Properties

Label 4005.2.a.p.1.1
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.51468\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51468 q^{2} +4.32363 q^{4} +1.00000 q^{5} -2.83060 q^{7} -5.84320 q^{8} +O(q^{10})\) \(q-2.51468 q^{2} +4.32363 q^{4} +1.00000 q^{5} -2.83060 q^{7} -5.84320 q^{8} -2.51468 q^{10} +1.32852 q^{11} -5.12107 q^{13} +7.11806 q^{14} +6.04654 q^{16} -4.61208 q^{17} +1.84782 q^{19} +4.32363 q^{20} -3.34081 q^{22} +2.29047 q^{23} +1.00000 q^{25} +12.8779 q^{26} -12.2385 q^{28} -0.167368 q^{29} +9.85168 q^{31} -3.51873 q^{32} +11.5979 q^{34} -2.83060 q^{35} -0.207451 q^{37} -4.64669 q^{38} -5.84320 q^{40} -5.20162 q^{41} +8.88527 q^{43} +5.74404 q^{44} -5.75981 q^{46} +5.91188 q^{47} +1.01229 q^{49} -2.51468 q^{50} -22.1416 q^{52} +3.11452 q^{53} +1.32852 q^{55} +16.5398 q^{56} +0.420877 q^{58} +7.20896 q^{59} +12.1210 q^{61} -24.7739 q^{62} -3.24458 q^{64} -5.12107 q^{65} +9.69323 q^{67} -19.9409 q^{68} +7.11806 q^{70} -0.991867 q^{71} -12.1815 q^{73} +0.521675 q^{74} +7.98932 q^{76} -3.76051 q^{77} -8.00154 q^{79} +6.04654 q^{80} +13.0804 q^{82} -14.9877 q^{83} -4.61208 q^{85} -22.3437 q^{86} -7.76282 q^{88} -1.00000 q^{89} +14.4957 q^{91} +9.90316 q^{92} -14.8665 q^{94} +1.84782 q^{95} +1.80568 q^{97} -2.54559 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51468 −1.77815 −0.889075 0.457762i \(-0.848651\pi\)
−0.889075 + 0.457762i \(0.848651\pi\)
\(3\) 0 0
\(4\) 4.32363 2.16182
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.83060 −1.06987 −0.534933 0.844895i \(-0.679663\pi\)
−0.534933 + 0.844895i \(0.679663\pi\)
\(8\) −5.84320 −2.06588
\(9\) 0 0
\(10\) −2.51468 −0.795213
\(11\) 1.32852 0.400564 0.200282 0.979738i \(-0.435814\pi\)
0.200282 + 0.979738i \(0.435814\pi\)
\(12\) 0 0
\(13\) −5.12107 −1.42033 −0.710165 0.704036i \(-0.751379\pi\)
−0.710165 + 0.704036i \(0.751379\pi\)
\(14\) 7.11806 1.90238
\(15\) 0 0
\(16\) 6.04654 1.51164
\(17\) −4.61208 −1.11859 −0.559297 0.828968i \(-0.688929\pi\)
−0.559297 + 0.828968i \(0.688929\pi\)
\(18\) 0 0
\(19\) 1.84782 0.423920 0.211960 0.977278i \(-0.432015\pi\)
0.211960 + 0.977278i \(0.432015\pi\)
\(20\) 4.32363 0.966794
\(21\) 0 0
\(22\) −3.34081 −0.712263
\(23\) 2.29047 0.477596 0.238798 0.971069i \(-0.423247\pi\)
0.238798 + 0.971069i \(0.423247\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 12.8779 2.52556
\(27\) 0 0
\(28\) −12.2385 −2.31285
\(29\) −0.167368 −0.0310794 −0.0155397 0.999879i \(-0.504947\pi\)
−0.0155397 + 0.999879i \(0.504947\pi\)
\(30\) 0 0
\(31\) 9.85168 1.76941 0.884707 0.466148i \(-0.154359\pi\)
0.884707 + 0.466148i \(0.154359\pi\)
\(32\) −3.51873 −0.622030
\(33\) 0 0
\(34\) 11.5979 1.98903
\(35\) −2.83060 −0.478458
\(36\) 0 0
\(37\) −0.207451 −0.0341048 −0.0170524 0.999855i \(-0.505428\pi\)
−0.0170524 + 0.999855i \(0.505428\pi\)
\(38\) −4.64669 −0.753793
\(39\) 0 0
\(40\) −5.84320 −0.923892
\(41\) −5.20162 −0.812357 −0.406178 0.913794i \(-0.633139\pi\)
−0.406178 + 0.913794i \(0.633139\pi\)
\(42\) 0 0
\(43\) 8.88527 1.35499 0.677496 0.735527i \(-0.263065\pi\)
0.677496 + 0.735527i \(0.263065\pi\)
\(44\) 5.74404 0.865946
\(45\) 0 0
\(46\) −5.75981 −0.849238
\(47\) 5.91188 0.862336 0.431168 0.902272i \(-0.358102\pi\)
0.431168 + 0.902272i \(0.358102\pi\)
\(48\) 0 0
\(49\) 1.01229 0.144613
\(50\) −2.51468 −0.355630
\(51\) 0 0
\(52\) −22.1416 −3.07049
\(53\) 3.11452 0.427812 0.213906 0.976854i \(-0.431381\pi\)
0.213906 + 0.976854i \(0.431381\pi\)
\(54\) 0 0
\(55\) 1.32852 0.179138
\(56\) 16.5398 2.21022
\(57\) 0 0
\(58\) 0.420877 0.0552639
\(59\) 7.20896 0.938526 0.469263 0.883058i \(-0.344520\pi\)
0.469263 + 0.883058i \(0.344520\pi\)
\(60\) 0 0
\(61\) 12.1210 1.55193 0.775966 0.630775i \(-0.217263\pi\)
0.775966 + 0.630775i \(0.217263\pi\)
\(62\) −24.7739 −3.14628
\(63\) 0 0
\(64\) −3.24458 −0.405573
\(65\) −5.12107 −0.635190
\(66\) 0 0
\(67\) 9.69323 1.18422 0.592108 0.805858i \(-0.298296\pi\)
0.592108 + 0.805858i \(0.298296\pi\)
\(68\) −19.9409 −2.41819
\(69\) 0 0
\(70\) 7.11806 0.850771
\(71\) −0.991867 −0.117713 −0.0588565 0.998266i \(-0.518745\pi\)
−0.0588565 + 0.998266i \(0.518745\pi\)
\(72\) 0 0
\(73\) −12.1815 −1.42573 −0.712867 0.701300i \(-0.752603\pi\)
−0.712867 + 0.701300i \(0.752603\pi\)
\(74\) 0.521675 0.0606435
\(75\) 0 0
\(76\) 7.98932 0.916437
\(77\) −3.76051 −0.428550
\(78\) 0 0
\(79\) −8.00154 −0.900244 −0.450122 0.892967i \(-0.648619\pi\)
−0.450122 + 0.892967i \(0.648619\pi\)
\(80\) 6.04654 0.676024
\(81\) 0 0
\(82\) 13.0804 1.44449
\(83\) −14.9877 −1.64511 −0.822557 0.568683i \(-0.807453\pi\)
−0.822557 + 0.568683i \(0.807453\pi\)
\(84\) 0 0
\(85\) −4.61208 −0.500250
\(86\) −22.3437 −2.40938
\(87\) 0 0
\(88\) −7.76282 −0.827519
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) 14.4957 1.51956
\(92\) 9.90316 1.03248
\(93\) 0 0
\(94\) −14.8665 −1.53336
\(95\) 1.84782 0.189583
\(96\) 0 0
\(97\) 1.80568 0.183339 0.0916697 0.995789i \(-0.470780\pi\)
0.0916697 + 0.995789i \(0.470780\pi\)
\(98\) −2.54559 −0.257143
\(99\) 0 0
\(100\) 4.32363 0.432363
\(101\) −7.12949 −0.709411 −0.354705 0.934978i \(-0.615419\pi\)
−0.354705 + 0.934978i \(0.615419\pi\)
\(102\) 0 0
\(103\) −4.87235 −0.480087 −0.240043 0.970762i \(-0.577162\pi\)
−0.240043 + 0.970762i \(0.577162\pi\)
\(104\) 29.9235 2.93424
\(105\) 0 0
\(106\) −7.83202 −0.760713
\(107\) 15.4342 1.49208 0.746042 0.665899i \(-0.231952\pi\)
0.746042 + 0.665899i \(0.231952\pi\)
\(108\) 0 0
\(109\) −16.8174 −1.61081 −0.805407 0.592722i \(-0.798053\pi\)
−0.805407 + 0.592722i \(0.798053\pi\)
\(110\) −3.34081 −0.318534
\(111\) 0 0
\(112\) −17.1153 −1.61725
\(113\) −20.6237 −1.94011 −0.970056 0.242880i \(-0.921908\pi\)
−0.970056 + 0.242880i \(0.921908\pi\)
\(114\) 0 0
\(115\) 2.29047 0.213587
\(116\) −0.723638 −0.0671881
\(117\) 0 0
\(118\) −18.1282 −1.66884
\(119\) 13.0549 1.19674
\(120\) 0 0
\(121\) −9.23503 −0.839548
\(122\) −30.4804 −2.75957
\(123\) 0 0
\(124\) 42.5950 3.82515
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −12.4045 −1.10072 −0.550362 0.834926i \(-0.685510\pi\)
−0.550362 + 0.834926i \(0.685510\pi\)
\(128\) 15.1966 1.34320
\(129\) 0 0
\(130\) 12.8779 1.12946
\(131\) −12.0122 −1.04951 −0.524755 0.851254i \(-0.675843\pi\)
−0.524755 + 0.851254i \(0.675843\pi\)
\(132\) 0 0
\(133\) −5.23045 −0.453537
\(134\) −24.3754 −2.10571
\(135\) 0 0
\(136\) 26.9493 2.31089
\(137\) 10.4285 0.890970 0.445485 0.895289i \(-0.353031\pi\)
0.445485 + 0.895289i \(0.353031\pi\)
\(138\) 0 0
\(139\) −7.42653 −0.629910 −0.314955 0.949107i \(-0.601989\pi\)
−0.314955 + 0.949107i \(0.601989\pi\)
\(140\) −12.2385 −1.03434
\(141\) 0 0
\(142\) 2.49423 0.209311
\(143\) −6.80345 −0.568933
\(144\) 0 0
\(145\) −0.167368 −0.0138992
\(146\) 30.6325 2.53517
\(147\) 0 0
\(148\) −0.896944 −0.0737283
\(149\) 1.06192 0.0869958 0.0434979 0.999054i \(-0.486150\pi\)
0.0434979 + 0.999054i \(0.486150\pi\)
\(150\) 0 0
\(151\) −22.5617 −1.83605 −0.918024 0.396525i \(-0.870216\pi\)
−0.918024 + 0.396525i \(0.870216\pi\)
\(152\) −10.7972 −0.875770
\(153\) 0 0
\(154\) 9.45649 0.762026
\(155\) 9.85168 0.791306
\(156\) 0 0
\(157\) 15.1708 1.21076 0.605379 0.795937i \(-0.293022\pi\)
0.605379 + 0.795937i \(0.293022\pi\)
\(158\) 20.1213 1.60077
\(159\) 0 0
\(160\) −3.51873 −0.278180
\(161\) −6.48340 −0.510964
\(162\) 0 0
\(163\) −15.0509 −1.17888 −0.589439 0.807813i \(-0.700651\pi\)
−0.589439 + 0.807813i \(0.700651\pi\)
\(164\) −22.4899 −1.75617
\(165\) 0 0
\(166\) 37.6893 2.92526
\(167\) −14.3817 −1.11289 −0.556445 0.830885i \(-0.687835\pi\)
−0.556445 + 0.830885i \(0.687835\pi\)
\(168\) 0 0
\(169\) 13.2254 1.01733
\(170\) 11.5979 0.889520
\(171\) 0 0
\(172\) 38.4167 2.92924
\(173\) 21.2741 1.61744 0.808720 0.588194i \(-0.200161\pi\)
0.808720 + 0.588194i \(0.200161\pi\)
\(174\) 0 0
\(175\) −2.83060 −0.213973
\(176\) 8.03296 0.605507
\(177\) 0 0
\(178\) 2.51468 0.188484
\(179\) −14.7720 −1.10411 −0.552057 0.833807i \(-0.686157\pi\)
−0.552057 + 0.833807i \(0.686157\pi\)
\(180\) 0 0
\(181\) 1.86322 0.138492 0.0692461 0.997600i \(-0.477941\pi\)
0.0692461 + 0.997600i \(0.477941\pi\)
\(182\) −36.4521 −2.70201
\(183\) 0 0
\(184\) −13.3837 −0.986659
\(185\) −0.207451 −0.0152521
\(186\) 0 0
\(187\) −6.12724 −0.448068
\(188\) 25.5608 1.86421
\(189\) 0 0
\(190\) −4.64669 −0.337107
\(191\) −10.5662 −0.764547 −0.382273 0.924049i \(-0.624859\pi\)
−0.382273 + 0.924049i \(0.624859\pi\)
\(192\) 0 0
\(193\) 0.0385817 0.00277717 0.00138859 0.999999i \(-0.499558\pi\)
0.00138859 + 0.999999i \(0.499558\pi\)
\(194\) −4.54072 −0.326005
\(195\) 0 0
\(196\) 4.37677 0.312626
\(197\) −1.23776 −0.0881868 −0.0440934 0.999027i \(-0.514040\pi\)
−0.0440934 + 0.999027i \(0.514040\pi\)
\(198\) 0 0
\(199\) 15.9428 1.13016 0.565078 0.825038i \(-0.308846\pi\)
0.565078 + 0.825038i \(0.308846\pi\)
\(200\) −5.84320 −0.413177
\(201\) 0 0
\(202\) 17.9284 1.26144
\(203\) 0.473751 0.0332508
\(204\) 0 0
\(205\) −5.20162 −0.363297
\(206\) 12.2524 0.853666
\(207\) 0 0
\(208\) −30.9648 −2.14702
\(209\) 2.45487 0.169807
\(210\) 0 0
\(211\) 23.8439 1.64148 0.820742 0.571299i \(-0.193560\pi\)
0.820742 + 0.571299i \(0.193560\pi\)
\(212\) 13.4660 0.924851
\(213\) 0 0
\(214\) −38.8122 −2.65315
\(215\) 8.88527 0.605971
\(216\) 0 0
\(217\) −27.8861 −1.89303
\(218\) 42.2904 2.86427
\(219\) 0 0
\(220\) 5.74404 0.387263
\(221\) 23.6188 1.58877
\(222\) 0 0
\(223\) −23.2041 −1.55386 −0.776929 0.629588i \(-0.783224\pi\)
−0.776929 + 0.629588i \(0.783224\pi\)
\(224\) 9.96012 0.665489
\(225\) 0 0
\(226\) 51.8620 3.44981
\(227\) 6.90337 0.458193 0.229096 0.973404i \(-0.426423\pi\)
0.229096 + 0.973404i \(0.426423\pi\)
\(228\) 0 0
\(229\) −13.8134 −0.912816 −0.456408 0.889770i \(-0.650864\pi\)
−0.456408 + 0.889770i \(0.650864\pi\)
\(230\) −5.75981 −0.379791
\(231\) 0 0
\(232\) 0.977965 0.0642066
\(233\) 1.20571 0.0789889 0.0394944 0.999220i \(-0.487425\pi\)
0.0394944 + 0.999220i \(0.487425\pi\)
\(234\) 0 0
\(235\) 5.91188 0.385648
\(236\) 31.1689 2.02892
\(237\) 0 0
\(238\) −32.8291 −2.12799
\(239\) −27.0870 −1.75211 −0.876055 0.482211i \(-0.839834\pi\)
−0.876055 + 0.482211i \(0.839834\pi\)
\(240\) 0 0
\(241\) 7.66571 0.493792 0.246896 0.969042i \(-0.420589\pi\)
0.246896 + 0.969042i \(0.420589\pi\)
\(242\) 23.2232 1.49284
\(243\) 0 0
\(244\) 52.4067 3.35499
\(245\) 1.01229 0.0646728
\(246\) 0 0
\(247\) −9.46284 −0.602106
\(248\) −57.5654 −3.65540
\(249\) 0 0
\(250\) −2.51468 −0.159043
\(251\) −10.6839 −0.674363 −0.337182 0.941440i \(-0.609474\pi\)
−0.337182 + 0.941440i \(0.609474\pi\)
\(252\) 0 0
\(253\) 3.04294 0.191308
\(254\) 31.1935 1.95725
\(255\) 0 0
\(256\) −31.7254 −1.98284
\(257\) 0.623084 0.0388669 0.0194335 0.999811i \(-0.493814\pi\)
0.0194335 + 0.999811i \(0.493814\pi\)
\(258\) 0 0
\(259\) 0.587212 0.0364876
\(260\) −22.1416 −1.37317
\(261\) 0 0
\(262\) 30.2068 1.86618
\(263\) 13.6749 0.843228 0.421614 0.906775i \(-0.361464\pi\)
0.421614 + 0.906775i \(0.361464\pi\)
\(264\) 0 0
\(265\) 3.11452 0.191323
\(266\) 13.1529 0.806457
\(267\) 0 0
\(268\) 41.9100 2.56006
\(269\) −3.83259 −0.233677 −0.116838 0.993151i \(-0.537276\pi\)
−0.116838 + 0.993151i \(0.537276\pi\)
\(270\) 0 0
\(271\) 24.2650 1.47399 0.736995 0.675898i \(-0.236244\pi\)
0.736995 + 0.675898i \(0.236244\pi\)
\(272\) −27.8871 −1.69091
\(273\) 0 0
\(274\) −26.2245 −1.58428
\(275\) 1.32852 0.0801128
\(276\) 0 0
\(277\) 18.2047 1.09382 0.546908 0.837193i \(-0.315805\pi\)
0.546908 + 0.837193i \(0.315805\pi\)
\(278\) 18.6754 1.12007
\(279\) 0 0
\(280\) 16.5398 0.988440
\(281\) 4.11252 0.245332 0.122666 0.992448i \(-0.460856\pi\)
0.122666 + 0.992448i \(0.460856\pi\)
\(282\) 0 0
\(283\) −6.51597 −0.387334 −0.193667 0.981067i \(-0.562038\pi\)
−0.193667 + 0.981067i \(0.562038\pi\)
\(284\) −4.28847 −0.254474
\(285\) 0 0
\(286\) 17.1085 1.01165
\(287\) 14.7237 0.869113
\(288\) 0 0
\(289\) 4.27127 0.251251
\(290\) 0.420877 0.0247148
\(291\) 0 0
\(292\) −52.6682 −3.08217
\(293\) −18.8557 −1.10156 −0.550781 0.834650i \(-0.685670\pi\)
−0.550781 + 0.834650i \(0.685670\pi\)
\(294\) 0 0
\(295\) 7.20896 0.419722
\(296\) 1.21218 0.0704566
\(297\) 0 0
\(298\) −2.67039 −0.154692
\(299\) −11.7297 −0.678344
\(300\) 0 0
\(301\) −25.1506 −1.44966
\(302\) 56.7356 3.26477
\(303\) 0 0
\(304\) 11.1729 0.640812
\(305\) 12.1210 0.694045
\(306\) 0 0
\(307\) 13.6486 0.778966 0.389483 0.921034i \(-0.372654\pi\)
0.389483 + 0.921034i \(0.372654\pi\)
\(308\) −16.2591 −0.926446
\(309\) 0 0
\(310\) −24.7739 −1.40706
\(311\) −25.7543 −1.46040 −0.730198 0.683236i \(-0.760572\pi\)
−0.730198 + 0.683236i \(0.760572\pi\)
\(312\) 0 0
\(313\) 11.1065 0.627776 0.313888 0.949460i \(-0.398368\pi\)
0.313888 + 0.949460i \(0.398368\pi\)
\(314\) −38.1496 −2.15291
\(315\) 0 0
\(316\) −34.5957 −1.94616
\(317\) −11.4835 −0.644977 −0.322488 0.946573i \(-0.604519\pi\)
−0.322488 + 0.946573i \(0.604519\pi\)
\(318\) 0 0
\(319\) −0.222352 −0.0124493
\(320\) −3.24458 −0.181378
\(321\) 0 0
\(322\) 16.3037 0.908570
\(323\) −8.52231 −0.474194
\(324\) 0 0
\(325\) −5.12107 −0.284066
\(326\) 37.8483 2.09622
\(327\) 0 0
\(328\) 30.3941 1.67824
\(329\) −16.7342 −0.922584
\(330\) 0 0
\(331\) 15.6240 0.858773 0.429386 0.903121i \(-0.358730\pi\)
0.429386 + 0.903121i \(0.358730\pi\)
\(332\) −64.8013 −3.55643
\(333\) 0 0
\(334\) 36.1654 1.97888
\(335\) 9.69323 0.529598
\(336\) 0 0
\(337\) 8.62551 0.469861 0.234931 0.972012i \(-0.424514\pi\)
0.234931 + 0.972012i \(0.424514\pi\)
\(338\) −33.2576 −1.80897
\(339\) 0 0
\(340\) −19.9409 −1.08145
\(341\) 13.0882 0.708763
\(342\) 0 0
\(343\) 16.9488 0.915150
\(344\) −51.9185 −2.79926
\(345\) 0 0
\(346\) −53.4976 −2.87605
\(347\) −18.8508 −1.01197 −0.505983 0.862544i \(-0.668870\pi\)
−0.505983 + 0.862544i \(0.668870\pi\)
\(348\) 0 0
\(349\) −20.2101 −1.08182 −0.540910 0.841080i \(-0.681920\pi\)
−0.540910 + 0.841080i \(0.681920\pi\)
\(350\) 7.11806 0.380476
\(351\) 0 0
\(352\) −4.67471 −0.249163
\(353\) 25.4587 1.35503 0.677514 0.735510i \(-0.263057\pi\)
0.677514 + 0.735510i \(0.263057\pi\)
\(354\) 0 0
\(355\) −0.991867 −0.0526428
\(356\) −4.32363 −0.229152
\(357\) 0 0
\(358\) 37.1470 1.96328
\(359\) 12.7517 0.673011 0.336505 0.941682i \(-0.390755\pi\)
0.336505 + 0.941682i \(0.390755\pi\)
\(360\) 0 0
\(361\) −15.5855 −0.820292
\(362\) −4.68541 −0.246260
\(363\) 0 0
\(364\) 62.6741 3.28501
\(365\) −12.1815 −0.637607
\(366\) 0 0
\(367\) −27.0102 −1.40992 −0.704961 0.709246i \(-0.749036\pi\)
−0.704961 + 0.709246i \(0.749036\pi\)
\(368\) 13.8494 0.721951
\(369\) 0 0
\(370\) 0.521675 0.0271206
\(371\) −8.81595 −0.457701
\(372\) 0 0
\(373\) −27.1822 −1.40744 −0.703720 0.710478i \(-0.748479\pi\)
−0.703720 + 0.710478i \(0.748479\pi\)
\(374\) 15.4081 0.796733
\(375\) 0 0
\(376\) −34.5443 −1.78149
\(377\) 0.857103 0.0441430
\(378\) 0 0
\(379\) −7.72849 −0.396986 −0.198493 0.980102i \(-0.563605\pi\)
−0.198493 + 0.980102i \(0.563605\pi\)
\(380\) 7.98932 0.409843
\(381\) 0 0
\(382\) 26.5708 1.35948
\(383\) −28.0352 −1.43253 −0.716267 0.697827i \(-0.754151\pi\)
−0.716267 + 0.697827i \(0.754151\pi\)
\(384\) 0 0
\(385\) −3.76051 −0.191653
\(386\) −0.0970208 −0.00493823
\(387\) 0 0
\(388\) 7.80711 0.396346
\(389\) 0.595763 0.0302064 0.0151032 0.999886i \(-0.495192\pi\)
0.0151032 + 0.999886i \(0.495192\pi\)
\(390\) 0 0
\(391\) −10.5638 −0.534236
\(392\) −5.91501 −0.298753
\(393\) 0 0
\(394\) 3.11258 0.156809
\(395\) −8.00154 −0.402601
\(396\) 0 0
\(397\) −35.5629 −1.78485 −0.892426 0.451193i \(-0.850999\pi\)
−0.892426 + 0.451193i \(0.850999\pi\)
\(398\) −40.0911 −2.00959
\(399\) 0 0
\(400\) 6.04654 0.302327
\(401\) 0.912908 0.0455884 0.0227942 0.999740i \(-0.492744\pi\)
0.0227942 + 0.999740i \(0.492744\pi\)
\(402\) 0 0
\(403\) −50.4511 −2.51315
\(404\) −30.8253 −1.53362
\(405\) 0 0
\(406\) −1.19134 −0.0591250
\(407\) −0.275604 −0.0136612
\(408\) 0 0
\(409\) −7.04632 −0.348418 −0.174209 0.984709i \(-0.555737\pi\)
−0.174209 + 0.984709i \(0.555737\pi\)
\(410\) 13.0804 0.645997
\(411\) 0 0
\(412\) −21.0662 −1.03786
\(413\) −20.4057 −1.00410
\(414\) 0 0
\(415\) −14.9877 −0.735717
\(416\) 18.0197 0.883487
\(417\) 0 0
\(418\) −6.17323 −0.301942
\(419\) −27.1256 −1.32517 −0.662587 0.748985i \(-0.730541\pi\)
−0.662587 + 0.748985i \(0.730541\pi\)
\(420\) 0 0
\(421\) 0.264561 0.0128939 0.00644696 0.999979i \(-0.497948\pi\)
0.00644696 + 0.999979i \(0.497948\pi\)
\(422\) −59.9600 −2.91881
\(423\) 0 0
\(424\) −18.1988 −0.883810
\(425\) −4.61208 −0.223719
\(426\) 0 0
\(427\) −34.3096 −1.66036
\(428\) 66.7320 3.22561
\(429\) 0 0
\(430\) −22.3437 −1.07751
\(431\) 20.5851 0.991549 0.495774 0.868451i \(-0.334884\pi\)
0.495774 + 0.868451i \(0.334884\pi\)
\(432\) 0 0
\(433\) −26.3333 −1.26550 −0.632749 0.774357i \(-0.718074\pi\)
−0.632749 + 0.774357i \(0.718074\pi\)
\(434\) 70.1248 3.36610
\(435\) 0 0
\(436\) −72.7122 −3.48228
\(437\) 4.23239 0.202463
\(438\) 0 0
\(439\) 36.9387 1.76299 0.881494 0.472195i \(-0.156538\pi\)
0.881494 + 0.472195i \(0.156538\pi\)
\(440\) −7.76282 −0.370078
\(441\) 0 0
\(442\) −59.3938 −2.82507
\(443\) 6.92362 0.328951 0.164476 0.986381i \(-0.447407\pi\)
0.164476 + 0.986381i \(0.447407\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) 58.3509 2.76299
\(447\) 0 0
\(448\) 9.18411 0.433909
\(449\) 13.7840 0.650509 0.325255 0.945626i \(-0.394550\pi\)
0.325255 + 0.945626i \(0.394550\pi\)
\(450\) 0 0
\(451\) −6.91046 −0.325401
\(452\) −89.1692 −4.19417
\(453\) 0 0
\(454\) −17.3598 −0.814735
\(455\) 14.4957 0.679569
\(456\) 0 0
\(457\) −32.0535 −1.49940 −0.749700 0.661778i \(-0.769802\pi\)
−0.749700 + 0.661778i \(0.769802\pi\)
\(458\) 34.7364 1.62312
\(459\) 0 0
\(460\) 9.90316 0.461737
\(461\) 27.4316 1.27762 0.638809 0.769365i \(-0.279427\pi\)
0.638809 + 0.769365i \(0.279427\pi\)
\(462\) 0 0
\(463\) −11.4729 −0.533193 −0.266596 0.963808i \(-0.585899\pi\)
−0.266596 + 0.963808i \(0.585899\pi\)
\(464\) −1.01200 −0.0469808
\(465\) 0 0
\(466\) −3.03199 −0.140454
\(467\) 18.2580 0.844880 0.422440 0.906391i \(-0.361174\pi\)
0.422440 + 0.906391i \(0.361174\pi\)
\(468\) 0 0
\(469\) −27.4376 −1.26695
\(470\) −14.8665 −0.685741
\(471\) 0 0
\(472\) −42.1234 −1.93889
\(473\) 11.8043 0.542761
\(474\) 0 0
\(475\) 1.84782 0.0847840
\(476\) 56.4448 2.58714
\(477\) 0 0
\(478\) 68.1151 3.11551
\(479\) −42.7672 −1.95408 −0.977042 0.213048i \(-0.931661\pi\)
−0.977042 + 0.213048i \(0.931661\pi\)
\(480\) 0 0
\(481\) 1.06237 0.0484400
\(482\) −19.2768 −0.878036
\(483\) 0 0
\(484\) −39.9289 −1.81495
\(485\) 1.80568 0.0819918
\(486\) 0 0
\(487\) −35.4303 −1.60550 −0.802751 0.596314i \(-0.796631\pi\)
−0.802751 + 0.596314i \(0.796631\pi\)
\(488\) −70.8254 −3.20611
\(489\) 0 0
\(490\) −2.54559 −0.114998
\(491\) −10.3361 −0.466463 −0.233232 0.972421i \(-0.574930\pi\)
−0.233232 + 0.972421i \(0.574930\pi\)
\(492\) 0 0
\(493\) 0.771914 0.0347653
\(494\) 23.7960 1.07063
\(495\) 0 0
\(496\) 59.5686 2.67471
\(497\) 2.80758 0.125937
\(498\) 0 0
\(499\) −29.1616 −1.30545 −0.652726 0.757594i \(-0.726375\pi\)
−0.652726 + 0.757594i \(0.726375\pi\)
\(500\) 4.32363 0.193359
\(501\) 0 0
\(502\) 26.8667 1.19912
\(503\) −35.1802 −1.56861 −0.784303 0.620378i \(-0.786979\pi\)
−0.784303 + 0.620378i \(0.786979\pi\)
\(504\) 0 0
\(505\) −7.12949 −0.317258
\(506\) −7.65203 −0.340174
\(507\) 0 0
\(508\) −53.6326 −2.37956
\(509\) 11.1436 0.493932 0.246966 0.969024i \(-0.420566\pi\)
0.246966 + 0.969024i \(0.420566\pi\)
\(510\) 0 0
\(511\) 34.4808 1.52534
\(512\) 49.3862 2.18258
\(513\) 0 0
\(514\) −1.56686 −0.0691112
\(515\) −4.87235 −0.214701
\(516\) 0 0
\(517\) 7.85405 0.345421
\(518\) −1.47665 −0.0648804
\(519\) 0 0
\(520\) 29.9235 1.31223
\(521\) 27.8902 1.22189 0.610947 0.791672i \(-0.290789\pi\)
0.610947 + 0.791672i \(0.290789\pi\)
\(522\) 0 0
\(523\) −19.0875 −0.834637 −0.417319 0.908760i \(-0.637030\pi\)
−0.417319 + 0.908760i \(0.637030\pi\)
\(524\) −51.9363 −2.26885
\(525\) 0 0
\(526\) −34.3879 −1.49939
\(527\) −45.4367 −1.97925
\(528\) 0 0
\(529\) −17.7537 −0.771902
\(530\) −7.83202 −0.340201
\(531\) 0 0
\(532\) −22.6145 −0.980465
\(533\) 26.6379 1.15381
\(534\) 0 0
\(535\) 15.4342 0.667280
\(536\) −56.6395 −2.44646
\(537\) 0 0
\(538\) 9.63774 0.415513
\(539\) 1.34485 0.0579266
\(540\) 0 0
\(541\) 36.2025 1.55647 0.778233 0.627975i \(-0.216116\pi\)
0.778233 + 0.627975i \(0.216116\pi\)
\(542\) −61.0187 −2.62098
\(543\) 0 0
\(544\) 16.2287 0.695799
\(545\) −16.8174 −0.720378
\(546\) 0 0
\(547\) 10.3493 0.442504 0.221252 0.975217i \(-0.428986\pi\)
0.221252 + 0.975217i \(0.428986\pi\)
\(548\) 45.0892 1.92612
\(549\) 0 0
\(550\) −3.34081 −0.142453
\(551\) −0.309267 −0.0131752
\(552\) 0 0
\(553\) 22.6492 0.963140
\(554\) −45.7791 −1.94497
\(555\) 0 0
\(556\) −32.1096 −1.36175
\(557\) 27.7262 1.17479 0.587397 0.809299i \(-0.300153\pi\)
0.587397 + 0.809299i \(0.300153\pi\)
\(558\) 0 0
\(559\) −45.5021 −1.92453
\(560\) −17.1153 −0.723255
\(561\) 0 0
\(562\) −10.3417 −0.436238
\(563\) −37.3785 −1.57532 −0.787659 0.616112i \(-0.788707\pi\)
−0.787659 + 0.616112i \(0.788707\pi\)
\(564\) 0 0
\(565\) −20.6237 −0.867645
\(566\) 16.3856 0.688739
\(567\) 0 0
\(568\) 5.79568 0.243181
\(569\) 13.8419 0.580285 0.290142 0.956983i \(-0.406297\pi\)
0.290142 + 0.956983i \(0.406297\pi\)
\(570\) 0 0
\(571\) 11.9908 0.501797 0.250899 0.968013i \(-0.419274\pi\)
0.250899 + 0.968013i \(0.419274\pi\)
\(572\) −29.4156 −1.22993
\(573\) 0 0
\(574\) −37.0255 −1.54541
\(575\) 2.29047 0.0955192
\(576\) 0 0
\(577\) −11.9615 −0.497962 −0.248981 0.968508i \(-0.580096\pi\)
−0.248981 + 0.968508i \(0.580096\pi\)
\(578\) −10.7409 −0.446763
\(579\) 0 0
\(580\) −0.723638 −0.0300474
\(581\) 42.4241 1.76005
\(582\) 0 0
\(583\) 4.13770 0.171366
\(584\) 71.1788 2.94540
\(585\) 0 0
\(586\) 47.4161 1.95874
\(587\) −5.14399 −0.212315 −0.106158 0.994349i \(-0.533855\pi\)
−0.106158 + 0.994349i \(0.533855\pi\)
\(588\) 0 0
\(589\) 18.2042 0.750090
\(590\) −18.1282 −0.746328
\(591\) 0 0
\(592\) −1.25436 −0.0515540
\(593\) 25.9237 1.06456 0.532279 0.846569i \(-0.321336\pi\)
0.532279 + 0.846569i \(0.321336\pi\)
\(594\) 0 0
\(595\) 13.0549 0.535201
\(596\) 4.59135 0.188069
\(597\) 0 0
\(598\) 29.4964 1.20620
\(599\) −15.8637 −0.648175 −0.324087 0.946027i \(-0.605057\pi\)
−0.324087 + 0.946027i \(0.605057\pi\)
\(600\) 0 0
\(601\) 19.9231 0.812678 0.406339 0.913722i \(-0.366805\pi\)
0.406339 + 0.913722i \(0.366805\pi\)
\(602\) 63.2459 2.57771
\(603\) 0 0
\(604\) −97.5487 −3.96920
\(605\) −9.23503 −0.375457
\(606\) 0 0
\(607\) 9.07779 0.368456 0.184228 0.982884i \(-0.441021\pi\)
0.184228 + 0.982884i \(0.441021\pi\)
\(608\) −6.50200 −0.263691
\(609\) 0 0
\(610\) −30.4804 −1.23412
\(611\) −30.2751 −1.22480
\(612\) 0 0
\(613\) 11.0839 0.447674 0.223837 0.974627i \(-0.428142\pi\)
0.223837 + 0.974627i \(0.428142\pi\)
\(614\) −34.3219 −1.38512
\(615\) 0 0
\(616\) 21.9734 0.885334
\(617\) 15.0662 0.606542 0.303271 0.952904i \(-0.401921\pi\)
0.303271 + 0.952904i \(0.401921\pi\)
\(618\) 0 0
\(619\) 42.8816 1.72356 0.861778 0.507286i \(-0.169351\pi\)
0.861778 + 0.507286i \(0.169351\pi\)
\(620\) 42.5950 1.71066
\(621\) 0 0
\(622\) 64.7640 2.59680
\(623\) 2.83060 0.113406
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −27.9293 −1.11628
\(627\) 0 0
\(628\) 65.5928 2.61744
\(629\) 0.956782 0.0381494
\(630\) 0 0
\(631\) −0.952046 −0.0379004 −0.0189502 0.999820i \(-0.506032\pi\)
−0.0189502 + 0.999820i \(0.506032\pi\)
\(632\) 46.7546 1.85980
\(633\) 0 0
\(634\) 28.8773 1.14686
\(635\) −12.4045 −0.492259
\(636\) 0 0
\(637\) −5.18400 −0.205398
\(638\) 0.559144 0.0221367
\(639\) 0 0
\(640\) 15.1966 0.600697
\(641\) −2.20464 −0.0870782 −0.0435391 0.999052i \(-0.513863\pi\)
−0.0435391 + 0.999052i \(0.513863\pi\)
\(642\) 0 0
\(643\) −12.6354 −0.498292 −0.249146 0.968466i \(-0.580150\pi\)
−0.249146 + 0.968466i \(0.580150\pi\)
\(644\) −28.0319 −1.10461
\(645\) 0 0
\(646\) 21.4309 0.843188
\(647\) −12.1752 −0.478656 −0.239328 0.970939i \(-0.576927\pi\)
−0.239328 + 0.970939i \(0.576927\pi\)
\(648\) 0 0
\(649\) 9.57725 0.375940
\(650\) 12.8779 0.505112
\(651\) 0 0
\(652\) −65.0746 −2.54852
\(653\) 18.0294 0.705545 0.352773 0.935709i \(-0.385239\pi\)
0.352773 + 0.935709i \(0.385239\pi\)
\(654\) 0 0
\(655\) −12.0122 −0.469355
\(656\) −31.4518 −1.22799
\(657\) 0 0
\(658\) 42.0811 1.64049
\(659\) −13.5430 −0.527562 −0.263781 0.964583i \(-0.584970\pi\)
−0.263781 + 0.964583i \(0.584970\pi\)
\(660\) 0 0
\(661\) −12.2540 −0.476627 −0.238314 0.971188i \(-0.576595\pi\)
−0.238314 + 0.971188i \(0.576595\pi\)
\(662\) −39.2894 −1.52703
\(663\) 0 0
\(664\) 87.5762 3.39861
\(665\) −5.23045 −0.202828
\(666\) 0 0
\(667\) −0.383351 −0.0148434
\(668\) −62.1812 −2.40586
\(669\) 0 0
\(670\) −24.3754 −0.941704
\(671\) 16.1030 0.621648
\(672\) 0 0
\(673\) −2.00909 −0.0774448 −0.0387224 0.999250i \(-0.512329\pi\)
−0.0387224 + 0.999250i \(0.512329\pi\)
\(674\) −21.6904 −0.835484
\(675\) 0 0
\(676\) 57.1816 2.19929
\(677\) −20.3448 −0.781913 −0.390956 0.920409i \(-0.627856\pi\)
−0.390956 + 0.920409i \(0.627856\pi\)
\(678\) 0 0
\(679\) −5.11116 −0.196148
\(680\) 26.9493 1.03346
\(681\) 0 0
\(682\) −32.9126 −1.26029
\(683\) 15.6710 0.599636 0.299818 0.953996i \(-0.403074\pi\)
0.299818 + 0.953996i \(0.403074\pi\)
\(684\) 0 0
\(685\) 10.4285 0.398454
\(686\) −42.6209 −1.62727
\(687\) 0 0
\(688\) 53.7252 2.04825
\(689\) −15.9497 −0.607634
\(690\) 0 0
\(691\) −9.63284 −0.366450 −0.183225 0.983071i \(-0.558654\pi\)
−0.183225 + 0.983071i \(0.558654\pi\)
\(692\) 91.9814 3.49661
\(693\) 0 0
\(694\) 47.4039 1.79943
\(695\) −7.42653 −0.281704
\(696\) 0 0
\(697\) 23.9903 0.908697
\(698\) 50.8220 1.92364
\(699\) 0 0
\(700\) −12.2385 −0.462571
\(701\) −13.8413 −0.522779 −0.261390 0.965233i \(-0.584181\pi\)
−0.261390 + 0.965233i \(0.584181\pi\)
\(702\) 0 0
\(703\) −0.383334 −0.0144577
\(704\) −4.31050 −0.162458
\(705\) 0 0
\(706\) −64.0205 −2.40944
\(707\) 20.1807 0.758974
\(708\) 0 0
\(709\) 19.8323 0.744817 0.372409 0.928069i \(-0.378532\pi\)
0.372409 + 0.928069i \(0.378532\pi\)
\(710\) 2.49423 0.0936069
\(711\) 0 0
\(712\) 5.84320 0.218983
\(713\) 22.5650 0.845065
\(714\) 0 0
\(715\) −6.80345 −0.254434
\(716\) −63.8688 −2.38689
\(717\) 0 0
\(718\) −32.0666 −1.19671
\(719\) −16.3095 −0.608243 −0.304122 0.952633i \(-0.598363\pi\)
−0.304122 + 0.952633i \(0.598363\pi\)
\(720\) 0 0
\(721\) 13.7917 0.513628
\(722\) 39.1927 1.45860
\(723\) 0 0
\(724\) 8.05589 0.299395
\(725\) −0.167368 −0.00621589
\(726\) 0 0
\(727\) −2.99661 −0.111138 −0.0555691 0.998455i \(-0.517697\pi\)
−0.0555691 + 0.998455i \(0.517697\pi\)
\(728\) −84.7013 −3.13924
\(729\) 0 0
\(730\) 30.6325 1.13376
\(731\) −40.9796 −1.51568
\(732\) 0 0
\(733\) 46.6651 1.72362 0.861808 0.507235i \(-0.169333\pi\)
0.861808 + 0.507235i \(0.169333\pi\)
\(734\) 67.9222 2.50705
\(735\) 0 0
\(736\) −8.05956 −0.297079
\(737\) 12.8777 0.474355
\(738\) 0 0
\(739\) 10.7663 0.396045 0.198022 0.980198i \(-0.436548\pi\)
0.198022 + 0.980198i \(0.436548\pi\)
\(740\) −0.896944 −0.0329723
\(741\) 0 0
\(742\) 22.1693 0.813861
\(743\) 48.3152 1.77251 0.886257 0.463194i \(-0.153297\pi\)
0.886257 + 0.463194i \(0.153297\pi\)
\(744\) 0 0
\(745\) 1.06192 0.0389057
\(746\) 68.3546 2.50264
\(747\) 0 0
\(748\) −26.4920 −0.968642
\(749\) −43.6881 −1.59633
\(750\) 0 0
\(751\) −20.6257 −0.752641 −0.376321 0.926490i \(-0.622811\pi\)
−0.376321 + 0.926490i \(0.622811\pi\)
\(752\) 35.7464 1.30354
\(753\) 0 0
\(754\) −2.15534 −0.0784929
\(755\) −22.5617 −0.821105
\(756\) 0 0
\(757\) 17.1099 0.621871 0.310936 0.950431i \(-0.399358\pi\)
0.310936 + 0.950431i \(0.399358\pi\)
\(758\) 19.4347 0.705901
\(759\) 0 0
\(760\) −10.7972 −0.391656
\(761\) 5.86395 0.212568 0.106284 0.994336i \(-0.466105\pi\)
0.106284 + 0.994336i \(0.466105\pi\)
\(762\) 0 0
\(763\) 47.6033 1.72335
\(764\) −45.6846 −1.65281
\(765\) 0 0
\(766\) 70.4997 2.54726
\(767\) −36.9176 −1.33302
\(768\) 0 0
\(769\) 18.3365 0.661231 0.330615 0.943766i \(-0.392744\pi\)
0.330615 + 0.943766i \(0.392744\pi\)
\(770\) 9.45649 0.340788
\(771\) 0 0
\(772\) 0.166813 0.00600374
\(773\) −0.361308 −0.0129954 −0.00649768 0.999979i \(-0.502068\pi\)
−0.00649768 + 0.999979i \(0.502068\pi\)
\(774\) 0 0
\(775\) 9.85168 0.353883
\(776\) −10.5510 −0.378758
\(777\) 0 0
\(778\) −1.49816 −0.0537115
\(779\) −9.61168 −0.344374
\(780\) 0 0
\(781\) −1.31772 −0.0471516
\(782\) 26.5647 0.949952
\(783\) 0 0
\(784\) 6.12085 0.218602
\(785\) 15.1708 0.541467
\(786\) 0 0
\(787\) 24.4430 0.871300 0.435650 0.900116i \(-0.356519\pi\)
0.435650 + 0.900116i \(0.356519\pi\)
\(788\) −5.35163 −0.190644
\(789\) 0 0
\(790\) 20.1213 0.715885
\(791\) 58.3774 2.07566
\(792\) 0 0
\(793\) −62.0724 −2.20425
\(794\) 89.4296 3.17374
\(795\) 0 0
\(796\) 68.9309 2.44319
\(797\) −8.59641 −0.304500 −0.152250 0.988342i \(-0.548652\pi\)
−0.152250 + 0.988342i \(0.548652\pi\)
\(798\) 0 0
\(799\) −27.2661 −0.964604
\(800\) −3.51873 −0.124406
\(801\) 0 0
\(802\) −2.29567 −0.0810631
\(803\) −16.1833 −0.571097
\(804\) 0 0
\(805\) −6.48340 −0.228510
\(806\) 126.869 4.46876
\(807\) 0 0
\(808\) 41.6591 1.46556
\(809\) −52.3619 −1.84094 −0.920472 0.390808i \(-0.872196\pi\)
−0.920472 + 0.390808i \(0.872196\pi\)
\(810\) 0 0
\(811\) 9.71912 0.341285 0.170642 0.985333i \(-0.445416\pi\)
0.170642 + 0.985333i \(0.445416\pi\)
\(812\) 2.04833 0.0718822
\(813\) 0 0
\(814\) 0.693056 0.0242916
\(815\) −15.0509 −0.527210
\(816\) 0 0
\(817\) 16.4184 0.574408
\(818\) 17.7193 0.619540
\(819\) 0 0
\(820\) −22.4899 −0.785382
\(821\) −11.4338 −0.399044 −0.199522 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(822\) 0 0
\(823\) −14.3109 −0.498845 −0.249422 0.968395i \(-0.580241\pi\)
−0.249422 + 0.968395i \(0.580241\pi\)
\(824\) 28.4701 0.991804
\(825\) 0 0
\(826\) 51.3138 1.78544
\(827\) −3.13835 −0.109131 −0.0545655 0.998510i \(-0.517377\pi\)
−0.0545655 + 0.998510i \(0.517377\pi\)
\(828\) 0 0
\(829\) −45.3160 −1.57389 −0.786944 0.617024i \(-0.788338\pi\)
−0.786944 + 0.617024i \(0.788338\pi\)
\(830\) 37.6893 1.30821
\(831\) 0 0
\(832\) 16.6157 0.576047
\(833\) −4.66876 −0.161763
\(834\) 0 0
\(835\) −14.3817 −0.497699
\(836\) 10.6140 0.367092
\(837\) 0 0
\(838\) 68.2124 2.35636
\(839\) 43.2811 1.49423 0.747115 0.664695i \(-0.231439\pi\)
0.747115 + 0.664695i \(0.231439\pi\)
\(840\) 0 0
\(841\) −28.9720 −0.999034
\(842\) −0.665287 −0.0229273
\(843\) 0 0
\(844\) 103.092 3.54859
\(845\) 13.2254 0.454966
\(846\) 0 0
\(847\) 26.1407 0.898204
\(848\) 18.8321 0.646696
\(849\) 0 0
\(850\) 11.5979 0.397805
\(851\) −0.475161 −0.0162883
\(852\) 0 0
\(853\) 51.6286 1.76773 0.883864 0.467744i \(-0.154933\pi\)
0.883864 + 0.467744i \(0.154933\pi\)
\(854\) 86.2779 2.95237
\(855\) 0 0
\(856\) −90.1854 −3.08247
\(857\) −29.9889 −1.02440 −0.512201 0.858866i \(-0.671170\pi\)
−0.512201 + 0.858866i \(0.671170\pi\)
\(858\) 0 0
\(859\) 4.50797 0.153810 0.0769049 0.997038i \(-0.475496\pi\)
0.0769049 + 0.997038i \(0.475496\pi\)
\(860\) 38.4167 1.31000
\(861\) 0 0
\(862\) −51.7650 −1.76312
\(863\) −29.1380 −0.991870 −0.495935 0.868360i \(-0.665175\pi\)
−0.495935 + 0.868360i \(0.665175\pi\)
\(864\) 0 0
\(865\) 21.2741 0.723341
\(866\) 66.2200 2.25025
\(867\) 0 0
\(868\) −120.569 −4.09239
\(869\) −10.6302 −0.360605
\(870\) 0 0
\(871\) −49.6397 −1.68198
\(872\) 98.2674 3.32776
\(873\) 0 0
\(874\) −10.6431 −0.360009
\(875\) −2.83060 −0.0956917
\(876\) 0 0
\(877\) −17.6137 −0.594772 −0.297386 0.954757i \(-0.596115\pi\)
−0.297386 + 0.954757i \(0.596115\pi\)
\(878\) −92.8892 −3.13486
\(879\) 0 0
\(880\) 8.03296 0.270791
\(881\) −27.6785 −0.932512 −0.466256 0.884650i \(-0.654398\pi\)
−0.466256 + 0.884650i \(0.654398\pi\)
\(882\) 0 0
\(883\) 23.7126 0.797994 0.398997 0.916952i \(-0.369358\pi\)
0.398997 + 0.916952i \(0.369358\pi\)
\(884\) 102.119 3.43463
\(885\) 0 0
\(886\) −17.4107 −0.584925
\(887\) 28.0883 0.943112 0.471556 0.881836i \(-0.343692\pi\)
0.471556 + 0.881836i \(0.343692\pi\)
\(888\) 0 0
\(889\) 35.1122 1.17763
\(890\) 2.51468 0.0842924
\(891\) 0 0
\(892\) −100.326 −3.35916
\(893\) 10.9241 0.365562
\(894\) 0 0
\(895\) −14.7720 −0.493774
\(896\) −43.0154 −1.43704
\(897\) 0 0
\(898\) −34.6625 −1.15670
\(899\) −1.64885 −0.0549924
\(900\) 0 0
\(901\) −14.3644 −0.478547
\(902\) 17.3776 0.578612
\(903\) 0 0
\(904\) 120.508 4.00805
\(905\) 1.86322 0.0619356
\(906\) 0 0
\(907\) −19.9123 −0.661178 −0.330589 0.943775i \(-0.607247\pi\)
−0.330589 + 0.943775i \(0.607247\pi\)
\(908\) 29.8476 0.990529
\(909\) 0 0
\(910\) −36.4521 −1.20837
\(911\) 17.1810 0.569233 0.284617 0.958641i \(-0.408134\pi\)
0.284617 + 0.958641i \(0.408134\pi\)
\(912\) 0 0
\(913\) −19.9115 −0.658973
\(914\) 80.6045 2.66616
\(915\) 0 0
\(916\) −59.7242 −1.97334
\(917\) 34.0017 1.12283
\(918\) 0 0
\(919\) 3.26343 0.107651 0.0538253 0.998550i \(-0.482859\pi\)
0.0538253 + 0.998550i \(0.482859\pi\)
\(920\) −13.3837 −0.441247
\(921\) 0 0
\(922\) −68.9819 −2.27180
\(923\) 5.07942 0.167191
\(924\) 0 0
\(925\) −0.207451 −0.00682096
\(926\) 28.8508 0.948097
\(927\) 0 0
\(928\) 0.588923 0.0193324
\(929\) −52.8522 −1.73402 −0.867012 0.498288i \(-0.833962\pi\)
−0.867012 + 0.498288i \(0.833962\pi\)
\(930\) 0 0
\(931\) 1.87053 0.0613042
\(932\) 5.21306 0.170759
\(933\) 0 0
\(934\) −45.9131 −1.50232
\(935\) −6.12724 −0.200382
\(936\) 0 0
\(937\) −32.9905 −1.07775 −0.538876 0.842385i \(-0.681151\pi\)
−0.538876 + 0.842385i \(0.681151\pi\)
\(938\) 68.9970 2.25283
\(939\) 0 0
\(940\) 25.5608 0.833701
\(941\) 8.91420 0.290595 0.145297 0.989388i \(-0.453586\pi\)
0.145297 + 0.989388i \(0.453586\pi\)
\(942\) 0 0
\(943\) −11.9142 −0.387979
\(944\) 43.5893 1.41871
\(945\) 0 0
\(946\) −29.6840 −0.965110
\(947\) −18.7920 −0.610659 −0.305329 0.952247i \(-0.598767\pi\)
−0.305329 + 0.952247i \(0.598767\pi\)
\(948\) 0 0
\(949\) 62.3821 2.02501
\(950\) −4.64669 −0.150759
\(951\) 0 0
\(952\) −76.2827 −2.47234
\(953\) 13.2480 0.429145 0.214573 0.976708i \(-0.431164\pi\)
0.214573 + 0.976708i \(0.431164\pi\)
\(954\) 0 0
\(955\) −10.5662 −0.341916
\(956\) −117.114 −3.78774
\(957\) 0 0
\(958\) 107.546 3.47465
\(959\) −29.5190 −0.953219
\(960\) 0 0
\(961\) 66.0555 2.13082
\(962\) −2.67153 −0.0861337
\(963\) 0 0
\(964\) 33.1437 1.06749
\(965\) 0.0385817 0.00124199
\(966\) 0 0
\(967\) 23.7207 0.762808 0.381404 0.924409i \(-0.375441\pi\)
0.381404 + 0.924409i \(0.375441\pi\)
\(968\) 53.9622 1.73441
\(969\) 0 0
\(970\) −4.54072 −0.145794
\(971\) 12.4868 0.400720 0.200360 0.979722i \(-0.435789\pi\)
0.200360 + 0.979722i \(0.435789\pi\)
\(972\) 0 0
\(973\) 21.0215 0.673919
\(974\) 89.0961 2.85482
\(975\) 0 0
\(976\) 73.2900 2.34596
\(977\) 2.08604 0.0667383 0.0333692 0.999443i \(-0.489376\pi\)
0.0333692 + 0.999443i \(0.489376\pi\)
\(978\) 0 0
\(979\) −1.32852 −0.0424597
\(980\) 4.37677 0.139811
\(981\) 0 0
\(982\) 25.9921 0.829442
\(983\) 32.8063 1.04636 0.523180 0.852222i \(-0.324746\pi\)
0.523180 + 0.852222i \(0.324746\pi\)
\(984\) 0 0
\(985\) −1.23776 −0.0394383
\(986\) −1.94112 −0.0618179
\(987\) 0 0
\(988\) −40.9138 −1.30164
\(989\) 20.3515 0.647139
\(990\) 0 0
\(991\) 15.6986 0.498683 0.249341 0.968416i \(-0.419786\pi\)
0.249341 + 0.968416i \(0.419786\pi\)
\(992\) −34.6654 −1.10063
\(993\) 0 0
\(994\) −7.06017 −0.223935
\(995\) 15.9428 0.505421
\(996\) 0 0
\(997\) −32.8993 −1.04193 −0.520966 0.853578i \(-0.674428\pi\)
−0.520966 + 0.853578i \(0.674428\pi\)
\(998\) 73.3322 2.32129
\(999\) 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 \(a_p\))