Properties

Label 4014.2.a.l.1.2
Level 4014
Weight 2
Character 4014.1
Self dual Yes
Analytic conductor 32.052
Analytic rank 0
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0519513713\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.30278\)
Character \(\chi\) = 4014.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +2.60555 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +2.60555 q^{7} +1.00000 q^{8} +6.30278 q^{11} +5.30278 q^{13} +2.60555 q^{14} +1.00000 q^{16} +4.60555 q^{17} +0.697224 q^{19} +6.30278 q^{22} -4.00000 q^{23} -5.00000 q^{25} +5.30278 q^{26} +2.60555 q^{28} +1.69722 q^{29} -0.605551 q^{31} +1.00000 q^{32} +4.60555 q^{34} -2.60555 q^{37} +0.697224 q^{38} -4.00000 q^{41} -6.90833 q^{43} +6.30278 q^{44} -4.00000 q^{46} +4.30278 q^{47} -0.211103 q^{49} -5.00000 q^{50} +5.30278 q^{52} -3.90833 q^{53} +2.60555 q^{56} +1.69722 q^{58} -3.30278 q^{59} -6.30278 q^{61} -0.605551 q^{62} +1.00000 q^{64} -2.60555 q^{67} +4.60555 q^{68} -3.21110 q^{71} +1.90833 q^{73} -2.60555 q^{74} +0.697224 q^{76} +16.4222 q^{77} -9.51388 q^{79} -4.00000 q^{82} +9.21110 q^{83} -6.90833 q^{86} +6.30278 q^{88} +2.78890 q^{89} +13.8167 q^{91} -4.00000 q^{92} +4.30278 q^{94} -15.2111 q^{97} -0.211103 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{4} - 2q^{7} + 2q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{4} - 2q^{7} + 2q^{8} + 9q^{11} + 7q^{13} - 2q^{14} + 2q^{16} + 2q^{17} + 5q^{19} + 9q^{22} - 8q^{23} - 10q^{25} + 7q^{26} - 2q^{28} + 7q^{29} + 6q^{31} + 2q^{32} + 2q^{34} + 2q^{37} + 5q^{38} - 8q^{41} - 3q^{43} + 9q^{44} - 8q^{46} + 5q^{47} + 14q^{49} - 10q^{50} + 7q^{52} + 3q^{53} - 2q^{56} + 7q^{58} - 3q^{59} - 9q^{61} + 6q^{62} + 2q^{64} + 2q^{67} + 2q^{68} + 8q^{71} - 7q^{73} + 2q^{74} + 5q^{76} + 4q^{77} - q^{79} - 8q^{82} + 4q^{83} - 3q^{86} + 9q^{88} + 20q^{89} + 6q^{91} - 8q^{92} + 5q^{94} - 16q^{97} + 14q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 2.60555 0.984806 0.492403 0.870367i \(-0.336119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 6.30278 1.90036 0.950179 0.311704i \(-0.100900\pi\)
0.950179 + 0.311704i \(0.100900\pi\)
\(12\) 0 0
\(13\) 5.30278 1.47073 0.735363 0.677674i \(-0.237012\pi\)
0.735363 + 0.677674i \(0.237012\pi\)
\(14\) 2.60555 0.696363
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.60555 1.11701 0.558505 0.829501i \(-0.311375\pi\)
0.558505 + 0.829501i \(0.311375\pi\)
\(18\) 0 0
\(19\) 0.697224 0.159954 0.0799771 0.996797i \(-0.474515\pi\)
0.0799771 + 0.996797i \(0.474515\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 6.30278 1.34376
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 5.30278 1.03996
\(27\) 0 0
\(28\) 2.60555 0.492403
\(29\) 1.69722 0.315167 0.157583 0.987506i \(-0.449630\pi\)
0.157583 + 0.987506i \(0.449630\pi\)
\(30\) 0 0
\(31\) −0.605551 −0.108760 −0.0543801 0.998520i \(-0.517318\pi\)
−0.0543801 + 0.998520i \(0.517318\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 4.60555 0.789846
\(35\) 0 0
\(36\) 0 0
\(37\) −2.60555 −0.428350 −0.214175 0.976795i \(-0.568706\pi\)
−0.214175 + 0.976795i \(0.568706\pi\)
\(38\) 0.697224 0.113105
\(39\) 0 0
\(40\) 0 0
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 0 0
\(43\) −6.90833 −1.05351 −0.526755 0.850017i \(-0.676591\pi\)
−0.526755 + 0.850017i \(0.676591\pi\)
\(44\) 6.30278 0.950179
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 4.30278 0.627624 0.313812 0.949485i \(-0.398394\pi\)
0.313812 + 0.949485i \(0.398394\pi\)
\(48\) 0 0
\(49\) −0.211103 −0.0301575
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 5.30278 0.735363
\(53\) −3.90833 −0.536850 −0.268425 0.963301i \(-0.586503\pi\)
−0.268425 + 0.963301i \(0.586503\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.60555 0.348181
\(57\) 0 0
\(58\) 1.69722 0.222856
\(59\) −3.30278 −0.429985 −0.214992 0.976616i \(-0.568973\pi\)
−0.214992 + 0.976616i \(0.568973\pi\)
\(60\) 0 0
\(61\) −6.30278 −0.806988 −0.403494 0.914982i \(-0.632204\pi\)
−0.403494 + 0.914982i \(0.632204\pi\)
\(62\) −0.605551 −0.0769051
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.60555 −0.318319 −0.159159 0.987253i \(-0.550878\pi\)
−0.159159 + 0.987253i \(0.550878\pi\)
\(68\) 4.60555 0.558505
\(69\) 0 0
\(70\) 0 0
\(71\) −3.21110 −0.381088 −0.190544 0.981679i \(-0.561025\pi\)
−0.190544 + 0.981679i \(0.561025\pi\)
\(72\) 0 0
\(73\) 1.90833 0.223353 0.111676 0.993745i \(-0.464378\pi\)
0.111676 + 0.993745i \(0.464378\pi\)
\(74\) −2.60555 −0.302889
\(75\) 0 0
\(76\) 0.697224 0.0799771
\(77\) 16.4222 1.87148
\(78\) 0 0
\(79\) −9.51388 −1.07039 −0.535197 0.844727i \(-0.679763\pi\)
−0.535197 + 0.844727i \(0.679763\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −4.00000 −0.441726
\(83\) 9.21110 1.01105 0.505525 0.862812i \(-0.331299\pi\)
0.505525 + 0.862812i \(0.331299\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −6.90833 −0.744944
\(87\) 0 0
\(88\) 6.30278 0.671878
\(89\) 2.78890 0.295623 0.147811 0.989016i \(-0.452777\pi\)
0.147811 + 0.989016i \(0.452777\pi\)
\(90\) 0 0
\(91\) 13.8167 1.44838
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) 4.30278 0.443797
\(95\) 0 0
\(96\) 0 0
\(97\) −15.2111 −1.54445 −0.772227 0.635347i \(-0.780857\pi\)
−0.772227 + 0.635347i \(0.780857\pi\)
\(98\) −0.211103 −0.0213246
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 0.0916731 0.00912181 0.00456091 0.999990i \(-0.498548\pi\)
0.00456091 + 0.999990i \(0.498548\pi\)
\(102\) 0 0
\(103\) 7.90833 0.779231 0.389615 0.920978i \(-0.372608\pi\)
0.389615 + 0.920978i \(0.372608\pi\)
\(104\) 5.30278 0.519980
\(105\) 0 0
\(106\) −3.90833 −0.379610
\(107\) −9.90833 −0.957874 −0.478937 0.877849i \(-0.658978\pi\)
−0.478937 + 0.877849i \(0.658978\pi\)
\(108\) 0 0
\(109\) −12.6056 −1.20739 −0.603696 0.797214i \(-0.706306\pi\)
−0.603696 + 0.797214i \(0.706306\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.60555 0.246201
\(113\) 19.3028 1.81585 0.907926 0.419130i \(-0.137665\pi\)
0.907926 + 0.419130i \(0.137665\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.69722 0.157583
\(117\) 0 0
\(118\) −3.30278 −0.304045
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) 28.7250 2.61136
\(122\) −6.30278 −0.570626
\(123\) 0 0
\(124\) −0.605551 −0.0543801
\(125\) 0 0
\(126\) 0 0
\(127\) −7.21110 −0.639882 −0.319941 0.947437i \(-0.603663\pi\)
−0.319941 + 0.947437i \(0.603663\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −12.4222 −1.08533 −0.542667 0.839948i \(-0.682585\pi\)
−0.542667 + 0.839948i \(0.682585\pi\)
\(132\) 0 0
\(133\) 1.81665 0.157524
\(134\) −2.60555 −0.225085
\(135\) 0 0
\(136\) 4.60555 0.394923
\(137\) 3.69722 0.315875 0.157938 0.987449i \(-0.449516\pi\)
0.157938 + 0.987449i \(0.449516\pi\)
\(138\) 0 0
\(139\) −1.09167 −0.0925945 −0.0462973 0.998928i \(-0.514742\pi\)
−0.0462973 + 0.998928i \(0.514742\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.21110 −0.269470
\(143\) 33.4222 2.79491
\(144\) 0 0
\(145\) 0 0
\(146\) 1.90833 0.157934
\(147\) 0 0
\(148\) −2.60555 −0.214175
\(149\) −9.21110 −0.754603 −0.377301 0.926090i \(-0.623148\pi\)
−0.377301 + 0.926090i \(0.623148\pi\)
\(150\) 0 0
\(151\) 18.5139 1.50664 0.753319 0.657655i \(-0.228452\pi\)
0.753319 + 0.657655i \(0.228452\pi\)
\(152\) 0.697224 0.0565524
\(153\) 0 0
\(154\) 16.4222 1.32334
\(155\) 0 0
\(156\) 0 0
\(157\) 6.30278 0.503016 0.251508 0.967855i \(-0.419073\pi\)
0.251508 + 0.967855i \(0.419073\pi\)
\(158\) −9.51388 −0.756884
\(159\) 0 0
\(160\) 0 0
\(161\) −10.4222 −0.821385
\(162\) 0 0
\(163\) 1.39445 0.109222 0.0546108 0.998508i \(-0.482608\pi\)
0.0546108 + 0.998508i \(0.482608\pi\)
\(164\) −4.00000 −0.312348
\(165\) 0 0
\(166\) 9.21110 0.714920
\(167\) −4.60555 −0.356388 −0.178194 0.983995i \(-0.557026\pi\)
−0.178194 + 0.983995i \(0.557026\pi\)
\(168\) 0 0
\(169\) 15.1194 1.16303
\(170\) 0 0
\(171\) 0 0
\(172\) −6.90833 −0.526755
\(173\) 23.0278 1.75077 0.875384 0.483428i \(-0.160609\pi\)
0.875384 + 0.483428i \(0.160609\pi\)
\(174\) 0 0
\(175\) −13.0278 −0.984806
\(176\) 6.30278 0.475090
\(177\) 0 0
\(178\) 2.78890 0.209037
\(179\) −1.21110 −0.0905221 −0.0452610 0.998975i \(-0.514412\pi\)
−0.0452610 + 0.998975i \(0.514412\pi\)
\(180\) 0 0
\(181\) 8.60555 0.639646 0.319823 0.947477i \(-0.396377\pi\)
0.319823 + 0.947477i \(0.396377\pi\)
\(182\) 13.8167 1.02416
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) 0 0
\(186\) 0 0
\(187\) 29.0278 2.12272
\(188\) 4.30278 0.313812
\(189\) 0 0
\(190\) 0 0
\(191\) 13.8167 0.999738 0.499869 0.866101i \(-0.333381\pi\)
0.499869 + 0.866101i \(0.333381\pi\)
\(192\) 0 0
\(193\) −20.4222 −1.47002 −0.735011 0.678055i \(-0.762823\pi\)
−0.735011 + 0.678055i \(0.762823\pi\)
\(194\) −15.2111 −1.09209
\(195\) 0 0
\(196\) −0.211103 −0.0150788
\(197\) −1.69722 −0.120922 −0.0604611 0.998171i \(-0.519257\pi\)
−0.0604611 + 0.998171i \(0.519257\pi\)
\(198\) 0 0
\(199\) −18.4222 −1.30592 −0.652958 0.757394i \(-0.726472\pi\)
−0.652958 + 0.757394i \(0.726472\pi\)
\(200\) −5.00000 −0.353553
\(201\) 0 0
\(202\) 0.0916731 0.00645010
\(203\) 4.42221 0.310378
\(204\) 0 0
\(205\) 0 0
\(206\) 7.90833 0.550999
\(207\) 0 0
\(208\) 5.30278 0.367681
\(209\) 4.39445 0.303970
\(210\) 0 0
\(211\) 1.69722 0.116842 0.0584209 0.998292i \(-0.481393\pi\)
0.0584209 + 0.998292i \(0.481393\pi\)
\(212\) −3.90833 −0.268425
\(213\) 0 0
\(214\) −9.90833 −0.677319
\(215\) 0 0
\(216\) 0 0
\(217\) −1.57779 −0.107108
\(218\) −12.6056 −0.853756
\(219\) 0 0
\(220\) 0 0
\(221\) 24.4222 1.64282
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) 2.60555 0.174091
\(225\) 0 0
\(226\) 19.3028 1.28400
\(227\) −17.0278 −1.13017 −0.565086 0.825032i \(-0.691157\pi\)
−0.565086 + 0.825032i \(0.691157\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.69722 0.111428
\(233\) −8.30278 −0.543933 −0.271966 0.962307i \(-0.587674\pi\)
−0.271966 + 0.962307i \(0.587674\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.30278 −0.214992
\(237\) 0 0
\(238\) 12.0000 0.777844
\(239\) 23.7250 1.53464 0.767321 0.641264i \(-0.221589\pi\)
0.767321 + 0.641264i \(0.221589\pi\)
\(240\) 0 0
\(241\) 13.5139 0.870505 0.435253 0.900308i \(-0.356659\pi\)
0.435253 + 0.900308i \(0.356659\pi\)
\(242\) 28.7250 1.84651
\(243\) 0 0
\(244\) −6.30278 −0.403494
\(245\) 0 0
\(246\) 0 0
\(247\) 3.69722 0.235249
\(248\) −0.605551 −0.0384525
\(249\) 0 0
\(250\) 0 0
\(251\) 6.42221 0.405366 0.202683 0.979244i \(-0.435034\pi\)
0.202683 + 0.979244i \(0.435034\pi\)
\(252\) 0 0
\(253\) −25.2111 −1.58501
\(254\) −7.21110 −0.452465
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) −6.78890 −0.421842
\(260\) 0 0
\(261\) 0 0
\(262\) −12.4222 −0.767446
\(263\) −14.6056 −0.900617 −0.450308 0.892873i \(-0.648686\pi\)
−0.450308 + 0.892873i \(0.648686\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.81665 0.111386
\(267\) 0 0
\(268\) −2.60555 −0.159159
\(269\) −21.0278 −1.28208 −0.641042 0.767505i \(-0.721498\pi\)
−0.641042 + 0.767505i \(0.721498\pi\)
\(270\) 0 0
\(271\) −10.1194 −0.614712 −0.307356 0.951595i \(-0.599444\pi\)
−0.307356 + 0.951595i \(0.599444\pi\)
\(272\) 4.60555 0.279253
\(273\) 0 0
\(274\) 3.69722 0.223357
\(275\) −31.5139 −1.90036
\(276\) 0 0
\(277\) −3.57779 −0.214969 −0.107484 0.994207i \(-0.534280\pi\)
−0.107484 + 0.994207i \(0.534280\pi\)
\(278\) −1.09167 −0.0654742
\(279\) 0 0
\(280\) 0 0
\(281\) 7.39445 0.441116 0.220558 0.975374i \(-0.429212\pi\)
0.220558 + 0.975374i \(0.429212\pi\)
\(282\) 0 0
\(283\) −19.3028 −1.14743 −0.573715 0.819055i \(-0.694498\pi\)
−0.573715 + 0.819055i \(0.694498\pi\)
\(284\) −3.21110 −0.190544
\(285\) 0 0
\(286\) 33.4222 1.97630
\(287\) −10.4222 −0.615203
\(288\) 0 0
\(289\) 4.21110 0.247712
\(290\) 0 0
\(291\) 0 0
\(292\) 1.90833 0.111676
\(293\) 30.2389 1.76657 0.883287 0.468834i \(-0.155326\pi\)
0.883287 + 0.468834i \(0.155326\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.60555 −0.151445
\(297\) 0 0
\(298\) −9.21110 −0.533585
\(299\) −21.2111 −1.22667
\(300\) 0 0
\(301\) −18.0000 −1.03750
\(302\) 18.5139 1.06535
\(303\) 0 0
\(304\) 0.697224 0.0399886
\(305\) 0 0
\(306\) 0 0
\(307\) −3.02776 −0.172803 −0.0864016 0.996260i \(-0.527537\pi\)
−0.0864016 + 0.996260i \(0.527537\pi\)
\(308\) 16.4222 0.935742
\(309\) 0 0
\(310\) 0 0
\(311\) 3.39445 0.192482 0.0962408 0.995358i \(-0.469318\pi\)
0.0962408 + 0.995358i \(0.469318\pi\)
\(312\) 0 0
\(313\) −20.0000 −1.13047 −0.565233 0.824931i \(-0.691214\pi\)
−0.565233 + 0.824931i \(0.691214\pi\)
\(314\) 6.30278 0.355686
\(315\) 0 0
\(316\) −9.51388 −0.535197
\(317\) −13.3028 −0.747158 −0.373579 0.927598i \(-0.621870\pi\)
−0.373579 + 0.927598i \(0.621870\pi\)
\(318\) 0 0
\(319\) 10.6972 0.598930
\(320\) 0 0
\(321\) 0 0
\(322\) −10.4222 −0.580807
\(323\) 3.21110 0.178671
\(324\) 0 0
\(325\) −26.5139 −1.47073
\(326\) 1.39445 0.0772314
\(327\) 0 0
\(328\) −4.00000 −0.220863
\(329\) 11.2111 0.618088
\(330\) 0 0
\(331\) −4.78890 −0.263222 −0.131611 0.991301i \(-0.542015\pi\)
−0.131611 + 0.991301i \(0.542015\pi\)
\(332\) 9.21110 0.505525
\(333\) 0 0
\(334\) −4.60555 −0.252005
\(335\) 0 0
\(336\) 0 0
\(337\) −9.21110 −0.501761 −0.250880 0.968018i \(-0.580720\pi\)
−0.250880 + 0.968018i \(0.580720\pi\)
\(338\) 15.1194 0.822389
\(339\) 0 0
\(340\) 0 0
\(341\) −3.81665 −0.206683
\(342\) 0 0
\(343\) −18.7889 −1.01451
\(344\) −6.90833 −0.372472
\(345\) 0 0
\(346\) 23.0278 1.23798
\(347\) 18.4222 0.988956 0.494478 0.869190i \(-0.335359\pi\)
0.494478 + 0.869190i \(0.335359\pi\)
\(348\) 0 0
\(349\) −32.6056 −1.74534 −0.872668 0.488315i \(-0.837612\pi\)
−0.872668 + 0.488315i \(0.837612\pi\)
\(350\) −13.0278 −0.696363
\(351\) 0 0
\(352\) 6.30278 0.335939
\(353\) 22.6056 1.20317 0.601586 0.798808i \(-0.294536\pi\)
0.601586 + 0.798808i \(0.294536\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.78890 0.147811
\(357\) 0 0
\(358\) −1.21110 −0.0640088
\(359\) 5.48612 0.289546 0.144773 0.989465i \(-0.453755\pi\)
0.144773 + 0.989465i \(0.453755\pi\)
\(360\) 0 0
\(361\) −18.5139 −0.974415
\(362\) 8.60555 0.452298
\(363\) 0 0
\(364\) 13.8167 0.724189
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) 0 0
\(371\) −10.1833 −0.528693
\(372\) 0 0
\(373\) 30.8444 1.59706 0.798532 0.601953i \(-0.205611\pi\)
0.798532 + 0.601953i \(0.205611\pi\)
\(374\) 29.0278 1.50099
\(375\) 0 0
\(376\) 4.30278 0.221899
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) 36.3305 1.86617 0.933087 0.359651i \(-0.117104\pi\)
0.933087 + 0.359651i \(0.117104\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 13.8167 0.706922
\(383\) −11.8167 −0.603803 −0.301901 0.953339i \(-0.597621\pi\)
−0.301901 + 0.953339i \(0.597621\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −20.4222 −1.03946
\(387\) 0 0
\(388\) −15.2111 −0.772227
\(389\) 21.9361 1.11220 0.556102 0.831114i \(-0.312296\pi\)
0.556102 + 0.831114i \(0.312296\pi\)
\(390\) 0 0
\(391\) −18.4222 −0.931651
\(392\) −0.211103 −0.0106623
\(393\) 0 0
\(394\) −1.69722 −0.0855049
\(395\) 0 0
\(396\) 0 0
\(397\) −19.5139 −0.979373 −0.489687 0.871898i \(-0.662889\pi\)
−0.489687 + 0.871898i \(0.662889\pi\)
\(398\) −18.4222 −0.923422
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −2.97224 −0.148427 −0.0742134 0.997242i \(-0.523645\pi\)
−0.0742134 + 0.997242i \(0.523645\pi\)
\(402\) 0 0
\(403\) −3.21110 −0.159956
\(404\) 0.0916731 0.00456091
\(405\) 0 0
\(406\) 4.42221 0.219470
\(407\) −16.4222 −0.814018
\(408\) 0 0
\(409\) 24.2389 1.19853 0.599267 0.800549i \(-0.295459\pi\)
0.599267 + 0.800549i \(0.295459\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 7.90833 0.389615
\(413\) −8.60555 −0.423451
\(414\) 0 0
\(415\) 0 0
\(416\) 5.30278 0.259990
\(417\) 0 0
\(418\) 4.39445 0.214940
\(419\) 3.39445 0.165830 0.0829148 0.996557i \(-0.473577\pi\)
0.0829148 + 0.996557i \(0.473577\pi\)
\(420\) 0 0
\(421\) −19.7250 −0.961337 −0.480668 0.876902i \(-0.659606\pi\)
−0.480668 + 0.876902i \(0.659606\pi\)
\(422\) 1.69722 0.0826196
\(423\) 0 0
\(424\) −3.90833 −0.189805
\(425\) −23.0278 −1.11701
\(426\) 0 0
\(427\) −16.4222 −0.794726
\(428\) −9.90833 −0.478937
\(429\) 0 0
\(430\) 0 0
\(431\) 25.8167 1.24354 0.621772 0.783198i \(-0.286413\pi\)
0.621772 + 0.783198i \(0.286413\pi\)
\(432\) 0 0
\(433\) 21.5416 1.03522 0.517612 0.855615i \(-0.326821\pi\)
0.517612 + 0.855615i \(0.326821\pi\)
\(434\) −1.57779 −0.0757366
\(435\) 0 0
\(436\) −12.6056 −0.603696
\(437\) −2.78890 −0.133411
\(438\) 0 0
\(439\) −15.6333 −0.746137 −0.373069 0.927804i \(-0.621694\pi\)
−0.373069 + 0.927804i \(0.621694\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 24.4222 1.16165
\(443\) −8.60555 −0.408862 −0.204431 0.978881i \(-0.565534\pi\)
−0.204431 + 0.978881i \(0.565534\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.00000 −0.0473514
\(447\) 0 0
\(448\) 2.60555 0.123101
\(449\) −0.788897 −0.0372304 −0.0186152 0.999827i \(-0.505926\pi\)
−0.0186152 + 0.999827i \(0.505926\pi\)
\(450\) 0 0
\(451\) −25.2111 −1.18714
\(452\) 19.3028 0.907926
\(453\) 0 0
\(454\) −17.0278 −0.799152
\(455\) 0 0
\(456\) 0 0
\(457\) 10.1833 0.476357 0.238178 0.971221i \(-0.423450\pi\)
0.238178 + 0.971221i \(0.423450\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) 27.7250 1.29128 0.645641 0.763641i \(-0.276590\pi\)
0.645641 + 0.763641i \(0.276590\pi\)
\(462\) 0 0
\(463\) 3.21110 0.149233 0.0746163 0.997212i \(-0.476227\pi\)
0.0746163 + 0.997212i \(0.476227\pi\)
\(464\) 1.69722 0.0787917
\(465\) 0 0
\(466\) −8.30278 −0.384619
\(467\) −2.09167 −0.0967911 −0.0483955 0.998828i \(-0.515411\pi\)
−0.0483955 + 0.998828i \(0.515411\pi\)
\(468\) 0 0
\(469\) −6.78890 −0.313482
\(470\) 0 0
\(471\) 0 0
\(472\) −3.30278 −0.152023
\(473\) −43.5416 −2.00205
\(474\) 0 0
\(475\) −3.48612 −0.159954
\(476\) 12.0000 0.550019
\(477\) 0 0
\(478\) 23.7250 1.08516
\(479\) 36.9083 1.68638 0.843192 0.537612i \(-0.180674\pi\)
0.843192 + 0.537612i \(0.180674\pi\)
\(480\) 0 0
\(481\) −13.8167 −0.629985
\(482\) 13.5139 0.615540
\(483\) 0 0
\(484\) 28.7250 1.30568
\(485\) 0 0
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) −6.30278 −0.285313
\(489\) 0 0
\(490\) 0 0
\(491\) −13.9361 −0.628927 −0.314463 0.949270i \(-0.601825\pi\)
−0.314463 + 0.949270i \(0.601825\pi\)
\(492\) 0 0
\(493\) 7.81665 0.352044
\(494\) 3.69722 0.166346
\(495\) 0 0
\(496\) −0.605551 −0.0271901
\(497\) −8.36669 −0.375297
\(498\) 0 0
\(499\) −6.30278 −0.282151 −0.141075 0.989999i \(-0.545056\pi\)
−0.141075 + 0.989999i \(0.545056\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 6.42221 0.286637
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −25.2111 −1.12077
\(507\) 0 0
\(508\) −7.21110 −0.319941
\(509\) −27.7527 −1.23012 −0.615059 0.788481i \(-0.710868\pi\)
−0.615059 + 0.788481i \(0.710868\pi\)
\(510\) 0 0
\(511\) 4.97224 0.219959
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 0 0
\(516\) 0 0
\(517\) 27.1194 1.19271
\(518\) −6.78890 −0.298287
\(519\) 0 0
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −5.57779 −0.243900 −0.121950 0.992536i \(-0.538915\pi\)
−0.121950 + 0.992536i \(0.538915\pi\)
\(524\) −12.4222 −0.542667
\(525\) 0 0
\(526\) −14.6056 −0.636832
\(527\) −2.78890 −0.121486
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 1.81665 0.0787619
\(533\) −21.2111 −0.918755
\(534\) 0 0
\(535\) 0 0
\(536\) −2.60555 −0.112543
\(537\) 0 0
\(538\) −21.0278 −0.906571
\(539\) −1.33053 −0.0573101
\(540\) 0 0
\(541\) 8.27502 0.355771 0.177885 0.984051i \(-0.443074\pi\)
0.177885 + 0.984051i \(0.443074\pi\)
\(542\) −10.1194 −0.434667
\(543\) 0 0
\(544\) 4.60555 0.197461
\(545\) 0 0
\(546\) 0 0
\(547\) 9.72498 0.415810 0.207905 0.978149i \(-0.433335\pi\)
0.207905 + 0.978149i \(0.433335\pi\)
\(548\) 3.69722 0.157938
\(549\) 0 0
\(550\) −31.5139 −1.34376
\(551\) 1.18335 0.0504122
\(552\) 0 0
\(553\) −24.7889 −1.05413
\(554\) −3.57779 −0.152006
\(555\) 0 0
\(556\) −1.09167 −0.0462973
\(557\) 38.4222 1.62800 0.814001 0.580864i \(-0.197285\pi\)
0.814001 + 0.580864i \(0.197285\pi\)
\(558\) 0 0
\(559\) −36.6333 −1.54942
\(560\) 0 0
\(561\) 0 0
\(562\) 7.39445 0.311916
\(563\) 42.5416 1.79292 0.896458 0.443129i \(-0.146131\pi\)
0.896458 + 0.443129i \(0.146131\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −19.3028 −0.811356
\(567\) 0 0
\(568\) −3.21110 −0.134735
\(569\) −33.5416 −1.40614 −0.703069 0.711121i \(-0.748188\pi\)
−0.703069 + 0.711121i \(0.748188\pi\)
\(570\) 0 0
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) 33.4222 1.39745
\(573\) 0 0
\(574\) −10.4222 −0.435014
\(575\) 20.0000 0.834058
\(576\) 0 0
\(577\) −42.9638 −1.78861 −0.894304 0.447460i \(-0.852329\pi\)
−0.894304 + 0.447460i \(0.852329\pi\)
\(578\) 4.21110 0.175159
\(579\) 0 0
\(580\) 0 0
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) −24.6333 −1.02021
\(584\) 1.90833 0.0789671
\(585\) 0 0
\(586\) 30.2389 1.24916
\(587\) −14.9361 −0.616478 −0.308239 0.951309i \(-0.599740\pi\)
−0.308239 + 0.951309i \(0.599740\pi\)
\(588\) 0 0
\(589\) −0.422205 −0.0173967
\(590\) 0 0
\(591\) 0 0
\(592\) −2.60555 −0.107087
\(593\) −32.4222 −1.33142 −0.665710 0.746210i \(-0.731871\pi\)
−0.665710 + 0.746210i \(0.731871\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.21110 −0.377301
\(597\) 0 0
\(598\) −21.2111 −0.867386
\(599\) 9.88057 0.403709 0.201855 0.979416i \(-0.435303\pi\)
0.201855 + 0.979416i \(0.435303\pi\)
\(600\) 0 0
\(601\) 21.8167 0.889920 0.444960 0.895550i \(-0.353218\pi\)
0.444960 + 0.895550i \(0.353218\pi\)
\(602\) −18.0000 −0.733625
\(603\) 0 0
\(604\) 18.5139 0.753319
\(605\) 0 0
\(606\) 0 0
\(607\) 32.8444 1.33311 0.666557 0.745454i \(-0.267767\pi\)
0.666557 + 0.745454i \(0.267767\pi\)
\(608\) 0.697224 0.0282762
\(609\) 0 0
\(610\) 0 0
\(611\) 22.8167 0.923063
\(612\) 0 0
\(613\) 0.486122 0.0196343 0.00981714 0.999952i \(-0.496875\pi\)
0.00981714 + 0.999952i \(0.496875\pi\)
\(614\) −3.02776 −0.122190
\(615\) 0 0
\(616\) 16.4222 0.661669
\(617\) 18.4222 0.741650 0.370825 0.928703i \(-0.379075\pi\)
0.370825 + 0.928703i \(0.379075\pi\)
\(618\) 0 0
\(619\) 10.4222 0.418904 0.209452 0.977819i \(-0.432832\pi\)
0.209452 + 0.977819i \(0.432832\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 3.39445 0.136105
\(623\) 7.26662 0.291131
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −20.0000 −0.799361
\(627\) 0 0
\(628\) 6.30278 0.251508
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 34.1194 1.35827 0.679137 0.734012i \(-0.262354\pi\)
0.679137 + 0.734012i \(0.262354\pi\)
\(632\) −9.51388 −0.378442
\(633\) 0 0
\(634\) −13.3028 −0.528321
\(635\) 0 0
\(636\) 0 0
\(637\) −1.11943 −0.0443534
\(638\) 10.6972 0.423507
\(639\) 0 0
\(640\) 0 0
\(641\) −40.5139 −1.60020 −0.800101 0.599865i \(-0.795221\pi\)
−0.800101 + 0.599865i \(0.795221\pi\)
\(642\) 0 0
\(643\) 30.3028 1.19502 0.597512 0.801860i \(-0.296156\pi\)
0.597512 + 0.801860i \(0.296156\pi\)
\(644\) −10.4222 −0.410692
\(645\) 0 0
\(646\) 3.21110 0.126339
\(647\) 24.0917 0.947141 0.473571 0.880756i \(-0.342965\pi\)
0.473571 + 0.880756i \(0.342965\pi\)
\(648\) 0 0
\(649\) −20.8167 −0.817125
\(650\) −26.5139 −1.03996
\(651\) 0 0
\(652\) 1.39445 0.0546108
\(653\) −7.63331 −0.298714 −0.149357 0.988783i \(-0.547720\pi\)
−0.149357 + 0.988783i \(0.547720\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.00000 −0.156174
\(657\) 0 0
\(658\) 11.2111 0.437054
\(659\) −21.6333 −0.842714 −0.421357 0.906895i \(-0.638446\pi\)
−0.421357 + 0.906895i \(0.638446\pi\)
\(660\) 0 0
\(661\) −37.9361 −1.47554 −0.737771 0.675051i \(-0.764122\pi\)
−0.737771 + 0.675051i \(0.764122\pi\)
\(662\) −4.78890 −0.186126
\(663\) 0 0
\(664\) 9.21110 0.357460
\(665\) 0 0
\(666\) 0 0
\(667\) −6.78890 −0.262867
\(668\) −4.60555 −0.178194
\(669\) 0 0
\(670\) 0 0
\(671\) −39.7250 −1.53357
\(672\) 0 0
\(673\) 11.1194 0.428623 0.214311 0.976765i \(-0.431249\pi\)
0.214311 + 0.976765i \(0.431249\pi\)
\(674\) −9.21110 −0.354798
\(675\) 0 0
\(676\) 15.1194 0.581517
\(677\) −20.7889 −0.798982 −0.399491 0.916737i \(-0.630813\pi\)
−0.399491 + 0.916737i \(0.630813\pi\)
\(678\) 0 0
\(679\) −39.6333 −1.52099
\(680\) 0 0
\(681\) 0 0
\(682\) −3.81665 −0.146147
\(683\) −45.8167 −1.75313 −0.876563 0.481288i \(-0.840169\pi\)
−0.876563 + 0.481288i \(0.840169\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −18.7889 −0.717363
\(687\) 0 0
\(688\) −6.90833 −0.263377
\(689\) −20.7250 −0.789559
\(690\) 0 0
\(691\) −0.183346 −0.00697482 −0.00348741 0.999994i \(-0.501110\pi\)
−0.00348741 + 0.999994i \(0.501110\pi\)
\(692\) 23.0278 0.875384
\(693\) 0 0
\(694\) 18.4222 0.699297
\(695\) 0 0
\(696\) 0 0
\(697\) −18.4222 −0.697791
\(698\) −32.6056 −1.23414
\(699\) 0 0
\(700\) −13.0278 −0.492403
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) −1.81665 −0.0685164
\(704\) 6.30278 0.237545
\(705\) 0 0
\(706\) 22.6056 0.850771
\(707\) 0.238859 0.00898321
\(708\) 0 0
\(709\) −3.57779 −0.134367 −0.0671835 0.997741i \(-0.521401\pi\)
−0.0671835 + 0.997741i \(0.521401\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 2.78890 0.104518
\(713\) 2.42221 0.0907123
\(714\) 0 0
\(715\) 0 0
\(716\) −1.21110 −0.0452610
\(717\) 0 0
\(718\) 5.48612 0.204740
\(719\) 21.2111 0.791041 0.395520 0.918457i \(-0.370564\pi\)
0.395520 + 0.918457i \(0.370564\pi\)
\(720\) 0 0
\(721\) 20.6056 0.767391
\(722\) −18.5139 −0.689015
\(723\) 0 0
\(724\) 8.60555 0.319823
\(725\) −8.48612 −0.315167
\(726\) 0 0
\(727\) −14.1833 −0.526031 −0.263016 0.964792i \(-0.584717\pi\)
−0.263016 + 0.964792i \(0.584717\pi\)
\(728\) 13.8167 0.512079
\(729\) 0 0
\(730\) 0 0
\(731\) −31.8167 −1.17678
\(732\) 0 0
\(733\) 20.4222 0.754311 0.377156 0.926150i \(-0.376902\pi\)
0.377156 + 0.926150i \(0.376902\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −16.4222 −0.604920
\(738\) 0 0
\(739\) 43.4500 1.59833 0.799166 0.601110i \(-0.205275\pi\)
0.799166 + 0.601110i \(0.205275\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −10.1833 −0.373842
\(743\) 16.9361 0.621325 0.310662 0.950520i \(-0.399449\pi\)
0.310662 + 0.950520i \(0.399449\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 30.8444 1.12929
\(747\) 0 0
\(748\) 29.0278 1.06136
\(749\) −25.8167 −0.943320
\(750\) 0 0
\(751\) 43.4500 1.58551 0.792756 0.609539i \(-0.208646\pi\)
0.792756 + 0.609539i \(0.208646\pi\)
\(752\) 4.30278 0.156906
\(753\) 0 0
\(754\) 9.00000 0.327761
\(755\) 0 0
\(756\) 0 0
\(757\) −6.33053 −0.230087 −0.115044 0.993360i \(-0.536701\pi\)
−0.115044 + 0.993360i \(0.536701\pi\)
\(758\) 36.3305 1.31958
\(759\) 0 0
\(760\) 0 0
\(761\) −26.0917 −0.945822 −0.472911 0.881110i \(-0.656797\pi\)
−0.472911 + 0.881110i \(0.656797\pi\)
\(762\) 0 0
\(763\) −32.8444 −1.18905
\(764\) 13.8167 0.499869
\(765\) 0 0
\(766\) −11.8167 −0.426953
\(767\) −17.5139 −0.632389
\(768\) 0 0
\(769\) −34.1194 −1.23038 −0.615189 0.788380i \(-0.710920\pi\)
−0.615189 + 0.788380i \(0.710920\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −20.4222 −0.735011
\(773\) −28.2389 −1.01568 −0.507841 0.861451i \(-0.669556\pi\)
−0.507841 + 0.861451i \(0.669556\pi\)
\(774\) 0 0
\(775\) 3.02776 0.108760
\(776\) −15.2111 −0.546047
\(777\) 0 0
\(778\) 21.9361 0.786447
\(779\) −2.78890 −0.0999226
\(780\) 0 0
\(781\) −20.2389 −0.724203
\(782\) −18.4222 −0.658777
\(783\) 0 0
\(784\) −0.211103 −0.00753938
\(785\) 0 0
\(786\) 0 0
\(787\) 29.2111 1.04126 0.520632 0.853781i \(-0.325696\pi\)
0.520632 + 0.853781i \(0.325696\pi\)
\(788\) −1.69722 −0.0604611
\(789\) 0 0
\(790\) 0 0
\(791\) 50.2944 1.78826
\(792\) 0 0
\(793\) −33.4222 −1.18686
\(794\) −19.5139 −0.692522
\(795\) 0 0
\(796\) −18.4222 −0.652958
\(797\) −12.4222 −0.440017 −0.220009 0.975498i \(-0.570609\pi\)
−0.220009 + 0.975498i \(0.570609\pi\)
\(798\) 0 0
\(799\) 19.8167 0.701063
\(800\) −5.00000 −0.176777
\(801\) 0 0
\(802\) −2.97224 −0.104954
\(803\) 12.0278 0.424450
\(804\) 0 0
\(805\) 0 0
\(806\) −3.21110 −0.113106
\(807\) 0 0
\(808\) 0.0916731 0.00322505
\(809\) 14.8444 0.521902 0.260951 0.965352i \(-0.415964\pi\)
0.260951 + 0.965352i \(0.415964\pi\)
\(810\) 0 0
\(811\) 4.23886 0.148846 0.0744232 0.997227i \(-0.476288\pi\)
0.0744232 + 0.997227i \(0.476288\pi\)
\(812\) 4.42221 0.155189
\(813\) 0 0
\(814\) −16.4222 −0.575598
\(815\) 0 0
\(816\) 0 0
\(817\) −4.81665 −0.168513
\(818\) 24.2389 0.847492
\(819\) 0 0
\(820\) 0 0
\(821\) −1.45837 −0.0508973 −0.0254487 0.999676i \(-0.508101\pi\)
−0.0254487 + 0.999676i \(0.508101\pi\)
\(822\) 0 0
\(823\) −51.2666 −1.78704 −0.893521 0.449022i \(-0.851773\pi\)
−0.893521 + 0.449022i \(0.851773\pi\)
\(824\) 7.90833 0.275500
\(825\) 0 0
\(826\) −8.60555 −0.299425
\(827\) 46.9361 1.63213 0.816064 0.577962i \(-0.196152\pi\)
0.816064 + 0.577962i \(0.196152\pi\)
\(828\) 0 0
\(829\) −51.5139 −1.78915 −0.894575 0.446917i \(-0.852522\pi\)
−0.894575 + 0.446917i \(0.852522\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 5.30278 0.183841
\(833\) −0.972244 −0.0336862
\(834\) 0 0
\(835\) 0 0
\(836\) 4.39445 0.151985
\(837\) 0 0
\(838\) 3.39445 0.117259
\(839\) −16.6056 −0.573287 −0.286644 0.958037i \(-0.592540\pi\)
−0.286644 + 0.958037i \(0.592540\pi\)
\(840\) 0 0
\(841\) −26.1194 −0.900670
\(842\) −19.7250 −0.679768
\(843\) 0 0
\(844\) 1.69722 0.0584209
\(845\) 0 0
\(846\) 0 0
\(847\) 74.8444 2.57168
\(848\) −3.90833 −0.134212
\(849\) 0 0
\(850\) −23.0278 −0.789846
\(851\) 10.4222 0.357269
\(852\) 0 0
\(853\) 28.1194 0.962791 0.481395 0.876504i \(-0.340130\pi\)
0.481395 + 0.876504i \(0.340130\pi\)
\(854\) −16.4222 −0.561956
\(855\) 0 0
\(856\) −9.90833 −0.338660
\(857\) −7.39445 −0.252590 −0.126295 0.991993i \(-0.540309\pi\)
−0.126295 + 0.991993i \(0.540309\pi\)
\(858\) 0 0
\(859\) −55.0278 −1.87752 −0.938761 0.344568i \(-0.888025\pi\)
−0.938761 + 0.344568i \(0.888025\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 25.8167 0.879319
\(863\) 35.2111 1.19860 0.599300 0.800525i \(-0.295446\pi\)
0.599300 + 0.800525i \(0.295446\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 21.5416 0.732015
\(867\) 0 0
\(868\) −1.57779 −0.0535538
\(869\) −59.9638 −2.03413
\(870\) 0 0
\(871\) −13.8167 −0.468159
\(872\) −12.6056 −0.426878
\(873\) 0 0
\(874\) −2.78890 −0.0943359
\(875\) 0 0
\(876\) 0 0
\(877\) 40.1194 1.35474 0.677368 0.735644i \(-0.263120\pi\)
0.677368 + 0.735644i \(0.263120\pi\)
\(878\) −15.6333 −0.527599
\(879\) 0 0
\(880\) 0 0
\(881\) 18.7889 0.633014 0.316507 0.948590i \(-0.397490\pi\)
0.316507 + 0.948590i \(0.397490\pi\)
\(882\) 0 0
\(883\) 32.0555 1.07875 0.539377 0.842064i \(-0.318660\pi\)
0.539377 + 0.842064i \(0.318660\pi\)
\(884\) 24.4222 0.821408
\(885\) 0 0
\(886\) −8.60555 −0.289109
\(887\) −0.275019 −0.00923424 −0.00461712 0.999989i \(-0.501470\pi\)
−0.00461712 + 0.999989i \(0.501470\pi\)
\(888\) 0 0
\(889\) −18.7889 −0.630159
\(890\) 0 0
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) 3.00000 0.100391
\(894\) 0 0
\(895\) 0 0
\(896\) 2.60555 0.0870454
\(897\) 0 0
\(898\) −0.788897 −0.0263258
\(899\) −1.02776 −0.0342776
\(900\) 0 0
\(901\) −18.0000 −0.599667
\(902\) −25.2111 −0.839438
\(903\) 0 0
\(904\) 19.3028 0.642001
\(905\) 0 0
\(906\) 0 0
\(907\) 28.3305 0.940700 0.470350 0.882480i \(-0.344128\pi\)
0.470350 + 0.882480i \(0.344128\pi\)
\(908\) −17.0278 −0.565086
\(909\) 0 0
\(910\) 0 0
\(911\) 9.57779 0.317327 0.158663 0.987333i \(-0.449282\pi\)
0.158663 + 0.987333i \(0.449282\pi\)
\(912\) 0 0
\(913\) 58.0555 1.92136
\(914\) 10.1833 0.336835
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) −32.3667 −1.06884
\(918\) 0 0
\(919\) −7.54163 −0.248776 −0.124388 0.992234i \(-0.539697\pi\)
−0.124388 + 0.992234i \(0.539697\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 27.7250 0.913074
\(923\) −17.0278 −0.560475
\(924\) 0 0
\(925\) 13.0278 0.428350
\(926\) 3.21110 0.105523
\(927\) 0 0
\(928\) 1.69722 0.0557141
\(929\) −22.9722 −0.753695 −0.376847 0.926275i \(-0.622992\pi\)
−0.376847 + 0.926275i \(0.622992\pi\)
\(930\) 0 0
\(931\) −0.147186 −0.00482382
\(932\) −8.30278 −0.271966
\(933\) 0 0
\(934\) −2.09167 −0.0684416
\(935\) 0 0
\(936\) 0 0
\(937\) −24.7889 −0.809818 −0.404909 0.914357i \(-0.632697\pi\)
−0.404909 + 0.914357i \(0.632697\pi\)
\(938\) −6.78890 −0.221665
\(939\) 0 0
\(940\) 0 0
\(941\) 49.1194 1.60125 0.800624 0.599167i \(-0.204502\pi\)
0.800624 + 0.599167i \(0.204502\pi\)
\(942\) 0 0
\(943\) 16.0000 0.521032
\(944\) −3.30278 −0.107496
\(945\) 0 0
\(946\) −43.5416 −1.41566
\(947\) −25.8167 −0.838929 −0.419464 0.907772i \(-0.637782\pi\)
−0.419464 + 0.907772i \(0.637782\pi\)
\(948\) 0 0
\(949\) 10.1194 0.328491
\(950\) −3.48612 −0.113105
\(951\) 0 0
\(952\) 12.0000 0.388922
\(953\) 44.0555 1.42710 0.713549 0.700605i \(-0.247087\pi\)
0.713549 + 0.700605i \(0.247087\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 23.7250 0.767321
\(957\) 0 0
\(958\) 36.9083 1.19245
\(959\) 9.63331 0.311076
\(960\) 0 0
\(961\) −30.6333 −0.988171
\(962\) −13.8167 −0.445467
\(963\) 0 0
\(964\) 13.5139 0.435253
\(965\) 0 0
\(966\) 0 0
\(967\) 12.0917 0.388842 0.194421 0.980918i \(-0.437717\pi\)
0.194421 + 0.980918i \(0.437717\pi\)
\(968\) 28.7250 0.923256
\(969\) 0 0
\(970\) 0 0
\(971\) −36.7250 −1.17856 −0.589280 0.807929i \(-0.700589\pi\)
−0.589280 + 0.807929i \(0.700589\pi\)
\(972\) 0 0
\(973\) −2.84441 −0.0911876
\(974\) −4.00000 −0.128168
\(975\) 0 0
\(976\) −6.30278 −0.201747
\(977\) −30.7250 −0.982979 −0.491490 0.870883i \(-0.663547\pi\)
−0.491490 + 0.870883i \(0.663547\pi\)
\(978\) 0 0
\(979\) 17.5778 0.561789
\(980\) 0 0
\(981\) 0 0
\(982\) −13.9361 −0.444718
\(983\) −36.7889 −1.17338 −0.586692 0.809810i \(-0.699570\pi\)
−0.586692 + 0.809810i \(0.699570\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 7.81665 0.248933
\(987\) 0 0
\(988\) 3.69722 0.117624
\(989\) 27.6333 0.878688
\(990\) 0 0
\(991\) 30.8806 0.980954 0.490477 0.871454i \(-0.336823\pi\)
0.490477 + 0.871454i \(0.336823\pi\)
\(992\) −0.605551 −0.0192263
\(993\) 0 0
\(994\) −8.36669 −0.265375
\(995\) 0 0
\(996\) 0 0
\(997\) 11.8167 0.374237 0.187119 0.982337i \(-0.440085\pi\)
0.187119 + 0.982337i \(0.440085\pi\)
\(998\) −6.30278 −0.199511
\(999\) 0 0
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 \(a_p\))