Properties

Label 6027.2.a.bk.1.13
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-2.13271\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.13271 q^{2} +1.00000 q^{3} +2.54845 q^{4} -0.889988 q^{5} +2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.13271 q^{2} +1.00000 q^{3} +2.54845 q^{4} -0.889988 q^{5} +2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} -1.89809 q^{10} +3.41733 q^{11} +2.54845 q^{12} -6.24747 q^{13} -0.889988 q^{15} -2.60231 q^{16} -7.99996 q^{17} +2.13271 q^{18} +0.0729909 q^{19} -2.26809 q^{20} +7.28817 q^{22} +1.57406 q^{23} +1.16968 q^{24} -4.20792 q^{25} -13.3240 q^{26} +1.00000 q^{27} -0.756839 q^{29} -1.89809 q^{30} -2.56122 q^{31} -7.88933 q^{32} +3.41733 q^{33} -17.0616 q^{34} +2.54845 q^{36} -11.1697 q^{37} +0.155668 q^{38} -6.24747 q^{39} -1.04100 q^{40} -1.00000 q^{41} -6.17260 q^{43} +8.70889 q^{44} -0.889988 q^{45} +3.35702 q^{46} -1.59757 q^{47} -2.60231 q^{48} -8.97427 q^{50} -7.99996 q^{51} -15.9214 q^{52} +9.15967 q^{53} +2.13271 q^{54} -3.04138 q^{55} +0.0729909 q^{57} -1.61412 q^{58} +0.919674 q^{59} -2.26809 q^{60} +8.51853 q^{61} -5.46234 q^{62} -11.6210 q^{64} +5.56017 q^{65} +7.28817 q^{66} +2.41279 q^{67} -20.3875 q^{68} +1.57406 q^{69} +8.88392 q^{71} +1.16968 q^{72} -3.64101 q^{73} -23.8216 q^{74} -4.20792 q^{75} +0.186014 q^{76} -13.3240 q^{78} +11.7568 q^{79} +2.31602 q^{80} +1.00000 q^{81} -2.13271 q^{82} -4.03102 q^{83} +7.11987 q^{85} -13.1644 q^{86} -0.756839 q^{87} +3.99719 q^{88} +8.44697 q^{89} -1.89809 q^{90} +4.01141 q^{92} -2.56122 q^{93} -3.40716 q^{94} -0.0649610 q^{95} -7.88933 q^{96} +9.05668 q^{97} +3.41733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.13271 1.50805 0.754027 0.656844i \(-0.228109\pi\)
0.754027 + 0.656844i \(0.228109\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.54845 1.27422
\(5\) −0.889988 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(6\) 2.13271 0.870675
\(7\) 0 0
\(8\) 1.16968 0.413545
\(9\) 1.00000 0.333333
\(10\) −1.89809 −0.600227
\(11\) 3.41733 1.03036 0.515182 0.857081i \(-0.327724\pi\)
0.515182 + 0.857081i \(0.327724\pi\)
\(12\) 2.54845 0.735674
\(13\) −6.24747 −1.73274 −0.866368 0.499406i \(-0.833552\pi\)
−0.866368 + 0.499406i \(0.833552\pi\)
\(14\) 0 0
\(15\) −0.889988 −0.229794
\(16\) −2.60231 −0.650577
\(17\) −7.99996 −1.94027 −0.970137 0.242556i \(-0.922014\pi\)
−0.970137 + 0.242556i \(0.922014\pi\)
\(18\) 2.13271 0.502684
\(19\) 0.0729909 0.0167453 0.00837263 0.999965i \(-0.497335\pi\)
0.00837263 + 0.999965i \(0.497335\pi\)
\(20\) −2.26809 −0.507160
\(21\) 0 0
\(22\) 7.28817 1.55384
\(23\) 1.57406 0.328215 0.164107 0.986443i \(-0.447526\pi\)
0.164107 + 0.986443i \(0.447526\pi\)
\(24\) 1.16968 0.238760
\(25\) −4.20792 −0.841584
\(26\) −13.3240 −2.61306
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.756839 −0.140541 −0.0702707 0.997528i \(-0.522386\pi\)
−0.0702707 + 0.997528i \(0.522386\pi\)
\(30\) −1.89809 −0.346541
\(31\) −2.56122 −0.460009 −0.230004 0.973190i \(-0.573874\pi\)
−0.230004 + 0.973190i \(0.573874\pi\)
\(32\) −7.88933 −1.39465
\(33\) 3.41733 0.594881
\(34\) −17.0616 −2.92604
\(35\) 0 0
\(36\) 2.54845 0.424741
\(37\) −11.1697 −1.83628 −0.918140 0.396257i \(-0.870309\pi\)
−0.918140 + 0.396257i \(0.870309\pi\)
\(38\) 0.155668 0.0252527
\(39\) −6.24747 −1.00040
\(40\) −1.04100 −0.164597
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −6.17260 −0.941312 −0.470656 0.882317i \(-0.655983\pi\)
−0.470656 + 0.882317i \(0.655983\pi\)
\(44\) 8.70889 1.31291
\(45\) −0.889988 −0.132672
\(46\) 3.35702 0.494965
\(47\) −1.59757 −0.233030 −0.116515 0.993189i \(-0.537172\pi\)
−0.116515 + 0.993189i \(0.537172\pi\)
\(48\) −2.60231 −0.375611
\(49\) 0 0
\(50\) −8.97427 −1.26915
\(51\) −7.99996 −1.12022
\(52\) −15.9214 −2.20789
\(53\) 9.15967 1.25818 0.629088 0.777334i \(-0.283428\pi\)
0.629088 + 0.777334i \(0.283428\pi\)
\(54\) 2.13271 0.290225
\(55\) −3.04138 −0.410100
\(56\) 0 0
\(57\) 0.0729909 0.00966788
\(58\) −1.61412 −0.211944
\(59\) 0.919674 0.119731 0.0598657 0.998206i \(-0.480933\pi\)
0.0598657 + 0.998206i \(0.480933\pi\)
\(60\) −2.26809 −0.292809
\(61\) 8.51853 1.09069 0.545343 0.838213i \(-0.316399\pi\)
0.545343 + 0.838213i \(0.316399\pi\)
\(62\) −5.46234 −0.693717
\(63\) 0 0
\(64\) −11.6210 −1.45263
\(65\) 5.56017 0.689655
\(66\) 7.28817 0.897112
\(67\) 2.41279 0.294770 0.147385 0.989079i \(-0.452914\pi\)
0.147385 + 0.989079i \(0.452914\pi\)
\(68\) −20.3875 −2.47235
\(69\) 1.57406 0.189495
\(70\) 0 0
\(71\) 8.88392 1.05433 0.527163 0.849764i \(-0.323256\pi\)
0.527163 + 0.849764i \(0.323256\pi\)
\(72\) 1.16968 0.137848
\(73\) −3.64101 −0.426148 −0.213074 0.977036i \(-0.568348\pi\)
−0.213074 + 0.977036i \(0.568348\pi\)
\(74\) −23.8216 −2.76921
\(75\) −4.20792 −0.485889
\(76\) 0.186014 0.0213372
\(77\) 0 0
\(78\) −13.3240 −1.50865
\(79\) 11.7568 1.32274 0.661371 0.750059i \(-0.269975\pi\)
0.661371 + 0.750059i \(0.269975\pi\)
\(80\) 2.31602 0.258939
\(81\) 1.00000 0.111111
\(82\) −2.13271 −0.235518
\(83\) −4.03102 −0.442462 −0.221231 0.975221i \(-0.571008\pi\)
−0.221231 + 0.975221i \(0.571008\pi\)
\(84\) 0 0
\(85\) 7.11987 0.772258
\(86\) −13.1644 −1.41955
\(87\) −0.756839 −0.0811417
\(88\) 3.99719 0.426101
\(89\) 8.44697 0.895377 0.447688 0.894190i \(-0.352247\pi\)
0.447688 + 0.894190i \(0.352247\pi\)
\(90\) −1.89809 −0.200076
\(91\) 0 0
\(92\) 4.01141 0.418219
\(93\) −2.56122 −0.265586
\(94\) −3.40716 −0.351421
\(95\) −0.0649610 −0.00666486
\(96\) −7.88933 −0.805201
\(97\) 9.05668 0.919567 0.459783 0.888031i \(-0.347927\pi\)
0.459783 + 0.888031i \(0.347927\pi\)
\(98\) 0 0
\(99\) 3.41733 0.343455
\(100\) −10.7237 −1.07237
\(101\) −10.8514 −1.07976 −0.539879 0.841742i \(-0.681530\pi\)
−0.539879 + 0.841742i \(0.681530\pi\)
\(102\) −17.0616 −1.68935
\(103\) 3.12953 0.308362 0.154181 0.988043i \(-0.450726\pi\)
0.154181 + 0.988043i \(0.450726\pi\)
\(104\) −7.30755 −0.716564
\(105\) 0 0
\(106\) 19.5349 1.89740
\(107\) 3.35731 0.324564 0.162282 0.986744i \(-0.448115\pi\)
0.162282 + 0.986744i \(0.448115\pi\)
\(108\) 2.54845 0.245225
\(109\) 0.403889 0.0386856 0.0193428 0.999813i \(-0.493843\pi\)
0.0193428 + 0.999813i \(0.493843\pi\)
\(110\) −6.48638 −0.618453
\(111\) −11.1697 −1.06018
\(112\) 0 0
\(113\) 5.43878 0.511637 0.255818 0.966725i \(-0.417655\pi\)
0.255818 + 0.966725i \(0.417655\pi\)
\(114\) 0.155668 0.0145797
\(115\) −1.40090 −0.130634
\(116\) −1.92877 −0.179081
\(117\) −6.24747 −0.577579
\(118\) 1.96140 0.180561
\(119\) 0 0
\(120\) −1.04100 −0.0950301
\(121\) 0.678140 0.0616491
\(122\) 18.1675 1.64481
\(123\) −1.00000 −0.0901670
\(124\) −6.52713 −0.586154
\(125\) 8.19494 0.732978
\(126\) 0 0
\(127\) −5.15902 −0.457789 −0.228895 0.973451i \(-0.573511\pi\)
−0.228895 + 0.973451i \(0.573511\pi\)
\(128\) −9.00561 −0.795991
\(129\) −6.17260 −0.543467
\(130\) 11.8582 1.04004
\(131\) −11.9242 −1.04182 −0.520911 0.853611i \(-0.674408\pi\)
−0.520911 + 0.853611i \(0.674408\pi\)
\(132\) 8.70889 0.758011
\(133\) 0 0
\(134\) 5.14579 0.444528
\(135\) −0.889988 −0.0765980
\(136\) −9.35740 −0.802390
\(137\) 4.57666 0.391010 0.195505 0.980703i \(-0.437365\pi\)
0.195505 + 0.980703i \(0.437365\pi\)
\(138\) 3.35702 0.285768
\(139\) −14.6408 −1.24181 −0.620906 0.783885i \(-0.713235\pi\)
−0.620906 + 0.783885i \(0.713235\pi\)
\(140\) 0 0
\(141\) −1.59757 −0.134540
\(142\) 18.9468 1.58998
\(143\) −21.3497 −1.78535
\(144\) −2.60231 −0.216859
\(145\) 0.673578 0.0559376
\(146\) −7.76522 −0.642654
\(147\) 0 0
\(148\) −28.4653 −2.33983
\(149\) 2.31277 0.189470 0.0947348 0.995503i \(-0.469800\pi\)
0.0947348 + 0.995503i \(0.469800\pi\)
\(150\) −8.97427 −0.732746
\(151\) 1.08733 0.0884857 0.0442428 0.999021i \(-0.485912\pi\)
0.0442428 + 0.999021i \(0.485912\pi\)
\(152\) 0.0853761 0.00692491
\(153\) −7.99996 −0.646758
\(154\) 0 0
\(155\) 2.27945 0.183090
\(156\) −15.9214 −1.27473
\(157\) −24.5214 −1.95702 −0.978512 0.206192i \(-0.933893\pi\)
−0.978512 + 0.206192i \(0.933893\pi\)
\(158\) 25.0738 1.99477
\(159\) 9.15967 0.726409
\(160\) 7.02141 0.555091
\(161\) 0 0
\(162\) 2.13271 0.167561
\(163\) −20.7325 −1.62390 −0.811948 0.583730i \(-0.801593\pi\)
−0.811948 + 0.583730i \(0.801593\pi\)
\(164\) −2.54845 −0.199000
\(165\) −3.04138 −0.236771
\(166\) −8.59700 −0.667257
\(167\) 9.83140 0.760776 0.380388 0.924827i \(-0.375790\pi\)
0.380388 + 0.924827i \(0.375790\pi\)
\(168\) 0 0
\(169\) 26.0309 2.00238
\(170\) 15.1846 1.16461
\(171\) 0.0729909 0.00558175
\(172\) −15.7305 −1.19944
\(173\) −19.3348 −1.47000 −0.734998 0.678070i \(-0.762817\pi\)
−0.734998 + 0.678070i \(0.762817\pi\)
\(174\) −1.61412 −0.122366
\(175\) 0 0
\(176\) −8.89294 −0.670331
\(177\) 0.919674 0.0691269
\(178\) 18.0149 1.35028
\(179\) 16.3998 1.22578 0.612888 0.790170i \(-0.290008\pi\)
0.612888 + 0.790170i \(0.290008\pi\)
\(180\) −2.26809 −0.169053
\(181\) −16.4233 −1.22073 −0.610366 0.792119i \(-0.708978\pi\)
−0.610366 + 0.792119i \(0.708978\pi\)
\(182\) 0 0
\(183\) 8.51853 0.629708
\(184\) 1.84115 0.135731
\(185\) 9.94086 0.730866
\(186\) −5.46234 −0.400518
\(187\) −27.3385 −1.99919
\(188\) −4.07133 −0.296932
\(189\) 0 0
\(190\) −0.138543 −0.0100510
\(191\) −25.9485 −1.87757 −0.938785 0.344503i \(-0.888047\pi\)
−0.938785 + 0.344503i \(0.888047\pi\)
\(192\) −11.6210 −0.838675
\(193\) 26.2201 1.88737 0.943683 0.330850i \(-0.107335\pi\)
0.943683 + 0.330850i \(0.107335\pi\)
\(194\) 19.3153 1.38676
\(195\) 5.56017 0.398172
\(196\) 0 0
\(197\) 5.03749 0.358906 0.179453 0.983767i \(-0.442567\pi\)
0.179453 + 0.983767i \(0.442567\pi\)
\(198\) 7.28817 0.517948
\(199\) 2.53705 0.179847 0.0899234 0.995949i \(-0.471338\pi\)
0.0899234 + 0.995949i \(0.471338\pi\)
\(200\) −4.92193 −0.348033
\(201\) 2.41279 0.170185
\(202\) −23.1430 −1.62833
\(203\) 0 0
\(204\) −20.3875 −1.42741
\(205\) 0.889988 0.0621595
\(206\) 6.67438 0.465026
\(207\) 1.57406 0.109405
\(208\) 16.2578 1.12728
\(209\) 0.249434 0.0172537
\(210\) 0 0
\(211\) −23.1162 −1.59139 −0.795693 0.605700i \(-0.792893\pi\)
−0.795693 + 0.605700i \(0.792893\pi\)
\(212\) 23.3429 1.60320
\(213\) 8.88392 0.608716
\(214\) 7.16017 0.489459
\(215\) 5.49354 0.374656
\(216\) 1.16968 0.0795867
\(217\) 0 0
\(218\) 0.861378 0.0583399
\(219\) −3.64101 −0.246037
\(220\) −7.75081 −0.522559
\(221\) 49.9795 3.36198
\(222\) −23.8216 −1.59880
\(223\) 0.239630 0.0160468 0.00802341 0.999968i \(-0.497446\pi\)
0.00802341 + 0.999968i \(0.497446\pi\)
\(224\) 0 0
\(225\) −4.20792 −0.280528
\(226\) 11.5993 0.771576
\(227\) 3.70162 0.245685 0.122843 0.992426i \(-0.460799\pi\)
0.122843 + 0.992426i \(0.460799\pi\)
\(228\) 0.186014 0.0123190
\(229\) −6.25848 −0.413572 −0.206786 0.978386i \(-0.566300\pi\)
−0.206786 + 0.978386i \(0.566300\pi\)
\(230\) −2.98770 −0.197003
\(231\) 0 0
\(232\) −0.885260 −0.0581202
\(233\) −25.6456 −1.68010 −0.840050 0.542509i \(-0.817474\pi\)
−0.840050 + 0.542509i \(0.817474\pi\)
\(234\) −13.3240 −0.871020
\(235\) 1.42182 0.0927493
\(236\) 2.34374 0.152565
\(237\) 11.7568 0.763686
\(238\) 0 0
\(239\) −17.7843 −1.15037 −0.575185 0.818023i \(-0.695070\pi\)
−0.575185 + 0.818023i \(0.695070\pi\)
\(240\) 2.31602 0.149499
\(241\) 7.64067 0.492179 0.246089 0.969247i \(-0.420854\pi\)
0.246089 + 0.969247i \(0.420854\pi\)
\(242\) 1.44627 0.0929700
\(243\) 1.00000 0.0641500
\(244\) 21.7090 1.38978
\(245\) 0 0
\(246\) −2.13271 −0.135977
\(247\) −0.456008 −0.0290151
\(248\) −2.99581 −0.190234
\(249\) −4.03102 −0.255456
\(250\) 17.4774 1.10537
\(251\) −2.01280 −0.127047 −0.0635235 0.997980i \(-0.520234\pi\)
−0.0635235 + 0.997980i \(0.520234\pi\)
\(252\) 0 0
\(253\) 5.37909 0.338180
\(254\) −11.0027 −0.690370
\(255\) 7.11987 0.445863
\(256\) 4.03570 0.252231
\(257\) −6.23662 −0.389030 −0.194515 0.980900i \(-0.562313\pi\)
−0.194515 + 0.980900i \(0.562313\pi\)
\(258\) −13.1644 −0.819577
\(259\) 0 0
\(260\) 14.1698 0.878775
\(261\) −0.756839 −0.0468472
\(262\) −25.4309 −1.57112
\(263\) −8.13880 −0.501860 −0.250930 0.968005i \(-0.580736\pi\)
−0.250930 + 0.968005i \(0.580736\pi\)
\(264\) 3.99719 0.246010
\(265\) −8.15199 −0.500773
\(266\) 0 0
\(267\) 8.44697 0.516946
\(268\) 6.14888 0.375603
\(269\) 25.6694 1.56509 0.782544 0.622595i \(-0.213921\pi\)
0.782544 + 0.622595i \(0.213921\pi\)
\(270\) −1.89809 −0.115514
\(271\) 30.0299 1.82419 0.912093 0.409983i \(-0.134465\pi\)
0.912093 + 0.409983i \(0.134465\pi\)
\(272\) 20.8184 1.26230
\(273\) 0 0
\(274\) 9.76068 0.589664
\(275\) −14.3799 −0.867138
\(276\) 4.01141 0.241459
\(277\) −10.2884 −0.618169 −0.309085 0.951035i \(-0.600023\pi\)
−0.309085 + 0.951035i \(0.600023\pi\)
\(278\) −31.2245 −1.87272
\(279\) −2.56122 −0.153336
\(280\) 0 0
\(281\) 11.9838 0.714894 0.357447 0.933933i \(-0.383647\pi\)
0.357447 + 0.933933i \(0.383647\pi\)
\(282\) −3.40716 −0.202893
\(283\) 15.2539 0.906752 0.453376 0.891319i \(-0.350219\pi\)
0.453376 + 0.891319i \(0.350219\pi\)
\(284\) 22.6402 1.34345
\(285\) −0.0649610 −0.00384796
\(286\) −45.5326 −2.69240
\(287\) 0 0
\(288\) −7.88933 −0.464883
\(289\) 46.9993 2.76467
\(290\) 1.43655 0.0843569
\(291\) 9.05668 0.530912
\(292\) −9.27893 −0.543008
\(293\) 29.2216 1.70714 0.853571 0.520976i \(-0.174432\pi\)
0.853571 + 0.520976i \(0.174432\pi\)
\(294\) 0 0
\(295\) −0.818499 −0.0476548
\(296\) −13.0649 −0.759384
\(297\) 3.41733 0.198294
\(298\) 4.93247 0.285730
\(299\) −9.83390 −0.568709
\(300\) −10.7237 −0.619131
\(301\) 0 0
\(302\) 2.31896 0.133441
\(303\) −10.8514 −0.623399
\(304\) −0.189945 −0.0108941
\(305\) −7.58139 −0.434109
\(306\) −17.0616 −0.975346
\(307\) 27.7393 1.58317 0.791584 0.611061i \(-0.209257\pi\)
0.791584 + 0.611061i \(0.209257\pi\)
\(308\) 0 0
\(309\) 3.12953 0.178033
\(310\) 4.86141 0.276110
\(311\) 13.6882 0.776187 0.388093 0.921620i \(-0.373134\pi\)
0.388093 + 0.921620i \(0.373134\pi\)
\(312\) −7.30755 −0.413708
\(313\) −21.4280 −1.21118 −0.605590 0.795777i \(-0.707063\pi\)
−0.605590 + 0.795777i \(0.707063\pi\)
\(314\) −52.2971 −2.95129
\(315\) 0 0
\(316\) 29.9616 1.68547
\(317\) −27.6310 −1.55191 −0.775956 0.630786i \(-0.782732\pi\)
−0.775956 + 0.630786i \(0.782732\pi\)
\(318\) 19.5349 1.09546
\(319\) −2.58637 −0.144809
\(320\) 10.3426 0.578168
\(321\) 3.35731 0.187387
\(322\) 0 0
\(323\) −0.583924 −0.0324904
\(324\) 2.54845 0.141580
\(325\) 26.2889 1.45824
\(326\) −44.2164 −2.44892
\(327\) 0.403889 0.0223351
\(328\) −1.16968 −0.0645848
\(329\) 0 0
\(330\) −6.48638 −0.357064
\(331\) −17.5293 −0.963498 −0.481749 0.876309i \(-0.659998\pi\)
−0.481749 + 0.876309i \(0.659998\pi\)
\(332\) −10.2729 −0.563796
\(333\) −11.1697 −0.612093
\(334\) 20.9675 1.14729
\(335\) −2.14736 −0.117323
\(336\) 0 0
\(337\) 13.3142 0.725272 0.362636 0.931931i \(-0.381877\pi\)
0.362636 + 0.931931i \(0.381877\pi\)
\(338\) 55.5163 3.01969
\(339\) 5.43878 0.295394
\(340\) 18.1446 0.984030
\(341\) −8.75253 −0.473976
\(342\) 0.155668 0.00841758
\(343\) 0 0
\(344\) −7.21997 −0.389275
\(345\) −1.40090 −0.0754217
\(346\) −41.2354 −2.21683
\(347\) −3.91557 −0.210199 −0.105099 0.994462i \(-0.533516\pi\)
−0.105099 + 0.994462i \(0.533516\pi\)
\(348\) −1.92877 −0.103393
\(349\) 20.1583 1.07905 0.539524 0.841970i \(-0.318604\pi\)
0.539524 + 0.841970i \(0.318604\pi\)
\(350\) 0 0
\(351\) −6.24747 −0.333465
\(352\) −26.9604 −1.43700
\(353\) −20.7285 −1.10327 −0.551633 0.834087i \(-0.685995\pi\)
−0.551633 + 0.834087i \(0.685995\pi\)
\(354\) 1.96140 0.104247
\(355\) −7.90658 −0.419638
\(356\) 21.5267 1.14091
\(357\) 0 0
\(358\) 34.9759 1.84854
\(359\) −34.7155 −1.83221 −0.916107 0.400934i \(-0.868686\pi\)
−0.916107 + 0.400934i \(0.868686\pi\)
\(360\) −1.04100 −0.0548656
\(361\) −18.9947 −0.999720
\(362\) −35.0261 −1.84093
\(363\) 0.678140 0.0355931
\(364\) 0 0
\(365\) 3.24046 0.169613
\(366\) 18.1675 0.949633
\(367\) 22.9795 1.19952 0.599761 0.800179i \(-0.295262\pi\)
0.599761 + 0.800179i \(0.295262\pi\)
\(368\) −4.09619 −0.213529
\(369\) −1.00000 −0.0520579
\(370\) 21.2010 1.10219
\(371\) 0 0
\(372\) −6.52713 −0.338416
\(373\) 9.55192 0.494580 0.247290 0.968942i \(-0.420460\pi\)
0.247290 + 0.968942i \(0.420460\pi\)
\(374\) −58.3051 −3.01488
\(375\) 8.19494 0.423185
\(376\) −1.86865 −0.0963683
\(377\) 4.72833 0.243521
\(378\) 0 0
\(379\) −16.6032 −0.852847 −0.426423 0.904524i \(-0.640227\pi\)
−0.426423 + 0.904524i \(0.640227\pi\)
\(380\) −0.165550 −0.00849253
\(381\) −5.15902 −0.264305
\(382\) −55.3407 −2.83148
\(383\) −37.5062 −1.91648 −0.958239 0.285969i \(-0.907685\pi\)
−0.958239 + 0.285969i \(0.907685\pi\)
\(384\) −9.00561 −0.459566
\(385\) 0 0
\(386\) 55.9199 2.84625
\(387\) −6.17260 −0.313771
\(388\) 23.0805 1.17173
\(389\) −1.49006 −0.0755488 −0.0377744 0.999286i \(-0.512027\pi\)
−0.0377744 + 0.999286i \(0.512027\pi\)
\(390\) 11.8582 0.600465
\(391\) −12.5924 −0.636826
\(392\) 0 0
\(393\) −11.9242 −0.601496
\(394\) 10.7435 0.541250
\(395\) −10.4634 −0.526471
\(396\) 8.70889 0.437638
\(397\) −6.71173 −0.336852 −0.168426 0.985714i \(-0.553868\pi\)
−0.168426 + 0.985714i \(0.553868\pi\)
\(398\) 5.41079 0.271218
\(399\) 0 0
\(400\) 10.9503 0.547515
\(401\) −3.68773 −0.184157 −0.0920783 0.995752i \(-0.529351\pi\)
−0.0920783 + 0.995752i \(0.529351\pi\)
\(402\) 5.14579 0.256648
\(403\) 16.0011 0.797074
\(404\) −27.6543 −1.37585
\(405\) −0.889988 −0.0442239
\(406\) 0 0
\(407\) −38.1704 −1.89204
\(408\) −9.35740 −0.463260
\(409\) 6.90268 0.341316 0.170658 0.985330i \(-0.445411\pi\)
0.170658 + 0.985330i \(0.445411\pi\)
\(410\) 1.89809 0.0937398
\(411\) 4.57666 0.225750
\(412\) 7.97544 0.392922
\(413\) 0 0
\(414\) 3.35702 0.164988
\(415\) 3.58756 0.176107
\(416\) 49.2883 2.41656
\(417\) −14.6408 −0.716961
\(418\) 0.531970 0.0260195
\(419\) −7.45445 −0.364174 −0.182087 0.983282i \(-0.558285\pi\)
−0.182087 + 0.983282i \(0.558285\pi\)
\(420\) 0 0
\(421\) 7.74992 0.377708 0.188854 0.982005i \(-0.439523\pi\)
0.188854 + 0.982005i \(0.439523\pi\)
\(422\) −49.3002 −2.39989
\(423\) −1.59757 −0.0776766
\(424\) 10.7139 0.520312
\(425\) 33.6632 1.63290
\(426\) 18.9468 0.917976
\(427\) 0 0
\(428\) 8.55594 0.413567
\(429\) −21.3497 −1.03077
\(430\) 11.7161 0.565001
\(431\) 8.87444 0.427467 0.213733 0.976892i \(-0.431438\pi\)
0.213733 + 0.976892i \(0.431438\pi\)
\(432\) −2.60231 −0.125204
\(433\) 15.3304 0.736734 0.368367 0.929681i \(-0.379917\pi\)
0.368367 + 0.929681i \(0.379917\pi\)
\(434\) 0 0
\(435\) 0.673578 0.0322956
\(436\) 1.02929 0.0492941
\(437\) 0.114892 0.00549604
\(438\) −7.76522 −0.371037
\(439\) −27.4686 −1.31100 −0.655501 0.755194i \(-0.727543\pi\)
−0.655501 + 0.755194i \(0.727543\pi\)
\(440\) −3.55745 −0.169595
\(441\) 0 0
\(442\) 106.592 5.07005
\(443\) −1.87494 −0.0890811 −0.0445406 0.999008i \(-0.514182\pi\)
−0.0445406 + 0.999008i \(0.514182\pi\)
\(444\) −28.4653 −1.35090
\(445\) −7.51770 −0.356373
\(446\) 0.511062 0.0241995
\(447\) 2.31277 0.109390
\(448\) 0 0
\(449\) 29.4978 1.39209 0.696043 0.718001i \(-0.254942\pi\)
0.696043 + 0.718001i \(0.254942\pi\)
\(450\) −8.97427 −0.423051
\(451\) −3.41733 −0.160916
\(452\) 13.8604 0.651940
\(453\) 1.08733 0.0510872
\(454\) 7.89449 0.370507
\(455\) 0 0
\(456\) 0.0853761 0.00399810
\(457\) 30.2742 1.41617 0.708084 0.706129i \(-0.249560\pi\)
0.708084 + 0.706129i \(0.249560\pi\)
\(458\) −13.3475 −0.623689
\(459\) −7.99996 −0.373406
\(460\) −3.57011 −0.166457
\(461\) −23.7455 −1.10594 −0.552968 0.833202i \(-0.686505\pi\)
−0.552968 + 0.833202i \(0.686505\pi\)
\(462\) 0 0
\(463\) −21.6384 −1.00562 −0.502811 0.864396i \(-0.667701\pi\)
−0.502811 + 0.864396i \(0.667701\pi\)
\(464\) 1.96953 0.0914330
\(465\) 2.27945 0.105707
\(466\) −54.6946 −2.53368
\(467\) −4.37189 −0.202307 −0.101153 0.994871i \(-0.532253\pi\)
−0.101153 + 0.994871i \(0.532253\pi\)
\(468\) −15.9214 −0.735965
\(469\) 0 0
\(470\) 3.03233 0.139871
\(471\) −24.5214 −1.12989
\(472\) 1.07572 0.0495142
\(473\) −21.0938 −0.969894
\(474\) 25.0738 1.15168
\(475\) −0.307140 −0.0140925
\(476\) 0 0
\(477\) 9.15967 0.419392
\(478\) −37.9287 −1.73482
\(479\) −16.5420 −0.755824 −0.377912 0.925842i \(-0.623358\pi\)
−0.377912 + 0.925842i \(0.623358\pi\)
\(480\) 7.02141 0.320482
\(481\) 69.7821 3.18179
\(482\) 16.2953 0.742232
\(483\) 0 0
\(484\) 1.72820 0.0785547
\(485\) −8.06034 −0.366001
\(486\) 2.13271 0.0967417
\(487\) −21.6708 −0.981998 −0.490999 0.871160i \(-0.663368\pi\)
−0.490999 + 0.871160i \(0.663368\pi\)
\(488\) 9.96396 0.451047
\(489\) −20.7325 −0.937557
\(490\) 0 0
\(491\) 2.65513 0.119824 0.0599121 0.998204i \(-0.480918\pi\)
0.0599121 + 0.998204i \(0.480918\pi\)
\(492\) −2.54845 −0.114893
\(493\) 6.05468 0.272689
\(494\) −0.972533 −0.0437563
\(495\) −3.04138 −0.136700
\(496\) 6.66508 0.299271
\(497\) 0 0
\(498\) −8.59700 −0.385241
\(499\) −3.67247 −0.164402 −0.0822012 0.996616i \(-0.526195\pi\)
−0.0822012 + 0.996616i \(0.526195\pi\)
\(500\) 20.8844 0.933978
\(501\) 9.83140 0.439234
\(502\) −4.29272 −0.191594
\(503\) 23.5718 1.05101 0.525506 0.850790i \(-0.323876\pi\)
0.525506 + 0.850790i \(0.323876\pi\)
\(504\) 0 0
\(505\) 9.65766 0.429760
\(506\) 11.4720 0.509994
\(507\) 26.0309 1.15607
\(508\) −13.1475 −0.583326
\(509\) −34.8559 −1.54496 −0.772481 0.635037i \(-0.780985\pi\)
−0.772481 + 0.635037i \(0.780985\pi\)
\(510\) 15.1846 0.672386
\(511\) 0 0
\(512\) 26.6182 1.17637
\(513\) 0.0729909 0.00322263
\(514\) −13.3009 −0.586677
\(515\) −2.78524 −0.122733
\(516\) −15.7305 −0.692498
\(517\) −5.45943 −0.240105
\(518\) 0 0
\(519\) −19.3348 −0.848702
\(520\) 6.50363 0.285203
\(521\) 39.0969 1.71287 0.856434 0.516257i \(-0.172675\pi\)
0.856434 + 0.516257i \(0.172675\pi\)
\(522\) −1.61412 −0.0706480
\(523\) −10.0083 −0.437632 −0.218816 0.975766i \(-0.570219\pi\)
−0.218816 + 0.975766i \(0.570219\pi\)
\(524\) −30.3882 −1.32752
\(525\) 0 0
\(526\) −17.3577 −0.756831
\(527\) 20.4896 0.892543
\(528\) −8.89294 −0.387016
\(529\) −20.5223 −0.892275
\(530\) −17.3858 −0.755192
\(531\) 0.919674 0.0399104
\(532\) 0 0
\(533\) 6.24747 0.270608
\(534\) 18.0149 0.779582
\(535\) −2.98797 −0.129181
\(536\) 2.82220 0.121900
\(537\) 16.3998 0.707702
\(538\) 54.7453 2.36024
\(539\) 0 0
\(540\) −2.26809 −0.0976030
\(541\) 22.2218 0.955390 0.477695 0.878526i \(-0.341472\pi\)
0.477695 + 0.878526i \(0.341472\pi\)
\(542\) 64.0450 2.75097
\(543\) −16.4233 −0.704790
\(544\) 63.1143 2.70600
\(545\) −0.359457 −0.0153974
\(546\) 0 0
\(547\) 26.4397 1.13048 0.565240 0.824927i \(-0.308784\pi\)
0.565240 + 0.824927i \(0.308784\pi\)
\(548\) 11.6634 0.498235
\(549\) 8.51853 0.363562
\(550\) −30.6680 −1.30769
\(551\) −0.0552424 −0.00235340
\(552\) 1.84115 0.0783645
\(553\) 0 0
\(554\) −21.9421 −0.932232
\(555\) 9.94086 0.421966
\(556\) −37.3112 −1.58235
\(557\) 25.7136 1.08952 0.544759 0.838593i \(-0.316621\pi\)
0.544759 + 0.838593i \(0.316621\pi\)
\(558\) −5.46234 −0.231239
\(559\) 38.5631 1.63105
\(560\) 0 0
\(561\) −27.3385 −1.15423
\(562\) 25.5580 1.07810
\(563\) 31.4548 1.32566 0.662830 0.748770i \(-0.269355\pi\)
0.662830 + 0.748770i \(0.269355\pi\)
\(564\) −4.07133 −0.171434
\(565\) −4.84045 −0.203639
\(566\) 32.5322 1.36743
\(567\) 0 0
\(568\) 10.3913 0.436011
\(569\) −26.4186 −1.10752 −0.553762 0.832675i \(-0.686808\pi\)
−0.553762 + 0.832675i \(0.686808\pi\)
\(570\) −0.138543 −0.00580293
\(571\) 4.76235 0.199298 0.0996491 0.995023i \(-0.468228\pi\)
0.0996491 + 0.995023i \(0.468228\pi\)
\(572\) −54.4085 −2.27493
\(573\) −25.9485 −1.08402
\(574\) 0 0
\(575\) −6.62353 −0.276220
\(576\) −11.6210 −0.484209
\(577\) −7.27641 −0.302921 −0.151460 0.988463i \(-0.548398\pi\)
−0.151460 + 0.988463i \(0.548398\pi\)
\(578\) 100.236 4.16926
\(579\) 26.2201 1.08967
\(580\) 1.71658 0.0712770
\(581\) 0 0
\(582\) 19.3153 0.800644
\(583\) 31.3016 1.29638
\(584\) −4.25882 −0.176231
\(585\) 5.56017 0.229885
\(586\) 62.3211 2.57446
\(587\) 1.48111 0.0611320 0.0305660 0.999533i \(-0.490269\pi\)
0.0305660 + 0.999533i \(0.490269\pi\)
\(588\) 0 0
\(589\) −0.186946 −0.00770296
\(590\) −1.74562 −0.0718660
\(591\) 5.03749 0.207215
\(592\) 29.0669 1.19464
\(593\) 0.770893 0.0316568 0.0158284 0.999875i \(-0.494961\pi\)
0.0158284 + 0.999875i \(0.494961\pi\)
\(594\) 7.28817 0.299037
\(595\) 0 0
\(596\) 5.89398 0.241427
\(597\) 2.53705 0.103835
\(598\) −20.9729 −0.857644
\(599\) 2.95056 0.120557 0.0602783 0.998182i \(-0.480801\pi\)
0.0602783 + 0.998182i \(0.480801\pi\)
\(600\) −4.92193 −0.200937
\(601\) −14.1523 −0.577285 −0.288642 0.957437i \(-0.593204\pi\)
−0.288642 + 0.957437i \(0.593204\pi\)
\(602\) 0 0
\(603\) 2.41279 0.0982565
\(604\) 2.77100 0.112751
\(605\) −0.603536 −0.0245372
\(606\) −23.1430 −0.940119
\(607\) −39.5171 −1.60395 −0.801975 0.597358i \(-0.796217\pi\)
−0.801975 + 0.597358i \(0.796217\pi\)
\(608\) −0.575849 −0.0233538
\(609\) 0 0
\(610\) −16.1689 −0.654660
\(611\) 9.98078 0.403779
\(612\) −20.3875 −0.824115
\(613\) 41.8648 1.69091 0.845453 0.534050i \(-0.179331\pi\)
0.845453 + 0.534050i \(0.179331\pi\)
\(614\) 59.1599 2.38750
\(615\) 0.889988 0.0358878
\(616\) 0 0
\(617\) 24.9542 1.00462 0.502310 0.864688i \(-0.332484\pi\)
0.502310 + 0.864688i \(0.332484\pi\)
\(618\) 6.67438 0.268483
\(619\) −5.05747 −0.203277 −0.101638 0.994821i \(-0.532408\pi\)
−0.101638 + 0.994821i \(0.532408\pi\)
\(620\) 5.80907 0.233298
\(621\) 1.57406 0.0631649
\(622\) 29.1929 1.17053
\(623\) 0 0
\(624\) 16.2578 0.650834
\(625\) 13.7462 0.549848
\(626\) −45.6996 −1.82652
\(627\) 0.249434 0.00996143
\(628\) −62.4916 −2.49369
\(629\) 89.3568 3.56289
\(630\) 0 0
\(631\) −16.8805 −0.672000 −0.336000 0.941862i \(-0.609074\pi\)
−0.336000 + 0.941862i \(0.609074\pi\)
\(632\) 13.7517 0.547013
\(633\) −23.1162 −0.918787
\(634\) −58.9289 −2.34037
\(635\) 4.59147 0.182207
\(636\) 23.3429 0.925608
\(637\) 0 0
\(638\) −5.51597 −0.218379
\(639\) 8.88392 0.351442
\(640\) 8.01489 0.316816
\(641\) −32.4571 −1.28198 −0.640990 0.767549i \(-0.721476\pi\)
−0.640990 + 0.767549i \(0.721476\pi\)
\(642\) 7.16017 0.282590
\(643\) −32.8318 −1.29476 −0.647381 0.762167i \(-0.724136\pi\)
−0.647381 + 0.762167i \(0.724136\pi\)
\(644\) 0 0
\(645\) 5.49354 0.216308
\(646\) −1.24534 −0.0489973
\(647\) 7.44564 0.292718 0.146359 0.989232i \(-0.453245\pi\)
0.146359 + 0.989232i \(0.453245\pi\)
\(648\) 1.16968 0.0459494
\(649\) 3.14283 0.123367
\(650\) 56.0665 2.19911
\(651\) 0 0
\(652\) −52.8357 −2.06921
\(653\) −14.6003 −0.571353 −0.285676 0.958326i \(-0.592218\pi\)
−0.285676 + 0.958326i \(0.592218\pi\)
\(654\) 0.861378 0.0336826
\(655\) 10.6124 0.414661
\(656\) 2.60231 0.101603
\(657\) −3.64101 −0.142049
\(658\) 0 0
\(659\) 7.79447 0.303629 0.151815 0.988409i \(-0.451488\pi\)
0.151815 + 0.988409i \(0.451488\pi\)
\(660\) −7.75081 −0.301700
\(661\) −13.7123 −0.533345 −0.266673 0.963787i \(-0.585924\pi\)
−0.266673 + 0.963787i \(0.585924\pi\)
\(662\) −37.3849 −1.45301
\(663\) 49.9795 1.94104
\(664\) −4.71501 −0.182978
\(665\) 0 0
\(666\) −23.8216 −0.923069
\(667\) −1.19131 −0.0461278
\(668\) 25.0548 0.969400
\(669\) 0.239630 0.00926464
\(670\) −4.57969 −0.176929
\(671\) 29.1106 1.12380
\(672\) 0 0
\(673\) −31.7957 −1.22563 −0.612817 0.790225i \(-0.709964\pi\)
−0.612817 + 0.790225i \(0.709964\pi\)
\(674\) 28.3953 1.09375
\(675\) −4.20792 −0.161963
\(676\) 66.3384 2.55148
\(677\) 15.6921 0.603095 0.301547 0.953451i \(-0.402497\pi\)
0.301547 + 0.953451i \(0.402497\pi\)
\(678\) 11.5993 0.445469
\(679\) 0 0
\(680\) 8.32798 0.319363
\(681\) 3.70162 0.141847
\(682\) −18.6666 −0.714781
\(683\) −45.4953 −1.74083 −0.870415 0.492320i \(-0.836149\pi\)
−0.870415 + 0.492320i \(0.836149\pi\)
\(684\) 0.186014 0.00711241
\(685\) −4.07317 −0.155628
\(686\) 0 0
\(687\) −6.25848 −0.238776
\(688\) 16.0630 0.612396
\(689\) −57.2247 −2.18009
\(690\) −2.98770 −0.113740
\(691\) 33.1928 1.26271 0.631356 0.775493i \(-0.282499\pi\)
0.631356 + 0.775493i \(0.282499\pi\)
\(692\) −49.2737 −1.87310
\(693\) 0 0
\(694\) −8.35077 −0.316991
\(695\) 13.0301 0.494260
\(696\) −0.885260 −0.0335557
\(697\) 7.99996 0.303020
\(698\) 42.9918 1.62726
\(699\) −25.6456 −0.970006
\(700\) 0 0
\(701\) 17.9370 0.677470 0.338735 0.940882i \(-0.390001\pi\)
0.338735 + 0.940882i \(0.390001\pi\)
\(702\) −13.3240 −0.502883
\(703\) −0.815283 −0.0307490
\(704\) −39.7129 −1.49674
\(705\) 1.42182 0.0535488
\(706\) −44.2078 −1.66378
\(707\) 0 0
\(708\) 2.34374 0.0880832
\(709\) −19.7437 −0.741492 −0.370746 0.928734i \(-0.620898\pi\)
−0.370746 + 0.928734i \(0.620898\pi\)
\(710\) −16.8624 −0.632836
\(711\) 11.7568 0.440914
\(712\) 9.88026 0.370278
\(713\) −4.03152 −0.150981
\(714\) 0 0
\(715\) 19.0009 0.710595
\(716\) 41.7940 1.56191
\(717\) −17.7843 −0.664167
\(718\) −74.0381 −2.76308
\(719\) −42.0245 −1.56725 −0.783625 0.621234i \(-0.786632\pi\)
−0.783625 + 0.621234i \(0.786632\pi\)
\(720\) 2.31602 0.0863131
\(721\) 0 0
\(722\) −40.5101 −1.50763
\(723\) 7.64067 0.284160
\(724\) −41.8539 −1.55549
\(725\) 3.18472 0.118277
\(726\) 1.44627 0.0536763
\(727\) 32.6634 1.21142 0.605709 0.795686i \(-0.292890\pi\)
0.605709 + 0.795686i \(0.292890\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.91095 0.255786
\(731\) 49.3805 1.82640
\(732\) 21.7090 0.802389
\(733\) 36.1097 1.33374 0.666870 0.745174i \(-0.267634\pi\)
0.666870 + 0.745174i \(0.267634\pi\)
\(734\) 49.0087 1.80894
\(735\) 0 0
\(736\) −12.4183 −0.457744
\(737\) 8.24531 0.303720
\(738\) −2.13271 −0.0785061
\(739\) 26.6713 0.981118 0.490559 0.871408i \(-0.336793\pi\)
0.490559 + 0.871408i \(0.336793\pi\)
\(740\) 25.3338 0.931288
\(741\) −0.456008 −0.0167519
\(742\) 0 0
\(743\) −32.0519 −1.17587 −0.587935 0.808908i \(-0.700059\pi\)
−0.587935 + 0.808908i \(0.700059\pi\)
\(744\) −2.99581 −0.109832
\(745\) −2.05834 −0.0754117
\(746\) 20.3715 0.745853
\(747\) −4.03102 −0.147487
\(748\) −69.6707 −2.54741
\(749\) 0 0
\(750\) 17.4774 0.638185
\(751\) 11.2233 0.409545 0.204772 0.978810i \(-0.434355\pi\)
0.204772 + 0.978810i \(0.434355\pi\)
\(752\) 4.15737 0.151604
\(753\) −2.01280 −0.0733506
\(754\) 10.0842 0.367243
\(755\) −0.967711 −0.0352186
\(756\) 0 0
\(757\) −11.3051 −0.410890 −0.205445 0.978669i \(-0.565864\pi\)
−0.205445 + 0.978669i \(0.565864\pi\)
\(758\) −35.4097 −1.28614
\(759\) 5.37909 0.195248
\(760\) −0.0759837 −0.00275622
\(761\) 14.9745 0.542826 0.271413 0.962463i \(-0.412509\pi\)
0.271413 + 0.962463i \(0.412509\pi\)
\(762\) −11.0027 −0.398586
\(763\) 0 0
\(764\) −66.1285 −2.39245
\(765\) 7.11987 0.257419
\(766\) −79.9898 −2.89015
\(767\) −5.74563 −0.207463
\(768\) 4.03570 0.145626
\(769\) −29.8781 −1.07743 −0.538716 0.842487i \(-0.681090\pi\)
−0.538716 + 0.842487i \(0.681090\pi\)
\(770\) 0 0
\(771\) −6.23662 −0.224606
\(772\) 66.8207 2.40493
\(773\) 6.39402 0.229977 0.114989 0.993367i \(-0.463317\pi\)
0.114989 + 0.993367i \(0.463317\pi\)
\(774\) −13.1644 −0.473183
\(775\) 10.7774 0.387136
\(776\) 10.5934 0.380282
\(777\) 0 0
\(778\) −3.17786 −0.113932
\(779\) −0.0729909 −0.00261517
\(780\) 14.1698 0.507361
\(781\) 30.3593 1.08634
\(782\) −26.8560 −0.960368
\(783\) −0.756839 −0.0270472
\(784\) 0 0
\(785\) 21.8238 0.778924
\(786\) −25.4309 −0.907089
\(787\) 40.7910 1.45404 0.727021 0.686615i \(-0.240904\pi\)
0.727021 + 0.686615i \(0.240904\pi\)
\(788\) 12.8378 0.457327
\(789\) −8.13880 −0.289749
\(790\) −22.3154 −0.793947
\(791\) 0 0
\(792\) 3.99719 0.142034
\(793\) −53.2193 −1.88987
\(794\) −14.3142 −0.507991
\(795\) −8.15199 −0.289121
\(796\) 6.46554 0.229165
\(797\) −33.0669 −1.17129 −0.585645 0.810567i \(-0.699159\pi\)
−0.585645 + 0.810567i \(0.699159\pi\)
\(798\) 0 0
\(799\) 12.7805 0.452142
\(800\) 33.1977 1.17371
\(801\) 8.44697 0.298459
\(802\) −7.86486 −0.277718
\(803\) −12.4425 −0.439088
\(804\) 6.14888 0.216854
\(805\) 0 0
\(806\) 34.1258 1.20203
\(807\) 25.6694 0.903604
\(808\) −12.6927 −0.446529
\(809\) 9.54220 0.335486 0.167743 0.985831i \(-0.446352\pi\)
0.167743 + 0.985831i \(0.446352\pi\)
\(810\) −1.89809 −0.0666919
\(811\) 2.64941 0.0930333 0.0465166 0.998918i \(-0.485188\pi\)
0.0465166 + 0.998918i \(0.485188\pi\)
\(812\) 0 0
\(813\) 30.0299 1.05319
\(814\) −81.4063 −2.85329
\(815\) 18.4517 0.646334
\(816\) 20.8184 0.728788
\(817\) −0.450543 −0.0157625
\(818\) 14.7214 0.514722
\(819\) 0 0
\(820\) 2.26809 0.0792051
\(821\) 39.2366 1.36937 0.684683 0.728841i \(-0.259941\pi\)
0.684683 + 0.728841i \(0.259941\pi\)
\(822\) 9.76068 0.340443
\(823\) −46.2425 −1.61191 −0.805956 0.591976i \(-0.798348\pi\)
−0.805956 + 0.591976i \(0.798348\pi\)
\(824\) 3.66055 0.127521
\(825\) −14.3799 −0.500642
\(826\) 0 0
\(827\) 19.5022 0.678158 0.339079 0.940758i \(-0.389885\pi\)
0.339079 + 0.940758i \(0.389885\pi\)
\(828\) 4.01141 0.139406
\(829\) −8.56705 −0.297546 −0.148773 0.988871i \(-0.547532\pi\)
−0.148773 + 0.988871i \(0.547532\pi\)
\(830\) 7.65123 0.265578
\(831\) −10.2884 −0.356900
\(832\) 72.6020 2.51702
\(833\) 0 0
\(834\) −31.2245 −1.08121
\(835\) −8.74983 −0.302800
\(836\) 0.635670 0.0219851
\(837\) −2.56122 −0.0885287
\(838\) −15.8982 −0.549193
\(839\) −43.6287 −1.50623 −0.753115 0.657888i \(-0.771450\pi\)
−0.753115 + 0.657888i \(0.771450\pi\)
\(840\) 0 0
\(841\) −28.4272 −0.980248
\(842\) 16.5283 0.569603
\(843\) 11.9838 0.412744
\(844\) −58.9105 −2.02778
\(845\) −23.1672 −0.796975
\(846\) −3.40716 −0.117140
\(847\) 0 0
\(848\) −23.8363 −0.818541
\(849\) 15.2539 0.523514
\(850\) 71.7938 2.46251
\(851\) −17.5817 −0.602694
\(852\) 22.6402 0.775641
\(853\) 3.06449 0.104926 0.0524630 0.998623i \(-0.483293\pi\)
0.0524630 + 0.998623i \(0.483293\pi\)
\(854\) 0 0
\(855\) −0.0649610 −0.00222162
\(856\) 3.92699 0.134222
\(857\) 10.5860 0.361610 0.180805 0.983519i \(-0.442130\pi\)
0.180805 + 0.983519i \(0.442130\pi\)
\(858\) −45.5326 −1.55446
\(859\) 7.65853 0.261306 0.130653 0.991428i \(-0.458293\pi\)
0.130653 + 0.991428i \(0.458293\pi\)
\(860\) 14.0000 0.477396
\(861\) 0 0
\(862\) 18.9266 0.644642
\(863\) 4.80094 0.163426 0.0817129 0.996656i \(-0.473961\pi\)
0.0817129 + 0.996656i \(0.473961\pi\)
\(864\) −7.88933 −0.268400
\(865\) 17.2077 0.585080
\(866\) 32.6954 1.11103
\(867\) 46.9993 1.59618
\(868\) 0 0
\(869\) 40.1768 1.36291
\(870\) 1.43655 0.0487035
\(871\) −15.0739 −0.510758
\(872\) 0.472422 0.0159982
\(873\) 9.05668 0.306522
\(874\) 0.245032 0.00828832
\(875\) 0 0
\(876\) −9.27893 −0.313506
\(877\) −52.0697 −1.75827 −0.879135 0.476573i \(-0.841879\pi\)
−0.879135 + 0.476573i \(0.841879\pi\)
\(878\) −58.5824 −1.97706
\(879\) 29.2216 0.985619
\(880\) 7.91461 0.266802
\(881\) 17.6360 0.594171 0.297085 0.954851i \(-0.403985\pi\)
0.297085 + 0.954851i \(0.403985\pi\)
\(882\) 0 0
\(883\) 12.2941 0.413731 0.206866 0.978369i \(-0.433674\pi\)
0.206866 + 0.978369i \(0.433674\pi\)
\(884\) 127.370 4.28392
\(885\) −0.818499 −0.0275135
\(886\) −3.99870 −0.134339
\(887\) 41.9487 1.40850 0.704251 0.709952i \(-0.251283\pi\)
0.704251 + 0.709952i \(0.251283\pi\)
\(888\) −13.0649 −0.438430
\(889\) 0 0
\(890\) −16.0331 −0.537430
\(891\) 3.41733 0.114485
\(892\) 0.610685 0.0204473
\(893\) −0.116608 −0.00390215
\(894\) 4.93247 0.164966
\(895\) −14.5956 −0.487877
\(896\) 0 0
\(897\) −9.83390 −0.328344
\(898\) 62.9101 2.09934
\(899\) 1.93843 0.0646503
\(900\) −10.7237 −0.357456
\(901\) −73.2769 −2.44121
\(902\) −7.28817 −0.242670
\(903\) 0 0
\(904\) 6.36163 0.211585
\(905\) 14.6165 0.485870
\(906\) 2.31896 0.0770422
\(907\) −0.531208 −0.0176385 −0.00881923 0.999961i \(-0.502807\pi\)
−0.00881923 + 0.999961i \(0.502807\pi\)
\(908\) 9.43340 0.313058
\(909\) −10.8514 −0.359920
\(910\) 0 0
\(911\) −19.0477 −0.631078 −0.315539 0.948913i \(-0.602185\pi\)
−0.315539 + 0.948913i \(0.602185\pi\)
\(912\) −0.189945 −0.00628970
\(913\) −13.7753 −0.455897
\(914\) 64.5661 2.13566
\(915\) −7.58139 −0.250633
\(916\) −15.9494 −0.526984
\(917\) 0 0
\(918\) −17.0616 −0.563116
\(919\) 9.06567 0.299049 0.149524 0.988758i \(-0.452226\pi\)
0.149524 + 0.988758i \(0.452226\pi\)
\(920\) −1.63860 −0.0540231
\(921\) 27.7393 0.914042
\(922\) −50.6422 −1.66781
\(923\) −55.5020 −1.82687
\(924\) 0 0
\(925\) 47.0010 1.54538
\(926\) −46.1484 −1.51653
\(927\) 3.12953 0.102787
\(928\) 5.97095 0.196006
\(929\) 9.91561 0.325321 0.162660 0.986682i \(-0.447993\pi\)
0.162660 + 0.986682i \(0.447993\pi\)
\(930\) 4.86141 0.159412
\(931\) 0 0
\(932\) −65.3565 −2.14082
\(933\) 13.6882 0.448131
\(934\) −9.32397 −0.305090
\(935\) 24.3309 0.795707
\(936\) −7.30755 −0.238855
\(937\) −22.9798 −0.750718 −0.375359 0.926879i \(-0.622481\pi\)
−0.375359 + 0.926879i \(0.622481\pi\)
\(938\) 0 0
\(939\) −21.4280 −0.699275
\(940\) 3.62344 0.118183
\(941\) −13.1179 −0.427630 −0.213815 0.976874i \(-0.568589\pi\)
−0.213815 + 0.976874i \(0.568589\pi\)
\(942\) −52.2971 −1.70393
\(943\) −1.57406 −0.0512585
\(944\) −2.39327 −0.0778944
\(945\) 0 0
\(946\) −44.9869 −1.46265
\(947\) −27.6733 −0.899262 −0.449631 0.893214i \(-0.648445\pi\)
−0.449631 + 0.893214i \(0.648445\pi\)
\(948\) 29.9616 0.973107
\(949\) 22.7471 0.738403
\(950\) −0.655040 −0.0212523
\(951\) −27.6310 −0.895997
\(952\) 0 0
\(953\) −14.5017 −0.469757 −0.234878 0.972025i \(-0.575469\pi\)
−0.234878 + 0.972025i \(0.575469\pi\)
\(954\) 19.5349 0.632466
\(955\) 23.0939 0.747301
\(956\) −45.3224 −1.46583
\(957\) −2.58637 −0.0836054
\(958\) −35.2793 −1.13982
\(959\) 0 0
\(960\) 10.3426 0.333805
\(961\) −24.4402 −0.788392
\(962\) 148.825 4.79831
\(963\) 3.35731 0.108188
\(964\) 19.4719 0.627146
\(965\) −23.3356 −0.751200
\(966\) 0 0
\(967\) −4.81409 −0.154811 −0.0774054 0.997000i \(-0.524664\pi\)
−0.0774054 + 0.997000i \(0.524664\pi\)
\(968\) 0.793207 0.0254946
\(969\) −0.583924 −0.0187583
\(970\) −17.1904 −0.551949
\(971\) 56.7999 1.82279 0.911397 0.411527i \(-0.135005\pi\)
0.911397 + 0.411527i \(0.135005\pi\)
\(972\) 2.54845 0.0817415
\(973\) 0 0
\(974\) −46.2175 −1.48090
\(975\) 26.2889 0.841917
\(976\) −22.1678 −0.709575
\(977\) 26.0244 0.832595 0.416297 0.909229i \(-0.363328\pi\)
0.416297 + 0.909229i \(0.363328\pi\)
\(978\) −44.2164 −1.41389
\(979\) 28.8661 0.922564
\(980\) 0 0
\(981\) 0.403889 0.0128952
\(982\) 5.66261 0.180701
\(983\) −59.1340 −1.88608 −0.943041 0.332677i \(-0.892048\pi\)
−0.943041 + 0.332677i \(0.892048\pi\)
\(984\) −1.16968 −0.0372881
\(985\) −4.48331 −0.142850
\(986\) 12.9129 0.411230
\(987\) 0 0
\(988\) −1.16211 −0.0369718
\(989\) −9.71604 −0.308952
\(990\) −6.48638 −0.206151
\(991\) 41.2982 1.31188 0.655941 0.754812i \(-0.272272\pi\)
0.655941 + 0.754812i \(0.272272\pi\)
\(992\) 20.2063 0.641550
\(993\) −17.5293 −0.556276
\(994\) 0 0
\(995\) −2.25794 −0.0715817
\(996\) −10.2729 −0.325508
\(997\) 12.4930 0.395657 0.197828 0.980237i \(-0.436611\pi\)
0.197828 + 0.980237i \(0.436611\pi\)
\(998\) −7.83231 −0.247927
\(999\) −11.1697 −0.353392
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 \(a_p\))