Properties

Label 8018.2.a.f.1.3
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 1.3
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-3.15270 q^{3}\) \(+1.00000 q^{4}\) \(-2.25930 q^{5}\) \(+3.15270 q^{6}\) \(-1.49908 q^{7}\) \(-1.00000 q^{8}\) \(+6.93949 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-3.15270 q^{3}\) \(+1.00000 q^{4}\) \(-2.25930 q^{5}\) \(+3.15270 q^{6}\) \(-1.49908 q^{7}\) \(-1.00000 q^{8}\) \(+6.93949 q^{9}\) \(+2.25930 q^{10}\) \(-3.03780 q^{11}\) \(-3.15270 q^{12}\) \(+3.87845 q^{13}\) \(+1.49908 q^{14}\) \(+7.12289 q^{15}\) \(+1.00000 q^{16}\) \(-3.17671 q^{17}\) \(-6.93949 q^{18}\) \(-1.00000 q^{19}\) \(-2.25930 q^{20}\) \(+4.72616 q^{21}\) \(+3.03780 q^{22}\) \(+3.24887 q^{23}\) \(+3.15270 q^{24}\) \(+0.104448 q^{25}\) \(-3.87845 q^{26}\) \(-12.4200 q^{27}\) \(-1.49908 q^{28}\) \(+1.46754 q^{29}\) \(-7.12289 q^{30}\) \(-10.7748 q^{31}\) \(-1.00000 q^{32}\) \(+9.57725 q^{33}\) \(+3.17671 q^{34}\) \(+3.38689 q^{35}\) \(+6.93949 q^{36}\) \(+3.23320 q^{37}\) \(+1.00000 q^{38}\) \(-12.2276 q^{39}\) \(+2.25930 q^{40}\) \(+3.81474 q^{41}\) \(-4.72616 q^{42}\) \(+1.14203 q^{43}\) \(-3.03780 q^{44}\) \(-15.6784 q^{45}\) \(-3.24887 q^{46}\) \(-0.559156 q^{47}\) \(-3.15270 q^{48}\) \(-4.75275 q^{49}\) \(-0.104448 q^{50}\) \(+10.0152 q^{51}\) \(+3.87845 q^{52}\) \(-1.40524 q^{53}\) \(+12.4200 q^{54}\) \(+6.86330 q^{55}\) \(+1.49908 q^{56}\) \(+3.15270 q^{57}\) \(-1.46754 q^{58}\) \(-0.460242 q^{59}\) \(+7.12289 q^{60}\) \(-2.40804 q^{61}\) \(+10.7748 q^{62}\) \(-10.4029 q^{63}\) \(+1.00000 q^{64}\) \(-8.76260 q^{65}\) \(-9.57725 q^{66}\) \(-9.34516 q^{67}\) \(-3.17671 q^{68}\) \(-10.2427 q^{69}\) \(-3.38689 q^{70}\) \(+4.71211 q^{71}\) \(-6.93949 q^{72}\) \(-8.63876 q^{73}\) \(-3.23320 q^{74}\) \(-0.329294 q^{75}\) \(-1.00000 q^{76}\) \(+4.55392 q^{77}\) \(+12.2276 q^{78}\) \(+6.74778 q^{79}\) \(-2.25930 q^{80}\) \(+18.3380 q^{81}\) \(-3.81474 q^{82}\) \(+2.80787 q^{83}\) \(+4.72616 q^{84}\) \(+7.17716 q^{85}\) \(-1.14203 q^{86}\) \(-4.62671 q^{87}\) \(+3.03780 q^{88}\) \(+16.9928 q^{89}\) \(+15.6784 q^{90}\) \(-5.81413 q^{91}\) \(+3.24887 q^{92}\) \(+33.9698 q^{93}\) \(+0.559156 q^{94}\) \(+2.25930 q^{95}\) \(+3.15270 q^{96}\) \(+7.51517 q^{97}\) \(+4.75275 q^{98}\) \(-21.0808 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.15270 −1.82021 −0.910105 0.414378i \(-0.863999\pi\)
−0.910105 + 0.414378i \(0.863999\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.25930 −1.01039 −0.505195 0.863005i \(-0.668580\pi\)
−0.505195 + 0.863005i \(0.668580\pi\)
\(6\) 3.15270 1.28708
\(7\) −1.49908 −0.566601 −0.283300 0.959031i \(-0.591429\pi\)
−0.283300 + 0.959031i \(0.591429\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.93949 2.31316
\(10\) 2.25930 0.714454
\(11\) −3.03780 −0.915930 −0.457965 0.888970i \(-0.651422\pi\)
−0.457965 + 0.888970i \(0.651422\pi\)
\(12\) −3.15270 −0.910105
\(13\) 3.87845 1.07569 0.537844 0.843044i \(-0.319239\pi\)
0.537844 + 0.843044i \(0.319239\pi\)
\(14\) 1.49908 0.400647
\(15\) 7.12289 1.83912
\(16\) 1.00000 0.250000
\(17\) −3.17671 −0.770466 −0.385233 0.922819i \(-0.625879\pi\)
−0.385233 + 0.922819i \(0.625879\pi\)
\(18\) −6.93949 −1.63565
\(19\) −1.00000 −0.229416
\(20\) −2.25930 −0.505195
\(21\) 4.72616 1.03133
\(22\) 3.03780 0.647661
\(23\) 3.24887 0.677437 0.338719 0.940888i \(-0.390007\pi\)
0.338719 + 0.940888i \(0.390007\pi\)
\(24\) 3.15270 0.643541
\(25\) 0.104448 0.0208897
\(26\) −3.87845 −0.760627
\(27\) −12.4200 −2.39023
\(28\) −1.49908 −0.283300
\(29\) 1.46754 0.272516 0.136258 0.990673i \(-0.456492\pi\)
0.136258 + 0.990673i \(0.456492\pi\)
\(30\) −7.12289 −1.30046
\(31\) −10.7748 −1.93522 −0.967608 0.252456i \(-0.918762\pi\)
−0.967608 + 0.252456i \(0.918762\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.57725 1.66719
\(34\) 3.17671 0.544802
\(35\) 3.38689 0.572488
\(36\) 6.93949 1.15658
\(37\) 3.23320 0.531536 0.265768 0.964037i \(-0.414375\pi\)
0.265768 + 0.964037i \(0.414375\pi\)
\(38\) 1.00000 0.162221
\(39\) −12.2276 −1.95798
\(40\) 2.25930 0.357227
\(41\) 3.81474 0.595763 0.297881 0.954603i \(-0.403720\pi\)
0.297881 + 0.954603i \(0.403720\pi\)
\(42\) −4.72616 −0.729262
\(43\) 1.14203 0.174158 0.0870792 0.996201i \(-0.472247\pi\)
0.0870792 + 0.996201i \(0.472247\pi\)
\(44\) −3.03780 −0.457965
\(45\) −15.6784 −2.33720
\(46\) −3.24887 −0.479020
\(47\) −0.559156 −0.0815613 −0.0407807 0.999168i \(-0.512984\pi\)
−0.0407807 + 0.999168i \(0.512984\pi\)
\(48\) −3.15270 −0.455052
\(49\) −4.75275 −0.678964
\(50\) −0.104448 −0.0147712
\(51\) 10.0152 1.40241
\(52\) 3.87845 0.537844
\(53\) −1.40524 −0.193024 −0.0965120 0.995332i \(-0.530769\pi\)
−0.0965120 + 0.995332i \(0.530769\pi\)
\(54\) 12.4200 1.69015
\(55\) 6.86330 0.925448
\(56\) 1.49908 0.200324
\(57\) 3.15270 0.417585
\(58\) −1.46754 −0.192698
\(59\) −0.460242 −0.0599184 −0.0299592 0.999551i \(-0.509538\pi\)
−0.0299592 + 0.999551i \(0.509538\pi\)
\(60\) 7.12289 0.919561
\(61\) −2.40804 −0.308319 −0.154159 0.988046i \(-0.549267\pi\)
−0.154159 + 0.988046i \(0.549267\pi\)
\(62\) 10.7748 1.36840
\(63\) −10.4029 −1.31064
\(64\) 1.00000 0.125000
\(65\) −8.76260 −1.08687
\(66\) −9.57725 −1.17888
\(67\) −9.34516 −1.14169 −0.570847 0.821057i \(-0.693385\pi\)
−0.570847 + 0.821057i \(0.693385\pi\)
\(68\) −3.17671 −0.385233
\(69\) −10.2427 −1.23308
\(70\) −3.38689 −0.404810
\(71\) 4.71211 0.559225 0.279612 0.960113i \(-0.409794\pi\)
0.279612 + 0.960113i \(0.409794\pi\)
\(72\) −6.93949 −0.817826
\(73\) −8.63876 −1.01109 −0.505545 0.862800i \(-0.668709\pi\)
−0.505545 + 0.862800i \(0.668709\pi\)
\(74\) −3.23320 −0.375852
\(75\) −0.329294 −0.0380236
\(76\) −1.00000 −0.114708
\(77\) 4.55392 0.518967
\(78\) 12.2276 1.38450
\(79\) 6.74778 0.759184 0.379592 0.925154i \(-0.376064\pi\)
0.379592 + 0.925154i \(0.376064\pi\)
\(80\) −2.25930 −0.252598
\(81\) 18.3380 2.03756
\(82\) −3.81474 −0.421268
\(83\) 2.80787 0.308203 0.154102 0.988055i \(-0.450752\pi\)
0.154102 + 0.988055i \(0.450752\pi\)
\(84\) 4.72616 0.515666
\(85\) 7.17716 0.778472
\(86\) −1.14203 −0.123149
\(87\) −4.62671 −0.496035
\(88\) 3.03780 0.323830
\(89\) 16.9928 1.80123 0.900615 0.434617i \(-0.143116\pi\)
0.900615 + 0.434617i \(0.143116\pi\)
\(90\) 15.6784 1.65265
\(91\) −5.81413 −0.609486
\(92\) 3.24887 0.338719
\(93\) 33.9698 3.52250
\(94\) 0.559156 0.0576726
\(95\) 2.25930 0.231800
\(96\) 3.15270 0.321771
\(97\) 7.51517 0.763049 0.381525 0.924359i \(-0.375399\pi\)
0.381525 + 0.924359i \(0.375399\pi\)
\(98\) 4.75275 0.480100
\(99\) −21.0808 −2.11870
\(100\) 0.104448 0.0104448
\(101\) 16.6574 1.65748 0.828738 0.559637i \(-0.189059\pi\)
0.828738 + 0.559637i \(0.189059\pi\)
\(102\) −10.0152 −0.991654
\(103\) −0.337757 −0.0332801 −0.0166401 0.999862i \(-0.505297\pi\)
−0.0166401 + 0.999862i \(0.505297\pi\)
\(104\) −3.87845 −0.380313
\(105\) −10.6778 −1.04205
\(106\) 1.40524 0.136489
\(107\) −10.1160 −0.977954 −0.488977 0.872297i \(-0.662630\pi\)
−0.488977 + 0.872297i \(0.662630\pi\)
\(108\) −12.4200 −1.19512
\(109\) −6.73026 −0.644642 −0.322321 0.946630i \(-0.604463\pi\)
−0.322321 + 0.946630i \(0.604463\pi\)
\(110\) −6.86330 −0.654390
\(111\) −10.1933 −0.967506
\(112\) −1.49908 −0.141650
\(113\) −2.15323 −0.202559 −0.101279 0.994858i \(-0.532294\pi\)
−0.101279 + 0.994858i \(0.532294\pi\)
\(114\) −3.15270 −0.295277
\(115\) −7.34019 −0.684476
\(116\) 1.46754 0.136258
\(117\) 26.9145 2.48824
\(118\) 0.460242 0.0423687
\(119\) 4.76216 0.436547
\(120\) −7.12289 −0.650228
\(121\) −1.77179 −0.161071
\(122\) 2.40804 0.218014
\(123\) −12.0267 −1.08441
\(124\) −10.7748 −0.967608
\(125\) 11.0605 0.989284
\(126\) 10.4029 0.926762
\(127\) −10.6611 −0.946022 −0.473011 0.881057i \(-0.656833\pi\)
−0.473011 + 0.881057i \(0.656833\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.60048 −0.317005
\(130\) 8.76260 0.768530
\(131\) 11.7544 1.02699 0.513495 0.858093i \(-0.328351\pi\)
0.513495 + 0.858093i \(0.328351\pi\)
\(132\) 9.57725 0.833593
\(133\) 1.49908 0.129987
\(134\) 9.34516 0.807299
\(135\) 28.0605 2.41507
\(136\) 3.17671 0.272401
\(137\) 2.68977 0.229803 0.114901 0.993377i \(-0.463345\pi\)
0.114901 + 0.993377i \(0.463345\pi\)
\(138\) 10.2427 0.871917
\(139\) 8.43676 0.715596 0.357798 0.933799i \(-0.383528\pi\)
0.357798 + 0.933799i \(0.383528\pi\)
\(140\) 3.38689 0.286244
\(141\) 1.76285 0.148459
\(142\) −4.71211 −0.395432
\(143\) −11.7820 −0.985256
\(144\) 6.93949 0.578291
\(145\) −3.31562 −0.275347
\(146\) 8.63876 0.714949
\(147\) 14.9840 1.23586
\(148\) 3.23320 0.265768
\(149\) 10.2635 0.840817 0.420409 0.907335i \(-0.361887\pi\)
0.420409 + 0.907335i \(0.361887\pi\)
\(150\) 0.329294 0.0268867
\(151\) 15.1541 1.23323 0.616613 0.787267i \(-0.288504\pi\)
0.616613 + 0.787267i \(0.288504\pi\)
\(152\) 1.00000 0.0811107
\(153\) −22.0448 −1.78221
\(154\) −4.55392 −0.366965
\(155\) 24.3436 1.95533
\(156\) −12.2276 −0.978990
\(157\) 6.87183 0.548432 0.274216 0.961668i \(-0.411582\pi\)
0.274216 + 0.961668i \(0.411582\pi\)
\(158\) −6.74778 −0.536824
\(159\) 4.43028 0.351344
\(160\) 2.25930 0.178614
\(161\) −4.87034 −0.383836
\(162\) −18.3380 −1.44077
\(163\) −14.3771 −1.12611 −0.563053 0.826421i \(-0.690373\pi\)
−0.563053 + 0.826421i \(0.690373\pi\)
\(164\) 3.81474 0.297881
\(165\) −21.6379 −1.68451
\(166\) −2.80787 −0.217933
\(167\) 21.1353 1.63550 0.817749 0.575575i \(-0.195222\pi\)
0.817749 + 0.575575i \(0.195222\pi\)
\(168\) −4.72616 −0.364631
\(169\) 2.04239 0.157107
\(170\) −7.17716 −0.550463
\(171\) −6.93949 −0.530676
\(172\) 1.14203 0.0870792
\(173\) 16.6634 1.26689 0.633447 0.773786i \(-0.281640\pi\)
0.633447 + 0.773786i \(0.281640\pi\)
\(174\) 4.62671 0.350750
\(175\) −0.156577 −0.0118361
\(176\) −3.03780 −0.228983
\(177\) 1.45100 0.109064
\(178\) −16.9928 −1.27366
\(179\) −1.54908 −0.115784 −0.0578918 0.998323i \(-0.518438\pi\)
−0.0578918 + 0.998323i \(0.518438\pi\)
\(180\) −15.6784 −1.16860
\(181\) 11.7252 0.871525 0.435762 0.900062i \(-0.356479\pi\)
0.435762 + 0.900062i \(0.356479\pi\)
\(182\) 5.81413 0.430972
\(183\) 7.59183 0.561204
\(184\) −3.24887 −0.239510
\(185\) −7.30479 −0.537059
\(186\) −33.9698 −2.49078
\(187\) 9.65021 0.705694
\(188\) −0.559156 −0.0407807
\(189\) 18.6186 1.35431
\(190\) −2.25930 −0.163907
\(191\) 10.5849 0.765900 0.382950 0.923769i \(-0.374908\pi\)
0.382950 + 0.923769i \(0.374908\pi\)
\(192\) −3.15270 −0.227526
\(193\) −23.4035 −1.68462 −0.842311 0.538991i \(-0.818806\pi\)
−0.842311 + 0.538991i \(0.818806\pi\)
\(194\) −7.51517 −0.539557
\(195\) 27.6258 1.97832
\(196\) −4.75275 −0.339482
\(197\) 25.3147 1.80360 0.901800 0.432153i \(-0.142246\pi\)
0.901800 + 0.432153i \(0.142246\pi\)
\(198\) 21.0808 1.49814
\(199\) −7.13772 −0.505979 −0.252990 0.967469i \(-0.581414\pi\)
−0.252990 + 0.967469i \(0.581414\pi\)
\(200\) −0.104448 −0.00738562
\(201\) 29.4625 2.07812
\(202\) −16.6574 −1.17201
\(203\) −2.19997 −0.154408
\(204\) 10.0152 0.701205
\(205\) −8.61866 −0.601953
\(206\) 0.337757 0.0235326
\(207\) 22.5455 1.56702
\(208\) 3.87845 0.268922
\(209\) 3.03780 0.210129
\(210\) 10.6778 0.736839
\(211\) −1.00000 −0.0688428
\(212\) −1.40524 −0.0965120
\(213\) −14.8559 −1.01791
\(214\) 10.1160 0.691518
\(215\) −2.58020 −0.175968
\(216\) 12.4200 0.845074
\(217\) 16.1524 1.09650
\(218\) 6.73026 0.455831
\(219\) 27.2354 1.84040
\(220\) 6.86330 0.462724
\(221\) −12.3207 −0.828782
\(222\) 10.1933 0.684130
\(223\) 8.20659 0.549554 0.274777 0.961508i \(-0.411396\pi\)
0.274777 + 0.961508i \(0.411396\pi\)
\(224\) 1.49908 0.100162
\(225\) 0.724818 0.0483212
\(226\) 2.15323 0.143231
\(227\) −9.18561 −0.609671 −0.304835 0.952405i \(-0.598601\pi\)
−0.304835 + 0.952405i \(0.598601\pi\)
\(228\) 3.15270 0.208792
\(229\) 16.8078 1.11069 0.555345 0.831620i \(-0.312586\pi\)
0.555345 + 0.831620i \(0.312586\pi\)
\(230\) 7.34019 0.483998
\(231\) −14.3571 −0.944628
\(232\) −1.46754 −0.0963488
\(233\) −26.7715 −1.75386 −0.876929 0.480620i \(-0.840411\pi\)
−0.876929 + 0.480620i \(0.840411\pi\)
\(234\) −26.9145 −1.75945
\(235\) 1.26330 0.0824088
\(236\) −0.460242 −0.0299592
\(237\) −21.2737 −1.38187
\(238\) −4.76216 −0.308685
\(239\) 8.00344 0.517700 0.258850 0.965918i \(-0.416657\pi\)
0.258850 + 0.965918i \(0.416657\pi\)
\(240\) 7.12289 0.459781
\(241\) 2.93960 0.189356 0.0946781 0.995508i \(-0.469818\pi\)
0.0946781 + 0.995508i \(0.469818\pi\)
\(242\) 1.77179 0.113895
\(243\) −20.5542 −1.31855
\(244\) −2.40804 −0.154159
\(245\) 10.7379 0.686019
\(246\) 12.0267 0.766796
\(247\) −3.87845 −0.246780
\(248\) 10.7748 0.684202
\(249\) −8.85234 −0.560995
\(250\) −11.0605 −0.699530
\(251\) 4.64008 0.292879 0.146440 0.989220i \(-0.453219\pi\)
0.146440 + 0.989220i \(0.453219\pi\)
\(252\) −10.4029 −0.655320
\(253\) −9.86942 −0.620485
\(254\) 10.6611 0.668938
\(255\) −22.6274 −1.41698
\(256\) 1.00000 0.0625000
\(257\) 22.2718 1.38928 0.694639 0.719358i \(-0.255564\pi\)
0.694639 + 0.719358i \(0.255564\pi\)
\(258\) 3.60048 0.224156
\(259\) −4.84685 −0.301168
\(260\) −8.76260 −0.543433
\(261\) 10.1840 0.630373
\(262\) −11.7544 −0.726191
\(263\) −31.1446 −1.92046 −0.960228 0.279217i \(-0.909925\pi\)
−0.960228 + 0.279217i \(0.909925\pi\)
\(264\) −9.57725 −0.589439
\(265\) 3.17485 0.195030
\(266\) −1.49908 −0.0919148
\(267\) −53.5730 −3.27862
\(268\) −9.34516 −0.570847
\(269\) 16.5378 1.00833 0.504164 0.863608i \(-0.331801\pi\)
0.504164 + 0.863608i \(0.331801\pi\)
\(270\) −28.0605 −1.70771
\(271\) −2.78737 −0.169321 −0.0846604 0.996410i \(-0.526981\pi\)
−0.0846604 + 0.996410i \(0.526981\pi\)
\(272\) −3.17671 −0.192617
\(273\) 18.3302 1.10939
\(274\) −2.68977 −0.162495
\(275\) −0.317293 −0.0191335
\(276\) −10.2427 −0.616539
\(277\) −6.01882 −0.361636 −0.180818 0.983517i \(-0.557874\pi\)
−0.180818 + 0.983517i \(0.557874\pi\)
\(278\) −8.43676 −0.506003
\(279\) −74.7718 −4.47647
\(280\) −3.38689 −0.202405
\(281\) 22.4994 1.34220 0.671102 0.741365i \(-0.265821\pi\)
0.671102 + 0.741365i \(0.265821\pi\)
\(282\) −1.76285 −0.104976
\(283\) 24.3138 1.44531 0.722654 0.691210i \(-0.242922\pi\)
0.722654 + 0.691210i \(0.242922\pi\)
\(284\) 4.71211 0.279612
\(285\) −7.12289 −0.421924
\(286\) 11.7820 0.696681
\(287\) −5.71862 −0.337560
\(288\) −6.93949 −0.408913
\(289\) −6.90849 −0.406382
\(290\) 3.31562 0.194700
\(291\) −23.6930 −1.38891
\(292\) −8.63876 −0.505545
\(293\) −7.79302 −0.455273 −0.227636 0.973746i \(-0.573100\pi\)
−0.227636 + 0.973746i \(0.573100\pi\)
\(294\) −14.9840 −0.873882
\(295\) 1.03983 0.0605410
\(296\) −3.23320 −0.187926
\(297\) 37.7295 2.18928
\(298\) −10.2635 −0.594548
\(299\) 12.6006 0.728712
\(300\) −0.329294 −0.0190118
\(301\) −1.71200 −0.0986782
\(302\) −15.1541 −0.872022
\(303\) −52.5158 −3.01695
\(304\) −1.00000 −0.0573539
\(305\) 5.44050 0.311522
\(306\) 22.0448 1.26022
\(307\) 9.44315 0.538949 0.269475 0.963008i \(-0.413150\pi\)
0.269475 + 0.963008i \(0.413150\pi\)
\(308\) 4.55392 0.259483
\(309\) 1.06484 0.0605768
\(310\) −24.3436 −1.38262
\(311\) −25.0081 −1.41808 −0.709040 0.705168i \(-0.750871\pi\)
−0.709040 + 0.705168i \(0.750871\pi\)
\(312\) 12.2276 0.692250
\(313\) −5.70980 −0.322737 −0.161368 0.986894i \(-0.551591\pi\)
−0.161368 + 0.986894i \(0.551591\pi\)
\(314\) −6.87183 −0.387800
\(315\) 23.5032 1.32426
\(316\) 6.74778 0.379592
\(317\) −23.9285 −1.34396 −0.671979 0.740570i \(-0.734555\pi\)
−0.671979 + 0.740570i \(0.734555\pi\)
\(318\) −4.43028 −0.248438
\(319\) −4.45809 −0.249605
\(320\) −2.25930 −0.126299
\(321\) 31.8928 1.78008
\(322\) 4.87034 0.271413
\(323\) 3.17671 0.176757
\(324\) 18.3380 1.01878
\(325\) 0.405098 0.0224708
\(326\) 14.3771 0.796277
\(327\) 21.2185 1.17338
\(328\) −3.81474 −0.210634
\(329\) 0.838223 0.0462127
\(330\) 21.6379 1.19113
\(331\) −8.34775 −0.458834 −0.229417 0.973328i \(-0.573682\pi\)
−0.229417 + 0.973328i \(0.573682\pi\)
\(332\) 2.80787 0.154102
\(333\) 22.4368 1.22953
\(334\) −21.1353 −1.15647
\(335\) 21.1136 1.15356
\(336\) 4.72616 0.257833
\(337\) −1.60844 −0.0876174 −0.0438087 0.999040i \(-0.513949\pi\)
−0.0438087 + 0.999040i \(0.513949\pi\)
\(338\) −2.04239 −0.111091
\(339\) 6.78848 0.368699
\(340\) 7.17716 0.389236
\(341\) 32.7318 1.77252
\(342\) 6.93949 0.375244
\(343\) 17.6184 0.951302
\(344\) −1.14203 −0.0615743
\(345\) 23.1414 1.24589
\(346\) −16.6634 −0.895829
\(347\) −10.7805 −0.578727 −0.289364 0.957219i \(-0.593444\pi\)
−0.289364 + 0.957219i \(0.593444\pi\)
\(348\) −4.62671 −0.248018
\(349\) 17.7810 0.951796 0.475898 0.879501i \(-0.342123\pi\)
0.475898 + 0.879501i \(0.342123\pi\)
\(350\) 0.156577 0.00836939
\(351\) −48.1704 −2.57114
\(352\) 3.03780 0.161915
\(353\) 13.5785 0.722713 0.361357 0.932428i \(-0.382314\pi\)
0.361357 + 0.932428i \(0.382314\pi\)
\(354\) −1.45100 −0.0771199
\(355\) −10.6461 −0.565036
\(356\) 16.9928 0.900615
\(357\) −15.0136 −0.794607
\(358\) 1.54908 0.0818714
\(359\) 5.04359 0.266190 0.133095 0.991103i \(-0.457508\pi\)
0.133095 + 0.991103i \(0.457508\pi\)
\(360\) 15.6784 0.826324
\(361\) 1.00000 0.0526316
\(362\) −11.7252 −0.616261
\(363\) 5.58590 0.293184
\(364\) −5.81413 −0.304743
\(365\) 19.5176 1.02160
\(366\) −7.59183 −0.396831
\(367\) 2.74679 0.143381 0.0716907 0.997427i \(-0.477161\pi\)
0.0716907 + 0.997427i \(0.477161\pi\)
\(368\) 3.24887 0.169359
\(369\) 26.4724 1.37810
\(370\) 7.30479 0.379758
\(371\) 2.10657 0.109368
\(372\) 33.9698 1.76125
\(373\) 10.2367 0.530037 0.265018 0.964243i \(-0.414622\pi\)
0.265018 + 0.964243i \(0.414622\pi\)
\(374\) −9.65021 −0.499001
\(375\) −34.8705 −1.80070
\(376\) 0.559156 0.0288363
\(377\) 5.69179 0.293142
\(378\) −18.6186 −0.957639
\(379\) 3.38717 0.173987 0.0869937 0.996209i \(-0.472274\pi\)
0.0869937 + 0.996209i \(0.472274\pi\)
\(380\) 2.25930 0.115900
\(381\) 33.6113 1.72196
\(382\) −10.5849 −0.541573
\(383\) −8.12315 −0.415074 −0.207537 0.978227i \(-0.566545\pi\)
−0.207537 + 0.978227i \(0.566545\pi\)
\(384\) 3.15270 0.160885
\(385\) −10.2887 −0.524359
\(386\) 23.4035 1.19121
\(387\) 7.92512 0.402856
\(388\) 7.51517 0.381525
\(389\) 10.6628 0.540626 0.270313 0.962772i \(-0.412873\pi\)
0.270313 + 0.962772i \(0.412873\pi\)
\(390\) −27.6258 −1.39889
\(391\) −10.3207 −0.521942
\(392\) 4.75275 0.240050
\(393\) −37.0581 −1.86934
\(394\) −25.3147 −1.27534
\(395\) −15.2453 −0.767073
\(396\) −21.0808 −1.05935
\(397\) 1.32452 0.0664760 0.0332380 0.999447i \(-0.489418\pi\)
0.0332380 + 0.999447i \(0.489418\pi\)
\(398\) 7.13772 0.357781
\(399\) −4.72616 −0.236604
\(400\) 0.104448 0.00522242
\(401\) −17.3827 −0.868053 −0.434026 0.900900i \(-0.642908\pi\)
−0.434026 + 0.900900i \(0.642908\pi\)
\(402\) −29.4625 −1.46945
\(403\) −41.7897 −2.08169
\(404\) 16.6574 0.828738
\(405\) −41.4311 −2.05873
\(406\) 2.19997 0.109183
\(407\) −9.82182 −0.486850
\(408\) −10.0152 −0.495827
\(409\) 12.0300 0.594844 0.297422 0.954746i \(-0.403873\pi\)
0.297422 + 0.954746i \(0.403873\pi\)
\(410\) 8.61866 0.425645
\(411\) −8.48003 −0.418289
\(412\) −0.337757 −0.0166401
\(413\) 0.689941 0.0339498
\(414\) −22.5455 −1.10805
\(415\) −6.34382 −0.311406
\(416\) −3.87845 −0.190157
\(417\) −26.5985 −1.30254
\(418\) −3.03780 −0.148584
\(419\) 9.89216 0.483264 0.241632 0.970368i \(-0.422317\pi\)
0.241632 + 0.970368i \(0.422317\pi\)
\(420\) −10.6778 −0.521024
\(421\) −28.3477 −1.38158 −0.690792 0.723053i \(-0.742738\pi\)
−0.690792 + 0.723053i \(0.742738\pi\)
\(422\) 1.00000 0.0486792
\(423\) −3.88026 −0.188665
\(424\) 1.40524 0.0682443
\(425\) −0.331803 −0.0160948
\(426\) 14.8559 0.719769
\(427\) 3.60986 0.174694
\(428\) −10.1160 −0.488977
\(429\) 37.1449 1.79337
\(430\) 2.58020 0.124428
\(431\) 0.658752 0.0317310 0.0158655 0.999874i \(-0.494950\pi\)
0.0158655 + 0.999874i \(0.494950\pi\)
\(432\) −12.4200 −0.597558
\(433\) 6.23777 0.299768 0.149884 0.988704i \(-0.452110\pi\)
0.149884 + 0.988704i \(0.452110\pi\)
\(434\) −16.1524 −0.775339
\(435\) 10.4531 0.501190
\(436\) −6.73026 −0.322321
\(437\) −3.24887 −0.155415
\(438\) −27.2354 −1.30136
\(439\) −40.6260 −1.93897 −0.969487 0.245141i \(-0.921166\pi\)
−0.969487 + 0.245141i \(0.921166\pi\)
\(440\) −6.86330 −0.327195
\(441\) −32.9816 −1.57055
\(442\) 12.3207 0.586037
\(443\) 10.7549 0.510979 0.255489 0.966812i \(-0.417763\pi\)
0.255489 + 0.966812i \(0.417763\pi\)
\(444\) −10.1933 −0.483753
\(445\) −38.3918 −1.81995
\(446\) −8.20659 −0.388593
\(447\) −32.3576 −1.53046
\(448\) −1.49908 −0.0708251
\(449\) −37.2453 −1.75771 −0.878857 0.477085i \(-0.841693\pi\)
−0.878857 + 0.477085i \(0.841693\pi\)
\(450\) −0.724818 −0.0341683
\(451\) −11.5884 −0.545677
\(452\) −2.15323 −0.101279
\(453\) −47.7764 −2.24473
\(454\) 9.18561 0.431102
\(455\) 13.1359 0.615819
\(456\) −3.15270 −0.147638
\(457\) −17.6885 −0.827432 −0.413716 0.910406i \(-0.635769\pi\)
−0.413716 + 0.910406i \(0.635769\pi\)
\(458\) −16.8078 −0.785377
\(459\) 39.4548 1.84159
\(460\) −7.34019 −0.342238
\(461\) −0.994485 −0.0463178 −0.0231589 0.999732i \(-0.507372\pi\)
−0.0231589 + 0.999732i \(0.507372\pi\)
\(462\) 14.3571 0.667953
\(463\) −5.07023 −0.235634 −0.117817 0.993035i \(-0.537590\pi\)
−0.117817 + 0.993035i \(0.537590\pi\)
\(464\) 1.46754 0.0681289
\(465\) −76.7480 −3.55910
\(466\) 26.7715 1.24016
\(467\) −6.05126 −0.280019 −0.140009 0.990150i \(-0.544713\pi\)
−0.140009 + 0.990150i \(0.544713\pi\)
\(468\) 26.9145 1.24412
\(469\) 14.0092 0.646884
\(470\) −1.26330 −0.0582718
\(471\) −21.6648 −0.998260
\(472\) 0.460242 0.0211843
\(473\) −3.46926 −0.159517
\(474\) 21.2737 0.977133
\(475\) −0.104448 −0.00479242
\(476\) 4.76216 0.218273
\(477\) −9.75162 −0.446496
\(478\) −8.00344 −0.366069
\(479\) 17.5383 0.801346 0.400673 0.916221i \(-0.368776\pi\)
0.400673 + 0.916221i \(0.368776\pi\)
\(480\) −7.12289 −0.325114
\(481\) 12.5398 0.571767
\(482\) −2.93960 −0.133895
\(483\) 15.3547 0.698663
\(484\) −1.77179 −0.0805357
\(485\) −16.9790 −0.770978
\(486\) 20.5542 0.932356
\(487\) 16.2677 0.737162 0.368581 0.929596i \(-0.379844\pi\)
0.368581 + 0.929596i \(0.379844\pi\)
\(488\) 2.40804 0.109007
\(489\) 45.3268 2.04975
\(490\) −10.7379 −0.485088
\(491\) 26.8743 1.21282 0.606410 0.795152i \(-0.292609\pi\)
0.606410 + 0.795152i \(0.292609\pi\)
\(492\) −12.0267 −0.542207
\(493\) −4.66196 −0.209964
\(494\) 3.87845 0.174500
\(495\) 47.6278 2.14071
\(496\) −10.7748 −0.483804
\(497\) −7.06386 −0.316857
\(498\) 8.85234 0.396683
\(499\) 27.3801 1.22570 0.612850 0.790199i \(-0.290023\pi\)
0.612850 + 0.790199i \(0.290023\pi\)
\(500\) 11.0605 0.494642
\(501\) −66.6331 −2.97695
\(502\) −4.64008 −0.207097
\(503\) −30.1377 −1.34377 −0.671887 0.740654i \(-0.734516\pi\)
−0.671887 + 0.740654i \(0.734516\pi\)
\(504\) 10.4029 0.463381
\(505\) −37.6342 −1.67470
\(506\) 9.86942 0.438749
\(507\) −6.43902 −0.285967
\(508\) −10.6611 −0.473011
\(509\) 3.93003 0.174196 0.0870978 0.996200i \(-0.472241\pi\)
0.0870978 + 0.996200i \(0.472241\pi\)
\(510\) 22.6274 1.00196
\(511\) 12.9502 0.572884
\(512\) −1.00000 −0.0441942
\(513\) 12.4200 0.548356
\(514\) −22.2718 −0.982369
\(515\) 0.763094 0.0336260
\(516\) −3.60048 −0.158502
\(517\) 1.69860 0.0747045
\(518\) 4.84685 0.212958
\(519\) −52.5346 −2.30601
\(520\) 8.76260 0.384265
\(521\) 23.3312 1.02216 0.511079 0.859534i \(-0.329246\pi\)
0.511079 + 0.859534i \(0.329246\pi\)
\(522\) −10.1840 −0.445741
\(523\) −25.0647 −1.09600 −0.548002 0.836477i \(-0.684611\pi\)
−0.548002 + 0.836477i \(0.684611\pi\)
\(524\) 11.7544 0.513495
\(525\) 0.493639 0.0215442
\(526\) 31.1446 1.35797
\(527\) 34.2286 1.49102
\(528\) 9.57725 0.416796
\(529\) −12.4448 −0.541079
\(530\) −3.17485 −0.137907
\(531\) −3.19384 −0.138601
\(532\) 1.49908 0.0649936
\(533\) 14.7953 0.640856
\(534\) 53.5730 2.31833
\(535\) 22.8552 0.988116
\(536\) 9.34516 0.403650
\(537\) 4.88378 0.210750
\(538\) −16.5378 −0.712995
\(539\) 14.4379 0.621883
\(540\) 28.0605 1.20753
\(541\) 11.5126 0.494966 0.247483 0.968892i \(-0.420397\pi\)
0.247483 + 0.968892i \(0.420397\pi\)
\(542\) 2.78737 0.119728
\(543\) −36.9659 −1.58636
\(544\) 3.17671 0.136200
\(545\) 15.2057 0.651341
\(546\) −18.3302 −0.784459
\(547\) −16.0788 −0.687480 −0.343740 0.939065i \(-0.611694\pi\)
−0.343740 + 0.939065i \(0.611694\pi\)
\(548\) 2.68977 0.114901
\(549\) −16.7106 −0.713191
\(550\) 0.317293 0.0135294
\(551\) −1.46754 −0.0625194
\(552\) 10.2427 0.435959
\(553\) −10.1155 −0.430154
\(554\) 6.01882 0.255715
\(555\) 23.0298 0.977559
\(556\) 8.43676 0.357798
\(557\) 17.7042 0.750153 0.375077 0.926994i \(-0.377616\pi\)
0.375077 + 0.926994i \(0.377616\pi\)
\(558\) 74.7718 3.16534
\(559\) 4.42932 0.187340
\(560\) 3.38689 0.143122
\(561\) −30.4242 −1.28451
\(562\) −22.4994 −0.949081
\(563\) −38.4061 −1.61862 −0.809311 0.587380i \(-0.800159\pi\)
−0.809311 + 0.587380i \(0.800159\pi\)
\(564\) 1.76285 0.0742294
\(565\) 4.86480 0.204664
\(566\) −24.3138 −1.02199
\(567\) −27.4902 −1.15448
\(568\) −4.71211 −0.197716
\(569\) 27.1065 1.13636 0.568182 0.822903i \(-0.307647\pi\)
0.568182 + 0.822903i \(0.307647\pi\)
\(570\) 7.12289 0.298345
\(571\) 19.5831 0.819527 0.409764 0.912192i \(-0.365611\pi\)
0.409764 + 0.912192i \(0.365611\pi\)
\(572\) −11.7820 −0.492628
\(573\) −33.3711 −1.39410
\(574\) 5.71862 0.238691
\(575\) 0.339340 0.0141514
\(576\) 6.93949 0.289145
\(577\) 22.4007 0.932553 0.466277 0.884639i \(-0.345595\pi\)
0.466277 + 0.884639i \(0.345595\pi\)
\(578\) 6.90849 0.287355
\(579\) 73.7842 3.06637
\(580\) −3.31562 −0.137674
\(581\) −4.20923 −0.174628
\(582\) 23.6930 0.982108
\(583\) 4.26882 0.176797
\(584\) 8.63876 0.357474
\(585\) −60.8079 −2.51410
\(586\) 7.79302 0.321927
\(587\) 9.08578 0.375010 0.187505 0.982264i \(-0.439960\pi\)
0.187505 + 0.982264i \(0.439960\pi\)
\(588\) 14.9840 0.617928
\(589\) 10.7748 0.443969
\(590\) −1.03983 −0.0428089
\(591\) −79.8096 −3.28293
\(592\) 3.23320 0.132884
\(593\) −11.6694 −0.479205 −0.239603 0.970871i \(-0.577017\pi\)
−0.239603 + 0.970871i \(0.577017\pi\)
\(594\) −37.7295 −1.54806
\(595\) −10.7592 −0.441083
\(596\) 10.2635 0.420409
\(597\) 22.5030 0.920988
\(598\) −12.6006 −0.515277
\(599\) 7.53912 0.308040 0.154020 0.988068i \(-0.450778\pi\)
0.154020 + 0.988068i \(0.450778\pi\)
\(600\) 0.329294 0.0134434
\(601\) −18.0846 −0.737687 −0.368843 0.929492i \(-0.620246\pi\)
−0.368843 + 0.929492i \(0.620246\pi\)
\(602\) 1.71200 0.0697760
\(603\) −64.8506 −2.64092
\(604\) 15.1541 0.616613
\(605\) 4.00300 0.162745
\(606\) 52.5158 2.13331
\(607\) −40.6126 −1.64841 −0.824207 0.566289i \(-0.808379\pi\)
−0.824207 + 0.566289i \(0.808379\pi\)
\(608\) 1.00000 0.0405554
\(609\) 6.93583 0.281054
\(610\) −5.44050 −0.220279
\(611\) −2.16866 −0.0877346
\(612\) −22.0448 −0.891107
\(613\) −6.59984 −0.266565 −0.133283 0.991078i \(-0.542552\pi\)
−0.133283 + 0.991078i \(0.542552\pi\)
\(614\) −9.44315 −0.381095
\(615\) 27.1720 1.09568
\(616\) −4.55392 −0.183482
\(617\) −14.7725 −0.594718 −0.297359 0.954766i \(-0.596106\pi\)
−0.297359 + 0.954766i \(0.596106\pi\)
\(618\) −1.06484 −0.0428343
\(619\) 29.9294 1.20297 0.601483 0.798886i \(-0.294577\pi\)
0.601483 + 0.798886i \(0.294577\pi\)
\(620\) 24.3436 0.977663
\(621\) −40.3510 −1.61923
\(622\) 25.0081 1.00273
\(623\) −25.4736 −1.02058
\(624\) −12.2276 −0.489495
\(625\) −25.5113 −1.02045
\(626\) 5.70980 0.228209
\(627\) −9.57725 −0.382479
\(628\) 6.87183 0.274216
\(629\) −10.2710 −0.409530
\(630\) −23.5032 −0.936392
\(631\) 21.0636 0.838529 0.419264 0.907864i \(-0.362288\pi\)
0.419264 + 0.907864i \(0.362288\pi\)
\(632\) −6.74778 −0.268412
\(633\) 3.15270 0.125308
\(634\) 23.9285 0.950322
\(635\) 24.0867 0.955852
\(636\) 4.43028 0.175672
\(637\) −18.4333 −0.730354
\(638\) 4.45809 0.176498
\(639\) 32.6996 1.29358
\(640\) 2.25930 0.0893068
\(641\) −26.4473 −1.04461 −0.522303 0.852760i \(-0.674927\pi\)
−0.522303 + 0.852760i \(0.674927\pi\)
\(642\) −31.8928 −1.25871
\(643\) 20.1647 0.795218 0.397609 0.917555i \(-0.369840\pi\)
0.397609 + 0.917555i \(0.369840\pi\)
\(644\) −4.87034 −0.191918
\(645\) 8.13457 0.320299
\(646\) −3.17671 −0.124986
\(647\) 0.169917 0.00668012 0.00334006 0.999994i \(-0.498937\pi\)
0.00334006 + 0.999994i \(0.498937\pi\)
\(648\) −18.3380 −0.720385
\(649\) 1.39812 0.0548811
\(650\) −0.405098 −0.0158892
\(651\) −50.9235 −1.99585
\(652\) −14.3771 −0.563053
\(653\) −16.4578 −0.644045 −0.322023 0.946732i \(-0.604363\pi\)
−0.322023 + 0.946732i \(0.604363\pi\)
\(654\) −21.2185 −0.829708
\(655\) −26.5568 −1.03766
\(656\) 3.81474 0.148941
\(657\) −59.9486 −2.33882
\(658\) −0.838223 −0.0326773
\(659\) −49.0828 −1.91199 −0.955997 0.293377i \(-0.905221\pi\)
−0.955997 + 0.293377i \(0.905221\pi\)
\(660\) −21.6379 −0.842254
\(661\) −39.6746 −1.54316 −0.771581 0.636131i \(-0.780534\pi\)
−0.771581 + 0.636131i \(0.780534\pi\)
\(662\) 8.34775 0.324444
\(663\) 38.8435 1.50856
\(664\) −2.80787 −0.108966
\(665\) −3.38689 −0.131338
\(666\) −22.4368 −0.869408
\(667\) 4.76786 0.184612
\(668\) 21.1353 0.817749
\(669\) −25.8729 −1.00030
\(670\) −21.1136 −0.815688
\(671\) 7.31515 0.282398
\(672\) −4.72616 −0.182315
\(673\) −26.3186 −1.01451 −0.507253 0.861797i \(-0.669339\pi\)
−0.507253 + 0.861797i \(0.669339\pi\)
\(674\) 1.60844 0.0619549
\(675\) −1.29725 −0.0499311
\(676\) 2.04239 0.0785533
\(677\) −35.5174 −1.36505 −0.682523 0.730864i \(-0.739117\pi\)
−0.682523 + 0.730864i \(0.739117\pi\)
\(678\) −6.78848 −0.260710
\(679\) −11.2659 −0.432344
\(680\) −7.17716 −0.275231
\(681\) 28.9594 1.10973
\(682\) −32.7318 −1.25336
\(683\) −8.86575 −0.339238 −0.169619 0.985510i \(-0.554254\pi\)
−0.169619 + 0.985510i \(0.554254\pi\)
\(684\) −6.93949 −0.265338
\(685\) −6.07701 −0.232191
\(686\) −17.6184 −0.672672
\(687\) −52.9899 −2.02169
\(688\) 1.14203 0.0435396
\(689\) −5.45014 −0.207634
\(690\) −23.1414 −0.880977
\(691\) −31.5448 −1.20002 −0.600010 0.799992i \(-0.704837\pi\)
−0.600010 + 0.799992i \(0.704837\pi\)
\(692\) 16.6634 0.633447
\(693\) 31.6018 1.20045
\(694\) 10.7805 0.409222
\(695\) −19.0612 −0.723032
\(696\) 4.62671 0.175375
\(697\) −12.1184 −0.459015
\(698\) −17.7810 −0.673021
\(699\) 84.4023 3.19239
\(700\) −0.156577 −0.00591805
\(701\) 21.4138 0.808789 0.404394 0.914585i \(-0.367482\pi\)
0.404394 + 0.914585i \(0.367482\pi\)
\(702\) 48.1704 1.81807
\(703\) −3.23320 −0.121943
\(704\) −3.03780 −0.114491
\(705\) −3.98281 −0.150001
\(706\) −13.5785 −0.511035
\(707\) −24.9709 −0.939127
\(708\) 1.45100 0.0545320
\(709\) −33.0551 −1.24141 −0.620704 0.784045i \(-0.713153\pi\)
−0.620704 + 0.784045i \(0.713153\pi\)
\(710\) 10.6461 0.399541
\(711\) 46.8261 1.75612
\(712\) −16.9928 −0.636831
\(713\) −35.0061 −1.31099
\(714\) 15.0136 0.561872
\(715\) 26.6190 0.995494
\(716\) −1.54908 −0.0578918
\(717\) −25.2324 −0.942322
\(718\) −5.04359 −0.188225
\(719\) −24.0967 −0.898656 −0.449328 0.893367i \(-0.648336\pi\)
−0.449328 + 0.893367i \(0.648336\pi\)
\(720\) −15.6784 −0.584300
\(721\) 0.506326 0.0188566
\(722\) −1.00000 −0.0372161
\(723\) −9.26765 −0.344668
\(724\) 11.7252 0.435762
\(725\) 0.153282 0.00569276
\(726\) −5.58590 −0.207312
\(727\) 31.5674 1.17077 0.585385 0.810755i \(-0.300943\pi\)
0.585385 + 0.810755i \(0.300943\pi\)
\(728\) 5.81413 0.215486
\(729\) 9.78700 0.362482
\(730\) −19.5176 −0.722378
\(731\) −3.62791 −0.134183
\(732\) 7.59183 0.280602
\(733\) 4.64204 0.171458 0.0857289 0.996319i \(-0.472678\pi\)
0.0857289 + 0.996319i \(0.472678\pi\)
\(734\) −2.74679 −0.101386
\(735\) −33.8533 −1.24870
\(736\) −3.24887 −0.119755
\(737\) 28.3887 1.04571
\(738\) −26.4724 −0.974461
\(739\) 8.89853 0.327338 0.163669 0.986515i \(-0.447667\pi\)
0.163669 + 0.986515i \(0.447667\pi\)
\(740\) −7.30479 −0.268529
\(741\) 12.2276 0.449191
\(742\) −2.10657 −0.0773345
\(743\) −24.1062 −0.884369 −0.442185 0.896924i \(-0.645796\pi\)
−0.442185 + 0.896924i \(0.645796\pi\)
\(744\) −33.9698 −1.24539
\(745\) −23.1883 −0.849554
\(746\) −10.2367 −0.374792
\(747\) 19.4851 0.712924
\(748\) 9.65021 0.352847
\(749\) 15.1648 0.554109
\(750\) 34.8705 1.27329
\(751\) 20.2780 0.739954 0.369977 0.929041i \(-0.379366\pi\)
0.369977 + 0.929041i \(0.379366\pi\)
\(752\) −0.559156 −0.0203903
\(753\) −14.6288 −0.533102
\(754\) −5.69179 −0.207283
\(755\) −34.2378 −1.24604
\(756\) 18.6186 0.677153
\(757\) −1.50610 −0.0547403 −0.0273701 0.999625i \(-0.508713\pi\)
−0.0273701 + 0.999625i \(0.508713\pi\)
\(758\) −3.38717 −0.123028
\(759\) 31.1153 1.12941
\(760\) −2.25930 −0.0819535
\(761\) −4.24719 −0.153961 −0.0769803 0.997033i \(-0.524528\pi\)
−0.0769803 + 0.997033i \(0.524528\pi\)
\(762\) −33.6113 −1.21761
\(763\) 10.0892 0.365255
\(764\) 10.5849 0.382950
\(765\) 49.8058 1.80073
\(766\) 8.12315 0.293501
\(767\) −1.78503 −0.0644535
\(768\) −3.15270 −0.113763
\(769\) −23.5607 −0.849621 −0.424811 0.905282i \(-0.639659\pi\)
−0.424811 + 0.905282i \(0.639659\pi\)
\(770\) 10.2887 0.370778
\(771\) −70.2163 −2.52878
\(772\) −23.4035 −0.842311
\(773\) 25.7501 0.926166 0.463083 0.886315i \(-0.346743\pi\)
0.463083 + 0.886315i \(0.346743\pi\)
\(774\) −7.92512 −0.284863
\(775\) −1.12541 −0.0404260
\(776\) −7.51517 −0.269779
\(777\) 15.2806 0.548190
\(778\) −10.6628 −0.382281
\(779\) −3.81474 −0.136677
\(780\) 27.6258 0.989162
\(781\) −14.3144 −0.512211
\(782\) 10.3207 0.369069
\(783\) −18.2269 −0.651375
\(784\) −4.75275 −0.169741
\(785\) −15.5255 −0.554130
\(786\) 37.0581 1.32182
\(787\) −11.0332 −0.393293 −0.196646 0.980474i \(-0.563005\pi\)
−0.196646 + 0.980474i \(0.563005\pi\)
\(788\) 25.3147 0.901800
\(789\) 98.1893 3.49563
\(790\) 15.2453 0.542402
\(791\) 3.22787 0.114770
\(792\) 21.0808 0.749072
\(793\) −9.33948 −0.331655
\(794\) −1.32452 −0.0470056
\(795\) −10.0093 −0.354995
\(796\) −7.13772 −0.252990
\(797\) 0.460893 0.0163257 0.00816284 0.999967i \(-0.497402\pi\)
0.00816284 + 0.999967i \(0.497402\pi\)
\(798\) 4.72616 0.167304
\(799\) 1.77628 0.0628403
\(800\) −0.104448 −0.00369281
\(801\) 117.921 4.16654
\(802\) 17.3827 0.613806
\(803\) 26.2428 0.926088
\(804\) 29.4625 1.03906
\(805\) 11.0036 0.387825
\(806\) 41.7897 1.47198
\(807\) −52.1386 −1.83537
\(808\) −16.6574 −0.586006
\(809\) −7.17518 −0.252266 −0.126133 0.992013i \(-0.540257\pi\)
−0.126133 + 0.992013i \(0.540257\pi\)
\(810\) 41.4311 1.45574
\(811\) −17.1640 −0.602708 −0.301354 0.953512i \(-0.597439\pi\)
−0.301354 + 0.953512i \(0.597439\pi\)
\(812\) −2.19997 −0.0772038
\(813\) 8.78773 0.308199
\(814\) 9.82182 0.344255
\(815\) 32.4823 1.13781
\(816\) 10.0152 0.350603
\(817\) −1.14203 −0.0399547
\(818\) −12.0300 −0.420618
\(819\) −40.3471 −1.40984
\(820\) −8.61866 −0.300977
\(821\) 19.2335 0.671254 0.335627 0.941995i \(-0.391052\pi\)
0.335627 + 0.941995i \(0.391052\pi\)
\(822\) 8.48003 0.295775
\(823\) 4.57979 0.159642 0.0798208 0.996809i \(-0.474565\pi\)
0.0798208 + 0.996809i \(0.474565\pi\)
\(824\) 0.337757 0.0117663
\(825\) 1.00033 0.0348270
\(826\) −0.689941 −0.0240061
\(827\) −6.43071 −0.223618 −0.111809 0.993730i \(-0.535664\pi\)
−0.111809 + 0.993730i \(0.535664\pi\)
\(828\) 22.5455 0.783511
\(829\) −14.4554 −0.502057 −0.251028 0.967980i \(-0.580769\pi\)
−0.251028 + 0.967980i \(0.580769\pi\)
\(830\) 6.34382 0.220197
\(831\) 18.9755 0.658253
\(832\) 3.87845 0.134461
\(833\) 15.0981 0.523119
\(834\) 26.5985 0.921032
\(835\) −47.7510 −1.65249
\(836\) 3.03780 0.105064
\(837\) 133.823 4.62561
\(838\) −9.89216 −0.341719
\(839\) −42.9259 −1.48197 −0.740983 0.671524i \(-0.765640\pi\)
−0.740983 + 0.671524i \(0.765640\pi\)
\(840\) 10.6778 0.368420
\(841\) −26.8463 −0.925735
\(842\) 28.3477 0.976928
\(843\) −70.9338 −2.44309
\(844\) −1.00000 −0.0344214
\(845\) −4.61437 −0.158739
\(846\) 3.88026 0.133406
\(847\) 2.65606 0.0912632
\(848\) −1.40524 −0.0482560
\(849\) −76.6541 −2.63076
\(850\) 0.331803 0.0113807
\(851\) 10.5043 0.360082
\(852\) −14.8559 −0.508953
\(853\) 28.5584 0.977821 0.488910 0.872334i \(-0.337395\pi\)
0.488910 + 0.872334i \(0.337395\pi\)
\(854\) −3.60986 −0.123527
\(855\) 15.6784 0.536190
\(856\) 10.1160 0.345759
\(857\) 24.1466 0.824832 0.412416 0.910996i \(-0.364685\pi\)
0.412416 + 0.910996i \(0.364685\pi\)
\(858\) −37.1449 −1.26811
\(859\) 25.3168 0.863799 0.431900 0.901922i \(-0.357843\pi\)
0.431900 + 0.901922i \(0.357843\pi\)
\(860\) −2.58020 −0.0879840
\(861\) 18.0291 0.614429
\(862\) −0.658752 −0.0224372
\(863\) −13.1854 −0.448837 −0.224418 0.974493i \(-0.572048\pi\)
−0.224418 + 0.974493i \(0.572048\pi\)
\(864\) 12.4200 0.422537
\(865\) −37.6476 −1.28006
\(866\) −6.23777 −0.211968
\(867\) 21.7804 0.739700
\(868\) 16.1524 0.548248
\(869\) −20.4984 −0.695360
\(870\) −10.4531 −0.354395
\(871\) −36.2448 −1.22811
\(872\) 6.73026 0.227915
\(873\) 52.1514 1.76506
\(874\) 3.24887 0.109895
\(875\) −16.5807 −0.560529
\(876\) 27.2354 0.920198
\(877\) 32.5095 1.09777 0.548885 0.835898i \(-0.315053\pi\)
0.548885 + 0.835898i \(0.315053\pi\)
\(878\) 40.6260 1.37106
\(879\) 24.5690 0.828692
\(880\) 6.86330 0.231362
\(881\) 32.6841 1.10115 0.550577 0.834784i \(-0.314408\pi\)
0.550577 + 0.834784i \(0.314408\pi\)
\(882\) 32.9816 1.11055
\(883\) −10.3084 −0.346905 −0.173453 0.984842i \(-0.555492\pi\)
−0.173453 + 0.984842i \(0.555492\pi\)
\(884\) −12.3207 −0.414391
\(885\) −3.27825 −0.110197
\(886\) −10.7549 −0.361317
\(887\) −44.9688 −1.50990 −0.754952 0.655780i \(-0.772340\pi\)
−0.754952 + 0.655780i \(0.772340\pi\)
\(888\) 10.1933 0.342065
\(889\) 15.9819 0.536017
\(890\) 38.3918 1.28690
\(891\) −55.7072 −1.86626
\(892\) 8.20659 0.274777
\(893\) 0.559156 0.0187115
\(894\) 32.3576 1.08220
\(895\) 3.49984 0.116987
\(896\) 1.49908 0.0500809
\(897\) −39.7259 −1.32641
\(898\) 37.2453 1.24289
\(899\) −15.8125 −0.527377
\(900\) 0.724818 0.0241606
\(901\) 4.46403 0.148718
\(902\) 11.5884 0.385852
\(903\) 5.39742 0.179615
\(904\) 2.15323 0.0716154
\(905\) −26.4907 −0.880581
\(906\) 47.7764 1.58726
\(907\) −37.9192 −1.25908 −0.629542 0.776966i \(-0.716758\pi\)
−0.629542 + 0.776966i \(0.716758\pi\)
\(908\) −9.18561 −0.304835
\(909\) 115.594 3.83401
\(910\) −13.1359 −0.435450
\(911\) 18.4120 0.610018 0.305009 0.952350i \(-0.401341\pi\)
0.305009 + 0.952350i \(0.401341\pi\)
\(912\) 3.15270 0.104396
\(913\) −8.52973 −0.282293
\(914\) 17.6885 0.585083
\(915\) −17.1522 −0.567036
\(916\) 16.8078 0.555345
\(917\) −17.6209 −0.581893
\(918\) −39.4548 −1.30220
\(919\) 55.5232 1.83154 0.915771 0.401701i \(-0.131581\pi\)
0.915771 + 0.401701i \(0.131581\pi\)
\(920\) 7.34019 0.241999
\(921\) −29.7714 −0.981000
\(922\) 0.994485 0.0327516
\(923\) 18.2757 0.601552
\(924\) −14.3571 −0.472314
\(925\) 0.337703 0.0111036
\(926\) 5.07023 0.166618
\(927\) −2.34386 −0.0769824
\(928\) −1.46754 −0.0481744
\(929\) 20.5845 0.675355 0.337677 0.941262i \(-0.390359\pi\)
0.337677 + 0.941262i \(0.390359\pi\)
\(930\) 76.7480 2.51666
\(931\) 4.75275 0.155765
\(932\) −26.7715 −0.876929
\(933\) 78.8429 2.58120
\(934\) 6.05126 0.198003
\(935\) −21.8028 −0.713026
\(936\) −26.9145 −0.879727
\(937\) 22.4599 0.733732 0.366866 0.930274i \(-0.380431\pi\)
0.366866 + 0.930274i \(0.380431\pi\)
\(938\) −14.0092 −0.457416
\(939\) 18.0013 0.587449
\(940\) 1.26330 0.0412044
\(941\) −22.4106 −0.730565 −0.365282 0.930897i \(-0.619028\pi\)
−0.365282 + 0.930897i \(0.619028\pi\)
\(942\) 21.6648 0.705877
\(943\) 12.3936 0.403592
\(944\) −0.460242 −0.0149796
\(945\) −42.0651 −1.36838
\(946\) 3.46926 0.112795
\(947\) −16.5309 −0.537184 −0.268592 0.963254i \(-0.586558\pi\)
−0.268592 + 0.963254i \(0.586558\pi\)
\(948\) −21.2737 −0.690937
\(949\) −33.5050 −1.08762
\(950\) 0.104448 0.00338875
\(951\) 75.4392 2.44628
\(952\) −4.76216 −0.154343
\(953\) −57.4110 −1.85972 −0.929862 0.367908i \(-0.880074\pi\)
−0.929862 + 0.367908i \(0.880074\pi\)
\(954\) 9.75162 0.315720
\(955\) −23.9146 −0.773858
\(956\) 8.00344 0.258850
\(957\) 14.0550 0.454334
\(958\) −17.5383 −0.566637
\(959\) −4.03220 −0.130206
\(960\) 7.12289 0.229890
\(961\) 85.0970 2.74506
\(962\) −12.5398 −0.404300
\(963\) −70.2001 −2.26217
\(964\) 2.93960 0.0946781
\(965\) 52.8757 1.70213
\(966\) −15.3547 −0.494029
\(967\) −4.38110 −0.140887 −0.0704434 0.997516i \(-0.522441\pi\)
−0.0704434 + 0.997516i \(0.522441\pi\)
\(968\) 1.77179 0.0569473
\(969\) −10.0152 −0.321735
\(970\) 16.9790 0.545164
\(971\) −23.2502 −0.746136 −0.373068 0.927804i \(-0.621694\pi\)
−0.373068 + 0.927804i \(0.621694\pi\)
\(972\) −20.5542 −0.659276
\(973\) −12.6474 −0.405457
\(974\) −16.2677 −0.521252
\(975\) −1.27715 −0.0409015
\(976\) −2.40804 −0.0770796
\(977\) −28.6740 −0.917361 −0.458681 0.888601i \(-0.651678\pi\)
−0.458681 + 0.888601i \(0.651678\pi\)
\(978\) −45.3268 −1.44939
\(979\) −51.6206 −1.64980
\(980\) 10.7379 0.343009
\(981\) −46.7046 −1.49116
\(982\) −26.8743 −0.857593
\(983\) −6.82114 −0.217561 −0.108780 0.994066i \(-0.534694\pi\)
−0.108780 + 0.994066i \(0.534694\pi\)
\(984\) 12.0267 0.383398
\(985\) −57.1936 −1.82234
\(986\) 4.66196 0.148467
\(987\) −2.64266 −0.0841168
\(988\) −3.87845 −0.123390
\(989\) 3.71032 0.117981
\(990\) −47.6278 −1.51371
\(991\) 15.7644 0.500773 0.250386 0.968146i \(-0.419442\pi\)
0.250386 + 0.968146i \(0.419442\pi\)
\(992\) 10.7748 0.342101
\(993\) 26.3179 0.835173
\(994\) 7.06386 0.224052
\(995\) 16.1263 0.511237
\(996\) −8.85234 −0.280497
\(997\) 18.7961 0.595278 0.297639 0.954678i \(-0.403801\pi\)
0.297639 + 0.954678i \(0.403801\pi\)
\(998\) −27.3801 −0.866701
\(999\) −40.1564 −1.27049
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 \(a_p\))