Properties

Label 6008.2.a.e.1.29
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 1.29
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.416230 q^{3} +3.95581 q^{5} +2.52758 q^{7} -2.82675 q^{9} +O(q^{10})\) \(q+0.416230 q^{3} +3.95581 q^{5} +2.52758 q^{7} -2.82675 q^{9} +3.42008 q^{11} -3.31267 q^{13} +1.64653 q^{15} -7.23883 q^{17} +4.52109 q^{19} +1.05206 q^{21} +7.20387 q^{23} +10.6484 q^{25} -2.42527 q^{27} +7.29186 q^{29} -4.45184 q^{31} +1.42354 q^{33} +9.99863 q^{35} -6.53567 q^{37} -1.37884 q^{39} +4.03924 q^{41} -9.48256 q^{43} -11.1821 q^{45} -0.0683152 q^{47} -0.611316 q^{49} -3.01302 q^{51} +9.07518 q^{53} +13.5292 q^{55} +1.88181 q^{57} +8.40101 q^{59} +3.48581 q^{61} -7.14486 q^{63} -13.1043 q^{65} +7.25056 q^{67} +2.99847 q^{69} +3.26703 q^{71} +11.2983 q^{73} +4.43219 q^{75} +8.64454 q^{77} +10.5574 q^{79} +7.47078 q^{81} +1.52092 q^{83} -28.6354 q^{85} +3.03510 q^{87} -8.80313 q^{89} -8.37306 q^{91} -1.85299 q^{93} +17.8845 q^{95} -2.44088 q^{97} -9.66772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 0.416230 0.240311 0.120155 0.992755i \(-0.461661\pi\)
0.120155 + 0.992755i \(0.461661\pi\)
\(4\) 0 0
\(5\) 3.95581 1.76909 0.884545 0.466455i \(-0.154469\pi\)
0.884545 + 0.466455i \(0.154469\pi\)
\(6\) 0 0
\(7\) 2.52758 0.955337 0.477669 0.878540i \(-0.341482\pi\)
0.477669 + 0.878540i \(0.341482\pi\)
\(8\) 0 0
\(9\) −2.82675 −0.942251
\(10\) 0 0
\(11\) 3.42008 1.03119 0.515596 0.856832i \(-0.327570\pi\)
0.515596 + 0.856832i \(0.327570\pi\)
\(12\) 0 0
\(13\) −3.31267 −0.918771 −0.459385 0.888237i \(-0.651930\pi\)
−0.459385 + 0.888237i \(0.651930\pi\)
\(14\) 0 0
\(15\) 1.64653 0.425131
\(16\) 0 0
\(17\) −7.23883 −1.75567 −0.877837 0.478959i \(-0.841014\pi\)
−0.877837 + 0.478959i \(0.841014\pi\)
\(18\) 0 0
\(19\) 4.52109 1.03721 0.518604 0.855014i \(-0.326452\pi\)
0.518604 + 0.855014i \(0.326452\pi\)
\(20\) 0 0
\(21\) 1.05206 0.229578
\(22\) 0 0
\(23\) 7.20387 1.50211 0.751055 0.660240i \(-0.229545\pi\)
0.751055 + 0.660240i \(0.229545\pi\)
\(24\) 0 0
\(25\) 10.6484 2.12968
\(26\) 0 0
\(27\) −2.42527 −0.466744
\(28\) 0 0
\(29\) 7.29186 1.35406 0.677032 0.735953i \(-0.263266\pi\)
0.677032 + 0.735953i \(0.263266\pi\)
\(30\) 0 0
\(31\) −4.45184 −0.799573 −0.399787 0.916608i \(-0.630916\pi\)
−0.399787 + 0.916608i \(0.630916\pi\)
\(32\) 0 0
\(33\) 1.42354 0.247807
\(34\) 0 0
\(35\) 9.99863 1.69008
\(36\) 0 0
\(37\) −6.53567 −1.07446 −0.537229 0.843436i \(-0.680529\pi\)
−0.537229 + 0.843436i \(0.680529\pi\)
\(38\) 0 0
\(39\) −1.37884 −0.220790
\(40\) 0 0
\(41\) 4.03924 0.630823 0.315412 0.948955i \(-0.397857\pi\)
0.315412 + 0.948955i \(0.397857\pi\)
\(42\) 0 0
\(43\) −9.48256 −1.44608 −0.723038 0.690808i \(-0.757255\pi\)
−0.723038 + 0.690808i \(0.757255\pi\)
\(44\) 0 0
\(45\) −11.1821 −1.66693
\(46\) 0 0
\(47\) −0.0683152 −0.00996480 −0.00498240 0.999988i \(-0.501586\pi\)
−0.00498240 + 0.999988i \(0.501586\pi\)
\(48\) 0 0
\(49\) −0.611316 −0.0873308
\(50\) 0 0
\(51\) −3.01302 −0.421907
\(52\) 0 0
\(53\) 9.07518 1.24657 0.623286 0.781994i \(-0.285797\pi\)
0.623286 + 0.781994i \(0.285797\pi\)
\(54\) 0 0
\(55\) 13.5292 1.82427
\(56\) 0 0
\(57\) 1.88181 0.249252
\(58\) 0 0
\(59\) 8.40101 1.09372 0.546859 0.837225i \(-0.315823\pi\)
0.546859 + 0.837225i \(0.315823\pi\)
\(60\) 0 0
\(61\) 3.48581 0.446312 0.223156 0.974783i \(-0.428364\pi\)
0.223156 + 0.974783i \(0.428364\pi\)
\(62\) 0 0
\(63\) −7.14486 −0.900167
\(64\) 0 0
\(65\) −13.1043 −1.62539
\(66\) 0 0
\(67\) 7.25056 0.885797 0.442899 0.896572i \(-0.353950\pi\)
0.442899 + 0.896572i \(0.353950\pi\)
\(68\) 0 0
\(69\) 2.99847 0.360973
\(70\) 0 0
\(71\) 3.26703 0.387725 0.193862 0.981029i \(-0.437898\pi\)
0.193862 + 0.981029i \(0.437898\pi\)
\(72\) 0 0
\(73\) 11.2983 1.32236 0.661182 0.750225i \(-0.270055\pi\)
0.661182 + 0.750225i \(0.270055\pi\)
\(74\) 0 0
\(75\) 4.43219 0.511785
\(76\) 0 0
\(77\) 8.64454 0.985137
\(78\) 0 0
\(79\) 10.5574 1.18780 0.593899 0.804540i \(-0.297588\pi\)
0.593899 + 0.804540i \(0.297588\pi\)
\(80\) 0 0
\(81\) 7.47078 0.830087
\(82\) 0 0
\(83\) 1.52092 0.166942 0.0834712 0.996510i \(-0.473399\pi\)
0.0834712 + 0.996510i \(0.473399\pi\)
\(84\) 0 0
\(85\) −28.6354 −3.10595
\(86\) 0 0
\(87\) 3.03510 0.325396
\(88\) 0 0
\(89\) −8.80313 −0.933130 −0.466565 0.884487i \(-0.654509\pi\)
−0.466565 + 0.884487i \(0.654509\pi\)
\(90\) 0 0
\(91\) −8.37306 −0.877736
\(92\) 0 0
\(93\) −1.85299 −0.192146
\(94\) 0 0
\(95\) 17.8845 1.83492
\(96\) 0 0
\(97\) −2.44088 −0.247833 −0.123917 0.992293i \(-0.539546\pi\)
−0.123917 + 0.992293i \(0.539546\pi\)
\(98\) 0 0
\(99\) −9.66772 −0.971642
\(100\) 0 0
\(101\) 9.56249 0.951503 0.475752 0.879580i \(-0.342176\pi\)
0.475752 + 0.879580i \(0.342176\pi\)
\(102\) 0 0
\(103\) −18.1103 −1.78446 −0.892232 0.451578i \(-0.850861\pi\)
−0.892232 + 0.451578i \(0.850861\pi\)
\(104\) 0 0
\(105\) 4.16174 0.406144
\(106\) 0 0
\(107\) 8.61886 0.833217 0.416608 0.909086i \(-0.363219\pi\)
0.416608 + 0.909086i \(0.363219\pi\)
\(108\) 0 0
\(109\) 7.48252 0.716695 0.358348 0.933588i \(-0.383340\pi\)
0.358348 + 0.933588i \(0.383340\pi\)
\(110\) 0 0
\(111\) −2.72035 −0.258204
\(112\) 0 0
\(113\) 20.0448 1.88565 0.942826 0.333284i \(-0.108157\pi\)
0.942826 + 0.333284i \(0.108157\pi\)
\(114\) 0 0
\(115\) 28.4971 2.65737
\(116\) 0 0
\(117\) 9.36411 0.865712
\(118\) 0 0
\(119\) −18.2968 −1.67726
\(120\) 0 0
\(121\) 0.696945 0.0633587
\(122\) 0 0
\(123\) 1.68125 0.151594
\(124\) 0 0
\(125\) 22.3440 1.99851
\(126\) 0 0
\(127\) 20.1367 1.78685 0.893423 0.449217i \(-0.148297\pi\)
0.893423 + 0.449217i \(0.148297\pi\)
\(128\) 0 0
\(129\) −3.94693 −0.347508
\(130\) 0 0
\(131\) −3.66923 −0.320582 −0.160291 0.987070i \(-0.551243\pi\)
−0.160291 + 0.987070i \(0.551243\pi\)
\(132\) 0 0
\(133\) 11.4274 0.990884
\(134\) 0 0
\(135\) −9.59390 −0.825712
\(136\) 0 0
\(137\) 11.6612 0.996285 0.498143 0.867095i \(-0.334016\pi\)
0.498143 + 0.867095i \(0.334016\pi\)
\(138\) 0 0
\(139\) 4.78719 0.406045 0.203022 0.979174i \(-0.434924\pi\)
0.203022 + 0.979174i \(0.434924\pi\)
\(140\) 0 0
\(141\) −0.0284349 −0.00239465
\(142\) 0 0
\(143\) −11.3296 −0.947430
\(144\) 0 0
\(145\) 28.8452 2.39546
\(146\) 0 0
\(147\) −0.254448 −0.0209865
\(148\) 0 0
\(149\) −2.28138 −0.186898 −0.0934492 0.995624i \(-0.529789\pi\)
−0.0934492 + 0.995624i \(0.529789\pi\)
\(150\) 0 0
\(151\) −12.6729 −1.03130 −0.515651 0.856799i \(-0.672450\pi\)
−0.515651 + 0.856799i \(0.672450\pi\)
\(152\) 0 0
\(153\) 20.4624 1.65429
\(154\) 0 0
\(155\) −17.6106 −1.41452
\(156\) 0 0
\(157\) 2.94428 0.234979 0.117489 0.993074i \(-0.462515\pi\)
0.117489 + 0.993074i \(0.462515\pi\)
\(158\) 0 0
\(159\) 3.77737 0.299565
\(160\) 0 0
\(161\) 18.2084 1.43502
\(162\) 0 0
\(163\) −11.7301 −0.918773 −0.459387 0.888236i \(-0.651931\pi\)
−0.459387 + 0.888236i \(0.651931\pi\)
\(164\) 0 0
\(165\) 5.63125 0.438392
\(166\) 0 0
\(167\) 3.66363 0.283500 0.141750 0.989902i \(-0.454727\pi\)
0.141750 + 0.989902i \(0.454727\pi\)
\(168\) 0 0
\(169\) −2.02619 −0.155861
\(170\) 0 0
\(171\) −12.7800 −0.977310
\(172\) 0 0
\(173\) −19.7203 −1.49930 −0.749652 0.661832i \(-0.769779\pi\)
−0.749652 + 0.661832i \(0.769779\pi\)
\(174\) 0 0
\(175\) 26.9147 2.03456
\(176\) 0 0
\(177\) 3.49676 0.262832
\(178\) 0 0
\(179\) −21.3864 −1.59850 −0.799248 0.601002i \(-0.794768\pi\)
−0.799248 + 0.601002i \(0.794768\pi\)
\(180\) 0 0
\(181\) −20.5412 −1.52681 −0.763406 0.645919i \(-0.776475\pi\)
−0.763406 + 0.645919i \(0.776475\pi\)
\(182\) 0 0
\(183\) 1.45090 0.107254
\(184\) 0 0
\(185\) −25.8538 −1.90081
\(186\) 0 0
\(187\) −24.7574 −1.81044
\(188\) 0 0
\(189\) −6.13008 −0.445898
\(190\) 0 0
\(191\) −6.33691 −0.458523 −0.229261 0.973365i \(-0.573631\pi\)
−0.229261 + 0.973365i \(0.573631\pi\)
\(192\) 0 0
\(193\) −2.00200 −0.144107 −0.0720536 0.997401i \(-0.522955\pi\)
−0.0720536 + 0.997401i \(0.522955\pi\)
\(194\) 0 0
\(195\) −5.45441 −0.390598
\(196\) 0 0
\(197\) −8.57793 −0.611152 −0.305576 0.952168i \(-0.598849\pi\)
−0.305576 + 0.952168i \(0.598849\pi\)
\(198\) 0 0
\(199\) −11.4115 −0.808942 −0.404471 0.914551i \(-0.632544\pi\)
−0.404471 + 0.914551i \(0.632544\pi\)
\(200\) 0 0
\(201\) 3.01790 0.212867
\(202\) 0 0
\(203\) 18.4308 1.29359
\(204\) 0 0
\(205\) 15.9784 1.11598
\(206\) 0 0
\(207\) −20.3635 −1.41536
\(208\) 0 0
\(209\) 15.4625 1.06956
\(210\) 0 0
\(211\) −26.1333 −1.79909 −0.899544 0.436831i \(-0.856101\pi\)
−0.899544 + 0.436831i \(0.856101\pi\)
\(212\) 0 0
\(213\) 1.35984 0.0931744
\(214\) 0 0
\(215\) −37.5112 −2.55824
\(216\) 0 0
\(217\) −11.2524 −0.763862
\(218\) 0 0
\(219\) 4.70269 0.317778
\(220\) 0 0
\(221\) 23.9799 1.61306
\(222\) 0 0
\(223\) 17.3328 1.16069 0.580346 0.814370i \(-0.302917\pi\)
0.580346 + 0.814370i \(0.302917\pi\)
\(224\) 0 0
\(225\) −30.1004 −2.00669
\(226\) 0 0
\(227\) −0.144305 −0.00957789 −0.00478894 0.999989i \(-0.501524\pi\)
−0.00478894 + 0.999989i \(0.501524\pi\)
\(228\) 0 0
\(229\) −14.5673 −0.962637 −0.481319 0.876546i \(-0.659842\pi\)
−0.481319 + 0.876546i \(0.659842\pi\)
\(230\) 0 0
\(231\) 3.59812 0.236739
\(232\) 0 0
\(233\) 18.4715 1.21011 0.605055 0.796184i \(-0.293151\pi\)
0.605055 + 0.796184i \(0.293151\pi\)
\(234\) 0 0
\(235\) −0.270242 −0.0176286
\(236\) 0 0
\(237\) 4.39430 0.285440
\(238\) 0 0
\(239\) −24.6859 −1.59680 −0.798400 0.602127i \(-0.794320\pi\)
−0.798400 + 0.602127i \(0.794320\pi\)
\(240\) 0 0
\(241\) 3.94882 0.254366 0.127183 0.991879i \(-0.459406\pi\)
0.127183 + 0.991879i \(0.459406\pi\)
\(242\) 0 0
\(243\) 10.3854 0.666223
\(244\) 0 0
\(245\) −2.41825 −0.154496
\(246\) 0 0
\(247\) −14.9769 −0.952957
\(248\) 0 0
\(249\) 0.633052 0.0401180
\(250\) 0 0
\(251\) −10.4129 −0.657259 −0.328629 0.944459i \(-0.606587\pi\)
−0.328629 + 0.944459i \(0.606587\pi\)
\(252\) 0 0
\(253\) 24.6378 1.54897
\(254\) 0 0
\(255\) −11.9189 −0.746392
\(256\) 0 0
\(257\) −1.99666 −0.124548 −0.0622740 0.998059i \(-0.519835\pi\)
−0.0622740 + 0.998059i \(0.519835\pi\)
\(258\) 0 0
\(259\) −16.5195 −1.02647
\(260\) 0 0
\(261\) −20.6123 −1.27587
\(262\) 0 0
\(263\) −4.62185 −0.284996 −0.142498 0.989795i \(-0.545513\pi\)
−0.142498 + 0.989795i \(0.545513\pi\)
\(264\) 0 0
\(265\) 35.8997 2.20530
\(266\) 0 0
\(267\) −3.66413 −0.224241
\(268\) 0 0
\(269\) 14.2497 0.868822 0.434411 0.900715i \(-0.356957\pi\)
0.434411 + 0.900715i \(0.356957\pi\)
\(270\) 0 0
\(271\) −21.6060 −1.31247 −0.656235 0.754557i \(-0.727852\pi\)
−0.656235 + 0.754557i \(0.727852\pi\)
\(272\) 0 0
\(273\) −3.48512 −0.210929
\(274\) 0 0
\(275\) 36.4184 2.19611
\(276\) 0 0
\(277\) −14.3677 −0.863273 −0.431637 0.902048i \(-0.642064\pi\)
−0.431637 + 0.902048i \(0.642064\pi\)
\(278\) 0 0
\(279\) 12.5842 0.753398
\(280\) 0 0
\(281\) 3.43523 0.204929 0.102464 0.994737i \(-0.467327\pi\)
0.102464 + 0.994737i \(0.467327\pi\)
\(282\) 0 0
\(283\) 3.31349 0.196966 0.0984832 0.995139i \(-0.468601\pi\)
0.0984832 + 0.995139i \(0.468601\pi\)
\(284\) 0 0
\(285\) 7.44409 0.440950
\(286\) 0 0
\(287\) 10.2095 0.602649
\(288\) 0 0
\(289\) 35.4007 2.08239
\(290\) 0 0
\(291\) −1.01597 −0.0595570
\(292\) 0 0
\(293\) 7.90794 0.461987 0.230993 0.972955i \(-0.425802\pi\)
0.230993 + 0.972955i \(0.425802\pi\)
\(294\) 0 0
\(295\) 33.2328 1.93489
\(296\) 0 0
\(297\) −8.29462 −0.481303
\(298\) 0 0
\(299\) −23.8641 −1.38009
\(300\) 0 0
\(301\) −23.9680 −1.38149
\(302\) 0 0
\(303\) 3.98020 0.228656
\(304\) 0 0
\(305\) 13.7892 0.789566
\(306\) 0 0
\(307\) 10.4809 0.598175 0.299087 0.954226i \(-0.403318\pi\)
0.299087 + 0.954226i \(0.403318\pi\)
\(308\) 0 0
\(309\) −7.53807 −0.428826
\(310\) 0 0
\(311\) −4.32281 −0.245124 −0.122562 0.992461i \(-0.539111\pi\)
−0.122562 + 0.992461i \(0.539111\pi\)
\(312\) 0 0
\(313\) 16.4570 0.930205 0.465103 0.885257i \(-0.346017\pi\)
0.465103 + 0.885257i \(0.346017\pi\)
\(314\) 0 0
\(315\) −28.2637 −1.59248
\(316\) 0 0
\(317\) −24.1651 −1.35725 −0.678623 0.734487i \(-0.737423\pi\)
−0.678623 + 0.734487i \(0.737423\pi\)
\(318\) 0 0
\(319\) 24.9388 1.39630
\(320\) 0 0
\(321\) 3.58743 0.200231
\(322\) 0 0
\(323\) −32.7274 −1.82100
\(324\) 0 0
\(325\) −35.2747 −1.95669
\(326\) 0 0
\(327\) 3.11445 0.172230
\(328\) 0 0
\(329\) −0.172672 −0.00951974
\(330\) 0 0
\(331\) 13.1035 0.720234 0.360117 0.932907i \(-0.382737\pi\)
0.360117 + 0.932907i \(0.382737\pi\)
\(332\) 0 0
\(333\) 18.4747 1.01241
\(334\) 0 0
\(335\) 28.6818 1.56705
\(336\) 0 0
\(337\) 7.16212 0.390146 0.195073 0.980789i \(-0.437506\pi\)
0.195073 + 0.980789i \(0.437506\pi\)
\(338\) 0 0
\(339\) 8.34324 0.453143
\(340\) 0 0
\(341\) −15.2256 −0.824514
\(342\) 0 0
\(343\) −19.2382 −1.03877
\(344\) 0 0
\(345\) 11.8614 0.638594
\(346\) 0 0
\(347\) −2.74633 −0.147431 −0.0737154 0.997279i \(-0.523486\pi\)
−0.0737154 + 0.997279i \(0.523486\pi\)
\(348\) 0 0
\(349\) −21.7346 −1.16343 −0.581715 0.813393i \(-0.697618\pi\)
−0.581715 + 0.813393i \(0.697618\pi\)
\(350\) 0 0
\(351\) 8.03414 0.428830
\(352\) 0 0
\(353\) 32.7124 1.74110 0.870551 0.492078i \(-0.163762\pi\)
0.870551 + 0.492078i \(0.163762\pi\)
\(354\) 0 0
\(355\) 12.9237 0.685920
\(356\) 0 0
\(357\) −7.61567 −0.403064
\(358\) 0 0
\(359\) 16.6087 0.876573 0.438287 0.898835i \(-0.355585\pi\)
0.438287 + 0.898835i \(0.355585\pi\)
\(360\) 0 0
\(361\) 1.44023 0.0758015
\(362\) 0 0
\(363\) 0.290090 0.0152258
\(364\) 0 0
\(365\) 44.6938 2.33938
\(366\) 0 0
\(367\) −3.70718 −0.193513 −0.0967566 0.995308i \(-0.530847\pi\)
−0.0967566 + 0.995308i \(0.530847\pi\)
\(368\) 0 0
\(369\) −11.4179 −0.594394
\(370\) 0 0
\(371\) 22.9383 1.19090
\(372\) 0 0
\(373\) −5.39864 −0.279531 −0.139765 0.990185i \(-0.544635\pi\)
−0.139765 + 0.990185i \(0.544635\pi\)
\(374\) 0 0
\(375\) 9.30024 0.480262
\(376\) 0 0
\(377\) −24.1556 −1.24407
\(378\) 0 0
\(379\) −5.09265 −0.261592 −0.130796 0.991409i \(-0.541753\pi\)
−0.130796 + 0.991409i \(0.541753\pi\)
\(380\) 0 0
\(381\) 8.38152 0.429398
\(382\) 0 0
\(383\) 32.8186 1.67695 0.838476 0.544938i \(-0.183447\pi\)
0.838476 + 0.544938i \(0.183447\pi\)
\(384\) 0 0
\(385\) 34.1961 1.74280
\(386\) 0 0
\(387\) 26.8048 1.36257
\(388\) 0 0
\(389\) −35.8011 −1.81519 −0.907594 0.419849i \(-0.862083\pi\)
−0.907594 + 0.419849i \(0.862083\pi\)
\(390\) 0 0
\(391\) −52.1476 −2.63722
\(392\) 0 0
\(393\) −1.52725 −0.0770394
\(394\) 0 0
\(395\) 41.7629 2.10132
\(396\) 0 0
\(397\) 33.2770 1.67012 0.835061 0.550157i \(-0.185432\pi\)
0.835061 + 0.550157i \(0.185432\pi\)
\(398\) 0 0
\(399\) 4.75644 0.238120
\(400\) 0 0
\(401\) −21.2385 −1.06060 −0.530299 0.847811i \(-0.677920\pi\)
−0.530299 + 0.847811i \(0.677920\pi\)
\(402\) 0 0
\(403\) 14.7475 0.734624
\(404\) 0 0
\(405\) 29.5530 1.46850
\(406\) 0 0
\(407\) −22.3525 −1.10797
\(408\) 0 0
\(409\) 14.5580 0.719849 0.359924 0.932981i \(-0.382802\pi\)
0.359924 + 0.932981i \(0.382802\pi\)
\(410\) 0 0
\(411\) 4.85376 0.239418
\(412\) 0 0
\(413\) 21.2343 1.04487
\(414\) 0 0
\(415\) 6.01645 0.295336
\(416\) 0 0
\(417\) 1.99258 0.0975769
\(418\) 0 0
\(419\) 26.7092 1.30483 0.652416 0.757861i \(-0.273756\pi\)
0.652416 + 0.757861i \(0.273756\pi\)
\(420\) 0 0
\(421\) −27.3395 −1.33245 −0.666223 0.745752i \(-0.732090\pi\)
−0.666223 + 0.745752i \(0.732090\pi\)
\(422\) 0 0
\(423\) 0.193110 0.00938934
\(424\) 0 0
\(425\) −77.0820 −3.73902
\(426\) 0 0
\(427\) 8.81067 0.426378
\(428\) 0 0
\(429\) −4.71573 −0.227678
\(430\) 0 0
\(431\) −25.8344 −1.24440 −0.622199 0.782859i \(-0.713761\pi\)
−0.622199 + 0.782859i \(0.713761\pi\)
\(432\) 0 0
\(433\) 4.10488 0.197268 0.0986340 0.995124i \(-0.468553\pi\)
0.0986340 + 0.995124i \(0.468553\pi\)
\(434\) 0 0
\(435\) 12.0062 0.575656
\(436\) 0 0
\(437\) 32.5693 1.55800
\(438\) 0 0
\(439\) −28.5009 −1.36027 −0.680137 0.733085i \(-0.738080\pi\)
−0.680137 + 0.733085i \(0.738080\pi\)
\(440\) 0 0
\(441\) 1.72804 0.0822876
\(442\) 0 0
\(443\) −2.09069 −0.0993316 −0.0496658 0.998766i \(-0.515816\pi\)
−0.0496658 + 0.998766i \(0.515816\pi\)
\(444\) 0 0
\(445\) −34.8235 −1.65079
\(446\) 0 0
\(447\) −0.949582 −0.0449137
\(448\) 0 0
\(449\) −20.2633 −0.956285 −0.478143 0.878282i \(-0.658690\pi\)
−0.478143 + 0.878282i \(0.658690\pi\)
\(450\) 0 0
\(451\) 13.8145 0.650500
\(452\) 0 0
\(453\) −5.27483 −0.247833
\(454\) 0 0
\(455\) −33.1222 −1.55279
\(456\) 0 0
\(457\) −15.3056 −0.715968 −0.357984 0.933728i \(-0.616536\pi\)
−0.357984 + 0.933728i \(0.616536\pi\)
\(458\) 0 0
\(459\) 17.5561 0.819450
\(460\) 0 0
\(461\) 36.0225 1.67773 0.838867 0.544336i \(-0.183218\pi\)
0.838867 + 0.544336i \(0.183218\pi\)
\(462\) 0 0
\(463\) −22.9678 −1.06740 −0.533702 0.845673i \(-0.679200\pi\)
−0.533702 + 0.845673i \(0.679200\pi\)
\(464\) 0 0
\(465\) −7.33007 −0.339924
\(466\) 0 0
\(467\) 1.03068 0.0476941 0.0238471 0.999716i \(-0.492409\pi\)
0.0238471 + 0.999716i \(0.492409\pi\)
\(468\) 0 0
\(469\) 18.3264 0.846235
\(470\) 0 0
\(471\) 1.22550 0.0564679
\(472\) 0 0
\(473\) −32.4311 −1.49118
\(474\) 0 0
\(475\) 48.1423 2.20892
\(476\) 0 0
\(477\) −25.6533 −1.17458
\(478\) 0 0
\(479\) 37.6486 1.72021 0.860103 0.510120i \(-0.170399\pi\)
0.860103 + 0.510120i \(0.170399\pi\)
\(480\) 0 0
\(481\) 21.6506 0.987180
\(482\) 0 0
\(483\) 7.57888 0.344851
\(484\) 0 0
\(485\) −9.65563 −0.438439
\(486\) 0 0
\(487\) 26.2919 1.19140 0.595700 0.803207i \(-0.296875\pi\)
0.595700 + 0.803207i \(0.296875\pi\)
\(488\) 0 0
\(489\) −4.88243 −0.220791
\(490\) 0 0
\(491\) −2.92374 −0.131947 −0.0659733 0.997821i \(-0.521015\pi\)
−0.0659733 + 0.997821i \(0.521015\pi\)
\(492\) 0 0
\(493\) −52.7846 −2.37730
\(494\) 0 0
\(495\) −38.2436 −1.71892
\(496\) 0 0
\(497\) 8.25769 0.370408
\(498\) 0 0
\(499\) 5.40783 0.242088 0.121044 0.992647i \(-0.461376\pi\)
0.121044 + 0.992647i \(0.461376\pi\)
\(500\) 0 0
\(501\) 1.52491 0.0681282
\(502\) 0 0
\(503\) 13.6924 0.610513 0.305257 0.952270i \(-0.401258\pi\)
0.305257 + 0.952270i \(0.401258\pi\)
\(504\) 0 0
\(505\) 37.8273 1.68329
\(506\) 0 0
\(507\) −0.843362 −0.0374550
\(508\) 0 0
\(509\) 38.1325 1.69020 0.845098 0.534612i \(-0.179542\pi\)
0.845098 + 0.534612i \(0.179542\pi\)
\(510\) 0 0
\(511\) 28.5574 1.26330
\(512\) 0 0
\(513\) −10.9649 −0.484111
\(514\) 0 0
\(515\) −71.6409 −3.15688
\(516\) 0 0
\(517\) −0.233643 −0.0102756
\(518\) 0 0
\(519\) −8.20818 −0.360299
\(520\) 0 0
\(521\) −21.2455 −0.930781 −0.465390 0.885105i \(-0.654086\pi\)
−0.465390 + 0.885105i \(0.654086\pi\)
\(522\) 0 0
\(523\) 2.96494 0.129648 0.0648238 0.997897i \(-0.479351\pi\)
0.0648238 + 0.997897i \(0.479351\pi\)
\(524\) 0 0
\(525\) 11.2027 0.488927
\(526\) 0 0
\(527\) 32.2261 1.40379
\(528\) 0 0
\(529\) 28.8957 1.25633
\(530\) 0 0
\(531\) −23.7476 −1.03056
\(532\) 0 0
\(533\) −13.3807 −0.579582
\(534\) 0 0
\(535\) 34.0945 1.47404
\(536\) 0 0
\(537\) −8.90167 −0.384136
\(538\) 0 0
\(539\) −2.09075 −0.0900549
\(540\) 0 0
\(541\) −1.64629 −0.0707795 −0.0353898 0.999374i \(-0.511267\pi\)
−0.0353898 + 0.999374i \(0.511267\pi\)
\(542\) 0 0
\(543\) −8.54986 −0.366910
\(544\) 0 0
\(545\) 29.5994 1.26790
\(546\) 0 0
\(547\) −22.8332 −0.976279 −0.488139 0.872766i \(-0.662324\pi\)
−0.488139 + 0.872766i \(0.662324\pi\)
\(548\) 0 0
\(549\) −9.85351 −0.420537
\(550\) 0 0
\(551\) 32.9671 1.40445
\(552\) 0 0
\(553\) 26.6847 1.13475
\(554\) 0 0
\(555\) −10.7612 −0.456786
\(556\) 0 0
\(557\) 2.83084 0.119947 0.0599733 0.998200i \(-0.480898\pi\)
0.0599733 + 0.998200i \(0.480898\pi\)
\(558\) 0 0
\(559\) 31.4126 1.32861
\(560\) 0 0
\(561\) −10.3048 −0.435068
\(562\) 0 0
\(563\) −16.2716 −0.685766 −0.342883 0.939378i \(-0.611403\pi\)
−0.342883 + 0.939378i \(0.611403\pi\)
\(564\) 0 0
\(565\) 79.2932 3.33589
\(566\) 0 0
\(567\) 18.8830 0.793013
\(568\) 0 0
\(569\) −27.0818 −1.13533 −0.567664 0.823260i \(-0.692153\pi\)
−0.567664 + 0.823260i \(0.692153\pi\)
\(570\) 0 0
\(571\) −30.6590 −1.28304 −0.641520 0.767107i \(-0.721696\pi\)
−0.641520 + 0.767107i \(0.721696\pi\)
\(572\) 0 0
\(573\) −2.63761 −0.110188
\(574\) 0 0
\(575\) 76.7097 3.19901
\(576\) 0 0
\(577\) 2.19730 0.0914749 0.0457374 0.998953i \(-0.485436\pi\)
0.0457374 + 0.998953i \(0.485436\pi\)
\(578\) 0 0
\(579\) −0.833293 −0.0346305
\(580\) 0 0
\(581\) 3.84425 0.159486
\(582\) 0 0
\(583\) 31.0378 1.28546
\(584\) 0 0
\(585\) 37.0426 1.53152
\(586\) 0 0
\(587\) 4.26846 0.176178 0.0880891 0.996113i \(-0.471924\pi\)
0.0880891 + 0.996113i \(0.471924\pi\)
\(588\) 0 0
\(589\) −20.1271 −0.829324
\(590\) 0 0
\(591\) −3.57040 −0.146867
\(592\) 0 0
\(593\) −12.2142 −0.501578 −0.250789 0.968042i \(-0.580690\pi\)
−0.250789 + 0.968042i \(0.580690\pi\)
\(594\) 0 0
\(595\) −72.3784 −2.96723
\(596\) 0 0
\(597\) −4.74983 −0.194398
\(598\) 0 0
\(599\) −33.3761 −1.36371 −0.681856 0.731487i \(-0.738827\pi\)
−0.681856 + 0.731487i \(0.738827\pi\)
\(600\) 0 0
\(601\) 40.8036 1.66441 0.832206 0.554466i \(-0.187078\pi\)
0.832206 + 0.554466i \(0.187078\pi\)
\(602\) 0 0
\(603\) −20.4955 −0.834643
\(604\) 0 0
\(605\) 2.75698 0.112087
\(606\) 0 0
\(607\) −29.2049 −1.18539 −0.592695 0.805427i \(-0.701936\pi\)
−0.592695 + 0.805427i \(0.701936\pi\)
\(608\) 0 0
\(609\) 7.67146 0.310863
\(610\) 0 0
\(611\) 0.226306 0.00915536
\(612\) 0 0
\(613\) −26.8257 −1.08348 −0.541741 0.840546i \(-0.682235\pi\)
−0.541741 + 0.840546i \(0.682235\pi\)
\(614\) 0 0
\(615\) 6.65072 0.268183
\(616\) 0 0
\(617\) 13.5959 0.547349 0.273675 0.961822i \(-0.411761\pi\)
0.273675 + 0.961822i \(0.411761\pi\)
\(618\) 0 0
\(619\) −31.7095 −1.27451 −0.637257 0.770651i \(-0.719931\pi\)
−0.637257 + 0.770651i \(0.719931\pi\)
\(620\) 0 0
\(621\) −17.4713 −0.701101
\(622\) 0 0
\(623\) −22.2507 −0.891454
\(624\) 0 0
\(625\) 35.1464 1.40586
\(626\) 0 0
\(627\) 6.43595 0.257027
\(628\) 0 0
\(629\) 47.3106 1.88640
\(630\) 0 0
\(631\) −34.6540 −1.37956 −0.689778 0.724021i \(-0.742292\pi\)
−0.689778 + 0.724021i \(0.742292\pi\)
\(632\) 0 0
\(633\) −10.8775 −0.432340
\(634\) 0 0
\(635\) 79.6570 3.16109
\(636\) 0 0
\(637\) 2.02509 0.0802370
\(638\) 0 0
\(639\) −9.23508 −0.365334
\(640\) 0 0
\(641\) −16.3012 −0.643857 −0.321929 0.946764i \(-0.604331\pi\)
−0.321929 + 0.946764i \(0.604331\pi\)
\(642\) 0 0
\(643\) 10.2511 0.404264 0.202132 0.979358i \(-0.435213\pi\)
0.202132 + 0.979358i \(0.435213\pi\)
\(644\) 0 0
\(645\) −15.6133 −0.614773
\(646\) 0 0
\(647\) −28.0119 −1.10126 −0.550630 0.834749i \(-0.685612\pi\)
−0.550630 + 0.834749i \(0.685612\pi\)
\(648\) 0 0
\(649\) 28.7321 1.12783
\(650\) 0 0
\(651\) −4.68359 −0.183564
\(652\) 0 0
\(653\) −42.7086 −1.67132 −0.835659 0.549249i \(-0.814914\pi\)
−0.835659 + 0.549249i \(0.814914\pi\)
\(654\) 0 0
\(655\) −14.5148 −0.567139
\(656\) 0 0
\(657\) −31.9375 −1.24600
\(658\) 0 0
\(659\) −23.5297 −0.916586 −0.458293 0.888801i \(-0.651539\pi\)
−0.458293 + 0.888801i \(0.651539\pi\)
\(660\) 0 0
\(661\) −30.6562 −1.19239 −0.596194 0.802840i \(-0.703321\pi\)
−0.596194 + 0.802840i \(0.703321\pi\)
\(662\) 0 0
\(663\) 9.98116 0.387636
\(664\) 0 0
\(665\) 45.2047 1.75296
\(666\) 0 0
\(667\) 52.5296 2.03395
\(668\) 0 0
\(669\) 7.21445 0.278927
\(670\) 0 0
\(671\) 11.9217 0.460233
\(672\) 0 0
\(673\) −43.7867 −1.68785 −0.843926 0.536459i \(-0.819762\pi\)
−0.843926 + 0.536459i \(0.819762\pi\)
\(674\) 0 0
\(675\) −25.8253 −0.994015
\(676\) 0 0
\(677\) 33.6766 1.29430 0.647148 0.762364i \(-0.275961\pi\)
0.647148 + 0.762364i \(0.275961\pi\)
\(678\) 0 0
\(679\) −6.16952 −0.236764
\(680\) 0 0
\(681\) −0.0600643 −0.00230167
\(682\) 0 0
\(683\) 19.0664 0.729557 0.364778 0.931094i \(-0.381145\pi\)
0.364778 + 0.931094i \(0.381145\pi\)
\(684\) 0 0
\(685\) 46.1295 1.76252
\(686\) 0 0
\(687\) −6.06337 −0.231332
\(688\) 0 0
\(689\) −30.0631 −1.14531
\(690\) 0 0
\(691\) 18.3146 0.696722 0.348361 0.937361i \(-0.386738\pi\)
0.348361 + 0.937361i \(0.386738\pi\)
\(692\) 0 0
\(693\) −24.4360 −0.928246
\(694\) 0 0
\(695\) 18.9372 0.718329
\(696\) 0 0
\(697\) −29.2394 −1.10752
\(698\) 0 0
\(699\) 7.68841 0.290803
\(700\) 0 0
\(701\) −18.0765 −0.682740 −0.341370 0.939929i \(-0.610891\pi\)
−0.341370 + 0.939929i \(0.610891\pi\)
\(702\) 0 0
\(703\) −29.5483 −1.11444
\(704\) 0 0
\(705\) −0.112483 −0.00423635
\(706\) 0 0
\(707\) 24.1700 0.909006
\(708\) 0 0
\(709\) 24.6654 0.926327 0.463164 0.886273i \(-0.346714\pi\)
0.463164 + 0.886273i \(0.346714\pi\)
\(710\) 0 0
\(711\) −29.8431 −1.11920
\(712\) 0 0
\(713\) −32.0704 −1.20105
\(714\) 0 0
\(715\) −44.8177 −1.67609
\(716\) 0 0
\(717\) −10.2750 −0.383728
\(718\) 0 0
\(719\) 11.6829 0.435699 0.217849 0.975982i \(-0.430096\pi\)
0.217849 + 0.975982i \(0.430096\pi\)
\(720\) 0 0
\(721\) −45.7754 −1.70476
\(722\) 0 0
\(723\) 1.64362 0.0611269
\(724\) 0 0
\(725\) 77.6467 2.88372
\(726\) 0 0
\(727\) 19.9582 0.740210 0.370105 0.928990i \(-0.379322\pi\)
0.370105 + 0.928990i \(0.379322\pi\)
\(728\) 0 0
\(729\) −18.0896 −0.669987
\(730\) 0 0
\(731\) 68.6426 2.53884
\(732\) 0 0
\(733\) −48.0802 −1.77588 −0.887941 0.459957i \(-0.847865\pi\)
−0.887941 + 0.459957i \(0.847865\pi\)
\(734\) 0 0
\(735\) −1.00655 −0.0371271
\(736\) 0 0
\(737\) 24.7975 0.913428
\(738\) 0 0
\(739\) −43.9960 −1.61842 −0.809209 0.587521i \(-0.800104\pi\)
−0.809209 + 0.587521i \(0.800104\pi\)
\(740\) 0 0
\(741\) −6.23384 −0.229006
\(742\) 0 0
\(743\) 16.0686 0.589500 0.294750 0.955574i \(-0.404764\pi\)
0.294750 + 0.955574i \(0.404764\pi\)
\(744\) 0 0
\(745\) −9.02471 −0.330640
\(746\) 0 0
\(747\) −4.29926 −0.157302
\(748\) 0 0
\(749\) 21.7849 0.796003
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −4.33418 −0.157946
\(754\) 0 0
\(755\) −50.1314 −1.82447
\(756\) 0 0
\(757\) −3.40087 −0.123607 −0.0618034 0.998088i \(-0.519685\pi\)
−0.0618034 + 0.998088i \(0.519685\pi\)
\(758\) 0 0
\(759\) 10.2550 0.372233
\(760\) 0 0
\(761\) 15.0807 0.546674 0.273337 0.961918i \(-0.411873\pi\)
0.273337 + 0.961918i \(0.411873\pi\)
\(762\) 0 0
\(763\) 18.9127 0.684685
\(764\) 0 0
\(765\) 80.9452 2.92658
\(766\) 0 0
\(767\) −27.8298 −1.00488
\(768\) 0 0
\(769\) 37.8490 1.36487 0.682436 0.730946i \(-0.260921\pi\)
0.682436 + 0.730946i \(0.260921\pi\)
\(770\) 0 0
\(771\) −0.831069 −0.0299302
\(772\) 0 0
\(773\) −1.68818 −0.0607198 −0.0303599 0.999539i \(-0.509665\pi\)
−0.0303599 + 0.999539i \(0.509665\pi\)
\(774\) 0 0
\(775\) −47.4049 −1.70283
\(776\) 0 0
\(777\) −6.87590 −0.246672
\(778\) 0 0
\(779\) 18.2618 0.654295
\(780\) 0 0
\(781\) 11.1735 0.399819
\(782\) 0 0
\(783\) −17.6847 −0.632001
\(784\) 0 0
\(785\) 11.6470 0.415699
\(786\) 0 0
\(787\) 21.1509 0.753949 0.376975 0.926224i \(-0.376964\pi\)
0.376975 + 0.926224i \(0.376964\pi\)
\(788\) 0 0
\(789\) −1.92376 −0.0684875
\(790\) 0 0
\(791\) 50.6648 1.80143
\(792\) 0 0
\(793\) −11.5473 −0.410058
\(794\) 0 0
\(795\) 14.9425 0.529957
\(796\) 0 0
\(797\) 53.5742 1.89770 0.948848 0.315733i \(-0.102250\pi\)
0.948848 + 0.315733i \(0.102250\pi\)
\(798\) 0 0
\(799\) 0.494522 0.0174949
\(800\) 0 0
\(801\) 24.8843 0.879242
\(802\) 0 0
\(803\) 38.6410 1.36361
\(804\) 0 0
\(805\) 72.0288 2.53868
\(806\) 0 0
\(807\) 5.93117 0.208787
\(808\) 0 0
\(809\) 28.8424 1.01404 0.507022 0.861933i \(-0.330746\pi\)
0.507022 + 0.861933i \(0.330746\pi\)
\(810\) 0 0
\(811\) −40.4030 −1.41874 −0.709371 0.704835i \(-0.751021\pi\)
−0.709371 + 0.704835i \(0.751021\pi\)
\(812\) 0 0
\(813\) −8.99307 −0.315401
\(814\) 0 0
\(815\) −46.4021 −1.62539
\(816\) 0 0
\(817\) −42.8715 −1.49988
\(818\) 0 0
\(819\) 23.6686 0.827047
\(820\) 0 0
\(821\) 50.4957 1.76231 0.881157 0.472824i \(-0.156765\pi\)
0.881157 + 0.472824i \(0.156765\pi\)
\(822\) 0 0
\(823\) 47.2314 1.64638 0.823191 0.567764i \(-0.192192\pi\)
0.823191 + 0.567764i \(0.192192\pi\)
\(824\) 0 0
\(825\) 15.1584 0.527749
\(826\) 0 0
\(827\) −14.3757 −0.499892 −0.249946 0.968260i \(-0.580413\pi\)
−0.249946 + 0.968260i \(0.580413\pi\)
\(828\) 0 0
\(829\) −1.41240 −0.0490548 −0.0245274 0.999699i \(-0.507808\pi\)
−0.0245274 + 0.999699i \(0.507808\pi\)
\(830\) 0 0
\(831\) −5.98029 −0.207454
\(832\) 0 0
\(833\) 4.42521 0.153325
\(834\) 0 0
\(835\) 14.4926 0.501537
\(836\) 0 0
\(837\) 10.7969 0.373196
\(838\) 0 0
\(839\) −0.522791 −0.0180488 −0.00902438 0.999959i \(-0.502873\pi\)
−0.00902438 + 0.999959i \(0.502873\pi\)
\(840\) 0 0
\(841\) 24.1713 0.833492
\(842\) 0 0
\(843\) 1.42985 0.0492466
\(844\) 0 0
\(845\) −8.01521 −0.275732
\(846\) 0 0
\(847\) 1.76159 0.0605289
\(848\) 0 0
\(849\) 1.37918 0.0473332
\(850\) 0 0
\(851\) −47.0821 −1.61395
\(852\) 0 0
\(853\) −3.31887 −0.113636 −0.0568180 0.998385i \(-0.518095\pi\)
−0.0568180 + 0.998385i \(0.518095\pi\)
\(854\) 0 0
\(855\) −50.5552 −1.72895
\(856\) 0 0
\(857\) 4.52657 0.154625 0.0773124 0.997007i \(-0.475366\pi\)
0.0773124 + 0.997007i \(0.475366\pi\)
\(858\) 0 0
\(859\) 13.2237 0.451186 0.225593 0.974222i \(-0.427568\pi\)
0.225593 + 0.974222i \(0.427568\pi\)
\(860\) 0 0
\(861\) 4.24951 0.144823
\(862\) 0 0
\(863\) 10.4020 0.354089 0.177044 0.984203i \(-0.443346\pi\)
0.177044 + 0.984203i \(0.443346\pi\)
\(864\) 0 0
\(865\) −78.0095 −2.65240
\(866\) 0 0
\(867\) 14.7348 0.500421
\(868\) 0 0
\(869\) 36.1071 1.22485
\(870\) 0 0
\(871\) −24.0187 −0.813844
\(872\) 0 0
\(873\) 6.89975 0.233521
\(874\) 0 0
\(875\) 56.4763 1.90925
\(876\) 0 0
\(877\) 32.1045 1.08409 0.542047 0.840348i \(-0.317650\pi\)
0.542047 + 0.840348i \(0.317650\pi\)
\(878\) 0 0
\(879\) 3.29152 0.111020
\(880\) 0 0
\(881\) −46.1835 −1.55596 −0.777981 0.628288i \(-0.783756\pi\)
−0.777981 + 0.628288i \(0.783756\pi\)
\(882\) 0 0
\(883\) −15.3369 −0.516127 −0.258063 0.966128i \(-0.583084\pi\)
−0.258063 + 0.966128i \(0.583084\pi\)
\(884\) 0 0
\(885\) 13.8325 0.464974
\(886\) 0 0
\(887\) −27.1206 −0.910620 −0.455310 0.890333i \(-0.650472\pi\)
−0.455310 + 0.890333i \(0.650472\pi\)
\(888\) 0 0
\(889\) 50.8973 1.70704
\(890\) 0 0
\(891\) 25.5507 0.855980
\(892\) 0 0
\(893\) −0.308859 −0.0103356
\(894\) 0 0
\(895\) −84.6005 −2.82788
\(896\) 0 0
\(897\) −9.93295 −0.331652
\(898\) 0 0
\(899\) −32.4622 −1.08267
\(900\) 0 0
\(901\) −65.6937 −2.18857
\(902\) 0 0
\(903\) −9.97620 −0.331987
\(904\) 0 0
\(905\) −81.2568 −2.70107
\(906\) 0 0
\(907\) 16.8042 0.557976 0.278988 0.960295i \(-0.410001\pi\)
0.278988 + 0.960295i \(0.410001\pi\)
\(908\) 0 0
\(909\) −27.0308 −0.896554
\(910\) 0 0
\(911\) 40.9944 1.35820 0.679102 0.734044i \(-0.262369\pi\)
0.679102 + 0.734044i \(0.262369\pi\)
\(912\) 0 0
\(913\) 5.20166 0.172150
\(914\) 0 0
\(915\) 5.73947 0.189741
\(916\) 0 0
\(917\) −9.27430 −0.306264
\(918\) 0 0
\(919\) −2.07414 −0.0684197 −0.0342098 0.999415i \(-0.510891\pi\)
−0.0342098 + 0.999415i \(0.510891\pi\)
\(920\) 0 0
\(921\) 4.36246 0.143748
\(922\) 0 0
\(923\) −10.8226 −0.356230
\(924\) 0 0
\(925\) −69.5944 −2.28825
\(926\) 0 0
\(927\) 51.1934 1.68141
\(928\) 0 0
\(929\) −30.3153 −0.994612 −0.497306 0.867575i \(-0.665677\pi\)
−0.497306 + 0.867575i \(0.665677\pi\)
\(930\) 0 0
\(931\) −2.76381 −0.0905803
\(932\) 0 0
\(933\) −1.79929 −0.0589060
\(934\) 0 0
\(935\) −97.9354 −3.20283
\(936\) 0 0
\(937\) −15.0261 −0.490881 −0.245440 0.969412i \(-0.578933\pi\)
−0.245440 + 0.969412i \(0.578933\pi\)
\(938\) 0 0
\(939\) 6.84991 0.223538
\(940\) 0 0
\(941\) −25.7935 −0.840843 −0.420422 0.907329i \(-0.638118\pi\)
−0.420422 + 0.907329i \(0.638118\pi\)
\(942\) 0 0
\(943\) 29.0981 0.947566
\(944\) 0 0
\(945\) −24.2494 −0.788833
\(946\) 0 0
\(947\) 47.9193 1.55717 0.778584 0.627540i \(-0.215938\pi\)
0.778584 + 0.627540i \(0.215938\pi\)
\(948\) 0 0
\(949\) −37.4276 −1.21495
\(950\) 0 0
\(951\) −10.0582 −0.326161
\(952\) 0 0
\(953\) −45.9750 −1.48928 −0.744638 0.667469i \(-0.767378\pi\)
−0.744638 + 0.667469i \(0.767378\pi\)
\(954\) 0 0
\(955\) −25.0676 −0.811168
\(956\) 0 0
\(957\) 10.3803 0.335546
\(958\) 0 0
\(959\) 29.4747 0.951788
\(960\) 0 0
\(961\) −11.1812 −0.360683
\(962\) 0 0
\(963\) −24.3634 −0.785099
\(964\) 0 0
\(965\) −7.91952 −0.254938
\(966\) 0 0
\(967\) 41.1328 1.32274 0.661371 0.750059i \(-0.269975\pi\)
0.661371 + 0.750059i \(0.269975\pi\)
\(968\) 0 0
\(969\) −13.6221 −0.437606
\(970\) 0 0
\(971\) −7.13673 −0.229028 −0.114514 0.993422i \(-0.536531\pi\)
−0.114514 + 0.993422i \(0.536531\pi\)
\(972\) 0 0
\(973\) 12.1000 0.387909
\(974\) 0 0
\(975\) −14.6824 −0.470213
\(976\) 0 0
\(977\) −31.7605 −1.01611 −0.508054 0.861325i \(-0.669635\pi\)
−0.508054 + 0.861325i \(0.669635\pi\)
\(978\) 0 0
\(979\) −30.1074 −0.962237
\(980\) 0 0
\(981\) −21.1512 −0.675306
\(982\) 0 0
\(983\) 16.0639 0.512359 0.256180 0.966629i \(-0.417536\pi\)
0.256180 + 0.966629i \(0.417536\pi\)
\(984\) 0 0
\(985\) −33.9326 −1.08118
\(986\) 0 0
\(987\) −0.0718715 −0.00228770
\(988\) 0 0
\(989\) −68.3111 −2.17217
\(990\) 0 0
\(991\) −19.7424 −0.627138 −0.313569 0.949565i \(-0.601525\pi\)
−0.313569 + 0.949565i \(0.601525\pi\)
\(992\) 0 0
\(993\) 5.45408 0.173080
\(994\) 0 0
\(995\) −45.1418 −1.43109
\(996\) 0 0
\(997\) −12.2962 −0.389426 −0.194713 0.980860i \(-0.562378\pi\)
−0.194713 + 0.980860i \(0.562378\pi\)
\(998\) 0 0
\(999\) 15.8508 0.501497
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 \(a_p\))