Properties

Label 4017.2.a.j.1.13
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0202075 q^{2} -1.00000 q^{3} -1.99959 q^{4} -1.35659 q^{5} -0.0202075 q^{6} -0.669195 q^{7} -0.0808216 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.0202075 q^{2} -1.00000 q^{3} -1.99959 q^{4} -1.35659 q^{5} -0.0202075 q^{6} -0.669195 q^{7} -0.0808216 q^{8} +1.00000 q^{9} -0.0274131 q^{10} +3.21751 q^{11} +1.99959 q^{12} +1.00000 q^{13} -0.0135227 q^{14} +1.35659 q^{15} +3.99755 q^{16} -0.412109 q^{17} +0.0202075 q^{18} +1.46743 q^{19} +2.71262 q^{20} +0.669195 q^{21} +0.0650177 q^{22} -2.51016 q^{23} +0.0808216 q^{24} -3.15968 q^{25} +0.0202075 q^{26} -1.00000 q^{27} +1.33812 q^{28} +1.53778 q^{29} +0.0274131 q^{30} +2.21745 q^{31} +0.242423 q^{32} -3.21751 q^{33} -0.00832767 q^{34} +0.907820 q^{35} -1.99959 q^{36} -4.89090 q^{37} +0.0296529 q^{38} -1.00000 q^{39} +0.109641 q^{40} -9.85948 q^{41} +0.0135227 q^{42} -7.39732 q^{43} -6.43371 q^{44} -1.35659 q^{45} -0.0507240 q^{46} -0.629405 q^{47} -3.99755 q^{48} -6.55218 q^{49} -0.0638490 q^{50} +0.412109 q^{51} -1.99959 q^{52} +6.18867 q^{53} -0.0202075 q^{54} -4.36483 q^{55} +0.0540854 q^{56} -1.46743 q^{57} +0.0310746 q^{58} -0.139569 q^{59} -2.71262 q^{60} +10.2963 q^{61} +0.0448090 q^{62} -0.669195 q^{63} -7.99020 q^{64} -1.35659 q^{65} -0.0650177 q^{66} +9.27090 q^{67} +0.824049 q^{68} +2.51016 q^{69} +0.0183447 q^{70} -14.2096 q^{71} -0.0808216 q^{72} +2.85045 q^{73} -0.0988325 q^{74} +3.15968 q^{75} -2.93425 q^{76} -2.15314 q^{77} -0.0202075 q^{78} -3.10012 q^{79} -5.42302 q^{80} +1.00000 q^{81} -0.199235 q^{82} +7.16852 q^{83} -1.33812 q^{84} +0.559061 q^{85} -0.149481 q^{86} -1.53778 q^{87} -0.260044 q^{88} +12.7296 q^{89} -0.0274131 q^{90} -0.669195 q^{91} +5.01930 q^{92} -2.21745 q^{93} -0.0127187 q^{94} -1.99069 q^{95} -0.242423 q^{96} +2.47992 q^{97} -0.132403 q^{98} +3.21751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0202075 0.0142888 0.00714441 0.999974i \(-0.497726\pi\)
0.00714441 + 0.999974i \(0.497726\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99959 −0.999796
\(5\) −1.35659 −0.606684 −0.303342 0.952882i \(-0.598102\pi\)
−0.303342 + 0.952882i \(0.598102\pi\)
\(6\) −0.0202075 −0.00824966
\(7\) −0.669195 −0.252932 −0.126466 0.991971i \(-0.540363\pi\)
−0.126466 + 0.991971i \(0.540363\pi\)
\(8\) −0.0808216 −0.0285747
\(9\) 1.00000 0.333333
\(10\) −0.0274131 −0.00866880
\(11\) 3.21751 0.970116 0.485058 0.874482i \(-0.338798\pi\)
0.485058 + 0.874482i \(0.338798\pi\)
\(12\) 1.99959 0.577232
\(13\) 1.00000 0.277350
\(14\) −0.0135227 −0.00361410
\(15\) 1.35659 0.350269
\(16\) 3.99755 0.999388
\(17\) −0.412109 −0.0999511 −0.0499755 0.998750i \(-0.515914\pi\)
−0.0499755 + 0.998750i \(0.515914\pi\)
\(18\) 0.0202075 0.00476294
\(19\) 1.46743 0.336651 0.168325 0.985732i \(-0.446164\pi\)
0.168325 + 0.985732i \(0.446164\pi\)
\(20\) 2.71262 0.606560
\(21\) 0.669195 0.146030
\(22\) 0.0650177 0.0138618
\(23\) −2.51016 −0.523405 −0.261702 0.965149i \(-0.584284\pi\)
−0.261702 + 0.965149i \(0.584284\pi\)
\(24\) 0.0808216 0.0164976
\(25\) −3.15968 −0.631935
\(26\) 0.0202075 0.00396301
\(27\) −1.00000 −0.192450
\(28\) 1.33812 0.252880
\(29\) 1.53778 0.285558 0.142779 0.989755i \(-0.454396\pi\)
0.142779 + 0.989755i \(0.454396\pi\)
\(30\) 0.0274131 0.00500493
\(31\) 2.21745 0.398266 0.199133 0.979972i \(-0.436187\pi\)
0.199133 + 0.979972i \(0.436187\pi\)
\(32\) 0.242423 0.0428548
\(33\) −3.21751 −0.560097
\(34\) −0.00832767 −0.00142818
\(35\) 0.907820 0.153450
\(36\) −1.99959 −0.333265
\(37\) −4.89090 −0.804058 −0.402029 0.915627i \(-0.631695\pi\)
−0.402029 + 0.915627i \(0.631695\pi\)
\(38\) 0.0296529 0.00481034
\(39\) −1.00000 −0.160128
\(40\) 0.109641 0.0173358
\(41\) −9.85948 −1.53979 −0.769896 0.638170i \(-0.779692\pi\)
−0.769896 + 0.638170i \(0.779692\pi\)
\(42\) 0.0135227 0.00208660
\(43\) −7.39732 −1.12808 −0.564041 0.825747i \(-0.690754\pi\)
−0.564041 + 0.825747i \(0.690754\pi\)
\(44\) −6.43371 −0.969918
\(45\) −1.35659 −0.202228
\(46\) −0.0507240 −0.00747884
\(47\) −0.629405 −0.0918082 −0.0459041 0.998946i \(-0.514617\pi\)
−0.0459041 + 0.998946i \(0.514617\pi\)
\(48\) −3.99755 −0.576997
\(49\) −6.55218 −0.936026
\(50\) −0.0638490 −0.00902961
\(51\) 0.412109 0.0577068
\(52\) −1.99959 −0.277293
\(53\) 6.18867 0.850079 0.425039 0.905175i \(-0.360260\pi\)
0.425039 + 0.905175i \(0.360260\pi\)
\(54\) −0.0202075 −0.00274989
\(55\) −4.36483 −0.588554
\(56\) 0.0540854 0.00722746
\(57\) −1.46743 −0.194365
\(58\) 0.0310746 0.00408029
\(59\) −0.139569 −0.0181703 −0.00908516 0.999959i \(-0.502892\pi\)
−0.00908516 + 0.999959i \(0.502892\pi\)
\(60\) −2.71262 −0.350197
\(61\) 10.2963 1.31831 0.659155 0.752007i \(-0.270914\pi\)
0.659155 + 0.752007i \(0.270914\pi\)
\(62\) 0.0448090 0.00569075
\(63\) −0.669195 −0.0843106
\(64\) −7.99020 −0.998775
\(65\) −1.35659 −0.168264
\(66\) −0.0650177 −0.00800313
\(67\) 9.27090 1.13262 0.566310 0.824192i \(-0.308370\pi\)
0.566310 + 0.824192i \(0.308370\pi\)
\(68\) 0.824049 0.0999307
\(69\) 2.51016 0.302188
\(70\) 0.0183447 0.00219261
\(71\) −14.2096 −1.68637 −0.843186 0.537622i \(-0.819323\pi\)
−0.843186 + 0.537622i \(0.819323\pi\)
\(72\) −0.0808216 −0.00952491
\(73\) 2.85045 0.333620 0.166810 0.985989i \(-0.446653\pi\)
0.166810 + 0.985989i \(0.446653\pi\)
\(74\) −0.0988325 −0.0114890
\(75\) 3.15968 0.364848
\(76\) −2.93425 −0.336582
\(77\) −2.15314 −0.245373
\(78\) −0.0202075 −0.00228804
\(79\) −3.10012 −0.348791 −0.174395 0.984676i \(-0.555797\pi\)
−0.174395 + 0.984676i \(0.555797\pi\)
\(80\) −5.42302 −0.606312
\(81\) 1.00000 0.111111
\(82\) −0.199235 −0.0220018
\(83\) 7.16852 0.786847 0.393424 0.919357i \(-0.371291\pi\)
0.393424 + 0.919357i \(0.371291\pi\)
\(84\) −1.33812 −0.146000
\(85\) 0.559061 0.0606387
\(86\) −0.149481 −0.0161190
\(87\) −1.53778 −0.164867
\(88\) −0.260044 −0.0277208
\(89\) 12.7296 1.34934 0.674668 0.738121i \(-0.264287\pi\)
0.674668 + 0.738121i \(0.264287\pi\)
\(90\) −0.0274131 −0.00288960
\(91\) −0.669195 −0.0701507
\(92\) 5.01930 0.523298
\(93\) −2.21745 −0.229939
\(94\) −0.0127187 −0.00131183
\(95\) −1.99069 −0.204240
\(96\) −0.242423 −0.0247422
\(97\) 2.47992 0.251797 0.125899 0.992043i \(-0.459819\pi\)
0.125899 + 0.992043i \(0.459819\pi\)
\(98\) −0.132403 −0.0133747
\(99\) 3.21751 0.323372
\(100\) 6.31806 0.631806
\(101\) 6.78688 0.675320 0.337660 0.941268i \(-0.390365\pi\)
0.337660 + 0.941268i \(0.390365\pi\)
\(102\) 0.00832767 0.000824562 0
\(103\) −1.00000 −0.0985329
\(104\) −0.0808216 −0.00792521
\(105\) −0.907820 −0.0885941
\(106\) 0.125057 0.0121466
\(107\) 1.10023 0.106363 0.0531817 0.998585i \(-0.483064\pi\)
0.0531817 + 0.998585i \(0.483064\pi\)
\(108\) 1.99959 0.192411
\(109\) 9.61416 0.920870 0.460435 0.887694i \(-0.347694\pi\)
0.460435 + 0.887694i \(0.347694\pi\)
\(110\) −0.0882021 −0.00840974
\(111\) 4.89090 0.464223
\(112\) −2.67514 −0.252777
\(113\) 15.0634 1.41705 0.708524 0.705687i \(-0.249361\pi\)
0.708524 + 0.705687i \(0.249361\pi\)
\(114\) −0.0296529 −0.00277725
\(115\) 3.40525 0.317541
\(116\) −3.07493 −0.285500
\(117\) 1.00000 0.0924500
\(118\) −0.00282033 −0.000259632 0
\(119\) 0.275781 0.0252808
\(120\) −0.109641 −0.0100088
\(121\) −0.647619 −0.0588744
\(122\) 0.208063 0.0188371
\(123\) 9.85948 0.888999
\(124\) −4.43399 −0.398184
\(125\) 11.0693 0.990068
\(126\) −0.0135227 −0.00120470
\(127\) 0.702217 0.0623117 0.0311558 0.999515i \(-0.490081\pi\)
0.0311558 + 0.999515i \(0.490081\pi\)
\(128\) −0.646309 −0.0571261
\(129\) 7.39732 0.651298
\(130\) −0.0274131 −0.00240429
\(131\) −4.71494 −0.411946 −0.205973 0.978558i \(-0.566036\pi\)
−0.205973 + 0.978558i \(0.566036\pi\)
\(132\) 6.43371 0.559983
\(133\) −0.981993 −0.0851496
\(134\) 0.187341 0.0161838
\(135\) 1.35659 0.116756
\(136\) 0.0333073 0.00285608
\(137\) −20.0334 −1.71157 −0.855786 0.517330i \(-0.826926\pi\)
−0.855786 + 0.517330i \(0.826926\pi\)
\(138\) 0.0507240 0.00431791
\(139\) 0.331543 0.0281211 0.0140605 0.999901i \(-0.495524\pi\)
0.0140605 + 0.999901i \(0.495524\pi\)
\(140\) −1.81527 −0.153418
\(141\) 0.629405 0.0530055
\(142\) −0.287140 −0.0240963
\(143\) 3.21751 0.269062
\(144\) 3.99755 0.333129
\(145\) −2.08613 −0.173243
\(146\) 0.0576003 0.00476704
\(147\) 6.55218 0.540415
\(148\) 9.77979 0.803894
\(149\) −8.86060 −0.725888 −0.362944 0.931811i \(-0.618228\pi\)
−0.362944 + 0.931811i \(0.618228\pi\)
\(150\) 0.0638490 0.00521325
\(151\) −2.09091 −0.170156 −0.0850780 0.996374i \(-0.527114\pi\)
−0.0850780 + 0.996374i \(0.527114\pi\)
\(152\) −0.118600 −0.00961970
\(153\) −0.412109 −0.0333170
\(154\) −0.0435095 −0.00350610
\(155\) −3.00816 −0.241621
\(156\) 1.99959 0.160095
\(157\) 4.75966 0.379862 0.189931 0.981797i \(-0.439174\pi\)
0.189931 + 0.981797i \(0.439174\pi\)
\(158\) −0.0626456 −0.00498381
\(159\) −6.18867 −0.490793
\(160\) −0.328868 −0.0259993
\(161\) 1.67979 0.132386
\(162\) 0.0202075 0.00158765
\(163\) 11.8482 0.928020 0.464010 0.885830i \(-0.346410\pi\)
0.464010 + 0.885830i \(0.346410\pi\)
\(164\) 19.7149 1.53948
\(165\) 4.36483 0.339802
\(166\) 0.144858 0.0112431
\(167\) −4.87516 −0.377251 −0.188626 0.982049i \(-0.560403\pi\)
−0.188626 + 0.982049i \(0.560403\pi\)
\(168\) −0.0540854 −0.00417278
\(169\) 1.00000 0.0769231
\(170\) 0.0112972 0.000866456 0
\(171\) 1.46743 0.112217
\(172\) 14.7916 1.12785
\(173\) 19.1852 1.45862 0.729311 0.684182i \(-0.239841\pi\)
0.729311 + 0.684182i \(0.239841\pi\)
\(174\) −0.0310746 −0.00235576
\(175\) 2.11444 0.159836
\(176\) 12.8622 0.969522
\(177\) 0.139569 0.0104906
\(178\) 0.257233 0.0192804
\(179\) 7.06520 0.528078 0.264039 0.964512i \(-0.414945\pi\)
0.264039 + 0.964512i \(0.414945\pi\)
\(180\) 2.71262 0.202187
\(181\) 22.0915 1.64205 0.821023 0.570896i \(-0.193404\pi\)
0.821023 + 0.570896i \(0.193404\pi\)
\(182\) −0.0135227 −0.00100237
\(183\) −10.2963 −0.761127
\(184\) 0.202875 0.0149562
\(185\) 6.63492 0.487809
\(186\) −0.0448090 −0.00328556
\(187\) −1.32597 −0.0969642
\(188\) 1.25855 0.0917894
\(189\) 0.669195 0.0486767
\(190\) −0.0402267 −0.00291836
\(191\) 25.4055 1.83827 0.919137 0.393938i \(-0.128888\pi\)
0.919137 + 0.393938i \(0.128888\pi\)
\(192\) 7.99020 0.576643
\(193\) 8.22803 0.592267 0.296133 0.955147i \(-0.404303\pi\)
0.296133 + 0.955147i \(0.404303\pi\)
\(194\) 0.0501128 0.00359789
\(195\) 1.35659 0.0971471
\(196\) 13.1017 0.935834
\(197\) −8.33876 −0.594112 −0.297056 0.954860i \(-0.596005\pi\)
−0.297056 + 0.954860i \(0.596005\pi\)
\(198\) 0.0650177 0.00462061
\(199\) −23.0763 −1.63583 −0.817917 0.575336i \(-0.804871\pi\)
−0.817917 + 0.575336i \(0.804871\pi\)
\(200\) 0.255370 0.0180574
\(201\) −9.27090 −0.653919
\(202\) 0.137146 0.00964953
\(203\) −1.02907 −0.0722267
\(204\) −0.824049 −0.0576950
\(205\) 13.3752 0.934166
\(206\) −0.0202075 −0.00140792
\(207\) −2.51016 −0.174468
\(208\) 3.99755 0.277180
\(209\) 4.72146 0.326590
\(210\) −0.0183447 −0.00126591
\(211\) −10.5659 −0.727389 −0.363694 0.931518i \(-0.618485\pi\)
−0.363694 + 0.931518i \(0.618485\pi\)
\(212\) −12.3748 −0.849905
\(213\) 14.2096 0.973627
\(214\) 0.0222329 0.00151981
\(215\) 10.0351 0.684388
\(216\) 0.0808216 0.00549921
\(217\) −1.48391 −0.100734
\(218\) 0.194278 0.0131581
\(219\) −2.85045 −0.192616
\(220\) 8.72788 0.588433
\(221\) −0.412109 −0.0277214
\(222\) 0.0988325 0.00663321
\(223\) 28.2176 1.88959 0.944795 0.327663i \(-0.106261\pi\)
0.944795 + 0.327663i \(0.106261\pi\)
\(224\) −0.162228 −0.0108393
\(225\) −3.15968 −0.210645
\(226\) 0.304393 0.0202479
\(227\) 14.7710 0.980385 0.490193 0.871614i \(-0.336926\pi\)
0.490193 + 0.871614i \(0.336926\pi\)
\(228\) 2.93425 0.194326
\(229\) −13.2331 −0.874469 −0.437235 0.899348i \(-0.644042\pi\)
−0.437235 + 0.899348i \(0.644042\pi\)
\(230\) 0.0688114 0.00453729
\(231\) 2.15314 0.141666
\(232\) −0.124286 −0.00815975
\(233\) 17.4974 1.14629 0.573146 0.819453i \(-0.305723\pi\)
0.573146 + 0.819453i \(0.305723\pi\)
\(234\) 0.0202075 0.00132100
\(235\) 0.853842 0.0556985
\(236\) 0.279081 0.0181666
\(237\) 3.10012 0.201374
\(238\) 0.00557283 0.000361233 0
\(239\) −3.73994 −0.241917 −0.120958 0.992658i \(-0.538597\pi\)
−0.120958 + 0.992658i \(0.538597\pi\)
\(240\) 5.42302 0.350054
\(241\) −13.4418 −0.865866 −0.432933 0.901426i \(-0.642521\pi\)
−0.432933 + 0.901426i \(0.642521\pi\)
\(242\) −0.0130867 −0.000841247 0
\(243\) −1.00000 −0.0641500
\(244\) −20.5885 −1.31804
\(245\) 8.88859 0.567871
\(246\) 0.199235 0.0127028
\(247\) 1.46743 0.0933701
\(248\) −0.179218 −0.0113803
\(249\) −7.16852 −0.454287
\(250\) 0.223682 0.0141469
\(251\) 18.0635 1.14016 0.570078 0.821590i \(-0.306913\pi\)
0.570078 + 0.821590i \(0.306913\pi\)
\(252\) 1.33812 0.0842934
\(253\) −8.07647 −0.507764
\(254\) 0.0141900 0.000890361 0
\(255\) −0.559061 −0.0350098
\(256\) 15.9673 0.997959
\(257\) −8.08677 −0.504439 −0.252220 0.967670i \(-0.581161\pi\)
−0.252220 + 0.967670i \(0.581161\pi\)
\(258\) 0.149481 0.00930629
\(259\) 3.27296 0.203372
\(260\) 2.71262 0.168229
\(261\) 1.53778 0.0951861
\(262\) −0.0952770 −0.00588623
\(263\) 13.8974 0.856952 0.428476 0.903553i \(-0.359051\pi\)
0.428476 + 0.903553i \(0.359051\pi\)
\(264\) 0.260044 0.0160046
\(265\) −8.39546 −0.515729
\(266\) −0.0198436 −0.00121669
\(267\) −12.7296 −0.779040
\(268\) −18.5380 −1.13239
\(269\) −25.2702 −1.54075 −0.770375 0.637591i \(-0.779931\pi\)
−0.770375 + 0.637591i \(0.779931\pi\)
\(270\) 0.0274131 0.00166831
\(271\) −17.9074 −1.08780 −0.543900 0.839150i \(-0.683053\pi\)
−0.543900 + 0.839150i \(0.683053\pi\)
\(272\) −1.64743 −0.0998899
\(273\) 0.669195 0.0405015
\(274\) −0.404825 −0.0244564
\(275\) −10.1663 −0.613050
\(276\) −5.01930 −0.302126
\(277\) 6.84895 0.411514 0.205757 0.978603i \(-0.434034\pi\)
0.205757 + 0.978603i \(0.434034\pi\)
\(278\) 0.00669963 0.000401817 0
\(279\) 2.21745 0.132755
\(280\) −0.0733714 −0.00438478
\(281\) 8.38429 0.500165 0.250082 0.968225i \(-0.419542\pi\)
0.250082 + 0.968225i \(0.419542\pi\)
\(282\) 0.0127187 0.000757386 0
\(283\) −20.7591 −1.23400 −0.616999 0.786964i \(-0.711652\pi\)
−0.616999 + 0.786964i \(0.711652\pi\)
\(284\) 28.4134 1.68603
\(285\) 1.99069 0.117918
\(286\) 0.0650177 0.00384458
\(287\) 6.59791 0.389462
\(288\) 0.242423 0.0142849
\(289\) −16.8302 −0.990010
\(290\) −0.0421553 −0.00247545
\(291\) −2.47992 −0.145375
\(292\) −5.69973 −0.333552
\(293\) −4.87749 −0.284946 −0.142473 0.989799i \(-0.545505\pi\)
−0.142473 + 0.989799i \(0.545505\pi\)
\(294\) 0.132403 0.00772189
\(295\) 0.189337 0.0110236
\(296\) 0.395290 0.0229758
\(297\) −3.21751 −0.186699
\(298\) −0.179050 −0.0103721
\(299\) −2.51016 −0.145166
\(300\) −6.31806 −0.364773
\(301\) 4.95025 0.285328
\(302\) −0.0422520 −0.00243133
\(303\) −6.78688 −0.389896
\(304\) 5.86611 0.336444
\(305\) −13.9679 −0.799797
\(306\) −0.00832767 −0.000476061 0
\(307\) 33.2405 1.89714 0.948568 0.316574i \(-0.102533\pi\)
0.948568 + 0.316574i \(0.102533\pi\)
\(308\) 4.30540 0.245323
\(309\) 1.00000 0.0568880
\(310\) −0.0607873 −0.00345249
\(311\) 0.937263 0.0531473 0.0265737 0.999647i \(-0.491540\pi\)
0.0265737 + 0.999647i \(0.491540\pi\)
\(312\) 0.0808216 0.00457562
\(313\) 5.88969 0.332905 0.166452 0.986049i \(-0.446769\pi\)
0.166452 + 0.986049i \(0.446769\pi\)
\(314\) 0.0961806 0.00542779
\(315\) 0.907820 0.0511499
\(316\) 6.19898 0.348720
\(317\) 22.2657 1.25057 0.625283 0.780398i \(-0.284984\pi\)
0.625283 + 0.780398i \(0.284984\pi\)
\(318\) −0.125057 −0.00701286
\(319\) 4.94782 0.277025
\(320\) 10.8394 0.605940
\(321\) −1.10023 −0.0614089
\(322\) 0.0339442 0.00189164
\(323\) −0.604739 −0.0336486
\(324\) −1.99959 −0.111088
\(325\) −3.15968 −0.175267
\(326\) 0.239421 0.0132603
\(327\) −9.61416 −0.531664
\(328\) 0.796858 0.0439991
\(329\) 0.421194 0.0232212
\(330\) 0.0882021 0.00485537
\(331\) −7.09028 −0.389717 −0.194858 0.980831i \(-0.562425\pi\)
−0.194858 + 0.980831i \(0.562425\pi\)
\(332\) −14.3341 −0.786687
\(333\) −4.89090 −0.268019
\(334\) −0.0985146 −0.00539048
\(335\) −12.5768 −0.687142
\(336\) 2.67514 0.145941
\(337\) 21.5009 1.17123 0.585615 0.810589i \(-0.300853\pi\)
0.585615 + 0.810589i \(0.300853\pi\)
\(338\) 0.0202075 0.00109914
\(339\) −15.0634 −0.818133
\(340\) −1.11789 −0.0606263
\(341\) 7.13467 0.386364
\(342\) 0.0296529 0.00160345
\(343\) 9.06904 0.489682
\(344\) 0.597863 0.0322346
\(345\) −3.40525 −0.183332
\(346\) 0.387684 0.0208420
\(347\) 36.7394 1.97227 0.986137 0.165935i \(-0.0530641\pi\)
0.986137 + 0.165935i \(0.0530641\pi\)
\(348\) 3.07493 0.164833
\(349\) −22.5384 −1.20645 −0.603227 0.797569i \(-0.706119\pi\)
−0.603227 + 0.797569i \(0.706119\pi\)
\(350\) 0.0427274 0.00228388
\(351\) −1.00000 −0.0533761
\(352\) 0.780000 0.0415742
\(353\) 34.9553 1.86048 0.930242 0.366945i \(-0.119596\pi\)
0.930242 + 0.366945i \(0.119596\pi\)
\(354\) 0.00282033 0.000149899 0
\(355\) 19.2766 1.02309
\(356\) −25.4540 −1.34906
\(357\) −0.275781 −0.0145959
\(358\) 0.142770 0.00754561
\(359\) 0.657556 0.0347045 0.0173522 0.999849i \(-0.494476\pi\)
0.0173522 + 0.999849i \(0.494476\pi\)
\(360\) 0.109641 0.00577861
\(361\) −16.8467 −0.886666
\(362\) 0.446412 0.0234629
\(363\) 0.647619 0.0339912
\(364\) 1.33812 0.0701363
\(365\) −3.86688 −0.202402
\(366\) −0.208063 −0.0108756
\(367\) 19.9068 1.03913 0.519563 0.854432i \(-0.326095\pi\)
0.519563 + 0.854432i \(0.326095\pi\)
\(368\) −10.0345 −0.523084
\(369\) −9.85948 −0.513264
\(370\) 0.134075 0.00697022
\(371\) −4.14142 −0.215012
\(372\) 4.43399 0.229892
\(373\) 2.93929 0.152190 0.0760952 0.997101i \(-0.475755\pi\)
0.0760952 + 0.997101i \(0.475755\pi\)
\(374\) −0.0267944 −0.00138550
\(375\) −11.0693 −0.571616
\(376\) 0.0508695 0.00262339
\(377\) 1.53778 0.0791996
\(378\) 0.0135227 0.000695534 0
\(379\) 6.96146 0.357586 0.178793 0.983887i \(-0.442781\pi\)
0.178793 + 0.983887i \(0.442781\pi\)
\(380\) 3.98056 0.204199
\(381\) −0.702217 −0.0359757
\(382\) 0.513380 0.0262668
\(383\) 9.74605 0.498000 0.249000 0.968503i \(-0.419898\pi\)
0.249000 + 0.968503i \(0.419898\pi\)
\(384\) 0.646309 0.0329818
\(385\) 2.92092 0.148864
\(386\) 0.166268 0.00846279
\(387\) −7.39732 −0.376027
\(388\) −4.95882 −0.251746
\(389\) 0.318499 0.0161485 0.00807426 0.999967i \(-0.497430\pi\)
0.00807426 + 0.999967i \(0.497430\pi\)
\(390\) 0.0274131 0.00138812
\(391\) 1.03446 0.0523149
\(392\) 0.529557 0.0267467
\(393\) 4.71494 0.237837
\(394\) −0.168505 −0.00848916
\(395\) 4.20558 0.211606
\(396\) −6.43371 −0.323306
\(397\) −33.0063 −1.65654 −0.828269 0.560331i \(-0.810674\pi\)
−0.828269 + 0.560331i \(0.810674\pi\)
\(398\) −0.466313 −0.0233741
\(399\) 0.981993 0.0491612
\(400\) −12.6310 −0.631548
\(401\) 23.8329 1.19016 0.595078 0.803668i \(-0.297121\pi\)
0.595078 + 0.803668i \(0.297121\pi\)
\(402\) −0.187341 −0.00934373
\(403\) 2.21745 0.110459
\(404\) −13.5710 −0.675182
\(405\) −1.35659 −0.0674093
\(406\) −0.0207949 −0.00103204
\(407\) −15.7365 −0.780030
\(408\) −0.0333073 −0.00164896
\(409\) 11.1597 0.551810 0.275905 0.961185i \(-0.411022\pi\)
0.275905 + 0.961185i \(0.411022\pi\)
\(410\) 0.270279 0.0133481
\(411\) 20.0334 0.988177
\(412\) 1.99959 0.0985128
\(413\) 0.0933987 0.00459585
\(414\) −0.0507240 −0.00249295
\(415\) −9.72471 −0.477367
\(416\) 0.242423 0.0118858
\(417\) −0.331543 −0.0162357
\(418\) 0.0954087 0.00466659
\(419\) −9.11466 −0.445280 −0.222640 0.974901i \(-0.571467\pi\)
−0.222640 + 0.974901i \(0.571467\pi\)
\(420\) 1.81527 0.0885761
\(421\) −1.07048 −0.0521721 −0.0260861 0.999660i \(-0.508304\pi\)
−0.0260861 + 0.999660i \(0.508304\pi\)
\(422\) −0.213511 −0.0103935
\(423\) −0.629405 −0.0306027
\(424\) −0.500178 −0.0242908
\(425\) 1.30213 0.0631626
\(426\) 0.287140 0.0139120
\(427\) −6.89025 −0.333443
\(428\) −2.20001 −0.106342
\(429\) −3.21751 −0.155343
\(430\) 0.202784 0.00977911
\(431\) 36.6214 1.76399 0.881996 0.471256i \(-0.156199\pi\)
0.881996 + 0.471256i \(0.156199\pi\)
\(432\) −3.99755 −0.192332
\(433\) −27.5878 −1.32579 −0.662893 0.748714i \(-0.730672\pi\)
−0.662893 + 0.748714i \(0.730672\pi\)
\(434\) −0.0299860 −0.00143937
\(435\) 2.08613 0.100022
\(436\) −19.2244 −0.920682
\(437\) −3.68347 −0.176205
\(438\) −0.0576003 −0.00275225
\(439\) −1.08940 −0.0519942 −0.0259971 0.999662i \(-0.508276\pi\)
−0.0259971 + 0.999662i \(0.508276\pi\)
\(440\) 0.352772 0.0168178
\(441\) −6.55218 −0.312009
\(442\) −0.00832767 −0.000396107 0
\(443\) 4.50168 0.213881 0.106941 0.994265i \(-0.465895\pi\)
0.106941 + 0.994265i \(0.465895\pi\)
\(444\) −9.77979 −0.464128
\(445\) −17.2688 −0.818620
\(446\) 0.570206 0.0270000
\(447\) 8.86060 0.419092
\(448\) 5.34700 0.252622
\(449\) 21.5728 1.01808 0.509042 0.860742i \(-0.330000\pi\)
0.509042 + 0.860742i \(0.330000\pi\)
\(450\) −0.0638490 −0.00300987
\(451\) −31.7230 −1.49378
\(452\) −30.1207 −1.41676
\(453\) 2.09091 0.0982396
\(454\) 0.298484 0.0140086
\(455\) 0.907820 0.0425592
\(456\) 0.118600 0.00555394
\(457\) −9.40343 −0.439874 −0.219937 0.975514i \(-0.570585\pi\)
−0.219937 + 0.975514i \(0.570585\pi\)
\(458\) −0.267408 −0.0124951
\(459\) 0.412109 0.0192356
\(460\) −6.80911 −0.317476
\(461\) −15.9182 −0.741384 −0.370692 0.928756i \(-0.620880\pi\)
−0.370692 + 0.928756i \(0.620880\pi\)
\(462\) 0.0435095 0.00202425
\(463\) 34.4701 1.60196 0.800981 0.598690i \(-0.204312\pi\)
0.800981 + 0.598690i \(0.204312\pi\)
\(464\) 6.14734 0.285383
\(465\) 3.00816 0.139500
\(466\) 0.353578 0.0163792
\(467\) −2.20259 −0.101924 −0.0509619 0.998701i \(-0.516229\pi\)
−0.0509619 + 0.998701i \(0.516229\pi\)
\(468\) −1.99959 −0.0924312
\(469\) −6.20404 −0.286476
\(470\) 0.0172540 0.000795866 0
\(471\) −4.75966 −0.219314
\(472\) 0.0112802 0.000519212 0
\(473\) −23.8010 −1.09437
\(474\) 0.0626456 0.00287741
\(475\) −4.63659 −0.212741
\(476\) −0.551449 −0.0252756
\(477\) 6.18867 0.283360
\(478\) −0.0755747 −0.00345671
\(479\) −0.364505 −0.0166547 −0.00832734 0.999965i \(-0.502651\pi\)
−0.00832734 + 0.999965i \(0.502651\pi\)
\(480\) 0.328868 0.0150107
\(481\) −4.89090 −0.223006
\(482\) −0.271626 −0.0123722
\(483\) −1.67979 −0.0764329
\(484\) 1.29497 0.0588624
\(485\) −3.36422 −0.152761
\(486\) −0.0202075 −0.000916629 0
\(487\) −11.2699 −0.510688 −0.255344 0.966850i \(-0.582189\pi\)
−0.255344 + 0.966850i \(0.582189\pi\)
\(488\) −0.832166 −0.0376704
\(489\) −11.8482 −0.535793
\(490\) 0.179616 0.00811422
\(491\) 12.1942 0.550318 0.275159 0.961399i \(-0.411269\pi\)
0.275159 + 0.961399i \(0.411269\pi\)
\(492\) −19.7149 −0.888817
\(493\) −0.633732 −0.0285418
\(494\) 0.0296529 0.00133415
\(495\) −4.36483 −0.196185
\(496\) 8.86437 0.398022
\(497\) 9.50900 0.426537
\(498\) −0.144858 −0.00649122
\(499\) 5.76878 0.258246 0.129123 0.991629i \(-0.458784\pi\)
0.129123 + 0.991629i \(0.458784\pi\)
\(500\) −22.1341 −0.989866
\(501\) 4.87516 0.217806
\(502\) 0.365017 0.0162915
\(503\) 20.6020 0.918596 0.459298 0.888282i \(-0.348101\pi\)
0.459298 + 0.888282i \(0.348101\pi\)
\(504\) 0.0540854 0.00240915
\(505\) −9.20699 −0.409706
\(506\) −0.163205 −0.00725535
\(507\) −1.00000 −0.0444116
\(508\) −1.40415 −0.0622989
\(509\) 38.0763 1.68770 0.843851 0.536577i \(-0.180283\pi\)
0.843851 + 0.536577i \(0.180283\pi\)
\(510\) −0.0112972 −0.000500248 0
\(511\) −1.90751 −0.0843831
\(512\) 1.61528 0.0713858
\(513\) −1.46743 −0.0647884
\(514\) −0.163413 −0.00720784
\(515\) 1.35659 0.0597783
\(516\) −14.7916 −0.651165
\(517\) −2.02512 −0.0890646
\(518\) 0.0661382 0.00290595
\(519\) −19.1852 −0.842136
\(520\) 0.109641 0.00480809
\(521\) −11.6539 −0.510568 −0.255284 0.966866i \(-0.582169\pi\)
−0.255284 + 0.966866i \(0.582169\pi\)
\(522\) 0.0310746 0.00136010
\(523\) 17.5619 0.767928 0.383964 0.923348i \(-0.374559\pi\)
0.383964 + 0.923348i \(0.374559\pi\)
\(524\) 9.42796 0.411862
\(525\) −2.11444 −0.0922816
\(526\) 0.280832 0.0122448
\(527\) −0.913831 −0.0398071
\(528\) −12.8622 −0.559754
\(529\) −16.6991 −0.726047
\(530\) −0.169651 −0.00736916
\(531\) −0.139569 −0.00605677
\(532\) 1.96359 0.0851322
\(533\) −9.85948 −0.427061
\(534\) −0.257233 −0.0111316
\(535\) −1.49256 −0.0645289
\(536\) −0.749289 −0.0323643
\(537\) −7.06520 −0.304886
\(538\) −0.510646 −0.0220155
\(539\) −21.0817 −0.908054
\(540\) −2.71262 −0.116732
\(541\) −40.8942 −1.75818 −0.879091 0.476655i \(-0.841849\pi\)
−0.879091 + 0.476655i \(0.841849\pi\)
\(542\) −0.361864 −0.0155434
\(543\) −22.0915 −0.948035
\(544\) −0.0999049 −0.00428339
\(545\) −13.0424 −0.558676
\(546\) 0.0135227 0.000578719 0
\(547\) 10.9531 0.468321 0.234160 0.972198i \(-0.424766\pi\)
0.234160 + 0.972198i \(0.424766\pi\)
\(548\) 40.0587 1.71122
\(549\) 10.2963 0.439437
\(550\) −0.205435 −0.00875977
\(551\) 2.25657 0.0961333
\(552\) −0.202875 −0.00863494
\(553\) 2.07458 0.0882203
\(554\) 0.138400 0.00588005
\(555\) −6.63492 −0.281637
\(556\) −0.662950 −0.0281153
\(557\) 13.2321 0.560661 0.280330 0.959904i \(-0.409556\pi\)
0.280330 + 0.959904i \(0.409556\pi\)
\(558\) 0.0448090 0.00189692
\(559\) −7.39732 −0.312873
\(560\) 3.62906 0.153356
\(561\) 1.32597 0.0559823
\(562\) 0.169425 0.00714677
\(563\) 9.76492 0.411542 0.205771 0.978600i \(-0.434030\pi\)
0.205771 + 0.978600i \(0.434030\pi\)
\(564\) −1.25855 −0.0529946
\(565\) −20.4348 −0.859699
\(566\) −0.419488 −0.0176324
\(567\) −0.669195 −0.0281035
\(568\) 1.14844 0.0481876
\(569\) 12.8799 0.539952 0.269976 0.962867i \(-0.412984\pi\)
0.269976 + 0.962867i \(0.412984\pi\)
\(570\) 0.0402267 0.00168491
\(571\) 0.898136 0.0375858 0.0187929 0.999823i \(-0.494018\pi\)
0.0187929 + 0.999823i \(0.494018\pi\)
\(572\) −6.43371 −0.269007
\(573\) −25.4055 −1.06133
\(574\) 0.133327 0.00556496
\(575\) 7.93129 0.330758
\(576\) −7.99020 −0.332925
\(577\) −7.34101 −0.305610 −0.152805 0.988256i \(-0.548831\pi\)
−0.152805 + 0.988256i \(0.548831\pi\)
\(578\) −0.340095 −0.0141461
\(579\) −8.22803 −0.341945
\(580\) 4.17140 0.173208
\(581\) −4.79714 −0.199019
\(582\) −0.0501128 −0.00207724
\(583\) 19.9121 0.824675
\(584\) −0.230378 −0.00953310
\(585\) −1.35659 −0.0560879
\(586\) −0.0985616 −0.00407154
\(587\) 33.9953 1.40314 0.701568 0.712603i \(-0.252484\pi\)
0.701568 + 0.712603i \(0.252484\pi\)
\(588\) −13.1017 −0.540304
\(589\) 3.25394 0.134076
\(590\) 0.00382602 0.000157515 0
\(591\) 8.33876 0.343011
\(592\) −19.5516 −0.803566
\(593\) −4.30992 −0.176987 −0.0884936 0.996077i \(-0.528205\pi\)
−0.0884936 + 0.996077i \(0.528205\pi\)
\(594\) −0.0650177 −0.00266771
\(595\) −0.374121 −0.0153374
\(596\) 17.7176 0.725740
\(597\) 23.0763 0.944449
\(598\) −0.0507240 −0.00207426
\(599\) −38.3299 −1.56612 −0.783059 0.621947i \(-0.786342\pi\)
−0.783059 + 0.621947i \(0.786342\pi\)
\(600\) −0.255370 −0.0104254
\(601\) 24.4229 0.996229 0.498115 0.867111i \(-0.334026\pi\)
0.498115 + 0.867111i \(0.334026\pi\)
\(602\) 0.100032 0.00407700
\(603\) 9.27090 0.377540
\(604\) 4.18097 0.170121
\(605\) 0.878551 0.0357182
\(606\) −0.137146 −0.00557116
\(607\) 20.1126 0.816347 0.408173 0.912904i \(-0.366166\pi\)
0.408173 + 0.912904i \(0.366166\pi\)
\(608\) 0.355738 0.0144271
\(609\) 1.02907 0.0417001
\(610\) −0.282255 −0.0114282
\(611\) −0.629405 −0.0254630
\(612\) 0.824049 0.0333102
\(613\) −22.0132 −0.889105 −0.444552 0.895753i \(-0.646637\pi\)
−0.444552 + 0.895753i \(0.646637\pi\)
\(614\) 0.671706 0.0271078
\(615\) −13.3752 −0.539341
\(616\) 0.174020 0.00701148
\(617\) −11.0599 −0.445255 −0.222628 0.974904i \(-0.571463\pi\)
−0.222628 + 0.974904i \(0.571463\pi\)
\(618\) 0.0202075 0.000812863 0
\(619\) 31.4113 1.26253 0.631264 0.775568i \(-0.282536\pi\)
0.631264 + 0.775568i \(0.282536\pi\)
\(620\) 6.01509 0.241572
\(621\) 2.51016 0.100729
\(622\) 0.0189397 0.000759413 0
\(623\) −8.51859 −0.341290
\(624\) −3.99755 −0.160030
\(625\) 0.781924 0.0312769
\(626\) 0.119016 0.00475682
\(627\) −4.72146 −0.188557
\(628\) −9.51738 −0.379785
\(629\) 2.01558 0.0803665
\(630\) 0.0183447 0.000730871 0
\(631\) 30.1770 1.20133 0.600663 0.799502i \(-0.294903\pi\)
0.600663 + 0.799502i \(0.294903\pi\)
\(632\) 0.250557 0.00996661
\(633\) 10.5659 0.419958
\(634\) 0.449933 0.0178691
\(635\) −0.952617 −0.0378035
\(636\) 12.3748 0.490693
\(637\) −6.55218 −0.259607
\(638\) 0.0999828 0.00395836
\(639\) −14.2096 −0.562124
\(640\) 0.876773 0.0346575
\(641\) −2.38863 −0.0943451 −0.0471726 0.998887i \(-0.515021\pi\)
−0.0471726 + 0.998887i \(0.515021\pi\)
\(642\) −0.0222329 −0.000877462 0
\(643\) −45.2987 −1.78641 −0.893203 0.449653i \(-0.851548\pi\)
−0.893203 + 0.449653i \(0.851548\pi\)
\(644\) −3.35889 −0.132359
\(645\) −10.0351 −0.395132
\(646\) −0.0122202 −0.000480799 0
\(647\) −35.4412 −1.39334 −0.696669 0.717393i \(-0.745335\pi\)
−0.696669 + 0.717393i \(0.745335\pi\)
\(648\) −0.0808216 −0.00317497
\(649\) −0.449064 −0.0176273
\(650\) −0.0638490 −0.00250436
\(651\) 1.48391 0.0581588
\(652\) −23.6915 −0.927831
\(653\) 27.4506 1.07423 0.537113 0.843510i \(-0.319515\pi\)
0.537113 + 0.843510i \(0.319515\pi\)
\(654\) −0.194278 −0.00759686
\(655\) 6.39622 0.249921
\(656\) −39.4137 −1.53885
\(657\) 2.85045 0.111207
\(658\) 0.00851127 0.000331804 0
\(659\) 26.5574 1.03453 0.517265 0.855825i \(-0.326950\pi\)
0.517265 + 0.855825i \(0.326950\pi\)
\(660\) −8.72788 −0.339732
\(661\) 12.7434 0.495660 0.247830 0.968804i \(-0.420283\pi\)
0.247830 + 0.968804i \(0.420283\pi\)
\(662\) −0.143276 −0.00556860
\(663\) 0.412109 0.0160050
\(664\) −0.579371 −0.0224840
\(665\) 1.33216 0.0516589
\(666\) −0.0988325 −0.00382968
\(667\) −3.86007 −0.149463
\(668\) 9.74833 0.377174
\(669\) −28.2176 −1.09096
\(670\) −0.254144 −0.00981846
\(671\) 33.1286 1.27891
\(672\) 0.162228 0.00625810
\(673\) 48.0470 1.85207 0.926037 0.377432i \(-0.123193\pi\)
0.926037 + 0.377432i \(0.123193\pi\)
\(674\) 0.434479 0.0167355
\(675\) 3.15968 0.121616
\(676\) −1.99959 −0.0769074
\(677\) −49.6558 −1.90843 −0.954214 0.299124i \(-0.903306\pi\)
−0.954214 + 0.299124i \(0.903306\pi\)
\(678\) −0.304393 −0.0116902
\(679\) −1.65955 −0.0636876
\(680\) −0.0451842 −0.00173273
\(681\) −14.7710 −0.566026
\(682\) 0.144174 0.00552069
\(683\) 3.43157 0.131305 0.0656527 0.997843i \(-0.479087\pi\)
0.0656527 + 0.997843i \(0.479087\pi\)
\(684\) −2.93425 −0.112194
\(685\) 27.1771 1.03838
\(686\) 0.183262 0.00699699
\(687\) 13.2331 0.504875
\(688\) −29.5712 −1.12739
\(689\) 6.18867 0.235769
\(690\) −0.0688114 −0.00261961
\(691\) 32.9966 1.25525 0.627624 0.778516i \(-0.284027\pi\)
0.627624 + 0.778516i \(0.284027\pi\)
\(692\) −38.3625 −1.45832
\(693\) −2.15314 −0.0817911
\(694\) 0.742409 0.0281815
\(695\) −0.449766 −0.0170606
\(696\) 0.124286 0.00471103
\(697\) 4.06318 0.153904
\(698\) −0.455444 −0.0172388
\(699\) −17.4974 −0.661813
\(700\) −4.22801 −0.159804
\(701\) 31.2184 1.17910 0.589551 0.807731i \(-0.299305\pi\)
0.589551 + 0.807731i \(0.299305\pi\)
\(702\) −0.0202075 −0.000762681 0
\(703\) −7.17702 −0.270687
\(704\) −25.7086 −0.968928
\(705\) −0.853842 −0.0321575
\(706\) 0.706358 0.0265841
\(707\) −4.54174 −0.170810
\(708\) −0.279081 −0.0104885
\(709\) 1.56114 0.0586297 0.0293148 0.999570i \(-0.490667\pi\)
0.0293148 + 0.999570i \(0.490667\pi\)
\(710\) 0.389530 0.0146188
\(711\) −3.10012 −0.116264
\(712\) −1.02883 −0.0385569
\(713\) −5.56616 −0.208454
\(714\) −0.00557283 −0.000208558 0
\(715\) −4.36483 −0.163235
\(716\) −14.1275 −0.527970
\(717\) 3.73994 0.139671
\(718\) 0.0132875 0.000495886 0
\(719\) −17.0771 −0.636868 −0.318434 0.947945i \(-0.603157\pi\)
−0.318434 + 0.947945i \(0.603157\pi\)
\(720\) −5.42302 −0.202104
\(721\) 0.669195 0.0249221
\(722\) −0.340428 −0.0126694
\(723\) 13.4418 0.499908
\(724\) −44.1739 −1.64171
\(725\) −4.85888 −0.180454
\(726\) 0.0130867 0.000485694 0
\(727\) 5.01960 0.186166 0.0930832 0.995658i \(-0.470328\pi\)
0.0930832 + 0.995658i \(0.470328\pi\)
\(728\) 0.0540854 0.00200454
\(729\) 1.00000 0.0370370
\(730\) −0.0781398 −0.00289208
\(731\) 3.04850 0.112753
\(732\) 20.5885 0.760971
\(733\) −10.8302 −0.400023 −0.200011 0.979794i \(-0.564098\pi\)
−0.200011 + 0.979794i \(0.564098\pi\)
\(734\) 0.402266 0.0148479
\(735\) −8.88859 −0.327861
\(736\) −0.608522 −0.0224304
\(737\) 29.8292 1.09877
\(738\) −0.199235 −0.00733394
\(739\) −27.0598 −0.995411 −0.497706 0.867346i \(-0.665824\pi\)
−0.497706 + 0.867346i \(0.665824\pi\)
\(740\) −13.2671 −0.487709
\(741\) −1.46743 −0.0539072
\(742\) −0.0836876 −0.00307227
\(743\) −23.0780 −0.846648 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(744\) 0.179218 0.00657044
\(745\) 12.0202 0.440385
\(746\) 0.0593955 0.00217462
\(747\) 7.16852 0.262282
\(748\) 2.65139 0.0969444
\(749\) −0.736269 −0.0269027
\(750\) −0.223682 −0.00816772
\(751\) 28.7314 1.04842 0.524211 0.851588i \(-0.324360\pi\)
0.524211 + 0.851588i \(0.324360\pi\)
\(752\) −2.51608 −0.0917519
\(753\) −18.0635 −0.658270
\(754\) 0.0310746 0.00113167
\(755\) 2.83650 0.103231
\(756\) −1.33812 −0.0486668
\(757\) 24.2231 0.880403 0.440202 0.897899i \(-0.354907\pi\)
0.440202 + 0.897899i \(0.354907\pi\)
\(758\) 0.140673 0.00510949
\(759\) 8.07647 0.293157
\(760\) 0.160891 0.00583611
\(761\) −7.63999 −0.276949 −0.138475 0.990366i \(-0.544220\pi\)
−0.138475 + 0.990366i \(0.544220\pi\)
\(762\) −0.0141900 −0.000514050 0
\(763\) −6.43374 −0.232917
\(764\) −50.8005 −1.83790
\(765\) 0.559061 0.0202129
\(766\) 0.196943 0.00711584
\(767\) −0.139569 −0.00503954
\(768\) −15.9673 −0.576172
\(769\) 14.2856 0.515153 0.257576 0.966258i \(-0.417076\pi\)
0.257576 + 0.966258i \(0.417076\pi\)
\(770\) 0.0590244 0.00212709
\(771\) 8.08677 0.291238
\(772\) −16.4527 −0.592146
\(773\) 31.5313 1.13410 0.567051 0.823683i \(-0.308084\pi\)
0.567051 + 0.823683i \(0.308084\pi\)
\(774\) −0.149481 −0.00537299
\(775\) −7.00642 −0.251678
\(776\) −0.200431 −0.00719505
\(777\) −3.27296 −0.117417
\(778\) 0.00643605 0.000230743 0
\(779\) −14.4680 −0.518372
\(780\) −2.71262 −0.0971273
\(781\) −45.7196 −1.63598
\(782\) 0.0209038 0.000747518 0
\(783\) −1.53778 −0.0549557
\(784\) −26.1927 −0.935452
\(785\) −6.45689 −0.230456
\(786\) 0.0952770 0.00339842
\(787\) −50.4778 −1.79934 −0.899669 0.436573i \(-0.856192\pi\)
−0.899669 + 0.436573i \(0.856192\pi\)
\(788\) 16.6741 0.593991
\(789\) −13.8974 −0.494761
\(790\) 0.0849841 0.00302360
\(791\) −10.0804 −0.358416
\(792\) −0.260044 −0.00924027
\(793\) 10.2963 0.365634
\(794\) −0.666973 −0.0236700
\(795\) 8.39546 0.297756
\(796\) 46.1431 1.63550
\(797\) −13.6255 −0.482640 −0.241320 0.970446i \(-0.577580\pi\)
−0.241320 + 0.970446i \(0.577580\pi\)
\(798\) 0.0198436 0.000702455 0
\(799\) 0.259383 0.00917632
\(800\) −0.765979 −0.0270815
\(801\) 12.7296 0.449779
\(802\) 0.481602 0.0170059
\(803\) 9.17135 0.323650
\(804\) 18.5380 0.653785
\(805\) −2.27877 −0.0803162
\(806\) 0.0448090 0.00157833
\(807\) 25.2702 0.889553
\(808\) −0.548526 −0.0192971
\(809\) 31.0541 1.09180 0.545902 0.837849i \(-0.316187\pi\)
0.545902 + 0.837849i \(0.316187\pi\)
\(810\) −0.0274131 −0.000963200 0
\(811\) −22.0253 −0.773412 −0.386706 0.922203i \(-0.626387\pi\)
−0.386706 + 0.922203i \(0.626387\pi\)
\(812\) 2.05773 0.0722120
\(813\) 17.9074 0.628041
\(814\) −0.317995 −0.0111457
\(815\) −16.0731 −0.563015
\(816\) 1.64743 0.0576714
\(817\) −10.8550 −0.379769
\(818\) 0.225509 0.00788472
\(819\) −0.669195 −0.0233836
\(820\) −26.7450 −0.933975
\(821\) 37.6478 1.31392 0.656959 0.753927i \(-0.271843\pi\)
0.656959 + 0.753927i \(0.271843\pi\)
\(822\) 0.404825 0.0141199
\(823\) −50.6340 −1.76499 −0.882495 0.470322i \(-0.844138\pi\)
−0.882495 + 0.470322i \(0.844138\pi\)
\(824\) 0.0808216 0.00281555
\(825\) 10.1663 0.353945
\(826\) 0.00188735 6.56693e−5 0
\(827\) 21.7174 0.755187 0.377594 0.925971i \(-0.376752\pi\)
0.377594 + 0.925971i \(0.376752\pi\)
\(828\) 5.01930 0.174433
\(829\) −12.4278 −0.431636 −0.215818 0.976434i \(-0.569242\pi\)
−0.215818 + 0.976434i \(0.569242\pi\)
\(830\) −0.196512 −0.00682102
\(831\) −6.84895 −0.237588
\(832\) −7.99020 −0.277010
\(833\) 2.70021 0.0935568
\(834\) −0.00669963 −0.000231989 0
\(835\) 6.61357 0.228872
\(836\) −9.44099 −0.326523
\(837\) −2.21745 −0.0766463
\(838\) −0.184184 −0.00636253
\(839\) 6.88073 0.237549 0.118775 0.992921i \(-0.462103\pi\)
0.118775 + 0.992921i \(0.462103\pi\)
\(840\) 0.0733714 0.00253155
\(841\) −26.6352 −0.918457
\(842\) −0.0216317 −0.000745478 0
\(843\) −8.38429 −0.288770
\(844\) 21.1276 0.727240
\(845\) −1.35659 −0.0466680
\(846\) −0.0127187 −0.000437277 0
\(847\) 0.433383 0.0148912
\(848\) 24.7395 0.849558
\(849\) 20.7591 0.712449
\(850\) 0.0263127 0.000902519 0
\(851\) 12.2769 0.420848
\(852\) −28.4134 −0.973428
\(853\) 0.499965 0.0171185 0.00855924 0.999963i \(-0.497275\pi\)
0.00855924 + 0.999963i \(0.497275\pi\)
\(854\) −0.139234 −0.00476450
\(855\) −1.99069 −0.0680801
\(856\) −0.0889225 −0.00303931
\(857\) −25.0494 −0.855670 −0.427835 0.903857i \(-0.640724\pi\)
−0.427835 + 0.903857i \(0.640724\pi\)
\(858\) −0.0650177 −0.00221967
\(859\) 4.07147 0.138917 0.0694584 0.997585i \(-0.477873\pi\)
0.0694584 + 0.997585i \(0.477873\pi\)
\(860\) −20.0661 −0.684249
\(861\) −6.59791 −0.224856
\(862\) 0.740026 0.0252054
\(863\) 17.5738 0.598220 0.299110 0.954219i \(-0.403310\pi\)
0.299110 + 0.954219i \(0.403310\pi\)
\(864\) −0.242423 −0.00824741
\(865\) −26.0263 −0.884922
\(866\) −0.557480 −0.0189439
\(867\) 16.8302 0.571582
\(868\) 2.96721 0.100714
\(869\) −9.97468 −0.338368
\(870\) 0.0421553 0.00142920
\(871\) 9.27090 0.314132
\(872\) −0.777031 −0.0263136
\(873\) 2.47992 0.0839325
\(874\) −0.0744337 −0.00251776
\(875\) −7.40751 −0.250420
\(876\) 5.69973 0.192576
\(877\) −41.5051 −1.40153 −0.700765 0.713393i \(-0.747158\pi\)
−0.700765 + 0.713393i \(0.747158\pi\)
\(878\) −0.0220140 −0.000742936 0
\(879\) 4.87749 0.164514
\(880\) −17.4486 −0.588193
\(881\) 37.9012 1.27692 0.638462 0.769653i \(-0.279571\pi\)
0.638462 + 0.769653i \(0.279571\pi\)
\(882\) −0.132403 −0.00445824
\(883\) 9.28018 0.312303 0.156151 0.987733i \(-0.450091\pi\)
0.156151 + 0.987733i \(0.450091\pi\)
\(884\) 0.824049 0.0277158
\(885\) −0.189337 −0.00636450
\(886\) 0.0909675 0.00305611
\(887\) 38.3684 1.28828 0.644142 0.764906i \(-0.277215\pi\)
0.644142 + 0.764906i \(0.277215\pi\)
\(888\) −0.395290 −0.0132651
\(889\) −0.469920 −0.0157606
\(890\) −0.348959 −0.0116971
\(891\) 3.21751 0.107791
\(892\) −56.4237 −1.88920
\(893\) −0.923605 −0.0309073
\(894\) 0.179050 0.00598833
\(895\) −9.58455 −0.320376
\(896\) 0.432506 0.0144490
\(897\) 2.51016 0.0838118
\(898\) 0.435931 0.0145472
\(899\) 3.40995 0.113728
\(900\) 6.31806 0.210602
\(901\) −2.55040 −0.0849663
\(902\) −0.641041 −0.0213443
\(903\) −4.95025 −0.164734
\(904\) −1.21745 −0.0404918
\(905\) −29.9690 −0.996202
\(906\) 0.0422520 0.00140373
\(907\) −37.0199 −1.22923 −0.614613 0.788829i \(-0.710688\pi\)
−0.614613 + 0.788829i \(0.710688\pi\)
\(908\) −29.5360 −0.980185
\(909\) 6.78688 0.225107
\(910\) 0.0183447 0.000608122 0
\(911\) 53.1472 1.76085 0.880423 0.474190i \(-0.157259\pi\)
0.880423 + 0.474190i \(0.157259\pi\)
\(912\) −5.86611 −0.194246
\(913\) 23.0648 0.763334
\(914\) −0.190019 −0.00628528
\(915\) 13.9679 0.461763
\(916\) 26.4608 0.874291
\(917\) 3.15521 0.104194
\(918\) 0.00832767 0.000274854 0
\(919\) 41.0216 1.35318 0.676588 0.736362i \(-0.263458\pi\)
0.676588 + 0.736362i \(0.263458\pi\)
\(920\) −0.275218 −0.00907365
\(921\) −33.2405 −1.09531
\(922\) −0.321666 −0.0105935
\(923\) −14.2096 −0.467715
\(924\) −4.30540 −0.141637
\(925\) 15.4536 0.508113
\(926\) 0.696553 0.0228902
\(927\) −1.00000 −0.0328443
\(928\) 0.372793 0.0122375
\(929\) −20.4971 −0.672489 −0.336245 0.941775i \(-0.609157\pi\)
−0.336245 + 0.941775i \(0.609157\pi\)
\(930\) 0.0607873 0.00199329
\(931\) −9.61483 −0.315113
\(932\) −34.9877 −1.14606
\(933\) −0.937263 −0.0306846
\(934\) −0.0445088 −0.00145637
\(935\) 1.79879 0.0588266
\(936\) −0.0808216 −0.00264174
\(937\) −21.7457 −0.710400 −0.355200 0.934790i \(-0.615587\pi\)
−0.355200 + 0.934790i \(0.615587\pi\)
\(938\) −0.125368 −0.00409340
\(939\) −5.88969 −0.192203
\(940\) −1.70733 −0.0556871
\(941\) 10.3186 0.336376 0.168188 0.985755i \(-0.446208\pi\)
0.168188 + 0.985755i \(0.446208\pi\)
\(942\) −0.0961806 −0.00313373
\(943\) 24.7489 0.805934
\(944\) −0.557933 −0.0181592
\(945\) −0.907820 −0.0295314
\(946\) −0.480957 −0.0156373
\(947\) 50.8447 1.65223 0.826116 0.563500i \(-0.190546\pi\)
0.826116 + 0.563500i \(0.190546\pi\)
\(948\) −6.19898 −0.201333
\(949\) 2.85045 0.0925295
\(950\) −0.0936936 −0.00303982
\(951\) −22.2657 −0.722014
\(952\) −0.0222891 −0.000722392 0
\(953\) 39.9839 1.29521 0.647603 0.761978i \(-0.275772\pi\)
0.647603 + 0.761978i \(0.275772\pi\)
\(954\) 0.125057 0.00404888
\(955\) −34.4647 −1.11525
\(956\) 7.47835 0.241867
\(957\) −4.94782 −0.159940
\(958\) −0.00736573 −0.000237976 0
\(959\) 13.4063 0.432911
\(960\) −10.8394 −0.349840
\(961\) −26.0829 −0.841384
\(962\) −0.0988325 −0.00318649
\(963\) 1.10023 0.0354545
\(964\) 26.8782 0.865689
\(965\) −11.1620 −0.359318
\(966\) −0.0339442 −0.00109214
\(967\) 8.37209 0.269228 0.134614 0.990898i \(-0.457021\pi\)
0.134614 + 0.990898i \(0.457021\pi\)
\(968\) 0.0523416 0.00168232
\(969\) 0.604739 0.0194270
\(970\) −0.0679823 −0.00218278
\(971\) −39.0151 −1.25205 −0.626027 0.779801i \(-0.715320\pi\)
−0.626027 + 0.779801i \(0.715320\pi\)
\(972\) 1.99959 0.0641369
\(973\) −0.221867 −0.00711272
\(974\) −0.227736 −0.00729714
\(975\) 3.15968 0.101191
\(976\) 41.1601 1.31750
\(977\) −5.37413 −0.171934 −0.0859668 0.996298i \(-0.527398\pi\)
−0.0859668 + 0.996298i \(0.527398\pi\)
\(978\) −0.239421 −0.00765585
\(979\) 40.9577 1.30901
\(980\) −17.7736 −0.567755
\(981\) 9.61416 0.306957
\(982\) 0.246414 0.00786340
\(983\) 8.26308 0.263551 0.131776 0.991280i \(-0.457932\pi\)
0.131776 + 0.991280i \(0.457932\pi\)
\(984\) −0.796858 −0.0254029
\(985\) 11.3122 0.360438
\(986\) −0.0128061 −0.000407830 0
\(987\) −0.421194 −0.0134068
\(988\) −2.93425 −0.0933510
\(989\) 18.5685 0.590443
\(990\) −0.0882021 −0.00280325
\(991\) −30.3789 −0.965018 −0.482509 0.875891i \(-0.660274\pi\)
−0.482509 + 0.875891i \(0.660274\pi\)
\(992\) 0.537562 0.0170676
\(993\) 7.09028 0.225003
\(994\) 0.192153 0.00609471
\(995\) 31.3049 0.992434
\(996\) 14.3341 0.454194
\(997\) −48.9090 −1.54896 −0.774482 0.632596i \(-0.781989\pi\)
−0.774482 + 0.632596i \(0.781989\pi\)
\(998\) 0.116572 0.00369003
\(999\) 4.89090 0.154741
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 \(a_p\))