Properties

Label 6034.2.a.n.1.8
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.920246 q^{3}\) \(+1.00000 q^{4}\) \(+2.96551 q^{5}\) \(+0.920246 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.15315 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.920246 q^{3}\) \(+1.00000 q^{4}\) \(+2.96551 q^{5}\) \(+0.920246 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.15315 q^{9}\) \(-2.96551 q^{10}\) \(-3.73387 q^{11}\) \(-0.920246 q^{12}\) \(-4.18929 q^{13}\) \(+1.00000 q^{14}\) \(-2.72900 q^{15}\) \(+1.00000 q^{16}\) \(+5.64502 q^{17}\) \(+2.15315 q^{18}\) \(+1.59892 q^{19}\) \(+2.96551 q^{20}\) \(+0.920246 q^{21}\) \(+3.73387 q^{22}\) \(+4.99189 q^{23}\) \(+0.920246 q^{24}\) \(+3.79427 q^{25}\) \(+4.18929 q^{26}\) \(+4.74216 q^{27}\) \(-1.00000 q^{28}\) \(-0.281679 q^{29}\) \(+2.72900 q^{30}\) \(-0.595843 q^{31}\) \(-1.00000 q^{32}\) \(+3.43608 q^{33}\) \(-5.64502 q^{34}\) \(-2.96551 q^{35}\) \(-2.15315 q^{36}\) \(-1.75109 q^{37}\) \(-1.59892 q^{38}\) \(+3.85518 q^{39}\) \(-2.96551 q^{40}\) \(+1.43359 q^{41}\) \(-0.920246 q^{42}\) \(+7.07586 q^{43}\) \(-3.73387 q^{44}\) \(-6.38519 q^{45}\) \(-4.99189 q^{46}\) \(-8.92805 q^{47}\) \(-0.920246 q^{48}\) \(+1.00000 q^{49}\) \(-3.79427 q^{50}\) \(-5.19480 q^{51}\) \(-4.18929 q^{52}\) \(-10.7665 q^{53}\) \(-4.74216 q^{54}\) \(-11.0729 q^{55}\) \(+1.00000 q^{56}\) \(-1.47140 q^{57}\) \(+0.281679 q^{58}\) \(+2.59695 q^{59}\) \(-2.72900 q^{60}\) \(-11.3867 q^{61}\) \(+0.595843 q^{62}\) \(+2.15315 q^{63}\) \(+1.00000 q^{64}\) \(-12.4234 q^{65}\) \(-3.43608 q^{66}\) \(-0.827398 q^{67}\) \(+5.64502 q^{68}\) \(-4.59377 q^{69}\) \(+2.96551 q^{70}\) \(-8.62062 q^{71}\) \(+2.15315 q^{72}\) \(+0.950530 q^{73}\) \(+1.75109 q^{74}\) \(-3.49166 q^{75}\) \(+1.59892 q^{76}\) \(+3.73387 q^{77}\) \(-3.85518 q^{78}\) \(+13.6713 q^{79}\) \(+2.96551 q^{80}\) \(+2.09549 q^{81}\) \(-1.43359 q^{82}\) \(+10.7904 q^{83}\) \(+0.920246 q^{84}\) \(+16.7404 q^{85}\) \(-7.07586 q^{86}\) \(+0.259214 q^{87}\) \(+3.73387 q^{88}\) \(-5.53491 q^{89}\) \(+6.38519 q^{90}\) \(+4.18929 q^{91}\) \(+4.99189 q^{92}\) \(+0.548322 q^{93}\) \(+8.92805 q^{94}\) \(+4.74161 q^{95}\) \(+0.920246 q^{96}\) \(+4.82510 q^{97}\) \(-1.00000 q^{98}\) \(+8.03958 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.920246 −0.531304 −0.265652 0.964069i \(-0.585587\pi\)
−0.265652 + 0.964069i \(0.585587\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.96551 1.32622 0.663109 0.748523i \(-0.269237\pi\)
0.663109 + 0.748523i \(0.269237\pi\)
\(6\) 0.920246 0.375689
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.15315 −0.717716
\(10\) −2.96551 −0.937778
\(11\) −3.73387 −1.12580 −0.562902 0.826523i \(-0.690315\pi\)
−0.562902 + 0.826523i \(0.690315\pi\)
\(12\) −0.920246 −0.265652
\(13\) −4.18929 −1.16190 −0.580950 0.813939i \(-0.697319\pi\)
−0.580950 + 0.813939i \(0.697319\pi\)
\(14\) 1.00000 0.267261
\(15\) −2.72900 −0.704625
\(16\) 1.00000 0.250000
\(17\) 5.64502 1.36912 0.684559 0.728958i \(-0.259995\pi\)
0.684559 + 0.728958i \(0.259995\pi\)
\(18\) 2.15315 0.507502
\(19\) 1.59892 0.366817 0.183408 0.983037i \(-0.441287\pi\)
0.183408 + 0.983037i \(0.441287\pi\)
\(20\) 2.96551 0.663109
\(21\) 0.920246 0.200814
\(22\) 3.73387 0.796064
\(23\) 4.99189 1.04088 0.520441 0.853898i \(-0.325768\pi\)
0.520441 + 0.853898i \(0.325768\pi\)
\(24\) 0.920246 0.187844
\(25\) 3.79427 0.758854
\(26\) 4.18929 0.821588
\(27\) 4.74216 0.912630
\(28\) −1.00000 −0.188982
\(29\) −0.281679 −0.0523066 −0.0261533 0.999658i \(-0.508326\pi\)
−0.0261533 + 0.999658i \(0.508326\pi\)
\(30\) 2.72900 0.498245
\(31\) −0.595843 −0.107017 −0.0535083 0.998567i \(-0.517040\pi\)
−0.0535083 + 0.998567i \(0.517040\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.43608 0.598145
\(34\) −5.64502 −0.968112
\(35\) −2.96551 −0.501263
\(36\) −2.15315 −0.358858
\(37\) −1.75109 −0.287878 −0.143939 0.989587i \(-0.545977\pi\)
−0.143939 + 0.989587i \(0.545977\pi\)
\(38\) −1.59892 −0.259379
\(39\) 3.85518 0.617323
\(40\) −2.96551 −0.468889
\(41\) 1.43359 0.223889 0.111945 0.993714i \(-0.464292\pi\)
0.111945 + 0.993714i \(0.464292\pi\)
\(42\) −0.920246 −0.141997
\(43\) 7.07586 1.07906 0.539529 0.841967i \(-0.318602\pi\)
0.539529 + 0.841967i \(0.318602\pi\)
\(44\) −3.73387 −0.562902
\(45\) −6.38519 −0.951848
\(46\) −4.99189 −0.736014
\(47\) −8.92805 −1.30229 −0.651145 0.758953i \(-0.725711\pi\)
−0.651145 + 0.758953i \(0.725711\pi\)
\(48\) −0.920246 −0.132826
\(49\) 1.00000 0.142857
\(50\) −3.79427 −0.536591
\(51\) −5.19480 −0.727418
\(52\) −4.18929 −0.580950
\(53\) −10.7665 −1.47889 −0.739447 0.673214i \(-0.764913\pi\)
−0.739447 + 0.673214i \(0.764913\pi\)
\(54\) −4.74216 −0.645327
\(55\) −11.0729 −1.49306
\(56\) 1.00000 0.133631
\(57\) −1.47140 −0.194891
\(58\) 0.281679 0.0369863
\(59\) 2.59695 0.338094 0.169047 0.985608i \(-0.445931\pi\)
0.169047 + 0.985608i \(0.445931\pi\)
\(60\) −2.72900 −0.352313
\(61\) −11.3867 −1.45792 −0.728960 0.684556i \(-0.759996\pi\)
−0.728960 + 0.684556i \(0.759996\pi\)
\(62\) 0.595843 0.0756721
\(63\) 2.15315 0.271271
\(64\) 1.00000 0.125000
\(65\) −12.4234 −1.54093
\(66\) −3.43608 −0.422952
\(67\) −0.827398 −0.101083 −0.0505414 0.998722i \(-0.516095\pi\)
−0.0505414 + 0.998722i \(0.516095\pi\)
\(68\) 5.64502 0.684559
\(69\) −4.59377 −0.553025
\(70\) 2.96551 0.354447
\(71\) −8.62062 −1.02308 −0.511540 0.859260i \(-0.670925\pi\)
−0.511540 + 0.859260i \(0.670925\pi\)
\(72\) 2.15315 0.253751
\(73\) 0.950530 0.111251 0.0556256 0.998452i \(-0.482285\pi\)
0.0556256 + 0.998452i \(0.482285\pi\)
\(74\) 1.75109 0.203561
\(75\) −3.49166 −0.403182
\(76\) 1.59892 0.183408
\(77\) 3.73387 0.425514
\(78\) −3.85518 −0.436513
\(79\) 13.6713 1.53814 0.769070 0.639165i \(-0.220720\pi\)
0.769070 + 0.639165i \(0.220720\pi\)
\(80\) 2.96551 0.331555
\(81\) 2.09549 0.232832
\(82\) −1.43359 −0.158314
\(83\) 10.7904 1.18440 0.592199 0.805792i \(-0.298260\pi\)
0.592199 + 0.805792i \(0.298260\pi\)
\(84\) 0.920246 0.100407
\(85\) 16.7404 1.81575
\(86\) −7.07586 −0.763009
\(87\) 0.259214 0.0277907
\(88\) 3.73387 0.398032
\(89\) −5.53491 −0.586699 −0.293350 0.956005i \(-0.594770\pi\)
−0.293350 + 0.956005i \(0.594770\pi\)
\(90\) 6.38519 0.673058
\(91\) 4.18929 0.439157
\(92\) 4.99189 0.520441
\(93\) 0.548322 0.0568583
\(94\) 8.92805 0.920858
\(95\) 4.74161 0.486479
\(96\) 0.920246 0.0939222
\(97\) 4.82510 0.489914 0.244957 0.969534i \(-0.421226\pi\)
0.244957 + 0.969534i \(0.421226\pi\)
\(98\) −1.00000 −0.101015
\(99\) 8.03958 0.808008
\(100\) 3.79427 0.379427
\(101\) 11.0551 1.10002 0.550010 0.835158i \(-0.314624\pi\)
0.550010 + 0.835158i \(0.314624\pi\)
\(102\) 5.19480 0.514362
\(103\) 14.8392 1.46215 0.731075 0.682297i \(-0.239019\pi\)
0.731075 + 0.682297i \(0.239019\pi\)
\(104\) 4.18929 0.410794
\(105\) 2.72900 0.266323
\(106\) 10.7665 1.04574
\(107\) −5.78284 −0.559048 −0.279524 0.960139i \(-0.590177\pi\)
−0.279524 + 0.960139i \(0.590177\pi\)
\(108\) 4.74216 0.456315
\(109\) −1.51331 −0.144949 −0.0724744 0.997370i \(-0.523090\pi\)
−0.0724744 + 0.997370i \(0.523090\pi\)
\(110\) 11.0729 1.05575
\(111\) 1.61144 0.152951
\(112\) −1.00000 −0.0944911
\(113\) 3.08038 0.289777 0.144889 0.989448i \(-0.453718\pi\)
0.144889 + 0.989448i \(0.453718\pi\)
\(114\) 1.47140 0.137809
\(115\) 14.8035 1.38044
\(116\) −0.281679 −0.0261533
\(117\) 9.02016 0.833914
\(118\) −2.59695 −0.239069
\(119\) −5.64502 −0.517478
\(120\) 2.72900 0.249123
\(121\) 2.94181 0.267437
\(122\) 11.3867 1.03091
\(123\) −1.31926 −0.118953
\(124\) −0.595843 −0.0535083
\(125\) −3.57561 −0.319812
\(126\) −2.15315 −0.191818
\(127\) −0.225215 −0.0199846 −0.00999231 0.999950i \(-0.503181\pi\)
−0.00999231 + 0.999950i \(0.503181\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.51153 −0.573308
\(130\) 12.4234 1.08960
\(131\) −12.8742 −1.12483 −0.562413 0.826857i \(-0.690127\pi\)
−0.562413 + 0.826857i \(0.690127\pi\)
\(132\) 3.43608 0.299072
\(133\) −1.59892 −0.138644
\(134\) 0.827398 0.0714763
\(135\) 14.0629 1.21035
\(136\) −5.64502 −0.484056
\(137\) −11.8084 −1.00886 −0.504429 0.863453i \(-0.668297\pi\)
−0.504429 + 0.863453i \(0.668297\pi\)
\(138\) 4.59377 0.391048
\(139\) −3.68604 −0.312646 −0.156323 0.987706i \(-0.549964\pi\)
−0.156323 + 0.987706i \(0.549964\pi\)
\(140\) −2.96551 −0.250632
\(141\) 8.21601 0.691912
\(142\) 8.62062 0.723426
\(143\) 15.6423 1.30807
\(144\) −2.15315 −0.179429
\(145\) −0.835324 −0.0693699
\(146\) −0.950530 −0.0786664
\(147\) −0.920246 −0.0759006
\(148\) −1.75109 −0.143939
\(149\) 3.42446 0.280543 0.140271 0.990113i \(-0.455202\pi\)
0.140271 + 0.990113i \(0.455202\pi\)
\(150\) 3.49166 0.285093
\(151\) 21.8871 1.78115 0.890575 0.454837i \(-0.150303\pi\)
0.890575 + 0.454837i \(0.150303\pi\)
\(152\) −1.59892 −0.129689
\(153\) −12.1546 −0.982637
\(154\) −3.73387 −0.300884
\(155\) −1.76698 −0.141927
\(156\) 3.85518 0.308661
\(157\) 2.80024 0.223484 0.111742 0.993737i \(-0.464357\pi\)
0.111742 + 0.993737i \(0.464357\pi\)
\(158\) −13.6713 −1.08763
\(159\) 9.90784 0.785743
\(160\) −2.96551 −0.234444
\(161\) −4.99189 −0.393416
\(162\) −2.09549 −0.164637
\(163\) 5.01493 0.392800 0.196400 0.980524i \(-0.437075\pi\)
0.196400 + 0.980524i \(0.437075\pi\)
\(164\) 1.43359 0.111945
\(165\) 10.1897 0.793271
\(166\) −10.7904 −0.837495
\(167\) 4.31481 0.333890 0.166945 0.985966i \(-0.446610\pi\)
0.166945 + 0.985966i \(0.446610\pi\)
\(168\) −0.920246 −0.0709985
\(169\) 4.55016 0.350012
\(170\) −16.7404 −1.28393
\(171\) −3.44270 −0.263270
\(172\) 7.07586 0.539529
\(173\) 9.90231 0.752858 0.376429 0.926445i \(-0.377152\pi\)
0.376429 + 0.926445i \(0.377152\pi\)
\(174\) −0.259214 −0.0196510
\(175\) −3.79427 −0.286820
\(176\) −3.73387 −0.281451
\(177\) −2.38983 −0.179631
\(178\) 5.53491 0.414859
\(179\) 17.3323 1.29548 0.647740 0.761861i \(-0.275714\pi\)
0.647740 + 0.761861i \(0.275714\pi\)
\(180\) −6.38519 −0.475924
\(181\) 0.496174 0.0368803 0.0184402 0.999830i \(-0.494130\pi\)
0.0184402 + 0.999830i \(0.494130\pi\)
\(182\) −4.18929 −0.310531
\(183\) 10.4786 0.774599
\(184\) −4.99189 −0.368007
\(185\) −5.19290 −0.381789
\(186\) −0.548322 −0.0402049
\(187\) −21.0778 −1.54136
\(188\) −8.92805 −0.651145
\(189\) −4.74216 −0.344942
\(190\) −4.74161 −0.343993
\(191\) 12.9619 0.937890 0.468945 0.883227i \(-0.344634\pi\)
0.468945 + 0.883227i \(0.344634\pi\)
\(192\) −0.920246 −0.0664130
\(193\) 16.1898 1.16537 0.582685 0.812698i \(-0.302002\pi\)
0.582685 + 0.812698i \(0.302002\pi\)
\(194\) −4.82510 −0.346422
\(195\) 11.4326 0.818704
\(196\) 1.00000 0.0714286
\(197\) 19.3336 1.37746 0.688731 0.725017i \(-0.258168\pi\)
0.688731 + 0.725017i \(0.258168\pi\)
\(198\) −8.03958 −0.571348
\(199\) −4.28872 −0.304019 −0.152010 0.988379i \(-0.548574\pi\)
−0.152010 + 0.988379i \(0.548574\pi\)
\(200\) −3.79427 −0.268295
\(201\) 0.761410 0.0537057
\(202\) −11.0551 −0.777832
\(203\) 0.281679 0.0197700
\(204\) −5.19480 −0.363709
\(205\) 4.25133 0.296926
\(206\) −14.8392 −1.03390
\(207\) −10.7483 −0.747057
\(208\) −4.18929 −0.290475
\(209\) −5.97015 −0.412964
\(210\) −2.72900 −0.188319
\(211\) 13.5601 0.933518 0.466759 0.884384i \(-0.345421\pi\)
0.466759 + 0.884384i \(0.345421\pi\)
\(212\) −10.7665 −0.739447
\(213\) 7.93309 0.543566
\(214\) 5.78284 0.395307
\(215\) 20.9835 1.43107
\(216\) −4.74216 −0.322663
\(217\) 0.595843 0.0404484
\(218\) 1.51331 0.102494
\(219\) −0.874721 −0.0591082
\(220\) −11.0729 −0.746531
\(221\) −23.6486 −1.59078
\(222\) −1.61144 −0.108153
\(223\) 12.1396 0.812926 0.406463 0.913667i \(-0.366762\pi\)
0.406463 + 0.913667i \(0.366762\pi\)
\(224\) 1.00000 0.0668153
\(225\) −8.16963 −0.544642
\(226\) −3.08038 −0.204904
\(227\) 13.9190 0.923840 0.461920 0.886922i \(-0.347161\pi\)
0.461920 + 0.886922i \(0.347161\pi\)
\(228\) −1.47140 −0.0974456
\(229\) −12.5004 −0.826048 −0.413024 0.910720i \(-0.635527\pi\)
−0.413024 + 0.910720i \(0.635527\pi\)
\(230\) −14.8035 −0.976116
\(231\) −3.43608 −0.226078
\(232\) 0.281679 0.0184932
\(233\) −0.392089 −0.0256866 −0.0128433 0.999918i \(-0.504088\pi\)
−0.0128433 + 0.999918i \(0.504088\pi\)
\(234\) −9.02016 −0.589666
\(235\) −26.4763 −1.72712
\(236\) 2.59695 0.169047
\(237\) −12.5809 −0.817220
\(238\) 5.64502 0.365912
\(239\) 17.1919 1.11205 0.556026 0.831165i \(-0.312325\pi\)
0.556026 + 0.831165i \(0.312325\pi\)
\(240\) −2.72900 −0.176156
\(241\) −5.92629 −0.381746 −0.190873 0.981615i \(-0.561132\pi\)
−0.190873 + 0.981615i \(0.561132\pi\)
\(242\) −2.94181 −0.189106
\(243\) −16.1549 −1.03633
\(244\) −11.3867 −0.728960
\(245\) 2.96551 0.189460
\(246\) 1.31926 0.0841127
\(247\) −6.69833 −0.426204
\(248\) 0.595843 0.0378361
\(249\) −9.92980 −0.629275
\(250\) 3.57561 0.226141
\(251\) 26.0565 1.64467 0.822336 0.569002i \(-0.192670\pi\)
0.822336 + 0.569002i \(0.192670\pi\)
\(252\) 2.15315 0.135636
\(253\) −18.6391 −1.17183
\(254\) 0.225215 0.0141313
\(255\) −15.4053 −0.964715
\(256\) 1.00000 0.0625000
\(257\) −7.88491 −0.491847 −0.245923 0.969289i \(-0.579091\pi\)
−0.245923 + 0.969289i \(0.579091\pi\)
\(258\) 6.51153 0.405390
\(259\) 1.75109 0.108808
\(260\) −12.4234 −0.770467
\(261\) 0.606497 0.0375412
\(262\) 12.8742 0.795371
\(263\) 3.97875 0.245340 0.122670 0.992447i \(-0.460854\pi\)
0.122670 + 0.992447i \(0.460854\pi\)
\(264\) −3.43608 −0.211476
\(265\) −31.9283 −1.96134
\(266\) 1.59892 0.0980359
\(267\) 5.09348 0.311716
\(268\) −0.827398 −0.0505414
\(269\) −7.78372 −0.474582 −0.237291 0.971439i \(-0.576259\pi\)
−0.237291 + 0.971439i \(0.576259\pi\)
\(270\) −14.0629 −0.855844
\(271\) 13.3878 0.813254 0.406627 0.913594i \(-0.366705\pi\)
0.406627 + 0.913594i \(0.366705\pi\)
\(272\) 5.64502 0.342279
\(273\) −3.85518 −0.233326
\(274\) 11.8084 0.713371
\(275\) −14.1673 −0.854322
\(276\) −4.59377 −0.276512
\(277\) 15.3841 0.924344 0.462172 0.886790i \(-0.347070\pi\)
0.462172 + 0.886790i \(0.347070\pi\)
\(278\) 3.68604 0.221074
\(279\) 1.28294 0.0768075
\(280\) 2.96551 0.177223
\(281\) 23.8750 1.42427 0.712133 0.702045i \(-0.247729\pi\)
0.712133 + 0.702045i \(0.247729\pi\)
\(282\) −8.21601 −0.489256
\(283\) −25.3162 −1.50489 −0.752445 0.658656i \(-0.771125\pi\)
−0.752445 + 0.658656i \(0.771125\pi\)
\(284\) −8.62062 −0.511540
\(285\) −4.36345 −0.258468
\(286\) −15.6423 −0.924947
\(287\) −1.43359 −0.0846222
\(288\) 2.15315 0.126875
\(289\) 14.8662 0.874483
\(290\) 0.835324 0.0490519
\(291\) −4.44027 −0.260293
\(292\) 0.950530 0.0556256
\(293\) −9.72297 −0.568022 −0.284011 0.958821i \(-0.591665\pi\)
−0.284011 + 0.958821i \(0.591665\pi\)
\(294\) 0.920246 0.0536698
\(295\) 7.70129 0.448387
\(296\) 1.75109 0.101780
\(297\) −17.7066 −1.02744
\(298\) −3.42446 −0.198374
\(299\) −20.9125 −1.20940
\(300\) −3.49166 −0.201591
\(301\) −7.07586 −0.407846
\(302\) −21.8871 −1.25946
\(303\) −10.1734 −0.584446
\(304\) 1.59892 0.0917042
\(305\) −33.7675 −1.93352
\(306\) 12.1546 0.694829
\(307\) −16.3176 −0.931295 −0.465648 0.884970i \(-0.654179\pi\)
−0.465648 + 0.884970i \(0.654179\pi\)
\(308\) 3.73387 0.212757
\(309\) −13.6557 −0.776846
\(310\) 1.76698 0.100358
\(311\) 30.4396 1.72607 0.863035 0.505144i \(-0.168561\pi\)
0.863035 + 0.505144i \(0.168561\pi\)
\(312\) −3.85518 −0.218256
\(313\) 3.79828 0.214691 0.107346 0.994222i \(-0.465765\pi\)
0.107346 + 0.994222i \(0.465765\pi\)
\(314\) −2.80024 −0.158027
\(315\) 6.38519 0.359765
\(316\) 13.6713 0.769070
\(317\) 31.4929 1.76882 0.884408 0.466715i \(-0.154563\pi\)
0.884408 + 0.466715i \(0.154563\pi\)
\(318\) −9.90784 −0.555604
\(319\) 1.05176 0.0588870
\(320\) 2.96551 0.165777
\(321\) 5.32164 0.297025
\(322\) 4.99189 0.278187
\(323\) 9.02591 0.502215
\(324\) 2.09549 0.116416
\(325\) −15.8953 −0.881713
\(326\) −5.01493 −0.277751
\(327\) 1.39262 0.0770119
\(328\) −1.43359 −0.0791568
\(329\) 8.92805 0.492220
\(330\) −10.1897 −0.560927
\(331\) 17.6665 0.971041 0.485520 0.874225i \(-0.338630\pi\)
0.485520 + 0.874225i \(0.338630\pi\)
\(332\) 10.7904 0.592199
\(333\) 3.77037 0.206615
\(334\) −4.31481 −0.236096
\(335\) −2.45366 −0.134058
\(336\) 0.920246 0.0502035
\(337\) 34.6562 1.88785 0.943923 0.330166i \(-0.107105\pi\)
0.943923 + 0.330166i \(0.107105\pi\)
\(338\) −4.55016 −0.247496
\(339\) −2.83470 −0.153960
\(340\) 16.7404 0.907874
\(341\) 2.22480 0.120480
\(342\) 3.44270 0.186160
\(343\) −1.00000 −0.0539949
\(344\) −7.07586 −0.381505
\(345\) −13.6229 −0.733431
\(346\) −9.90231 −0.532351
\(347\) −33.2148 −1.78306 −0.891532 0.452959i \(-0.850369\pi\)
−0.891532 + 0.452959i \(0.850369\pi\)
\(348\) 0.259214 0.0138953
\(349\) 7.55703 0.404518 0.202259 0.979332i \(-0.435172\pi\)
0.202259 + 0.979332i \(0.435172\pi\)
\(350\) 3.79427 0.202812
\(351\) −19.8663 −1.06038
\(352\) 3.73387 0.199016
\(353\) −15.2892 −0.813760 −0.406880 0.913482i \(-0.633383\pi\)
−0.406880 + 0.913482i \(0.633383\pi\)
\(354\) 2.38983 0.127018
\(355\) −25.5646 −1.35683
\(356\) −5.53491 −0.293350
\(357\) 5.19480 0.274938
\(358\) −17.3323 −0.916043
\(359\) 6.70872 0.354073 0.177036 0.984204i \(-0.443349\pi\)
0.177036 + 0.984204i \(0.443349\pi\)
\(360\) 6.38519 0.336529
\(361\) −16.4435 −0.865446
\(362\) −0.496174 −0.0260783
\(363\) −2.70718 −0.142090
\(364\) 4.18929 0.219579
\(365\) 2.81881 0.147543
\(366\) −10.4786 −0.547724
\(367\) 14.1782 0.740094 0.370047 0.929013i \(-0.379342\pi\)
0.370047 + 0.929013i \(0.379342\pi\)
\(368\) 4.99189 0.260220
\(369\) −3.08673 −0.160689
\(370\) 5.19290 0.269966
\(371\) 10.7665 0.558970
\(372\) 0.548322 0.0284292
\(373\) −9.62992 −0.498618 −0.249309 0.968424i \(-0.580204\pi\)
−0.249309 + 0.968424i \(0.580204\pi\)
\(374\) 21.0778 1.08991
\(375\) 3.29044 0.169917
\(376\) 8.92805 0.460429
\(377\) 1.18004 0.0607750
\(378\) 4.74216 0.243911
\(379\) 0.704386 0.0361819 0.0180909 0.999836i \(-0.494241\pi\)
0.0180909 + 0.999836i \(0.494241\pi\)
\(380\) 4.74161 0.243239
\(381\) 0.207253 0.0106179
\(382\) −12.9619 −0.663188
\(383\) 11.5952 0.592489 0.296245 0.955112i \(-0.404266\pi\)
0.296245 + 0.955112i \(0.404266\pi\)
\(384\) 0.920246 0.0469611
\(385\) 11.0729 0.564325
\(386\) −16.1898 −0.824040
\(387\) −15.2354 −0.774457
\(388\) 4.82510 0.244957
\(389\) −4.89619 −0.248247 −0.124123 0.992267i \(-0.539612\pi\)
−0.124123 + 0.992267i \(0.539612\pi\)
\(390\) −11.4326 −0.578911
\(391\) 28.1793 1.42509
\(392\) −1.00000 −0.0505076
\(393\) 11.8474 0.597624
\(394\) −19.3336 −0.974013
\(395\) 40.5424 2.03991
\(396\) 8.03958 0.404004
\(397\) 23.3345 1.17112 0.585562 0.810627i \(-0.300874\pi\)
0.585562 + 0.810627i \(0.300874\pi\)
\(398\) 4.28872 0.214974
\(399\) 1.47140 0.0736620
\(400\) 3.79427 0.189714
\(401\) 24.8657 1.24173 0.620866 0.783917i \(-0.286781\pi\)
0.620866 + 0.783917i \(0.286781\pi\)
\(402\) −0.761410 −0.0379757
\(403\) 2.49616 0.124343
\(404\) 11.0551 0.550010
\(405\) 6.21419 0.308786
\(406\) −0.281679 −0.0139795
\(407\) 6.53837 0.324095
\(408\) 5.19480 0.257181
\(409\) 0.240956 0.0119145 0.00595726 0.999982i \(-0.498104\pi\)
0.00595726 + 0.999982i \(0.498104\pi\)
\(410\) −4.25133 −0.209958
\(411\) 10.8666 0.536011
\(412\) 14.8392 0.731075
\(413\) −2.59695 −0.127788
\(414\) 10.7483 0.528249
\(415\) 31.9990 1.57077
\(416\) 4.18929 0.205397
\(417\) 3.39207 0.166110
\(418\) 5.97015 0.292010
\(419\) 6.22872 0.304293 0.152146 0.988358i \(-0.451381\pi\)
0.152146 + 0.988358i \(0.451381\pi\)
\(420\) 2.72900 0.133162
\(421\) 2.28185 0.111210 0.0556052 0.998453i \(-0.482291\pi\)
0.0556052 + 0.998453i \(0.482291\pi\)
\(422\) −13.5601 −0.660097
\(423\) 19.2234 0.934674
\(424\) 10.7665 0.522868
\(425\) 21.4187 1.03896
\(426\) −7.93309 −0.384360
\(427\) 11.3867 0.551042
\(428\) −5.78284 −0.279524
\(429\) −14.3947 −0.694985
\(430\) −20.9835 −1.01192
\(431\) 1.00000 0.0481683
\(432\) 4.74216 0.228157
\(433\) −7.69716 −0.369902 −0.184951 0.982748i \(-0.559213\pi\)
−0.184951 + 0.982748i \(0.559213\pi\)
\(434\) −0.595843 −0.0286014
\(435\) 0.768704 0.0368565
\(436\) −1.51331 −0.0724744
\(437\) 7.98162 0.381813
\(438\) 0.874721 0.0417958
\(439\) 15.6183 0.745420 0.372710 0.927948i \(-0.378429\pi\)
0.372710 + 0.927948i \(0.378429\pi\)
\(440\) 11.0729 0.527877
\(441\) −2.15315 −0.102531
\(442\) 23.6486 1.12485
\(443\) 21.4825 1.02067 0.510333 0.859977i \(-0.329522\pi\)
0.510333 + 0.859977i \(0.329522\pi\)
\(444\) 1.61144 0.0764755
\(445\) −16.4139 −0.778091
\(446\) −12.1396 −0.574825
\(447\) −3.15135 −0.149054
\(448\) −1.00000 −0.0472456
\(449\) 5.15008 0.243047 0.121524 0.992589i \(-0.461222\pi\)
0.121524 + 0.992589i \(0.461222\pi\)
\(450\) 8.16963 0.385120
\(451\) −5.35285 −0.252056
\(452\) 3.08038 0.144889
\(453\) −20.1415 −0.946332
\(454\) −13.9190 −0.653253
\(455\) 12.4234 0.582418
\(456\) 1.47140 0.0689045
\(457\) −24.1714 −1.13069 −0.565346 0.824854i \(-0.691257\pi\)
−0.565346 + 0.824854i \(0.691257\pi\)
\(458\) 12.5004 0.584104
\(459\) 26.7696 1.24950
\(460\) 14.8035 0.690218
\(461\) −19.9699 −0.930090 −0.465045 0.885287i \(-0.653962\pi\)
−0.465045 + 0.885287i \(0.653962\pi\)
\(462\) 3.43608 0.159861
\(463\) 24.5172 1.13941 0.569706 0.821849i \(-0.307057\pi\)
0.569706 + 0.821849i \(0.307057\pi\)
\(464\) −0.281679 −0.0130766
\(465\) 1.62606 0.0754065
\(466\) 0.392089 0.0181632
\(467\) 4.73023 0.218889 0.109444 0.993993i \(-0.465093\pi\)
0.109444 + 0.993993i \(0.465093\pi\)
\(468\) 9.02016 0.416957
\(469\) 0.827398 0.0382057
\(470\) 26.4763 1.22126
\(471\) −2.57691 −0.118738
\(472\) −2.59695 −0.119534
\(473\) −26.4203 −1.21481
\(474\) 12.5809 0.577862
\(475\) 6.06672 0.278360
\(476\) −5.64502 −0.258739
\(477\) 23.1819 1.06143
\(478\) −17.1919 −0.786340
\(479\) −15.6484 −0.714993 −0.357497 0.933914i \(-0.616370\pi\)
−0.357497 + 0.933914i \(0.616370\pi\)
\(480\) 2.72900 0.124561
\(481\) 7.33585 0.334486
\(482\) 5.92629 0.269935
\(483\) 4.59377 0.209024
\(484\) 2.94181 0.133718
\(485\) 14.3089 0.649733
\(486\) 16.1549 0.732799
\(487\) −35.3945 −1.60388 −0.801939 0.597406i \(-0.796198\pi\)
−0.801939 + 0.597406i \(0.796198\pi\)
\(488\) 11.3867 0.515453
\(489\) −4.61497 −0.208696
\(490\) −2.96551 −0.133968
\(491\) 12.5717 0.567354 0.283677 0.958920i \(-0.408446\pi\)
0.283677 + 0.958920i \(0.408446\pi\)
\(492\) −1.31926 −0.0594767
\(493\) −1.59009 −0.0716138
\(494\) 6.69833 0.301372
\(495\) 23.8415 1.07159
\(496\) −0.595843 −0.0267541
\(497\) 8.62062 0.386688
\(498\) 9.92980 0.444965
\(499\) −23.1265 −1.03529 −0.517643 0.855597i \(-0.673190\pi\)
−0.517643 + 0.855597i \(0.673190\pi\)
\(500\) −3.57561 −0.159906
\(501\) −3.97069 −0.177397
\(502\) −26.0565 −1.16296
\(503\) −9.56311 −0.426398 −0.213199 0.977009i \(-0.568388\pi\)
−0.213199 + 0.977009i \(0.568388\pi\)
\(504\) −2.15315 −0.0959088
\(505\) 32.7840 1.45887
\(506\) 18.6391 0.828609
\(507\) −4.18726 −0.185963
\(508\) −0.225215 −0.00999231
\(509\) −7.03707 −0.311912 −0.155956 0.987764i \(-0.549846\pi\)
−0.155956 + 0.987764i \(0.549846\pi\)
\(510\) 15.4053 0.682156
\(511\) −0.950530 −0.0420490
\(512\) −1.00000 −0.0441942
\(513\) 7.58232 0.334768
\(514\) 7.88491 0.347788
\(515\) 44.0059 1.93913
\(516\) −6.51153 −0.286654
\(517\) 33.3362 1.46613
\(518\) −1.75109 −0.0769387
\(519\) −9.11256 −0.399997
\(520\) 12.4234 0.544802
\(521\) 28.7774 1.26076 0.630380 0.776286i \(-0.282899\pi\)
0.630380 + 0.776286i \(0.282899\pi\)
\(522\) −0.606497 −0.0265457
\(523\) −9.00158 −0.393612 −0.196806 0.980442i \(-0.563057\pi\)
−0.196806 + 0.980442i \(0.563057\pi\)
\(524\) −12.8742 −0.562413
\(525\) 3.49166 0.152389
\(526\) −3.97875 −0.173482
\(527\) −3.36354 −0.146518
\(528\) 3.43608 0.149536
\(529\) 1.91900 0.0834346
\(530\) 31.9283 1.38687
\(531\) −5.59162 −0.242656
\(532\) −1.59892 −0.0693218
\(533\) −6.00573 −0.260137
\(534\) −5.09348 −0.220416
\(535\) −17.1491 −0.741420
\(536\) 0.827398 0.0357382
\(537\) −15.9500 −0.688294
\(538\) 7.78372 0.335580
\(539\) −3.73387 −0.160829
\(540\) 14.0629 0.605173
\(541\) 0.811603 0.0348935 0.0174468 0.999848i \(-0.494446\pi\)
0.0174468 + 0.999848i \(0.494446\pi\)
\(542\) −13.3878 −0.575057
\(543\) −0.456602 −0.0195947
\(544\) −5.64502 −0.242028
\(545\) −4.48774 −0.192234
\(546\) 3.85518 0.164986
\(547\) 4.85868 0.207742 0.103871 0.994591i \(-0.466877\pi\)
0.103871 + 0.994591i \(0.466877\pi\)
\(548\) −11.8084 −0.504429
\(549\) 24.5173 1.04637
\(550\) 14.1673 0.604097
\(551\) −0.450382 −0.0191869
\(552\) 4.59377 0.195524
\(553\) −13.6713 −0.581362
\(554\) −15.3841 −0.653610
\(555\) 4.77874 0.202846
\(556\) −3.68604 −0.156323
\(557\) −42.9449 −1.81964 −0.909818 0.415008i \(-0.863779\pi\)
−0.909818 + 0.415008i \(0.863779\pi\)
\(558\) −1.28294 −0.0543111
\(559\) −29.6428 −1.25376
\(560\) −2.96551 −0.125316
\(561\) 19.3967 0.818931
\(562\) −23.8750 −1.00711
\(563\) −17.0067 −0.716747 −0.358374 0.933578i \(-0.616669\pi\)
−0.358374 + 0.933578i \(0.616669\pi\)
\(564\) 8.21601 0.345956
\(565\) 9.13490 0.384308
\(566\) 25.3162 1.06412
\(567\) −2.09549 −0.0880021
\(568\) 8.62062 0.361713
\(569\) 33.9507 1.42329 0.711644 0.702540i \(-0.247951\pi\)
0.711644 + 0.702540i \(0.247951\pi\)
\(570\) 4.36345 0.182765
\(571\) −11.3356 −0.474378 −0.237189 0.971464i \(-0.576226\pi\)
−0.237189 + 0.971464i \(0.576226\pi\)
\(572\) 15.6423 0.654037
\(573\) −11.9281 −0.498305
\(574\) 1.43359 0.0598369
\(575\) 18.9406 0.789877
\(576\) −2.15315 −0.0897145
\(577\) 25.9991 1.08236 0.541179 0.840908i \(-0.317978\pi\)
0.541179 + 0.840908i \(0.317978\pi\)
\(578\) −14.8662 −0.618353
\(579\) −14.8986 −0.619166
\(580\) −0.835324 −0.0346850
\(581\) −10.7904 −0.447660
\(582\) 4.44027 0.184055
\(583\) 40.2008 1.66495
\(584\) −0.950530 −0.0393332
\(585\) 26.7494 1.10595
\(586\) 9.72297 0.401652
\(587\) 32.4335 1.33867 0.669336 0.742960i \(-0.266579\pi\)
0.669336 + 0.742960i \(0.266579\pi\)
\(588\) −0.920246 −0.0379503
\(589\) −0.952703 −0.0392554
\(590\) −7.70129 −0.317057
\(591\) −17.7917 −0.731852
\(592\) −1.75109 −0.0719696
\(593\) 8.70949 0.357656 0.178828 0.983880i \(-0.442769\pi\)
0.178828 + 0.983880i \(0.442769\pi\)
\(594\) 17.7066 0.726512
\(595\) −16.7404 −0.686288
\(596\) 3.42446 0.140271
\(597\) 3.94668 0.161527
\(598\) 20.9125 0.855175
\(599\) −30.4873 −1.24568 −0.622838 0.782351i \(-0.714021\pi\)
−0.622838 + 0.782351i \(0.714021\pi\)
\(600\) 3.49166 0.142547
\(601\) −33.5614 −1.36900 −0.684499 0.729014i \(-0.739979\pi\)
−0.684499 + 0.729014i \(0.739979\pi\)
\(602\) 7.07586 0.288390
\(603\) 1.78151 0.0725487
\(604\) 21.8871 0.890575
\(605\) 8.72397 0.354680
\(606\) 10.1734 0.413265
\(607\) 23.0581 0.935898 0.467949 0.883756i \(-0.344993\pi\)
0.467949 + 0.883756i \(0.344993\pi\)
\(608\) −1.59892 −0.0648446
\(609\) −0.259214 −0.0105039
\(610\) 33.7675 1.36721
\(611\) 37.4022 1.51313
\(612\) −12.1546 −0.491319
\(613\) 5.78694 0.233732 0.116866 0.993148i \(-0.462715\pi\)
0.116866 + 0.993148i \(0.462715\pi\)
\(614\) 16.3176 0.658525
\(615\) −3.91227 −0.157758
\(616\) −3.73387 −0.150442
\(617\) 7.82002 0.314822 0.157411 0.987533i \(-0.449685\pi\)
0.157411 + 0.987533i \(0.449685\pi\)
\(618\) 13.6557 0.549313
\(619\) −38.0806 −1.53059 −0.765294 0.643681i \(-0.777407\pi\)
−0.765294 + 0.643681i \(0.777407\pi\)
\(620\) −1.76698 −0.0709636
\(621\) 23.6724 0.949939
\(622\) −30.4396 −1.22052
\(623\) 5.53491 0.221752
\(624\) 3.85518 0.154331
\(625\) −29.5749 −1.18299
\(626\) −3.79828 −0.151810
\(627\) 5.49401 0.219410
\(628\) 2.80024 0.111742
\(629\) −9.88496 −0.394139
\(630\) −6.38519 −0.254392
\(631\) 42.7598 1.70224 0.851121 0.524969i \(-0.175923\pi\)
0.851121 + 0.524969i \(0.175923\pi\)
\(632\) −13.6713 −0.543815
\(633\) −12.4787 −0.495982
\(634\) −31.4929 −1.25074
\(635\) −0.667879 −0.0265040
\(636\) 9.90784 0.392872
\(637\) −4.18929 −0.165986
\(638\) −1.05176 −0.0416394
\(639\) 18.5615 0.734280
\(640\) −2.96551 −0.117222
\(641\) −8.44630 −0.333609 −0.166804 0.985990i \(-0.553345\pi\)
−0.166804 + 0.985990i \(0.553345\pi\)
\(642\) −5.32164 −0.210028
\(643\) 20.1993 0.796584 0.398292 0.917259i \(-0.369603\pi\)
0.398292 + 0.917259i \(0.369603\pi\)
\(644\) −4.99189 −0.196708
\(645\) −19.3100 −0.760332
\(646\) −9.02591 −0.355120
\(647\) 18.1854 0.714943 0.357471 0.933924i \(-0.383639\pi\)
0.357471 + 0.933924i \(0.383639\pi\)
\(648\) −2.09549 −0.0823185
\(649\) −9.69668 −0.380628
\(650\) 15.8953 0.623465
\(651\) −0.548322 −0.0214904
\(652\) 5.01493 0.196400
\(653\) −19.3459 −0.757063 −0.378531 0.925588i \(-0.623571\pi\)
−0.378531 + 0.925588i \(0.623571\pi\)
\(654\) −1.39262 −0.0544556
\(655\) −38.1787 −1.49176
\(656\) 1.43359 0.0559723
\(657\) −2.04663 −0.0798467
\(658\) −8.92805 −0.348052
\(659\) 28.1137 1.09515 0.547576 0.836756i \(-0.315551\pi\)
0.547576 + 0.836756i \(0.315551\pi\)
\(660\) 10.1897 0.396635
\(661\) 33.8790 1.31774 0.658870 0.752256i \(-0.271035\pi\)
0.658870 + 0.752256i \(0.271035\pi\)
\(662\) −17.6665 −0.686630
\(663\) 21.7625 0.845187
\(664\) −10.7904 −0.418748
\(665\) −4.74161 −0.183872
\(666\) −3.77037 −0.146099
\(667\) −1.40611 −0.0544449
\(668\) 4.31481 0.166945
\(669\) −11.1714 −0.431911
\(670\) 2.45366 0.0947932
\(671\) 42.5166 1.64133
\(672\) −0.920246 −0.0354993
\(673\) −43.9445 −1.69394 −0.846969 0.531643i \(-0.821575\pi\)
−0.846969 + 0.531643i \(0.821575\pi\)
\(674\) −34.6562 −1.33491
\(675\) 17.9931 0.692553
\(676\) 4.55016 0.175006
\(677\) −29.0469 −1.11636 −0.558182 0.829718i \(-0.688501\pi\)
−0.558182 + 0.829718i \(0.688501\pi\)
\(678\) 2.83470 0.108866
\(679\) −4.82510 −0.185170
\(680\) −16.7404 −0.641964
\(681\) −12.8089 −0.490840
\(682\) −2.22480 −0.0851920
\(683\) −4.86375 −0.186106 −0.0930531 0.995661i \(-0.529663\pi\)
−0.0930531 + 0.995661i \(0.529663\pi\)
\(684\) −3.44270 −0.131635
\(685\) −35.0179 −1.33797
\(686\) 1.00000 0.0381802
\(687\) 11.5034 0.438883
\(688\) 7.07586 0.269765
\(689\) 45.1041 1.71833
\(690\) 13.6229 0.518614
\(691\) 22.6241 0.860660 0.430330 0.902672i \(-0.358397\pi\)
0.430330 + 0.902672i \(0.358397\pi\)
\(692\) 9.90231 0.376429
\(693\) −8.03958 −0.305398
\(694\) 33.2148 1.26082
\(695\) −10.9310 −0.414637
\(696\) −0.259214 −0.00982550
\(697\) 8.09265 0.306531
\(698\) −7.55703 −0.286038
\(699\) 0.360819 0.0136474
\(700\) −3.79427 −0.143410
\(701\) −21.4443 −0.809939 −0.404969 0.914330i \(-0.632718\pi\)
−0.404969 + 0.914330i \(0.632718\pi\)
\(702\) 19.8663 0.749805
\(703\) −2.79986 −0.105599
\(704\) −3.73387 −0.140726
\(705\) 24.3647 0.917627
\(706\) 15.2892 0.575415
\(707\) −11.0551 −0.415769
\(708\) −2.38983 −0.0898154
\(709\) 36.4867 1.37029 0.685143 0.728408i \(-0.259740\pi\)
0.685143 + 0.728408i \(0.259740\pi\)
\(710\) 25.5646 0.959421
\(711\) −29.4363 −1.10395
\(712\) 5.53491 0.207430
\(713\) −2.97438 −0.111392
\(714\) −5.19480 −0.194411
\(715\) 46.3874 1.73479
\(716\) 17.3323 0.647740
\(717\) −15.8208 −0.590838
\(718\) −6.70872 −0.250367
\(719\) 20.5648 0.766938 0.383469 0.923554i \(-0.374729\pi\)
0.383469 + 0.923554i \(0.374729\pi\)
\(720\) −6.38519 −0.237962
\(721\) −14.8392 −0.552641
\(722\) 16.4435 0.611962
\(723\) 5.45365 0.202823
\(724\) 0.496174 0.0184402
\(725\) −1.06877 −0.0396931
\(726\) 2.70718 0.100473
\(727\) 3.06023 0.113497 0.0567487 0.998388i \(-0.481927\pi\)
0.0567487 + 0.998388i \(0.481927\pi\)
\(728\) −4.18929 −0.155265
\(729\) 8.57998 0.317777
\(730\) −2.81881 −0.104329
\(731\) 39.9433 1.47736
\(732\) 10.4786 0.387300
\(733\) 2.35676 0.0870491 0.0435245 0.999052i \(-0.486141\pi\)
0.0435245 + 0.999052i \(0.486141\pi\)
\(734\) −14.1782 −0.523326
\(735\) −2.72900 −0.100661
\(736\) −4.99189 −0.184004
\(737\) 3.08940 0.113799
\(738\) 3.08673 0.113624
\(739\) −34.2481 −1.25984 −0.629918 0.776661i \(-0.716912\pi\)
−0.629918 + 0.776661i \(0.716912\pi\)
\(740\) −5.19290 −0.190895
\(741\) 6.16411 0.226444
\(742\) −10.7665 −0.395251
\(743\) −26.3559 −0.966903 −0.483452 0.875371i \(-0.660617\pi\)
−0.483452 + 0.875371i \(0.660617\pi\)
\(744\) −0.548322 −0.0201025
\(745\) 10.1553 0.372061
\(746\) 9.62992 0.352576
\(747\) −23.2333 −0.850061
\(748\) −21.0778 −0.770680
\(749\) 5.78284 0.211300
\(750\) −3.29044 −0.120150
\(751\) 10.4102 0.379874 0.189937 0.981796i \(-0.439172\pi\)
0.189937 + 0.981796i \(0.439172\pi\)
\(752\) −8.92805 −0.325573
\(753\) −23.9784 −0.873821
\(754\) −1.18004 −0.0429744
\(755\) 64.9066 2.36219
\(756\) −4.74216 −0.172471
\(757\) −11.1410 −0.404928 −0.202464 0.979290i \(-0.564895\pi\)
−0.202464 + 0.979290i \(0.564895\pi\)
\(758\) −0.704386 −0.0255844
\(759\) 17.1525 0.622598
\(760\) −4.74161 −0.171996
\(761\) 27.5200 0.997598 0.498799 0.866718i \(-0.333775\pi\)
0.498799 + 0.866718i \(0.333775\pi\)
\(762\) −0.207253 −0.00750800
\(763\) 1.51331 0.0547855
\(764\) 12.9619 0.468945
\(765\) −36.0445 −1.30319
\(766\) −11.5952 −0.418953
\(767\) −10.8794 −0.392832
\(768\) −0.920246 −0.0332065
\(769\) 1.61368 0.0581907 0.0290953 0.999577i \(-0.490737\pi\)
0.0290953 + 0.999577i \(0.490737\pi\)
\(770\) −11.0729 −0.399038
\(771\) 7.25605 0.261320
\(772\) 16.1898 0.582685
\(773\) 23.5910 0.848510 0.424255 0.905543i \(-0.360536\pi\)
0.424255 + 0.905543i \(0.360536\pi\)
\(774\) 15.2354 0.547624
\(775\) −2.26079 −0.0812099
\(776\) −4.82510 −0.173211
\(777\) −1.61144 −0.0578100
\(778\) 4.89619 0.175537
\(779\) 2.29219 0.0821263
\(780\) 11.4326 0.409352
\(781\) 32.1883 1.15179
\(782\) −28.1793 −1.00769
\(783\) −1.33577 −0.0477365
\(784\) 1.00000 0.0357143
\(785\) 8.30416 0.296388
\(786\) −11.8474 −0.422584
\(787\) −11.4838 −0.409353 −0.204676 0.978830i \(-0.565614\pi\)
−0.204676 + 0.978830i \(0.565614\pi\)
\(788\) 19.3336 0.688731
\(789\) −3.66143 −0.130350
\(790\) −40.5424 −1.44243
\(791\) −3.08038 −0.109526
\(792\) −8.03958 −0.285674
\(793\) 47.7023 1.69396
\(794\) −23.3345 −0.828110
\(795\) 29.3818 1.04207
\(796\) −4.28872 −0.152010
\(797\) −13.7209 −0.486019 −0.243009 0.970024i \(-0.578135\pi\)
−0.243009 + 0.970024i \(0.578135\pi\)
\(798\) −1.47140 −0.0520869
\(799\) −50.3990 −1.78299
\(800\) −3.79427 −0.134148
\(801\) 11.9175 0.421083
\(802\) −24.8657 −0.878037
\(803\) −3.54916 −0.125247
\(804\) 0.761410 0.0268528
\(805\) −14.8035 −0.521756
\(806\) −2.49616 −0.0879234
\(807\) 7.16293 0.252147
\(808\) −11.0551 −0.388916
\(809\) −13.7223 −0.482450 −0.241225 0.970469i \(-0.577549\pi\)
−0.241225 + 0.970469i \(0.577549\pi\)
\(810\) −6.21419 −0.218344
\(811\) 11.5696 0.406265 0.203132 0.979151i \(-0.434888\pi\)
0.203132 + 0.979151i \(0.434888\pi\)
\(812\) 0.281679 0.00988501
\(813\) −12.3201 −0.432085
\(814\) −6.53837 −0.229170
\(815\) 14.8719 0.520938
\(816\) −5.19480 −0.181854
\(817\) 11.3137 0.395817
\(818\) −0.240956 −0.00842484
\(819\) −9.02016 −0.315190
\(820\) 4.25133 0.148463
\(821\) 13.9858 0.488107 0.244054 0.969762i \(-0.421523\pi\)
0.244054 + 0.969762i \(0.421523\pi\)
\(822\) −10.8666 −0.379017
\(823\) −19.1504 −0.667542 −0.333771 0.942654i \(-0.608321\pi\)
−0.333771 + 0.942654i \(0.608321\pi\)
\(824\) −14.8392 −0.516948
\(825\) 13.0374 0.453905
\(826\) 2.59695 0.0903595
\(827\) 49.3630 1.71652 0.858259 0.513216i \(-0.171546\pi\)
0.858259 + 0.513216i \(0.171546\pi\)
\(828\) −10.7483 −0.373529
\(829\) −2.76014 −0.0958635 −0.0479318 0.998851i \(-0.515263\pi\)
−0.0479318 + 0.998851i \(0.515263\pi\)
\(830\) −31.9990 −1.11070
\(831\) −14.1572 −0.491108
\(832\) −4.18929 −0.145238
\(833\) 5.64502 0.195588
\(834\) −3.39207 −0.117458
\(835\) 12.7956 0.442811
\(836\) −5.97015 −0.206482
\(837\) −2.82558 −0.0976665
\(838\) −6.22872 −0.215168
\(839\) 11.1669 0.385524 0.192762 0.981246i \(-0.438255\pi\)
0.192762 + 0.981246i \(0.438255\pi\)
\(840\) −2.72900 −0.0941595
\(841\) −28.9207 −0.997264
\(842\) −2.28185 −0.0786376
\(843\) −21.9709 −0.756718
\(844\) 13.5601 0.466759
\(845\) 13.4936 0.464192
\(846\) −19.2234 −0.660915
\(847\) −2.94181 −0.101082
\(848\) −10.7665 −0.369724
\(849\) 23.2971 0.799554
\(850\) −21.4187 −0.734656
\(851\) −8.74128 −0.299647
\(852\) 7.93309 0.271783
\(853\) −52.3890 −1.79376 −0.896882 0.442270i \(-0.854173\pi\)
−0.896882 + 0.442270i \(0.854173\pi\)
\(854\) −11.3867 −0.389646
\(855\) −10.2094 −0.349154
\(856\) 5.78284 0.197653
\(857\) −0.850670 −0.0290583 −0.0145292 0.999894i \(-0.504625\pi\)
−0.0145292 + 0.999894i \(0.504625\pi\)
\(858\) 14.3947 0.491428
\(859\) −1.82823 −0.0623785 −0.0311892 0.999513i \(-0.509929\pi\)
−0.0311892 + 0.999513i \(0.509929\pi\)
\(860\) 20.9835 0.715533
\(861\) 1.31926 0.0449601
\(862\) −1.00000 −0.0340601
\(863\) 17.4958 0.595563 0.297782 0.954634i \(-0.403753\pi\)
0.297782 + 0.954634i \(0.403753\pi\)
\(864\) −4.74216 −0.161332
\(865\) 29.3654 0.998455
\(866\) 7.69716 0.261560
\(867\) −13.6806 −0.464616
\(868\) 0.595843 0.0202242
\(869\) −51.0468 −1.73165
\(870\) −0.768704 −0.0260615
\(871\) 3.46621 0.117448
\(872\) 1.51331 0.0512471
\(873\) −10.3891 −0.351619
\(874\) −7.98162 −0.269982
\(875\) 3.57561 0.120878
\(876\) −0.874721 −0.0295541
\(877\) −15.9725 −0.539354 −0.269677 0.962951i \(-0.586917\pi\)
−0.269677 + 0.962951i \(0.586917\pi\)
\(878\) −15.6183 −0.527091
\(879\) 8.94752 0.301792
\(880\) −11.0729 −0.373266
\(881\) −7.31983 −0.246611 −0.123306 0.992369i \(-0.539350\pi\)
−0.123306 + 0.992369i \(0.539350\pi\)
\(882\) 2.15315 0.0725002
\(883\) −41.2582 −1.38845 −0.694224 0.719759i \(-0.744252\pi\)
−0.694224 + 0.719759i \(0.744252\pi\)
\(884\) −23.6486 −0.795389
\(885\) −7.08708 −0.238230
\(886\) −21.4825 −0.721720
\(887\) −38.7293 −1.30040 −0.650202 0.759762i \(-0.725316\pi\)
−0.650202 + 0.759762i \(0.725316\pi\)
\(888\) −1.61144 −0.0540763
\(889\) 0.225215 0.00755348
\(890\) 16.4139 0.550194
\(891\) −7.82428 −0.262123
\(892\) 12.1396 0.406463
\(893\) −14.2752 −0.477702
\(894\) 3.15135 0.105397
\(895\) 51.3993 1.71809
\(896\) 1.00000 0.0334077
\(897\) 19.2446 0.642560
\(898\) −5.15008 −0.171860
\(899\) 0.167837 0.00559767
\(900\) −8.16963 −0.272321
\(901\) −60.7772 −2.02478
\(902\) 5.35285 0.178230
\(903\) 6.51153 0.216690
\(904\) −3.08038 −0.102452
\(905\) 1.47141 0.0489113
\(906\) 20.1415 0.669158
\(907\) 3.54657 0.117762 0.0588810 0.998265i \(-0.481247\pi\)
0.0588810 + 0.998265i \(0.481247\pi\)
\(908\) 13.9190 0.461920
\(909\) −23.8032 −0.789502
\(910\) −12.4234 −0.411832
\(911\) −13.1576 −0.435932 −0.217966 0.975956i \(-0.569942\pi\)
−0.217966 + 0.975956i \(0.569942\pi\)
\(912\) −1.47140 −0.0487228
\(913\) −40.2899 −1.33340
\(914\) 24.1714 0.799520
\(915\) 31.0744 1.02729
\(916\) −12.5004 −0.413024
\(917\) 12.8742 0.425144
\(918\) −26.7696 −0.883528
\(919\) −24.0443 −0.793147 −0.396573 0.918003i \(-0.629801\pi\)
−0.396573 + 0.918003i \(0.629801\pi\)
\(920\) −14.8035 −0.488058
\(921\) 15.0162 0.494801
\(922\) 19.9699 0.657673
\(923\) 36.1143 1.18872
\(924\) −3.43608 −0.113039
\(925\) −6.64413 −0.218458
\(926\) −24.5172 −0.805686
\(927\) −31.9510 −1.04941
\(928\) 0.281679 0.00924658
\(929\) −9.38922 −0.308050 −0.154025 0.988067i \(-0.549224\pi\)
−0.154025 + 0.988067i \(0.549224\pi\)
\(930\) −1.62606 −0.0533205
\(931\) 1.59892 0.0524024
\(932\) −0.392089 −0.0128433
\(933\) −28.0119 −0.917068
\(934\) −4.73023 −0.154778
\(935\) −62.5064 −2.04418
\(936\) −9.02016 −0.294833
\(937\) −22.4978 −0.734970 −0.367485 0.930030i \(-0.619781\pi\)
−0.367485 + 0.930030i \(0.619781\pi\)
\(938\) −0.827398 −0.0270155
\(939\) −3.49535 −0.114066
\(940\) −26.4763 −0.863561
\(941\) 30.5767 0.996773 0.498386 0.866955i \(-0.333926\pi\)
0.498386 + 0.866955i \(0.333926\pi\)
\(942\) 2.57691 0.0839603
\(943\) 7.15633 0.233042
\(944\) 2.59695 0.0845235
\(945\) −14.0629 −0.457468
\(946\) 26.4203 0.859000
\(947\) −20.0129 −0.650331 −0.325166 0.945657i \(-0.605420\pi\)
−0.325166 + 0.945657i \(0.605420\pi\)
\(948\) −12.5809 −0.408610
\(949\) −3.98205 −0.129263
\(950\) −6.06672 −0.196831
\(951\) −28.9812 −0.939779
\(952\) 5.64502 0.182956
\(953\) 22.3561 0.724184 0.362092 0.932142i \(-0.382063\pi\)
0.362092 + 0.932142i \(0.382063\pi\)
\(954\) −23.1819 −0.750542
\(955\) 38.4387 1.24385
\(956\) 17.1919 0.556026
\(957\) −0.967874 −0.0312869
\(958\) 15.6484 0.505577
\(959\) 11.8084 0.381313
\(960\) −2.72900 −0.0880782
\(961\) −30.6450 −0.988547
\(962\) −7.33585 −0.236517
\(963\) 12.4513 0.401238
\(964\) −5.92629 −0.190873
\(965\) 48.0111 1.54553
\(966\) −4.59377 −0.147802
\(967\) −7.43118 −0.238971 −0.119485 0.992836i \(-0.538124\pi\)
−0.119485 + 0.992836i \(0.538124\pi\)
\(968\) −2.94181 −0.0945532
\(969\) −8.30606 −0.266829
\(970\) −14.3089 −0.459431
\(971\) 14.4503 0.463731 0.231866 0.972748i \(-0.425517\pi\)
0.231866 + 0.972748i \(0.425517\pi\)
\(972\) −16.1549 −0.518167
\(973\) 3.68604 0.118169
\(974\) 35.3945 1.13411
\(975\) 14.6276 0.468458
\(976\) −11.3867 −0.364480
\(977\) 28.9904 0.927486 0.463743 0.885970i \(-0.346506\pi\)
0.463743 + 0.885970i \(0.346506\pi\)
\(978\) 4.61497 0.147571
\(979\) 20.6667 0.660509
\(980\) 2.96551 0.0947299
\(981\) 3.25838 0.104032
\(982\) −12.5717 −0.401180
\(983\) 6.71003 0.214017 0.107008 0.994258i \(-0.465873\pi\)
0.107008 + 0.994258i \(0.465873\pi\)
\(984\) 1.31926 0.0420564
\(985\) 57.3341 1.82682
\(986\) 1.59009 0.0506386
\(987\) −8.21601 −0.261518
\(988\) −6.69833 −0.213102
\(989\) 35.3219 1.12317
\(990\) −23.8415 −0.757732
\(991\) −39.6410 −1.25924 −0.629619 0.776904i \(-0.716789\pi\)
−0.629619 + 0.776904i \(0.716789\pi\)
\(992\) 0.595843 0.0189180
\(993\) −16.2576 −0.515918
\(994\) −8.62062 −0.273430
\(995\) −12.7183 −0.403196
\(996\) −9.92980 −0.314638
\(997\) −11.2595 −0.356592 −0.178296 0.983977i \(-0.557058\pi\)
−0.178296 + 0.983977i \(0.557058\pi\)
\(998\) 23.1265 0.732057
\(999\) −8.30398 −0.262726
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 \(a_p\))