Properties

Label 8021.2.a.a.1.5
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56319 q^{2}\) \(+1.05402 q^{3}\) \(+4.56992 q^{4}\) \(+0.0841128 q^{5}\) \(-2.70164 q^{6}\) \(+2.43328 q^{7}\) \(-6.58720 q^{8}\) \(-1.88905 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56319 q^{2}\) \(+1.05402 q^{3}\) \(+4.56992 q^{4}\) \(+0.0841128 q^{5}\) \(-2.70164 q^{6}\) \(+2.43328 q^{7}\) \(-6.58720 q^{8}\) \(-1.88905 q^{9}\) \(-0.215597 q^{10}\) \(-0.162178 q^{11}\) \(+4.81678 q^{12}\) \(+1.00000 q^{13}\) \(-6.23694 q^{14}\) \(+0.0886564 q^{15}\) \(+7.74436 q^{16}\) \(+5.05225 q^{17}\) \(+4.84198 q^{18}\) \(-8.09735 q^{19}\) \(+0.384389 q^{20}\) \(+2.56472 q^{21}\) \(+0.415692 q^{22}\) \(-2.96158 q^{23}\) \(-6.94302 q^{24}\) \(-4.99293 q^{25}\) \(-2.56319 q^{26}\) \(-5.15314 q^{27}\) \(+11.1199 q^{28}\) \(+2.72251 q^{29}\) \(-0.227243 q^{30}\) \(+2.75712 q^{31}\) \(-6.67585 q^{32}\) \(-0.170938 q^{33}\) \(-12.9499 q^{34}\) \(+0.204670 q^{35}\) \(-8.63280 q^{36}\) \(+3.14706 q^{37}\) \(+20.7550 q^{38}\) \(+1.05402 q^{39}\) \(-0.554068 q^{40}\) \(+1.66523 q^{41}\) \(-6.57385 q^{42}\) \(+1.17209 q^{43}\) \(-0.741141 q^{44}\) \(-0.158893 q^{45}\) \(+7.59109 q^{46}\) \(+5.67144 q^{47}\) \(+8.16269 q^{48}\) \(-1.07917 q^{49}\) \(+12.7978 q^{50}\) \(+5.32516 q^{51}\) \(+4.56992 q^{52}\) \(-11.3659 q^{53}\) \(+13.2085 q^{54}\) \(-0.0136412 q^{55}\) \(-16.0285 q^{56}\) \(-8.53475 q^{57}\) \(-6.97831 q^{58}\) \(+11.3943 q^{59}\) \(+0.405153 q^{60}\) \(+2.50378 q^{61}\) \(-7.06701 q^{62}\) \(-4.59657 q^{63}\) \(+1.62272 q^{64}\) \(+0.0841128 q^{65}\) \(+0.438147 q^{66}\) \(-12.1937 q^{67}\) \(+23.0884 q^{68}\) \(-3.12156 q^{69}\) \(-0.524607 q^{70}\) \(+0.993322 q^{71}\) \(+12.4435 q^{72}\) \(-3.91407 q^{73}\) \(-8.06650 q^{74}\) \(-5.26263 q^{75}\) \(-37.0043 q^{76}\) \(-0.394624 q^{77}\) \(-2.70164 q^{78}\) \(+9.64741 q^{79}\) \(+0.651400 q^{80}\) \(+0.235635 q^{81}\) \(-4.26830 q^{82}\) \(-16.0923 q^{83}\) \(+11.7206 q^{84}\) \(+0.424959 q^{85}\) \(-3.00428 q^{86}\) \(+2.86958 q^{87}\) \(+1.06830 q^{88}\) \(+5.16841 q^{89}\) \(+0.407272 q^{90}\) \(+2.43328 q^{91}\) \(-13.5342 q^{92}\) \(+2.90605 q^{93}\) \(-14.5370 q^{94}\) \(-0.681091 q^{95}\) \(-7.03646 q^{96}\) \(-1.75817 q^{97}\) \(+2.76610 q^{98}\) \(+0.306362 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56319 −1.81245 −0.906223 0.422800i \(-0.861047\pi\)
−0.906223 + 0.422800i \(0.861047\pi\)
\(3\) 1.05402 0.608537 0.304269 0.952586i \(-0.401588\pi\)
0.304269 + 0.952586i \(0.401588\pi\)
\(4\) 4.56992 2.28496
\(5\) 0.0841128 0.0376164 0.0188082 0.999823i \(-0.494013\pi\)
0.0188082 + 0.999823i \(0.494013\pi\)
\(6\) −2.70164 −1.10294
\(7\) 2.43328 0.919692 0.459846 0.887999i \(-0.347905\pi\)
0.459846 + 0.887999i \(0.347905\pi\)
\(8\) −6.58720 −2.32893
\(9\) −1.88905 −0.629682
\(10\) −0.215597 −0.0681777
\(11\) −0.162178 −0.0488985 −0.0244492 0.999701i \(-0.507783\pi\)
−0.0244492 + 0.999701i \(0.507783\pi\)
\(12\) 4.81678 1.39049
\(13\) 1.00000 0.277350
\(14\) −6.23694 −1.66689
\(15\) 0.0886564 0.0228910
\(16\) 7.74436 1.93609
\(17\) 5.05225 1.22535 0.612675 0.790335i \(-0.290093\pi\)
0.612675 + 0.790335i \(0.290093\pi\)
\(18\) 4.84198 1.14127
\(19\) −8.09735 −1.85766 −0.928829 0.370508i \(-0.879184\pi\)
−0.928829 + 0.370508i \(0.879184\pi\)
\(20\) 0.384389 0.0859521
\(21\) 2.56472 0.559667
\(22\) 0.415692 0.0886259
\(23\) −2.96158 −0.617533 −0.308767 0.951138i \(-0.599916\pi\)
−0.308767 + 0.951138i \(0.599916\pi\)
\(24\) −6.94302 −1.41724
\(25\) −4.99293 −0.998585
\(26\) −2.56319 −0.502682
\(27\) −5.15314 −0.991723
\(28\) 11.1199 2.10146
\(29\) 2.72251 0.505558 0.252779 0.967524i \(-0.418655\pi\)
0.252779 + 0.967524i \(0.418655\pi\)
\(30\) −0.227243 −0.0414887
\(31\) 2.75712 0.495193 0.247596 0.968863i \(-0.420359\pi\)
0.247596 + 0.968863i \(0.420359\pi\)
\(32\) −6.67585 −1.18013
\(33\) −0.170938 −0.0297566
\(34\) −12.9499 −2.22088
\(35\) 0.204670 0.0345955
\(36\) −8.63280 −1.43880
\(37\) 3.14706 0.517374 0.258687 0.965961i \(-0.416710\pi\)
0.258687 + 0.965961i \(0.416710\pi\)
\(38\) 20.7550 3.36691
\(39\) 1.05402 0.168778
\(40\) −0.554068 −0.0876058
\(41\) 1.66523 0.260065 0.130033 0.991510i \(-0.458492\pi\)
0.130033 + 0.991510i \(0.458492\pi\)
\(42\) −6.57385 −1.01437
\(43\) 1.17209 0.178742 0.0893709 0.995998i \(-0.471514\pi\)
0.0893709 + 0.995998i \(0.471514\pi\)
\(44\) −0.741141 −0.111731
\(45\) −0.158893 −0.0236864
\(46\) 7.59109 1.11925
\(47\) 5.67144 0.827264 0.413632 0.910444i \(-0.364260\pi\)
0.413632 + 0.910444i \(0.364260\pi\)
\(48\) 8.16269 1.17818
\(49\) −1.07917 −0.154166
\(50\) 12.7978 1.80988
\(51\) 5.32516 0.745672
\(52\) 4.56992 0.633734
\(53\) −11.3659 −1.56122 −0.780610 0.625018i \(-0.785091\pi\)
−0.780610 + 0.625018i \(0.785091\pi\)
\(54\) 13.2085 1.79744
\(55\) −0.0136412 −0.00183939
\(56\) −16.0285 −2.14189
\(57\) −8.53475 −1.13045
\(58\) −6.97831 −0.916296
\(59\) 11.3943 1.48341 0.741706 0.670725i \(-0.234017\pi\)
0.741706 + 0.670725i \(0.234017\pi\)
\(60\) 0.405153 0.0523050
\(61\) 2.50378 0.320576 0.160288 0.987070i \(-0.448758\pi\)
0.160288 + 0.987070i \(0.448758\pi\)
\(62\) −7.06701 −0.897511
\(63\) −4.59657 −0.579114
\(64\) 1.62272 0.202840
\(65\) 0.0841128 0.0104329
\(66\) 0.438147 0.0539322
\(67\) −12.1937 −1.48970 −0.744849 0.667233i \(-0.767479\pi\)
−0.744849 + 0.667233i \(0.767479\pi\)
\(68\) 23.0884 2.79988
\(69\) −3.12156 −0.375792
\(70\) −0.524607 −0.0627025
\(71\) 0.993322 0.117886 0.0589428 0.998261i \(-0.481227\pi\)
0.0589428 + 0.998261i \(0.481227\pi\)
\(72\) 12.4435 1.46648
\(73\) −3.91407 −0.458108 −0.229054 0.973414i \(-0.573563\pi\)
−0.229054 + 0.973414i \(0.573563\pi\)
\(74\) −8.06650 −0.937712
\(75\) −5.26263 −0.607676
\(76\) −37.0043 −4.24468
\(77\) −0.394624 −0.0449716
\(78\) −2.70164 −0.305901
\(79\) 9.64741 1.08542 0.542709 0.839921i \(-0.317398\pi\)
0.542709 + 0.839921i \(0.317398\pi\)
\(80\) 0.651400 0.0728287
\(81\) 0.235635 0.0261817
\(82\) −4.26830 −0.471355
\(83\) −16.0923 −1.76636 −0.883181 0.469033i \(-0.844602\pi\)
−0.883181 + 0.469033i \(0.844602\pi\)
\(84\) 11.7206 1.27882
\(85\) 0.424959 0.0460933
\(86\) −3.00428 −0.323960
\(87\) 2.86958 0.307651
\(88\) 1.06830 0.113881
\(89\) 5.16841 0.547851 0.273925 0.961751i \(-0.411678\pi\)
0.273925 + 0.961751i \(0.411678\pi\)
\(90\) 0.407272 0.0429303
\(91\) 2.43328 0.255077
\(92\) −13.5342 −1.41104
\(93\) 2.90605 0.301343
\(94\) −14.5370 −1.49937
\(95\) −0.681091 −0.0698784
\(96\) −7.03646 −0.718156
\(97\) −1.75817 −0.178515 −0.0892575 0.996009i \(-0.528449\pi\)
−0.0892575 + 0.996009i \(0.528449\pi\)
\(98\) 2.76610 0.279418
\(99\) 0.306362 0.0307905
\(100\) −22.8173 −2.28173
\(101\) −13.9901 −1.39207 −0.696035 0.718007i \(-0.745054\pi\)
−0.696035 + 0.718007i \(0.745054\pi\)
\(102\) −13.6494 −1.35149
\(103\) 12.6200 1.24349 0.621745 0.783220i \(-0.286424\pi\)
0.621745 + 0.783220i \(0.286424\pi\)
\(104\) −6.58720 −0.645928
\(105\) 0.215726 0.0210527
\(106\) 29.1328 2.82963
\(107\) −2.55646 −0.247143 −0.123571 0.992336i \(-0.539435\pi\)
−0.123571 + 0.992336i \(0.539435\pi\)
\(108\) −23.5495 −2.26605
\(109\) 5.82804 0.558225 0.279112 0.960258i \(-0.409960\pi\)
0.279112 + 0.960258i \(0.409960\pi\)
\(110\) 0.0349651 0.00333379
\(111\) 3.31706 0.314841
\(112\) 18.8442 1.78061
\(113\) 14.8308 1.39516 0.697581 0.716506i \(-0.254260\pi\)
0.697581 + 0.716506i \(0.254260\pi\)
\(114\) 21.8761 2.04889
\(115\) −0.249107 −0.0232294
\(116\) 12.4417 1.15518
\(117\) −1.88905 −0.174642
\(118\) −29.2057 −2.68861
\(119\) 12.2935 1.12695
\(120\) −0.583997 −0.0533114
\(121\) −10.9737 −0.997609
\(122\) −6.41764 −0.581026
\(123\) 1.75518 0.158260
\(124\) 12.5998 1.13150
\(125\) −0.840533 −0.0751796
\(126\) 11.7819 1.04961
\(127\) −4.83880 −0.429374 −0.214687 0.976683i \(-0.568873\pi\)
−0.214687 + 0.976683i \(0.568873\pi\)
\(128\) 9.19236 0.812497
\(129\) 1.23540 0.108771
\(130\) −0.215597 −0.0189091
\(131\) 11.0811 0.968161 0.484081 0.875023i \(-0.339154\pi\)
0.484081 + 0.875023i \(0.339154\pi\)
\(132\) −0.781176 −0.0679926
\(133\) −19.7031 −1.70847
\(134\) 31.2547 2.70000
\(135\) −0.433445 −0.0373050
\(136\) −33.2802 −2.85375
\(137\) 18.0796 1.54464 0.772321 0.635232i \(-0.219096\pi\)
0.772321 + 0.635232i \(0.219096\pi\)
\(138\) 8.00115 0.681103
\(139\) −18.7593 −1.59114 −0.795570 0.605861i \(-0.792829\pi\)
−0.795570 + 0.605861i \(0.792829\pi\)
\(140\) 0.935325 0.0790494
\(141\) 5.97780 0.503421
\(142\) −2.54607 −0.213661
\(143\) −0.162178 −0.0135620
\(144\) −14.6295 −1.21912
\(145\) 0.228998 0.0190173
\(146\) 10.0325 0.830295
\(147\) −1.13746 −0.0938161
\(148\) 14.3818 1.18218
\(149\) 18.8950 1.54794 0.773970 0.633222i \(-0.218268\pi\)
0.773970 + 0.633222i \(0.218268\pi\)
\(150\) 13.4891 1.10138
\(151\) −15.8221 −1.28758 −0.643792 0.765201i \(-0.722640\pi\)
−0.643792 + 0.765201i \(0.722640\pi\)
\(152\) 53.3388 4.32635
\(153\) −9.54393 −0.771581
\(154\) 1.01149 0.0815085
\(155\) 0.231909 0.0186274
\(156\) 4.81678 0.385651
\(157\) −4.76282 −0.380114 −0.190057 0.981773i \(-0.560867\pi\)
−0.190057 + 0.981773i \(0.560867\pi\)
\(158\) −24.7281 −1.96726
\(159\) −11.9798 −0.950061
\(160\) −0.561524 −0.0443924
\(161\) −7.20636 −0.567940
\(162\) −0.603977 −0.0474529
\(163\) 4.90733 0.384372 0.192186 0.981359i \(-0.438442\pi\)
0.192186 + 0.981359i \(0.438442\pi\)
\(164\) 7.60998 0.594240
\(165\) −0.0143781 −0.00111934
\(166\) 41.2476 3.20143
\(167\) −12.7232 −0.984548 −0.492274 0.870440i \(-0.663834\pi\)
−0.492274 + 0.870440i \(0.663834\pi\)
\(168\) −16.8943 −1.30342
\(169\) 1.00000 0.0769231
\(170\) −1.08925 −0.0835416
\(171\) 15.2963 1.16973
\(172\) 5.35636 0.408418
\(173\) −20.9766 −1.59482 −0.797410 0.603438i \(-0.793797\pi\)
−0.797410 + 0.603438i \(0.793797\pi\)
\(174\) −7.35526 −0.557601
\(175\) −12.1492 −0.918391
\(176\) −1.25596 −0.0946719
\(177\) 12.0098 0.902712
\(178\) −13.2476 −0.992950
\(179\) −20.3371 −1.52006 −0.760032 0.649885i \(-0.774817\pi\)
−0.760032 + 0.649885i \(0.774817\pi\)
\(180\) −0.726129 −0.0541225
\(181\) −19.4189 −1.44340 −0.721699 0.692207i \(-0.756639\pi\)
−0.721699 + 0.692207i \(0.756639\pi\)
\(182\) −6.23694 −0.462313
\(183\) 2.63902 0.195082
\(184\) 19.5085 1.43819
\(185\) 0.264708 0.0194617
\(186\) −7.44875 −0.546169
\(187\) −0.819364 −0.0599178
\(188\) 25.9180 1.89027
\(189\) −12.5390 −0.912079
\(190\) 1.74576 0.126651
\(191\) −17.7881 −1.28710 −0.643552 0.765403i \(-0.722540\pi\)
−0.643552 + 0.765403i \(0.722540\pi\)
\(192\) 1.71038 0.123436
\(193\) 1.91929 0.138153 0.0690767 0.997611i \(-0.477995\pi\)
0.0690767 + 0.997611i \(0.477995\pi\)
\(194\) 4.50651 0.323549
\(195\) 0.0886564 0.00634882
\(196\) −4.93170 −0.352265
\(197\) −21.8610 −1.55753 −0.778767 0.627313i \(-0.784155\pi\)
−0.778767 + 0.627313i \(0.784155\pi\)
\(198\) −0.785262 −0.0558062
\(199\) −0.509438 −0.0361131 −0.0180566 0.999837i \(-0.505748\pi\)
−0.0180566 + 0.999837i \(0.505748\pi\)
\(200\) 32.8894 2.32563
\(201\) −12.8524 −0.906537
\(202\) 35.8593 2.52305
\(203\) 6.62462 0.464957
\(204\) 24.3356 1.70383
\(205\) 0.140067 0.00978272
\(206\) −32.3475 −2.25376
\(207\) 5.59457 0.388850
\(208\) 7.74436 0.536975
\(209\) 1.31321 0.0908367
\(210\) −0.552945 −0.0381568
\(211\) −26.3841 −1.81636 −0.908179 0.418582i \(-0.862527\pi\)
−0.908179 + 0.418582i \(0.862527\pi\)
\(212\) −51.9411 −3.56733
\(213\) 1.04698 0.0717378
\(214\) 6.55269 0.447933
\(215\) 0.0985877 0.00672363
\(216\) 33.9448 2.30965
\(217\) 6.70883 0.455425
\(218\) −14.9383 −1.01175
\(219\) −4.12550 −0.278776
\(220\) −0.0623395 −0.00420293
\(221\) 5.05225 0.339851
\(222\) −8.50224 −0.570633
\(223\) −26.1695 −1.75244 −0.876218 0.481914i \(-0.839942\pi\)
−0.876218 + 0.481914i \(0.839942\pi\)
\(224\) −16.2442 −1.08536
\(225\) 9.43187 0.628791
\(226\) −38.0140 −2.52866
\(227\) −27.6146 −1.83284 −0.916422 0.400214i \(-0.868936\pi\)
−0.916422 + 0.400214i \(0.868936\pi\)
\(228\) −39.0032 −2.58305
\(229\) 10.8224 0.715162 0.357581 0.933882i \(-0.383602\pi\)
0.357581 + 0.933882i \(0.383602\pi\)
\(230\) 0.638508 0.0421020
\(231\) −0.415941 −0.0273669
\(232\) −17.9337 −1.17741
\(233\) 3.48179 0.228100 0.114050 0.993475i \(-0.463618\pi\)
0.114050 + 0.993475i \(0.463618\pi\)
\(234\) 4.84198 0.316530
\(235\) 0.477041 0.0311187
\(236\) 52.0711 3.38954
\(237\) 10.1685 0.660518
\(238\) −31.5106 −2.04253
\(239\) 6.27071 0.405619 0.202809 0.979218i \(-0.434993\pi\)
0.202809 + 0.979218i \(0.434993\pi\)
\(240\) 0.686587 0.0443190
\(241\) −6.70910 −0.432171 −0.216086 0.976374i \(-0.569329\pi\)
−0.216086 + 0.976374i \(0.569329\pi\)
\(242\) 28.1276 1.80811
\(243\) 15.7078 1.00766
\(244\) 11.4421 0.732503
\(245\) −0.0907716 −0.00579919
\(246\) −4.49886 −0.286837
\(247\) −8.09735 −0.515222
\(248\) −18.1617 −1.15327
\(249\) −16.9616 −1.07490
\(250\) 2.15444 0.136259
\(251\) 13.2362 0.835461 0.417730 0.908571i \(-0.362826\pi\)
0.417730 + 0.908571i \(0.362826\pi\)
\(252\) −21.0060 −1.32325
\(253\) 0.480304 0.0301964
\(254\) 12.4027 0.778218
\(255\) 0.447914 0.0280495
\(256\) −26.8072 −1.67545
\(257\) 1.92955 0.120362 0.0601811 0.998187i \(-0.480832\pi\)
0.0601811 + 0.998187i \(0.480832\pi\)
\(258\) −3.16657 −0.197142
\(259\) 7.65767 0.475824
\(260\) 0.384389 0.0238388
\(261\) −5.14295 −0.318341
\(262\) −28.4030 −1.75474
\(263\) 8.73721 0.538760 0.269380 0.963034i \(-0.413181\pi\)
0.269380 + 0.963034i \(0.413181\pi\)
\(264\) 1.12601 0.0693008
\(265\) −0.956014 −0.0587275
\(266\) 50.5027 3.09652
\(267\) 5.44760 0.333388
\(268\) −55.7243 −3.40390
\(269\) 3.83682 0.233935 0.116968 0.993136i \(-0.462683\pi\)
0.116968 + 0.993136i \(0.462683\pi\)
\(270\) 1.11100 0.0676134
\(271\) −2.01716 −0.122534 −0.0612670 0.998121i \(-0.519514\pi\)
−0.0612670 + 0.998121i \(0.519514\pi\)
\(272\) 39.1264 2.37239
\(273\) 2.56472 0.155224
\(274\) −46.3413 −2.79958
\(275\) 0.809742 0.0488293
\(276\) −14.2653 −0.858671
\(277\) −23.9421 −1.43854 −0.719269 0.694731i \(-0.755523\pi\)
−0.719269 + 0.694731i \(0.755523\pi\)
\(278\) 48.0835 2.88386
\(279\) −5.20832 −0.311814
\(280\) −1.34820 −0.0805703
\(281\) 20.0033 1.19330 0.596648 0.802503i \(-0.296499\pi\)
0.596648 + 0.802503i \(0.296499\pi\)
\(282\) −15.3222 −0.912424
\(283\) −5.14058 −0.305576 −0.152788 0.988259i \(-0.548825\pi\)
−0.152788 + 0.988259i \(0.548825\pi\)
\(284\) 4.53940 0.269364
\(285\) −0.717882 −0.0425236
\(286\) 0.415692 0.0245804
\(287\) 4.05197 0.239180
\(288\) 12.6110 0.743109
\(289\) 8.52522 0.501484
\(290\) −0.586965 −0.0344678
\(291\) −1.85314 −0.108633
\(292\) −17.8870 −1.04676
\(293\) 8.08624 0.472403 0.236202 0.971704i \(-0.424097\pi\)
0.236202 + 0.971704i \(0.424097\pi\)
\(294\) 2.91552 0.170037
\(295\) 0.958407 0.0558006
\(296\) −20.7303 −1.20492
\(297\) 0.835726 0.0484937
\(298\) −48.4314 −2.80556
\(299\) −2.96158 −0.171273
\(300\) −24.0498 −1.38852
\(301\) 2.85202 0.164387
\(302\) 40.5550 2.33368
\(303\) −14.7459 −0.847127
\(304\) −62.7088 −3.59659
\(305\) 0.210600 0.0120589
\(306\) 24.4629 1.39845
\(307\) 31.9480 1.82337 0.911684 0.410893i \(-0.134783\pi\)
0.911684 + 0.410893i \(0.134783\pi\)
\(308\) −1.80340 −0.102758
\(309\) 13.3017 0.756710
\(310\) −0.594426 −0.0337611
\(311\) −2.01011 −0.113983 −0.0569914 0.998375i \(-0.518151\pi\)
−0.0569914 + 0.998375i \(0.518151\pi\)
\(312\) −6.94302 −0.393071
\(313\) −23.6852 −1.33876 −0.669382 0.742918i \(-0.733441\pi\)
−0.669382 + 0.742918i \(0.733441\pi\)
\(314\) 12.2080 0.688937
\(315\) −0.386631 −0.0217842
\(316\) 44.0879 2.48014
\(317\) −5.30415 −0.297911 −0.148955 0.988844i \(-0.547591\pi\)
−0.148955 + 0.988844i \(0.547591\pi\)
\(318\) 30.7065 1.72193
\(319\) −0.441531 −0.0247210
\(320\) 0.136492 0.00763012
\(321\) −2.69456 −0.150396
\(322\) 18.4712 1.02936
\(323\) −40.9098 −2.27628
\(324\) 1.07684 0.0598242
\(325\) −4.99293 −0.276958
\(326\) −12.5784 −0.696653
\(327\) 6.14286 0.339701
\(328\) −10.9692 −0.605673
\(329\) 13.8002 0.760828
\(330\) 0.0368538 0.00202873
\(331\) −19.4226 −1.06757 −0.533783 0.845622i \(-0.679230\pi\)
−0.533783 + 0.845622i \(0.679230\pi\)
\(332\) −73.5407 −4.03607
\(333\) −5.94494 −0.325781
\(334\) 32.6118 1.78444
\(335\) −1.02565 −0.0560371
\(336\) 19.8621 1.08357
\(337\) −20.3786 −1.11009 −0.555046 0.831820i \(-0.687299\pi\)
−0.555046 + 0.831820i \(0.687299\pi\)
\(338\) −2.56319 −0.139419
\(339\) 15.6319 0.849008
\(340\) 1.94203 0.105321
\(341\) −0.447144 −0.0242142
\(342\) −39.2072 −2.12008
\(343\) −19.6588 −1.06148
\(344\) −7.72078 −0.416276
\(345\) −0.262564 −0.0141359
\(346\) 53.7669 2.89052
\(347\) 0.653318 0.0350720 0.0175360 0.999846i \(-0.494418\pi\)
0.0175360 + 0.999846i \(0.494418\pi\)
\(348\) 13.1137 0.702971
\(349\) 11.1535 0.597034 0.298517 0.954404i \(-0.403508\pi\)
0.298517 + 0.954404i \(0.403508\pi\)
\(350\) 31.1406 1.66453
\(351\) −5.15314 −0.275054
\(352\) 1.08268 0.0577068
\(353\) 11.2836 0.600567 0.300284 0.953850i \(-0.402919\pi\)
0.300284 + 0.953850i \(0.402919\pi\)
\(354\) −30.7834 −1.63612
\(355\) 0.0835511 0.00443443
\(356\) 23.6193 1.25182
\(357\) 12.9576 0.685788
\(358\) 52.1277 2.75504
\(359\) 12.5778 0.663832 0.331916 0.943309i \(-0.392305\pi\)
0.331916 + 0.943309i \(0.392305\pi\)
\(360\) 1.04666 0.0551638
\(361\) 46.5670 2.45090
\(362\) 49.7744 2.61608
\(363\) −11.5665 −0.607082
\(364\) 11.1199 0.582841
\(365\) −0.329224 −0.0172324
\(366\) −6.76431 −0.353576
\(367\) 38.0020 1.98369 0.991843 0.127465i \(-0.0406839\pi\)
0.991843 + 0.127465i \(0.0406839\pi\)
\(368\) −22.9356 −1.19560
\(369\) −3.14570 −0.163759
\(370\) −0.678496 −0.0352733
\(371\) −27.6563 −1.43584
\(372\) 13.2804 0.688558
\(373\) −29.4321 −1.52394 −0.761969 0.647613i \(-0.775767\pi\)
−0.761969 + 0.647613i \(0.775767\pi\)
\(374\) 2.10018 0.108598
\(375\) −0.885937 −0.0457496
\(376\) −37.3589 −1.92664
\(377\) 2.72251 0.140217
\(378\) 32.1398 1.65310
\(379\) −13.1455 −0.675241 −0.337620 0.941282i \(-0.609622\pi\)
−0.337620 + 0.941282i \(0.609622\pi\)
\(380\) −3.11253 −0.159670
\(381\) −5.10018 −0.261290
\(382\) 45.5943 2.33281
\(383\) 1.58464 0.0809713 0.0404856 0.999180i \(-0.487110\pi\)
0.0404856 + 0.999180i \(0.487110\pi\)
\(384\) 9.68891 0.494435
\(385\) −0.0331929 −0.00169167
\(386\) −4.91949 −0.250396
\(387\) −2.21413 −0.112551
\(388\) −8.03470 −0.407900
\(389\) −15.1295 −0.767097 −0.383549 0.923521i \(-0.625298\pi\)
−0.383549 + 0.923521i \(0.625298\pi\)
\(390\) −0.227243 −0.0115069
\(391\) −14.9627 −0.756694
\(392\) 7.10867 0.359042
\(393\) 11.6797 0.589163
\(394\) 56.0339 2.82295
\(395\) 0.811471 0.0408295
\(396\) 1.40005 0.0703552
\(397\) 10.6022 0.532109 0.266055 0.963958i \(-0.414280\pi\)
0.266055 + 0.963958i \(0.414280\pi\)
\(398\) 1.30578 0.0654531
\(399\) −20.7674 −1.03967
\(400\) −38.6670 −1.93335
\(401\) 20.2709 1.01228 0.506139 0.862452i \(-0.331072\pi\)
0.506139 + 0.862452i \(0.331072\pi\)
\(402\) 32.9431 1.64305
\(403\) 2.75712 0.137342
\(404\) −63.9339 −3.18083
\(405\) 0.0198200 0.000984861 0
\(406\) −16.9801 −0.842711
\(407\) −0.510384 −0.0252988
\(408\) −35.0779 −1.73661
\(409\) 8.32678 0.411733 0.205866 0.978580i \(-0.433999\pi\)
0.205866 + 0.978580i \(0.433999\pi\)
\(410\) −0.359019 −0.0177307
\(411\) 19.0562 0.939973
\(412\) 57.6726 2.84133
\(413\) 27.7255 1.36428
\(414\) −14.3399 −0.704769
\(415\) −1.35357 −0.0664441
\(416\) −6.67585 −0.327310
\(417\) −19.7726 −0.968269
\(418\) −3.36601 −0.164637
\(419\) 18.4411 0.900906 0.450453 0.892800i \(-0.351262\pi\)
0.450453 + 0.892800i \(0.351262\pi\)
\(420\) 0.985850 0.0481045
\(421\) −32.2867 −1.57356 −0.786778 0.617236i \(-0.788253\pi\)
−0.786778 + 0.617236i \(0.788253\pi\)
\(422\) 67.6274 3.29205
\(423\) −10.7136 −0.520913
\(424\) 74.8691 3.63596
\(425\) −25.2255 −1.22362
\(426\) −2.68360 −0.130021
\(427\) 6.09238 0.294831
\(428\) −11.6828 −0.564712
\(429\) −0.170938 −0.00825299
\(430\) −0.252699 −0.0121862
\(431\) −22.2633 −1.07239 −0.536193 0.844096i \(-0.680138\pi\)
−0.536193 + 0.844096i \(0.680138\pi\)
\(432\) −39.9078 −1.92006
\(433\) −6.42569 −0.308799 −0.154399 0.988009i \(-0.549344\pi\)
−0.154399 + 0.988009i \(0.549344\pi\)
\(434\) −17.1960 −0.825433
\(435\) 0.241368 0.0115727
\(436\) 26.6337 1.27552
\(437\) 23.9810 1.14717
\(438\) 10.5744 0.505266
\(439\) 0.157339 0.00750940 0.00375470 0.999993i \(-0.498805\pi\)
0.00375470 + 0.999993i \(0.498805\pi\)
\(440\) 0.0898576 0.00428379
\(441\) 2.03859 0.0970759
\(442\) −12.9499 −0.615962
\(443\) −5.80318 −0.275717 −0.137859 0.990452i \(-0.544022\pi\)
−0.137859 + 0.990452i \(0.544022\pi\)
\(444\) 15.1587 0.719400
\(445\) 0.434730 0.0206082
\(446\) 67.0772 3.17620
\(447\) 19.9157 0.941979
\(448\) 3.94853 0.186551
\(449\) 22.7312 1.07275 0.536376 0.843979i \(-0.319793\pi\)
0.536376 + 0.843979i \(0.319793\pi\)
\(450\) −24.1756 −1.13965
\(451\) −0.270064 −0.0127168
\(452\) 67.7755 3.18789
\(453\) −16.6768 −0.783543
\(454\) 70.7813 3.32193
\(455\) 0.204670 0.00959507
\(456\) 56.2200 2.63274
\(457\) 37.1000 1.73546 0.867732 0.497033i \(-0.165577\pi\)
0.867732 + 0.497033i \(0.165577\pi\)
\(458\) −27.7397 −1.29619
\(459\) −26.0350 −1.21521
\(460\) −1.13840 −0.0530782
\(461\) 10.3805 0.483466 0.241733 0.970343i \(-0.422284\pi\)
0.241733 + 0.970343i \(0.422284\pi\)
\(462\) 1.06613 0.0496010
\(463\) −40.4103 −1.87803 −0.939014 0.343879i \(-0.888259\pi\)
−0.939014 + 0.343879i \(0.888259\pi\)
\(464\) 21.0841 0.978805
\(465\) 0.244436 0.0113355
\(466\) −8.92447 −0.413418
\(467\) −13.9827 −0.647043 −0.323522 0.946221i \(-0.604867\pi\)
−0.323522 + 0.946221i \(0.604867\pi\)
\(468\) −8.63280 −0.399051
\(469\) −29.6707 −1.37006
\(470\) −1.22274 −0.0564010
\(471\) −5.02010 −0.231314
\(472\) −75.0565 −3.45476
\(473\) −0.190087 −0.00874021
\(474\) −26.0639 −1.19715
\(475\) 40.4294 1.85503
\(476\) 56.1805 2.57503
\(477\) 21.4706 0.983072
\(478\) −16.0730 −0.735162
\(479\) 11.5789 0.529054 0.264527 0.964378i \(-0.414784\pi\)
0.264527 + 0.964378i \(0.414784\pi\)
\(480\) −0.591857 −0.0270144
\(481\) 3.14706 0.143494
\(482\) 17.1967 0.783287
\(483\) −7.59563 −0.345613
\(484\) −50.1490 −2.27950
\(485\) −0.147885 −0.00671509
\(486\) −40.2620 −1.82632
\(487\) −16.0663 −0.728033 −0.364017 0.931392i \(-0.618595\pi\)
−0.364017 + 0.931392i \(0.618595\pi\)
\(488\) −16.4929 −0.746597
\(489\) 5.17241 0.233905
\(490\) 0.232665 0.0105107
\(491\) 16.8237 0.759243 0.379621 0.925142i \(-0.376054\pi\)
0.379621 + 0.925142i \(0.376054\pi\)
\(492\) 8.02105 0.361617
\(493\) 13.7548 0.619485
\(494\) 20.7550 0.933812
\(495\) 0.0257690 0.00115823
\(496\) 21.3521 0.958738
\(497\) 2.41703 0.108418
\(498\) 43.4757 1.94819
\(499\) −16.1601 −0.723426 −0.361713 0.932290i \(-0.617808\pi\)
−0.361713 + 0.932290i \(0.617808\pi\)
\(500\) −3.84117 −0.171782
\(501\) −13.4104 −0.599134
\(502\) −33.9268 −1.51423
\(503\) 10.8909 0.485601 0.242801 0.970076i \(-0.421934\pi\)
0.242801 + 0.970076i \(0.421934\pi\)
\(504\) 30.2785 1.34871
\(505\) −1.17675 −0.0523647
\(506\) −1.23111 −0.0547294
\(507\) 1.05402 0.0468106
\(508\) −22.1130 −0.981104
\(509\) −27.1967 −1.20547 −0.602736 0.797940i \(-0.705923\pi\)
−0.602736 + 0.797940i \(0.705923\pi\)
\(510\) −1.14809 −0.0508382
\(511\) −9.52402 −0.421318
\(512\) 50.3271 2.22416
\(513\) 41.7268 1.84228
\(514\) −4.94580 −0.218150
\(515\) 1.06151 0.0467756
\(516\) 5.64570 0.248538
\(517\) −0.919782 −0.0404520
\(518\) −19.6280 −0.862406
\(519\) −22.1097 −0.970507
\(520\) −0.554068 −0.0242975
\(521\) 12.5391 0.549347 0.274674 0.961537i \(-0.411430\pi\)
0.274674 + 0.961537i \(0.411430\pi\)
\(522\) 13.1823 0.576975
\(523\) −4.83062 −0.211228 −0.105614 0.994407i \(-0.533681\pi\)
−0.105614 + 0.994407i \(0.533681\pi\)
\(524\) 50.6399 2.21221
\(525\) −12.8054 −0.558875
\(526\) −22.3951 −0.976473
\(527\) 13.9296 0.606785
\(528\) −1.32381 −0.0576114
\(529\) −14.2290 −0.618653
\(530\) 2.45044 0.106440
\(531\) −21.5244 −0.934078
\(532\) −90.0416 −3.90380
\(533\) 1.66523 0.0721292
\(534\) −13.9632 −0.604247
\(535\) −0.215031 −0.00929662
\(536\) 80.3223 3.46940
\(537\) −21.4356 −0.925016
\(538\) −9.83450 −0.423995
\(539\) 0.175017 0.00753851
\(540\) −1.98081 −0.0852406
\(541\) 8.68482 0.373390 0.186695 0.982418i \(-0.440222\pi\)
0.186695 + 0.982418i \(0.440222\pi\)
\(542\) 5.17037 0.222086
\(543\) −20.4679 −0.878362
\(544\) −33.7280 −1.44608
\(545\) 0.490213 0.0209984
\(546\) −6.57385 −0.281335
\(547\) −9.15039 −0.391242 −0.195621 0.980680i \(-0.562672\pi\)
−0.195621 + 0.980680i \(0.562672\pi\)
\(548\) 82.6223 3.52945
\(549\) −4.72975 −0.201861
\(550\) −2.07552 −0.0885005
\(551\) −22.0451 −0.939154
\(552\) 20.5623 0.875192
\(553\) 23.4748 0.998251
\(554\) 61.3679 2.60727
\(555\) 0.279007 0.0118432
\(556\) −85.7284 −3.63570
\(557\) 32.7189 1.38634 0.693172 0.720772i \(-0.256213\pi\)
0.693172 + 0.720772i \(0.256213\pi\)
\(558\) 13.3499 0.565146
\(559\) 1.17209 0.0495741
\(560\) 1.58504 0.0669800
\(561\) −0.863624 −0.0364622
\(562\) −51.2721 −2.16278
\(563\) 29.2587 1.23311 0.616554 0.787313i \(-0.288528\pi\)
0.616554 + 0.787313i \(0.288528\pi\)
\(564\) 27.3181 1.15030
\(565\) 1.24746 0.0524809
\(566\) 13.1763 0.553839
\(567\) 0.573366 0.0240791
\(568\) −6.54320 −0.274547
\(569\) −35.5532 −1.49047 −0.745233 0.666804i \(-0.767662\pi\)
−0.745233 + 0.666804i \(0.767662\pi\)
\(570\) 1.84006 0.0770718
\(571\) −36.3596 −1.52160 −0.760800 0.648986i \(-0.775193\pi\)
−0.760800 + 0.648986i \(0.775193\pi\)
\(572\) −0.741141 −0.0309887
\(573\) −18.7490 −0.783251
\(574\) −10.3859 −0.433501
\(575\) 14.7870 0.616659
\(576\) −3.06540 −0.127725
\(577\) −31.7975 −1.32375 −0.661874 0.749615i \(-0.730239\pi\)
−0.661874 + 0.749615i \(0.730239\pi\)
\(578\) −21.8517 −0.908912
\(579\) 2.02296 0.0840715
\(580\) 1.04650 0.0434537
\(581\) −39.1571 −1.62451
\(582\) 4.74995 0.196892
\(583\) 1.84329 0.0763413
\(584\) 25.7828 1.06690
\(585\) −0.158893 −0.00656942
\(586\) −20.7265 −0.856205
\(587\) 27.1549 1.12080 0.560402 0.828221i \(-0.310647\pi\)
0.560402 + 0.828221i \(0.310647\pi\)
\(588\) −5.19810 −0.214366
\(589\) −22.3253 −0.919899
\(590\) −2.45658 −0.101136
\(591\) −23.0419 −0.947818
\(592\) 24.3720 1.00168
\(593\) −7.65149 −0.314209 −0.157104 0.987582i \(-0.550216\pi\)
−0.157104 + 0.987582i \(0.550216\pi\)
\(594\) −2.14212 −0.0878923
\(595\) 1.03404 0.0423916
\(596\) 86.3488 3.53698
\(597\) −0.536957 −0.0219762
\(598\) 7.59109 0.310423
\(599\) 29.0795 1.18815 0.594077 0.804408i \(-0.297517\pi\)
0.594077 + 0.804408i \(0.297517\pi\)
\(600\) 34.6660 1.41523
\(601\) 11.5734 0.472090 0.236045 0.971742i \(-0.424149\pi\)
0.236045 + 0.971742i \(0.424149\pi\)
\(602\) −7.31025 −0.297944
\(603\) 23.0345 0.938036
\(604\) −72.3057 −2.94208
\(605\) −0.923029 −0.0375265
\(606\) 37.7964 1.53537
\(607\) 21.2582 0.862844 0.431422 0.902150i \(-0.358012\pi\)
0.431422 + 0.902150i \(0.358012\pi\)
\(608\) 54.0566 2.19229
\(609\) 6.98247 0.282944
\(610\) −0.539806 −0.0218561
\(611\) 5.67144 0.229442
\(612\) −43.6151 −1.76303
\(613\) −4.12714 −0.166694 −0.0833468 0.996521i \(-0.526561\pi\)
−0.0833468 + 0.996521i \(0.526561\pi\)
\(614\) −81.8886 −3.30476
\(615\) 0.147633 0.00595315
\(616\) 2.59946 0.104735
\(617\) 1.00000 0.0402585
\(618\) −34.0949 −1.37150
\(619\) −2.36523 −0.0950664 −0.0475332 0.998870i \(-0.515136\pi\)
−0.0475332 + 0.998870i \(0.515136\pi\)
\(620\) 1.05981 0.0425629
\(621\) 15.2615 0.612422
\(622\) 5.15228 0.206588
\(623\) 12.5762 0.503854
\(624\) 8.16269 0.326769
\(625\) 24.8939 0.995757
\(626\) 60.7095 2.42644
\(627\) 1.38415 0.0552775
\(628\) −21.7657 −0.868547
\(629\) 15.8997 0.633964
\(630\) 0.991007 0.0394826
\(631\) 26.3967 1.05084 0.525419 0.850844i \(-0.323909\pi\)
0.525419 + 0.850844i \(0.323909\pi\)
\(632\) −63.5494 −2.52786
\(633\) −27.8093 −1.10532
\(634\) 13.5955 0.539947
\(635\) −0.407005 −0.0161515
\(636\) −54.7468 −2.17085
\(637\) −1.07917 −0.0427581
\(638\) 1.13173 0.0448055
\(639\) −1.87643 −0.0742304
\(640\) 0.773195 0.0305632
\(641\) 31.3876 1.23974 0.619869 0.784706i \(-0.287186\pi\)
0.619869 + 0.784706i \(0.287186\pi\)
\(642\) 6.90666 0.272584
\(643\) 6.83377 0.269498 0.134749 0.990880i \(-0.456977\pi\)
0.134749 + 0.990880i \(0.456977\pi\)
\(644\) −32.9325 −1.29772
\(645\) 0.103913 0.00409158
\(646\) 104.859 4.12564
\(647\) −27.2791 −1.07245 −0.536226 0.844074i \(-0.680151\pi\)
−0.536226 + 0.844074i \(0.680151\pi\)
\(648\) −1.55218 −0.0609752
\(649\) −1.84791 −0.0725366
\(650\) 12.7978 0.501971
\(651\) 7.07123 0.277143
\(652\) 22.4261 0.878275
\(653\) 12.6502 0.495042 0.247521 0.968883i \(-0.420384\pi\)
0.247521 + 0.968883i \(0.420384\pi\)
\(654\) −15.7453 −0.615689
\(655\) 0.932064 0.0364188
\(656\) 12.8961 0.503510
\(657\) 7.39386 0.288462
\(658\) −35.3724 −1.37896
\(659\) −18.8611 −0.734726 −0.367363 0.930078i \(-0.619739\pi\)
−0.367363 + 0.930078i \(0.619739\pi\)
\(660\) −0.0657069 −0.00255764
\(661\) 10.7509 0.418161 0.209080 0.977898i \(-0.432953\pi\)
0.209080 + 0.977898i \(0.432953\pi\)
\(662\) 49.7839 1.93490
\(663\) 5.32516 0.206812
\(664\) 106.003 4.11372
\(665\) −1.65728 −0.0642666
\(666\) 15.2380 0.590460
\(667\) −8.06295 −0.312199
\(668\) −58.1439 −2.24965
\(669\) −27.5831 −1.06642
\(670\) 2.62892 0.101564
\(671\) −0.406057 −0.0156757
\(672\) −17.1217 −0.660482
\(673\) −8.25785 −0.318317 −0.159158 0.987253i \(-0.550878\pi\)
−0.159158 + 0.987253i \(0.550878\pi\)
\(674\) 52.2341 2.01198
\(675\) 25.7293 0.990319
\(676\) 4.56992 0.175766
\(677\) −33.7330 −1.29647 −0.648233 0.761442i \(-0.724492\pi\)
−0.648233 + 0.761442i \(0.724492\pi\)
\(678\) −40.0675 −1.53878
\(679\) −4.27811 −0.164179
\(680\) −2.79929 −0.107348
\(681\) −29.1063 −1.11535
\(682\) 1.14611 0.0438869
\(683\) −16.4285 −0.628620 −0.314310 0.949320i \(-0.601773\pi\)
−0.314310 + 0.949320i \(0.601773\pi\)
\(684\) 69.9028 2.67280
\(685\) 1.52072 0.0581039
\(686\) 50.3893 1.92387
\(687\) 11.4070 0.435203
\(688\) 9.07708 0.346060
\(689\) −11.3659 −0.433005
\(690\) 0.672999 0.0256206
\(691\) 43.2571 1.64558 0.822788 0.568348i \(-0.192417\pi\)
0.822788 + 0.568348i \(0.192417\pi\)
\(692\) −95.8614 −3.64410
\(693\) 0.745463 0.0283178
\(694\) −1.67458 −0.0635661
\(695\) −1.57790 −0.0598530
\(696\) −18.9025 −0.716496
\(697\) 8.41316 0.318671
\(698\) −28.5885 −1.08209
\(699\) 3.66987 0.138807
\(700\) −55.5208 −2.09849
\(701\) −23.7760 −0.898009 −0.449004 0.893530i \(-0.648221\pi\)
−0.449004 + 0.893530i \(0.648221\pi\)
\(702\) 13.2085 0.498521
\(703\) −25.4828 −0.961103
\(704\) −0.263170 −0.00991858
\(705\) 0.502809 0.0189369
\(706\) −28.9221 −1.08850
\(707\) −34.0419 −1.28028
\(708\) 54.8839 2.06266
\(709\) −13.7453 −0.516217 −0.258109 0.966116i \(-0.583099\pi\)
−0.258109 + 0.966116i \(0.583099\pi\)
\(710\) −0.214157 −0.00803717
\(711\) −18.2244 −0.683469
\(712\) −34.0454 −1.27590
\(713\) −8.16544 −0.305798
\(714\) −33.2127 −1.24295
\(715\) −0.0136412 −0.000510154 0
\(716\) −92.9389 −3.47329
\(717\) 6.60945 0.246834
\(718\) −32.2393 −1.20316
\(719\) −39.6978 −1.48048 −0.740239 0.672344i \(-0.765288\pi\)
−0.740239 + 0.672344i \(0.765288\pi\)
\(720\) −1.23052 −0.0458590
\(721\) 30.7080 1.14363
\(722\) −119.360 −4.44212
\(723\) −7.07151 −0.262992
\(724\) −88.7431 −3.29811
\(725\) −13.5933 −0.504842
\(726\) 29.6470 1.10030
\(727\) −17.4362 −0.646674 −0.323337 0.946284i \(-0.604805\pi\)
−0.323337 + 0.946284i \(0.604805\pi\)
\(728\) −16.0285 −0.594055
\(729\) 15.8494 0.587014
\(730\) 0.843862 0.0312327
\(731\) 5.92169 0.219021
\(732\) 12.0601 0.445756
\(733\) −6.52643 −0.241059 −0.120530 0.992710i \(-0.538459\pi\)
−0.120530 + 0.992710i \(0.538459\pi\)
\(734\) −97.4061 −3.59533
\(735\) −0.0956749 −0.00352902
\(736\) 19.7711 0.728772
\(737\) 1.97755 0.0728440
\(738\) 8.06301 0.296804
\(739\) −14.0205 −0.515753 −0.257876 0.966178i \(-0.583023\pi\)
−0.257876 + 0.966178i \(0.583023\pi\)
\(740\) 1.20970 0.0444693
\(741\) −8.53475 −0.313532
\(742\) 70.8882 2.60239
\(743\) 50.2932 1.84508 0.922539 0.385904i \(-0.126110\pi\)
0.922539 + 0.385904i \(0.126110\pi\)
\(744\) −19.1427 −0.701806
\(745\) 1.58931 0.0582279
\(746\) 75.4400 2.76206
\(747\) 30.3991 1.11225
\(748\) −3.74443 −0.136910
\(749\) −6.22058 −0.227295
\(750\) 2.27082 0.0829187
\(751\) −34.3004 −1.25164 −0.625820 0.779968i \(-0.715235\pi\)
−0.625820 + 0.779968i \(0.715235\pi\)
\(752\) 43.9217 1.60166
\(753\) 13.9512 0.508409
\(754\) −6.97831 −0.254135
\(755\) −1.33084 −0.0484342
\(756\) −57.3024 −2.08407
\(757\) 28.9380 1.05177 0.525884 0.850556i \(-0.323734\pi\)
0.525884 + 0.850556i \(0.323734\pi\)
\(758\) 33.6944 1.22384
\(759\) 0.506249 0.0183757
\(760\) 4.48648 0.162742
\(761\) 8.47740 0.307306 0.153653 0.988125i \(-0.450896\pi\)
0.153653 + 0.988125i \(0.450896\pi\)
\(762\) 13.0727 0.473575
\(763\) 14.1812 0.513395
\(764\) −81.2904 −2.94098
\(765\) −0.802767 −0.0290241
\(766\) −4.06172 −0.146756
\(767\) 11.3943 0.411425
\(768\) −28.2552 −1.01957
\(769\) −19.6412 −0.708280 −0.354140 0.935192i \(-0.615226\pi\)
−0.354140 + 0.935192i \(0.615226\pi\)
\(770\) 0.0850797 0.00306606
\(771\) 2.03378 0.0732449
\(772\) 8.77100 0.315675
\(773\) −15.0632 −0.541786 −0.270893 0.962609i \(-0.587319\pi\)
−0.270893 + 0.962609i \(0.587319\pi\)
\(774\) 5.67523 0.203992
\(775\) −13.7661 −0.494492
\(776\) 11.5814 0.415748
\(777\) 8.07132 0.289557
\(778\) 38.7798 1.39032
\(779\) −13.4840 −0.483113
\(780\) 0.405153 0.0145068
\(781\) −0.161095 −0.00576443
\(782\) 38.3521 1.37147
\(783\) −14.0295 −0.501373
\(784\) −8.35744 −0.298480
\(785\) −0.400614 −0.0142985
\(786\) −29.9372 −1.06783
\(787\) −41.0309 −1.46259 −0.731297 0.682059i \(-0.761085\pi\)
−0.731297 + 0.682059i \(0.761085\pi\)
\(788\) −99.9033 −3.55891
\(789\) 9.20918 0.327855
\(790\) −2.07995 −0.0740014
\(791\) 36.0874 1.28312
\(792\) −2.01806 −0.0717088
\(793\) 2.50378 0.0889117
\(794\) −27.1754 −0.964419
\(795\) −1.00766 −0.0357379
\(796\) −2.32809 −0.0825171
\(797\) −35.9829 −1.27458 −0.637290 0.770624i \(-0.719945\pi\)
−0.637290 + 0.770624i \(0.719945\pi\)
\(798\) 53.2307 1.88435
\(799\) 28.6535 1.01369
\(800\) 33.3320 1.17846
\(801\) −9.76337 −0.344972
\(802\) −51.9580 −1.83470
\(803\) 0.634776 0.0224008
\(804\) −58.7344 −2.07140
\(805\) −0.606147 −0.0213639
\(806\) −7.06701 −0.248925
\(807\) 4.04408 0.142358
\(808\) 92.1558 3.24203
\(809\) −0.991303 −0.0348524 −0.0174262 0.999848i \(-0.505547\pi\)
−0.0174262 + 0.999848i \(0.505547\pi\)
\(810\) −0.0508022 −0.00178501
\(811\) 16.9943 0.596751 0.298375 0.954449i \(-0.403555\pi\)
0.298375 + 0.954449i \(0.403555\pi\)
\(812\) 30.2740 1.06241
\(813\) −2.12613 −0.0745665
\(814\) 1.30821 0.0458527
\(815\) 0.412769 0.0144587
\(816\) 41.2400 1.44369
\(817\) −9.49081 −0.332041
\(818\) −21.3431 −0.746244
\(819\) −4.59657 −0.160617
\(820\) 0.640097 0.0223532
\(821\) −16.4244 −0.573214 −0.286607 0.958048i \(-0.592527\pi\)
−0.286607 + 0.958048i \(0.592527\pi\)
\(822\) −48.8446 −1.70365
\(823\) 10.7494 0.374700 0.187350 0.982293i \(-0.440010\pi\)
0.187350 + 0.982293i \(0.440010\pi\)
\(824\) −83.1307 −2.89599
\(825\) 0.853483 0.0297145
\(826\) −71.0656 −2.47269
\(827\) 30.9104 1.07486 0.537431 0.843308i \(-0.319395\pi\)
0.537431 + 0.843308i \(0.319395\pi\)
\(828\) 25.5668 0.888507
\(829\) 36.4665 1.26654 0.633268 0.773933i \(-0.281713\pi\)
0.633268 + 0.773933i \(0.281713\pi\)
\(830\) 3.46945 0.120426
\(831\) −25.2354 −0.875405
\(832\) 1.62272 0.0562578
\(833\) −5.45221 −0.188908
\(834\) 50.6809 1.75494
\(835\) −1.07018 −0.0370351
\(836\) 6.00128 0.207558
\(837\) −14.2078 −0.491094
\(838\) −47.2679 −1.63284
\(839\) −35.8042 −1.23610 −0.618048 0.786140i \(-0.712076\pi\)
−0.618048 + 0.786140i \(0.712076\pi\)
\(840\) −1.42103 −0.0490301
\(841\) −21.5879 −0.744411
\(842\) 82.7568 2.85199
\(843\) 21.0838 0.726165
\(844\) −120.573 −4.15031
\(845\) 0.0841128 0.00289357
\(846\) 27.4610 0.944128
\(847\) −26.7020 −0.917493
\(848\) −88.0213 −3.02266
\(849\) −5.41826 −0.185954
\(850\) 64.6577 2.21774
\(851\) −9.32029 −0.319495
\(852\) 4.78461 0.163918
\(853\) −0.171577 −0.00587468 −0.00293734 0.999996i \(-0.500935\pi\)
−0.00293734 + 0.999996i \(0.500935\pi\)
\(854\) −15.6159 −0.534365
\(855\) 1.28661 0.0440012
\(856\) 16.8399 0.575577
\(857\) 0.194608 0.00664768 0.00332384 0.999994i \(-0.498942\pi\)
0.00332384 + 0.999994i \(0.498942\pi\)
\(858\) 0.438147 0.0149581
\(859\) 55.1624 1.88212 0.941058 0.338245i \(-0.109833\pi\)
0.941058 + 0.338245i \(0.109833\pi\)
\(860\) 0.450538 0.0153632
\(861\) 4.27085 0.145550
\(862\) 57.0650 1.94364
\(863\) −15.3478 −0.522444 −0.261222 0.965279i \(-0.584126\pi\)
−0.261222 + 0.965279i \(0.584126\pi\)
\(864\) 34.4016 1.17037
\(865\) −1.76440 −0.0599914
\(866\) 16.4702 0.559681
\(867\) 8.98574 0.305172
\(868\) 30.6588 1.04063
\(869\) −1.56460 −0.0530753
\(870\) −0.618672 −0.0209749
\(871\) −12.1937 −0.413168
\(872\) −38.3904 −1.30006
\(873\) 3.32126 0.112408
\(874\) −61.4677 −2.07918
\(875\) −2.04525 −0.0691421
\(876\) −18.8532 −0.636992
\(877\) 48.1700 1.62659 0.813293 0.581854i \(-0.197673\pi\)
0.813293 + 0.581854i \(0.197673\pi\)
\(878\) −0.403290 −0.0136104
\(879\) 8.52304 0.287475
\(880\) −0.105643 −0.00356122
\(881\) −56.0075 −1.88694 −0.943471 0.331455i \(-0.892460\pi\)
−0.943471 + 0.331455i \(0.892460\pi\)
\(882\) −5.22529 −0.175945
\(883\) 22.4813 0.756557 0.378278 0.925692i \(-0.376516\pi\)
0.378278 + 0.925692i \(0.376516\pi\)
\(884\) 23.0884 0.776547
\(885\) 1.01018 0.0339568
\(886\) 14.8746 0.499723
\(887\) −44.1393 −1.48205 −0.741026 0.671476i \(-0.765661\pi\)
−0.741026 + 0.671476i \(0.765661\pi\)
\(888\) −21.8501 −0.733242
\(889\) −11.7741 −0.394892
\(890\) −1.11429 −0.0373512
\(891\) −0.0382149 −0.00128025
\(892\) −119.592 −4.00425
\(893\) −45.9236 −1.53677
\(894\) −51.0476 −1.70729
\(895\) −1.71061 −0.0571794
\(896\) 22.3675 0.747247
\(897\) −3.12156 −0.104226
\(898\) −58.2643 −1.94430
\(899\) 7.50629 0.250349
\(900\) 43.1029 1.43676
\(901\) −57.4231 −1.91304
\(902\) 0.692224 0.0230485
\(903\) 3.00608 0.100036
\(904\) −97.6932 −3.24923
\(905\) −1.63338 −0.0542954
\(906\) 42.7457 1.42013
\(907\) −52.5801 −1.74589 −0.872947 0.487815i \(-0.837794\pi\)
−0.872947 + 0.487815i \(0.837794\pi\)
\(908\) −126.197 −4.18798
\(909\) 26.4280 0.876562
\(910\) −0.524607 −0.0173905
\(911\) −39.8202 −1.31930 −0.659651 0.751572i \(-0.729296\pi\)
−0.659651 + 0.751572i \(0.729296\pi\)
\(912\) −66.0962 −2.18866
\(913\) 2.60982 0.0863724
\(914\) −95.0941 −3.14543
\(915\) 0.221976 0.00733829
\(916\) 49.4574 1.63412
\(917\) 26.9634 0.890410
\(918\) 66.7325 2.20250
\(919\) 38.9332 1.28429 0.642144 0.766584i \(-0.278045\pi\)
0.642144 + 0.766584i \(0.278045\pi\)
\(920\) 1.64092 0.0540995
\(921\) 33.6737 1.10959
\(922\) −26.6071 −0.876257
\(923\) 0.993322 0.0326956
\(924\) −1.90082 −0.0625323
\(925\) −15.7130 −0.516641
\(926\) 103.579 3.40382
\(927\) −23.8398 −0.783003
\(928\) −18.1751 −0.596626
\(929\) 12.0482 0.395287 0.197644 0.980274i \(-0.436671\pi\)
0.197644 + 0.980274i \(0.436671\pi\)
\(930\) −0.626536 −0.0205449
\(931\) 8.73837 0.286389
\(932\) 15.9115 0.521199
\(933\) −2.11869 −0.0693628
\(934\) 35.8403 1.17273
\(935\) −0.0689190 −0.00225389
\(936\) 12.4435 0.406729
\(937\) −51.0642 −1.66820 −0.834098 0.551617i \(-0.814011\pi\)
−0.834098 + 0.551617i \(0.814011\pi\)
\(938\) 76.0514 2.48317
\(939\) −24.9646 −0.814688
\(940\) 2.18004 0.0711051
\(941\) −53.0808 −1.73039 −0.865193 0.501439i \(-0.832804\pi\)
−0.865193 + 0.501439i \(0.832804\pi\)
\(942\) 12.8674 0.419244
\(943\) −4.93172 −0.160599
\(944\) 88.2416 2.87202
\(945\) −1.05469 −0.0343091
\(946\) 0.487228 0.0158412
\(947\) −38.7293 −1.25853 −0.629266 0.777190i \(-0.716645\pi\)
−0.629266 + 0.777190i \(0.716645\pi\)
\(948\) 46.4695 1.50926
\(949\) −3.91407 −0.127056
\(950\) −103.628 −3.36214
\(951\) −5.59067 −0.181290
\(952\) −80.9798 −2.62457
\(953\) 54.8400 1.77644 0.888221 0.459416i \(-0.151941\pi\)
0.888221 + 0.459416i \(0.151941\pi\)
\(954\) −55.0332 −1.78177
\(955\) −1.49621 −0.0484162
\(956\) 28.6567 0.926824
\(957\) −0.465382 −0.0150437
\(958\) −29.6789 −0.958882
\(959\) 43.9926 1.42060
\(960\) 0.143865 0.00464321
\(961\) −23.3983 −0.754784
\(962\) −8.06650 −0.260074
\(963\) 4.82928 0.155621
\(964\) −30.6601 −0.987494
\(965\) 0.161437 0.00519683
\(966\) 19.4690 0.626405
\(967\) 4.28014 0.137640 0.0688201 0.997629i \(-0.478077\pi\)
0.0688201 + 0.997629i \(0.478077\pi\)
\(968\) 72.2859 2.32336
\(969\) −43.1197 −1.38520
\(970\) 0.379056 0.0121707
\(971\) −49.2148 −1.57938 −0.789689 0.613507i \(-0.789758\pi\)
−0.789689 + 0.613507i \(0.789758\pi\)
\(972\) 71.7834 2.30245
\(973\) −45.6465 −1.46336
\(974\) 41.1809 1.31952
\(975\) −5.26263 −0.168539
\(976\) 19.3901 0.620663
\(977\) 26.5332 0.848873 0.424436 0.905458i \(-0.360472\pi\)
0.424436 + 0.905458i \(0.360472\pi\)
\(978\) −13.2579 −0.423940
\(979\) −0.838203 −0.0267891
\(980\) −0.414820 −0.0132509
\(981\) −11.0094 −0.351504
\(982\) −43.1223 −1.37609
\(983\) −44.4747 −1.41852 −0.709261 0.704946i \(-0.750971\pi\)
−0.709261 + 0.704946i \(0.750971\pi\)
\(984\) −11.5617 −0.368575
\(985\) −1.83879 −0.0585888
\(986\) −35.2561 −1.12278
\(987\) 14.5456 0.462993
\(988\) −37.0043 −1.17726
\(989\) −3.47124 −0.110379
\(990\) −0.0660506 −0.00209923
\(991\) 19.4891 0.619092 0.309546 0.950884i \(-0.399823\pi\)
0.309546 + 0.950884i \(0.399823\pi\)
\(992\) −18.4061 −0.584394
\(993\) −20.4718 −0.649653
\(994\) −6.19529 −0.196503
\(995\) −0.0428503 −0.00135844
\(996\) −77.5132 −2.45610
\(997\) 60.6275 1.92009 0.960046 0.279842i \(-0.0902822\pi\)
0.960046 + 0.279842i \(0.0902822\pi\)
\(998\) 41.4214 1.31117
\(999\) −16.2172 −0.513091
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 \(a_p\))