Properties

Label 6013.2.a.e.1.14
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.11721 q^{2}\) \(+0.0595888 q^{3}\) \(+2.48258 q^{4}\) \(-0.217642 q^{5}\) \(-0.126162 q^{6}\) \(+1.00000 q^{7}\) \(-1.02172 q^{8}\) \(-2.99645 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.11721 q^{2}\) \(+0.0595888 q^{3}\) \(+2.48258 q^{4}\) \(-0.217642 q^{5}\) \(-0.126162 q^{6}\) \(+1.00000 q^{7}\) \(-1.02172 q^{8}\) \(-2.99645 q^{9}\) \(+0.460795 q^{10}\) \(-6.48236 q^{11}\) \(+0.147934 q^{12}\) \(-1.76262 q^{13}\) \(-2.11721 q^{14}\) \(-0.0129691 q^{15}\) \(-2.80196 q^{16}\) \(-3.36526 q^{17}\) \(+6.34411 q^{18}\) \(+2.28368 q^{19}\) \(-0.540315 q^{20}\) \(+0.0595888 q^{21}\) \(+13.7245 q^{22}\) \(+4.32025 q^{23}\) \(-0.0608833 q^{24}\) \(-4.95263 q^{25}\) \(+3.73184 q^{26}\) \(-0.357321 q^{27}\) \(+2.48258 q^{28}\) \(-9.07084 q^{29}\) \(+0.0274582 q^{30}\) \(-4.78988 q^{31}\) \(+7.97578 q^{32}\) \(-0.386276 q^{33}\) \(+7.12496 q^{34}\) \(-0.217642 q^{35}\) \(-7.43892 q^{36}\) \(-5.25246 q^{37}\) \(-4.83503 q^{38}\) \(-0.105032 q^{39}\) \(+0.222370 q^{40}\) \(+10.4507 q^{41}\) \(-0.126162 q^{42}\) \(-9.64737 q^{43}\) \(-16.0930 q^{44}\) \(+0.652155 q^{45}\) \(-9.14689 q^{46}\) \(-1.63389 q^{47}\) \(-0.166965 q^{48}\) \(+1.00000 q^{49}\) \(+10.4858 q^{50}\) \(-0.200532 q^{51}\) \(-4.37585 q^{52}\) \(+1.70108 q^{53}\) \(+0.756524 q^{54}\) \(+1.41084 q^{55}\) \(-1.02172 q^{56}\) \(+0.136082 q^{57}\) \(+19.2049 q^{58}\) \(-2.35256 q^{59}\) \(-0.0321967 q^{60}\) \(-9.12822 q^{61}\) \(+10.1412 q^{62}\) \(-2.99645 q^{63}\) \(-11.2825 q^{64}\) \(+0.383621 q^{65}\) \(+0.817828 q^{66}\) \(-5.08291 q^{67}\) \(-8.35453 q^{68}\) \(+0.257439 q^{69}\) \(+0.460795 q^{70}\) \(-6.42142 q^{71}\) \(+3.06154 q^{72}\) \(-11.3025 q^{73}\) \(+11.1206 q^{74}\) \(-0.295121 q^{75}\) \(+5.66942 q^{76}\) \(-6.48236 q^{77}\) \(+0.222376 q^{78}\) \(+7.17326 q^{79}\) \(+0.609825 q^{80}\) \(+8.96806 q^{81}\) \(-22.1264 q^{82}\) \(+3.43556 q^{83}\) \(+0.147934 q^{84}\) \(+0.732424 q^{85}\) \(+20.4255 q^{86}\) \(-0.540520 q^{87}\) \(+6.62318 q^{88}\) \(+1.17943 q^{89}\) \(-1.38075 q^{90}\) \(-1.76262 q^{91}\) \(+10.7254 q^{92}\) \(-0.285423 q^{93}\) \(+3.45928 q^{94}\) \(-0.497026 q^{95}\) \(+0.475267 q^{96}\) \(-17.0817 q^{97}\) \(-2.11721 q^{98}\) \(+19.4241 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11721 −1.49709 −0.748547 0.663082i \(-0.769248\pi\)
−0.748547 + 0.663082i \(0.769248\pi\)
\(3\) 0.0595888 0.0344036 0.0172018 0.999852i \(-0.494524\pi\)
0.0172018 + 0.999852i \(0.494524\pi\)
\(4\) 2.48258 1.24129
\(5\) −0.217642 −0.0973327 −0.0486663 0.998815i \(-0.515497\pi\)
−0.0486663 + 0.998815i \(0.515497\pi\)
\(6\) −0.126162 −0.0515054
\(7\) 1.00000 0.377964
\(8\) −1.02172 −0.361234
\(9\) −2.99645 −0.998816
\(10\) 0.460795 0.145716
\(11\) −6.48236 −1.95451 −0.977253 0.212078i \(-0.931977\pi\)
−0.977253 + 0.212078i \(0.931977\pi\)
\(12\) 0.147934 0.0427048
\(13\) −1.76262 −0.488863 −0.244432 0.969667i \(-0.578601\pi\)
−0.244432 + 0.969667i \(0.578601\pi\)
\(14\) −2.11721 −0.565848
\(15\) −0.0129691 −0.00334859
\(16\) −2.80196 −0.700489
\(17\) −3.36526 −0.816195 −0.408098 0.912938i \(-0.633808\pi\)
−0.408098 + 0.912938i \(0.633808\pi\)
\(18\) 6.34411 1.49532
\(19\) 2.28368 0.523912 0.261956 0.965080i \(-0.415632\pi\)
0.261956 + 0.965080i \(0.415632\pi\)
\(20\) −0.540315 −0.120818
\(21\) 0.0595888 0.0130033
\(22\) 13.7245 2.92608
\(23\) 4.32025 0.900835 0.450418 0.892818i \(-0.351275\pi\)
0.450418 + 0.892818i \(0.351275\pi\)
\(24\) −0.0608833 −0.0124277
\(25\) −4.95263 −0.990526
\(26\) 3.73184 0.731874
\(27\) −0.357321 −0.0687665
\(28\) 2.48258 0.469164
\(29\) −9.07084 −1.68441 −0.842207 0.539155i \(-0.818744\pi\)
−0.842207 + 0.539155i \(0.818744\pi\)
\(30\) 0.0274582 0.00501316
\(31\) −4.78988 −0.860287 −0.430144 0.902760i \(-0.641537\pi\)
−0.430144 + 0.902760i \(0.641537\pi\)
\(32\) 7.97578 1.40993
\(33\) −0.386276 −0.0672420
\(34\) 7.12496 1.22192
\(35\) −0.217642 −0.0367883
\(36\) −7.43892 −1.23982
\(37\) −5.25246 −0.863499 −0.431750 0.901993i \(-0.642104\pi\)
−0.431750 + 0.901993i \(0.642104\pi\)
\(38\) −4.83503 −0.784346
\(39\) −0.105032 −0.0168187
\(40\) 0.222370 0.0351599
\(41\) 10.4507 1.63213 0.816066 0.577959i \(-0.196151\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(42\) −0.126162 −0.0194672
\(43\) −9.64737 −1.47121 −0.735605 0.677410i \(-0.763102\pi\)
−0.735605 + 0.677410i \(0.763102\pi\)
\(44\) −16.0930 −2.42611
\(45\) 0.652155 0.0972175
\(46\) −9.14689 −1.34863
\(47\) −1.63389 −0.238327 −0.119163 0.992875i \(-0.538021\pi\)
−0.119163 + 0.992875i \(0.538021\pi\)
\(48\) −0.166965 −0.0240993
\(49\) 1.00000 0.142857
\(50\) 10.4858 1.48291
\(51\) −0.200532 −0.0280801
\(52\) −4.37585 −0.606821
\(53\) 1.70108 0.233661 0.116831 0.993152i \(-0.462727\pi\)
0.116831 + 0.993152i \(0.462727\pi\)
\(54\) 0.756524 0.102950
\(55\) 1.41084 0.190237
\(56\) −1.02172 −0.136534
\(57\) 0.136082 0.0180245
\(58\) 19.2049 2.52172
\(59\) −2.35256 −0.306278 −0.153139 0.988205i \(-0.548938\pi\)
−0.153139 + 0.988205i \(0.548938\pi\)
\(60\) −0.0321967 −0.00415658
\(61\) −9.12822 −1.16875 −0.584374 0.811484i \(-0.698660\pi\)
−0.584374 + 0.811484i \(0.698660\pi\)
\(62\) 10.1412 1.28793
\(63\) −2.99645 −0.377517
\(64\) −11.2825 −1.41031
\(65\) 0.383621 0.0475824
\(66\) 0.817828 0.100668
\(67\) −5.08291 −0.620976 −0.310488 0.950577i \(-0.600492\pi\)
−0.310488 + 0.950577i \(0.600492\pi\)
\(68\) −8.35453 −1.01314
\(69\) 0.257439 0.0309920
\(70\) 0.460795 0.0550755
\(71\) −6.42142 −0.762083 −0.381041 0.924558i \(-0.624434\pi\)
−0.381041 + 0.924558i \(0.624434\pi\)
\(72\) 3.06154 0.360806
\(73\) −11.3025 −1.32285 −0.661427 0.750010i \(-0.730049\pi\)
−0.661427 + 0.750010i \(0.730049\pi\)
\(74\) 11.1206 1.29274
\(75\) −0.295121 −0.0340777
\(76\) 5.66942 0.650327
\(77\) −6.48236 −0.738734
\(78\) 0.222376 0.0251791
\(79\) 7.17326 0.807055 0.403528 0.914968i \(-0.367784\pi\)
0.403528 + 0.914968i \(0.367784\pi\)
\(80\) 0.609825 0.0681805
\(81\) 8.96806 0.996451
\(82\) −22.1264 −2.44345
\(83\) 3.43556 0.377101 0.188551 0.982063i \(-0.439621\pi\)
0.188551 + 0.982063i \(0.439621\pi\)
\(84\) 0.147934 0.0161409
\(85\) 0.732424 0.0794425
\(86\) 20.4255 2.20254
\(87\) −0.540520 −0.0579499
\(88\) 6.62318 0.706033
\(89\) 1.17943 0.125019 0.0625094 0.998044i \(-0.480090\pi\)
0.0625094 + 0.998044i \(0.480090\pi\)
\(90\) −1.38075 −0.145544
\(91\) −1.76262 −0.184773
\(92\) 10.7254 1.11820
\(93\) −0.285423 −0.0295970
\(94\) 3.45928 0.356798
\(95\) −0.497026 −0.0509938
\(96\) 0.475267 0.0485067
\(97\) −17.0817 −1.73439 −0.867193 0.497973i \(-0.834078\pi\)
−0.867193 + 0.497973i \(0.834078\pi\)
\(98\) −2.11721 −0.213871
\(99\) 19.4241 1.95219
\(100\) −12.2953 −1.22953
\(101\) 17.2815 1.71957 0.859784 0.510657i \(-0.170598\pi\)
0.859784 + 0.510657i \(0.170598\pi\)
\(102\) 0.424568 0.0420385
\(103\) −7.02745 −0.692435 −0.346218 0.938154i \(-0.612534\pi\)
−0.346218 + 0.938154i \(0.612534\pi\)
\(104\) 1.80091 0.176594
\(105\) −0.0129691 −0.00126565
\(106\) −3.60155 −0.349813
\(107\) 9.30497 0.899545 0.449773 0.893143i \(-0.351505\pi\)
0.449773 + 0.893143i \(0.351505\pi\)
\(108\) −0.887078 −0.0853591
\(109\) 7.46946 0.715444 0.357722 0.933828i \(-0.383554\pi\)
0.357722 + 0.933828i \(0.383554\pi\)
\(110\) −2.98704 −0.284803
\(111\) −0.312988 −0.0297075
\(112\) −2.80196 −0.264760
\(113\) 11.3575 1.06842 0.534210 0.845352i \(-0.320609\pi\)
0.534210 + 0.845352i \(0.320609\pi\)
\(114\) −0.288114 −0.0269843
\(115\) −0.940271 −0.0876807
\(116\) −22.5191 −2.09085
\(117\) 5.28161 0.488285
\(118\) 4.98087 0.458527
\(119\) −3.36526 −0.308493
\(120\) 0.0132508 0.00120963
\(121\) 31.0210 2.82009
\(122\) 19.3264 1.74973
\(123\) 0.622747 0.0561512
\(124\) −11.8913 −1.06787
\(125\) 2.16612 0.193743
\(126\) 6.34411 0.565179
\(127\) −4.77108 −0.423365 −0.211682 0.977339i \(-0.567894\pi\)
−0.211682 + 0.977339i \(0.567894\pi\)
\(128\) 7.93585 0.701436
\(129\) −0.574875 −0.0506149
\(130\) −0.812207 −0.0712353
\(131\) −9.59927 −0.838692 −0.419346 0.907827i \(-0.637741\pi\)
−0.419346 + 0.907827i \(0.637741\pi\)
\(132\) −0.958961 −0.0834669
\(133\) 2.28368 0.198020
\(134\) 10.7616 0.929659
\(135\) 0.0777683 0.00669323
\(136\) 3.43837 0.294837
\(137\) 11.6660 0.996698 0.498349 0.866977i \(-0.333940\pi\)
0.498349 + 0.866977i \(0.333940\pi\)
\(138\) −0.545052 −0.0463979
\(139\) 5.18473 0.439763 0.219882 0.975527i \(-0.429433\pi\)
0.219882 + 0.975527i \(0.429433\pi\)
\(140\) −0.540315 −0.0456649
\(141\) −0.0973613 −0.00819930
\(142\) 13.5955 1.14091
\(143\) 11.4259 0.955486
\(144\) 8.39592 0.699660
\(145\) 1.97420 0.163948
\(146\) 23.9297 1.98044
\(147\) 0.0595888 0.00491480
\(148\) −13.0397 −1.07185
\(149\) 9.52641 0.780434 0.390217 0.920723i \(-0.372400\pi\)
0.390217 + 0.920723i \(0.372400\pi\)
\(150\) 0.624834 0.0510175
\(151\) −8.59419 −0.699385 −0.349693 0.936864i \(-0.613714\pi\)
−0.349693 + 0.936864i \(0.613714\pi\)
\(152\) −2.33329 −0.189255
\(153\) 10.0838 0.815229
\(154\) 13.7245 1.10595
\(155\) 1.04248 0.0837341
\(156\) −0.260752 −0.0208768
\(157\) −17.4332 −1.39132 −0.695660 0.718371i \(-0.744888\pi\)
−0.695660 + 0.718371i \(0.744888\pi\)
\(158\) −15.1873 −1.20824
\(159\) 0.101365 0.00803879
\(160\) −1.73587 −0.137232
\(161\) 4.32025 0.340484
\(162\) −18.9873 −1.49178
\(163\) 7.80360 0.611225 0.305613 0.952156i \(-0.401139\pi\)
0.305613 + 0.952156i \(0.401139\pi\)
\(164\) 25.9448 2.02595
\(165\) 0.0840701 0.00654485
\(166\) −7.27380 −0.564556
\(167\) −4.36425 −0.337716 −0.168858 0.985640i \(-0.554008\pi\)
−0.168858 + 0.985640i \(0.554008\pi\)
\(168\) −0.0608833 −0.00469725
\(169\) −9.89317 −0.761013
\(170\) −1.55069 −0.118933
\(171\) −6.84293 −0.523292
\(172\) −23.9504 −1.82620
\(173\) −2.13481 −0.162307 −0.0811533 0.996702i \(-0.525860\pi\)
−0.0811533 + 0.996702i \(0.525860\pi\)
\(174\) 1.14440 0.0867564
\(175\) −4.95263 −0.374384
\(176\) 18.1633 1.36911
\(177\) −0.140186 −0.0105371
\(178\) −2.49709 −0.187165
\(179\) −6.27980 −0.469375 −0.234687 0.972071i \(-0.575407\pi\)
−0.234687 + 0.972071i \(0.575407\pi\)
\(180\) 1.61903 0.120675
\(181\) 8.83302 0.656553 0.328277 0.944582i \(-0.393532\pi\)
0.328277 + 0.944582i \(0.393532\pi\)
\(182\) 3.73184 0.276622
\(183\) −0.543940 −0.0402092
\(184\) −4.41410 −0.325412
\(185\) 1.14316 0.0840467
\(186\) 0.604300 0.0443095
\(187\) 21.8148 1.59526
\(188\) −4.05626 −0.295833
\(189\) −0.357321 −0.0259913
\(190\) 1.05231 0.0763425
\(191\) 4.74801 0.343554 0.171777 0.985136i \(-0.445049\pi\)
0.171777 + 0.985136i \(0.445049\pi\)
\(192\) −0.672310 −0.0485198
\(193\) −0.244290 −0.0175843 −0.00879217 0.999961i \(-0.502799\pi\)
−0.00879217 + 0.999961i \(0.502799\pi\)
\(194\) 36.1656 2.59654
\(195\) 0.0228595 0.00163700
\(196\) 2.48258 0.177327
\(197\) 11.4463 0.815518 0.407759 0.913090i \(-0.366310\pi\)
0.407759 + 0.913090i \(0.366310\pi\)
\(198\) −41.1248 −2.92261
\(199\) −13.1190 −0.929982 −0.464991 0.885315i \(-0.653943\pi\)
−0.464991 + 0.885315i \(0.653943\pi\)
\(200\) 5.06022 0.357812
\(201\) −0.302884 −0.0213638
\(202\) −36.5885 −2.57436
\(203\) −9.07084 −0.636648
\(204\) −0.497836 −0.0348555
\(205\) −2.27453 −0.158860
\(206\) 14.8786 1.03664
\(207\) −12.9454 −0.899769
\(208\) 4.93879 0.342443
\(209\) −14.8036 −1.02399
\(210\) 0.0274582 0.00189480
\(211\) 21.8108 1.50152 0.750760 0.660576i \(-0.229688\pi\)
0.750760 + 0.660576i \(0.229688\pi\)
\(212\) 4.22307 0.290042
\(213\) −0.382645 −0.0262184
\(214\) −19.7006 −1.34670
\(215\) 2.09968 0.143197
\(216\) 0.365083 0.0248408
\(217\) −4.78988 −0.325158
\(218\) −15.8144 −1.07109
\(219\) −0.673500 −0.0455109
\(220\) 3.50252 0.236140
\(221\) 5.93168 0.399008
\(222\) 0.662661 0.0444749
\(223\) 2.63188 0.176244 0.0881220 0.996110i \(-0.471913\pi\)
0.0881220 + 0.996110i \(0.471913\pi\)
\(224\) 7.97578 0.532904
\(225\) 14.8403 0.989354
\(226\) −24.0461 −1.59952
\(227\) −19.5609 −1.29830 −0.649151 0.760660i \(-0.724876\pi\)
−0.649151 + 0.760660i \(0.724876\pi\)
\(228\) 0.337834 0.0223736
\(229\) 2.91229 0.192450 0.0962249 0.995360i \(-0.469323\pi\)
0.0962249 + 0.995360i \(0.469323\pi\)
\(230\) 1.99075 0.131266
\(231\) −0.386276 −0.0254151
\(232\) 9.26789 0.608467
\(233\) −13.8129 −0.904911 −0.452456 0.891787i \(-0.649452\pi\)
−0.452456 + 0.891787i \(0.649452\pi\)
\(234\) −11.1823 −0.731008
\(235\) 0.355603 0.0231970
\(236\) −5.84043 −0.380180
\(237\) 0.427446 0.0277656
\(238\) 7.12496 0.461843
\(239\) −17.0656 −1.10388 −0.551940 0.833884i \(-0.686112\pi\)
−0.551940 + 0.833884i \(0.686112\pi\)
\(240\) 0.0363387 0.00234565
\(241\) 8.46587 0.545334 0.272667 0.962108i \(-0.412094\pi\)
0.272667 + 0.962108i \(0.412094\pi\)
\(242\) −65.6780 −4.22194
\(243\) 1.60636 0.103048
\(244\) −22.6615 −1.45076
\(245\) −0.217642 −0.0139047
\(246\) −1.31849 −0.0840636
\(247\) −4.02526 −0.256121
\(248\) 4.89393 0.310765
\(249\) 0.204721 0.0129736
\(250\) −4.58612 −0.290052
\(251\) 2.54112 0.160394 0.0801969 0.996779i \(-0.474445\pi\)
0.0801969 + 0.996779i \(0.474445\pi\)
\(252\) −7.43892 −0.468608
\(253\) −28.0054 −1.76069
\(254\) 10.1014 0.633817
\(255\) 0.0436442 0.00273311
\(256\) 5.76312 0.360195
\(257\) 19.0147 1.18610 0.593052 0.805164i \(-0.297923\pi\)
0.593052 + 0.805164i \(0.297923\pi\)
\(258\) 1.21713 0.0757753
\(259\) −5.25246 −0.326372
\(260\) 0.952371 0.0590635
\(261\) 27.1803 1.68242
\(262\) 20.3237 1.25560
\(263\) −19.9647 −1.23107 −0.615537 0.788108i \(-0.711061\pi\)
−0.615537 + 0.788108i \(0.711061\pi\)
\(264\) 0.394667 0.0242901
\(265\) −0.370227 −0.0227429
\(266\) −4.83503 −0.296455
\(267\) 0.0702805 0.00430110
\(268\) −12.6187 −0.770811
\(269\) −10.1215 −0.617119 −0.308560 0.951205i \(-0.599847\pi\)
−0.308560 + 0.951205i \(0.599847\pi\)
\(270\) −0.164652 −0.0100204
\(271\) −32.2546 −1.95933 −0.979663 0.200649i \(-0.935695\pi\)
−0.979663 + 0.200649i \(0.935695\pi\)
\(272\) 9.42931 0.571736
\(273\) −0.105032 −0.00635685
\(274\) −24.6995 −1.49215
\(275\) 32.1047 1.93599
\(276\) 0.639112 0.0384700
\(277\) −16.6210 −0.998660 −0.499330 0.866412i \(-0.666420\pi\)
−0.499330 + 0.866412i \(0.666420\pi\)
\(278\) −10.9772 −0.658367
\(279\) 14.3526 0.859269
\(280\) 0.222370 0.0132892
\(281\) −2.60751 −0.155551 −0.0777755 0.996971i \(-0.524782\pi\)
−0.0777755 + 0.996971i \(0.524782\pi\)
\(282\) 0.206134 0.0122751
\(283\) −2.48118 −0.147491 −0.0737455 0.997277i \(-0.523495\pi\)
−0.0737455 + 0.997277i \(0.523495\pi\)
\(284\) −15.9417 −0.945966
\(285\) −0.0296172 −0.00175437
\(286\) −24.1911 −1.43045
\(287\) 10.4507 0.616888
\(288\) −23.8990 −1.40826
\(289\) −5.67503 −0.333825
\(290\) −4.17980 −0.245446
\(291\) −1.01788 −0.0596691
\(292\) −28.0593 −1.64204
\(293\) 11.0299 0.644374 0.322187 0.946676i \(-0.395582\pi\)
0.322187 + 0.946676i \(0.395582\pi\)
\(294\) −0.126162 −0.00735792
\(295\) 0.512018 0.0298108
\(296\) 5.36656 0.311925
\(297\) 2.31628 0.134404
\(298\) −20.1694 −1.16838
\(299\) −7.61497 −0.440385
\(300\) −0.732662 −0.0423003
\(301\) −9.64737 −0.556065
\(302\) 18.1957 1.04705
\(303\) 1.02978 0.0591593
\(304\) −6.39877 −0.366995
\(305\) 1.98669 0.113757
\(306\) −21.3496 −1.22047
\(307\) 21.7046 1.23875 0.619373 0.785097i \(-0.287387\pi\)
0.619373 + 0.785097i \(0.287387\pi\)
\(308\) −16.0930 −0.916983
\(309\) −0.418757 −0.0238223
\(310\) −2.20715 −0.125358
\(311\) 3.32174 0.188359 0.0941794 0.995555i \(-0.469977\pi\)
0.0941794 + 0.995555i \(0.469977\pi\)
\(312\) 0.107314 0.00607547
\(313\) 17.1896 0.971614 0.485807 0.874066i \(-0.338526\pi\)
0.485807 + 0.874066i \(0.338526\pi\)
\(314\) 36.9097 2.08294
\(315\) 0.652155 0.0367448
\(316\) 17.8082 1.00179
\(317\) 14.9223 0.838120 0.419060 0.907959i \(-0.362360\pi\)
0.419060 + 0.907959i \(0.362360\pi\)
\(318\) −0.214612 −0.0120348
\(319\) 58.8005 3.29219
\(320\) 2.45555 0.137269
\(321\) 0.554472 0.0309476
\(322\) −9.14689 −0.509736
\(323\) −7.68518 −0.427615
\(324\) 22.2639 1.23688
\(325\) 8.72962 0.484232
\(326\) −16.5219 −0.915061
\(327\) 0.445096 0.0246139
\(328\) −10.6778 −0.589581
\(329\) −1.63389 −0.0900791
\(330\) −0.177994 −0.00979825
\(331\) 24.0942 1.32433 0.662167 0.749356i \(-0.269637\pi\)
0.662167 + 0.749356i \(0.269637\pi\)
\(332\) 8.52905 0.468092
\(333\) 15.7387 0.862477
\(334\) 9.24003 0.505592
\(335\) 1.10626 0.0604412
\(336\) −0.166965 −0.00910870
\(337\) −4.75104 −0.258805 −0.129403 0.991592i \(-0.541306\pi\)
−0.129403 + 0.991592i \(0.541306\pi\)
\(338\) 20.9459 1.13931
\(339\) 0.676777 0.0367575
\(340\) 1.81830 0.0986112
\(341\) 31.0497 1.68144
\(342\) 14.4879 0.783417
\(343\) 1.00000 0.0539949
\(344\) 9.85695 0.531451
\(345\) −0.0560296 −0.00301653
\(346\) 4.51984 0.242988
\(347\) 21.5673 1.15779 0.578896 0.815401i \(-0.303484\pi\)
0.578896 + 0.815401i \(0.303484\pi\)
\(348\) −1.34189 −0.0719326
\(349\) 1.14669 0.0613810 0.0306905 0.999529i \(-0.490229\pi\)
0.0306905 + 0.999529i \(0.490229\pi\)
\(350\) 10.4858 0.560488
\(351\) 0.629822 0.0336174
\(352\) −51.7019 −2.75572
\(353\) −36.1542 −1.92430 −0.962148 0.272527i \(-0.912141\pi\)
−0.962148 + 0.272527i \(0.912141\pi\)
\(354\) 0.296804 0.0157750
\(355\) 1.39757 0.0741755
\(356\) 2.92802 0.155185
\(357\) −0.200532 −0.0106133
\(358\) 13.2957 0.702698
\(359\) 7.30795 0.385699 0.192849 0.981228i \(-0.438227\pi\)
0.192849 + 0.981228i \(0.438227\pi\)
\(360\) −0.666322 −0.0351182
\(361\) −13.7848 −0.725516
\(362\) −18.7014 −0.982922
\(363\) 1.84850 0.0970213
\(364\) −4.37585 −0.229357
\(365\) 2.45990 0.128757
\(366\) 1.15163 0.0601969
\(367\) 8.26315 0.431333 0.215667 0.976467i \(-0.430808\pi\)
0.215667 + 0.976467i \(0.430808\pi\)
\(368\) −12.1052 −0.631025
\(369\) −31.3151 −1.63020
\(370\) −2.42031 −0.125826
\(371\) 1.70108 0.0883157
\(372\) −0.708585 −0.0367384
\(373\) 9.42895 0.488213 0.244106 0.969748i \(-0.421505\pi\)
0.244106 + 0.969748i \(0.421505\pi\)
\(374\) −46.1866 −2.38825
\(375\) 0.129076 0.00666547
\(376\) 1.66938 0.0860917
\(377\) 15.9885 0.823448
\(378\) 0.756524 0.0389114
\(379\) −29.3093 −1.50552 −0.752758 0.658298i \(-0.771277\pi\)
−0.752758 + 0.658298i \(0.771277\pi\)
\(380\) −1.23391 −0.0632981
\(381\) −0.284303 −0.0145653
\(382\) −10.0525 −0.514333
\(383\) −3.08427 −0.157599 −0.0787994 0.996890i \(-0.525109\pi\)
−0.0787994 + 0.996890i \(0.525109\pi\)
\(384\) 0.472887 0.0241319
\(385\) 1.41084 0.0719029
\(386\) 0.517212 0.0263254
\(387\) 28.9079 1.46947
\(388\) −42.4067 −2.15288
\(389\) 9.10273 0.461527 0.230763 0.973010i \(-0.425878\pi\)
0.230763 + 0.973010i \(0.425878\pi\)
\(390\) −0.0483984 −0.00245075
\(391\) −14.5388 −0.735258
\(392\) −1.02172 −0.0516048
\(393\) −0.572009 −0.0288540
\(394\) −24.2343 −1.22091
\(395\) −1.56121 −0.0785528
\(396\) 48.2218 2.42324
\(397\) 26.1887 1.31437 0.657186 0.753728i \(-0.271747\pi\)
0.657186 + 0.753728i \(0.271747\pi\)
\(398\) 27.7757 1.39227
\(399\) 0.136082 0.00681261
\(400\) 13.8771 0.693853
\(401\) −3.59029 −0.179291 −0.0896453 0.995974i \(-0.528573\pi\)
−0.0896453 + 0.995974i \(0.528573\pi\)
\(402\) 0.641270 0.0319836
\(403\) 8.44274 0.420563
\(404\) 42.9026 2.13448
\(405\) −1.95183 −0.0969872
\(406\) 19.2049 0.953122
\(407\) 34.0484 1.68771
\(408\) 0.204888 0.0101435
\(409\) 17.9430 0.887226 0.443613 0.896218i \(-0.353696\pi\)
0.443613 + 0.896218i \(0.353696\pi\)
\(410\) 4.81565 0.237828
\(411\) 0.695165 0.0342900
\(412\) −17.4462 −0.859513
\(413\) −2.35256 −0.115762
\(414\) 27.4082 1.34704
\(415\) −0.747723 −0.0367043
\(416\) −14.0583 −0.689264
\(417\) 0.308952 0.0151294
\(418\) 31.3424 1.53301
\(419\) −31.8687 −1.55689 −0.778443 0.627715i \(-0.783990\pi\)
−0.778443 + 0.627715i \(0.783990\pi\)
\(420\) −0.0321967 −0.00157104
\(421\) 22.7319 1.10788 0.553942 0.832555i \(-0.313123\pi\)
0.553942 + 0.832555i \(0.313123\pi\)
\(422\) −46.1781 −2.24792
\(423\) 4.89586 0.238045
\(424\) −1.73803 −0.0844064
\(425\) 16.6669 0.808463
\(426\) 0.810140 0.0392514
\(427\) −9.12822 −0.441746
\(428\) 23.1003 1.11660
\(429\) 0.680858 0.0328722
\(430\) −4.44546 −0.214379
\(431\) −20.6156 −0.993017 −0.496509 0.868032i \(-0.665385\pi\)
−0.496509 + 0.868032i \(0.665385\pi\)
\(432\) 1.00120 0.0481702
\(433\) −28.3262 −1.36127 −0.680635 0.732623i \(-0.738296\pi\)
−0.680635 + 0.732623i \(0.738296\pi\)
\(434\) 10.1412 0.486792
\(435\) 0.117640 0.00564042
\(436\) 18.5435 0.888074
\(437\) 9.86608 0.471959
\(438\) 1.42594 0.0681341
\(439\) 8.67275 0.413928 0.206964 0.978349i \(-0.433642\pi\)
0.206964 + 0.978349i \(0.433642\pi\)
\(440\) −1.44149 −0.0687201
\(441\) −2.99645 −0.142688
\(442\) −12.5586 −0.597352
\(443\) 10.7649 0.511456 0.255728 0.966749i \(-0.417685\pi\)
0.255728 + 0.966749i \(0.417685\pi\)
\(444\) −0.777017 −0.0368756
\(445\) −0.256693 −0.0121684
\(446\) −5.57225 −0.263854
\(447\) 0.567667 0.0268497
\(448\) −11.2825 −0.533047
\(449\) −20.9528 −0.988823 −0.494411 0.869228i \(-0.664616\pi\)
−0.494411 + 0.869228i \(0.664616\pi\)
\(450\) −31.4201 −1.48116
\(451\) −67.7455 −3.19001
\(452\) 28.1958 1.32622
\(453\) −0.512117 −0.0240614
\(454\) 41.4145 1.94368
\(455\) 0.383621 0.0179844
\(456\) −0.139038 −0.00651105
\(457\) −17.8034 −0.832807 −0.416403 0.909180i \(-0.636710\pi\)
−0.416403 + 0.909180i \(0.636710\pi\)
\(458\) −6.16594 −0.288115
\(459\) 1.20248 0.0561269
\(460\) −2.33430 −0.108837
\(461\) 24.5697 1.14432 0.572162 0.820141i \(-0.306105\pi\)
0.572162 + 0.820141i \(0.306105\pi\)
\(462\) 0.817828 0.0380488
\(463\) −7.91931 −0.368042 −0.184021 0.982922i \(-0.558911\pi\)
−0.184021 + 0.982922i \(0.558911\pi\)
\(464\) 25.4161 1.17991
\(465\) 0.0621202 0.00288075
\(466\) 29.2448 1.35474
\(467\) −13.4611 −0.622904 −0.311452 0.950262i \(-0.600815\pi\)
−0.311452 + 0.950262i \(0.600815\pi\)
\(468\) 13.1120 0.606103
\(469\) −5.08291 −0.234707
\(470\) −0.752887 −0.0347281
\(471\) −1.03882 −0.0478664
\(472\) 2.40367 0.110638
\(473\) 62.5378 2.87549
\(474\) −0.904993 −0.0415677
\(475\) −11.3102 −0.518949
\(476\) −8.35453 −0.382929
\(477\) −5.09720 −0.233385
\(478\) 36.1314 1.65261
\(479\) −15.8429 −0.723882 −0.361941 0.932201i \(-0.617886\pi\)
−0.361941 + 0.932201i \(0.617886\pi\)
\(480\) −0.103438 −0.00472129
\(481\) 9.25810 0.422133
\(482\) −17.9240 −0.816417
\(483\) 0.257439 0.0117139
\(484\) 77.0121 3.50055
\(485\) 3.71771 0.168812
\(486\) −3.40100 −0.154272
\(487\) 10.5448 0.477830 0.238915 0.971040i \(-0.423208\pi\)
0.238915 + 0.971040i \(0.423208\pi\)
\(488\) 9.32652 0.422192
\(489\) 0.465007 0.0210283
\(490\) 0.460795 0.0208166
\(491\) 8.13835 0.367279 0.183639 0.982994i \(-0.441212\pi\)
0.183639 + 0.982994i \(0.441212\pi\)
\(492\) 1.54602 0.0696999
\(493\) 30.5257 1.37481
\(494\) 8.52233 0.383438
\(495\) −4.22750 −0.190012
\(496\) 13.4210 0.602622
\(497\) −6.42142 −0.288040
\(498\) −0.433437 −0.0194228
\(499\) 36.8607 1.65011 0.825055 0.565052i \(-0.191144\pi\)
0.825055 + 0.565052i \(0.191144\pi\)
\(500\) 5.37756 0.240492
\(501\) −0.260060 −0.0116186
\(502\) −5.38008 −0.240125
\(503\) 37.6896 1.68050 0.840248 0.542202i \(-0.182409\pi\)
0.840248 + 0.542202i \(0.182409\pi\)
\(504\) 3.06154 0.136372
\(505\) −3.76118 −0.167370
\(506\) 59.2934 2.63591
\(507\) −0.589522 −0.0261816
\(508\) −11.8446 −0.525519
\(509\) −20.2812 −0.898947 −0.449474 0.893294i \(-0.648388\pi\)
−0.449474 + 0.893294i \(0.648388\pi\)
\(510\) −0.0924040 −0.00409172
\(511\) −11.3025 −0.499992
\(512\) −28.0734 −1.24068
\(513\) −0.816007 −0.0360276
\(514\) −40.2581 −1.77571
\(515\) 1.52947 0.0673966
\(516\) −1.42717 −0.0628278
\(517\) 10.5914 0.465811
\(518\) 11.1206 0.488610
\(519\) −0.127211 −0.00558393
\(520\) −0.391955 −0.0171884
\(521\) −19.0089 −0.832797 −0.416398 0.909182i \(-0.636708\pi\)
−0.416398 + 0.909182i \(0.636708\pi\)
\(522\) −57.5465 −2.51874
\(523\) 27.4550 1.20052 0.600262 0.799803i \(-0.295063\pi\)
0.600262 + 0.799803i \(0.295063\pi\)
\(524\) −23.8309 −1.04106
\(525\) −0.295121 −0.0128801
\(526\) 42.2694 1.84303
\(527\) 16.1192 0.702163
\(528\) 1.08233 0.0471023
\(529\) −4.33541 −0.188496
\(530\) 0.783849 0.0340482
\(531\) 7.04934 0.305915
\(532\) 5.66942 0.245801
\(533\) −18.4207 −0.797889
\(534\) −0.148799 −0.00643915
\(535\) −2.02516 −0.0875552
\(536\) 5.19333 0.224318
\(537\) −0.374206 −0.0161482
\(538\) 21.4294 0.923886
\(539\) −6.48236 −0.279215
\(540\) 0.193066 0.00830823
\(541\) 31.2465 1.34339 0.671696 0.740827i \(-0.265566\pi\)
0.671696 + 0.740827i \(0.265566\pi\)
\(542\) 68.2897 2.93330
\(543\) 0.526349 0.0225878
\(544\) −26.8406 −1.15078
\(545\) −1.62567 −0.0696361
\(546\) 0.222376 0.00951681
\(547\) −1.74443 −0.0745863 −0.0372932 0.999304i \(-0.511874\pi\)
−0.0372932 + 0.999304i \(0.511874\pi\)
\(548\) 28.9619 1.23719
\(549\) 27.3522 1.16737
\(550\) −67.9725 −2.89836
\(551\) −20.7149 −0.882485
\(552\) −0.263031 −0.0111953
\(553\) 7.17326 0.305038
\(554\) 35.1902 1.49509
\(555\) 0.0681194 0.00289151
\(556\) 12.8715 0.545874
\(557\) −9.64378 −0.408620 −0.204310 0.978906i \(-0.565495\pi\)
−0.204310 + 0.978906i \(0.565495\pi\)
\(558\) −30.3875 −1.28641
\(559\) 17.0047 0.719221
\(560\) 0.609825 0.0257698
\(561\) 1.29992 0.0548826
\(562\) 5.52065 0.232875
\(563\) 1.40870 0.0593698 0.0296849 0.999559i \(-0.490550\pi\)
0.0296849 + 0.999559i \(0.490550\pi\)
\(564\) −0.241707 −0.0101777
\(565\) −2.47186 −0.103992
\(566\) 5.25319 0.220808
\(567\) 8.96806 0.376623
\(568\) 6.56092 0.275290
\(569\) 20.2389 0.848458 0.424229 0.905555i \(-0.360545\pi\)
0.424229 + 0.905555i \(0.360545\pi\)
\(570\) 0.0627058 0.00262646
\(571\) 4.64069 0.194207 0.0971033 0.995274i \(-0.469042\pi\)
0.0971033 + 0.995274i \(0.469042\pi\)
\(572\) 28.3658 1.18604
\(573\) 0.282928 0.0118195
\(574\) −22.1264 −0.923539
\(575\) −21.3966 −0.892301
\(576\) 33.8074 1.40864
\(577\) −29.3050 −1.21998 −0.609991 0.792409i \(-0.708827\pi\)
−0.609991 + 0.792409i \(0.708827\pi\)
\(578\) 12.0152 0.499767
\(579\) −0.0145569 −0.000604965 0
\(580\) 4.90111 0.203508
\(581\) 3.43556 0.142531
\(582\) 2.15506 0.0893302
\(583\) −11.0270 −0.456692
\(584\) 11.5480 0.477859
\(585\) −1.14950 −0.0475260
\(586\) −23.3526 −0.964689
\(587\) 40.8916 1.68778 0.843888 0.536520i \(-0.180261\pi\)
0.843888 + 0.536520i \(0.180261\pi\)
\(588\) 0.147934 0.00610069
\(589\) −10.9385 −0.450715
\(590\) −1.08405 −0.0446296
\(591\) 0.682073 0.0280567
\(592\) 14.7172 0.604872
\(593\) 10.2466 0.420776 0.210388 0.977618i \(-0.432527\pi\)
0.210388 + 0.977618i \(0.432527\pi\)
\(594\) −4.90406 −0.201216
\(595\) 0.732424 0.0300264
\(596\) 23.6501 0.968745
\(597\) −0.781746 −0.0319947
\(598\) 16.1225 0.659298
\(599\) −0.338809 −0.0138433 −0.00692167 0.999976i \(-0.502203\pi\)
−0.00692167 + 0.999976i \(0.502203\pi\)
\(600\) 0.301532 0.0123100
\(601\) −43.9287 −1.79189 −0.895944 0.444166i \(-0.853500\pi\)
−0.895944 + 0.444166i \(0.853500\pi\)
\(602\) 20.4255 0.832482
\(603\) 15.2307 0.620241
\(604\) −21.3358 −0.868140
\(605\) −6.75149 −0.274487
\(606\) −2.18026 −0.0885671
\(607\) 39.2534 1.59325 0.796623 0.604476i \(-0.206617\pi\)
0.796623 + 0.604476i \(0.206617\pi\)
\(608\) 18.2141 0.738681
\(609\) −0.540520 −0.0219030
\(610\) −4.20624 −0.170306
\(611\) 2.87992 0.116509
\(612\) 25.0339 1.01194
\(613\) −12.7386 −0.514506 −0.257253 0.966344i \(-0.582817\pi\)
−0.257253 + 0.966344i \(0.582817\pi\)
\(614\) −45.9532 −1.85452
\(615\) −0.135536 −0.00546535
\(616\) 6.62318 0.266856
\(617\) −27.1520 −1.09310 −0.546549 0.837427i \(-0.684059\pi\)
−0.546549 + 0.837427i \(0.684059\pi\)
\(618\) 0.886597 0.0356642
\(619\) −34.9457 −1.40459 −0.702293 0.711888i \(-0.747840\pi\)
−0.702293 + 0.711888i \(0.747840\pi\)
\(620\) 2.58804 0.103938
\(621\) −1.54372 −0.0619473
\(622\) −7.03283 −0.281991
\(623\) 1.17943 0.0472527
\(624\) 0.294296 0.0117813
\(625\) 24.2917 0.971669
\(626\) −36.3940 −1.45460
\(627\) −0.882131 −0.0352289
\(628\) −43.2793 −1.72703
\(629\) 17.6759 0.704784
\(630\) −1.38075 −0.0550103
\(631\) 15.5446 0.618821 0.309411 0.950929i \(-0.399868\pi\)
0.309411 + 0.950929i \(0.399868\pi\)
\(632\) −7.32909 −0.291536
\(633\) 1.29968 0.0516577
\(634\) −31.5936 −1.25474
\(635\) 1.03839 0.0412072
\(636\) 0.251648 0.00997847
\(637\) −1.76262 −0.0698376
\(638\) −124.493 −4.92872
\(639\) 19.2415 0.761181
\(640\) −1.72718 −0.0682727
\(641\) −0.426687 −0.0168531 −0.00842657 0.999964i \(-0.502682\pi\)
−0.00842657 + 0.999964i \(0.502682\pi\)
\(642\) −1.17393 −0.0463315
\(643\) 7.50108 0.295814 0.147907 0.989001i \(-0.452746\pi\)
0.147907 + 0.989001i \(0.452746\pi\)
\(644\) 10.7254 0.422639
\(645\) 0.125117 0.00492649
\(646\) 16.2711 0.640179
\(647\) −10.4776 −0.411915 −0.205958 0.978561i \(-0.566031\pi\)
−0.205958 + 0.978561i \(0.566031\pi\)
\(648\) −9.16287 −0.359952
\(649\) 15.2502 0.598622
\(650\) −18.4824 −0.724941
\(651\) −0.285423 −0.0111866
\(652\) 19.3731 0.758708
\(653\) 25.6587 1.00410 0.502050 0.864838i \(-0.332579\pi\)
0.502050 + 0.864838i \(0.332579\pi\)
\(654\) −0.942361 −0.0368492
\(655\) 2.08921 0.0816321
\(656\) −29.2825 −1.14329
\(657\) 33.8673 1.32129
\(658\) 3.45928 0.134857
\(659\) 24.6107 0.958696 0.479348 0.877625i \(-0.340873\pi\)
0.479348 + 0.877625i \(0.340873\pi\)
\(660\) 0.208711 0.00812405
\(661\) −7.59168 −0.295282 −0.147641 0.989041i \(-0.547168\pi\)
−0.147641 + 0.989041i \(0.547168\pi\)
\(662\) −51.0124 −1.98265
\(663\) 0.353462 0.0137273
\(664\) −3.51019 −0.136222
\(665\) −0.497026 −0.0192738
\(666\) −33.3222 −1.29121
\(667\) −39.1883 −1.51738
\(668\) −10.8346 −0.419203
\(669\) 0.156831 0.00606343
\(670\) −2.34218 −0.0904862
\(671\) 59.1724 2.28433
\(672\) 0.475267 0.0183338
\(673\) −0.166041 −0.00640042 −0.00320021 0.999995i \(-0.501019\pi\)
−0.00320021 + 0.999995i \(0.501019\pi\)
\(674\) 10.0589 0.387456
\(675\) 1.76968 0.0681150
\(676\) −24.5606 −0.944638
\(677\) 26.7521 1.02817 0.514084 0.857740i \(-0.328132\pi\)
0.514084 + 0.857740i \(0.328132\pi\)
\(678\) −1.43288 −0.0550294
\(679\) −17.0817 −0.655536
\(680\) −0.748334 −0.0286973
\(681\) −1.16561 −0.0446662
\(682\) −65.7388 −2.51727
\(683\) −4.78958 −0.183268 −0.0916340 0.995793i \(-0.529209\pi\)
−0.0916340 + 0.995793i \(0.529209\pi\)
\(684\) −16.9881 −0.649557
\(685\) −2.53903 −0.0970112
\(686\) −2.11721 −0.0808355
\(687\) 0.173540 0.00662097
\(688\) 27.0315 1.03057
\(689\) −2.99836 −0.114228
\(690\) 0.118626 0.00451603
\(691\) 24.7193 0.940365 0.470182 0.882569i \(-0.344188\pi\)
0.470182 + 0.882569i \(0.344188\pi\)
\(692\) −5.29983 −0.201469
\(693\) 19.4241 0.737859
\(694\) −45.6625 −1.73332
\(695\) −1.12842 −0.0428033
\(696\) 0.552262 0.0209335
\(697\) −35.1695 −1.33214
\(698\) −2.42779 −0.0918931
\(699\) −0.823092 −0.0311322
\(700\) −12.2953 −0.464719
\(701\) −21.8019 −0.823447 −0.411723 0.911309i \(-0.635073\pi\)
−0.411723 + 0.911309i \(0.635073\pi\)
\(702\) −1.33347 −0.0503284
\(703\) −11.9949 −0.452398
\(704\) 73.1372 2.75646
\(705\) 0.0211900 0.000798060 0
\(706\) 76.5461 2.88085
\(707\) 17.2815 0.649936
\(708\) −0.348024 −0.0130795
\(709\) 8.49774 0.319139 0.159570 0.987187i \(-0.448989\pi\)
0.159570 + 0.987187i \(0.448989\pi\)
\(710\) −2.95896 −0.111048
\(711\) −21.4943 −0.806100
\(712\) −1.20505 −0.0451610
\(713\) −20.6935 −0.774977
\(714\) 0.424568 0.0158891
\(715\) −2.48677 −0.0930000
\(716\) −15.5901 −0.582630
\(717\) −1.01692 −0.0379774
\(718\) −15.4725 −0.577428
\(719\) 14.6774 0.547374 0.273687 0.961819i \(-0.411757\pi\)
0.273687 + 0.961819i \(0.411757\pi\)
\(720\) −1.82731 −0.0680998
\(721\) −7.02745 −0.261716
\(722\) 29.1853 1.08617
\(723\) 0.504471 0.0187615
\(724\) 21.9287 0.814973
\(725\) 44.9245 1.66846
\(726\) −3.91367 −0.145250
\(727\) −6.62906 −0.245858 −0.122929 0.992415i \(-0.539229\pi\)
−0.122929 + 0.992415i \(0.539229\pi\)
\(728\) 1.80091 0.0667462
\(729\) −26.8084 −0.992905
\(730\) −5.20812 −0.192761
\(731\) 32.4659 1.20080
\(732\) −1.35037 −0.0499112
\(733\) 9.10716 0.336381 0.168190 0.985755i \(-0.446208\pi\)
0.168190 + 0.985755i \(0.446208\pi\)
\(734\) −17.4948 −0.645746
\(735\) −0.0129691 −0.000478371 0
\(736\) 34.4574 1.27012
\(737\) 32.9492 1.21370
\(738\) 66.3007 2.44056
\(739\) 11.0180 0.405305 0.202653 0.979251i \(-0.435044\pi\)
0.202653 + 0.979251i \(0.435044\pi\)
\(740\) 2.83798 0.104326
\(741\) −0.239861 −0.00881150
\(742\) −3.60155 −0.132217
\(743\) −14.9881 −0.549861 −0.274930 0.961464i \(-0.588655\pi\)
−0.274930 + 0.961464i \(0.588655\pi\)
\(744\) 0.291623 0.0106914
\(745\) −2.07335 −0.0759617
\(746\) −19.9631 −0.730900
\(747\) −10.2945 −0.376655
\(748\) 54.1571 1.98018
\(749\) 9.30497 0.339996
\(750\) −0.273281 −0.00997883
\(751\) −21.4583 −0.783026 −0.391513 0.920173i \(-0.628048\pi\)
−0.391513 + 0.920173i \(0.628048\pi\)
\(752\) 4.57808 0.166945
\(753\) 0.151422 0.00551812
\(754\) −33.8509 −1.23278
\(755\) 1.87046 0.0680731
\(756\) −0.887078 −0.0322627
\(757\) 40.9067 1.48678 0.743389 0.668859i \(-0.233217\pi\)
0.743389 + 0.668859i \(0.233217\pi\)
\(758\) 62.0539 2.25390
\(759\) −1.66881 −0.0605740
\(760\) 0.507823 0.0184207
\(761\) 48.7549 1.76736 0.883682 0.468087i \(-0.155057\pi\)
0.883682 + 0.468087i \(0.155057\pi\)
\(762\) 0.601929 0.0218056
\(763\) 7.46946 0.270412
\(764\) 11.7873 0.426450
\(765\) −2.19467 −0.0793485
\(766\) 6.53005 0.235940
\(767\) 4.14668 0.149728
\(768\) 0.343417 0.0123920
\(769\) −35.2238 −1.27020 −0.635101 0.772429i \(-0.719041\pi\)
−0.635101 + 0.772429i \(0.719041\pi\)
\(770\) −2.98704 −0.107645
\(771\) 1.13306 0.0408063
\(772\) −0.606468 −0.0218273
\(773\) −38.6719 −1.39093 −0.695465 0.718560i \(-0.744802\pi\)
−0.695465 + 0.718560i \(0.744802\pi\)
\(774\) −61.2040 −2.19993
\(775\) 23.7225 0.852137
\(776\) 17.4528 0.626519
\(777\) −0.312988 −0.0112284
\(778\) −19.2724 −0.690949
\(779\) 23.8662 0.855094
\(780\) 0.0567506 0.00203200
\(781\) 41.6260 1.48949
\(782\) 30.7816 1.10075
\(783\) 3.24120 0.115831
\(784\) −2.80196 −0.100070
\(785\) 3.79420 0.135421
\(786\) 1.21106 0.0431972
\(787\) 43.6273 1.55515 0.777573 0.628793i \(-0.216451\pi\)
0.777573 + 0.628793i \(0.216451\pi\)
\(788\) 28.4165 1.01229
\(789\) −1.18967 −0.0423534
\(790\) 3.30540 0.117601
\(791\) 11.3575 0.403825
\(792\) −19.8460 −0.705198
\(793\) 16.0896 0.571358
\(794\) −55.4470 −1.96774
\(795\) −0.0220614 −0.000782437 0
\(796\) −32.5690 −1.15438
\(797\) −0.673246 −0.0238476 −0.0119238 0.999929i \(-0.503796\pi\)
−0.0119238 + 0.999929i \(0.503796\pi\)
\(798\) −0.288114 −0.0101991
\(799\) 5.49845 0.194521
\(800\) −39.5011 −1.39657
\(801\) −3.53409 −0.124871
\(802\) 7.60140 0.268415
\(803\) 73.2667 2.58552
\(804\) −0.751934 −0.0265187
\(805\) −0.940271 −0.0331402
\(806\) −17.8751 −0.629622
\(807\) −0.603128 −0.0212311
\(808\) −17.6569 −0.621166
\(809\) 36.8340 1.29502 0.647508 0.762059i \(-0.275811\pi\)
0.647508 + 0.762059i \(0.275811\pi\)
\(810\) 4.13243 0.145199
\(811\) −1.64876 −0.0578957 −0.0289479 0.999581i \(-0.509216\pi\)
−0.0289479 + 0.999581i \(0.509216\pi\)
\(812\) −22.5191 −0.790265
\(813\) −1.92201 −0.0674079
\(814\) −72.0875 −2.52667
\(815\) −1.69839 −0.0594922
\(816\) 0.561881 0.0196698
\(817\) −22.0315 −0.770785
\(818\) −37.9892 −1.32826
\(819\) 5.28161 0.184554
\(820\) −5.64669 −0.197191
\(821\) −0.143069 −0.00499314 −0.00249657 0.999997i \(-0.500795\pi\)
−0.00249657 + 0.999997i \(0.500795\pi\)
\(822\) −1.47181 −0.0513353
\(823\) 2.19352 0.0764613 0.0382307 0.999269i \(-0.487828\pi\)
0.0382307 + 0.999269i \(0.487828\pi\)
\(824\) 7.18011 0.250131
\(825\) 1.91308 0.0666050
\(826\) 4.98087 0.173307
\(827\) −20.7132 −0.720269 −0.360134 0.932900i \(-0.617269\pi\)
−0.360134 + 0.932900i \(0.617269\pi\)
\(828\) −32.1380 −1.11687
\(829\) 41.2445 1.43248 0.716240 0.697854i \(-0.245862\pi\)
0.716240 + 0.697854i \(0.245862\pi\)
\(830\) 1.58309 0.0549498
\(831\) −0.990426 −0.0343575
\(832\) 19.8868 0.689449
\(833\) −3.36526 −0.116599
\(834\) −0.654116 −0.0226502
\(835\) 0.949846 0.0328708
\(836\) −36.7512 −1.27107
\(837\) 1.71152 0.0591589
\(838\) 67.4727 2.33080
\(839\) 2.79736 0.0965755 0.0482877 0.998833i \(-0.484624\pi\)
0.0482877 + 0.998833i \(0.484624\pi\)
\(840\) 0.0132508 0.000457195 0
\(841\) 53.2802 1.83725
\(842\) −48.1281 −1.65861
\(843\) −0.155378 −0.00535152
\(844\) 54.1471 1.86382
\(845\) 2.15317 0.0740714
\(846\) −10.3656 −0.356375
\(847\) 31.0210 1.06589
\(848\) −4.76635 −0.163677
\(849\) −0.147851 −0.00507422
\(850\) −35.2873 −1.21035
\(851\) −22.6920 −0.777871
\(852\) −0.949946 −0.0325446
\(853\) 52.7964 1.80771 0.903857 0.427835i \(-0.140723\pi\)
0.903857 + 0.427835i \(0.140723\pi\)
\(854\) 19.3264 0.661335
\(855\) 1.48931 0.0509334
\(856\) −9.50711 −0.324946
\(857\) 44.0863 1.50596 0.752980 0.658044i \(-0.228616\pi\)
0.752980 + 0.658044i \(0.228616\pi\)
\(858\) −1.44152 −0.0492127
\(859\) −1.00000 −0.0341196
\(860\) 5.21262 0.177749
\(861\) 0.622747 0.0212232
\(862\) 43.6475 1.48664
\(863\) 5.54964 0.188912 0.0944560 0.995529i \(-0.469889\pi\)
0.0944560 + 0.995529i \(0.469889\pi\)
\(864\) −2.84991 −0.0969560
\(865\) 0.464625 0.0157977
\(866\) 59.9725 2.03795
\(867\) −0.338168 −0.0114848
\(868\) −11.8913 −0.403615
\(869\) −46.4997 −1.57739
\(870\) −0.249069 −0.00844423
\(871\) 8.95924 0.303572
\(872\) −7.63172 −0.258443
\(873\) 51.1845 1.73233
\(874\) −20.8886 −0.706566
\(875\) 2.16612 0.0732281
\(876\) −1.67202 −0.0564923
\(877\) −33.9048 −1.14488 −0.572441 0.819946i \(-0.694004\pi\)
−0.572441 + 0.819946i \(0.694004\pi\)
\(878\) −18.3620 −0.619688
\(879\) 0.657259 0.0221688
\(880\) −3.95310 −0.133259
\(881\) 45.7117 1.54006 0.770032 0.638005i \(-0.220240\pi\)
0.770032 + 0.638005i \(0.220240\pi\)
\(882\) 6.34411 0.213617
\(883\) 36.8708 1.24080 0.620401 0.784285i \(-0.286970\pi\)
0.620401 + 0.784285i \(0.286970\pi\)
\(884\) 14.7259 0.495285
\(885\) 0.0305105 0.00102560
\(886\) −22.7916 −0.765698
\(887\) −36.9820 −1.24173 −0.620867 0.783916i \(-0.713219\pi\)
−0.620867 + 0.783916i \(0.713219\pi\)
\(888\) 0.319787 0.0107313
\(889\) −4.77108 −0.160017
\(890\) 0.543473 0.0182173
\(891\) −58.1342 −1.94757
\(892\) 6.53386 0.218770
\(893\) −3.73128 −0.124862
\(894\) −1.20187 −0.0401966
\(895\) 1.36675 0.0456855
\(896\) 7.93585 0.265118
\(897\) −0.453767 −0.0151508
\(898\) 44.3614 1.48036
\(899\) 43.4482 1.44908
\(900\) 36.8423 1.22808
\(901\) −5.72458 −0.190713
\(902\) 143.431 4.77574
\(903\) −0.574875 −0.0191307
\(904\) −11.6042 −0.385949
\(905\) −1.92244 −0.0639041
\(906\) 1.08426 0.0360221
\(907\) −20.4566 −0.679251 −0.339626 0.940561i \(-0.610300\pi\)
−0.339626 + 0.940561i \(0.610300\pi\)
\(908\) −48.5615 −1.61157
\(909\) −51.7830 −1.71753
\(910\) −0.812207 −0.0269244
\(911\) −26.4667 −0.876882 −0.438441 0.898760i \(-0.644469\pi\)
−0.438441 + 0.898760i \(0.644469\pi\)
\(912\) −0.381295 −0.0126259
\(913\) −22.2705 −0.737047
\(914\) 37.6935 1.24679
\(915\) 0.118384 0.00391367
\(916\) 7.23000 0.238886
\(917\) −9.59927 −0.316996
\(918\) −2.54590 −0.0840272
\(919\) 19.8580 0.655054 0.327527 0.944842i \(-0.393785\pi\)
0.327527 + 0.944842i \(0.393785\pi\)
\(920\) 0.960697 0.0316732
\(921\) 1.29335 0.0426173
\(922\) −52.0191 −1.71316
\(923\) 11.3185 0.372554
\(924\) −0.958961 −0.0315475
\(925\) 26.0135 0.855319
\(926\) 16.7668 0.550993
\(927\) 21.0574 0.691616
\(928\) −72.3470 −2.37491
\(929\) −22.6708 −0.743805 −0.371902 0.928272i \(-0.621294\pi\)
−0.371902 + 0.928272i \(0.621294\pi\)
\(930\) −0.131521 −0.00431276
\(931\) 2.28368 0.0748446
\(932\) −34.2916 −1.12326
\(933\) 0.197939 0.00648022
\(934\) 28.4999 0.932545
\(935\) −4.74783 −0.155271
\(936\) −5.39634 −0.176385
\(937\) −22.6353 −0.739462 −0.369731 0.929139i \(-0.620550\pi\)
−0.369731 + 0.929139i \(0.620550\pi\)
\(938\) 10.7616 0.351378
\(939\) 1.02431 0.0334270
\(940\) 0.882814 0.0287942
\(941\) −48.7597 −1.58952 −0.794760 0.606923i \(-0.792403\pi\)
−0.794760 + 0.606923i \(0.792403\pi\)
\(942\) 2.19941 0.0716605
\(943\) 45.1498 1.47028
\(944\) 6.59178 0.214544
\(945\) 0.0777683 0.00252980
\(946\) −132.406 −4.30488
\(947\) 4.63379 0.150578 0.0752890 0.997162i \(-0.476012\pi\)
0.0752890 + 0.997162i \(0.476012\pi\)
\(948\) 1.06117 0.0344652
\(949\) 19.9220 0.646694
\(950\) 23.9461 0.776915
\(951\) 0.889202 0.0288343
\(952\) 3.43837 0.111438
\(953\) −39.9812 −1.29512 −0.647559 0.762016i \(-0.724210\pi\)
−0.647559 + 0.762016i \(0.724210\pi\)
\(954\) 10.7918 0.349399
\(955\) −1.03337 −0.0334390
\(956\) −42.3666 −1.37023
\(957\) 3.50385 0.113263
\(958\) 33.5428 1.08372
\(959\) 11.6660 0.376716
\(960\) 0.146323 0.00472256
\(961\) −8.05708 −0.259906
\(962\) −19.6013 −0.631973
\(963\) −27.8819 −0.898481
\(964\) 21.0172 0.676918
\(965\) 0.0531678 0.00171153
\(966\) −0.545052 −0.0175368
\(967\) 7.80533 0.251002 0.125501 0.992093i \(-0.459946\pi\)
0.125501 + 0.992093i \(0.459946\pi\)
\(968\) −31.6949 −1.01871
\(969\) −0.457950 −0.0147115
\(970\) −7.87117 −0.252728
\(971\) −3.13358 −0.100562 −0.0502808 0.998735i \(-0.516012\pi\)
−0.0502808 + 0.998735i \(0.516012\pi\)
\(972\) 3.98791 0.127912
\(973\) 5.18473 0.166215
\(974\) −22.3255 −0.715356
\(975\) 0.520187 0.0166593
\(976\) 25.5769 0.818696
\(977\) −8.36532 −0.267630 −0.133815 0.991006i \(-0.542723\pi\)
−0.133815 + 0.991006i \(0.542723\pi\)
\(978\) −0.984518 −0.0314814
\(979\) −7.64546 −0.244350
\(980\) −0.540315 −0.0172597
\(981\) −22.3818 −0.714597
\(982\) −17.2306 −0.549851
\(983\) 33.8004 1.07806 0.539032 0.842285i \(-0.318790\pi\)
0.539032 + 0.842285i \(0.318790\pi\)
\(984\) −0.636275 −0.0202837
\(985\) −2.49121 −0.0793765
\(986\) −64.6294 −2.05822
\(987\) −0.0973613 −0.00309905
\(988\) −9.99304 −0.317921
\(989\) −41.6791 −1.32532
\(990\) 8.95051 0.284466
\(991\) 12.2818 0.390144 0.195072 0.980789i \(-0.437506\pi\)
0.195072 + 0.980789i \(0.437506\pi\)
\(992\) −38.2030 −1.21295
\(993\) 1.43574 0.0455619
\(994\) 13.5955 0.431223
\(995\) 2.85526 0.0905177
\(996\) 0.508235 0.0161041
\(997\) −26.4235 −0.836840 −0.418420 0.908254i \(-0.637416\pi\)
−0.418420 + 0.908254i \(0.637416\pi\)
\(998\) −78.0418 −2.47037
\(999\) 1.87682 0.0593798
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 \(a_p\))