Properties

Label 6027.2.a.bm.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
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: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.69180\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69180 q^{2} +1.00000 q^{3} +5.24578 q^{4} -3.62847 q^{5} -2.69180 q^{6} -8.73699 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.69180 q^{2} +1.00000 q^{3} +5.24578 q^{4} -3.62847 q^{5} -2.69180 q^{6} -8.73699 q^{8} +1.00000 q^{9} +9.76712 q^{10} +3.79578 q^{11} +5.24578 q^{12} +0.986924 q^{13} -3.62847 q^{15} +13.0267 q^{16} +1.05753 q^{17} -2.69180 q^{18} -2.81023 q^{19} -19.0342 q^{20} -10.2175 q^{22} -5.66437 q^{23} -8.73699 q^{24} +8.16582 q^{25} -2.65660 q^{26} +1.00000 q^{27} -2.21857 q^{29} +9.76712 q^{30} +10.4547 q^{31} -17.5912 q^{32} +3.79578 q^{33} -2.84664 q^{34} +5.24578 q^{36} -7.86953 q^{37} +7.56457 q^{38} +0.986924 q^{39} +31.7019 q^{40} +1.00000 q^{41} +4.16152 q^{43} +19.9118 q^{44} -3.62847 q^{45} +15.2473 q^{46} -5.08902 q^{47} +13.0267 q^{48} -21.9807 q^{50} +1.05753 q^{51} +5.17719 q^{52} -9.17461 q^{53} -2.69180 q^{54} -13.7729 q^{55} -2.81023 q^{57} +5.97193 q^{58} -7.58471 q^{59} -19.0342 q^{60} +5.96328 q^{61} -28.1420 q^{62} +21.2985 q^{64} -3.58103 q^{65} -10.2175 q^{66} -15.6363 q^{67} +5.54754 q^{68} -5.66437 q^{69} +11.6213 q^{71} -8.73699 q^{72} -3.75487 q^{73} +21.1832 q^{74} +8.16582 q^{75} -14.7418 q^{76} -2.65660 q^{78} -4.83413 q^{79} -47.2669 q^{80} +1.00000 q^{81} -2.69180 q^{82} +7.04509 q^{83} -3.83720 q^{85} -11.2020 q^{86} -2.21857 q^{87} -33.1637 q^{88} +9.53384 q^{89} +9.76712 q^{90} -29.7140 q^{92} +10.4547 q^{93} +13.6986 q^{94} +10.1968 q^{95} -17.5912 q^{96} +14.2834 q^{97} +3.79578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69180 −1.90339 −0.951695 0.307046i \(-0.900659\pi\)
−0.951695 + 0.307046i \(0.900659\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.24578 2.62289
\(5\) −3.62847 −1.62270 −0.811351 0.584559i \(-0.801268\pi\)
−0.811351 + 0.584559i \(0.801268\pi\)
\(6\) −2.69180 −1.09892
\(7\) 0 0
\(8\) −8.73699 −3.08899
\(9\) 1.00000 0.333333
\(10\) 9.76712 3.08863
\(11\) 3.79578 1.14447 0.572235 0.820090i \(-0.306077\pi\)
0.572235 + 0.820090i \(0.306077\pi\)
\(12\) 5.24578 1.51433
\(13\) 0.986924 0.273723 0.136862 0.990590i \(-0.456298\pi\)
0.136862 + 0.990590i \(0.456298\pi\)
\(14\) 0 0
\(15\) −3.62847 −0.936868
\(16\) 13.0267 3.25666
\(17\) 1.05753 0.256488 0.128244 0.991743i \(-0.459066\pi\)
0.128244 + 0.991743i \(0.459066\pi\)
\(18\) −2.69180 −0.634463
\(19\) −2.81023 −0.644711 −0.322355 0.946619i \(-0.604475\pi\)
−0.322355 + 0.946619i \(0.604475\pi\)
\(20\) −19.0342 −4.25617
\(21\) 0 0
\(22\) −10.2175 −2.17837
\(23\) −5.66437 −1.18110 −0.590551 0.807000i \(-0.701090\pi\)
−0.590551 + 0.807000i \(0.701090\pi\)
\(24\) −8.73699 −1.78343
\(25\) 8.16582 1.63316
\(26\) −2.65660 −0.521002
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.21857 −0.411977 −0.205989 0.978554i \(-0.566041\pi\)
−0.205989 + 0.978554i \(0.566041\pi\)
\(30\) 9.76712 1.78322
\(31\) 10.4547 1.87773 0.938863 0.344291i \(-0.111881\pi\)
0.938863 + 0.344291i \(0.111881\pi\)
\(32\) −17.5912 −3.10971
\(33\) 3.79578 0.660760
\(34\) −2.84664 −0.488196
\(35\) 0 0
\(36\) 5.24578 0.874297
\(37\) −7.86953 −1.29374 −0.646871 0.762599i \(-0.723923\pi\)
−0.646871 + 0.762599i \(0.723923\pi\)
\(38\) 7.56457 1.22714
\(39\) 0.986924 0.158034
\(40\) 31.7019 5.01251
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 4.16152 0.634625 0.317313 0.948321i \(-0.397220\pi\)
0.317313 + 0.948321i \(0.397220\pi\)
\(44\) 19.9118 3.00182
\(45\) −3.62847 −0.540901
\(46\) 15.2473 2.24810
\(47\) −5.08902 −0.742309 −0.371155 0.928571i \(-0.621038\pi\)
−0.371155 + 0.928571i \(0.621038\pi\)
\(48\) 13.0267 1.88024
\(49\) 0 0
\(50\) −21.9807 −3.10854
\(51\) 1.05753 0.148083
\(52\) 5.17719 0.717946
\(53\) −9.17461 −1.26023 −0.630115 0.776502i \(-0.716992\pi\)
−0.630115 + 0.776502i \(0.716992\pi\)
\(54\) −2.69180 −0.366307
\(55\) −13.7729 −1.85713
\(56\) 0 0
\(57\) −2.81023 −0.372224
\(58\) 5.97193 0.784153
\(59\) −7.58471 −0.987446 −0.493723 0.869619i \(-0.664364\pi\)
−0.493723 + 0.869619i \(0.664364\pi\)
\(60\) −19.0342 −2.45730
\(61\) 5.96328 0.763520 0.381760 0.924262i \(-0.375318\pi\)
0.381760 + 0.924262i \(0.375318\pi\)
\(62\) −28.1420 −3.57404
\(63\) 0 0
\(64\) 21.2985 2.66232
\(65\) −3.58103 −0.444172
\(66\) −10.2175 −1.25768
\(67\) −15.6363 −1.91027 −0.955137 0.296165i \(-0.904292\pi\)
−0.955137 + 0.296165i \(0.904292\pi\)
\(68\) 5.54754 0.672739
\(69\) −5.66437 −0.681909
\(70\) 0 0
\(71\) 11.6213 1.37920 0.689600 0.724190i \(-0.257786\pi\)
0.689600 + 0.724190i \(0.257786\pi\)
\(72\) −8.73699 −1.02966
\(73\) −3.75487 −0.439475 −0.219737 0.975559i \(-0.570520\pi\)
−0.219737 + 0.975559i \(0.570520\pi\)
\(74\) 21.1832 2.46250
\(75\) 8.16582 0.942907
\(76\) −14.7418 −1.69101
\(77\) 0 0
\(78\) −2.65660 −0.300801
\(79\) −4.83413 −0.543883 −0.271941 0.962314i \(-0.587666\pi\)
−0.271941 + 0.962314i \(0.587666\pi\)
\(80\) −47.2669 −5.28460
\(81\) 1.00000 0.111111
\(82\) −2.69180 −0.297259
\(83\) 7.04509 0.773299 0.386649 0.922227i \(-0.373632\pi\)
0.386649 + 0.922227i \(0.373632\pi\)
\(84\) 0 0
\(85\) −3.83720 −0.416203
\(86\) −11.2020 −1.20794
\(87\) −2.21857 −0.237855
\(88\) −33.1637 −3.53526
\(89\) 9.53384 1.01059 0.505293 0.862948i \(-0.331385\pi\)
0.505293 + 0.862948i \(0.331385\pi\)
\(90\) 9.76712 1.02954
\(91\) 0 0
\(92\) −29.7140 −3.09790
\(93\) 10.4547 1.08411
\(94\) 13.6986 1.41290
\(95\) 10.1968 1.04617
\(96\) −17.5912 −1.79539
\(97\) 14.2834 1.45026 0.725130 0.688612i \(-0.241779\pi\)
0.725130 + 0.688612i \(0.241779\pi\)
\(98\) 0 0
\(99\) 3.79578 0.381490
\(100\) 42.8361 4.28361
\(101\) 1.27838 0.127203 0.0636017 0.997975i \(-0.479741\pi\)
0.0636017 + 0.997975i \(0.479741\pi\)
\(102\) −2.84664 −0.281860
\(103\) 11.9906 1.18147 0.590737 0.806864i \(-0.298837\pi\)
0.590737 + 0.806864i \(0.298837\pi\)
\(104\) −8.62274 −0.845529
\(105\) 0 0
\(106\) 24.6962 2.39871
\(107\) −18.0089 −1.74098 −0.870491 0.492185i \(-0.836198\pi\)
−0.870491 + 0.492185i \(0.836198\pi\)
\(108\) 5.24578 0.504775
\(109\) −14.0107 −1.34198 −0.670992 0.741464i \(-0.734132\pi\)
−0.670992 + 0.741464i \(0.734132\pi\)
\(110\) 37.0738 3.53485
\(111\) −7.86953 −0.746943
\(112\) 0 0
\(113\) 13.5638 1.27597 0.637986 0.770048i \(-0.279768\pi\)
0.637986 + 0.770048i \(0.279768\pi\)
\(114\) 7.56457 0.708487
\(115\) 20.5530 1.91658
\(116\) −11.6381 −1.08057
\(117\) 0.986924 0.0912411
\(118\) 20.4165 1.87949
\(119\) 0 0
\(120\) 31.7019 2.89398
\(121\) 3.40793 0.309812
\(122\) −16.0519 −1.45328
\(123\) 1.00000 0.0901670
\(124\) 54.8433 4.92507
\(125\) −11.4871 −1.02744
\(126\) 0 0
\(127\) 12.6460 1.12215 0.561076 0.827764i \(-0.310387\pi\)
0.561076 + 0.827764i \(0.310387\pi\)
\(128\) −22.1491 −1.95772
\(129\) 4.16152 0.366401
\(130\) 9.63940 0.845431
\(131\) 21.8687 1.91068 0.955340 0.295509i \(-0.0954893\pi\)
0.955340 + 0.295509i \(0.0954893\pi\)
\(132\) 19.9118 1.73310
\(133\) 0 0
\(134\) 42.0897 3.63599
\(135\) −3.62847 −0.312289
\(136\) −9.23959 −0.792288
\(137\) −4.28037 −0.365697 −0.182848 0.983141i \(-0.558532\pi\)
−0.182848 + 0.983141i \(0.558532\pi\)
\(138\) 15.2473 1.29794
\(139\) 0.0145030 0.00123013 0.000615064 1.00000i \(-0.499804\pi\)
0.000615064 1.00000i \(0.499804\pi\)
\(140\) 0 0
\(141\) −5.08902 −0.428572
\(142\) −31.2823 −2.62515
\(143\) 3.74614 0.313268
\(144\) 13.0267 1.08555
\(145\) 8.05001 0.668517
\(146\) 10.1074 0.836491
\(147\) 0 0
\(148\) −41.2818 −3.39335
\(149\) −14.7596 −1.20915 −0.604577 0.796547i \(-0.706658\pi\)
−0.604577 + 0.796547i \(0.706658\pi\)
\(150\) −21.9807 −1.79472
\(151\) −6.86221 −0.558438 −0.279219 0.960227i \(-0.590076\pi\)
−0.279219 + 0.960227i \(0.590076\pi\)
\(152\) 24.5529 1.99151
\(153\) 1.05753 0.0854958
\(154\) 0 0
\(155\) −37.9347 −3.04699
\(156\) 5.17719 0.414507
\(157\) 4.17576 0.333262 0.166631 0.986019i \(-0.446711\pi\)
0.166631 + 0.986019i \(0.446711\pi\)
\(158\) 13.0125 1.03522
\(159\) −9.17461 −0.727594
\(160\) 63.8290 5.04613
\(161\) 0 0
\(162\) −2.69180 −0.211488
\(163\) −23.5210 −1.84231 −0.921155 0.389195i \(-0.872753\pi\)
−0.921155 + 0.389195i \(0.872753\pi\)
\(164\) 5.24578 0.409627
\(165\) −13.7729 −1.07222
\(166\) −18.9640 −1.47189
\(167\) −15.7070 −1.21544 −0.607722 0.794150i \(-0.707917\pi\)
−0.607722 + 0.794150i \(0.707917\pi\)
\(168\) 0 0
\(169\) −12.0260 −0.925076
\(170\) 10.3290 0.792196
\(171\) −2.81023 −0.214904
\(172\) 21.8304 1.66455
\(173\) −5.89269 −0.448013 −0.224006 0.974588i \(-0.571914\pi\)
−0.224006 + 0.974588i \(0.571914\pi\)
\(174\) 5.97193 0.452731
\(175\) 0 0
\(176\) 49.4463 3.72715
\(177\) −7.58471 −0.570102
\(178\) −25.6632 −1.92354
\(179\) 4.67222 0.349218 0.174609 0.984638i \(-0.444134\pi\)
0.174609 + 0.984638i \(0.444134\pi\)
\(180\) −19.0342 −1.41872
\(181\) −13.2354 −0.983776 −0.491888 0.870658i \(-0.663693\pi\)
−0.491888 + 0.870658i \(0.663693\pi\)
\(182\) 0 0
\(183\) 5.96328 0.440818
\(184\) 49.4895 3.64841
\(185\) 28.5544 2.09936
\(186\) −28.1420 −2.06348
\(187\) 4.01413 0.293542
\(188\) −26.6959 −1.94700
\(189\) 0 0
\(190\) −27.4478 −1.99127
\(191\) 18.4336 1.33381 0.666903 0.745145i \(-0.267620\pi\)
0.666903 + 0.745145i \(0.267620\pi\)
\(192\) 21.2985 1.53709
\(193\) 11.4648 0.825254 0.412627 0.910900i \(-0.364611\pi\)
0.412627 + 0.910900i \(0.364611\pi\)
\(194\) −38.4481 −2.76041
\(195\) −3.58103 −0.256443
\(196\) 0 0
\(197\) 2.88305 0.205408 0.102704 0.994712i \(-0.467250\pi\)
0.102704 + 0.994712i \(0.467250\pi\)
\(198\) −10.2175 −0.726124
\(199\) 18.6674 1.32330 0.661650 0.749813i \(-0.269856\pi\)
0.661650 + 0.749813i \(0.269856\pi\)
\(200\) −71.3446 −5.04483
\(201\) −15.6363 −1.10290
\(202\) −3.44114 −0.242118
\(203\) 0 0
\(204\) 5.54754 0.388406
\(205\) −3.62847 −0.253424
\(206\) −32.2764 −2.24880
\(207\) −5.66437 −0.393701
\(208\) 12.8563 0.891425
\(209\) −10.6670 −0.737852
\(210\) 0 0
\(211\) −3.09415 −0.213010 −0.106505 0.994312i \(-0.533966\pi\)
−0.106505 + 0.994312i \(0.533966\pi\)
\(212\) −48.1280 −3.30544
\(213\) 11.6213 0.796282
\(214\) 48.4762 3.31377
\(215\) −15.1000 −1.02981
\(216\) −8.73699 −0.594477
\(217\) 0 0
\(218\) 37.7141 2.55432
\(219\) −3.75487 −0.253731
\(220\) −72.2495 −4.87106
\(221\) 1.04370 0.0702066
\(222\) 21.1832 1.42172
\(223\) 20.2026 1.35286 0.676432 0.736505i \(-0.263525\pi\)
0.676432 + 0.736505i \(0.263525\pi\)
\(224\) 0 0
\(225\) 8.16582 0.544388
\(226\) −36.5109 −2.42867
\(227\) −23.1892 −1.53912 −0.769559 0.638575i \(-0.779524\pi\)
−0.769559 + 0.638575i \(0.779524\pi\)
\(228\) −14.7418 −0.976302
\(229\) −14.8334 −0.980219 −0.490109 0.871661i \(-0.663043\pi\)
−0.490109 + 0.871661i \(0.663043\pi\)
\(230\) −55.3245 −3.64799
\(231\) 0 0
\(232\) 19.3836 1.27259
\(233\) 23.8864 1.56485 0.782426 0.622744i \(-0.213982\pi\)
0.782426 + 0.622744i \(0.213982\pi\)
\(234\) −2.65660 −0.173667
\(235\) 18.4654 1.20455
\(236\) −39.7877 −2.58996
\(237\) −4.83413 −0.314011
\(238\) 0 0
\(239\) 17.1844 1.11156 0.555782 0.831328i \(-0.312419\pi\)
0.555782 + 0.831328i \(0.312419\pi\)
\(240\) −47.2669 −3.05106
\(241\) 6.16967 0.397423 0.198712 0.980058i \(-0.436324\pi\)
0.198712 + 0.980058i \(0.436324\pi\)
\(242\) −9.17345 −0.589692
\(243\) 1.00000 0.0641500
\(244\) 31.2821 2.00263
\(245\) 0 0
\(246\) −2.69180 −0.171623
\(247\) −2.77348 −0.176472
\(248\) −91.3429 −5.80028
\(249\) 7.04509 0.446464
\(250\) 30.9209 1.95561
\(251\) −21.2207 −1.33944 −0.669720 0.742614i \(-0.733586\pi\)
−0.669720 + 0.742614i \(0.733586\pi\)
\(252\) 0 0
\(253\) −21.5007 −1.35174
\(254\) −34.0405 −2.13589
\(255\) −3.83720 −0.240295
\(256\) 17.0238 1.06399
\(257\) 23.2708 1.45159 0.725796 0.687910i \(-0.241472\pi\)
0.725796 + 0.687910i \(0.241472\pi\)
\(258\) −11.2020 −0.697404
\(259\) 0 0
\(260\) −18.7853 −1.16501
\(261\) −2.21857 −0.137326
\(262\) −58.8662 −3.63677
\(263\) −30.5369 −1.88299 −0.941493 0.337033i \(-0.890577\pi\)
−0.941493 + 0.337033i \(0.890577\pi\)
\(264\) −33.1637 −2.04108
\(265\) 33.2898 2.04498
\(266\) 0 0
\(267\) 9.53384 0.583462
\(268\) −82.0244 −5.01044
\(269\) −4.54700 −0.277235 −0.138618 0.990346i \(-0.544266\pi\)
−0.138618 + 0.990346i \(0.544266\pi\)
\(270\) 9.76712 0.594408
\(271\) −21.0582 −1.27919 −0.639597 0.768711i \(-0.720899\pi\)
−0.639597 + 0.768711i \(0.720899\pi\)
\(272\) 13.7760 0.835294
\(273\) 0 0
\(274\) 11.5219 0.696063
\(275\) 30.9956 1.86911
\(276\) −29.7140 −1.78857
\(277\) −1.16773 −0.0701620 −0.0350810 0.999384i \(-0.511169\pi\)
−0.0350810 + 0.999384i \(0.511169\pi\)
\(278\) −0.0390392 −0.00234141
\(279\) 10.4547 0.625909
\(280\) 0 0
\(281\) −16.8177 −1.00326 −0.501631 0.865082i \(-0.667266\pi\)
−0.501631 + 0.865082i \(0.667266\pi\)
\(282\) 13.6986 0.815740
\(283\) 32.2924 1.91958 0.959791 0.280715i \(-0.0905717\pi\)
0.959791 + 0.280715i \(0.0905717\pi\)
\(284\) 60.9630 3.61749
\(285\) 10.1968 0.604008
\(286\) −10.0839 −0.596271
\(287\) 0 0
\(288\) −17.5912 −1.03657
\(289\) −15.8816 −0.934214
\(290\) −21.6690 −1.27245
\(291\) 14.2834 0.837309
\(292\) −19.6972 −1.15269
\(293\) −22.4014 −1.30871 −0.654353 0.756189i \(-0.727059\pi\)
−0.654353 + 0.756189i \(0.727059\pi\)
\(294\) 0 0
\(295\) 27.5209 1.60233
\(296\) 68.7560 3.99636
\(297\) 3.79578 0.220253
\(298\) 39.7299 2.30149
\(299\) −5.59030 −0.323295
\(300\) 42.8361 2.47314
\(301\) 0 0
\(302\) 18.4717 1.06293
\(303\) 1.27838 0.0734409
\(304\) −36.6079 −2.09961
\(305\) −21.6376 −1.23897
\(306\) −2.84664 −0.162732
\(307\) −15.5675 −0.888481 −0.444241 0.895907i \(-0.646526\pi\)
−0.444241 + 0.895907i \(0.646526\pi\)
\(308\) 0 0
\(309\) 11.9906 0.682124
\(310\) 102.113 5.79961
\(311\) −20.2286 −1.14706 −0.573531 0.819184i \(-0.694427\pi\)
−0.573531 + 0.819184i \(0.694427\pi\)
\(312\) −8.62274 −0.488167
\(313\) −13.2244 −0.747490 −0.373745 0.927532i \(-0.621926\pi\)
−0.373745 + 0.927532i \(0.621926\pi\)
\(314\) −11.2403 −0.634328
\(315\) 0 0
\(316\) −25.3588 −1.42654
\(317\) −17.4307 −0.979004 −0.489502 0.872002i \(-0.662821\pi\)
−0.489502 + 0.872002i \(0.662821\pi\)
\(318\) 24.6962 1.38489
\(319\) −8.42118 −0.471496
\(320\) −77.2812 −4.32015
\(321\) −18.0089 −1.00516
\(322\) 0 0
\(323\) −2.97189 −0.165360
\(324\) 5.24578 0.291432
\(325\) 8.05904 0.447035
\(326\) 63.3139 3.50663
\(327\) −14.0107 −0.774795
\(328\) −8.73699 −0.482420
\(329\) 0 0
\(330\) 37.0738 2.04085
\(331\) 20.7539 1.14074 0.570369 0.821389i \(-0.306800\pi\)
0.570369 + 0.821389i \(0.306800\pi\)
\(332\) 36.9570 2.02828
\(333\) −7.86953 −0.431248
\(334\) 42.2801 2.31346
\(335\) 56.7358 3.09981
\(336\) 0 0
\(337\) −3.56654 −0.194282 −0.0971409 0.995271i \(-0.530970\pi\)
−0.0971409 + 0.995271i \(0.530970\pi\)
\(338\) 32.3715 1.76078
\(339\) 13.5638 0.736682
\(340\) −20.1291 −1.09165
\(341\) 39.6839 2.14900
\(342\) 7.56457 0.409045
\(343\) 0 0
\(344\) −36.3591 −1.96035
\(345\) 20.5530 1.10654
\(346\) 15.8619 0.852743
\(347\) 11.9328 0.640586 0.320293 0.947319i \(-0.396219\pi\)
0.320293 + 0.947319i \(0.396219\pi\)
\(348\) −11.6381 −0.623868
\(349\) −6.91055 −0.369913 −0.184957 0.982747i \(-0.559214\pi\)
−0.184957 + 0.982747i \(0.559214\pi\)
\(350\) 0 0
\(351\) 0.986924 0.0526781
\(352\) −66.7721 −3.55897
\(353\) 3.75498 0.199858 0.0999288 0.994995i \(-0.468139\pi\)
0.0999288 + 0.994995i \(0.468139\pi\)
\(354\) 20.4165 1.08513
\(355\) −42.1677 −2.23803
\(356\) 50.0125 2.65066
\(357\) 0 0
\(358\) −12.5767 −0.664698
\(359\) 9.38283 0.495207 0.247603 0.968861i \(-0.420357\pi\)
0.247603 + 0.968861i \(0.420357\pi\)
\(360\) 31.7019 1.67084
\(361\) −11.1026 −0.584348
\(362\) 35.6269 1.87251
\(363\) 3.40793 0.178870
\(364\) 0 0
\(365\) 13.6245 0.713136
\(366\) −16.0519 −0.839049
\(367\) −26.7028 −1.39388 −0.696938 0.717132i \(-0.745455\pi\)
−0.696938 + 0.717132i \(0.745455\pi\)
\(368\) −73.7877 −3.84645
\(369\) 1.00000 0.0520579
\(370\) −76.8626 −3.99590
\(371\) 0 0
\(372\) 54.8433 2.84349
\(373\) 6.05227 0.313375 0.156687 0.987648i \(-0.449919\pi\)
0.156687 + 0.987648i \(0.449919\pi\)
\(374\) −10.8052 −0.558725
\(375\) −11.4871 −0.593190
\(376\) 44.4627 2.29299
\(377\) −2.18956 −0.112768
\(378\) 0 0
\(379\) −4.68737 −0.240774 −0.120387 0.992727i \(-0.538414\pi\)
−0.120387 + 0.992727i \(0.538414\pi\)
\(380\) 53.4904 2.74400
\(381\) 12.6460 0.647875
\(382\) −49.6194 −2.53875
\(383\) −34.5205 −1.76391 −0.881957 0.471330i \(-0.843774\pi\)
−0.881957 + 0.471330i \(0.843774\pi\)
\(384\) −22.1491 −1.13029
\(385\) 0 0
\(386\) −30.8609 −1.57078
\(387\) 4.16152 0.211542
\(388\) 74.9277 3.80388
\(389\) 1.71421 0.0869137 0.0434569 0.999055i \(-0.486163\pi\)
0.0434569 + 0.999055i \(0.486163\pi\)
\(390\) 9.63940 0.488110
\(391\) −5.99021 −0.302938
\(392\) 0 0
\(393\) 21.8687 1.10313
\(394\) −7.76058 −0.390972
\(395\) 17.5405 0.882560
\(396\) 19.9118 1.00061
\(397\) 14.5925 0.732377 0.366189 0.930541i \(-0.380662\pi\)
0.366189 + 0.930541i \(0.380662\pi\)
\(398\) −50.2490 −2.51876
\(399\) 0 0
\(400\) 106.373 5.31866
\(401\) 10.9102 0.544829 0.272415 0.962180i \(-0.412178\pi\)
0.272415 + 0.962180i \(0.412178\pi\)
\(402\) 42.0897 2.09924
\(403\) 10.3180 0.513978
\(404\) 6.70609 0.333641
\(405\) −3.62847 −0.180300
\(406\) 0 0
\(407\) −29.8710 −1.48065
\(408\) −9.23959 −0.457428
\(409\) −14.5454 −0.719224 −0.359612 0.933102i \(-0.617091\pi\)
−0.359612 + 0.933102i \(0.617091\pi\)
\(410\) 9.76712 0.482364
\(411\) −4.28037 −0.211135
\(412\) 62.9003 3.09888
\(413\) 0 0
\(414\) 15.2473 0.749365
\(415\) −25.5629 −1.25483
\(416\) −17.3611 −0.851199
\(417\) 0.0145030 0.000710215 0
\(418\) 28.7134 1.40442
\(419\) −18.6549 −0.911353 −0.455676 0.890146i \(-0.650603\pi\)
−0.455676 + 0.890146i \(0.650603\pi\)
\(420\) 0 0
\(421\) −30.2812 −1.47582 −0.737909 0.674900i \(-0.764187\pi\)
−0.737909 + 0.674900i \(0.764187\pi\)
\(422\) 8.32884 0.405441
\(423\) −5.08902 −0.247436
\(424\) 80.1584 3.89284
\(425\) 8.63555 0.418886
\(426\) −31.2823 −1.51563
\(427\) 0 0
\(428\) −94.4705 −4.56640
\(429\) 3.74614 0.180865
\(430\) 40.6460 1.96013
\(431\) 12.4541 0.599895 0.299948 0.953956i \(-0.403031\pi\)
0.299948 + 0.953956i \(0.403031\pi\)
\(432\) 13.0267 0.626745
\(433\) −6.80377 −0.326968 −0.163484 0.986546i \(-0.552273\pi\)
−0.163484 + 0.986546i \(0.552273\pi\)
\(434\) 0 0
\(435\) 8.05001 0.385968
\(436\) −73.4972 −3.51988
\(437\) 15.9182 0.761469
\(438\) 10.1074 0.482948
\(439\) −23.6472 −1.12862 −0.564310 0.825563i \(-0.690858\pi\)
−0.564310 + 0.825563i \(0.690858\pi\)
\(440\) 120.333 5.73667
\(441\) 0 0
\(442\) −2.80942 −0.133631
\(443\) 14.4599 0.687009 0.343505 0.939151i \(-0.388386\pi\)
0.343505 + 0.939151i \(0.388386\pi\)
\(444\) −41.2818 −1.95915
\(445\) −34.5933 −1.63988
\(446\) −54.3812 −2.57503
\(447\) −14.7596 −0.698105
\(448\) 0 0
\(449\) −14.7644 −0.696777 −0.348388 0.937350i \(-0.613271\pi\)
−0.348388 + 0.937350i \(0.613271\pi\)
\(450\) −21.9807 −1.03618
\(451\) 3.79578 0.178736
\(452\) 71.1525 3.34673
\(453\) −6.86221 −0.322415
\(454\) 62.4205 2.92954
\(455\) 0 0
\(456\) 24.5529 1.14980
\(457\) −7.93084 −0.370989 −0.185495 0.982645i \(-0.559389\pi\)
−0.185495 + 0.982645i \(0.559389\pi\)
\(458\) 39.9285 1.86574
\(459\) 1.05753 0.0493610
\(460\) 107.817 5.02697
\(461\) 9.83013 0.457835 0.228917 0.973446i \(-0.426481\pi\)
0.228917 + 0.973446i \(0.426481\pi\)
\(462\) 0 0
\(463\) −6.47631 −0.300980 −0.150490 0.988612i \(-0.548085\pi\)
−0.150490 + 0.988612i \(0.548085\pi\)
\(464\) −28.9005 −1.34167
\(465\) −37.9347 −1.75918
\(466\) −64.2975 −2.97852
\(467\) 2.17951 0.100856 0.0504278 0.998728i \(-0.483942\pi\)
0.0504278 + 0.998728i \(0.483942\pi\)
\(468\) 5.17719 0.239315
\(469\) 0 0
\(470\) −49.7050 −2.29272
\(471\) 4.17576 0.192409
\(472\) 66.2676 3.05021
\(473\) 15.7962 0.726310
\(474\) 13.0125 0.597685
\(475\) −22.9478 −1.05292
\(476\) 0 0
\(477\) −9.17461 −0.420076
\(478\) −46.2569 −2.11574
\(479\) −23.3346 −1.06619 −0.533093 0.846057i \(-0.678970\pi\)
−0.533093 + 0.846057i \(0.678970\pi\)
\(480\) 63.8290 2.91338
\(481\) −7.76663 −0.354128
\(482\) −16.6075 −0.756451
\(483\) 0 0
\(484\) 17.8772 0.812602
\(485\) −51.8270 −2.35334
\(486\) −2.69180 −0.122102
\(487\) −0.181820 −0.00823903 −0.00411952 0.999992i \(-0.501311\pi\)
−0.00411952 + 0.999992i \(0.501311\pi\)
\(488\) −52.1011 −2.35851
\(489\) −23.5210 −1.06366
\(490\) 0 0
\(491\) 19.2932 0.870688 0.435344 0.900264i \(-0.356627\pi\)
0.435344 + 0.900264i \(0.356627\pi\)
\(492\) 5.24578 0.236498
\(493\) −2.34619 −0.105667
\(494\) 7.46565 0.335896
\(495\) −13.7729 −0.619045
\(496\) 136.190 6.11512
\(497\) 0 0
\(498\) −18.9640 −0.849795
\(499\) 9.27958 0.415411 0.207706 0.978191i \(-0.433400\pi\)
0.207706 + 0.978191i \(0.433400\pi\)
\(500\) −60.2587 −2.69485
\(501\) −15.7070 −0.701737
\(502\) 57.1219 2.54948
\(503\) 19.7484 0.880537 0.440269 0.897866i \(-0.354883\pi\)
0.440269 + 0.897866i \(0.354883\pi\)
\(504\) 0 0
\(505\) −4.63856 −0.206413
\(506\) 57.8755 2.57288
\(507\) −12.0260 −0.534093
\(508\) 66.3383 2.94328
\(509\) 10.5926 0.469510 0.234755 0.972055i \(-0.424571\pi\)
0.234755 + 0.972055i \(0.424571\pi\)
\(510\) 10.3290 0.457375
\(511\) 0 0
\(512\) −1.52644 −0.0674599
\(513\) −2.81023 −0.124075
\(514\) −62.6403 −2.76294
\(515\) −43.5077 −1.91718
\(516\) 21.8304 0.961030
\(517\) −19.3168 −0.849551
\(518\) 0 0
\(519\) −5.89269 −0.258660
\(520\) 31.2874 1.37204
\(521\) 27.2068 1.19195 0.595976 0.803002i \(-0.296765\pi\)
0.595976 + 0.803002i \(0.296765\pi\)
\(522\) 5.97193 0.261384
\(523\) −43.2412 −1.89081 −0.945403 0.325904i \(-0.894331\pi\)
−0.945403 + 0.325904i \(0.894331\pi\)
\(524\) 114.719 5.01150
\(525\) 0 0
\(526\) 82.1992 3.58406
\(527\) 11.0561 0.481613
\(528\) 49.4463 2.15187
\(529\) 9.08504 0.395002
\(530\) −89.6095 −3.89239
\(531\) −7.58471 −0.329149
\(532\) 0 0
\(533\) 0.986924 0.0427484
\(534\) −25.6632 −1.11055
\(535\) 65.3446 2.82510
\(536\) 136.614 5.90082
\(537\) 4.67222 0.201621
\(538\) 12.2396 0.527687
\(539\) 0 0
\(540\) −19.0342 −0.819100
\(541\) 11.1859 0.480919 0.240459 0.970659i \(-0.422702\pi\)
0.240459 + 0.970659i \(0.422702\pi\)
\(542\) 56.6844 2.43480
\(543\) −13.2354 −0.567983
\(544\) −18.6031 −0.797601
\(545\) 50.8375 2.17764
\(546\) 0 0
\(547\) 34.4215 1.47176 0.735878 0.677115i \(-0.236770\pi\)
0.735878 + 0.677115i \(0.236770\pi\)
\(548\) −22.4539 −0.959183
\(549\) 5.96328 0.254507
\(550\) −83.4340 −3.55764
\(551\) 6.23468 0.265606
\(552\) 49.4895 2.10641
\(553\) 0 0
\(554\) 3.14329 0.133546
\(555\) 28.5544 1.21207
\(556\) 0.0760796 0.00322649
\(557\) 37.0851 1.57134 0.785672 0.618643i \(-0.212317\pi\)
0.785672 + 0.618643i \(0.212317\pi\)
\(558\) −28.1420 −1.19135
\(559\) 4.10710 0.173712
\(560\) 0 0
\(561\) 4.01413 0.169477
\(562\) 45.2699 1.90960
\(563\) 0.795779 0.0335381 0.0167690 0.999859i \(-0.494662\pi\)
0.0167690 + 0.999859i \(0.494662\pi\)
\(564\) −26.6959 −1.12410
\(565\) −49.2157 −2.07052
\(566\) −86.9246 −3.65371
\(567\) 0 0
\(568\) −101.536 −4.26034
\(569\) 11.2518 0.471701 0.235850 0.971789i \(-0.424212\pi\)
0.235850 + 0.971789i \(0.424212\pi\)
\(570\) −27.4478 −1.14966
\(571\) −39.0794 −1.63542 −0.817711 0.575629i \(-0.804757\pi\)
−0.817711 + 0.575629i \(0.804757\pi\)
\(572\) 19.6514 0.821668
\(573\) 18.4336 0.770073
\(574\) 0 0
\(575\) −46.2542 −1.92893
\(576\) 21.2985 0.887439
\(577\) −11.3745 −0.473527 −0.236763 0.971567i \(-0.576087\pi\)
−0.236763 + 0.971567i \(0.576087\pi\)
\(578\) 42.7502 1.77817
\(579\) 11.4648 0.476461
\(580\) 42.2286 1.75345
\(581\) 0 0
\(582\) −38.4481 −1.59372
\(583\) −34.8248 −1.44229
\(584\) 32.8063 1.35753
\(585\) −3.58103 −0.148057
\(586\) 60.3002 2.49098
\(587\) −1.19831 −0.0494595 −0.0247297 0.999694i \(-0.507873\pi\)
−0.0247297 + 0.999694i \(0.507873\pi\)
\(588\) 0 0
\(589\) −29.3802 −1.21059
\(590\) −74.0808 −3.04986
\(591\) 2.88305 0.118593
\(592\) −102.514 −4.21329
\(593\) 24.6608 1.01270 0.506349 0.862329i \(-0.330995\pi\)
0.506349 + 0.862329i \(0.330995\pi\)
\(594\) −10.2175 −0.419228
\(595\) 0 0
\(596\) −77.4256 −3.17148
\(597\) 18.6674 0.764008
\(598\) 15.0480 0.615357
\(599\) −25.4843 −1.04126 −0.520630 0.853783i \(-0.674303\pi\)
−0.520630 + 0.853783i \(0.674303\pi\)
\(600\) −71.3446 −2.91263
\(601\) −0.495078 −0.0201947 −0.0100973 0.999949i \(-0.503214\pi\)
−0.0100973 + 0.999949i \(0.503214\pi\)
\(602\) 0 0
\(603\) −15.6363 −0.636758
\(604\) −35.9976 −1.46472
\(605\) −12.3656 −0.502732
\(606\) −3.44114 −0.139787
\(607\) −47.8430 −1.94189 −0.970943 0.239309i \(-0.923079\pi\)
−0.970943 + 0.239309i \(0.923079\pi\)
\(608\) 49.4352 2.00486
\(609\) 0 0
\(610\) 58.2441 2.35823
\(611\) −5.02247 −0.203187
\(612\) 5.54754 0.224246
\(613\) −38.3710 −1.54979 −0.774895 0.632090i \(-0.782197\pi\)
−0.774895 + 0.632090i \(0.782197\pi\)
\(614\) 41.9044 1.69113
\(615\) −3.62847 −0.146314
\(616\) 0 0
\(617\) −9.52594 −0.383500 −0.191750 0.981444i \(-0.561416\pi\)
−0.191750 + 0.981444i \(0.561416\pi\)
\(618\) −32.2764 −1.29835
\(619\) −33.0989 −1.33036 −0.665179 0.746684i \(-0.731645\pi\)
−0.665179 + 0.746684i \(0.731645\pi\)
\(620\) −198.997 −7.99192
\(621\) −5.66437 −0.227303
\(622\) 54.4515 2.18330
\(623\) 0 0
\(624\) 12.8563 0.514665
\(625\) 0.851461 0.0340584
\(626\) 35.5976 1.42276
\(627\) −10.6670 −0.425999
\(628\) 21.9051 0.874110
\(629\) −8.32223 −0.331829
\(630\) 0 0
\(631\) −7.62134 −0.303401 −0.151700 0.988427i \(-0.548475\pi\)
−0.151700 + 0.988427i \(0.548475\pi\)
\(632\) 42.2358 1.68005
\(633\) −3.09415 −0.122982
\(634\) 46.9199 1.86343
\(635\) −45.8857 −1.82092
\(636\) −48.1280 −1.90840
\(637\) 0 0
\(638\) 22.6681 0.897440
\(639\) 11.6213 0.459733
\(640\) 80.3673 3.17680
\(641\) −33.7943 −1.33479 −0.667397 0.744702i \(-0.732592\pi\)
−0.667397 + 0.744702i \(0.732592\pi\)
\(642\) 48.4762 1.91320
\(643\) 6.60324 0.260406 0.130203 0.991487i \(-0.458437\pi\)
0.130203 + 0.991487i \(0.458437\pi\)
\(644\) 0 0
\(645\) −15.1000 −0.594560
\(646\) 7.99972 0.314745
\(647\) −12.2008 −0.479663 −0.239832 0.970815i \(-0.577092\pi\)
−0.239832 + 0.970815i \(0.577092\pi\)
\(648\) −8.73699 −0.343221
\(649\) −28.7899 −1.13010
\(650\) −21.6933 −0.850881
\(651\) 0 0
\(652\) −123.386 −4.83218
\(653\) −37.3586 −1.46195 −0.730977 0.682402i \(-0.760936\pi\)
−0.730977 + 0.682402i \(0.760936\pi\)
\(654\) 37.7141 1.47474
\(655\) −79.3501 −3.10046
\(656\) 13.0267 0.508605
\(657\) −3.75487 −0.146492
\(658\) 0 0
\(659\) 17.0668 0.664829 0.332414 0.943133i \(-0.392137\pi\)
0.332414 + 0.943133i \(0.392137\pi\)
\(660\) −72.2495 −2.81231
\(661\) 9.34986 0.363668 0.181834 0.983329i \(-0.441797\pi\)
0.181834 + 0.983329i \(0.441797\pi\)
\(662\) −55.8653 −2.17127
\(663\) 1.04370 0.0405338
\(664\) −61.5528 −2.38871
\(665\) 0 0
\(666\) 21.1832 0.820832
\(667\) 12.5668 0.486587
\(668\) −82.3955 −3.18798
\(669\) 20.2026 0.781076
\(670\) −152.721 −5.90014
\(671\) 22.6353 0.873825
\(672\) 0 0
\(673\) 7.36902 0.284055 0.142027 0.989863i \(-0.454638\pi\)
0.142027 + 0.989863i \(0.454638\pi\)
\(674\) 9.60040 0.369794
\(675\) 8.16582 0.314302
\(676\) −63.0857 −2.42637
\(677\) 18.2593 0.701762 0.350881 0.936420i \(-0.385882\pi\)
0.350881 + 0.936420i \(0.385882\pi\)
\(678\) −36.5109 −1.40219
\(679\) 0 0
\(680\) 33.5256 1.28565
\(681\) −23.1892 −0.888610
\(682\) −106.821 −4.09039
\(683\) 5.22095 0.199774 0.0998870 0.994999i \(-0.468152\pi\)
0.0998870 + 0.994999i \(0.468152\pi\)
\(684\) −14.7418 −0.563668
\(685\) 15.5312 0.593417
\(686\) 0 0
\(687\) −14.8334 −0.565929
\(688\) 54.2107 2.06676
\(689\) −9.05464 −0.344954
\(690\) −55.3245 −2.10617
\(691\) −1.84487 −0.0701823 −0.0350912 0.999384i \(-0.511172\pi\)
−0.0350912 + 0.999384i \(0.511172\pi\)
\(692\) −30.9117 −1.17509
\(693\) 0 0
\(694\) −32.1207 −1.21928
\(695\) −0.0526237 −0.00199613
\(696\) 19.3836 0.734733
\(697\) 1.05753 0.0400566
\(698\) 18.6018 0.704089
\(699\) 23.8864 0.903468
\(700\) 0 0
\(701\) −30.6724 −1.15848 −0.579240 0.815157i \(-0.696651\pi\)
−0.579240 + 0.815157i \(0.696651\pi\)
\(702\) −2.65660 −0.100267
\(703\) 22.1152 0.834090
\(704\) 80.8445 3.04694
\(705\) 18.4654 0.695446
\(706\) −10.1077 −0.380407
\(707\) 0 0
\(708\) −39.7877 −1.49531
\(709\) −29.3623 −1.10273 −0.551363 0.834266i \(-0.685892\pi\)
−0.551363 + 0.834266i \(0.685892\pi\)
\(710\) 113.507 4.25984
\(711\) −4.83413 −0.181294
\(712\) −83.2971 −3.12169
\(713\) −59.2195 −2.21779
\(714\) 0 0
\(715\) −13.5928 −0.508341
\(716\) 24.5094 0.915961
\(717\) 17.1844 0.641762
\(718\) −25.2567 −0.942572
\(719\) 13.0625 0.487148 0.243574 0.969882i \(-0.421680\pi\)
0.243574 + 0.969882i \(0.421680\pi\)
\(720\) −47.2669 −1.76153
\(721\) 0 0
\(722\) 29.8860 1.11224
\(723\) 6.16967 0.229452
\(724\) −69.4298 −2.58034
\(725\) −18.1164 −0.672826
\(726\) −9.17345 −0.340459
\(727\) −18.2556 −0.677064 −0.338532 0.940955i \(-0.609930\pi\)
−0.338532 + 0.940955i \(0.609930\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −36.6743 −1.35738
\(731\) 4.40091 0.162773
\(732\) 31.2821 1.15622
\(733\) 21.0158 0.776235 0.388117 0.921610i \(-0.373126\pi\)
0.388117 + 0.921610i \(0.373126\pi\)
\(734\) 71.8786 2.65309
\(735\) 0 0
\(736\) 99.6427 3.67288
\(737\) −59.3518 −2.18625
\(738\) −2.69180 −0.0990865
\(739\) 42.2094 1.55270 0.776348 0.630304i \(-0.217070\pi\)
0.776348 + 0.630304i \(0.217070\pi\)
\(740\) 149.790 5.50639
\(741\) −2.77348 −0.101886
\(742\) 0 0
\(743\) −52.7446 −1.93501 −0.967505 0.252852i \(-0.918632\pi\)
−0.967505 + 0.252852i \(0.918632\pi\)
\(744\) −91.3429 −3.34879
\(745\) 53.5548 1.96210
\(746\) −16.2915 −0.596474
\(747\) 7.04509 0.257766
\(748\) 21.0572 0.769929
\(749\) 0 0
\(750\) 30.9209 1.12907
\(751\) −26.7511 −0.976160 −0.488080 0.872799i \(-0.662303\pi\)
−0.488080 + 0.872799i \(0.662303\pi\)
\(752\) −66.2929 −2.41745
\(753\) −21.2207 −0.773326
\(754\) 5.89384 0.214641
\(755\) 24.8993 0.906179
\(756\) 0 0
\(757\) 46.6901 1.69698 0.848489 0.529212i \(-0.177512\pi\)
0.848489 + 0.529212i \(0.177512\pi\)
\(758\) 12.6175 0.458287
\(759\) −21.5007 −0.780425
\(760\) −89.0896 −3.23162
\(761\) 39.3776 1.42744 0.713718 0.700433i \(-0.247010\pi\)
0.713718 + 0.700433i \(0.247010\pi\)
\(762\) −34.0405 −1.23316
\(763\) 0 0
\(764\) 96.6984 3.49843
\(765\) −3.83720 −0.138734
\(766\) 92.9222 3.35742
\(767\) −7.48553 −0.270287
\(768\) 17.0238 0.614293
\(769\) −40.4050 −1.45704 −0.728520 0.685025i \(-0.759791\pi\)
−0.728520 + 0.685025i \(0.759791\pi\)
\(770\) 0 0
\(771\) 23.2708 0.838077
\(772\) 60.1418 2.16455
\(773\) −16.5528 −0.595364 −0.297682 0.954665i \(-0.596214\pi\)
−0.297682 + 0.954665i \(0.596214\pi\)
\(774\) −11.2020 −0.402646
\(775\) 85.3715 3.06663
\(776\) −124.794 −4.47984
\(777\) 0 0
\(778\) −4.61430 −0.165431
\(779\) −2.81023 −0.100687
\(780\) −18.7853 −0.672621
\(781\) 44.1120 1.57845
\(782\) 16.1244 0.576609
\(783\) −2.21857 −0.0792851
\(784\) 0 0
\(785\) −15.1516 −0.540785
\(786\) −58.8662 −2.09969
\(787\) −41.3752 −1.47487 −0.737433 0.675420i \(-0.763962\pi\)
−0.737433 + 0.675420i \(0.763962\pi\)
\(788\) 15.1238 0.538764
\(789\) −30.5369 −1.08714
\(790\) −47.2156 −1.67985
\(791\) 0 0
\(792\) −33.1637 −1.17842
\(793\) 5.88530 0.208993
\(794\) −39.2801 −1.39400
\(795\) 33.2898 1.18067
\(796\) 97.9253 3.47087
\(797\) −30.5376 −1.08170 −0.540849 0.841119i \(-0.681897\pi\)
−0.540849 + 0.841119i \(0.681897\pi\)
\(798\) 0 0
\(799\) −5.38176 −0.190393
\(800\) −143.646 −5.07866
\(801\) 9.53384 0.336862
\(802\) −29.3680 −1.03702
\(803\) −14.2527 −0.502965
\(804\) −82.0244 −2.89278
\(805\) 0 0
\(806\) −27.7741 −0.978299
\(807\) −4.54700 −0.160062
\(808\) −11.1692 −0.392930
\(809\) −23.0463 −0.810264 −0.405132 0.914258i \(-0.632774\pi\)
−0.405132 + 0.914258i \(0.632774\pi\)
\(810\) 9.76712 0.343182
\(811\) −16.0147 −0.562352 −0.281176 0.959656i \(-0.590725\pi\)
−0.281176 + 0.959656i \(0.590725\pi\)
\(812\) 0 0
\(813\) −21.0582 −0.738543
\(814\) 80.4067 2.81825
\(815\) 85.3455 2.98952
\(816\) 13.7760 0.482257
\(817\) −11.6948 −0.409150
\(818\) 39.1533 1.36896
\(819\) 0 0
\(820\) −19.0342 −0.664702
\(821\) 26.8925 0.938553 0.469277 0.883051i \(-0.344515\pi\)
0.469277 + 0.883051i \(0.344515\pi\)
\(822\) 11.5219 0.401872
\(823\) −49.1148 −1.71203 −0.856017 0.516947i \(-0.827068\pi\)
−0.856017 + 0.516947i \(0.827068\pi\)
\(824\) −104.762 −3.64956
\(825\) 30.9956 1.07913
\(826\) 0 0
\(827\) −5.37580 −0.186935 −0.0934675 0.995622i \(-0.529795\pi\)
−0.0934675 + 0.995622i \(0.529795\pi\)
\(828\) −29.7140 −1.03263
\(829\) 24.9271 0.865754 0.432877 0.901453i \(-0.357498\pi\)
0.432877 + 0.901453i \(0.357498\pi\)
\(830\) 68.8102 2.38844
\(831\) −1.16773 −0.0405081
\(832\) 21.0200 0.728739
\(833\) 0 0
\(834\) −0.0390392 −0.00135182
\(835\) 56.9924 1.97230
\(836\) −55.9567 −1.93530
\(837\) 10.4547 0.361369
\(838\) 50.2153 1.73466
\(839\) −12.8146 −0.442408 −0.221204 0.975228i \(-0.570999\pi\)
−0.221204 + 0.975228i \(0.570999\pi\)
\(840\) 0 0
\(841\) −24.0780 −0.830275
\(842\) 81.5110 2.80906
\(843\) −16.8177 −0.579233
\(844\) −16.2312 −0.558702
\(845\) 43.6359 1.50112
\(846\) 13.6986 0.470968
\(847\) 0 0
\(848\) −119.514 −4.10414
\(849\) 32.2924 1.10827
\(850\) −23.2452 −0.797303
\(851\) 44.5759 1.52804
\(852\) 60.9630 2.08856
\(853\) −55.5740 −1.90282 −0.951409 0.307930i \(-0.900364\pi\)
−0.951409 + 0.307930i \(0.900364\pi\)
\(854\) 0 0
\(855\) 10.1968 0.348724
\(856\) 157.343 5.37788
\(857\) −18.9766 −0.648228 −0.324114 0.946018i \(-0.605066\pi\)
−0.324114 + 0.946018i \(0.605066\pi\)
\(858\) −10.0839 −0.344257
\(859\) 6.24592 0.213108 0.106554 0.994307i \(-0.466018\pi\)
0.106554 + 0.994307i \(0.466018\pi\)
\(860\) −79.2110 −2.70107
\(861\) 0 0
\(862\) −33.5241 −1.14183
\(863\) −33.6361 −1.14499 −0.572494 0.819909i \(-0.694024\pi\)
−0.572494 + 0.819909i \(0.694024\pi\)
\(864\) −17.5912 −0.598463
\(865\) 21.3815 0.726991
\(866\) 18.3144 0.622348
\(867\) −15.8816 −0.539369
\(868\) 0 0
\(869\) −18.3493 −0.622457
\(870\) −21.6690 −0.734648
\(871\) −15.4318 −0.522887
\(872\) 122.412 4.14538
\(873\) 14.2834 0.483420
\(874\) −42.8485 −1.44937
\(875\) 0 0
\(876\) −19.6972 −0.665508
\(877\) −12.4187 −0.419351 −0.209676 0.977771i \(-0.567241\pi\)
−0.209676 + 0.977771i \(0.567241\pi\)
\(878\) 63.6535 2.14820
\(879\) −22.4014 −0.755582
\(880\) −179.414 −6.04806
\(881\) 20.7551 0.699258 0.349629 0.936888i \(-0.386308\pi\)
0.349629 + 0.936888i \(0.386308\pi\)
\(882\) 0 0
\(883\) −6.14363 −0.206750 −0.103375 0.994642i \(-0.532964\pi\)
−0.103375 + 0.994642i \(0.532964\pi\)
\(884\) 5.47500 0.184144
\(885\) 27.5209 0.925106
\(886\) −38.9231 −1.30765
\(887\) 15.6800 0.526482 0.263241 0.964730i \(-0.415209\pi\)
0.263241 + 0.964730i \(0.415209\pi\)
\(888\) 68.7560 2.30730
\(889\) 0 0
\(890\) 93.1182 3.12133
\(891\) 3.79578 0.127163
\(892\) 105.978 3.54841
\(893\) 14.3013 0.478575
\(894\) 39.7299 1.32877
\(895\) −16.9530 −0.566677
\(896\) 0 0
\(897\) −5.59030 −0.186655
\(898\) 39.7429 1.32624
\(899\) −23.1945 −0.773581
\(900\) 42.8361 1.42787
\(901\) −9.70238 −0.323233
\(902\) −10.2175 −0.340205
\(903\) 0 0
\(904\) −118.506 −3.94146
\(905\) 48.0241 1.59638
\(906\) 18.4717 0.613680
\(907\) −51.5516 −1.71174 −0.855871 0.517190i \(-0.826978\pi\)
−0.855871 + 0.517190i \(0.826978\pi\)
\(908\) −121.645 −4.03694
\(909\) 1.27838 0.0424011
\(910\) 0 0
\(911\) −25.3620 −0.840280 −0.420140 0.907459i \(-0.638019\pi\)
−0.420140 + 0.907459i \(0.638019\pi\)
\(912\) −36.6079 −1.21221
\(913\) 26.7416 0.885017
\(914\) 21.3482 0.706137
\(915\) −21.6376 −0.715317
\(916\) −77.8128 −2.57101
\(917\) 0 0
\(918\) −2.84664 −0.0939533
\(919\) −14.9540 −0.493288 −0.246644 0.969106i \(-0.579328\pi\)
−0.246644 + 0.969106i \(0.579328\pi\)
\(920\) −179.571 −5.92029
\(921\) −15.5675 −0.512965
\(922\) −26.4607 −0.871438
\(923\) 11.4694 0.377519
\(924\) 0 0
\(925\) −64.2611 −2.11289
\(926\) 17.4329 0.572882
\(927\) 11.9906 0.393825
\(928\) 39.0271 1.28113
\(929\) 22.0282 0.722722 0.361361 0.932426i \(-0.382312\pi\)
0.361361 + 0.932426i \(0.382312\pi\)
\(930\) 102.113 3.34841
\(931\) 0 0
\(932\) 125.303 4.10443
\(933\) −20.2286 −0.662256
\(934\) −5.86680 −0.191967
\(935\) −14.5652 −0.476332
\(936\) −8.62274 −0.281843
\(937\) 15.4016 0.503149 0.251575 0.967838i \(-0.419052\pi\)
0.251575 + 0.967838i \(0.419052\pi\)
\(938\) 0 0
\(939\) −13.2244 −0.431564
\(940\) 96.8652 3.15940
\(941\) 21.8930 0.713692 0.356846 0.934163i \(-0.383852\pi\)
0.356846 + 0.934163i \(0.383852\pi\)
\(942\) −11.2403 −0.366229
\(943\) −5.66437 −0.184457
\(944\) −98.8034 −3.21578
\(945\) 0 0
\(946\) −42.5202 −1.38245
\(947\) −24.2765 −0.788881 −0.394441 0.918921i \(-0.629062\pi\)
−0.394441 + 0.918921i \(0.629062\pi\)
\(948\) −25.3588 −0.823616
\(949\) −3.70577 −0.120294
\(950\) 61.7709 2.00411
\(951\) −17.4307 −0.565228
\(952\) 0 0
\(953\) 26.1321 0.846503 0.423251 0.906012i \(-0.360889\pi\)
0.423251 + 0.906012i \(0.360889\pi\)
\(954\) 24.6962 0.799569
\(955\) −66.8857 −2.16437
\(956\) 90.1455 2.91551
\(957\) −8.42118 −0.272218
\(958\) 62.8121 2.02937
\(959\) 0 0
\(960\) −77.2812 −2.49424
\(961\) 78.3015 2.52586
\(962\) 20.9062 0.674043
\(963\) −18.0089 −0.580327
\(964\) 32.3647 1.04240
\(965\) −41.5997 −1.33914
\(966\) 0 0
\(967\) −22.4692 −0.722561 −0.361280 0.932457i \(-0.617660\pi\)
−0.361280 + 0.932457i \(0.617660\pi\)
\(968\) −29.7750 −0.957005
\(969\) −2.97189 −0.0954708
\(970\) 139.508 4.47933
\(971\) −6.12283 −0.196491 −0.0982454 0.995162i \(-0.531323\pi\)
−0.0982454 + 0.995162i \(0.531323\pi\)
\(972\) 5.24578 0.168258
\(973\) 0 0
\(974\) 0.489422 0.0156821
\(975\) 8.05904 0.258096
\(976\) 77.6816 2.48653
\(977\) 6.50369 0.208071 0.104036 0.994574i \(-0.466824\pi\)
0.104036 + 0.994574i \(0.466824\pi\)
\(978\) 63.3139 2.02456
\(979\) 36.1884 1.15658
\(980\) 0 0
\(981\) −14.0107 −0.447328
\(982\) −51.9333 −1.65726
\(983\) −45.8232 −1.46153 −0.730766 0.682628i \(-0.760837\pi\)
−0.730766 + 0.682628i \(0.760837\pi\)
\(984\) −8.73699 −0.278525
\(985\) −10.4611 −0.333317
\(986\) 6.31547 0.201125
\(987\) 0 0
\(988\) −14.5491 −0.462868
\(989\) −23.5724 −0.749557
\(990\) 37.0738 1.17828
\(991\) 23.9854 0.761920 0.380960 0.924591i \(-0.375594\pi\)
0.380960 + 0.924591i \(0.375594\pi\)
\(992\) −183.911 −5.83918
\(993\) 20.7539 0.658605
\(994\) 0 0
\(995\) −67.7343 −2.14732
\(996\) 36.9570 1.17103
\(997\) −9.44196 −0.299030 −0.149515 0.988759i \(-0.547771\pi\)
−0.149515 + 0.988759i \(0.547771\pi\)
\(998\) −24.9788 −0.790689
\(999\) −7.86953 −0.248981
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 \(a_p\))