Properties

Label 8018.2.a.f.1.17
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.656283 q^{3}\) \(+1.00000 q^{4}\) \(-1.22883 q^{5}\) \(+0.656283 q^{6}\) \(+2.46640 q^{7}\) \(-1.00000 q^{8}\) \(-2.56929 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.656283 q^{3}\) \(+1.00000 q^{4}\) \(-1.22883 q^{5}\) \(+0.656283 q^{6}\) \(+2.46640 q^{7}\) \(-1.00000 q^{8}\) \(-2.56929 q^{9}\) \(+1.22883 q^{10}\) \(+2.53318 q^{11}\) \(-0.656283 q^{12}\) \(+2.77706 q^{13}\) \(-2.46640 q^{14}\) \(+0.806463 q^{15}\) \(+1.00000 q^{16}\) \(-0.964185 q^{17}\) \(+2.56929 q^{18}\) \(-1.00000 q^{19}\) \(-1.22883 q^{20}\) \(-1.61866 q^{21}\) \(-2.53318 q^{22}\) \(+3.35525 q^{23}\) \(+0.656283 q^{24}\) \(-3.48997 q^{25}\) \(-2.77706 q^{26}\) \(+3.65503 q^{27}\) \(+2.46640 q^{28}\) \(+0.507372 q^{29}\) \(-0.806463 q^{30}\) \(+5.13456 q^{31}\) \(-1.00000 q^{32}\) \(-1.66248 q^{33}\) \(+0.964185 q^{34}\) \(-3.03080 q^{35}\) \(-2.56929 q^{36}\) \(-8.07137 q^{37}\) \(+1.00000 q^{38}\) \(-1.82253 q^{39}\) \(+1.22883 q^{40}\) \(-1.46881 q^{41}\) \(+1.61866 q^{42}\) \(-12.6564 q^{43}\) \(+2.53318 q^{44}\) \(+3.15724 q^{45}\) \(-3.35525 q^{46}\) \(-2.57855 q^{47}\) \(-0.656283 q^{48}\) \(-0.916878 q^{49}\) \(+3.48997 q^{50}\) \(+0.632778 q^{51}\) \(+2.77706 q^{52}\) \(-1.67655 q^{53}\) \(-3.65503 q^{54}\) \(-3.11286 q^{55}\) \(-2.46640 q^{56}\) \(+0.656283 q^{57}\) \(-0.507372 q^{58}\) \(-0.559232 q^{59}\) \(+0.806463 q^{60}\) \(-3.22268 q^{61}\) \(-5.13456 q^{62}\) \(-6.33690 q^{63}\) \(+1.00000 q^{64}\) \(-3.41254 q^{65}\) \(+1.66248 q^{66}\) \(+4.20151 q^{67}\) \(-0.964185 q^{68}\) \(-2.20199 q^{69}\) \(+3.03080 q^{70}\) \(+4.84164 q^{71}\) \(+2.56929 q^{72}\) \(-8.59432 q^{73}\) \(+8.07137 q^{74}\) \(+2.29041 q^{75}\) \(-1.00000 q^{76}\) \(+6.24783 q^{77}\) \(+1.82253 q^{78}\) \(+15.0772 q^{79}\) \(-1.22883 q^{80}\) \(+5.30914 q^{81}\) \(+1.46881 q^{82}\) \(+14.5687 q^{83}\) \(-1.61866 q^{84}\) \(+1.18482 q^{85}\) \(+12.6564 q^{86}\) \(-0.332979 q^{87}\) \(-2.53318 q^{88}\) \(-15.3041 q^{89}\) \(-3.15724 q^{90}\) \(+6.84932 q^{91}\) \(+3.35525 q^{92}\) \(-3.36972 q^{93}\) \(+2.57855 q^{94}\) \(+1.22883 q^{95}\) \(+0.656283 q^{96}\) \(+2.84413 q^{97}\) \(+0.916878 q^{98}\) \(-6.50848 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.656283 −0.378905 −0.189453 0.981890i \(-0.560671\pi\)
−0.189453 + 0.981890i \(0.560671\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.22883 −0.549552 −0.274776 0.961508i \(-0.588604\pi\)
−0.274776 + 0.961508i \(0.588604\pi\)
\(6\) 0.656283 0.267926
\(7\) 2.46640 0.932211 0.466106 0.884729i \(-0.345657\pi\)
0.466106 + 0.884729i \(0.345657\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.56929 −0.856431
\(10\) 1.22883 0.388592
\(11\) 2.53318 0.763783 0.381891 0.924207i \(-0.375273\pi\)
0.381891 + 0.924207i \(0.375273\pi\)
\(12\) −0.656283 −0.189453
\(13\) 2.77706 0.770217 0.385108 0.922871i \(-0.374164\pi\)
0.385108 + 0.922871i \(0.374164\pi\)
\(14\) −2.46640 −0.659173
\(15\) 0.806463 0.208228
\(16\) 1.00000 0.250000
\(17\) −0.964185 −0.233849 −0.116925 0.993141i \(-0.537304\pi\)
−0.116925 + 0.993141i \(0.537304\pi\)
\(18\) 2.56929 0.605588
\(19\) −1.00000 −0.229416
\(20\) −1.22883 −0.274776
\(21\) −1.61866 −0.353220
\(22\) −2.53318 −0.540076
\(23\) 3.35525 0.699618 0.349809 0.936821i \(-0.386246\pi\)
0.349809 + 0.936821i \(0.386246\pi\)
\(24\) 0.656283 0.133963
\(25\) −3.48997 −0.697993
\(26\) −2.77706 −0.544625
\(27\) 3.65503 0.703411
\(28\) 2.46640 0.466106
\(29\) 0.507372 0.0942165 0.0471083 0.998890i \(-0.484999\pi\)
0.0471083 + 0.998890i \(0.484999\pi\)
\(30\) −0.806463 −0.147239
\(31\) 5.13456 0.922194 0.461097 0.887350i \(-0.347456\pi\)
0.461097 + 0.887350i \(0.347456\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.66248 −0.289401
\(34\) 0.964185 0.165356
\(35\) −3.03080 −0.512298
\(36\) −2.56929 −0.428215
\(37\) −8.07137 −1.32693 −0.663463 0.748209i \(-0.730914\pi\)
−0.663463 + 0.748209i \(0.730914\pi\)
\(38\) 1.00000 0.162221
\(39\) −1.82253 −0.291839
\(40\) 1.22883 0.194296
\(41\) −1.46881 −0.229390 −0.114695 0.993401i \(-0.536589\pi\)
−0.114695 + 0.993401i \(0.536589\pi\)
\(42\) 1.61866 0.249764
\(43\) −12.6564 −1.93008 −0.965041 0.262100i \(-0.915585\pi\)
−0.965041 + 0.262100i \(0.915585\pi\)
\(44\) 2.53318 0.381891
\(45\) 3.15724 0.470653
\(46\) −3.35525 −0.494705
\(47\) −2.57855 −0.376120 −0.188060 0.982158i \(-0.560220\pi\)
−0.188060 + 0.982158i \(0.560220\pi\)
\(48\) −0.656283 −0.0947263
\(49\) −0.916878 −0.130983
\(50\) 3.48997 0.493556
\(51\) 0.632778 0.0886067
\(52\) 2.77706 0.385108
\(53\) −1.67655 −0.230292 −0.115146 0.993349i \(-0.536734\pi\)
−0.115146 + 0.993349i \(0.536734\pi\)
\(54\) −3.65503 −0.497387
\(55\) −3.11286 −0.419738
\(56\) −2.46640 −0.329586
\(57\) 0.656283 0.0869268
\(58\) −0.507372 −0.0666211
\(59\) −0.559232 −0.0728058 −0.0364029 0.999337i \(-0.511590\pi\)
−0.0364029 + 0.999337i \(0.511590\pi\)
\(60\) 0.806463 0.104114
\(61\) −3.22268 −0.412622 −0.206311 0.978486i \(-0.566146\pi\)
−0.206311 + 0.978486i \(0.566146\pi\)
\(62\) −5.13456 −0.652090
\(63\) −6.33690 −0.798374
\(64\) 1.00000 0.125000
\(65\) −3.41254 −0.423274
\(66\) 1.66248 0.204638
\(67\) 4.20151 0.513296 0.256648 0.966505i \(-0.417382\pi\)
0.256648 + 0.966505i \(0.417382\pi\)
\(68\) −0.964185 −0.116925
\(69\) −2.20199 −0.265089
\(70\) 3.03080 0.362249
\(71\) 4.84164 0.574597 0.287298 0.957841i \(-0.407243\pi\)
0.287298 + 0.957841i \(0.407243\pi\)
\(72\) 2.56929 0.302794
\(73\) −8.59432 −1.00589 −0.502945 0.864319i \(-0.667750\pi\)
−0.502945 + 0.864319i \(0.667750\pi\)
\(74\) 8.07137 0.938278
\(75\) 2.29041 0.264473
\(76\) −1.00000 −0.114708
\(77\) 6.24783 0.712007
\(78\) 1.82253 0.206361
\(79\) 15.0772 1.69632 0.848161 0.529738i \(-0.177710\pi\)
0.848161 + 0.529738i \(0.177710\pi\)
\(80\) −1.22883 −0.137388
\(81\) 5.30914 0.589905
\(82\) 1.46881 0.162203
\(83\) 14.5687 1.59912 0.799559 0.600587i \(-0.205067\pi\)
0.799559 + 0.600587i \(0.205067\pi\)
\(84\) −1.61866 −0.176610
\(85\) 1.18482 0.128512
\(86\) 12.6564 1.36477
\(87\) −0.332979 −0.0356991
\(88\) −2.53318 −0.270038
\(89\) −15.3041 −1.62223 −0.811117 0.584884i \(-0.801140\pi\)
−0.811117 + 0.584884i \(0.801140\pi\)
\(90\) −3.15724 −0.332802
\(91\) 6.84932 0.718004
\(92\) 3.35525 0.349809
\(93\) −3.36972 −0.349424
\(94\) 2.57855 0.265957
\(95\) 1.22883 0.126076
\(96\) 0.656283 0.0669816
\(97\) 2.84413 0.288777 0.144389 0.989521i \(-0.453878\pi\)
0.144389 + 0.989521i \(0.453878\pi\)
\(98\) 0.916878 0.0926187
\(99\) −6.50848 −0.654127
\(100\) −3.48997 −0.348997
\(101\) −2.40413 −0.239220 −0.119610 0.992821i \(-0.538164\pi\)
−0.119610 + 0.992821i \(0.538164\pi\)
\(102\) −0.632778 −0.0626544
\(103\) 1.08381 0.106791 0.0533954 0.998573i \(-0.482996\pi\)
0.0533954 + 0.998573i \(0.482996\pi\)
\(104\) −2.77706 −0.272313
\(105\) 1.98906 0.194112
\(106\) 1.67655 0.162841
\(107\) 5.41633 0.523616 0.261808 0.965120i \(-0.415681\pi\)
0.261808 + 0.965120i \(0.415681\pi\)
\(108\) 3.65503 0.351706
\(109\) −14.2925 −1.36897 −0.684486 0.729026i \(-0.739973\pi\)
−0.684486 + 0.729026i \(0.739973\pi\)
\(110\) 3.11286 0.296800
\(111\) 5.29711 0.502779
\(112\) 2.46640 0.233053
\(113\) 4.36519 0.410642 0.205321 0.978695i \(-0.434176\pi\)
0.205321 + 0.978695i \(0.434176\pi\)
\(114\) −0.656283 −0.0614665
\(115\) −4.12305 −0.384476
\(116\) 0.507372 0.0471083
\(117\) −7.13507 −0.659637
\(118\) 0.559232 0.0514815
\(119\) −2.37806 −0.217997
\(120\) −0.806463 −0.0736197
\(121\) −4.58300 −0.416636
\(122\) 3.22268 0.291768
\(123\) 0.963958 0.0869171
\(124\) 5.13456 0.461097
\(125\) 10.4328 0.933135
\(126\) 6.33690 0.564536
\(127\) −4.68023 −0.415303 −0.207652 0.978203i \(-0.566582\pi\)
−0.207652 + 0.978203i \(0.566582\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.30618 0.731318
\(130\) 3.41254 0.299300
\(131\) −11.5458 −1.00876 −0.504382 0.863481i \(-0.668280\pi\)
−0.504382 + 0.863481i \(0.668280\pi\)
\(132\) −1.66248 −0.144701
\(133\) −2.46640 −0.213864
\(134\) −4.20151 −0.362955
\(135\) −4.49143 −0.386561
\(136\) 0.964185 0.0826782
\(137\) −16.0140 −1.36817 −0.684086 0.729402i \(-0.739799\pi\)
−0.684086 + 0.729402i \(0.739799\pi\)
\(138\) 2.20199 0.187446
\(139\) −6.76188 −0.573535 −0.286768 0.958000i \(-0.592581\pi\)
−0.286768 + 0.958000i \(0.592581\pi\)
\(140\) −3.03080 −0.256149
\(141\) 1.69226 0.142514
\(142\) −4.84164 −0.406301
\(143\) 7.03478 0.588278
\(144\) −2.56929 −0.214108
\(145\) −0.623476 −0.0517768
\(146\) 8.59432 0.711271
\(147\) 0.601732 0.0496300
\(148\) −8.07137 −0.663463
\(149\) 20.2752 1.66101 0.830505 0.557011i \(-0.188052\pi\)
0.830505 + 0.557011i \(0.188052\pi\)
\(150\) −2.29041 −0.187011
\(151\) −5.05919 −0.411711 −0.205855 0.978582i \(-0.565998\pi\)
−0.205855 + 0.978582i \(0.565998\pi\)
\(152\) 1.00000 0.0811107
\(153\) 2.47727 0.200276
\(154\) −6.24783 −0.503465
\(155\) −6.30952 −0.506793
\(156\) −1.82253 −0.145920
\(157\) 4.42653 0.353276 0.176638 0.984276i \(-0.443478\pi\)
0.176638 + 0.984276i \(0.443478\pi\)
\(158\) −15.0772 −1.19948
\(159\) 1.10029 0.0872588
\(160\) 1.22883 0.0971479
\(161\) 8.27538 0.652192
\(162\) −5.30914 −0.417126
\(163\) 15.4583 1.21078 0.605392 0.795927i \(-0.293016\pi\)
0.605392 + 0.795927i \(0.293016\pi\)
\(164\) −1.46881 −0.114695
\(165\) 2.04292 0.159041
\(166\) −14.5687 −1.13075
\(167\) −14.6812 −1.13607 −0.568034 0.823005i \(-0.692296\pi\)
−0.568034 + 0.823005i \(0.692296\pi\)
\(168\) 1.61866 0.124882
\(169\) −5.28796 −0.406767
\(170\) −1.18482 −0.0908718
\(171\) 2.56929 0.196479
\(172\) −12.6564 −0.965041
\(173\) 2.84477 0.216284 0.108142 0.994135i \(-0.465510\pi\)
0.108142 + 0.994135i \(0.465510\pi\)
\(174\) 0.332979 0.0252431
\(175\) −8.60765 −0.650677
\(176\) 2.53318 0.190946
\(177\) 0.367014 0.0275865
\(178\) 15.3041 1.14709
\(179\) 3.45578 0.258297 0.129149 0.991625i \(-0.458776\pi\)
0.129149 + 0.991625i \(0.458776\pi\)
\(180\) 3.15724 0.235326
\(181\) −12.8494 −0.955089 −0.477545 0.878607i \(-0.658473\pi\)
−0.477545 + 0.878607i \(0.658473\pi\)
\(182\) −6.84932 −0.507706
\(183\) 2.11499 0.156345
\(184\) −3.35525 −0.247352
\(185\) 9.91838 0.729214
\(186\) 3.36972 0.247080
\(187\) −2.44245 −0.178610
\(188\) −2.57855 −0.188060
\(189\) 9.01477 0.655728
\(190\) −1.22883 −0.0891490
\(191\) 25.9589 1.87832 0.939159 0.343484i \(-0.111607\pi\)
0.939159 + 0.343484i \(0.111607\pi\)
\(192\) −0.656283 −0.0473632
\(193\) −13.2961 −0.957075 −0.478537 0.878067i \(-0.658833\pi\)
−0.478537 + 0.878067i \(0.658833\pi\)
\(194\) −2.84413 −0.204196
\(195\) 2.23959 0.160381
\(196\) −0.916878 −0.0654913
\(197\) 2.67231 0.190394 0.0951972 0.995458i \(-0.469652\pi\)
0.0951972 + 0.995458i \(0.469652\pi\)
\(198\) 6.50848 0.462538
\(199\) −7.84768 −0.556307 −0.278154 0.960537i \(-0.589722\pi\)
−0.278154 + 0.960537i \(0.589722\pi\)
\(200\) 3.48997 0.246778
\(201\) −2.75738 −0.194491
\(202\) 2.40413 0.169154
\(203\) 1.25138 0.0878297
\(204\) 0.632778 0.0443033
\(205\) 1.80493 0.126062
\(206\) −1.08381 −0.0755124
\(207\) −8.62062 −0.599174
\(208\) 2.77706 0.192554
\(209\) −2.53318 −0.175224
\(210\) −1.98906 −0.137258
\(211\) −1.00000 −0.0688428
\(212\) −1.67655 −0.115146
\(213\) −3.17749 −0.217718
\(214\) −5.41633 −0.370253
\(215\) 15.5526 1.06068
\(216\) −3.65503 −0.248693
\(217\) 12.6639 0.859679
\(218\) 14.2925 0.968009
\(219\) 5.64031 0.381137
\(220\) −3.11286 −0.209869
\(221\) −2.67759 −0.180115
\(222\) −5.29711 −0.355518
\(223\) 3.87038 0.259180 0.129590 0.991568i \(-0.458634\pi\)
0.129590 + 0.991568i \(0.458634\pi\)
\(224\) −2.46640 −0.164793
\(225\) 8.96674 0.597783
\(226\) −4.36519 −0.290368
\(227\) 16.7652 1.11275 0.556374 0.830932i \(-0.312192\pi\)
0.556374 + 0.830932i \(0.312192\pi\)
\(228\) 0.656283 0.0434634
\(229\) 0.445190 0.0294190 0.0147095 0.999892i \(-0.495318\pi\)
0.0147095 + 0.999892i \(0.495318\pi\)
\(230\) 4.12305 0.271866
\(231\) −4.10035 −0.269783
\(232\) −0.507372 −0.0333106
\(233\) −18.5171 −1.21309 −0.606547 0.795048i \(-0.707446\pi\)
−0.606547 + 0.795048i \(0.707446\pi\)
\(234\) 7.13507 0.466434
\(235\) 3.16861 0.206697
\(236\) −0.559232 −0.0364029
\(237\) −9.89494 −0.642746
\(238\) 2.37806 0.154147
\(239\) −1.71529 −0.110953 −0.0554765 0.998460i \(-0.517668\pi\)
−0.0554765 + 0.998460i \(0.517668\pi\)
\(240\) 0.806463 0.0520570
\(241\) 21.1313 1.36118 0.680592 0.732662i \(-0.261723\pi\)
0.680592 + 0.732662i \(0.261723\pi\)
\(242\) 4.58300 0.294606
\(243\) −14.4494 −0.926929
\(244\) −3.22268 −0.206311
\(245\) 1.12669 0.0719817
\(246\) −0.963958 −0.0614597
\(247\) −2.77706 −0.176700
\(248\) −5.13456 −0.326045
\(249\) −9.56117 −0.605914
\(250\) −10.4328 −0.659826
\(251\) −7.75851 −0.489713 −0.244856 0.969559i \(-0.578741\pi\)
−0.244856 + 0.969559i \(0.578741\pi\)
\(252\) −6.33690 −0.399187
\(253\) 8.49945 0.534356
\(254\) 4.68023 0.293664
\(255\) −0.777580 −0.0486939
\(256\) 1.00000 0.0625000
\(257\) 1.14498 0.0714222 0.0357111 0.999362i \(-0.488630\pi\)
0.0357111 + 0.999362i \(0.488630\pi\)
\(258\) −8.30618 −0.517120
\(259\) −19.9072 −1.23697
\(260\) −3.41254 −0.211637
\(261\) −1.30359 −0.0806899
\(262\) 11.5458 0.713304
\(263\) 25.3912 1.56569 0.782843 0.622219i \(-0.213769\pi\)
0.782843 + 0.622219i \(0.213769\pi\)
\(264\) 1.66248 0.102319
\(265\) 2.06020 0.126557
\(266\) 2.46640 0.151225
\(267\) 10.0438 0.614673
\(268\) 4.20151 0.256648
\(269\) 3.37381 0.205705 0.102852 0.994697i \(-0.467203\pi\)
0.102852 + 0.994697i \(0.467203\pi\)
\(270\) 4.49143 0.273340
\(271\) 26.0833 1.58445 0.792223 0.610232i \(-0.208924\pi\)
0.792223 + 0.610232i \(0.208924\pi\)
\(272\) −0.964185 −0.0584623
\(273\) −4.49510 −0.272056
\(274\) 16.0140 0.967443
\(275\) −8.84071 −0.533115
\(276\) −2.20199 −0.132544
\(277\) 9.79155 0.588317 0.294159 0.955757i \(-0.404961\pi\)
0.294159 + 0.955757i \(0.404961\pi\)
\(278\) 6.76188 0.405551
\(279\) −13.1922 −0.789795
\(280\) 3.03080 0.181125
\(281\) −16.1406 −0.962865 −0.481433 0.876483i \(-0.659883\pi\)
−0.481433 + 0.876483i \(0.659883\pi\)
\(282\) −1.69226 −0.100773
\(283\) −19.1946 −1.14100 −0.570501 0.821297i \(-0.693251\pi\)
−0.570501 + 0.821297i \(0.693251\pi\)
\(284\) 4.84164 0.287298
\(285\) −0.806463 −0.0477708
\(286\) −7.03478 −0.415975
\(287\) −3.62268 −0.213840
\(288\) 2.56929 0.151397
\(289\) −16.0703 −0.945315
\(290\) 0.623476 0.0366118
\(291\) −1.86655 −0.109419
\(292\) −8.59432 −0.502945
\(293\) −21.6518 −1.26491 −0.632455 0.774597i \(-0.717953\pi\)
−0.632455 + 0.774597i \(0.717953\pi\)
\(294\) −0.601732 −0.0350937
\(295\) 0.687203 0.0400105
\(296\) 8.07137 0.469139
\(297\) 9.25886 0.537253
\(298\) −20.2752 −1.17451
\(299\) 9.31771 0.538857
\(300\) 2.29041 0.132237
\(301\) −31.2157 −1.79924
\(302\) 5.05919 0.291124
\(303\) 1.57779 0.0906415
\(304\) −1.00000 −0.0573539
\(305\) 3.96014 0.226757
\(306\) −2.47727 −0.141616
\(307\) −0.731919 −0.0417728 −0.0208864 0.999782i \(-0.506649\pi\)
−0.0208864 + 0.999782i \(0.506649\pi\)
\(308\) 6.24783 0.356003
\(309\) −0.711284 −0.0404636
\(310\) 6.30952 0.358357
\(311\) −21.8823 −1.24083 −0.620414 0.784274i \(-0.713036\pi\)
−0.620414 + 0.784274i \(0.713036\pi\)
\(312\) 1.82253 0.103181
\(313\) −19.2489 −1.08801 −0.544007 0.839081i \(-0.683093\pi\)
−0.544007 + 0.839081i \(0.683093\pi\)
\(314\) −4.42653 −0.249804
\(315\) 7.78700 0.438748
\(316\) 15.0772 0.848161
\(317\) −20.9236 −1.17518 −0.587592 0.809157i \(-0.699924\pi\)
−0.587592 + 0.809157i \(0.699924\pi\)
\(318\) −1.10029 −0.0617013
\(319\) 1.28526 0.0719610
\(320\) −1.22883 −0.0686939
\(321\) −3.55465 −0.198401
\(322\) −8.27538 −0.461169
\(323\) 0.964185 0.0536487
\(324\) 5.30914 0.294952
\(325\) −9.69183 −0.537606
\(326\) −15.4583 −0.856154
\(327\) 9.37991 0.518710
\(328\) 1.46881 0.0811017
\(329\) −6.35973 −0.350623
\(330\) −2.04292 −0.112459
\(331\) −26.3706 −1.44946 −0.724729 0.689034i \(-0.758035\pi\)
−0.724729 + 0.689034i \(0.758035\pi\)
\(332\) 14.5687 0.799559
\(333\) 20.7377 1.13642
\(334\) 14.6812 0.803322
\(335\) −5.16296 −0.282083
\(336\) −1.61866 −0.0883049
\(337\) −22.0621 −1.20180 −0.600900 0.799324i \(-0.705191\pi\)
−0.600900 + 0.799324i \(0.705191\pi\)
\(338\) 5.28796 0.287627
\(339\) −2.86480 −0.155595
\(340\) 1.18482 0.0642561
\(341\) 13.0068 0.704356
\(342\) −2.56929 −0.138931
\(343\) −19.5262 −1.05431
\(344\) 12.6564 0.682387
\(345\) 2.70589 0.145680
\(346\) −2.84477 −0.152936
\(347\) −5.03597 −0.270345 −0.135172 0.990822i \(-0.543159\pi\)
−0.135172 + 0.990822i \(0.543159\pi\)
\(348\) −0.332979 −0.0178496
\(349\) −6.92267 −0.370562 −0.185281 0.982686i \(-0.559320\pi\)
−0.185281 + 0.982686i \(0.559320\pi\)
\(350\) 8.60765 0.460098
\(351\) 10.1502 0.541779
\(352\) −2.53318 −0.135019
\(353\) 21.3368 1.13564 0.567822 0.823151i \(-0.307786\pi\)
0.567822 + 0.823151i \(0.307786\pi\)
\(354\) −0.367014 −0.0195066
\(355\) −5.94957 −0.315771
\(356\) −15.3041 −0.811117
\(357\) 1.56068 0.0826001
\(358\) −3.45578 −0.182644
\(359\) 32.2705 1.70317 0.851586 0.524215i \(-0.175641\pi\)
0.851586 + 0.524215i \(0.175641\pi\)
\(360\) −3.15724 −0.166401
\(361\) 1.00000 0.0526316
\(362\) 12.8494 0.675350
\(363\) 3.00774 0.157866
\(364\) 6.84932 0.359002
\(365\) 10.5610 0.552788
\(366\) −2.11499 −0.110552
\(367\) 31.8609 1.66312 0.831562 0.555432i \(-0.187447\pi\)
0.831562 + 0.555432i \(0.187447\pi\)
\(368\) 3.35525 0.174904
\(369\) 3.77381 0.196457
\(370\) −9.91838 −0.515632
\(371\) −4.13504 −0.214681
\(372\) −3.36972 −0.174712
\(373\) 3.93302 0.203644 0.101822 0.994803i \(-0.467533\pi\)
0.101822 + 0.994803i \(0.467533\pi\)
\(374\) 2.44245 0.126296
\(375\) −6.84685 −0.353570
\(376\) 2.57855 0.132979
\(377\) 1.40900 0.0725671
\(378\) −9.01477 −0.463670
\(379\) −16.4831 −0.846682 −0.423341 0.905970i \(-0.639143\pi\)
−0.423341 + 0.905970i \(0.639143\pi\)
\(380\) 1.22883 0.0630379
\(381\) 3.07156 0.157361
\(382\) −25.9589 −1.32817
\(383\) −5.90876 −0.301924 −0.150962 0.988540i \(-0.548237\pi\)
−0.150962 + 0.988540i \(0.548237\pi\)
\(384\) 0.656283 0.0334908
\(385\) −7.67755 −0.391284
\(386\) 13.2961 0.676754
\(387\) 32.5180 1.65298
\(388\) 2.84413 0.144389
\(389\) −26.5021 −1.34371 −0.671854 0.740683i \(-0.734502\pi\)
−0.671854 + 0.740683i \(0.734502\pi\)
\(390\) −2.23959 −0.113406
\(391\) −3.23508 −0.163605
\(392\) 0.916878 0.0463093
\(393\) 7.57733 0.382226
\(394\) −2.67231 −0.134629
\(395\) −18.5274 −0.932217
\(396\) −6.50848 −0.327064
\(397\) −29.4443 −1.47777 −0.738883 0.673834i \(-0.764646\pi\)
−0.738883 + 0.673834i \(0.764646\pi\)
\(398\) 7.84768 0.393369
\(399\) 1.61866 0.0810341
\(400\) −3.48997 −0.174498
\(401\) −16.0740 −0.802696 −0.401348 0.915926i \(-0.631458\pi\)
−0.401348 + 0.915926i \(0.631458\pi\)
\(402\) 2.75738 0.137526
\(403\) 14.2590 0.710289
\(404\) −2.40413 −0.119610
\(405\) −6.52406 −0.324183
\(406\) −1.25138 −0.0621050
\(407\) −20.4462 −1.01348
\(408\) −0.632778 −0.0313272
\(409\) −15.5578 −0.769282 −0.384641 0.923066i \(-0.625675\pi\)
−0.384641 + 0.923066i \(0.625675\pi\)
\(410\) −1.80493 −0.0891391
\(411\) 10.5097 0.518407
\(412\) 1.08381 0.0533954
\(413\) −1.37929 −0.0678703
\(414\) 8.62062 0.423680
\(415\) −17.9025 −0.878798
\(416\) −2.77706 −0.136156
\(417\) 4.43771 0.217315
\(418\) 2.53318 0.123902
\(419\) 30.8745 1.50832 0.754159 0.656692i \(-0.228045\pi\)
0.754159 + 0.656692i \(0.228045\pi\)
\(420\) 1.98906 0.0970562
\(421\) 17.9081 0.872786 0.436393 0.899756i \(-0.356256\pi\)
0.436393 + 0.899756i \(0.356256\pi\)
\(422\) 1.00000 0.0486792
\(423\) 6.62505 0.322121
\(424\) 1.67655 0.0814204
\(425\) 3.36497 0.163225
\(426\) 3.17749 0.153950
\(427\) −7.94842 −0.384651
\(428\) 5.41633 0.261808
\(429\) −4.61681 −0.222902
\(430\) −15.5526 −0.750014
\(431\) 28.5173 1.37363 0.686816 0.726831i \(-0.259008\pi\)
0.686816 + 0.726831i \(0.259008\pi\)
\(432\) 3.65503 0.175853
\(433\) −37.7724 −1.81523 −0.907614 0.419806i \(-0.862098\pi\)
−0.907614 + 0.419806i \(0.862098\pi\)
\(434\) −12.6639 −0.607885
\(435\) 0.409177 0.0196185
\(436\) −14.2925 −0.684486
\(437\) −3.35525 −0.160503
\(438\) −5.64031 −0.269504
\(439\) −4.71110 −0.224849 −0.112424 0.993660i \(-0.535862\pi\)
−0.112424 + 0.993660i \(0.535862\pi\)
\(440\) 3.11286 0.148400
\(441\) 2.35573 0.112178
\(442\) 2.67759 0.127360
\(443\) 32.4557 1.54202 0.771008 0.636826i \(-0.219753\pi\)
0.771008 + 0.636826i \(0.219753\pi\)
\(444\) 5.29711 0.251389
\(445\) 18.8062 0.891501
\(446\) −3.87038 −0.183268
\(447\) −13.3063 −0.629365
\(448\) 2.46640 0.116526
\(449\) −12.9548 −0.611376 −0.305688 0.952132i \(-0.598886\pi\)
−0.305688 + 0.952132i \(0.598886\pi\)
\(450\) −8.96674 −0.422696
\(451\) −3.72077 −0.175204
\(452\) 4.36519 0.205321
\(453\) 3.32026 0.155999
\(454\) −16.7652 −0.786832
\(455\) −8.41669 −0.394580
\(456\) −0.656283 −0.0307333
\(457\) −36.6463 −1.71424 −0.857121 0.515115i \(-0.827749\pi\)
−0.857121 + 0.515115i \(0.827749\pi\)
\(458\) −0.445190 −0.0208024
\(459\) −3.52413 −0.164492
\(460\) −4.12305 −0.192238
\(461\) 28.7701 1.33996 0.669978 0.742381i \(-0.266303\pi\)
0.669978 + 0.742381i \(0.266303\pi\)
\(462\) 4.10035 0.190765
\(463\) −34.5158 −1.60409 −0.802043 0.597266i \(-0.796254\pi\)
−0.802043 + 0.597266i \(0.796254\pi\)
\(464\) 0.507372 0.0235541
\(465\) 4.14083 0.192027
\(466\) 18.5171 0.857787
\(467\) 16.3066 0.754581 0.377291 0.926095i \(-0.376856\pi\)
0.377291 + 0.926095i \(0.376856\pi\)
\(468\) −7.13507 −0.329819
\(469\) 10.3626 0.478501
\(470\) −3.16861 −0.146157
\(471\) −2.90506 −0.133858
\(472\) 0.559232 0.0257407
\(473\) −32.0609 −1.47416
\(474\) 9.89494 0.454490
\(475\) 3.48997 0.160131
\(476\) −2.37806 −0.108998
\(477\) 4.30755 0.197229
\(478\) 1.71529 0.0784556
\(479\) −5.46908 −0.249888 −0.124944 0.992164i \(-0.539875\pi\)
−0.124944 + 0.992164i \(0.539875\pi\)
\(480\) −0.806463 −0.0368098
\(481\) −22.4146 −1.02202
\(482\) −21.1313 −0.962503
\(483\) −5.43099 −0.247119
\(484\) −4.58300 −0.208318
\(485\) −3.49496 −0.158698
\(486\) 14.4494 0.655438
\(487\) 20.2075 0.915689 0.457845 0.889032i \(-0.348622\pi\)
0.457845 + 0.889032i \(0.348622\pi\)
\(488\) 3.22268 0.145884
\(489\) −10.1450 −0.458773
\(490\) −1.12669 −0.0508987
\(491\) −28.7727 −1.29850 −0.649248 0.760577i \(-0.724916\pi\)
−0.649248 + 0.760577i \(0.724916\pi\)
\(492\) 0.963958 0.0434586
\(493\) −0.489200 −0.0220325
\(494\) 2.77706 0.124946
\(495\) 7.99785 0.359477
\(496\) 5.13456 0.230548
\(497\) 11.9414 0.535646
\(498\) 9.56117 0.428446
\(499\) −30.5754 −1.36874 −0.684372 0.729133i \(-0.739924\pi\)
−0.684372 + 0.729133i \(0.739924\pi\)
\(500\) 10.4328 0.466567
\(501\) 9.63505 0.430462
\(502\) 7.75851 0.346279
\(503\) −17.2476 −0.769034 −0.384517 0.923118i \(-0.625632\pi\)
−0.384517 + 0.923118i \(0.625632\pi\)
\(504\) 6.33690 0.282268
\(505\) 2.95427 0.131463
\(506\) −8.49945 −0.377847
\(507\) 3.47040 0.154126
\(508\) −4.68023 −0.207652
\(509\) −9.55011 −0.423301 −0.211651 0.977345i \(-0.567884\pi\)
−0.211651 + 0.977345i \(0.567884\pi\)
\(510\) 0.777580 0.0344318
\(511\) −21.1970 −0.937701
\(512\) −1.00000 −0.0441942
\(513\) −3.65503 −0.161374
\(514\) −1.14498 −0.0505031
\(515\) −1.33182 −0.0586870
\(516\) 8.30618 0.365659
\(517\) −6.53194 −0.287274
\(518\) 19.9072 0.874673
\(519\) −1.86697 −0.0819510
\(520\) 3.41254 0.149650
\(521\) −34.9260 −1.53014 −0.765068 0.643950i \(-0.777295\pi\)
−0.765068 + 0.643950i \(0.777295\pi\)
\(522\) 1.30359 0.0570564
\(523\) −29.9788 −1.31088 −0.655441 0.755246i \(-0.727517\pi\)
−0.655441 + 0.755246i \(0.727517\pi\)
\(524\) −11.5458 −0.504382
\(525\) 5.64905 0.246545
\(526\) −25.3912 −1.10711
\(527\) −4.95066 −0.215654
\(528\) −1.66248 −0.0723503
\(529\) −11.7423 −0.510535
\(530\) −2.06020 −0.0894895
\(531\) 1.43683 0.0623531
\(532\) −2.46640 −0.106932
\(533\) −4.07898 −0.176680
\(534\) −10.0438 −0.434639
\(535\) −6.65577 −0.287754
\(536\) −4.20151 −0.181478
\(537\) −2.26797 −0.0978703
\(538\) −3.37381 −0.145455
\(539\) −2.32262 −0.100042
\(540\) −4.49143 −0.193280
\(541\) 36.7983 1.58208 0.791041 0.611763i \(-0.209539\pi\)
0.791041 + 0.611763i \(0.209539\pi\)
\(542\) −26.0833 −1.12037
\(543\) 8.43285 0.361888
\(544\) 0.964185 0.0413391
\(545\) 17.5631 0.752320
\(546\) 4.49510 0.192372
\(547\) 1.26217 0.0539664 0.0269832 0.999636i \(-0.491410\pi\)
0.0269832 + 0.999636i \(0.491410\pi\)
\(548\) −16.0140 −0.684086
\(549\) 8.28001 0.353382
\(550\) 8.84071 0.376969
\(551\) −0.507372 −0.0216148
\(552\) 2.20199 0.0937231
\(553\) 37.1865 1.58133
\(554\) −9.79155 −0.416003
\(555\) −6.50927 −0.276303
\(556\) −6.76188 −0.286768
\(557\) 7.59417 0.321775 0.160888 0.986973i \(-0.448564\pi\)
0.160888 + 0.986973i \(0.448564\pi\)
\(558\) 13.1922 0.558470
\(559\) −35.1475 −1.48658
\(560\) −3.03080 −0.128074
\(561\) 1.60294 0.0676763
\(562\) 16.1406 0.680849
\(563\) 28.7440 1.21141 0.605707 0.795688i \(-0.292891\pi\)
0.605707 + 0.795688i \(0.292891\pi\)
\(564\) 1.69226 0.0712570
\(565\) −5.36409 −0.225669
\(566\) 19.1946 0.806810
\(567\) 13.0945 0.549916
\(568\) −4.84164 −0.203151
\(569\) −26.2671 −1.10117 −0.550586 0.834778i \(-0.685596\pi\)
−0.550586 + 0.834778i \(0.685596\pi\)
\(570\) 0.806463 0.0337790
\(571\) 24.2872 1.01639 0.508194 0.861243i \(-0.330313\pi\)
0.508194 + 0.861243i \(0.330313\pi\)
\(572\) 7.03478 0.294139
\(573\) −17.0364 −0.711704
\(574\) 3.62268 0.151208
\(575\) −11.7097 −0.488329
\(576\) −2.56929 −0.107054
\(577\) 24.1157 1.00395 0.501975 0.864882i \(-0.332607\pi\)
0.501975 + 0.864882i \(0.332607\pi\)
\(578\) 16.0703 0.668438
\(579\) 8.72601 0.362641
\(580\) −0.623476 −0.0258884
\(581\) 35.9321 1.49072
\(582\) 1.86655 0.0773711
\(583\) −4.24700 −0.175893
\(584\) 8.59432 0.355636
\(585\) 8.76782 0.362505
\(586\) 21.6518 0.894426
\(587\) −18.2212 −0.752068 −0.376034 0.926606i \(-0.622712\pi\)
−0.376034 + 0.926606i \(0.622712\pi\)
\(588\) 0.601732 0.0248150
\(589\) −5.13456 −0.211566
\(590\) −0.687203 −0.0282917
\(591\) −1.75379 −0.0721414
\(592\) −8.07137 −0.331731
\(593\) 24.6583 1.01260 0.506298 0.862359i \(-0.331014\pi\)
0.506298 + 0.862359i \(0.331014\pi\)
\(594\) −9.25886 −0.379896
\(595\) 2.92225 0.119800
\(596\) 20.2752 0.830505
\(597\) 5.15030 0.210788
\(598\) −9.31771 −0.381030
\(599\) −1.97385 −0.0806495 −0.0403247 0.999187i \(-0.512839\pi\)
−0.0403247 + 0.999187i \(0.512839\pi\)
\(600\) −2.29041 −0.0935054
\(601\) −4.08788 −0.166748 −0.0833741 0.996518i \(-0.526570\pi\)
−0.0833741 + 0.996518i \(0.526570\pi\)
\(602\) 31.2157 1.27226
\(603\) −10.7949 −0.439603
\(604\) −5.05919 −0.205855
\(605\) 5.63174 0.228963
\(606\) −1.57779 −0.0640932
\(607\) −28.6796 −1.16407 −0.582035 0.813164i \(-0.697743\pi\)
−0.582035 + 0.813164i \(0.697743\pi\)
\(608\) 1.00000 0.0405554
\(609\) −0.821260 −0.0332791
\(610\) −3.96014 −0.160342
\(611\) −7.16078 −0.289694
\(612\) 2.47727 0.100138
\(613\) 0.249598 0.0100812 0.00504059 0.999987i \(-0.498396\pi\)
0.00504059 + 0.999987i \(0.498396\pi\)
\(614\) 0.731919 0.0295378
\(615\) −1.18454 −0.0477654
\(616\) −6.24783 −0.251732
\(617\) −8.63308 −0.347555 −0.173777 0.984785i \(-0.555597\pi\)
−0.173777 + 0.984785i \(0.555597\pi\)
\(618\) 0.711284 0.0286121
\(619\) −1.09586 −0.0440463 −0.0220231 0.999757i \(-0.507011\pi\)
−0.0220231 + 0.999757i \(0.507011\pi\)
\(620\) −6.30952 −0.253397
\(621\) 12.2635 0.492119
\(622\) 21.8823 0.877398
\(623\) −37.7461 −1.51226
\(624\) −1.82253 −0.0729598
\(625\) 4.62969 0.185188
\(626\) 19.2489 0.769342
\(627\) 1.66248 0.0663932
\(628\) 4.42653 0.176638
\(629\) 7.78230 0.310300
\(630\) −7.78700 −0.310242
\(631\) 18.1954 0.724348 0.362174 0.932111i \(-0.382035\pi\)
0.362174 + 0.932111i \(0.382035\pi\)
\(632\) −15.0772 −0.599741
\(633\) 0.656283 0.0260849
\(634\) 20.9236 0.830981
\(635\) 5.75123 0.228231
\(636\) 1.10029 0.0436294
\(637\) −2.54622 −0.100885
\(638\) −1.28526 −0.0508841
\(639\) −12.4396 −0.492103
\(640\) 1.22883 0.0485740
\(641\) 33.4455 1.32102 0.660509 0.750818i \(-0.270341\pi\)
0.660509 + 0.750818i \(0.270341\pi\)
\(642\) 3.55465 0.140291
\(643\) −17.2875 −0.681753 −0.340876 0.940108i \(-0.610724\pi\)
−0.340876 + 0.940108i \(0.610724\pi\)
\(644\) 8.27538 0.326096
\(645\) −10.2069 −0.401897
\(646\) −0.964185 −0.0379354
\(647\) 25.7407 1.01197 0.505986 0.862541i \(-0.331129\pi\)
0.505986 + 0.862541i \(0.331129\pi\)
\(648\) −5.30914 −0.208563
\(649\) −1.41664 −0.0556078
\(650\) 9.69183 0.380145
\(651\) −8.31108 −0.325737
\(652\) 15.4583 0.605392
\(653\) 0.984346 0.0385204 0.0192602 0.999815i \(-0.493869\pi\)
0.0192602 + 0.999815i \(0.493869\pi\)
\(654\) −9.37991 −0.366784
\(655\) 14.1879 0.554368
\(656\) −1.46881 −0.0573475
\(657\) 22.0813 0.861475
\(658\) 6.35973 0.247928
\(659\) −46.4564 −1.80968 −0.904842 0.425746i \(-0.860012\pi\)
−0.904842 + 0.425746i \(0.860012\pi\)
\(660\) 2.04292 0.0795205
\(661\) −30.8462 −1.19978 −0.599888 0.800084i \(-0.704788\pi\)
−0.599888 + 0.800084i \(0.704788\pi\)
\(662\) 26.3706 1.02492
\(663\) 1.75726 0.0682463
\(664\) −14.5687 −0.565374
\(665\) 3.03080 0.117529
\(666\) −20.7377 −0.803570
\(667\) 1.70236 0.0659156
\(668\) −14.6812 −0.568034
\(669\) −2.54006 −0.0982045
\(670\) 5.16296 0.199463
\(671\) −8.16364 −0.315154
\(672\) 1.61866 0.0624410
\(673\) 10.6344 0.409925 0.204963 0.978770i \(-0.434293\pi\)
0.204963 + 0.978770i \(0.434293\pi\)
\(674\) 22.0621 0.849802
\(675\) −12.7559 −0.490976
\(676\) −5.28796 −0.203383
\(677\) 5.33569 0.205067 0.102534 0.994730i \(-0.467305\pi\)
0.102534 + 0.994730i \(0.467305\pi\)
\(678\) 2.86480 0.110022
\(679\) 7.01475 0.269201
\(680\) −1.18482 −0.0454359
\(681\) −11.0027 −0.421626
\(682\) −13.0068 −0.498055
\(683\) −38.0068 −1.45429 −0.727145 0.686483i \(-0.759153\pi\)
−0.727145 + 0.686483i \(0.759153\pi\)
\(684\) 2.56929 0.0982394
\(685\) 19.6786 0.751881
\(686\) 19.5262 0.745513
\(687\) −0.292171 −0.0111470
\(688\) −12.6564 −0.482520
\(689\) −4.65587 −0.177375
\(690\) −2.70589 −0.103011
\(691\) 25.4522 0.968247 0.484124 0.875000i \(-0.339139\pi\)
0.484124 + 0.875000i \(0.339139\pi\)
\(692\) 2.84477 0.108142
\(693\) −16.0525 −0.609784
\(694\) 5.03597 0.191163
\(695\) 8.30923 0.315187
\(696\) 0.332979 0.0126216
\(697\) 1.41621 0.0536427
\(698\) 6.92267 0.262027
\(699\) 12.1524 0.459647
\(700\) −8.60765 −0.325338
\(701\) 23.8630 0.901293 0.450647 0.892702i \(-0.351193\pi\)
0.450647 + 0.892702i \(0.351193\pi\)
\(702\) −10.1502 −0.383096
\(703\) 8.07137 0.304418
\(704\) 2.53318 0.0954728
\(705\) −2.07951 −0.0783188
\(706\) −21.3368 −0.803022
\(707\) −5.92953 −0.223003
\(708\) 0.367014 0.0137932
\(709\) −4.16387 −0.156378 −0.0781888 0.996939i \(-0.524914\pi\)
−0.0781888 + 0.996939i \(0.524914\pi\)
\(710\) 5.94957 0.223284
\(711\) −38.7379 −1.45278
\(712\) 15.3041 0.573546
\(713\) 17.2277 0.645183
\(714\) −1.56068 −0.0584071
\(715\) −8.64458 −0.323289
\(716\) 3.45578 0.129149
\(717\) 1.12572 0.0420407
\(718\) −32.2705 −1.20432
\(719\) −0.560009 −0.0208848 −0.0104424 0.999945i \(-0.503324\pi\)
−0.0104424 + 0.999945i \(0.503324\pi\)
\(720\) 3.15724 0.117663
\(721\) 2.67310 0.0995515
\(722\) −1.00000 −0.0372161
\(723\) −13.8681 −0.515760
\(724\) −12.8494 −0.477545
\(725\) −1.77071 −0.0657625
\(726\) −3.00774 −0.111628
\(727\) −19.6820 −0.729966 −0.364983 0.931014i \(-0.618925\pi\)
−0.364983 + 0.931014i \(0.618925\pi\)
\(728\) −6.84932 −0.253853
\(729\) −6.44453 −0.238686
\(730\) −10.5610 −0.390880
\(731\) 12.2031 0.451348
\(732\) 2.11499 0.0781724
\(733\) −18.4815 −0.682629 −0.341314 0.939949i \(-0.610872\pi\)
−0.341314 + 0.939949i \(0.610872\pi\)
\(734\) −31.8609 −1.17601
\(735\) −0.739429 −0.0272742
\(736\) −3.35525 −0.123676
\(737\) 10.6432 0.392047
\(738\) −3.77381 −0.138916
\(739\) −46.4157 −1.70743 −0.853715 0.520741i \(-0.825656\pi\)
−0.853715 + 0.520741i \(0.825656\pi\)
\(740\) 9.91838 0.364607
\(741\) 1.82253 0.0669525
\(742\) 4.13504 0.151802
\(743\) −48.5036 −1.77942 −0.889712 0.456522i \(-0.849095\pi\)
−0.889712 + 0.456522i \(0.849095\pi\)
\(744\) 3.36972 0.123540
\(745\) −24.9149 −0.912811
\(746\) −3.93302 −0.143998
\(747\) −37.4311 −1.36953
\(748\) −2.44245 −0.0893050
\(749\) 13.3588 0.488121
\(750\) 6.84685 0.250011
\(751\) 52.9738 1.93304 0.966521 0.256588i \(-0.0825983\pi\)
0.966521 + 0.256588i \(0.0825983\pi\)
\(752\) −2.57855 −0.0940301
\(753\) 5.09178 0.185555
\(754\) −1.40900 −0.0513127
\(755\) 6.21691 0.226256
\(756\) 9.01477 0.327864
\(757\) −2.75771 −0.100231 −0.0501153 0.998743i \(-0.515959\pi\)
−0.0501153 + 0.998743i \(0.515959\pi\)
\(758\) 16.4831 0.598695
\(759\) −5.57805 −0.202470
\(760\) −1.22883 −0.0445745
\(761\) −42.9698 −1.55765 −0.778827 0.627239i \(-0.784185\pi\)
−0.778827 + 0.627239i \(0.784185\pi\)
\(762\) −3.07156 −0.111271
\(763\) −35.2509 −1.27617
\(764\) 25.9589 0.939159
\(765\) −3.04416 −0.110062
\(766\) 5.90876 0.213492
\(767\) −1.55302 −0.0560762
\(768\) −0.656283 −0.0236816
\(769\) −6.64548 −0.239642 −0.119821 0.992796i \(-0.538232\pi\)
−0.119821 + 0.992796i \(0.538232\pi\)
\(770\) 7.67755 0.276680
\(771\) −0.751434 −0.0270622
\(772\) −13.2961 −0.478537
\(773\) −13.2313 −0.475897 −0.237949 0.971278i \(-0.576475\pi\)
−0.237949 + 0.971278i \(0.576475\pi\)
\(774\) −32.5180 −1.16883
\(775\) −17.9194 −0.643685
\(776\) −2.84413 −0.102098
\(777\) 13.0648 0.468696
\(778\) 26.5021 0.950145
\(779\) 1.46881 0.0526257
\(780\) 2.23959 0.0801903
\(781\) 12.2647 0.438867
\(782\) 3.23508 0.115686
\(783\) 1.85446 0.0662730
\(784\) −0.916878 −0.0327457
\(785\) −5.43948 −0.194143
\(786\) −7.57733 −0.270274
\(787\) −52.1463 −1.85882 −0.929408 0.369054i \(-0.879682\pi\)
−0.929408 + 0.369054i \(0.879682\pi\)
\(788\) 2.67231 0.0951972
\(789\) −16.6638 −0.593247
\(790\) 18.5274 0.659177
\(791\) 10.7663 0.382805
\(792\) 6.50848 0.231269
\(793\) −8.94957 −0.317808
\(794\) 29.4443 1.04494
\(795\) −1.35208 −0.0479532
\(796\) −7.84768 −0.278154
\(797\) −19.7145 −0.698324 −0.349162 0.937062i \(-0.613534\pi\)
−0.349162 + 0.937062i \(0.613534\pi\)
\(798\) −1.61866 −0.0572998
\(799\) 2.48620 0.0879554
\(800\) 3.48997 0.123389
\(801\) 39.3208 1.38933
\(802\) 16.0740 0.567592
\(803\) −21.7710 −0.768281
\(804\) −2.75738 −0.0972454
\(805\) −10.1691 −0.358413
\(806\) −14.2590 −0.502250
\(807\) −2.21418 −0.0779427
\(808\) 2.40413 0.0845769
\(809\) −14.5695 −0.512237 −0.256119 0.966645i \(-0.582444\pi\)
−0.256119 + 0.966645i \(0.582444\pi\)
\(810\) 6.52406 0.229232
\(811\) 1.76128 0.0618471 0.0309235 0.999522i \(-0.490155\pi\)
0.0309235 + 0.999522i \(0.490155\pi\)
\(812\) 1.25138 0.0439148
\(813\) −17.1180 −0.600355
\(814\) 20.4462 0.716641
\(815\) −18.9956 −0.665389
\(816\) 0.632778 0.0221517
\(817\) 12.6564 0.442791
\(818\) 15.5578 0.543965
\(819\) −17.5979 −0.614921
\(820\) 1.80493 0.0630309
\(821\) −36.4323 −1.27149 −0.635747 0.771897i \(-0.719308\pi\)
−0.635747 + 0.771897i \(0.719308\pi\)
\(822\) −10.5097 −0.366569
\(823\) 36.2487 1.26355 0.631775 0.775151i \(-0.282326\pi\)
0.631775 + 0.775151i \(0.282326\pi\)
\(824\) −1.08381 −0.0377562
\(825\) 5.80201 0.202000
\(826\) 1.37929 0.0479916
\(827\) −10.9360 −0.380282 −0.190141 0.981757i \(-0.560894\pi\)
−0.190141 + 0.981757i \(0.560894\pi\)
\(828\) −8.62062 −0.299587
\(829\) −39.1854 −1.36097 −0.680483 0.732764i \(-0.738230\pi\)
−0.680483 + 0.732764i \(0.738230\pi\)
\(830\) 17.9025 0.621404
\(831\) −6.42603 −0.222916
\(832\) 2.77706 0.0962771
\(833\) 0.884040 0.0306302
\(834\) −4.43771 −0.153665
\(835\) 18.0408 0.624328
\(836\) −2.53318 −0.0876119
\(837\) 18.7670 0.648682
\(838\) −30.8745 −1.06654
\(839\) −45.2169 −1.56106 −0.780530 0.625119i \(-0.785051\pi\)
−0.780530 + 0.625119i \(0.785051\pi\)
\(840\) −1.98906 −0.0686291
\(841\) −28.7426 −0.991123
\(842\) −17.9081 −0.617153
\(843\) 10.5928 0.364835
\(844\) −1.00000 −0.0344214
\(845\) 6.49803 0.223539
\(846\) −6.62505 −0.227774
\(847\) −11.3035 −0.388393
\(848\) −1.67655 −0.0575729
\(849\) 12.5971 0.432332
\(850\) −3.36497 −0.115418
\(851\) −27.0815 −0.928341
\(852\) −3.17749 −0.108859
\(853\) 14.0127 0.479786 0.239893 0.970799i \(-0.422888\pi\)
0.239893 + 0.970799i \(0.422888\pi\)
\(854\) 7.94842 0.271989
\(855\) −3.15724 −0.107975
\(856\) −5.41633 −0.185126
\(857\) 56.7653 1.93907 0.969533 0.244960i \(-0.0787748\pi\)
0.969533 + 0.244960i \(0.0787748\pi\)
\(858\) 4.61681 0.157615
\(859\) −40.7536 −1.39049 −0.695247 0.718771i \(-0.744705\pi\)
−0.695247 + 0.718771i \(0.744705\pi\)
\(860\) 15.5526 0.530340
\(861\) 2.37750 0.0810251
\(862\) −28.5173 −0.971304
\(863\) 10.2198 0.347885 0.173943 0.984756i \(-0.444349\pi\)
0.173943 + 0.984756i \(0.444349\pi\)
\(864\) −3.65503 −0.124347
\(865\) −3.49575 −0.118859
\(866\) 37.7724 1.28356
\(867\) 10.5467 0.358185
\(868\) 12.6639 0.429840
\(869\) 38.1934 1.29562
\(870\) −0.409177 −0.0138724
\(871\) 11.6678 0.395349
\(872\) 14.2925 0.484004
\(873\) −7.30739 −0.247318
\(874\) 3.35525 0.113493
\(875\) 25.7314 0.869878
\(876\) 5.64031 0.190568
\(877\) −22.5041 −0.759911 −0.379955 0.925005i \(-0.624061\pi\)
−0.379955 + 0.925005i \(0.624061\pi\)
\(878\) 4.71110 0.158992
\(879\) 14.2097 0.479281
\(880\) −3.11286 −0.104934
\(881\) −44.2344 −1.49029 −0.745147 0.666900i \(-0.767621\pi\)
−0.745147 + 0.666900i \(0.767621\pi\)
\(882\) −2.35573 −0.0793215
\(883\) −20.1243 −0.677236 −0.338618 0.940924i \(-0.609959\pi\)
−0.338618 + 0.940924i \(0.609959\pi\)
\(884\) −2.67759 −0.0900573
\(885\) −0.451000 −0.0151602
\(886\) −32.4557 −1.09037
\(887\) 11.4870 0.385697 0.192848 0.981229i \(-0.438227\pi\)
0.192848 + 0.981229i \(0.438227\pi\)
\(888\) −5.29711 −0.177759
\(889\) −11.5433 −0.387150
\(890\) −18.8062 −0.630386
\(891\) 13.4490 0.450559
\(892\) 3.87038 0.129590
\(893\) 2.57855 0.0862879
\(894\) 13.3063 0.445029
\(895\) −4.24659 −0.141948
\(896\) −2.46640 −0.0823966
\(897\) −6.11506 −0.204176
\(898\) 12.9548 0.432308
\(899\) 2.60513 0.0868859
\(900\) 8.96674 0.298891
\(901\) 1.61650 0.0538536
\(902\) 3.72077 0.123888
\(903\) 20.4863 0.681743
\(904\) −4.36519 −0.145184
\(905\) 15.7898 0.524871
\(906\) −3.32026 −0.110308
\(907\) 40.8797 1.35739 0.678695 0.734421i \(-0.262546\pi\)
0.678695 + 0.734421i \(0.262546\pi\)
\(908\) 16.7652 0.556374
\(909\) 6.17690 0.204875
\(910\) 8.41669 0.279010
\(911\) −26.9274 −0.892143 −0.446071 0.894997i \(-0.647177\pi\)
−0.446071 + 0.894997i \(0.647177\pi\)
\(912\) 0.656283 0.0217317
\(913\) 36.9050 1.22138
\(914\) 36.6463 1.21215
\(915\) −2.59898 −0.0859195
\(916\) 0.445190 0.0147095
\(917\) −28.4766 −0.940381
\(918\) 3.52413 0.116314
\(919\) 21.1727 0.698424 0.349212 0.937044i \(-0.386449\pi\)
0.349212 + 0.937044i \(0.386449\pi\)
\(920\) 4.12305 0.135933
\(921\) 0.480346 0.0158279
\(922\) −28.7701 −0.947492
\(923\) 13.4455 0.442564
\(924\) −4.10035 −0.134892
\(925\) 28.1688 0.926185
\(926\) 34.5158 1.13426
\(927\) −2.78462 −0.0914589
\(928\) −0.507372 −0.0166553
\(929\) 36.8654 1.20952 0.604758 0.796410i \(-0.293270\pi\)
0.604758 + 0.796410i \(0.293270\pi\)
\(930\) −4.14083 −0.135783
\(931\) 0.916878 0.0300495
\(932\) −18.5171 −0.606547
\(933\) 14.3610 0.470156
\(934\) −16.3066 −0.533569
\(935\) 3.00137 0.0981554
\(936\) 7.13507 0.233217
\(937\) −25.4699 −0.832067 −0.416033 0.909349i \(-0.636580\pi\)
−0.416033 + 0.909349i \(0.636580\pi\)
\(938\) −10.3626 −0.338351
\(939\) 12.6327 0.412254
\(940\) 3.16861 0.103349
\(941\) −20.5582 −0.670179 −0.335089 0.942186i \(-0.608767\pi\)
−0.335089 + 0.942186i \(0.608767\pi\)
\(942\) 2.90506 0.0946519
\(943\) −4.92824 −0.160485
\(944\) −0.559232 −0.0182014
\(945\) −11.0777 −0.360356
\(946\) 32.0609 1.04239
\(947\) −48.2835 −1.56900 −0.784502 0.620127i \(-0.787081\pi\)
−0.784502 + 0.620127i \(0.787081\pi\)
\(948\) −9.89494 −0.321373
\(949\) −23.8669 −0.774752
\(950\) −3.48997 −0.113229
\(951\) 13.7318 0.445284
\(952\) 2.37806 0.0770735
\(953\) −35.6738 −1.15559 −0.577794 0.816183i \(-0.696086\pi\)
−0.577794 + 0.816183i \(0.696086\pi\)
\(954\) −4.30755 −0.139462
\(955\) −31.8991 −1.03223
\(956\) −1.71529 −0.0554765
\(957\) −0.843497 −0.0272664
\(958\) 5.46908 0.176698
\(959\) −39.4970 −1.27542
\(960\) 0.806463 0.0260285
\(961\) −4.63631 −0.149558
\(962\) 22.4146 0.722677
\(963\) −13.9161 −0.448441
\(964\) 21.1313 0.680592
\(965\) 16.3387 0.525962
\(966\) 5.43099 0.174739
\(967\) 30.2767 0.973632 0.486816 0.873505i \(-0.338158\pi\)
0.486816 + 0.873505i \(0.338158\pi\)
\(968\) 4.58300 0.147303
\(969\) −0.632778 −0.0203278
\(970\) 3.49496 0.112216
\(971\) −9.19295 −0.295016 −0.147508 0.989061i \(-0.547125\pi\)
−0.147508 + 0.989061i \(0.547125\pi\)
\(972\) −14.4494 −0.463465
\(973\) −16.6775 −0.534656
\(974\) −20.2075 −0.647490
\(975\) 6.36058 0.203702
\(976\) −3.22268 −0.103156
\(977\) −23.0252 −0.736642 −0.368321 0.929699i \(-0.620067\pi\)
−0.368321 + 0.929699i \(0.620067\pi\)
\(978\) 10.1450 0.324401
\(979\) −38.7681 −1.23903
\(980\) 1.12669 0.0359908
\(981\) 36.7216 1.17243
\(982\) 28.7727 0.918175
\(983\) −33.3707 −1.06436 −0.532179 0.846632i \(-0.678627\pi\)
−0.532179 + 0.846632i \(0.678627\pi\)
\(984\) −0.963958 −0.0307298
\(985\) −3.28383 −0.104632
\(986\) 0.489200 0.0155793
\(987\) 4.17379 0.132853
\(988\) −2.77706 −0.0883499
\(989\) −42.4654 −1.35032
\(990\) −7.99785 −0.254188
\(991\) −9.97660 −0.316917 −0.158459 0.987366i \(-0.550652\pi\)
−0.158459 + 0.987366i \(0.550652\pi\)
\(992\) −5.13456 −0.163022
\(993\) 17.3066 0.549208
\(994\) −11.9414 −0.378759
\(995\) 9.64350 0.305720
\(996\) −9.56117 −0.302957
\(997\) −16.3622 −0.518197 −0.259099 0.965851i \(-0.583425\pi\)
−0.259099 + 0.965851i \(0.583425\pi\)
\(998\) 30.5754 0.967848
\(999\) −29.5011 −0.933374
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 \(a_p\))