Properties

Label 8018.2.a.d.1.23
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 1.23
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.37784 q^{3} +1.00000 q^{4} +3.53697 q^{5} +1.37784 q^{6} -2.08526 q^{7} +1.00000 q^{8} -1.10156 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.37784 q^{3} +1.00000 q^{4} +3.53697 q^{5} +1.37784 q^{6} -2.08526 q^{7} +1.00000 q^{8} -1.10156 q^{9} +3.53697 q^{10} -3.14295 q^{11} +1.37784 q^{12} -3.99759 q^{13} -2.08526 q^{14} +4.87337 q^{15} +1.00000 q^{16} -6.01813 q^{17} -1.10156 q^{18} +1.00000 q^{19} +3.53697 q^{20} -2.87314 q^{21} -3.14295 q^{22} -6.22231 q^{23} +1.37784 q^{24} +7.51017 q^{25} -3.99759 q^{26} -5.65129 q^{27} -2.08526 q^{28} -6.86242 q^{29} +4.87337 q^{30} +6.59507 q^{31} +1.00000 q^{32} -4.33048 q^{33} -6.01813 q^{34} -7.37550 q^{35} -1.10156 q^{36} -3.67195 q^{37} +1.00000 q^{38} -5.50802 q^{39} +3.53697 q^{40} +8.95892 q^{41} -2.87314 q^{42} +0.304255 q^{43} -3.14295 q^{44} -3.89620 q^{45} -6.22231 q^{46} +0.829211 q^{47} +1.37784 q^{48} -2.65170 q^{49} +7.51017 q^{50} -8.29200 q^{51} -3.99759 q^{52} +3.90013 q^{53} -5.65129 q^{54} -11.1165 q^{55} -2.08526 q^{56} +1.37784 q^{57} -6.86242 q^{58} -10.5452 q^{59} +4.87337 q^{60} +2.06867 q^{61} +6.59507 q^{62} +2.29705 q^{63} +1.00000 q^{64} -14.1394 q^{65} -4.33048 q^{66} +4.91181 q^{67} -6.01813 q^{68} -8.57334 q^{69} -7.37550 q^{70} -1.61616 q^{71} -1.10156 q^{72} -2.42349 q^{73} -3.67195 q^{74} +10.3478 q^{75} +1.00000 q^{76} +6.55387 q^{77} -5.50802 q^{78} -2.78453 q^{79} +3.53697 q^{80} -4.48186 q^{81} +8.95892 q^{82} +12.8628 q^{83} -2.87314 q^{84} -21.2859 q^{85} +0.304255 q^{86} -9.45530 q^{87} -3.14295 q^{88} -3.09295 q^{89} -3.89620 q^{90} +8.33600 q^{91} -6.22231 q^{92} +9.08693 q^{93} +0.829211 q^{94} +3.53697 q^{95} +1.37784 q^{96} +2.90999 q^{97} -2.65170 q^{98} +3.46217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

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
\(3\) 1.37784 0.795495 0.397747 0.917495i \(-0.369792\pi\)
0.397747 + 0.917495i \(0.369792\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.53697 1.58178 0.790891 0.611957i \(-0.209617\pi\)
0.790891 + 0.611957i \(0.209617\pi\)
\(6\) 1.37784 0.562500
\(7\) −2.08526 −0.788153 −0.394076 0.919078i \(-0.628935\pi\)
−0.394076 + 0.919078i \(0.628935\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.10156 −0.367188
\(10\) 3.53697 1.11849
\(11\) −3.14295 −0.947636 −0.473818 0.880623i \(-0.657125\pi\)
−0.473818 + 0.880623i \(0.657125\pi\)
\(12\) 1.37784 0.397747
\(13\) −3.99759 −1.10873 −0.554366 0.832273i \(-0.687039\pi\)
−0.554366 + 0.832273i \(0.687039\pi\)
\(14\) −2.08526 −0.557308
\(15\) 4.87337 1.25830
\(16\) 1.00000 0.250000
\(17\) −6.01813 −1.45961 −0.729805 0.683655i \(-0.760389\pi\)
−0.729805 + 0.683655i \(0.760389\pi\)
\(18\) −1.10156 −0.259641
\(19\) 1.00000 0.229416
\(20\) 3.53697 0.790891
\(21\) −2.87314 −0.626971
\(22\) −3.14295 −0.670080
\(23\) −6.22231 −1.29744 −0.648721 0.761026i \(-0.724696\pi\)
−0.648721 + 0.761026i \(0.724696\pi\)
\(24\) 1.37784 0.281250
\(25\) 7.51017 1.50203
\(26\) −3.99759 −0.783991
\(27\) −5.65129 −1.08759
\(28\) −2.08526 −0.394076
\(29\) −6.86242 −1.27432 −0.637160 0.770732i \(-0.719891\pi\)
−0.637160 + 0.770732i \(0.719891\pi\)
\(30\) 4.87337 0.889752
\(31\) 6.59507 1.18451 0.592255 0.805751i \(-0.298238\pi\)
0.592255 + 0.805751i \(0.298238\pi\)
\(32\) 1.00000 0.176777
\(33\) −4.33048 −0.753840
\(34\) −6.01813 −1.03210
\(35\) −7.37550 −1.24669
\(36\) −1.10156 −0.183594
\(37\) −3.67195 −0.603665 −0.301833 0.953361i \(-0.597598\pi\)
−0.301833 + 0.953361i \(0.597598\pi\)
\(38\) 1.00000 0.162221
\(39\) −5.50802 −0.881990
\(40\) 3.53697 0.559244
\(41\) 8.95892 1.39915 0.699574 0.714560i \(-0.253373\pi\)
0.699574 + 0.714560i \(0.253373\pi\)
\(42\) −2.87314 −0.443336
\(43\) 0.304255 0.0463985 0.0231993 0.999731i \(-0.492615\pi\)
0.0231993 + 0.999731i \(0.492615\pi\)
\(44\) −3.14295 −0.473818
\(45\) −3.89620 −0.580812
\(46\) −6.22231 −0.917430
\(47\) 0.829211 0.120953 0.0604764 0.998170i \(-0.480738\pi\)
0.0604764 + 0.998170i \(0.480738\pi\)
\(48\) 1.37784 0.198874
\(49\) −2.65170 −0.378815
\(50\) 7.51017 1.06210
\(51\) −8.29200 −1.16111
\(52\) −3.99759 −0.554366
\(53\) 3.90013 0.535724 0.267862 0.963457i \(-0.413683\pi\)
0.267862 + 0.963457i \(0.413683\pi\)
\(54\) −5.65129 −0.769043
\(55\) −11.1165 −1.49895
\(56\) −2.08526 −0.278654
\(57\) 1.37784 0.182499
\(58\) −6.86242 −0.901080
\(59\) −10.5452 −1.37287 −0.686434 0.727192i \(-0.740825\pi\)
−0.686434 + 0.727192i \(0.740825\pi\)
\(60\) 4.87337 0.629150
\(61\) 2.06867 0.264866 0.132433 0.991192i \(-0.457721\pi\)
0.132433 + 0.991192i \(0.457721\pi\)
\(62\) 6.59507 0.837575
\(63\) 2.29705 0.289401
\(64\) 1.00000 0.125000
\(65\) −14.1394 −1.75377
\(66\) −4.33048 −0.533045
\(67\) 4.91181 0.600073 0.300037 0.953928i \(-0.403001\pi\)
0.300037 + 0.953928i \(0.403001\pi\)
\(68\) −6.01813 −0.729805
\(69\) −8.57334 −1.03211
\(70\) −7.37550 −0.881540
\(71\) −1.61616 −0.191803 −0.0959016 0.995391i \(-0.530573\pi\)
−0.0959016 + 0.995391i \(0.530573\pi\)
\(72\) −1.10156 −0.129821
\(73\) −2.42349 −0.283648 −0.141824 0.989892i \(-0.545297\pi\)
−0.141824 + 0.989892i \(0.545297\pi\)
\(74\) −3.67195 −0.426856
\(75\) 10.3478 1.19486
\(76\) 1.00000 0.114708
\(77\) 6.55387 0.746883
\(78\) −5.50802 −0.623661
\(79\) −2.78453 −0.313284 −0.156642 0.987655i \(-0.550067\pi\)
−0.156642 + 0.987655i \(0.550067\pi\)
\(80\) 3.53697 0.395446
\(81\) −4.48186 −0.497985
\(82\) 8.95892 0.989347
\(83\) 12.8628 1.41187 0.705937 0.708275i \(-0.250526\pi\)
0.705937 + 0.708275i \(0.250526\pi\)
\(84\) −2.87314 −0.313486
\(85\) −21.2859 −2.30878
\(86\) 0.304255 0.0328087
\(87\) −9.45530 −1.01371
\(88\) −3.14295 −0.335040
\(89\) −3.09295 −0.327852 −0.163926 0.986473i \(-0.552416\pi\)
−0.163926 + 0.986473i \(0.552416\pi\)
\(90\) −3.89620 −0.410696
\(91\) 8.33600 0.873850
\(92\) −6.22231 −0.648721
\(93\) 9.08693 0.942271
\(94\) 0.829211 0.0855266
\(95\) 3.53697 0.362886
\(96\) 1.37784 0.140625
\(97\) 2.90999 0.295465 0.147732 0.989027i \(-0.452803\pi\)
0.147732 + 0.989027i \(0.452803\pi\)
\(98\) −2.65170 −0.267863
\(99\) 3.46217 0.347961
\(100\) 7.51017 0.751017
\(101\) −1.30507 −0.129859 −0.0649296 0.997890i \(-0.520682\pi\)
−0.0649296 + 0.997890i \(0.520682\pi\)
\(102\) −8.29200 −0.821030
\(103\) −12.3411 −1.21601 −0.608003 0.793935i \(-0.708029\pi\)
−0.608003 + 0.793935i \(0.708029\pi\)
\(104\) −3.99759 −0.391996
\(105\) −10.1622 −0.991732
\(106\) 3.90013 0.378814
\(107\) 1.14970 0.111146 0.0555729 0.998455i \(-0.482301\pi\)
0.0555729 + 0.998455i \(0.482301\pi\)
\(108\) −5.65129 −0.543795
\(109\) 4.57273 0.437988 0.218994 0.975726i \(-0.429722\pi\)
0.218994 + 0.975726i \(0.429722\pi\)
\(110\) −11.1165 −1.05992
\(111\) −5.05935 −0.480212
\(112\) −2.08526 −0.197038
\(113\) −1.47352 −0.138617 −0.0693087 0.997595i \(-0.522079\pi\)
−0.0693087 + 0.997595i \(0.522079\pi\)
\(114\) 1.37784 0.129046
\(115\) −22.0082 −2.05227
\(116\) −6.86242 −0.637160
\(117\) 4.40360 0.407113
\(118\) −10.5452 −0.970764
\(119\) 12.5493 1.15040
\(120\) 4.87337 0.444876
\(121\) −1.12184 −0.101985
\(122\) 2.06867 0.187288
\(123\) 12.3439 1.11301
\(124\) 6.59507 0.592255
\(125\) 8.87841 0.794109
\(126\) 2.29705 0.204637
\(127\) −12.0006 −1.06488 −0.532442 0.846467i \(-0.678725\pi\)
−0.532442 + 0.846467i \(0.678725\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.419215 0.0369098
\(130\) −14.1394 −1.24010
\(131\) −8.37543 −0.731765 −0.365882 0.930661i \(-0.619233\pi\)
−0.365882 + 0.930661i \(0.619233\pi\)
\(132\) −4.33048 −0.376920
\(133\) −2.08526 −0.180815
\(134\) 4.91181 0.424316
\(135\) −19.9885 −1.72033
\(136\) −6.01813 −0.516050
\(137\) −10.7677 −0.919944 −0.459972 0.887933i \(-0.652141\pi\)
−0.459972 + 0.887933i \(0.652141\pi\)
\(138\) −8.57334 −0.729811
\(139\) 1.42665 0.121007 0.0605035 0.998168i \(-0.480729\pi\)
0.0605035 + 0.998168i \(0.480729\pi\)
\(140\) −7.37550 −0.623343
\(141\) 1.14252 0.0962174
\(142\) −1.61616 −0.135625
\(143\) 12.5642 1.05067
\(144\) −1.10156 −0.0917971
\(145\) −24.2722 −2.01570
\(146\) −2.42349 −0.200569
\(147\) −3.65362 −0.301345
\(148\) −3.67195 −0.301833
\(149\) −1.66215 −0.136169 −0.0680843 0.997680i \(-0.521689\pi\)
−0.0680843 + 0.997680i \(0.521689\pi\)
\(150\) 10.3478 0.844894
\(151\) 5.77068 0.469611 0.234806 0.972042i \(-0.424555\pi\)
0.234806 + 0.972042i \(0.424555\pi\)
\(152\) 1.00000 0.0811107
\(153\) 6.62935 0.535952
\(154\) 6.55387 0.528126
\(155\) 23.3266 1.87364
\(156\) −5.50802 −0.440995
\(157\) −7.85464 −0.626869 −0.313434 0.949610i \(-0.601480\pi\)
−0.313434 + 0.949610i \(0.601480\pi\)
\(158\) −2.78453 −0.221526
\(159\) 5.37374 0.426166
\(160\) 3.53697 0.279622
\(161\) 12.9751 1.02258
\(162\) −4.48186 −0.352128
\(163\) −4.10851 −0.321803 −0.160902 0.986970i \(-0.551440\pi\)
−0.160902 + 0.986970i \(0.551440\pi\)
\(164\) 8.95892 0.699574
\(165\) −15.3168 −1.19241
\(166\) 12.8628 0.998345
\(167\) 7.06678 0.546844 0.273422 0.961894i \(-0.411845\pi\)
0.273422 + 0.961894i \(0.411845\pi\)
\(168\) −2.87314 −0.221668
\(169\) 2.98071 0.229285
\(170\) −21.2859 −1.63256
\(171\) −1.10156 −0.0842388
\(172\) 0.304255 0.0231993
\(173\) 9.71788 0.738837 0.369418 0.929263i \(-0.379557\pi\)
0.369418 + 0.929263i \(0.379557\pi\)
\(174\) −9.45530 −0.716804
\(175\) −15.6606 −1.18383
\(176\) −3.14295 −0.236909
\(177\) −14.5296 −1.09211
\(178\) −3.09295 −0.231826
\(179\) −24.7875 −1.85270 −0.926352 0.376659i \(-0.877073\pi\)
−0.926352 + 0.376659i \(0.877073\pi\)
\(180\) −3.89620 −0.290406
\(181\) −2.42472 −0.180228 −0.0901142 0.995931i \(-0.528723\pi\)
−0.0901142 + 0.995931i \(0.528723\pi\)
\(182\) 8.33600 0.617905
\(183\) 2.85029 0.210699
\(184\) −6.22231 −0.458715
\(185\) −12.9876 −0.954867
\(186\) 9.08693 0.666286
\(187\) 18.9147 1.38318
\(188\) 0.829211 0.0604764
\(189\) 11.7844 0.857188
\(190\) 3.53697 0.256599
\(191\) 19.0532 1.37864 0.689322 0.724455i \(-0.257909\pi\)
0.689322 + 0.724455i \(0.257909\pi\)
\(192\) 1.37784 0.0994368
\(193\) −6.16409 −0.443701 −0.221850 0.975081i \(-0.571210\pi\)
−0.221850 + 0.975081i \(0.571210\pi\)
\(194\) 2.90999 0.208925
\(195\) −19.4817 −1.39512
\(196\) −2.65170 −0.189407
\(197\) 3.38890 0.241449 0.120725 0.992686i \(-0.461478\pi\)
0.120725 + 0.992686i \(0.461478\pi\)
\(198\) 3.46217 0.246046
\(199\) 7.72991 0.547959 0.273979 0.961736i \(-0.411660\pi\)
0.273979 + 0.961736i \(0.411660\pi\)
\(200\) 7.51017 0.531049
\(201\) 6.76768 0.477355
\(202\) −1.30507 −0.0918243
\(203\) 14.3099 1.00436
\(204\) −8.29200 −0.580556
\(205\) 31.6874 2.21315
\(206\) −12.3411 −0.859846
\(207\) 6.85428 0.476406
\(208\) −3.99759 −0.277183
\(209\) −3.14295 −0.217403
\(210\) −10.1622 −0.701261
\(211\) −1.00000 −0.0688428
\(212\) 3.90013 0.267862
\(213\) −2.22681 −0.152578
\(214\) 1.14970 0.0785920
\(215\) 1.07614 0.0733924
\(216\) −5.65129 −0.384521
\(217\) −13.7524 −0.933575
\(218\) 4.57273 0.309704
\(219\) −3.33917 −0.225640
\(220\) −11.1165 −0.749477
\(221\) 24.0580 1.61832
\(222\) −5.05935 −0.339562
\(223\) −4.53033 −0.303373 −0.151687 0.988429i \(-0.548470\pi\)
−0.151687 + 0.988429i \(0.548470\pi\)
\(224\) −2.08526 −0.139327
\(225\) −8.27294 −0.551529
\(226\) −1.47352 −0.0980173
\(227\) −4.60548 −0.305676 −0.152838 0.988251i \(-0.548841\pi\)
−0.152838 + 0.988251i \(0.548841\pi\)
\(228\) 1.37784 0.0912495
\(229\) −18.8360 −1.24472 −0.622359 0.782732i \(-0.713826\pi\)
−0.622359 + 0.782732i \(0.713826\pi\)
\(230\) −22.0082 −1.45117
\(231\) 9.03016 0.594141
\(232\) −6.86242 −0.450540
\(233\) 13.9203 0.911951 0.455976 0.889992i \(-0.349290\pi\)
0.455976 + 0.889992i \(0.349290\pi\)
\(234\) 4.40360 0.287872
\(235\) 2.93290 0.191321
\(236\) −10.5452 −0.686434
\(237\) −3.83663 −0.249216
\(238\) 12.5493 0.813453
\(239\) −1.61370 −0.104382 −0.0521909 0.998637i \(-0.516620\pi\)
−0.0521909 + 0.998637i \(0.516620\pi\)
\(240\) 4.87337 0.314575
\(241\) −5.33913 −0.343924 −0.171962 0.985104i \(-0.555011\pi\)
−0.171962 + 0.985104i \(0.555011\pi\)
\(242\) −1.12184 −0.0721143
\(243\) 10.7786 0.691447
\(244\) 2.06867 0.132433
\(245\) −9.37900 −0.599203
\(246\) 12.3439 0.787020
\(247\) −3.99759 −0.254360
\(248\) 6.59507 0.418787
\(249\) 17.7228 1.12314
\(250\) 8.87841 0.561520
\(251\) −15.5928 −0.984208 −0.492104 0.870536i \(-0.663772\pi\)
−0.492104 + 0.870536i \(0.663772\pi\)
\(252\) 2.29705 0.144700
\(253\) 19.5565 1.22950
\(254\) −12.0006 −0.752986
\(255\) −29.3286 −1.83663
\(256\) 1.00000 0.0625000
\(257\) 16.7444 1.04449 0.522244 0.852796i \(-0.325095\pi\)
0.522244 + 0.852796i \(0.325095\pi\)
\(258\) 0.419215 0.0260992
\(259\) 7.65696 0.475781
\(260\) −14.1394 −0.876886
\(261\) 7.55940 0.467915
\(262\) −8.37543 −0.517436
\(263\) 16.0204 0.987858 0.493929 0.869502i \(-0.335560\pi\)
0.493929 + 0.869502i \(0.335560\pi\)
\(264\) −4.33048 −0.266523
\(265\) 13.7947 0.847399
\(266\) −2.08526 −0.127855
\(267\) −4.26158 −0.260804
\(268\) 4.91181 0.300037
\(269\) −18.2562 −1.11310 −0.556551 0.830813i \(-0.687876\pi\)
−0.556551 + 0.830813i \(0.687876\pi\)
\(270\) −19.9885 −1.21646
\(271\) 19.6564 1.19404 0.597022 0.802225i \(-0.296351\pi\)
0.597022 + 0.802225i \(0.296351\pi\)
\(272\) −6.01813 −0.364902
\(273\) 11.4856 0.695143
\(274\) −10.7677 −0.650499
\(275\) −23.6041 −1.42338
\(276\) −8.57334 −0.516054
\(277\) −20.4390 −1.22806 −0.614030 0.789283i \(-0.710452\pi\)
−0.614030 + 0.789283i \(0.710452\pi\)
\(278\) 1.42665 0.0855649
\(279\) −7.26490 −0.434938
\(280\) −7.37550 −0.440770
\(281\) 6.65167 0.396805 0.198403 0.980121i \(-0.436425\pi\)
0.198403 + 0.980121i \(0.436425\pi\)
\(282\) 1.14252 0.0680360
\(283\) −9.99361 −0.594058 −0.297029 0.954868i \(-0.595996\pi\)
−0.297029 + 0.954868i \(0.595996\pi\)
\(284\) −1.61616 −0.0959016
\(285\) 4.87337 0.288674
\(286\) 12.5642 0.742939
\(287\) −18.6816 −1.10274
\(288\) −1.10156 −0.0649103
\(289\) 19.2178 1.13046
\(290\) −24.2722 −1.42531
\(291\) 4.00949 0.235041
\(292\) −2.42349 −0.141824
\(293\) 11.8689 0.693387 0.346694 0.937978i \(-0.387304\pi\)
0.346694 + 0.937978i \(0.387304\pi\)
\(294\) −3.65362 −0.213083
\(295\) −37.2981 −2.17158
\(296\) −3.67195 −0.213428
\(297\) 17.7617 1.03064
\(298\) −1.66215 −0.0962858
\(299\) 24.8742 1.43851
\(300\) 10.3478 0.597430
\(301\) −0.634451 −0.0365691
\(302\) 5.77068 0.332065
\(303\) −1.79817 −0.103302
\(304\) 1.00000 0.0573539
\(305\) 7.31682 0.418960
\(306\) 6.62935 0.378975
\(307\) 0.203433 0.0116105 0.00580526 0.999983i \(-0.498152\pi\)
0.00580526 + 0.999983i \(0.498152\pi\)
\(308\) 6.55387 0.373441
\(309\) −17.0040 −0.967326
\(310\) 23.3266 1.32486
\(311\) 6.86918 0.389515 0.194758 0.980851i \(-0.437608\pi\)
0.194758 + 0.980851i \(0.437608\pi\)
\(312\) −5.50802 −0.311830
\(313\) 13.2839 0.750852 0.375426 0.926852i \(-0.377496\pi\)
0.375426 + 0.926852i \(0.377496\pi\)
\(314\) −7.85464 −0.443263
\(315\) 8.12459 0.457769
\(316\) −2.78453 −0.156642
\(317\) 2.61783 0.147032 0.0735161 0.997294i \(-0.476578\pi\)
0.0735161 + 0.997294i \(0.476578\pi\)
\(318\) 5.37374 0.301345
\(319\) 21.5683 1.20759
\(320\) 3.53697 0.197723
\(321\) 1.58410 0.0884159
\(322\) 12.9751 0.723075
\(323\) −6.01813 −0.334857
\(324\) −4.48186 −0.248992
\(325\) −30.0226 −1.66535
\(326\) −4.10851 −0.227549
\(327\) 6.30048 0.348417
\(328\) 8.95892 0.494674
\(329\) −1.72912 −0.0953294
\(330\) −15.3168 −0.843161
\(331\) 1.55037 0.0852161 0.0426081 0.999092i \(-0.486433\pi\)
0.0426081 + 0.999092i \(0.486433\pi\)
\(332\) 12.8628 0.705937
\(333\) 4.04489 0.221659
\(334\) 7.06678 0.386677
\(335\) 17.3729 0.949185
\(336\) −2.87314 −0.156743
\(337\) −2.68537 −0.146281 −0.0731406 0.997322i \(-0.523302\pi\)
−0.0731406 + 0.997322i \(0.523302\pi\)
\(338\) 2.98071 0.162129
\(339\) −2.03028 −0.110269
\(340\) −21.2859 −1.15439
\(341\) −20.7280 −1.12248
\(342\) −1.10156 −0.0595658
\(343\) 20.1263 1.08672
\(344\) 0.304255 0.0164044
\(345\) −30.3237 −1.63257
\(346\) 9.71788 0.522436
\(347\) 31.9733 1.71642 0.858209 0.513300i \(-0.171577\pi\)
0.858209 + 0.513300i \(0.171577\pi\)
\(348\) −9.45530 −0.506857
\(349\) −10.4598 −0.559899 −0.279949 0.960015i \(-0.590318\pi\)
−0.279949 + 0.960015i \(0.590318\pi\)
\(350\) −15.6606 −0.837096
\(351\) 22.5915 1.20585
\(352\) −3.14295 −0.167520
\(353\) 16.4897 0.877659 0.438829 0.898570i \(-0.355393\pi\)
0.438829 + 0.898570i \(0.355393\pi\)
\(354\) −14.5296 −0.772238
\(355\) −5.71632 −0.303391
\(356\) −3.09295 −0.163926
\(357\) 17.2909 0.915134
\(358\) −24.7875 −1.31006
\(359\) 22.9622 1.21190 0.605949 0.795504i \(-0.292794\pi\)
0.605949 + 0.795504i \(0.292794\pi\)
\(360\) −3.89620 −0.205348
\(361\) 1.00000 0.0526316
\(362\) −2.42472 −0.127441
\(363\) −1.54571 −0.0811286
\(364\) 8.33600 0.436925
\(365\) −8.57180 −0.448669
\(366\) 2.85029 0.148987
\(367\) 11.1602 0.582558 0.291279 0.956638i \(-0.405919\pi\)
0.291279 + 0.956638i \(0.405919\pi\)
\(368\) −6.22231 −0.324361
\(369\) −9.86883 −0.513751
\(370\) −12.9876 −0.675193
\(371\) −8.13277 −0.422233
\(372\) 9.08693 0.471135
\(373\) −22.3744 −1.15850 −0.579250 0.815150i \(-0.696655\pi\)
−0.579250 + 0.815150i \(0.696655\pi\)
\(374\) 18.9147 0.978056
\(375\) 12.2330 0.631710
\(376\) 0.829211 0.0427633
\(377\) 27.4331 1.41288
\(378\) 11.7844 0.606123
\(379\) −24.4532 −1.25608 −0.628039 0.778182i \(-0.716142\pi\)
−0.628039 + 0.778182i \(0.716142\pi\)
\(380\) 3.53697 0.181443
\(381\) −16.5349 −0.847109
\(382\) 19.0532 0.974849
\(383\) −25.9429 −1.32562 −0.662811 0.748787i \(-0.730637\pi\)
−0.662811 + 0.748787i \(0.730637\pi\)
\(384\) 1.37784 0.0703125
\(385\) 23.1808 1.18141
\(386\) −6.16409 −0.313744
\(387\) −0.335157 −0.0170370
\(388\) 2.90999 0.147732
\(389\) 24.6340 1.24899 0.624497 0.781028i \(-0.285304\pi\)
0.624497 + 0.781028i \(0.285304\pi\)
\(390\) −19.4817 −0.986496
\(391\) 37.4467 1.89376
\(392\) −2.65170 −0.133931
\(393\) −11.5400 −0.582115
\(394\) 3.38890 0.170730
\(395\) −9.84882 −0.495548
\(396\) 3.46217 0.173980
\(397\) 13.3044 0.667728 0.333864 0.942621i \(-0.391647\pi\)
0.333864 + 0.942621i \(0.391647\pi\)
\(398\) 7.72991 0.387465
\(399\) −2.87314 −0.143837
\(400\) 7.51017 0.375509
\(401\) 16.5602 0.826977 0.413489 0.910509i \(-0.364310\pi\)
0.413489 + 0.910509i \(0.364310\pi\)
\(402\) 6.76768 0.337541
\(403\) −26.3644 −1.31330
\(404\) −1.30507 −0.0649296
\(405\) −15.8522 −0.787703
\(406\) 14.3099 0.710189
\(407\) 11.5408 0.572055
\(408\) −8.29200 −0.410515
\(409\) 26.6765 1.31907 0.659534 0.751675i \(-0.270754\pi\)
0.659534 + 0.751675i \(0.270754\pi\)
\(410\) 31.6874 1.56493
\(411\) −14.8361 −0.731811
\(412\) −12.3411 −0.608003
\(413\) 21.9894 1.08203
\(414\) 6.85428 0.336870
\(415\) 45.4953 2.23328
\(416\) −3.99759 −0.195998
\(417\) 1.96569 0.0962604
\(418\) −3.14295 −0.153727
\(419\) −27.4551 −1.34127 −0.670635 0.741788i \(-0.733978\pi\)
−0.670635 + 0.741788i \(0.733978\pi\)
\(420\) −10.1622 −0.495866
\(421\) 11.2610 0.548828 0.274414 0.961612i \(-0.411516\pi\)
0.274414 + 0.961612i \(0.411516\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −0.913430 −0.0444125
\(424\) 3.90013 0.189407
\(425\) −45.1972 −2.19238
\(426\) −2.22681 −0.107889
\(427\) −4.31370 −0.208755
\(428\) 1.14970 0.0555729
\(429\) 17.3115 0.835806
\(430\) 1.07614 0.0518962
\(431\) 18.3117 0.882041 0.441021 0.897497i \(-0.354617\pi\)
0.441021 + 0.897497i \(0.354617\pi\)
\(432\) −5.65129 −0.271898
\(433\) −17.6693 −0.849134 −0.424567 0.905396i \(-0.639574\pi\)
−0.424567 + 0.905396i \(0.639574\pi\)
\(434\) −13.7524 −0.660137
\(435\) −33.4431 −1.60348
\(436\) 4.57273 0.218994
\(437\) −6.22231 −0.297654
\(438\) −3.33917 −0.159552
\(439\) 13.3069 0.635106 0.317553 0.948241i \(-0.397139\pi\)
0.317553 + 0.948241i \(0.397139\pi\)
\(440\) −11.1165 −0.529960
\(441\) 2.92102 0.139096
\(442\) 24.0580 1.14432
\(443\) 15.0992 0.717385 0.358693 0.933456i \(-0.383223\pi\)
0.358693 + 0.933456i \(0.383223\pi\)
\(444\) −5.05935 −0.240106
\(445\) −10.9397 −0.518590
\(446\) −4.53033 −0.214517
\(447\) −2.29017 −0.108321
\(448\) −2.08526 −0.0985191
\(449\) 7.48980 0.353465 0.176733 0.984259i \(-0.443447\pi\)
0.176733 + 0.984259i \(0.443447\pi\)
\(450\) −8.27294 −0.389990
\(451\) −28.1575 −1.32588
\(452\) −1.47352 −0.0693087
\(453\) 7.95106 0.373573
\(454\) −4.60548 −0.216146
\(455\) 29.4842 1.38224
\(456\) 1.37784 0.0645231
\(457\) −13.3573 −0.624827 −0.312413 0.949946i \(-0.601137\pi\)
−0.312413 + 0.949946i \(0.601137\pi\)
\(458\) −18.8360 −0.880149
\(459\) 34.0102 1.58746
\(460\) −22.0082 −1.02614
\(461\) −29.7300 −1.38467 −0.692333 0.721578i \(-0.743417\pi\)
−0.692333 + 0.721578i \(0.743417\pi\)
\(462\) 9.03016 0.420121
\(463\) −15.9808 −0.742691 −0.371345 0.928495i \(-0.621103\pi\)
−0.371345 + 0.928495i \(0.621103\pi\)
\(464\) −6.86242 −0.318580
\(465\) 32.1402 1.49047
\(466\) 13.9203 0.644847
\(467\) 10.1118 0.467920 0.233960 0.972246i \(-0.424832\pi\)
0.233960 + 0.972246i \(0.424832\pi\)
\(468\) 4.40360 0.203557
\(469\) −10.2424 −0.472950
\(470\) 2.93290 0.135284
\(471\) −10.8224 −0.498671
\(472\) −10.5452 −0.485382
\(473\) −0.956261 −0.0439689
\(474\) −3.83663 −0.176222
\(475\) 7.51017 0.344590
\(476\) 12.5493 0.575198
\(477\) −4.29625 −0.196712
\(478\) −1.61370 −0.0738091
\(479\) −18.6733 −0.853203 −0.426602 0.904440i \(-0.640289\pi\)
−0.426602 + 0.904440i \(0.640289\pi\)
\(480\) 4.87337 0.222438
\(481\) 14.6790 0.669303
\(482\) −5.33913 −0.243191
\(483\) 17.8776 0.813459
\(484\) −1.12184 −0.0509925
\(485\) 10.2926 0.467361
\(486\) 10.7786 0.488927
\(487\) 7.80494 0.353676 0.176838 0.984240i \(-0.443413\pi\)
0.176838 + 0.984240i \(0.443413\pi\)
\(488\) 2.06867 0.0936442
\(489\) −5.66085 −0.255993
\(490\) −9.37900 −0.423700
\(491\) 30.4261 1.37311 0.686556 0.727077i \(-0.259122\pi\)
0.686556 + 0.727077i \(0.259122\pi\)
\(492\) 12.3439 0.556507
\(493\) 41.2989 1.86001
\(494\) −3.99759 −0.179860
\(495\) 12.2456 0.550398
\(496\) 6.59507 0.296127
\(497\) 3.37011 0.151170
\(498\) 17.7228 0.794178
\(499\) −27.5678 −1.23411 −0.617053 0.786922i \(-0.711673\pi\)
−0.617053 + 0.786922i \(0.711673\pi\)
\(500\) 8.87841 0.397055
\(501\) 9.73687 0.435011
\(502\) −15.5928 −0.695940
\(503\) −21.2454 −0.947283 −0.473642 0.880718i \(-0.657061\pi\)
−0.473642 + 0.880718i \(0.657061\pi\)
\(504\) 2.29705 0.102319
\(505\) −4.61599 −0.205409
\(506\) 19.5565 0.869390
\(507\) 4.10693 0.182395
\(508\) −12.0006 −0.532442
\(509\) −8.63307 −0.382654 −0.191327 0.981526i \(-0.561279\pi\)
−0.191327 + 0.981526i \(0.561279\pi\)
\(510\) −29.3286 −1.29869
\(511\) 5.05359 0.223558
\(512\) 1.00000 0.0441942
\(513\) −5.65129 −0.249510
\(514\) 16.7444 0.738564
\(515\) −43.6502 −1.92346
\(516\) 0.419215 0.0184549
\(517\) −2.60617 −0.114619
\(518\) 7.65696 0.336428
\(519\) 13.3897 0.587741
\(520\) −14.1394 −0.620052
\(521\) 39.7373 1.74092 0.870461 0.492237i \(-0.163821\pi\)
0.870461 + 0.492237i \(0.163821\pi\)
\(522\) 7.55940 0.330866
\(523\) −12.5368 −0.548196 −0.274098 0.961702i \(-0.588379\pi\)
−0.274098 + 0.961702i \(0.588379\pi\)
\(524\) −8.37543 −0.365882
\(525\) −21.5778 −0.941733
\(526\) 16.0204 0.698521
\(527\) −39.6900 −1.72892
\(528\) −4.33048 −0.188460
\(529\) 15.7172 0.683357
\(530\) 13.7947 0.599201
\(531\) 11.6162 0.504101
\(532\) −2.08526 −0.0904073
\(533\) −35.8141 −1.55128
\(534\) −4.26158 −0.184417
\(535\) 4.06646 0.175809
\(536\) 4.91181 0.212158
\(537\) −34.1531 −1.47382
\(538\) −18.2562 −0.787082
\(539\) 8.33419 0.358979
\(540\) −19.9885 −0.860166
\(541\) 29.9048 1.28571 0.642855 0.765988i \(-0.277750\pi\)
0.642855 + 0.765988i \(0.277750\pi\)
\(542\) 19.6564 0.844317
\(543\) −3.34087 −0.143371
\(544\) −6.01813 −0.258025
\(545\) 16.1736 0.692802
\(546\) 11.4856 0.491540
\(547\) 17.3234 0.740696 0.370348 0.928893i \(-0.379238\pi\)
0.370348 + 0.928893i \(0.379238\pi\)
\(548\) −10.7677 −0.459972
\(549\) −2.27877 −0.0972556
\(550\) −23.6041 −1.00648
\(551\) −6.86242 −0.292349
\(552\) −8.57334 −0.364905
\(553\) 5.80647 0.246916
\(554\) −20.4390 −0.868369
\(555\) −17.8948 −0.759592
\(556\) 1.42665 0.0605035
\(557\) −29.8705 −1.26565 −0.632827 0.774293i \(-0.718106\pi\)
−0.632827 + 0.774293i \(0.718106\pi\)
\(558\) −7.26490 −0.307548
\(559\) −1.21629 −0.0514435
\(560\) −7.37550 −0.311672
\(561\) 26.0614 1.10031
\(562\) 6.65167 0.280584
\(563\) 21.5489 0.908178 0.454089 0.890956i \(-0.349965\pi\)
0.454089 + 0.890956i \(0.349965\pi\)
\(564\) 1.14252 0.0481087
\(565\) −5.21181 −0.219263
\(566\) −9.99361 −0.420063
\(567\) 9.34583 0.392488
\(568\) −1.61616 −0.0678126
\(569\) −27.9037 −1.16979 −0.584893 0.811111i \(-0.698863\pi\)
−0.584893 + 0.811111i \(0.698863\pi\)
\(570\) 4.87337 0.204123
\(571\) 32.8503 1.37474 0.687371 0.726307i \(-0.258765\pi\)
0.687371 + 0.726307i \(0.258765\pi\)
\(572\) 12.5642 0.525337
\(573\) 26.2523 1.09670
\(574\) −18.6816 −0.779757
\(575\) −46.7307 −1.94880
\(576\) −1.10156 −0.0458985
\(577\) −5.47732 −0.228024 −0.114012 0.993479i \(-0.536370\pi\)
−0.114012 + 0.993479i \(0.536370\pi\)
\(578\) 19.2178 0.799356
\(579\) −8.49311 −0.352962
\(580\) −24.2722 −1.00785
\(581\) −26.8222 −1.11277
\(582\) 4.00949 0.166199
\(583\) −12.2579 −0.507672
\(584\) −2.42349 −0.100285
\(585\) 15.5754 0.643964
\(586\) 11.8689 0.490299
\(587\) −11.0692 −0.456873 −0.228437 0.973559i \(-0.573361\pi\)
−0.228437 + 0.973559i \(0.573361\pi\)
\(588\) −3.65362 −0.150673
\(589\) 6.59507 0.271745
\(590\) −37.2981 −1.53554
\(591\) 4.66935 0.192071
\(592\) −3.67195 −0.150916
\(593\) −14.4974 −0.595337 −0.297669 0.954669i \(-0.596209\pi\)
−0.297669 + 0.954669i \(0.596209\pi\)
\(594\) 17.7617 0.728773
\(595\) 44.3867 1.81968
\(596\) −1.66215 −0.0680843
\(597\) 10.6506 0.435898
\(598\) 24.8742 1.01718
\(599\) 17.2497 0.704802 0.352401 0.935849i \(-0.385365\pi\)
0.352401 + 0.935849i \(0.385365\pi\)
\(600\) 10.3478 0.422447
\(601\) −27.1951 −1.10931 −0.554655 0.832081i \(-0.687150\pi\)
−0.554655 + 0.832081i \(0.687150\pi\)
\(602\) −0.634451 −0.0258583
\(603\) −5.41068 −0.220340
\(604\) 5.77068 0.234806
\(605\) −3.96790 −0.161318
\(606\) −1.79817 −0.0730458
\(607\) 29.3930 1.19303 0.596513 0.802604i \(-0.296553\pi\)
0.596513 + 0.802604i \(0.296553\pi\)
\(608\) 1.00000 0.0405554
\(609\) 19.7167 0.798962
\(610\) 7.31682 0.296250
\(611\) −3.31484 −0.134104
\(612\) 6.62935 0.267976
\(613\) −26.7405 −1.08004 −0.540020 0.841652i \(-0.681583\pi\)
−0.540020 + 0.841652i \(0.681583\pi\)
\(614\) 0.203433 0.00820988
\(615\) 43.6601 1.76055
\(616\) 6.55387 0.264063
\(617\) −2.53854 −0.102198 −0.0510989 0.998694i \(-0.516272\pi\)
−0.0510989 + 0.998694i \(0.516272\pi\)
\(618\) −17.0040 −0.684003
\(619\) 4.50555 0.181093 0.0905467 0.995892i \(-0.471139\pi\)
0.0905467 + 0.995892i \(0.471139\pi\)
\(620\) 23.3266 0.936818
\(621\) 35.1641 1.41109
\(622\) 6.86918 0.275429
\(623\) 6.44959 0.258398
\(624\) −5.50802 −0.220497
\(625\) −6.14817 −0.245927
\(626\) 13.2839 0.530933
\(627\) −4.33048 −0.172943
\(628\) −7.85464 −0.313434
\(629\) 22.0983 0.881116
\(630\) 8.12459 0.323691
\(631\) 14.0791 0.560478 0.280239 0.959930i \(-0.409586\pi\)
0.280239 + 0.959930i \(0.409586\pi\)
\(632\) −2.78453 −0.110763
\(633\) −1.37784 −0.0547641
\(634\) 2.61783 0.103967
\(635\) −42.4459 −1.68441
\(636\) 5.37374 0.213083
\(637\) 10.6004 0.420004
\(638\) 21.5683 0.853896
\(639\) 1.78031 0.0704278
\(640\) 3.53697 0.139811
\(641\) −24.3660 −0.962399 −0.481199 0.876611i \(-0.659799\pi\)
−0.481199 + 0.876611i \(0.659799\pi\)
\(642\) 1.58410 0.0625195
\(643\) 45.0314 1.77586 0.887932 0.459975i \(-0.152142\pi\)
0.887932 + 0.459975i \(0.152142\pi\)
\(644\) 12.9751 0.511292
\(645\) 1.48275 0.0583832
\(646\) −6.01813 −0.236780
\(647\) −7.60264 −0.298891 −0.149445 0.988770i \(-0.547749\pi\)
−0.149445 + 0.988770i \(0.547749\pi\)
\(648\) −4.48186 −0.176064
\(649\) 33.1431 1.30098
\(650\) −30.0226 −1.17758
\(651\) −18.9486 −0.742654
\(652\) −4.10851 −0.160902
\(653\) −21.0806 −0.824948 −0.412474 0.910969i \(-0.635335\pi\)
−0.412474 + 0.910969i \(0.635335\pi\)
\(654\) 6.30048 0.246368
\(655\) −29.6237 −1.15749
\(656\) 8.95892 0.349787
\(657\) 2.66963 0.104152
\(658\) −1.72912 −0.0674081
\(659\) 28.7679 1.12064 0.560320 0.828276i \(-0.310678\pi\)
0.560320 + 0.828276i \(0.310678\pi\)
\(660\) −15.3168 −0.596205
\(661\) −29.5633 −1.14988 −0.574940 0.818196i \(-0.694975\pi\)
−0.574940 + 0.818196i \(0.694975\pi\)
\(662\) 1.55037 0.0602569
\(663\) 33.1480 1.28736
\(664\) 12.8628 0.499173
\(665\) −7.37550 −0.286009
\(666\) 4.04489 0.156736
\(667\) 42.7001 1.65336
\(668\) 7.06678 0.273422
\(669\) −6.24206 −0.241332
\(670\) 17.3729 0.671175
\(671\) −6.50173 −0.250997
\(672\) −2.87314 −0.110834
\(673\) −19.2315 −0.741318 −0.370659 0.928769i \(-0.620868\pi\)
−0.370659 + 0.928769i \(0.620868\pi\)
\(674\) −2.68537 −0.103436
\(675\) −42.4422 −1.63360
\(676\) 2.98071 0.114643
\(677\) 13.8011 0.530421 0.265210 0.964191i \(-0.414559\pi\)
0.265210 + 0.964191i \(0.414559\pi\)
\(678\) −2.03028 −0.0779723
\(679\) −6.06808 −0.232871
\(680\) −21.2859 −0.816279
\(681\) −6.34560 −0.243164
\(682\) −20.7280 −0.793716
\(683\) −19.4834 −0.745511 −0.372756 0.927930i \(-0.621587\pi\)
−0.372756 + 0.927930i \(0.621587\pi\)
\(684\) −1.10156 −0.0421194
\(685\) −38.0850 −1.45515
\(686\) 20.1263 0.768425
\(687\) −25.9529 −0.990167
\(688\) 0.304255 0.0115996
\(689\) −15.5911 −0.593974
\(690\) −30.3237 −1.15440
\(691\) 37.7494 1.43605 0.718027 0.696015i \(-0.245045\pi\)
0.718027 + 0.696015i \(0.245045\pi\)
\(692\) 9.71788 0.369418
\(693\) −7.21951 −0.274246
\(694\) 31.9733 1.21369
\(695\) 5.04603 0.191407
\(696\) −9.45530 −0.358402
\(697\) −53.9159 −2.04221
\(698\) −10.4598 −0.395908
\(699\) 19.1799 0.725452
\(700\) −15.6606 −0.591917
\(701\) −28.1212 −1.06212 −0.531061 0.847334i \(-0.678206\pi\)
−0.531061 + 0.847334i \(0.678206\pi\)
\(702\) 22.5915 0.852662
\(703\) −3.67195 −0.138490
\(704\) −3.14295 −0.118455
\(705\) 4.04105 0.152195
\(706\) 16.4897 0.620598
\(707\) 2.72140 0.102349
\(708\) −14.5296 −0.546054
\(709\) −8.69213 −0.326440 −0.163220 0.986590i \(-0.552188\pi\)
−0.163220 + 0.986590i \(0.552188\pi\)
\(710\) −5.71632 −0.214530
\(711\) 3.06734 0.115034
\(712\) −3.09295 −0.115913
\(713\) −41.0366 −1.53683
\(714\) 17.2909 0.647097
\(715\) 44.4394 1.66194
\(716\) −24.7875 −0.926352
\(717\) −2.22342 −0.0830352
\(718\) 22.9622 0.856941
\(719\) 18.3861 0.685686 0.342843 0.939393i \(-0.388610\pi\)
0.342843 + 0.939393i \(0.388610\pi\)
\(720\) −3.89620 −0.145203
\(721\) 25.7344 0.958399
\(722\) 1.00000 0.0372161
\(723\) −7.35646 −0.273590
\(724\) −2.42472 −0.0901142
\(725\) −51.5380 −1.91407
\(726\) −1.54571 −0.0573666
\(727\) 17.5555 0.651097 0.325548 0.945525i \(-0.394451\pi\)
0.325548 + 0.945525i \(0.394451\pi\)
\(728\) 8.33600 0.308953
\(729\) 28.2967 1.04803
\(730\) −8.57180 −0.317257
\(731\) −1.83105 −0.0677237
\(732\) 2.85029 0.105350
\(733\) −46.1061 −1.70297 −0.851483 0.524382i \(-0.824296\pi\)
−0.851483 + 0.524382i \(0.824296\pi\)
\(734\) 11.1602 0.411931
\(735\) −12.9227 −0.476662
\(736\) −6.22231 −0.229358
\(737\) −15.4376 −0.568651
\(738\) −9.86883 −0.363277
\(739\) 22.4589 0.826162 0.413081 0.910694i \(-0.364453\pi\)
0.413081 + 0.910694i \(0.364453\pi\)
\(740\) −12.9876 −0.477433
\(741\) −5.50802 −0.202342
\(742\) −8.13277 −0.298564
\(743\) −49.4864 −1.81548 −0.907741 0.419531i \(-0.862194\pi\)
−0.907741 + 0.419531i \(0.862194\pi\)
\(744\) 9.08693 0.333143
\(745\) −5.87898 −0.215389
\(746\) −22.3744 −0.819183
\(747\) −14.1692 −0.518423
\(748\) 18.9147 0.691590
\(749\) −2.39742 −0.0875999
\(750\) 12.2330 0.446686
\(751\) −20.0847 −0.732900 −0.366450 0.930438i \(-0.619427\pi\)
−0.366450 + 0.930438i \(0.619427\pi\)
\(752\) 0.829211 0.0302382
\(753\) −21.4843 −0.782932
\(754\) 27.4331 0.999056
\(755\) 20.4107 0.742823
\(756\) 11.7844 0.428594
\(757\) −26.3031 −0.956003 −0.478002 0.878359i \(-0.658639\pi\)
−0.478002 + 0.878359i \(0.658639\pi\)
\(758\) −24.4532 −0.888181
\(759\) 26.9456 0.978064
\(760\) 3.53697 0.128299
\(761\) −28.8315 −1.04514 −0.522570 0.852597i \(-0.675027\pi\)
−0.522570 + 0.852597i \(0.675027\pi\)
\(762\) −16.5349 −0.598997
\(763\) −9.53532 −0.345202
\(764\) 19.0532 0.689322
\(765\) 23.4478 0.847759
\(766\) −25.9429 −0.937356
\(767\) 42.1553 1.52214
\(768\) 1.37784 0.0497184
\(769\) 17.7757 0.641007 0.320503 0.947247i \(-0.396148\pi\)
0.320503 + 0.947247i \(0.396148\pi\)
\(770\) 23.1808 0.835380
\(771\) 23.0711 0.830884
\(772\) −6.16409 −0.221850
\(773\) −1.54444 −0.0555497 −0.0277749 0.999614i \(-0.508842\pi\)
−0.0277749 + 0.999614i \(0.508842\pi\)
\(774\) −0.335157 −0.0120470
\(775\) 49.5301 1.77917
\(776\) 2.90999 0.104463
\(777\) 10.5500 0.378481
\(778\) 24.6340 0.883171
\(779\) 8.95892 0.320987
\(780\) −19.4817 −0.697558
\(781\) 5.07952 0.181760
\(782\) 37.4467 1.33909
\(783\) 38.7815 1.38594
\(784\) −2.65170 −0.0947037
\(785\) −27.7817 −0.991570
\(786\) −11.5400 −0.411617
\(787\) −14.7378 −0.525345 −0.262673 0.964885i \(-0.584604\pi\)
−0.262673 + 0.964885i \(0.584604\pi\)
\(788\) 3.38890 0.120725
\(789\) 22.0734 0.785835
\(790\) −9.84882 −0.350405
\(791\) 3.07267 0.109252
\(792\) 3.46217 0.123023
\(793\) −8.26968 −0.293665
\(794\) 13.3044 0.472155
\(795\) 19.0068 0.674101
\(796\) 7.72991 0.273979
\(797\) −14.7054 −0.520892 −0.260446 0.965488i \(-0.583870\pi\)
−0.260446 + 0.965488i \(0.583870\pi\)
\(798\) −2.87314 −0.101708
\(799\) −4.99030 −0.176544
\(800\) 7.51017 0.265525
\(801\) 3.40708 0.120383
\(802\) 16.5602 0.584761
\(803\) 7.61691 0.268795
\(804\) 6.76768 0.238678
\(805\) 45.8927 1.61750
\(806\) −26.3644 −0.928645
\(807\) −25.1541 −0.885467
\(808\) −1.30507 −0.0459122
\(809\) 21.3092 0.749191 0.374596 0.927188i \(-0.377782\pi\)
0.374596 + 0.927188i \(0.377782\pi\)
\(810\) −15.8522 −0.556990
\(811\) 55.7967 1.95929 0.979644 0.200745i \(-0.0643363\pi\)
0.979644 + 0.200745i \(0.0643363\pi\)
\(812\) 14.3099 0.502179
\(813\) 27.0834 0.949856
\(814\) 11.5408 0.404504
\(815\) −14.5317 −0.509022
\(816\) −8.29200 −0.290278
\(817\) 0.304255 0.0106446
\(818\) 26.6765 0.932721
\(819\) −9.18264 −0.320867
\(820\) 31.6874 1.10657
\(821\) −36.2826 −1.26627 −0.633136 0.774041i \(-0.718232\pi\)
−0.633136 + 0.774041i \(0.718232\pi\)
\(822\) −14.8361 −0.517468
\(823\) 40.4131 1.40871 0.704356 0.709847i \(-0.251236\pi\)
0.704356 + 0.709847i \(0.251236\pi\)
\(824\) −12.3411 −0.429923
\(825\) −32.5227 −1.13229
\(826\) 21.9894 0.765110
\(827\) −14.6019 −0.507759 −0.253879 0.967236i \(-0.581707\pi\)
−0.253879 + 0.967236i \(0.581707\pi\)
\(828\) 6.85428 0.238203
\(829\) −47.6614 −1.65535 −0.827674 0.561209i \(-0.810336\pi\)
−0.827674 + 0.561209i \(0.810336\pi\)
\(830\) 45.4953 1.57916
\(831\) −28.1616 −0.976915
\(832\) −3.99759 −0.138591
\(833\) 15.9583 0.552922
\(834\) 1.96569 0.0680664
\(835\) 24.9950 0.864987
\(836\) −3.14295 −0.108701
\(837\) −37.2706 −1.28826
\(838\) −27.4551 −0.948421
\(839\) 30.1178 1.03978 0.519890 0.854233i \(-0.325973\pi\)
0.519890 + 0.854233i \(0.325973\pi\)
\(840\) −10.1622 −0.350630
\(841\) 18.0928 0.623891
\(842\) 11.2610 0.388080
\(843\) 9.16491 0.315656
\(844\) −1.00000 −0.0344214
\(845\) 10.5427 0.362679
\(846\) −0.913430 −0.0314044
\(847\) 2.33932 0.0803798
\(848\) 3.90013 0.133931
\(849\) −13.7696 −0.472570
\(850\) −45.1972 −1.55025
\(851\) 22.8480 0.783221
\(852\) −2.22681 −0.0762892
\(853\) −33.0738 −1.13243 −0.566213 0.824259i \(-0.691592\pi\)
−0.566213 + 0.824259i \(0.691592\pi\)
\(854\) −4.31370 −0.147612
\(855\) −3.89620 −0.133247
\(856\) 1.14970 0.0392960
\(857\) −42.3024 −1.44502 −0.722512 0.691358i \(-0.757013\pi\)
−0.722512 + 0.691358i \(0.757013\pi\)
\(858\) 17.3115 0.591004
\(859\) −21.3341 −0.727909 −0.363955 0.931417i \(-0.618574\pi\)
−0.363955 + 0.931417i \(0.618574\pi\)
\(860\) 1.07614 0.0366962
\(861\) −25.7403 −0.877226
\(862\) 18.3117 0.623697
\(863\) −32.4571 −1.10485 −0.552427 0.833561i \(-0.686298\pi\)
−0.552427 + 0.833561i \(0.686298\pi\)
\(864\) −5.65129 −0.192261
\(865\) 34.3719 1.16868
\(866\) −17.6693 −0.600429
\(867\) 26.4790 0.899276
\(868\) −13.7524 −0.466787
\(869\) 8.75166 0.296880
\(870\) −33.4431 −1.13383
\(871\) −19.6354 −0.665320
\(872\) 4.57273 0.154852
\(873\) −3.20554 −0.108491
\(874\) −6.22231 −0.210473
\(875\) −18.5138 −0.625880
\(876\) −3.33917 −0.112820
\(877\) 0.468896 0.0158335 0.00791675 0.999969i \(-0.497480\pi\)
0.00791675 + 0.999969i \(0.497480\pi\)
\(878\) 13.3069 0.449087
\(879\) 16.3534 0.551586
\(880\) −11.1165 −0.374739
\(881\) −36.5735 −1.23219 −0.616096 0.787671i \(-0.711287\pi\)
−0.616096 + 0.787671i \(0.711287\pi\)
\(882\) 2.92102 0.0983560
\(883\) −34.1591 −1.14954 −0.574772 0.818313i \(-0.694909\pi\)
−0.574772 + 0.818313i \(0.694909\pi\)
\(884\) 24.0580 0.809158
\(885\) −51.3907 −1.72748
\(886\) 15.0992 0.507268
\(887\) −48.8571 −1.64046 −0.820230 0.572034i \(-0.806155\pi\)
−0.820230 + 0.572034i \(0.806155\pi\)
\(888\) −5.05935 −0.169781
\(889\) 25.0244 0.839291
\(890\) −10.9397 −0.366699
\(891\) 14.0863 0.471908
\(892\) −4.53033 −0.151687
\(893\) 0.829211 0.0277485
\(894\) −2.29017 −0.0765948
\(895\) −87.6727 −2.93057
\(896\) −2.08526 −0.0696635
\(897\) 34.2727 1.14433
\(898\) 7.48980 0.249938
\(899\) −45.2581 −1.50944
\(900\) −8.27294 −0.275765
\(901\) −23.4715 −0.781948
\(902\) −28.1575 −0.937541
\(903\) −0.874170 −0.0290906
\(904\) −1.47352 −0.0490087
\(905\) −8.57618 −0.285082
\(906\) 7.95106 0.264156
\(907\) −0.521839 −0.0173274 −0.00866370 0.999962i \(-0.502758\pi\)
−0.00866370 + 0.999962i \(0.502758\pi\)
\(908\) −4.60548 −0.152838
\(909\) 1.43762 0.0476828
\(910\) 29.4842 0.977391
\(911\) −12.0419 −0.398967 −0.199484 0.979901i \(-0.563926\pi\)
−0.199484 + 0.979901i \(0.563926\pi\)
\(912\) 1.37784 0.0456247
\(913\) −40.4271 −1.33794
\(914\) −13.3573 −0.441819
\(915\) 10.0814 0.333280
\(916\) −18.8360 −0.622359
\(917\) 17.4649 0.576743
\(918\) 34.0102 1.12250
\(919\) 45.3593 1.49626 0.748132 0.663550i \(-0.230951\pi\)
0.748132 + 0.663550i \(0.230951\pi\)
\(920\) −22.0082 −0.725587
\(921\) 0.280297 0.00923611
\(922\) −29.7300 −0.979106
\(923\) 6.46075 0.212658
\(924\) 9.03016 0.297071
\(925\) −27.5770 −0.906726
\(926\) −15.9808 −0.525162
\(927\) 13.5945 0.446503
\(928\) −6.86242 −0.225270
\(929\) −21.1047 −0.692421 −0.346211 0.938157i \(-0.612532\pi\)
−0.346211 + 0.938157i \(0.612532\pi\)
\(930\) 32.1402 1.05392
\(931\) −2.65170 −0.0869061
\(932\) 13.9203 0.455976
\(933\) 9.46461 0.309857
\(934\) 10.1118 0.330869
\(935\) 66.9008 2.18789
\(936\) 4.40360 0.143936
\(937\) 21.8671 0.714368 0.357184 0.934034i \(-0.383737\pi\)
0.357184 + 0.934034i \(0.383737\pi\)
\(938\) −10.2424 −0.334426
\(939\) 18.3031 0.597299
\(940\) 2.93290 0.0956606
\(941\) 9.59255 0.312708 0.156354 0.987701i \(-0.450026\pi\)
0.156354 + 0.987701i \(0.450026\pi\)
\(942\) −10.8224 −0.352614
\(943\) −55.7452 −1.81531
\(944\) −10.5452 −0.343217
\(945\) 41.6811 1.35588
\(946\) −0.956261 −0.0310907
\(947\) −34.1196 −1.10874 −0.554368 0.832271i \(-0.687040\pi\)
−0.554368 + 0.832271i \(0.687040\pi\)
\(948\) −3.83663 −0.124608
\(949\) 9.68810 0.314489
\(950\) 7.51017 0.243662
\(951\) 3.60695 0.116963
\(952\) 12.5493 0.406726
\(953\) −41.1267 −1.33223 −0.666113 0.745851i \(-0.732043\pi\)
−0.666113 + 0.745851i \(0.732043\pi\)
\(954\) −4.29625 −0.139096
\(955\) 67.3908 2.18071
\(956\) −1.61370 −0.0521909
\(957\) 29.7176 0.960633
\(958\) −18.6733 −0.603306
\(959\) 22.4534 0.725057
\(960\) 4.87337 0.157287
\(961\) 12.4949 0.403062
\(962\) 14.6790 0.473268
\(963\) −1.26647 −0.0408115
\(964\) −5.33913 −0.171962
\(965\) −21.8022 −0.701838
\(966\) 17.8776 0.575203
\(967\) −48.9448 −1.57396 −0.786980 0.616979i \(-0.788357\pi\)
−0.786980 + 0.616979i \(0.788357\pi\)
\(968\) −1.12184 −0.0360572
\(969\) −8.29200 −0.266377
\(970\) 10.2926 0.330474
\(971\) −51.4521 −1.65118 −0.825589 0.564272i \(-0.809157\pi\)
−0.825589 + 0.564272i \(0.809157\pi\)
\(972\) 10.7786 0.345723
\(973\) −2.97494 −0.0953720
\(974\) 7.80494 0.250087
\(975\) −41.3662 −1.32478
\(976\) 2.06867 0.0662165
\(977\) −16.1395 −0.516349 −0.258175 0.966098i \(-0.583121\pi\)
−0.258175 + 0.966098i \(0.583121\pi\)
\(978\) −5.66085 −0.181014
\(979\) 9.72100 0.310684
\(980\) −9.37900 −0.299601
\(981\) −5.03716 −0.160824
\(982\) 30.4261 0.970937
\(983\) −17.2121 −0.548981 −0.274490 0.961590i \(-0.588509\pi\)
−0.274490 + 0.961590i \(0.588509\pi\)
\(984\) 12.3439 0.393510
\(985\) 11.9864 0.381920
\(986\) 41.2989 1.31523
\(987\) −2.38244 −0.0758340
\(988\) −3.99759 −0.127180
\(989\) −1.89317 −0.0601994
\(990\) 12.2456 0.389190
\(991\) −6.25321 −0.198640 −0.0993198 0.995056i \(-0.531667\pi\)
−0.0993198 + 0.995056i \(0.531667\pi\)
\(992\) 6.59507 0.209394
\(993\) 2.13616 0.0677890
\(994\) 3.37011 0.106893
\(995\) 27.3405 0.866751
\(996\) 17.7228 0.561569
\(997\) −10.4092 −0.329663 −0.164832 0.986322i \(-0.552708\pi\)
−0.164832 + 0.986322i \(0.552708\pi\)
\(998\) −27.5678 −0.872644
\(999\) 20.7513 0.656541
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 \(a_p\))