Properties

Label 4031.2.a.c.1.17
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.44140 q^{2}\) \(+2.16928 q^{3}\) \(+0.0776255 q^{4}\) \(+0.0237256 q^{5}\) \(-3.12680 q^{6}\) \(+1.29161 q^{7}\) \(+2.77090 q^{8}\) \(+1.70580 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.44140 q^{2}\) \(+2.16928 q^{3}\) \(+0.0776255 q^{4}\) \(+0.0237256 q^{5}\) \(-3.12680 q^{6}\) \(+1.29161 q^{7}\) \(+2.77090 q^{8}\) \(+1.70580 q^{9}\) \(-0.0341981 q^{10}\) \(+2.85722 q^{11}\) \(+0.168392 q^{12}\) \(+3.27002 q^{13}\) \(-1.86173 q^{14}\) \(+0.0514677 q^{15}\) \(-4.14923 q^{16}\) \(-2.63441 q^{17}\) \(-2.45873 q^{18}\) \(-6.32493 q^{19}\) \(+0.00184172 q^{20}\) \(+2.80188 q^{21}\) \(-4.11839 q^{22}\) \(-5.18950 q^{23}\) \(+6.01088 q^{24}\) \(-4.99944 q^{25}\) \(-4.71340 q^{26}\) \(-2.80750 q^{27}\) \(+0.100262 q^{28}\) \(-1.00000 q^{29}\) \(-0.0741854 q^{30}\) \(-5.53067 q^{31}\) \(+0.438871 q^{32}\) \(+6.19813 q^{33}\) \(+3.79722 q^{34}\) \(+0.0306444 q^{35}\) \(+0.132413 q^{36}\) \(+1.80794 q^{37}\) \(+9.11673 q^{38}\) \(+7.09360 q^{39}\) \(+0.0657415 q^{40}\) \(-3.80735 q^{41}\) \(-4.03862 q^{42}\) \(-8.83651 q^{43}\) \(+0.221793 q^{44}\) \(+0.0404711 q^{45}\) \(+7.48013 q^{46}\) \(-12.4492 q^{47}\) \(-9.00085 q^{48}\) \(-5.33173 q^{49}\) \(+7.20617 q^{50}\) \(-5.71477 q^{51}\) \(+0.253837 q^{52}\) \(-4.75313 q^{53}\) \(+4.04672 q^{54}\) \(+0.0677895 q^{55}\) \(+3.57894 q^{56}\) \(-13.7206 q^{57}\) \(+1.44140 q^{58}\) \(-7.95235 q^{59}\) \(+0.00399520 q^{60}\) \(-1.44128 q^{61}\) \(+7.97190 q^{62}\) \(+2.20323 q^{63}\) \(+7.66586 q^{64}\) \(+0.0775833 q^{65}\) \(-8.93397 q^{66}\) \(+8.26135 q^{67}\) \(-0.204497 q^{68}\) \(-11.2575 q^{69}\) \(-0.0441707 q^{70}\) \(-5.47640 q^{71}\) \(+4.72660 q^{72}\) \(+3.62545 q^{73}\) \(-2.60595 q^{74}\) \(-10.8452 q^{75}\) \(-0.490976 q^{76}\) \(+3.69043 q^{77}\) \(-10.2247 q^{78}\) \(+16.7698 q^{79}\) \(-0.0984430 q^{80}\) \(-11.2076 q^{81}\) \(+5.48790 q^{82}\) \(+16.7752 q^{83}\) \(+0.217497 q^{84}\) \(-0.0625030 q^{85}\) \(+12.7369 q^{86}\) \(-2.16928 q^{87}\) \(+7.91709 q^{88}\) \(+9.86238 q^{89}\) \(-0.0583349 q^{90}\) \(+4.22360 q^{91}\) \(-0.402837 q^{92}\) \(-11.9976 q^{93}\) \(+17.9442 q^{94}\) \(-0.150063 q^{95}\) \(+0.952037 q^{96}\) \(-6.95404 q^{97}\) \(+7.68515 q^{98}\) \(+4.87384 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44140 −1.01922 −0.509611 0.860405i \(-0.670211\pi\)
−0.509611 + 0.860405i \(0.670211\pi\)
\(3\) 2.16928 1.25244 0.626219 0.779648i \(-0.284602\pi\)
0.626219 + 0.779648i \(0.284602\pi\)
\(4\) 0.0776255 0.0388128
\(5\) 0.0237256 0.0106104 0.00530522 0.999986i \(-0.498311\pi\)
0.00530522 + 0.999986i \(0.498311\pi\)
\(6\) −3.12680 −1.27651
\(7\) 1.29161 0.488184 0.244092 0.969752i \(-0.421510\pi\)
0.244092 + 0.969752i \(0.421510\pi\)
\(8\) 2.77090 0.979663
\(9\) 1.70580 0.568599
\(10\) −0.0341981 −0.0108144
\(11\) 2.85722 0.861485 0.430743 0.902475i \(-0.358252\pi\)
0.430743 + 0.902475i \(0.358252\pi\)
\(12\) 0.168392 0.0486105
\(13\) 3.27002 0.906940 0.453470 0.891271i \(-0.350186\pi\)
0.453470 + 0.891271i \(0.350186\pi\)
\(14\) −1.86173 −0.497568
\(15\) 0.0514677 0.0132889
\(16\) −4.14923 −1.03731
\(17\) −2.63441 −0.638937 −0.319469 0.947597i \(-0.603504\pi\)
−0.319469 + 0.947597i \(0.603504\pi\)
\(18\) −2.45873 −0.579528
\(19\) −6.32493 −1.45104 −0.725519 0.688202i \(-0.758400\pi\)
−0.725519 + 0.688202i \(0.758400\pi\)
\(20\) 0.00184172 0.000411820 0
\(21\) 2.80188 0.611420
\(22\) −4.11839 −0.878044
\(23\) −5.18950 −1.08209 −0.541043 0.840995i \(-0.681970\pi\)
−0.541043 + 0.840995i \(0.681970\pi\)
\(24\) 6.01088 1.22697
\(25\) −4.99944 −0.999887
\(26\) −4.71340 −0.924373
\(27\) −2.80750 −0.540303
\(28\) 0.100262 0.0189478
\(29\) −1.00000 −0.185695
\(30\) −0.0741854 −0.0135443
\(31\) −5.53067 −0.993338 −0.496669 0.867940i \(-0.665444\pi\)
−0.496669 + 0.867940i \(0.665444\pi\)
\(32\) 0.438871 0.0775822
\(33\) 6.19813 1.07896
\(34\) 3.79722 0.651219
\(35\) 0.0306444 0.00517984
\(36\) 0.132413 0.0220689
\(37\) 1.80794 0.297223 0.148611 0.988896i \(-0.452520\pi\)
0.148611 + 0.988896i \(0.452520\pi\)
\(38\) 9.11673 1.47893
\(39\) 7.09360 1.13589
\(40\) 0.0657415 0.0103946
\(41\) −3.80735 −0.594608 −0.297304 0.954783i \(-0.596087\pi\)
−0.297304 + 0.954783i \(0.596087\pi\)
\(42\) −4.03862 −0.623172
\(43\) −8.83651 −1.34755 −0.673777 0.738934i \(-0.735329\pi\)
−0.673777 + 0.738934i \(0.735329\pi\)
\(44\) 0.221793 0.0334366
\(45\) 0.0404711 0.00603308
\(46\) 7.48013 1.10288
\(47\) −12.4492 −1.81590 −0.907952 0.419075i \(-0.862354\pi\)
−0.907952 + 0.419075i \(0.862354\pi\)
\(48\) −9.00085 −1.29916
\(49\) −5.33173 −0.761676
\(50\) 7.20617 1.01911
\(51\) −5.71477 −0.800229
\(52\) 0.253837 0.0352008
\(53\) −4.75313 −0.652892 −0.326446 0.945216i \(-0.605851\pi\)
−0.326446 + 0.945216i \(0.605851\pi\)
\(54\) 4.04672 0.550689
\(55\) 0.0677895 0.00914073
\(56\) 3.57894 0.478256
\(57\) −13.7206 −1.81733
\(58\) 1.44140 0.189265
\(59\) −7.95235 −1.03531 −0.517654 0.855590i \(-0.673194\pi\)
−0.517654 + 0.855590i \(0.673194\pi\)
\(60\) 0.00399520 0.000515779 0
\(61\) −1.44128 −0.184536 −0.0922682 0.995734i \(-0.529412\pi\)
−0.0922682 + 0.995734i \(0.529412\pi\)
\(62\) 7.97190 1.01243
\(63\) 2.20323 0.277581
\(64\) 7.66586 0.958233
\(65\) 0.0775833 0.00962303
\(66\) −8.93397 −1.09970
\(67\) 8.26135 1.00928 0.504642 0.863329i \(-0.331624\pi\)
0.504642 + 0.863329i \(0.331624\pi\)
\(68\) −0.204497 −0.0247989
\(69\) −11.2575 −1.35524
\(70\) −0.0441707 −0.00527941
\(71\) −5.47640 −0.649929 −0.324964 0.945726i \(-0.605352\pi\)
−0.324964 + 0.945726i \(0.605352\pi\)
\(72\) 4.72660 0.557035
\(73\) 3.62545 0.424327 0.212163 0.977234i \(-0.431949\pi\)
0.212163 + 0.977234i \(0.431949\pi\)
\(74\) −2.60595 −0.302936
\(75\) −10.8452 −1.25230
\(76\) −0.490976 −0.0563188
\(77\) 3.69043 0.420563
\(78\) −10.2247 −1.15772
\(79\) 16.7698 1.88675 0.943374 0.331730i \(-0.107632\pi\)
0.943374 + 0.331730i \(0.107632\pi\)
\(80\) −0.0984430 −0.0110063
\(81\) −11.2076 −1.24529
\(82\) 5.48790 0.606037
\(83\) 16.7752 1.84131 0.920656 0.390374i \(-0.127654\pi\)
0.920656 + 0.390374i \(0.127654\pi\)
\(84\) 0.217497 0.0237309
\(85\) −0.0625030 −0.00677940
\(86\) 12.7369 1.37346
\(87\) −2.16928 −0.232572
\(88\) 7.91709 0.843965
\(89\) 9.86238 1.04541 0.522705 0.852514i \(-0.324923\pi\)
0.522705 + 0.852514i \(0.324923\pi\)
\(90\) −0.0583349 −0.00614904
\(91\) 4.22360 0.442754
\(92\) −0.402837 −0.0419987
\(93\) −11.9976 −1.24409
\(94\) 17.9442 1.85081
\(95\) −0.150063 −0.0153961
\(96\) 0.952037 0.0971668
\(97\) −6.95404 −0.706076 −0.353038 0.935609i \(-0.614851\pi\)
−0.353038 + 0.935609i \(0.614851\pi\)
\(98\) 7.68515 0.776317
\(99\) 4.87384 0.489839
\(100\) −0.388084 −0.0388084
\(101\) −15.7816 −1.57033 −0.785166 0.619285i \(-0.787422\pi\)
−0.785166 + 0.619285i \(0.787422\pi\)
\(102\) 8.23726 0.815610
\(103\) −0.497893 −0.0490589 −0.0245294 0.999699i \(-0.507809\pi\)
−0.0245294 + 0.999699i \(0.507809\pi\)
\(104\) 9.06091 0.888496
\(105\) 0.0664764 0.00648743
\(106\) 6.85114 0.665442
\(107\) −8.37042 −0.809199 −0.404599 0.914494i \(-0.632589\pi\)
−0.404599 + 0.914494i \(0.632589\pi\)
\(108\) −0.217933 −0.0209706
\(109\) −7.74654 −0.741984 −0.370992 0.928636i \(-0.620982\pi\)
−0.370992 + 0.928636i \(0.620982\pi\)
\(110\) −0.0977115 −0.00931643
\(111\) 3.92193 0.372253
\(112\) −5.35920 −0.506396
\(113\) 11.6979 1.10045 0.550223 0.835018i \(-0.314543\pi\)
0.550223 + 0.835018i \(0.314543\pi\)
\(114\) 19.7768 1.85227
\(115\) −0.123124 −0.0114814
\(116\) −0.0776255 −0.00720735
\(117\) 5.57799 0.515685
\(118\) 11.4625 1.05521
\(119\) −3.40263 −0.311919
\(120\) 0.142612 0.0130186
\(121\) −2.83628 −0.257843
\(122\) 2.07745 0.188083
\(123\) −8.25922 −0.744709
\(124\) −0.429321 −0.0385542
\(125\) −0.237243 −0.0212197
\(126\) −3.17573 −0.282916
\(127\) 19.5139 1.73158 0.865790 0.500407i \(-0.166816\pi\)
0.865790 + 0.500407i \(0.166816\pi\)
\(128\) −11.9273 −1.05423
\(129\) −19.1689 −1.68773
\(130\) −0.111828 −0.00980800
\(131\) 21.9921 1.92146 0.960728 0.277492i \(-0.0895031\pi\)
0.960728 + 0.277492i \(0.0895031\pi\)
\(132\) 0.481133 0.0418773
\(133\) −8.16937 −0.708374
\(134\) −11.9079 −1.02868
\(135\) −0.0666097 −0.00573285
\(136\) −7.29969 −0.625943
\(137\) 2.79068 0.238424 0.119212 0.992869i \(-0.461963\pi\)
0.119212 + 0.992869i \(0.461963\pi\)
\(138\) 16.2265 1.38129
\(139\) −1.00000 −0.0848189
\(140\) 0.00237878 0.000201044 0
\(141\) −27.0059 −2.27430
\(142\) 7.89366 0.662422
\(143\) 9.34318 0.781316
\(144\) −7.07773 −0.589811
\(145\) −0.0237256 −0.00197031
\(146\) −5.22572 −0.432483
\(147\) −11.5660 −0.953952
\(148\) 0.140342 0.0115360
\(149\) 16.7366 1.37111 0.685557 0.728019i \(-0.259559\pi\)
0.685557 + 0.728019i \(0.259559\pi\)
\(150\) 15.6322 1.27637
\(151\) −18.4167 −1.49873 −0.749363 0.662159i \(-0.769640\pi\)
−0.749363 + 0.662159i \(0.769640\pi\)
\(152\) −17.5258 −1.42153
\(153\) −4.49376 −0.363299
\(154\) −5.31937 −0.428647
\(155\) −0.131219 −0.0105397
\(156\) 0.550645 0.0440868
\(157\) −3.27599 −0.261452 −0.130726 0.991419i \(-0.541731\pi\)
−0.130726 + 0.991419i \(0.541731\pi\)
\(158\) −24.1719 −1.92302
\(159\) −10.3109 −0.817706
\(160\) 0.0104125 0.000823181 0
\(161\) −6.70283 −0.528257
\(162\) 16.1547 1.26923
\(163\) 7.71572 0.604341 0.302171 0.953254i \(-0.402289\pi\)
0.302171 + 0.953254i \(0.402289\pi\)
\(164\) −0.295547 −0.0230784
\(165\) 0.147055 0.0114482
\(166\) −24.1797 −1.87671
\(167\) −7.06534 −0.546732 −0.273366 0.961910i \(-0.588137\pi\)
−0.273366 + 0.961910i \(0.588137\pi\)
\(168\) 7.76374 0.598985
\(169\) −2.30697 −0.177459
\(170\) 0.0900916 0.00690971
\(171\) −10.7890 −0.825058
\(172\) −0.685938 −0.0523023
\(173\) 5.53623 0.420912 0.210456 0.977603i \(-0.432505\pi\)
0.210456 + 0.977603i \(0.432505\pi\)
\(174\) 3.12680 0.237042
\(175\) −6.45734 −0.488129
\(176\) −11.8553 −0.893624
\(177\) −17.2509 −1.29666
\(178\) −14.2156 −1.06550
\(179\) 8.51694 0.636586 0.318293 0.947992i \(-0.396890\pi\)
0.318293 + 0.947992i \(0.396890\pi\)
\(180\) 0.00314159 0.000234160 0
\(181\) 9.46279 0.703364 0.351682 0.936120i \(-0.385610\pi\)
0.351682 + 0.936120i \(0.385610\pi\)
\(182\) −6.08789 −0.451264
\(183\) −3.12654 −0.231120
\(184\) −14.3796 −1.06008
\(185\) 0.0428944 0.00315366
\(186\) 17.2933 1.26801
\(187\) −7.52708 −0.550435
\(188\) −0.966376 −0.0704802
\(189\) −3.62620 −0.263767
\(190\) 0.216300 0.0156921
\(191\) −1.04842 −0.0758610 −0.0379305 0.999280i \(-0.512077\pi\)
−0.0379305 + 0.999280i \(0.512077\pi\)
\(192\) 16.6294 1.20013
\(193\) −12.1742 −0.876317 −0.438159 0.898898i \(-0.644369\pi\)
−0.438159 + 0.898898i \(0.644369\pi\)
\(194\) 10.0235 0.719648
\(195\) 0.168300 0.0120522
\(196\) −0.413879 −0.0295628
\(197\) −16.0708 −1.14500 −0.572498 0.819906i \(-0.694025\pi\)
−0.572498 + 0.819906i \(0.694025\pi\)
\(198\) −7.02514 −0.499255
\(199\) −8.15113 −0.577818 −0.288909 0.957357i \(-0.593293\pi\)
−0.288909 + 0.957357i \(0.593293\pi\)
\(200\) −13.8530 −0.979553
\(201\) 17.9212 1.26407
\(202\) 22.7476 1.60052
\(203\) −1.29161 −0.0906535
\(204\) −0.443612 −0.0310591
\(205\) −0.0903318 −0.00630905
\(206\) 0.717662 0.0500019
\(207\) −8.85222 −0.615272
\(208\) −13.5680 −0.940775
\(209\) −18.0717 −1.25005
\(210\) −0.0958188 −0.00661213
\(211\) 7.85756 0.540937 0.270469 0.962729i \(-0.412821\pi\)
0.270469 + 0.962729i \(0.412821\pi\)
\(212\) −0.368964 −0.0253405
\(213\) −11.8799 −0.813995
\(214\) 12.0651 0.824753
\(215\) −0.209652 −0.0142981
\(216\) −7.77931 −0.529315
\(217\) −7.14350 −0.484932
\(218\) 11.1658 0.756246
\(219\) 7.86464 0.531443
\(220\) 0.00526219 0.000354777 0
\(221\) −8.61456 −0.579478
\(222\) −5.65305 −0.379408
\(223\) −5.31289 −0.355777 −0.177889 0.984051i \(-0.556927\pi\)
−0.177889 + 0.984051i \(0.556927\pi\)
\(224\) 0.566852 0.0378744
\(225\) −8.52802 −0.568535
\(226\) −16.8613 −1.12160
\(227\) 5.65697 0.375466 0.187733 0.982220i \(-0.439886\pi\)
0.187733 + 0.982220i \(0.439886\pi\)
\(228\) −1.06507 −0.0705357
\(229\) −17.8459 −1.17929 −0.589645 0.807662i \(-0.700732\pi\)
−0.589645 + 0.807662i \(0.700732\pi\)
\(230\) 0.177471 0.0117021
\(231\) 8.00559 0.526729
\(232\) −2.77090 −0.181919
\(233\) 8.17627 0.535646 0.267823 0.963468i \(-0.413696\pi\)
0.267823 + 0.963468i \(0.413696\pi\)
\(234\) −8.04009 −0.525597
\(235\) −0.295365 −0.0192675
\(236\) −0.617305 −0.0401831
\(237\) 36.3784 2.36303
\(238\) 4.90455 0.317915
\(239\) 15.9450 1.03140 0.515699 0.856770i \(-0.327532\pi\)
0.515699 + 0.856770i \(0.327532\pi\)
\(240\) −0.213551 −0.0137847
\(241\) 19.3879 1.24888 0.624441 0.781072i \(-0.285327\pi\)
0.624441 + 0.781072i \(0.285327\pi\)
\(242\) 4.08820 0.262799
\(243\) −15.8901 −1.01935
\(244\) −0.111880 −0.00716236
\(245\) −0.126499 −0.00808171
\(246\) 11.9048 0.759024
\(247\) −20.6826 −1.31600
\(248\) −15.3250 −0.973137
\(249\) 36.3901 2.30613
\(250\) 0.341961 0.0216275
\(251\) 3.92085 0.247482 0.123741 0.992315i \(-0.460511\pi\)
0.123741 + 0.992315i \(0.460511\pi\)
\(252\) 0.171027 0.0107737
\(253\) −14.8276 −0.932200
\(254\) −28.1273 −1.76486
\(255\) −0.135587 −0.00849077
\(256\) 1.86024 0.116265
\(257\) −7.58448 −0.473107 −0.236554 0.971618i \(-0.576018\pi\)
−0.236554 + 0.971618i \(0.576018\pi\)
\(258\) 27.6300 1.72017
\(259\) 2.33515 0.145099
\(260\) 0.00602244 0.000373496 0
\(261\) −1.70580 −0.105586
\(262\) −31.6993 −1.95839
\(263\) 6.86867 0.423540 0.211770 0.977320i \(-0.432077\pi\)
0.211770 + 0.977320i \(0.432077\pi\)
\(264\) 17.1744 1.05701
\(265\) −0.112771 −0.00692747
\(266\) 11.7753 0.721990
\(267\) 21.3943 1.30931
\(268\) 0.641292 0.0391731
\(269\) 15.9476 0.972345 0.486173 0.873863i \(-0.338393\pi\)
0.486173 + 0.873863i \(0.338393\pi\)
\(270\) 0.0960110 0.00584304
\(271\) −9.26938 −0.563075 −0.281537 0.959550i \(-0.590844\pi\)
−0.281537 + 0.959550i \(0.590844\pi\)
\(272\) 10.9307 0.662773
\(273\) 9.16220 0.554521
\(274\) −4.02248 −0.243007
\(275\) −14.2845 −0.861388
\(276\) −0.873869 −0.0526007
\(277\) 0.202309 0.0121555 0.00607777 0.999982i \(-0.498065\pi\)
0.00607777 + 0.999982i \(0.498065\pi\)
\(278\) 1.44140 0.0864493
\(279\) −9.43420 −0.564811
\(280\) 0.0849126 0.00507450
\(281\) 26.8704 1.60296 0.801478 0.598024i \(-0.204047\pi\)
0.801478 + 0.598024i \(0.204047\pi\)
\(282\) 38.9262 2.31802
\(283\) −3.93348 −0.233821 −0.116911 0.993142i \(-0.537299\pi\)
−0.116911 + 0.993142i \(0.537299\pi\)
\(284\) −0.425108 −0.0252255
\(285\) −0.325529 −0.0192827
\(286\) −13.4672 −0.796334
\(287\) −4.91762 −0.290278
\(288\) 0.748625 0.0441131
\(289\) −10.0599 −0.591759
\(290\) 0.0341981 0.00200818
\(291\) −15.0853 −0.884316
\(292\) 0.281428 0.0164693
\(293\) −13.0407 −0.761844 −0.380922 0.924607i \(-0.624393\pi\)
−0.380922 + 0.924607i \(0.624393\pi\)
\(294\) 16.6713 0.972288
\(295\) −0.188675 −0.0109851
\(296\) 5.00962 0.291178
\(297\) −8.02164 −0.465463
\(298\) −24.1241 −1.39747
\(299\) −16.9698 −0.981387
\(300\) −0.841864 −0.0486051
\(301\) −11.4134 −0.657855
\(302\) 26.5457 1.52753
\(303\) −34.2349 −1.96674
\(304\) 26.2436 1.50517
\(305\) −0.0341952 −0.00195801
\(306\) 6.47729 0.370282
\(307\) 4.23978 0.241977 0.120988 0.992654i \(-0.461394\pi\)
0.120988 + 0.992654i \(0.461394\pi\)
\(308\) 0.286471 0.0163232
\(309\) −1.08007 −0.0614432
\(310\) 0.189138 0.0107423
\(311\) 22.6470 1.28420 0.642098 0.766623i \(-0.278064\pi\)
0.642098 + 0.766623i \(0.278064\pi\)
\(312\) 19.6557 1.11278
\(313\) 10.2916 0.581713 0.290856 0.956767i \(-0.406060\pi\)
0.290856 + 0.956767i \(0.406060\pi\)
\(314\) 4.72200 0.266478
\(315\) 0.0522730 0.00294525
\(316\) 1.30176 0.0732299
\(317\) −19.8157 −1.11296 −0.556480 0.830861i \(-0.687849\pi\)
−0.556480 + 0.830861i \(0.687849\pi\)
\(318\) 14.8621 0.833424
\(319\) −2.85722 −0.159974
\(320\) 0.181878 0.0101673
\(321\) −18.1578 −1.01347
\(322\) 9.66144 0.538411
\(323\) 16.6624 0.927122
\(324\) −0.869999 −0.0483333
\(325\) −16.3483 −0.906838
\(326\) −11.1214 −0.615958
\(327\) −16.8044 −0.929288
\(328\) −10.5498 −0.582515
\(329\) −16.0796 −0.886495
\(330\) −0.211964 −0.0116682
\(331\) −27.5993 −1.51700 −0.758498 0.651675i \(-0.774067\pi\)
−0.758498 + 0.651675i \(0.774067\pi\)
\(332\) 1.30218 0.0714664
\(333\) 3.08397 0.169000
\(334\) 10.1840 0.557241
\(335\) 0.196006 0.0107089
\(336\) −11.6256 −0.634230
\(337\) 13.8453 0.754203 0.377101 0.926172i \(-0.376921\pi\)
0.377101 + 0.926172i \(0.376921\pi\)
\(338\) 3.32526 0.180870
\(339\) 25.3761 1.37824
\(340\) −0.00485182 −0.000263127 0
\(341\) −15.8024 −0.855746
\(342\) 15.5513 0.840917
\(343\) −15.9278 −0.860022
\(344\) −24.4851 −1.32015
\(345\) −0.267091 −0.0143797
\(346\) −7.97991 −0.429003
\(347\) 4.21277 0.226153 0.113077 0.993586i \(-0.463929\pi\)
0.113077 + 0.993586i \(0.463929\pi\)
\(348\) −0.168392 −0.00902675
\(349\) 33.4756 1.79191 0.895954 0.444146i \(-0.146493\pi\)
0.895954 + 0.444146i \(0.146493\pi\)
\(350\) 9.30759 0.497512
\(351\) −9.18057 −0.490023
\(352\) 1.25395 0.0668359
\(353\) −14.4749 −0.770419 −0.385210 0.922829i \(-0.625871\pi\)
−0.385210 + 0.922829i \(0.625871\pi\)
\(354\) 24.8654 1.32158
\(355\) −0.129931 −0.00689603
\(356\) 0.765572 0.0405752
\(357\) −7.38128 −0.390659
\(358\) −12.2763 −0.648823
\(359\) 6.42843 0.339280 0.169640 0.985506i \(-0.445740\pi\)
0.169640 + 0.985506i \(0.445740\pi\)
\(360\) 0.112142 0.00591038
\(361\) 21.0047 1.10551
\(362\) −13.6396 −0.716884
\(363\) −6.15269 −0.322932
\(364\) 0.327859 0.0171845
\(365\) 0.0860162 0.00450229
\(366\) 4.50658 0.235563
\(367\) −26.1769 −1.36642 −0.683212 0.730221i \(-0.739417\pi\)
−0.683212 + 0.730221i \(0.739417\pi\)
\(368\) 21.5324 1.12245
\(369\) −6.49456 −0.338093
\(370\) −0.0618279 −0.00321428
\(371\) −6.13920 −0.318732
\(372\) −0.931320 −0.0482867
\(373\) −16.8675 −0.873366 −0.436683 0.899615i \(-0.643847\pi\)
−0.436683 + 0.899615i \(0.643847\pi\)
\(374\) 10.8495 0.561015
\(375\) −0.514648 −0.0265763
\(376\) −34.4956 −1.77897
\(377\) −3.27002 −0.168415
\(378\) 5.22680 0.268837
\(379\) −9.79954 −0.503369 −0.251684 0.967809i \(-0.580984\pi\)
−0.251684 + 0.967809i \(0.580984\pi\)
\(380\) −0.0116487 −0.000597567 0
\(381\) 42.3313 2.16870
\(382\) 1.51119 0.0773192
\(383\) 33.7504 1.72456 0.862282 0.506429i \(-0.169035\pi\)
0.862282 + 0.506429i \(0.169035\pi\)
\(384\) −25.8737 −1.32036
\(385\) 0.0875578 0.00446236
\(386\) 17.5478 0.893161
\(387\) −15.0733 −0.766218
\(388\) −0.539811 −0.0274048
\(389\) 27.7919 1.40911 0.704553 0.709651i \(-0.251147\pi\)
0.704553 + 0.709651i \(0.251147\pi\)
\(390\) −0.242588 −0.0122839
\(391\) 13.6712 0.691384
\(392\) −14.7737 −0.746186
\(393\) 47.7071 2.40650
\(394\) 23.1644 1.16700
\(395\) 0.397874 0.0200192
\(396\) 0.378334 0.0190120
\(397\) 13.4653 0.675802 0.337901 0.941182i \(-0.390283\pi\)
0.337901 + 0.941182i \(0.390283\pi\)
\(398\) 11.7490 0.588925
\(399\) −17.7217 −0.887194
\(400\) 20.7438 1.03719
\(401\) 11.7256 0.585550 0.292775 0.956181i \(-0.405421\pi\)
0.292775 + 0.956181i \(0.405421\pi\)
\(402\) −25.8316 −1.28836
\(403\) −18.0854 −0.900899
\(404\) −1.22506 −0.0609489
\(405\) −0.265909 −0.0132131
\(406\) 1.86173 0.0923960
\(407\) 5.16567 0.256053
\(408\) −15.8351 −0.783954
\(409\) 39.1642 1.93654 0.968272 0.249898i \(-0.0803971\pi\)
0.968272 + 0.249898i \(0.0803971\pi\)
\(410\) 0.130204 0.00643032
\(411\) 6.05378 0.298611
\(412\) −0.0386492 −0.00190411
\(413\) −10.2714 −0.505421
\(414\) 12.7596 0.627099
\(415\) 0.398001 0.0195371
\(416\) 1.43512 0.0703624
\(417\) −2.16928 −0.106230
\(418\) 26.0485 1.27408
\(419\) 14.0821 0.687956 0.343978 0.938978i \(-0.388225\pi\)
0.343978 + 0.938978i \(0.388225\pi\)
\(420\) 0.00516026 0.000251795 0
\(421\) 13.5069 0.658286 0.329143 0.944280i \(-0.393240\pi\)
0.329143 + 0.944280i \(0.393240\pi\)
\(422\) −11.3259 −0.551335
\(423\) −21.2358 −1.03252
\(424\) −13.1705 −0.639614
\(425\) 13.1705 0.638865
\(426\) 17.1236 0.829641
\(427\) −1.86157 −0.0900877
\(428\) −0.649758 −0.0314072
\(429\) 20.2680 0.978549
\(430\) 0.302192 0.0145730
\(431\) −25.7758 −1.24157 −0.620787 0.783979i \(-0.713187\pi\)
−0.620787 + 0.783979i \(0.713187\pi\)
\(432\) 11.6489 0.560460
\(433\) −3.31352 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(434\) 10.2966 0.494253
\(435\) −0.0514677 −0.00246769
\(436\) −0.601329 −0.0287984
\(437\) 32.8232 1.57015
\(438\) −11.3361 −0.541658
\(439\) 13.5199 0.645270 0.322635 0.946523i \(-0.395431\pi\)
0.322635 + 0.946523i \(0.395431\pi\)
\(440\) 0.187838 0.00895483
\(441\) −9.09485 −0.433088
\(442\) 12.4170 0.590616
\(443\) 2.35544 0.111910 0.0559552 0.998433i \(-0.482180\pi\)
0.0559552 + 0.998433i \(0.482180\pi\)
\(444\) 0.304442 0.0144482
\(445\) 0.233991 0.0110922
\(446\) 7.65798 0.362616
\(447\) 36.3064 1.71723
\(448\) 9.90133 0.467794
\(449\) 4.42492 0.208825 0.104413 0.994534i \(-0.466704\pi\)
0.104413 + 0.994534i \(0.466704\pi\)
\(450\) 12.2923 0.579463
\(451\) −10.8784 −0.512246
\(452\) 0.908056 0.0427113
\(453\) −39.9510 −1.87706
\(454\) −8.15394 −0.382683
\(455\) 0.100208 0.00469781
\(456\) −38.0184 −1.78037
\(457\) −37.2863 −1.74418 −0.872089 0.489348i \(-0.837235\pi\)
−0.872089 + 0.489348i \(0.837235\pi\)
\(458\) 25.7230 1.20196
\(459\) 7.39608 0.345220
\(460\) −0.00955758 −0.000445624 0
\(461\) 3.78948 0.176494 0.0882469 0.996099i \(-0.471874\pi\)
0.0882469 + 0.996099i \(0.471874\pi\)
\(462\) −11.5392 −0.536854
\(463\) 5.94468 0.276273 0.138136 0.990413i \(-0.455889\pi\)
0.138136 + 0.990413i \(0.455889\pi\)
\(464\) 4.14923 0.192623
\(465\) −0.284651 −0.0132004
\(466\) −11.7853 −0.545942
\(467\) −15.8081 −0.731510 −0.365755 0.930711i \(-0.619189\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(468\) 0.432994 0.0200152
\(469\) 10.6705 0.492717
\(470\) 0.425739 0.0196379
\(471\) −7.10655 −0.327453
\(472\) −22.0352 −1.01425
\(473\) −25.2479 −1.16090
\(474\) −52.4358 −2.40846
\(475\) 31.6211 1.45087
\(476\) −0.264131 −0.0121064
\(477\) −8.10786 −0.371234
\(478\) −22.9831 −1.05122
\(479\) 15.0571 0.687975 0.343988 0.938974i \(-0.388222\pi\)
0.343988 + 0.938974i \(0.388222\pi\)
\(480\) 0.0225877 0.00103098
\(481\) 5.91198 0.269563
\(482\) −27.9456 −1.27289
\(483\) −14.5403 −0.661608
\(484\) −0.220167 −0.0100076
\(485\) −0.164989 −0.00749177
\(486\) 22.9039 1.03894
\(487\) −16.7173 −0.757532 −0.378766 0.925492i \(-0.623652\pi\)
−0.378766 + 0.925492i \(0.623652\pi\)
\(488\) −3.99364 −0.180783
\(489\) 16.7376 0.756900
\(490\) 0.182335 0.00823706
\(491\) −20.5445 −0.927159 −0.463579 0.886055i \(-0.653435\pi\)
−0.463579 + 0.886055i \(0.653435\pi\)
\(492\) −0.641126 −0.0289042
\(493\) 2.63441 0.118648
\(494\) 29.8119 1.34130
\(495\) 0.115635 0.00519741
\(496\) 22.9480 1.03040
\(497\) −7.07339 −0.317285
\(498\) −52.4526 −2.35046
\(499\) −35.2627 −1.57857 −0.789287 0.614025i \(-0.789549\pi\)
−0.789287 + 0.614025i \(0.789549\pi\)
\(500\) −0.0184161 −0.000823594 0
\(501\) −15.3267 −0.684748
\(502\) −5.65151 −0.252239
\(503\) −2.94724 −0.131411 −0.0657055 0.997839i \(-0.520930\pi\)
−0.0657055 + 0.997839i \(0.520930\pi\)
\(504\) 6.10494 0.271936
\(505\) −0.374430 −0.0166619
\(506\) 21.3724 0.950119
\(507\) −5.00448 −0.222257
\(508\) 1.51478 0.0672074
\(509\) −32.5256 −1.44167 −0.720836 0.693106i \(-0.756242\pi\)
−0.720836 + 0.693106i \(0.756242\pi\)
\(510\) 0.195434 0.00865398
\(511\) 4.68268 0.207150
\(512\) 21.1732 0.935734
\(513\) 17.7572 0.784000
\(514\) 10.9323 0.482201
\(515\) −0.0118128 −0.000520536 0
\(516\) −1.48800 −0.0655054
\(517\) −35.5702 −1.56437
\(518\) −3.36588 −0.147888
\(519\) 12.0097 0.527166
\(520\) 0.214976 0.00942732
\(521\) −21.0994 −0.924380 −0.462190 0.886781i \(-0.652936\pi\)
−0.462190 + 0.886781i \(0.652936\pi\)
\(522\) 2.45873 0.107616
\(523\) −2.03896 −0.0891576 −0.0445788 0.999006i \(-0.514195\pi\)
−0.0445788 + 0.999006i \(0.514195\pi\)
\(524\) 1.70715 0.0745770
\(525\) −14.0078 −0.611351
\(526\) −9.90048 −0.431681
\(527\) 14.5700 0.634681
\(528\) −25.7174 −1.11921
\(529\) 3.93089 0.170908
\(530\) 0.162548 0.00706062
\(531\) −13.5651 −0.588674
\(532\) −0.634151 −0.0274939
\(533\) −12.4501 −0.539274
\(534\) −30.8377 −1.33448
\(535\) −0.198594 −0.00858595
\(536\) 22.8914 0.988759
\(537\) 18.4757 0.797284
\(538\) −22.9869 −0.991035
\(539\) −15.2340 −0.656173
\(540\) −0.00517061 −0.000222508 0
\(541\) −16.7240 −0.719021 −0.359511 0.933141i \(-0.617056\pi\)
−0.359511 + 0.933141i \(0.617056\pi\)
\(542\) 13.3609 0.573898
\(543\) 20.5275 0.880919
\(544\) −1.15616 −0.0495702
\(545\) −0.183792 −0.00787277
\(546\) −13.2064 −0.565180
\(547\) 32.9566 1.40912 0.704562 0.709643i \(-0.251144\pi\)
0.704562 + 0.709643i \(0.251144\pi\)
\(548\) 0.216628 0.00925388
\(549\) −2.45852 −0.104927
\(550\) 20.5896 0.877945
\(551\) 6.32493 0.269451
\(552\) −31.1935 −1.32768
\(553\) 21.6601 0.921081
\(554\) −0.291607 −0.0123892
\(555\) 0.0930502 0.00394976
\(556\) −0.0776255 −0.00329205
\(557\) 30.8339 1.30647 0.653236 0.757154i \(-0.273411\pi\)
0.653236 + 0.757154i \(0.273411\pi\)
\(558\) 13.5984 0.575668
\(559\) −28.8956 −1.22215
\(560\) −0.127150 −0.00537308
\(561\) −16.3284 −0.689385
\(562\) −38.7310 −1.63377
\(563\) −34.0004 −1.43295 −0.716474 0.697614i \(-0.754245\pi\)
−0.716474 + 0.697614i \(0.754245\pi\)
\(564\) −2.09634 −0.0882720
\(565\) 0.277540 0.0116762
\(566\) 5.66971 0.238316
\(567\) −14.4760 −0.607933
\(568\) −15.1746 −0.636711
\(569\) 3.02396 0.126771 0.0633856 0.997989i \(-0.479810\pi\)
0.0633856 + 0.997989i \(0.479810\pi\)
\(570\) 0.469217 0.0196533
\(571\) 0.857273 0.0358757 0.0179379 0.999839i \(-0.494290\pi\)
0.0179379 + 0.999839i \(0.494290\pi\)
\(572\) 0.725269 0.0303250
\(573\) −2.27432 −0.0950111
\(574\) 7.08825 0.295858
\(575\) 25.9446 1.08196
\(576\) 13.0764 0.544850
\(577\) −40.7432 −1.69616 −0.848082 0.529866i \(-0.822242\pi\)
−0.848082 + 0.529866i \(0.822242\pi\)
\(578\) 14.5003 0.603134
\(579\) −26.4093 −1.09753
\(580\) −0.00184172 −7.64731e−5 0
\(581\) 21.6670 0.898900
\(582\) 21.7439 0.901314
\(583\) −13.5807 −0.562457
\(584\) 10.0458 0.415697
\(585\) 0.132341 0.00547164
\(586\) 18.7968 0.776488
\(587\) −19.5934 −0.808705 −0.404353 0.914603i \(-0.632503\pi\)
−0.404353 + 0.914603i \(0.632503\pi\)
\(588\) −0.897820 −0.0370255
\(589\) 34.9811 1.44137
\(590\) 0.271955 0.0111962
\(591\) −34.8621 −1.43403
\(592\) −7.50153 −0.308311
\(593\) 1.62330 0.0666611 0.0333305 0.999444i \(-0.489389\pi\)
0.0333305 + 0.999444i \(0.489389\pi\)
\(594\) 11.5624 0.474410
\(595\) −0.0807297 −0.00330959
\(596\) 1.29919 0.0532167
\(597\) −17.6821 −0.723681
\(598\) 24.4602 1.00025
\(599\) −42.3633 −1.73092 −0.865458 0.500981i \(-0.832973\pi\)
−0.865458 + 0.500981i \(0.832973\pi\)
\(600\) −30.0510 −1.22683
\(601\) −39.5236 −1.61220 −0.806100 0.591780i \(-0.798425\pi\)
−0.806100 + 0.591780i \(0.798425\pi\)
\(602\) 16.4512 0.670500
\(603\) 14.0922 0.573878
\(604\) −1.42960 −0.0581697
\(605\) −0.0672925 −0.00273583
\(606\) 49.3460 2.00455
\(607\) 42.8241 1.73818 0.869088 0.494658i \(-0.164706\pi\)
0.869088 + 0.494658i \(0.164706\pi\)
\(608\) −2.77583 −0.112575
\(609\) −2.80188 −0.113538
\(610\) 0.0492888 0.00199565
\(611\) −40.7091 −1.64692
\(612\) −0.348830 −0.0141006
\(613\) −3.16702 −0.127915 −0.0639573 0.997953i \(-0.520372\pi\)
−0.0639573 + 0.997953i \(0.520372\pi\)
\(614\) −6.11120 −0.246628
\(615\) −0.195955 −0.00790168
\(616\) 10.2258 0.412010
\(617\) 20.9486 0.843360 0.421680 0.906745i \(-0.361441\pi\)
0.421680 + 0.906745i \(0.361441\pi\)
\(618\) 1.55681 0.0626242
\(619\) −18.9591 −0.762029 −0.381014 0.924569i \(-0.624425\pi\)
−0.381014 + 0.924569i \(0.624425\pi\)
\(620\) −0.0101859 −0.000409077 0
\(621\) 14.5695 0.584654
\(622\) −32.6434 −1.30888
\(623\) 12.7384 0.510353
\(624\) −29.4330 −1.17826
\(625\) 24.9916 0.999662
\(626\) −14.8342 −0.592894
\(627\) −39.2027 −1.56561
\(628\) −0.254300 −0.0101477
\(629\) −4.76283 −0.189907
\(630\) −0.0753462 −0.00300186
\(631\) −14.0990 −0.561274 −0.280637 0.959814i \(-0.590546\pi\)
−0.280637 + 0.959814i \(0.590546\pi\)
\(632\) 46.4675 1.84838
\(633\) 17.0453 0.677490
\(634\) 28.5623 1.13435
\(635\) 0.462980 0.0183728
\(636\) −0.800388 −0.0317374
\(637\) −17.4349 −0.690795
\(638\) 4.11839 0.163049
\(639\) −9.34162 −0.369549
\(640\) −0.282983 −0.0111859
\(641\) −0.143017 −0.00564884 −0.00282442 0.999996i \(-0.500899\pi\)
−0.00282442 + 0.999996i \(0.500899\pi\)
\(642\) 26.1726 1.03295
\(643\) −12.4764 −0.492022 −0.246011 0.969267i \(-0.579120\pi\)
−0.246011 + 0.969267i \(0.579120\pi\)
\(644\) −0.520310 −0.0205031
\(645\) −0.454794 −0.0179075
\(646\) −24.0172 −0.944943
\(647\) −28.2334 −1.10997 −0.554984 0.831861i \(-0.687276\pi\)
−0.554984 + 0.831861i \(0.687276\pi\)
\(648\) −31.0553 −1.21997
\(649\) −22.7216 −0.891902
\(650\) 23.5643 0.924269
\(651\) −15.4963 −0.607347
\(652\) 0.598936 0.0234562
\(653\) −29.5921 −1.15803 −0.579014 0.815318i \(-0.696562\pi\)
−0.579014 + 0.815318i \(0.696562\pi\)
\(654\) 24.2219 0.947150
\(655\) 0.521776 0.0203875
\(656\) 15.7975 0.616791
\(657\) 6.18428 0.241272
\(658\) 23.1770 0.903535
\(659\) 28.3564 1.10461 0.552304 0.833643i \(-0.313749\pi\)
0.552304 + 0.833643i \(0.313749\pi\)
\(660\) 0.0114152 0.000444336 0
\(661\) −11.3046 −0.439696 −0.219848 0.975534i \(-0.570556\pi\)
−0.219848 + 0.975534i \(0.570556\pi\)
\(662\) 39.7816 1.54616
\(663\) −18.6874 −0.725759
\(664\) 46.4824 1.80387
\(665\) −0.193823 −0.00751615
\(666\) −4.44522 −0.172249
\(667\) 5.18950 0.200938
\(668\) −0.548450 −0.0212202
\(669\) −11.5252 −0.445589
\(670\) −0.282522 −0.0109148
\(671\) −4.11804 −0.158975
\(672\) 1.22966 0.0474353
\(673\) −17.0891 −0.658735 −0.329367 0.944202i \(-0.606835\pi\)
−0.329367 + 0.944202i \(0.606835\pi\)
\(674\) −19.9566 −0.768700
\(675\) 14.0359 0.540242
\(676\) −0.179080 −0.00688769
\(677\) −28.8172 −1.10753 −0.553767 0.832672i \(-0.686810\pi\)
−0.553767 + 0.832672i \(0.686810\pi\)
\(678\) −36.5770 −1.40473
\(679\) −8.98194 −0.344695
\(680\) −0.173190 −0.00664152
\(681\) 12.2716 0.470248
\(682\) 22.7775 0.872195
\(683\) 10.6669 0.408158 0.204079 0.978954i \(-0.434580\pi\)
0.204079 + 0.978954i \(0.434580\pi\)
\(684\) −0.837505 −0.0320228
\(685\) 0.0662106 0.00252978
\(686\) 22.9583 0.876553
\(687\) −38.7128 −1.47699
\(688\) 36.6647 1.39783
\(689\) −15.5428 −0.592134
\(690\) 0.384985 0.0146561
\(691\) 10.5226 0.400300 0.200150 0.979765i \(-0.435857\pi\)
0.200150 + 0.979765i \(0.435857\pi\)
\(692\) 0.429753 0.0163368
\(693\) 6.29512 0.239132
\(694\) −6.07227 −0.230500
\(695\) −0.0237256 −0.000899965 0
\(696\) −6.01088 −0.227842
\(697\) 10.0301 0.379917
\(698\) −48.2516 −1.82635
\(699\) 17.7367 0.670862
\(700\) −0.501254 −0.0189456
\(701\) −5.17967 −0.195633 −0.0978167 0.995204i \(-0.531186\pi\)
−0.0978167 + 0.995204i \(0.531186\pi\)
\(702\) 13.2328 0.499442
\(703\) −11.4351 −0.431282
\(704\) 21.9031 0.825503
\(705\) −0.640732 −0.0241314
\(706\) 20.8640 0.785228
\(707\) −20.3838 −0.766611
\(708\) −1.33911 −0.0503268
\(709\) 11.9938 0.450435 0.225218 0.974308i \(-0.427691\pi\)
0.225218 + 0.974308i \(0.427691\pi\)
\(710\) 0.187282 0.00702858
\(711\) 28.6058 1.07280
\(712\) 27.3277 1.02415
\(713\) 28.7014 1.07488
\(714\) 10.6394 0.398168
\(715\) 0.221673 0.00829009
\(716\) 0.661132 0.0247077
\(717\) 34.5893 1.29176
\(718\) −9.26592 −0.345801
\(719\) 22.1622 0.826511 0.413256 0.910615i \(-0.364392\pi\)
0.413256 + 0.910615i \(0.364392\pi\)
\(720\) −0.167924 −0.00625815
\(721\) −0.643086 −0.0239498
\(722\) −30.2762 −1.12676
\(723\) 42.0578 1.56415
\(724\) 0.734554 0.0272995
\(725\) 4.99944 0.185674
\(726\) 8.86847 0.329140
\(727\) 29.8138 1.10573 0.552866 0.833270i \(-0.313534\pi\)
0.552866 + 0.833270i \(0.313534\pi\)
\(728\) 11.7032 0.433749
\(729\) −0.847182 −0.0313771
\(730\) −0.123983 −0.00458883
\(731\) 23.2789 0.861003
\(732\) −0.242699 −0.00897041
\(733\) −14.3713 −0.530816 −0.265408 0.964136i \(-0.585507\pi\)
−0.265408 + 0.964136i \(0.585507\pi\)
\(734\) 37.7313 1.39269
\(735\) −0.274412 −0.0101218
\(736\) −2.27752 −0.0839506
\(737\) 23.6045 0.869484
\(738\) 9.36124 0.344592
\(739\) −12.0779 −0.444293 −0.222147 0.975013i \(-0.571306\pi\)
−0.222147 + 0.975013i \(0.571306\pi\)
\(740\) 0.00332970 0.000122402 0
\(741\) −44.8665 −1.64821
\(742\) 8.84903 0.324858
\(743\) 30.2748 1.11067 0.555337 0.831626i \(-0.312589\pi\)
0.555337 + 0.831626i \(0.312589\pi\)
\(744\) −33.2442 −1.21879
\(745\) 0.397086 0.0145481
\(746\) 24.3128 0.890154
\(747\) 28.6150 1.04697
\(748\) −0.584294 −0.0213639
\(749\) −10.8113 −0.395038
\(750\) 0.741812 0.0270871
\(751\) −17.2916 −0.630980 −0.315490 0.948929i \(-0.602169\pi\)
−0.315490 + 0.948929i \(0.602169\pi\)
\(752\) 51.6546 1.88365
\(753\) 8.50545 0.309956
\(754\) 4.71340 0.171652
\(755\) −0.436947 −0.0159021
\(756\) −0.281486 −0.0102375
\(757\) −5.14268 −0.186914 −0.0934569 0.995623i \(-0.529792\pi\)
−0.0934569 + 0.995623i \(0.529792\pi\)
\(758\) 14.1250 0.513044
\(759\) −32.1652 −1.16752
\(760\) −0.415810 −0.0150830
\(761\) −2.61328 −0.0947313 −0.0473657 0.998878i \(-0.515083\pi\)
−0.0473657 + 0.998878i \(0.515083\pi\)
\(762\) −61.0161 −2.21038
\(763\) −10.0055 −0.362225
\(764\) −0.0813841 −0.00294437
\(765\) −0.106617 −0.00385476
\(766\) −48.6477 −1.75771
\(767\) −26.0043 −0.938962
\(768\) 4.03539 0.145615
\(769\) −43.4797 −1.56792 −0.783959 0.620813i \(-0.786803\pi\)
−0.783959 + 0.620813i \(0.786803\pi\)
\(770\) −0.126206 −0.00454813
\(771\) −16.4529 −0.592537
\(772\) −0.945027 −0.0340123
\(773\) 3.95881 0.142389 0.0711943 0.997462i \(-0.477319\pi\)
0.0711943 + 0.997462i \(0.477319\pi\)
\(774\) 21.7266 0.780946
\(775\) 27.6503 0.993227
\(776\) −19.2690 −0.691717
\(777\) 5.06561 0.181728
\(778\) −40.0592 −1.43619
\(779\) 24.0812 0.862799
\(780\) 0.0130644 0.000467780 0
\(781\) −15.6473 −0.559904
\(782\) −19.7057 −0.704674
\(783\) 2.80750 0.100332
\(784\) 22.1226 0.790092
\(785\) −0.0777249 −0.00277412
\(786\) −68.7648 −2.45276
\(787\) −40.1335 −1.43061 −0.715303 0.698815i \(-0.753711\pi\)
−0.715303 + 0.698815i \(0.753711\pi\)
\(788\) −1.24750 −0.0444404
\(789\) 14.9001 0.530457
\(790\) −0.573494 −0.0204040
\(791\) 15.1092 0.537220
\(792\) 13.5049 0.479877
\(793\) −4.71300 −0.167363
\(794\) −19.4088 −0.688792
\(795\) −0.244632 −0.00867622
\(796\) −0.632736 −0.0224267
\(797\) 24.6515 0.873202 0.436601 0.899655i \(-0.356182\pi\)
0.436601 + 0.899655i \(0.356182\pi\)
\(798\) 25.5440 0.904247
\(799\) 32.7963 1.16025
\(800\) −2.19411 −0.0775735
\(801\) 16.8232 0.594419
\(802\) −16.9013 −0.596805
\(803\) 10.3587 0.365551
\(804\) 1.39114 0.0490619
\(805\) −0.159029 −0.00560503
\(806\) 26.0683 0.918215
\(807\) 34.5950 1.21780
\(808\) −43.7294 −1.53840
\(809\) 23.6805 0.832562 0.416281 0.909236i \(-0.363333\pi\)
0.416281 + 0.909236i \(0.363333\pi\)
\(810\) 0.383280 0.0134671
\(811\) 0.268429 0.00942581 0.00471291 0.999989i \(-0.498500\pi\)
0.00471291 + 0.999989i \(0.498500\pi\)
\(812\) −0.100262 −0.00351851
\(813\) −20.1079 −0.705215
\(814\) −7.44579 −0.260975
\(815\) 0.183060 0.00641232
\(816\) 23.7119 0.830082
\(817\) 55.8903 1.95535
\(818\) −56.4511 −1.97377
\(819\) 7.20460 0.251749
\(820\) −0.00701205 −0.000244871 0
\(821\) −13.3248 −0.465038 −0.232519 0.972592i \(-0.574697\pi\)
−0.232519 + 0.972592i \(0.574697\pi\)
\(822\) −8.72590 −0.304351
\(823\) 25.0905 0.874598 0.437299 0.899316i \(-0.355935\pi\)
0.437299 + 0.899316i \(0.355935\pi\)
\(824\) −1.37961 −0.0480612
\(825\) −30.9872 −1.07883
\(826\) 14.8051 0.515136
\(827\) −12.1457 −0.422348 −0.211174 0.977449i \(-0.567729\pi\)
−0.211174 + 0.977449i \(0.567729\pi\)
\(828\) −0.687158 −0.0238804
\(829\) −27.9464 −0.970617 −0.485309 0.874343i \(-0.661293\pi\)
−0.485309 + 0.874343i \(0.661293\pi\)
\(830\) −0.573678 −0.0199127
\(831\) 0.438865 0.0152240
\(832\) 25.0675 0.869060
\(833\) 14.0459 0.486663
\(834\) 3.12680 0.108272
\(835\) −0.167630 −0.00580106
\(836\) −1.40283 −0.0485178
\(837\) 15.5274 0.536704
\(838\) −20.2979 −0.701180
\(839\) 48.9226 1.68900 0.844498 0.535558i \(-0.179899\pi\)
0.844498 + 0.535558i \(0.179899\pi\)
\(840\) 0.184200 0.00635549
\(841\) 1.00000 0.0344828
\(842\) −19.4688 −0.670939
\(843\) 58.2896 2.00760
\(844\) 0.609947 0.0209953
\(845\) −0.0547344 −0.00188292
\(846\) 30.6092 1.05237
\(847\) −3.66337 −0.125875
\(848\) 19.7218 0.677249
\(849\) −8.53284 −0.292846
\(850\) −18.9840 −0.651145
\(851\) −9.38228 −0.321620
\(852\) −0.922181 −0.0315934
\(853\) −31.5562 −1.08046 −0.540232 0.841516i \(-0.681664\pi\)
−0.540232 + 0.841516i \(0.681664\pi\)
\(854\) 2.68326 0.0918194
\(855\) −0.255977 −0.00875422
\(856\) −23.1936 −0.792742
\(857\) −42.8914 −1.46514 −0.732571 0.680691i \(-0.761680\pi\)
−0.732571 + 0.680691i \(0.761680\pi\)
\(858\) −29.2142 −0.997358
\(859\) 9.26195 0.316014 0.158007 0.987438i \(-0.449493\pi\)
0.158007 + 0.987438i \(0.449493\pi\)
\(860\) −0.0162743 −0.000554950 0
\(861\) −10.6677 −0.363555
\(862\) 37.1531 1.26544
\(863\) −14.6948 −0.500216 −0.250108 0.968218i \(-0.580466\pi\)
−0.250108 + 0.968218i \(0.580466\pi\)
\(864\) −1.23213 −0.0419179
\(865\) 0.131351 0.00446606
\(866\) 4.77609 0.162298
\(867\) −21.8228 −0.741141
\(868\) −0.554517 −0.0188215
\(869\) 47.9150 1.62541
\(870\) 0.0741854 0.00251512
\(871\) 27.0148 0.915361
\(872\) −21.4649 −0.726894
\(873\) −11.8622 −0.401474
\(874\) −47.3113 −1.60033
\(875\) −0.306426 −0.0103591
\(876\) 0.610496 0.0206268
\(877\) −22.3081 −0.753290 −0.376645 0.926358i \(-0.622922\pi\)
−0.376645 + 0.926358i \(0.622922\pi\)
\(878\) −19.4876 −0.657673
\(879\) −28.2889 −0.954162
\(880\) −0.281274 −0.00948174
\(881\) 42.2608 1.42380 0.711902 0.702279i \(-0.247834\pi\)
0.711902 + 0.702279i \(0.247834\pi\)
\(882\) 13.1093 0.441413
\(883\) −38.1070 −1.28240 −0.641202 0.767372i \(-0.721564\pi\)
−0.641202 + 0.767372i \(0.721564\pi\)
\(884\) −0.668709 −0.0224911
\(885\) −0.409289 −0.0137581
\(886\) −3.39512 −0.114061
\(887\) 24.0823 0.808606 0.404303 0.914625i \(-0.367514\pi\)
0.404303 + 0.914625i \(0.367514\pi\)
\(888\) 10.8673 0.364682
\(889\) 25.2045 0.845330
\(890\) −0.337274 −0.0113055
\(891\) −32.0228 −1.07280
\(892\) −0.412416 −0.0138087
\(893\) 78.7403 2.63495
\(894\) −52.3320 −1.75024
\(895\) 0.202070 0.00675445
\(896\) −15.4055 −0.514660
\(897\) −36.8122 −1.22912
\(898\) −6.37807 −0.212839
\(899\) 5.53067 0.184458
\(900\) −0.661992 −0.0220664
\(901\) 12.5217 0.417157
\(902\) 15.6802 0.522092
\(903\) −24.7588 −0.823922
\(904\) 32.4138 1.07807
\(905\) 0.224511 0.00746299
\(906\) 57.5852 1.91314
\(907\) −21.9045 −0.727326 −0.363663 0.931531i \(-0.618474\pi\)
−0.363663 + 0.931531i \(0.618474\pi\)
\(908\) 0.439125 0.0145729
\(909\) −26.9203 −0.892889
\(910\) −0.144439 −0.00478811
\(911\) −24.6992 −0.818319 −0.409160 0.912463i \(-0.634178\pi\)
−0.409160 + 0.912463i \(0.634178\pi\)
\(912\) 56.9297 1.88513
\(913\) 47.9304 1.58626
\(914\) 53.7443 1.77770
\(915\) −0.0741791 −0.00245228
\(916\) −1.38530 −0.0457715
\(917\) 28.4053 0.938024
\(918\) −10.6607 −0.351855
\(919\) −14.9096 −0.491823 −0.245912 0.969292i \(-0.579087\pi\)
−0.245912 + 0.969292i \(0.579087\pi\)
\(920\) −0.341165 −0.0112479
\(921\) 9.19729 0.303061
\(922\) −5.46215 −0.179886
\(923\) −17.9079 −0.589447
\(924\) 0.621438 0.0204438
\(925\) −9.03866 −0.297189
\(926\) −8.56864 −0.281583
\(927\) −0.849304 −0.0278948
\(928\) −0.438871 −0.0144067
\(929\) 35.2255 1.15571 0.577856 0.816139i \(-0.303890\pi\)
0.577856 + 0.816139i \(0.303890\pi\)
\(930\) 0.410295 0.0134541
\(931\) 33.7228 1.10522
\(932\) 0.634687 0.0207899
\(933\) 49.1279 1.60837
\(934\) 22.7857 0.745570
\(935\) −0.178585 −0.00584035
\(936\) 15.4561 0.505197
\(937\) −26.5636 −0.867796 −0.433898 0.900962i \(-0.642862\pi\)
−0.433898 + 0.900962i \(0.642862\pi\)
\(938\) −15.3804 −0.502188
\(939\) 22.3253 0.728559
\(940\) −0.0229279 −0.000747825 0
\(941\) 32.4804 1.05883 0.529415 0.848363i \(-0.322411\pi\)
0.529415 + 0.848363i \(0.322411\pi\)
\(942\) 10.2434 0.333747
\(943\) 19.7582 0.643416
\(944\) 32.9961 1.07393
\(945\) −0.0860340 −0.00279869
\(946\) 36.3922 1.18321
\(947\) −12.0046 −0.390098 −0.195049 0.980793i \(-0.562487\pi\)
−0.195049 + 0.980793i \(0.562487\pi\)
\(948\) 2.82390 0.0917159
\(949\) 11.8553 0.384839
\(950\) −45.5785 −1.47876
\(951\) −42.9859 −1.39391
\(952\) −9.42838 −0.305575
\(953\) 10.0335 0.325017 0.162508 0.986707i \(-0.448042\pi\)
0.162508 + 0.986707i \(0.448042\pi\)
\(954\) 11.6867 0.378369
\(955\) −0.0248744 −0.000804918 0
\(956\) 1.23774 0.0400314
\(957\) −6.19813 −0.200357
\(958\) −21.7032 −0.701199
\(959\) 3.60448 0.116395
\(960\) 0.394544 0.0127339
\(961\) −0.411638 −0.0132786
\(962\) −8.52152 −0.274745
\(963\) −14.2782 −0.460109
\(964\) 1.50499 0.0484726
\(965\) −0.288840 −0.00929810
\(966\) 20.9584 0.674326
\(967\) 27.1988 0.874656 0.437328 0.899302i \(-0.355925\pi\)
0.437328 + 0.899302i \(0.355925\pi\)
\(968\) −7.85905 −0.252599
\(969\) 36.1455 1.16116
\(970\) 0.237815 0.00763578
\(971\) 38.7602 1.24387 0.621937 0.783067i \(-0.286346\pi\)
0.621937 + 0.783067i \(0.286346\pi\)
\(972\) −1.23348 −0.0395638
\(973\) −1.29161 −0.0414072
\(974\) 24.0962 0.772093
\(975\) −35.4640 −1.13576
\(976\) 5.98017 0.191421
\(977\) −13.2799 −0.424860 −0.212430 0.977176i \(-0.568138\pi\)
−0.212430 + 0.977176i \(0.568138\pi\)
\(978\) −24.1255 −0.771449
\(979\) 28.1790 0.900605
\(980\) −0.00981953 −0.000313674 0
\(981\) −13.2140 −0.421891
\(982\) 29.6127 0.944981
\(983\) 33.2638 1.06095 0.530476 0.847700i \(-0.322013\pi\)
0.530476 + 0.847700i \(0.322013\pi\)
\(984\) −22.8855 −0.729564
\(985\) −0.381289 −0.0121489
\(986\) −3.79722 −0.120928
\(987\) −34.8812 −1.11028
\(988\) −1.60550 −0.0510778
\(989\) 45.8570 1.45817
\(990\) −0.166676 −0.00529731
\(991\) −29.3560 −0.932523 −0.466262 0.884647i \(-0.654399\pi\)
−0.466262 + 0.884647i \(0.654399\pi\)
\(992\) −2.42725 −0.0770654
\(993\) −59.8708 −1.89994
\(994\) 10.1956 0.323384
\(995\) −0.193391 −0.00613090
\(996\) 2.82480 0.0895072
\(997\) −20.9366 −0.663070 −0.331535 0.943443i \(-0.607566\pi\)
−0.331535 + 0.943443i \(0.607566\pi\)
\(998\) 50.8275 1.60892
\(999\) −5.07577 −0.160590
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 \(a_p\))