Properties

Label 6004.2.a.g.1.5
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.14389 q^{3}\) \(+2.12568 q^{5}\) \(-4.35707 q^{7}\) \(+1.59626 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.14389 q^{3}\) \(+2.12568 q^{5}\) \(-4.35707 q^{7}\) \(+1.59626 q^{9}\) \(+2.62997 q^{11}\) \(+1.60555 q^{13}\) \(-4.55722 q^{15}\) \(-7.43738 q^{17}\) \(+1.00000 q^{19}\) \(+9.34107 q^{21}\) \(+6.34749 q^{23}\) \(-0.481487 q^{25}\) \(+3.00946 q^{27}\) \(-6.78691 q^{29}\) \(+5.19656 q^{31}\) \(-5.63836 q^{33}\) \(-9.26173 q^{35}\) \(+9.25264 q^{37}\) \(-3.44212 q^{39}\) \(-10.6249 q^{41}\) \(+1.30088 q^{43}\) \(+3.39314 q^{45}\) \(+13.2589 q^{47}\) \(+11.9840 q^{49}\) \(+15.9449 q^{51}\) \(-4.96110 q^{53}\) \(+5.59047 q^{55}\) \(-2.14389 q^{57}\) \(-9.67374 q^{59}\) \(+0.0771850 q^{61}\) \(-6.95502 q^{63}\) \(+3.41289 q^{65}\) \(+8.62707 q^{67}\) \(-13.6083 q^{69}\) \(-10.4767 q^{71}\) \(-6.36465 q^{73}\) \(+1.03225 q^{75}\) \(-11.4589 q^{77}\) \(-1.00000 q^{79}\) \(-11.2407 q^{81}\) \(-0.269206 q^{83}\) \(-15.8095 q^{85}\) \(+14.5504 q^{87}\) \(+13.0122 q^{89}\) \(-6.99549 q^{91}\) \(-11.1408 q^{93}\) \(+2.12568 q^{95}\) \(-5.91056 q^{97}\) \(+4.19812 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.14389 −1.23778 −0.618888 0.785480i \(-0.712416\pi\)
−0.618888 + 0.785480i \(0.712416\pi\)
\(4\) 0 0
\(5\) 2.12568 0.950633 0.475316 0.879815i \(-0.342334\pi\)
0.475316 + 0.879815i \(0.342334\pi\)
\(6\) 0 0
\(7\) −4.35707 −1.64682 −0.823408 0.567449i \(-0.807930\pi\)
−0.823408 + 0.567449i \(0.807930\pi\)
\(8\) 0 0
\(9\) 1.59626 0.532088
\(10\) 0 0
\(11\) 2.62997 0.792965 0.396483 0.918042i \(-0.370231\pi\)
0.396483 + 0.918042i \(0.370231\pi\)
\(12\) 0 0
\(13\) 1.60555 0.445300 0.222650 0.974898i \(-0.428529\pi\)
0.222650 + 0.974898i \(0.428529\pi\)
\(14\) 0 0
\(15\) −4.55722 −1.17667
\(16\) 0 0
\(17\) −7.43738 −1.80383 −0.901914 0.431915i \(-0.857838\pi\)
−0.901914 + 0.431915i \(0.857838\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 9.34107 2.03839
\(22\) 0 0
\(23\) 6.34749 1.32354 0.661771 0.749706i \(-0.269805\pi\)
0.661771 + 0.749706i \(0.269805\pi\)
\(24\) 0 0
\(25\) −0.481487 −0.0962973
\(26\) 0 0
\(27\) 3.00946 0.579170
\(28\) 0 0
\(29\) −6.78691 −1.26030 −0.630149 0.776475i \(-0.717006\pi\)
−0.630149 + 0.776475i \(0.717006\pi\)
\(30\) 0 0
\(31\) 5.19656 0.933329 0.466664 0.884434i \(-0.345456\pi\)
0.466664 + 0.884434i \(0.345456\pi\)
\(32\) 0 0
\(33\) −5.63836 −0.981513
\(34\) 0 0
\(35\) −9.26173 −1.56552
\(36\) 0 0
\(37\) 9.25264 1.52112 0.760562 0.649265i \(-0.224923\pi\)
0.760562 + 0.649265i \(0.224923\pi\)
\(38\) 0 0
\(39\) −3.44212 −0.551181
\(40\) 0 0
\(41\) −10.6249 −1.65933 −0.829667 0.558259i \(-0.811470\pi\)
−0.829667 + 0.558259i \(0.811470\pi\)
\(42\) 0 0
\(43\) 1.30088 0.198383 0.0991913 0.995068i \(-0.468374\pi\)
0.0991913 + 0.995068i \(0.468374\pi\)
\(44\) 0 0
\(45\) 3.39314 0.505820
\(46\) 0 0
\(47\) 13.2589 1.93401 0.967003 0.254766i \(-0.0819985\pi\)
0.967003 + 0.254766i \(0.0819985\pi\)
\(48\) 0 0
\(49\) 11.9840 1.71200
\(50\) 0 0
\(51\) 15.9449 2.23273
\(52\) 0 0
\(53\) −4.96110 −0.681460 −0.340730 0.940161i \(-0.610674\pi\)
−0.340730 + 0.940161i \(0.610674\pi\)
\(54\) 0 0
\(55\) 5.59047 0.753819
\(56\) 0 0
\(57\) −2.14389 −0.283965
\(58\) 0 0
\(59\) −9.67374 −1.25941 −0.629707 0.776833i \(-0.716825\pi\)
−0.629707 + 0.776833i \(0.716825\pi\)
\(60\) 0 0
\(61\) 0.0771850 0.00988252 0.00494126 0.999988i \(-0.498427\pi\)
0.00494126 + 0.999988i \(0.498427\pi\)
\(62\) 0 0
\(63\) −6.95502 −0.876251
\(64\) 0 0
\(65\) 3.41289 0.423316
\(66\) 0 0
\(67\) 8.62707 1.05396 0.526982 0.849876i \(-0.323323\pi\)
0.526982 + 0.849876i \(0.323323\pi\)
\(68\) 0 0
\(69\) −13.6083 −1.63825
\(70\) 0 0
\(71\) −10.4767 −1.24336 −0.621679 0.783273i \(-0.713549\pi\)
−0.621679 + 0.783273i \(0.713549\pi\)
\(72\) 0 0
\(73\) −6.36465 −0.744926 −0.372463 0.928047i \(-0.621487\pi\)
−0.372463 + 0.928047i \(0.621487\pi\)
\(74\) 0 0
\(75\) 1.03225 0.119194
\(76\) 0 0
\(77\) −11.4589 −1.30587
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −11.2407 −1.24897
\(82\) 0 0
\(83\) −0.269206 −0.0295492 −0.0147746 0.999891i \(-0.504703\pi\)
−0.0147746 + 0.999891i \(0.504703\pi\)
\(84\) 0 0
\(85\) −15.8095 −1.71478
\(86\) 0 0
\(87\) 14.5504 1.55996
\(88\) 0 0
\(89\) 13.0122 1.37929 0.689644 0.724149i \(-0.257767\pi\)
0.689644 + 0.724149i \(0.257767\pi\)
\(90\) 0 0
\(91\) −6.99549 −0.733327
\(92\) 0 0
\(93\) −11.1408 −1.15525
\(94\) 0 0
\(95\) 2.12568 0.218090
\(96\) 0 0
\(97\) −5.91056 −0.600126 −0.300063 0.953919i \(-0.597008\pi\)
−0.300063 + 0.953919i \(0.597008\pi\)
\(98\) 0 0
\(99\) 4.19812 0.421927
\(100\) 0 0
\(101\) 15.3724 1.52961 0.764803 0.644264i \(-0.222836\pi\)
0.764803 + 0.644264i \(0.222836\pi\)
\(102\) 0 0
\(103\) 15.3785 1.51529 0.757643 0.652669i \(-0.226351\pi\)
0.757643 + 0.652669i \(0.226351\pi\)
\(104\) 0 0
\(105\) 19.8561 1.93776
\(106\) 0 0
\(107\) −12.5103 −1.20942 −0.604709 0.796446i \(-0.706711\pi\)
−0.604709 + 0.796446i \(0.706711\pi\)
\(108\) 0 0
\(109\) 8.72744 0.835937 0.417969 0.908462i \(-0.362742\pi\)
0.417969 + 0.908462i \(0.362742\pi\)
\(110\) 0 0
\(111\) −19.8366 −1.88281
\(112\) 0 0
\(113\) −2.86294 −0.269323 −0.134661 0.990892i \(-0.542995\pi\)
−0.134661 + 0.990892i \(0.542995\pi\)
\(114\) 0 0
\(115\) 13.4927 1.25820
\(116\) 0 0
\(117\) 2.56288 0.236938
\(118\) 0 0
\(119\) 32.4051 2.97057
\(120\) 0 0
\(121\) −4.08326 −0.371206
\(122\) 0 0
\(123\) 22.7787 2.05388
\(124\) 0 0
\(125\) −11.6519 −1.04218
\(126\) 0 0
\(127\) 13.0048 1.15399 0.576994 0.816749i \(-0.304226\pi\)
0.576994 + 0.816749i \(0.304226\pi\)
\(128\) 0 0
\(129\) −2.78895 −0.245553
\(130\) 0 0
\(131\) −10.0451 −0.877641 −0.438821 0.898575i \(-0.644604\pi\)
−0.438821 + 0.898575i \(0.644604\pi\)
\(132\) 0 0
\(133\) −4.35707 −0.377806
\(134\) 0 0
\(135\) 6.39714 0.550578
\(136\) 0 0
\(137\) 7.67431 0.655661 0.327830 0.944737i \(-0.393683\pi\)
0.327830 + 0.944737i \(0.393683\pi\)
\(138\) 0 0
\(139\) −9.24532 −0.784178 −0.392089 0.919927i \(-0.628247\pi\)
−0.392089 + 0.919927i \(0.628247\pi\)
\(140\) 0 0
\(141\) −28.4256 −2.39386
\(142\) 0 0
\(143\) 4.22255 0.353107
\(144\) 0 0
\(145\) −14.4268 −1.19808
\(146\) 0 0
\(147\) −25.6924 −2.11908
\(148\) 0 0
\(149\) −12.3267 −1.00985 −0.504923 0.863165i \(-0.668479\pi\)
−0.504923 + 0.863165i \(0.668479\pi\)
\(150\) 0 0
\(151\) 5.46737 0.444928 0.222464 0.974941i \(-0.428590\pi\)
0.222464 + 0.974941i \(0.428590\pi\)
\(152\) 0 0
\(153\) −11.8720 −0.959795
\(154\) 0 0
\(155\) 11.0462 0.887253
\(156\) 0 0
\(157\) −5.28258 −0.421596 −0.210798 0.977530i \(-0.567606\pi\)
−0.210798 + 0.977530i \(0.567606\pi\)
\(158\) 0 0
\(159\) 10.6361 0.843494
\(160\) 0 0
\(161\) −27.6564 −2.17963
\(162\) 0 0
\(163\) −22.5062 −1.76282 −0.881410 0.472352i \(-0.843405\pi\)
−0.881410 + 0.472352i \(0.843405\pi\)
\(164\) 0 0
\(165\) −11.9854 −0.933058
\(166\) 0 0
\(167\) −24.5736 −1.90156 −0.950782 0.309860i \(-0.899718\pi\)
−0.950782 + 0.309860i \(0.899718\pi\)
\(168\) 0 0
\(169\) −10.4222 −0.801708
\(170\) 0 0
\(171\) 1.59626 0.122069
\(172\) 0 0
\(173\) 12.8035 0.973434 0.486717 0.873560i \(-0.338194\pi\)
0.486717 + 0.873560i \(0.338194\pi\)
\(174\) 0 0
\(175\) 2.09787 0.158584
\(176\) 0 0
\(177\) 20.7394 1.55887
\(178\) 0 0
\(179\) −2.11092 −0.157777 −0.0788887 0.996883i \(-0.525137\pi\)
−0.0788887 + 0.996883i \(0.525137\pi\)
\(180\) 0 0
\(181\) 2.71295 0.201652 0.100826 0.994904i \(-0.467851\pi\)
0.100826 + 0.994904i \(0.467851\pi\)
\(182\) 0 0
\(183\) −0.165476 −0.0122323
\(184\) 0 0
\(185\) 19.6681 1.44603
\(186\) 0 0
\(187\) −19.5601 −1.43037
\(188\) 0 0
\(189\) −13.1124 −0.953787
\(190\) 0 0
\(191\) 15.8457 1.14655 0.573277 0.819362i \(-0.305672\pi\)
0.573277 + 0.819362i \(0.305672\pi\)
\(192\) 0 0
\(193\) 4.80511 0.345879 0.172940 0.984932i \(-0.444673\pi\)
0.172940 + 0.984932i \(0.444673\pi\)
\(194\) 0 0
\(195\) −7.31685 −0.523971
\(196\) 0 0
\(197\) −10.2230 −0.728358 −0.364179 0.931329i \(-0.618650\pi\)
−0.364179 + 0.931329i \(0.618650\pi\)
\(198\) 0 0
\(199\) −2.55409 −0.181055 −0.0905273 0.995894i \(-0.528855\pi\)
−0.0905273 + 0.995894i \(0.528855\pi\)
\(200\) 0 0
\(201\) −18.4955 −1.30457
\(202\) 0 0
\(203\) 29.5710 2.07548
\(204\) 0 0
\(205\) −22.5852 −1.57742
\(206\) 0 0
\(207\) 10.1323 0.704241
\(208\) 0 0
\(209\) 2.62997 0.181919
\(210\) 0 0
\(211\) −24.8781 −1.71268 −0.856338 0.516415i \(-0.827266\pi\)
−0.856338 + 0.516415i \(0.827266\pi\)
\(212\) 0 0
\(213\) 22.4609 1.53900
\(214\) 0 0
\(215\) 2.76526 0.188589
\(216\) 0 0
\(217\) −22.6417 −1.53702
\(218\) 0 0
\(219\) 13.6451 0.922051
\(220\) 0 0
\(221\) −11.9411 −0.803244
\(222\) 0 0
\(223\) 18.8472 1.26210 0.631050 0.775742i \(-0.282624\pi\)
0.631050 + 0.775742i \(0.282624\pi\)
\(224\) 0 0
\(225\) −0.768579 −0.0512386
\(226\) 0 0
\(227\) 13.0581 0.866695 0.433347 0.901227i \(-0.357332\pi\)
0.433347 + 0.901227i \(0.357332\pi\)
\(228\) 0 0
\(229\) 3.20186 0.211585 0.105792 0.994388i \(-0.466262\pi\)
0.105792 + 0.994388i \(0.466262\pi\)
\(230\) 0 0
\(231\) 24.5667 1.61637
\(232\) 0 0
\(233\) 7.72987 0.506400 0.253200 0.967414i \(-0.418517\pi\)
0.253200 + 0.967414i \(0.418517\pi\)
\(234\) 0 0
\(235\) 28.1841 1.83853
\(236\) 0 0
\(237\) 2.14389 0.139261
\(238\) 0 0
\(239\) 17.0828 1.10499 0.552497 0.833515i \(-0.313675\pi\)
0.552497 + 0.833515i \(0.313675\pi\)
\(240\) 0 0
\(241\) −24.4878 −1.57740 −0.788700 0.614778i \(-0.789246\pi\)
−0.788700 + 0.614778i \(0.789246\pi\)
\(242\) 0 0
\(243\) 15.0705 0.966774
\(244\) 0 0
\(245\) 25.4742 1.62749
\(246\) 0 0
\(247\) 1.60555 0.102159
\(248\) 0 0
\(249\) 0.577147 0.0365752
\(250\) 0 0
\(251\) −16.6351 −1.05000 −0.524999 0.851103i \(-0.675934\pi\)
−0.524999 + 0.851103i \(0.675934\pi\)
\(252\) 0 0
\(253\) 16.6937 1.04952
\(254\) 0 0
\(255\) 33.8938 2.12251
\(256\) 0 0
\(257\) −32.0134 −1.99694 −0.998472 0.0552644i \(-0.982400\pi\)
−0.998472 + 0.0552644i \(0.982400\pi\)
\(258\) 0 0
\(259\) −40.3144 −2.50501
\(260\) 0 0
\(261\) −10.8337 −0.670588
\(262\) 0 0
\(263\) −10.5677 −0.651635 −0.325817 0.945433i \(-0.605639\pi\)
−0.325817 + 0.945433i \(0.605639\pi\)
\(264\) 0 0
\(265\) −10.5457 −0.647818
\(266\) 0 0
\(267\) −27.8967 −1.70725
\(268\) 0 0
\(269\) −25.8886 −1.57846 −0.789228 0.614100i \(-0.789519\pi\)
−0.789228 + 0.614100i \(0.789519\pi\)
\(270\) 0 0
\(271\) −9.75807 −0.592761 −0.296380 0.955070i \(-0.595780\pi\)
−0.296380 + 0.955070i \(0.595780\pi\)
\(272\) 0 0
\(273\) 14.9976 0.907694
\(274\) 0 0
\(275\) −1.26629 −0.0763604
\(276\) 0 0
\(277\) 7.32901 0.440358 0.220179 0.975460i \(-0.429336\pi\)
0.220179 + 0.975460i \(0.429336\pi\)
\(278\) 0 0
\(279\) 8.29507 0.496613
\(280\) 0 0
\(281\) 0.0135689 0.000809454 0 0.000404727 1.00000i \(-0.499871\pi\)
0.000404727 1.00000i \(0.499871\pi\)
\(282\) 0 0
\(283\) −11.3812 −0.676542 −0.338271 0.941049i \(-0.609842\pi\)
−0.338271 + 0.941049i \(0.609842\pi\)
\(284\) 0 0
\(285\) −4.55722 −0.269947
\(286\) 0 0
\(287\) 46.2935 2.73262
\(288\) 0 0
\(289\) 38.3146 2.25380
\(290\) 0 0
\(291\) 12.6716 0.742821
\(292\) 0 0
\(293\) 16.6159 0.970714 0.485357 0.874316i \(-0.338690\pi\)
0.485357 + 0.874316i \(0.338690\pi\)
\(294\) 0 0
\(295\) −20.5633 −1.19724
\(296\) 0 0
\(297\) 7.91478 0.459262
\(298\) 0 0
\(299\) 10.1912 0.589373
\(300\) 0 0
\(301\) −5.66803 −0.326700
\(302\) 0 0
\(303\) −32.9566 −1.89331
\(304\) 0 0
\(305\) 0.164070 0.00939465
\(306\) 0 0
\(307\) 5.25463 0.299897 0.149949 0.988694i \(-0.452089\pi\)
0.149949 + 0.988694i \(0.452089\pi\)
\(308\) 0 0
\(309\) −32.9698 −1.87558
\(310\) 0 0
\(311\) 30.5038 1.72971 0.864857 0.502018i \(-0.167409\pi\)
0.864857 + 0.502018i \(0.167409\pi\)
\(312\) 0 0
\(313\) 14.1889 0.802006 0.401003 0.916077i \(-0.368662\pi\)
0.401003 + 0.916077i \(0.368662\pi\)
\(314\) 0 0
\(315\) −14.7842 −0.832993
\(316\) 0 0
\(317\) −34.8894 −1.95958 −0.979792 0.200020i \(-0.935899\pi\)
−0.979792 + 0.200020i \(0.935899\pi\)
\(318\) 0 0
\(319\) −17.8494 −0.999372
\(320\) 0 0
\(321\) 26.8208 1.49699
\(322\) 0 0
\(323\) −7.43738 −0.413827
\(324\) 0 0
\(325\) −0.773051 −0.0428812
\(326\) 0 0
\(327\) −18.7107 −1.03470
\(328\) 0 0
\(329\) −57.7698 −3.18495
\(330\) 0 0
\(331\) −22.4092 −1.23172 −0.615860 0.787856i \(-0.711191\pi\)
−0.615860 + 0.787856i \(0.711191\pi\)
\(332\) 0 0
\(333\) 14.7696 0.809371
\(334\) 0 0
\(335\) 18.3384 1.00193
\(336\) 0 0
\(337\) −24.8371 −1.35296 −0.676481 0.736460i \(-0.736496\pi\)
−0.676481 + 0.736460i \(0.736496\pi\)
\(338\) 0 0
\(339\) 6.13783 0.333361
\(340\) 0 0
\(341\) 13.6668 0.740098
\(342\) 0 0
\(343\) −21.7158 −1.17254
\(344\) 0 0
\(345\) −28.9269 −1.55737
\(346\) 0 0
\(347\) −1.89664 −0.101817 −0.0509086 0.998703i \(-0.516212\pi\)
−0.0509086 + 0.998703i \(0.516212\pi\)
\(348\) 0 0
\(349\) −12.1821 −0.652095 −0.326048 0.945353i \(-0.605717\pi\)
−0.326048 + 0.945353i \(0.605717\pi\)
\(350\) 0 0
\(351\) 4.83184 0.257904
\(352\) 0 0
\(353\) 2.72479 0.145026 0.0725130 0.997367i \(-0.476898\pi\)
0.0725130 + 0.997367i \(0.476898\pi\)
\(354\) 0 0
\(355\) −22.2701 −1.18198
\(356\) 0 0
\(357\) −69.4731 −3.67690
\(358\) 0 0
\(359\) −30.6161 −1.61586 −0.807929 0.589280i \(-0.799412\pi\)
−0.807929 + 0.589280i \(0.799412\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 8.75407 0.459469
\(364\) 0 0
\(365\) −13.5292 −0.708151
\(366\) 0 0
\(367\) −31.4506 −1.64171 −0.820855 0.571137i \(-0.806503\pi\)
−0.820855 + 0.571137i \(0.806503\pi\)
\(368\) 0 0
\(369\) −16.9602 −0.882911
\(370\) 0 0
\(371\) 21.6159 1.12224
\(372\) 0 0
\(373\) −18.2606 −0.945500 −0.472750 0.881196i \(-0.656739\pi\)
−0.472750 + 0.881196i \(0.656739\pi\)
\(374\) 0 0
\(375\) 24.9804 1.28998
\(376\) 0 0
\(377\) −10.8967 −0.561210
\(378\) 0 0
\(379\) 18.2307 0.936448 0.468224 0.883610i \(-0.344894\pi\)
0.468224 + 0.883610i \(0.344894\pi\)
\(380\) 0 0
\(381\) −27.8808 −1.42838
\(382\) 0 0
\(383\) 7.22982 0.369426 0.184713 0.982792i \(-0.440864\pi\)
0.184713 + 0.982792i \(0.440864\pi\)
\(384\) 0 0
\(385\) −24.3581 −1.24140
\(386\) 0 0
\(387\) 2.07655 0.105557
\(388\) 0 0
\(389\) 17.9081 0.907975 0.453987 0.891008i \(-0.350001\pi\)
0.453987 + 0.891008i \(0.350001\pi\)
\(390\) 0 0
\(391\) −47.2086 −2.38744
\(392\) 0 0
\(393\) 21.5355 1.08632
\(394\) 0 0
\(395\) −2.12568 −0.106955
\(396\) 0 0
\(397\) −5.98507 −0.300382 −0.150191 0.988657i \(-0.547989\pi\)
−0.150191 + 0.988657i \(0.547989\pi\)
\(398\) 0 0
\(399\) 9.34107 0.467638
\(400\) 0 0
\(401\) −8.00498 −0.399750 −0.199875 0.979821i \(-0.564054\pi\)
−0.199875 + 0.979821i \(0.564054\pi\)
\(402\) 0 0
\(403\) 8.34333 0.415611
\(404\) 0 0
\(405\) −23.8942 −1.18731
\(406\) 0 0
\(407\) 24.3341 1.20620
\(408\) 0 0
\(409\) −17.5025 −0.865445 −0.432722 0.901527i \(-0.642447\pi\)
−0.432722 + 0.901527i \(0.642447\pi\)
\(410\) 0 0
\(411\) −16.4529 −0.811560
\(412\) 0 0
\(413\) 42.1491 2.07402
\(414\) 0 0
\(415\) −0.572245 −0.0280904
\(416\) 0 0
\(417\) 19.8209 0.970636
\(418\) 0 0
\(419\) 22.1126 1.08027 0.540136 0.841578i \(-0.318373\pi\)
0.540136 + 0.841578i \(0.318373\pi\)
\(420\) 0 0
\(421\) 13.3413 0.650213 0.325106 0.945677i \(-0.394600\pi\)
0.325106 + 0.945677i \(0.394600\pi\)
\(422\) 0 0
\(423\) 21.1646 1.02906
\(424\) 0 0
\(425\) 3.58100 0.173704
\(426\) 0 0
\(427\) −0.336300 −0.0162747
\(428\) 0 0
\(429\) −9.05268 −0.437067
\(430\) 0 0
\(431\) 7.71926 0.371824 0.185912 0.982566i \(-0.440476\pi\)
0.185912 + 0.982566i \(0.440476\pi\)
\(432\) 0 0
\(433\) −7.36989 −0.354174 −0.177087 0.984195i \(-0.556667\pi\)
−0.177087 + 0.984195i \(0.556667\pi\)
\(434\) 0 0
\(435\) 30.9294 1.48295
\(436\) 0 0
\(437\) 6.34749 0.303641
\(438\) 0 0
\(439\) 3.26857 0.156000 0.0780001 0.996953i \(-0.475147\pi\)
0.0780001 + 0.996953i \(0.475147\pi\)
\(440\) 0 0
\(441\) 19.1297 0.910937
\(442\) 0 0
\(443\) −37.7130 −1.79180 −0.895900 0.444256i \(-0.853468\pi\)
−0.895900 + 0.444256i \(0.853468\pi\)
\(444\) 0 0
\(445\) 27.6597 1.31120
\(446\) 0 0
\(447\) 26.4271 1.24996
\(448\) 0 0
\(449\) −40.1857 −1.89648 −0.948240 0.317555i \(-0.897138\pi\)
−0.948240 + 0.317555i \(0.897138\pi\)
\(450\) 0 0
\(451\) −27.9432 −1.31579
\(452\) 0 0
\(453\) −11.7214 −0.550721
\(454\) 0 0
\(455\) −14.8702 −0.697125
\(456\) 0 0
\(457\) 16.1353 0.754776 0.377388 0.926055i \(-0.376822\pi\)
0.377388 + 0.926055i \(0.376822\pi\)
\(458\) 0 0
\(459\) −22.3825 −1.04472
\(460\) 0 0
\(461\) −38.2154 −1.77987 −0.889934 0.456090i \(-0.849250\pi\)
−0.889934 + 0.456090i \(0.849250\pi\)
\(462\) 0 0
\(463\) −24.8069 −1.15288 −0.576438 0.817141i \(-0.695558\pi\)
−0.576438 + 0.817141i \(0.695558\pi\)
\(464\) 0 0
\(465\) −23.6819 −1.09822
\(466\) 0 0
\(467\) 6.85118 0.317035 0.158517 0.987356i \(-0.449329\pi\)
0.158517 + 0.987356i \(0.449329\pi\)
\(468\) 0 0
\(469\) −37.5887 −1.73569
\(470\) 0 0
\(471\) 11.3253 0.521841
\(472\) 0 0
\(473\) 3.42128 0.157311
\(474\) 0 0
\(475\) −0.481487 −0.0220921
\(476\) 0 0
\(477\) −7.91922 −0.362596
\(478\) 0 0
\(479\) −24.1668 −1.10421 −0.552105 0.833774i \(-0.686175\pi\)
−0.552105 + 0.833774i \(0.686175\pi\)
\(480\) 0 0
\(481\) 14.8556 0.677356
\(482\) 0 0
\(483\) 59.2923 2.69789
\(484\) 0 0
\(485\) −12.5640 −0.570500
\(486\) 0 0
\(487\) −31.0689 −1.40787 −0.703934 0.710265i \(-0.748575\pi\)
−0.703934 + 0.710265i \(0.748575\pi\)
\(488\) 0 0
\(489\) 48.2508 2.18197
\(490\) 0 0
\(491\) −0.377765 −0.0170483 −0.00852414 0.999964i \(-0.502713\pi\)
−0.00852414 + 0.999964i \(0.502713\pi\)
\(492\) 0 0
\(493\) 50.4768 2.27336
\(494\) 0 0
\(495\) 8.92386 0.401098
\(496\) 0 0
\(497\) 45.6477 2.04758
\(498\) 0 0
\(499\) −22.0949 −0.989101 −0.494551 0.869149i \(-0.664667\pi\)
−0.494551 + 0.869149i \(0.664667\pi\)
\(500\) 0 0
\(501\) 52.6832 2.35371
\(502\) 0 0
\(503\) 24.9086 1.11062 0.555309 0.831644i \(-0.312600\pi\)
0.555309 + 0.831644i \(0.312600\pi\)
\(504\) 0 0
\(505\) 32.6767 1.45409
\(506\) 0 0
\(507\) 22.3441 0.992335
\(508\) 0 0
\(509\) −1.71529 −0.0760290 −0.0380145 0.999277i \(-0.512103\pi\)
−0.0380145 + 0.999277i \(0.512103\pi\)
\(510\) 0 0
\(511\) 27.7312 1.22676
\(512\) 0 0
\(513\) 3.00946 0.132871
\(514\) 0 0
\(515\) 32.6897 1.44048
\(516\) 0 0
\(517\) 34.8704 1.53360
\(518\) 0 0
\(519\) −27.4493 −1.20489
\(520\) 0 0
\(521\) −16.6626 −0.730002 −0.365001 0.931007i \(-0.618931\pi\)
−0.365001 + 0.931007i \(0.618931\pi\)
\(522\) 0 0
\(523\) −2.13944 −0.0935512 −0.0467756 0.998905i \(-0.514895\pi\)
−0.0467756 + 0.998905i \(0.514895\pi\)
\(524\) 0 0
\(525\) −4.49760 −0.196291
\(526\) 0 0
\(527\) −38.6487 −1.68357
\(528\) 0 0
\(529\) 17.2906 0.751765
\(530\) 0 0
\(531\) −15.4418 −0.670118
\(532\) 0 0
\(533\) −17.0588 −0.738901
\(534\) 0 0
\(535\) −26.5929 −1.14971
\(536\) 0 0
\(537\) 4.52557 0.195293
\(538\) 0 0
\(539\) 31.5176 1.35756
\(540\) 0 0
\(541\) 26.5841 1.14294 0.571469 0.820624i \(-0.306374\pi\)
0.571469 + 0.820624i \(0.306374\pi\)
\(542\) 0 0
\(543\) −5.81626 −0.249600
\(544\) 0 0
\(545\) 18.5517 0.794669
\(546\) 0 0
\(547\) −19.5487 −0.835844 −0.417922 0.908483i \(-0.637241\pi\)
−0.417922 + 0.908483i \(0.637241\pi\)
\(548\) 0 0
\(549\) 0.123207 0.00525837
\(550\) 0 0
\(551\) −6.78691 −0.289132
\(552\) 0 0
\(553\) 4.35707 0.185281
\(554\) 0 0
\(555\) −42.1663 −1.78986
\(556\) 0 0
\(557\) −15.5728 −0.659839 −0.329919 0.944009i \(-0.607022\pi\)
−0.329919 + 0.944009i \(0.607022\pi\)
\(558\) 0 0
\(559\) 2.08863 0.0883398
\(560\) 0 0
\(561\) 41.9346 1.77048
\(562\) 0 0
\(563\) −14.7846 −0.623098 −0.311549 0.950230i \(-0.600848\pi\)
−0.311549 + 0.950230i \(0.600848\pi\)
\(564\) 0 0
\(565\) −6.08569 −0.256027
\(566\) 0 0
\(567\) 48.9766 2.05683
\(568\) 0 0
\(569\) −21.5807 −0.904710 −0.452355 0.891838i \(-0.649416\pi\)
−0.452355 + 0.891838i \(0.649416\pi\)
\(570\) 0 0
\(571\) 15.2869 0.639739 0.319869 0.947462i \(-0.396361\pi\)
0.319869 + 0.947462i \(0.396361\pi\)
\(572\) 0 0
\(573\) −33.9714 −1.41918
\(574\) 0 0
\(575\) −3.05623 −0.127454
\(576\) 0 0
\(577\) −23.4394 −0.975797 −0.487898 0.872900i \(-0.662236\pi\)
−0.487898 + 0.872900i \(0.662236\pi\)
\(578\) 0 0
\(579\) −10.3016 −0.428121
\(580\) 0 0
\(581\) 1.17295 0.0486620
\(582\) 0 0
\(583\) −13.0475 −0.540374
\(584\) 0 0
\(585\) 5.44786 0.225241
\(586\) 0 0
\(587\) −20.0445 −0.827327 −0.413663 0.910430i \(-0.635751\pi\)
−0.413663 + 0.910430i \(0.635751\pi\)
\(588\) 0 0
\(589\) 5.19656 0.214120
\(590\) 0 0
\(591\) 21.9170 0.901543
\(592\) 0 0
\(593\) 15.9108 0.653377 0.326689 0.945132i \(-0.394067\pi\)
0.326689 + 0.945132i \(0.394067\pi\)
\(594\) 0 0
\(595\) 68.8830 2.82393
\(596\) 0 0
\(597\) 5.47568 0.224105
\(598\) 0 0
\(599\) −41.0020 −1.67530 −0.837649 0.546209i \(-0.816070\pi\)
−0.837649 + 0.546209i \(0.816070\pi\)
\(600\) 0 0
\(601\) −25.3062 −1.03226 −0.516131 0.856509i \(-0.672628\pi\)
−0.516131 + 0.856509i \(0.672628\pi\)
\(602\) 0 0
\(603\) 13.7711 0.560802
\(604\) 0 0
\(605\) −8.67971 −0.352880
\(606\) 0 0
\(607\) 23.8276 0.967134 0.483567 0.875307i \(-0.339341\pi\)
0.483567 + 0.875307i \(0.339341\pi\)
\(608\) 0 0
\(609\) −63.3970 −2.56898
\(610\) 0 0
\(611\) 21.2878 0.861212
\(612\) 0 0
\(613\) 20.2971 0.819792 0.409896 0.912132i \(-0.365565\pi\)
0.409896 + 0.912132i \(0.365565\pi\)
\(614\) 0 0
\(615\) 48.4201 1.95249
\(616\) 0 0
\(617\) 23.9811 0.965442 0.482721 0.875774i \(-0.339649\pi\)
0.482721 + 0.875774i \(0.339649\pi\)
\(618\) 0 0
\(619\) 10.7967 0.433958 0.216979 0.976176i \(-0.430380\pi\)
0.216979 + 0.976176i \(0.430380\pi\)
\(620\) 0 0
\(621\) 19.1025 0.766557
\(622\) 0 0
\(623\) −56.6949 −2.27143
\(624\) 0 0
\(625\) −22.3607 −0.894429
\(626\) 0 0
\(627\) −5.63836 −0.225175
\(628\) 0 0
\(629\) −68.8154 −2.74385
\(630\) 0 0
\(631\) −29.4905 −1.17400 −0.587000 0.809587i \(-0.699691\pi\)
−0.587000 + 0.809587i \(0.699691\pi\)
\(632\) 0 0
\(633\) 53.3358 2.11991
\(634\) 0 0
\(635\) 27.6440 1.09702
\(636\) 0 0
\(637\) 19.2410 0.762355
\(638\) 0 0
\(639\) −16.7236 −0.661575
\(640\) 0 0
\(641\) −11.8446 −0.467833 −0.233916 0.972257i \(-0.575154\pi\)
−0.233916 + 0.972257i \(0.575154\pi\)
\(642\) 0 0
\(643\) 21.3846 0.843327 0.421663 0.906752i \(-0.361446\pi\)
0.421663 + 0.906752i \(0.361446\pi\)
\(644\) 0 0
\(645\) −5.92841 −0.233431
\(646\) 0 0
\(647\) 37.5431 1.47597 0.737985 0.674817i \(-0.235777\pi\)
0.737985 + 0.674817i \(0.235777\pi\)
\(648\) 0 0
\(649\) −25.4416 −0.998671
\(650\) 0 0
\(651\) 48.5414 1.90249
\(652\) 0 0
\(653\) −35.7235 −1.39797 −0.698984 0.715137i \(-0.746364\pi\)
−0.698984 + 0.715137i \(0.746364\pi\)
\(654\) 0 0
\(655\) −21.3526 −0.834314
\(656\) 0 0
\(657\) −10.1597 −0.396366
\(658\) 0 0
\(659\) −32.7924 −1.27741 −0.638706 0.769451i \(-0.720530\pi\)
−0.638706 + 0.769451i \(0.720530\pi\)
\(660\) 0 0
\(661\) −15.8731 −0.617391 −0.308696 0.951161i \(-0.599892\pi\)
−0.308696 + 0.951161i \(0.599892\pi\)
\(662\) 0 0
\(663\) 25.6004 0.994236
\(664\) 0 0
\(665\) −9.26173 −0.359154
\(666\) 0 0
\(667\) −43.0798 −1.66806
\(668\) 0 0
\(669\) −40.4063 −1.56220
\(670\) 0 0
\(671\) 0.202994 0.00783650
\(672\) 0 0
\(673\) 16.0180 0.617448 0.308724 0.951152i \(-0.400098\pi\)
0.308724 + 0.951152i \(0.400098\pi\)
\(674\) 0 0
\(675\) −1.44901 −0.0557726
\(676\) 0 0
\(677\) 28.6912 1.10269 0.551346 0.834277i \(-0.314114\pi\)
0.551346 + 0.834277i \(0.314114\pi\)
\(678\) 0 0
\(679\) 25.7527 0.988298
\(680\) 0 0
\(681\) −27.9951 −1.07277
\(682\) 0 0
\(683\) 38.7196 1.48157 0.740783 0.671744i \(-0.234455\pi\)
0.740783 + 0.671744i \(0.234455\pi\)
\(684\) 0 0
\(685\) 16.3131 0.623292
\(686\) 0 0
\(687\) −6.86443 −0.261894
\(688\) 0 0
\(689\) −7.96530 −0.303454
\(690\) 0 0
\(691\) −40.1229 −1.52635 −0.763174 0.646193i \(-0.776360\pi\)
−0.763174 + 0.646193i \(0.776360\pi\)
\(692\) 0 0
\(693\) −18.2915 −0.694836
\(694\) 0 0
\(695\) −19.6526 −0.745465
\(696\) 0 0
\(697\) 79.0215 2.99315
\(698\) 0 0
\(699\) −16.5720 −0.626810
\(700\) 0 0
\(701\) −34.4368 −1.30066 −0.650329 0.759652i \(-0.725369\pi\)
−0.650329 + 0.759652i \(0.725369\pi\)
\(702\) 0 0
\(703\) 9.25264 0.348970
\(704\) 0 0
\(705\) −60.4236 −2.27569
\(706\) 0 0
\(707\) −66.9784 −2.51898
\(708\) 0 0
\(709\) −5.82146 −0.218630 −0.109315 0.994007i \(-0.534866\pi\)
−0.109315 + 0.994007i \(0.534866\pi\)
\(710\) 0 0
\(711\) −1.59626 −0.0598645
\(712\) 0 0
\(713\) 32.9851 1.23530
\(714\) 0 0
\(715\) 8.97578 0.335675
\(716\) 0 0
\(717\) −36.6236 −1.36773
\(718\) 0 0
\(719\) 30.6248 1.14211 0.571055 0.820911i \(-0.306534\pi\)
0.571055 + 0.820911i \(0.306534\pi\)
\(720\) 0 0
\(721\) −67.0050 −2.49540
\(722\) 0 0
\(723\) 52.4992 1.95247
\(724\) 0 0
\(725\) 3.26781 0.121363
\(726\) 0 0
\(727\) 1.31811 0.0488860 0.0244430 0.999701i \(-0.492219\pi\)
0.0244430 + 0.999701i \(0.492219\pi\)
\(728\) 0 0
\(729\) 1.41267 0.0523211
\(730\) 0 0
\(731\) −9.67515 −0.357848
\(732\) 0 0
\(733\) 4.24944 0.156957 0.0784783 0.996916i \(-0.474994\pi\)
0.0784783 + 0.996916i \(0.474994\pi\)
\(734\) 0 0
\(735\) −54.6139 −2.01446
\(736\) 0 0
\(737\) 22.6889 0.835758
\(738\) 0 0
\(739\) 38.8400 1.42875 0.714375 0.699763i \(-0.246711\pi\)
0.714375 + 0.699763i \(0.246711\pi\)
\(740\) 0 0
\(741\) −3.44212 −0.126450
\(742\) 0 0
\(743\) 33.1921 1.21770 0.608850 0.793285i \(-0.291631\pi\)
0.608850 + 0.793285i \(0.291631\pi\)
\(744\) 0 0
\(745\) −26.2027 −0.959992
\(746\) 0 0
\(747\) −0.429723 −0.0157227
\(748\) 0 0
\(749\) 54.5083 1.99169
\(750\) 0 0
\(751\) −12.0409 −0.439380 −0.219690 0.975570i \(-0.570505\pi\)
−0.219690 + 0.975570i \(0.570505\pi\)
\(752\) 0 0
\(753\) 35.6638 1.29966
\(754\) 0 0
\(755\) 11.6219 0.422963
\(756\) 0 0
\(757\) −4.07712 −0.148185 −0.0740927 0.997251i \(-0.523606\pi\)
−0.0740927 + 0.997251i \(0.523606\pi\)
\(758\) 0 0
\(759\) −35.7894 −1.29907
\(760\) 0 0
\(761\) 21.7769 0.789411 0.394706 0.918808i \(-0.370847\pi\)
0.394706 + 0.918808i \(0.370847\pi\)
\(762\) 0 0
\(763\) −38.0260 −1.37663
\(764\) 0 0
\(765\) −25.2361 −0.912412
\(766\) 0 0
\(767\) −15.5317 −0.560816
\(768\) 0 0
\(769\) 46.6151 1.68098 0.840491 0.541825i \(-0.182267\pi\)
0.840491 + 0.541825i \(0.182267\pi\)
\(770\) 0 0
\(771\) 68.6333 2.47177
\(772\) 0 0
\(773\) 12.6364 0.454498 0.227249 0.973837i \(-0.427027\pi\)
0.227249 + 0.973837i \(0.427027\pi\)
\(774\) 0 0
\(775\) −2.50207 −0.0898771
\(776\) 0 0
\(777\) 86.4296 3.10064
\(778\) 0 0
\(779\) −10.6249 −0.380677
\(780\) 0 0
\(781\) −27.5534 −0.985939
\(782\) 0 0
\(783\) −20.4249 −0.729927
\(784\) 0 0
\(785\) −11.2291 −0.400783
\(786\) 0 0
\(787\) −6.47695 −0.230878 −0.115439 0.993315i \(-0.536828\pi\)
−0.115439 + 0.993315i \(0.536828\pi\)
\(788\) 0 0
\(789\) 22.6561 0.806577
\(790\) 0 0
\(791\) 12.4740 0.443525
\(792\) 0 0
\(793\) 0.123924 0.00440068
\(794\) 0 0
\(795\) 22.6088 0.801853
\(796\) 0 0
\(797\) −31.0359 −1.09935 −0.549675 0.835379i \(-0.685248\pi\)
−0.549675 + 0.835379i \(0.685248\pi\)
\(798\) 0 0
\(799\) −98.6112 −3.48861
\(800\) 0 0
\(801\) 20.7708 0.733902
\(802\) 0 0
\(803\) −16.7388 −0.590701
\(804\) 0 0
\(805\) −58.7887 −2.07203
\(806\) 0 0
\(807\) 55.5023 1.95377
\(808\) 0 0
\(809\) −27.6555 −0.972316 −0.486158 0.873871i \(-0.661602\pi\)
−0.486158 + 0.873871i \(0.661602\pi\)
\(810\) 0 0
\(811\) 12.3852 0.434905 0.217452 0.976071i \(-0.430225\pi\)
0.217452 + 0.976071i \(0.430225\pi\)
\(812\) 0 0
\(813\) 20.9202 0.733704
\(814\) 0 0
\(815\) −47.8409 −1.67579
\(816\) 0 0
\(817\) 1.30088 0.0455121
\(818\) 0 0
\(819\) −11.1666 −0.390194
\(820\) 0 0
\(821\) −42.6582 −1.48878 −0.744391 0.667744i \(-0.767260\pi\)
−0.744391 + 0.667744i \(0.767260\pi\)
\(822\) 0 0
\(823\) −31.8548 −1.11039 −0.555194 0.831721i \(-0.687356\pi\)
−0.555194 + 0.831721i \(0.687356\pi\)
\(824\) 0 0
\(825\) 2.71480 0.0945171
\(826\) 0 0
\(827\) −19.4568 −0.676578 −0.338289 0.941042i \(-0.609848\pi\)
−0.338289 + 0.941042i \(0.609848\pi\)
\(828\) 0 0
\(829\) 8.11597 0.281879 0.140940 0.990018i \(-0.454988\pi\)
0.140940 + 0.990018i \(0.454988\pi\)
\(830\) 0 0
\(831\) −15.7126 −0.545064
\(832\) 0 0
\(833\) −89.1298 −3.08816
\(834\) 0 0
\(835\) −52.2357 −1.80769
\(836\) 0 0
\(837\) 15.6388 0.540556
\(838\) 0 0
\(839\) −28.4402 −0.981864 −0.490932 0.871198i \(-0.663344\pi\)
−0.490932 + 0.871198i \(0.663344\pi\)
\(840\) 0 0
\(841\) 17.0621 0.588349
\(842\) 0 0
\(843\) −0.0290903 −0.00100192
\(844\) 0 0
\(845\) −22.1543 −0.762130
\(846\) 0 0
\(847\) 17.7911 0.611308
\(848\) 0 0
\(849\) 24.4000 0.837407
\(850\) 0 0
\(851\) 58.7310 2.01327
\(852\) 0 0
\(853\) 55.4942 1.90008 0.950042 0.312122i \(-0.101040\pi\)
0.950042 + 0.312122i \(0.101040\pi\)
\(854\) 0 0
\(855\) 3.39314 0.116043
\(856\) 0 0
\(857\) 28.3573 0.968667 0.484334 0.874883i \(-0.339062\pi\)
0.484334 + 0.874883i \(0.339062\pi\)
\(858\) 0 0
\(859\) 34.2990 1.17027 0.585133 0.810937i \(-0.301042\pi\)
0.585133 + 0.810937i \(0.301042\pi\)
\(860\) 0 0
\(861\) −99.2481 −3.38237
\(862\) 0 0
\(863\) 23.1331 0.787459 0.393729 0.919226i \(-0.371185\pi\)
0.393729 + 0.919226i \(0.371185\pi\)
\(864\) 0 0
\(865\) 27.2162 0.925378
\(866\) 0 0
\(867\) −82.1422 −2.78969
\(868\) 0 0
\(869\) −2.62997 −0.0892156
\(870\) 0 0
\(871\) 13.8512 0.469330
\(872\) 0 0
\(873\) −9.43480 −0.319320
\(874\) 0 0
\(875\) 50.7680 1.71627
\(876\) 0 0
\(877\) 17.7369 0.598933 0.299467 0.954107i \(-0.403191\pi\)
0.299467 + 0.954107i \(0.403191\pi\)
\(878\) 0 0
\(879\) −35.6227 −1.20153
\(880\) 0 0
\(881\) 10.9644 0.369401 0.184700 0.982795i \(-0.440869\pi\)
0.184700 + 0.982795i \(0.440869\pi\)
\(882\) 0 0
\(883\) 49.5814 1.66855 0.834274 0.551350i \(-0.185887\pi\)
0.834274 + 0.551350i \(0.185887\pi\)
\(884\) 0 0
\(885\) 44.0854 1.48191
\(886\) 0 0
\(887\) −26.6259 −0.894011 −0.447005 0.894531i \(-0.647510\pi\)
−0.447005 + 0.894531i \(0.647510\pi\)
\(888\) 0 0
\(889\) −56.6627 −1.90041
\(890\) 0 0
\(891\) −29.5628 −0.990390
\(892\) 0 0
\(893\) 13.2589 0.443691
\(894\) 0 0
\(895\) −4.48713 −0.149988
\(896\) 0 0
\(897\) −21.8488 −0.729511
\(898\) 0 0
\(899\) −35.2685 −1.17627
\(900\) 0 0
\(901\) 36.8976 1.22924
\(902\) 0 0
\(903\) 12.1516 0.404381
\(904\) 0 0
\(905\) 5.76686 0.191697
\(906\) 0 0
\(907\) −34.6956 −1.15205 −0.576025 0.817432i \(-0.695397\pi\)
−0.576025 + 0.817432i \(0.695397\pi\)
\(908\) 0 0
\(909\) 24.5383 0.813884
\(910\) 0 0
\(911\) −31.3442 −1.03848 −0.519240 0.854629i \(-0.673785\pi\)
−0.519240 + 0.854629i \(0.673785\pi\)
\(912\) 0 0
\(913\) −0.708002 −0.0234315
\(914\) 0 0
\(915\) −0.351749 −0.0116285
\(916\) 0 0
\(917\) 43.7670 1.44531
\(918\) 0 0
\(919\) −5.00119 −0.164974 −0.0824871 0.996592i \(-0.526286\pi\)
−0.0824871 + 0.996592i \(0.526286\pi\)
\(920\) 0 0
\(921\) −11.2653 −0.371206
\(922\) 0 0
\(923\) −16.8209 −0.553666
\(924\) 0 0
\(925\) −4.45502 −0.146480
\(926\) 0 0
\(927\) 24.5481 0.806265
\(928\) 0 0
\(929\) 19.5074 0.640018 0.320009 0.947414i \(-0.396314\pi\)
0.320009 + 0.947414i \(0.396314\pi\)
\(930\) 0 0
\(931\) 11.9840 0.392761
\(932\) 0 0
\(933\) −65.3969 −2.14100
\(934\) 0 0
\(935\) −41.5784 −1.35976
\(936\) 0 0
\(937\) 4.20144 0.137255 0.0686275 0.997642i \(-0.478138\pi\)
0.0686275 + 0.997642i \(0.478138\pi\)
\(938\) 0 0
\(939\) −30.4195 −0.992704
\(940\) 0 0
\(941\) −11.0142 −0.359054 −0.179527 0.983753i \(-0.557457\pi\)
−0.179527 + 0.983753i \(0.557457\pi\)
\(942\) 0 0
\(943\) −67.4415 −2.19620
\(944\) 0 0
\(945\) −27.8728 −0.906701
\(946\) 0 0
\(947\) 26.2525 0.853091 0.426546 0.904466i \(-0.359730\pi\)
0.426546 + 0.904466i \(0.359730\pi\)
\(948\) 0 0
\(949\) −10.2188 −0.331715
\(950\) 0 0
\(951\) 74.7990 2.42552
\(952\) 0 0
\(953\) 20.3400 0.658879 0.329439 0.944177i \(-0.393140\pi\)
0.329439 + 0.944177i \(0.393140\pi\)
\(954\) 0 0
\(955\) 33.6829 1.08995
\(956\) 0 0
\(957\) 38.2670 1.23700
\(958\) 0 0
\(959\) −33.4375 −1.07975
\(960\) 0 0
\(961\) −3.99581 −0.128897
\(962\) 0 0
\(963\) −19.9698 −0.643517
\(964\) 0 0
\(965\) 10.2141 0.328804
\(966\) 0 0
\(967\) 27.8742 0.896375 0.448188 0.893940i \(-0.352070\pi\)
0.448188 + 0.893940i \(0.352070\pi\)
\(968\) 0 0
\(969\) 15.9449 0.512224
\(970\) 0 0
\(971\) 36.8990 1.18415 0.592073 0.805885i \(-0.298310\pi\)
0.592073 + 0.805885i \(0.298310\pi\)
\(972\) 0 0
\(973\) 40.2825 1.29140
\(974\) 0 0
\(975\) 1.65734 0.0530773
\(976\) 0 0
\(977\) 12.0080 0.384169 0.192084 0.981378i \(-0.438475\pi\)
0.192084 + 0.981378i \(0.438475\pi\)
\(978\) 0 0
\(979\) 34.2216 1.09373
\(980\) 0 0
\(981\) 13.9313 0.444792
\(982\) 0 0
\(983\) 10.3993 0.331687 0.165844 0.986152i \(-0.446965\pi\)
0.165844 + 0.986152i \(0.446965\pi\)
\(984\) 0 0
\(985\) −21.7308 −0.692401
\(986\) 0 0
\(987\) 123.852 3.94225
\(988\) 0 0
\(989\) 8.25733 0.262568
\(990\) 0 0
\(991\) −23.7903 −0.755724 −0.377862 0.925862i \(-0.623341\pi\)
−0.377862 + 0.925862i \(0.623341\pi\)
\(992\) 0 0
\(993\) 48.0428 1.52459
\(994\) 0 0
\(995\) −5.42917 −0.172116
\(996\) 0 0
\(997\) −15.9782 −0.506035 −0.253018 0.967462i \(-0.581423\pi\)
−0.253018 + 0.967462i \(0.581423\pi\)
\(998\) 0 0
\(999\) 27.8454 0.880990
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 \(a_p\))