Properties

Label 6027.2.a.bc.1.6
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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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: \(8\)
Coefficient field: 8.8.7457527933.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.70821\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.66803 q^{2} +1.00000 q^{3} +0.782321 q^{4} +4.32429 q^{5} +1.66803 q^{6} -2.03112 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.66803 q^{2} +1.00000 q^{3} +0.782321 q^{4} +4.32429 q^{5} +1.66803 q^{6} -2.03112 q^{8} +1.00000 q^{9} +7.21304 q^{10} +5.84934 q^{11} +0.782321 q^{12} +4.56081 q^{13} +4.32429 q^{15} -4.95262 q^{16} +1.48730 q^{17} +1.66803 q^{18} -7.25900 q^{19} +3.38298 q^{20} +9.75686 q^{22} +3.99375 q^{23} -2.03112 q^{24} +13.6995 q^{25} +7.60756 q^{26} +1.00000 q^{27} -3.99637 q^{29} +7.21304 q^{30} -3.33775 q^{31} -4.19886 q^{32} +5.84934 q^{33} +2.48086 q^{34} +0.782321 q^{36} +0.681013 q^{37} -12.1082 q^{38} +4.56081 q^{39} -8.78317 q^{40} +1.00000 q^{41} -7.66175 q^{43} +4.57606 q^{44} +4.32429 q^{45} +6.66169 q^{46} -6.16952 q^{47} -4.95262 q^{48} +22.8512 q^{50} +1.48730 q^{51} +3.56801 q^{52} -2.70607 q^{53} +1.66803 q^{54} +25.2942 q^{55} -7.25900 q^{57} -6.66606 q^{58} +0.715360 q^{59} +3.38298 q^{60} +3.33773 q^{61} -5.56747 q^{62} +2.90141 q^{64} +19.7223 q^{65} +9.75686 q^{66} -7.99827 q^{67} +1.16355 q^{68} +3.99375 q^{69} +7.51068 q^{71} -2.03112 q^{72} -0.453895 q^{73} +1.13595 q^{74} +13.6995 q^{75} -5.67887 q^{76} +7.60756 q^{78} -6.22766 q^{79} -21.4166 q^{80} +1.00000 q^{81} +1.66803 q^{82} -7.75509 q^{83} +6.43153 q^{85} -12.7800 q^{86} -3.99637 q^{87} -11.8807 q^{88} +14.2235 q^{89} +7.21304 q^{90} +3.12439 q^{92} -3.33775 q^{93} -10.2909 q^{94} -31.3900 q^{95} -4.19886 q^{96} -7.48789 q^{97} +5.84934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + 8q^{10} + 11q^{11} + 13q^{12} + 10q^{13} + 7q^{15} - 17q^{16} + 3q^{17} + q^{18} + 6q^{19} + 11q^{20} + 15q^{22} + 14q^{23} + 6q^{24} + 25q^{25} + 24q^{26} + 8q^{27} + 2q^{29} + 8q^{30} + 16q^{31} + 3q^{32} + 11q^{33} - 4q^{34} + 13q^{36} - 20q^{37} + 10q^{38} + 10q^{39} - 3q^{40} + 8q^{41} + 7q^{43} + 7q^{45} - 5q^{46} + 14q^{47} - 17q^{48} - 5q^{50} + 3q^{51} + 23q^{52} + 7q^{53} + q^{54} + 48q^{55} + 6q^{57} - 20q^{58} + 22q^{59} + 11q^{60} - 33q^{62} - 10q^{64} - 14q^{65} + 15q^{66} + 12q^{67} - 27q^{68} + 14q^{69} - 5q^{71} + 6q^{72} + 2q^{73} + 6q^{74} + 25q^{75} + 43q^{76} + 24q^{78} - 15q^{79} - 7q^{80} + 8q^{81} + q^{82} + 15q^{83} - 43q^{85} + 31q^{86} + 2q^{87} + 17q^{88} + 29q^{89} + 8q^{90} + 19q^{92} + 16q^{93} + 20q^{94} + 14q^{95} + 3q^{96} + 19q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.66803 1.17947 0.589737 0.807595i \(-0.299231\pi\)
0.589737 + 0.807595i \(0.299231\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.782321 0.391160
\(5\) 4.32429 1.93388 0.966941 0.255001i \(-0.0820757\pi\)
0.966941 + 0.255001i \(0.0820757\pi\)
\(6\) 1.66803 0.680970
\(7\) 0 0
\(8\) −2.03112 −0.718111
\(9\) 1.00000 0.333333
\(10\) 7.21304 2.28096
\(11\) 5.84934 1.76364 0.881821 0.471585i \(-0.156318\pi\)
0.881821 + 0.471585i \(0.156318\pi\)
\(12\) 0.782321 0.225837
\(13\) 4.56081 1.26494 0.632470 0.774585i \(-0.282041\pi\)
0.632470 + 0.774585i \(0.282041\pi\)
\(14\) 0 0
\(15\) 4.32429 1.11653
\(16\) −4.95262 −1.23815
\(17\) 1.48730 0.360724 0.180362 0.983600i \(-0.442273\pi\)
0.180362 + 0.983600i \(0.442273\pi\)
\(18\) 1.66803 0.393158
\(19\) −7.25900 −1.66533 −0.832665 0.553778i \(-0.813186\pi\)
−0.832665 + 0.553778i \(0.813186\pi\)
\(20\) 3.38298 0.756458
\(21\) 0 0
\(22\) 9.75686 2.08017
\(23\) 3.99375 0.832754 0.416377 0.909192i \(-0.363300\pi\)
0.416377 + 0.909192i \(0.363300\pi\)
\(24\) −2.03112 −0.414602
\(25\) 13.6995 2.73990
\(26\) 7.60756 1.49196
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −3.99637 −0.742107 −0.371053 0.928612i \(-0.621003\pi\)
−0.371053 + 0.928612i \(0.621003\pi\)
\(30\) 7.21304 1.31692
\(31\) −3.33775 −0.599478 −0.299739 0.954021i \(-0.596900\pi\)
−0.299739 + 0.954021i \(0.596900\pi\)
\(32\) −4.19886 −0.742260
\(33\) 5.84934 1.01824
\(34\) 2.48086 0.425465
\(35\) 0 0
\(36\) 0.782321 0.130387
\(37\) 0.681013 0.111958 0.0559789 0.998432i \(-0.482172\pi\)
0.0559789 + 0.998432i \(0.482172\pi\)
\(38\) −12.1082 −1.96421
\(39\) 4.56081 0.730313
\(40\) −8.78317 −1.38874
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −7.66175 −1.16841 −0.584203 0.811607i \(-0.698593\pi\)
−0.584203 + 0.811607i \(0.698593\pi\)
\(44\) 4.57606 0.689867
\(45\) 4.32429 0.644627
\(46\) 6.66169 0.982213
\(47\) −6.16952 −0.899917 −0.449958 0.893050i \(-0.648561\pi\)
−0.449958 + 0.893050i \(0.648561\pi\)
\(48\) −4.95262 −0.714849
\(49\) 0 0
\(50\) 22.8512 3.23164
\(51\) 1.48730 0.208264
\(52\) 3.56801 0.494794
\(53\) −2.70607 −0.371707 −0.185853 0.982577i \(-0.559505\pi\)
−0.185853 + 0.982577i \(0.559505\pi\)
\(54\) 1.66803 0.226990
\(55\) 25.2942 3.41067
\(56\) 0 0
\(57\) −7.25900 −0.961478
\(58\) −6.66606 −0.875296
\(59\) 0.715360 0.0931319 0.0465660 0.998915i \(-0.485172\pi\)
0.0465660 + 0.998915i \(0.485172\pi\)
\(60\) 3.38298 0.436741
\(61\) 3.33773 0.427353 0.213677 0.976904i \(-0.431456\pi\)
0.213677 + 0.976904i \(0.431456\pi\)
\(62\) −5.56747 −0.707069
\(63\) 0 0
\(64\) 2.90141 0.362677
\(65\) 19.7223 2.44624
\(66\) 9.75686 1.20099
\(67\) −7.99827 −0.977145 −0.488572 0.872523i \(-0.662482\pi\)
−0.488572 + 0.872523i \(0.662482\pi\)
\(68\) 1.16355 0.141101
\(69\) 3.99375 0.480791
\(70\) 0 0
\(71\) 7.51068 0.891354 0.445677 0.895194i \(-0.352963\pi\)
0.445677 + 0.895194i \(0.352963\pi\)
\(72\) −2.03112 −0.239370
\(73\) −0.453895 −0.0531244 −0.0265622 0.999647i \(-0.508456\pi\)
−0.0265622 + 0.999647i \(0.508456\pi\)
\(74\) 1.13595 0.132051
\(75\) 13.6995 1.58188
\(76\) −5.67887 −0.651411
\(77\) 0 0
\(78\) 7.60756 0.861386
\(79\) −6.22766 −0.700666 −0.350333 0.936625i \(-0.613932\pi\)
−0.350333 + 0.936625i \(0.613932\pi\)
\(80\) −21.4166 −2.39444
\(81\) 1.00000 0.111111
\(82\) 1.66803 0.184203
\(83\) −7.75509 −0.851232 −0.425616 0.904904i \(-0.639943\pi\)
−0.425616 + 0.904904i \(0.639943\pi\)
\(84\) 0 0
\(85\) 6.43153 0.697597
\(86\) −12.7800 −1.37811
\(87\) −3.99637 −0.428456
\(88\) −11.8807 −1.26649
\(89\) 14.2235 1.50769 0.753846 0.657051i \(-0.228196\pi\)
0.753846 + 0.657051i \(0.228196\pi\)
\(90\) 7.21304 0.760321
\(91\) 0 0
\(92\) 3.12439 0.325740
\(93\) −3.33775 −0.346109
\(94\) −10.2909 −1.06143
\(95\) −31.3900 −3.22055
\(96\) −4.19886 −0.428544
\(97\) −7.48789 −0.760280 −0.380140 0.924929i \(-0.624124\pi\)
−0.380140 + 0.924929i \(0.624124\pi\)
\(98\) 0 0
\(99\) 5.84934 0.587881
\(100\) 10.7174 1.07174
\(101\) −12.1787 −1.21183 −0.605915 0.795529i \(-0.707193\pi\)
−0.605915 + 0.795529i \(0.707193\pi\)
\(102\) 2.48086 0.245642
\(103\) 11.2578 1.10926 0.554630 0.832097i \(-0.312860\pi\)
0.554630 + 0.832097i \(0.312860\pi\)
\(104\) −9.26356 −0.908367
\(105\) 0 0
\(106\) −4.51380 −0.438419
\(107\) −16.9596 −1.63954 −0.819772 0.572691i \(-0.805900\pi\)
−0.819772 + 0.572691i \(0.805900\pi\)
\(108\) 0.782321 0.0752788
\(109\) −15.8268 −1.51593 −0.757967 0.652293i \(-0.773807\pi\)
−0.757967 + 0.652293i \(0.773807\pi\)
\(110\) 42.1915 4.02280
\(111\) 0.681013 0.0646389
\(112\) 0 0
\(113\) 0.0411977 0.00387555 0.00193778 0.999998i \(-0.499383\pi\)
0.00193778 + 0.999998i \(0.499383\pi\)
\(114\) −12.1082 −1.13404
\(115\) 17.2701 1.61045
\(116\) −3.12644 −0.290283
\(117\) 4.56081 0.421647
\(118\) 1.19324 0.109847
\(119\) 0 0
\(120\) −8.78317 −0.801790
\(121\) 23.2147 2.11043
\(122\) 5.56744 0.504052
\(123\) 1.00000 0.0901670
\(124\) −2.61119 −0.234492
\(125\) 37.6191 3.36476
\(126\) 0 0
\(127\) −6.47454 −0.574522 −0.287261 0.957852i \(-0.592745\pi\)
−0.287261 + 0.957852i \(0.592745\pi\)
\(128\) 13.2374 1.17003
\(129\) −7.66175 −0.674580
\(130\) 32.8973 2.88528
\(131\) −13.6986 −1.19685 −0.598425 0.801179i \(-0.704207\pi\)
−0.598425 + 0.801179i \(0.704207\pi\)
\(132\) 4.57606 0.398295
\(133\) 0 0
\(134\) −13.3414 −1.15252
\(135\) 4.32429 0.372176
\(136\) −3.02090 −0.259040
\(137\) 0.100390 0.00857690 0.00428845 0.999991i \(-0.498635\pi\)
0.00428845 + 0.999991i \(0.498635\pi\)
\(138\) 6.66169 0.567081
\(139\) 14.5020 1.23005 0.615023 0.788509i \(-0.289147\pi\)
0.615023 + 0.788509i \(0.289147\pi\)
\(140\) 0 0
\(141\) −6.16952 −0.519567
\(142\) 12.5280 1.05133
\(143\) 26.6777 2.23090
\(144\) −4.95262 −0.412718
\(145\) −17.2815 −1.43515
\(146\) −0.757110 −0.0626589
\(147\) 0 0
\(148\) 0.532771 0.0437935
\(149\) −6.42022 −0.525965 −0.262982 0.964801i \(-0.584706\pi\)
−0.262982 + 0.964801i \(0.584706\pi\)
\(150\) 22.8512 1.86579
\(151\) −6.61736 −0.538513 −0.269256 0.963069i \(-0.586778\pi\)
−0.269256 + 0.963069i \(0.586778\pi\)
\(152\) 14.7439 1.19589
\(153\) 1.48730 0.120241
\(154\) 0 0
\(155\) −14.4334 −1.15932
\(156\) 3.56801 0.285670
\(157\) 5.84014 0.466094 0.233047 0.972465i \(-0.425130\pi\)
0.233047 + 0.972465i \(0.425130\pi\)
\(158\) −10.3879 −0.826418
\(159\) −2.70607 −0.214605
\(160\) −18.1571 −1.43544
\(161\) 0 0
\(162\) 1.66803 0.131053
\(163\) 13.2696 1.03935 0.519677 0.854363i \(-0.326052\pi\)
0.519677 + 0.854363i \(0.326052\pi\)
\(164\) 0.782321 0.0610890
\(165\) 25.2942 1.96915
\(166\) −12.9357 −1.00401
\(167\) −0.628977 −0.0486717 −0.0243359 0.999704i \(-0.507747\pi\)
−0.0243359 + 0.999704i \(0.507747\pi\)
\(168\) 0 0
\(169\) 7.80095 0.600073
\(170\) 10.7280 0.822798
\(171\) −7.25900 −0.555110
\(172\) −5.99395 −0.457034
\(173\) 18.9619 1.44164 0.720822 0.693120i \(-0.243765\pi\)
0.720822 + 0.693120i \(0.243765\pi\)
\(174\) −6.66606 −0.505352
\(175\) 0 0
\(176\) −28.9695 −2.18366
\(177\) 0.715360 0.0537698
\(178\) 23.7253 1.77828
\(179\) 4.54253 0.339525 0.169762 0.985485i \(-0.445700\pi\)
0.169762 + 0.985485i \(0.445700\pi\)
\(180\) 3.38298 0.252153
\(181\) 15.5935 1.15905 0.579526 0.814954i \(-0.303238\pi\)
0.579526 + 0.814954i \(0.303238\pi\)
\(182\) 0 0
\(183\) 3.33773 0.246732
\(184\) −8.11180 −0.598010
\(185\) 2.94490 0.216513
\(186\) −5.56747 −0.408226
\(187\) 8.69974 0.636188
\(188\) −4.82654 −0.352012
\(189\) 0 0
\(190\) −52.3595 −3.79856
\(191\) −9.20449 −0.666013 −0.333007 0.942924i \(-0.608063\pi\)
−0.333007 + 0.942924i \(0.608063\pi\)
\(192\) 2.90141 0.209392
\(193\) 18.1234 1.30455 0.652276 0.757982i \(-0.273814\pi\)
0.652276 + 0.757982i \(0.273814\pi\)
\(194\) −12.4900 −0.896731
\(195\) 19.7223 1.41234
\(196\) 0 0
\(197\) −22.1458 −1.57782 −0.788910 0.614509i \(-0.789354\pi\)
−0.788910 + 0.614509i \(0.789354\pi\)
\(198\) 9.75686 0.693390
\(199\) 18.5760 1.31682 0.658410 0.752660i \(-0.271229\pi\)
0.658410 + 0.752660i \(0.271229\pi\)
\(200\) −27.8254 −1.96755
\(201\) −7.99827 −0.564155
\(202\) −20.3145 −1.42932
\(203\) 0 0
\(204\) 1.16355 0.0814646
\(205\) 4.32429 0.302022
\(206\) 18.7783 1.30834
\(207\) 3.99375 0.277585
\(208\) −22.5879 −1.56619
\(209\) −42.4604 −2.93704
\(210\) 0 0
\(211\) −13.4151 −0.923531 −0.461765 0.887002i \(-0.652784\pi\)
−0.461765 + 0.887002i \(0.652784\pi\)
\(212\) −2.11701 −0.145397
\(213\) 7.51068 0.514624
\(214\) −28.2891 −1.93380
\(215\) −33.1317 −2.25956
\(216\) −2.03112 −0.138201
\(217\) 0 0
\(218\) −26.3996 −1.78801
\(219\) −0.453895 −0.0306714
\(220\) 19.7882 1.33412
\(221\) 6.78330 0.456294
\(222\) 1.13595 0.0762399
\(223\) 10.4122 0.697255 0.348627 0.937261i \(-0.386648\pi\)
0.348627 + 0.937261i \(0.386648\pi\)
\(224\) 0 0
\(225\) 13.6995 0.913299
\(226\) 0.0687189 0.00457111
\(227\) 10.5305 0.698934 0.349467 0.936949i \(-0.386363\pi\)
0.349467 + 0.936949i \(0.386363\pi\)
\(228\) −5.67887 −0.376092
\(229\) 13.6437 0.901598 0.450799 0.892625i \(-0.351139\pi\)
0.450799 + 0.892625i \(0.351139\pi\)
\(230\) 28.8071 1.89948
\(231\) 0 0
\(232\) 8.11712 0.532915
\(233\) 15.9722 1.04637 0.523186 0.852219i \(-0.324743\pi\)
0.523186 + 0.852219i \(0.324743\pi\)
\(234\) 7.60756 0.497321
\(235\) −26.6788 −1.74033
\(236\) 0.559641 0.0364295
\(237\) −6.22766 −0.404530
\(238\) 0 0
\(239\) −2.04562 −0.132320 −0.0661600 0.997809i \(-0.521075\pi\)
−0.0661600 + 0.997809i \(0.521075\pi\)
\(240\) −21.4166 −1.38243
\(241\) −23.6978 −1.52651 −0.763254 0.646099i \(-0.776400\pi\)
−0.763254 + 0.646099i \(0.776400\pi\)
\(242\) 38.7229 2.48920
\(243\) 1.00000 0.0641500
\(244\) 2.61118 0.167164
\(245\) 0 0
\(246\) 1.66803 0.106350
\(247\) −33.1069 −2.10654
\(248\) 6.77939 0.430492
\(249\) −7.75509 −0.491459
\(250\) 62.7498 3.96865
\(251\) 13.4627 0.849760 0.424880 0.905250i \(-0.360316\pi\)
0.424880 + 0.905250i \(0.360316\pi\)
\(252\) 0 0
\(253\) 23.3608 1.46868
\(254\) −10.7997 −0.677634
\(255\) 6.43153 0.402758
\(256\) 16.2775 1.01734
\(257\) −10.3493 −0.645569 −0.322785 0.946472i \(-0.604619\pi\)
−0.322785 + 0.946472i \(0.604619\pi\)
\(258\) −12.7800 −0.795650
\(259\) 0 0
\(260\) 15.4291 0.956874
\(261\) −3.99637 −0.247369
\(262\) −22.8496 −1.41166
\(263\) −0.788038 −0.0485925 −0.0242962 0.999705i \(-0.507734\pi\)
−0.0242962 + 0.999705i \(0.507734\pi\)
\(264\) −11.8807 −0.731208
\(265\) −11.7018 −0.718837
\(266\) 0 0
\(267\) 14.2235 0.870467
\(268\) −6.25722 −0.382220
\(269\) −19.3210 −1.17802 −0.589010 0.808126i \(-0.700482\pi\)
−0.589010 + 0.808126i \(0.700482\pi\)
\(270\) 7.21304 0.438972
\(271\) −16.0597 −0.975560 −0.487780 0.872966i \(-0.662193\pi\)
−0.487780 + 0.872966i \(0.662193\pi\)
\(272\) −7.36604 −0.446632
\(273\) 0 0
\(274\) 0.167454 0.0101162
\(275\) 80.1330 4.83220
\(276\) 3.12439 0.188066
\(277\) 4.09759 0.246201 0.123100 0.992394i \(-0.460716\pi\)
0.123100 + 0.992394i \(0.460716\pi\)
\(278\) 24.1898 1.45081
\(279\) −3.33775 −0.199826
\(280\) 0 0
\(281\) 8.67302 0.517389 0.258694 0.965959i \(-0.416708\pi\)
0.258694 + 0.965959i \(0.416708\pi\)
\(282\) −10.2909 −0.612816
\(283\) −15.3327 −0.911433 −0.455716 0.890125i \(-0.650617\pi\)
−0.455716 + 0.890125i \(0.650617\pi\)
\(284\) 5.87576 0.348662
\(285\) −31.3900 −1.85939
\(286\) 44.4992 2.63129
\(287\) 0 0
\(288\) −4.19886 −0.247420
\(289\) −14.7879 −0.869878
\(290\) −28.8260 −1.69272
\(291\) −7.48789 −0.438948
\(292\) −0.355091 −0.0207802
\(293\) −0.0222887 −0.00130212 −0.000651059 1.00000i \(-0.500207\pi\)
−0.000651059 1.00000i \(0.500207\pi\)
\(294\) 0 0
\(295\) 3.09342 0.180106
\(296\) −1.38322 −0.0803981
\(297\) 5.84934 0.339413
\(298\) −10.7091 −0.620362
\(299\) 18.2147 1.05338
\(300\) 10.7174 0.618769
\(301\) 0 0
\(302\) −11.0379 −0.635162
\(303\) −12.1787 −0.699651
\(304\) 35.9510 2.06193
\(305\) 14.4333 0.826450
\(306\) 2.48086 0.141822
\(307\) 3.14402 0.179439 0.0897195 0.995967i \(-0.471403\pi\)
0.0897195 + 0.995967i \(0.471403\pi\)
\(308\) 0 0
\(309\) 11.2578 0.640431
\(310\) −24.0753 −1.36739
\(311\) −26.5894 −1.50774 −0.753872 0.657021i \(-0.771816\pi\)
−0.753872 + 0.657021i \(0.771816\pi\)
\(312\) −9.26356 −0.524446
\(313\) −6.25270 −0.353423 −0.176712 0.984263i \(-0.556546\pi\)
−0.176712 + 0.984263i \(0.556546\pi\)
\(314\) 9.74153 0.549746
\(315\) 0 0
\(316\) −4.87203 −0.274073
\(317\) 22.0285 1.23724 0.618621 0.785689i \(-0.287691\pi\)
0.618621 + 0.785689i \(0.287691\pi\)
\(318\) −4.51380 −0.253121
\(319\) −23.3761 −1.30881
\(320\) 12.5466 0.701374
\(321\) −16.9596 −0.946591
\(322\) 0 0
\(323\) −10.7963 −0.600724
\(324\) 0.782321 0.0434623
\(325\) 62.4807 3.46581
\(326\) 22.1341 1.22589
\(327\) −15.8268 −0.875225
\(328\) −2.03112 −0.112150
\(329\) 0 0
\(330\) 42.1915 2.32257
\(331\) 31.0654 1.70751 0.853756 0.520674i \(-0.174319\pi\)
0.853756 + 0.520674i \(0.174319\pi\)
\(332\) −6.06697 −0.332968
\(333\) 0.681013 0.0373193
\(334\) −1.04915 −0.0574070
\(335\) −34.5869 −1.88968
\(336\) 0 0
\(337\) −20.5844 −1.12130 −0.560652 0.828052i \(-0.689449\pi\)
−0.560652 + 0.828052i \(0.689449\pi\)
\(338\) 13.0122 0.707771
\(339\) 0.0411977 0.00223755
\(340\) 5.03152 0.272872
\(341\) −19.5236 −1.05726
\(342\) −12.1082 −0.654738
\(343\) 0 0
\(344\) 15.5620 0.839045
\(345\) 17.2701 0.929793
\(346\) 31.6289 1.70038
\(347\) −13.6978 −0.735336 −0.367668 0.929957i \(-0.619844\pi\)
−0.367668 + 0.929957i \(0.619844\pi\)
\(348\) −3.12644 −0.167595
\(349\) 19.6067 1.04952 0.524761 0.851250i \(-0.324155\pi\)
0.524761 + 0.851250i \(0.324155\pi\)
\(350\) 0 0
\(351\) 4.56081 0.243438
\(352\) −24.5605 −1.30908
\(353\) 6.16984 0.328387 0.164194 0.986428i \(-0.447498\pi\)
0.164194 + 0.986428i \(0.447498\pi\)
\(354\) 1.19324 0.0634201
\(355\) 32.4784 1.72377
\(356\) 11.1274 0.589749
\(357\) 0 0
\(358\) 7.57707 0.400461
\(359\) −23.6085 −1.24601 −0.623003 0.782219i \(-0.714088\pi\)
−0.623003 + 0.782219i \(0.714088\pi\)
\(360\) −8.78317 −0.462914
\(361\) 33.6931 1.77332
\(362\) 26.0103 1.36707
\(363\) 23.2147 1.21846
\(364\) 0 0
\(365\) −1.96277 −0.102736
\(366\) 5.56744 0.291015
\(367\) 25.2440 1.31773 0.658864 0.752262i \(-0.271037\pi\)
0.658864 + 0.752262i \(0.271037\pi\)
\(368\) −19.7795 −1.03108
\(369\) 1.00000 0.0520579
\(370\) 4.91218 0.255372
\(371\) 0 0
\(372\) −2.61119 −0.135384
\(373\) 20.9243 1.08342 0.541708 0.840566i \(-0.317778\pi\)
0.541708 + 0.840566i \(0.317778\pi\)
\(374\) 14.5114 0.750367
\(375\) 37.6191 1.94264
\(376\) 12.5311 0.646240
\(377\) −18.2267 −0.938720
\(378\) 0 0
\(379\) −28.3554 −1.45652 −0.728261 0.685300i \(-0.759671\pi\)
−0.728261 + 0.685300i \(0.759671\pi\)
\(380\) −24.5571 −1.25975
\(381\) −6.47454 −0.331701
\(382\) −15.3534 −0.785546
\(383\) 1.47971 0.0756094 0.0378047 0.999285i \(-0.487964\pi\)
0.0378047 + 0.999285i \(0.487964\pi\)
\(384\) 13.2374 0.675516
\(385\) 0 0
\(386\) 30.2304 1.53869
\(387\) −7.66175 −0.389469
\(388\) −5.85793 −0.297391
\(389\) 13.4225 0.680549 0.340275 0.940326i \(-0.389480\pi\)
0.340275 + 0.940326i \(0.389480\pi\)
\(390\) 32.8973 1.66582
\(391\) 5.93991 0.300394
\(392\) 0 0
\(393\) −13.6986 −0.691002
\(394\) −36.9398 −1.86100
\(395\) −26.9302 −1.35501
\(396\) 4.57606 0.229956
\(397\) 0.598620 0.0300439 0.0150219 0.999887i \(-0.495218\pi\)
0.0150219 + 0.999887i \(0.495218\pi\)
\(398\) 30.9853 1.55315
\(399\) 0 0
\(400\) −67.8483 −3.39242
\(401\) −11.6312 −0.580835 −0.290418 0.956900i \(-0.593794\pi\)
−0.290418 + 0.956900i \(0.593794\pi\)
\(402\) −13.3414 −0.665406
\(403\) −15.2228 −0.758304
\(404\) −9.52769 −0.474020
\(405\) 4.32429 0.214876
\(406\) 0 0
\(407\) 3.98347 0.197454
\(408\) −3.02090 −0.149557
\(409\) 30.0222 1.48450 0.742250 0.670123i \(-0.233758\pi\)
0.742250 + 0.670123i \(0.233758\pi\)
\(410\) 7.21304 0.356227
\(411\) 0.100390 0.00495188
\(412\) 8.80717 0.433898
\(413\) 0 0
\(414\) 6.66169 0.327404
\(415\) −33.5353 −1.64618
\(416\) −19.1502 −0.938915
\(417\) 14.5020 0.710167
\(418\) −70.8251 −3.46417
\(419\) 8.22375 0.401756 0.200878 0.979616i \(-0.435620\pi\)
0.200878 + 0.979616i \(0.435620\pi\)
\(420\) 0 0
\(421\) −0.696747 −0.0339574 −0.0169787 0.999856i \(-0.505405\pi\)
−0.0169787 + 0.999856i \(0.505405\pi\)
\(422\) −22.3767 −1.08928
\(423\) −6.16952 −0.299972
\(424\) 5.49636 0.266927
\(425\) 20.3753 0.988347
\(426\) 12.5280 0.606985
\(427\) 0 0
\(428\) −13.2678 −0.641324
\(429\) 26.6777 1.28801
\(430\) −55.2646 −2.66509
\(431\) −27.0930 −1.30502 −0.652512 0.757779i \(-0.726285\pi\)
−0.652512 + 0.757779i \(0.726285\pi\)
\(432\) −4.95262 −0.238283
\(433\) 15.1891 0.729943 0.364972 0.931019i \(-0.381079\pi\)
0.364972 + 0.931019i \(0.381079\pi\)
\(434\) 0 0
\(435\) −17.2815 −0.828582
\(436\) −12.3816 −0.592973
\(437\) −28.9906 −1.38681
\(438\) −0.757110 −0.0361761
\(439\) 26.1419 1.24769 0.623843 0.781550i \(-0.285570\pi\)
0.623843 + 0.781550i \(0.285570\pi\)
\(440\) −51.3757 −2.44924
\(441\) 0 0
\(442\) 11.3147 0.538187
\(443\) −2.63221 −0.125060 −0.0625300 0.998043i \(-0.519917\pi\)
−0.0625300 + 0.998043i \(0.519917\pi\)
\(444\) 0.532771 0.0252842
\(445\) 61.5067 2.91570
\(446\) 17.3679 0.822394
\(447\) −6.42022 −0.303666
\(448\) 0 0
\(449\) −10.7630 −0.507935 −0.253968 0.967213i \(-0.581736\pi\)
−0.253968 + 0.967213i \(0.581736\pi\)
\(450\) 22.8512 1.07721
\(451\) 5.84934 0.275435
\(452\) 0.0322298 0.00151596
\(453\) −6.61736 −0.310911
\(454\) 17.5652 0.824375
\(455\) 0 0
\(456\) 14.7439 0.690448
\(457\) −12.8296 −0.600143 −0.300071 0.953917i \(-0.597011\pi\)
−0.300071 + 0.953917i \(0.597011\pi\)
\(458\) 22.7580 1.06341
\(459\) 1.48730 0.0694213
\(460\) 13.5108 0.629944
\(461\) −32.7222 −1.52403 −0.762013 0.647562i \(-0.775789\pi\)
−0.762013 + 0.647562i \(0.775789\pi\)
\(462\) 0 0
\(463\) −1.48288 −0.0689155 −0.0344577 0.999406i \(-0.510970\pi\)
−0.0344577 + 0.999406i \(0.510970\pi\)
\(464\) 19.7925 0.918842
\(465\) −14.4334 −0.669333
\(466\) 26.6420 1.23417
\(467\) 22.6643 1.04878 0.524390 0.851478i \(-0.324293\pi\)
0.524390 + 0.851478i \(0.324293\pi\)
\(468\) 3.56801 0.164931
\(469\) 0 0
\(470\) −44.5010 −2.05268
\(471\) 5.84014 0.269100
\(472\) −1.45299 −0.0668791
\(473\) −44.8162 −2.06065
\(474\) −10.3879 −0.477133
\(475\) −99.4446 −4.56283
\(476\) 0 0
\(477\) −2.70607 −0.123902
\(478\) −3.41215 −0.156068
\(479\) −11.8541 −0.541628 −0.270814 0.962632i \(-0.587293\pi\)
−0.270814 + 0.962632i \(0.587293\pi\)
\(480\) −18.1571 −0.828754
\(481\) 3.10597 0.141620
\(482\) −39.5286 −1.80048
\(483\) 0 0
\(484\) 18.1614 0.825517
\(485\) −32.3798 −1.47029
\(486\) 1.66803 0.0756633
\(487\) −35.4706 −1.60732 −0.803662 0.595086i \(-0.797118\pi\)
−0.803662 + 0.595086i \(0.797118\pi\)
\(488\) −6.77935 −0.306887
\(489\) 13.2696 0.600072
\(490\) 0 0
\(491\) −2.57948 −0.116410 −0.0582052 0.998305i \(-0.518538\pi\)
−0.0582052 + 0.998305i \(0.518538\pi\)
\(492\) 0.782321 0.0352697
\(493\) −5.94381 −0.267696
\(494\) −55.2233 −2.48461
\(495\) 25.2942 1.13689
\(496\) 16.5306 0.742246
\(497\) 0 0
\(498\) −12.9357 −0.579663
\(499\) 15.4774 0.692863 0.346432 0.938075i \(-0.387393\pi\)
0.346432 + 0.938075i \(0.387393\pi\)
\(500\) 29.4302 1.31616
\(501\) −0.628977 −0.0281006
\(502\) 22.4562 1.00227
\(503\) 5.92655 0.264252 0.132126 0.991233i \(-0.457820\pi\)
0.132126 + 0.991233i \(0.457820\pi\)
\(504\) 0 0
\(505\) −52.6644 −2.34354
\(506\) 38.9665 1.73227
\(507\) 7.80095 0.346452
\(508\) −5.06516 −0.224730
\(509\) −32.1538 −1.42519 −0.712597 0.701573i \(-0.752481\pi\)
−0.712597 + 0.701573i \(0.752481\pi\)
\(510\) 10.7280 0.475043
\(511\) 0 0
\(512\) 0.676573 0.0299006
\(513\) −7.25900 −0.320493
\(514\) −17.2629 −0.761432
\(515\) 48.6818 2.14518
\(516\) −5.99395 −0.263869
\(517\) −36.0876 −1.58713
\(518\) 0 0
\(519\) 18.9619 0.832334
\(520\) −40.0583 −1.75667
\(521\) 4.96065 0.217330 0.108665 0.994078i \(-0.465342\pi\)
0.108665 + 0.994078i \(0.465342\pi\)
\(522\) −6.66606 −0.291765
\(523\) 17.8989 0.782664 0.391332 0.920250i \(-0.372014\pi\)
0.391332 + 0.920250i \(0.372014\pi\)
\(524\) −10.7167 −0.468161
\(525\) 0 0
\(526\) −1.31447 −0.0573136
\(527\) −4.96425 −0.216246
\(528\) −28.9695 −1.26074
\(529\) −7.04997 −0.306520
\(530\) −19.5190 −0.847850
\(531\) 0.715360 0.0310440
\(532\) 0 0
\(533\) 4.56081 0.197550
\(534\) 23.7253 1.02669
\(535\) −73.3381 −3.17068
\(536\) 16.2455 0.701698
\(537\) 4.54253 0.196025
\(538\) −32.2279 −1.38945
\(539\) 0 0
\(540\) 3.38298 0.145580
\(541\) 31.0548 1.33515 0.667576 0.744542i \(-0.267332\pi\)
0.667576 + 0.744542i \(0.267332\pi\)
\(542\) −26.7881 −1.15065
\(543\) 15.5935 0.669179
\(544\) −6.24497 −0.267751
\(545\) −68.4398 −2.93164
\(546\) 0 0
\(547\) −14.2599 −0.609709 −0.304854 0.952399i \(-0.598608\pi\)
−0.304854 + 0.952399i \(0.598608\pi\)
\(548\) 0.0785372 0.00335494
\(549\) 3.33773 0.142451
\(550\) 133.664 5.69946
\(551\) 29.0096 1.23585
\(552\) −8.11180 −0.345261
\(553\) 0 0
\(554\) 6.83490 0.290387
\(555\) 2.94490 0.125004
\(556\) 11.3452 0.481145
\(557\) −22.0405 −0.933885 −0.466942 0.884288i \(-0.654644\pi\)
−0.466942 + 0.884288i \(0.654644\pi\)
\(558\) −5.56747 −0.235690
\(559\) −34.9438 −1.47796
\(560\) 0 0
\(561\) 8.69974 0.367303
\(562\) 14.4668 0.610247
\(563\) −31.1001 −1.31071 −0.655356 0.755320i \(-0.727481\pi\)
−0.655356 + 0.755320i \(0.727481\pi\)
\(564\) −4.82654 −0.203234
\(565\) 0.178151 0.00749486
\(566\) −25.5753 −1.07501
\(567\) 0 0
\(568\) −15.2551 −0.640091
\(569\) 8.53952 0.357995 0.178998 0.983849i \(-0.442715\pi\)
0.178998 + 0.983849i \(0.442715\pi\)
\(570\) −52.3595 −2.19310
\(571\) −0.459320 −0.0192220 −0.00961098 0.999954i \(-0.503059\pi\)
−0.00961098 + 0.999954i \(0.503059\pi\)
\(572\) 20.8705 0.872640
\(573\) −9.20449 −0.384523
\(574\) 0 0
\(575\) 54.7123 2.28166
\(576\) 2.90141 0.120892
\(577\) −25.7043 −1.07008 −0.535042 0.844825i \(-0.679704\pi\)
−0.535042 + 0.844825i \(0.679704\pi\)
\(578\) −24.6667 −1.02600
\(579\) 18.1234 0.753183
\(580\) −13.5196 −0.561372
\(581\) 0 0
\(582\) −12.4900 −0.517728
\(583\) −15.8287 −0.655558
\(584\) 0.921917 0.0381492
\(585\) 19.7223 0.815415
\(586\) −0.0371782 −0.00153582
\(587\) 28.9538 1.19505 0.597526 0.801849i \(-0.296150\pi\)
0.597526 + 0.801849i \(0.296150\pi\)
\(588\) 0 0
\(589\) 24.2287 0.998328
\(590\) 5.15992 0.212431
\(591\) −22.1458 −0.910955
\(592\) −3.37280 −0.138621
\(593\) −3.54980 −0.145773 −0.0728865 0.997340i \(-0.523221\pi\)
−0.0728865 + 0.997340i \(0.523221\pi\)
\(594\) 9.75686 0.400329
\(595\) 0 0
\(596\) −5.02267 −0.205736
\(597\) 18.5760 0.760266
\(598\) 30.3827 1.24244
\(599\) 25.4327 1.03915 0.519576 0.854424i \(-0.326090\pi\)
0.519576 + 0.854424i \(0.326090\pi\)
\(600\) −27.8254 −1.13597
\(601\) 32.6848 1.33324 0.666621 0.745397i \(-0.267740\pi\)
0.666621 + 0.745397i \(0.267740\pi\)
\(602\) 0 0
\(603\) −7.99827 −0.325715
\(604\) −5.17690 −0.210645
\(605\) 100.387 4.08133
\(606\) −20.3145 −0.825220
\(607\) 23.9828 0.973432 0.486716 0.873560i \(-0.338195\pi\)
0.486716 + 0.873560i \(0.338195\pi\)
\(608\) 30.4795 1.23611
\(609\) 0 0
\(610\) 24.0752 0.974777
\(611\) −28.1380 −1.13834
\(612\) 1.16355 0.0470336
\(613\) −38.2382 −1.54442 −0.772212 0.635364i \(-0.780850\pi\)
−0.772212 + 0.635364i \(0.780850\pi\)
\(614\) 5.24432 0.211644
\(615\) 4.32429 0.174372
\(616\) 0 0
\(617\) −4.29122 −0.172758 −0.0863790 0.996262i \(-0.527530\pi\)
−0.0863790 + 0.996262i \(0.527530\pi\)
\(618\) 18.7783 0.755372
\(619\) −20.2026 −0.812009 −0.406005 0.913871i \(-0.633078\pi\)
−0.406005 + 0.913871i \(0.633078\pi\)
\(620\) −11.2916 −0.453480
\(621\) 3.99375 0.160264
\(622\) −44.3518 −1.77835
\(623\) 0 0
\(624\) −22.5879 −0.904240
\(625\) 94.1786 3.76715
\(626\) −10.4297 −0.416854
\(627\) −42.4604 −1.69570
\(628\) 4.56886 0.182318
\(629\) 1.01287 0.0403859
\(630\) 0 0
\(631\) 33.0298 1.31490 0.657448 0.753500i \(-0.271636\pi\)
0.657448 + 0.753500i \(0.271636\pi\)
\(632\) 12.6491 0.503156
\(633\) −13.4151 −0.533201
\(634\) 36.7441 1.45930
\(635\) −27.9978 −1.11106
\(636\) −2.11701 −0.0839450
\(637\) 0 0
\(638\) −38.9920 −1.54371
\(639\) 7.51068 0.297118
\(640\) 57.2422 2.26270
\(641\) −21.8364 −0.862487 −0.431243 0.902236i \(-0.641925\pi\)
−0.431243 + 0.902236i \(0.641925\pi\)
\(642\) −28.2891 −1.11648
\(643\) 22.4974 0.887209 0.443605 0.896223i \(-0.353699\pi\)
0.443605 + 0.896223i \(0.353699\pi\)
\(644\) 0 0
\(645\) −33.1317 −1.30456
\(646\) −18.0086 −0.708539
\(647\) −13.4779 −0.529871 −0.264936 0.964266i \(-0.585351\pi\)
−0.264936 + 0.964266i \(0.585351\pi\)
\(648\) −2.03112 −0.0797901
\(649\) 4.18438 0.164251
\(650\) 104.220 4.08783
\(651\) 0 0
\(652\) 10.3811 0.406554
\(653\) −36.2358 −1.41802 −0.709008 0.705200i \(-0.750857\pi\)
−0.709008 + 0.705200i \(0.750857\pi\)
\(654\) −26.3996 −1.03231
\(655\) −59.2367 −2.31457
\(656\) −4.95262 −0.193367
\(657\) −0.453895 −0.0177081
\(658\) 0 0
\(659\) −10.3387 −0.402737 −0.201369 0.979516i \(-0.564539\pi\)
−0.201369 + 0.979516i \(0.564539\pi\)
\(660\) 19.7882 0.770255
\(661\) 26.6528 1.03667 0.518337 0.855177i \(-0.326551\pi\)
0.518337 + 0.855177i \(0.326551\pi\)
\(662\) 51.8181 2.01397
\(663\) 6.78330 0.263441
\(664\) 15.7516 0.611279
\(665\) 0 0
\(666\) 1.13595 0.0440171
\(667\) −15.9605 −0.617993
\(668\) −0.492062 −0.0190384
\(669\) 10.4122 0.402560
\(670\) −57.6919 −2.22883
\(671\) 19.5235 0.753698
\(672\) 0 0
\(673\) 1.94492 0.0749711 0.0374856 0.999297i \(-0.488065\pi\)
0.0374856 + 0.999297i \(0.488065\pi\)
\(674\) −34.3354 −1.32255
\(675\) 13.6995 0.527294
\(676\) 6.10284 0.234725
\(677\) 16.1164 0.619402 0.309701 0.950834i \(-0.399771\pi\)
0.309701 + 0.950834i \(0.399771\pi\)
\(678\) 0.0687189 0.00263913
\(679\) 0 0
\(680\) −13.0632 −0.500952
\(681\) 10.5305 0.403530
\(682\) −32.5660 −1.24702
\(683\) 32.2129 1.23259 0.616295 0.787515i \(-0.288633\pi\)
0.616295 + 0.787515i \(0.288633\pi\)
\(684\) −5.67887 −0.217137
\(685\) 0.434116 0.0165867
\(686\) 0 0
\(687\) 13.6437 0.520538
\(688\) 37.9457 1.44667
\(689\) −12.3418 −0.470187
\(690\) 28.8071 1.09667
\(691\) −15.9137 −0.605384 −0.302692 0.953088i \(-0.597885\pi\)
−0.302692 + 0.953088i \(0.597885\pi\)
\(692\) 14.8343 0.563914
\(693\) 0 0
\(694\) −22.8483 −0.867310
\(695\) 62.7110 2.37876
\(696\) 8.11712 0.307679
\(697\) 1.48730 0.0563356
\(698\) 32.7045 1.23788
\(699\) 15.9722 0.604123
\(700\) 0 0
\(701\) 7.53082 0.284435 0.142218 0.989835i \(-0.454577\pi\)
0.142218 + 0.989835i \(0.454577\pi\)
\(702\) 7.60756 0.287129
\(703\) −4.94347 −0.186447
\(704\) 16.9714 0.639632
\(705\) −26.6788 −1.00478
\(706\) 10.2915 0.387325
\(707\) 0 0
\(708\) 0.559641 0.0210326
\(709\) 3.97882 0.149428 0.0747138 0.997205i \(-0.476196\pi\)
0.0747138 + 0.997205i \(0.476196\pi\)
\(710\) 54.1749 2.03315
\(711\) −6.22766 −0.233555
\(712\) −28.8898 −1.08269
\(713\) −13.3301 −0.499218
\(714\) 0 0
\(715\) 115.362 4.31430
\(716\) 3.55372 0.132809
\(717\) −2.04562 −0.0763950
\(718\) −39.3796 −1.46963
\(719\) −34.2235 −1.27632 −0.638161 0.769903i \(-0.720305\pi\)
−0.638161 + 0.769903i \(0.720305\pi\)
\(720\) −21.4166 −0.798148
\(721\) 0 0
\(722\) 56.2011 2.09159
\(723\) −23.6978 −0.881330
\(724\) 12.1991 0.453375
\(725\) −54.7482 −2.03330
\(726\) 38.7229 1.43714
\(727\) −28.3533 −1.05156 −0.525782 0.850619i \(-0.676227\pi\)
−0.525782 + 0.850619i \(0.676227\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −3.27396 −0.121175
\(731\) −11.3953 −0.421472
\(732\) 2.61118 0.0965120
\(733\) 21.1863 0.782532 0.391266 0.920278i \(-0.372037\pi\)
0.391266 + 0.920278i \(0.372037\pi\)
\(734\) 42.1078 1.55423
\(735\) 0 0
\(736\) −16.7692 −0.618120
\(737\) −46.7846 −1.72333
\(738\) 1.66803 0.0614010
\(739\) 5.01966 0.184651 0.0923257 0.995729i \(-0.470570\pi\)
0.0923257 + 0.995729i \(0.470570\pi\)
\(740\) 2.30385 0.0846914
\(741\) −33.1069 −1.21621
\(742\) 0 0
\(743\) 5.80215 0.212860 0.106430 0.994320i \(-0.466058\pi\)
0.106430 + 0.994320i \(0.466058\pi\)
\(744\) 6.77939 0.248544
\(745\) −27.7629 −1.01715
\(746\) 34.9023 1.27786
\(747\) −7.75509 −0.283744
\(748\) 6.80598 0.248851
\(749\) 0 0
\(750\) 62.7498 2.29130
\(751\) −4.60198 −0.167929 −0.0839643 0.996469i \(-0.526758\pi\)
−0.0839643 + 0.996469i \(0.526758\pi\)
\(752\) 30.5552 1.11424
\(753\) 13.4627 0.490609
\(754\) −30.4026 −1.10720
\(755\) −28.6154 −1.04142
\(756\) 0 0
\(757\) −9.87582 −0.358943 −0.179471 0.983763i \(-0.557439\pi\)
−0.179471 + 0.983763i \(0.557439\pi\)
\(758\) −47.2977 −1.71793
\(759\) 23.3608 0.847943
\(760\) 63.7571 2.31271
\(761\) 19.2921 0.699339 0.349670 0.936873i \(-0.386294\pi\)
0.349670 + 0.936873i \(0.386294\pi\)
\(762\) −10.7997 −0.391232
\(763\) 0 0
\(764\) −7.20086 −0.260518
\(765\) 6.43153 0.232532
\(766\) 2.46819 0.0891794
\(767\) 3.26262 0.117806
\(768\) 16.2775 0.587363
\(769\) −25.6251 −0.924066 −0.462033 0.886863i \(-0.652880\pi\)
−0.462033 + 0.886863i \(0.652880\pi\)
\(770\) 0 0
\(771\) −10.3493 −0.372719
\(772\) 14.1783 0.510289
\(773\) −16.4298 −0.590938 −0.295469 0.955352i \(-0.595476\pi\)
−0.295469 + 0.955352i \(0.595476\pi\)
\(774\) −12.7800 −0.459369
\(775\) −45.7255 −1.64251
\(776\) 15.2088 0.545965
\(777\) 0 0
\(778\) 22.3892 0.802691
\(779\) −7.25900 −0.260081
\(780\) 15.4291 0.552451
\(781\) 43.9325 1.57203
\(782\) 9.90795 0.354308
\(783\) −3.99637 −0.142819
\(784\) 0 0
\(785\) 25.2545 0.901371
\(786\) −22.8496 −0.815019
\(787\) 4.68820 0.167116 0.0835582 0.996503i \(-0.473372\pi\)
0.0835582 + 0.996503i \(0.473372\pi\)
\(788\) −17.3251 −0.617181
\(789\) −0.788038 −0.0280549
\(790\) −44.9204 −1.59820
\(791\) 0 0
\(792\) −11.8807 −0.422163
\(793\) 15.2228 0.540576
\(794\) 0.998516 0.0354360
\(795\) −11.7018 −0.415021
\(796\) 14.5324 0.515087
\(797\) 5.03067 0.178196 0.0890978 0.996023i \(-0.471602\pi\)
0.0890978 + 0.996023i \(0.471602\pi\)
\(798\) 0 0
\(799\) −9.17594 −0.324621
\(800\) −57.5222 −2.03372
\(801\) 14.2235 0.502564
\(802\) −19.4012 −0.685081
\(803\) −2.65499 −0.0936924
\(804\) −6.25722 −0.220675
\(805\) 0 0
\(806\) −25.3921 −0.894400
\(807\) −19.3210 −0.680131
\(808\) 24.7365 0.870229
\(809\) 0.167803 0.00589965 0.00294982 0.999996i \(-0.499061\pi\)
0.00294982 + 0.999996i \(0.499061\pi\)
\(810\) 7.21304 0.253440
\(811\) −47.1839 −1.65685 −0.828426 0.560098i \(-0.810763\pi\)
−0.828426 + 0.560098i \(0.810763\pi\)
\(812\) 0 0
\(813\) −16.0597 −0.563240
\(814\) 6.64455 0.232891
\(815\) 57.3816 2.00999
\(816\) −7.36604 −0.257863
\(817\) 55.6167 1.94578
\(818\) 50.0779 1.75093
\(819\) 0 0
\(820\) 3.38298 0.118139
\(821\) 26.6236 0.929169 0.464585 0.885529i \(-0.346204\pi\)
0.464585 + 0.885529i \(0.346204\pi\)
\(822\) 0.167454 0.00584061
\(823\) −17.5847 −0.612964 −0.306482 0.951876i \(-0.599152\pi\)
−0.306482 + 0.951876i \(0.599152\pi\)
\(824\) −22.8659 −0.796571
\(825\) 80.1330 2.78987
\(826\) 0 0
\(827\) 21.5130 0.748082 0.374041 0.927412i \(-0.377972\pi\)
0.374041 + 0.927412i \(0.377972\pi\)
\(828\) 3.12439 0.108580
\(829\) 29.8147 1.03551 0.517754 0.855529i \(-0.326768\pi\)
0.517754 + 0.855529i \(0.326768\pi\)
\(830\) −55.9378 −1.94163
\(831\) 4.09759 0.142144
\(832\) 13.2328 0.458764
\(833\) 0 0
\(834\) 24.1898 0.837625
\(835\) −2.71988 −0.0941253
\(836\) −33.2176 −1.14886
\(837\) −3.33775 −0.115370
\(838\) 13.7174 0.473861
\(839\) 12.9236 0.446171 0.223085 0.974799i \(-0.428387\pi\)
0.223085 + 0.974799i \(0.428387\pi\)
\(840\) 0 0
\(841\) −13.0291 −0.449278
\(842\) −1.16219 −0.0400519
\(843\) 8.67302 0.298715
\(844\) −10.4949 −0.361249
\(845\) 33.7336 1.16047
\(846\) −10.2909 −0.353810
\(847\) 0 0
\(848\) 13.4021 0.460230
\(849\) −15.3327 −0.526216
\(850\) 33.9866 1.16573
\(851\) 2.71980 0.0932334
\(852\) 5.87576 0.201300
\(853\) −5.26193 −0.180165 −0.0900824 0.995934i \(-0.528713\pi\)
−0.0900824 + 0.995934i \(0.528713\pi\)
\(854\) 0 0
\(855\) −31.3900 −1.07352
\(856\) 34.4470 1.17737
\(857\) −36.4007 −1.24342 −0.621712 0.783246i \(-0.713563\pi\)
−0.621712 + 0.783246i \(0.713563\pi\)
\(858\) 44.4992 1.51918
\(859\) 7.06055 0.240903 0.120451 0.992719i \(-0.461566\pi\)
0.120451 + 0.992719i \(0.461566\pi\)
\(860\) −25.9196 −0.883850
\(861\) 0 0
\(862\) −45.1919 −1.53924
\(863\) 18.9497 0.645054 0.322527 0.946560i \(-0.395468\pi\)
0.322527 + 0.946560i \(0.395468\pi\)
\(864\) −4.19886 −0.142848
\(865\) 81.9966 2.78797
\(866\) 25.3359 0.860950
\(867\) −14.7879 −0.502224
\(868\) 0 0
\(869\) −36.4277 −1.23572
\(870\) −28.8260 −0.977292
\(871\) −36.4786 −1.23603
\(872\) 32.1462 1.08861
\(873\) −7.48789 −0.253427
\(874\) −48.3572 −1.63571
\(875\) 0 0
\(876\) −0.355091 −0.0119974
\(877\) −35.6780 −1.20476 −0.602380 0.798209i \(-0.705781\pi\)
−0.602380 + 0.798209i \(0.705781\pi\)
\(878\) 43.6055 1.47161
\(879\) −0.0222887 −0.000751778 0
\(880\) −125.273 −4.22294
\(881\) 15.4830 0.521635 0.260818 0.965388i \(-0.416008\pi\)
0.260818 + 0.965388i \(0.416008\pi\)
\(882\) 0 0
\(883\) −45.3288 −1.52543 −0.762717 0.646732i \(-0.776135\pi\)
−0.762717 + 0.646732i \(0.776135\pi\)
\(884\) 5.30671 0.178484
\(885\) 3.09342 0.103984
\(886\) −4.39060 −0.147505
\(887\) 50.8827 1.70847 0.854237 0.519884i \(-0.174025\pi\)
0.854237 + 0.519884i \(0.174025\pi\)
\(888\) −1.38322 −0.0464179
\(889\) 0 0
\(890\) 102.595 3.43899
\(891\) 5.84934 0.195960
\(892\) 8.14571 0.272738
\(893\) 44.7845 1.49866
\(894\) −10.7091 −0.358166
\(895\) 19.6432 0.656601
\(896\) 0 0
\(897\) 18.2147 0.608172
\(898\) −17.9529 −0.599097
\(899\) 13.3389 0.444877
\(900\) 10.7174 0.357247
\(901\) −4.02474 −0.134084
\(902\) 9.75686 0.324868
\(903\) 0 0
\(904\) −0.0836776 −0.00278308
\(905\) 67.4307 2.24147
\(906\) −11.0379 −0.366711
\(907\) −32.7943 −1.08892 −0.544458 0.838788i \(-0.683265\pi\)
−0.544458 + 0.838788i \(0.683265\pi\)
\(908\) 8.23823 0.273395
\(909\) −12.1787 −0.403944
\(910\) 0 0
\(911\) 24.4758 0.810920 0.405460 0.914113i \(-0.367111\pi\)
0.405460 + 0.914113i \(0.367111\pi\)
\(912\) 35.9510 1.19046
\(913\) −45.3622 −1.50127
\(914\) −21.4001 −0.707853
\(915\) 14.4333 0.477151
\(916\) 10.6737 0.352669
\(917\) 0 0
\(918\) 2.48086 0.0818807
\(919\) −5.45846 −0.180058 −0.0900289 0.995939i \(-0.528696\pi\)
−0.0900289 + 0.995939i \(0.528696\pi\)
\(920\) −35.0778 −1.15648
\(921\) 3.14402 0.103599
\(922\) −54.5816 −1.79755
\(923\) 34.2548 1.12751
\(924\) 0 0
\(925\) 9.32953 0.306753
\(926\) −2.47349 −0.0812841
\(927\) 11.2578 0.369753
\(928\) 16.7802 0.550836
\(929\) −38.6111 −1.26679 −0.633395 0.773829i \(-0.718339\pi\)
−0.633395 + 0.773829i \(0.718339\pi\)
\(930\) −24.0753 −0.789462
\(931\) 0 0
\(932\) 12.4954 0.409299
\(933\) −26.5894 −0.870496
\(934\) 37.8048 1.23701
\(935\) 37.6202 1.23031
\(936\) −9.26356 −0.302789
\(937\) −7.88640 −0.257638 −0.128819 0.991668i \(-0.541119\pi\)
−0.128819 + 0.991668i \(0.541119\pi\)
\(938\) 0 0
\(939\) −6.25270 −0.204049
\(940\) −20.8714 −0.680749
\(941\) −0.520002 −0.0169516 −0.00847579 0.999964i \(-0.502698\pi\)
−0.00847579 + 0.999964i \(0.502698\pi\)
\(942\) 9.74153 0.317396
\(943\) 3.99375 0.130054
\(944\) −3.54290 −0.115312
\(945\) 0 0
\(946\) −74.7547 −2.43048
\(947\) −7.62438 −0.247759 −0.123879 0.992297i \(-0.539534\pi\)
−0.123879 + 0.992297i \(0.539534\pi\)
\(948\) −4.87203 −0.158236
\(949\) −2.07013 −0.0671992
\(950\) −165.877 −5.38175
\(951\) 22.0285 0.714322
\(952\) 0 0
\(953\) 15.0822 0.488559 0.244279 0.969705i \(-0.421449\pi\)
0.244279 + 0.969705i \(0.421449\pi\)
\(954\) −4.51380 −0.146140
\(955\) −39.8029 −1.28799
\(956\) −1.60033 −0.0517584
\(957\) −23.3761 −0.755642
\(958\) −19.7730 −0.638836
\(959\) 0 0
\(960\) 12.5466 0.404939
\(961\) −19.8594 −0.640626
\(962\) 5.18084 0.167037
\(963\) −16.9596 −0.546514
\(964\) −18.5393 −0.597109
\(965\) 78.3709 2.52285
\(966\) 0 0
\(967\) 34.1646 1.09866 0.549330 0.835606i \(-0.314883\pi\)
0.549330 + 0.835606i \(0.314883\pi\)
\(968\) −47.1520 −1.51552
\(969\) −10.7963 −0.346828
\(970\) −54.0105 −1.73417
\(971\) 53.8374 1.72773 0.863863 0.503727i \(-0.168038\pi\)
0.863863 + 0.503727i \(0.168038\pi\)
\(972\) 0.782321 0.0250929
\(973\) 0 0
\(974\) −59.1659 −1.89580
\(975\) 62.4807 2.00098
\(976\) −16.5305 −0.529129
\(977\) −42.6087 −1.36317 −0.681587 0.731737i \(-0.738710\pi\)
−0.681587 + 0.731737i \(0.738710\pi\)
\(978\) 22.1341 0.707769
\(979\) 83.1983 2.65903
\(980\) 0 0
\(981\) −15.8268 −0.505311
\(982\) −4.30265 −0.137303
\(983\) 26.9565 0.859780 0.429890 0.902881i \(-0.358552\pi\)
0.429890 + 0.902881i \(0.358552\pi\)
\(984\) −2.03112 −0.0647499
\(985\) −95.7647 −3.05132
\(986\) −9.91444 −0.315740
\(987\) 0 0
\(988\) −25.9002 −0.823996
\(989\) −30.5991 −0.972996
\(990\) 42.1915 1.34093
\(991\) −38.6693 −1.22837 −0.614185 0.789162i \(-0.710515\pi\)
−0.614185 + 0.789162i \(0.710515\pi\)
\(992\) 14.0147 0.444969
\(993\) 31.0654 0.985832
\(994\) 0 0
\(995\) 80.3281 2.54657
\(996\) −6.06697 −0.192239
\(997\) −18.0152 −0.570548 −0.285274 0.958446i \(-0.592085\pi\)
−0.285274 + 0.958446i \(0.592085\pi\)
\(998\) 25.8167 0.817215
\(999\) 0.681013 0.0215463
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 \(a_p\))