Properties

Label 8046.2.a.h.1.4
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.836154\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.63508 q^{5} +4.18187 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.63508 q^{5} +4.18187 q^{7} +1.00000 q^{8} -1.63508 q^{10} -0.197300 q^{11} -5.53420 q^{13} +4.18187 q^{14} +1.00000 q^{16} +6.24995 q^{17} -1.76358 q^{19} -1.63508 q^{20} -0.197300 q^{22} -1.25693 q^{23} -2.32651 q^{25} -5.53420 q^{26} +4.18187 q^{28} -6.46749 q^{29} -9.67005 q^{31} +1.00000 q^{32} +6.24995 q^{34} -6.83770 q^{35} -8.61274 q^{37} -1.76358 q^{38} -1.63508 q^{40} -7.00464 q^{41} +4.69520 q^{43} -0.197300 q^{44} -1.25693 q^{46} -6.92211 q^{47} +10.4880 q^{49} -2.32651 q^{50} -5.53420 q^{52} -5.96851 q^{53} +0.322602 q^{55} +4.18187 q^{56} -6.46749 q^{58} +4.41785 q^{59} +6.34679 q^{61} -9.67005 q^{62} +1.00000 q^{64} +9.04888 q^{65} -15.3102 q^{67} +6.24995 q^{68} -6.83770 q^{70} +8.52896 q^{71} -0.842454 q^{73} -8.61274 q^{74} -1.76358 q^{76} -0.825083 q^{77} -2.79367 q^{79} -1.63508 q^{80} -7.00464 q^{82} +1.68295 q^{83} -10.2192 q^{85} +4.69520 q^{86} -0.197300 q^{88} +0.518659 q^{89} -23.1433 q^{91} -1.25693 q^{92} -6.92211 q^{94} +2.88360 q^{95} +2.99290 q^{97} +10.4880 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.63508 −0.731231 −0.365615 0.930766i \(-0.619141\pi\)
−0.365615 + 0.930766i \(0.619141\pi\)
\(6\) 0 0
\(7\) 4.18187 1.58060 0.790299 0.612721i \(-0.209925\pi\)
0.790299 + 0.612721i \(0.209925\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.63508 −0.517058
\(11\) −0.197300 −0.0594882 −0.0297441 0.999558i \(-0.509469\pi\)
−0.0297441 + 0.999558i \(0.509469\pi\)
\(12\) 0 0
\(13\) −5.53420 −1.53491 −0.767456 0.641101i \(-0.778478\pi\)
−0.767456 + 0.641101i \(0.778478\pi\)
\(14\) 4.18187 1.11765
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.24995 1.51584 0.757918 0.652350i \(-0.226217\pi\)
0.757918 + 0.652350i \(0.226217\pi\)
\(18\) 0 0
\(19\) −1.76358 −0.404593 −0.202297 0.979324i \(-0.564841\pi\)
−0.202297 + 0.979324i \(0.564841\pi\)
\(20\) −1.63508 −0.365615
\(21\) 0 0
\(22\) −0.197300 −0.0420645
\(23\) −1.25693 −0.262088 −0.131044 0.991377i \(-0.541833\pi\)
−0.131044 + 0.991377i \(0.541833\pi\)
\(24\) 0 0
\(25\) −2.32651 −0.465302
\(26\) −5.53420 −1.08535
\(27\) 0 0
\(28\) 4.18187 0.790299
\(29\) −6.46749 −1.20098 −0.600492 0.799631i \(-0.705029\pi\)
−0.600492 + 0.799631i \(0.705029\pi\)
\(30\) 0 0
\(31\) −9.67005 −1.73679 −0.868396 0.495871i \(-0.834849\pi\)
−0.868396 + 0.495871i \(0.834849\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.24995 1.07186
\(35\) −6.83770 −1.15578
\(36\) 0 0
\(37\) −8.61274 −1.41593 −0.707963 0.706250i \(-0.750386\pi\)
−0.707963 + 0.706250i \(0.750386\pi\)
\(38\) −1.76358 −0.286091
\(39\) 0 0
\(40\) −1.63508 −0.258529
\(41\) −7.00464 −1.09394 −0.546971 0.837152i \(-0.684219\pi\)
−0.546971 + 0.837152i \(0.684219\pi\)
\(42\) 0 0
\(43\) 4.69520 0.716011 0.358006 0.933719i \(-0.383457\pi\)
0.358006 + 0.933719i \(0.383457\pi\)
\(44\) −0.197300 −0.0297441
\(45\) 0 0
\(46\) −1.25693 −0.185324
\(47\) −6.92211 −1.00969 −0.504847 0.863209i \(-0.668451\pi\)
−0.504847 + 0.863209i \(0.668451\pi\)
\(48\) 0 0
\(49\) 10.4880 1.49829
\(50\) −2.32651 −0.329018
\(51\) 0 0
\(52\) −5.53420 −0.767456
\(53\) −5.96851 −0.819838 −0.409919 0.912122i \(-0.634443\pi\)
−0.409919 + 0.912122i \(0.634443\pi\)
\(54\) 0 0
\(55\) 0.322602 0.0434996
\(56\) 4.18187 0.558826
\(57\) 0 0
\(58\) −6.46749 −0.849224
\(59\) 4.41785 0.575155 0.287577 0.957757i \(-0.407150\pi\)
0.287577 + 0.957757i \(0.407150\pi\)
\(60\) 0 0
\(61\) 6.34679 0.812623 0.406311 0.913735i \(-0.366815\pi\)
0.406311 + 0.913735i \(0.366815\pi\)
\(62\) −9.67005 −1.22810
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 9.04888 1.12237
\(66\) 0 0
\(67\) −15.3102 −1.87044 −0.935222 0.354062i \(-0.884800\pi\)
−0.935222 + 0.354062i \(0.884800\pi\)
\(68\) 6.24995 0.757918
\(69\) 0 0
\(70\) −6.83770 −0.817261
\(71\) 8.52896 1.01220 0.506100 0.862475i \(-0.331087\pi\)
0.506100 + 0.862475i \(0.331087\pi\)
\(72\) 0 0
\(73\) −0.842454 −0.0986018 −0.0493009 0.998784i \(-0.515699\pi\)
−0.0493009 + 0.998784i \(0.515699\pi\)
\(74\) −8.61274 −1.00121
\(75\) 0 0
\(76\) −1.76358 −0.202297
\(77\) −0.825083 −0.0940269
\(78\) 0 0
\(79\) −2.79367 −0.314313 −0.157156 0.987574i \(-0.550233\pi\)
−0.157156 + 0.987574i \(0.550233\pi\)
\(80\) −1.63508 −0.182808
\(81\) 0 0
\(82\) −7.00464 −0.773533
\(83\) 1.68295 0.184728 0.0923641 0.995725i \(-0.470558\pi\)
0.0923641 + 0.995725i \(0.470558\pi\)
\(84\) 0 0
\(85\) −10.2192 −1.10843
\(86\) 4.69520 0.506296
\(87\) 0 0
\(88\) −0.197300 −0.0210323
\(89\) 0.518659 0.0549777 0.0274889 0.999622i \(-0.491249\pi\)
0.0274889 + 0.999622i \(0.491249\pi\)
\(90\) 0 0
\(91\) −23.1433 −2.42608
\(92\) −1.25693 −0.131044
\(93\) 0 0
\(94\) −6.92211 −0.713961
\(95\) 2.88360 0.295851
\(96\) 0 0
\(97\) 2.99290 0.303883 0.151941 0.988390i \(-0.451447\pi\)
0.151941 + 0.988390i \(0.451447\pi\)
\(98\) 10.4880 1.05945
\(99\) 0 0
\(100\) −2.32651 −0.232651
\(101\) 4.86820 0.484404 0.242202 0.970226i \(-0.422130\pi\)
0.242202 + 0.970226i \(0.422130\pi\)
\(102\) 0 0
\(103\) 7.84368 0.772860 0.386430 0.922319i \(-0.373708\pi\)
0.386430 + 0.922319i \(0.373708\pi\)
\(104\) −5.53420 −0.542673
\(105\) 0 0
\(106\) −5.96851 −0.579713
\(107\) −1.68404 −0.162802 −0.0814012 0.996681i \(-0.525940\pi\)
−0.0814012 + 0.996681i \(0.525940\pi\)
\(108\) 0 0
\(109\) −10.7457 −1.02925 −0.514627 0.857414i \(-0.672070\pi\)
−0.514627 + 0.857414i \(0.672070\pi\)
\(110\) 0.322602 0.0307589
\(111\) 0 0
\(112\) 4.18187 0.395149
\(113\) 10.3413 0.972826 0.486413 0.873729i \(-0.338305\pi\)
0.486413 + 0.873729i \(0.338305\pi\)
\(114\) 0 0
\(115\) 2.05519 0.191647
\(116\) −6.46749 −0.600492
\(117\) 0 0
\(118\) 4.41785 0.406696
\(119\) 26.1365 2.39593
\(120\) 0 0
\(121\) −10.9611 −0.996461
\(122\) 6.34679 0.574611
\(123\) 0 0
\(124\) −9.67005 −0.868396
\(125\) 11.9794 1.07147
\(126\) 0 0
\(127\) 7.37977 0.654849 0.327424 0.944877i \(-0.393819\pi\)
0.327424 + 0.944877i \(0.393819\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 9.04888 0.793639
\(131\) −9.07961 −0.793289 −0.396645 0.917972i \(-0.629825\pi\)
−0.396645 + 0.917972i \(0.629825\pi\)
\(132\) 0 0
\(133\) −7.37507 −0.639499
\(134\) −15.3102 −1.32260
\(135\) 0 0
\(136\) 6.24995 0.535929
\(137\) 12.7245 1.08713 0.543563 0.839368i \(-0.317075\pi\)
0.543563 + 0.839368i \(0.317075\pi\)
\(138\) 0 0
\(139\) 1.66714 0.141405 0.0707026 0.997497i \(-0.477476\pi\)
0.0707026 + 0.997497i \(0.477476\pi\)
\(140\) −6.83770 −0.577891
\(141\) 0 0
\(142\) 8.52896 0.715734
\(143\) 1.09190 0.0913092
\(144\) 0 0
\(145\) 10.5749 0.878196
\(146\) −0.842454 −0.0697220
\(147\) 0 0
\(148\) −8.61274 −0.707963
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) −17.2820 −1.40639 −0.703193 0.710999i \(-0.748243\pi\)
−0.703193 + 0.710999i \(0.748243\pi\)
\(152\) −1.76358 −0.143045
\(153\) 0 0
\(154\) −0.825083 −0.0664871
\(155\) 15.8113 1.27000
\(156\) 0 0
\(157\) −16.9018 −1.34891 −0.674457 0.738314i \(-0.735622\pi\)
−0.674457 + 0.738314i \(0.735622\pi\)
\(158\) −2.79367 −0.222253
\(159\) 0 0
\(160\) −1.63508 −0.129265
\(161\) −5.25632 −0.414256
\(162\) 0 0
\(163\) 11.9163 0.933355 0.466678 0.884428i \(-0.345451\pi\)
0.466678 + 0.884428i \(0.345451\pi\)
\(164\) −7.00464 −0.546971
\(165\) 0 0
\(166\) 1.68295 0.130623
\(167\) 14.7560 1.14186 0.570929 0.821000i \(-0.306583\pi\)
0.570929 + 0.821000i \(0.306583\pi\)
\(168\) 0 0
\(169\) 17.6274 1.35596
\(170\) −10.2192 −0.783775
\(171\) 0 0
\(172\) 4.69520 0.358006
\(173\) −24.6303 −1.87260 −0.936302 0.351195i \(-0.885776\pi\)
−0.936302 + 0.351195i \(0.885776\pi\)
\(174\) 0 0
\(175\) −9.72915 −0.735455
\(176\) −0.197300 −0.0148721
\(177\) 0 0
\(178\) 0.518659 0.0388751
\(179\) 20.1909 1.50914 0.754568 0.656221i \(-0.227846\pi\)
0.754568 + 0.656221i \(0.227846\pi\)
\(180\) 0 0
\(181\) −18.5876 −1.38160 −0.690801 0.723045i \(-0.742742\pi\)
−0.690801 + 0.723045i \(0.742742\pi\)
\(182\) −23.1433 −1.71550
\(183\) 0 0
\(184\) −1.25693 −0.0926622
\(185\) 14.0825 1.03537
\(186\) 0 0
\(187\) −1.23312 −0.0901743
\(188\) −6.92211 −0.504847
\(189\) 0 0
\(190\) 2.88360 0.209198
\(191\) 22.5264 1.62995 0.814976 0.579495i \(-0.196750\pi\)
0.814976 + 0.579495i \(0.196750\pi\)
\(192\) 0 0
\(193\) −3.61836 −0.260455 −0.130228 0.991484i \(-0.541571\pi\)
−0.130228 + 0.991484i \(0.541571\pi\)
\(194\) 2.99290 0.214878
\(195\) 0 0
\(196\) 10.4880 0.749145
\(197\) −22.2957 −1.58851 −0.794253 0.607587i \(-0.792138\pi\)
−0.794253 + 0.607587i \(0.792138\pi\)
\(198\) 0 0
\(199\) −11.0975 −0.786680 −0.393340 0.919393i \(-0.628680\pi\)
−0.393340 + 0.919393i \(0.628680\pi\)
\(200\) −2.32651 −0.164509
\(201\) 0 0
\(202\) 4.86820 0.342525
\(203\) −27.0462 −1.89827
\(204\) 0 0
\(205\) 11.4532 0.799923
\(206\) 7.84368 0.546495
\(207\) 0 0
\(208\) −5.53420 −0.383728
\(209\) 0.347955 0.0240685
\(210\) 0 0
\(211\) −12.6815 −0.873030 −0.436515 0.899697i \(-0.643787\pi\)
−0.436515 + 0.899697i \(0.643787\pi\)
\(212\) −5.96851 −0.409919
\(213\) 0 0
\(214\) −1.68404 −0.115119
\(215\) −7.67703 −0.523569
\(216\) 0 0
\(217\) −40.4389 −2.74517
\(218\) −10.7457 −0.727793
\(219\) 0 0
\(220\) 0.322602 0.0217498
\(221\) −34.5885 −2.32667
\(222\) 0 0
\(223\) −4.65351 −0.311622 −0.155811 0.987787i \(-0.549799\pi\)
−0.155811 + 0.987787i \(0.549799\pi\)
\(224\) 4.18187 0.279413
\(225\) 0 0
\(226\) 10.3413 0.687892
\(227\) 13.2197 0.877425 0.438713 0.898627i \(-0.355435\pi\)
0.438713 + 0.898627i \(0.355435\pi\)
\(228\) 0 0
\(229\) −4.02383 −0.265902 −0.132951 0.991123i \(-0.542445\pi\)
−0.132951 + 0.991123i \(0.542445\pi\)
\(230\) 2.05519 0.135515
\(231\) 0 0
\(232\) −6.46749 −0.424612
\(233\) −7.44022 −0.487425 −0.243712 0.969848i \(-0.578365\pi\)
−0.243712 + 0.969848i \(0.578365\pi\)
\(234\) 0 0
\(235\) 11.3182 0.738319
\(236\) 4.41785 0.287577
\(237\) 0 0
\(238\) 26.1365 1.69418
\(239\) −25.1146 −1.62453 −0.812263 0.583291i \(-0.801765\pi\)
−0.812263 + 0.583291i \(0.801765\pi\)
\(240\) 0 0
\(241\) −5.39031 −0.347220 −0.173610 0.984814i \(-0.555543\pi\)
−0.173610 + 0.984814i \(0.555543\pi\)
\(242\) −10.9611 −0.704604
\(243\) 0 0
\(244\) 6.34679 0.406311
\(245\) −17.1488 −1.09560
\(246\) 0 0
\(247\) 9.76002 0.621015
\(248\) −9.67005 −0.614049
\(249\) 0 0
\(250\) 11.9794 0.757646
\(251\) 27.5070 1.73623 0.868113 0.496366i \(-0.165333\pi\)
0.868113 + 0.496366i \(0.165333\pi\)
\(252\) 0 0
\(253\) 0.247993 0.0155912
\(254\) 7.37977 0.463048
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −8.27868 −0.516410 −0.258205 0.966090i \(-0.583131\pi\)
−0.258205 + 0.966090i \(0.583131\pi\)
\(258\) 0 0
\(259\) −36.0173 −2.23801
\(260\) 9.04888 0.561187
\(261\) 0 0
\(262\) −9.07961 −0.560940
\(263\) 19.6577 1.21214 0.606072 0.795410i \(-0.292744\pi\)
0.606072 + 0.795410i \(0.292744\pi\)
\(264\) 0 0
\(265\) 9.75900 0.599491
\(266\) −7.37507 −0.452194
\(267\) 0 0
\(268\) −15.3102 −0.935222
\(269\) 3.61876 0.220640 0.110320 0.993896i \(-0.464812\pi\)
0.110320 + 0.993896i \(0.464812\pi\)
\(270\) 0 0
\(271\) 16.2770 0.988756 0.494378 0.869247i \(-0.335396\pi\)
0.494378 + 0.869247i \(0.335396\pi\)
\(272\) 6.24995 0.378959
\(273\) 0 0
\(274\) 12.7245 0.768714
\(275\) 0.459020 0.0276800
\(276\) 0 0
\(277\) 9.87391 0.593266 0.296633 0.954992i \(-0.404136\pi\)
0.296633 + 0.954992i \(0.404136\pi\)
\(278\) 1.66714 0.0999886
\(279\) 0 0
\(280\) −6.83770 −0.408630
\(281\) −5.71542 −0.340953 −0.170477 0.985362i \(-0.554531\pi\)
−0.170477 + 0.985362i \(0.554531\pi\)
\(282\) 0 0
\(283\) −11.6035 −0.689754 −0.344877 0.938648i \(-0.612079\pi\)
−0.344877 + 0.938648i \(0.612079\pi\)
\(284\) 8.52896 0.506100
\(285\) 0 0
\(286\) 1.09190 0.0645653
\(287\) −29.2925 −1.72908
\(288\) 0 0
\(289\) 22.0619 1.29776
\(290\) 10.5749 0.620978
\(291\) 0 0
\(292\) −0.842454 −0.0493009
\(293\) 1.62266 0.0947967 0.0473983 0.998876i \(-0.484907\pi\)
0.0473983 + 0.998876i \(0.484907\pi\)
\(294\) 0 0
\(295\) −7.22354 −0.420571
\(296\) −8.61274 −0.500605
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 6.95612 0.402283
\(300\) 0 0
\(301\) 19.6347 1.13173
\(302\) −17.2820 −0.994465
\(303\) 0 0
\(304\) −1.76358 −0.101148
\(305\) −10.3775 −0.594215
\(306\) 0 0
\(307\) −9.46804 −0.540369 −0.270185 0.962809i \(-0.587085\pi\)
−0.270185 + 0.962809i \(0.587085\pi\)
\(308\) −0.825083 −0.0470135
\(309\) 0 0
\(310\) 15.8113 0.898023
\(311\) −18.2503 −1.03488 −0.517440 0.855720i \(-0.673115\pi\)
−0.517440 + 0.855720i \(0.673115\pi\)
\(312\) 0 0
\(313\) 17.6571 0.998037 0.499018 0.866591i \(-0.333694\pi\)
0.499018 + 0.866591i \(0.333694\pi\)
\(314\) −16.9018 −0.953826
\(315\) 0 0
\(316\) −2.79367 −0.157156
\(317\) −15.3212 −0.860526 −0.430263 0.902704i \(-0.641579\pi\)
−0.430263 + 0.902704i \(0.641579\pi\)
\(318\) 0 0
\(319\) 1.27604 0.0714444
\(320\) −1.63508 −0.0914038
\(321\) 0 0
\(322\) −5.25632 −0.292923
\(323\) −11.0223 −0.613297
\(324\) 0 0
\(325\) 12.8754 0.714197
\(326\) 11.9163 0.659982
\(327\) 0 0
\(328\) −7.00464 −0.386767
\(329\) −28.9474 −1.59592
\(330\) 0 0
\(331\) 10.9330 0.600932 0.300466 0.953793i \(-0.402858\pi\)
0.300466 + 0.953793i \(0.402858\pi\)
\(332\) 1.68295 0.0923641
\(333\) 0 0
\(334\) 14.7560 0.807415
\(335\) 25.0335 1.36773
\(336\) 0 0
\(337\) 2.19251 0.119434 0.0597169 0.998215i \(-0.480980\pi\)
0.0597169 + 0.998215i \(0.480980\pi\)
\(338\) 17.6274 0.958806
\(339\) 0 0
\(340\) −10.2192 −0.554213
\(341\) 1.90790 0.103319
\(342\) 0 0
\(343\) 14.5865 0.787595
\(344\) 4.69520 0.253148
\(345\) 0 0
\(346\) −24.6303 −1.32413
\(347\) −22.7847 −1.22315 −0.611574 0.791187i \(-0.709463\pi\)
−0.611574 + 0.791187i \(0.709463\pi\)
\(348\) 0 0
\(349\) −19.0409 −1.01924 −0.509618 0.860401i \(-0.670213\pi\)
−0.509618 + 0.860401i \(0.670213\pi\)
\(350\) −9.72915 −0.520045
\(351\) 0 0
\(352\) −0.197300 −0.0105161
\(353\) 15.2629 0.812365 0.406182 0.913792i \(-0.366860\pi\)
0.406182 + 0.913792i \(0.366860\pi\)
\(354\) 0 0
\(355\) −13.9455 −0.740152
\(356\) 0.518659 0.0274889
\(357\) 0 0
\(358\) 20.1909 1.06712
\(359\) −1.35972 −0.0717635 −0.0358817 0.999356i \(-0.511424\pi\)
−0.0358817 + 0.999356i \(0.511424\pi\)
\(360\) 0 0
\(361\) −15.8898 −0.836304
\(362\) −18.5876 −0.976941
\(363\) 0 0
\(364\) −23.1433 −1.21304
\(365\) 1.37748 0.0721006
\(366\) 0 0
\(367\) 5.15305 0.268987 0.134494 0.990914i \(-0.457059\pi\)
0.134494 + 0.990914i \(0.457059\pi\)
\(368\) −1.25693 −0.0655221
\(369\) 0 0
\(370\) 14.0825 0.732116
\(371\) −24.9595 −1.29583
\(372\) 0 0
\(373\) 4.71232 0.243995 0.121997 0.992530i \(-0.461070\pi\)
0.121997 + 0.992530i \(0.461070\pi\)
\(374\) −1.23312 −0.0637629
\(375\) 0 0
\(376\) −6.92211 −0.356981
\(377\) 35.7924 1.84340
\(378\) 0 0
\(379\) 16.9403 0.870166 0.435083 0.900390i \(-0.356719\pi\)
0.435083 + 0.900390i \(0.356719\pi\)
\(380\) 2.88360 0.147926
\(381\) 0 0
\(382\) 22.5264 1.15255
\(383\) −6.39895 −0.326971 −0.163486 0.986546i \(-0.552274\pi\)
−0.163486 + 0.986546i \(0.552274\pi\)
\(384\) 0 0
\(385\) 1.34908 0.0687554
\(386\) −3.61836 −0.184170
\(387\) 0 0
\(388\) 2.99290 0.151941
\(389\) 1.08628 0.0550767 0.0275384 0.999621i \(-0.491233\pi\)
0.0275384 + 0.999621i \(0.491233\pi\)
\(390\) 0 0
\(391\) −7.85576 −0.397283
\(392\) 10.4880 0.529725
\(393\) 0 0
\(394\) −22.2957 −1.12324
\(395\) 4.56789 0.229835
\(396\) 0 0
\(397\) 25.3461 1.27208 0.636042 0.771654i \(-0.280570\pi\)
0.636042 + 0.771654i \(0.280570\pi\)
\(398\) −11.0975 −0.556267
\(399\) 0 0
\(400\) −2.32651 −0.116325
\(401\) 2.08150 0.103945 0.0519725 0.998649i \(-0.483449\pi\)
0.0519725 + 0.998649i \(0.483449\pi\)
\(402\) 0 0
\(403\) 53.5161 2.66582
\(404\) 4.86820 0.242202
\(405\) 0 0
\(406\) −27.0462 −1.34228
\(407\) 1.69929 0.0842309
\(408\) 0 0
\(409\) 1.78094 0.0880617 0.0440309 0.999030i \(-0.485980\pi\)
0.0440309 + 0.999030i \(0.485980\pi\)
\(410\) 11.4532 0.565631
\(411\) 0 0
\(412\) 7.84368 0.386430
\(413\) 18.4749 0.909088
\(414\) 0 0
\(415\) −2.75177 −0.135079
\(416\) −5.53420 −0.271337
\(417\) 0 0
\(418\) 0.347955 0.0170190
\(419\) 20.4936 1.00118 0.500589 0.865685i \(-0.333117\pi\)
0.500589 + 0.865685i \(0.333117\pi\)
\(420\) 0 0
\(421\) −13.6932 −0.667364 −0.333682 0.942686i \(-0.608291\pi\)
−0.333682 + 0.942686i \(0.608291\pi\)
\(422\) −12.6815 −0.617326
\(423\) 0 0
\(424\) −5.96851 −0.289857
\(425\) −14.5406 −0.705321
\(426\) 0 0
\(427\) 26.5414 1.28443
\(428\) −1.68404 −0.0814012
\(429\) 0 0
\(430\) −7.67703 −0.370219
\(431\) 22.2846 1.07341 0.536707 0.843769i \(-0.319668\pi\)
0.536707 + 0.843769i \(0.319668\pi\)
\(432\) 0 0
\(433\) −22.4806 −1.08035 −0.540175 0.841552i \(-0.681642\pi\)
−0.540175 + 0.841552i \(0.681642\pi\)
\(434\) −40.4389 −1.94113
\(435\) 0 0
\(436\) −10.7457 −0.514627
\(437\) 2.21670 0.106039
\(438\) 0 0
\(439\) −24.1239 −1.15137 −0.575686 0.817671i \(-0.695265\pi\)
−0.575686 + 0.817671i \(0.695265\pi\)
\(440\) 0.322602 0.0153794
\(441\) 0 0
\(442\) −34.5885 −1.64521
\(443\) 29.6812 1.41020 0.705098 0.709110i \(-0.250903\pi\)
0.705098 + 0.709110i \(0.250903\pi\)
\(444\) 0 0
\(445\) −0.848050 −0.0402014
\(446\) −4.65351 −0.220350
\(447\) 0 0
\(448\) 4.18187 0.197575
\(449\) −25.7344 −1.21448 −0.607240 0.794519i \(-0.707723\pi\)
−0.607240 + 0.794519i \(0.707723\pi\)
\(450\) 0 0
\(451\) 1.38202 0.0650766
\(452\) 10.3413 0.486413
\(453\) 0 0
\(454\) 13.2197 0.620433
\(455\) 37.8412 1.77402
\(456\) 0 0
\(457\) 0.610859 0.0285748 0.0142874 0.999898i \(-0.495452\pi\)
0.0142874 + 0.999898i \(0.495452\pi\)
\(458\) −4.02383 −0.188021
\(459\) 0 0
\(460\) 2.05519 0.0958235
\(461\) 11.9751 0.557734 0.278867 0.960330i \(-0.410041\pi\)
0.278867 + 0.960330i \(0.410041\pi\)
\(462\) 0 0
\(463\) −12.6330 −0.587103 −0.293552 0.955943i \(-0.594837\pi\)
−0.293552 + 0.955943i \(0.594837\pi\)
\(464\) −6.46749 −0.300246
\(465\) 0 0
\(466\) −7.44022 −0.344661
\(467\) −6.77417 −0.313471 −0.156736 0.987641i \(-0.550097\pi\)
−0.156736 + 0.987641i \(0.550097\pi\)
\(468\) 0 0
\(469\) −64.0254 −2.95642
\(470\) 11.3182 0.522070
\(471\) 0 0
\(472\) 4.41785 0.203348
\(473\) −0.926363 −0.0425942
\(474\) 0 0
\(475\) 4.10299 0.188258
\(476\) 26.1365 1.19796
\(477\) 0 0
\(478\) −25.1146 −1.14871
\(479\) 12.1625 0.555719 0.277859 0.960622i \(-0.410375\pi\)
0.277859 + 0.960622i \(0.410375\pi\)
\(480\) 0 0
\(481\) 47.6647 2.17332
\(482\) −5.39031 −0.245522
\(483\) 0 0
\(484\) −10.9611 −0.498231
\(485\) −4.89363 −0.222208
\(486\) 0 0
\(487\) −14.0747 −0.637783 −0.318892 0.947791i \(-0.603311\pi\)
−0.318892 + 0.947791i \(0.603311\pi\)
\(488\) 6.34679 0.287306
\(489\) 0 0
\(490\) −17.1488 −0.774703
\(491\) 19.2146 0.867141 0.433571 0.901120i \(-0.357253\pi\)
0.433571 + 0.901120i \(0.357253\pi\)
\(492\) 0 0
\(493\) −40.4215 −1.82049
\(494\) 9.76002 0.439124
\(495\) 0 0
\(496\) −9.67005 −0.434198
\(497\) 35.6670 1.59988
\(498\) 0 0
\(499\) 35.5569 1.59175 0.795874 0.605463i \(-0.207012\pi\)
0.795874 + 0.605463i \(0.207012\pi\)
\(500\) 11.9794 0.535737
\(501\) 0 0
\(502\) 27.5070 1.22770
\(503\) 7.48503 0.333741 0.166871 0.985979i \(-0.446634\pi\)
0.166871 + 0.985979i \(0.446634\pi\)
\(504\) 0 0
\(505\) −7.95990 −0.354211
\(506\) 0.247993 0.0110246
\(507\) 0 0
\(508\) 7.37977 0.327424
\(509\) 6.17672 0.273778 0.136889 0.990586i \(-0.456290\pi\)
0.136889 + 0.990586i \(0.456290\pi\)
\(510\) 0 0
\(511\) −3.52303 −0.155850
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −8.27868 −0.365157
\(515\) −12.8251 −0.565139
\(516\) 0 0
\(517\) 1.36573 0.0600649
\(518\) −36.0173 −1.58251
\(519\) 0 0
\(520\) 9.04888 0.396819
\(521\) 4.67763 0.204930 0.102465 0.994737i \(-0.467327\pi\)
0.102465 + 0.994737i \(0.467327\pi\)
\(522\) 0 0
\(523\) −6.80751 −0.297672 −0.148836 0.988862i \(-0.547553\pi\)
−0.148836 + 0.988862i \(0.547553\pi\)
\(524\) −9.07961 −0.396645
\(525\) 0 0
\(526\) 19.6577 0.857115
\(527\) −60.4373 −2.63269
\(528\) 0 0
\(529\) −21.4201 −0.931310
\(530\) 9.75900 0.423904
\(531\) 0 0
\(532\) −7.37507 −0.319750
\(533\) 38.7651 1.67910
\(534\) 0 0
\(535\) 2.75354 0.119046
\(536\) −15.3102 −0.661302
\(537\) 0 0
\(538\) 3.61876 0.156016
\(539\) −2.06929 −0.0891306
\(540\) 0 0
\(541\) −37.6664 −1.61940 −0.809702 0.586841i \(-0.800371\pi\)
−0.809702 + 0.586841i \(0.800371\pi\)
\(542\) 16.2770 0.699156
\(543\) 0 0
\(544\) 6.24995 0.267964
\(545\) 17.5702 0.752623
\(546\) 0 0
\(547\) −34.8485 −1.49001 −0.745007 0.667056i \(-0.767554\pi\)
−0.745007 + 0.667056i \(0.767554\pi\)
\(548\) 12.7245 0.543563
\(549\) 0 0
\(550\) 0.459020 0.0195727
\(551\) 11.4060 0.485910
\(552\) 0 0
\(553\) −11.6828 −0.496802
\(554\) 9.87391 0.419502
\(555\) 0 0
\(556\) 1.66714 0.0707026
\(557\) −11.6360 −0.493034 −0.246517 0.969138i \(-0.579286\pi\)
−0.246517 + 0.969138i \(0.579286\pi\)
\(558\) 0 0
\(559\) −25.9842 −1.09901
\(560\) −6.83770 −0.288945
\(561\) 0 0
\(562\) −5.71542 −0.241090
\(563\) −24.7461 −1.04292 −0.521462 0.853274i \(-0.674613\pi\)
−0.521462 + 0.853274i \(0.674613\pi\)
\(564\) 0 0
\(565\) −16.9088 −0.711360
\(566\) −11.6035 −0.487730
\(567\) 0 0
\(568\) 8.52896 0.357867
\(569\) 8.14143 0.341306 0.170653 0.985331i \(-0.445412\pi\)
0.170653 + 0.985331i \(0.445412\pi\)
\(570\) 0 0
\(571\) 1.63240 0.0683138 0.0341569 0.999416i \(-0.489125\pi\)
0.0341569 + 0.999416i \(0.489125\pi\)
\(572\) 1.09190 0.0456546
\(573\) 0 0
\(574\) −29.2925 −1.22264
\(575\) 2.92426 0.121950
\(576\) 0 0
\(577\) 9.01805 0.375426 0.187713 0.982224i \(-0.439892\pi\)
0.187713 + 0.982224i \(0.439892\pi\)
\(578\) 22.0619 0.917652
\(579\) 0 0
\(580\) 10.5749 0.439098
\(581\) 7.03789 0.291981
\(582\) 0 0
\(583\) 1.17759 0.0487707
\(584\) −0.842454 −0.0348610
\(585\) 0 0
\(586\) 1.62266 0.0670314
\(587\) −42.4374 −1.75158 −0.875789 0.482694i \(-0.839658\pi\)
−0.875789 + 0.482694i \(0.839658\pi\)
\(588\) 0 0
\(589\) 17.0539 0.702695
\(590\) −7.22354 −0.297388
\(591\) 0 0
\(592\) −8.61274 −0.353981
\(593\) 40.5390 1.66474 0.832369 0.554222i \(-0.186984\pi\)
0.832369 + 0.554222i \(0.186984\pi\)
\(594\) 0 0
\(595\) −42.7352 −1.75197
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) 6.95612 0.284457
\(599\) 11.4659 0.468484 0.234242 0.972178i \(-0.424739\pi\)
0.234242 + 0.972178i \(0.424739\pi\)
\(600\) 0 0
\(601\) 36.0785 1.47167 0.735837 0.677159i \(-0.236789\pi\)
0.735837 + 0.677159i \(0.236789\pi\)
\(602\) 19.6347 0.800251
\(603\) 0 0
\(604\) −17.2820 −0.703193
\(605\) 17.9222 0.728643
\(606\) 0 0
\(607\) −37.2834 −1.51329 −0.756643 0.653828i \(-0.773162\pi\)
−0.756643 + 0.653828i \(0.773162\pi\)
\(608\) −1.76358 −0.0715227
\(609\) 0 0
\(610\) −10.3775 −0.420173
\(611\) 38.3084 1.54979
\(612\) 0 0
\(613\) −0.666270 −0.0269104 −0.0134552 0.999909i \(-0.504283\pi\)
−0.0134552 + 0.999909i \(0.504283\pi\)
\(614\) −9.46804 −0.382099
\(615\) 0 0
\(616\) −0.825083 −0.0332435
\(617\) −41.1430 −1.65635 −0.828177 0.560467i \(-0.810622\pi\)
−0.828177 + 0.560467i \(0.810622\pi\)
\(618\) 0 0
\(619\) −0.736346 −0.0295962 −0.0147981 0.999891i \(-0.504711\pi\)
−0.0147981 + 0.999891i \(0.504711\pi\)
\(620\) 15.8113 0.634998
\(621\) 0 0
\(622\) −18.2503 −0.731770
\(623\) 2.16896 0.0868977
\(624\) 0 0
\(625\) −7.95481 −0.318193
\(626\) 17.6571 0.705719
\(627\) 0 0
\(628\) −16.9018 −0.674457
\(629\) −53.8292 −2.14631
\(630\) 0 0
\(631\) 46.8071 1.86336 0.931681 0.363277i \(-0.118342\pi\)
0.931681 + 0.363277i \(0.118342\pi\)
\(632\) −2.79367 −0.111126
\(633\) 0 0
\(634\) −15.3212 −0.608483
\(635\) −12.0665 −0.478845
\(636\) 0 0
\(637\) −58.0429 −2.29974
\(638\) 1.27604 0.0505188
\(639\) 0 0
\(640\) −1.63508 −0.0646323
\(641\) −20.0532 −0.792052 −0.396026 0.918239i \(-0.629611\pi\)
−0.396026 + 0.918239i \(0.629611\pi\)
\(642\) 0 0
\(643\) 48.7277 1.92163 0.960817 0.277182i \(-0.0894005\pi\)
0.960817 + 0.277182i \(0.0894005\pi\)
\(644\) −5.25632 −0.207128
\(645\) 0 0
\(646\) −11.0223 −0.433666
\(647\) −21.8927 −0.860692 −0.430346 0.902664i \(-0.641608\pi\)
−0.430346 + 0.902664i \(0.641608\pi\)
\(648\) 0 0
\(649\) −0.871641 −0.0342149
\(650\) 12.8754 0.505014
\(651\) 0 0
\(652\) 11.9163 0.466678
\(653\) 29.9921 1.17368 0.586840 0.809703i \(-0.300372\pi\)
0.586840 + 0.809703i \(0.300372\pi\)
\(654\) 0 0
\(655\) 14.8459 0.580077
\(656\) −7.00464 −0.273485
\(657\) 0 0
\(658\) −28.9474 −1.12849
\(659\) −42.8025 −1.66735 −0.833675 0.552255i \(-0.813767\pi\)
−0.833675 + 0.552255i \(0.813767\pi\)
\(660\) 0 0
\(661\) 37.7037 1.46651 0.733253 0.679956i \(-0.238001\pi\)
0.733253 + 0.679956i \(0.238001\pi\)
\(662\) 10.9330 0.424923
\(663\) 0 0
\(664\) 1.68295 0.0653113
\(665\) 12.0588 0.467621
\(666\) 0 0
\(667\) 8.12920 0.314764
\(668\) 14.7560 0.570929
\(669\) 0 0
\(670\) 25.0335 0.967128
\(671\) −1.25222 −0.0483415
\(672\) 0 0
\(673\) −7.65651 −0.295137 −0.147568 0.989052i \(-0.547145\pi\)
−0.147568 + 0.989052i \(0.547145\pi\)
\(674\) 2.19251 0.0844525
\(675\) 0 0
\(676\) 17.6274 0.677978
\(677\) −51.3670 −1.97420 −0.987098 0.160118i \(-0.948812\pi\)
−0.987098 + 0.160118i \(0.948812\pi\)
\(678\) 0 0
\(679\) 12.5159 0.480317
\(680\) −10.2192 −0.391887
\(681\) 0 0
\(682\) 1.90790 0.0730573
\(683\) 6.92554 0.264998 0.132499 0.991183i \(-0.457700\pi\)
0.132499 + 0.991183i \(0.457700\pi\)
\(684\) 0 0
\(685\) −20.8056 −0.794940
\(686\) 14.5865 0.556914
\(687\) 0 0
\(688\) 4.69520 0.179003
\(689\) 33.0310 1.25838
\(690\) 0 0
\(691\) 9.16011 0.348467 0.174233 0.984704i \(-0.444255\pi\)
0.174233 + 0.984704i \(0.444255\pi\)
\(692\) −24.6303 −0.936302
\(693\) 0 0
\(694\) −22.7847 −0.864896
\(695\) −2.72591 −0.103400
\(696\) 0 0
\(697\) −43.7787 −1.65823
\(698\) −19.0409 −0.720709
\(699\) 0 0
\(700\) −9.72915 −0.367727
\(701\) 14.6149 0.551995 0.275998 0.961158i \(-0.410992\pi\)
0.275998 + 0.961158i \(0.410992\pi\)
\(702\) 0 0
\(703\) 15.1893 0.572874
\(704\) −0.197300 −0.00743603
\(705\) 0 0
\(706\) 15.2629 0.574429
\(707\) 20.3582 0.765648
\(708\) 0 0
\(709\) −42.3835 −1.59175 −0.795873 0.605464i \(-0.792988\pi\)
−0.795873 + 0.605464i \(0.792988\pi\)
\(710\) −13.9455 −0.523367
\(711\) 0 0
\(712\) 0.518659 0.0194376
\(713\) 12.1546 0.455193
\(714\) 0 0
\(715\) −1.78534 −0.0667681
\(716\) 20.1909 0.754568
\(717\) 0 0
\(718\) −1.35972 −0.0507444
\(719\) −20.0259 −0.746841 −0.373420 0.927662i \(-0.621815\pi\)
−0.373420 + 0.927662i \(0.621815\pi\)
\(720\) 0 0
\(721\) 32.8012 1.22158
\(722\) −15.8898 −0.591356
\(723\) 0 0
\(724\) −18.5876 −0.690801
\(725\) 15.0467 0.558820
\(726\) 0 0
\(727\) 10.9223 0.405088 0.202544 0.979273i \(-0.435079\pi\)
0.202544 + 0.979273i \(0.435079\pi\)
\(728\) −23.1433 −0.857748
\(729\) 0 0
\(730\) 1.37748 0.0509828
\(731\) 29.3448 1.08535
\(732\) 0 0
\(733\) 33.8316 1.24960 0.624799 0.780785i \(-0.285181\pi\)
0.624799 + 0.780785i \(0.285181\pi\)
\(734\) 5.15305 0.190203
\(735\) 0 0
\(736\) −1.25693 −0.0463311
\(737\) 3.02071 0.111269
\(738\) 0 0
\(739\) −18.9760 −0.698045 −0.349023 0.937114i \(-0.613486\pi\)
−0.349023 + 0.937114i \(0.613486\pi\)
\(740\) 14.0825 0.517684
\(741\) 0 0
\(742\) −24.9595 −0.916293
\(743\) −15.2042 −0.557786 −0.278893 0.960322i \(-0.589968\pi\)
−0.278893 + 0.960322i \(0.589968\pi\)
\(744\) 0 0
\(745\) 1.63508 0.0599047
\(746\) 4.71232 0.172530
\(747\) 0 0
\(748\) −1.23312 −0.0450872
\(749\) −7.04244 −0.257325
\(750\) 0 0
\(751\) −3.34506 −0.122063 −0.0610316 0.998136i \(-0.519439\pi\)
−0.0610316 + 0.998136i \(0.519439\pi\)
\(752\) −6.92211 −0.252423
\(753\) 0 0
\(754\) 35.7924 1.30348
\(755\) 28.2574 1.02839
\(756\) 0 0
\(757\) −42.2280 −1.53480 −0.767401 0.641167i \(-0.778450\pi\)
−0.767401 + 0.641167i \(0.778450\pi\)
\(758\) 16.9403 0.615301
\(759\) 0 0
\(760\) 2.88360 0.104599
\(761\) −27.8189 −1.00844 −0.504218 0.863577i \(-0.668219\pi\)
−0.504218 + 0.863577i \(0.668219\pi\)
\(762\) 0 0
\(763\) −44.9373 −1.62684
\(764\) 22.5264 0.814976
\(765\) 0 0
\(766\) −6.39895 −0.231203
\(767\) −24.4493 −0.882812
\(768\) 0 0
\(769\) 35.7072 1.28764 0.643818 0.765179i \(-0.277349\pi\)
0.643818 + 0.765179i \(0.277349\pi\)
\(770\) 1.34908 0.0486174
\(771\) 0 0
\(772\) −3.61836 −0.130228
\(773\) −52.1349 −1.87516 −0.937580 0.347769i \(-0.886939\pi\)
−0.937580 + 0.347769i \(0.886939\pi\)
\(774\) 0 0
\(775\) 22.4975 0.808133
\(776\) 2.99290 0.107439
\(777\) 0 0
\(778\) 1.08628 0.0389451
\(779\) 12.3533 0.442601
\(780\) 0 0
\(781\) −1.68276 −0.0602140
\(782\) −7.85576 −0.280921
\(783\) 0 0
\(784\) 10.4880 0.374572
\(785\) 27.6359 0.986367
\(786\) 0 0
\(787\) −29.2235 −1.04170 −0.520852 0.853647i \(-0.674386\pi\)
−0.520852 + 0.853647i \(0.674386\pi\)
\(788\) −22.2957 −0.794253
\(789\) 0 0
\(790\) 4.56789 0.162518
\(791\) 43.2459 1.53765
\(792\) 0 0
\(793\) −35.1244 −1.24730
\(794\) 25.3461 0.899500
\(795\) 0 0
\(796\) −11.0975 −0.393340
\(797\) 16.9257 0.599538 0.299769 0.954012i \(-0.403090\pi\)
0.299769 + 0.954012i \(0.403090\pi\)
\(798\) 0 0
\(799\) −43.2628 −1.53053
\(800\) −2.32651 −0.0822545
\(801\) 0 0
\(802\) 2.08150 0.0735002
\(803\) 0.166216 0.00586564
\(804\) 0 0
\(805\) 8.59452 0.302917
\(806\) 53.5161 1.88502
\(807\) 0 0
\(808\) 4.86820 0.171263
\(809\) −33.6153 −1.18185 −0.590926 0.806726i \(-0.701237\pi\)
−0.590926 + 0.806726i \(0.701237\pi\)
\(810\) 0 0
\(811\) 50.8551 1.78577 0.892883 0.450289i \(-0.148679\pi\)
0.892883 + 0.450289i \(0.148679\pi\)
\(812\) −27.0462 −0.949136
\(813\) 0 0
\(814\) 1.69929 0.0595602
\(815\) −19.4841 −0.682498
\(816\) 0 0
\(817\) −8.28037 −0.289693
\(818\) 1.78094 0.0622691
\(819\) 0 0
\(820\) 11.4532 0.399962
\(821\) 10.0302 0.350056 0.175028 0.984563i \(-0.443998\pi\)
0.175028 + 0.984563i \(0.443998\pi\)
\(822\) 0 0
\(823\) −17.0828 −0.595470 −0.297735 0.954649i \(-0.596231\pi\)
−0.297735 + 0.954649i \(0.596231\pi\)
\(824\) 7.84368 0.273247
\(825\) 0 0
\(826\) 18.4749 0.642823
\(827\) 33.6331 1.16954 0.584768 0.811201i \(-0.301186\pi\)
0.584768 + 0.811201i \(0.301186\pi\)
\(828\) 0 0
\(829\) −29.4770 −1.02378 −0.511889 0.859052i \(-0.671054\pi\)
−0.511889 + 0.859052i \(0.671054\pi\)
\(830\) −2.75177 −0.0955152
\(831\) 0 0
\(832\) −5.53420 −0.191864
\(833\) 65.5496 2.27116
\(834\) 0 0
\(835\) −24.1273 −0.834961
\(836\) 0.347955 0.0120343
\(837\) 0 0
\(838\) 20.4936 0.707940
\(839\) 22.2593 0.768476 0.384238 0.923234i \(-0.374464\pi\)
0.384238 + 0.923234i \(0.374464\pi\)
\(840\) 0 0
\(841\) 12.8285 0.442362
\(842\) −13.6932 −0.471897
\(843\) 0 0
\(844\) −12.6815 −0.436515
\(845\) −28.8223 −0.991516
\(846\) 0 0
\(847\) −45.8378 −1.57500
\(848\) −5.96851 −0.204960
\(849\) 0 0
\(850\) −14.5406 −0.498737
\(851\) 10.8256 0.371098
\(852\) 0 0
\(853\) −6.65495 −0.227861 −0.113931 0.993489i \(-0.536344\pi\)
−0.113931 + 0.993489i \(0.536344\pi\)
\(854\) 26.5414 0.908229
\(855\) 0 0
\(856\) −1.68404 −0.0575593
\(857\) 47.2482 1.61397 0.806983 0.590574i \(-0.201099\pi\)
0.806983 + 0.590574i \(0.201099\pi\)
\(858\) 0 0
\(859\) 33.1021 1.12943 0.564714 0.825287i \(-0.308987\pi\)
0.564714 + 0.825287i \(0.308987\pi\)
\(860\) −7.67703 −0.261785
\(861\) 0 0
\(862\) 22.2846 0.759018
\(863\) 5.50067 0.187245 0.0936225 0.995608i \(-0.470155\pi\)
0.0936225 + 0.995608i \(0.470155\pi\)
\(864\) 0 0
\(865\) 40.2725 1.36931
\(866\) −22.4806 −0.763923
\(867\) 0 0
\(868\) −40.4389 −1.37259
\(869\) 0.551192 0.0186979
\(870\) 0 0
\(871\) 84.7300 2.87097
\(872\) −10.7457 −0.363897
\(873\) 0 0
\(874\) 2.21670 0.0749810
\(875\) 50.0964 1.69357
\(876\) 0 0
\(877\) 22.7687 0.768844 0.384422 0.923157i \(-0.374401\pi\)
0.384422 + 0.923157i \(0.374401\pi\)
\(878\) −24.1239 −0.814143
\(879\) 0 0
\(880\) 0.322602 0.0108749
\(881\) −35.0854 −1.18206 −0.591029 0.806650i \(-0.701278\pi\)
−0.591029 + 0.806650i \(0.701278\pi\)
\(882\) 0 0
\(883\) −13.7453 −0.462565 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(884\) −34.5885 −1.16334
\(885\) 0 0
\(886\) 29.6812 0.997159
\(887\) −27.4555 −0.921865 −0.460932 0.887435i \(-0.652485\pi\)
−0.460932 + 0.887435i \(0.652485\pi\)
\(888\) 0 0
\(889\) 30.8612 1.03505
\(890\) −0.848050 −0.0284267
\(891\) 0 0
\(892\) −4.65351 −0.155811
\(893\) 12.2077 0.408515
\(894\) 0 0
\(895\) −33.0137 −1.10353
\(896\) 4.18187 0.139706
\(897\) 0 0
\(898\) −25.7344 −0.858767
\(899\) 62.5410 2.08586
\(900\) 0 0
\(901\) −37.3029 −1.24274
\(902\) 1.38202 0.0460161
\(903\) 0 0
\(904\) 10.3413 0.343946
\(905\) 30.3922 1.01027
\(906\) 0 0
\(907\) 2.38802 0.0792927 0.0396464 0.999214i \(-0.487377\pi\)
0.0396464 + 0.999214i \(0.487377\pi\)
\(908\) 13.2197 0.438713
\(909\) 0 0
\(910\) 37.8412 1.25442
\(911\) −27.0356 −0.895729 −0.447864 0.894101i \(-0.647815\pi\)
−0.447864 + 0.894101i \(0.647815\pi\)
\(912\) 0 0
\(913\) −0.332047 −0.0109891
\(914\) 0.610859 0.0202054
\(915\) 0 0
\(916\) −4.02383 −0.132951
\(917\) −37.9697 −1.25387
\(918\) 0 0
\(919\) 3.17380 0.104694 0.0523470 0.998629i \(-0.483330\pi\)
0.0523470 + 0.998629i \(0.483330\pi\)
\(920\) 2.05519 0.0677575
\(921\) 0 0
\(922\) 11.9751 0.394377
\(923\) −47.2010 −1.55364
\(924\) 0 0
\(925\) 20.0376 0.658833
\(926\) −12.6330 −0.415145
\(927\) 0 0
\(928\) −6.46749 −0.212306
\(929\) 56.2318 1.84490 0.922452 0.386112i \(-0.126182\pi\)
0.922452 + 0.386112i \(0.126182\pi\)
\(930\) 0 0
\(931\) −18.4965 −0.606198
\(932\) −7.44022 −0.243712
\(933\) 0 0
\(934\) −6.77417 −0.221658
\(935\) 2.01624 0.0659382
\(936\) 0 0
\(937\) −27.0832 −0.884770 −0.442385 0.896825i \(-0.645868\pi\)
−0.442385 + 0.896825i \(0.645868\pi\)
\(938\) −64.0254 −2.09050
\(939\) 0 0
\(940\) 11.3182 0.369159
\(941\) 37.6898 1.22865 0.614326 0.789052i \(-0.289428\pi\)
0.614326 + 0.789052i \(0.289428\pi\)
\(942\) 0 0
\(943\) 8.80436 0.286709
\(944\) 4.41785 0.143789
\(945\) 0 0
\(946\) −0.926363 −0.0301187
\(947\) −42.1198 −1.36871 −0.684354 0.729150i \(-0.739916\pi\)
−0.684354 + 0.729150i \(0.739916\pi\)
\(948\) 0 0
\(949\) 4.66231 0.151345
\(950\) 4.10299 0.133118
\(951\) 0 0
\(952\) 26.1365 0.847088
\(953\) −6.25412 −0.202591 −0.101295 0.994856i \(-0.532299\pi\)
−0.101295 + 0.994856i \(0.532299\pi\)
\(954\) 0 0
\(955\) −36.8325 −1.19187
\(956\) −25.1146 −0.812263
\(957\) 0 0
\(958\) 12.1625 0.392952
\(959\) 53.2121 1.71831
\(960\) 0 0
\(961\) 62.5099 2.01645
\(962\) 47.6647 1.53677
\(963\) 0 0
\(964\) −5.39031 −0.173610
\(965\) 5.91631 0.190453
\(966\) 0 0
\(967\) 31.9859 1.02860 0.514298 0.857611i \(-0.328052\pi\)
0.514298 + 0.857611i \(0.328052\pi\)
\(968\) −10.9611 −0.352302
\(969\) 0 0
\(970\) −4.89363 −0.157125
\(971\) 33.2640 1.06749 0.533747 0.845644i \(-0.320783\pi\)
0.533747 + 0.845644i \(0.320783\pi\)
\(972\) 0 0
\(973\) 6.97177 0.223505
\(974\) −14.0747 −0.450981
\(975\) 0 0
\(976\) 6.34679 0.203156
\(977\) 15.1642 0.485145 0.242573 0.970133i \(-0.422009\pi\)
0.242573 + 0.970133i \(0.422009\pi\)
\(978\) 0 0
\(979\) −0.102331 −0.00327053
\(980\) −17.1488 −0.547798
\(981\) 0 0
\(982\) 19.2146 0.613162
\(983\) 20.6179 0.657609 0.328804 0.944398i \(-0.393354\pi\)
0.328804 + 0.944398i \(0.393354\pi\)
\(984\) 0 0
\(985\) 36.4554 1.16156
\(986\) −40.4215 −1.28728
\(987\) 0 0
\(988\) 9.76002 0.310508
\(989\) −5.90155 −0.187658
\(990\) 0 0
\(991\) 36.9640 1.17420 0.587101 0.809514i \(-0.300269\pi\)
0.587101 + 0.809514i \(0.300269\pi\)
\(992\) −9.67005 −0.307024
\(993\) 0 0
\(994\) 35.6670 1.13129
\(995\) 18.1453 0.575244
\(996\) 0 0
\(997\) 36.7817 1.16489 0.582444 0.812871i \(-0.302096\pi\)
0.582444 + 0.812871i \(0.302096\pi\)
\(998\) 35.5569 1.12554
\(999\) 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 \(a_p\))