Properties

Label 8018.2.a.d.1.17
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
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: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+0.180143 q^{3}\) \(+1.00000 q^{4}\) \(+0.229721 q^{5}\) \(+0.180143 q^{6}\) \(-1.11361 q^{7}\) \(+1.00000 q^{8}\) \(-2.96755 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+0.180143 q^{3}\) \(+1.00000 q^{4}\) \(+0.229721 q^{5}\) \(+0.180143 q^{6}\) \(-1.11361 q^{7}\) \(+1.00000 q^{8}\) \(-2.96755 q^{9}\) \(+0.229721 q^{10}\) \(-4.26991 q^{11}\) \(+0.180143 q^{12}\) \(+5.52427 q^{13}\) \(-1.11361 q^{14}\) \(+0.0413825 q^{15}\) \(+1.00000 q^{16}\) \(+3.05989 q^{17}\) \(-2.96755 q^{18}\) \(+1.00000 q^{19}\) \(+0.229721 q^{20}\) \(-0.200608 q^{21}\) \(-4.26991 q^{22}\) \(-0.559549 q^{23}\) \(+0.180143 q^{24}\) \(-4.94723 q^{25}\) \(+5.52427 q^{26}\) \(-1.07501 q^{27}\) \(-1.11361 q^{28}\) \(-4.00049 q^{29}\) \(+0.0413825 q^{30}\) \(+9.37372 q^{31}\) \(+1.00000 q^{32}\) \(-0.769192 q^{33}\) \(+3.05989 q^{34}\) \(-0.255818 q^{35}\) \(-2.96755 q^{36}\) \(+4.95059 q^{37}\) \(+1.00000 q^{38}\) \(+0.995156 q^{39}\) \(+0.229721 q^{40}\) \(-10.1260 q^{41}\) \(-0.200608 q^{42}\) \(-12.2198 q^{43}\) \(-4.26991 q^{44}\) \(-0.681707 q^{45}\) \(-0.559549 q^{46}\) \(-6.32808 q^{47}\) \(+0.180143 q^{48}\) \(-5.75988 q^{49}\) \(-4.94723 q^{50}\) \(+0.551216 q^{51}\) \(+5.52427 q^{52}\) \(-0.623348 q^{53}\) \(-1.07501 q^{54}\) \(-0.980886 q^{55}\) \(-1.11361 q^{56}\) \(+0.180143 q^{57}\) \(-4.00049 q^{58}\) \(+2.85480 q^{59}\) \(+0.0413825 q^{60}\) \(-12.0077 q^{61}\) \(+9.37372 q^{62}\) \(+3.30468 q^{63}\) \(+1.00000 q^{64}\) \(+1.26904 q^{65}\) \(-0.769192 q^{66}\) \(-9.26742 q^{67}\) \(+3.05989 q^{68}\) \(-0.100799 q^{69}\) \(-0.255818 q^{70}\) \(+8.20192 q^{71}\) \(-2.96755 q^{72}\) \(+15.2736 q^{73}\) \(+4.95059 q^{74}\) \(-0.891207 q^{75}\) \(+1.00000 q^{76}\) \(+4.75499 q^{77}\) \(+0.995156 q^{78}\) \(-4.06243 q^{79}\) \(+0.229721 q^{80}\) \(+8.70899 q^{81}\) \(-10.1260 q^{82}\) \(+4.31169 q^{83}\) \(-0.200608 q^{84}\) \(+0.702920 q^{85}\) \(-12.2198 q^{86}\) \(-0.720658 q^{87}\) \(-4.26991 q^{88}\) \(-2.30328 q^{89}\) \(-0.681707 q^{90}\) \(-6.15185 q^{91}\) \(-0.559549 q^{92}\) \(+1.68861 q^{93}\) \(-6.32808 q^{94}\) \(+0.229721 q^{95}\) \(+0.180143 q^{96}\) \(-2.67655 q^{97}\) \(-5.75988 q^{98}\) \(+12.6712 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.180143 0.104005 0.0520027 0.998647i \(-0.483440\pi\)
0.0520027 + 0.998647i \(0.483440\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.229721 0.102734 0.0513671 0.998680i \(-0.483642\pi\)
0.0513671 + 0.998680i \(0.483642\pi\)
\(6\) 0.180143 0.0735429
\(7\) −1.11361 −0.420903 −0.210452 0.977604i \(-0.567493\pi\)
−0.210452 + 0.977604i \(0.567493\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.96755 −0.989183
\(10\) 0.229721 0.0726440
\(11\) −4.26991 −1.28743 −0.643713 0.765267i \(-0.722607\pi\)
−0.643713 + 0.765267i \(0.722607\pi\)
\(12\) 0.180143 0.0520027
\(13\) 5.52427 1.53216 0.766078 0.642748i \(-0.222206\pi\)
0.766078 + 0.642748i \(0.222206\pi\)
\(14\) −1.11361 −0.297624
\(15\) 0.0413825 0.0106849
\(16\) 1.00000 0.250000
\(17\) 3.05989 0.742132 0.371066 0.928607i \(-0.378992\pi\)
0.371066 + 0.928607i \(0.378992\pi\)
\(18\) −2.96755 −0.699458
\(19\) 1.00000 0.229416
\(20\) 0.229721 0.0513671
\(21\) −0.200608 −0.0437762
\(22\) −4.26991 −0.910347
\(23\) −0.559549 −0.116674 −0.0583370 0.998297i \(-0.518580\pi\)
−0.0583370 + 0.998297i \(0.518580\pi\)
\(24\) 0.180143 0.0367715
\(25\) −4.94723 −0.989446
\(26\) 5.52427 1.08340
\(27\) −1.07501 −0.206886
\(28\) −1.11361 −0.210452
\(29\) −4.00049 −0.742872 −0.371436 0.928459i \(-0.621134\pi\)
−0.371436 + 0.928459i \(0.621134\pi\)
\(30\) 0.0413825 0.00755537
\(31\) 9.37372 1.68357 0.841785 0.539813i \(-0.181505\pi\)
0.841785 + 0.539813i \(0.181505\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.769192 −0.133899
\(34\) 3.05989 0.524767
\(35\) −0.255818 −0.0432412
\(36\) −2.96755 −0.494591
\(37\) 4.95059 0.813871 0.406936 0.913457i \(-0.366597\pi\)
0.406936 + 0.913457i \(0.366597\pi\)
\(38\) 1.00000 0.162221
\(39\) 0.995156 0.159352
\(40\) 0.229721 0.0363220
\(41\) −10.1260 −1.58142 −0.790710 0.612190i \(-0.790289\pi\)
−0.790710 + 0.612190i \(0.790289\pi\)
\(42\) −0.200608 −0.0309545
\(43\) −12.2198 −1.86351 −0.931753 0.363094i \(-0.881721\pi\)
−0.931753 + 0.363094i \(0.881721\pi\)
\(44\) −4.26991 −0.643713
\(45\) −0.681707 −0.101623
\(46\) −0.559549 −0.0825010
\(47\) −6.32808 −0.923046 −0.461523 0.887128i \(-0.652697\pi\)
−0.461523 + 0.887128i \(0.652697\pi\)
\(48\) 0.180143 0.0260013
\(49\) −5.75988 −0.822840
\(50\) −4.94723 −0.699644
\(51\) 0.551216 0.0771857
\(52\) 5.52427 0.766078
\(53\) −0.623348 −0.0856234 −0.0428117 0.999083i \(-0.513632\pi\)
−0.0428117 + 0.999083i \(0.513632\pi\)
\(54\) −1.07501 −0.146290
\(55\) −0.980886 −0.132263
\(56\) −1.11361 −0.148812
\(57\) 0.180143 0.0238605
\(58\) −4.00049 −0.525290
\(59\) 2.85480 0.371663 0.185832 0.982582i \(-0.440502\pi\)
0.185832 + 0.982582i \(0.440502\pi\)
\(60\) 0.0413825 0.00534245
\(61\) −12.0077 −1.53743 −0.768716 0.639590i \(-0.779104\pi\)
−0.768716 + 0.639590i \(0.779104\pi\)
\(62\) 9.37372 1.19046
\(63\) 3.30468 0.416350
\(64\) 1.00000 0.125000
\(65\) 1.26904 0.157405
\(66\) −0.769192 −0.0946810
\(67\) −9.26742 −1.13220 −0.566098 0.824338i \(-0.691547\pi\)
−0.566098 + 0.824338i \(0.691547\pi\)
\(68\) 3.05989 0.371066
\(69\) −0.100799 −0.0121347
\(70\) −0.255818 −0.0305761
\(71\) 8.20192 0.973389 0.486694 0.873572i \(-0.338202\pi\)
0.486694 + 0.873572i \(0.338202\pi\)
\(72\) −2.96755 −0.349729
\(73\) 15.2736 1.78765 0.893823 0.448421i \(-0.148013\pi\)
0.893823 + 0.448421i \(0.148013\pi\)
\(74\) 4.95059 0.575494
\(75\) −0.891207 −0.102908
\(76\) 1.00000 0.114708
\(77\) 4.75499 0.541882
\(78\) 0.995156 0.112679
\(79\) −4.06243 −0.457059 −0.228529 0.973537i \(-0.573392\pi\)
−0.228529 + 0.973537i \(0.573392\pi\)
\(80\) 0.229721 0.0256835
\(81\) 8.70899 0.967666
\(82\) −10.1260 −1.11823
\(83\) 4.31169 0.473269 0.236635 0.971599i \(-0.423956\pi\)
0.236635 + 0.971599i \(0.423956\pi\)
\(84\) −0.200608 −0.0218881
\(85\) 0.702920 0.0762423
\(86\) −12.2198 −1.31770
\(87\) −0.720658 −0.0772627
\(88\) −4.26991 −0.455174
\(89\) −2.30328 −0.244148 −0.122074 0.992521i \(-0.538954\pi\)
−0.122074 + 0.992521i \(0.538954\pi\)
\(90\) −0.681707 −0.0718582
\(91\) −6.15185 −0.644889
\(92\) −0.559549 −0.0583370
\(93\) 1.68861 0.175100
\(94\) −6.32808 −0.652692
\(95\) 0.229721 0.0235688
\(96\) 0.180143 0.0183857
\(97\) −2.67655 −0.271762 −0.135881 0.990725i \(-0.543387\pi\)
−0.135881 + 0.990725i \(0.543387\pi\)
\(98\) −5.75988 −0.581836
\(99\) 12.6712 1.27350
\(100\) −4.94723 −0.494723
\(101\) −1.51488 −0.150736 −0.0753679 0.997156i \(-0.524013\pi\)
−0.0753679 + 0.997156i \(0.524013\pi\)
\(102\) 0.551216 0.0545785
\(103\) 6.71149 0.661302 0.330651 0.943753i \(-0.392732\pi\)
0.330651 + 0.943753i \(0.392732\pi\)
\(104\) 5.52427 0.541699
\(105\) −0.0460838 −0.00449731
\(106\) −0.623348 −0.0605449
\(107\) 18.0314 1.74316 0.871578 0.490256i \(-0.163097\pi\)
0.871578 + 0.490256i \(0.163097\pi\)
\(108\) −1.07501 −0.103443
\(109\) −3.09897 −0.296828 −0.148414 0.988925i \(-0.547417\pi\)
−0.148414 + 0.988925i \(0.547417\pi\)
\(110\) −0.980886 −0.0935238
\(111\) 0.891811 0.0846470
\(112\) −1.11361 −0.105226
\(113\) −5.13579 −0.483134 −0.241567 0.970384i \(-0.577661\pi\)
−0.241567 + 0.970384i \(0.577661\pi\)
\(114\) 0.180143 0.0168719
\(115\) −0.128540 −0.0119864
\(116\) −4.00049 −0.371436
\(117\) −16.3935 −1.51558
\(118\) 2.85480 0.262806
\(119\) −3.40751 −0.312366
\(120\) 0.0413825 0.00377769
\(121\) 7.23210 0.657464
\(122\) −12.0077 −1.08713
\(123\) −1.82413 −0.164476
\(124\) 9.37372 0.841785
\(125\) −2.28508 −0.204384
\(126\) 3.30468 0.294404
\(127\) −12.5240 −1.11133 −0.555664 0.831407i \(-0.687536\pi\)
−0.555664 + 0.831407i \(0.687536\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.20131 −0.193815
\(130\) 1.26904 0.111302
\(131\) −2.57515 −0.224992 −0.112496 0.993652i \(-0.535885\pi\)
−0.112496 + 0.993652i \(0.535885\pi\)
\(132\) −0.769192 −0.0669496
\(133\) −1.11361 −0.0965619
\(134\) −9.26742 −0.800583
\(135\) −0.246952 −0.0212542
\(136\) 3.05989 0.262383
\(137\) −4.92632 −0.420884 −0.210442 0.977606i \(-0.567490\pi\)
−0.210442 + 0.977606i \(0.567490\pi\)
\(138\) −0.100799 −0.00858055
\(139\) −16.8290 −1.42741 −0.713707 0.700444i \(-0.752985\pi\)
−0.713707 + 0.700444i \(0.752985\pi\)
\(140\) −0.255818 −0.0216206
\(141\) −1.13996 −0.0960017
\(142\) 8.20192 0.688290
\(143\) −23.5881 −1.97254
\(144\) −2.96755 −0.247296
\(145\) −0.918994 −0.0763183
\(146\) 15.2736 1.26406
\(147\) −1.03760 −0.0855798
\(148\) 4.95059 0.406936
\(149\) −19.6430 −1.60922 −0.804609 0.593805i \(-0.797625\pi\)
−0.804609 + 0.593805i \(0.797625\pi\)
\(150\) −0.891207 −0.0727667
\(151\) −8.52109 −0.693437 −0.346718 0.937969i \(-0.612704\pi\)
−0.346718 + 0.937969i \(0.612704\pi\)
\(152\) 1.00000 0.0811107
\(153\) −9.08037 −0.734104
\(154\) 4.75499 0.383168
\(155\) 2.15334 0.172960
\(156\) 0.995156 0.0796762
\(157\) −8.73492 −0.697123 −0.348561 0.937286i \(-0.613330\pi\)
−0.348561 + 0.937286i \(0.613330\pi\)
\(158\) −4.06243 −0.323189
\(159\) −0.112292 −0.00890530
\(160\) 0.229721 0.0181610
\(161\) 0.623117 0.0491085
\(162\) 8.70899 0.684243
\(163\) −5.89902 −0.462047 −0.231024 0.972948i \(-0.574207\pi\)
−0.231024 + 0.972948i \(0.574207\pi\)
\(164\) −10.1260 −0.790710
\(165\) −0.176699 −0.0137560
\(166\) 4.31169 0.334652
\(167\) 4.96906 0.384518 0.192259 0.981344i \(-0.438419\pi\)
0.192259 + 0.981344i \(0.438419\pi\)
\(168\) −0.200608 −0.0154772
\(169\) 17.5175 1.34750
\(170\) 0.702920 0.0539115
\(171\) −2.96755 −0.226934
\(172\) −12.2198 −0.931753
\(173\) −16.4703 −1.25222 −0.626108 0.779736i \(-0.715353\pi\)
−0.626108 + 0.779736i \(0.715353\pi\)
\(174\) −0.720658 −0.0546330
\(175\) 5.50926 0.416461
\(176\) −4.26991 −0.321856
\(177\) 0.514271 0.0386550
\(178\) −2.30328 −0.172638
\(179\) 0.150726 0.0112658 0.00563289 0.999984i \(-0.498207\pi\)
0.00563289 + 0.999984i \(0.498207\pi\)
\(180\) −0.681707 −0.0508115
\(181\) −26.2189 −1.94884 −0.974418 0.224744i \(-0.927845\pi\)
−0.974418 + 0.224744i \(0.927845\pi\)
\(182\) −6.15185 −0.456006
\(183\) −2.16310 −0.159901
\(184\) −0.559549 −0.0412505
\(185\) 1.13725 0.0836124
\(186\) 1.68861 0.123815
\(187\) −13.0654 −0.955439
\(188\) −6.32808 −0.461523
\(189\) 1.19714 0.0870789
\(190\) 0.229721 0.0166657
\(191\) 3.97821 0.287853 0.143927 0.989588i \(-0.454027\pi\)
0.143927 + 0.989588i \(0.454027\pi\)
\(192\) 0.180143 0.0130007
\(193\) −19.4922 −1.40308 −0.701540 0.712630i \(-0.747504\pi\)
−0.701540 + 0.712630i \(0.747504\pi\)
\(194\) −2.67655 −0.192165
\(195\) 0.228608 0.0163709
\(196\) −5.75988 −0.411420
\(197\) 0.443923 0.0316282 0.0158141 0.999875i \(-0.494966\pi\)
0.0158141 + 0.999875i \(0.494966\pi\)
\(198\) 12.6712 0.900500
\(199\) −1.10002 −0.0779783 −0.0389892 0.999240i \(-0.512414\pi\)
−0.0389892 + 0.999240i \(0.512414\pi\)
\(200\) −4.94723 −0.349822
\(201\) −1.66946 −0.117754
\(202\) −1.51488 −0.106586
\(203\) 4.45496 0.312677
\(204\) 0.551216 0.0385929
\(205\) −2.32616 −0.162466
\(206\) 6.71149 0.467611
\(207\) 1.66049 0.115412
\(208\) 5.52427 0.383039
\(209\) −4.26991 −0.295356
\(210\) −0.0460838 −0.00318008
\(211\) −1.00000 −0.0688428
\(212\) −0.623348 −0.0428117
\(213\) 1.47752 0.101238
\(214\) 18.0314 1.23260
\(215\) −2.80715 −0.191446
\(216\) −1.07501 −0.0731452
\(217\) −10.4386 −0.708620
\(218\) −3.09897 −0.209889
\(219\) 2.75144 0.185925
\(220\) −0.980886 −0.0661313
\(221\) 16.9036 1.13706
\(222\) 0.891811 0.0598545
\(223\) −20.3912 −1.36550 −0.682748 0.730654i \(-0.739215\pi\)
−0.682748 + 0.730654i \(0.739215\pi\)
\(224\) −1.11361 −0.0744059
\(225\) 14.6811 0.978743
\(226\) −5.13579 −0.341628
\(227\) 15.0417 0.998356 0.499178 0.866500i \(-0.333635\pi\)
0.499178 + 0.866500i \(0.333635\pi\)
\(228\) 0.180143 0.0119302
\(229\) −14.5838 −0.963725 −0.481862 0.876247i \(-0.660039\pi\)
−0.481862 + 0.876247i \(0.660039\pi\)
\(230\) −0.128540 −0.00847568
\(231\) 0.856577 0.0563586
\(232\) −4.00049 −0.262645
\(233\) 17.6557 1.15667 0.578333 0.815801i \(-0.303703\pi\)
0.578333 + 0.815801i \(0.303703\pi\)
\(234\) −16.3935 −1.07168
\(235\) −1.45369 −0.0948284
\(236\) 2.85480 0.185832
\(237\) −0.731816 −0.0475366
\(238\) −3.40751 −0.220876
\(239\) 4.26804 0.276077 0.138038 0.990427i \(-0.455920\pi\)
0.138038 + 0.990427i \(0.455920\pi\)
\(240\) 0.0413825 0.00267123
\(241\) −19.2029 −1.23697 −0.618483 0.785798i \(-0.712253\pi\)
−0.618483 + 0.785798i \(0.712253\pi\)
\(242\) 7.23210 0.464897
\(243\) 4.79389 0.307528
\(244\) −12.0077 −0.768716
\(245\) −1.32316 −0.0845338
\(246\) −1.82413 −0.116302
\(247\) 5.52427 0.351501
\(248\) 9.37372 0.595232
\(249\) 0.776719 0.0492226
\(250\) −2.28508 −0.144521
\(251\) 1.45843 0.0920550 0.0460275 0.998940i \(-0.485344\pi\)
0.0460275 + 0.998940i \(0.485344\pi\)
\(252\) 3.30468 0.208175
\(253\) 2.38922 0.150209
\(254\) −12.5240 −0.785828
\(255\) 0.126626 0.00792961
\(256\) 1.00000 0.0625000
\(257\) 12.5816 0.784820 0.392410 0.919790i \(-0.371641\pi\)
0.392410 + 0.919790i \(0.371641\pi\)
\(258\) −2.20131 −0.137048
\(259\) −5.51300 −0.342561
\(260\) 1.26904 0.0787024
\(261\) 11.8716 0.734836
\(262\) −2.57515 −0.159094
\(263\) 27.4585 1.69316 0.846582 0.532259i \(-0.178657\pi\)
0.846582 + 0.532259i \(0.178657\pi\)
\(264\) −0.769192 −0.0473405
\(265\) −0.143196 −0.00879645
\(266\) −1.11361 −0.0682795
\(267\) −0.414920 −0.0253927
\(268\) −9.26742 −0.566098
\(269\) −0.813377 −0.0495924 −0.0247962 0.999693i \(-0.507894\pi\)
−0.0247962 + 0.999693i \(0.507894\pi\)
\(270\) −0.246952 −0.0150290
\(271\) −0.269699 −0.0163830 −0.00819152 0.999966i \(-0.502607\pi\)
−0.00819152 + 0.999966i \(0.502607\pi\)
\(272\) 3.05989 0.185533
\(273\) −1.10821 −0.0670720
\(274\) −4.92632 −0.297610
\(275\) 21.1242 1.27384
\(276\) −0.100799 −0.00606737
\(277\) 6.75257 0.405723 0.202861 0.979207i \(-0.434976\pi\)
0.202861 + 0.979207i \(0.434976\pi\)
\(278\) −16.8290 −1.00933
\(279\) −27.8170 −1.66536
\(280\) −0.255818 −0.0152881
\(281\) −12.3044 −0.734017 −0.367009 0.930218i \(-0.619618\pi\)
−0.367009 + 0.930218i \(0.619618\pi\)
\(282\) −1.13996 −0.0678835
\(283\) 21.2192 1.26135 0.630674 0.776047i \(-0.282778\pi\)
0.630674 + 0.776047i \(0.282778\pi\)
\(284\) 8.20192 0.486694
\(285\) 0.0413825 0.00245129
\(286\) −23.5881 −1.39479
\(287\) 11.2764 0.665625
\(288\) −2.96755 −0.174864
\(289\) −7.63708 −0.449240
\(290\) −0.918994 −0.0539652
\(291\) −0.482160 −0.0282647
\(292\) 15.2736 0.893823
\(293\) −4.08543 −0.238673 −0.119337 0.992854i \(-0.538077\pi\)
−0.119337 + 0.992854i \(0.538077\pi\)
\(294\) −1.03760 −0.0605141
\(295\) 0.655807 0.0381825
\(296\) 4.95059 0.287747
\(297\) 4.59019 0.266350
\(298\) −19.6430 −1.13789
\(299\) −3.09110 −0.178763
\(300\) −0.891207 −0.0514538
\(301\) 13.6081 0.784356
\(302\) −8.52109 −0.490334
\(303\) −0.272894 −0.0156773
\(304\) 1.00000 0.0573539
\(305\) −2.75842 −0.157947
\(306\) −9.08037 −0.519090
\(307\) −2.86108 −0.163290 −0.0816452 0.996661i \(-0.526017\pi\)
−0.0816452 + 0.996661i \(0.526017\pi\)
\(308\) 4.75499 0.270941
\(309\) 1.20902 0.0687790
\(310\) 2.15334 0.122301
\(311\) −7.66583 −0.434690 −0.217345 0.976095i \(-0.569740\pi\)
−0.217345 + 0.976095i \(0.569740\pi\)
\(312\) 0.995156 0.0563396
\(313\) −4.17760 −0.236132 −0.118066 0.993006i \(-0.537669\pi\)
−0.118066 + 0.993006i \(0.537669\pi\)
\(314\) −8.73492 −0.492940
\(315\) 0.759153 0.0427734
\(316\) −4.06243 −0.228529
\(317\) 28.2365 1.58592 0.792961 0.609272i \(-0.208538\pi\)
0.792961 + 0.609272i \(0.208538\pi\)
\(318\) −0.112292 −0.00629700
\(319\) 17.0817 0.956392
\(320\) 0.229721 0.0128418
\(321\) 3.24822 0.181298
\(322\) 0.623117 0.0347250
\(323\) 3.05989 0.170257
\(324\) 8.70899 0.483833
\(325\) −27.3298 −1.51598
\(326\) −5.89902 −0.326717
\(327\) −0.558257 −0.0308717
\(328\) −10.1260 −0.559117
\(329\) 7.04699 0.388513
\(330\) −0.176699 −0.00972698
\(331\) −20.2332 −1.11212 −0.556058 0.831144i \(-0.687687\pi\)
−0.556058 + 0.831144i \(0.687687\pi\)
\(332\) 4.31169 0.236635
\(333\) −14.6911 −0.805068
\(334\) 4.96906 0.271895
\(335\) −2.12892 −0.116315
\(336\) −0.200608 −0.0109441
\(337\) −26.6353 −1.45092 −0.725459 0.688265i \(-0.758372\pi\)
−0.725459 + 0.688265i \(0.758372\pi\)
\(338\) 17.5175 0.952827
\(339\) −0.925175 −0.0502486
\(340\) 0.702920 0.0381212
\(341\) −40.0249 −2.16747
\(342\) −2.96755 −0.160467
\(343\) 14.2095 0.767240
\(344\) −12.2198 −0.658849
\(345\) −0.0231555 −0.00124665
\(346\) −16.4703 −0.885451
\(347\) −6.57563 −0.352999 −0.176499 0.984301i \(-0.556477\pi\)
−0.176499 + 0.984301i \(0.556477\pi\)
\(348\) −0.720658 −0.0386313
\(349\) −13.3044 −0.712168 −0.356084 0.934454i \(-0.615888\pi\)
−0.356084 + 0.934454i \(0.615888\pi\)
\(350\) 5.50926 0.294482
\(351\) −5.93864 −0.316981
\(352\) −4.26991 −0.227587
\(353\) −8.67801 −0.461884 −0.230942 0.972968i \(-0.574181\pi\)
−0.230942 + 0.972968i \(0.574181\pi\)
\(354\) 0.514271 0.0273332
\(355\) 1.88415 0.100000
\(356\) −2.30328 −0.122074
\(357\) −0.613838 −0.0324877
\(358\) 0.150726 0.00796610
\(359\) 7.49472 0.395556 0.197778 0.980247i \(-0.436627\pi\)
0.197778 + 0.980247i \(0.436627\pi\)
\(360\) −0.681707 −0.0359291
\(361\) 1.00000 0.0526316
\(362\) −26.2189 −1.37803
\(363\) 1.30281 0.0683798
\(364\) −6.15185 −0.322445
\(365\) 3.50867 0.183652
\(366\) −2.16310 −0.113067
\(367\) −11.4329 −0.596793 −0.298397 0.954442i \(-0.596452\pi\)
−0.298397 + 0.954442i \(0.596452\pi\)
\(368\) −0.559549 −0.0291685
\(369\) 30.0495 1.56431
\(370\) 1.13725 0.0591229
\(371\) 0.694164 0.0360392
\(372\) 1.68861 0.0875501
\(373\) 22.2220 1.15061 0.575306 0.817938i \(-0.304883\pi\)
0.575306 + 0.817938i \(0.304883\pi\)
\(374\) −13.0654 −0.675598
\(375\) −0.411641 −0.0212570
\(376\) −6.32808 −0.326346
\(377\) −22.0998 −1.13820
\(378\) 1.19714 0.0615741
\(379\) −12.2328 −0.628357 −0.314179 0.949364i \(-0.601729\pi\)
−0.314179 + 0.949364i \(0.601729\pi\)
\(380\) 0.229721 0.0117844
\(381\) −2.25611 −0.115584
\(382\) 3.97821 0.203543
\(383\) −31.6357 −1.61651 −0.808254 0.588833i \(-0.799587\pi\)
−0.808254 + 0.588833i \(0.799587\pi\)
\(384\) 0.180143 0.00919286
\(385\) 1.09232 0.0556698
\(386\) −19.4922 −0.992128
\(387\) 36.2629 1.84335
\(388\) −2.67655 −0.135881
\(389\) −33.3039 −1.68857 −0.844287 0.535892i \(-0.819975\pi\)
−0.844287 + 0.535892i \(0.819975\pi\)
\(390\) 0.228608 0.0115760
\(391\) −1.71216 −0.0865876
\(392\) −5.75988 −0.290918
\(393\) −0.463895 −0.0234004
\(394\) 0.443923 0.0223645
\(395\) −0.933223 −0.0469556
\(396\) 12.6712 0.636749
\(397\) −17.2426 −0.865379 −0.432690 0.901543i \(-0.642435\pi\)
−0.432690 + 0.901543i \(0.642435\pi\)
\(398\) −1.10002 −0.0551390
\(399\) −0.200608 −0.0100430
\(400\) −4.94723 −0.247361
\(401\) 3.51519 0.175540 0.0877701 0.996141i \(-0.472026\pi\)
0.0877701 + 0.996141i \(0.472026\pi\)
\(402\) −1.66946 −0.0832649
\(403\) 51.7829 2.57949
\(404\) −1.51488 −0.0753679
\(405\) 2.00064 0.0994124
\(406\) 4.45496 0.221096
\(407\) −21.1385 −1.04780
\(408\) 0.551216 0.0272893
\(409\) 3.69626 0.182768 0.0913841 0.995816i \(-0.470871\pi\)
0.0913841 + 0.995816i \(0.470871\pi\)
\(410\) −2.32616 −0.114881
\(411\) −0.887440 −0.0437742
\(412\) 6.71149 0.330651
\(413\) −3.17912 −0.156434
\(414\) 1.66049 0.0816086
\(415\) 0.990484 0.0486210
\(416\) 5.52427 0.270849
\(417\) −3.03161 −0.148459
\(418\) −4.26991 −0.208848
\(419\) 6.28854 0.307215 0.153608 0.988132i \(-0.450911\pi\)
0.153608 + 0.988132i \(0.450911\pi\)
\(420\) −0.0460838 −0.00224866
\(421\) 30.0515 1.46462 0.732310 0.680971i \(-0.238442\pi\)
0.732310 + 0.680971i \(0.238442\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 18.7789 0.913061
\(424\) −0.623348 −0.0302724
\(425\) −15.1380 −0.734299
\(426\) 1.47752 0.0715859
\(427\) 13.3719 0.647111
\(428\) 18.0314 0.871578
\(429\) −4.24922 −0.205154
\(430\) −2.80715 −0.135373
\(431\) −2.18952 −0.105466 −0.0527328 0.998609i \(-0.516793\pi\)
−0.0527328 + 0.998609i \(0.516793\pi\)
\(432\) −1.07501 −0.0517214
\(433\) 18.0306 0.866496 0.433248 0.901275i \(-0.357367\pi\)
0.433248 + 0.901275i \(0.357367\pi\)
\(434\) −10.4386 −0.501070
\(435\) −0.165550 −0.00793752
\(436\) −3.09897 −0.148414
\(437\) −0.559549 −0.0267669
\(438\) 2.75144 0.131469
\(439\) −28.5483 −1.36254 −0.681268 0.732034i \(-0.738571\pi\)
−0.681268 + 0.732034i \(0.738571\pi\)
\(440\) −0.980886 −0.0467619
\(441\) 17.0927 0.813940
\(442\) 16.9036 0.804024
\(443\) 21.4218 1.01778 0.508889 0.860832i \(-0.330056\pi\)
0.508889 + 0.860832i \(0.330056\pi\)
\(444\) 0.891811 0.0423235
\(445\) −0.529112 −0.0250823
\(446\) −20.3912 −0.965551
\(447\) −3.53854 −0.167367
\(448\) −1.11361 −0.0526129
\(449\) 18.6241 0.878925 0.439463 0.898261i \(-0.355169\pi\)
0.439463 + 0.898261i \(0.355169\pi\)
\(450\) 14.6811 0.692076
\(451\) 43.2372 2.03596
\(452\) −5.13579 −0.241567
\(453\) −1.53501 −0.0721211
\(454\) 15.0417 0.705944
\(455\) −1.41321 −0.0662522
\(456\) 0.180143 0.00843595
\(457\) −10.6850 −0.499826 −0.249913 0.968268i \(-0.580402\pi\)
−0.249913 + 0.968268i \(0.580402\pi\)
\(458\) −14.5838 −0.681456
\(459\) −3.28941 −0.153537
\(460\) −0.128540 −0.00599321
\(461\) −17.8639 −0.832003 −0.416001 0.909364i \(-0.636569\pi\)
−0.416001 + 0.909364i \(0.636569\pi\)
\(462\) 0.856577 0.0398516
\(463\) 34.8728 1.62068 0.810338 0.585962i \(-0.199283\pi\)
0.810338 + 0.585962i \(0.199283\pi\)
\(464\) −4.00049 −0.185718
\(465\) 0.387908 0.0179888
\(466\) 17.6557 0.817887
\(467\) 27.8937 1.29077 0.645384 0.763858i \(-0.276697\pi\)
0.645384 + 0.763858i \(0.276697\pi\)
\(468\) −16.3935 −0.757791
\(469\) 10.3202 0.476545
\(470\) −1.45369 −0.0670538
\(471\) −1.57353 −0.0725045
\(472\) 2.85480 0.131403
\(473\) 52.1775 2.39912
\(474\) −0.731816 −0.0336134
\(475\) −4.94723 −0.226994
\(476\) −3.40751 −0.156183
\(477\) 1.84982 0.0846972
\(478\) 4.26804 0.195216
\(479\) 32.8962 1.50306 0.751532 0.659696i \(-0.229315\pi\)
0.751532 + 0.659696i \(0.229315\pi\)
\(480\) 0.0413825 0.00188884
\(481\) 27.3484 1.24698
\(482\) −19.2029 −0.874668
\(483\) 0.112250 0.00510755
\(484\) 7.23210 0.328732
\(485\) −0.614858 −0.0279193
\(486\) 4.79389 0.217455
\(487\) −40.1341 −1.81865 −0.909326 0.416085i \(-0.863402\pi\)
−0.909326 + 0.416085i \(0.863402\pi\)
\(488\) −12.0077 −0.543565
\(489\) −1.06267 −0.0480554
\(490\) −1.32316 −0.0597745
\(491\) 22.5398 1.01721 0.508603 0.861001i \(-0.330162\pi\)
0.508603 + 0.861001i \(0.330162\pi\)
\(492\) −1.82413 −0.0822381
\(493\) −12.2410 −0.551309
\(494\) 5.52427 0.248548
\(495\) 2.91083 0.130832
\(496\) 9.37372 0.420892
\(497\) −9.13371 −0.409703
\(498\) 0.776719 0.0348056
\(499\) 3.63815 0.162866 0.0814330 0.996679i \(-0.474050\pi\)
0.0814330 + 0.996679i \(0.474050\pi\)
\(500\) −2.28508 −0.102192
\(501\) 0.895140 0.0399919
\(502\) 1.45843 0.0650927
\(503\) 20.2758 0.904052 0.452026 0.892005i \(-0.350701\pi\)
0.452026 + 0.892005i \(0.350701\pi\)
\(504\) 3.30468 0.147202
\(505\) −0.347998 −0.0154857
\(506\) 2.38922 0.106214
\(507\) 3.15565 0.140147
\(508\) −12.5240 −0.555664
\(509\) −38.9237 −1.72526 −0.862632 0.505832i \(-0.831186\pi\)
−0.862632 + 0.505832i \(0.831186\pi\)
\(510\) 0.126626 0.00560708
\(511\) −17.0088 −0.752426
\(512\) 1.00000 0.0441942
\(513\) −1.07501 −0.0474628
\(514\) 12.5816 0.554951
\(515\) 1.54177 0.0679384
\(516\) −2.20131 −0.0969073
\(517\) 27.0203 1.18835
\(518\) −5.51300 −0.242227
\(519\) −2.96701 −0.130237
\(520\) 1.26904 0.0556510
\(521\) 25.0557 1.09771 0.548854 0.835918i \(-0.315064\pi\)
0.548854 + 0.835918i \(0.315064\pi\)
\(522\) 11.8716 0.519608
\(523\) −0.879046 −0.0384380 −0.0192190 0.999815i \(-0.506118\pi\)
−0.0192190 + 0.999815i \(0.506118\pi\)
\(524\) −2.57515 −0.112496
\(525\) 0.992453 0.0433142
\(526\) 27.4585 1.19725
\(527\) 28.6825 1.24943
\(528\) −0.769192 −0.0334748
\(529\) −22.6869 −0.986387
\(530\) −0.143196 −0.00622003
\(531\) −8.47176 −0.367643
\(532\) −1.11361 −0.0482809
\(533\) −55.9389 −2.42298
\(534\) −0.414920 −0.0179553
\(535\) 4.14217 0.179082
\(536\) −9.26742 −0.400291
\(537\) 0.0271521 0.00117170
\(538\) −0.813377 −0.0350672
\(539\) 24.5942 1.05935
\(540\) −0.246952 −0.0106271
\(541\) 11.7477 0.505072 0.252536 0.967588i \(-0.418735\pi\)
0.252536 + 0.967588i \(0.418735\pi\)
\(542\) −0.269699 −0.0115846
\(543\) −4.72314 −0.202689
\(544\) 3.05989 0.131192
\(545\) −0.711898 −0.0304944
\(546\) −1.10821 −0.0474270
\(547\) 25.4968 1.09017 0.545083 0.838382i \(-0.316498\pi\)
0.545083 + 0.838382i \(0.316498\pi\)
\(548\) −4.92632 −0.210442
\(549\) 35.6335 1.52080
\(550\) 21.1242 0.900739
\(551\) −4.00049 −0.170426
\(552\) −0.100799 −0.00429028
\(553\) 4.52394 0.192378
\(554\) 6.75257 0.286889
\(555\) 0.204868 0.00869614
\(556\) −16.8290 −0.713707
\(557\) −17.3617 −0.735641 −0.367820 0.929897i \(-0.619896\pi\)
−0.367820 + 0.929897i \(0.619896\pi\)
\(558\) −27.8170 −1.17759
\(559\) −67.5055 −2.85518
\(560\) −0.255818 −0.0108103
\(561\) −2.35364 −0.0993708
\(562\) −12.3044 −0.519029
\(563\) 15.6627 0.660105 0.330053 0.943963i \(-0.392933\pi\)
0.330053 + 0.943963i \(0.392933\pi\)
\(564\) −1.13996 −0.0480009
\(565\) −1.17980 −0.0496344
\(566\) 21.2192 0.891908
\(567\) −9.69838 −0.407294
\(568\) 8.20192 0.344145
\(569\) 33.3860 1.39962 0.699808 0.714331i \(-0.253269\pi\)
0.699808 + 0.714331i \(0.253269\pi\)
\(570\) 0.0413825 0.00173332
\(571\) 7.59220 0.317724 0.158862 0.987301i \(-0.449218\pi\)
0.158862 + 0.987301i \(0.449218\pi\)
\(572\) −23.5881 −0.986268
\(573\) 0.716646 0.0299383
\(574\) 11.2764 0.470668
\(575\) 2.76822 0.115443
\(576\) −2.96755 −0.123648
\(577\) −21.1446 −0.880262 −0.440131 0.897934i \(-0.645068\pi\)
−0.440131 + 0.897934i \(0.645068\pi\)
\(578\) −7.63708 −0.317661
\(579\) −3.51138 −0.145928
\(580\) −0.918994 −0.0381592
\(581\) −4.80152 −0.199201
\(582\) −0.482160 −0.0199862
\(583\) 2.66164 0.110234
\(584\) 15.2736 0.632028
\(585\) −3.76593 −0.155702
\(586\) −4.08543 −0.168768
\(587\) 34.8324 1.43769 0.718844 0.695172i \(-0.244672\pi\)
0.718844 + 0.695172i \(0.244672\pi\)
\(588\) −1.03760 −0.0427899
\(589\) 9.37372 0.386237
\(590\) 0.655807 0.0269991
\(591\) 0.0799695 0.00328951
\(592\) 4.95059 0.203468
\(593\) 9.49659 0.389978 0.194989 0.980805i \(-0.437533\pi\)
0.194989 + 0.980805i \(0.437533\pi\)
\(594\) 4.59019 0.188338
\(595\) −0.782775 −0.0320907
\(596\) −19.6430 −0.804609
\(597\) −0.198160 −0.00811016
\(598\) −3.09110 −0.126404
\(599\) 2.83024 0.115641 0.0578203 0.998327i \(-0.481585\pi\)
0.0578203 + 0.998327i \(0.481585\pi\)
\(600\) −0.891207 −0.0363834
\(601\) 15.2341 0.621411 0.310705 0.950506i \(-0.399435\pi\)
0.310705 + 0.950506i \(0.399435\pi\)
\(602\) 13.6081 0.554623
\(603\) 27.5015 1.11995
\(604\) −8.52109 −0.346718
\(605\) 1.66136 0.0675440
\(606\) −0.272894 −0.0110855
\(607\) 7.71824 0.313274 0.156637 0.987656i \(-0.449935\pi\)
0.156637 + 0.987656i \(0.449935\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0.802529 0.0325201
\(610\) −2.75842 −0.111685
\(611\) −34.9580 −1.41425
\(612\) −9.08037 −0.367052
\(613\) −14.0496 −0.567458 −0.283729 0.958904i \(-0.591572\pi\)
−0.283729 + 0.958904i \(0.591572\pi\)
\(614\) −2.86108 −0.115464
\(615\) −0.419040 −0.0168973
\(616\) 4.75499 0.191584
\(617\) 24.6093 0.990732 0.495366 0.868684i \(-0.335034\pi\)
0.495366 + 0.868684i \(0.335034\pi\)
\(618\) 1.20902 0.0486341
\(619\) 25.3138 1.01745 0.508723 0.860930i \(-0.330118\pi\)
0.508723 + 0.860930i \(0.330118\pi\)
\(620\) 2.15334 0.0864801
\(621\) 0.601521 0.0241382
\(622\) −7.66583 −0.307372
\(623\) 2.56495 0.102763
\(624\) 0.995156 0.0398381
\(625\) 24.2112 0.968448
\(626\) −4.17760 −0.166970
\(627\) −0.769192 −0.0307186
\(628\) −8.73492 −0.348561
\(629\) 15.1482 0.604000
\(630\) 0.759153 0.0302454
\(631\) 47.2848 1.88238 0.941190 0.337878i \(-0.109709\pi\)
0.941190 + 0.337878i \(0.109709\pi\)
\(632\) −4.06243 −0.161595
\(633\) −0.180143 −0.00716003
\(634\) 28.2365 1.12142
\(635\) −2.87703 −0.114171
\(636\) −0.112292 −0.00445265
\(637\) −31.8191 −1.26072
\(638\) 17.0817 0.676271
\(639\) −24.3396 −0.962860
\(640\) 0.229721 0.00908051
\(641\) 0.909587 0.0359265 0.0179633 0.999839i \(-0.494282\pi\)
0.0179633 + 0.999839i \(0.494282\pi\)
\(642\) 3.24822 0.128197
\(643\) −34.6847 −1.36783 −0.683915 0.729562i \(-0.739724\pi\)
−0.683915 + 0.729562i \(0.739724\pi\)
\(644\) 0.623117 0.0245543
\(645\) −0.505686 −0.0199114
\(646\) 3.05989 0.120390
\(647\) 0.935069 0.0367614 0.0183807 0.999831i \(-0.494149\pi\)
0.0183807 + 0.999831i \(0.494149\pi\)
\(648\) 8.70899 0.342121
\(649\) −12.1897 −0.478489
\(650\) −27.3298 −1.07196
\(651\) −1.88044 −0.0737003
\(652\) −5.89902 −0.231024
\(653\) −12.8674 −0.503540 −0.251770 0.967787i \(-0.581013\pi\)
−0.251770 + 0.967787i \(0.581013\pi\)
\(654\) −0.558257 −0.0218296
\(655\) −0.591566 −0.0231144
\(656\) −10.1260 −0.395355
\(657\) −45.3253 −1.76831
\(658\) 7.04699 0.274720
\(659\) −3.02116 −0.117688 −0.0588439 0.998267i \(-0.518741\pi\)
−0.0588439 + 0.998267i \(0.518741\pi\)
\(660\) −0.176699 −0.00687801
\(661\) 34.2100 1.33061 0.665307 0.746570i \(-0.268301\pi\)
0.665307 + 0.746570i \(0.268301\pi\)
\(662\) −20.2332 −0.786385
\(663\) 3.04507 0.118261
\(664\) 4.31169 0.167326
\(665\) −0.255818 −0.00992020
\(666\) −14.6911 −0.569269
\(667\) 2.23847 0.0866739
\(668\) 4.96906 0.192259
\(669\) −3.67332 −0.142019
\(670\) −2.12892 −0.0822472
\(671\) 51.2719 1.97933
\(672\) −0.200608 −0.00773862
\(673\) −4.36989 −0.168447 −0.0842234 0.996447i \(-0.526841\pi\)
−0.0842234 + 0.996447i \(0.526841\pi\)
\(674\) −26.6353 −1.02595
\(675\) 5.31832 0.204702
\(676\) 17.5175 0.673750
\(677\) 27.0152 1.03828 0.519140 0.854689i \(-0.326252\pi\)
0.519140 + 0.854689i \(0.326252\pi\)
\(678\) −0.925175 −0.0355311
\(679\) 2.98062 0.114386
\(680\) 0.702920 0.0269557
\(681\) 2.70966 0.103834
\(682\) −40.0249 −1.53263
\(683\) 17.6562 0.675595 0.337797 0.941219i \(-0.390318\pi\)
0.337797 + 0.941219i \(0.390318\pi\)
\(684\) −2.96755 −0.113467
\(685\) −1.13168 −0.0432392
\(686\) 14.2095 0.542520
\(687\) −2.62716 −0.100233
\(688\) −12.2198 −0.465876
\(689\) −3.44354 −0.131188
\(690\) −0.0231555 −0.000881516 0
\(691\) −20.7315 −0.788664 −0.394332 0.918968i \(-0.629024\pi\)
−0.394332 + 0.918968i \(0.629024\pi\)
\(692\) −16.4703 −0.626108
\(693\) −14.1107 −0.536020
\(694\) −6.57563 −0.249608
\(695\) −3.86596 −0.146644
\(696\) −0.720658 −0.0273165
\(697\) −30.9845 −1.17362
\(698\) −13.3044 −0.503579
\(699\) 3.18055 0.120300
\(700\) 5.50926 0.208231
\(701\) −17.2579 −0.651820 −0.325910 0.945401i \(-0.605671\pi\)
−0.325910 + 0.945401i \(0.605671\pi\)
\(702\) −5.93864 −0.224140
\(703\) 4.95059 0.186715
\(704\) −4.26991 −0.160928
\(705\) −0.261872 −0.00986266
\(706\) −8.67801 −0.326601
\(707\) 1.68697 0.0634452
\(708\) 0.514271 0.0193275
\(709\) −38.7954 −1.45699 −0.728497 0.685049i \(-0.759781\pi\)
−0.728497 + 0.685049i \(0.759781\pi\)
\(710\) 1.88415 0.0707109
\(711\) 12.0554 0.452115
\(712\) −2.30328 −0.0863192
\(713\) −5.24506 −0.196429
\(714\) −0.613838 −0.0229723
\(715\) −5.41867 −0.202647
\(716\) 0.150726 0.00563289
\(717\) 0.768856 0.0287135
\(718\) 7.49472 0.279701
\(719\) −18.4676 −0.688727 −0.344364 0.938836i \(-0.611905\pi\)
−0.344364 + 0.938836i \(0.611905\pi\)
\(720\) −0.681707 −0.0254057
\(721\) −7.47395 −0.278344
\(722\) 1.00000 0.0372161
\(723\) −3.45926 −0.128651
\(724\) −26.2189 −0.974418
\(725\) 19.7913 0.735031
\(726\) 1.30281 0.0483518
\(727\) −3.11969 −0.115703 −0.0578514 0.998325i \(-0.518425\pi\)
−0.0578514 + 0.998325i \(0.518425\pi\)
\(728\) −6.15185 −0.228003
\(729\) −25.2634 −0.935681
\(730\) 3.50867 0.129862
\(731\) −37.3913 −1.38297
\(732\) −2.16310 −0.0799506
\(733\) 52.9978 1.95752 0.978759 0.205012i \(-0.0657233\pi\)
0.978759 + 0.205012i \(0.0657233\pi\)
\(734\) −11.4329 −0.421997
\(735\) −0.238358 −0.00879197
\(736\) −0.559549 −0.0206253
\(737\) 39.5710 1.45762
\(738\) 30.0495 1.10614
\(739\) 7.47621 0.275017 0.137508 0.990501i \(-0.456091\pi\)
0.137508 + 0.990501i \(0.456091\pi\)
\(740\) 1.13725 0.0418062
\(741\) 0.995156 0.0365580
\(742\) 0.694164 0.0254836
\(743\) −46.1925 −1.69464 −0.847318 0.531085i \(-0.821784\pi\)
−0.847318 + 0.531085i \(0.821784\pi\)
\(744\) 1.68861 0.0619073
\(745\) −4.51240 −0.165322
\(746\) 22.2220 0.813606
\(747\) −12.7952 −0.468150
\(748\) −13.0654 −0.477720
\(749\) −20.0798 −0.733701
\(750\) −0.411641 −0.0150310
\(751\) 16.1242 0.588380 0.294190 0.955747i \(-0.404950\pi\)
0.294190 + 0.955747i \(0.404950\pi\)
\(752\) −6.32808 −0.230761
\(753\) 0.262725 0.00957422
\(754\) −22.0998 −0.804825
\(755\) −1.95747 −0.0712397
\(756\) 1.19714 0.0435395
\(757\) 31.3916 1.14095 0.570474 0.821316i \(-0.306760\pi\)
0.570474 + 0.821316i \(0.306760\pi\)
\(758\) −12.2328 −0.444316
\(759\) 0.430401 0.0156226
\(760\) 0.229721 0.00833284
\(761\) 12.4286 0.450537 0.225268 0.974297i \(-0.427674\pi\)
0.225268 + 0.974297i \(0.427674\pi\)
\(762\) −2.25611 −0.0817303
\(763\) 3.45103 0.124936
\(764\) 3.97821 0.143927
\(765\) −2.08595 −0.0754176
\(766\) −31.6357 −1.14304
\(767\) 15.7707 0.569446
\(768\) 0.180143 0.00650034
\(769\) 23.4742 0.846500 0.423250 0.906013i \(-0.360889\pi\)
0.423250 + 0.906013i \(0.360889\pi\)
\(770\) 1.09232 0.0393645
\(771\) 2.26649 0.0816255
\(772\) −19.4922 −0.701540
\(773\) 49.3268 1.77416 0.887082 0.461613i \(-0.152729\pi\)
0.887082 + 0.461613i \(0.152729\pi\)
\(774\) 36.2629 1.30344
\(775\) −46.3739 −1.66580
\(776\) −2.67655 −0.0960825
\(777\) −0.993126 −0.0356282
\(778\) −33.3039 −1.19400
\(779\) −10.1260 −0.362803
\(780\) 0.228608 0.00818547
\(781\) −35.0214 −1.25317
\(782\) −1.71216 −0.0612266
\(783\) 4.30056 0.153690
\(784\) −5.75988 −0.205710
\(785\) −2.00659 −0.0716183
\(786\) −0.463895 −0.0165466
\(787\) 10.4308 0.371818 0.185909 0.982567i \(-0.440477\pi\)
0.185909 + 0.982567i \(0.440477\pi\)
\(788\) 0.443923 0.0158141
\(789\) 4.94645 0.176098
\(790\) −0.933223 −0.0332026
\(791\) 5.71924 0.203353
\(792\) 12.6712 0.450250
\(793\) −66.3339 −2.35559
\(794\) −17.2426 −0.611916
\(795\) −0.0257957 −0.000914878 0
\(796\) −1.10002 −0.0389892
\(797\) 8.25571 0.292432 0.146216 0.989253i \(-0.453291\pi\)
0.146216 + 0.989253i \(0.453291\pi\)
\(798\) −0.200608 −0.00710144
\(799\) −19.3632 −0.685022
\(800\) −4.94723 −0.174911
\(801\) 6.83511 0.241507
\(802\) 3.51519 0.124126
\(803\) −65.2171 −2.30146
\(804\) −1.66946 −0.0588772
\(805\) 0.143143 0.00504512
\(806\) 51.7829 1.82397
\(807\) −0.146524 −0.00515788
\(808\) −1.51488 −0.0532932
\(809\) −4.02957 −0.141672 −0.0708361 0.997488i \(-0.522567\pi\)
−0.0708361 + 0.997488i \(0.522567\pi\)
\(810\) 2.00064 0.0702951
\(811\) −7.86026 −0.276011 −0.138006 0.990431i \(-0.544069\pi\)
−0.138006 + 0.990431i \(0.544069\pi\)
\(812\) 4.45496 0.156339
\(813\) −0.0485843 −0.00170392
\(814\) −21.1385 −0.740905
\(815\) −1.35513 −0.0474680
\(816\) 0.551216 0.0192964
\(817\) −12.2198 −0.427517
\(818\) 3.69626 0.129237
\(819\) 18.2559 0.637914
\(820\) −2.32616 −0.0812330
\(821\) −28.1334 −0.981864 −0.490932 0.871198i \(-0.663344\pi\)
−0.490932 + 0.871198i \(0.663344\pi\)
\(822\) −0.887440 −0.0309530
\(823\) 14.5052 0.505621 0.252810 0.967516i \(-0.418645\pi\)
0.252810 + 0.967516i \(0.418645\pi\)
\(824\) 6.71149 0.233806
\(825\) 3.80537 0.132486
\(826\) −3.17912 −0.110616
\(827\) 1.43755 0.0499886 0.0249943 0.999688i \(-0.492043\pi\)
0.0249943 + 0.999688i \(0.492043\pi\)
\(828\) 1.66049 0.0577060
\(829\) −3.82894 −0.132984 −0.0664922 0.997787i \(-0.521181\pi\)
−0.0664922 + 0.997787i \(0.521181\pi\)
\(830\) 0.990484 0.0343802
\(831\) 1.21643 0.0421974
\(832\) 5.52427 0.191519
\(833\) −17.6246 −0.610656
\(834\) −3.03161 −0.104976
\(835\) 1.14150 0.0395031
\(836\) −4.26991 −0.147678
\(837\) −10.0768 −0.348306
\(838\) 6.28854 0.217234
\(839\) −5.82105 −0.200965 −0.100482 0.994939i \(-0.532039\pi\)
−0.100482 + 0.994939i \(0.532039\pi\)
\(840\) −0.0460838 −0.00159004
\(841\) −12.9961 −0.448142
\(842\) 30.0515 1.03564
\(843\) −2.21654 −0.0763418
\(844\) −1.00000 −0.0344214
\(845\) 4.02413 0.138434
\(846\) 18.7789 0.645632
\(847\) −8.05371 −0.276729
\(848\) −0.623348 −0.0214059
\(849\) 3.82248 0.131187
\(850\) −15.1380 −0.519228
\(851\) −2.77010 −0.0949577
\(852\) 1.47752 0.0506188
\(853\) −14.0942 −0.482576 −0.241288 0.970454i \(-0.577570\pi\)
−0.241288 + 0.970454i \(0.577570\pi\)
\(854\) 13.3719 0.457576
\(855\) −0.681707 −0.0233139
\(856\) 18.0314 0.616299
\(857\) −2.59336 −0.0885875 −0.0442938 0.999019i \(-0.514104\pi\)
−0.0442938 + 0.999019i \(0.514104\pi\)
\(858\) −4.24922 −0.145066
\(859\) −48.2396 −1.64592 −0.822958 0.568103i \(-0.807678\pi\)
−0.822958 + 0.568103i \(0.807678\pi\)
\(860\) −2.80715 −0.0957229
\(861\) 2.03136 0.0692286
\(862\) −2.18952 −0.0745755
\(863\) −27.8447 −0.947845 −0.473922 0.880567i \(-0.657162\pi\)
−0.473922 + 0.880567i \(0.657162\pi\)
\(864\) −1.07501 −0.0365726
\(865\) −3.78358 −0.128645
\(866\) 18.0306 0.612705
\(867\) −1.37576 −0.0467234
\(868\) −10.4386 −0.354310
\(869\) 17.3462 0.588429
\(870\) −0.165550 −0.00561267
\(871\) −51.1957 −1.73470
\(872\) −3.09897 −0.104944
\(873\) 7.94279 0.268823
\(874\) −0.559549 −0.0189270
\(875\) 2.54468 0.0860260
\(876\) 2.75144 0.0929624
\(877\) 29.6613 1.00159 0.500795 0.865566i \(-0.333041\pi\)
0.500795 + 0.865566i \(0.333041\pi\)
\(878\) −28.5483 −0.963458
\(879\) −0.735960 −0.0248233
\(880\) −0.980886 −0.0330656
\(881\) −0.579311 −0.0195175 −0.00975874 0.999952i \(-0.503106\pi\)
−0.00975874 + 0.999952i \(0.503106\pi\)
\(882\) 17.0927 0.575542
\(883\) 46.2508 1.55646 0.778232 0.627977i \(-0.216117\pi\)
0.778232 + 0.627977i \(0.216117\pi\)
\(884\) 16.9036 0.568531
\(885\) 0.118139 0.00397119
\(886\) 21.4218 0.719678
\(887\) 58.8398 1.97565 0.987824 0.155575i \(-0.0497229\pi\)
0.987824 + 0.155575i \(0.0497229\pi\)
\(888\) 0.891811 0.0299272
\(889\) 13.9468 0.467762
\(890\) −0.529112 −0.0177359
\(891\) −37.1866 −1.24580
\(892\) −20.3912 −0.682748
\(893\) −6.32808 −0.211761
\(894\) −3.53854 −0.118347
\(895\) 0.0346248 0.00115738
\(896\) −1.11361 −0.0372030
\(897\) −0.556838 −0.0185923
\(898\) 18.6241 0.621494
\(899\) −37.4994 −1.25068
\(900\) 14.6811 0.489371
\(901\) −1.90737 −0.0635439
\(902\) 43.2372 1.43964
\(903\) 2.45139 0.0815772
\(904\) −5.13579 −0.170814
\(905\) −6.02302 −0.200212
\(906\) −1.53501 −0.0509973
\(907\) 39.6193 1.31554 0.657768 0.753221i \(-0.271501\pi\)
0.657768 + 0.753221i \(0.271501\pi\)
\(908\) 15.0417 0.499178
\(909\) 4.49547 0.149105
\(910\) −1.41321 −0.0468474
\(911\) 17.3758 0.575687 0.287843 0.957677i \(-0.407062\pi\)
0.287843 + 0.957677i \(0.407062\pi\)
\(912\) 0.180143 0.00596512
\(913\) −18.4105 −0.609299
\(914\) −10.6850 −0.353430
\(915\) −0.496910 −0.0164273
\(916\) −14.5838 −0.481862
\(917\) 2.86771 0.0947000
\(918\) −3.28941 −0.108567
\(919\) 52.2347 1.72306 0.861532 0.507703i \(-0.169505\pi\)
0.861532 + 0.507703i \(0.169505\pi\)
\(920\) −0.128540 −0.00423784
\(921\) −0.515402 −0.0169831
\(922\) −17.8639 −0.588315
\(923\) 45.3096 1.49138
\(924\) 0.856577 0.0281793
\(925\) −24.4917 −0.805281
\(926\) 34.8728 1.14599
\(927\) −19.9167 −0.654149
\(928\) −4.00049 −0.131322
\(929\) 3.72749 0.122295 0.0611474 0.998129i \(-0.480524\pi\)
0.0611474 + 0.998129i \(0.480524\pi\)
\(930\) 0.387908 0.0127200
\(931\) −5.75988 −0.188773
\(932\) 17.6557 0.578333
\(933\) −1.38094 −0.0452101
\(934\) 27.8937 0.912711
\(935\) −3.00140 −0.0981563
\(936\) −16.3935 −0.535839
\(937\) 8.87541 0.289947 0.144974 0.989436i \(-0.453690\pi\)
0.144974 + 0.989436i \(0.453690\pi\)
\(938\) 10.3202 0.336968
\(939\) −0.752563 −0.0245590
\(940\) −1.45369 −0.0474142
\(941\) 49.6865 1.61973 0.809867 0.586614i \(-0.199539\pi\)
0.809867 + 0.586614i \(0.199539\pi\)
\(942\) −1.57353 −0.0512684
\(943\) 5.66601 0.184511
\(944\) 2.85480 0.0929159
\(945\) 0.275007 0.00894598
\(946\) 52.1775 1.69644
\(947\) 21.3104 0.692495 0.346248 0.938143i \(-0.387456\pi\)
0.346248 + 0.938143i \(0.387456\pi\)
\(948\) −0.731816 −0.0237683
\(949\) 84.3757 2.73895
\(950\) −4.94723 −0.160509
\(951\) 5.08660 0.164944
\(952\) −3.40751 −0.110438
\(953\) 25.2963 0.819429 0.409715 0.912214i \(-0.365628\pi\)
0.409715 + 0.912214i \(0.365628\pi\)
\(954\) 1.84982 0.0598900
\(955\) 0.913878 0.0295724
\(956\) 4.26804 0.138038
\(957\) 3.07714 0.0994699
\(958\) 32.8962 1.06283
\(959\) 5.48598 0.177152
\(960\) 0.0413825 0.00133561
\(961\) 56.8666 1.83441
\(962\) 27.3484 0.881746
\(963\) −53.5089 −1.72430
\(964\) −19.2029 −0.618483
\(965\) −4.47777 −0.144144
\(966\) 0.112250 0.00361158
\(967\) 26.3850 0.848483 0.424241 0.905549i \(-0.360541\pi\)
0.424241 + 0.905549i \(0.360541\pi\)
\(968\) 7.23210 0.232449
\(969\) 0.551216 0.0177076
\(970\) −0.614858 −0.0197419
\(971\) −36.0319 −1.15632 −0.578160 0.815924i \(-0.696229\pi\)
−0.578160 + 0.815924i \(0.696229\pi\)
\(972\) 4.79389 0.153764
\(973\) 18.7408 0.600804
\(974\) −40.1341 −1.28598
\(975\) −4.92326 −0.157671
\(976\) −12.0077 −0.384358
\(977\) −10.8656 −0.347620 −0.173810 0.984779i \(-0.555608\pi\)
−0.173810 + 0.984779i \(0.555608\pi\)
\(978\) −1.06267 −0.0339803
\(979\) 9.83481 0.314322
\(980\) −1.32316 −0.0422669
\(981\) 9.19635 0.293617
\(982\) 22.5398 0.719273
\(983\) −40.6673 −1.29708 −0.648542 0.761179i \(-0.724621\pi\)
−0.648542 + 0.761179i \(0.724621\pi\)
\(984\) −1.82413 −0.0581512
\(985\) 0.101978 0.00324930
\(986\) −12.2410 −0.389834
\(987\) 1.26946 0.0404075
\(988\) 5.52427 0.175750
\(989\) 6.83759 0.217423
\(990\) 2.91083 0.0925121
\(991\) −6.98112 −0.221763 −0.110881 0.993834i \(-0.535367\pi\)
−0.110881 + 0.993834i \(0.535367\pi\)
\(992\) 9.37372 0.297616
\(993\) −3.64486 −0.115666
\(994\) −9.13371 −0.289704
\(995\) −0.252697 −0.00801104
\(996\) 0.776719 0.0246113
\(997\) −4.59083 −0.145393 −0.0726966 0.997354i \(-0.523160\pi\)
−0.0726966 + 0.997354i \(0.523160\pi\)
\(998\) 3.63815 0.115164
\(999\) −5.32193 −0.168378
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 \(a_p\))