Properties

Label 6008.2.a.e.1.34
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.34
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.38028 q^{3} -3.43256 q^{5} +3.30717 q^{7} -1.09484 q^{9} +O(q^{10})\) \(q+1.38028 q^{3} -3.43256 q^{5} +3.30717 q^{7} -1.09484 q^{9} -0.715209 q^{11} +5.15563 q^{13} -4.73789 q^{15} -1.52677 q^{17} +7.44406 q^{19} +4.56481 q^{21} -3.93916 q^{23} +6.78248 q^{25} -5.65201 q^{27} -4.20561 q^{29} +6.78288 q^{31} -0.987187 q^{33} -11.3521 q^{35} -5.07948 q^{37} +7.11620 q^{39} +1.57167 q^{41} -1.14412 q^{43} +3.75809 q^{45} +4.06761 q^{47} +3.93737 q^{49} -2.10737 q^{51} +3.64581 q^{53} +2.45500 q^{55} +10.2749 q^{57} +12.5592 q^{59} -5.54003 q^{61} -3.62081 q^{63} -17.6970 q^{65} -2.31555 q^{67} -5.43713 q^{69} +6.03969 q^{71} -6.14485 q^{73} +9.36170 q^{75} -2.36532 q^{77} +12.9617 q^{79} -4.51682 q^{81} +8.06286 q^{83} +5.24074 q^{85} -5.80490 q^{87} -15.5246 q^{89} +17.0506 q^{91} +9.36225 q^{93} -25.5522 q^{95} +4.13304 q^{97} +0.783037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.38028 0.796903 0.398452 0.917189i \(-0.369548\pi\)
0.398452 + 0.917189i \(0.369548\pi\)
\(4\) 0 0
\(5\) −3.43256 −1.53509 −0.767544 0.640996i \(-0.778521\pi\)
−0.767544 + 0.640996i \(0.778521\pi\)
\(6\) 0 0
\(7\) 3.30717 1.24999 0.624996 0.780628i \(-0.285100\pi\)
0.624996 + 0.780628i \(0.285100\pi\)
\(8\) 0 0
\(9\) −1.09484 −0.364945
\(10\) 0 0
\(11\) −0.715209 −0.215644 −0.107822 0.994170i \(-0.534388\pi\)
−0.107822 + 0.994170i \(0.534388\pi\)
\(12\) 0 0
\(13\) 5.15563 1.42992 0.714958 0.699168i \(-0.246446\pi\)
0.714958 + 0.699168i \(0.246446\pi\)
\(14\) 0 0
\(15\) −4.73789 −1.22332
\(16\) 0 0
\(17\) −1.52677 −0.370297 −0.185148 0.982711i \(-0.559277\pi\)
−0.185148 + 0.982711i \(0.559277\pi\)
\(18\) 0 0
\(19\) 7.44406 1.70779 0.853893 0.520449i \(-0.174235\pi\)
0.853893 + 0.520449i \(0.174235\pi\)
\(20\) 0 0
\(21\) 4.56481 0.996123
\(22\) 0 0
\(23\) −3.93916 −0.821372 −0.410686 0.911777i \(-0.634711\pi\)
−0.410686 + 0.911777i \(0.634711\pi\)
\(24\) 0 0
\(25\) 6.78248 1.35650
\(26\) 0 0
\(27\) −5.65201 −1.08773
\(28\) 0 0
\(29\) −4.20561 −0.780961 −0.390481 0.920611i \(-0.627691\pi\)
−0.390481 + 0.920611i \(0.627691\pi\)
\(30\) 0 0
\(31\) 6.78288 1.21824 0.609121 0.793078i \(-0.291523\pi\)
0.609121 + 0.793078i \(0.291523\pi\)
\(32\) 0 0
\(33\) −0.987187 −0.171847
\(34\) 0 0
\(35\) −11.3521 −1.91885
\(36\) 0 0
\(37\) −5.07948 −0.835061 −0.417530 0.908663i \(-0.637104\pi\)
−0.417530 + 0.908663i \(0.637104\pi\)
\(38\) 0 0
\(39\) 7.11620 1.13950
\(40\) 0 0
\(41\) 1.57167 0.245453 0.122727 0.992441i \(-0.460836\pi\)
0.122727 + 0.992441i \(0.460836\pi\)
\(42\) 0 0
\(43\) −1.14412 −0.174476 −0.0872381 0.996187i \(-0.527804\pi\)
−0.0872381 + 0.996187i \(0.527804\pi\)
\(44\) 0 0
\(45\) 3.75809 0.560223
\(46\) 0 0
\(47\) 4.06761 0.593322 0.296661 0.954983i \(-0.404127\pi\)
0.296661 + 0.954983i \(0.404127\pi\)
\(48\) 0 0
\(49\) 3.93737 0.562482
\(50\) 0 0
\(51\) −2.10737 −0.295091
\(52\) 0 0
\(53\) 3.64581 0.500790 0.250395 0.968144i \(-0.419439\pi\)
0.250395 + 0.968144i \(0.419439\pi\)
\(54\) 0 0
\(55\) 2.45500 0.331032
\(56\) 0 0
\(57\) 10.2749 1.36094
\(58\) 0 0
\(59\) 12.5592 1.63507 0.817536 0.575877i \(-0.195339\pi\)
0.817536 + 0.575877i \(0.195339\pi\)
\(60\) 0 0
\(61\) −5.54003 −0.709328 −0.354664 0.934994i \(-0.615405\pi\)
−0.354664 + 0.934994i \(0.615405\pi\)
\(62\) 0 0
\(63\) −3.62081 −0.456179
\(64\) 0 0
\(65\) −17.6970 −2.19505
\(66\) 0 0
\(67\) −2.31555 −0.282890 −0.141445 0.989946i \(-0.545175\pi\)
−0.141445 + 0.989946i \(0.545175\pi\)
\(68\) 0 0
\(69\) −5.43713 −0.654554
\(70\) 0 0
\(71\) 6.03969 0.716780 0.358390 0.933572i \(-0.383326\pi\)
0.358390 + 0.933572i \(0.383326\pi\)
\(72\) 0 0
\(73\) −6.14485 −0.719201 −0.359600 0.933106i \(-0.617087\pi\)
−0.359600 + 0.933106i \(0.617087\pi\)
\(74\) 0 0
\(75\) 9.36170 1.08100
\(76\) 0 0
\(77\) −2.36532 −0.269553
\(78\) 0 0
\(79\) 12.9617 1.45830 0.729152 0.684351i \(-0.239915\pi\)
0.729152 + 0.684351i \(0.239915\pi\)
\(80\) 0 0
\(81\) −4.51682 −0.501869
\(82\) 0 0
\(83\) 8.06286 0.885014 0.442507 0.896765i \(-0.354089\pi\)
0.442507 + 0.896765i \(0.354089\pi\)
\(84\) 0 0
\(85\) 5.24074 0.568438
\(86\) 0 0
\(87\) −5.80490 −0.622351
\(88\) 0 0
\(89\) −15.5246 −1.64560 −0.822802 0.568328i \(-0.807590\pi\)
−0.822802 + 0.568328i \(0.807590\pi\)
\(90\) 0 0
\(91\) 17.0506 1.78738
\(92\) 0 0
\(93\) 9.36225 0.970820
\(94\) 0 0
\(95\) −25.5522 −2.62160
\(96\) 0 0
\(97\) 4.13304 0.419647 0.209824 0.977739i \(-0.432711\pi\)
0.209824 + 0.977739i \(0.432711\pi\)
\(98\) 0 0
\(99\) 0.783037 0.0786982
\(100\) 0 0
\(101\) −3.07921 −0.306393 −0.153197 0.988196i \(-0.548957\pi\)
−0.153197 + 0.988196i \(0.548957\pi\)
\(102\) 0 0
\(103\) −12.9048 −1.27155 −0.635775 0.771874i \(-0.719319\pi\)
−0.635775 + 0.771874i \(0.719319\pi\)
\(104\) 0 0
\(105\) −15.6690 −1.52914
\(106\) 0 0
\(107\) 18.1027 1.75006 0.875029 0.484071i \(-0.160842\pi\)
0.875029 + 0.484071i \(0.160842\pi\)
\(108\) 0 0
\(109\) −1.37607 −0.131804 −0.0659018 0.997826i \(-0.520992\pi\)
−0.0659018 + 0.997826i \(0.520992\pi\)
\(110\) 0 0
\(111\) −7.01108 −0.665463
\(112\) 0 0
\(113\) 17.9587 1.68941 0.844707 0.535228i \(-0.179774\pi\)
0.844707 + 0.535228i \(0.179774\pi\)
\(114\) 0 0
\(115\) 13.5214 1.26088
\(116\) 0 0
\(117\) −5.64457 −0.521841
\(118\) 0 0
\(119\) −5.04929 −0.462868
\(120\) 0 0
\(121\) −10.4885 −0.953498
\(122\) 0 0
\(123\) 2.16934 0.195602
\(124\) 0 0
\(125\) −6.11848 −0.547253
\(126\) 0 0
\(127\) 20.8271 1.84810 0.924052 0.382267i \(-0.124857\pi\)
0.924052 + 0.382267i \(0.124857\pi\)
\(128\) 0 0
\(129\) −1.57920 −0.139041
\(130\) 0 0
\(131\) 6.81472 0.595404 0.297702 0.954659i \(-0.403780\pi\)
0.297702 + 0.954659i \(0.403780\pi\)
\(132\) 0 0
\(133\) 24.6188 2.13472
\(134\) 0 0
\(135\) 19.4009 1.66976
\(136\) 0 0
\(137\) −13.4759 −1.15133 −0.575664 0.817686i \(-0.695256\pi\)
−0.575664 + 0.817686i \(0.695256\pi\)
\(138\) 0 0
\(139\) −11.6302 −0.986460 −0.493230 0.869899i \(-0.664184\pi\)
−0.493230 + 0.869899i \(0.664184\pi\)
\(140\) 0 0
\(141\) 5.61443 0.472820
\(142\) 0 0
\(143\) −3.68736 −0.308352
\(144\) 0 0
\(145\) 14.4360 1.19884
\(146\) 0 0
\(147\) 5.43466 0.448243
\(148\) 0 0
\(149\) −15.7126 −1.28723 −0.643614 0.765350i \(-0.722566\pi\)
−0.643614 + 0.765350i \(0.722566\pi\)
\(150\) 0 0
\(151\) 6.13637 0.499371 0.249685 0.968327i \(-0.419673\pi\)
0.249685 + 0.968327i \(0.419673\pi\)
\(152\) 0 0
\(153\) 1.67157 0.135138
\(154\) 0 0
\(155\) −23.2827 −1.87011
\(156\) 0 0
\(157\) 6.25511 0.499213 0.249606 0.968347i \(-0.419699\pi\)
0.249606 + 0.968347i \(0.419699\pi\)
\(158\) 0 0
\(159\) 5.03222 0.399081
\(160\) 0 0
\(161\) −13.0275 −1.02671
\(162\) 0 0
\(163\) 24.7242 1.93655 0.968274 0.249891i \(-0.0803947\pi\)
0.968274 + 0.249891i \(0.0803947\pi\)
\(164\) 0 0
\(165\) 3.38858 0.263801
\(166\) 0 0
\(167\) 0.736630 0.0570021 0.0285011 0.999594i \(-0.490927\pi\)
0.0285011 + 0.999594i \(0.490927\pi\)
\(168\) 0 0
\(169\) 13.5805 1.04466
\(170\) 0 0
\(171\) −8.15003 −0.623249
\(172\) 0 0
\(173\) 12.0400 0.915387 0.457694 0.889110i \(-0.348676\pi\)
0.457694 + 0.889110i \(0.348676\pi\)
\(174\) 0 0
\(175\) 22.4308 1.69561
\(176\) 0 0
\(177\) 17.3352 1.30299
\(178\) 0 0
\(179\) 13.6240 1.01831 0.509154 0.860676i \(-0.329958\pi\)
0.509154 + 0.860676i \(0.329958\pi\)
\(180\) 0 0
\(181\) 11.7372 0.872421 0.436210 0.899845i \(-0.356320\pi\)
0.436210 + 0.899845i \(0.356320\pi\)
\(182\) 0 0
\(183\) −7.64677 −0.565266
\(184\) 0 0
\(185\) 17.4356 1.28189
\(186\) 0 0
\(187\) 1.09196 0.0798521
\(188\) 0 0
\(189\) −18.6921 −1.35965
\(190\) 0 0
\(191\) −1.41855 −0.102643 −0.0513215 0.998682i \(-0.516343\pi\)
−0.0513215 + 0.998682i \(0.516343\pi\)
\(192\) 0 0
\(193\) 13.5267 0.973672 0.486836 0.873493i \(-0.338151\pi\)
0.486836 + 0.873493i \(0.338151\pi\)
\(194\) 0 0
\(195\) −24.4268 −1.74924
\(196\) 0 0
\(197\) −6.85311 −0.488264 −0.244132 0.969742i \(-0.578503\pi\)
−0.244132 + 0.969742i \(0.578503\pi\)
\(198\) 0 0
\(199\) 23.9050 1.69458 0.847291 0.531129i \(-0.178232\pi\)
0.847291 + 0.531129i \(0.178232\pi\)
\(200\) 0 0
\(201\) −3.19610 −0.225436
\(202\) 0 0
\(203\) −13.9087 −0.976196
\(204\) 0 0
\(205\) −5.39484 −0.376792
\(206\) 0 0
\(207\) 4.31274 0.299756
\(208\) 0 0
\(209\) −5.32406 −0.368273
\(210\) 0 0
\(211\) 11.0715 0.762192 0.381096 0.924536i \(-0.375547\pi\)
0.381096 + 0.924536i \(0.375547\pi\)
\(212\) 0 0
\(213\) 8.33645 0.571204
\(214\) 0 0
\(215\) 3.92725 0.267836
\(216\) 0 0
\(217\) 22.4321 1.52279
\(218\) 0 0
\(219\) −8.48160 −0.573133
\(220\) 0 0
\(221\) −7.87148 −0.529493
\(222\) 0 0
\(223\) 15.8141 1.05899 0.529494 0.848314i \(-0.322382\pi\)
0.529494 + 0.848314i \(0.322382\pi\)
\(224\) 0 0
\(225\) −7.42571 −0.495047
\(226\) 0 0
\(227\) −11.9752 −0.794822 −0.397411 0.917641i \(-0.630091\pi\)
−0.397411 + 0.917641i \(0.630091\pi\)
\(228\) 0 0
\(229\) 6.96277 0.460113 0.230056 0.973177i \(-0.426109\pi\)
0.230056 + 0.973177i \(0.426109\pi\)
\(230\) 0 0
\(231\) −3.26479 −0.214808
\(232\) 0 0
\(233\) −19.3936 −1.27052 −0.635258 0.772300i \(-0.719106\pi\)
−0.635258 + 0.772300i \(0.719106\pi\)
\(234\) 0 0
\(235\) −13.9623 −0.910801
\(236\) 0 0
\(237\) 17.8907 1.16213
\(238\) 0 0
\(239\) 15.1021 0.976876 0.488438 0.872599i \(-0.337567\pi\)
0.488438 + 0.872599i \(0.337567\pi\)
\(240\) 0 0
\(241\) −14.5806 −0.939222 −0.469611 0.882873i \(-0.655606\pi\)
−0.469611 + 0.882873i \(0.655606\pi\)
\(242\) 0 0
\(243\) 10.7216 0.687788
\(244\) 0 0
\(245\) −13.5153 −0.863459
\(246\) 0 0
\(247\) 38.3789 2.44199
\(248\) 0 0
\(249\) 11.1290 0.705271
\(250\) 0 0
\(251\) −4.72647 −0.298332 −0.149166 0.988812i \(-0.547659\pi\)
−0.149166 + 0.988812i \(0.547659\pi\)
\(252\) 0 0
\(253\) 2.81733 0.177124
\(254\) 0 0
\(255\) 7.23367 0.452990
\(256\) 0 0
\(257\) 0.0945381 0.00589713 0.00294856 0.999996i \(-0.499061\pi\)
0.00294856 + 0.999996i \(0.499061\pi\)
\(258\) 0 0
\(259\) −16.7987 −1.04382
\(260\) 0 0
\(261\) 4.60445 0.285008
\(262\) 0 0
\(263\) 15.6136 0.962774 0.481387 0.876508i \(-0.340133\pi\)
0.481387 + 0.876508i \(0.340133\pi\)
\(264\) 0 0
\(265\) −12.5145 −0.768757
\(266\) 0 0
\(267\) −21.4282 −1.31139
\(268\) 0 0
\(269\) 12.0602 0.735323 0.367662 0.929960i \(-0.380158\pi\)
0.367662 + 0.929960i \(0.380158\pi\)
\(270\) 0 0
\(271\) −4.82291 −0.292971 −0.146485 0.989213i \(-0.546796\pi\)
−0.146485 + 0.989213i \(0.546796\pi\)
\(272\) 0 0
\(273\) 23.5345 1.42437
\(274\) 0 0
\(275\) −4.85089 −0.292520
\(276\) 0 0
\(277\) −10.8417 −0.651415 −0.325707 0.945471i \(-0.605602\pi\)
−0.325707 + 0.945471i \(0.605602\pi\)
\(278\) 0 0
\(279\) −7.42614 −0.444592
\(280\) 0 0
\(281\) −11.5903 −0.691420 −0.345710 0.938341i \(-0.612362\pi\)
−0.345710 + 0.938341i \(0.612362\pi\)
\(282\) 0 0
\(283\) −12.2298 −0.726989 −0.363494 0.931596i \(-0.618416\pi\)
−0.363494 + 0.931596i \(0.618416\pi\)
\(284\) 0 0
\(285\) −35.2691 −2.08916
\(286\) 0 0
\(287\) 5.19777 0.306815
\(288\) 0 0
\(289\) −14.6690 −0.862880
\(290\) 0 0
\(291\) 5.70475 0.334418
\(292\) 0 0
\(293\) 11.8915 0.694710 0.347355 0.937734i \(-0.387080\pi\)
0.347355 + 0.937734i \(0.387080\pi\)
\(294\) 0 0
\(295\) −43.1103 −2.50998
\(296\) 0 0
\(297\) 4.04237 0.234562
\(298\) 0 0
\(299\) −20.3089 −1.17449
\(300\) 0 0
\(301\) −3.78379 −0.218094
\(302\) 0 0
\(303\) −4.25017 −0.244166
\(304\) 0 0
\(305\) 19.0165 1.08888
\(306\) 0 0
\(307\) −22.9784 −1.31144 −0.655722 0.755002i \(-0.727636\pi\)
−0.655722 + 0.755002i \(0.727636\pi\)
\(308\) 0 0
\(309\) −17.8122 −1.01330
\(310\) 0 0
\(311\) 10.1728 0.576848 0.288424 0.957503i \(-0.406869\pi\)
0.288424 + 0.957503i \(0.406869\pi\)
\(312\) 0 0
\(313\) 10.0258 0.566692 0.283346 0.959018i \(-0.408556\pi\)
0.283346 + 0.959018i \(0.408556\pi\)
\(314\) 0 0
\(315\) 12.4287 0.700275
\(316\) 0 0
\(317\) 21.3486 1.19906 0.599528 0.800354i \(-0.295355\pi\)
0.599528 + 0.800354i \(0.295355\pi\)
\(318\) 0 0
\(319\) 3.00789 0.168409
\(320\) 0 0
\(321\) 24.9868 1.39463
\(322\) 0 0
\(323\) −11.3654 −0.632387
\(324\) 0 0
\(325\) 34.9680 1.93967
\(326\) 0 0
\(327\) −1.89936 −0.105035
\(328\) 0 0
\(329\) 13.4523 0.741648
\(330\) 0 0
\(331\) 23.7276 1.30419 0.652093 0.758139i \(-0.273891\pi\)
0.652093 + 0.758139i \(0.273891\pi\)
\(332\) 0 0
\(333\) 5.56120 0.304752
\(334\) 0 0
\(335\) 7.94827 0.434261
\(336\) 0 0
\(337\) 22.0819 1.20288 0.601438 0.798919i \(-0.294595\pi\)
0.601438 + 0.798919i \(0.294595\pi\)
\(338\) 0 0
\(339\) 24.7880 1.34630
\(340\) 0 0
\(341\) −4.85118 −0.262706
\(342\) 0 0
\(343\) −10.1286 −0.546895
\(344\) 0 0
\(345\) 18.6633 1.00480
\(346\) 0 0
\(347\) 23.7902 1.27712 0.638562 0.769570i \(-0.279529\pi\)
0.638562 + 0.769570i \(0.279529\pi\)
\(348\) 0 0
\(349\) 23.9757 1.28339 0.641695 0.766960i \(-0.278232\pi\)
0.641695 + 0.766960i \(0.278232\pi\)
\(350\) 0 0
\(351\) −29.1397 −1.55536
\(352\) 0 0
\(353\) 1.63502 0.0870233 0.0435117 0.999053i \(-0.486145\pi\)
0.0435117 + 0.999053i \(0.486145\pi\)
\(354\) 0 0
\(355\) −20.7316 −1.10032
\(356\) 0 0
\(357\) −6.96942 −0.368861
\(358\) 0 0
\(359\) −12.8539 −0.678405 −0.339202 0.940713i \(-0.610157\pi\)
−0.339202 + 0.940713i \(0.610157\pi\)
\(360\) 0 0
\(361\) 36.4141 1.91653
\(362\) 0 0
\(363\) −14.4770 −0.759845
\(364\) 0 0
\(365\) 21.0926 1.10404
\(366\) 0 0
\(367\) 27.2219 1.42097 0.710486 0.703711i \(-0.248475\pi\)
0.710486 + 0.703711i \(0.248475\pi\)
\(368\) 0 0
\(369\) −1.72072 −0.0895770
\(370\) 0 0
\(371\) 12.0573 0.625984
\(372\) 0 0
\(373\) 16.3061 0.844298 0.422149 0.906527i \(-0.361276\pi\)
0.422149 + 0.906527i \(0.361276\pi\)
\(374\) 0 0
\(375\) −8.44519 −0.436108
\(376\) 0 0
\(377\) −21.6826 −1.11671
\(378\) 0 0
\(379\) −6.96706 −0.357874 −0.178937 0.983861i \(-0.557266\pi\)
−0.178937 + 0.983861i \(0.557266\pi\)
\(380\) 0 0
\(381\) 28.7471 1.47276
\(382\) 0 0
\(383\) −28.0321 −1.43238 −0.716188 0.697907i \(-0.754115\pi\)
−0.716188 + 0.697907i \(0.754115\pi\)
\(384\) 0 0
\(385\) 8.11910 0.413788
\(386\) 0 0
\(387\) 1.25262 0.0636743
\(388\) 0 0
\(389\) 25.1118 1.27322 0.636610 0.771186i \(-0.280336\pi\)
0.636610 + 0.771186i \(0.280336\pi\)
\(390\) 0 0
\(391\) 6.01420 0.304151
\(392\) 0 0
\(393\) 9.40619 0.474480
\(394\) 0 0
\(395\) −44.4918 −2.23863
\(396\) 0 0
\(397\) −13.0339 −0.654154 −0.327077 0.944998i \(-0.606064\pi\)
−0.327077 + 0.944998i \(0.606064\pi\)
\(398\) 0 0
\(399\) 33.9807 1.70116
\(400\) 0 0
\(401\) −12.2412 −0.611296 −0.305648 0.952145i \(-0.598873\pi\)
−0.305648 + 0.952145i \(0.598873\pi\)
\(402\) 0 0
\(403\) 34.9700 1.74198
\(404\) 0 0
\(405\) 15.5043 0.770414
\(406\) 0 0
\(407\) 3.63289 0.180076
\(408\) 0 0
\(409\) −5.12069 −0.253202 −0.126601 0.991954i \(-0.540407\pi\)
−0.126601 + 0.991954i \(0.540407\pi\)
\(410\) 0 0
\(411\) −18.6005 −0.917497
\(412\) 0 0
\(413\) 41.5355 2.04383
\(414\) 0 0
\(415\) −27.6763 −1.35857
\(416\) 0 0
\(417\) −16.0529 −0.786113
\(418\) 0 0
\(419\) −1.48489 −0.0725419 −0.0362709 0.999342i \(-0.511548\pi\)
−0.0362709 + 0.999342i \(0.511548\pi\)
\(420\) 0 0
\(421\) −1.32660 −0.0646545 −0.0323272 0.999477i \(-0.510292\pi\)
−0.0323272 + 0.999477i \(0.510292\pi\)
\(422\) 0 0
\(423\) −4.45337 −0.216530
\(424\) 0 0
\(425\) −10.3553 −0.502306
\(426\) 0 0
\(427\) −18.3218 −0.886655
\(428\) 0 0
\(429\) −5.08957 −0.245727
\(430\) 0 0
\(431\) 1.11034 0.0534832 0.0267416 0.999642i \(-0.491487\pi\)
0.0267416 + 0.999642i \(0.491487\pi\)
\(432\) 0 0
\(433\) −18.7731 −0.902179 −0.451089 0.892479i \(-0.648964\pi\)
−0.451089 + 0.892479i \(0.648964\pi\)
\(434\) 0 0
\(435\) 19.9257 0.955363
\(436\) 0 0
\(437\) −29.3234 −1.40273
\(438\) 0 0
\(439\) −1.77248 −0.0845960 −0.0422980 0.999105i \(-0.513468\pi\)
−0.0422980 + 0.999105i \(0.513468\pi\)
\(440\) 0 0
\(441\) −4.31078 −0.205275
\(442\) 0 0
\(443\) −23.5716 −1.11992 −0.559961 0.828519i \(-0.689184\pi\)
−0.559961 + 0.828519i \(0.689184\pi\)
\(444\) 0 0
\(445\) 53.2891 2.52615
\(446\) 0 0
\(447\) −21.6878 −1.02580
\(448\) 0 0
\(449\) 11.3934 0.537688 0.268844 0.963184i \(-0.413358\pi\)
0.268844 + 0.963184i \(0.413358\pi\)
\(450\) 0 0
\(451\) −1.12407 −0.0529304
\(452\) 0 0
\(453\) 8.46989 0.397950
\(454\) 0 0
\(455\) −58.5271 −2.74379
\(456\) 0 0
\(457\) −37.3769 −1.74842 −0.874209 0.485549i \(-0.838620\pi\)
−0.874209 + 0.485549i \(0.838620\pi\)
\(458\) 0 0
\(459\) 8.62933 0.402783
\(460\) 0 0
\(461\) 28.6343 1.33363 0.666817 0.745221i \(-0.267656\pi\)
0.666817 + 0.745221i \(0.267656\pi\)
\(462\) 0 0
\(463\) 1.79462 0.0834032 0.0417016 0.999130i \(-0.486722\pi\)
0.0417016 + 0.999130i \(0.486722\pi\)
\(464\) 0 0
\(465\) −32.1365 −1.49029
\(466\) 0 0
\(467\) 25.7225 1.19029 0.595147 0.803617i \(-0.297094\pi\)
0.595147 + 0.803617i \(0.297094\pi\)
\(468\) 0 0
\(469\) −7.65792 −0.353610
\(470\) 0 0
\(471\) 8.63379 0.397824
\(472\) 0 0
\(473\) 0.818283 0.0376247
\(474\) 0 0
\(475\) 50.4892 2.31660
\(476\) 0 0
\(477\) −3.99156 −0.182761
\(478\) 0 0
\(479\) −24.5167 −1.12020 −0.560099 0.828426i \(-0.689237\pi\)
−0.560099 + 0.828426i \(0.689237\pi\)
\(480\) 0 0
\(481\) −26.1879 −1.19407
\(482\) 0 0
\(483\) −17.9815 −0.818188
\(484\) 0 0
\(485\) −14.1869 −0.644195
\(486\) 0 0
\(487\) 1.10226 0.0499482 0.0249741 0.999688i \(-0.492050\pi\)
0.0249741 + 0.999688i \(0.492050\pi\)
\(488\) 0 0
\(489\) 34.1262 1.54324
\(490\) 0 0
\(491\) 23.1395 1.04427 0.522136 0.852862i \(-0.325135\pi\)
0.522136 + 0.852862i \(0.325135\pi\)
\(492\) 0 0
\(493\) 6.42100 0.289187
\(494\) 0 0
\(495\) −2.68782 −0.120809
\(496\) 0 0
\(497\) 19.9743 0.895969
\(498\) 0 0
\(499\) −27.4595 −1.22926 −0.614628 0.788817i \(-0.710694\pi\)
−0.614628 + 0.788817i \(0.710694\pi\)
\(500\) 0 0
\(501\) 1.01675 0.0454252
\(502\) 0 0
\(503\) 15.2079 0.678086 0.339043 0.940771i \(-0.389897\pi\)
0.339043 + 0.940771i \(0.389897\pi\)
\(504\) 0 0
\(505\) 10.5696 0.470341
\(506\) 0 0
\(507\) 18.7449 0.832491
\(508\) 0 0
\(509\) 21.6588 0.960011 0.480005 0.877266i \(-0.340635\pi\)
0.480005 + 0.877266i \(0.340635\pi\)
\(510\) 0 0
\(511\) −20.3221 −0.898996
\(512\) 0 0
\(513\) −42.0739 −1.85761
\(514\) 0 0
\(515\) 44.2966 1.95194
\(516\) 0 0
\(517\) −2.90919 −0.127946
\(518\) 0 0
\(519\) 16.6186 0.729475
\(520\) 0 0
\(521\) −23.3182 −1.02159 −0.510795 0.859703i \(-0.670649\pi\)
−0.510795 + 0.859703i \(0.670649\pi\)
\(522\) 0 0
\(523\) −11.9308 −0.521698 −0.260849 0.965380i \(-0.584002\pi\)
−0.260849 + 0.965380i \(0.584002\pi\)
\(524\) 0 0
\(525\) 30.9607 1.35124
\(526\) 0 0
\(527\) −10.3559 −0.451111
\(528\) 0 0
\(529\) −7.48300 −0.325348
\(530\) 0 0
\(531\) −13.7503 −0.596712
\(532\) 0 0
\(533\) 8.10294 0.350977
\(534\) 0 0
\(535\) −62.1388 −2.68649
\(536\) 0 0
\(537\) 18.8049 0.811492
\(538\) 0 0
\(539\) −2.81604 −0.121296
\(540\) 0 0
\(541\) −30.0986 −1.29404 −0.647021 0.762472i \(-0.723985\pi\)
−0.647021 + 0.762472i \(0.723985\pi\)
\(542\) 0 0
\(543\) 16.2006 0.695235
\(544\) 0 0
\(545\) 4.72344 0.202330
\(546\) 0 0
\(547\) −11.1630 −0.477296 −0.238648 0.971106i \(-0.576704\pi\)
−0.238648 + 0.971106i \(0.576704\pi\)
\(548\) 0 0
\(549\) 6.06542 0.258866
\(550\) 0 0
\(551\) −31.3068 −1.33371
\(552\) 0 0
\(553\) 42.8665 1.82287
\(554\) 0 0
\(555\) 24.0660 1.02154
\(556\) 0 0
\(557\) −16.1492 −0.684264 −0.342132 0.939652i \(-0.611149\pi\)
−0.342132 + 0.939652i \(0.611149\pi\)
\(558\) 0 0
\(559\) −5.89865 −0.249486
\(560\) 0 0
\(561\) 1.50721 0.0636344
\(562\) 0 0
\(563\) 2.34711 0.0989191 0.0494595 0.998776i \(-0.484250\pi\)
0.0494595 + 0.998776i \(0.484250\pi\)
\(564\) 0 0
\(565\) −61.6444 −2.59340
\(566\) 0 0
\(567\) −14.9379 −0.627333
\(568\) 0 0
\(569\) 9.18458 0.385038 0.192519 0.981293i \(-0.438334\pi\)
0.192519 + 0.981293i \(0.438334\pi\)
\(570\) 0 0
\(571\) −24.8042 −1.03802 −0.519012 0.854767i \(-0.673700\pi\)
−0.519012 + 0.854767i \(0.673700\pi\)
\(572\) 0 0
\(573\) −1.95800 −0.0817965
\(574\) 0 0
\(575\) −26.7173 −1.11419
\(576\) 0 0
\(577\) −26.8202 −1.11654 −0.558269 0.829660i \(-0.688534\pi\)
−0.558269 + 0.829660i \(0.688534\pi\)
\(578\) 0 0
\(579\) 18.6706 0.775922
\(580\) 0 0
\(581\) 26.6653 1.10626
\(582\) 0 0
\(583\) −2.60752 −0.107992
\(584\) 0 0
\(585\) 19.3753 0.801072
\(586\) 0 0
\(587\) −36.2607 −1.49664 −0.748319 0.663339i \(-0.769139\pi\)
−0.748319 + 0.663339i \(0.769139\pi\)
\(588\) 0 0
\(589\) 50.4922 2.08049
\(590\) 0 0
\(591\) −9.45918 −0.389099
\(592\) 0 0
\(593\) −13.5126 −0.554895 −0.277448 0.960741i \(-0.589489\pi\)
−0.277448 + 0.960741i \(0.589489\pi\)
\(594\) 0 0
\(595\) 17.3320 0.710543
\(596\) 0 0
\(597\) 32.9956 1.35042
\(598\) 0 0
\(599\) 26.2268 1.07160 0.535800 0.844345i \(-0.320010\pi\)
0.535800 + 0.844345i \(0.320010\pi\)
\(600\) 0 0
\(601\) −16.9506 −0.691428 −0.345714 0.938340i \(-0.612363\pi\)
−0.345714 + 0.938340i \(0.612363\pi\)
\(602\) 0 0
\(603\) 2.53515 0.103239
\(604\) 0 0
\(605\) 36.0023 1.46370
\(606\) 0 0
\(607\) −37.2591 −1.51230 −0.756149 0.654399i \(-0.772922\pi\)
−0.756149 + 0.654399i \(0.772922\pi\)
\(608\) 0 0
\(609\) −19.1978 −0.777934
\(610\) 0 0
\(611\) 20.9711 0.848400
\(612\) 0 0
\(613\) −14.4194 −0.582393 −0.291197 0.956663i \(-0.594053\pi\)
−0.291197 + 0.956663i \(0.594053\pi\)
\(614\) 0 0
\(615\) −7.44638 −0.300267
\(616\) 0 0
\(617\) 27.0114 1.08744 0.543719 0.839267i \(-0.317016\pi\)
0.543719 + 0.839267i \(0.317016\pi\)
\(618\) 0 0
\(619\) 18.4323 0.740855 0.370427 0.928861i \(-0.379211\pi\)
0.370427 + 0.928861i \(0.379211\pi\)
\(620\) 0 0
\(621\) 22.2642 0.893431
\(622\) 0 0
\(623\) −51.3425 −2.05699
\(624\) 0 0
\(625\) −12.9104 −0.516414
\(626\) 0 0
\(627\) −7.34868 −0.293478
\(628\) 0 0
\(629\) 7.75520 0.309220
\(630\) 0 0
\(631\) −2.25049 −0.0895906 −0.0447953 0.998996i \(-0.514264\pi\)
−0.0447953 + 0.998996i \(0.514264\pi\)
\(632\) 0 0
\(633\) 15.2817 0.607393
\(634\) 0 0
\(635\) −71.4902 −2.83700
\(636\) 0 0
\(637\) 20.2996 0.804301
\(638\) 0 0
\(639\) −6.61247 −0.261585
\(640\) 0 0
\(641\) 16.7234 0.660533 0.330267 0.943888i \(-0.392861\pi\)
0.330267 + 0.943888i \(0.392861\pi\)
\(642\) 0 0
\(643\) 3.08542 0.121677 0.0608386 0.998148i \(-0.480622\pi\)
0.0608386 + 0.998148i \(0.480622\pi\)
\(644\) 0 0
\(645\) 5.42070 0.213440
\(646\) 0 0
\(647\) −38.4215 −1.51050 −0.755252 0.655435i \(-0.772485\pi\)
−0.755252 + 0.655435i \(0.772485\pi\)
\(648\) 0 0
\(649\) −8.98248 −0.352593
\(650\) 0 0
\(651\) 30.9626 1.21352
\(652\) 0 0
\(653\) −3.35524 −0.131301 −0.0656503 0.997843i \(-0.520912\pi\)
−0.0656503 + 0.997843i \(0.520912\pi\)
\(654\) 0 0
\(655\) −23.3919 −0.913998
\(656\) 0 0
\(657\) 6.72761 0.262469
\(658\) 0 0
\(659\) −21.8296 −0.850359 −0.425179 0.905109i \(-0.639789\pi\)
−0.425179 + 0.905109i \(0.639789\pi\)
\(660\) 0 0
\(661\) −35.8057 −1.39268 −0.696340 0.717712i \(-0.745189\pi\)
−0.696340 + 0.717712i \(0.745189\pi\)
\(662\) 0 0
\(663\) −10.8648 −0.421954
\(664\) 0 0
\(665\) −84.5055 −3.27698
\(666\) 0 0
\(667\) 16.5666 0.641460
\(668\) 0 0
\(669\) 21.8278 0.843910
\(670\) 0 0
\(671\) 3.96228 0.152962
\(672\) 0 0
\(673\) −43.1693 −1.66406 −0.832028 0.554734i \(-0.812820\pi\)
−0.832028 + 0.554734i \(0.812820\pi\)
\(674\) 0 0
\(675\) −38.3346 −1.47550
\(676\) 0 0
\(677\) 6.38497 0.245394 0.122697 0.992444i \(-0.460846\pi\)
0.122697 + 0.992444i \(0.460846\pi\)
\(678\) 0 0
\(679\) 13.6687 0.524556
\(680\) 0 0
\(681\) −16.5291 −0.633396
\(682\) 0 0
\(683\) −19.5133 −0.746656 −0.373328 0.927699i \(-0.621783\pi\)
−0.373328 + 0.927699i \(0.621783\pi\)
\(684\) 0 0
\(685\) 46.2570 1.76739
\(686\) 0 0
\(687\) 9.61055 0.366665
\(688\) 0 0
\(689\) 18.7964 0.716088
\(690\) 0 0
\(691\) −16.9634 −0.645319 −0.322659 0.946515i \(-0.604577\pi\)
−0.322659 + 0.946515i \(0.604577\pi\)
\(692\) 0 0
\(693\) 2.58964 0.0983721
\(694\) 0 0
\(695\) 39.9214 1.51430
\(696\) 0 0
\(697\) −2.39958 −0.0908905
\(698\) 0 0
\(699\) −26.7685 −1.01248
\(700\) 0 0
\(701\) −2.32280 −0.0877311 −0.0438655 0.999037i \(-0.513967\pi\)
−0.0438655 + 0.999037i \(0.513967\pi\)
\(702\) 0 0
\(703\) −37.8120 −1.42610
\(704\) 0 0
\(705\) −19.2719 −0.725820
\(706\) 0 0
\(707\) −10.1835 −0.382989
\(708\) 0 0
\(709\) −36.4777 −1.36995 −0.684974 0.728568i \(-0.740186\pi\)
−0.684974 + 0.728568i \(0.740186\pi\)
\(710\) 0 0
\(711\) −14.1909 −0.532202
\(712\) 0 0
\(713\) −26.7189 −1.00063
\(714\) 0 0
\(715\) 12.6571 0.473348
\(716\) 0 0
\(717\) 20.8451 0.778475
\(718\) 0 0
\(719\) −8.31384 −0.310054 −0.155027 0.987910i \(-0.549546\pi\)
−0.155027 + 0.987910i \(0.549546\pi\)
\(720\) 0 0
\(721\) −42.6785 −1.58943
\(722\) 0 0
\(723\) −20.1253 −0.748469
\(724\) 0 0
\(725\) −28.5244 −1.05937
\(726\) 0 0
\(727\) 27.7570 1.02945 0.514725 0.857356i \(-0.327894\pi\)
0.514725 + 0.857356i \(0.327894\pi\)
\(728\) 0 0
\(729\) 28.3492 1.04997
\(730\) 0 0
\(731\) 1.74681 0.0646080
\(732\) 0 0
\(733\) 45.2015 1.66955 0.834777 0.550588i \(-0.185597\pi\)
0.834777 + 0.550588i \(0.185597\pi\)
\(734\) 0 0
\(735\) −18.6548 −0.688093
\(736\) 0 0
\(737\) 1.65610 0.0610034
\(738\) 0 0
\(739\) 19.7131 0.725159 0.362580 0.931953i \(-0.381896\pi\)
0.362580 + 0.931953i \(0.381896\pi\)
\(740\) 0 0
\(741\) 52.9734 1.94603
\(742\) 0 0
\(743\) 2.33662 0.0857224 0.0428612 0.999081i \(-0.486353\pi\)
0.0428612 + 0.999081i \(0.486353\pi\)
\(744\) 0 0
\(745\) 53.9346 1.97601
\(746\) 0 0
\(747\) −8.82751 −0.322982
\(748\) 0 0
\(749\) 59.8688 2.18756
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −6.52384 −0.237742
\(754\) 0 0
\(755\) −21.0635 −0.766579
\(756\) 0 0
\(757\) −35.4457 −1.28830 −0.644148 0.764901i \(-0.722788\pi\)
−0.644148 + 0.764901i \(0.722788\pi\)
\(758\) 0 0
\(759\) 3.88869 0.141150
\(760\) 0 0
\(761\) −26.7618 −0.970116 −0.485058 0.874482i \(-0.661201\pi\)
−0.485058 + 0.874482i \(0.661201\pi\)
\(762\) 0 0
\(763\) −4.55090 −0.164753
\(764\) 0 0
\(765\) −5.73775 −0.207449
\(766\) 0 0
\(767\) 64.7508 2.33801
\(768\) 0 0
\(769\) 1.18115 0.0425934 0.0212967 0.999773i \(-0.493221\pi\)
0.0212967 + 0.999773i \(0.493221\pi\)
\(770\) 0 0
\(771\) 0.130489 0.00469944
\(772\) 0 0
\(773\) 6.27705 0.225770 0.112885 0.993608i \(-0.463991\pi\)
0.112885 + 0.993608i \(0.463991\pi\)
\(774\) 0 0
\(775\) 46.0048 1.65254
\(776\) 0 0
\(777\) −23.1868 −0.831823
\(778\) 0 0
\(779\) 11.6996 0.419181
\(780\) 0 0
\(781\) −4.31964 −0.154569
\(782\) 0 0
\(783\) 23.7701 0.849475
\(784\) 0 0
\(785\) −21.4711 −0.766335
\(786\) 0 0
\(787\) −12.1036 −0.431447 −0.215724 0.976454i \(-0.569211\pi\)
−0.215724 + 0.976454i \(0.569211\pi\)
\(788\) 0 0
\(789\) 21.5510 0.767237
\(790\) 0 0
\(791\) 59.3926 2.11176
\(792\) 0 0
\(793\) −28.5623 −1.01428
\(794\) 0 0
\(795\) −17.2734 −0.612625
\(796\) 0 0
\(797\) −53.8903 −1.90889 −0.954446 0.298383i \(-0.903553\pi\)
−0.954446 + 0.298383i \(0.903553\pi\)
\(798\) 0 0
\(799\) −6.21031 −0.219705
\(800\) 0 0
\(801\) 16.9969 0.600556
\(802\) 0 0
\(803\) 4.39486 0.155091
\(804\) 0 0
\(805\) 44.7176 1.57609
\(806\) 0 0
\(807\) 16.6464 0.585981
\(808\) 0 0
\(809\) 18.4573 0.648923 0.324461 0.945899i \(-0.394817\pi\)
0.324461 + 0.945899i \(0.394817\pi\)
\(810\) 0 0
\(811\) 49.7375 1.74652 0.873260 0.487254i \(-0.162002\pi\)
0.873260 + 0.487254i \(0.162002\pi\)
\(812\) 0 0
\(813\) −6.65694 −0.233469
\(814\) 0 0
\(815\) −84.8673 −2.97277
\(816\) 0 0
\(817\) −8.51688 −0.297968
\(818\) 0 0
\(819\) −18.6676 −0.652297
\(820\) 0 0
\(821\) 40.4080 1.41025 0.705125 0.709083i \(-0.250891\pi\)
0.705125 + 0.709083i \(0.250891\pi\)
\(822\) 0 0
\(823\) 28.5688 0.995845 0.497923 0.867221i \(-0.334096\pi\)
0.497923 + 0.867221i \(0.334096\pi\)
\(824\) 0 0
\(825\) −6.69557 −0.233110
\(826\) 0 0
\(827\) 15.8368 0.550698 0.275349 0.961344i \(-0.411207\pi\)
0.275349 + 0.961344i \(0.411207\pi\)
\(828\) 0 0
\(829\) 27.5314 0.956204 0.478102 0.878304i \(-0.341325\pi\)
0.478102 + 0.878304i \(0.341325\pi\)
\(830\) 0 0
\(831\) −14.9645 −0.519114
\(832\) 0 0
\(833\) −6.01147 −0.208285
\(834\) 0 0
\(835\) −2.52853 −0.0875033
\(836\) 0 0
\(837\) −38.3369 −1.32512
\(838\) 0 0
\(839\) −2.77127 −0.0956750 −0.0478375 0.998855i \(-0.515233\pi\)
−0.0478375 + 0.998855i \(0.515233\pi\)
\(840\) 0 0
\(841\) −11.3129 −0.390099
\(842\) 0 0
\(843\) −15.9978 −0.550994
\(844\) 0 0
\(845\) −46.6161 −1.60364
\(846\) 0 0
\(847\) −34.6872 −1.19187
\(848\) 0 0
\(849\) −16.8806 −0.579340
\(850\) 0 0
\(851\) 20.0089 0.685896
\(852\) 0 0
\(853\) 3.26328 0.111733 0.0558664 0.998438i \(-0.482208\pi\)
0.0558664 + 0.998438i \(0.482208\pi\)
\(854\) 0 0
\(855\) 27.9755 0.956742
\(856\) 0 0
\(857\) 2.70878 0.0925301 0.0462650 0.998929i \(-0.485268\pi\)
0.0462650 + 0.998929i \(0.485268\pi\)
\(858\) 0 0
\(859\) 38.1510 1.30170 0.650848 0.759208i \(-0.274414\pi\)
0.650848 + 0.759208i \(0.274414\pi\)
\(860\) 0 0
\(861\) 7.17436 0.244502
\(862\) 0 0
\(863\) −3.41001 −0.116078 −0.0580391 0.998314i \(-0.518485\pi\)
−0.0580391 + 0.998314i \(0.518485\pi\)
\(864\) 0 0
\(865\) −41.3282 −1.40520
\(866\) 0 0
\(867\) −20.2472 −0.687632
\(868\) 0 0
\(869\) −9.27032 −0.314474
\(870\) 0 0
\(871\) −11.9381 −0.404508
\(872\) 0 0
\(873\) −4.52501 −0.153148
\(874\) 0 0
\(875\) −20.2348 −0.684063
\(876\) 0 0
\(877\) 18.6335 0.629210 0.314605 0.949223i \(-0.398128\pi\)
0.314605 + 0.949223i \(0.398128\pi\)
\(878\) 0 0
\(879\) 16.4136 0.553617
\(880\) 0 0
\(881\) 37.7308 1.27118 0.635592 0.772025i \(-0.280756\pi\)
0.635592 + 0.772025i \(0.280756\pi\)
\(882\) 0 0
\(883\) −12.9761 −0.436681 −0.218340 0.975873i \(-0.570064\pi\)
−0.218340 + 0.975873i \(0.570064\pi\)
\(884\) 0 0
\(885\) −59.5042 −2.00021
\(886\) 0 0
\(887\) −47.7085 −1.60190 −0.800948 0.598734i \(-0.795671\pi\)
−0.800948 + 0.598734i \(0.795671\pi\)
\(888\) 0 0
\(889\) 68.8786 2.31012
\(890\) 0 0
\(891\) 3.23047 0.108225
\(892\) 0 0
\(893\) 30.2795 1.01327
\(894\) 0 0
\(895\) −46.7653 −1.56319
\(896\) 0 0
\(897\) −28.0319 −0.935957
\(898\) 0 0
\(899\) −28.5261 −0.951399
\(900\) 0 0
\(901\) −5.56632 −0.185441
\(902\) 0 0
\(903\) −5.22268 −0.173800
\(904\) 0 0
\(905\) −40.2887 −1.33924
\(906\) 0 0
\(907\) 40.5414 1.34615 0.673077 0.739572i \(-0.264972\pi\)
0.673077 + 0.739572i \(0.264972\pi\)
\(908\) 0 0
\(909\) 3.37124 0.111817
\(910\) 0 0
\(911\) −31.0323 −1.02815 −0.514073 0.857747i \(-0.671864\pi\)
−0.514073 + 0.857747i \(0.671864\pi\)
\(912\) 0 0
\(913\) −5.76663 −0.190848
\(914\) 0 0
\(915\) 26.2480 0.867733
\(916\) 0 0
\(917\) 22.5374 0.744251
\(918\) 0 0
\(919\) 49.2321 1.62402 0.812009 0.583644i \(-0.198374\pi\)
0.812009 + 0.583644i \(0.198374\pi\)
\(920\) 0 0
\(921\) −31.7165 −1.04509
\(922\) 0 0
\(923\) 31.1384 1.02493
\(924\) 0 0
\(925\) −34.4515 −1.13276
\(926\) 0 0
\(927\) 14.1287 0.464047
\(928\) 0 0
\(929\) −46.5816 −1.52829 −0.764146 0.645043i \(-0.776839\pi\)
−0.764146 + 0.645043i \(0.776839\pi\)
\(930\) 0 0
\(931\) 29.3100 0.960598
\(932\) 0 0
\(933\) 14.0413 0.459692
\(934\) 0 0
\(935\) −3.74823 −0.122580
\(936\) 0 0
\(937\) −35.6760 −1.16548 −0.582742 0.812657i \(-0.698020\pi\)
−0.582742 + 0.812657i \(0.698020\pi\)
\(938\) 0 0
\(939\) 13.8384 0.451598
\(940\) 0 0
\(941\) 42.4784 1.38476 0.692379 0.721534i \(-0.256563\pi\)
0.692379 + 0.721534i \(0.256563\pi\)
\(942\) 0 0
\(943\) −6.19105 −0.201608
\(944\) 0 0
\(945\) 64.1619 2.08719
\(946\) 0 0
\(947\) 36.4930 1.18586 0.592932 0.805252i \(-0.297970\pi\)
0.592932 + 0.805252i \(0.297970\pi\)
\(948\) 0 0
\(949\) −31.6806 −1.02840
\(950\) 0 0
\(951\) 29.4669 0.955531
\(952\) 0 0
\(953\) 41.3087 1.33812 0.669061 0.743208i \(-0.266697\pi\)
0.669061 + 0.743208i \(0.266697\pi\)
\(954\) 0 0
\(955\) 4.86928 0.157566
\(956\) 0 0
\(957\) 4.15172 0.134206
\(958\) 0 0
\(959\) −44.5672 −1.43915
\(960\) 0 0
\(961\) 15.0075 0.484112
\(962\) 0 0
\(963\) −19.8195 −0.638676
\(964\) 0 0
\(965\) −46.4312 −1.49467
\(966\) 0 0
\(967\) 22.5504 0.725172 0.362586 0.931950i \(-0.381894\pi\)
0.362586 + 0.931950i \(0.381894\pi\)
\(968\) 0 0
\(969\) −15.6874 −0.503951
\(970\) 0 0
\(971\) −33.4442 −1.07328 −0.536638 0.843813i \(-0.680306\pi\)
−0.536638 + 0.843813i \(0.680306\pi\)
\(972\) 0 0
\(973\) −38.4630 −1.23307
\(974\) 0 0
\(975\) 48.2655 1.54573
\(976\) 0 0
\(977\) −35.1927 −1.12591 −0.562957 0.826486i \(-0.690336\pi\)
−0.562957 + 0.826486i \(0.690336\pi\)
\(978\) 0 0
\(979\) 11.1033 0.354864
\(980\) 0 0
\(981\) 1.50657 0.0481011
\(982\) 0 0
\(983\) 6.33888 0.202179 0.101089 0.994877i \(-0.467767\pi\)
0.101089 + 0.994877i \(0.467767\pi\)
\(984\) 0 0
\(985\) 23.5237 0.749528
\(986\) 0 0
\(987\) 18.5679 0.591021
\(988\) 0 0
\(989\) 4.50686 0.143310
\(990\) 0 0
\(991\) −32.1283 −1.02059 −0.510294 0.860000i \(-0.670463\pi\)
−0.510294 + 0.860000i \(0.670463\pi\)
\(992\) 0 0
\(993\) 32.7506 1.03931
\(994\) 0 0
\(995\) −82.0555 −2.60133
\(996\) 0 0
\(997\) 14.6952 0.465402 0.232701 0.972548i \(-0.425244\pi\)
0.232701 + 0.972548i \(0.425244\pi\)
\(998\) 0 0
\(999\) 28.7092 0.908320
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 \(a_p\))