Properties

Label 8018.2.a.d.1.18
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

Related objects

Downloads

Learn more about

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: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+0.460726 q^{3}\) \(+1.00000 q^{4}\) \(+0.645126 q^{5}\) \(+0.460726 q^{6}\) \(+1.69833 q^{7}\) \(+1.00000 q^{8}\) \(-2.78773 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+0.460726 q^{3}\) \(+1.00000 q^{4}\) \(+0.645126 q^{5}\) \(+0.460726 q^{6}\) \(+1.69833 q^{7}\) \(+1.00000 q^{8}\) \(-2.78773 q^{9}\) \(+0.645126 q^{10}\) \(+0.878525 q^{11}\) \(+0.460726 q^{12}\) \(-2.21021 q^{13}\) \(+1.69833 q^{14}\) \(+0.297226 q^{15}\) \(+1.00000 q^{16}\) \(-3.24512 q^{17}\) \(-2.78773 q^{18}\) \(+1.00000 q^{19}\) \(+0.645126 q^{20}\) \(+0.782465 q^{21}\) \(+0.878525 q^{22}\) \(-0.250785 q^{23}\) \(+0.460726 q^{24}\) \(-4.58381 q^{25}\) \(-2.21021 q^{26}\) \(-2.66656 q^{27}\) \(+1.69833 q^{28}\) \(-6.95706 q^{29}\) \(+0.297226 q^{30}\) \(-5.17048 q^{31}\) \(+1.00000 q^{32}\) \(+0.404759 q^{33}\) \(-3.24512 q^{34}\) \(+1.09564 q^{35}\) \(-2.78773 q^{36}\) \(+4.12685 q^{37}\) \(+1.00000 q^{38}\) \(-1.01830 q^{39}\) \(+0.645126 q^{40}\) \(-4.51052 q^{41}\) \(+0.782465 q^{42}\) \(+0.863349 q^{43}\) \(+0.878525 q^{44}\) \(-1.79844 q^{45}\) \(-0.250785 q^{46}\) \(-8.45380 q^{47}\) \(+0.460726 q^{48}\) \(-4.11567 q^{49}\) \(-4.58381 q^{50}\) \(-1.49511 q^{51}\) \(-2.21021 q^{52}\) \(+1.10404 q^{53}\) \(-2.66656 q^{54}\) \(+0.566760 q^{55}\) \(+1.69833 q^{56}\) \(+0.460726 q^{57}\) \(-6.95706 q^{58}\) \(-11.4249 q^{59}\) \(+0.297226 q^{60}\) \(+7.83485 q^{61}\) \(-5.17048 q^{62}\) \(-4.73449 q^{63}\) \(+1.00000 q^{64}\) \(-1.42586 q^{65}\) \(+0.404759 q^{66}\) \(-4.12175 q^{67}\) \(-3.24512 q^{68}\) \(-0.115543 q^{69}\) \(+1.09564 q^{70}\) \(-6.15084 q^{71}\) \(-2.78773 q^{72}\) \(-0.0206681 q^{73}\) \(+4.12685 q^{74}\) \(-2.11188 q^{75}\) \(+1.00000 q^{76}\) \(+1.49203 q^{77}\) \(-1.01830 q^{78}\) \(+3.73317 q^{79}\) \(+0.645126 q^{80}\) \(+7.13464 q^{81}\) \(-4.51052 q^{82}\) \(+12.2527 q^{83}\) \(+0.782465 q^{84}\) \(-2.09351 q^{85}\) \(+0.863349 q^{86}\) \(-3.20530 q^{87}\) \(+0.878525 q^{88}\) \(+0.944202 q^{89}\) \(-1.79844 q^{90}\) \(-3.75366 q^{91}\) \(-0.250785 q^{92}\) \(-2.38217 q^{93}\) \(-8.45380 q^{94}\) \(+0.645126 q^{95}\) \(+0.460726 q^{96}\) \(-8.08209 q^{97}\) \(-4.11567 q^{98}\) \(-2.44909 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.460726 0.266000 0.133000 0.991116i \(-0.457539\pi\)
0.133000 + 0.991116i \(0.457539\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.645126 0.288509 0.144255 0.989541i \(-0.453922\pi\)
0.144255 + 0.989541i \(0.453922\pi\)
\(6\) 0.460726 0.188091
\(7\) 1.69833 0.641909 0.320954 0.947095i \(-0.395996\pi\)
0.320954 + 0.947095i \(0.395996\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.78773 −0.929244
\(10\) 0.645126 0.204007
\(11\) 0.878525 0.264885 0.132443 0.991191i \(-0.457718\pi\)
0.132443 + 0.991191i \(0.457718\pi\)
\(12\) 0.460726 0.133000
\(13\) −2.21021 −0.613001 −0.306500 0.951871i \(-0.599158\pi\)
−0.306500 + 0.951871i \(0.599158\pi\)
\(14\) 1.69833 0.453898
\(15\) 0.297226 0.0767435
\(16\) 1.00000 0.250000
\(17\) −3.24512 −0.787056 −0.393528 0.919313i \(-0.628746\pi\)
−0.393528 + 0.919313i \(0.628746\pi\)
\(18\) −2.78773 −0.657075
\(19\) 1.00000 0.229416
\(20\) 0.645126 0.144255
\(21\) 0.782465 0.170748
\(22\) 0.878525 0.187302
\(23\) −0.250785 −0.0522923 −0.0261462 0.999658i \(-0.508324\pi\)
−0.0261462 + 0.999658i \(0.508324\pi\)
\(24\) 0.460726 0.0940453
\(25\) −4.58381 −0.916762
\(26\) −2.21021 −0.433457
\(27\) −2.66656 −0.513179
\(28\) 1.69833 0.320954
\(29\) −6.95706 −1.29189 −0.645947 0.763383i \(-0.723537\pi\)
−0.645947 + 0.763383i \(0.723537\pi\)
\(30\) 0.297226 0.0542659
\(31\) −5.17048 −0.928645 −0.464322 0.885666i \(-0.653702\pi\)
−0.464322 + 0.885666i \(0.653702\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.404759 0.0704596
\(34\) −3.24512 −0.556533
\(35\) 1.09564 0.185197
\(36\) −2.78773 −0.464622
\(37\) 4.12685 0.678450 0.339225 0.940705i \(-0.389835\pi\)
0.339225 + 0.940705i \(0.389835\pi\)
\(38\) 1.00000 0.162221
\(39\) −1.01830 −0.163058
\(40\) 0.645126 0.102003
\(41\) −4.51052 −0.704424 −0.352212 0.935920i \(-0.614570\pi\)
−0.352212 + 0.935920i \(0.614570\pi\)
\(42\) 0.782465 0.120737
\(43\) 0.863349 0.131660 0.0658298 0.997831i \(-0.479031\pi\)
0.0658298 + 0.997831i \(0.479031\pi\)
\(44\) 0.878525 0.132443
\(45\) −1.79844 −0.268095
\(46\) −0.250785 −0.0369763
\(47\) −8.45380 −1.23311 −0.616557 0.787311i \(-0.711473\pi\)
−0.616557 + 0.787311i \(0.711473\pi\)
\(48\) 0.460726 0.0665001
\(49\) −4.11567 −0.587953
\(50\) −4.58381 −0.648249
\(51\) −1.49511 −0.209357
\(52\) −2.21021 −0.306500
\(53\) 1.10404 0.151652 0.0758260 0.997121i \(-0.475841\pi\)
0.0758260 + 0.997121i \(0.475841\pi\)
\(54\) −2.66656 −0.362873
\(55\) 0.566760 0.0764218
\(56\) 1.69833 0.226949
\(57\) 0.460726 0.0610247
\(58\) −6.95706 −0.913506
\(59\) −11.4249 −1.48739 −0.743696 0.668518i \(-0.766929\pi\)
−0.743696 + 0.668518i \(0.766929\pi\)
\(60\) 0.297226 0.0383718
\(61\) 7.83485 1.00315 0.501575 0.865114i \(-0.332754\pi\)
0.501575 + 0.865114i \(0.332754\pi\)
\(62\) −5.17048 −0.656651
\(63\) −4.73449 −0.596490
\(64\) 1.00000 0.125000
\(65\) −1.42586 −0.176856
\(66\) 0.404759 0.0498224
\(67\) −4.12175 −0.503552 −0.251776 0.967786i \(-0.581015\pi\)
−0.251776 + 0.967786i \(0.581015\pi\)
\(68\) −3.24512 −0.393528
\(69\) −0.115543 −0.0139098
\(70\) 1.09564 0.130954
\(71\) −6.15084 −0.729971 −0.364985 0.931013i \(-0.618926\pi\)
−0.364985 + 0.931013i \(0.618926\pi\)
\(72\) −2.78773 −0.328537
\(73\) −0.0206681 −0.00241902 −0.00120951 0.999999i \(-0.500385\pi\)
−0.00120951 + 0.999999i \(0.500385\pi\)
\(74\) 4.12685 0.479736
\(75\) −2.11188 −0.243859
\(76\) 1.00000 0.114708
\(77\) 1.49203 0.170032
\(78\) −1.01830 −0.115300
\(79\) 3.73317 0.420014 0.210007 0.977700i \(-0.432651\pi\)
0.210007 + 0.977700i \(0.432651\pi\)
\(80\) 0.645126 0.0721273
\(81\) 7.13464 0.792738
\(82\) −4.51052 −0.498103
\(83\) 12.2527 1.34491 0.672453 0.740140i \(-0.265241\pi\)
0.672453 + 0.740140i \(0.265241\pi\)
\(84\) 0.782465 0.0853739
\(85\) −2.09351 −0.227073
\(86\) 0.863349 0.0930974
\(87\) −3.20530 −0.343644
\(88\) 0.878525 0.0936511
\(89\) 0.944202 0.100085 0.0500426 0.998747i \(-0.484064\pi\)
0.0500426 + 0.998747i \(0.484064\pi\)
\(90\) −1.79844 −0.189572
\(91\) −3.75366 −0.393490
\(92\) −0.250785 −0.0261462
\(93\) −2.38217 −0.247020
\(94\) −8.45380 −0.871943
\(95\) 0.645126 0.0661885
\(96\) 0.460726 0.0470227
\(97\) −8.08209 −0.820612 −0.410306 0.911948i \(-0.634578\pi\)
−0.410306 + 0.911948i \(0.634578\pi\)
\(98\) −4.11567 −0.415746
\(99\) −2.44909 −0.246143
\(100\) −4.58381 −0.458381
\(101\) 0.959342 0.0954581 0.0477290 0.998860i \(-0.484802\pi\)
0.0477290 + 0.998860i \(0.484802\pi\)
\(102\) −1.49511 −0.148038
\(103\) −3.43349 −0.338312 −0.169156 0.985589i \(-0.554104\pi\)
−0.169156 + 0.985589i \(0.554104\pi\)
\(104\) −2.21021 −0.216728
\(105\) 0.504789 0.0492623
\(106\) 1.10404 0.107234
\(107\) 6.03026 0.582967 0.291483 0.956576i \(-0.405851\pi\)
0.291483 + 0.956576i \(0.405851\pi\)
\(108\) −2.66656 −0.256590
\(109\) −6.44518 −0.617337 −0.308668 0.951170i \(-0.599883\pi\)
−0.308668 + 0.951170i \(0.599883\pi\)
\(110\) 0.566760 0.0540384
\(111\) 1.90135 0.180468
\(112\) 1.69833 0.160477
\(113\) 16.3812 1.54101 0.770506 0.637433i \(-0.220004\pi\)
0.770506 + 0.637433i \(0.220004\pi\)
\(114\) 0.460726 0.0431509
\(115\) −0.161788 −0.0150868
\(116\) −6.95706 −0.645947
\(117\) 6.16146 0.569627
\(118\) −11.4249 −1.05174
\(119\) −5.51128 −0.505218
\(120\) 0.297226 0.0271329
\(121\) −10.2282 −0.929836
\(122\) 7.83485 0.709334
\(123\) −2.07811 −0.187377
\(124\) −5.17048 −0.464322
\(125\) −6.18277 −0.553004
\(126\) −4.73449 −0.421782
\(127\) −8.38429 −0.743985 −0.371993 0.928236i \(-0.621325\pi\)
−0.371993 + 0.928236i \(0.621325\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.397768 0.0350215
\(130\) −1.42586 −0.125056
\(131\) 11.5878 1.01243 0.506215 0.862408i \(-0.331044\pi\)
0.506215 + 0.862408i \(0.331044\pi\)
\(132\) 0.404759 0.0352298
\(133\) 1.69833 0.147264
\(134\) −4.12175 −0.356065
\(135\) −1.72027 −0.148057
\(136\) −3.24512 −0.278266
\(137\) 17.7090 1.51299 0.756493 0.654002i \(-0.226911\pi\)
0.756493 + 0.654002i \(0.226911\pi\)
\(138\) −0.115543 −0.00983570
\(139\) −13.7301 −1.16457 −0.582286 0.812984i \(-0.697842\pi\)
−0.582286 + 0.812984i \(0.697842\pi\)
\(140\) 1.09564 0.0925983
\(141\) −3.89489 −0.328008
\(142\) −6.15084 −0.516167
\(143\) −1.94172 −0.162375
\(144\) −2.78773 −0.232311
\(145\) −4.48818 −0.372723
\(146\) −0.0206681 −0.00171050
\(147\) −1.89620 −0.156396
\(148\) 4.12685 0.339225
\(149\) −11.9151 −0.976123 −0.488061 0.872809i \(-0.662296\pi\)
−0.488061 + 0.872809i \(0.662296\pi\)
\(150\) −2.11188 −0.172434
\(151\) 4.00395 0.325837 0.162918 0.986640i \(-0.447909\pi\)
0.162918 + 0.986640i \(0.447909\pi\)
\(152\) 1.00000 0.0811107
\(153\) 9.04651 0.731367
\(154\) 1.49203 0.120231
\(155\) −3.33561 −0.267923
\(156\) −1.01830 −0.0815292
\(157\) −21.5010 −1.71597 −0.857983 0.513678i \(-0.828282\pi\)
−0.857983 + 0.513678i \(0.828282\pi\)
\(158\) 3.73317 0.296995
\(159\) 0.508661 0.0403395
\(160\) 0.645126 0.0510017
\(161\) −0.425916 −0.0335669
\(162\) 7.13464 0.560550
\(163\) −17.7351 −1.38912 −0.694560 0.719435i \(-0.744401\pi\)
−0.694560 + 0.719435i \(0.744401\pi\)
\(164\) −4.51052 −0.352212
\(165\) 0.261121 0.0203282
\(166\) 12.2527 0.950991
\(167\) 9.68545 0.749483 0.374741 0.927129i \(-0.377732\pi\)
0.374741 + 0.927129i \(0.377732\pi\)
\(168\) 0.782465 0.0603685
\(169\) −8.11499 −0.624230
\(170\) −2.09351 −0.160565
\(171\) −2.78773 −0.213183
\(172\) 0.863349 0.0658298
\(173\) 22.6120 1.71916 0.859579 0.511003i \(-0.170726\pi\)
0.859579 + 0.511003i \(0.170726\pi\)
\(174\) −3.20530 −0.242993
\(175\) −7.78483 −0.588478
\(176\) 0.878525 0.0662213
\(177\) −5.26374 −0.395647
\(178\) 0.944202 0.0707709
\(179\) −1.85040 −0.138306 −0.0691528 0.997606i \(-0.522030\pi\)
−0.0691528 + 0.997606i \(0.522030\pi\)
\(180\) −1.79844 −0.134048
\(181\) 17.8420 1.32619 0.663093 0.748537i \(-0.269243\pi\)
0.663093 + 0.748537i \(0.269243\pi\)
\(182\) −3.75366 −0.278240
\(183\) 3.60972 0.266838
\(184\) −0.250785 −0.0184881
\(185\) 2.66234 0.195739
\(186\) −2.38217 −0.174669
\(187\) −2.85092 −0.208480
\(188\) −8.45380 −0.616557
\(189\) −4.52870 −0.329414
\(190\) 0.645126 0.0468024
\(191\) −17.5088 −1.26689 −0.633445 0.773788i \(-0.718360\pi\)
−0.633445 + 0.773788i \(0.718360\pi\)
\(192\) 0.460726 0.0332500
\(193\) 18.8884 1.35961 0.679807 0.733391i \(-0.262064\pi\)
0.679807 + 0.733391i \(0.262064\pi\)
\(194\) −8.08209 −0.580260
\(195\) −0.656931 −0.0470438
\(196\) −4.11567 −0.293977
\(197\) 16.3478 1.16474 0.582368 0.812926i \(-0.302126\pi\)
0.582368 + 0.812926i \(0.302126\pi\)
\(198\) −2.44909 −0.174049
\(199\) 6.35334 0.450377 0.225188 0.974315i \(-0.427700\pi\)
0.225188 + 0.974315i \(0.427700\pi\)
\(200\) −4.58381 −0.324124
\(201\) −1.89900 −0.133945
\(202\) 0.959342 0.0674990
\(203\) −11.8154 −0.829277
\(204\) −1.49511 −0.104679
\(205\) −2.90985 −0.203233
\(206\) −3.43349 −0.239223
\(207\) 0.699122 0.0485923
\(208\) −2.21021 −0.153250
\(209\) 0.878525 0.0607689
\(210\) 0.504789 0.0348337
\(211\) −1.00000 −0.0688428
\(212\) 1.10404 0.0758260
\(213\) −2.83385 −0.194172
\(214\) 6.03026 0.412220
\(215\) 0.556969 0.0379850
\(216\) −2.66656 −0.181436
\(217\) −8.78118 −0.596105
\(218\) −6.44518 −0.436523
\(219\) −0.00952234 −0.000643460 0
\(220\) 0.566760 0.0382109
\(221\) 7.17237 0.482466
\(222\) 1.90135 0.127610
\(223\) −0.300471 −0.0201211 −0.0100605 0.999949i \(-0.503202\pi\)
−0.0100605 + 0.999949i \(0.503202\pi\)
\(224\) 1.69833 0.113474
\(225\) 12.7784 0.851896
\(226\) 16.3812 1.08966
\(227\) 24.1346 1.60187 0.800934 0.598753i \(-0.204337\pi\)
0.800934 + 0.598753i \(0.204337\pi\)
\(228\) 0.460726 0.0305123
\(229\) 18.5855 1.22816 0.614082 0.789242i \(-0.289527\pi\)
0.614082 + 0.789242i \(0.289527\pi\)
\(230\) −0.161788 −0.0106680
\(231\) 0.687415 0.0452286
\(232\) −6.95706 −0.456753
\(233\) −20.7966 −1.36243 −0.681215 0.732084i \(-0.738548\pi\)
−0.681215 + 0.732084i \(0.738548\pi\)
\(234\) 6.16146 0.402787
\(235\) −5.45377 −0.355764
\(236\) −11.4249 −0.743696
\(237\) 1.71997 0.111724
\(238\) −5.51128 −0.357243
\(239\) −8.68185 −0.561582 −0.280791 0.959769i \(-0.590597\pi\)
−0.280791 + 0.959769i \(0.590597\pi\)
\(240\) 0.297226 0.0191859
\(241\) −5.50361 −0.354519 −0.177259 0.984164i \(-0.556723\pi\)
−0.177259 + 0.984164i \(0.556723\pi\)
\(242\) −10.2282 −0.657493
\(243\) 11.2868 0.724048
\(244\) 7.83485 0.501575
\(245\) −2.65513 −0.169630
\(246\) −2.07811 −0.132496
\(247\) −2.21021 −0.140632
\(248\) −5.17048 −0.328326
\(249\) 5.64512 0.357745
\(250\) −6.18277 −0.391033
\(251\) −13.7081 −0.865249 −0.432624 0.901574i \(-0.642412\pi\)
−0.432624 + 0.901574i \(0.642412\pi\)
\(252\) −4.73449 −0.298245
\(253\) −0.220321 −0.0138515
\(254\) −8.38429 −0.526077
\(255\) −0.964534 −0.0604015
\(256\) 1.00000 0.0625000
\(257\) −16.3600 −1.02051 −0.510255 0.860023i \(-0.670449\pi\)
−0.510255 + 0.860023i \(0.670449\pi\)
\(258\) 0.397768 0.0247639
\(259\) 7.00875 0.435503
\(260\) −1.42586 −0.0884282
\(261\) 19.3944 1.20048
\(262\) 11.5878 0.715895
\(263\) −15.2573 −0.940807 −0.470404 0.882451i \(-0.655892\pi\)
−0.470404 + 0.882451i \(0.655892\pi\)
\(264\) 0.404759 0.0249112
\(265\) 0.712247 0.0437530
\(266\) 1.69833 0.104131
\(267\) 0.435018 0.0266227
\(268\) −4.12175 −0.251776
\(269\) 2.66337 0.162388 0.0811942 0.996698i \(-0.474127\pi\)
0.0811942 + 0.996698i \(0.474127\pi\)
\(270\) −1.72027 −0.104692
\(271\) −11.1873 −0.679578 −0.339789 0.940502i \(-0.610356\pi\)
−0.339789 + 0.940502i \(0.610356\pi\)
\(272\) −3.24512 −0.196764
\(273\) −1.72941 −0.104669
\(274\) 17.7090 1.06984
\(275\) −4.02699 −0.242837
\(276\) −0.115543 −0.00695489
\(277\) 13.7972 0.828994 0.414497 0.910051i \(-0.363958\pi\)
0.414497 + 0.910051i \(0.363958\pi\)
\(278\) −13.7301 −0.823477
\(279\) 14.4139 0.862938
\(280\) 1.09564 0.0654769
\(281\) −20.6065 −1.22928 −0.614641 0.788807i \(-0.710699\pi\)
−0.614641 + 0.788807i \(0.710699\pi\)
\(282\) −3.89489 −0.231937
\(283\) −15.6785 −0.931989 −0.465995 0.884788i \(-0.654303\pi\)
−0.465995 + 0.884788i \(0.654303\pi\)
\(284\) −6.15084 −0.364985
\(285\) 0.297226 0.0176062
\(286\) −1.94172 −0.114816
\(287\) −7.66035 −0.452176
\(288\) −2.78773 −0.164269
\(289\) −6.46922 −0.380542
\(290\) −4.48818 −0.263555
\(291\) −3.72363 −0.218283
\(292\) −0.0206681 −0.00120951
\(293\) 15.5027 0.905677 0.452839 0.891592i \(-0.350411\pi\)
0.452839 + 0.891592i \(0.350411\pi\)
\(294\) −1.89620 −0.110589
\(295\) −7.37048 −0.429126
\(296\) 4.12685 0.239868
\(297\) −2.34264 −0.135934
\(298\) −11.9151 −0.690223
\(299\) 0.554287 0.0320552
\(300\) −2.11188 −0.121930
\(301\) 1.46625 0.0845134
\(302\) 4.00395 0.230402
\(303\) 0.441994 0.0253919
\(304\) 1.00000 0.0573539
\(305\) 5.05446 0.289418
\(306\) 9.04651 0.517155
\(307\) 1.42294 0.0812113 0.0406056 0.999175i \(-0.487071\pi\)
0.0406056 + 0.999175i \(0.487071\pi\)
\(308\) 1.49203 0.0850161
\(309\) −1.58190 −0.0899910
\(310\) −3.33561 −0.189450
\(311\) 1.66714 0.0945350 0.0472675 0.998882i \(-0.484949\pi\)
0.0472675 + 0.998882i \(0.484949\pi\)
\(312\) −1.01830 −0.0576498
\(313\) 29.0193 1.64027 0.820134 0.572172i \(-0.193899\pi\)
0.820134 + 0.572172i \(0.193899\pi\)
\(314\) −21.5010 −1.21337
\(315\) −3.05434 −0.172093
\(316\) 3.73317 0.210007
\(317\) −20.7912 −1.16775 −0.583876 0.811843i \(-0.698464\pi\)
−0.583876 + 0.811843i \(0.698464\pi\)
\(318\) 0.508661 0.0285243
\(319\) −6.11195 −0.342203
\(320\) 0.645126 0.0360636
\(321\) 2.77830 0.155069
\(322\) −0.425916 −0.0237354
\(323\) −3.24512 −0.180563
\(324\) 7.13464 0.396369
\(325\) 10.1312 0.561976
\(326\) −17.7351 −0.982256
\(327\) −2.96946 −0.164212
\(328\) −4.51052 −0.249052
\(329\) −14.3573 −0.791546
\(330\) 0.261121 0.0143742
\(331\) 1.45503 0.0799757 0.0399878 0.999200i \(-0.487268\pi\)
0.0399878 + 0.999200i \(0.487268\pi\)
\(332\) 12.2527 0.672453
\(333\) −11.5045 −0.630445
\(334\) 9.68545 0.529964
\(335\) −2.65905 −0.145279
\(336\) 0.782465 0.0426870
\(337\) −21.9574 −1.19610 −0.598048 0.801461i \(-0.704057\pi\)
−0.598048 + 0.801461i \(0.704057\pi\)
\(338\) −8.11499 −0.441397
\(339\) 7.54724 0.409910
\(340\) −2.09351 −0.113536
\(341\) −4.54239 −0.245984
\(342\) −2.78773 −0.150743
\(343\) −18.8781 −1.01932
\(344\) 0.863349 0.0465487
\(345\) −0.0745400 −0.00401310
\(346\) 22.6120 1.21563
\(347\) −16.7802 −0.900809 −0.450404 0.892825i \(-0.648720\pi\)
−0.450404 + 0.892825i \(0.648720\pi\)
\(348\) −3.20530 −0.171822
\(349\) 31.6741 1.69548 0.847738 0.530415i \(-0.177964\pi\)
0.847738 + 0.530415i \(0.177964\pi\)
\(350\) −7.78483 −0.416117
\(351\) 5.89364 0.314579
\(352\) 0.878525 0.0468255
\(353\) 8.97346 0.477609 0.238804 0.971068i \(-0.423245\pi\)
0.238804 + 0.971068i \(0.423245\pi\)
\(354\) −5.26374 −0.279764
\(355\) −3.96807 −0.210603
\(356\) 0.944202 0.0500426
\(357\) −2.53919 −0.134388
\(358\) −1.85040 −0.0977968
\(359\) −11.1130 −0.586524 −0.293262 0.956032i \(-0.594741\pi\)
−0.293262 + 0.956032i \(0.594741\pi\)
\(360\) −1.79844 −0.0947860
\(361\) 1.00000 0.0526316
\(362\) 17.8420 0.937755
\(363\) −4.71240 −0.247337
\(364\) −3.75366 −0.196745
\(365\) −0.0133335 −0.000697909 0
\(366\) 3.60972 0.188683
\(367\) 22.3538 1.16686 0.583429 0.812164i \(-0.301711\pi\)
0.583429 + 0.812164i \(0.301711\pi\)
\(368\) −0.250785 −0.0130731
\(369\) 12.5741 0.654582
\(370\) 2.66234 0.138408
\(371\) 1.87503 0.0973467
\(372\) −2.38217 −0.123510
\(373\) −0.703120 −0.0364062 −0.0182031 0.999834i \(-0.505795\pi\)
−0.0182031 + 0.999834i \(0.505795\pi\)
\(374\) −2.85092 −0.147417
\(375\) −2.84856 −0.147099
\(376\) −8.45380 −0.435971
\(377\) 15.3765 0.791931
\(378\) −4.52870 −0.232931
\(379\) 4.45597 0.228888 0.114444 0.993430i \(-0.463491\pi\)
0.114444 + 0.993430i \(0.463491\pi\)
\(380\) 0.645126 0.0330943
\(381\) −3.86286 −0.197900
\(382\) −17.5088 −0.895827
\(383\) 15.3346 0.783560 0.391780 0.920059i \(-0.371859\pi\)
0.391780 + 0.920059i \(0.371859\pi\)
\(384\) 0.460726 0.0235113
\(385\) 0.962545 0.0490558
\(386\) 18.8884 0.961392
\(387\) −2.40679 −0.122344
\(388\) −8.08209 −0.410306
\(389\) 0.666043 0.0337697 0.0168849 0.999857i \(-0.494625\pi\)
0.0168849 + 0.999857i \(0.494625\pi\)
\(390\) −0.656931 −0.0332650
\(391\) 0.813827 0.0411570
\(392\) −4.11567 −0.207873
\(393\) 5.33879 0.269306
\(394\) 16.3478 0.823592
\(395\) 2.40837 0.121178
\(396\) −2.44909 −0.123072
\(397\) −27.5420 −1.38230 −0.691148 0.722714i \(-0.742895\pi\)
−0.691148 + 0.722714i \(0.742895\pi\)
\(398\) 6.35334 0.318464
\(399\) 0.782465 0.0391722
\(400\) −4.58381 −0.229191
\(401\) 25.4611 1.27146 0.635732 0.771910i \(-0.280698\pi\)
0.635732 + 0.771910i \(0.280698\pi\)
\(402\) −1.89900 −0.0947134
\(403\) 11.4278 0.569260
\(404\) 0.959342 0.0477290
\(405\) 4.60274 0.228712
\(406\) −11.8154 −0.586388
\(407\) 3.62554 0.179711
\(408\) −1.49511 −0.0740190
\(409\) −12.7346 −0.629685 −0.314842 0.949144i \(-0.601952\pi\)
−0.314842 + 0.949144i \(0.601952\pi\)
\(410\) −2.90985 −0.143707
\(411\) 8.15902 0.402455
\(412\) −3.43349 −0.169156
\(413\) −19.4032 −0.954770
\(414\) 0.699122 0.0343600
\(415\) 7.90452 0.388017
\(416\) −2.21021 −0.108364
\(417\) −6.32582 −0.309777
\(418\) 0.878525 0.0429701
\(419\) 35.7455 1.74628 0.873141 0.487469i \(-0.162080\pi\)
0.873141 + 0.487469i \(0.162080\pi\)
\(420\) 0.504789 0.0246312
\(421\) 9.41270 0.458747 0.229374 0.973338i \(-0.426332\pi\)
0.229374 + 0.973338i \(0.426332\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 23.5669 1.14586
\(424\) 1.10404 0.0536171
\(425\) 14.8750 0.721544
\(426\) −2.83385 −0.137301
\(427\) 13.3062 0.643930
\(428\) 6.03026 0.291483
\(429\) −0.894601 −0.0431918
\(430\) 0.556969 0.0268594
\(431\) −26.0702 −1.25576 −0.627880 0.778310i \(-0.716077\pi\)
−0.627880 + 0.778310i \(0.716077\pi\)
\(432\) −2.66656 −0.128295
\(433\) 16.2636 0.781578 0.390789 0.920480i \(-0.372202\pi\)
0.390789 + 0.920480i \(0.372202\pi\)
\(434\) −8.78118 −0.421510
\(435\) −2.06782 −0.0991444
\(436\) −6.44518 −0.308668
\(437\) −0.250785 −0.0119967
\(438\) −0.00952234 −0.000454995 0
\(439\) −31.8460 −1.51993 −0.759964 0.649965i \(-0.774783\pi\)
−0.759964 + 0.649965i \(0.774783\pi\)
\(440\) 0.566760 0.0270192
\(441\) 11.4734 0.546352
\(442\) 7.17237 0.341155
\(443\) 33.2149 1.57809 0.789044 0.614337i \(-0.210576\pi\)
0.789044 + 0.614337i \(0.210576\pi\)
\(444\) 1.90135 0.0902339
\(445\) 0.609129 0.0288755
\(446\) −0.300471 −0.0142277
\(447\) −5.48960 −0.259649
\(448\) 1.69833 0.0802386
\(449\) 31.3215 1.47815 0.739077 0.673621i \(-0.235262\pi\)
0.739077 + 0.673621i \(0.235262\pi\)
\(450\) 12.7784 0.602381
\(451\) −3.96260 −0.186592
\(452\) 16.3812 0.770506
\(453\) 1.84472 0.0866727
\(454\) 24.1346 1.13269
\(455\) −2.42158 −0.113526
\(456\) 0.460726 0.0215755
\(457\) −36.4027 −1.70285 −0.851424 0.524479i \(-0.824260\pi\)
−0.851424 + 0.524479i \(0.824260\pi\)
\(458\) 18.5855 0.868443
\(459\) 8.65329 0.403901
\(460\) −0.161788 −0.00754341
\(461\) −20.5792 −0.958467 −0.479234 0.877687i \(-0.659085\pi\)
−0.479234 + 0.877687i \(0.659085\pi\)
\(462\) 0.687415 0.0319815
\(463\) 10.6034 0.492782 0.246391 0.969170i \(-0.420755\pi\)
0.246391 + 0.969170i \(0.420755\pi\)
\(464\) −6.95706 −0.322973
\(465\) −1.53680 −0.0712675
\(466\) −20.7966 −0.963383
\(467\) −2.51857 −0.116545 −0.0582727 0.998301i \(-0.518559\pi\)
−0.0582727 + 0.998301i \(0.518559\pi\)
\(468\) 6.16146 0.284814
\(469\) −7.00010 −0.323234
\(470\) −5.45377 −0.251563
\(471\) −9.90606 −0.456447
\(472\) −11.4249 −0.525872
\(473\) 0.758474 0.0348747
\(474\) 1.71997 0.0790008
\(475\) −4.58381 −0.210320
\(476\) −5.51128 −0.252609
\(477\) −3.07777 −0.140922
\(478\) −8.68185 −0.397099
\(479\) −28.5571 −1.30481 −0.652405 0.757871i \(-0.726240\pi\)
−0.652405 + 0.757871i \(0.726240\pi\)
\(480\) 0.297226 0.0135665
\(481\) −9.12118 −0.415890
\(482\) −5.50361 −0.250683
\(483\) −0.196231 −0.00892880
\(484\) −10.2282 −0.464918
\(485\) −5.21397 −0.236754
\(486\) 11.2868 0.511979
\(487\) 11.9271 0.540469 0.270235 0.962795i \(-0.412899\pi\)
0.270235 + 0.962795i \(0.412899\pi\)
\(488\) 7.83485 0.354667
\(489\) −8.17102 −0.369506
\(490\) −2.65513 −0.119946
\(491\) −26.7750 −1.20834 −0.604170 0.796856i \(-0.706495\pi\)
−0.604170 + 0.796856i \(0.706495\pi\)
\(492\) −2.07811 −0.0936886
\(493\) 22.5765 1.01679
\(494\) −2.21021 −0.0994418
\(495\) −1.57997 −0.0710145
\(496\) −5.17048 −0.232161
\(497\) −10.4462 −0.468575
\(498\) 5.64512 0.252964
\(499\) 34.3714 1.53868 0.769339 0.638841i \(-0.220586\pi\)
0.769339 + 0.638841i \(0.220586\pi\)
\(500\) −6.18277 −0.276502
\(501\) 4.46234 0.199363
\(502\) −13.7081 −0.611823
\(503\) −24.1789 −1.07809 −0.539043 0.842278i \(-0.681214\pi\)
−0.539043 + 0.842278i \(0.681214\pi\)
\(504\) −4.73449 −0.210891
\(505\) 0.618896 0.0275405
\(506\) −0.220321 −0.00979447
\(507\) −3.73879 −0.166045
\(508\) −8.38429 −0.371993
\(509\) 4.62230 0.204880 0.102440 0.994739i \(-0.467335\pi\)
0.102440 + 0.994739i \(0.467335\pi\)
\(510\) −0.964534 −0.0427103
\(511\) −0.0351013 −0.00155279
\(512\) 1.00000 0.0441942
\(513\) −2.66656 −0.117731
\(514\) −16.3600 −0.721610
\(515\) −2.21503 −0.0976061
\(516\) 0.397768 0.0175107
\(517\) −7.42687 −0.326634
\(518\) 7.00875 0.307947
\(519\) 10.4179 0.457297
\(520\) −1.42586 −0.0625281
\(521\) −21.2661 −0.931685 −0.465842 0.884868i \(-0.654249\pi\)
−0.465842 + 0.884868i \(0.654249\pi\)
\(522\) 19.3944 0.848870
\(523\) −6.44365 −0.281761 −0.140880 0.990027i \(-0.544993\pi\)
−0.140880 + 0.990027i \(0.544993\pi\)
\(524\) 11.5878 0.506215
\(525\) −3.58667 −0.156535
\(526\) −15.2573 −0.665251
\(527\) 16.7788 0.730896
\(528\) 0.404759 0.0176149
\(529\) −22.9371 −0.997266
\(530\) 0.712247 0.0309380
\(531\) 31.8495 1.38215
\(532\) 1.69833 0.0736320
\(533\) 9.96917 0.431813
\(534\) 0.435018 0.0188251
\(535\) 3.89028 0.168191
\(536\) −4.12175 −0.178033
\(537\) −0.852528 −0.0367893
\(538\) 2.66337 0.114826
\(539\) −3.61572 −0.155740
\(540\) −1.72027 −0.0740285
\(541\) −1.05796 −0.0454854 −0.0227427 0.999741i \(-0.507240\pi\)
−0.0227427 + 0.999741i \(0.507240\pi\)
\(542\) −11.1873 −0.480534
\(543\) 8.22028 0.352766
\(544\) −3.24512 −0.139133
\(545\) −4.15796 −0.178107
\(546\) −1.72941 −0.0740118
\(547\) 16.0363 0.685661 0.342830 0.939397i \(-0.388614\pi\)
0.342830 + 0.939397i \(0.388614\pi\)
\(548\) 17.7090 0.756493
\(549\) −21.8414 −0.932170
\(550\) −4.02699 −0.171712
\(551\) −6.95706 −0.296381
\(552\) −0.115543 −0.00491785
\(553\) 6.34016 0.269611
\(554\) 13.7972 0.586187
\(555\) 1.22661 0.0520666
\(556\) −13.7301 −0.582286
\(557\) 2.07876 0.0880798 0.0440399 0.999030i \(-0.485977\pi\)
0.0440399 + 0.999030i \(0.485977\pi\)
\(558\) 14.4139 0.610189
\(559\) −1.90818 −0.0807074
\(560\) 1.09564 0.0462991
\(561\) −1.31349 −0.0554556
\(562\) −20.6065 −0.869234
\(563\) −10.9676 −0.462231 −0.231116 0.972926i \(-0.574238\pi\)
−0.231116 + 0.972926i \(0.574238\pi\)
\(564\) −3.89489 −0.164004
\(565\) 10.5679 0.444596
\(566\) −15.6785 −0.659016
\(567\) 12.1170 0.508865
\(568\) −6.15084 −0.258084
\(569\) 0.865205 0.0362713 0.0181356 0.999836i \(-0.494227\pi\)
0.0181356 + 0.999836i \(0.494227\pi\)
\(570\) 0.297226 0.0124494
\(571\) 24.5838 1.02880 0.514400 0.857551i \(-0.328015\pi\)
0.514400 + 0.857551i \(0.328015\pi\)
\(572\) −1.94172 −0.0811874
\(573\) −8.06675 −0.336993
\(574\) −7.66035 −0.319737
\(575\) 1.14955 0.0479396
\(576\) −2.78773 −0.116155
\(577\) 12.1607 0.506257 0.253128 0.967433i \(-0.418541\pi\)
0.253128 + 0.967433i \(0.418541\pi\)
\(578\) −6.46922 −0.269084
\(579\) 8.70236 0.361658
\(580\) −4.48818 −0.186361
\(581\) 20.8091 0.863306
\(582\) −3.72363 −0.154349
\(583\) 0.969929 0.0401704
\(584\) −0.0206681 −0.000855252 0
\(585\) 3.97492 0.164343
\(586\) 15.5027 0.640411
\(587\) 30.0892 1.24191 0.620957 0.783845i \(-0.286744\pi\)
0.620957 + 0.783845i \(0.286744\pi\)
\(588\) −1.89620 −0.0781979
\(589\) −5.17048 −0.213046
\(590\) −7.37048 −0.303438
\(591\) 7.53187 0.309820
\(592\) 4.12685 0.169612
\(593\) −30.8823 −1.26819 −0.634093 0.773257i \(-0.718626\pi\)
−0.634093 + 0.773257i \(0.718626\pi\)
\(594\) −2.34264 −0.0961196
\(595\) −3.55547 −0.145760
\(596\) −11.9151 −0.488061
\(597\) 2.92715 0.119800
\(598\) 0.554287 0.0226665
\(599\) −28.0460 −1.14593 −0.572964 0.819581i \(-0.694206\pi\)
−0.572964 + 0.819581i \(0.694206\pi\)
\(600\) −2.11188 −0.0862172
\(601\) −22.7623 −0.928493 −0.464246 0.885706i \(-0.653675\pi\)
−0.464246 + 0.885706i \(0.653675\pi\)
\(602\) 1.46625 0.0597600
\(603\) 11.4903 0.467923
\(604\) 4.00395 0.162918
\(605\) −6.59847 −0.268266
\(606\) 0.441994 0.0179548
\(607\) −46.9739 −1.90661 −0.953306 0.302005i \(-0.902344\pi\)
−0.953306 + 0.302005i \(0.902344\pi\)
\(608\) 1.00000 0.0405554
\(609\) −5.44365 −0.220588
\(610\) 5.05446 0.204649
\(611\) 18.6846 0.755899
\(612\) 9.04651 0.365684
\(613\) −48.8112 −1.97147 −0.985733 0.168315i \(-0.946168\pi\)
−0.985733 + 0.168315i \(0.946168\pi\)
\(614\) 1.42294 0.0574250
\(615\) −1.34064 −0.0540600
\(616\) 1.49203 0.0601154
\(617\) 22.6779 0.912978 0.456489 0.889729i \(-0.349107\pi\)
0.456489 + 0.889729i \(0.349107\pi\)
\(618\) −1.58190 −0.0636333
\(619\) 20.5635 0.826518 0.413259 0.910614i \(-0.364391\pi\)
0.413259 + 0.910614i \(0.364391\pi\)
\(620\) −3.33561 −0.133961
\(621\) 0.668733 0.0268354
\(622\) 1.66714 0.0668463
\(623\) 1.60357 0.0642455
\(624\) −1.01830 −0.0407646
\(625\) 18.9304 0.757216
\(626\) 29.0193 1.15984
\(627\) 0.404759 0.0161645
\(628\) −21.5010 −0.857983
\(629\) −13.3921 −0.533978
\(630\) −3.05434 −0.121688
\(631\) 19.1828 0.763655 0.381827 0.924234i \(-0.375295\pi\)
0.381827 + 0.924234i \(0.375295\pi\)
\(632\) 3.73317 0.148498
\(633\) −0.460726 −0.0183122
\(634\) −20.7912 −0.825725
\(635\) −5.40892 −0.214647
\(636\) 0.508661 0.0201697
\(637\) 9.09648 0.360416
\(638\) −6.11195 −0.241974
\(639\) 17.1469 0.678321
\(640\) 0.645126 0.0255008
\(641\) 11.3206 0.447136 0.223568 0.974688i \(-0.428230\pi\)
0.223568 + 0.974688i \(0.428230\pi\)
\(642\) 2.77830 0.109651
\(643\) −6.07447 −0.239554 −0.119777 0.992801i \(-0.538218\pi\)
−0.119777 + 0.992801i \(0.538218\pi\)
\(644\) −0.425916 −0.0167834
\(645\) 0.256610 0.0101040
\(646\) −3.24512 −0.127677
\(647\) −7.00039 −0.275214 −0.137607 0.990487i \(-0.543941\pi\)
−0.137607 + 0.990487i \(0.543941\pi\)
\(648\) 7.13464 0.280275
\(649\) −10.0370 −0.393988
\(650\) 10.1312 0.397377
\(651\) −4.04572 −0.158564
\(652\) −17.7351 −0.694560
\(653\) 13.6085 0.532540 0.266270 0.963898i \(-0.414209\pi\)
0.266270 + 0.963898i \(0.414209\pi\)
\(654\) −2.96946 −0.116115
\(655\) 7.47558 0.292095
\(656\) −4.51052 −0.176106
\(657\) 0.0576171 0.00224786
\(658\) −14.3573 −0.559708
\(659\) 8.07413 0.314523 0.157262 0.987557i \(-0.449733\pi\)
0.157262 + 0.987557i \(0.449733\pi\)
\(660\) 0.261121 0.0101641
\(661\) −14.9075 −0.579836 −0.289918 0.957052i \(-0.593628\pi\)
−0.289918 + 0.957052i \(0.593628\pi\)
\(662\) 1.45503 0.0565513
\(663\) 3.30450 0.128336
\(664\) 12.2527 0.475496
\(665\) 1.09564 0.0424870
\(666\) −11.5045 −0.445792
\(667\) 1.74473 0.0675561
\(668\) 9.68545 0.374741
\(669\) −0.138435 −0.00535221
\(670\) −2.65905 −0.102728
\(671\) 6.88311 0.265719
\(672\) 0.782465 0.0301842
\(673\) −9.77470 −0.376787 −0.188394 0.982094i \(-0.560328\pi\)
−0.188394 + 0.982094i \(0.560328\pi\)
\(674\) −21.9574 −0.845767
\(675\) 12.2230 0.470464
\(676\) −8.11499 −0.312115
\(677\) −41.7106 −1.60307 −0.801535 0.597948i \(-0.795983\pi\)
−0.801535 + 0.597948i \(0.795983\pi\)
\(678\) 7.54724 0.289850
\(679\) −13.7261 −0.526758
\(680\) −2.09351 −0.0802824
\(681\) 11.1194 0.426097
\(682\) −4.54239 −0.173937
\(683\) 45.3543 1.73543 0.867717 0.497059i \(-0.165587\pi\)
0.867717 + 0.497059i \(0.165587\pi\)
\(684\) −2.78773 −0.106592
\(685\) 11.4246 0.436510
\(686\) −18.8781 −0.720769
\(687\) 8.56282 0.326692
\(688\) 0.863349 0.0329149
\(689\) −2.44016 −0.0929627
\(690\) −0.0745400 −0.00283769
\(691\) −25.0269 −0.952067 −0.476034 0.879427i \(-0.657926\pi\)
−0.476034 + 0.879427i \(0.657926\pi\)
\(692\) 22.6120 0.859579
\(693\) −4.15937 −0.158001
\(694\) −16.7802 −0.636968
\(695\) −8.85765 −0.335990
\(696\) −3.20530 −0.121496
\(697\) 14.6372 0.554422
\(698\) 31.6741 1.19888
\(699\) −9.58153 −0.362407
\(700\) −7.78483 −0.294239
\(701\) 5.83789 0.220494 0.110247 0.993904i \(-0.464836\pi\)
0.110247 + 0.993904i \(0.464836\pi\)
\(702\) 5.89364 0.222441
\(703\) 4.12685 0.155647
\(704\) 0.878525 0.0331107
\(705\) −2.51269 −0.0946335
\(706\) 8.97346 0.337721
\(707\) 1.62928 0.0612753
\(708\) −5.26374 −0.197823
\(709\) −7.39188 −0.277608 −0.138804 0.990320i \(-0.544326\pi\)
−0.138804 + 0.990320i \(0.544326\pi\)
\(710\) −3.96807 −0.148919
\(711\) −10.4071 −0.390296
\(712\) 0.944202 0.0353855
\(713\) 1.29668 0.0485610
\(714\) −2.53919 −0.0950268
\(715\) −1.25265 −0.0468466
\(716\) −1.85040 −0.0691528
\(717\) −3.99996 −0.149381
\(718\) −11.1130 −0.414735
\(719\) −37.4008 −1.39482 −0.697408 0.716675i \(-0.745663\pi\)
−0.697408 + 0.716675i \(0.745663\pi\)
\(720\) −1.79844 −0.0670238
\(721\) −5.83120 −0.217165
\(722\) 1.00000 0.0372161
\(723\) −2.53566 −0.0943021
\(724\) 17.8420 0.663093
\(725\) 31.8898 1.18436
\(726\) −4.71240 −0.174893
\(727\) 3.91838 0.145325 0.0726623 0.997357i \(-0.476850\pi\)
0.0726623 + 0.997357i \(0.476850\pi\)
\(728\) −3.75366 −0.139120
\(729\) −16.2038 −0.600141
\(730\) −0.0133335 −0.000493496 0
\(731\) −2.80167 −0.103623
\(732\) 3.60972 0.133419
\(733\) 20.3180 0.750464 0.375232 0.926931i \(-0.377563\pi\)
0.375232 + 0.926931i \(0.377563\pi\)
\(734\) 22.3538 0.825094
\(735\) −1.22329 −0.0451216
\(736\) −0.250785 −0.00924407
\(737\) −3.62106 −0.133384
\(738\) 12.5741 0.462859
\(739\) −22.6161 −0.831946 −0.415973 0.909377i \(-0.636559\pi\)
−0.415973 + 0.909377i \(0.636559\pi\)
\(740\) 2.66234 0.0978695
\(741\) −1.01830 −0.0374082
\(742\) 1.87503 0.0688345
\(743\) 41.6489 1.52795 0.763975 0.645246i \(-0.223245\pi\)
0.763975 + 0.645246i \(0.223245\pi\)
\(744\) −2.38217 −0.0873347
\(745\) −7.68674 −0.281620
\(746\) −0.703120 −0.0257431
\(747\) −34.1571 −1.24974
\(748\) −2.85092 −0.104240
\(749\) 10.2414 0.374212
\(750\) −2.84856 −0.104015
\(751\) −3.07181 −0.112092 −0.0560460 0.998428i \(-0.517849\pi\)
−0.0560460 + 0.998428i \(0.517849\pi\)
\(752\) −8.45380 −0.308278
\(753\) −6.31569 −0.230156
\(754\) 15.3765 0.559980
\(755\) 2.58305 0.0940069
\(756\) −4.52870 −0.164707
\(757\) 11.4073 0.414605 0.207303 0.978277i \(-0.433532\pi\)
0.207303 + 0.978277i \(0.433532\pi\)
\(758\) 4.45597 0.161848
\(759\) −0.101508 −0.00368450
\(760\) 0.645126 0.0234012
\(761\) −3.48416 −0.126301 −0.0631503 0.998004i \(-0.520115\pi\)
−0.0631503 + 0.998004i \(0.520115\pi\)
\(762\) −3.86286 −0.139937
\(763\) −10.9461 −0.396274
\(764\) −17.5088 −0.633445
\(765\) 5.83614 0.211006
\(766\) 15.3346 0.554061
\(767\) 25.2513 0.911772
\(768\) 0.460726 0.0166250
\(769\) −18.2702 −0.658839 −0.329419 0.944184i \(-0.606853\pi\)
−0.329419 + 0.944184i \(0.606853\pi\)
\(770\) 0.962545 0.0346877
\(771\) −7.53749 −0.271456
\(772\) 18.8884 0.679807
\(773\) −12.8306 −0.461484 −0.230742 0.973015i \(-0.574115\pi\)
−0.230742 + 0.973015i \(0.574115\pi\)
\(774\) −2.40679 −0.0865102
\(775\) 23.7005 0.851347
\(776\) −8.08209 −0.290130
\(777\) 3.22911 0.115844
\(778\) 0.666043 0.0238788
\(779\) −4.51052 −0.161606
\(780\) −0.656931 −0.0235219
\(781\) −5.40367 −0.193359
\(782\) 0.813827 0.0291024
\(783\) 18.5514 0.662973
\(784\) −4.11567 −0.146988
\(785\) −13.8708 −0.495072
\(786\) 5.33879 0.190428
\(787\) 15.2580 0.543888 0.271944 0.962313i \(-0.412333\pi\)
0.271944 + 0.962313i \(0.412333\pi\)
\(788\) 16.3478 0.582368
\(789\) −7.02945 −0.250255
\(790\) 2.40837 0.0856858
\(791\) 27.8207 0.989189
\(792\) −2.44909 −0.0870247
\(793\) −17.3166 −0.614931
\(794\) −27.5420 −0.977430
\(795\) 0.328151 0.0116383
\(796\) 6.35334 0.225188
\(797\) −35.9817 −1.27454 −0.637269 0.770641i \(-0.719936\pi\)
−0.637269 + 0.770641i \(0.719936\pi\)
\(798\) 0.782465 0.0276990
\(799\) 27.4336 0.970530
\(800\) −4.58381 −0.162062
\(801\) −2.63218 −0.0930035
\(802\) 25.4611 0.899061
\(803\) −0.0181575 −0.000640763 0
\(804\) −1.89900 −0.0669725
\(805\) −0.274770 −0.00968436
\(806\) 11.4278 0.402528
\(807\) 1.22708 0.0431954
\(808\) 0.959342 0.0337495
\(809\) 34.3670 1.20828 0.604139 0.796879i \(-0.293517\pi\)
0.604139 + 0.796879i \(0.293517\pi\)
\(810\) 4.60274 0.161724
\(811\) −21.2131 −0.744892 −0.372446 0.928054i \(-0.621481\pi\)
−0.372446 + 0.928054i \(0.621481\pi\)
\(812\) −11.8154 −0.414639
\(813\) −5.15426 −0.180768
\(814\) 3.62554 0.127075
\(815\) −11.4414 −0.400774
\(816\) −1.49511 −0.0523393
\(817\) 0.863349 0.0302048
\(818\) −12.7346 −0.445254
\(819\) 10.4642 0.365649
\(820\) −2.90985 −0.101616
\(821\) −35.5049 −1.23913 −0.619566 0.784945i \(-0.712691\pi\)
−0.619566 + 0.784945i \(0.712691\pi\)
\(822\) 8.15902 0.284578
\(823\) −18.7535 −0.653706 −0.326853 0.945075i \(-0.605988\pi\)
−0.326853 + 0.945075i \(0.605988\pi\)
\(824\) −3.43349 −0.119611
\(825\) −1.85534 −0.0645947
\(826\) −19.4032 −0.675124
\(827\) −21.5994 −0.751086 −0.375543 0.926805i \(-0.622544\pi\)
−0.375543 + 0.926805i \(0.622544\pi\)
\(828\) 0.699122 0.0242962
\(829\) 20.3139 0.705532 0.352766 0.935711i \(-0.385241\pi\)
0.352766 + 0.935711i \(0.385241\pi\)
\(830\) 7.90452 0.274370
\(831\) 6.35673 0.220513
\(832\) −2.21021 −0.0766251
\(833\) 13.3558 0.462752
\(834\) −6.32582 −0.219045
\(835\) 6.24834 0.216233
\(836\) 0.878525 0.0303844
\(837\) 13.7874 0.476561
\(838\) 35.7455 1.23481
\(839\) −18.6544 −0.644022 −0.322011 0.946736i \(-0.604359\pi\)
−0.322011 + 0.946736i \(0.604359\pi\)
\(840\) 0.504789 0.0174169
\(841\) 19.4006 0.668988
\(842\) 9.41270 0.324383
\(843\) −9.49396 −0.326989
\(844\) −1.00000 −0.0344214
\(845\) −5.23519 −0.180096
\(846\) 23.5669 0.810247
\(847\) −17.3709 −0.596870
\(848\) 1.10404 0.0379130
\(849\) −7.22349 −0.247909
\(850\) 14.8750 0.510208
\(851\) −1.03495 −0.0354777
\(852\) −2.83385 −0.0970862
\(853\) 49.2044 1.68473 0.842363 0.538910i \(-0.181164\pi\)
0.842363 + 0.538910i \(0.181164\pi\)
\(854\) 13.3062 0.455327
\(855\) −1.79844 −0.0615053
\(856\) 6.03026 0.206110
\(857\) 15.6583 0.534876 0.267438 0.963575i \(-0.413823\pi\)
0.267438 + 0.963575i \(0.413823\pi\)
\(858\) −0.894601 −0.0305412
\(859\) 12.4783 0.425754 0.212877 0.977079i \(-0.431717\pi\)
0.212877 + 0.977079i \(0.431717\pi\)
\(860\) 0.556969 0.0189925
\(861\) −3.52932 −0.120279
\(862\) −26.0702 −0.887956
\(863\) −13.8419 −0.471183 −0.235591 0.971852i \(-0.575703\pi\)
−0.235591 + 0.971852i \(0.575703\pi\)
\(864\) −2.66656 −0.0907182
\(865\) 14.5876 0.495993
\(866\) 16.2636 0.552659
\(867\) −2.98054 −0.101224
\(868\) −8.78118 −0.298053
\(869\) 3.27968 0.111256
\(870\) −2.06782 −0.0701057
\(871\) 9.10992 0.308678
\(872\) −6.44518 −0.218261
\(873\) 22.5307 0.762549
\(874\) −0.250785 −0.00848294
\(875\) −10.5004 −0.354978
\(876\) −0.00952234 −0.000321730 0
\(877\) 19.5952 0.661683 0.330841 0.943686i \(-0.392667\pi\)
0.330841 + 0.943686i \(0.392667\pi\)
\(878\) −31.8460 −1.07475
\(879\) 7.14250 0.240910
\(880\) 0.566760 0.0191055
\(881\) 5.60531 0.188848 0.0944239 0.995532i \(-0.469899\pi\)
0.0944239 + 0.995532i \(0.469899\pi\)
\(882\) 11.4734 0.386329
\(883\) −12.3954 −0.417139 −0.208570 0.978008i \(-0.566881\pi\)
−0.208570 + 0.978008i \(0.566881\pi\)
\(884\) 7.17237 0.241233
\(885\) −3.39577 −0.114148
\(886\) 33.2149 1.11588
\(887\) 36.5755 1.22808 0.614042 0.789273i \(-0.289542\pi\)
0.614042 + 0.789273i \(0.289542\pi\)
\(888\) 1.90135 0.0638050
\(889\) −14.2393 −0.477571
\(890\) 0.609129 0.0204181
\(891\) 6.26796 0.209985
\(892\) −0.300471 −0.0100605
\(893\) −8.45380 −0.282896
\(894\) −5.48960 −0.183600
\(895\) −1.19374 −0.0399024
\(896\) 1.69833 0.0567372
\(897\) 0.255374 0.00852670
\(898\) 31.3215 1.04521
\(899\) 35.9713 1.19971
\(900\) 12.7784 0.425948
\(901\) −3.58275 −0.119359
\(902\) −3.96260 −0.131940
\(903\) 0.675541 0.0224806
\(904\) 16.3812 0.544830
\(905\) 11.5103 0.382617
\(906\) 1.84472 0.0612869
\(907\) 5.29724 0.175892 0.0879459 0.996125i \(-0.471970\pi\)
0.0879459 + 0.996125i \(0.471970\pi\)
\(908\) 24.1346 0.800934
\(909\) −2.67439 −0.0887038
\(910\) −2.42158 −0.0802747
\(911\) 51.5586 1.70821 0.854106 0.520099i \(-0.174105\pi\)
0.854106 + 0.520099i \(0.174105\pi\)
\(912\) 0.460726 0.0152562
\(913\) 10.7643 0.356246
\(914\) −36.4027 −1.20409
\(915\) 2.32872 0.0769852
\(916\) 18.5855 0.614082
\(917\) 19.6799 0.649887
\(918\) 8.65329 0.285601
\(919\) −10.7944 −0.356074 −0.178037 0.984024i \(-0.556975\pi\)
−0.178037 + 0.984024i \(0.556975\pi\)
\(920\) −0.161788 −0.00533400
\(921\) 0.655584 0.0216022
\(922\) −20.5792 −0.677739
\(923\) 13.5946 0.447473
\(924\) 0.687415 0.0226143
\(925\) −18.9167 −0.621977
\(926\) 10.6034 0.348450
\(927\) 9.57165 0.314374
\(928\) −6.95706 −0.228377
\(929\) 42.5967 1.39755 0.698776 0.715341i \(-0.253728\pi\)
0.698776 + 0.715341i \(0.253728\pi\)
\(930\) −1.53680 −0.0503937
\(931\) −4.11567 −0.134886
\(932\) −20.7966 −0.681215
\(933\) 0.768096 0.0251463
\(934\) −2.51857 −0.0824100
\(935\) −1.83920 −0.0601483
\(936\) 6.16146 0.201394
\(937\) −9.40348 −0.307198 −0.153599 0.988133i \(-0.549086\pi\)
−0.153599 + 0.988133i \(0.549086\pi\)
\(938\) −7.00010 −0.228561
\(939\) 13.3699 0.436312
\(940\) −5.45377 −0.177882
\(941\) −14.8997 −0.485715 −0.242858 0.970062i \(-0.578085\pi\)
−0.242858 + 0.970062i \(0.578085\pi\)
\(942\) −9.90606 −0.322757
\(943\) 1.13117 0.0368360
\(944\) −11.4249 −0.371848
\(945\) −2.92158 −0.0950390
\(946\) 0.758474 0.0246601
\(947\) −34.8195 −1.13148 −0.565741 0.824583i \(-0.691410\pi\)
−0.565741 + 0.824583i \(0.691410\pi\)
\(948\) 1.71997 0.0558620
\(949\) 0.0456808 0.00148286
\(950\) −4.58381 −0.148719
\(951\) −9.57906 −0.310622
\(952\) −5.51128 −0.178622
\(953\) −23.7351 −0.768856 −0.384428 0.923155i \(-0.625601\pi\)
−0.384428 + 0.923155i \(0.625601\pi\)
\(954\) −3.07777 −0.0996466
\(955\) −11.2954 −0.365509
\(956\) −8.68185 −0.280791
\(957\) −2.81593 −0.0910262
\(958\) −28.5571 −0.922640
\(959\) 30.0758 0.971198
\(960\) 0.297226 0.00959294
\(961\) −4.26618 −0.137619
\(962\) −9.12118 −0.294079
\(963\) −16.8107 −0.541718
\(964\) −5.50361 −0.177259
\(965\) 12.1854 0.392261
\(966\) −0.196231 −0.00631362
\(967\) −5.78042 −0.185886 −0.0929429 0.995671i \(-0.529627\pi\)
−0.0929429 + 0.995671i \(0.529627\pi\)
\(968\) −10.2282 −0.328747
\(969\) −1.49511 −0.0480298
\(970\) −5.21397 −0.167410
\(971\) −2.26732 −0.0727617 −0.0363809 0.999338i \(-0.511583\pi\)
−0.0363809 + 0.999338i \(0.511583\pi\)
\(972\) 11.2868 0.362024
\(973\) −23.3183 −0.747549
\(974\) 11.9271 0.382169
\(975\) 4.66769 0.149486
\(976\) 7.83485 0.250787
\(977\) −51.3263 −1.64207 −0.821036 0.570876i \(-0.806604\pi\)
−0.821036 + 0.570876i \(0.806604\pi\)
\(978\) −8.17102 −0.261280
\(979\) 0.829505 0.0265111
\(980\) −2.65513 −0.0848150
\(981\) 17.9674 0.573656
\(982\) −26.7750 −0.854425
\(983\) 47.6101 1.51852 0.759262 0.650785i \(-0.225560\pi\)
0.759262 + 0.650785i \(0.225560\pi\)
\(984\) −2.07811 −0.0662478
\(985\) 10.5464 0.336037
\(986\) 22.5765 0.718981
\(987\) −6.61480 −0.210551
\(988\) −2.21021 −0.0703160
\(989\) −0.216515 −0.00688479
\(990\) −1.57997 −0.0502148
\(991\) 4.39478 0.139605 0.0698024 0.997561i \(-0.477763\pi\)
0.0698024 + 0.997561i \(0.477763\pi\)
\(992\) −5.17048 −0.164163
\(993\) 0.670370 0.0212736
\(994\) −10.4462 −0.331332
\(995\) 4.09871 0.129938
\(996\) 5.64512 0.178873
\(997\) −18.5491 −0.587457 −0.293728 0.955889i \(-0.594896\pi\)
−0.293728 + 0.955889i \(0.594896\pi\)
\(998\) 34.3714 1.08801
\(999\) −11.0045 −0.348166
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 \(a_p\))