Properties

Label 6008.2.a.e.1.35
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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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 1.35
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.61660 q^{3} -2.04999 q^{5} -3.31441 q^{7} -0.386600 q^{9} +O(q^{10})\) \(q+1.61660 q^{3} -2.04999 q^{5} -3.31441 q^{7} -0.386600 q^{9} -2.70219 q^{11} -2.54782 q^{13} -3.31402 q^{15} -6.55636 q^{17} +7.23359 q^{19} -5.35808 q^{21} +2.74290 q^{23} -0.797524 q^{25} -5.47478 q^{27} -5.48790 q^{29} +7.20213 q^{31} -4.36837 q^{33} +6.79451 q^{35} +3.67337 q^{37} -4.11881 q^{39} -8.99074 q^{41} +11.5595 q^{43} +0.792527 q^{45} -1.90614 q^{47} +3.98529 q^{49} -10.5990 q^{51} -3.98817 q^{53} +5.53948 q^{55} +11.6938 q^{57} -4.53997 q^{59} +11.9172 q^{61} +1.28135 q^{63} +5.22301 q^{65} -4.99427 q^{67} +4.43417 q^{69} +9.44385 q^{71} +4.74839 q^{73} -1.28928 q^{75} +8.95617 q^{77} +5.82553 q^{79} -7.69074 q^{81} -16.6455 q^{83} +13.4405 q^{85} -8.87175 q^{87} -7.87937 q^{89} +8.44451 q^{91} +11.6430 q^{93} -14.8288 q^{95} +17.2804 q^{97} +1.04467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 1.61660 0.933345 0.466673 0.884430i \(-0.345453\pi\)
0.466673 + 0.884430i \(0.345453\pi\)
\(4\) 0 0
\(5\) −2.04999 −0.916785 −0.458393 0.888750i \(-0.651575\pi\)
−0.458393 + 0.888750i \(0.651575\pi\)
\(6\) 0 0
\(7\) −3.31441 −1.25273 −0.626364 0.779531i \(-0.715458\pi\)
−0.626364 + 0.779531i \(0.715458\pi\)
\(8\) 0 0
\(9\) −0.386600 −0.128867
\(10\) 0 0
\(11\) −2.70219 −0.814742 −0.407371 0.913263i \(-0.633554\pi\)
−0.407371 + 0.913263i \(0.633554\pi\)
\(12\) 0 0
\(13\) −2.54782 −0.706638 −0.353319 0.935503i \(-0.614947\pi\)
−0.353319 + 0.935503i \(0.614947\pi\)
\(14\) 0 0
\(15\) −3.31402 −0.855677
\(16\) 0 0
\(17\) −6.55636 −1.59015 −0.795075 0.606511i \(-0.792569\pi\)
−0.795075 + 0.606511i \(0.792569\pi\)
\(18\) 0 0
\(19\) 7.23359 1.65950 0.829749 0.558136i \(-0.188483\pi\)
0.829749 + 0.558136i \(0.188483\pi\)
\(20\) 0 0
\(21\) −5.35808 −1.16923
\(22\) 0 0
\(23\) 2.74290 0.571934 0.285967 0.958240i \(-0.407685\pi\)
0.285967 + 0.958240i \(0.407685\pi\)
\(24\) 0 0
\(25\) −0.797524 −0.159505
\(26\) 0 0
\(27\) −5.47478 −1.05362
\(28\) 0 0
\(29\) −5.48790 −1.01908 −0.509539 0.860448i \(-0.670184\pi\)
−0.509539 + 0.860448i \(0.670184\pi\)
\(30\) 0 0
\(31\) 7.20213 1.29354 0.646771 0.762684i \(-0.276119\pi\)
0.646771 + 0.762684i \(0.276119\pi\)
\(32\) 0 0
\(33\) −4.36837 −0.760435
\(34\) 0 0
\(35\) 6.79451 1.14848
\(36\) 0 0
\(37\) 3.67337 0.603898 0.301949 0.953324i \(-0.402363\pi\)
0.301949 + 0.953324i \(0.402363\pi\)
\(38\) 0 0
\(39\) −4.11881 −0.659537
\(40\) 0 0
\(41\) −8.99074 −1.40412 −0.702058 0.712119i \(-0.747735\pi\)
−0.702058 + 0.712119i \(0.747735\pi\)
\(42\) 0 0
\(43\) 11.5595 1.76281 0.881404 0.472363i \(-0.156599\pi\)
0.881404 + 0.472363i \(0.156599\pi\)
\(44\) 0 0
\(45\) 0.792527 0.118143
\(46\) 0 0
\(47\) −1.90614 −0.278040 −0.139020 0.990290i \(-0.544395\pi\)
−0.139020 + 0.990290i \(0.544395\pi\)
\(48\) 0 0
\(49\) 3.98529 0.569327
\(50\) 0 0
\(51\) −10.5990 −1.48416
\(52\) 0 0
\(53\) −3.98817 −0.547818 −0.273909 0.961756i \(-0.588317\pi\)
−0.273909 + 0.961756i \(0.588317\pi\)
\(54\) 0 0
\(55\) 5.53948 0.746943
\(56\) 0 0
\(57\) 11.6938 1.54889
\(58\) 0 0
\(59\) −4.53997 −0.591054 −0.295527 0.955334i \(-0.595495\pi\)
−0.295527 + 0.955334i \(0.595495\pi\)
\(60\) 0 0
\(61\) 11.9172 1.52584 0.762919 0.646494i \(-0.223766\pi\)
0.762919 + 0.646494i \(0.223766\pi\)
\(62\) 0 0
\(63\) 1.28135 0.161435
\(64\) 0 0
\(65\) 5.22301 0.647835
\(66\) 0 0
\(67\) −4.99427 −0.610147 −0.305073 0.952329i \(-0.598681\pi\)
−0.305073 + 0.952329i \(0.598681\pi\)
\(68\) 0 0
\(69\) 4.43417 0.533812
\(70\) 0 0
\(71\) 9.44385 1.12078 0.560389 0.828229i \(-0.310652\pi\)
0.560389 + 0.828229i \(0.310652\pi\)
\(72\) 0 0
\(73\) 4.74839 0.555757 0.277879 0.960616i \(-0.410369\pi\)
0.277879 + 0.960616i \(0.410369\pi\)
\(74\) 0 0
\(75\) −1.28928 −0.148873
\(76\) 0 0
\(77\) 8.95617 1.02065
\(78\) 0 0
\(79\) 5.82553 0.655423 0.327712 0.944778i \(-0.393723\pi\)
0.327712 + 0.944778i \(0.393723\pi\)
\(80\) 0 0
\(81\) −7.69074 −0.854527
\(82\) 0 0
\(83\) −16.6455 −1.82709 −0.913543 0.406742i \(-0.866665\pi\)
−0.913543 + 0.406742i \(0.866665\pi\)
\(84\) 0 0
\(85\) 13.4405 1.45783
\(86\) 0 0
\(87\) −8.87175 −0.951152
\(88\) 0 0
\(89\) −7.87937 −0.835212 −0.417606 0.908628i \(-0.637131\pi\)
−0.417606 + 0.908628i \(0.637131\pi\)
\(90\) 0 0
\(91\) 8.44451 0.885225
\(92\) 0 0
\(93\) 11.6430 1.20732
\(94\) 0 0
\(95\) −14.8288 −1.52140
\(96\) 0 0
\(97\) 17.2804 1.75456 0.877282 0.479976i \(-0.159354\pi\)
0.877282 + 0.479976i \(0.159354\pi\)
\(98\) 0 0
\(99\) 1.04467 0.104993
\(100\) 0 0
\(101\) 3.49106 0.347373 0.173687 0.984801i \(-0.444432\pi\)
0.173687 + 0.984801i \(0.444432\pi\)
\(102\) 0 0
\(103\) 16.0886 1.58526 0.792631 0.609702i \(-0.208711\pi\)
0.792631 + 0.609702i \(0.208711\pi\)
\(104\) 0 0
\(105\) 10.9840 1.07193
\(106\) 0 0
\(107\) −5.25993 −0.508497 −0.254249 0.967139i \(-0.581828\pi\)
−0.254249 + 0.967139i \(0.581828\pi\)
\(108\) 0 0
\(109\) −15.0242 −1.43906 −0.719530 0.694461i \(-0.755643\pi\)
−0.719530 + 0.694461i \(0.755643\pi\)
\(110\) 0 0
\(111\) 5.93837 0.563645
\(112\) 0 0
\(113\) 9.52896 0.896410 0.448205 0.893931i \(-0.352064\pi\)
0.448205 + 0.893931i \(0.352064\pi\)
\(114\) 0 0
\(115\) −5.62292 −0.524340
\(116\) 0 0
\(117\) 0.984986 0.0910619
\(118\) 0 0
\(119\) 21.7304 1.99203
\(120\) 0 0
\(121\) −3.69815 −0.336196
\(122\) 0 0
\(123\) −14.5344 −1.31053
\(124\) 0 0
\(125\) 11.8849 1.06302
\(126\) 0 0
\(127\) −1.54355 −0.136968 −0.0684841 0.997652i \(-0.521816\pi\)
−0.0684841 + 0.997652i \(0.521816\pi\)
\(128\) 0 0
\(129\) 18.6871 1.64531
\(130\) 0 0
\(131\) 15.1053 1.31976 0.659880 0.751371i \(-0.270607\pi\)
0.659880 + 0.751371i \(0.270607\pi\)
\(132\) 0 0
\(133\) −23.9750 −2.07890
\(134\) 0 0
\(135\) 11.2233 0.965945
\(136\) 0 0
\(137\) 4.20609 0.359350 0.179675 0.983726i \(-0.442495\pi\)
0.179675 + 0.983726i \(0.442495\pi\)
\(138\) 0 0
\(139\) −3.70026 −0.313852 −0.156926 0.987610i \(-0.550158\pi\)
−0.156926 + 0.987610i \(0.550158\pi\)
\(140\) 0 0
\(141\) −3.08148 −0.259507
\(142\) 0 0
\(143\) 6.88470 0.575727
\(144\) 0 0
\(145\) 11.2502 0.934276
\(146\) 0 0
\(147\) 6.44263 0.531379
\(148\) 0 0
\(149\) 15.0949 1.23662 0.618309 0.785935i \(-0.287818\pi\)
0.618309 + 0.785935i \(0.287818\pi\)
\(150\) 0 0
\(151\) 18.0387 1.46797 0.733983 0.679168i \(-0.237659\pi\)
0.733983 + 0.679168i \(0.237659\pi\)
\(152\) 0 0
\(153\) 2.53468 0.204917
\(154\) 0 0
\(155\) −14.7643 −1.18590
\(156\) 0 0
\(157\) 8.07079 0.644119 0.322060 0.946719i \(-0.395625\pi\)
0.322060 + 0.946719i \(0.395625\pi\)
\(158\) 0 0
\(159\) −6.44729 −0.511303
\(160\) 0 0
\(161\) −9.09108 −0.716477
\(162\) 0 0
\(163\) 12.2448 0.959088 0.479544 0.877518i \(-0.340802\pi\)
0.479544 + 0.877518i \(0.340802\pi\)
\(164\) 0 0
\(165\) 8.95513 0.697156
\(166\) 0 0
\(167\) −5.48478 −0.424425 −0.212213 0.977224i \(-0.568067\pi\)
−0.212213 + 0.977224i \(0.568067\pi\)
\(168\) 0 0
\(169\) −6.50862 −0.500663
\(170\) 0 0
\(171\) −2.79650 −0.213854
\(172\) 0 0
\(173\) 13.0680 0.993541 0.496771 0.867882i \(-0.334519\pi\)
0.496771 + 0.867882i \(0.334519\pi\)
\(174\) 0 0
\(175\) 2.64332 0.199816
\(176\) 0 0
\(177\) −7.33932 −0.551657
\(178\) 0 0
\(179\) −12.2795 −0.917813 −0.458907 0.888484i \(-0.651759\pi\)
−0.458907 + 0.888484i \(0.651759\pi\)
\(180\) 0 0
\(181\) −22.9869 −1.70860 −0.854301 0.519778i \(-0.826015\pi\)
−0.854301 + 0.519778i \(0.826015\pi\)
\(182\) 0 0
\(183\) 19.2653 1.42413
\(184\) 0 0
\(185\) −7.53038 −0.553645
\(186\) 0 0
\(187\) 17.7165 1.29556
\(188\) 0 0
\(189\) 18.1457 1.31990
\(190\) 0 0
\(191\) 23.4040 1.69345 0.846727 0.532027i \(-0.178570\pi\)
0.846727 + 0.532027i \(0.178570\pi\)
\(192\) 0 0
\(193\) −19.1512 −1.37853 −0.689266 0.724508i \(-0.742067\pi\)
−0.689266 + 0.724508i \(0.742067\pi\)
\(194\) 0 0
\(195\) 8.44353 0.604654
\(196\) 0 0
\(197\) −4.19224 −0.298685 −0.149342 0.988786i \(-0.547716\pi\)
−0.149342 + 0.988786i \(0.547716\pi\)
\(198\) 0 0
\(199\) −20.8199 −1.47588 −0.737941 0.674865i \(-0.764202\pi\)
−0.737941 + 0.674865i \(0.764202\pi\)
\(200\) 0 0
\(201\) −8.07374 −0.569477
\(202\) 0 0
\(203\) 18.1891 1.27663
\(204\) 0 0
\(205\) 18.4310 1.28727
\(206\) 0 0
\(207\) −1.06040 −0.0737031
\(208\) 0 0
\(209\) −19.5465 −1.35206
\(210\) 0 0
\(211\) −5.75813 −0.396406 −0.198203 0.980161i \(-0.563511\pi\)
−0.198203 + 0.980161i \(0.563511\pi\)
\(212\) 0 0
\(213\) 15.2669 1.04607
\(214\) 0 0
\(215\) −23.6969 −1.61612
\(216\) 0 0
\(217\) −23.8708 −1.62046
\(218\) 0 0
\(219\) 7.67626 0.518714
\(220\) 0 0
\(221\) 16.7044 1.12366
\(222\) 0 0
\(223\) −0.927334 −0.0620989 −0.0310494 0.999518i \(-0.509885\pi\)
−0.0310494 + 0.999518i \(0.509885\pi\)
\(224\) 0 0
\(225\) 0.308322 0.0205548
\(226\) 0 0
\(227\) 6.06352 0.402450 0.201225 0.979545i \(-0.435508\pi\)
0.201225 + 0.979545i \(0.435508\pi\)
\(228\) 0 0
\(229\) 27.8171 1.83820 0.919102 0.394020i \(-0.128916\pi\)
0.919102 + 0.394020i \(0.128916\pi\)
\(230\) 0 0
\(231\) 14.4786 0.952619
\(232\) 0 0
\(233\) 27.7198 1.81599 0.907993 0.418984i \(-0.137614\pi\)
0.907993 + 0.418984i \(0.137614\pi\)
\(234\) 0 0
\(235\) 3.90759 0.254903
\(236\) 0 0
\(237\) 9.41756 0.611736
\(238\) 0 0
\(239\) 4.42799 0.286423 0.143212 0.989692i \(-0.454257\pi\)
0.143212 + 0.989692i \(0.454257\pi\)
\(240\) 0 0
\(241\) −10.8707 −0.700243 −0.350121 0.936704i \(-0.613860\pi\)
−0.350121 + 0.936704i \(0.613860\pi\)
\(242\) 0 0
\(243\) 3.99148 0.256054
\(244\) 0 0
\(245\) −8.16983 −0.521951
\(246\) 0 0
\(247\) −18.4299 −1.17266
\(248\) 0 0
\(249\) −26.9092 −1.70530
\(250\) 0 0
\(251\) −14.9029 −0.940664 −0.470332 0.882490i \(-0.655866\pi\)
−0.470332 + 0.882490i \(0.655866\pi\)
\(252\) 0 0
\(253\) −7.41184 −0.465978
\(254\) 0 0
\(255\) 21.7279 1.36066
\(256\) 0 0
\(257\) −25.1208 −1.56699 −0.783497 0.621395i \(-0.786566\pi\)
−0.783497 + 0.621395i \(0.786566\pi\)
\(258\) 0 0
\(259\) −12.1750 −0.756520
\(260\) 0 0
\(261\) 2.12162 0.131325
\(262\) 0 0
\(263\) 7.65430 0.471984 0.235992 0.971755i \(-0.424166\pi\)
0.235992 + 0.971755i \(0.424166\pi\)
\(264\) 0 0
\(265\) 8.17573 0.502231
\(266\) 0 0
\(267\) −12.7378 −0.779541
\(268\) 0 0
\(269\) 18.1152 1.10450 0.552251 0.833678i \(-0.313769\pi\)
0.552251 + 0.833678i \(0.313769\pi\)
\(270\) 0 0
\(271\) 2.71643 0.165011 0.0825057 0.996591i \(-0.473708\pi\)
0.0825057 + 0.996591i \(0.473708\pi\)
\(272\) 0 0
\(273\) 13.6514 0.826220
\(274\) 0 0
\(275\) 2.15506 0.129955
\(276\) 0 0
\(277\) −2.94112 −0.176715 −0.0883573 0.996089i \(-0.528162\pi\)
−0.0883573 + 0.996089i \(0.528162\pi\)
\(278\) 0 0
\(279\) −2.78434 −0.166694
\(280\) 0 0
\(281\) 31.4638 1.87697 0.938487 0.345313i \(-0.112227\pi\)
0.938487 + 0.345313i \(0.112227\pi\)
\(282\) 0 0
\(283\) 25.4770 1.51445 0.757226 0.653153i \(-0.226554\pi\)
0.757226 + 0.653153i \(0.226554\pi\)
\(284\) 0 0
\(285\) −23.9723 −1.42000
\(286\) 0 0
\(287\) 29.7990 1.75898
\(288\) 0 0
\(289\) 25.9858 1.52858
\(290\) 0 0
\(291\) 27.9356 1.63761
\(292\) 0 0
\(293\) −2.07049 −0.120959 −0.0604796 0.998169i \(-0.519263\pi\)
−0.0604796 + 0.998169i \(0.519263\pi\)
\(294\) 0 0
\(295\) 9.30691 0.541869
\(296\) 0 0
\(297\) 14.7939 0.858430
\(298\) 0 0
\(299\) −6.98840 −0.404150
\(300\) 0 0
\(301\) −38.3129 −2.20832
\(302\) 0 0
\(303\) 5.64365 0.324219
\(304\) 0 0
\(305\) −24.4301 −1.39887
\(306\) 0 0
\(307\) −4.53913 −0.259062 −0.129531 0.991575i \(-0.541347\pi\)
−0.129531 + 0.991575i \(0.541347\pi\)
\(308\) 0 0
\(309\) 26.0089 1.47960
\(310\) 0 0
\(311\) −18.5129 −1.04977 −0.524885 0.851173i \(-0.675892\pi\)
−0.524885 + 0.851173i \(0.675892\pi\)
\(312\) 0 0
\(313\) 23.5749 1.33253 0.666265 0.745715i \(-0.267892\pi\)
0.666265 + 0.745715i \(0.267892\pi\)
\(314\) 0 0
\(315\) −2.62676 −0.148001
\(316\) 0 0
\(317\) −19.6279 −1.10242 −0.551208 0.834368i \(-0.685833\pi\)
−0.551208 + 0.834368i \(0.685833\pi\)
\(318\) 0 0
\(319\) 14.8294 0.830285
\(320\) 0 0
\(321\) −8.50322 −0.474603
\(322\) 0 0
\(323\) −47.4260 −2.63885
\(324\) 0 0
\(325\) 2.03195 0.112712
\(326\) 0 0
\(327\) −24.2882 −1.34314
\(328\) 0 0
\(329\) 6.31774 0.348308
\(330\) 0 0
\(331\) 3.19153 0.175422 0.0877112 0.996146i \(-0.472045\pi\)
0.0877112 + 0.996146i \(0.472045\pi\)
\(332\) 0 0
\(333\) −1.42012 −0.0778222
\(334\) 0 0
\(335\) 10.2382 0.559373
\(336\) 0 0
\(337\) −29.9156 −1.62961 −0.814804 0.579736i \(-0.803156\pi\)
−0.814804 + 0.579736i \(0.803156\pi\)
\(338\) 0 0
\(339\) 15.4045 0.836660
\(340\) 0 0
\(341\) −19.4616 −1.05390
\(342\) 0 0
\(343\) 9.99197 0.539516
\(344\) 0 0
\(345\) −9.09003 −0.489391
\(346\) 0 0
\(347\) −19.0454 −1.02241 −0.511205 0.859459i \(-0.670801\pi\)
−0.511205 + 0.859459i \(0.670801\pi\)
\(348\) 0 0
\(349\) −32.6177 −1.74599 −0.872993 0.487734i \(-0.837824\pi\)
−0.872993 + 0.487734i \(0.837824\pi\)
\(350\) 0 0
\(351\) 13.9488 0.744529
\(352\) 0 0
\(353\) 13.8073 0.734890 0.367445 0.930045i \(-0.380233\pi\)
0.367445 + 0.930045i \(0.380233\pi\)
\(354\) 0 0
\(355\) −19.3598 −1.02751
\(356\) 0 0
\(357\) 35.1294 1.85925
\(358\) 0 0
\(359\) −2.43331 −0.128425 −0.0642125 0.997936i \(-0.520454\pi\)
−0.0642125 + 0.997936i \(0.520454\pi\)
\(360\) 0 0
\(361\) 33.3248 1.75394
\(362\) 0 0
\(363\) −5.97844 −0.313787
\(364\) 0 0
\(365\) −9.73418 −0.509510
\(366\) 0 0
\(367\) −25.2729 −1.31923 −0.659616 0.751603i \(-0.729281\pi\)
−0.659616 + 0.751603i \(0.729281\pi\)
\(368\) 0 0
\(369\) 3.47581 0.180944
\(370\) 0 0
\(371\) 13.2184 0.686267
\(372\) 0 0
\(373\) 18.7704 0.971893 0.485947 0.873988i \(-0.338475\pi\)
0.485947 + 0.873988i \(0.338475\pi\)
\(374\) 0 0
\(375\) 19.2131 0.992162
\(376\) 0 0
\(377\) 13.9822 0.720119
\(378\) 0 0
\(379\) −6.93082 −0.356012 −0.178006 0.984029i \(-0.556965\pi\)
−0.178006 + 0.984029i \(0.556965\pi\)
\(380\) 0 0
\(381\) −2.49531 −0.127839
\(382\) 0 0
\(383\) 20.0711 1.02558 0.512792 0.858513i \(-0.328611\pi\)
0.512792 + 0.858513i \(0.328611\pi\)
\(384\) 0 0
\(385\) −18.3601 −0.935717
\(386\) 0 0
\(387\) −4.46890 −0.227167
\(388\) 0 0
\(389\) −30.0653 −1.52437 −0.762186 0.647358i \(-0.775874\pi\)
−0.762186 + 0.647358i \(0.775874\pi\)
\(390\) 0 0
\(391\) −17.9834 −0.909460
\(392\) 0 0
\(393\) 24.4193 1.23179
\(394\) 0 0
\(395\) −11.9423 −0.600882
\(396\) 0 0
\(397\) 24.7771 1.24353 0.621764 0.783204i \(-0.286416\pi\)
0.621764 + 0.783204i \(0.286416\pi\)
\(398\) 0 0
\(399\) −38.7581 −1.94033
\(400\) 0 0
\(401\) −25.6540 −1.28110 −0.640549 0.767917i \(-0.721293\pi\)
−0.640549 + 0.767917i \(0.721293\pi\)
\(402\) 0 0
\(403\) −18.3497 −0.914065
\(404\) 0 0
\(405\) 15.7660 0.783418
\(406\) 0 0
\(407\) −9.92615 −0.492021
\(408\) 0 0
\(409\) −6.42085 −0.317490 −0.158745 0.987320i \(-0.550745\pi\)
−0.158745 + 0.987320i \(0.550745\pi\)
\(410\) 0 0
\(411\) 6.79957 0.335398
\(412\) 0 0
\(413\) 15.0473 0.740429
\(414\) 0 0
\(415\) 34.1233 1.67505
\(416\) 0 0
\(417\) −5.98184 −0.292932
\(418\) 0 0
\(419\) 19.2524 0.940540 0.470270 0.882523i \(-0.344156\pi\)
0.470270 + 0.882523i \(0.344156\pi\)
\(420\) 0 0
\(421\) −36.7613 −1.79164 −0.895819 0.444419i \(-0.853410\pi\)
−0.895819 + 0.444419i \(0.853410\pi\)
\(422\) 0 0
\(423\) 0.736915 0.0358300
\(424\) 0 0
\(425\) 5.22885 0.253636
\(426\) 0 0
\(427\) −39.4984 −1.91146
\(428\) 0 0
\(429\) 11.1298 0.537352
\(430\) 0 0
\(431\) −6.75491 −0.325372 −0.162686 0.986678i \(-0.552016\pi\)
−0.162686 + 0.986678i \(0.552016\pi\)
\(432\) 0 0
\(433\) 4.54679 0.218505 0.109252 0.994014i \(-0.465154\pi\)
0.109252 + 0.994014i \(0.465154\pi\)
\(434\) 0 0
\(435\) 18.1870 0.872002
\(436\) 0 0
\(437\) 19.8410 0.949123
\(438\) 0 0
\(439\) −11.2422 −0.536562 −0.268281 0.963341i \(-0.586455\pi\)
−0.268281 + 0.963341i \(0.586455\pi\)
\(440\) 0 0
\(441\) −1.54071 −0.0733672
\(442\) 0 0
\(443\) 6.93494 0.329489 0.164744 0.986336i \(-0.447320\pi\)
0.164744 + 0.986336i \(0.447320\pi\)
\(444\) 0 0
\(445\) 16.1527 0.765710
\(446\) 0 0
\(447\) 24.4024 1.15419
\(448\) 0 0
\(449\) 14.6313 0.690495 0.345248 0.938512i \(-0.387795\pi\)
0.345248 + 0.938512i \(0.387795\pi\)
\(450\) 0 0
\(451\) 24.2947 1.14399
\(452\) 0 0
\(453\) 29.1613 1.37012
\(454\) 0 0
\(455\) −17.3112 −0.811561
\(456\) 0 0
\(457\) −3.79139 −0.177354 −0.0886768 0.996060i \(-0.528264\pi\)
−0.0886768 + 0.996060i \(0.528264\pi\)
\(458\) 0 0
\(459\) 35.8946 1.67542
\(460\) 0 0
\(461\) −7.87884 −0.366954 −0.183477 0.983024i \(-0.558735\pi\)
−0.183477 + 0.983024i \(0.558735\pi\)
\(462\) 0 0
\(463\) 24.2679 1.12783 0.563913 0.825834i \(-0.309295\pi\)
0.563913 + 0.825834i \(0.309295\pi\)
\(464\) 0 0
\(465\) −23.8680 −1.10685
\(466\) 0 0
\(467\) 41.8618 1.93713 0.968567 0.248754i \(-0.0800212\pi\)
0.968567 + 0.248754i \(0.0800212\pi\)
\(468\) 0 0
\(469\) 16.5530 0.764348
\(470\) 0 0
\(471\) 13.0473 0.601186
\(472\) 0 0
\(473\) −31.2360 −1.43623
\(474\) 0 0
\(475\) −5.76896 −0.264698
\(476\) 0 0
\(477\) 1.54183 0.0705954
\(478\) 0 0
\(479\) −36.0167 −1.64564 −0.822822 0.568299i \(-0.807602\pi\)
−0.822822 + 0.568299i \(0.807602\pi\)
\(480\) 0 0
\(481\) −9.35908 −0.426737
\(482\) 0 0
\(483\) −14.6966 −0.668721
\(484\) 0 0
\(485\) −35.4248 −1.60856
\(486\) 0 0
\(487\) 17.0178 0.771151 0.385575 0.922676i \(-0.374003\pi\)
0.385575 + 0.922676i \(0.374003\pi\)
\(488\) 0 0
\(489\) 19.7950 0.895160
\(490\) 0 0
\(491\) −30.2818 −1.36660 −0.683299 0.730139i \(-0.739455\pi\)
−0.683299 + 0.730139i \(0.739455\pi\)
\(492\) 0 0
\(493\) 35.9806 1.62049
\(494\) 0 0
\(495\) −2.14156 −0.0962560
\(496\) 0 0
\(497\) −31.3008 −1.40403
\(498\) 0 0
\(499\) −18.2197 −0.815625 −0.407813 0.913066i \(-0.633708\pi\)
−0.407813 + 0.913066i \(0.633708\pi\)
\(500\) 0 0
\(501\) −8.86670 −0.396135
\(502\) 0 0
\(503\) 19.8674 0.885846 0.442923 0.896560i \(-0.353942\pi\)
0.442923 + 0.896560i \(0.353942\pi\)
\(504\) 0 0
\(505\) −7.15665 −0.318467
\(506\) 0 0
\(507\) −10.5218 −0.467292
\(508\) 0 0
\(509\) 27.9308 1.23801 0.619006 0.785386i \(-0.287536\pi\)
0.619006 + 0.785386i \(0.287536\pi\)
\(510\) 0 0
\(511\) −15.7381 −0.696213
\(512\) 0 0
\(513\) −39.6023 −1.74848
\(514\) 0 0
\(515\) −32.9816 −1.45334
\(516\) 0 0
\(517\) 5.15077 0.226531
\(518\) 0 0
\(519\) 21.1257 0.927317
\(520\) 0 0
\(521\) 27.5902 1.20875 0.604374 0.796700i \(-0.293423\pi\)
0.604374 + 0.796700i \(0.293423\pi\)
\(522\) 0 0
\(523\) −31.7904 −1.39010 −0.695048 0.718964i \(-0.744617\pi\)
−0.695048 + 0.718964i \(0.744617\pi\)
\(524\) 0 0
\(525\) 4.27319 0.186497
\(526\) 0 0
\(527\) −47.2198 −2.05692
\(528\) 0 0
\(529\) −15.4765 −0.672892
\(530\) 0 0
\(531\) 1.75515 0.0761670
\(532\) 0 0
\(533\) 22.9068 0.992202
\(534\) 0 0
\(535\) 10.7828 0.466183
\(536\) 0 0
\(537\) −19.8511 −0.856637
\(538\) 0 0
\(539\) −10.7690 −0.463855
\(540\) 0 0
\(541\) 7.95275 0.341915 0.170958 0.985278i \(-0.445314\pi\)
0.170958 + 0.985278i \(0.445314\pi\)
\(542\) 0 0
\(543\) −37.1607 −1.59472
\(544\) 0 0
\(545\) 30.7996 1.31931
\(546\) 0 0
\(547\) 22.3760 0.956729 0.478365 0.878161i \(-0.341230\pi\)
0.478365 + 0.878161i \(0.341230\pi\)
\(548\) 0 0
\(549\) −4.60717 −0.196629
\(550\) 0 0
\(551\) −39.6972 −1.69116
\(552\) 0 0
\(553\) −19.3082 −0.821067
\(554\) 0 0
\(555\) −12.1736 −0.516742
\(556\) 0 0
\(557\) 28.2178 1.19563 0.597814 0.801635i \(-0.296036\pi\)
0.597814 + 0.801635i \(0.296036\pi\)
\(558\) 0 0
\(559\) −29.4515 −1.24567
\(560\) 0 0
\(561\) 28.6406 1.20921
\(562\) 0 0
\(563\) 10.2146 0.430492 0.215246 0.976560i \(-0.430945\pi\)
0.215246 + 0.976560i \(0.430945\pi\)
\(564\) 0 0
\(565\) −19.5343 −0.821815
\(566\) 0 0
\(567\) 25.4902 1.07049
\(568\) 0 0
\(569\) −40.0792 −1.68021 −0.840104 0.542426i \(-0.817506\pi\)
−0.840104 + 0.542426i \(0.817506\pi\)
\(570\) 0 0
\(571\) 21.5988 0.903880 0.451940 0.892048i \(-0.350732\pi\)
0.451940 + 0.892048i \(0.350732\pi\)
\(572\) 0 0
\(573\) 37.8349 1.58058
\(574\) 0 0
\(575\) −2.18753 −0.0912261
\(576\) 0 0
\(577\) −9.43358 −0.392725 −0.196363 0.980531i \(-0.562913\pi\)
−0.196363 + 0.980531i \(0.562913\pi\)
\(578\) 0 0
\(579\) −30.9598 −1.28665
\(580\) 0 0
\(581\) 55.1701 2.28884
\(582\) 0 0
\(583\) 10.7768 0.446330
\(584\) 0 0
\(585\) −2.01921 −0.0834842
\(586\) 0 0
\(587\) −7.03497 −0.290364 −0.145182 0.989405i \(-0.546377\pi\)
−0.145182 + 0.989405i \(0.546377\pi\)
\(588\) 0 0
\(589\) 52.0973 2.14663
\(590\) 0 0
\(591\) −6.77719 −0.278776
\(592\) 0 0
\(593\) −20.6993 −0.850016 −0.425008 0.905190i \(-0.639729\pi\)
−0.425008 + 0.905190i \(0.639729\pi\)
\(594\) 0 0
\(595\) −44.5473 −1.82626
\(596\) 0 0
\(597\) −33.6574 −1.37751
\(598\) 0 0
\(599\) −29.4031 −1.20138 −0.600690 0.799482i \(-0.705107\pi\)
−0.600690 + 0.799482i \(0.705107\pi\)
\(600\) 0 0
\(601\) 42.1879 1.72088 0.860440 0.509552i \(-0.170189\pi\)
0.860440 + 0.509552i \(0.170189\pi\)
\(602\) 0 0
\(603\) 1.93078 0.0786275
\(604\) 0 0
\(605\) 7.58119 0.308219
\(606\) 0 0
\(607\) −39.7096 −1.61176 −0.805882 0.592077i \(-0.798308\pi\)
−0.805882 + 0.592077i \(0.798308\pi\)
\(608\) 0 0
\(609\) 29.4046 1.19153
\(610\) 0 0
\(611\) 4.85651 0.196473
\(612\) 0 0
\(613\) 0.218377 0.00882018 0.00441009 0.999990i \(-0.498596\pi\)
0.00441009 + 0.999990i \(0.498596\pi\)
\(614\) 0 0
\(615\) 29.7955 1.20147
\(616\) 0 0
\(617\) 18.2193 0.733480 0.366740 0.930324i \(-0.380474\pi\)
0.366740 + 0.930324i \(0.380474\pi\)
\(618\) 0 0
\(619\) −45.7495 −1.83883 −0.919414 0.393291i \(-0.871336\pi\)
−0.919414 + 0.393291i \(0.871336\pi\)
\(620\) 0 0
\(621\) −15.0168 −0.602602
\(622\) 0 0
\(623\) 26.1155 1.04629
\(624\) 0 0
\(625\) −20.3763 −0.815053
\(626\) 0 0
\(627\) −31.5990 −1.26194
\(628\) 0 0
\(629\) −24.0839 −0.960288
\(630\) 0 0
\(631\) −31.9262 −1.27096 −0.635482 0.772116i \(-0.719198\pi\)
−0.635482 + 0.772116i \(0.719198\pi\)
\(632\) 0 0
\(633\) −9.30860 −0.369984
\(634\) 0 0
\(635\) 3.16428 0.125571
\(636\) 0 0
\(637\) −10.1538 −0.402308
\(638\) 0 0
\(639\) −3.65099 −0.144431
\(640\) 0 0
\(641\) −13.1182 −0.518139 −0.259070 0.965859i \(-0.583416\pi\)
−0.259070 + 0.965859i \(0.583416\pi\)
\(642\) 0 0
\(643\) −13.6792 −0.539453 −0.269727 0.962937i \(-0.586933\pi\)
−0.269727 + 0.962937i \(0.586933\pi\)
\(644\) 0 0
\(645\) −38.3085 −1.50840
\(646\) 0 0
\(647\) 43.6943 1.71780 0.858900 0.512144i \(-0.171148\pi\)
0.858900 + 0.512144i \(0.171148\pi\)
\(648\) 0 0
\(649\) 12.2679 0.481556
\(650\) 0 0
\(651\) −38.5896 −1.51244
\(652\) 0 0
\(653\) 45.1666 1.76751 0.883753 0.467953i \(-0.155008\pi\)
0.883753 + 0.467953i \(0.155008\pi\)
\(654\) 0 0
\(655\) −30.9659 −1.20994
\(656\) 0 0
\(657\) −1.83573 −0.0716185
\(658\) 0 0
\(659\) −42.8268 −1.66829 −0.834147 0.551543i \(-0.814039\pi\)
−0.834147 + 0.551543i \(0.814039\pi\)
\(660\) 0 0
\(661\) 15.6683 0.609426 0.304713 0.952444i \(-0.401439\pi\)
0.304713 + 0.952444i \(0.401439\pi\)
\(662\) 0 0
\(663\) 27.0044 1.04876
\(664\) 0 0
\(665\) 49.1487 1.90591
\(666\) 0 0
\(667\) −15.0528 −0.582845
\(668\) 0 0
\(669\) −1.49913 −0.0579597
\(670\) 0 0
\(671\) −32.2025 −1.24316
\(672\) 0 0
\(673\) −20.9804 −0.808737 −0.404368 0.914596i \(-0.632509\pi\)
−0.404368 + 0.914596i \(0.632509\pi\)
\(674\) 0 0
\(675\) 4.36627 0.168058
\(676\) 0 0
\(677\) −47.6345 −1.83074 −0.915371 0.402612i \(-0.868103\pi\)
−0.915371 + 0.402612i \(0.868103\pi\)
\(678\) 0 0
\(679\) −57.2744 −2.19799
\(680\) 0 0
\(681\) 9.80230 0.375625
\(682\) 0 0
\(683\) 6.69745 0.256271 0.128135 0.991757i \(-0.459101\pi\)
0.128135 + 0.991757i \(0.459101\pi\)
\(684\) 0 0
\(685\) −8.62245 −0.329447
\(686\) 0 0
\(687\) 44.9691 1.71568
\(688\) 0 0
\(689\) 10.1611 0.387109
\(690\) 0 0
\(691\) 20.5599 0.782134 0.391067 0.920362i \(-0.372106\pi\)
0.391067 + 0.920362i \(0.372106\pi\)
\(692\) 0 0
\(693\) −3.46245 −0.131528
\(694\) 0 0
\(695\) 7.58550 0.287735
\(696\) 0 0
\(697\) 58.9465 2.23276
\(698\) 0 0
\(699\) 44.8119 1.69494
\(700\) 0 0
\(701\) 29.9348 1.13062 0.565311 0.824878i \(-0.308756\pi\)
0.565311 + 0.824878i \(0.308756\pi\)
\(702\) 0 0
\(703\) 26.5716 1.00217
\(704\) 0 0
\(705\) 6.31701 0.237912
\(706\) 0 0
\(707\) −11.5708 −0.435164
\(708\) 0 0
\(709\) −9.93931 −0.373278 −0.186639 0.982429i \(-0.559760\pi\)
−0.186639 + 0.982429i \(0.559760\pi\)
\(710\) 0 0
\(711\) −2.25215 −0.0844621
\(712\) 0 0
\(713\) 19.7547 0.739820
\(714\) 0 0
\(715\) −14.1136 −0.527818
\(716\) 0 0
\(717\) 7.15830 0.267332
\(718\) 0 0
\(719\) 13.6533 0.509182 0.254591 0.967049i \(-0.418059\pi\)
0.254591 + 0.967049i \(0.418059\pi\)
\(720\) 0 0
\(721\) −53.3243 −1.98590
\(722\) 0 0
\(723\) −17.5736 −0.653568
\(724\) 0 0
\(725\) 4.37673 0.162548
\(726\) 0 0
\(727\) −25.3472 −0.940076 −0.470038 0.882646i \(-0.655760\pi\)
−0.470038 + 0.882646i \(0.655760\pi\)
\(728\) 0 0
\(729\) 29.5249 1.09351
\(730\) 0 0
\(731\) −75.7883 −2.80313
\(732\) 0 0
\(733\) 42.5680 1.57229 0.786143 0.618045i \(-0.212075\pi\)
0.786143 + 0.618045i \(0.212075\pi\)
\(734\) 0 0
\(735\) −13.2074 −0.487161
\(736\) 0 0
\(737\) 13.4955 0.497112
\(738\) 0 0
\(739\) 48.3247 1.77765 0.888826 0.458245i \(-0.151522\pi\)
0.888826 + 0.458245i \(0.151522\pi\)
\(740\) 0 0
\(741\) −29.7937 −1.09450
\(742\) 0 0
\(743\) −15.7506 −0.577832 −0.288916 0.957355i \(-0.593295\pi\)
−0.288916 + 0.957355i \(0.593295\pi\)
\(744\) 0 0
\(745\) −30.9444 −1.13371
\(746\) 0 0
\(747\) 6.43516 0.235450
\(748\) 0 0
\(749\) 17.4336 0.637009
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −24.0921 −0.877964
\(754\) 0 0
\(755\) −36.9791 −1.34581
\(756\) 0 0
\(757\) 37.5806 1.36589 0.682945 0.730470i \(-0.260699\pi\)
0.682945 + 0.730470i \(0.260699\pi\)
\(758\) 0 0
\(759\) −11.9820 −0.434919
\(760\) 0 0
\(761\) 16.6132 0.602227 0.301114 0.953588i \(-0.402642\pi\)
0.301114 + 0.953588i \(0.402642\pi\)
\(762\) 0 0
\(763\) 49.7964 1.80275
\(764\) 0 0
\(765\) −5.19609 −0.187865
\(766\) 0 0
\(767\) 11.5670 0.417661
\(768\) 0 0
\(769\) −14.3021 −0.515745 −0.257873 0.966179i \(-0.583022\pi\)
−0.257873 + 0.966179i \(0.583022\pi\)
\(770\) 0 0
\(771\) −40.6104 −1.46255
\(772\) 0 0
\(773\) 25.3207 0.910721 0.455360 0.890307i \(-0.349510\pi\)
0.455360 + 0.890307i \(0.349510\pi\)
\(774\) 0 0
\(775\) −5.74387 −0.206326
\(776\) 0 0
\(777\) −19.6822 −0.706094
\(778\) 0 0
\(779\) −65.0353 −2.33013
\(780\) 0 0
\(781\) −25.5191 −0.913145
\(782\) 0 0
\(783\) 30.0451 1.07372
\(784\) 0 0
\(785\) −16.5451 −0.590519
\(786\) 0 0
\(787\) 3.58611 0.127831 0.0639155 0.997955i \(-0.479641\pi\)
0.0639155 + 0.997955i \(0.479641\pi\)
\(788\) 0 0
\(789\) 12.3739 0.440524
\(790\) 0 0
\(791\) −31.5829 −1.12296
\(792\) 0 0
\(793\) −30.3628 −1.07821
\(794\) 0 0
\(795\) 13.2169 0.468755
\(796\) 0 0
\(797\) 0.0820483 0.00290630 0.00145315 0.999999i \(-0.499537\pi\)
0.00145315 + 0.999999i \(0.499537\pi\)
\(798\) 0 0
\(799\) 12.4974 0.442125
\(800\) 0 0
\(801\) 3.04616 0.107631
\(802\) 0 0
\(803\) −12.8311 −0.452799
\(804\) 0 0
\(805\) 18.6367 0.656856
\(806\) 0 0
\(807\) 29.2850 1.03088
\(808\) 0 0
\(809\) 45.1159 1.58619 0.793095 0.609098i \(-0.208468\pi\)
0.793095 + 0.609098i \(0.208468\pi\)
\(810\) 0 0
\(811\) 27.5799 0.968462 0.484231 0.874940i \(-0.339099\pi\)
0.484231 + 0.874940i \(0.339099\pi\)
\(812\) 0 0
\(813\) 4.39138 0.154013
\(814\) 0 0
\(815\) −25.1018 −0.879277
\(816\) 0 0
\(817\) 83.6167 2.92538
\(818\) 0 0
\(819\) −3.26464 −0.114076
\(820\) 0 0
\(821\) −32.9461 −1.14983 −0.574914 0.818214i \(-0.694965\pi\)
−0.574914 + 0.818214i \(0.694965\pi\)
\(822\) 0 0
\(823\) 29.6183 1.03243 0.516215 0.856459i \(-0.327341\pi\)
0.516215 + 0.856459i \(0.327341\pi\)
\(824\) 0 0
\(825\) 3.48388 0.121293
\(826\) 0 0
\(827\) 20.8483 0.724967 0.362484 0.931990i \(-0.381929\pi\)
0.362484 + 0.931990i \(0.381929\pi\)
\(828\) 0 0
\(829\) −0.762368 −0.0264781 −0.0132391 0.999912i \(-0.504214\pi\)
−0.0132391 + 0.999912i \(0.504214\pi\)
\(830\) 0 0
\(831\) −4.75462 −0.164936
\(832\) 0 0
\(833\) −26.1290 −0.905316
\(834\) 0 0
\(835\) 11.2438 0.389107
\(836\) 0 0
\(837\) −39.4301 −1.36290
\(838\) 0 0
\(839\) 45.5805 1.57361 0.786807 0.617199i \(-0.211733\pi\)
0.786807 + 0.617199i \(0.211733\pi\)
\(840\) 0 0
\(841\) 1.11708 0.0385200
\(842\) 0 0
\(843\) 50.8645 1.75187
\(844\) 0 0
\(845\) 13.3426 0.459001
\(846\) 0 0
\(847\) 12.2572 0.421162
\(848\) 0 0
\(849\) 41.1862 1.41351
\(850\) 0 0
\(851\) 10.0757 0.345390
\(852\) 0 0
\(853\) 19.8227 0.678717 0.339358 0.940657i \(-0.389790\pi\)
0.339358 + 0.940657i \(0.389790\pi\)
\(854\) 0 0
\(855\) 5.73281 0.196058
\(856\) 0 0
\(857\) −9.61034 −0.328283 −0.164141 0.986437i \(-0.552485\pi\)
−0.164141 + 0.986437i \(0.552485\pi\)
\(858\) 0 0
\(859\) −4.35296 −0.148521 −0.0742606 0.997239i \(-0.523660\pi\)
−0.0742606 + 0.997239i \(0.523660\pi\)
\(860\) 0 0
\(861\) 48.1730 1.64173
\(862\) 0 0
\(863\) 27.5206 0.936811 0.468405 0.883514i \(-0.344829\pi\)
0.468405 + 0.883514i \(0.344829\pi\)
\(864\) 0 0
\(865\) −26.7893 −0.910864
\(866\) 0 0
\(867\) 42.0087 1.42669
\(868\) 0 0
\(869\) −15.7417 −0.534001
\(870\) 0 0
\(871\) 12.7245 0.431153
\(872\) 0 0
\(873\) −6.68061 −0.226105
\(874\) 0 0
\(875\) −39.3914 −1.33167
\(876\) 0 0
\(877\) −26.0018 −0.878017 −0.439008 0.898483i \(-0.644670\pi\)
−0.439008 + 0.898483i \(0.644670\pi\)
\(878\) 0 0
\(879\) −3.34716 −0.112897
\(880\) 0 0
\(881\) 3.49450 0.117733 0.0588664 0.998266i \(-0.481251\pi\)
0.0588664 + 0.998266i \(0.481251\pi\)
\(882\) 0 0
\(883\) 38.2283 1.28648 0.643242 0.765663i \(-0.277589\pi\)
0.643242 + 0.765663i \(0.277589\pi\)
\(884\) 0 0
\(885\) 15.0456 0.505751
\(886\) 0 0
\(887\) −5.51887 −0.185306 −0.0926528 0.995698i \(-0.529535\pi\)
−0.0926528 + 0.995698i \(0.529535\pi\)
\(888\) 0 0
\(889\) 5.11597 0.171584
\(890\) 0 0
\(891\) 20.7819 0.696219
\(892\) 0 0
\(893\) −13.7883 −0.461407
\(894\) 0 0
\(895\) 25.1729 0.841438
\(896\) 0 0
\(897\) −11.2975 −0.377211
\(898\) 0 0
\(899\) −39.5246 −1.31822
\(900\) 0 0
\(901\) 26.1479 0.871112
\(902\) 0 0
\(903\) −61.9367 −2.06112
\(904\) 0 0
\(905\) 47.1230 1.56642
\(906\) 0 0
\(907\) 41.0948 1.36453 0.682266 0.731104i \(-0.260995\pi\)
0.682266 + 0.731104i \(0.260995\pi\)
\(908\) 0 0
\(909\) −1.34964 −0.0447648
\(910\) 0 0
\(911\) 34.2744 1.13556 0.567781 0.823180i \(-0.307802\pi\)
0.567781 + 0.823180i \(0.307802\pi\)
\(912\) 0 0
\(913\) 44.9795 1.48860
\(914\) 0 0
\(915\) −39.4938 −1.30562
\(916\) 0 0
\(917\) −50.0653 −1.65330
\(918\) 0 0
\(919\) 13.4356 0.443200 0.221600 0.975138i \(-0.428872\pi\)
0.221600 + 0.975138i \(0.428872\pi\)
\(920\) 0 0
\(921\) −7.33797 −0.241794
\(922\) 0 0
\(923\) −24.0612 −0.791985
\(924\) 0 0
\(925\) −2.92960 −0.0963246
\(926\) 0 0
\(927\) −6.21986 −0.204287
\(928\) 0 0
\(929\) −41.4250 −1.35911 −0.679556 0.733624i \(-0.737827\pi\)
−0.679556 + 0.733624i \(0.737827\pi\)
\(930\) 0 0
\(931\) 28.8280 0.944798
\(932\) 0 0
\(933\) −29.9280 −0.979797
\(934\) 0 0
\(935\) −36.3188 −1.18775
\(936\) 0 0
\(937\) −5.04066 −0.164671 −0.0823355 0.996605i \(-0.526238\pi\)
−0.0823355 + 0.996605i \(0.526238\pi\)
\(938\) 0 0
\(939\) 38.1112 1.24371
\(940\) 0 0
\(941\) 16.3377 0.532593 0.266296 0.963891i \(-0.414200\pi\)
0.266296 + 0.963891i \(0.414200\pi\)
\(942\) 0 0
\(943\) −24.6607 −0.803062
\(944\) 0 0
\(945\) −37.1985 −1.21007
\(946\) 0 0
\(947\) −2.67885 −0.0870510 −0.0435255 0.999052i \(-0.513859\pi\)
−0.0435255 + 0.999052i \(0.513859\pi\)
\(948\) 0 0
\(949\) −12.0980 −0.392719
\(950\) 0 0
\(951\) −31.7306 −1.02893
\(952\) 0 0
\(953\) −23.7815 −0.770359 −0.385179 0.922842i \(-0.625860\pi\)
−0.385179 + 0.922842i \(0.625860\pi\)
\(954\) 0 0
\(955\) −47.9781 −1.55253
\(956\) 0 0
\(957\) 23.9732 0.774943
\(958\) 0 0
\(959\) −13.9407 −0.450168
\(960\) 0 0
\(961\) 20.8707 0.673249
\(962\) 0 0
\(963\) 2.03349 0.0655283
\(964\) 0 0
\(965\) 39.2598 1.26382
\(966\) 0 0
\(967\) 15.2747 0.491202 0.245601 0.969371i \(-0.421015\pi\)
0.245601 + 0.969371i \(0.421015\pi\)
\(968\) 0 0
\(969\) −76.6689 −2.46296
\(970\) 0 0
\(971\) 11.1615 0.358191 0.179095 0.983832i \(-0.442683\pi\)
0.179095 + 0.983832i \(0.442683\pi\)
\(972\) 0 0
\(973\) 12.2642 0.393171
\(974\) 0 0
\(975\) 3.28485 0.105199
\(976\) 0 0
\(977\) 56.0371 1.79278 0.896392 0.443262i \(-0.146179\pi\)
0.896392 + 0.443262i \(0.146179\pi\)
\(978\) 0 0
\(979\) 21.2916 0.680482
\(980\) 0 0
\(981\) 5.80836 0.185447
\(982\) 0 0
\(983\) 45.1511 1.44010 0.720048 0.693925i \(-0.244120\pi\)
0.720048 + 0.693925i \(0.244120\pi\)
\(984\) 0 0
\(985\) 8.59407 0.273830
\(986\) 0 0
\(987\) 10.2133 0.325092
\(988\) 0 0
\(989\) 31.7065 1.00821
\(990\) 0 0
\(991\) −8.65024 −0.274784 −0.137392 0.990517i \(-0.543872\pi\)
−0.137392 + 0.990517i \(0.543872\pi\)
\(992\) 0 0
\(993\) 5.15943 0.163730
\(994\) 0 0
\(995\) 42.6806 1.35307
\(996\) 0 0
\(997\) −19.2339 −0.609143 −0.304572 0.952489i \(-0.598513\pi\)
−0.304572 + 0.952489i \(0.598513\pi\)
\(998\) 0 0
\(999\) −20.1109 −0.636280
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 \(a_p\))