Properties

Label 6008.2.a.e.1.8
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.49253 q^{3}\) \(-3.92718 q^{5}\) \(+2.18622 q^{7}\) \(+3.21269 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.49253 q^{3}\) \(-3.92718 q^{5}\) \(+2.18622 q^{7}\) \(+3.21269 q^{9}\) \(+3.47715 q^{11}\) \(+3.85586 q^{13}\) \(+9.78861 q^{15}\) \(-2.14678 q^{17}\) \(+7.07416 q^{19}\) \(-5.44922 q^{21}\) \(-0.572069 q^{23}\) \(+10.4227 q^{25}\) \(-0.530148 q^{27}\) \(+5.29014 q^{29}\) \(+8.09240 q^{31}\) \(-8.66688 q^{33}\) \(-8.58569 q^{35}\) \(+4.15971 q^{37}\) \(-9.61083 q^{39}\) \(+0.245191 q^{41}\) \(+5.43293 q^{43}\) \(-12.6168 q^{45}\) \(+1.50042 q^{47}\) \(-2.22043 q^{49}\) \(+5.35091 q^{51}\) \(-7.38122 q^{53}\) \(-13.6554 q^{55}\) \(-17.6325 q^{57}\) \(-10.9107 q^{59}\) \(+8.32991 q^{61}\) \(+7.02367 q^{63}\) \(-15.1426 q^{65}\) \(+5.93170 q^{67}\) \(+1.42590 q^{69}\) \(-6.26670 q^{71}\) \(+0.909284 q^{73}\) \(-25.9790 q^{75}\) \(+7.60182 q^{77}\) \(-9.07280 q^{79}\) \(-8.31668 q^{81}\) \(+12.2441 q^{83}\) \(+8.43080 q^{85}\) \(-13.1858 q^{87}\) \(+10.9607 q^{89}\) \(+8.42976 q^{91}\) \(-20.1705 q^{93}\) \(-27.7815 q^{95}\) \(-7.29623 q^{97}\) \(+11.1710 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.49253 −1.43906 −0.719531 0.694461i \(-0.755643\pi\)
−0.719531 + 0.694461i \(0.755643\pi\)
\(4\) 0 0
\(5\) −3.92718 −1.75629 −0.878144 0.478396i \(-0.841218\pi\)
−0.878144 + 0.478396i \(0.841218\pi\)
\(6\) 0 0
\(7\) 2.18622 0.826315 0.413157 0.910660i \(-0.364426\pi\)
0.413157 + 0.910660i \(0.364426\pi\)
\(8\) 0 0
\(9\) 3.21269 1.07090
\(10\) 0 0
\(11\) 3.47715 1.04840 0.524199 0.851596i \(-0.324365\pi\)
0.524199 + 0.851596i \(0.324365\pi\)
\(12\) 0 0
\(13\) 3.85586 1.06942 0.534711 0.845035i \(-0.320421\pi\)
0.534711 + 0.845035i \(0.320421\pi\)
\(14\) 0 0
\(15\) 9.78861 2.52741
\(16\) 0 0
\(17\) −2.14678 −0.520671 −0.260336 0.965518i \(-0.583833\pi\)
−0.260336 + 0.965518i \(0.583833\pi\)
\(18\) 0 0
\(19\) 7.07416 1.62292 0.811462 0.584406i \(-0.198672\pi\)
0.811462 + 0.584406i \(0.198672\pi\)
\(20\) 0 0
\(21\) −5.44922 −1.18912
\(22\) 0 0
\(23\) −0.572069 −0.119285 −0.0596423 0.998220i \(-0.518996\pi\)
−0.0596423 + 0.998220i \(0.518996\pi\)
\(24\) 0 0
\(25\) 10.4227 2.08455
\(26\) 0 0
\(27\) −0.530148 −0.102027
\(28\) 0 0
\(29\) 5.29014 0.982354 0.491177 0.871060i \(-0.336567\pi\)
0.491177 + 0.871060i \(0.336567\pi\)
\(30\) 0 0
\(31\) 8.09240 1.45344 0.726719 0.686935i \(-0.241044\pi\)
0.726719 + 0.686935i \(0.241044\pi\)
\(32\) 0 0
\(33\) −8.66688 −1.50871
\(34\) 0 0
\(35\) −8.58569 −1.45125
\(36\) 0 0
\(37\) 4.15971 0.683852 0.341926 0.939727i \(-0.388921\pi\)
0.341926 + 0.939727i \(0.388921\pi\)
\(38\) 0 0
\(39\) −9.61083 −1.53896
\(40\) 0 0
\(41\) 0.245191 0.0382924 0.0191462 0.999817i \(-0.493905\pi\)
0.0191462 + 0.999817i \(0.493905\pi\)
\(42\) 0 0
\(43\) 5.43293 0.828514 0.414257 0.910160i \(-0.364042\pi\)
0.414257 + 0.910160i \(0.364042\pi\)
\(44\) 0 0
\(45\) −12.6168 −1.88081
\(46\) 0 0
\(47\) 1.50042 0.218858 0.109429 0.993995i \(-0.465098\pi\)
0.109429 + 0.993995i \(0.465098\pi\)
\(48\) 0 0
\(49\) −2.22043 −0.317204
\(50\) 0 0
\(51\) 5.35091 0.749278
\(52\) 0 0
\(53\) −7.38122 −1.01389 −0.506944 0.861979i \(-0.669225\pi\)
−0.506944 + 0.861979i \(0.669225\pi\)
\(54\) 0 0
\(55\) −13.6554 −1.84129
\(56\) 0 0
\(57\) −17.6325 −2.33549
\(58\) 0 0
\(59\) −10.9107 −1.42045 −0.710227 0.703972i \(-0.751408\pi\)
−0.710227 + 0.703972i \(0.751408\pi\)
\(60\) 0 0
\(61\) 8.32991 1.06654 0.533268 0.845946i \(-0.320964\pi\)
0.533268 + 0.845946i \(0.320964\pi\)
\(62\) 0 0
\(63\) 7.02367 0.884899
\(64\) 0 0
\(65\) −15.1426 −1.87821
\(66\) 0 0
\(67\) 5.93170 0.724673 0.362336 0.932047i \(-0.381979\pi\)
0.362336 + 0.932047i \(0.381979\pi\)
\(68\) 0 0
\(69\) 1.42590 0.171658
\(70\) 0 0
\(71\) −6.26670 −0.743721 −0.371861 0.928289i \(-0.621280\pi\)
−0.371861 + 0.928289i \(0.621280\pi\)
\(72\) 0 0
\(73\) 0.909284 0.106424 0.0532118 0.998583i \(-0.483054\pi\)
0.0532118 + 0.998583i \(0.483054\pi\)
\(74\) 0 0
\(75\) −25.9790 −2.99980
\(76\) 0 0
\(77\) 7.60182 0.866307
\(78\) 0 0
\(79\) −9.07280 −1.02077 −0.510385 0.859946i \(-0.670497\pi\)
−0.510385 + 0.859946i \(0.670497\pi\)
\(80\) 0 0
\(81\) −8.31668 −0.924075
\(82\) 0 0
\(83\) 12.2441 1.34396 0.671980 0.740569i \(-0.265444\pi\)
0.671980 + 0.740569i \(0.265444\pi\)
\(84\) 0 0
\(85\) 8.43080 0.914449
\(86\) 0 0
\(87\) −13.1858 −1.41367
\(88\) 0 0
\(89\) 10.9607 1.16184 0.580918 0.813962i \(-0.302694\pi\)
0.580918 + 0.813962i \(0.302694\pi\)
\(90\) 0 0
\(91\) 8.42976 0.883679
\(92\) 0 0
\(93\) −20.1705 −2.09159
\(94\) 0 0
\(95\) −27.7815 −2.85032
\(96\) 0 0
\(97\) −7.29623 −0.740820 −0.370410 0.928868i \(-0.620783\pi\)
−0.370410 + 0.928868i \(0.620783\pi\)
\(98\) 0 0
\(99\) 11.1710 1.12273
\(100\) 0 0
\(101\) −2.15477 −0.214408 −0.107204 0.994237i \(-0.534190\pi\)
−0.107204 + 0.994237i \(0.534190\pi\)
\(102\) 0 0
\(103\) 15.8738 1.56410 0.782048 0.623218i \(-0.214175\pi\)
0.782048 + 0.623218i \(0.214175\pi\)
\(104\) 0 0
\(105\) 21.4001 2.08843
\(106\) 0 0
\(107\) 9.70889 0.938594 0.469297 0.883040i \(-0.344507\pi\)
0.469297 + 0.883040i \(0.344507\pi\)
\(108\) 0 0
\(109\) −0.266281 −0.0255051 −0.0127525 0.999919i \(-0.504059\pi\)
−0.0127525 + 0.999919i \(0.504059\pi\)
\(110\) 0 0
\(111\) −10.3682 −0.984105
\(112\) 0 0
\(113\) −7.96495 −0.749280 −0.374640 0.927170i \(-0.622234\pi\)
−0.374640 + 0.927170i \(0.622234\pi\)
\(114\) 0 0
\(115\) 2.24662 0.209498
\(116\) 0 0
\(117\) 12.3877 1.14524
\(118\) 0 0
\(119\) −4.69334 −0.430238
\(120\) 0 0
\(121\) 1.09054 0.0991398
\(122\) 0 0
\(123\) −0.611145 −0.0551051
\(124\) 0 0
\(125\) −21.2961 −1.90478
\(126\) 0 0
\(127\) −6.21230 −0.551253 −0.275626 0.961265i \(-0.588885\pi\)
−0.275626 + 0.961265i \(0.588885\pi\)
\(128\) 0 0
\(129\) −13.5417 −1.19228
\(130\) 0 0
\(131\) −14.7337 −1.28729 −0.643645 0.765324i \(-0.722579\pi\)
−0.643645 + 0.765324i \(0.722579\pi\)
\(132\) 0 0
\(133\) 15.4657 1.34105
\(134\) 0 0
\(135\) 2.08199 0.179189
\(136\) 0 0
\(137\) 9.14072 0.780945 0.390472 0.920615i \(-0.372312\pi\)
0.390472 + 0.920615i \(0.372312\pi\)
\(138\) 0 0
\(139\) 1.35070 0.114564 0.0572822 0.998358i \(-0.481757\pi\)
0.0572822 + 0.998358i \(0.481757\pi\)
\(140\) 0 0
\(141\) −3.73983 −0.314950
\(142\) 0 0
\(143\) 13.4074 1.12118
\(144\) 0 0
\(145\) −20.7753 −1.72530
\(146\) 0 0
\(147\) 5.53448 0.456476
\(148\) 0 0
\(149\) 12.3909 1.01510 0.507552 0.861621i \(-0.330550\pi\)
0.507552 + 0.861621i \(0.330550\pi\)
\(150\) 0 0
\(151\) −17.7936 −1.44802 −0.724012 0.689788i \(-0.757704\pi\)
−0.724012 + 0.689788i \(0.757704\pi\)
\(152\) 0 0
\(153\) −6.89695 −0.557586
\(154\) 0 0
\(155\) −31.7803 −2.55266
\(156\) 0 0
\(157\) 13.1429 1.04892 0.524459 0.851435i \(-0.324267\pi\)
0.524459 + 0.851435i \(0.324267\pi\)
\(158\) 0 0
\(159\) 18.3979 1.45905
\(160\) 0 0
\(161\) −1.25067 −0.0985667
\(162\) 0 0
\(163\) 6.93629 0.543292 0.271646 0.962397i \(-0.412432\pi\)
0.271646 + 0.962397i \(0.412432\pi\)
\(164\) 0 0
\(165\) 34.0364 2.64973
\(166\) 0 0
\(167\) −12.5044 −0.967622 −0.483811 0.875173i \(-0.660748\pi\)
−0.483811 + 0.875173i \(0.660748\pi\)
\(168\) 0 0
\(169\) 1.86762 0.143663
\(170\) 0 0
\(171\) 22.7271 1.73799
\(172\) 0 0
\(173\) 21.2106 1.61261 0.806307 0.591497i \(-0.201463\pi\)
0.806307 + 0.591497i \(0.201463\pi\)
\(174\) 0 0
\(175\) 22.7865 1.72249
\(176\) 0 0
\(177\) 27.1953 2.04412
\(178\) 0 0
\(179\) −18.3274 −1.36986 −0.684929 0.728610i \(-0.740167\pi\)
−0.684929 + 0.728610i \(0.740167\pi\)
\(180\) 0 0
\(181\) 11.4582 0.851685 0.425842 0.904797i \(-0.359978\pi\)
0.425842 + 0.904797i \(0.359978\pi\)
\(182\) 0 0
\(183\) −20.7625 −1.53481
\(184\) 0 0
\(185\) −16.3359 −1.20104
\(186\) 0 0
\(187\) −7.46467 −0.545871
\(188\) 0 0
\(189\) −1.15902 −0.0843064
\(190\) 0 0
\(191\) −7.23850 −0.523759 −0.261880 0.965101i \(-0.584342\pi\)
−0.261880 + 0.965101i \(0.584342\pi\)
\(192\) 0 0
\(193\) −6.26334 −0.450845 −0.225423 0.974261i \(-0.572376\pi\)
−0.225423 + 0.974261i \(0.572376\pi\)
\(194\) 0 0
\(195\) 37.7435 2.70286
\(196\) 0 0
\(197\) 5.18663 0.369532 0.184766 0.982783i \(-0.440847\pi\)
0.184766 + 0.982783i \(0.440847\pi\)
\(198\) 0 0
\(199\) −20.9473 −1.48491 −0.742456 0.669895i \(-0.766339\pi\)
−0.742456 + 0.669895i \(0.766339\pi\)
\(200\) 0 0
\(201\) −14.7849 −1.04285
\(202\) 0 0
\(203\) 11.5654 0.811734
\(204\) 0 0
\(205\) −0.962908 −0.0672524
\(206\) 0 0
\(207\) −1.83788 −0.127742
\(208\) 0 0
\(209\) 24.5979 1.70147
\(210\) 0 0
\(211\) −17.4373 −1.20043 −0.600217 0.799837i \(-0.704919\pi\)
−0.600217 + 0.799837i \(0.704919\pi\)
\(212\) 0 0
\(213\) 15.6199 1.07026
\(214\) 0 0
\(215\) −21.3361 −1.45511
\(216\) 0 0
\(217\) 17.6918 1.20100
\(218\) 0 0
\(219\) −2.26642 −0.153150
\(220\) 0 0
\(221\) −8.27768 −0.556817
\(222\) 0 0
\(223\) 7.61026 0.509621 0.254810 0.966991i \(-0.417987\pi\)
0.254810 + 0.966991i \(0.417987\pi\)
\(224\) 0 0
\(225\) 33.4851 2.23234
\(226\) 0 0
\(227\) 26.2180 1.74015 0.870074 0.492921i \(-0.164071\pi\)
0.870074 + 0.492921i \(0.164071\pi\)
\(228\) 0 0
\(229\) 13.1573 0.869462 0.434731 0.900560i \(-0.356843\pi\)
0.434731 + 0.900560i \(0.356843\pi\)
\(230\) 0 0
\(231\) −18.9477 −1.24667
\(232\) 0 0
\(233\) 3.87355 0.253764 0.126882 0.991918i \(-0.459503\pi\)
0.126882 + 0.991918i \(0.459503\pi\)
\(234\) 0 0
\(235\) −5.89241 −0.384378
\(236\) 0 0
\(237\) 22.6142 1.46895
\(238\) 0 0
\(239\) −20.4227 −1.32103 −0.660517 0.750812i \(-0.729663\pi\)
−0.660517 + 0.750812i \(0.729663\pi\)
\(240\) 0 0
\(241\) 9.40360 0.605739 0.302870 0.953032i \(-0.402055\pi\)
0.302870 + 0.953032i \(0.402055\pi\)
\(242\) 0 0
\(243\) 22.3200 1.43183
\(244\) 0 0
\(245\) 8.72002 0.557101
\(246\) 0 0
\(247\) 27.2769 1.73559
\(248\) 0 0
\(249\) −30.5186 −1.93404
\(250\) 0 0
\(251\) −26.3902 −1.66573 −0.832866 0.553475i \(-0.813301\pi\)
−0.832866 + 0.553475i \(0.813301\pi\)
\(252\) 0 0
\(253\) −1.98917 −0.125058
\(254\) 0 0
\(255\) −21.0140 −1.31595
\(256\) 0 0
\(257\) 19.8601 1.23884 0.619420 0.785060i \(-0.287368\pi\)
0.619420 + 0.785060i \(0.287368\pi\)
\(258\) 0 0
\(259\) 9.09405 0.565077
\(260\) 0 0
\(261\) 16.9956 1.05200
\(262\) 0 0
\(263\) 21.7481 1.34105 0.670523 0.741889i \(-0.266070\pi\)
0.670523 + 0.741889i \(0.266070\pi\)
\(264\) 0 0
\(265\) 28.9874 1.78068
\(266\) 0 0
\(267\) −27.3200 −1.67195
\(268\) 0 0
\(269\) 29.7942 1.81658 0.908291 0.418339i \(-0.137388\pi\)
0.908291 + 0.418339i \(0.137388\pi\)
\(270\) 0 0
\(271\) 4.81290 0.292363 0.146181 0.989258i \(-0.453302\pi\)
0.146181 + 0.989258i \(0.453302\pi\)
\(272\) 0 0
\(273\) −21.0114 −1.27167
\(274\) 0 0
\(275\) 36.2414 2.18544
\(276\) 0 0
\(277\) −1.87943 −0.112924 −0.0564620 0.998405i \(-0.517982\pi\)
−0.0564620 + 0.998405i \(0.517982\pi\)
\(278\) 0 0
\(279\) 25.9984 1.55648
\(280\) 0 0
\(281\) 13.0500 0.778498 0.389249 0.921133i \(-0.372735\pi\)
0.389249 + 0.921133i \(0.372735\pi\)
\(282\) 0 0
\(283\) 6.75429 0.401501 0.200751 0.979642i \(-0.435662\pi\)
0.200751 + 0.979642i \(0.435662\pi\)
\(284\) 0 0
\(285\) 69.2462 4.10179
\(286\) 0 0
\(287\) 0.536042 0.0316415
\(288\) 0 0
\(289\) −12.3913 −0.728902
\(290\) 0 0
\(291\) 18.1861 1.06609
\(292\) 0 0
\(293\) −20.1411 −1.17666 −0.588329 0.808622i \(-0.700214\pi\)
−0.588329 + 0.808622i \(0.700214\pi\)
\(294\) 0 0
\(295\) 42.8484 2.49473
\(296\) 0 0
\(297\) −1.84340 −0.106965
\(298\) 0 0
\(299\) −2.20582 −0.127566
\(300\) 0 0
\(301\) 11.8776 0.684613
\(302\) 0 0
\(303\) 5.37083 0.308546
\(304\) 0 0
\(305\) −32.7131 −1.87314
\(306\) 0 0
\(307\) 4.70210 0.268363 0.134182 0.990957i \(-0.457159\pi\)
0.134182 + 0.990957i \(0.457159\pi\)
\(308\) 0 0
\(309\) −39.5660 −2.25083
\(310\) 0 0
\(311\) 32.6084 1.84905 0.924527 0.381115i \(-0.124460\pi\)
0.924527 + 0.381115i \(0.124460\pi\)
\(312\) 0 0
\(313\) 2.32504 0.131419 0.0657096 0.997839i \(-0.479069\pi\)
0.0657096 + 0.997839i \(0.479069\pi\)
\(314\) 0 0
\(315\) −27.5832 −1.55414
\(316\) 0 0
\(317\) −13.3206 −0.748160 −0.374080 0.927396i \(-0.622041\pi\)
−0.374080 + 0.927396i \(0.622041\pi\)
\(318\) 0 0
\(319\) 18.3946 1.02990
\(320\) 0 0
\(321\) −24.1997 −1.35069
\(322\) 0 0
\(323\) −15.1867 −0.845009
\(324\) 0 0
\(325\) 40.1886 2.22926
\(326\) 0 0
\(327\) 0.663712 0.0367034
\(328\) 0 0
\(329\) 3.28025 0.180846
\(330\) 0 0
\(331\) −1.14348 −0.0628516 −0.0314258 0.999506i \(-0.510005\pi\)
−0.0314258 + 0.999506i \(0.510005\pi\)
\(332\) 0 0
\(333\) 13.3639 0.732336
\(334\) 0 0
\(335\) −23.2949 −1.27273
\(336\) 0 0
\(337\) −6.33761 −0.345232 −0.172616 0.984989i \(-0.555222\pi\)
−0.172616 + 0.984989i \(0.555222\pi\)
\(338\) 0 0
\(339\) 19.8529 1.07826
\(340\) 0 0
\(341\) 28.1385 1.52378
\(342\) 0 0
\(343\) −20.1579 −1.08843
\(344\) 0 0
\(345\) −5.59976 −0.301481
\(346\) 0 0
\(347\) 4.93567 0.264961 0.132480 0.991186i \(-0.457706\pi\)
0.132480 + 0.991186i \(0.457706\pi\)
\(348\) 0 0
\(349\) −8.75307 −0.468541 −0.234270 0.972171i \(-0.575270\pi\)
−0.234270 + 0.972171i \(0.575270\pi\)
\(350\) 0 0
\(351\) −2.04417 −0.109110
\(352\) 0 0
\(353\) 5.01433 0.266886 0.133443 0.991056i \(-0.457397\pi\)
0.133443 + 0.991056i \(0.457397\pi\)
\(354\) 0 0
\(355\) 24.6105 1.30619
\(356\) 0 0
\(357\) 11.6983 0.619139
\(358\) 0 0
\(359\) 31.8687 1.68197 0.840984 0.541060i \(-0.181977\pi\)
0.840984 + 0.541060i \(0.181977\pi\)
\(360\) 0 0
\(361\) 31.0437 1.63388
\(362\) 0 0
\(363\) −2.71820 −0.142668
\(364\) 0 0
\(365\) −3.57092 −0.186911
\(366\) 0 0
\(367\) 2.03363 0.106155 0.0530773 0.998590i \(-0.483097\pi\)
0.0530773 + 0.998590i \(0.483097\pi\)
\(368\) 0 0
\(369\) 0.787723 0.0410072
\(370\) 0 0
\(371\) −16.1370 −0.837791
\(372\) 0 0
\(373\) −23.3372 −1.20835 −0.604176 0.796851i \(-0.706498\pi\)
−0.604176 + 0.796851i \(0.706498\pi\)
\(374\) 0 0
\(375\) 53.0811 2.74110
\(376\) 0 0
\(377\) 20.3980 1.05055
\(378\) 0 0
\(379\) −27.0205 −1.38795 −0.693975 0.719999i \(-0.744142\pi\)
−0.693975 + 0.719999i \(0.744142\pi\)
\(380\) 0 0
\(381\) 15.4843 0.793287
\(382\) 0 0
\(383\) −8.47464 −0.433034 −0.216517 0.976279i \(-0.569470\pi\)
−0.216517 + 0.976279i \(0.569470\pi\)
\(384\) 0 0
\(385\) −29.8537 −1.52149
\(386\) 0 0
\(387\) 17.4543 0.887254
\(388\) 0 0
\(389\) 5.56427 0.282120 0.141060 0.990001i \(-0.454949\pi\)
0.141060 + 0.990001i \(0.454949\pi\)
\(390\) 0 0
\(391\) 1.22811 0.0621081
\(392\) 0 0
\(393\) 36.7242 1.85249
\(394\) 0 0
\(395\) 35.6305 1.79277
\(396\) 0 0
\(397\) −16.8815 −0.847257 −0.423628 0.905836i \(-0.639244\pi\)
−0.423628 + 0.905836i \(0.639244\pi\)
\(398\) 0 0
\(399\) −38.5487 −1.92985
\(400\) 0 0
\(401\) 33.8108 1.68843 0.844215 0.536005i \(-0.180067\pi\)
0.844215 + 0.536005i \(0.180067\pi\)
\(402\) 0 0
\(403\) 31.2031 1.55434
\(404\) 0 0
\(405\) 32.6611 1.62294
\(406\) 0 0
\(407\) 14.4639 0.716949
\(408\) 0 0
\(409\) 2.34695 0.116049 0.0580247 0.998315i \(-0.481520\pi\)
0.0580247 + 0.998315i \(0.481520\pi\)
\(410\) 0 0
\(411\) −22.7835 −1.12383
\(412\) 0 0
\(413\) −23.8533 −1.17374
\(414\) 0 0
\(415\) −48.0846 −2.36038
\(416\) 0 0
\(417\) −3.36665 −0.164865
\(418\) 0 0
\(419\) 4.68586 0.228919 0.114460 0.993428i \(-0.463486\pi\)
0.114460 + 0.993428i \(0.463486\pi\)
\(420\) 0 0
\(421\) −5.06792 −0.246996 −0.123498 0.992345i \(-0.539411\pi\)
−0.123498 + 0.992345i \(0.539411\pi\)
\(422\) 0 0
\(423\) 4.82038 0.234375
\(424\) 0 0
\(425\) −22.3754 −1.08536
\(426\) 0 0
\(427\) 18.2110 0.881294
\(428\) 0 0
\(429\) −33.4182 −1.61345
\(430\) 0 0
\(431\) 16.8409 0.811196 0.405598 0.914052i \(-0.367063\pi\)
0.405598 + 0.914052i \(0.367063\pi\)
\(432\) 0 0
\(433\) 19.0307 0.914556 0.457278 0.889324i \(-0.348825\pi\)
0.457278 + 0.889324i \(0.348825\pi\)
\(434\) 0 0
\(435\) 51.7831 2.48281
\(436\) 0 0
\(437\) −4.04691 −0.193590
\(438\) 0 0
\(439\) −35.0666 −1.67364 −0.836819 0.547479i \(-0.815587\pi\)
−0.836819 + 0.547479i \(0.815587\pi\)
\(440\) 0 0
\(441\) −7.13355 −0.339693
\(442\) 0 0
\(443\) −21.7054 −1.03126 −0.515628 0.856812i \(-0.672441\pi\)
−0.515628 + 0.856812i \(0.672441\pi\)
\(444\) 0 0
\(445\) −43.0448 −2.04052
\(446\) 0 0
\(447\) −30.8847 −1.46080
\(448\) 0 0
\(449\) −27.7769 −1.31087 −0.655436 0.755251i \(-0.727515\pi\)
−0.655436 + 0.755251i \(0.727515\pi\)
\(450\) 0 0
\(451\) 0.852564 0.0401457
\(452\) 0 0
\(453\) 44.3511 2.08380
\(454\) 0 0
\(455\) −33.1052 −1.55200
\(456\) 0 0
\(457\) −1.78593 −0.0835421 −0.0417710 0.999127i \(-0.513300\pi\)
−0.0417710 + 0.999127i \(0.513300\pi\)
\(458\) 0 0
\(459\) 1.13811 0.0531225
\(460\) 0 0
\(461\) 13.4279 0.625400 0.312700 0.949852i \(-0.398766\pi\)
0.312700 + 0.949852i \(0.398766\pi\)
\(462\) 0 0
\(463\) −38.4010 −1.78465 −0.892323 0.451398i \(-0.850926\pi\)
−0.892323 + 0.451398i \(0.850926\pi\)
\(464\) 0 0
\(465\) 79.2133 3.67343
\(466\) 0 0
\(467\) −34.1437 −1.57998 −0.789991 0.613118i \(-0.789915\pi\)
−0.789991 + 0.613118i \(0.789915\pi\)
\(468\) 0 0
\(469\) 12.9680 0.598808
\(470\) 0 0
\(471\) −32.7591 −1.50946
\(472\) 0 0
\(473\) 18.8911 0.868613
\(474\) 0 0
\(475\) 73.7322 3.38306
\(476\) 0 0
\(477\) −23.7136 −1.08577
\(478\) 0 0
\(479\) 16.7021 0.763139 0.381569 0.924340i \(-0.375384\pi\)
0.381569 + 0.924340i \(0.375384\pi\)
\(480\) 0 0
\(481\) 16.0392 0.731326
\(482\) 0 0
\(483\) 3.11733 0.141844
\(484\) 0 0
\(485\) 28.6536 1.30109
\(486\) 0 0
\(487\) 34.0061 1.54096 0.770482 0.637462i \(-0.220016\pi\)
0.770482 + 0.637462i \(0.220016\pi\)
\(488\) 0 0
\(489\) −17.2889 −0.781831
\(490\) 0 0
\(491\) −36.4410 −1.64456 −0.822280 0.569083i \(-0.807298\pi\)
−0.822280 + 0.569083i \(0.807298\pi\)
\(492\) 0 0
\(493\) −11.3568 −0.511483
\(494\) 0 0
\(495\) −43.8706 −1.97183
\(496\) 0 0
\(497\) −13.7004 −0.614548
\(498\) 0 0
\(499\) 19.7536 0.884294 0.442147 0.896943i \(-0.354217\pi\)
0.442147 + 0.896943i \(0.354217\pi\)
\(500\) 0 0
\(501\) 31.1676 1.39247
\(502\) 0 0
\(503\) 25.7793 1.14944 0.574721 0.818350i \(-0.305111\pi\)
0.574721 + 0.818350i \(0.305111\pi\)
\(504\) 0 0
\(505\) 8.46218 0.376562
\(506\) 0 0
\(507\) −4.65509 −0.206740
\(508\) 0 0
\(509\) −11.7842 −0.522324 −0.261162 0.965295i \(-0.584106\pi\)
−0.261162 + 0.965295i \(0.584106\pi\)
\(510\) 0 0
\(511\) 1.98790 0.0879395
\(512\) 0 0
\(513\) −3.75035 −0.165582
\(514\) 0 0
\(515\) −62.3395 −2.74700
\(516\) 0 0
\(517\) 5.21717 0.229451
\(518\) 0 0
\(519\) −52.8681 −2.32065
\(520\) 0 0
\(521\) −19.0809 −0.835949 −0.417974 0.908459i \(-0.637260\pi\)
−0.417974 + 0.908459i \(0.637260\pi\)
\(522\) 0 0
\(523\) −4.20785 −0.183997 −0.0919983 0.995759i \(-0.529325\pi\)
−0.0919983 + 0.995759i \(0.529325\pi\)
\(524\) 0 0
\(525\) −56.7959 −2.47878
\(526\) 0 0
\(527\) −17.3726 −0.756763
\(528\) 0 0
\(529\) −22.6727 −0.985771
\(530\) 0 0
\(531\) −35.0528 −1.52116
\(532\) 0 0
\(533\) 0.945420 0.0409507
\(534\) 0 0
\(535\) −38.1286 −1.64844
\(536\) 0 0
\(537\) 45.6817 1.97131
\(538\) 0 0
\(539\) −7.72075 −0.332556
\(540\) 0 0
\(541\) 1.17651 0.0505820 0.0252910 0.999680i \(-0.491949\pi\)
0.0252910 + 0.999680i \(0.491949\pi\)
\(542\) 0 0
\(543\) −28.5600 −1.22563
\(544\) 0 0
\(545\) 1.04573 0.0447943
\(546\) 0 0
\(547\) 1.24925 0.0534141 0.0267071 0.999643i \(-0.491498\pi\)
0.0267071 + 0.999643i \(0.491498\pi\)
\(548\) 0 0
\(549\) 26.7615 1.14215
\(550\) 0 0
\(551\) 37.4233 1.59429
\(552\) 0 0
\(553\) −19.8352 −0.843477
\(554\) 0 0
\(555\) 40.7178 1.72837
\(556\) 0 0
\(557\) 4.66180 0.197527 0.0987635 0.995111i \(-0.468511\pi\)
0.0987635 + 0.995111i \(0.468511\pi\)
\(558\) 0 0
\(559\) 20.9486 0.886031
\(560\) 0 0
\(561\) 18.6059 0.785542
\(562\) 0 0
\(563\) −9.89653 −0.417089 −0.208545 0.978013i \(-0.566873\pi\)
−0.208545 + 0.978013i \(0.566873\pi\)
\(564\) 0 0
\(565\) 31.2798 1.31595
\(566\) 0 0
\(567\) −18.1821 −0.763577
\(568\) 0 0
\(569\) 14.5155 0.608521 0.304260 0.952589i \(-0.401591\pi\)
0.304260 + 0.952589i \(0.401591\pi\)
\(570\) 0 0
\(571\) 27.2594 1.14077 0.570385 0.821377i \(-0.306794\pi\)
0.570385 + 0.821377i \(0.306794\pi\)
\(572\) 0 0
\(573\) 18.0422 0.753722
\(574\) 0 0
\(575\) −5.96253 −0.248655
\(576\) 0 0
\(577\) −37.2339 −1.55007 −0.775033 0.631920i \(-0.782267\pi\)
−0.775033 + 0.631920i \(0.782267\pi\)
\(578\) 0 0
\(579\) 15.6116 0.648794
\(580\) 0 0
\(581\) 26.7682 1.11053
\(582\) 0 0
\(583\) −25.6656 −1.06296
\(584\) 0 0
\(585\) −48.6487 −2.01138
\(586\) 0 0
\(587\) −19.9918 −0.825152 −0.412576 0.910923i \(-0.635371\pi\)
−0.412576 + 0.910923i \(0.635371\pi\)
\(588\) 0 0
\(589\) 57.2469 2.35882
\(590\) 0 0
\(591\) −12.9278 −0.531780
\(592\) 0 0
\(593\) −36.6630 −1.50557 −0.752785 0.658266i \(-0.771290\pi\)
−0.752785 + 0.658266i \(0.771290\pi\)
\(594\) 0 0
\(595\) 18.4316 0.755622
\(596\) 0 0
\(597\) 52.2116 2.13688
\(598\) 0 0
\(599\) 21.8396 0.892343 0.446172 0.894947i \(-0.352787\pi\)
0.446172 + 0.894947i \(0.352787\pi\)
\(600\) 0 0
\(601\) −0.564099 −0.0230101 −0.0115050 0.999934i \(-0.503662\pi\)
−0.0115050 + 0.999934i \(0.503662\pi\)
\(602\) 0 0
\(603\) 19.0568 0.776051
\(604\) 0 0
\(605\) −4.28274 −0.174118
\(606\) 0 0
\(607\) 42.3256 1.71794 0.858972 0.512022i \(-0.171103\pi\)
0.858972 + 0.512022i \(0.171103\pi\)
\(608\) 0 0
\(609\) −28.8271 −1.16814
\(610\) 0 0
\(611\) 5.78539 0.234052
\(612\) 0 0
\(613\) −19.1984 −0.775416 −0.387708 0.921782i \(-0.626733\pi\)
−0.387708 + 0.921782i \(0.626733\pi\)
\(614\) 0 0
\(615\) 2.40008 0.0967804
\(616\) 0 0
\(617\) 31.4840 1.26750 0.633750 0.773538i \(-0.281515\pi\)
0.633750 + 0.773538i \(0.281515\pi\)
\(618\) 0 0
\(619\) −26.3771 −1.06019 −0.530093 0.847939i \(-0.677843\pi\)
−0.530093 + 0.847939i \(0.677843\pi\)
\(620\) 0 0
\(621\) 0.303281 0.0121703
\(622\) 0 0
\(623\) 23.9626 0.960042
\(624\) 0 0
\(625\) 31.5199 1.26080
\(626\) 0 0
\(627\) −61.3109 −2.44852
\(628\) 0 0
\(629\) −8.92999 −0.356062
\(630\) 0 0
\(631\) 9.85443 0.392298 0.196149 0.980574i \(-0.437156\pi\)
0.196149 + 0.980574i \(0.437156\pi\)
\(632\) 0 0
\(633\) 43.4630 1.72750
\(634\) 0 0
\(635\) 24.3968 0.968159
\(636\) 0 0
\(637\) −8.56164 −0.339225
\(638\) 0 0
\(639\) −20.1330 −0.796450
\(640\) 0 0
\(641\) −0.555236 −0.0219305 −0.0109652 0.999940i \(-0.503490\pi\)
−0.0109652 + 0.999940i \(0.503490\pi\)
\(642\) 0 0
\(643\) −15.8519 −0.625136 −0.312568 0.949895i \(-0.601189\pi\)
−0.312568 + 0.949895i \(0.601189\pi\)
\(644\) 0 0
\(645\) 53.1808 2.09399
\(646\) 0 0
\(647\) −32.4741 −1.27669 −0.638345 0.769751i \(-0.720380\pi\)
−0.638345 + 0.769751i \(0.720380\pi\)
\(648\) 0 0
\(649\) −37.9382 −1.48920
\(650\) 0 0
\(651\) −44.0973 −1.72831
\(652\) 0 0
\(653\) 31.1028 1.21715 0.608573 0.793498i \(-0.291742\pi\)
0.608573 + 0.793498i \(0.291742\pi\)
\(654\) 0 0
\(655\) 57.8619 2.26085
\(656\) 0 0
\(657\) 2.92125 0.113969
\(658\) 0 0
\(659\) 12.9780 0.505551 0.252776 0.967525i \(-0.418657\pi\)
0.252776 + 0.967525i \(0.418657\pi\)
\(660\) 0 0
\(661\) 25.6740 0.998603 0.499301 0.866428i \(-0.333590\pi\)
0.499301 + 0.866428i \(0.333590\pi\)
\(662\) 0 0
\(663\) 20.6323 0.801294
\(664\) 0 0
\(665\) −60.7366 −2.35526
\(666\) 0 0
\(667\) −3.02633 −0.117180
\(668\) 0 0
\(669\) −18.9688 −0.733376
\(670\) 0 0
\(671\) 28.9643 1.11815
\(672\) 0 0
\(673\) −9.25271 −0.356666 −0.178333 0.983970i \(-0.557070\pi\)
−0.178333 + 0.983970i \(0.557070\pi\)
\(674\) 0 0
\(675\) −5.52559 −0.212680
\(676\) 0 0
\(677\) 49.2561 1.89307 0.946533 0.322607i \(-0.104559\pi\)
0.946533 + 0.322607i \(0.104559\pi\)
\(678\) 0 0
\(679\) −15.9512 −0.612151
\(680\) 0 0
\(681\) −65.3490 −2.50418
\(682\) 0 0
\(683\) −11.1109 −0.425148 −0.212574 0.977145i \(-0.568185\pi\)
−0.212574 + 0.977145i \(0.568185\pi\)
\(684\) 0 0
\(685\) −35.8973 −1.37156
\(686\) 0 0
\(687\) −32.7950 −1.25121
\(688\) 0 0
\(689\) −28.4609 −1.08427
\(690\) 0 0
\(691\) 47.2131 1.79607 0.898036 0.439922i \(-0.144994\pi\)
0.898036 + 0.439922i \(0.144994\pi\)
\(692\) 0 0
\(693\) 24.4223 0.927727
\(694\) 0 0
\(695\) −5.30442 −0.201208
\(696\) 0 0
\(697\) −0.526371 −0.0199377
\(698\) 0 0
\(699\) −9.65492 −0.365183
\(700\) 0 0
\(701\) −10.3819 −0.392119 −0.196060 0.980592i \(-0.562815\pi\)
−0.196060 + 0.980592i \(0.562815\pi\)
\(702\) 0 0
\(703\) 29.4264 1.10984
\(704\) 0 0
\(705\) 14.6870 0.553144
\(706\) 0 0
\(707\) −4.71082 −0.177168
\(708\) 0 0
\(709\) −15.3544 −0.576648 −0.288324 0.957533i \(-0.593098\pi\)
−0.288324 + 0.957533i \(0.593098\pi\)
\(710\) 0 0
\(711\) −29.1481 −1.09314
\(712\) 0 0
\(713\) −4.62941 −0.173373
\(714\) 0 0
\(715\) −52.6532 −1.96912
\(716\) 0 0
\(717\) 50.9041 1.90105
\(718\) 0 0
\(719\) −15.3370 −0.571974 −0.285987 0.958233i \(-0.592321\pi\)
−0.285987 + 0.958233i \(0.592321\pi\)
\(720\) 0 0
\(721\) 34.7038 1.29244
\(722\) 0 0
\(723\) −23.4387 −0.871696
\(724\) 0 0
\(725\) 55.1378 2.04777
\(726\) 0 0
\(727\) 8.20666 0.304368 0.152184 0.988352i \(-0.451369\pi\)
0.152184 + 0.988352i \(0.451369\pi\)
\(728\) 0 0
\(729\) −30.6832 −1.13641
\(730\) 0 0
\(731\) −11.6633 −0.431383
\(732\) 0 0
\(733\) 14.9200 0.551082 0.275541 0.961289i \(-0.411143\pi\)
0.275541 + 0.961289i \(0.411143\pi\)
\(734\) 0 0
\(735\) −21.7349 −0.801703
\(736\) 0 0
\(737\) 20.6254 0.759746
\(738\) 0 0
\(739\) −39.3144 −1.44620 −0.723102 0.690742i \(-0.757284\pi\)
−0.723102 + 0.690742i \(0.757284\pi\)
\(740\) 0 0
\(741\) −67.9885 −2.49762
\(742\) 0 0
\(743\) −43.4766 −1.59500 −0.797500 0.603319i \(-0.793845\pi\)
−0.797500 + 0.603319i \(0.793845\pi\)
\(744\) 0 0
\(745\) −48.6614 −1.78282
\(746\) 0 0
\(747\) 39.3364 1.43924
\(748\) 0 0
\(749\) 21.2258 0.775574
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 65.7782 2.39709
\(754\) 0 0
\(755\) 69.8787 2.54315
\(756\) 0 0
\(757\) 20.0740 0.729600 0.364800 0.931086i \(-0.381137\pi\)
0.364800 + 0.931086i \(0.381137\pi\)
\(758\) 0 0
\(759\) 4.95805 0.179966
\(760\) 0 0
\(761\) 16.5998 0.601742 0.300871 0.953665i \(-0.402723\pi\)
0.300871 + 0.953665i \(0.402723\pi\)
\(762\) 0 0
\(763\) −0.582149 −0.0210752
\(764\) 0 0
\(765\) 27.0856 0.979281
\(766\) 0 0
\(767\) −42.0702 −1.51907
\(768\) 0 0
\(769\) −24.4487 −0.881641 −0.440821 0.897595i \(-0.645313\pi\)
−0.440821 + 0.897595i \(0.645313\pi\)
\(770\) 0 0
\(771\) −49.5019 −1.78277
\(772\) 0 0
\(773\) −33.8832 −1.21869 −0.609347 0.792903i \(-0.708569\pi\)
−0.609347 + 0.792903i \(0.708569\pi\)
\(774\) 0 0
\(775\) 84.3451 3.02976
\(776\) 0 0
\(777\) −22.6672 −0.813181
\(778\) 0 0
\(779\) 1.73452 0.0621455
\(780\) 0 0
\(781\) −21.7902 −0.779716
\(782\) 0 0
\(783\) −2.80455 −0.100227
\(784\) 0 0
\(785\) −51.6146 −1.84220
\(786\) 0 0
\(787\) −8.39663 −0.299307 −0.149654 0.988738i \(-0.547816\pi\)
−0.149654 + 0.988738i \(0.547816\pi\)
\(788\) 0 0
\(789\) −54.2078 −1.92985
\(790\) 0 0
\(791\) −17.4132 −0.619141
\(792\) 0 0
\(793\) 32.1189 1.14058
\(794\) 0 0
\(795\) −72.2519 −2.56251
\(796\) 0 0
\(797\) 20.8862 0.739826 0.369913 0.929066i \(-0.379387\pi\)
0.369913 + 0.929066i \(0.379387\pi\)
\(798\) 0 0
\(799\) −3.22107 −0.113953
\(800\) 0 0
\(801\) 35.2135 1.24421
\(802\) 0 0
\(803\) 3.16171 0.111574
\(804\) 0 0
\(805\) 4.91161 0.173112
\(806\) 0 0
\(807\) −74.2628 −2.61417
\(808\) 0 0
\(809\) −2.28498 −0.0803355 −0.0401678 0.999193i \(-0.512789\pi\)
−0.0401678 + 0.999193i \(0.512789\pi\)
\(810\) 0 0
\(811\) −18.5733 −0.652198 −0.326099 0.945336i \(-0.605734\pi\)
−0.326099 + 0.945336i \(0.605734\pi\)
\(812\) 0 0
\(813\) −11.9963 −0.420728
\(814\) 0 0
\(815\) −27.2401 −0.954178
\(816\) 0 0
\(817\) 38.4334 1.34461
\(818\) 0 0
\(819\) 27.0823 0.946330
\(820\) 0 0
\(821\) −13.4261 −0.468575 −0.234287 0.972167i \(-0.575276\pi\)
−0.234287 + 0.972167i \(0.575276\pi\)
\(822\) 0 0
\(823\) 56.5702 1.97191 0.985957 0.167001i \(-0.0534082\pi\)
0.985957 + 0.167001i \(0.0534082\pi\)
\(824\) 0 0
\(825\) −90.3327 −3.14498
\(826\) 0 0
\(827\) 23.4792 0.816450 0.408225 0.912881i \(-0.366148\pi\)
0.408225 + 0.912881i \(0.366148\pi\)
\(828\) 0 0
\(829\) 2.60961 0.0906356 0.0453178 0.998973i \(-0.485570\pi\)
0.0453178 + 0.998973i \(0.485570\pi\)
\(830\) 0 0
\(831\) 4.68453 0.162504
\(832\) 0 0
\(833\) 4.76677 0.165159
\(834\) 0 0
\(835\) 49.1072 1.69942
\(836\) 0 0
\(837\) −4.29017 −0.148290
\(838\) 0 0
\(839\) −33.9247 −1.17121 −0.585606 0.810596i \(-0.699143\pi\)
−0.585606 + 0.810596i \(0.699143\pi\)
\(840\) 0 0
\(841\) −1.01442 −0.0349802
\(842\) 0 0
\(843\) −32.5275 −1.12031
\(844\) 0 0
\(845\) −7.33448 −0.252314
\(846\) 0 0
\(847\) 2.38416 0.0819207
\(848\) 0 0
\(849\) −16.8353 −0.577785
\(850\) 0 0
\(851\) −2.37964 −0.0815730
\(852\) 0 0
\(853\) −24.2402 −0.829970 −0.414985 0.909828i \(-0.636213\pi\)
−0.414985 + 0.909828i \(0.636213\pi\)
\(854\) 0 0
\(855\) −89.2535 −3.05240
\(856\) 0 0
\(857\) −20.8125 −0.710941 −0.355470 0.934688i \(-0.615679\pi\)
−0.355470 + 0.934688i \(0.615679\pi\)
\(858\) 0 0
\(859\) −30.8237 −1.05169 −0.525846 0.850580i \(-0.676251\pi\)
−0.525846 + 0.850580i \(0.676251\pi\)
\(860\) 0 0
\(861\) −1.33610 −0.0455341
\(862\) 0 0
\(863\) −43.5436 −1.48224 −0.741121 0.671372i \(-0.765705\pi\)
−0.741121 + 0.671372i \(0.765705\pi\)
\(864\) 0 0
\(865\) −83.2980 −2.83222
\(866\) 0 0
\(867\) 30.8857 1.04893
\(868\) 0 0
\(869\) −31.5474 −1.07017
\(870\) 0 0
\(871\) 22.8718 0.774981
\(872\) 0 0
\(873\) −23.4406 −0.793343
\(874\) 0 0
\(875\) −46.5581 −1.57395
\(876\) 0 0
\(877\) −55.6566 −1.87939 −0.939695 0.342014i \(-0.888891\pi\)
−0.939695 + 0.342014i \(0.888891\pi\)
\(878\) 0 0
\(879\) 50.2024 1.69328
\(880\) 0 0
\(881\) 2.58474 0.0870821 0.0435411 0.999052i \(-0.486136\pi\)
0.0435411 + 0.999052i \(0.486136\pi\)
\(882\) 0 0
\(883\) −8.56154 −0.288119 −0.144059 0.989569i \(-0.546016\pi\)
−0.144059 + 0.989569i \(0.546016\pi\)
\(884\) 0 0
\(885\) −106.801 −3.59007
\(886\) 0 0
\(887\) −45.2711 −1.52006 −0.760028 0.649891i \(-0.774815\pi\)
−0.760028 + 0.649891i \(0.774815\pi\)
\(888\) 0 0
\(889\) −13.5815 −0.455508
\(890\) 0 0
\(891\) −28.9183 −0.968799
\(892\) 0 0
\(893\) 10.6142 0.355190
\(894\) 0 0
\(895\) 71.9752 2.40586
\(896\) 0 0
\(897\) 5.49806 0.183575
\(898\) 0 0
\(899\) 42.8099 1.42779
\(900\) 0 0
\(901\) 15.8459 0.527902
\(902\) 0 0
\(903\) −29.6052 −0.985200
\(904\) 0 0
\(905\) −44.9986 −1.49580
\(906\) 0 0
\(907\) 35.5777 1.18134 0.590669 0.806914i \(-0.298864\pi\)
0.590669 + 0.806914i \(0.298864\pi\)
\(908\) 0 0
\(909\) −6.92263 −0.229609
\(910\) 0 0
\(911\) −13.1500 −0.435679 −0.217839 0.975985i \(-0.569901\pi\)
−0.217839 + 0.975985i \(0.569901\pi\)
\(912\) 0 0
\(913\) 42.5744 1.40901
\(914\) 0 0
\(915\) 81.5382 2.69557
\(916\) 0 0
\(917\) −32.2112 −1.06371
\(918\) 0 0
\(919\) −23.1987 −0.765255 −0.382628 0.923903i \(-0.624981\pi\)
−0.382628 + 0.923903i \(0.624981\pi\)
\(920\) 0 0
\(921\) −11.7201 −0.386191
\(922\) 0 0
\(923\) −24.1635 −0.795351
\(924\) 0 0
\(925\) 43.3556 1.42552
\(926\) 0 0
\(927\) 50.9978 1.67499
\(928\) 0 0
\(929\) −10.4634 −0.343292 −0.171646 0.985159i \(-0.554909\pi\)
−0.171646 + 0.985159i \(0.554909\pi\)
\(930\) 0 0
\(931\) −15.7077 −0.514797
\(932\) 0 0
\(933\) −81.2774 −2.66090
\(934\) 0 0
\(935\) 29.3151 0.958707
\(936\) 0 0
\(937\) −29.5114 −0.964094 −0.482047 0.876145i \(-0.660107\pi\)
−0.482047 + 0.876145i \(0.660107\pi\)
\(938\) 0 0
\(939\) −5.79523 −0.189120
\(940\) 0 0
\(941\) 44.6333 1.45500 0.727502 0.686105i \(-0.240681\pi\)
0.727502 + 0.686105i \(0.240681\pi\)
\(942\) 0 0
\(943\) −0.140266 −0.00456769
\(944\) 0 0
\(945\) 4.55169 0.148066
\(946\) 0 0
\(947\) 43.7330 1.42113 0.710566 0.703631i \(-0.248439\pi\)
0.710566 + 0.703631i \(0.248439\pi\)
\(948\) 0 0
\(949\) 3.50607 0.113812
\(950\) 0 0
\(951\) 33.2020 1.07665
\(952\) 0 0
\(953\) 31.2685 1.01289 0.506444 0.862273i \(-0.330960\pi\)
0.506444 + 0.862273i \(0.330960\pi\)
\(954\) 0 0
\(955\) 28.4269 0.919872
\(956\) 0 0
\(957\) −45.8490 −1.48209
\(958\) 0 0
\(959\) 19.9837 0.645306
\(960\) 0 0
\(961\) 34.4870 1.11248
\(962\) 0 0
\(963\) 31.1917 1.00514
\(964\) 0 0
\(965\) 24.5973 0.791815
\(966\) 0 0
\(967\) 3.81997 0.122842 0.0614210 0.998112i \(-0.480437\pi\)
0.0614210 + 0.998112i \(0.480437\pi\)
\(968\) 0 0
\(969\) 37.8532 1.21602
\(970\) 0 0
\(971\) 19.4527 0.624268 0.312134 0.950038i \(-0.398956\pi\)
0.312134 + 0.950038i \(0.398956\pi\)
\(972\) 0 0
\(973\) 2.95292 0.0946663
\(974\) 0 0
\(975\) −100.171 −3.20805
\(976\) 0 0
\(977\) 57.4235 1.83714 0.918571 0.395256i \(-0.129344\pi\)
0.918571 + 0.395256i \(0.129344\pi\)
\(978\) 0 0
\(979\) 38.1121 1.21807
\(980\) 0 0
\(981\) −0.855479 −0.0273133
\(982\) 0 0
\(983\) −7.00696 −0.223487 −0.111744 0.993737i \(-0.535644\pi\)
−0.111744 + 0.993737i \(0.535644\pi\)
\(984\) 0 0
\(985\) −20.3688 −0.649005
\(986\) 0 0
\(987\) −8.17610 −0.260248
\(988\) 0 0
\(989\) −3.10801 −0.0988290
\(990\) 0 0
\(991\) −9.87477 −0.313682 −0.156841 0.987624i \(-0.550131\pi\)
−0.156841 + 0.987624i \(0.550131\pi\)
\(992\) 0 0
\(993\) 2.85017 0.0904473
\(994\) 0 0
\(995\) 82.2637 2.60793
\(996\) 0 0
\(997\) 45.6262 1.44500 0.722498 0.691373i \(-0.242994\pi\)
0.722498 + 0.691373i \(0.242994\pi\)
\(998\) 0 0
\(999\) −2.20526 −0.0697713
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 \(a_p\))