Properties

Label 6027.2.a.bn.1.4
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.96907 q^{2} -1.00000 q^{3} +1.87725 q^{4} +4.10878 q^{5} +1.96907 q^{6} +0.241710 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.96907 q^{2} -1.00000 q^{3} +1.87725 q^{4} +4.10878 q^{5} +1.96907 q^{6} +0.241710 q^{8} +1.00000 q^{9} -8.09048 q^{10} +4.87993 q^{11} -1.87725 q^{12} +2.68737 q^{13} -4.10878 q^{15} -4.23044 q^{16} +3.34460 q^{17} -1.96907 q^{18} +0.186064 q^{19} +7.71319 q^{20} -9.60894 q^{22} +5.74714 q^{23} -0.241710 q^{24} +11.8820 q^{25} -5.29162 q^{26} -1.00000 q^{27} +2.28935 q^{29} +8.09048 q^{30} -0.783246 q^{31} +7.84662 q^{32} -4.87993 q^{33} -6.58576 q^{34} +1.87725 q^{36} +1.26983 q^{37} -0.366374 q^{38} -2.68737 q^{39} +0.993134 q^{40} +1.00000 q^{41} -11.2503 q^{43} +9.16084 q^{44} +4.10878 q^{45} -11.3165 q^{46} -2.29201 q^{47} +4.23044 q^{48} -23.3966 q^{50} -3.34460 q^{51} +5.04485 q^{52} +11.2502 q^{53} +1.96907 q^{54} +20.0506 q^{55} -0.186064 q^{57} -4.50789 q^{58} +11.9843 q^{59} -7.71319 q^{60} +1.36157 q^{61} +1.54227 q^{62} -6.98969 q^{64} +11.0418 q^{65} +9.60894 q^{66} -2.74258 q^{67} +6.27864 q^{68} -5.74714 q^{69} +6.59530 q^{71} +0.241710 q^{72} -3.81962 q^{73} -2.50039 q^{74} -11.8820 q^{75} +0.349289 q^{76} +5.29162 q^{78} -10.7548 q^{79} -17.3819 q^{80} +1.00000 q^{81} -1.96907 q^{82} -3.54877 q^{83} +13.7422 q^{85} +22.1526 q^{86} -2.28935 q^{87} +1.17953 q^{88} -9.08983 q^{89} -8.09048 q^{90} +10.7888 q^{92} +0.783246 q^{93} +4.51313 q^{94} +0.764497 q^{95} -7.84662 q^{96} +10.0278 q^{97} +4.87993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96907 −1.39234 −0.696172 0.717875i \(-0.745115\pi\)
−0.696172 + 0.717875i \(0.745115\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.87725 0.938623
\(5\) 4.10878 1.83750 0.918750 0.394839i \(-0.129200\pi\)
0.918750 + 0.394839i \(0.129200\pi\)
\(6\) 1.96907 0.803870
\(7\) 0 0
\(8\) 0.241710 0.0854575
\(9\) 1.00000 0.333333
\(10\) −8.09048 −2.55843
\(11\) 4.87993 1.47136 0.735678 0.677332i \(-0.236864\pi\)
0.735678 + 0.677332i \(0.236864\pi\)
\(12\) −1.87725 −0.541914
\(13\) 2.68737 0.745341 0.372671 0.927964i \(-0.378442\pi\)
0.372671 + 0.927964i \(0.378442\pi\)
\(14\) 0 0
\(15\) −4.10878 −1.06088
\(16\) −4.23044 −1.05761
\(17\) 3.34460 0.811184 0.405592 0.914054i \(-0.367065\pi\)
0.405592 + 0.914054i \(0.367065\pi\)
\(18\) −1.96907 −0.464115
\(19\) 0.186064 0.0426861 0.0213431 0.999772i \(-0.493206\pi\)
0.0213431 + 0.999772i \(0.493206\pi\)
\(20\) 7.71319 1.72472
\(21\) 0 0
\(22\) −9.60894 −2.04863
\(23\) 5.74714 1.19836 0.599181 0.800614i \(-0.295493\pi\)
0.599181 + 0.800614i \(0.295493\pi\)
\(24\) −0.241710 −0.0493389
\(25\) 11.8820 2.37641
\(26\) −5.29162 −1.03777
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.28935 0.425121 0.212561 0.977148i \(-0.431820\pi\)
0.212561 + 0.977148i \(0.431820\pi\)
\(30\) 8.09048 1.47711
\(31\) −0.783246 −0.140675 −0.0703376 0.997523i \(-0.522408\pi\)
−0.0703376 + 0.997523i \(0.522408\pi\)
\(32\) 7.84662 1.38710
\(33\) −4.87993 −0.849488
\(34\) −6.58576 −1.12945
\(35\) 0 0
\(36\) 1.87725 0.312874
\(37\) 1.26983 0.208759 0.104380 0.994538i \(-0.466714\pi\)
0.104380 + 0.994538i \(0.466714\pi\)
\(38\) −0.366374 −0.0594338
\(39\) −2.68737 −0.430323
\(40\) 0.993134 0.157028
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −11.2503 −1.71565 −0.857824 0.513944i \(-0.828184\pi\)
−0.857824 + 0.513944i \(0.828184\pi\)
\(44\) 9.16084 1.38105
\(45\) 4.10878 0.612500
\(46\) −11.3165 −1.66853
\(47\) −2.29201 −0.334324 −0.167162 0.985929i \(-0.553460\pi\)
−0.167162 + 0.985929i \(0.553460\pi\)
\(48\) 4.23044 0.610611
\(49\) 0 0
\(50\) −23.3966 −3.30878
\(51\) −3.34460 −0.468338
\(52\) 5.04485 0.699595
\(53\) 11.2502 1.54533 0.772667 0.634812i \(-0.218922\pi\)
0.772667 + 0.634812i \(0.218922\pi\)
\(54\) 1.96907 0.267957
\(55\) 20.0506 2.70362
\(56\) 0 0
\(57\) −0.186064 −0.0246448
\(58\) −4.50789 −0.591915
\(59\) 11.9843 1.56023 0.780113 0.625639i \(-0.215162\pi\)
0.780113 + 0.625639i \(0.215162\pi\)
\(60\) −7.71319 −0.995768
\(61\) 1.36157 0.174331 0.0871654 0.996194i \(-0.472219\pi\)
0.0871654 + 0.996194i \(0.472219\pi\)
\(62\) 1.54227 0.195868
\(63\) 0 0
\(64\) −6.98969 −0.873711
\(65\) 11.0418 1.36957
\(66\) 9.60894 1.18278
\(67\) −2.74258 −0.335059 −0.167529 0.985867i \(-0.553579\pi\)
−0.167529 + 0.985867i \(0.553579\pi\)
\(68\) 6.27864 0.761397
\(69\) −5.74714 −0.691875
\(70\) 0 0
\(71\) 6.59530 0.782719 0.391359 0.920238i \(-0.372005\pi\)
0.391359 + 0.920238i \(0.372005\pi\)
\(72\) 0.241710 0.0284858
\(73\) −3.81962 −0.447053 −0.223527 0.974698i \(-0.571757\pi\)
−0.223527 + 0.974698i \(0.571757\pi\)
\(74\) −2.50039 −0.290665
\(75\) −11.8820 −1.37202
\(76\) 0.349289 0.0400662
\(77\) 0 0
\(78\) 5.29162 0.599158
\(79\) −10.7548 −1.21001 −0.605003 0.796223i \(-0.706828\pi\)
−0.605003 + 0.796223i \(0.706828\pi\)
\(80\) −17.3819 −1.94336
\(81\) 1.00000 0.111111
\(82\) −1.96907 −0.217448
\(83\) −3.54877 −0.389528 −0.194764 0.980850i \(-0.562394\pi\)
−0.194764 + 0.980850i \(0.562394\pi\)
\(84\) 0 0
\(85\) 13.7422 1.49055
\(86\) 22.1526 2.38877
\(87\) −2.28935 −0.245444
\(88\) 1.17953 0.125738
\(89\) −9.08983 −0.963520 −0.481760 0.876303i \(-0.660002\pi\)
−0.481760 + 0.876303i \(0.660002\pi\)
\(90\) −8.09048 −0.852811
\(91\) 0 0
\(92\) 10.7888 1.12481
\(93\) 0.783246 0.0812189
\(94\) 4.51313 0.465494
\(95\) 0.764497 0.0784357
\(96\) −7.84662 −0.800842
\(97\) 10.0278 1.01817 0.509083 0.860717i \(-0.329985\pi\)
0.509083 + 0.860717i \(0.329985\pi\)
\(98\) 0 0
\(99\) 4.87993 0.490452
\(100\) 22.3055 2.23055
\(101\) 5.67306 0.564490 0.282245 0.959342i \(-0.408921\pi\)
0.282245 + 0.959342i \(0.408921\pi\)
\(102\) 6.58576 0.652087
\(103\) 8.59023 0.846421 0.423210 0.906031i \(-0.360903\pi\)
0.423210 + 0.906031i \(0.360903\pi\)
\(104\) 0.649564 0.0636950
\(105\) 0 0
\(106\) −22.1525 −2.15164
\(107\) −3.10612 −0.300279 −0.150140 0.988665i \(-0.547972\pi\)
−0.150140 + 0.988665i \(0.547972\pi\)
\(108\) −1.87725 −0.180638
\(109\) 10.4576 1.00166 0.500830 0.865546i \(-0.333028\pi\)
0.500830 + 0.865546i \(0.333028\pi\)
\(110\) −39.4810 −3.76437
\(111\) −1.26983 −0.120527
\(112\) 0 0
\(113\) −8.24364 −0.775497 −0.387748 0.921765i \(-0.626747\pi\)
−0.387748 + 0.921765i \(0.626747\pi\)
\(114\) 0.366374 0.0343141
\(115\) 23.6137 2.20199
\(116\) 4.29767 0.399029
\(117\) 2.68737 0.248447
\(118\) −23.5980 −2.17237
\(119\) 0 0
\(120\) −0.993134 −0.0906603
\(121\) 12.8138 1.16489
\(122\) −2.68103 −0.242729
\(123\) −1.00000 −0.0901670
\(124\) −1.47035 −0.132041
\(125\) 28.2768 2.52915
\(126\) 0 0
\(127\) 17.7620 1.57612 0.788060 0.615598i \(-0.211086\pi\)
0.788060 + 0.615598i \(0.211086\pi\)
\(128\) −1.93004 −0.170593
\(129\) 11.2503 0.990530
\(130\) −21.7421 −1.90691
\(131\) −12.1215 −1.05906 −0.529529 0.848292i \(-0.677631\pi\)
−0.529529 + 0.848292i \(0.677631\pi\)
\(132\) −9.16084 −0.797349
\(133\) 0 0
\(134\) 5.40033 0.466517
\(135\) −4.10878 −0.353627
\(136\) 0.808424 0.0693218
\(137\) 13.6412 1.16545 0.582725 0.812669i \(-0.301986\pi\)
0.582725 + 0.812669i \(0.301986\pi\)
\(138\) 11.3165 0.963328
\(139\) 7.04836 0.597834 0.298917 0.954279i \(-0.403375\pi\)
0.298917 + 0.954279i \(0.403375\pi\)
\(140\) 0 0
\(141\) 2.29201 0.193022
\(142\) −12.9866 −1.08981
\(143\) 13.1142 1.09666
\(144\) −4.23044 −0.352537
\(145\) 9.40642 0.781161
\(146\) 7.52112 0.622452
\(147\) 0 0
\(148\) 2.38379 0.195946
\(149\) −22.0836 −1.80916 −0.904579 0.426305i \(-0.859815\pi\)
−0.904579 + 0.426305i \(0.859815\pi\)
\(150\) 23.3966 1.91032
\(151\) −13.9955 −1.13894 −0.569469 0.822013i \(-0.692851\pi\)
−0.569469 + 0.822013i \(0.692851\pi\)
\(152\) 0.0449737 0.00364785
\(153\) 3.34460 0.270395
\(154\) 0 0
\(155\) −3.21818 −0.258491
\(156\) −5.04485 −0.403911
\(157\) −22.2994 −1.77968 −0.889841 0.456270i \(-0.849185\pi\)
−0.889841 + 0.456270i \(0.849185\pi\)
\(158\) 21.1769 1.68475
\(159\) −11.2502 −0.892199
\(160\) 32.2400 2.54880
\(161\) 0 0
\(162\) −1.96907 −0.154705
\(163\) −12.0403 −0.943070 −0.471535 0.881847i \(-0.656300\pi\)
−0.471535 + 0.881847i \(0.656300\pi\)
\(164\) 1.87725 0.146588
\(165\) −20.0506 −1.56093
\(166\) 6.98778 0.542357
\(167\) −8.09156 −0.626144 −0.313072 0.949729i \(-0.601358\pi\)
−0.313072 + 0.949729i \(0.601358\pi\)
\(168\) 0 0
\(169\) −5.77806 −0.444466
\(170\) −27.0594 −2.07536
\(171\) 0.186064 0.0142287
\(172\) −21.1195 −1.61035
\(173\) 6.27533 0.477104 0.238552 0.971130i \(-0.423327\pi\)
0.238552 + 0.971130i \(0.423327\pi\)
\(174\) 4.50789 0.341743
\(175\) 0 0
\(176\) −20.6443 −1.55612
\(177\) −11.9843 −0.900797
\(178\) 17.8985 1.34155
\(179\) 20.9156 1.56331 0.781654 0.623712i \(-0.214376\pi\)
0.781654 + 0.623712i \(0.214376\pi\)
\(180\) 7.71319 0.574907
\(181\) −1.55997 −0.115952 −0.0579758 0.998318i \(-0.518465\pi\)
−0.0579758 + 0.998318i \(0.518465\pi\)
\(182\) 0 0
\(183\) −1.36157 −0.100650
\(184\) 1.38914 0.102409
\(185\) 5.21746 0.383595
\(186\) −1.54227 −0.113085
\(187\) 16.3214 1.19354
\(188\) −4.30267 −0.313804
\(189\) 0 0
\(190\) −1.50535 −0.109210
\(191\) −17.2164 −1.24574 −0.622868 0.782327i \(-0.714033\pi\)
−0.622868 + 0.782327i \(0.714033\pi\)
\(192\) 6.98969 0.504437
\(193\) −15.9807 −1.15031 −0.575157 0.818043i \(-0.695059\pi\)
−0.575157 + 0.818043i \(0.695059\pi\)
\(194\) −19.7454 −1.41764
\(195\) −11.0418 −0.790719
\(196\) 0 0
\(197\) 9.32916 0.664675 0.332337 0.943161i \(-0.392163\pi\)
0.332337 + 0.943161i \(0.392163\pi\)
\(198\) −9.60894 −0.682878
\(199\) 12.6095 0.893866 0.446933 0.894567i \(-0.352516\pi\)
0.446933 + 0.894567i \(0.352516\pi\)
\(200\) 2.87201 0.203082
\(201\) 2.74258 0.193446
\(202\) −11.1707 −0.785965
\(203\) 0 0
\(204\) −6.27864 −0.439593
\(205\) 4.10878 0.286969
\(206\) −16.9148 −1.17851
\(207\) 5.74714 0.399454
\(208\) −11.3687 −0.788280
\(209\) 0.907982 0.0628064
\(210\) 0 0
\(211\) −15.9027 −1.09479 −0.547394 0.836875i \(-0.684380\pi\)
−0.547394 + 0.836875i \(0.684380\pi\)
\(212\) 21.1194 1.45049
\(213\) −6.59530 −0.451903
\(214\) 6.11617 0.418092
\(215\) −46.2248 −3.15250
\(216\) −0.241710 −0.0164463
\(217\) 0 0
\(218\) −20.5918 −1.39465
\(219\) 3.81962 0.258106
\(220\) 37.6398 2.53768
\(221\) 8.98816 0.604609
\(222\) 2.50039 0.167815
\(223\) −29.0062 −1.94240 −0.971199 0.238268i \(-0.923420\pi\)
−0.971199 + 0.238268i \(0.923420\pi\)
\(224\) 0 0
\(225\) 11.8820 0.792136
\(226\) 16.2323 1.07976
\(227\) −20.3453 −1.35036 −0.675182 0.737651i \(-0.735935\pi\)
−0.675182 + 0.737651i \(0.735935\pi\)
\(228\) −0.349289 −0.0231322
\(229\) −24.6741 −1.63051 −0.815257 0.579100i \(-0.803404\pi\)
−0.815257 + 0.579100i \(0.803404\pi\)
\(230\) −46.4971 −3.06593
\(231\) 0 0
\(232\) 0.553359 0.0363298
\(233\) 7.08960 0.464455 0.232227 0.972661i \(-0.425399\pi\)
0.232227 + 0.972661i \(0.425399\pi\)
\(234\) −5.29162 −0.345924
\(235\) −9.41736 −0.614321
\(236\) 22.4975 1.46446
\(237\) 10.7548 0.698598
\(238\) 0 0
\(239\) −19.3453 −1.25134 −0.625672 0.780086i \(-0.715175\pi\)
−0.625672 + 0.780086i \(0.715175\pi\)
\(240\) 17.3819 1.12200
\(241\) 26.5629 1.71107 0.855534 0.517747i \(-0.173229\pi\)
0.855534 + 0.517747i \(0.173229\pi\)
\(242\) −25.2312 −1.62192
\(243\) −1.00000 −0.0641500
\(244\) 2.55600 0.163631
\(245\) 0 0
\(246\) 1.96907 0.125543
\(247\) 0.500023 0.0318157
\(248\) −0.189319 −0.0120218
\(249\) 3.54877 0.224894
\(250\) −55.6790 −3.52145
\(251\) −25.9956 −1.64083 −0.820414 0.571770i \(-0.806257\pi\)
−0.820414 + 0.571770i \(0.806257\pi\)
\(252\) 0 0
\(253\) 28.0457 1.76322
\(254\) −34.9746 −2.19450
\(255\) −13.7422 −0.860570
\(256\) 17.7798 1.11124
\(257\) −21.1096 −1.31678 −0.658391 0.752676i \(-0.728763\pi\)
−0.658391 + 0.752676i \(0.728763\pi\)
\(258\) −22.1526 −1.37916
\(259\) 0 0
\(260\) 20.7282 1.28551
\(261\) 2.28935 0.141707
\(262\) 23.8681 1.47457
\(263\) −10.5110 −0.648136 −0.324068 0.946034i \(-0.605051\pi\)
−0.324068 + 0.946034i \(0.605051\pi\)
\(264\) −1.17953 −0.0725951
\(265\) 46.2245 2.83955
\(266\) 0 0
\(267\) 9.08983 0.556288
\(268\) −5.14849 −0.314494
\(269\) −21.1796 −1.29135 −0.645673 0.763614i \(-0.723423\pi\)
−0.645673 + 0.763614i \(0.723423\pi\)
\(270\) 8.09048 0.492371
\(271\) 2.53803 0.154175 0.0770873 0.997024i \(-0.475438\pi\)
0.0770873 + 0.997024i \(0.475438\pi\)
\(272\) −14.1491 −0.857916
\(273\) 0 0
\(274\) −26.8606 −1.62271
\(275\) 57.9836 3.49654
\(276\) −10.7888 −0.649410
\(277\) 20.2870 1.21893 0.609465 0.792813i \(-0.291384\pi\)
0.609465 + 0.792813i \(0.291384\pi\)
\(278\) −13.8787 −0.832390
\(279\) −0.783246 −0.0468917
\(280\) 0 0
\(281\) −18.2747 −1.09018 −0.545088 0.838379i \(-0.683504\pi\)
−0.545088 + 0.838379i \(0.683504\pi\)
\(282\) −4.51313 −0.268753
\(283\) 4.14431 0.246354 0.123177 0.992385i \(-0.460692\pi\)
0.123177 + 0.992385i \(0.460692\pi\)
\(284\) 12.3810 0.734678
\(285\) −0.764497 −0.0452849
\(286\) −25.8228 −1.52693
\(287\) 0 0
\(288\) 7.84662 0.462366
\(289\) −5.81366 −0.341980
\(290\) −18.5219 −1.08765
\(291\) −10.0278 −0.587839
\(292\) −7.17038 −0.419615
\(293\) −2.08588 −0.121859 −0.0609293 0.998142i \(-0.519406\pi\)
−0.0609293 + 0.998142i \(0.519406\pi\)
\(294\) 0 0
\(295\) 49.2409 2.86692
\(296\) 0.306932 0.0178401
\(297\) −4.87993 −0.283163
\(298\) 43.4842 2.51897
\(299\) 15.4447 0.893189
\(300\) −22.3055 −1.28781
\(301\) 0 0
\(302\) 27.5582 1.58579
\(303\) −5.67306 −0.325909
\(304\) −0.787134 −0.0451452
\(305\) 5.59438 0.320333
\(306\) −6.58576 −0.376483
\(307\) −6.30305 −0.359734 −0.179867 0.983691i \(-0.557567\pi\)
−0.179867 + 0.983691i \(0.557567\pi\)
\(308\) 0 0
\(309\) −8.59023 −0.488681
\(310\) 6.33684 0.359908
\(311\) −16.3846 −0.929083 −0.464541 0.885551i \(-0.653781\pi\)
−0.464541 + 0.885551i \(0.653781\pi\)
\(312\) −0.649564 −0.0367743
\(313\) 14.1093 0.797504 0.398752 0.917059i \(-0.369443\pi\)
0.398752 + 0.917059i \(0.369443\pi\)
\(314\) 43.9091 2.47793
\(315\) 0 0
\(316\) −20.1894 −1.13574
\(317\) 6.97987 0.392029 0.196014 0.980601i \(-0.437200\pi\)
0.196014 + 0.980601i \(0.437200\pi\)
\(318\) 22.1525 1.24225
\(319\) 11.1719 0.625505
\(320\) −28.7191 −1.60544
\(321\) 3.10612 0.173366
\(322\) 0 0
\(323\) 0.622311 0.0346263
\(324\) 1.87725 0.104291
\(325\) 31.9314 1.77124
\(326\) 23.7082 1.31308
\(327\) −10.4576 −0.578308
\(328\) 0.241710 0.0133462
\(329\) 0 0
\(330\) 39.4810 2.17336
\(331\) 10.6727 0.586626 0.293313 0.956016i \(-0.405242\pi\)
0.293313 + 0.956016i \(0.405242\pi\)
\(332\) −6.66192 −0.365620
\(333\) 1.26983 0.0695864
\(334\) 15.9329 0.871808
\(335\) −11.2686 −0.615671
\(336\) 0 0
\(337\) −5.30369 −0.288910 −0.144455 0.989511i \(-0.546143\pi\)
−0.144455 + 0.989511i \(0.546143\pi\)
\(338\) 11.3774 0.618850
\(339\) 8.24364 0.447733
\(340\) 25.7975 1.39907
\(341\) −3.82219 −0.206983
\(342\) −0.366374 −0.0198113
\(343\) 0 0
\(344\) −2.71930 −0.146615
\(345\) −23.6137 −1.27132
\(346\) −12.3566 −0.664293
\(347\) 5.01085 0.268996 0.134498 0.990914i \(-0.457058\pi\)
0.134498 + 0.990914i \(0.457058\pi\)
\(348\) −4.29767 −0.230379
\(349\) −30.8522 −1.65148 −0.825740 0.564051i \(-0.809242\pi\)
−0.825740 + 0.564051i \(0.809242\pi\)
\(350\) 0 0
\(351\) −2.68737 −0.143441
\(352\) 38.2910 2.04092
\(353\) 6.06809 0.322972 0.161486 0.986875i \(-0.448371\pi\)
0.161486 + 0.986875i \(0.448371\pi\)
\(354\) 23.5980 1.25422
\(355\) 27.0986 1.43825
\(356\) −17.0638 −0.904382
\(357\) 0 0
\(358\) −41.1844 −2.17666
\(359\) 14.9483 0.788940 0.394470 0.918909i \(-0.370928\pi\)
0.394470 + 0.918909i \(0.370928\pi\)
\(360\) 0.993134 0.0523427
\(361\) −18.9654 −0.998178
\(362\) 3.07169 0.161445
\(363\) −12.8138 −0.672548
\(364\) 0 0
\(365\) −15.6940 −0.821461
\(366\) 2.68103 0.140139
\(367\) −24.3316 −1.27010 −0.635051 0.772470i \(-0.719021\pi\)
−0.635051 + 0.772470i \(0.719021\pi\)
\(368\) −24.3129 −1.26740
\(369\) 1.00000 0.0520579
\(370\) −10.2736 −0.534097
\(371\) 0 0
\(372\) 1.47035 0.0762339
\(373\) −24.1138 −1.24856 −0.624281 0.781200i \(-0.714608\pi\)
−0.624281 + 0.781200i \(0.714608\pi\)
\(374\) −32.1381 −1.66182
\(375\) −28.2768 −1.46021
\(376\) −0.554003 −0.0285705
\(377\) 6.15232 0.316861
\(378\) 0 0
\(379\) 38.8760 1.99692 0.998462 0.0554442i \(-0.0176575\pi\)
0.998462 + 0.0554442i \(0.0176575\pi\)
\(380\) 1.43515 0.0736216
\(381\) −17.7620 −0.909973
\(382\) 33.9004 1.73449
\(383\) −2.85283 −0.145773 −0.0728865 0.997340i \(-0.523221\pi\)
−0.0728865 + 0.997340i \(0.523221\pi\)
\(384\) 1.93004 0.0984920
\(385\) 0 0
\(386\) 31.4671 1.60163
\(387\) −11.2503 −0.571882
\(388\) 18.8246 0.955675
\(389\) 3.62480 0.183785 0.0918924 0.995769i \(-0.470708\pi\)
0.0918924 + 0.995769i \(0.470708\pi\)
\(390\) 21.7421 1.10095
\(391\) 19.2219 0.972093
\(392\) 0 0
\(393\) 12.1215 0.611448
\(394\) −18.3698 −0.925456
\(395\) −44.1890 −2.22339
\(396\) 9.16084 0.460350
\(397\) 24.5418 1.23172 0.615859 0.787857i \(-0.288809\pi\)
0.615859 + 0.787857i \(0.288809\pi\)
\(398\) −24.8291 −1.24457
\(399\) 0 0
\(400\) −50.2662 −2.51331
\(401\) −16.6130 −0.829612 −0.414806 0.909910i \(-0.636151\pi\)
−0.414806 + 0.909910i \(0.636151\pi\)
\(402\) −5.40033 −0.269344
\(403\) −2.10487 −0.104851
\(404\) 10.6497 0.529844
\(405\) 4.10878 0.204167
\(406\) 0 0
\(407\) 6.19670 0.307159
\(408\) −0.808424 −0.0400230
\(409\) −6.47251 −0.320045 −0.160023 0.987113i \(-0.551157\pi\)
−0.160023 + 0.987113i \(0.551157\pi\)
\(410\) −8.09048 −0.399560
\(411\) −13.6412 −0.672873
\(412\) 16.1260 0.794470
\(413\) 0 0
\(414\) −11.3165 −0.556178
\(415\) −14.5811 −0.715758
\(416\) 21.0867 1.03386
\(417\) −7.04836 −0.345159
\(418\) −1.78788 −0.0874482
\(419\) −36.5645 −1.78629 −0.893145 0.449768i \(-0.851507\pi\)
−0.893145 + 0.449768i \(0.851507\pi\)
\(420\) 0 0
\(421\) 19.5817 0.954352 0.477176 0.878808i \(-0.341660\pi\)
0.477176 + 0.878808i \(0.341660\pi\)
\(422\) 31.3136 1.52432
\(423\) −2.29201 −0.111441
\(424\) 2.71929 0.132060
\(425\) 39.7407 1.92771
\(426\) 12.9866 0.629204
\(427\) 0 0
\(428\) −5.83094 −0.281849
\(429\) −13.1142 −0.633158
\(430\) 91.0199 4.38937
\(431\) −14.7266 −0.709358 −0.354679 0.934988i \(-0.615410\pi\)
−0.354679 + 0.934988i \(0.615410\pi\)
\(432\) 4.23044 0.203537
\(433\) −36.9867 −1.77747 −0.888734 0.458423i \(-0.848414\pi\)
−0.888734 + 0.458423i \(0.848414\pi\)
\(434\) 0 0
\(435\) −9.40642 −0.451003
\(436\) 19.6316 0.940181
\(437\) 1.06934 0.0511534
\(438\) −7.52112 −0.359373
\(439\) −37.3318 −1.78175 −0.890875 0.454248i \(-0.849908\pi\)
−0.890875 + 0.454248i \(0.849908\pi\)
\(440\) 4.84643 0.231044
\(441\) 0 0
\(442\) −17.6983 −0.841824
\(443\) 12.9322 0.614427 0.307214 0.951641i \(-0.400603\pi\)
0.307214 + 0.951641i \(0.400603\pi\)
\(444\) −2.38379 −0.113130
\(445\) −37.3481 −1.77047
\(446\) 57.1153 2.70449
\(447\) 22.0836 1.04452
\(448\) 0 0
\(449\) 16.2013 0.764585 0.382293 0.924041i \(-0.375135\pi\)
0.382293 + 0.924041i \(0.375135\pi\)
\(450\) −23.3966 −1.10293
\(451\) 4.87993 0.229787
\(452\) −15.4754 −0.727899
\(453\) 13.9955 0.657566
\(454\) 40.0613 1.88017
\(455\) 0 0
\(456\) −0.0449737 −0.00210609
\(457\) 34.1158 1.59587 0.797934 0.602745i \(-0.205926\pi\)
0.797934 + 0.602745i \(0.205926\pi\)
\(458\) 48.5852 2.27024
\(459\) −3.34460 −0.156113
\(460\) 44.3288 2.06684
\(461\) 4.85915 0.226313 0.113157 0.993577i \(-0.463904\pi\)
0.113157 + 0.993577i \(0.463904\pi\)
\(462\) 0 0
\(463\) 14.8794 0.691505 0.345752 0.938326i \(-0.387624\pi\)
0.345752 + 0.938326i \(0.387624\pi\)
\(464\) −9.68495 −0.449612
\(465\) 3.21818 0.149240
\(466\) −13.9599 −0.646681
\(467\) 10.9481 0.506616 0.253308 0.967386i \(-0.418481\pi\)
0.253308 + 0.967386i \(0.418481\pi\)
\(468\) 5.04485 0.233198
\(469\) 0 0
\(470\) 18.5435 0.855346
\(471\) 22.2994 1.02750
\(472\) 2.89673 0.133333
\(473\) −54.9005 −2.52433
\(474\) −21.1769 −0.972689
\(475\) 2.21083 0.101440
\(476\) 0 0
\(477\) 11.2502 0.515111
\(478\) 38.0923 1.74230
\(479\) −12.9076 −0.589765 −0.294882 0.955534i \(-0.595281\pi\)
−0.294882 + 0.955534i \(0.595281\pi\)
\(480\) −32.2400 −1.47155
\(481\) 3.41251 0.155597
\(482\) −52.3043 −2.38239
\(483\) 0 0
\(484\) 24.0546 1.09339
\(485\) 41.2019 1.87088
\(486\) 1.96907 0.0893189
\(487\) 36.1750 1.63925 0.819623 0.572903i \(-0.194183\pi\)
0.819623 + 0.572903i \(0.194183\pi\)
\(488\) 0.329105 0.0148979
\(489\) 12.0403 0.544482
\(490\) 0 0
\(491\) −26.5961 −1.20027 −0.600134 0.799900i \(-0.704886\pi\)
−0.600134 + 0.799900i \(0.704886\pi\)
\(492\) −1.87725 −0.0846328
\(493\) 7.65695 0.344852
\(494\) −0.984582 −0.0442984
\(495\) 20.0506 0.901206
\(496\) 3.31348 0.148779
\(497\) 0 0
\(498\) −6.98778 −0.313130
\(499\) 2.92760 0.131058 0.0655288 0.997851i \(-0.479127\pi\)
0.0655288 + 0.997851i \(0.479127\pi\)
\(500\) 53.0825 2.37392
\(501\) 8.09156 0.361504
\(502\) 51.1872 2.28460
\(503\) −24.7773 −1.10477 −0.552383 0.833590i \(-0.686281\pi\)
−0.552383 + 0.833590i \(0.686281\pi\)
\(504\) 0 0
\(505\) 23.3093 1.03725
\(506\) −55.2240 −2.45501
\(507\) 5.77806 0.256613
\(508\) 33.3436 1.47938
\(509\) −0.0377927 −0.00167513 −0.000837566 1.00000i \(-0.500267\pi\)
−0.000837566 1.00000i \(0.500267\pi\)
\(510\) 27.0594 1.19821
\(511\) 0 0
\(512\) −31.1496 −1.37663
\(513\) −0.186064 −0.00821494
\(514\) 41.5664 1.83341
\(515\) 35.2953 1.55530
\(516\) 21.1195 0.929734
\(517\) −11.1849 −0.491910
\(518\) 0 0
\(519\) −6.27533 −0.275456
\(520\) 2.66891 0.117040
\(521\) 31.0842 1.36182 0.680911 0.732366i \(-0.261584\pi\)
0.680911 + 0.732366i \(0.261584\pi\)
\(522\) −4.50789 −0.197305
\(523\) 3.42589 0.149804 0.0749018 0.997191i \(-0.476136\pi\)
0.0749018 + 0.997191i \(0.476136\pi\)
\(524\) −22.7550 −0.994057
\(525\) 0 0
\(526\) 20.6969 0.902428
\(527\) −2.61965 −0.114114
\(528\) 20.6443 0.898426
\(529\) 10.0297 0.436072
\(530\) −91.0195 −3.95363
\(531\) 11.9843 0.520075
\(532\) 0 0
\(533\) 2.68737 0.116403
\(534\) −17.8985 −0.774545
\(535\) −12.7623 −0.551764
\(536\) −0.662909 −0.0286333
\(537\) −20.9156 −0.902576
\(538\) 41.7042 1.79800
\(539\) 0 0
\(540\) −7.71319 −0.331923
\(541\) −18.9563 −0.814996 −0.407498 0.913206i \(-0.633599\pi\)
−0.407498 + 0.913206i \(0.633599\pi\)
\(542\) −4.99757 −0.214664
\(543\) 1.55997 0.0669447
\(544\) 26.2438 1.12519
\(545\) 42.9681 1.84055
\(546\) 0 0
\(547\) 29.9021 1.27852 0.639261 0.768989i \(-0.279240\pi\)
0.639261 + 0.768989i \(0.279240\pi\)
\(548\) 25.6080 1.09392
\(549\) 1.36157 0.0581103
\(550\) −114.174 −4.86839
\(551\) 0.425966 0.0181468
\(552\) −1.38914 −0.0591259
\(553\) 0 0
\(554\) −39.9466 −1.69717
\(555\) −5.21746 −0.221469
\(556\) 13.2315 0.561141
\(557\) 39.7964 1.68623 0.843114 0.537735i \(-0.180720\pi\)
0.843114 + 0.537735i \(0.180720\pi\)
\(558\) 1.54227 0.0652895
\(559\) −30.2335 −1.27874
\(560\) 0 0
\(561\) −16.3214 −0.689091
\(562\) 35.9842 1.51790
\(563\) −19.6406 −0.827754 −0.413877 0.910333i \(-0.635826\pi\)
−0.413877 + 0.910333i \(0.635826\pi\)
\(564\) 4.30267 0.181175
\(565\) −33.8713 −1.42498
\(566\) −8.16044 −0.343009
\(567\) 0 0
\(568\) 1.59415 0.0668892
\(569\) 19.4591 0.815766 0.407883 0.913034i \(-0.366267\pi\)
0.407883 + 0.913034i \(0.366267\pi\)
\(570\) 1.50535 0.0630522
\(571\) −12.9550 −0.542150 −0.271075 0.962558i \(-0.587379\pi\)
−0.271075 + 0.962558i \(0.587379\pi\)
\(572\) 24.6185 1.02935
\(573\) 17.2164 0.719226
\(574\) 0 0
\(575\) 68.2878 2.84780
\(576\) −6.98969 −0.291237
\(577\) −16.9641 −0.706225 −0.353113 0.935581i \(-0.614877\pi\)
−0.353113 + 0.935581i \(0.614877\pi\)
\(578\) 11.4475 0.476154
\(579\) 15.9807 0.664134
\(580\) 17.6582 0.733216
\(581\) 0 0
\(582\) 19.7454 0.818474
\(583\) 54.9002 2.27373
\(584\) −0.923243 −0.0382041
\(585\) 11.0418 0.456522
\(586\) 4.10725 0.169669
\(587\) 39.4502 1.62828 0.814142 0.580667i \(-0.197208\pi\)
0.814142 + 0.580667i \(0.197208\pi\)
\(588\) 0 0
\(589\) −0.145734 −0.00600488
\(590\) −96.9589 −3.99173
\(591\) −9.32916 −0.383750
\(592\) −5.37195 −0.220786
\(593\) 12.4924 0.513003 0.256501 0.966544i \(-0.417430\pi\)
0.256501 + 0.966544i \(0.417430\pi\)
\(594\) 9.60894 0.394260
\(595\) 0 0
\(596\) −41.4564 −1.69812
\(597\) −12.6095 −0.516074
\(598\) −30.4117 −1.24363
\(599\) −42.6285 −1.74175 −0.870876 0.491502i \(-0.836448\pi\)
−0.870876 + 0.491502i \(0.836448\pi\)
\(600\) −2.87201 −0.117249
\(601\) 45.6087 1.86042 0.930210 0.367028i \(-0.119625\pi\)
0.930210 + 0.367028i \(0.119625\pi\)
\(602\) 0 0
\(603\) −2.74258 −0.111686
\(604\) −26.2730 −1.06903
\(605\) 52.6489 2.14048
\(606\) 11.1707 0.453777
\(607\) 14.2458 0.578220 0.289110 0.957296i \(-0.406641\pi\)
0.289110 + 0.957296i \(0.406641\pi\)
\(608\) 1.45998 0.0592099
\(609\) 0 0
\(610\) −11.0157 −0.446014
\(611\) −6.15947 −0.249186
\(612\) 6.27864 0.253799
\(613\) 43.8828 1.77241 0.886206 0.463292i \(-0.153332\pi\)
0.886206 + 0.463292i \(0.153332\pi\)
\(614\) 12.4112 0.500874
\(615\) −4.10878 −0.165682
\(616\) 0 0
\(617\) 41.1419 1.65631 0.828154 0.560500i \(-0.189391\pi\)
0.828154 + 0.560500i \(0.189391\pi\)
\(618\) 16.9148 0.680413
\(619\) −17.9272 −0.720556 −0.360278 0.932845i \(-0.617318\pi\)
−0.360278 + 0.932845i \(0.617318\pi\)
\(620\) −6.04133 −0.242625
\(621\) −5.74714 −0.230625
\(622\) 32.2624 1.29360
\(623\) 0 0
\(624\) 11.3687 0.455114
\(625\) 56.7727 2.27091
\(626\) −27.7822 −1.11040
\(627\) −0.907982 −0.0362613
\(628\) −41.8614 −1.67045
\(629\) 4.24708 0.169342
\(630\) 0 0
\(631\) 10.2409 0.407685 0.203843 0.979004i \(-0.434657\pi\)
0.203843 + 0.979004i \(0.434657\pi\)
\(632\) −2.59954 −0.103404
\(633\) 15.9027 0.632077
\(634\) −13.7439 −0.545839
\(635\) 72.9800 2.89612
\(636\) −21.1194 −0.837438
\(637\) 0 0
\(638\) −21.9982 −0.870918
\(639\) 6.59530 0.260906
\(640\) −7.93010 −0.313465
\(641\) 26.1190 1.03164 0.515819 0.856697i \(-0.327488\pi\)
0.515819 + 0.856697i \(0.327488\pi\)
\(642\) −6.11617 −0.241386
\(643\) −21.4692 −0.846662 −0.423331 0.905975i \(-0.639139\pi\)
−0.423331 + 0.905975i \(0.639139\pi\)
\(644\) 0 0
\(645\) 46.2248 1.82010
\(646\) −1.22538 −0.0482117
\(647\) −0.229609 −0.00902684 −0.00451342 0.999990i \(-0.501437\pi\)
−0.00451342 + 0.999990i \(0.501437\pi\)
\(648\) 0.241710 0.00949528
\(649\) 58.4827 2.29565
\(650\) −62.8752 −2.46617
\(651\) 0 0
\(652\) −22.6026 −0.885187
\(653\) 15.5172 0.607234 0.303617 0.952794i \(-0.401806\pi\)
0.303617 + 0.952794i \(0.401806\pi\)
\(654\) 20.5918 0.805204
\(655\) −49.8044 −1.94602
\(656\) −4.23044 −0.165171
\(657\) −3.81962 −0.149018
\(658\) 0 0
\(659\) 43.0279 1.67613 0.838064 0.545571i \(-0.183687\pi\)
0.838064 + 0.545571i \(0.183687\pi\)
\(660\) −37.6398 −1.46513
\(661\) −43.4018 −1.68814 −0.844068 0.536236i \(-0.819846\pi\)
−0.844068 + 0.536236i \(0.819846\pi\)
\(662\) −21.0154 −0.816786
\(663\) −8.98816 −0.349071
\(664\) −0.857774 −0.0332881
\(665\) 0 0
\(666\) −2.50039 −0.0968883
\(667\) 13.1572 0.509449
\(668\) −15.1899 −0.587713
\(669\) 29.0062 1.12144
\(670\) 22.1887 0.857226
\(671\) 6.64436 0.256503
\(672\) 0 0
\(673\) −6.47233 −0.249490 −0.124745 0.992189i \(-0.539811\pi\)
−0.124745 + 0.992189i \(0.539811\pi\)
\(674\) 10.4433 0.402263
\(675\) −11.8820 −0.457340
\(676\) −10.8468 −0.417187
\(677\) −27.7353 −1.06595 −0.532977 0.846130i \(-0.678927\pi\)
−0.532977 + 0.846130i \(0.678927\pi\)
\(678\) −16.2323 −0.623399
\(679\) 0 0
\(680\) 3.32163 0.127379
\(681\) 20.3453 0.779633
\(682\) 7.52617 0.288192
\(683\) 20.3012 0.776803 0.388401 0.921490i \(-0.373027\pi\)
0.388401 + 0.921490i \(0.373027\pi\)
\(684\) 0.349289 0.0133554
\(685\) 56.0488 2.14151
\(686\) 0 0
\(687\) 24.6741 0.941378
\(688\) 47.5935 1.81449
\(689\) 30.2334 1.15180
\(690\) 46.4971 1.77012
\(691\) −38.7781 −1.47519 −0.737593 0.675245i \(-0.764038\pi\)
−0.737593 + 0.675245i \(0.764038\pi\)
\(692\) 11.7803 0.447821
\(693\) 0 0
\(694\) −9.86672 −0.374535
\(695\) 28.9601 1.09852
\(696\) −0.553359 −0.0209750
\(697\) 3.34460 0.126686
\(698\) 60.7502 2.29943
\(699\) −7.08960 −0.268153
\(700\) 0 0
\(701\) 5.57108 0.210417 0.105208 0.994450i \(-0.466449\pi\)
0.105208 + 0.994450i \(0.466449\pi\)
\(702\) 5.29162 0.199719
\(703\) 0.236271 0.00891112
\(704\) −34.1092 −1.28554
\(705\) 9.41736 0.354678
\(706\) −11.9485 −0.449688
\(707\) 0 0
\(708\) −22.4975 −0.845509
\(709\) −17.4267 −0.654473 −0.327236 0.944942i \(-0.606117\pi\)
−0.327236 + 0.944942i \(0.606117\pi\)
\(710\) −53.3592 −2.00253
\(711\) −10.7548 −0.403336
\(712\) −2.19710 −0.0823400
\(713\) −4.50143 −0.168580
\(714\) 0 0
\(715\) 53.8832 2.01512
\(716\) 39.2638 1.46736
\(717\) 19.3453 0.722464
\(718\) −29.4343 −1.09848
\(719\) 43.7743 1.63250 0.816252 0.577696i \(-0.196048\pi\)
0.816252 + 0.577696i \(0.196048\pi\)
\(720\) −17.3819 −0.647786
\(721\) 0 0
\(722\) 37.3442 1.38981
\(723\) −26.5629 −0.987885
\(724\) −2.92845 −0.108835
\(725\) 27.2021 1.01026
\(726\) 25.2312 0.936418
\(727\) 34.2841 1.27153 0.635763 0.771885i \(-0.280686\pi\)
0.635763 + 0.771885i \(0.280686\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 30.9026 1.14376
\(731\) −37.6276 −1.39171
\(732\) −2.55600 −0.0944724
\(733\) −20.6748 −0.763640 −0.381820 0.924237i \(-0.624703\pi\)
−0.381820 + 0.924237i \(0.624703\pi\)
\(734\) 47.9108 1.76842
\(735\) 0 0
\(736\) 45.0956 1.66225
\(737\) −13.3836 −0.492991
\(738\) −1.96907 −0.0724826
\(739\) −45.0202 −1.65610 −0.828048 0.560657i \(-0.810549\pi\)
−0.828048 + 0.560657i \(0.810549\pi\)
\(740\) 9.79446 0.360052
\(741\) −0.500023 −0.0183688
\(742\) 0 0
\(743\) −23.4216 −0.859256 −0.429628 0.903006i \(-0.641355\pi\)
−0.429628 + 0.903006i \(0.641355\pi\)
\(744\) 0.189319 0.00694076
\(745\) −90.7366 −3.32433
\(746\) 47.4817 1.73843
\(747\) −3.54877 −0.129843
\(748\) 30.6393 1.12029
\(749\) 0 0
\(750\) 55.6790 2.03311
\(751\) 24.0476 0.877509 0.438754 0.898607i \(-0.355420\pi\)
0.438754 + 0.898607i \(0.355420\pi\)
\(752\) 9.69621 0.353584
\(753\) 25.9956 0.947333
\(754\) −12.1144 −0.441179
\(755\) −57.5044 −2.09280
\(756\) 0 0
\(757\) −52.0114 −1.89039 −0.945194 0.326510i \(-0.894127\pi\)
−0.945194 + 0.326510i \(0.894127\pi\)
\(758\) −76.5496 −2.78041
\(759\) −28.0457 −1.01799
\(760\) 0.184787 0.00670292
\(761\) −16.0058 −0.580209 −0.290104 0.956995i \(-0.593690\pi\)
−0.290104 + 0.956995i \(0.593690\pi\)
\(762\) 34.9746 1.26700
\(763\) 0 0
\(764\) −32.3195 −1.16928
\(765\) 13.7422 0.496851
\(766\) 5.61743 0.202966
\(767\) 32.2063 1.16290
\(768\) −17.7798 −0.641572
\(769\) −42.7047 −1.53997 −0.769985 0.638062i \(-0.779737\pi\)
−0.769985 + 0.638062i \(0.779737\pi\)
\(770\) 0 0
\(771\) 21.1096 0.760244
\(772\) −29.9997 −1.07971
\(773\) 13.8164 0.496943 0.248471 0.968639i \(-0.420072\pi\)
0.248471 + 0.968639i \(0.420072\pi\)
\(774\) 22.1526 0.796257
\(775\) −9.30657 −0.334302
\(776\) 2.42382 0.0870100
\(777\) 0 0
\(778\) −7.13750 −0.255892
\(779\) 0.186064 0.00666645
\(780\) −20.7282 −0.742187
\(781\) 32.1847 1.15166
\(782\) −37.8493 −1.35349
\(783\) −2.28935 −0.0818147
\(784\) 0 0
\(785\) −91.6231 −3.27017
\(786\) −23.8681 −0.851346
\(787\) 5.73213 0.204328 0.102164 0.994768i \(-0.467423\pi\)
0.102164 + 0.994768i \(0.467423\pi\)
\(788\) 17.5131 0.623879
\(789\) 10.5110 0.374201
\(790\) 87.0113 3.09572
\(791\) 0 0
\(792\) 1.17953 0.0419128
\(793\) 3.65903 0.129936
\(794\) −48.3246 −1.71498
\(795\) −46.2245 −1.63942
\(796\) 23.6712 0.839004
\(797\) 4.96900 0.176011 0.0880055 0.996120i \(-0.471951\pi\)
0.0880055 + 0.996120i \(0.471951\pi\)
\(798\) 0 0
\(799\) −7.66586 −0.271198
\(800\) 93.2339 3.29631
\(801\) −9.08983 −0.321173
\(802\) 32.7121 1.15511
\(803\) −18.6395 −0.657774
\(804\) 5.14849 0.181573
\(805\) 0 0
\(806\) 4.14464 0.145989
\(807\) 21.1796 0.745559
\(808\) 1.37124 0.0482399
\(809\) 48.0152 1.68813 0.844063 0.536244i \(-0.180157\pi\)
0.844063 + 0.536244i \(0.180157\pi\)
\(810\) −8.09048 −0.284270
\(811\) 15.3782 0.540003 0.270001 0.962860i \(-0.412976\pi\)
0.270001 + 0.962860i \(0.412976\pi\)
\(812\) 0 0
\(813\) −2.53803 −0.0890127
\(814\) −12.2018 −0.427671
\(815\) −49.4709 −1.73289
\(816\) 14.1491 0.495318
\(817\) −2.09327 −0.0732343
\(818\) 12.7449 0.445613
\(819\) 0 0
\(820\) 7.71319 0.269356
\(821\) −8.08265 −0.282086 −0.141043 0.990003i \(-0.545046\pi\)
−0.141043 + 0.990003i \(0.545046\pi\)
\(822\) 26.8606 0.936871
\(823\) 37.3193 1.30087 0.650435 0.759562i \(-0.274587\pi\)
0.650435 + 0.759562i \(0.274587\pi\)
\(824\) 2.07635 0.0723330
\(825\) −57.9836 −2.01873
\(826\) 0 0
\(827\) −20.4901 −0.712510 −0.356255 0.934389i \(-0.615947\pi\)
−0.356255 + 0.934389i \(0.615947\pi\)
\(828\) 10.7888 0.374937
\(829\) −32.8011 −1.13923 −0.569614 0.821912i \(-0.692907\pi\)
−0.569614 + 0.821912i \(0.692907\pi\)
\(830\) 28.7112 0.996582
\(831\) −20.2870 −0.703749
\(832\) −18.7838 −0.651213
\(833\) 0 0
\(834\) 13.8787 0.480581
\(835\) −33.2464 −1.15054
\(836\) 1.70451 0.0589516
\(837\) 0.783246 0.0270730
\(838\) 71.9981 2.48713
\(839\) −10.1261 −0.349591 −0.174796 0.984605i \(-0.555926\pi\)
−0.174796 + 0.984605i \(0.555926\pi\)
\(840\) 0 0
\(841\) −23.7589 −0.819272
\(842\) −38.5577 −1.32879
\(843\) 18.2747 0.629413
\(844\) −29.8533 −1.02759
\(845\) −23.7408 −0.816707
\(846\) 4.51313 0.155165
\(847\) 0 0
\(848\) −47.5933 −1.63436
\(849\) −4.14431 −0.142232
\(850\) −78.2523 −2.68403
\(851\) 7.29791 0.250169
\(852\) −12.3810 −0.424167
\(853\) 5.07879 0.173894 0.0869472 0.996213i \(-0.472289\pi\)
0.0869472 + 0.996213i \(0.472289\pi\)
\(854\) 0 0
\(855\) 0.764497 0.0261452
\(856\) −0.750780 −0.0256611
\(857\) 8.24571 0.281668 0.140834 0.990033i \(-0.455022\pi\)
0.140834 + 0.990033i \(0.455022\pi\)
\(858\) 25.8228 0.881574
\(859\) 55.2489 1.88507 0.942533 0.334112i \(-0.108436\pi\)
0.942533 + 0.334112i \(0.108436\pi\)
\(860\) −86.7753 −2.95901
\(861\) 0 0
\(862\) 28.9978 0.987670
\(863\) 17.2958 0.588757 0.294378 0.955689i \(-0.404887\pi\)
0.294378 + 0.955689i \(0.404887\pi\)
\(864\) −7.84662 −0.266947
\(865\) 25.7839 0.876679
\(866\) 72.8295 2.47485
\(867\) 5.81366 0.197442
\(868\) 0 0
\(869\) −52.4826 −1.78035
\(870\) 18.5219 0.627952
\(871\) −7.37030 −0.249733
\(872\) 2.52772 0.0855993
\(873\) 10.0278 0.339389
\(874\) −2.10561 −0.0712232
\(875\) 0 0
\(876\) 7.17038 0.242265
\(877\) 45.7039 1.54331 0.771656 0.636040i \(-0.219429\pi\)
0.771656 + 0.636040i \(0.219429\pi\)
\(878\) 73.5091 2.48081
\(879\) 2.08588 0.0703550
\(880\) −84.8227 −2.85937
\(881\) 42.8769 1.44456 0.722279 0.691602i \(-0.243095\pi\)
0.722279 + 0.691602i \(0.243095\pi\)
\(882\) 0 0
\(883\) 20.6767 0.695826 0.347913 0.937527i \(-0.386890\pi\)
0.347913 + 0.937527i \(0.386890\pi\)
\(884\) 16.8730 0.567500
\(885\) −49.2409 −1.65521
\(886\) −25.4644 −0.855495
\(887\) 17.4997 0.587583 0.293791 0.955870i \(-0.405083\pi\)
0.293791 + 0.955870i \(0.405083\pi\)
\(888\) −0.306932 −0.0103000
\(889\) 0 0
\(890\) 73.5410 2.46510
\(891\) 4.87993 0.163484
\(892\) −54.4518 −1.82318
\(893\) −0.426462 −0.0142710
\(894\) −43.4842 −1.45433
\(895\) 85.9377 2.87258
\(896\) 0 0
\(897\) −15.4447 −0.515683
\(898\) −31.9015 −1.06457
\(899\) −1.79312 −0.0598040
\(900\) 22.3055 0.743517
\(901\) 37.6274 1.25355
\(902\) −9.60894 −0.319943
\(903\) 0 0
\(904\) −1.99257 −0.0662720
\(905\) −6.40956 −0.213061
\(906\) −27.5582 −0.915559
\(907\) −23.9979 −0.796837 −0.398418 0.917204i \(-0.630441\pi\)
−0.398418 + 0.917204i \(0.630441\pi\)
\(908\) −38.1931 −1.26748
\(909\) 5.67306 0.188163
\(910\) 0 0
\(911\) −13.1362 −0.435222 −0.217611 0.976036i \(-0.569826\pi\)
−0.217611 + 0.976036i \(0.569826\pi\)
\(912\) 0.787134 0.0260646
\(913\) −17.3178 −0.573134
\(914\) −67.1764 −2.22200
\(915\) −5.59438 −0.184944
\(916\) −46.3195 −1.53044
\(917\) 0 0
\(918\) 6.58576 0.217362
\(919\) 30.7304 1.01370 0.506852 0.862033i \(-0.330809\pi\)
0.506852 + 0.862033i \(0.330809\pi\)
\(920\) 5.70768 0.188177
\(921\) 6.30305 0.207693
\(922\) −9.56803 −0.315106
\(923\) 17.7240 0.583392
\(924\) 0 0
\(925\) 15.0882 0.496097
\(926\) −29.2986 −0.962813
\(927\) 8.59023 0.282140
\(928\) 17.9636 0.589686
\(929\) −30.6801 −1.00658 −0.503292 0.864117i \(-0.667878\pi\)
−0.503292 + 0.864117i \(0.667878\pi\)
\(930\) −6.33684 −0.207793
\(931\) 0 0
\(932\) 13.3089 0.435948
\(933\) 16.3846 0.536406
\(934\) −21.5575 −0.705384
\(935\) 67.0611 2.19313
\(936\) 0.649564 0.0212317
\(937\) −26.1785 −0.855214 −0.427607 0.903965i \(-0.640643\pi\)
−0.427607 + 0.903965i \(0.640643\pi\)
\(938\) 0 0
\(939\) −14.1093 −0.460439
\(940\) −17.6787 −0.576616
\(941\) 19.3605 0.631135 0.315567 0.948903i \(-0.397805\pi\)
0.315567 + 0.948903i \(0.397805\pi\)
\(942\) −43.9091 −1.43063
\(943\) 5.74714 0.187153
\(944\) −50.6989 −1.65011
\(945\) 0 0
\(946\) 108.103 3.51473
\(947\) 28.8451 0.937339 0.468670 0.883374i \(-0.344733\pi\)
0.468670 + 0.883374i \(0.344733\pi\)
\(948\) 20.1894 0.655720
\(949\) −10.2647 −0.333207
\(950\) −4.35328 −0.141239
\(951\) −6.97987 −0.226338
\(952\) 0 0
\(953\) −38.3762 −1.24313 −0.621563 0.783364i \(-0.713502\pi\)
−0.621563 + 0.783364i \(0.713502\pi\)
\(954\) −22.1525 −0.717212
\(955\) −70.7384 −2.28904
\(956\) −36.3159 −1.17454
\(957\) −11.1719 −0.361135
\(958\) 25.4161 0.821156
\(959\) 0 0
\(960\) 28.7191 0.926904
\(961\) −30.3865 −0.980210
\(962\) −6.71947 −0.216645
\(963\) −3.10612 −0.100093
\(964\) 49.8651 1.60605
\(965\) −65.6610 −2.11370
\(966\) 0 0
\(967\) −49.5741 −1.59419 −0.797097 0.603851i \(-0.793632\pi\)
−0.797097 + 0.603851i \(0.793632\pi\)
\(968\) 3.09722 0.0995484
\(969\) −0.622311 −0.0199915
\(970\) −81.1295 −2.60491
\(971\) −13.3866 −0.429596 −0.214798 0.976658i \(-0.568909\pi\)
−0.214798 + 0.976658i \(0.568909\pi\)
\(972\) −1.87725 −0.0602127
\(973\) 0 0
\(974\) −71.2312 −2.28240
\(975\) −31.9314 −1.02262
\(976\) −5.76003 −0.184374
\(977\) −9.38029 −0.300102 −0.150051 0.988678i \(-0.547944\pi\)
−0.150051 + 0.988678i \(0.547944\pi\)
\(978\) −23.7082 −0.758106
\(979\) −44.3578 −1.41768
\(980\) 0 0
\(981\) 10.4576 0.333886
\(982\) 52.3697 1.67119
\(983\) 0.842818 0.0268817 0.0134409 0.999910i \(-0.495722\pi\)
0.0134409 + 0.999910i \(0.495722\pi\)
\(984\) −0.241710 −0.00770544
\(985\) 38.3314 1.22134
\(986\) −15.0771 −0.480153
\(987\) 0 0
\(988\) 0.938667 0.0298630
\(989\) −64.6568 −2.05597
\(990\) −39.4810 −1.25479
\(991\) −59.1465 −1.87885 −0.939425 0.342755i \(-0.888640\pi\)
−0.939425 + 0.342755i \(0.888640\pi\)
\(992\) −6.14584 −0.195131
\(993\) −10.6727 −0.338689
\(994\) 0 0
\(995\) 51.8097 1.64248
\(996\) 6.66192 0.211091
\(997\) 1.87911 0.0595121 0.0297560 0.999557i \(-0.490527\pi\)
0.0297560 + 0.999557i \(0.490527\pi\)
\(998\) −5.76467 −0.182477
\(999\) −1.26983 −0.0401758
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 \(a_p\))