Properties

Label 8018.2.a.f.1.12
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.71717 q^{3} +1.00000 q^{4} +1.96614 q^{5} +1.71717 q^{6} +0.664883 q^{7} -1.00000 q^{8} -0.0513372 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.71717 q^{3} +1.00000 q^{4} +1.96614 q^{5} +1.71717 q^{6} +0.664883 q^{7} -1.00000 q^{8} -0.0513372 q^{9} -1.96614 q^{10} +5.44663 q^{11} -1.71717 q^{12} -0.0515753 q^{13} -0.664883 q^{14} -3.37618 q^{15} +1.00000 q^{16} -7.45253 q^{17} +0.0513372 q^{18} -1.00000 q^{19} +1.96614 q^{20} -1.14172 q^{21} -5.44663 q^{22} -0.569198 q^{23} +1.71717 q^{24} -1.13431 q^{25} +0.0515753 q^{26} +5.23966 q^{27} +0.664883 q^{28} -2.76138 q^{29} +3.37618 q^{30} +4.18029 q^{31} -1.00000 q^{32} -9.35277 q^{33} +7.45253 q^{34} +1.30725 q^{35} -0.0513372 q^{36} +3.80764 q^{37} +1.00000 q^{38} +0.0885634 q^{39} -1.96614 q^{40} +3.76344 q^{41} +1.14172 q^{42} +5.34950 q^{43} +5.44663 q^{44} -0.100936 q^{45} +0.569198 q^{46} +2.90711 q^{47} -1.71717 q^{48} -6.55793 q^{49} +1.13431 q^{50} +12.7972 q^{51} -0.0515753 q^{52} -4.82207 q^{53} -5.23966 q^{54} +10.7088 q^{55} -0.664883 q^{56} +1.71717 q^{57} +2.76138 q^{58} -0.401214 q^{59} -3.37618 q^{60} -7.28561 q^{61} -4.18029 q^{62} -0.0341332 q^{63} +1.00000 q^{64} -0.101404 q^{65} +9.35277 q^{66} -11.1051 q^{67} -7.45253 q^{68} +0.977408 q^{69} -1.30725 q^{70} -15.3423 q^{71} +0.0513372 q^{72} -0.623277 q^{73} -3.80764 q^{74} +1.94780 q^{75} -1.00000 q^{76} +3.62137 q^{77} -0.0885634 q^{78} -3.96744 q^{79} +1.96614 q^{80} -8.84335 q^{81} -3.76344 q^{82} +7.33098 q^{83} -1.14172 q^{84} -14.6527 q^{85} -5.34950 q^{86} +4.74175 q^{87} -5.44663 q^{88} +11.5704 q^{89} +0.100936 q^{90} -0.0342916 q^{91} -0.569198 q^{92} -7.17826 q^{93} -2.90711 q^{94} -1.96614 q^{95} +1.71717 q^{96} -1.39596 q^{97} +6.55793 q^{98} -0.279614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.71717 −0.991407 −0.495703 0.868492i \(-0.665090\pi\)
−0.495703 + 0.868492i \(0.665090\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.96614 0.879282 0.439641 0.898174i \(-0.355106\pi\)
0.439641 + 0.898174i \(0.355106\pi\)
\(6\) 1.71717 0.701031
\(7\) 0.664883 0.251302 0.125651 0.992074i \(-0.459898\pi\)
0.125651 + 0.992074i \(0.459898\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.0513372 −0.0171124
\(10\) −1.96614 −0.621747
\(11\) 5.44663 1.64222 0.821110 0.570770i \(-0.193355\pi\)
0.821110 + 0.570770i \(0.193355\pi\)
\(12\) −1.71717 −0.495703
\(13\) −0.0515753 −0.0143044 −0.00715221 0.999974i \(-0.502277\pi\)
−0.00715221 + 0.999974i \(0.502277\pi\)
\(14\) −0.664883 −0.177698
\(15\) −3.37618 −0.871727
\(16\) 1.00000 0.250000
\(17\) −7.45253 −1.80750 −0.903752 0.428057i \(-0.859198\pi\)
−0.903752 + 0.428057i \(0.859198\pi\)
\(18\) 0.0513372 0.0121003
\(19\) −1.00000 −0.229416
\(20\) 1.96614 0.439641
\(21\) −1.14172 −0.249143
\(22\) −5.44663 −1.16122
\(23\) −0.569198 −0.118686 −0.0593430 0.998238i \(-0.518901\pi\)
−0.0593430 + 0.998238i \(0.518901\pi\)
\(24\) 1.71717 0.350515
\(25\) −1.13431 −0.226863
\(26\) 0.0515753 0.0101147
\(27\) 5.23966 1.00837
\(28\) 0.664883 0.125651
\(29\) −2.76138 −0.512775 −0.256388 0.966574i \(-0.582532\pi\)
−0.256388 + 0.966574i \(0.582532\pi\)
\(30\) 3.37618 0.616404
\(31\) 4.18029 0.750803 0.375401 0.926862i \(-0.377505\pi\)
0.375401 + 0.926862i \(0.377505\pi\)
\(32\) −1.00000 −0.176777
\(33\) −9.35277 −1.62811
\(34\) 7.45253 1.27810
\(35\) 1.30725 0.220966
\(36\) −0.0513372 −0.00855620
\(37\) 3.80764 0.625972 0.312986 0.949758i \(-0.398671\pi\)
0.312986 + 0.949758i \(0.398671\pi\)
\(38\) 1.00000 0.162221
\(39\) 0.0885634 0.0141815
\(40\) −1.96614 −0.310873
\(41\) 3.76344 0.587751 0.293875 0.955844i \(-0.405055\pi\)
0.293875 + 0.955844i \(0.405055\pi\)
\(42\) 1.14172 0.176171
\(43\) 5.34950 0.815790 0.407895 0.913029i \(-0.366263\pi\)
0.407895 + 0.913029i \(0.366263\pi\)
\(44\) 5.44663 0.821110
\(45\) −0.100936 −0.0150466
\(46\) 0.569198 0.0839236
\(47\) 2.90711 0.424045 0.212022 0.977265i \(-0.431995\pi\)
0.212022 + 0.977265i \(0.431995\pi\)
\(48\) −1.71717 −0.247852
\(49\) −6.55793 −0.936847
\(50\) 1.13431 0.160416
\(51\) 12.7972 1.79197
\(52\) −0.0515753 −0.00715221
\(53\) −4.82207 −0.662363 −0.331181 0.943567i \(-0.607447\pi\)
−0.331181 + 0.943567i \(0.607447\pi\)
\(54\) −5.23966 −0.713027
\(55\) 10.7088 1.44397
\(56\) −0.664883 −0.0888488
\(57\) 1.71717 0.227444
\(58\) 2.76138 0.362587
\(59\) −0.401214 −0.0522336 −0.0261168 0.999659i \(-0.508314\pi\)
−0.0261168 + 0.999659i \(0.508314\pi\)
\(60\) −3.37618 −0.435863
\(61\) −7.28561 −0.932827 −0.466413 0.884567i \(-0.654454\pi\)
−0.466413 + 0.884567i \(0.654454\pi\)
\(62\) −4.18029 −0.530898
\(63\) −0.0341332 −0.00430038
\(64\) 1.00000 0.125000
\(65\) −0.101404 −0.0125776
\(66\) 9.35277 1.15125
\(67\) −11.1051 −1.35671 −0.678354 0.734735i \(-0.737306\pi\)
−0.678354 + 0.734735i \(0.737306\pi\)
\(68\) −7.45253 −0.903752
\(69\) 0.977408 0.117666
\(70\) −1.30725 −0.156246
\(71\) −15.3423 −1.82080 −0.910398 0.413735i \(-0.864224\pi\)
−0.910398 + 0.413735i \(0.864224\pi\)
\(72\) 0.0513372 0.00605015
\(73\) −0.623277 −0.0729490 −0.0364745 0.999335i \(-0.511613\pi\)
−0.0364745 + 0.999335i \(0.511613\pi\)
\(74\) −3.80764 −0.442629
\(75\) 1.94780 0.224913
\(76\) −1.00000 −0.114708
\(77\) 3.62137 0.412694
\(78\) −0.0885634 −0.0100278
\(79\) −3.96744 −0.446371 −0.223186 0.974776i \(-0.571646\pi\)
−0.223186 + 0.974776i \(0.571646\pi\)
\(80\) 1.96614 0.219821
\(81\) −8.84335 −0.982595
\(82\) −3.76344 −0.415602
\(83\) 7.33098 0.804679 0.402340 0.915490i \(-0.368197\pi\)
0.402340 + 0.915490i \(0.368197\pi\)
\(84\) −1.14172 −0.124571
\(85\) −14.6527 −1.58931
\(86\) −5.34950 −0.576851
\(87\) 4.74175 0.508369
\(88\) −5.44663 −0.580612
\(89\) 11.5704 1.22646 0.613230 0.789904i \(-0.289870\pi\)
0.613230 + 0.789904i \(0.289870\pi\)
\(90\) 0.100936 0.0106396
\(91\) −0.0342916 −0.00359473
\(92\) −0.569198 −0.0593430
\(93\) −7.17826 −0.744351
\(94\) −2.90711 −0.299845
\(95\) −1.96614 −0.201721
\(96\) 1.71717 0.175258
\(97\) −1.39596 −0.141738 −0.0708691 0.997486i \(-0.522577\pi\)
−0.0708691 + 0.997486i \(0.522577\pi\)
\(98\) 6.55793 0.662451
\(99\) −0.279614 −0.0281023
\(100\) −1.13431 −0.113431
\(101\) 0.815336 0.0811290 0.0405645 0.999177i \(-0.487084\pi\)
0.0405645 + 0.999177i \(0.487084\pi\)
\(102\) −12.7972 −1.26711
\(103\) −17.7362 −1.74760 −0.873800 0.486286i \(-0.838351\pi\)
−0.873800 + 0.486286i \(0.838351\pi\)
\(104\) 0.0515753 0.00505737
\(105\) −2.24477 −0.219067
\(106\) 4.82207 0.468361
\(107\) −9.25934 −0.895135 −0.447567 0.894250i \(-0.647709\pi\)
−0.447567 + 0.894250i \(0.647709\pi\)
\(108\) 5.23966 0.504186
\(109\) −14.4033 −1.37958 −0.689791 0.724008i \(-0.742298\pi\)
−0.689791 + 0.724008i \(0.742298\pi\)
\(110\) −10.7088 −1.02104
\(111\) −6.53835 −0.620593
\(112\) 0.664883 0.0628256
\(113\) 4.30841 0.405301 0.202651 0.979251i \(-0.435044\pi\)
0.202651 + 0.979251i \(0.435044\pi\)
\(114\) −1.71717 −0.160827
\(115\) −1.11912 −0.104358
\(116\) −2.76138 −0.256388
\(117\) 0.00264773 0.000244783 0
\(118\) 0.401214 0.0369347
\(119\) −4.95506 −0.454230
\(120\) 3.37618 0.308202
\(121\) 18.6657 1.69689
\(122\) 7.28561 0.659608
\(123\) −6.46246 −0.582700
\(124\) 4.18029 0.375401
\(125\) −12.0609 −1.07876
\(126\) 0.0341332 0.00304083
\(127\) 1.79062 0.158892 0.0794460 0.996839i \(-0.474685\pi\)
0.0794460 + 0.996839i \(0.474685\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.18598 −0.808780
\(130\) 0.101404 0.00889372
\(131\) 6.42765 0.561587 0.280793 0.959768i \(-0.409402\pi\)
0.280793 + 0.959768i \(0.409402\pi\)
\(132\) −9.35277 −0.814054
\(133\) −0.664883 −0.0576527
\(134\) 11.1051 0.959337
\(135\) 10.3019 0.886644
\(136\) 7.45253 0.639049
\(137\) 4.90431 0.419003 0.209502 0.977808i \(-0.432816\pi\)
0.209502 + 0.977808i \(0.432816\pi\)
\(138\) −0.977408 −0.0832025
\(139\) 16.7741 1.42276 0.711379 0.702809i \(-0.248071\pi\)
0.711379 + 0.702809i \(0.248071\pi\)
\(140\) 1.30725 0.110483
\(141\) −4.99199 −0.420401
\(142\) 15.3423 1.28750
\(143\) −0.280911 −0.0234910
\(144\) −0.0513372 −0.00427810
\(145\) −5.42925 −0.450874
\(146\) 0.623277 0.0515828
\(147\) 11.2611 0.928797
\(148\) 3.80764 0.312986
\(149\) 2.19033 0.179439 0.0897193 0.995967i \(-0.471403\pi\)
0.0897193 + 0.995967i \(0.471403\pi\)
\(150\) −1.94780 −0.159038
\(151\) 4.02446 0.327506 0.163753 0.986501i \(-0.447640\pi\)
0.163753 + 0.986501i \(0.447640\pi\)
\(152\) 1.00000 0.0811107
\(153\) 0.382592 0.0309307
\(154\) −3.62137 −0.291818
\(155\) 8.21902 0.660167
\(156\) 0.0885634 0.00709075
\(157\) 0.722109 0.0576306 0.0288153 0.999585i \(-0.490827\pi\)
0.0288153 + 0.999585i \(0.490827\pi\)
\(158\) 3.96744 0.315632
\(159\) 8.28031 0.656671
\(160\) −1.96614 −0.155437
\(161\) −0.378450 −0.0298260
\(162\) 8.84335 0.694799
\(163\) 2.08633 0.163414 0.0817069 0.996656i \(-0.473963\pi\)
0.0817069 + 0.996656i \(0.473963\pi\)
\(164\) 3.76344 0.293875
\(165\) −18.3888 −1.43157
\(166\) −7.33098 −0.568994
\(167\) −22.3102 −1.72642 −0.863209 0.504847i \(-0.831549\pi\)
−0.863209 + 0.504847i \(0.831549\pi\)
\(168\) 1.14172 0.0880853
\(169\) −12.9973 −0.999795
\(170\) 14.6527 1.12381
\(171\) 0.0513372 0.00392585
\(172\) 5.34950 0.407895
\(173\) −14.6786 −1.11599 −0.557996 0.829843i \(-0.688430\pi\)
−0.557996 + 0.829843i \(0.688430\pi\)
\(174\) −4.74175 −0.359471
\(175\) −0.754186 −0.0570111
\(176\) 5.44663 0.410555
\(177\) 0.688952 0.0517848
\(178\) −11.5704 −0.867238
\(179\) 3.49821 0.261469 0.130734 0.991417i \(-0.458266\pi\)
0.130734 + 0.991417i \(0.458266\pi\)
\(180\) −0.100936 −0.00752331
\(181\) −15.2807 −1.13581 −0.567904 0.823095i \(-0.692245\pi\)
−0.567904 + 0.823095i \(0.692245\pi\)
\(182\) 0.0342916 0.00254186
\(183\) 12.5106 0.924811
\(184\) 0.569198 0.0419618
\(185\) 7.48633 0.550406
\(186\) 7.17826 0.526336
\(187\) −40.5911 −2.96832
\(188\) 2.90711 0.212022
\(189\) 3.48376 0.253406
\(190\) 1.96614 0.142638
\(191\) 9.10809 0.659039 0.329519 0.944149i \(-0.393113\pi\)
0.329519 + 0.944149i \(0.393113\pi\)
\(192\) −1.71717 −0.123926
\(193\) 24.3418 1.75216 0.876080 0.482167i \(-0.160150\pi\)
0.876080 + 0.482167i \(0.160150\pi\)
\(194\) 1.39596 0.100224
\(195\) 0.174128 0.0124695
\(196\) −6.55793 −0.468424
\(197\) 3.04025 0.216609 0.108304 0.994118i \(-0.465458\pi\)
0.108304 + 0.994118i \(0.465458\pi\)
\(198\) 0.279614 0.0198713
\(199\) −7.69027 −0.545149 −0.272575 0.962135i \(-0.587875\pi\)
−0.272575 + 0.962135i \(0.587875\pi\)
\(200\) 1.13431 0.0802080
\(201\) 19.0694 1.34505
\(202\) −0.815336 −0.0573669
\(203\) −1.83600 −0.128862
\(204\) 12.7972 0.895986
\(205\) 7.39943 0.516799
\(206\) 17.7362 1.23574
\(207\) 0.0292210 0.00203100
\(208\) −0.0515753 −0.00357610
\(209\) −5.44663 −0.376751
\(210\) 2.24477 0.154904
\(211\) −1.00000 −0.0688428
\(212\) −4.82207 −0.331181
\(213\) 26.3453 1.80515
\(214\) 9.25934 0.632956
\(215\) 10.5178 0.717310
\(216\) −5.23966 −0.356513
\(217\) 2.77941 0.188678
\(218\) 14.4033 0.975512
\(219\) 1.07027 0.0723222
\(220\) 10.7088 0.721987
\(221\) 0.384366 0.0258553
\(222\) 6.53835 0.438825
\(223\) 7.97029 0.533730 0.266865 0.963734i \(-0.414012\pi\)
0.266865 + 0.963734i \(0.414012\pi\)
\(224\) −0.664883 −0.0444244
\(225\) 0.0582324 0.00388216
\(226\) −4.30841 −0.286591
\(227\) −12.4698 −0.827651 −0.413825 0.910356i \(-0.635808\pi\)
−0.413825 + 0.910356i \(0.635808\pi\)
\(228\) 1.71717 0.113722
\(229\) 10.0271 0.662608 0.331304 0.943524i \(-0.392511\pi\)
0.331304 + 0.943524i \(0.392511\pi\)
\(230\) 1.11912 0.0737926
\(231\) −6.21850 −0.409147
\(232\) 2.76138 0.181294
\(233\) 2.93800 0.192475 0.0962373 0.995358i \(-0.469319\pi\)
0.0962373 + 0.995358i \(0.469319\pi\)
\(234\) −0.00264773 −0.000173088 0
\(235\) 5.71576 0.372855
\(236\) −0.401214 −0.0261168
\(237\) 6.81275 0.442536
\(238\) 4.95506 0.321189
\(239\) 27.1772 1.75795 0.878973 0.476871i \(-0.158229\pi\)
0.878973 + 0.476871i \(0.158229\pi\)
\(240\) −3.37618 −0.217932
\(241\) 11.4352 0.736608 0.368304 0.929705i \(-0.379939\pi\)
0.368304 + 0.929705i \(0.379939\pi\)
\(242\) −18.6657 −1.19988
\(243\) −0.533453 −0.0342210
\(244\) −7.28561 −0.466413
\(245\) −12.8938 −0.823753
\(246\) 6.46246 0.412031
\(247\) 0.0515753 0.00328166
\(248\) −4.18029 −0.265449
\(249\) −12.5885 −0.797765
\(250\) 12.0609 0.762798
\(251\) 7.49421 0.473030 0.236515 0.971628i \(-0.423995\pi\)
0.236515 + 0.971628i \(0.423995\pi\)
\(252\) −0.0341332 −0.00215019
\(253\) −3.10021 −0.194908
\(254\) −1.79062 −0.112354
\(255\) 25.1611 1.57565
\(256\) 1.00000 0.0625000
\(257\) −11.2392 −0.701085 −0.350542 0.936547i \(-0.614003\pi\)
−0.350542 + 0.936547i \(0.614003\pi\)
\(258\) 9.18598 0.571894
\(259\) 2.53164 0.157308
\(260\) −0.101404 −0.00628881
\(261\) 0.141762 0.00877482
\(262\) −6.42765 −0.397102
\(263\) −28.5766 −1.76211 −0.881053 0.473018i \(-0.843165\pi\)
−0.881053 + 0.473018i \(0.843165\pi\)
\(264\) 9.35277 0.575623
\(265\) −9.48085 −0.582404
\(266\) 0.664883 0.0407666
\(267\) −19.8683 −1.21592
\(268\) −11.1051 −0.678354
\(269\) −25.3611 −1.54629 −0.773146 0.634228i \(-0.781318\pi\)
−0.773146 + 0.634228i \(0.781318\pi\)
\(270\) −10.3019 −0.626952
\(271\) 22.9209 1.39235 0.696174 0.717873i \(-0.254884\pi\)
0.696174 + 0.717873i \(0.254884\pi\)
\(272\) −7.45253 −0.451876
\(273\) 0.0588843 0.00356384
\(274\) −4.90431 −0.296280
\(275\) −6.17818 −0.372558
\(276\) 0.977408 0.0588330
\(277\) −12.2951 −0.738742 −0.369371 0.929282i \(-0.620427\pi\)
−0.369371 + 0.929282i \(0.620427\pi\)
\(278\) −16.7741 −1.00604
\(279\) −0.214604 −0.0128480
\(280\) −1.30725 −0.0781232
\(281\) −3.01077 −0.179607 −0.0898036 0.995959i \(-0.528624\pi\)
−0.0898036 + 0.995959i \(0.528624\pi\)
\(282\) 4.99199 0.297268
\(283\) −31.6362 −1.88057 −0.940287 0.340382i \(-0.889444\pi\)
−0.940287 + 0.340382i \(0.889444\pi\)
\(284\) −15.3423 −0.910398
\(285\) 3.37618 0.199988
\(286\) 0.280911 0.0166106
\(287\) 2.50225 0.147703
\(288\) 0.0513372 0.00302507
\(289\) 38.5402 2.26707
\(290\) 5.42925 0.318816
\(291\) 2.39709 0.140520
\(292\) −0.623277 −0.0364745
\(293\) −2.89410 −0.169075 −0.0845377 0.996420i \(-0.526941\pi\)
−0.0845377 + 0.996420i \(0.526941\pi\)
\(294\) −11.2611 −0.656758
\(295\) −0.788841 −0.0459281
\(296\) −3.80764 −0.221315
\(297\) 28.5384 1.65597
\(298\) −2.19033 −0.126882
\(299\) 0.0293566 0.00169773
\(300\) 1.94780 0.112457
\(301\) 3.55679 0.205010
\(302\) −4.02446 −0.231582
\(303\) −1.40007 −0.0804318
\(304\) −1.00000 −0.0573539
\(305\) −14.3245 −0.820218
\(306\) −0.382592 −0.0218713
\(307\) −19.0575 −1.08767 −0.543833 0.839193i \(-0.683028\pi\)
−0.543833 + 0.839193i \(0.683028\pi\)
\(308\) 3.62137 0.206347
\(309\) 30.4560 1.73258
\(310\) −8.21902 −0.466809
\(311\) 3.64366 0.206613 0.103306 0.994650i \(-0.467058\pi\)
0.103306 + 0.994650i \(0.467058\pi\)
\(312\) −0.0885634 −0.00501392
\(313\) 22.3322 1.26229 0.631146 0.775664i \(-0.282585\pi\)
0.631146 + 0.775664i \(0.282585\pi\)
\(314\) −0.722109 −0.0407510
\(315\) −0.0671106 −0.00378125
\(316\) −3.96744 −0.223186
\(317\) 8.40912 0.472303 0.236152 0.971716i \(-0.424114\pi\)
0.236152 + 0.971716i \(0.424114\pi\)
\(318\) −8.28031 −0.464337
\(319\) −15.0402 −0.842090
\(320\) 1.96614 0.109910
\(321\) 15.8998 0.887443
\(322\) 0.378450 0.0210902
\(323\) 7.45253 0.414670
\(324\) −8.84335 −0.491297
\(325\) 0.0585025 0.00324514
\(326\) −2.08633 −0.115551
\(327\) 24.7328 1.36773
\(328\) −3.76344 −0.207801
\(329\) 1.93289 0.106563
\(330\) 18.3888 1.01227
\(331\) 24.3203 1.33676 0.668381 0.743819i \(-0.266988\pi\)
0.668381 + 0.743819i \(0.266988\pi\)
\(332\) 7.33098 0.402340
\(333\) −0.195473 −0.0107119
\(334\) 22.3102 1.22076
\(335\) −21.8342 −1.19293
\(336\) −1.14172 −0.0622857
\(337\) −11.1676 −0.608339 −0.304169 0.952618i \(-0.598379\pi\)
−0.304169 + 0.952618i \(0.598379\pi\)
\(338\) 12.9973 0.706962
\(339\) −7.39826 −0.401818
\(340\) −14.6527 −0.794653
\(341\) 22.7685 1.23298
\(342\) −0.0513372 −0.00277600
\(343\) −9.01444 −0.486734
\(344\) −5.34950 −0.288425
\(345\) 1.92172 0.103462
\(346\) 14.6786 0.789126
\(347\) −20.9306 −1.12361 −0.561806 0.827269i \(-0.689893\pi\)
−0.561806 + 0.827269i \(0.689893\pi\)
\(348\) 4.74175 0.254185
\(349\) 1.95004 0.104383 0.0521917 0.998637i \(-0.483379\pi\)
0.0521917 + 0.998637i \(0.483379\pi\)
\(350\) 0.754186 0.0403129
\(351\) −0.270237 −0.0144242
\(352\) −5.44663 −0.290306
\(353\) 19.6958 1.04830 0.524150 0.851626i \(-0.324383\pi\)
0.524150 + 0.851626i \(0.324383\pi\)
\(354\) −0.688952 −0.0366174
\(355\) −30.1650 −1.60099
\(356\) 11.5704 0.613230
\(357\) 8.50867 0.450326
\(358\) −3.49821 −0.184886
\(359\) −13.0411 −0.688282 −0.344141 0.938918i \(-0.611830\pi\)
−0.344141 + 0.938918i \(0.611830\pi\)
\(360\) 0.100936 0.00531979
\(361\) 1.00000 0.0526316
\(362\) 15.2807 0.803137
\(363\) −32.0522 −1.68230
\(364\) −0.0342916 −0.00179737
\(365\) −1.22545 −0.0641428
\(366\) −12.5106 −0.653940
\(367\) 2.35542 0.122952 0.0614759 0.998109i \(-0.480419\pi\)
0.0614759 + 0.998109i \(0.480419\pi\)
\(368\) −0.569198 −0.0296715
\(369\) −0.193204 −0.0100578
\(370\) −7.48633 −0.389196
\(371\) −3.20612 −0.166453
\(372\) −7.17826 −0.372175
\(373\) 4.22862 0.218950 0.109475 0.993990i \(-0.465083\pi\)
0.109475 + 0.993990i \(0.465083\pi\)
\(374\) 40.5911 2.09892
\(375\) 20.7106 1.06949
\(376\) −2.90711 −0.149922
\(377\) 0.142419 0.00733495
\(378\) −3.48376 −0.179185
\(379\) −3.50916 −0.180253 −0.0901267 0.995930i \(-0.528727\pi\)
−0.0901267 + 0.995930i \(0.528727\pi\)
\(380\) −1.96614 −0.100861
\(381\) −3.07480 −0.157527
\(382\) −9.10809 −0.466011
\(383\) −13.3488 −0.682092 −0.341046 0.940047i \(-0.610781\pi\)
−0.341046 + 0.940047i \(0.610781\pi\)
\(384\) 1.71717 0.0876288
\(385\) 7.12011 0.362874
\(386\) −24.3418 −1.23896
\(387\) −0.274628 −0.0139601
\(388\) −1.39596 −0.0708691
\(389\) 0.558264 0.0283051 0.0141526 0.999900i \(-0.495495\pi\)
0.0141526 + 0.999900i \(0.495495\pi\)
\(390\) −0.174128 −0.00881730
\(391\) 4.24196 0.214525
\(392\) 6.55793 0.331225
\(393\) −11.0374 −0.556761
\(394\) −3.04025 −0.153165
\(395\) −7.80051 −0.392486
\(396\) −0.279614 −0.0140512
\(397\) −8.33658 −0.418401 −0.209201 0.977873i \(-0.567086\pi\)
−0.209201 + 0.977873i \(0.567086\pi\)
\(398\) 7.69027 0.385479
\(399\) 1.14172 0.0571573
\(400\) −1.13431 −0.0567156
\(401\) 28.0628 1.40139 0.700696 0.713460i \(-0.252873\pi\)
0.700696 + 0.713460i \(0.252873\pi\)
\(402\) −19.0694 −0.951094
\(403\) −0.215600 −0.0107398
\(404\) 0.815336 0.0405645
\(405\) −17.3872 −0.863978
\(406\) 1.83600 0.0911189
\(407\) 20.7388 1.02798
\(408\) −12.7972 −0.633557
\(409\) 19.5015 0.964286 0.482143 0.876093i \(-0.339859\pi\)
0.482143 + 0.876093i \(0.339859\pi\)
\(410\) −7.39943 −0.365432
\(411\) −8.42152 −0.415403
\(412\) −17.7362 −0.873800
\(413\) −0.266761 −0.0131264
\(414\) −0.0292210 −0.00143613
\(415\) 14.4137 0.707540
\(416\) 0.0515753 0.00252869
\(417\) −28.8039 −1.41053
\(418\) 5.44663 0.266403
\(419\) −17.2565 −0.843037 −0.421518 0.906820i \(-0.638503\pi\)
−0.421518 + 0.906820i \(0.638503\pi\)
\(420\) −2.24477 −0.109533
\(421\) −0.147683 −0.00719763 −0.00359881 0.999994i \(-0.501146\pi\)
−0.00359881 + 0.999994i \(0.501146\pi\)
\(422\) 1.00000 0.0486792
\(423\) −0.149243 −0.00725642
\(424\) 4.82207 0.234181
\(425\) 8.45350 0.410055
\(426\) −26.3453 −1.27643
\(427\) −4.84408 −0.234421
\(428\) −9.25934 −0.447567
\(429\) 0.482372 0.0232891
\(430\) −10.5178 −0.507215
\(431\) 8.58035 0.413301 0.206651 0.978415i \(-0.433744\pi\)
0.206651 + 0.978415i \(0.433744\pi\)
\(432\) 5.23966 0.252093
\(433\) −37.1097 −1.78338 −0.891688 0.452650i \(-0.850479\pi\)
−0.891688 + 0.452650i \(0.850479\pi\)
\(434\) −2.77941 −0.133416
\(435\) 9.32292 0.447000
\(436\) −14.4033 −0.689791
\(437\) 0.569198 0.0272284
\(438\) −1.07027 −0.0511395
\(439\) −23.4518 −1.11929 −0.559647 0.828731i \(-0.689063\pi\)
−0.559647 + 0.828731i \(0.689063\pi\)
\(440\) −10.7088 −0.510522
\(441\) 0.336666 0.0160317
\(442\) −0.384366 −0.0182824
\(443\) 2.40260 0.114151 0.0570755 0.998370i \(-0.481822\pi\)
0.0570755 + 0.998370i \(0.481822\pi\)
\(444\) −6.53835 −0.310296
\(445\) 22.7490 1.07840
\(446\) −7.97029 −0.377404
\(447\) −3.76116 −0.177897
\(448\) 0.664883 0.0314128
\(449\) −39.4123 −1.85998 −0.929990 0.367585i \(-0.880185\pi\)
−0.929990 + 0.367585i \(0.880185\pi\)
\(450\) −0.0582324 −0.00274510
\(451\) 20.4981 0.965216
\(452\) 4.30841 0.202651
\(453\) −6.91067 −0.324691
\(454\) 12.4698 0.585237
\(455\) −0.0674218 −0.00316078
\(456\) −1.71717 −0.0804137
\(457\) 29.3385 1.37240 0.686198 0.727415i \(-0.259278\pi\)
0.686198 + 0.727415i \(0.259278\pi\)
\(458\) −10.0271 −0.468535
\(459\) −39.0487 −1.82264
\(460\) −1.11912 −0.0521792
\(461\) 7.98018 0.371674 0.185837 0.982581i \(-0.440500\pi\)
0.185837 + 0.982581i \(0.440500\pi\)
\(462\) 6.21850 0.289311
\(463\) −37.4941 −1.74250 −0.871248 0.490843i \(-0.836689\pi\)
−0.871248 + 0.490843i \(0.836689\pi\)
\(464\) −2.76138 −0.128194
\(465\) −14.1134 −0.654495
\(466\) −2.93800 −0.136100
\(467\) −21.1682 −0.979549 −0.489775 0.871849i \(-0.662921\pi\)
−0.489775 + 0.871849i \(0.662921\pi\)
\(468\) 0.00264773 0.000122391 0
\(469\) −7.38362 −0.340944
\(470\) −5.71576 −0.263648
\(471\) −1.23998 −0.0571353
\(472\) 0.401214 0.0184674
\(473\) 29.1367 1.33971
\(474\) −6.81275 −0.312920
\(475\) 1.13431 0.0520458
\(476\) −4.95506 −0.227115
\(477\) 0.247552 0.0113346
\(478\) −27.1772 −1.24306
\(479\) 17.7815 0.812456 0.406228 0.913772i \(-0.366844\pi\)
0.406228 + 0.913772i \(0.366844\pi\)
\(480\) 3.37618 0.154101
\(481\) −0.196380 −0.00895416
\(482\) −11.4352 −0.520861
\(483\) 0.649862 0.0295698
\(484\) 18.6657 0.848443
\(485\) −2.74464 −0.124628
\(486\) 0.533453 0.0241979
\(487\) −15.8359 −0.717592 −0.358796 0.933416i \(-0.616813\pi\)
−0.358796 + 0.933416i \(0.616813\pi\)
\(488\) 7.28561 0.329804
\(489\) −3.58258 −0.162010
\(490\) 12.8938 0.582481
\(491\) 34.2367 1.54508 0.772540 0.634966i \(-0.218986\pi\)
0.772540 + 0.634966i \(0.218986\pi\)
\(492\) −6.46246 −0.291350
\(493\) 20.5793 0.926843
\(494\) −0.0515753 −0.00232048
\(495\) −0.549760 −0.0247099
\(496\) 4.18029 0.187701
\(497\) −10.2008 −0.457570
\(498\) 12.5885 0.564105
\(499\) 7.51190 0.336279 0.168139 0.985763i \(-0.446224\pi\)
0.168139 + 0.985763i \(0.446224\pi\)
\(500\) −12.0609 −0.539379
\(501\) 38.3104 1.71158
\(502\) −7.49421 −0.334483
\(503\) −39.2132 −1.74843 −0.874215 0.485539i \(-0.838623\pi\)
−0.874215 + 0.485539i \(0.838623\pi\)
\(504\) 0.0341332 0.00152042
\(505\) 1.60306 0.0713353
\(506\) 3.10021 0.137821
\(507\) 22.3186 0.991204
\(508\) 1.79062 0.0794460
\(509\) 5.10912 0.226458 0.113229 0.993569i \(-0.463881\pi\)
0.113229 + 0.993569i \(0.463881\pi\)
\(510\) −25.1611 −1.11415
\(511\) −0.414406 −0.0183323
\(512\) −1.00000 −0.0441942
\(513\) −5.23966 −0.231336
\(514\) 11.2392 0.495742
\(515\) −34.8718 −1.53663
\(516\) −9.18598 −0.404390
\(517\) 15.8339 0.696375
\(518\) −2.53164 −0.111234
\(519\) 25.2056 1.10640
\(520\) 0.101404 0.00444686
\(521\) −31.1713 −1.36564 −0.682820 0.730586i \(-0.739247\pi\)
−0.682820 + 0.730586i \(0.739247\pi\)
\(522\) −0.141762 −0.00620473
\(523\) −25.1686 −1.10054 −0.550272 0.834985i \(-0.685476\pi\)
−0.550272 + 0.834985i \(0.685476\pi\)
\(524\) 6.42765 0.280793
\(525\) 1.29506 0.0565212
\(526\) 28.5766 1.24600
\(527\) −31.1537 −1.35708
\(528\) −9.35277 −0.407027
\(529\) −22.6760 −0.985914
\(530\) 9.48085 0.411822
\(531\) 0.0205972 0.000893842 0
\(532\) −0.664883 −0.0288263
\(533\) −0.194101 −0.00840743
\(534\) 19.8683 0.859786
\(535\) −18.2051 −0.787076
\(536\) 11.1051 0.479669
\(537\) −6.00702 −0.259222
\(538\) 25.3611 1.09339
\(539\) −35.7186 −1.53851
\(540\) 10.3019 0.443322
\(541\) −14.6435 −0.629573 −0.314787 0.949162i \(-0.601933\pi\)
−0.314787 + 0.949162i \(0.601933\pi\)
\(542\) −22.9209 −0.984539
\(543\) 26.2396 1.12605
\(544\) 7.45253 0.319524
\(545\) −28.3188 −1.21304
\(546\) −0.0588843 −0.00252002
\(547\) −3.08583 −0.131940 −0.0659702 0.997822i \(-0.521014\pi\)
−0.0659702 + 0.997822i \(0.521014\pi\)
\(548\) 4.90431 0.209502
\(549\) 0.374023 0.0159629
\(550\) 6.17818 0.263438
\(551\) 2.76138 0.117639
\(552\) −0.977408 −0.0416012
\(553\) −2.63788 −0.112174
\(554\) 12.2951 0.522369
\(555\) −12.8553 −0.545676
\(556\) 16.7741 0.711379
\(557\) 10.9246 0.462891 0.231446 0.972848i \(-0.425654\pi\)
0.231446 + 0.972848i \(0.425654\pi\)
\(558\) 0.214604 0.00908493
\(559\) −0.275902 −0.0116694
\(560\) 1.30725 0.0552414
\(561\) 69.7018 2.94281
\(562\) 3.01077 0.127002
\(563\) −10.5361 −0.444045 −0.222023 0.975042i \(-0.571266\pi\)
−0.222023 + 0.975042i \(0.571266\pi\)
\(564\) −4.99199 −0.210200
\(565\) 8.47091 0.356374
\(566\) 31.6362 1.32977
\(567\) −5.87980 −0.246928
\(568\) 15.3423 0.643748
\(569\) −40.3961 −1.69349 −0.846746 0.531998i \(-0.821441\pi\)
−0.846746 + 0.531998i \(0.821441\pi\)
\(570\) −3.37618 −0.141413
\(571\) −41.3898 −1.73211 −0.866054 0.499950i \(-0.833352\pi\)
−0.866054 + 0.499950i \(0.833352\pi\)
\(572\) −0.280911 −0.0117455
\(573\) −15.6401 −0.653375
\(574\) −2.50225 −0.104442
\(575\) 0.645648 0.0269254
\(576\) −0.0513372 −0.00213905
\(577\) −7.58644 −0.315827 −0.157914 0.987453i \(-0.550477\pi\)
−0.157914 + 0.987453i \(0.550477\pi\)
\(578\) −38.5402 −1.60306
\(579\) −41.7989 −1.73710
\(580\) −5.42925 −0.225437
\(581\) 4.87424 0.202218
\(582\) −2.39709 −0.0993628
\(583\) −26.2640 −1.08775
\(584\) 0.623277 0.0257914
\(585\) 0.00520580 0.000215233 0
\(586\) 2.89410 0.119554
\(587\) 3.89266 0.160667 0.0803337 0.996768i \(-0.474401\pi\)
0.0803337 + 0.996768i \(0.474401\pi\)
\(588\) 11.2611 0.464398
\(589\) −4.18029 −0.172246
\(590\) 0.788841 0.0324761
\(591\) −5.22061 −0.214747
\(592\) 3.80764 0.156493
\(593\) −21.4182 −0.879540 −0.439770 0.898110i \(-0.644940\pi\)
−0.439770 + 0.898110i \(0.644940\pi\)
\(594\) −28.5384 −1.17095
\(595\) −9.74232 −0.399396
\(596\) 2.19033 0.0897193
\(597\) 13.2055 0.540465
\(598\) −0.0293566 −0.00120048
\(599\) 31.3344 1.28029 0.640145 0.768254i \(-0.278874\pi\)
0.640145 + 0.768254i \(0.278874\pi\)
\(600\) −1.94780 −0.0795188
\(601\) 39.0137 1.59140 0.795702 0.605688i \(-0.207102\pi\)
0.795702 + 0.605688i \(0.207102\pi\)
\(602\) −3.55679 −0.144964
\(603\) 0.570106 0.0232165
\(604\) 4.02446 0.163753
\(605\) 36.6994 1.49204
\(606\) 1.40007 0.0568739
\(607\) −16.4957 −0.669541 −0.334771 0.942300i \(-0.608659\pi\)
−0.334771 + 0.942300i \(0.608659\pi\)
\(608\) 1.00000 0.0405554
\(609\) 3.15271 0.127754
\(610\) 14.3245 0.579982
\(611\) −0.149935 −0.00606571
\(612\) 0.382592 0.0154654
\(613\) −7.40723 −0.299175 −0.149588 0.988748i \(-0.547795\pi\)
−0.149588 + 0.988748i \(0.547795\pi\)
\(614\) 19.0575 0.769096
\(615\) −12.7061 −0.512358
\(616\) −3.62137 −0.145909
\(617\) 21.7208 0.874446 0.437223 0.899353i \(-0.355962\pi\)
0.437223 + 0.899353i \(0.355962\pi\)
\(618\) −30.4560 −1.22512
\(619\) 31.9548 1.28437 0.642185 0.766549i \(-0.278028\pi\)
0.642185 + 0.766549i \(0.278028\pi\)
\(620\) 8.21902 0.330084
\(621\) −2.98240 −0.119680
\(622\) −3.64366 −0.146097
\(623\) 7.69297 0.308212
\(624\) 0.0885634 0.00354537
\(625\) −18.0418 −0.721671
\(626\) −22.3322 −0.892576
\(627\) 9.35277 0.373514
\(628\) 0.722109 0.0288153
\(629\) −28.3765 −1.13145
\(630\) 0.0671106 0.00267375
\(631\) 31.2137 1.24260 0.621298 0.783574i \(-0.286606\pi\)
0.621298 + 0.783574i \(0.286606\pi\)
\(632\) 3.96744 0.157816
\(633\) 1.71717 0.0682513
\(634\) −8.40912 −0.333969
\(635\) 3.52061 0.139711
\(636\) 8.28031 0.328336
\(637\) 0.338227 0.0134011
\(638\) 15.0402 0.595448
\(639\) 0.787630 0.0311582
\(640\) −1.96614 −0.0777183
\(641\) −6.61615 −0.261322 −0.130661 0.991427i \(-0.541710\pi\)
−0.130661 + 0.991427i \(0.541710\pi\)
\(642\) −15.8998 −0.627517
\(643\) 0.277025 0.0109248 0.00546240 0.999985i \(-0.498261\pi\)
0.00546240 + 0.999985i \(0.498261\pi\)
\(644\) −0.378450 −0.0149130
\(645\) −18.0609 −0.711146
\(646\) −7.45253 −0.293216
\(647\) 21.7579 0.855391 0.427695 0.903923i \(-0.359326\pi\)
0.427695 + 0.903923i \(0.359326\pi\)
\(648\) 8.84335 0.347400
\(649\) −2.18526 −0.0857791
\(650\) −0.0585025 −0.00229466
\(651\) −4.77271 −0.187057
\(652\) 2.08633 0.0817069
\(653\) −9.39540 −0.367670 −0.183835 0.982957i \(-0.558851\pi\)
−0.183835 + 0.982957i \(0.558851\pi\)
\(654\) −24.7328 −0.967129
\(655\) 12.6376 0.493793
\(656\) 3.76344 0.146938
\(657\) 0.0319973 0.00124833
\(658\) −1.93289 −0.0753517
\(659\) 24.2046 0.942878 0.471439 0.881899i \(-0.343735\pi\)
0.471439 + 0.881899i \(0.343735\pi\)
\(660\) −18.3888 −0.715783
\(661\) −22.5768 −0.878136 −0.439068 0.898454i \(-0.644691\pi\)
−0.439068 + 0.898454i \(0.644691\pi\)
\(662\) −24.3203 −0.945234
\(663\) −0.660021 −0.0256331
\(664\) −7.33098 −0.284497
\(665\) −1.30725 −0.0506930
\(666\) 0.195473 0.00757444
\(667\) 1.57177 0.0608592
\(668\) −22.3102 −0.863209
\(669\) −13.6863 −0.529143
\(670\) 21.8342 0.843528
\(671\) −39.6820 −1.53191
\(672\) 1.14172 0.0440426
\(673\) 19.6184 0.756234 0.378117 0.925758i \(-0.376572\pi\)
0.378117 + 0.925758i \(0.376572\pi\)
\(674\) 11.1676 0.430160
\(675\) −5.94341 −0.228762
\(676\) −12.9973 −0.499898
\(677\) −2.77541 −0.106668 −0.0533338 0.998577i \(-0.516985\pi\)
−0.0533338 + 0.998577i \(0.516985\pi\)
\(678\) 7.39826 0.284128
\(679\) −0.928150 −0.0356191
\(680\) 14.6527 0.561904
\(681\) 21.4128 0.820539
\(682\) −22.7685 −0.871851
\(683\) 17.7505 0.679205 0.339603 0.940569i \(-0.389707\pi\)
0.339603 + 0.940569i \(0.389707\pi\)
\(684\) 0.0513372 0.00196293
\(685\) 9.64254 0.368422
\(686\) 9.01444 0.344173
\(687\) −17.2182 −0.656914
\(688\) 5.34950 0.203948
\(689\) 0.248700 0.00947472
\(690\) −1.92172 −0.0731585
\(691\) −3.62867 −0.138041 −0.0690206 0.997615i \(-0.521987\pi\)
−0.0690206 + 0.997615i \(0.521987\pi\)
\(692\) −14.6786 −0.557996
\(693\) −0.185911 −0.00706218
\(694\) 20.9306 0.794513
\(695\) 32.9801 1.25101
\(696\) −4.74175 −0.179736
\(697\) −28.0471 −1.06236
\(698\) −1.95004 −0.0738102
\(699\) −5.04503 −0.190821
\(700\) −0.754186 −0.0285055
\(701\) 9.56454 0.361248 0.180624 0.983552i \(-0.442188\pi\)
0.180624 + 0.983552i \(0.442188\pi\)
\(702\) 0.270237 0.0101994
\(703\) −3.80764 −0.143608
\(704\) 5.44663 0.205277
\(705\) −9.81492 −0.369651
\(706\) −19.6958 −0.741259
\(707\) 0.542103 0.0203879
\(708\) 0.688952 0.0258924
\(709\) −30.7759 −1.15581 −0.577907 0.816102i \(-0.696131\pi\)
−0.577907 + 0.816102i \(0.696131\pi\)
\(710\) 30.1650 1.13207
\(711\) 0.203677 0.00763848
\(712\) −11.5704 −0.433619
\(713\) −2.37941 −0.0891097
\(714\) −8.50867 −0.318429
\(715\) −0.552310 −0.0206552
\(716\) 3.49821 0.130734
\(717\) −46.6678 −1.74284
\(718\) 13.0411 0.486689
\(719\) −10.4775 −0.390744 −0.195372 0.980729i \(-0.562591\pi\)
−0.195372 + 0.980729i \(0.562591\pi\)
\(720\) −0.100936 −0.00376166
\(721\) −11.7925 −0.439176
\(722\) −1.00000 −0.0372161
\(723\) −19.6362 −0.730278
\(724\) −15.2807 −0.567904
\(725\) 3.13227 0.116330
\(726\) 32.0522 1.18957
\(727\) 32.8219 1.21730 0.608649 0.793440i \(-0.291712\pi\)
0.608649 + 0.793440i \(0.291712\pi\)
\(728\) 0.0342916 0.00127093
\(729\) 27.4461 1.01652
\(730\) 1.22545 0.0453558
\(731\) −39.8673 −1.47454
\(732\) 12.5106 0.462405
\(733\) −15.1043 −0.557889 −0.278945 0.960307i \(-0.589985\pi\)
−0.278945 + 0.960307i \(0.589985\pi\)
\(734\) −2.35542 −0.0869401
\(735\) 22.1408 0.816675
\(736\) 0.569198 0.0209809
\(737\) −60.4855 −2.22801
\(738\) 0.193204 0.00711195
\(739\) −0.843562 −0.0310309 −0.0155155 0.999880i \(-0.504939\pi\)
−0.0155155 + 0.999880i \(0.504939\pi\)
\(740\) 7.48633 0.275203
\(741\) −0.0885634 −0.00325346
\(742\) 3.20612 0.117700
\(743\) 28.1547 1.03290 0.516448 0.856318i \(-0.327254\pi\)
0.516448 + 0.856318i \(0.327254\pi\)
\(744\) 7.17826 0.263168
\(745\) 4.30648 0.157777
\(746\) −4.22862 −0.154821
\(747\) −0.376352 −0.0137700
\(748\) −40.5911 −1.48416
\(749\) −6.15638 −0.224949
\(750\) −20.7106 −0.756243
\(751\) −43.1009 −1.57277 −0.786387 0.617734i \(-0.788051\pi\)
−0.786387 + 0.617734i \(0.788051\pi\)
\(752\) 2.90711 0.106011
\(753\) −12.8688 −0.468965
\(754\) −0.142419 −0.00518660
\(755\) 7.91263 0.287970
\(756\) 3.48376 0.126703
\(757\) 5.04390 0.183324 0.0916619 0.995790i \(-0.470782\pi\)
0.0916619 + 0.995790i \(0.470782\pi\)
\(758\) 3.50916 0.127458
\(759\) 5.32358 0.193234
\(760\) 1.96614 0.0713192
\(761\) 40.9204 1.48336 0.741681 0.670752i \(-0.234029\pi\)
0.741681 + 0.670752i \(0.234029\pi\)
\(762\) 3.07480 0.111388
\(763\) −9.57649 −0.346692
\(764\) 9.10809 0.329519
\(765\) 0.752227 0.0271968
\(766\) 13.3488 0.482312
\(767\) 0.0206927 0.000747171 0
\(768\) −1.71717 −0.0619629
\(769\) −33.5885 −1.21123 −0.605617 0.795757i \(-0.707073\pi\)
−0.605617 + 0.795757i \(0.707073\pi\)
\(770\) −7.12011 −0.256591
\(771\) 19.2997 0.695060
\(772\) 24.3418 0.876080
\(773\) 17.4791 0.628679 0.314340 0.949311i \(-0.398217\pi\)
0.314340 + 0.949311i \(0.398217\pi\)
\(774\) 0.274628 0.00987130
\(775\) −4.74176 −0.170329
\(776\) 1.39596 0.0501120
\(777\) −4.34724 −0.155956
\(778\) −0.558264 −0.0200147
\(779\) −3.76344 −0.134839
\(780\) 0.174128 0.00623477
\(781\) −83.5637 −2.99015
\(782\) −4.24196 −0.151692
\(783\) −14.4687 −0.517069
\(784\) −6.55793 −0.234212
\(785\) 1.41976 0.0506735
\(786\) 11.0374 0.393689
\(787\) −24.6448 −0.878493 −0.439246 0.898367i \(-0.644754\pi\)
−0.439246 + 0.898367i \(0.644754\pi\)
\(788\) 3.04025 0.108304
\(789\) 49.0707 1.74696
\(790\) 7.80051 0.277530
\(791\) 2.86459 0.101853
\(792\) 0.279614 0.00993567
\(793\) 0.375757 0.0133435
\(794\) 8.33658 0.295854
\(795\) 16.2802 0.577399
\(796\) −7.69027 −0.272575
\(797\) 30.0135 1.06313 0.531567 0.847016i \(-0.321603\pi\)
0.531567 + 0.847016i \(0.321603\pi\)
\(798\) −1.14172 −0.0404163
\(799\) −21.6653 −0.766462
\(800\) 1.13431 0.0401040
\(801\) −0.593992 −0.0209877
\(802\) −28.0628 −0.990933
\(803\) −3.39476 −0.119798
\(804\) 19.0694 0.672525
\(805\) −0.744084 −0.0262255
\(806\) 0.215600 0.00759418
\(807\) 43.5492 1.53300
\(808\) −0.815336 −0.0286834
\(809\) 31.1310 1.09451 0.547254 0.836966i \(-0.315673\pi\)
0.547254 + 0.836966i \(0.315673\pi\)
\(810\) 17.3872 0.610925
\(811\) −30.3583 −1.06603 −0.533013 0.846107i \(-0.678940\pi\)
−0.533013 + 0.846107i \(0.678940\pi\)
\(812\) −1.83600 −0.0644308
\(813\) −39.3591 −1.38038
\(814\) −20.7388 −0.726894
\(815\) 4.10200 0.143687
\(816\) 12.7972 0.447993
\(817\) −5.34950 −0.187155
\(818\) −19.5015 −0.681853
\(819\) 0.00176043 6.15145e−5 0
\(820\) 7.39943 0.258399
\(821\) 37.4264 1.30619 0.653094 0.757277i \(-0.273470\pi\)
0.653094 + 0.757277i \(0.273470\pi\)
\(822\) 8.42152 0.293734
\(823\) −34.6012 −1.20612 −0.603061 0.797695i \(-0.706052\pi\)
−0.603061 + 0.797695i \(0.706052\pi\)
\(824\) 17.7362 0.617870
\(825\) 10.6090 0.369357
\(826\) 0.266761 0.00928179
\(827\) −49.4218 −1.71857 −0.859283 0.511500i \(-0.829090\pi\)
−0.859283 + 0.511500i \(0.829090\pi\)
\(828\) 0.0292210 0.00101550
\(829\) −26.9608 −0.936387 −0.468194 0.883626i \(-0.655095\pi\)
−0.468194 + 0.883626i \(0.655095\pi\)
\(830\) −14.4137 −0.500307
\(831\) 21.1128 0.732394
\(832\) −0.0515753 −0.00178805
\(833\) 48.8731 1.69335
\(834\) 28.8039 0.997397
\(835\) −43.8649 −1.51801
\(836\) −5.44663 −0.188376
\(837\) 21.9033 0.757089
\(838\) 17.2565 0.596117
\(839\) 17.6134 0.608082 0.304041 0.952659i \(-0.401664\pi\)
0.304041 + 0.952659i \(0.401664\pi\)
\(840\) 2.24477 0.0774518
\(841\) −21.3748 −0.737061
\(842\) 0.147683 0.00508949
\(843\) 5.16999 0.178064
\(844\) −1.00000 −0.0344214
\(845\) −25.5545 −0.879102
\(846\) 0.149243 0.00513107
\(847\) 12.4105 0.426431
\(848\) −4.82207 −0.165591
\(849\) 54.3246 1.86441
\(850\) −8.45350 −0.289953
\(851\) −2.16730 −0.0742941
\(852\) 26.3453 0.902574
\(853\) −35.3787 −1.21135 −0.605673 0.795714i \(-0.707096\pi\)
−0.605673 + 0.795714i \(0.707096\pi\)
\(854\) 4.84408 0.165761
\(855\) 0.100936 0.00345193
\(856\) 9.25934 0.316478
\(857\) −9.75284 −0.333151 −0.166575 0.986029i \(-0.553271\pi\)
−0.166575 + 0.986029i \(0.553271\pi\)
\(858\) −0.482372 −0.0164679
\(859\) −43.9490 −1.49952 −0.749760 0.661710i \(-0.769831\pi\)
−0.749760 + 0.661710i \(0.769831\pi\)
\(860\) 10.5178 0.358655
\(861\) −4.29678 −0.146434
\(862\) −8.58035 −0.292248
\(863\) −36.7963 −1.25256 −0.626280 0.779598i \(-0.715423\pi\)
−0.626280 + 0.779598i \(0.715423\pi\)
\(864\) −5.23966 −0.178257
\(865\) −28.8601 −0.981273
\(866\) 37.1097 1.26104
\(867\) −66.1799 −2.24759
\(868\) 2.77941 0.0943392
\(869\) −21.6091 −0.733040
\(870\) −9.32292 −0.316077
\(871\) 0.572751 0.0194069
\(872\) 14.4033 0.487756
\(873\) 0.0716646 0.00242548
\(874\) −0.569198 −0.0192534
\(875\) −8.01908 −0.271094
\(876\) 1.07027 0.0361611
\(877\) −44.6268 −1.50694 −0.753470 0.657483i \(-0.771621\pi\)
−0.753470 + 0.657483i \(0.771621\pi\)
\(878\) 23.4518 0.791461
\(879\) 4.96966 0.167622
\(880\) 10.7088 0.360994
\(881\) 11.3536 0.382512 0.191256 0.981540i \(-0.438744\pi\)
0.191256 + 0.981540i \(0.438744\pi\)
\(882\) −0.336666 −0.0113361
\(883\) −41.2415 −1.38789 −0.693944 0.720029i \(-0.744129\pi\)
−0.693944 + 0.720029i \(0.744129\pi\)
\(884\) 0.384366 0.0129276
\(885\) 1.35457 0.0455334
\(886\) −2.40260 −0.0807169
\(887\) −18.4339 −0.618951 −0.309475 0.950907i \(-0.600153\pi\)
−0.309475 + 0.950907i \(0.600153\pi\)
\(888\) 6.53835 0.219413
\(889\) 1.19056 0.0399299
\(890\) −22.7490 −0.762547
\(891\) −48.1664 −1.61364
\(892\) 7.97029 0.266865
\(893\) −2.90711 −0.0972826
\(894\) 3.76116 0.125792
\(895\) 6.87796 0.229905
\(896\) −0.664883 −0.0222122
\(897\) −0.0504101 −0.00168314
\(898\) 39.4123 1.31520
\(899\) −11.5434 −0.384993
\(900\) 0.0582324 0.00194108
\(901\) 35.9366 1.19722
\(902\) −20.4981 −0.682511
\(903\) −6.10760 −0.203248
\(904\) −4.30841 −0.143296
\(905\) −30.0440 −0.998695
\(906\) 6.91067 0.229592
\(907\) 11.3421 0.376609 0.188305 0.982111i \(-0.439701\pi\)
0.188305 + 0.982111i \(0.439701\pi\)
\(908\) −12.4698 −0.413825
\(909\) −0.0418571 −0.00138831
\(910\) 0.0674218 0.00223501
\(911\) −38.3605 −1.27094 −0.635470 0.772125i \(-0.719194\pi\)
−0.635470 + 0.772125i \(0.719194\pi\)
\(912\) 1.71717 0.0568611
\(913\) 39.9291 1.32146
\(914\) −29.3385 −0.970430
\(915\) 24.5975 0.813170
\(916\) 10.0271 0.331304
\(917\) 4.27364 0.141128
\(918\) 39.0487 1.28880
\(919\) −53.0919 −1.75134 −0.875670 0.482910i \(-0.839580\pi\)
−0.875670 + 0.482910i \(0.839580\pi\)
\(920\) 1.11912 0.0368963
\(921\) 32.7248 1.07832
\(922\) −7.98018 −0.262813
\(923\) 0.791283 0.0260454
\(924\) −6.21850 −0.204574
\(925\) −4.31905 −0.142010
\(926\) 37.4941 1.23213
\(927\) 0.910526 0.0299056
\(928\) 2.76138 0.0906468
\(929\) −11.2355 −0.368625 −0.184313 0.982868i \(-0.559006\pi\)
−0.184313 + 0.982868i \(0.559006\pi\)
\(930\) 14.1134 0.462798
\(931\) 6.55793 0.214927
\(932\) 2.93800 0.0962373
\(933\) −6.25677 −0.204837
\(934\) 21.1682 0.692646
\(935\) −79.8076 −2.60999
\(936\) −0.00264773 −8.65438e−5 0
\(937\) −9.83497 −0.321295 −0.160647 0.987012i \(-0.551358\pi\)
−0.160647 + 0.987012i \(0.551358\pi\)
\(938\) 7.38362 0.241084
\(939\) −38.3482 −1.25145
\(940\) 5.71576 0.186428
\(941\) −0.178774 −0.00582786 −0.00291393 0.999996i \(-0.500928\pi\)
−0.00291393 + 0.999996i \(0.500928\pi\)
\(942\) 1.23998 0.0404008
\(943\) −2.14214 −0.0697577
\(944\) −0.401214 −0.0130584
\(945\) 6.84954 0.222816
\(946\) −29.1367 −0.947316
\(947\) −36.3394 −1.18087 −0.590436 0.807085i \(-0.701044\pi\)
−0.590436 + 0.807085i \(0.701044\pi\)
\(948\) 6.81275 0.221268
\(949\) 0.0321457 0.00104349
\(950\) −1.13431 −0.0368020
\(951\) −14.4399 −0.468245
\(952\) 4.95506 0.160594
\(953\) −1.70822 −0.0553347 −0.0276673 0.999617i \(-0.508808\pi\)
−0.0276673 + 0.999617i \(0.508808\pi\)
\(954\) −0.247552 −0.00801478
\(955\) 17.9077 0.579481
\(956\) 27.1772 0.878973
\(957\) 25.8266 0.834854
\(958\) −17.7815 −0.574493
\(959\) 3.26079 0.105297
\(960\) −3.37618 −0.108966
\(961\) −13.5252 −0.436295
\(962\) 0.196380 0.00633155
\(963\) 0.475349 0.0153179
\(964\) 11.4352 0.368304
\(965\) 47.8592 1.54064
\(966\) −0.649862 −0.0209090
\(967\) −39.2416 −1.26192 −0.630962 0.775814i \(-0.717339\pi\)
−0.630962 + 0.775814i \(0.717339\pi\)
\(968\) −18.6657 −0.599940
\(969\) −12.7972 −0.411106
\(970\) 2.74464 0.0881252
\(971\) 52.9983 1.70080 0.850399 0.526139i \(-0.176361\pi\)
0.850399 + 0.526139i \(0.176361\pi\)
\(972\) −0.533453 −0.0171105
\(973\) 11.1528 0.357542
\(974\) 15.8359 0.507414
\(975\) −0.100459 −0.00321725
\(976\) −7.28561 −0.233207
\(977\) −19.6760 −0.629491 −0.314746 0.949176i \(-0.601919\pi\)
−0.314746 + 0.949176i \(0.601919\pi\)
\(978\) 3.58258 0.114558
\(979\) 63.0197 2.01412
\(980\) −12.8938 −0.411877
\(981\) 0.739423 0.0236080
\(982\) −34.2367 −1.09254
\(983\) −39.5305 −1.26083 −0.630414 0.776259i \(-0.717115\pi\)
−0.630414 + 0.776259i \(0.717115\pi\)
\(984\) 6.46246 0.206016
\(985\) 5.97754 0.190460
\(986\) −20.5793 −0.655377
\(987\) −3.31909 −0.105648
\(988\) 0.0515753 0.00164083
\(989\) −3.04492 −0.0968229
\(990\) 0.549760 0.0174725
\(991\) −61.8294 −1.96407 −0.982037 0.188688i \(-0.939577\pi\)
−0.982037 + 0.188688i \(0.939577\pi\)
\(992\) −4.18029 −0.132724
\(993\) −41.7619 −1.32528
\(994\) 10.2008 0.323551
\(995\) −15.1201 −0.479340
\(996\) −12.5885 −0.398882
\(997\) −14.3653 −0.454954 −0.227477 0.973783i \(-0.573048\pi\)
−0.227477 + 0.973783i \(0.573048\pi\)
\(998\) −7.51190 −0.237785
\(999\) 19.9507 0.631213
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 \(a_p\))