Properties

Label 6003.2.a.t.1.10
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.424349 q^{2} -1.81993 q^{4} -2.43761 q^{5} +3.41293 q^{7} +1.62098 q^{8} +O(q^{10})\) \(q-0.424349 q^{2} -1.81993 q^{4} -2.43761 q^{5} +3.41293 q^{7} +1.62098 q^{8} +1.03440 q^{10} +5.84264 q^{11} -6.73637 q^{13} -1.44828 q^{14} +2.95199 q^{16} -4.57994 q^{17} +3.36654 q^{19} +4.43628 q^{20} -2.47932 q^{22} +1.00000 q^{23} +0.941962 q^{25} +2.85857 q^{26} -6.21129 q^{28} +1.00000 q^{29} -2.25875 q^{31} -4.49464 q^{32} +1.94349 q^{34} -8.31942 q^{35} -4.84124 q^{37} -1.42859 q^{38} -3.95133 q^{40} -4.80077 q^{41} +7.09307 q^{43} -10.6332 q^{44} -0.424349 q^{46} -3.50228 q^{47} +4.64812 q^{49} -0.399721 q^{50} +12.2597 q^{52} +0.803109 q^{53} -14.2421 q^{55} +5.53231 q^{56} -0.424349 q^{58} +8.37512 q^{59} -12.3218 q^{61} +0.958499 q^{62} -3.99669 q^{64} +16.4207 q^{65} +7.03184 q^{67} +8.33516 q^{68} +3.53034 q^{70} +6.87668 q^{71} -3.29707 q^{73} +2.05438 q^{74} -6.12686 q^{76} +19.9406 q^{77} -12.0450 q^{79} -7.19582 q^{80} +2.03720 q^{82} +15.2301 q^{83} +11.1641 q^{85} -3.00994 q^{86} +9.47082 q^{88} +7.50144 q^{89} -22.9908 q^{91} -1.81993 q^{92} +1.48619 q^{94} -8.20633 q^{95} -9.65226 q^{97} -1.97243 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.424349 −0.300060 −0.150030 0.988681i \(-0.547937\pi\)
−0.150030 + 0.988681i \(0.547937\pi\)
\(3\) 0 0
\(4\) −1.81993 −0.909964
\(5\) −2.43761 −1.09013 −0.545067 0.838392i \(-0.683496\pi\)
−0.545067 + 0.838392i \(0.683496\pi\)
\(6\) 0 0
\(7\) 3.41293 1.28997 0.644984 0.764196i \(-0.276864\pi\)
0.644984 + 0.764196i \(0.276864\pi\)
\(8\) 1.62098 0.573104
\(9\) 0 0
\(10\) 1.03440 0.327106
\(11\) 5.84264 1.76162 0.880811 0.473468i \(-0.156998\pi\)
0.880811 + 0.473468i \(0.156998\pi\)
\(12\) 0 0
\(13\) −6.73637 −1.86833 −0.934167 0.356837i \(-0.883855\pi\)
−0.934167 + 0.356837i \(0.883855\pi\)
\(14\) −1.44828 −0.387068
\(15\) 0 0
\(16\) 2.95199 0.737998
\(17\) −4.57994 −1.11080 −0.555399 0.831584i \(-0.687435\pi\)
−0.555399 + 0.831584i \(0.687435\pi\)
\(18\) 0 0
\(19\) 3.36654 0.772337 0.386169 0.922428i \(-0.373798\pi\)
0.386169 + 0.922428i \(0.373798\pi\)
\(20\) 4.43628 0.991983
\(21\) 0 0
\(22\) −2.47932 −0.528593
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0.941962 0.188392
\(26\) 2.85857 0.560612
\(27\) 0 0
\(28\) −6.21129 −1.17382
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −2.25875 −0.405684 −0.202842 0.979212i \(-0.565018\pi\)
−0.202842 + 0.979212i \(0.565018\pi\)
\(32\) −4.49464 −0.794548
\(33\) 0 0
\(34\) 1.94349 0.333306
\(35\) −8.31942 −1.40624
\(36\) 0 0
\(37\) −4.84124 −0.795895 −0.397948 0.917408i \(-0.630277\pi\)
−0.397948 + 0.917408i \(0.630277\pi\)
\(38\) −1.42859 −0.231748
\(39\) 0 0
\(40\) −3.95133 −0.624760
\(41\) −4.80077 −0.749754 −0.374877 0.927075i \(-0.622315\pi\)
−0.374877 + 0.927075i \(0.622315\pi\)
\(42\) 0 0
\(43\) 7.09307 1.08168 0.540841 0.841125i \(-0.318106\pi\)
0.540841 + 0.841125i \(0.318106\pi\)
\(44\) −10.6332 −1.60301
\(45\) 0 0
\(46\) −0.424349 −0.0625669
\(47\) −3.50228 −0.510860 −0.255430 0.966828i \(-0.582217\pi\)
−0.255430 + 0.966828i \(0.582217\pi\)
\(48\) 0 0
\(49\) 4.64812 0.664017
\(50\) −0.399721 −0.0565291
\(51\) 0 0
\(52\) 12.2597 1.70012
\(53\) 0.803109 0.110316 0.0551578 0.998478i \(-0.482434\pi\)
0.0551578 + 0.998478i \(0.482434\pi\)
\(54\) 0 0
\(55\) −14.2421 −1.92040
\(56\) 5.53231 0.739286
\(57\) 0 0
\(58\) −0.424349 −0.0557198
\(59\) 8.37512 1.09035 0.545174 0.838323i \(-0.316464\pi\)
0.545174 + 0.838323i \(0.316464\pi\)
\(60\) 0 0
\(61\) −12.3218 −1.57764 −0.788821 0.614623i \(-0.789308\pi\)
−0.788821 + 0.614623i \(0.789308\pi\)
\(62\) 0.958499 0.121729
\(63\) 0 0
\(64\) −3.99669 −0.499586
\(65\) 16.4207 2.03673
\(66\) 0 0
\(67\) 7.03184 0.859076 0.429538 0.903049i \(-0.358677\pi\)
0.429538 + 0.903049i \(0.358677\pi\)
\(68\) 8.33516 1.01079
\(69\) 0 0
\(70\) 3.53034 0.421956
\(71\) 6.87668 0.816112 0.408056 0.912957i \(-0.366207\pi\)
0.408056 + 0.912957i \(0.366207\pi\)
\(72\) 0 0
\(73\) −3.29707 −0.385893 −0.192946 0.981209i \(-0.561804\pi\)
−0.192946 + 0.981209i \(0.561804\pi\)
\(74\) 2.05438 0.238816
\(75\) 0 0
\(76\) −6.12686 −0.702799
\(77\) 19.9406 2.27244
\(78\) 0 0
\(79\) −12.0450 −1.35517 −0.677584 0.735445i \(-0.736973\pi\)
−0.677584 + 0.735445i \(0.736973\pi\)
\(80\) −7.19582 −0.804517
\(81\) 0 0
\(82\) 2.03720 0.224971
\(83\) 15.2301 1.67172 0.835858 0.548945i \(-0.184970\pi\)
0.835858 + 0.548945i \(0.184970\pi\)
\(84\) 0 0
\(85\) 11.1641 1.21092
\(86\) −3.00994 −0.324570
\(87\) 0 0
\(88\) 9.47082 1.00959
\(89\) 7.50144 0.795151 0.397575 0.917570i \(-0.369852\pi\)
0.397575 + 0.917570i \(0.369852\pi\)
\(90\) 0 0
\(91\) −22.9908 −2.41009
\(92\) −1.81993 −0.189741
\(93\) 0 0
\(94\) 1.48619 0.153289
\(95\) −8.20633 −0.841951
\(96\) 0 0
\(97\) −9.65226 −0.980038 −0.490019 0.871712i \(-0.663010\pi\)
−0.490019 + 0.871712i \(0.663010\pi\)
\(98\) −1.97243 −0.199245
\(99\) 0 0
\(100\) −1.71430 −0.171430
\(101\) 6.89515 0.686094 0.343047 0.939318i \(-0.388541\pi\)
0.343047 + 0.939318i \(0.388541\pi\)
\(102\) 0 0
\(103\) 15.4211 1.51948 0.759742 0.650224i \(-0.225325\pi\)
0.759742 + 0.650224i \(0.225325\pi\)
\(104\) −10.9195 −1.07075
\(105\) 0 0
\(106\) −0.340799 −0.0331013
\(107\) 14.2228 1.37497 0.687486 0.726198i \(-0.258714\pi\)
0.687486 + 0.726198i \(0.258714\pi\)
\(108\) 0 0
\(109\) 6.67649 0.639492 0.319746 0.947503i \(-0.396403\pi\)
0.319746 + 0.947503i \(0.396403\pi\)
\(110\) 6.04362 0.576237
\(111\) 0 0
\(112\) 10.0750 0.951994
\(113\) −11.2542 −1.05870 −0.529352 0.848402i \(-0.677565\pi\)
−0.529352 + 0.848402i \(0.677565\pi\)
\(114\) 0 0
\(115\) −2.43761 −0.227309
\(116\) −1.81993 −0.168976
\(117\) 0 0
\(118\) −3.55397 −0.327170
\(119\) −15.6310 −1.43289
\(120\) 0 0
\(121\) 23.1365 2.10331
\(122\) 5.22874 0.473388
\(123\) 0 0
\(124\) 4.11076 0.369157
\(125\) 9.89193 0.884761
\(126\) 0 0
\(127\) −17.8522 −1.58413 −0.792063 0.610440i \(-0.790993\pi\)
−0.792063 + 0.610440i \(0.790993\pi\)
\(128\) 10.6853 0.944454
\(129\) 0 0
\(130\) −6.96810 −0.611143
\(131\) −6.10711 −0.533581 −0.266790 0.963755i \(-0.585963\pi\)
−0.266790 + 0.963755i \(0.585963\pi\)
\(132\) 0 0
\(133\) 11.4898 0.996291
\(134\) −2.98395 −0.257774
\(135\) 0 0
\(136\) −7.42401 −0.636603
\(137\) −16.6372 −1.42141 −0.710707 0.703488i \(-0.751625\pi\)
−0.710707 + 0.703488i \(0.751625\pi\)
\(138\) 0 0
\(139\) −17.3748 −1.47371 −0.736855 0.676051i \(-0.763690\pi\)
−0.736855 + 0.676051i \(0.763690\pi\)
\(140\) 15.1407 1.27963
\(141\) 0 0
\(142\) −2.91811 −0.244883
\(143\) −39.3582 −3.29130
\(144\) 0 0
\(145\) −2.43761 −0.202433
\(146\) 1.39911 0.115791
\(147\) 0 0
\(148\) 8.81071 0.724236
\(149\) −15.5254 −1.27189 −0.635947 0.771733i \(-0.719390\pi\)
−0.635947 + 0.771733i \(0.719390\pi\)
\(150\) 0 0
\(151\) −2.45313 −0.199633 −0.0998165 0.995006i \(-0.531826\pi\)
−0.0998165 + 0.995006i \(0.531826\pi\)
\(152\) 5.45711 0.442630
\(153\) 0 0
\(154\) −8.46176 −0.681868
\(155\) 5.50596 0.442250
\(156\) 0 0
\(157\) −2.35821 −0.188205 −0.0941027 0.995562i \(-0.529998\pi\)
−0.0941027 + 0.995562i \(0.529998\pi\)
\(158\) 5.11129 0.406632
\(159\) 0 0
\(160\) 10.9562 0.866164
\(161\) 3.41293 0.268977
\(162\) 0 0
\(163\) −16.3414 −1.27996 −0.639978 0.768393i \(-0.721057\pi\)
−0.639978 + 0.768393i \(0.721057\pi\)
\(164\) 8.73705 0.682249
\(165\) 0 0
\(166\) −6.46287 −0.501616
\(167\) −5.89276 −0.455995 −0.227998 0.973662i \(-0.573218\pi\)
−0.227998 + 0.973662i \(0.573218\pi\)
\(168\) 0 0
\(169\) 32.3787 2.49067
\(170\) −4.73749 −0.363349
\(171\) 0 0
\(172\) −12.9089 −0.984292
\(173\) −1.20279 −0.0914467 −0.0457234 0.998954i \(-0.514559\pi\)
−0.0457234 + 0.998954i \(0.514559\pi\)
\(174\) 0 0
\(175\) 3.21485 0.243020
\(176\) 17.2474 1.30007
\(177\) 0 0
\(178\) −3.18323 −0.238593
\(179\) −15.5040 −1.15883 −0.579413 0.815034i \(-0.696718\pi\)
−0.579413 + 0.815034i \(0.696718\pi\)
\(180\) 0 0
\(181\) −23.2463 −1.72789 −0.863943 0.503590i \(-0.832012\pi\)
−0.863943 + 0.503590i \(0.832012\pi\)
\(182\) 9.75612 0.723172
\(183\) 0 0
\(184\) 1.62098 0.119500
\(185\) 11.8011 0.867633
\(186\) 0 0
\(187\) −26.7589 −1.95681
\(188\) 6.37389 0.464864
\(189\) 0 0
\(190\) 3.48235 0.252636
\(191\) 18.0430 1.30555 0.652773 0.757553i \(-0.273605\pi\)
0.652773 + 0.757553i \(0.273605\pi\)
\(192\) 0 0
\(193\) 6.24298 0.449380 0.224690 0.974430i \(-0.427863\pi\)
0.224690 + 0.974430i \(0.427863\pi\)
\(194\) 4.09593 0.294070
\(195\) 0 0
\(196\) −8.45925 −0.604232
\(197\) 14.9870 1.06778 0.533891 0.845553i \(-0.320729\pi\)
0.533891 + 0.845553i \(0.320729\pi\)
\(198\) 0 0
\(199\) −4.83185 −0.342521 −0.171260 0.985226i \(-0.554784\pi\)
−0.171260 + 0.985226i \(0.554784\pi\)
\(200\) 1.52690 0.107968
\(201\) 0 0
\(202\) −2.92595 −0.205869
\(203\) 3.41293 0.239541
\(204\) 0 0
\(205\) 11.7024 0.817332
\(206\) −6.54393 −0.455937
\(207\) 0 0
\(208\) −19.8857 −1.37883
\(209\) 19.6695 1.36057
\(210\) 0 0
\(211\) 9.98291 0.687252 0.343626 0.939107i \(-0.388345\pi\)
0.343626 + 0.939107i \(0.388345\pi\)
\(212\) −1.46160 −0.100383
\(213\) 0 0
\(214\) −6.03544 −0.412574
\(215\) −17.2902 −1.17918
\(216\) 0 0
\(217\) −7.70897 −0.523319
\(218\) −2.83316 −0.191886
\(219\) 0 0
\(220\) 25.9196 1.74750
\(221\) 30.8522 2.07534
\(222\) 0 0
\(223\) −3.51605 −0.235452 −0.117726 0.993046i \(-0.537561\pi\)
−0.117726 + 0.993046i \(0.537561\pi\)
\(224\) −15.3399 −1.02494
\(225\) 0 0
\(226\) 4.77570 0.317675
\(227\) −9.22552 −0.612319 −0.306160 0.951980i \(-0.599044\pi\)
−0.306160 + 0.951980i \(0.599044\pi\)
\(228\) 0 0
\(229\) −8.97788 −0.593275 −0.296638 0.954990i \(-0.595865\pi\)
−0.296638 + 0.954990i \(0.595865\pi\)
\(230\) 1.03440 0.0682063
\(231\) 0 0
\(232\) 1.62098 0.106423
\(233\) −10.5134 −0.688753 −0.344376 0.938832i \(-0.611910\pi\)
−0.344376 + 0.938832i \(0.611910\pi\)
\(234\) 0 0
\(235\) 8.53720 0.556905
\(236\) −15.2421 −0.992177
\(237\) 0 0
\(238\) 6.63302 0.429955
\(239\) 14.4794 0.936596 0.468298 0.883571i \(-0.344867\pi\)
0.468298 + 0.883571i \(0.344867\pi\)
\(240\) 0 0
\(241\) 1.76018 0.113383 0.0566917 0.998392i \(-0.481945\pi\)
0.0566917 + 0.998392i \(0.481945\pi\)
\(242\) −9.81793 −0.631121
\(243\) 0 0
\(244\) 22.4248 1.43560
\(245\) −11.3303 −0.723868
\(246\) 0 0
\(247\) −22.6783 −1.44298
\(248\) −3.66140 −0.232499
\(249\) 0 0
\(250\) −4.19763 −0.265482
\(251\) 11.6685 0.736506 0.368253 0.929726i \(-0.379956\pi\)
0.368253 + 0.929726i \(0.379956\pi\)
\(252\) 0 0
\(253\) 5.84264 0.367324
\(254\) 7.57556 0.475333
\(255\) 0 0
\(256\) 3.45909 0.216193
\(257\) 9.01106 0.562094 0.281047 0.959694i \(-0.409318\pi\)
0.281047 + 0.959694i \(0.409318\pi\)
\(258\) 0 0
\(259\) −16.5228 −1.02668
\(260\) −29.8844 −1.85335
\(261\) 0 0
\(262\) 2.59155 0.160106
\(263\) −21.3050 −1.31372 −0.656861 0.754012i \(-0.728116\pi\)
−0.656861 + 0.754012i \(0.728116\pi\)
\(264\) 0 0
\(265\) −1.95767 −0.120259
\(266\) −4.87568 −0.298947
\(267\) 0 0
\(268\) −12.7974 −0.781728
\(269\) 6.35901 0.387716 0.193858 0.981030i \(-0.437900\pi\)
0.193858 + 0.981030i \(0.437900\pi\)
\(270\) 0 0
\(271\) −27.4931 −1.67009 −0.835044 0.550183i \(-0.814558\pi\)
−0.835044 + 0.550183i \(0.814558\pi\)
\(272\) −13.5200 −0.819767
\(273\) 0 0
\(274\) 7.05999 0.426510
\(275\) 5.50355 0.331876
\(276\) 0 0
\(277\) −29.7357 −1.78664 −0.893322 0.449417i \(-0.851632\pi\)
−0.893322 + 0.449417i \(0.851632\pi\)
\(278\) 7.37298 0.442202
\(279\) 0 0
\(280\) −13.4856 −0.805921
\(281\) −11.1902 −0.667550 −0.333775 0.942653i \(-0.608323\pi\)
−0.333775 + 0.942653i \(0.608323\pi\)
\(282\) 0 0
\(283\) 17.7812 1.05698 0.528492 0.848938i \(-0.322758\pi\)
0.528492 + 0.848938i \(0.322758\pi\)
\(284\) −12.5151 −0.742632
\(285\) 0 0
\(286\) 16.7016 0.987587
\(287\) −16.3847 −0.967158
\(288\) 0 0
\(289\) 3.97586 0.233874
\(290\) 1.03440 0.0607420
\(291\) 0 0
\(292\) 6.00043 0.351148
\(293\) −15.5413 −0.907931 −0.453966 0.891019i \(-0.649991\pi\)
−0.453966 + 0.891019i \(0.649991\pi\)
\(294\) 0 0
\(295\) −20.4153 −1.18863
\(296\) −7.84757 −0.456131
\(297\) 0 0
\(298\) 6.58821 0.381645
\(299\) −6.73637 −0.389574
\(300\) 0 0
\(301\) 24.2082 1.39534
\(302\) 1.04098 0.0599019
\(303\) 0 0
\(304\) 9.93800 0.569984
\(305\) 30.0357 1.71984
\(306\) 0 0
\(307\) 14.1411 0.807075 0.403538 0.914963i \(-0.367780\pi\)
0.403538 + 0.914963i \(0.367780\pi\)
\(308\) −36.2904 −2.06784
\(309\) 0 0
\(310\) −2.33645 −0.132701
\(311\) 17.5960 0.997780 0.498890 0.866665i \(-0.333741\pi\)
0.498890 + 0.866665i \(0.333741\pi\)
\(312\) 0 0
\(313\) 0.544433 0.0307732 0.0153866 0.999882i \(-0.495102\pi\)
0.0153866 + 0.999882i \(0.495102\pi\)
\(314\) 1.00070 0.0564729
\(315\) 0 0
\(316\) 21.9210 1.23315
\(317\) 14.2193 0.798635 0.399318 0.916813i \(-0.369247\pi\)
0.399318 + 0.916813i \(0.369247\pi\)
\(318\) 0 0
\(319\) 5.84264 0.327125
\(320\) 9.74238 0.544616
\(321\) 0 0
\(322\) −1.44828 −0.0807093
\(323\) −15.4186 −0.857912
\(324\) 0 0
\(325\) −6.34540 −0.351980
\(326\) 6.93445 0.384064
\(327\) 0 0
\(328\) −7.78196 −0.429687
\(329\) −11.9530 −0.658992
\(330\) 0 0
\(331\) 10.3007 0.566176 0.283088 0.959094i \(-0.408641\pi\)
0.283088 + 0.959094i \(0.408641\pi\)
\(332\) −27.7176 −1.52120
\(333\) 0 0
\(334\) 2.50059 0.136826
\(335\) −17.1409 −0.936508
\(336\) 0 0
\(337\) −25.8924 −1.41045 −0.705224 0.708984i \(-0.749154\pi\)
−0.705224 + 0.708984i \(0.749154\pi\)
\(338\) −13.7399 −0.747350
\(339\) 0 0
\(340\) −20.3179 −1.10189
\(341\) −13.1971 −0.714661
\(342\) 0 0
\(343\) −8.02681 −0.433407
\(344\) 11.4977 0.619917
\(345\) 0 0
\(346\) 0.510404 0.0274395
\(347\) −13.4609 −0.722621 −0.361310 0.932446i \(-0.617670\pi\)
−0.361310 + 0.932446i \(0.617670\pi\)
\(348\) 0 0
\(349\) −28.3225 −1.51607 −0.758035 0.652213i \(-0.773841\pi\)
−0.758035 + 0.652213i \(0.773841\pi\)
\(350\) −1.36422 −0.0729207
\(351\) 0 0
\(352\) −26.2606 −1.39969
\(353\) −10.2989 −0.548156 −0.274078 0.961707i \(-0.588373\pi\)
−0.274078 + 0.961707i \(0.588373\pi\)
\(354\) 0 0
\(355\) −16.7627 −0.889671
\(356\) −13.6521 −0.723559
\(357\) 0 0
\(358\) 6.57912 0.347717
\(359\) −23.4510 −1.23770 −0.618849 0.785510i \(-0.712401\pi\)
−0.618849 + 0.785510i \(0.712401\pi\)
\(360\) 0 0
\(361\) −7.66640 −0.403495
\(362\) 9.86455 0.518469
\(363\) 0 0
\(364\) 41.8416 2.19309
\(365\) 8.03698 0.420675
\(366\) 0 0
\(367\) −19.1389 −0.999040 −0.499520 0.866302i \(-0.666490\pi\)
−0.499520 + 0.866302i \(0.666490\pi\)
\(368\) 2.95199 0.153883
\(369\) 0 0
\(370\) −5.00778 −0.260342
\(371\) 2.74096 0.142304
\(372\) 0 0
\(373\) −36.6987 −1.90019 −0.950094 0.311964i \(-0.899013\pi\)
−0.950094 + 0.311964i \(0.899013\pi\)
\(374\) 11.3551 0.587160
\(375\) 0 0
\(376\) −5.67713 −0.292776
\(377\) −6.73637 −0.346941
\(378\) 0 0
\(379\) −27.5791 −1.41664 −0.708322 0.705889i \(-0.750548\pi\)
−0.708322 + 0.705889i \(0.750548\pi\)
\(380\) 14.9349 0.766145
\(381\) 0 0
\(382\) −7.65654 −0.391743
\(383\) −22.2252 −1.13566 −0.567829 0.823147i \(-0.692216\pi\)
−0.567829 + 0.823147i \(0.692216\pi\)
\(384\) 0 0
\(385\) −48.6074 −2.47726
\(386\) −2.64920 −0.134841
\(387\) 0 0
\(388\) 17.5664 0.891800
\(389\) −8.46057 −0.428968 −0.214484 0.976728i \(-0.568807\pi\)
−0.214484 + 0.976728i \(0.568807\pi\)
\(390\) 0 0
\(391\) −4.57994 −0.231618
\(392\) 7.53453 0.380551
\(393\) 0 0
\(394\) −6.35973 −0.320399
\(395\) 29.3611 1.47732
\(396\) 0 0
\(397\) −27.9140 −1.40096 −0.700481 0.713671i \(-0.747031\pi\)
−0.700481 + 0.713671i \(0.747031\pi\)
\(398\) 2.05039 0.102777
\(399\) 0 0
\(400\) 2.78066 0.139033
\(401\) 5.92439 0.295850 0.147925 0.988999i \(-0.452741\pi\)
0.147925 + 0.988999i \(0.452741\pi\)
\(402\) 0 0
\(403\) 15.2158 0.757952
\(404\) −12.5487 −0.624320
\(405\) 0 0
\(406\) −1.44828 −0.0718767
\(407\) −28.2856 −1.40207
\(408\) 0 0
\(409\) 14.3485 0.709487 0.354744 0.934964i \(-0.384568\pi\)
0.354744 + 0.934964i \(0.384568\pi\)
\(410\) −4.96591 −0.245249
\(411\) 0 0
\(412\) −28.0653 −1.38268
\(413\) 28.5837 1.40651
\(414\) 0 0
\(415\) −37.1250 −1.82240
\(416\) 30.2776 1.48448
\(417\) 0 0
\(418\) −8.34673 −0.408252
\(419\) −36.2582 −1.77133 −0.885665 0.464325i \(-0.846297\pi\)
−0.885665 + 0.464325i \(0.846297\pi\)
\(420\) 0 0
\(421\) 17.7411 0.864650 0.432325 0.901718i \(-0.357693\pi\)
0.432325 + 0.901718i \(0.357693\pi\)
\(422\) −4.23624 −0.206217
\(423\) 0 0
\(424\) 1.30183 0.0632223
\(425\) −4.31413 −0.209266
\(426\) 0 0
\(427\) −42.0534 −2.03511
\(428\) −25.8845 −1.25118
\(429\) 0 0
\(430\) 7.33707 0.353825
\(431\) 18.7348 0.902422 0.451211 0.892417i \(-0.350992\pi\)
0.451211 + 0.892417i \(0.350992\pi\)
\(432\) 0 0
\(433\) 4.71993 0.226825 0.113413 0.993548i \(-0.463822\pi\)
0.113413 + 0.993548i \(0.463822\pi\)
\(434\) 3.27129 0.157027
\(435\) 0 0
\(436\) −12.1507 −0.581914
\(437\) 3.36654 0.161043
\(438\) 0 0
\(439\) 24.6405 1.17603 0.588014 0.808851i \(-0.299910\pi\)
0.588014 + 0.808851i \(0.299910\pi\)
\(440\) −23.0862 −1.10059
\(441\) 0 0
\(442\) −13.0921 −0.622727
\(443\) −11.2204 −0.533097 −0.266549 0.963821i \(-0.585883\pi\)
−0.266549 + 0.963821i \(0.585883\pi\)
\(444\) 0 0
\(445\) −18.2856 −0.866821
\(446\) 1.49203 0.0706499
\(447\) 0 0
\(448\) −13.6404 −0.644450
\(449\) −8.68202 −0.409730 −0.204865 0.978790i \(-0.565676\pi\)
−0.204865 + 0.978790i \(0.565676\pi\)
\(450\) 0 0
\(451\) −28.0492 −1.32078
\(452\) 20.4818 0.963382
\(453\) 0 0
\(454\) 3.91484 0.183733
\(455\) 56.0427 2.62732
\(456\) 0 0
\(457\) 37.9401 1.77476 0.887382 0.461035i \(-0.152522\pi\)
0.887382 + 0.461035i \(0.152522\pi\)
\(458\) 3.80976 0.178018
\(459\) 0 0
\(460\) 4.43628 0.206843
\(461\) 40.1649 1.87066 0.935332 0.353770i \(-0.115100\pi\)
0.935332 + 0.353770i \(0.115100\pi\)
\(462\) 0 0
\(463\) −29.2381 −1.35881 −0.679404 0.733764i \(-0.737762\pi\)
−0.679404 + 0.733764i \(0.737762\pi\)
\(464\) 2.95199 0.137043
\(465\) 0 0
\(466\) 4.46133 0.206667
\(467\) −32.6854 −1.51250 −0.756250 0.654283i \(-0.772971\pi\)
−0.756250 + 0.654283i \(0.772971\pi\)
\(468\) 0 0
\(469\) 23.9992 1.10818
\(470\) −3.62275 −0.167105
\(471\) 0 0
\(472\) 13.5759 0.624883
\(473\) 41.4423 1.90552
\(474\) 0 0
\(475\) 3.17115 0.145503
\(476\) 28.4474 1.30388
\(477\) 0 0
\(478\) −6.14433 −0.281035
\(479\) 2.99873 0.137016 0.0685078 0.997651i \(-0.478176\pi\)
0.0685078 + 0.997651i \(0.478176\pi\)
\(480\) 0 0
\(481\) 32.6124 1.48700
\(482\) −0.746932 −0.0340218
\(483\) 0 0
\(484\) −42.1067 −1.91394
\(485\) 23.5285 1.06837
\(486\) 0 0
\(487\) 5.57967 0.252839 0.126420 0.991977i \(-0.459651\pi\)
0.126420 + 0.991977i \(0.459651\pi\)
\(488\) −19.9734 −0.904153
\(489\) 0 0
\(490\) 4.80801 0.217204
\(491\) −15.3909 −0.694583 −0.347292 0.937757i \(-0.612899\pi\)
−0.347292 + 0.937757i \(0.612899\pi\)
\(492\) 0 0
\(493\) −4.57994 −0.206270
\(494\) 9.62350 0.432982
\(495\) 0 0
\(496\) −6.66782 −0.299394
\(497\) 23.4697 1.05276
\(498\) 0 0
\(499\) −0.711042 −0.0318306 −0.0159153 0.999873i \(-0.505066\pi\)
−0.0159153 + 0.999873i \(0.505066\pi\)
\(500\) −18.0026 −0.805101
\(501\) 0 0
\(502\) −4.95150 −0.220996
\(503\) 7.73183 0.344745 0.172373 0.985032i \(-0.444857\pi\)
0.172373 + 0.985032i \(0.444857\pi\)
\(504\) 0 0
\(505\) −16.8077 −0.747934
\(506\) −2.47932 −0.110219
\(507\) 0 0
\(508\) 32.4897 1.44150
\(509\) −29.1832 −1.29352 −0.646760 0.762693i \(-0.723877\pi\)
−0.646760 + 0.762693i \(0.723877\pi\)
\(510\) 0 0
\(511\) −11.2527 −0.497789
\(512\) −22.8384 −1.00932
\(513\) 0 0
\(514\) −3.82383 −0.168662
\(515\) −37.5907 −1.65644
\(516\) 0 0
\(517\) −20.4625 −0.899942
\(518\) 7.01145 0.308066
\(519\) 0 0
\(520\) 26.6176 1.16726
\(521\) 31.2501 1.36909 0.684547 0.728969i \(-0.260000\pi\)
0.684547 + 0.728969i \(0.260000\pi\)
\(522\) 0 0
\(523\) 8.76052 0.383071 0.191535 0.981486i \(-0.438653\pi\)
0.191535 + 0.981486i \(0.438653\pi\)
\(524\) 11.1145 0.485539
\(525\) 0 0
\(526\) 9.04075 0.394196
\(527\) 10.3449 0.450633
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0.830736 0.0360849
\(531\) 0 0
\(532\) −20.9106 −0.906588
\(533\) 32.3397 1.40079
\(534\) 0 0
\(535\) −34.6698 −1.49890
\(536\) 11.3985 0.492340
\(537\) 0 0
\(538\) −2.69844 −0.116338
\(539\) 27.1573 1.16975
\(540\) 0 0
\(541\) −27.5448 −1.18424 −0.592121 0.805849i \(-0.701709\pi\)
−0.592121 + 0.805849i \(0.701709\pi\)
\(542\) 11.6667 0.501127
\(543\) 0 0
\(544\) 20.5852 0.882583
\(545\) −16.2747 −0.697132
\(546\) 0 0
\(547\) 10.6989 0.457451 0.228725 0.973491i \(-0.426544\pi\)
0.228725 + 0.973491i \(0.426544\pi\)
\(548\) 30.2785 1.29343
\(549\) 0 0
\(550\) −2.33542 −0.0995829
\(551\) 3.36654 0.143419
\(552\) 0 0
\(553\) −41.1088 −1.74812
\(554\) 12.6183 0.536101
\(555\) 0 0
\(556\) 31.6209 1.34102
\(557\) −14.8501 −0.629217 −0.314608 0.949222i \(-0.601873\pi\)
−0.314608 + 0.949222i \(0.601873\pi\)
\(558\) 0 0
\(559\) −47.7815 −2.02094
\(560\) −24.5589 −1.03780
\(561\) 0 0
\(562\) 4.74855 0.200305
\(563\) −32.9448 −1.38846 −0.694229 0.719754i \(-0.744255\pi\)
−0.694229 + 0.719754i \(0.744255\pi\)
\(564\) 0 0
\(565\) 27.4333 1.15413
\(566\) −7.54545 −0.317159
\(567\) 0 0
\(568\) 11.1470 0.467717
\(569\) −0.826143 −0.0346337 −0.0173169 0.999850i \(-0.505512\pi\)
−0.0173169 + 0.999850i \(0.505512\pi\)
\(570\) 0 0
\(571\) 26.0145 1.08867 0.544337 0.838867i \(-0.316781\pi\)
0.544337 + 0.838867i \(0.316781\pi\)
\(572\) 71.6291 2.99496
\(573\) 0 0
\(574\) 6.95283 0.290206
\(575\) 0.941962 0.0392825
\(576\) 0 0
\(577\) −17.0333 −0.709104 −0.354552 0.935036i \(-0.615367\pi\)
−0.354552 + 0.935036i \(0.615367\pi\)
\(578\) −1.68715 −0.0701762
\(579\) 0 0
\(580\) 4.43628 0.184207
\(581\) 51.9792 2.15646
\(582\) 0 0
\(583\) 4.69228 0.194334
\(584\) −5.34449 −0.221157
\(585\) 0 0
\(586\) 6.59493 0.272434
\(587\) −4.52833 −0.186904 −0.0934522 0.995624i \(-0.529790\pi\)
−0.0934522 + 0.995624i \(0.529790\pi\)
\(588\) 0 0
\(589\) −7.60418 −0.313325
\(590\) 8.66322 0.356659
\(591\) 0 0
\(592\) −14.2913 −0.587369
\(593\) 32.9549 1.35330 0.676648 0.736307i \(-0.263432\pi\)
0.676648 + 0.736307i \(0.263432\pi\)
\(594\) 0 0
\(595\) 38.1024 1.56205
\(596\) 28.2552 1.15738
\(597\) 0 0
\(598\) 2.85857 0.116896
\(599\) 19.3328 0.789918 0.394959 0.918699i \(-0.370759\pi\)
0.394959 + 0.918699i \(0.370759\pi\)
\(600\) 0 0
\(601\) 20.3794 0.831294 0.415647 0.909526i \(-0.363555\pi\)
0.415647 + 0.909526i \(0.363555\pi\)
\(602\) −10.2727 −0.418685
\(603\) 0 0
\(604\) 4.46452 0.181659
\(605\) −56.3977 −2.29289
\(606\) 0 0
\(607\) 21.5119 0.873143 0.436571 0.899670i \(-0.356193\pi\)
0.436571 + 0.899670i \(0.356193\pi\)
\(608\) −15.1314 −0.613659
\(609\) 0 0
\(610\) −12.7456 −0.516056
\(611\) 23.5926 0.954456
\(612\) 0 0
\(613\) 8.08436 0.326524 0.163262 0.986583i \(-0.447798\pi\)
0.163262 + 0.986583i \(0.447798\pi\)
\(614\) −6.00076 −0.242171
\(615\) 0 0
\(616\) 32.3233 1.30234
\(617\) −5.79105 −0.233139 −0.116570 0.993183i \(-0.537190\pi\)
−0.116570 + 0.993183i \(0.537190\pi\)
\(618\) 0 0
\(619\) −22.5549 −0.906559 −0.453279 0.891368i \(-0.649746\pi\)
−0.453279 + 0.891368i \(0.649746\pi\)
\(620\) −10.0205 −0.402431
\(621\) 0 0
\(622\) −7.46687 −0.299394
\(623\) 25.6019 1.02572
\(624\) 0 0
\(625\) −28.8225 −1.15290
\(626\) −0.231030 −0.00923380
\(627\) 0 0
\(628\) 4.29177 0.171260
\(629\) 22.1726 0.884080
\(630\) 0 0
\(631\) 45.2346 1.80076 0.900381 0.435101i \(-0.143287\pi\)
0.900381 + 0.435101i \(0.143287\pi\)
\(632\) −19.5247 −0.776653
\(633\) 0 0
\(634\) −6.03395 −0.239639
\(635\) 43.5167 1.72691
\(636\) 0 0
\(637\) −31.3115 −1.24061
\(638\) −2.47932 −0.0981572
\(639\) 0 0
\(640\) −26.0466 −1.02958
\(641\) −23.2117 −0.916809 −0.458404 0.888744i \(-0.651579\pi\)
−0.458404 + 0.888744i \(0.651579\pi\)
\(642\) 0 0
\(643\) 7.33923 0.289431 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(644\) −6.21129 −0.244759
\(645\) 0 0
\(646\) 6.54285 0.257425
\(647\) 22.3876 0.880148 0.440074 0.897962i \(-0.354952\pi\)
0.440074 + 0.897962i \(0.354952\pi\)
\(648\) 0 0
\(649\) 48.9328 1.92078
\(650\) 2.69267 0.105615
\(651\) 0 0
\(652\) 29.7401 1.16471
\(653\) 19.8442 0.776564 0.388282 0.921541i \(-0.373069\pi\)
0.388282 + 0.921541i \(0.373069\pi\)
\(654\) 0 0
\(655\) 14.8868 0.581675
\(656\) −14.1718 −0.553317
\(657\) 0 0
\(658\) 5.07226 0.197737
\(659\) −10.2160 −0.397958 −0.198979 0.980004i \(-0.563763\pi\)
−0.198979 + 0.980004i \(0.563763\pi\)
\(660\) 0 0
\(661\) −12.0111 −0.467179 −0.233589 0.972335i \(-0.575047\pi\)
−0.233589 + 0.972335i \(0.575047\pi\)
\(662\) −4.37108 −0.169887
\(663\) 0 0
\(664\) 24.6877 0.958068
\(665\) −28.0077 −1.08609
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 10.7244 0.414939
\(669\) 0 0
\(670\) 7.27373 0.281009
\(671\) −71.9917 −2.77921
\(672\) 0 0
\(673\) 24.1569 0.931179 0.465590 0.885001i \(-0.345842\pi\)
0.465590 + 0.885001i \(0.345842\pi\)
\(674\) 10.9874 0.423220
\(675\) 0 0
\(676\) −58.9269 −2.26642
\(677\) −45.3916 −1.74454 −0.872271 0.489023i \(-0.837353\pi\)
−0.872271 + 0.489023i \(0.837353\pi\)
\(678\) 0 0
\(679\) −32.9425 −1.26422
\(680\) 18.0969 0.693983
\(681\) 0 0
\(682\) 5.60016 0.214441
\(683\) 29.6148 1.13318 0.566589 0.824000i \(-0.308263\pi\)
0.566589 + 0.824000i \(0.308263\pi\)
\(684\) 0 0
\(685\) 40.5551 1.54953
\(686\) 3.40617 0.130048
\(687\) 0 0
\(688\) 20.9387 0.798280
\(689\) −5.41004 −0.206106
\(690\) 0 0
\(691\) 25.0680 0.953633 0.476817 0.879003i \(-0.341791\pi\)
0.476817 + 0.879003i \(0.341791\pi\)
\(692\) 2.18900 0.0832132
\(693\) 0 0
\(694\) 5.71213 0.216830
\(695\) 42.3530 1.60654
\(696\) 0 0
\(697\) 21.9872 0.832826
\(698\) 12.0186 0.454912
\(699\) 0 0
\(700\) −5.85080 −0.221140
\(701\) −6.49421 −0.245283 −0.122641 0.992451i \(-0.539136\pi\)
−0.122641 + 0.992451i \(0.539136\pi\)
\(702\) 0 0
\(703\) −16.2982 −0.614700
\(704\) −23.3512 −0.880082
\(705\) 0 0
\(706\) 4.37034 0.164480
\(707\) 23.5327 0.885039
\(708\) 0 0
\(709\) 2.52860 0.0949635 0.0474817 0.998872i \(-0.484880\pi\)
0.0474817 + 0.998872i \(0.484880\pi\)
\(710\) 7.11323 0.266955
\(711\) 0 0
\(712\) 12.1597 0.455704
\(713\) −2.25875 −0.0845909
\(714\) 0 0
\(715\) 95.9401 3.58796
\(716\) 28.2162 1.05449
\(717\) 0 0
\(718\) 9.95142 0.371384
\(719\) −50.7768 −1.89366 −0.946828 0.321739i \(-0.895733\pi\)
−0.946828 + 0.321739i \(0.895733\pi\)
\(720\) 0 0
\(721\) 52.6312 1.96009
\(722\) 3.25323 0.121073
\(723\) 0 0
\(724\) 42.3066 1.57231
\(725\) 0.941962 0.0349836
\(726\) 0 0
\(727\) −40.8691 −1.51575 −0.757876 0.652399i \(-0.773763\pi\)
−0.757876 + 0.652399i \(0.773763\pi\)
\(728\) −37.2677 −1.38123
\(729\) 0 0
\(730\) −3.41049 −0.126228
\(731\) −32.4858 −1.20153
\(732\) 0 0
\(733\) −25.3863 −0.937665 −0.468832 0.883287i \(-0.655325\pi\)
−0.468832 + 0.883287i \(0.655325\pi\)
\(734\) 8.12156 0.299772
\(735\) 0 0
\(736\) −4.49464 −0.165675
\(737\) 41.0845 1.51337
\(738\) 0 0
\(739\) −21.1947 −0.779658 −0.389829 0.920887i \(-0.627466\pi\)
−0.389829 + 0.920887i \(0.627466\pi\)
\(740\) −21.4771 −0.789514
\(741\) 0 0
\(742\) −1.16312 −0.0426996
\(743\) −33.9818 −1.24667 −0.623336 0.781954i \(-0.714223\pi\)
−0.623336 + 0.781954i \(0.714223\pi\)
\(744\) 0 0
\(745\) 37.8450 1.38653
\(746\) 15.5731 0.570171
\(747\) 0 0
\(748\) 48.6994 1.78062
\(749\) 48.5416 1.77367
\(750\) 0 0
\(751\) 8.40956 0.306869 0.153435 0.988159i \(-0.450967\pi\)
0.153435 + 0.988159i \(0.450967\pi\)
\(752\) −10.3387 −0.377013
\(753\) 0 0
\(754\) 2.85857 0.104103
\(755\) 5.97979 0.217627
\(756\) 0 0
\(757\) 25.3310 0.920670 0.460335 0.887745i \(-0.347729\pi\)
0.460335 + 0.887745i \(0.347729\pi\)
\(758\) 11.7032 0.425079
\(759\) 0 0
\(760\) −13.3023 −0.482526
\(761\) 20.1122 0.729067 0.364534 0.931190i \(-0.381228\pi\)
0.364534 + 0.931190i \(0.381228\pi\)
\(762\) 0 0
\(763\) 22.7864 0.824924
\(764\) −32.8370 −1.18800
\(765\) 0 0
\(766\) 9.43126 0.340765
\(767\) −56.4179 −2.03713
\(768\) 0 0
\(769\) −28.2509 −1.01875 −0.509377 0.860543i \(-0.670124\pi\)
−0.509377 + 0.860543i \(0.670124\pi\)
\(770\) 20.6265 0.743327
\(771\) 0 0
\(772\) −11.3618 −0.408919
\(773\) −21.5840 −0.776323 −0.388161 0.921591i \(-0.626890\pi\)
−0.388161 + 0.921591i \(0.626890\pi\)
\(774\) 0 0
\(775\) −2.12766 −0.0764277
\(776\) −15.6461 −0.561664
\(777\) 0 0
\(778\) 3.59024 0.128716
\(779\) −16.1620 −0.579063
\(780\) 0 0
\(781\) 40.1780 1.43768
\(782\) 1.94349 0.0694992
\(783\) 0 0
\(784\) 13.7212 0.490044
\(785\) 5.74840 0.205169
\(786\) 0 0
\(787\) −35.3258 −1.25923 −0.629614 0.776908i \(-0.716787\pi\)
−0.629614 + 0.776908i \(0.716787\pi\)
\(788\) −27.2753 −0.971643
\(789\) 0 0
\(790\) −12.4593 −0.443283
\(791\) −38.4098 −1.36569
\(792\) 0 0
\(793\) 83.0041 2.94756
\(794\) 11.8453 0.420373
\(795\) 0 0
\(796\) 8.79362 0.311682
\(797\) 16.5841 0.587439 0.293719 0.955892i \(-0.405107\pi\)
0.293719 + 0.955892i \(0.405107\pi\)
\(798\) 0 0
\(799\) 16.0402 0.567462
\(800\) −4.23378 −0.149687
\(801\) 0 0
\(802\) −2.51401 −0.0887728
\(803\) −19.2636 −0.679797
\(804\) 0 0
\(805\) −8.31942 −0.293221
\(806\) −6.45680 −0.227431
\(807\) 0 0
\(808\) 11.1769 0.393203
\(809\) 46.3267 1.62876 0.814379 0.580333i \(-0.197078\pi\)
0.814379 + 0.580333i \(0.197078\pi\)
\(810\) 0 0
\(811\) −6.92923 −0.243318 −0.121659 0.992572i \(-0.538821\pi\)
−0.121659 + 0.992572i \(0.538821\pi\)
\(812\) −6.21129 −0.217974
\(813\) 0 0
\(814\) 12.0030 0.420704
\(815\) 39.8340 1.39532
\(816\) 0 0
\(817\) 23.8791 0.835424
\(818\) −6.08877 −0.212889
\(819\) 0 0
\(820\) −21.2976 −0.743743
\(821\) −12.4948 −0.436070 −0.218035 0.975941i \(-0.569965\pi\)
−0.218035 + 0.975941i \(0.569965\pi\)
\(822\) 0 0
\(823\) 20.6832 0.720971 0.360485 0.932765i \(-0.382611\pi\)
0.360485 + 0.932765i \(0.382611\pi\)
\(824\) 24.9973 0.870823
\(825\) 0 0
\(826\) −12.1295 −0.422039
\(827\) −37.9507 −1.31968 −0.659838 0.751408i \(-0.729375\pi\)
−0.659838 + 0.751408i \(0.729375\pi\)
\(828\) 0 0
\(829\) −23.1196 −0.802977 −0.401489 0.915864i \(-0.631507\pi\)
−0.401489 + 0.915864i \(0.631507\pi\)
\(830\) 15.7540 0.546828
\(831\) 0 0
\(832\) 26.9232 0.933393
\(833\) −21.2881 −0.737590
\(834\) 0 0
\(835\) 14.3643 0.497096
\(836\) −35.7970 −1.23807
\(837\) 0 0
\(838\) 15.3861 0.531505
\(839\) −35.3974 −1.22205 −0.611027 0.791609i \(-0.709243\pi\)
−0.611027 + 0.791609i \(0.709243\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −7.52844 −0.259447
\(843\) 0 0
\(844\) −18.1682 −0.625374
\(845\) −78.9267 −2.71516
\(846\) 0 0
\(847\) 78.9632 2.71321
\(848\) 2.37077 0.0814127
\(849\) 0 0
\(850\) 1.83070 0.0627924
\(851\) −4.84124 −0.165956
\(852\) 0 0
\(853\) 25.4871 0.872661 0.436331 0.899786i \(-0.356278\pi\)
0.436331 + 0.899786i \(0.356278\pi\)
\(854\) 17.8453 0.610655
\(855\) 0 0
\(856\) 23.0550 0.788002
\(857\) −26.7263 −0.912954 −0.456477 0.889735i \(-0.650889\pi\)
−0.456477 + 0.889735i \(0.650889\pi\)
\(858\) 0 0
\(859\) −44.6325 −1.52284 −0.761421 0.648257i \(-0.775498\pi\)
−0.761421 + 0.648257i \(0.775498\pi\)
\(860\) 31.4669 1.07301
\(861\) 0 0
\(862\) −7.95009 −0.270781
\(863\) 38.5205 1.31125 0.655626 0.755085i \(-0.272405\pi\)
0.655626 + 0.755085i \(0.272405\pi\)
\(864\) 0 0
\(865\) 2.93195 0.0996892
\(866\) −2.00290 −0.0680612
\(867\) 0 0
\(868\) 14.0298 0.476201
\(869\) −70.3746 −2.38730
\(870\) 0 0
\(871\) −47.3691 −1.60504
\(872\) 10.8225 0.366495
\(873\) 0 0
\(874\) −1.42859 −0.0483227
\(875\) 33.7605 1.14131
\(876\) 0 0
\(877\) −45.2033 −1.52641 −0.763203 0.646158i \(-0.776375\pi\)
−0.763203 + 0.646158i \(0.776375\pi\)
\(878\) −10.4562 −0.352879
\(879\) 0 0
\(880\) −42.0426 −1.41726
\(881\) −34.1314 −1.14992 −0.574959 0.818182i \(-0.694982\pi\)
−0.574959 + 0.818182i \(0.694982\pi\)
\(882\) 0 0
\(883\) 24.9724 0.840387 0.420193 0.907435i \(-0.361962\pi\)
0.420193 + 0.907435i \(0.361962\pi\)
\(884\) −56.1487 −1.88849
\(885\) 0 0
\(886\) 4.76137 0.159961
\(887\) −1.69868 −0.0570362 −0.0285181 0.999593i \(-0.509079\pi\)
−0.0285181 + 0.999593i \(0.509079\pi\)
\(888\) 0 0
\(889\) −60.9283 −2.04347
\(890\) 7.75948 0.260098
\(891\) 0 0
\(892\) 6.39896 0.214253
\(893\) −11.7906 −0.394556
\(894\) 0 0
\(895\) 37.7928 1.26328
\(896\) 36.4681 1.21832
\(897\) 0 0
\(898\) 3.68421 0.122944
\(899\) −2.25875 −0.0753335
\(900\) 0 0
\(901\) −3.67819 −0.122538
\(902\) 11.9026 0.396314
\(903\) 0 0
\(904\) −18.2428 −0.606748
\(905\) 56.6655 1.88363
\(906\) 0 0
\(907\) 20.6791 0.686639 0.343320 0.939219i \(-0.388449\pi\)
0.343320 + 0.939219i \(0.388449\pi\)
\(908\) 16.7898 0.557188
\(909\) 0 0
\(910\) −23.7817 −0.788354
\(911\) 56.7976 1.88179 0.940894 0.338700i \(-0.109987\pi\)
0.940894 + 0.338700i \(0.109987\pi\)
\(912\) 0 0
\(913\) 88.9838 2.94493
\(914\) −16.0999 −0.532536
\(915\) 0 0
\(916\) 16.3391 0.539859
\(917\) −20.8432 −0.688302
\(918\) 0 0
\(919\) −38.6718 −1.27567 −0.637833 0.770175i \(-0.720169\pi\)
−0.637833 + 0.770175i \(0.720169\pi\)
\(920\) −3.95133 −0.130272
\(921\) 0 0
\(922\) −17.0439 −0.561312
\(923\) −46.3239 −1.52477
\(924\) 0 0
\(925\) −4.56027 −0.149941
\(926\) 12.4072 0.407724
\(927\) 0 0
\(928\) −4.49464 −0.147544
\(929\) 39.0509 1.28122 0.640609 0.767867i \(-0.278682\pi\)
0.640609 + 0.767867i \(0.278682\pi\)
\(930\) 0 0
\(931\) 15.6481 0.512846
\(932\) 19.1335 0.626740
\(933\) 0 0
\(934\) 13.8700 0.453841
\(935\) 65.2280 2.13318
\(936\) 0 0
\(937\) −38.2425 −1.24933 −0.624664 0.780894i \(-0.714764\pi\)
−0.624664 + 0.780894i \(0.714764\pi\)
\(938\) −10.1840 −0.332521
\(939\) 0 0
\(940\) −15.5371 −0.506764
\(941\) 26.9386 0.878172 0.439086 0.898445i \(-0.355302\pi\)
0.439086 + 0.898445i \(0.355302\pi\)
\(942\) 0 0
\(943\) −4.80077 −0.156334
\(944\) 24.7233 0.804675
\(945\) 0 0
\(946\) −17.5860 −0.571770
\(947\) −16.4580 −0.534814 −0.267407 0.963584i \(-0.586167\pi\)
−0.267407 + 0.963584i \(0.586167\pi\)
\(948\) 0 0
\(949\) 22.2103 0.720976
\(950\) −1.34568 −0.0436595
\(951\) 0 0
\(952\) −25.3376 −0.821198
\(953\) −17.2466 −0.558672 −0.279336 0.960193i \(-0.590114\pi\)
−0.279336 + 0.960193i \(0.590114\pi\)
\(954\) 0 0
\(955\) −43.9819 −1.42322
\(956\) −26.3515 −0.852268
\(957\) 0 0
\(958\) −1.27251 −0.0411129
\(959\) −56.7817 −1.83358
\(960\) 0 0
\(961\) −25.8980 −0.835421
\(962\) −13.8390 −0.446189
\(963\) 0 0
\(964\) −3.20341 −0.103175
\(965\) −15.2180 −0.489884
\(966\) 0 0
\(967\) 47.6981 1.53387 0.766934 0.641726i \(-0.221781\pi\)
0.766934 + 0.641726i \(0.221781\pi\)
\(968\) 37.5038 1.20542
\(969\) 0 0
\(970\) −9.98429 −0.320576
\(971\) 26.3554 0.845784 0.422892 0.906180i \(-0.361015\pi\)
0.422892 + 0.906180i \(0.361015\pi\)
\(972\) 0 0
\(973\) −59.2990 −1.90104
\(974\) −2.36773 −0.0758670
\(975\) 0 0
\(976\) −36.3738 −1.16430
\(977\) −28.7208 −0.918858 −0.459429 0.888214i \(-0.651946\pi\)
−0.459429 + 0.888214i \(0.651946\pi\)
\(978\) 0 0
\(979\) 43.8282 1.40076
\(980\) 20.6204 0.658694
\(981\) 0 0
\(982\) 6.53113 0.208417
\(983\) −0.767884 −0.0244917 −0.0122458 0.999925i \(-0.503898\pi\)
−0.0122458 + 0.999925i \(0.503898\pi\)
\(984\) 0 0
\(985\) −36.5326 −1.16403
\(986\) 1.94349 0.0618935
\(987\) 0 0
\(988\) 41.2728 1.31306
\(989\) 7.09307 0.225546
\(990\) 0 0
\(991\) −29.3337 −0.931815 −0.465908 0.884833i \(-0.654272\pi\)
−0.465908 + 0.884833i \(0.654272\pi\)
\(992\) 10.1523 0.322335
\(993\) 0 0
\(994\) −9.95933 −0.315891
\(995\) 11.7782 0.373394
\(996\) 0 0
\(997\) −13.7965 −0.436940 −0.218470 0.975844i \(-0.570107\pi\)
−0.218470 + 0.975844i \(0.570107\pi\)
\(998\) 0.301730 0.00955110
\(999\) 0 0
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 \(a_p\))