Properties

Label 8027.2.a.f.1.13
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.47345 q^{2} -2.21693 q^{3} +4.11797 q^{4} -0.996079 q^{5} +5.48348 q^{6} +1.88032 q^{7} -5.23870 q^{8} +1.91479 q^{9} +O(q^{10})\) \(q-2.47345 q^{2} -2.21693 q^{3} +4.11797 q^{4} -0.996079 q^{5} +5.48348 q^{6} +1.88032 q^{7} -5.23870 q^{8} +1.91479 q^{9} +2.46376 q^{10} -1.24882 q^{11} -9.12926 q^{12} -0.803083 q^{13} -4.65088 q^{14} +2.20824 q^{15} +4.72174 q^{16} -0.930436 q^{17} -4.73613 q^{18} +6.20106 q^{19} -4.10182 q^{20} -4.16854 q^{21} +3.08890 q^{22} +1.00000 q^{23} +11.6138 q^{24} -4.00783 q^{25} +1.98639 q^{26} +2.40585 q^{27} +7.74309 q^{28} -1.98858 q^{29} -5.46198 q^{30} +9.15227 q^{31} -1.20160 q^{32} +2.76855 q^{33} +2.30139 q^{34} -1.87295 q^{35} +7.88503 q^{36} +0.596239 q^{37} -15.3380 q^{38} +1.78038 q^{39} +5.21816 q^{40} -8.17800 q^{41} +10.3107 q^{42} +6.27933 q^{43} -5.14261 q^{44} -1.90728 q^{45} -2.47345 q^{46} +5.78681 q^{47} -10.4678 q^{48} -3.46440 q^{49} +9.91317 q^{50} +2.06271 q^{51} -3.30707 q^{52} -4.20753 q^{53} -5.95075 q^{54} +1.24393 q^{55} -9.85042 q^{56} -13.7473 q^{57} +4.91866 q^{58} -5.45655 q^{59} +9.09346 q^{60} -4.99497 q^{61} -22.6377 q^{62} +3.60040 q^{63} -6.47138 q^{64} +0.799934 q^{65} -6.84788 q^{66} -1.85913 q^{67} -3.83151 q^{68} -2.21693 q^{69} +4.63264 q^{70} +1.82003 q^{71} -10.0310 q^{72} +10.1626 q^{73} -1.47477 q^{74} +8.88508 q^{75} +25.5358 q^{76} -2.34818 q^{77} -4.40369 q^{78} +11.3664 q^{79} -4.70322 q^{80} -11.0780 q^{81} +20.2279 q^{82} +10.6081 q^{83} -17.1659 q^{84} +0.926788 q^{85} -15.5316 q^{86} +4.40854 q^{87} +6.54220 q^{88} -0.00820211 q^{89} +4.71756 q^{90} -1.51005 q^{91} +4.11797 q^{92} -20.2899 q^{93} -14.3134 q^{94} -6.17674 q^{95} +2.66386 q^{96} +3.33566 q^{97} +8.56904 q^{98} -2.39123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47345 −1.74900 −0.874498 0.485030i \(-0.838809\pi\)
−0.874498 + 0.485030i \(0.838809\pi\)
\(3\) −2.21693 −1.27995 −0.639973 0.768397i \(-0.721054\pi\)
−0.639973 + 0.768397i \(0.721054\pi\)
\(4\) 4.11797 2.05899
\(5\) −0.996079 −0.445460 −0.222730 0.974880i \(-0.571497\pi\)
−0.222730 + 0.974880i \(0.571497\pi\)
\(6\) 5.48348 2.23862
\(7\) 1.88032 0.710693 0.355347 0.934735i \(-0.384363\pi\)
0.355347 + 0.934735i \(0.384363\pi\)
\(8\) −5.23870 −1.85216
\(9\) 1.91479 0.638262
\(10\) 2.46376 0.779108
\(11\) −1.24882 −0.376534 −0.188267 0.982118i \(-0.560287\pi\)
−0.188267 + 0.982118i \(0.560287\pi\)
\(12\) −9.12926 −2.63539
\(13\) −0.803083 −0.222735 −0.111368 0.993779i \(-0.535523\pi\)
−0.111368 + 0.993779i \(0.535523\pi\)
\(14\) −4.65088 −1.24300
\(15\) 2.20824 0.570165
\(16\) 4.72174 1.18043
\(17\) −0.930436 −0.225664 −0.112832 0.993614i \(-0.535992\pi\)
−0.112832 + 0.993614i \(0.535992\pi\)
\(18\) −4.73613 −1.11632
\(19\) 6.20106 1.42262 0.711310 0.702879i \(-0.248102\pi\)
0.711310 + 0.702879i \(0.248102\pi\)
\(20\) −4.10182 −0.917196
\(21\) −4.16854 −0.909649
\(22\) 3.08890 0.658556
\(23\) 1.00000 0.208514
\(24\) 11.6138 2.37066
\(25\) −4.00783 −0.801565
\(26\) 1.98639 0.389563
\(27\) 2.40585 0.463005
\(28\) 7.74309 1.46331
\(29\) −1.98858 −0.369270 −0.184635 0.982807i \(-0.559110\pi\)
−0.184635 + 0.982807i \(0.559110\pi\)
\(30\) −5.46198 −0.997216
\(31\) 9.15227 1.64380 0.821898 0.569635i \(-0.192915\pi\)
0.821898 + 0.569635i \(0.192915\pi\)
\(32\) −1.20160 −0.212414
\(33\) 2.76855 0.481943
\(34\) 2.30139 0.394685
\(35\) −1.87295 −0.316586
\(36\) 7.88503 1.31417
\(37\) 0.596239 0.0980211 0.0490106 0.998798i \(-0.484393\pi\)
0.0490106 + 0.998798i \(0.484393\pi\)
\(38\) −15.3380 −2.48816
\(39\) 1.78038 0.285089
\(40\) 5.21816 0.825063
\(41\) −8.17800 −1.27719 −0.638594 0.769544i \(-0.720484\pi\)
−0.638594 + 0.769544i \(0.720484\pi\)
\(42\) 10.3107 1.59097
\(43\) 6.27933 0.957589 0.478795 0.877927i \(-0.341074\pi\)
0.478795 + 0.877927i \(0.341074\pi\)
\(44\) −5.14261 −0.775278
\(45\) −1.90728 −0.284320
\(46\) −2.47345 −0.364691
\(47\) 5.78681 0.844093 0.422046 0.906574i \(-0.361312\pi\)
0.422046 + 0.906574i \(0.361312\pi\)
\(48\) −10.4678 −1.51089
\(49\) −3.46440 −0.494915
\(50\) 9.91317 1.40193
\(51\) 2.06271 0.288838
\(52\) −3.30707 −0.458608
\(53\) −4.20753 −0.577948 −0.288974 0.957337i \(-0.593314\pi\)
−0.288974 + 0.957337i \(0.593314\pi\)
\(54\) −5.95075 −0.809794
\(55\) 1.24393 0.167731
\(56\) −9.85042 −1.31632
\(57\) −13.7473 −1.82088
\(58\) 4.91866 0.645851
\(59\) −5.45655 −0.710382 −0.355191 0.934794i \(-0.615584\pi\)
−0.355191 + 0.934794i \(0.615584\pi\)
\(60\) 9.09346 1.17396
\(61\) −4.99497 −0.639541 −0.319770 0.947495i \(-0.603606\pi\)
−0.319770 + 0.947495i \(0.603606\pi\)
\(62\) −22.6377 −2.87499
\(63\) 3.60040 0.453608
\(64\) −6.47138 −0.808923
\(65\) 0.799934 0.0992196
\(66\) −6.84788 −0.842916
\(67\) −1.85913 −0.227129 −0.113565 0.993531i \(-0.536227\pi\)
−0.113565 + 0.993531i \(0.536227\pi\)
\(68\) −3.83151 −0.464639
\(69\) −2.21693 −0.266887
\(70\) 4.63264 0.553707
\(71\) 1.82003 0.215998 0.107999 0.994151i \(-0.465556\pi\)
0.107999 + 0.994151i \(0.465556\pi\)
\(72\) −10.0310 −1.18216
\(73\) 10.1626 1.18945 0.594724 0.803930i \(-0.297261\pi\)
0.594724 + 0.803930i \(0.297261\pi\)
\(74\) −1.47477 −0.171438
\(75\) 8.88508 1.02596
\(76\) 25.5358 2.92915
\(77\) −2.34818 −0.267600
\(78\) −4.40369 −0.498619
\(79\) 11.3664 1.27882 0.639411 0.768865i \(-0.279178\pi\)
0.639411 + 0.768865i \(0.279178\pi\)
\(80\) −4.70322 −0.525837
\(81\) −11.0780 −1.23088
\(82\) 20.2279 2.23380
\(83\) 10.6081 1.16439 0.582195 0.813049i \(-0.302194\pi\)
0.582195 + 0.813049i \(0.302194\pi\)
\(84\) −17.1659 −1.87295
\(85\) 0.926788 0.100524
\(86\) −15.5316 −1.67482
\(87\) 4.40854 0.472646
\(88\) 6.54220 0.697401
\(89\) −0.00820211 −0.000869422 0 −0.000434711 1.00000i \(-0.500138\pi\)
−0.000434711 1.00000i \(0.500138\pi\)
\(90\) 4.71756 0.497275
\(91\) −1.51005 −0.158296
\(92\) 4.11797 0.429328
\(93\) −20.2899 −2.10397
\(94\) −14.3134 −1.47631
\(95\) −6.17674 −0.633720
\(96\) 2.66386 0.271879
\(97\) 3.33566 0.338685 0.169342 0.985557i \(-0.445836\pi\)
0.169342 + 0.985557i \(0.445836\pi\)
\(98\) 8.56904 0.865604
\(99\) −2.39123 −0.240327
\(100\) −16.5041 −1.65041
\(101\) 14.0354 1.39658 0.698288 0.715817i \(-0.253945\pi\)
0.698288 + 0.715817i \(0.253945\pi\)
\(102\) −5.10202 −0.505176
\(103\) −7.69035 −0.757753 −0.378876 0.925447i \(-0.623689\pi\)
−0.378876 + 0.925447i \(0.623689\pi\)
\(104\) 4.20711 0.412541
\(105\) 4.15219 0.405212
\(106\) 10.4071 1.01083
\(107\) 11.2230 1.08497 0.542483 0.840067i \(-0.317484\pi\)
0.542483 + 0.840067i \(0.317484\pi\)
\(108\) 9.90721 0.953321
\(109\) −3.52532 −0.337665 −0.168832 0.985645i \(-0.554000\pi\)
−0.168832 + 0.985645i \(0.554000\pi\)
\(110\) −3.07679 −0.293360
\(111\) −1.32182 −0.125462
\(112\) 8.87837 0.838927
\(113\) −10.0578 −0.946159 −0.473080 0.881020i \(-0.656858\pi\)
−0.473080 + 0.881020i \(0.656858\pi\)
\(114\) 34.0033 3.18470
\(115\) −0.996079 −0.0928849
\(116\) −8.18891 −0.760321
\(117\) −1.53773 −0.142163
\(118\) 13.4965 1.24245
\(119\) −1.74952 −0.160378
\(120\) −11.5683 −1.05604
\(121\) −9.44044 −0.858222
\(122\) 12.3548 1.11855
\(123\) 18.1301 1.63473
\(124\) 37.6888 3.38455
\(125\) 8.97251 0.802526
\(126\) −8.90543 −0.793359
\(127\) 13.7835 1.22309 0.611543 0.791211i \(-0.290549\pi\)
0.611543 + 0.791211i \(0.290549\pi\)
\(128\) 18.4099 1.62722
\(129\) −13.9208 −1.22566
\(130\) −1.97860 −0.173535
\(131\) 4.21251 0.368049 0.184024 0.982922i \(-0.441087\pi\)
0.184024 + 0.982922i \(0.441087\pi\)
\(132\) 11.4008 0.992314
\(133\) 11.6600 1.01105
\(134\) 4.59848 0.397248
\(135\) −2.39641 −0.206250
\(136\) 4.87427 0.417966
\(137\) −4.96817 −0.424459 −0.212230 0.977220i \(-0.568072\pi\)
−0.212230 + 0.977220i \(0.568072\pi\)
\(138\) 5.48348 0.466784
\(139\) 12.1301 1.02886 0.514431 0.857532i \(-0.328003\pi\)
0.514431 + 0.857532i \(0.328003\pi\)
\(140\) −7.71273 −0.651845
\(141\) −12.8290 −1.08039
\(142\) −4.50177 −0.377780
\(143\) 1.00291 0.0838673
\(144\) 9.04111 0.753426
\(145\) 1.98078 0.164495
\(146\) −25.1368 −2.08034
\(147\) 7.68035 0.633464
\(148\) 2.45530 0.201824
\(149\) −11.4974 −0.941906 −0.470953 0.882158i \(-0.656090\pi\)
−0.470953 + 0.882158i \(0.656090\pi\)
\(150\) −21.9768 −1.79440
\(151\) 15.9740 1.29994 0.649972 0.759958i \(-0.274781\pi\)
0.649972 + 0.759958i \(0.274781\pi\)
\(152\) −32.4855 −2.63492
\(153\) −1.78158 −0.144033
\(154\) 5.80812 0.468031
\(155\) −9.11638 −0.732245
\(156\) 7.33155 0.586994
\(157\) 9.65439 0.770504 0.385252 0.922811i \(-0.374115\pi\)
0.385252 + 0.922811i \(0.374115\pi\)
\(158\) −28.1143 −2.23665
\(159\) 9.32780 0.739743
\(160\) 1.19689 0.0946222
\(161\) 1.88032 0.148190
\(162\) 27.4008 2.15281
\(163\) 4.16764 0.326434 0.163217 0.986590i \(-0.447813\pi\)
0.163217 + 0.986590i \(0.447813\pi\)
\(164\) −33.6768 −2.62971
\(165\) −2.75770 −0.214686
\(166\) −26.2386 −2.03651
\(167\) −18.4989 −1.43148 −0.715742 0.698365i \(-0.753911\pi\)
−0.715742 + 0.698365i \(0.753911\pi\)
\(168\) 21.8377 1.68482
\(169\) −12.3551 −0.950389
\(170\) −2.29237 −0.175816
\(171\) 11.8737 0.908004
\(172\) 25.8581 1.97166
\(173\) −2.67985 −0.203745 −0.101872 0.994797i \(-0.532483\pi\)
−0.101872 + 0.994797i \(0.532483\pi\)
\(174\) −10.9043 −0.826655
\(175\) −7.53599 −0.569667
\(176\) −5.89661 −0.444474
\(177\) 12.0968 0.909250
\(178\) 0.0202875 0.00152061
\(179\) −1.19995 −0.0896888 −0.0448444 0.998994i \(-0.514279\pi\)
−0.0448444 + 0.998994i \(0.514279\pi\)
\(180\) −7.85411 −0.585411
\(181\) −2.32566 −0.172865 −0.0864324 0.996258i \(-0.527547\pi\)
−0.0864324 + 0.996258i \(0.527547\pi\)
\(182\) 3.73504 0.276860
\(183\) 11.0735 0.818578
\(184\) −5.23870 −0.386202
\(185\) −0.593901 −0.0436645
\(186\) 50.1862 3.67983
\(187\) 1.16195 0.0849701
\(188\) 23.8299 1.73797
\(189\) 4.52376 0.329055
\(190\) 15.2779 1.10837
\(191\) 10.0552 0.727569 0.363785 0.931483i \(-0.381484\pi\)
0.363785 + 0.931483i \(0.381484\pi\)
\(192\) 14.3466 1.03538
\(193\) 11.0793 0.797506 0.398753 0.917058i \(-0.369443\pi\)
0.398753 + 0.917058i \(0.369443\pi\)
\(194\) −8.25059 −0.592358
\(195\) −1.77340 −0.126996
\(196\) −14.2663 −1.01902
\(197\) −17.0512 −1.21485 −0.607423 0.794378i \(-0.707797\pi\)
−0.607423 + 0.794378i \(0.707797\pi\)
\(198\) 5.91458 0.420331
\(199\) −12.2991 −0.871858 −0.435929 0.899981i \(-0.643580\pi\)
−0.435929 + 0.899981i \(0.643580\pi\)
\(200\) 20.9958 1.48463
\(201\) 4.12157 0.290713
\(202\) −34.7160 −2.44261
\(203\) −3.73916 −0.262438
\(204\) 8.49419 0.594712
\(205\) 8.14593 0.568937
\(206\) 19.0217 1.32531
\(207\) 1.91479 0.133087
\(208\) −3.79195 −0.262924
\(209\) −7.74401 −0.535665
\(210\) −10.2703 −0.708715
\(211\) −18.0793 −1.24463 −0.622315 0.782767i \(-0.713808\pi\)
−0.622315 + 0.782767i \(0.713808\pi\)
\(212\) −17.3265 −1.18999
\(213\) −4.03489 −0.276466
\(214\) −27.7595 −1.89760
\(215\) −6.25471 −0.426568
\(216\) −12.6035 −0.857560
\(217\) 17.2092 1.16823
\(218\) 8.71972 0.590574
\(219\) −22.5299 −1.52243
\(220\) 5.12245 0.345355
\(221\) 0.747217 0.0502633
\(222\) 3.26946 0.219432
\(223\) 1.42297 0.0952889 0.0476445 0.998864i \(-0.484829\pi\)
0.0476445 + 0.998864i \(0.484829\pi\)
\(224\) −2.25939 −0.150962
\(225\) −7.67413 −0.511608
\(226\) 24.8775 1.65483
\(227\) −2.02413 −0.134346 −0.0671732 0.997741i \(-0.521398\pi\)
−0.0671732 + 0.997741i \(0.521398\pi\)
\(228\) −56.6110 −3.74916
\(229\) 7.52010 0.496942 0.248471 0.968639i \(-0.420072\pi\)
0.248471 + 0.968639i \(0.420072\pi\)
\(230\) 2.46376 0.162455
\(231\) 5.20576 0.342514
\(232\) 10.4176 0.683947
\(233\) 2.01986 0.132326 0.0661628 0.997809i \(-0.478924\pi\)
0.0661628 + 0.997809i \(0.478924\pi\)
\(234\) 3.80351 0.248643
\(235\) −5.76412 −0.376010
\(236\) −22.4699 −1.46267
\(237\) −25.1986 −1.63682
\(238\) 4.32734 0.280500
\(239\) 2.95181 0.190937 0.0954684 0.995432i \(-0.469565\pi\)
0.0954684 + 0.995432i \(0.469565\pi\)
\(240\) 10.4267 0.673042
\(241\) −6.58757 −0.424343 −0.212171 0.977232i \(-0.568053\pi\)
−0.212171 + 0.977232i \(0.568053\pi\)
\(242\) 23.3505 1.50103
\(243\) 17.3415 1.11246
\(244\) −20.5691 −1.31680
\(245\) 3.45082 0.220465
\(246\) −44.8439 −2.85914
\(247\) −4.97996 −0.316867
\(248\) −47.9460 −3.04457
\(249\) −23.5174 −1.49036
\(250\) −22.1931 −1.40361
\(251\) −24.3433 −1.53653 −0.768267 0.640129i \(-0.778881\pi\)
−0.768267 + 0.640129i \(0.778881\pi\)
\(252\) 14.8264 0.933973
\(253\) −1.24882 −0.0785127
\(254\) −34.0928 −2.13917
\(255\) −2.05463 −0.128666
\(256\) −32.5931 −2.03707
\(257\) 27.9423 1.74299 0.871496 0.490402i \(-0.163150\pi\)
0.871496 + 0.490402i \(0.163150\pi\)
\(258\) 34.4326 2.14368
\(259\) 1.12112 0.0696630
\(260\) 3.29410 0.204292
\(261\) −3.80770 −0.235691
\(262\) −10.4194 −0.643716
\(263\) 8.05654 0.496788 0.248394 0.968659i \(-0.420097\pi\)
0.248394 + 0.968659i \(0.420097\pi\)
\(264\) −14.5036 −0.892636
\(265\) 4.19103 0.257453
\(266\) −28.8404 −1.76832
\(267\) 0.0181835 0.00111281
\(268\) −7.65586 −0.467656
\(269\) −4.58006 −0.279251 −0.139626 0.990204i \(-0.544590\pi\)
−0.139626 + 0.990204i \(0.544590\pi\)
\(270\) 5.92742 0.360731
\(271\) −26.1138 −1.58630 −0.793150 0.609026i \(-0.791560\pi\)
−0.793150 + 0.609026i \(0.791560\pi\)
\(272\) −4.39327 −0.266381
\(273\) 3.34768 0.202611
\(274\) 12.2885 0.742377
\(275\) 5.00506 0.301816
\(276\) −9.12926 −0.549517
\(277\) 1.98074 0.119011 0.0595055 0.998228i \(-0.481048\pi\)
0.0595055 + 0.998228i \(0.481048\pi\)
\(278\) −30.0032 −1.79947
\(279\) 17.5246 1.04917
\(280\) 9.81180 0.586367
\(281\) 12.3291 0.735494 0.367747 0.929926i \(-0.380129\pi\)
0.367747 + 0.929926i \(0.380129\pi\)
\(282\) 31.7318 1.88960
\(283\) −8.94343 −0.531632 −0.265816 0.964024i \(-0.585641\pi\)
−0.265816 + 0.964024i \(0.585641\pi\)
\(284\) 7.49484 0.444737
\(285\) 13.6934 0.811128
\(286\) −2.48064 −0.146684
\(287\) −15.3772 −0.907690
\(288\) −2.30080 −0.135576
\(289\) −16.1343 −0.949076
\(290\) −4.89937 −0.287701
\(291\) −7.39492 −0.433498
\(292\) 41.8495 2.44905
\(293\) −5.02944 −0.293823 −0.146911 0.989150i \(-0.546933\pi\)
−0.146911 + 0.989150i \(0.546933\pi\)
\(294\) −18.9970 −1.10793
\(295\) 5.43515 0.316447
\(296\) −3.12352 −0.181551
\(297\) −3.00447 −0.174337
\(298\) 28.4383 1.64739
\(299\) −0.803083 −0.0464435
\(300\) 36.5885 2.11244
\(301\) 11.8071 0.680552
\(302\) −39.5109 −2.27360
\(303\) −31.1156 −1.78754
\(304\) 29.2798 1.67931
\(305\) 4.97539 0.284890
\(306\) 4.40667 0.251912
\(307\) 3.91098 0.223212 0.111606 0.993753i \(-0.464401\pi\)
0.111606 + 0.993753i \(0.464401\pi\)
\(308\) −9.66974 −0.550985
\(309\) 17.0490 0.969883
\(310\) 22.5489 1.28069
\(311\) −9.26473 −0.525355 −0.262677 0.964884i \(-0.584605\pi\)
−0.262677 + 0.964884i \(0.584605\pi\)
\(312\) −9.32687 −0.528030
\(313\) 5.70321 0.322365 0.161182 0.986925i \(-0.448469\pi\)
0.161182 + 0.986925i \(0.448469\pi\)
\(314\) −23.8797 −1.34761
\(315\) −3.58629 −0.202064
\(316\) 46.8066 2.63307
\(317\) −17.3218 −0.972890 −0.486445 0.873711i \(-0.661707\pi\)
−0.486445 + 0.873711i \(0.661707\pi\)
\(318\) −23.0719 −1.29381
\(319\) 2.48338 0.139043
\(320\) 6.44601 0.360343
\(321\) −24.8806 −1.38870
\(322\) −4.65088 −0.259183
\(323\) −5.76968 −0.321034
\(324\) −45.6187 −2.53437
\(325\) 3.21862 0.178537
\(326\) −10.3085 −0.570932
\(327\) 7.81540 0.432193
\(328\) 42.8421 2.36556
\(329\) 10.8810 0.599891
\(330\) 6.82103 0.375486
\(331\) 0.926427 0.0509210 0.0254605 0.999676i \(-0.491895\pi\)
0.0254605 + 0.999676i \(0.491895\pi\)
\(332\) 43.6838 2.39746
\(333\) 1.14167 0.0625631
\(334\) 45.7560 2.50366
\(335\) 1.85184 0.101177
\(336\) −19.6827 −1.07378
\(337\) 11.6513 0.634687 0.317344 0.948311i \(-0.397209\pi\)
0.317344 + 0.948311i \(0.397209\pi\)
\(338\) 30.5597 1.66223
\(339\) 22.2975 1.21103
\(340\) 3.81648 0.206978
\(341\) −11.4295 −0.618945
\(342\) −29.3690 −1.58809
\(343\) −19.6764 −1.06243
\(344\) −32.8955 −1.77361
\(345\) 2.20824 0.118888
\(346\) 6.62847 0.356349
\(347\) 9.18483 0.493067 0.246534 0.969134i \(-0.420708\pi\)
0.246534 + 0.969134i \(0.420708\pi\)
\(348\) 18.1543 0.973170
\(349\) −1.00000 −0.0535288
\(350\) 18.6399 0.996345
\(351\) −1.93209 −0.103128
\(352\) 1.50058 0.0799812
\(353\) 1.27850 0.0680475 0.0340237 0.999421i \(-0.489168\pi\)
0.0340237 + 0.999421i \(0.489168\pi\)
\(354\) −29.9208 −1.59027
\(355\) −1.81290 −0.0962186
\(356\) −0.0337760 −0.00179013
\(357\) 3.87856 0.205275
\(358\) 2.96803 0.156865
\(359\) −12.2638 −0.647258 −0.323629 0.946184i \(-0.604903\pi\)
−0.323629 + 0.946184i \(0.604903\pi\)
\(360\) 9.99165 0.526606
\(361\) 19.4531 1.02385
\(362\) 5.75240 0.302340
\(363\) 20.9288 1.09848
\(364\) −6.21834 −0.325930
\(365\) −10.1228 −0.529852
\(366\) −27.3898 −1.43169
\(367\) 5.59851 0.292240 0.146120 0.989267i \(-0.453321\pi\)
0.146120 + 0.989267i \(0.453321\pi\)
\(368\) 4.72174 0.246138
\(369\) −15.6591 −0.815181
\(370\) 1.46899 0.0763690
\(371\) −7.91149 −0.410744
\(372\) −83.5534 −4.33204
\(373\) 31.0890 1.60973 0.804863 0.593461i \(-0.202239\pi\)
0.804863 + 0.593461i \(0.202239\pi\)
\(374\) −2.87403 −0.148612
\(375\) −19.8914 −1.02719
\(376\) −30.3154 −1.56340
\(377\) 1.59699 0.0822494
\(378\) −11.1893 −0.575515
\(379\) −31.6292 −1.62468 −0.812342 0.583181i \(-0.801808\pi\)
−0.812342 + 0.583181i \(0.801808\pi\)
\(380\) −25.4356 −1.30482
\(381\) −30.5571 −1.56549
\(382\) −24.8711 −1.27252
\(383\) −24.3120 −1.24228 −0.621142 0.783698i \(-0.713331\pi\)
−0.621142 + 0.783698i \(0.713331\pi\)
\(384\) −40.8134 −2.08275
\(385\) 2.33897 0.119205
\(386\) −27.4041 −1.39483
\(387\) 12.0236 0.611193
\(388\) 13.7361 0.697347
\(389\) −8.45824 −0.428850 −0.214425 0.976740i \(-0.568788\pi\)
−0.214425 + 0.976740i \(0.568788\pi\)
\(390\) 4.38642 0.222115
\(391\) −0.930436 −0.0470542
\(392\) 18.1490 0.916662
\(393\) −9.33885 −0.471083
\(394\) 42.1753 2.12476
\(395\) −11.3219 −0.569664
\(396\) −9.84699 −0.494830
\(397\) −19.2627 −0.966765 −0.483383 0.875409i \(-0.660592\pi\)
−0.483383 + 0.875409i \(0.660592\pi\)
\(398\) 30.4212 1.52488
\(399\) −25.8493 −1.29408
\(400\) −18.9239 −0.946195
\(401\) −25.2703 −1.26194 −0.630968 0.775809i \(-0.717342\pi\)
−0.630968 + 0.775809i \(0.717342\pi\)
\(402\) −10.1945 −0.508456
\(403\) −7.35003 −0.366131
\(404\) 57.7975 2.87553
\(405\) 11.0345 0.548310
\(406\) 9.24864 0.459002
\(407\) −0.744596 −0.0369083
\(408\) −10.8059 −0.534973
\(409\) −11.4224 −0.564801 −0.282401 0.959297i \(-0.591131\pi\)
−0.282401 + 0.959297i \(0.591131\pi\)
\(410\) −20.1486 −0.995068
\(411\) 11.0141 0.543285
\(412\) −31.6686 −1.56020
\(413\) −10.2600 −0.504864
\(414\) −4.73613 −0.232768
\(415\) −10.5665 −0.518689
\(416\) 0.964982 0.0473122
\(417\) −26.8916 −1.31689
\(418\) 19.1545 0.936875
\(419\) 21.0921 1.03041 0.515207 0.857066i \(-0.327715\pi\)
0.515207 + 0.857066i \(0.327715\pi\)
\(420\) 17.0986 0.834326
\(421\) −10.2148 −0.497838 −0.248919 0.968524i \(-0.580075\pi\)
−0.248919 + 0.968524i \(0.580075\pi\)
\(422\) 44.7183 2.17685
\(423\) 11.0805 0.538752
\(424\) 22.0420 1.07045
\(425\) 3.72903 0.180884
\(426\) 9.98011 0.483538
\(427\) −9.39214 −0.454517
\(428\) 46.2159 2.23393
\(429\) −2.22338 −0.107346
\(430\) 15.4707 0.746065
\(431\) 17.3087 0.833729 0.416865 0.908969i \(-0.363129\pi\)
0.416865 + 0.908969i \(0.363129\pi\)
\(432\) 11.3598 0.546548
\(433\) 3.03391 0.145801 0.0729003 0.997339i \(-0.476775\pi\)
0.0729003 + 0.997339i \(0.476775\pi\)
\(434\) −42.5661 −2.04324
\(435\) −4.39126 −0.210545
\(436\) −14.5172 −0.695247
\(437\) 6.20106 0.296637
\(438\) 55.7266 2.66272
\(439\) 18.3388 0.875261 0.437631 0.899155i \(-0.355818\pi\)
0.437631 + 0.899155i \(0.355818\pi\)
\(440\) −6.51655 −0.310664
\(441\) −6.63359 −0.315885
\(442\) −1.84821 −0.0879102
\(443\) 2.87170 0.136438 0.0682192 0.997670i \(-0.478268\pi\)
0.0682192 + 0.997670i \(0.478268\pi\)
\(444\) −5.44322 −0.258324
\(445\) 0.00816995 0.000387293 0
\(446\) −3.51964 −0.166660
\(447\) 25.4890 1.20559
\(448\) −12.1683 −0.574896
\(449\) 4.84889 0.228833 0.114417 0.993433i \(-0.463500\pi\)
0.114417 + 0.993433i \(0.463500\pi\)
\(450\) 18.9816 0.894801
\(451\) 10.2129 0.480905
\(452\) −41.4178 −1.94813
\(453\) −35.4132 −1.66386
\(454\) 5.00660 0.234971
\(455\) 1.50413 0.0705147
\(456\) 72.0181 3.37255
\(457\) −30.4075 −1.42240 −0.711201 0.702989i \(-0.751848\pi\)
−0.711201 + 0.702989i \(0.751848\pi\)
\(458\) −18.6006 −0.869149
\(459\) −2.23849 −0.104484
\(460\) −4.10182 −0.191249
\(461\) 24.2902 1.13131 0.565653 0.824643i \(-0.308624\pi\)
0.565653 + 0.824643i \(0.308624\pi\)
\(462\) −12.8762 −0.599055
\(463\) 13.3552 0.620666 0.310333 0.950628i \(-0.399559\pi\)
0.310333 + 0.950628i \(0.399559\pi\)
\(464\) −9.38955 −0.435899
\(465\) 20.2104 0.937235
\(466\) −4.99603 −0.231437
\(467\) −17.1338 −0.792859 −0.396430 0.918065i \(-0.629751\pi\)
−0.396430 + 0.918065i \(0.629751\pi\)
\(468\) −6.33233 −0.292712
\(469\) −3.49576 −0.161419
\(470\) 14.2573 0.657639
\(471\) −21.4031 −0.986204
\(472\) 28.5852 1.31574
\(473\) −7.84177 −0.360565
\(474\) 62.3275 2.86280
\(475\) −24.8528 −1.14032
\(476\) −7.20445 −0.330216
\(477\) −8.05651 −0.368882
\(478\) −7.30116 −0.333948
\(479\) 4.78030 0.218417 0.109209 0.994019i \(-0.465168\pi\)
0.109209 + 0.994019i \(0.465168\pi\)
\(480\) −2.65341 −0.121111
\(481\) −0.478829 −0.0218327
\(482\) 16.2940 0.742173
\(483\) −4.16854 −0.189675
\(484\) −38.8755 −1.76707
\(485\) −3.32258 −0.150871
\(486\) −42.8934 −1.94569
\(487\) −20.1740 −0.914170 −0.457085 0.889423i \(-0.651107\pi\)
−0.457085 + 0.889423i \(0.651107\pi\)
\(488\) 26.1672 1.18453
\(489\) −9.23936 −0.417818
\(490\) −8.53545 −0.385592
\(491\) −8.25587 −0.372582 −0.186291 0.982495i \(-0.559647\pi\)
−0.186291 + 0.982495i \(0.559647\pi\)
\(492\) 74.6591 3.36589
\(493\) 1.85025 0.0833309
\(494\) 12.3177 0.554199
\(495\) 2.38185 0.107056
\(496\) 43.2146 1.94039
\(497\) 3.42224 0.153508
\(498\) 58.1692 2.60663
\(499\) 12.2623 0.548934 0.274467 0.961597i \(-0.411499\pi\)
0.274467 + 0.961597i \(0.411499\pi\)
\(500\) 36.9485 1.65239
\(501\) 41.0107 1.83222
\(502\) 60.2120 2.68739
\(503\) 31.4085 1.40043 0.700217 0.713930i \(-0.253086\pi\)
0.700217 + 0.713930i \(0.253086\pi\)
\(504\) −18.8614 −0.840155
\(505\) −13.9804 −0.622119
\(506\) 3.08890 0.137318
\(507\) 27.3903 1.21645
\(508\) 56.7600 2.51832
\(509\) 30.4049 1.34767 0.673837 0.738880i \(-0.264645\pi\)
0.673837 + 0.738880i \(0.264645\pi\)
\(510\) 5.08202 0.225036
\(511\) 19.1090 0.845333
\(512\) 43.7979 1.93561
\(513\) 14.9188 0.658681
\(514\) −69.1140 −3.04849
\(515\) 7.66020 0.337549
\(516\) −57.3256 −2.52362
\(517\) −7.22669 −0.317830
\(518\) −2.77304 −0.121840
\(519\) 5.94103 0.260782
\(520\) −4.19061 −0.183771
\(521\) −34.6938 −1.51996 −0.759982 0.649944i \(-0.774792\pi\)
−0.759982 + 0.649944i \(0.774792\pi\)
\(522\) 9.41817 0.412222
\(523\) 35.2593 1.54178 0.770890 0.636968i \(-0.219812\pi\)
0.770890 + 0.636968i \(0.219812\pi\)
\(524\) 17.3470 0.757807
\(525\) 16.7068 0.729143
\(526\) −19.9275 −0.868880
\(527\) −8.51560 −0.370945
\(528\) 13.0724 0.568902
\(529\) 1.00000 0.0434783
\(530\) −10.3663 −0.450284
\(531\) −10.4481 −0.453410
\(532\) 48.0153 2.08173
\(533\) 6.56761 0.284475
\(534\) −0.0449761 −0.00194630
\(535\) −11.1790 −0.483309
\(536\) 9.73945 0.420680
\(537\) 2.66022 0.114797
\(538\) 11.3286 0.488409
\(539\) 4.32642 0.186352
\(540\) −9.86836 −0.424667
\(541\) −19.0635 −0.819604 −0.409802 0.912175i \(-0.634402\pi\)
−0.409802 + 0.912175i \(0.634402\pi\)
\(542\) 64.5912 2.77443
\(543\) 5.15582 0.221257
\(544\) 1.11801 0.0479343
\(545\) 3.51150 0.150416
\(546\) −8.28033 −0.354365
\(547\) −26.7725 −1.14471 −0.572354 0.820006i \(-0.693970\pi\)
−0.572354 + 0.820006i \(0.693970\pi\)
\(548\) −20.4588 −0.873955
\(549\) −9.56430 −0.408194
\(550\) −12.3798 −0.527876
\(551\) −12.3313 −0.525331
\(552\) 11.6138 0.494318
\(553\) 21.3725 0.908850
\(554\) −4.89926 −0.208150
\(555\) 1.31664 0.0558882
\(556\) 49.9514 2.11841
\(557\) −26.9576 −1.14223 −0.571115 0.820870i \(-0.693489\pi\)
−0.571115 + 0.820870i \(0.693489\pi\)
\(558\) −43.3463 −1.83500
\(559\) −5.04282 −0.213289
\(560\) −8.84356 −0.373708
\(561\) −2.57596 −0.108757
\(562\) −30.4955 −1.28638
\(563\) 23.1606 0.976103 0.488052 0.872815i \(-0.337708\pi\)
0.488052 + 0.872815i \(0.337708\pi\)
\(564\) −52.8293 −2.22451
\(565\) 10.0184 0.421476
\(566\) 22.1211 0.929821
\(567\) −20.8301 −0.874781
\(568\) −9.53461 −0.400063
\(569\) −2.35378 −0.0986755 −0.0493378 0.998782i \(-0.515711\pi\)
−0.0493378 + 0.998782i \(0.515711\pi\)
\(570\) −33.8700 −1.41866
\(571\) 8.63857 0.361513 0.180757 0.983528i \(-0.442145\pi\)
0.180757 + 0.983528i \(0.442145\pi\)
\(572\) 4.12994 0.172682
\(573\) −22.2917 −0.931249
\(574\) 38.0349 1.58754
\(575\) −4.00783 −0.167138
\(576\) −12.3913 −0.516304
\(577\) 18.7681 0.781326 0.390663 0.920534i \(-0.372246\pi\)
0.390663 + 0.920534i \(0.372246\pi\)
\(578\) 39.9074 1.65993
\(579\) −24.5621 −1.02076
\(580\) 8.15680 0.338693
\(581\) 19.9466 0.827524
\(582\) 18.2910 0.758186
\(583\) 5.25445 0.217617
\(584\) −53.2390 −2.20305
\(585\) 1.53170 0.0633281
\(586\) 12.4401 0.513895
\(587\) −16.1141 −0.665099 −0.332549 0.943086i \(-0.607909\pi\)
−0.332549 + 0.943086i \(0.607909\pi\)
\(588\) 31.6274 1.30429
\(589\) 56.7537 2.33850
\(590\) −13.4436 −0.553464
\(591\) 37.8013 1.55494
\(592\) 2.81529 0.115708
\(593\) 21.6882 0.890629 0.445315 0.895374i \(-0.353092\pi\)
0.445315 + 0.895374i \(0.353092\pi\)
\(594\) 7.43142 0.304915
\(595\) 1.74266 0.0714419
\(596\) −47.3461 −1.93937
\(597\) 27.2662 1.11593
\(598\) 1.98639 0.0812294
\(599\) −38.1893 −1.56037 −0.780186 0.625548i \(-0.784875\pi\)
−0.780186 + 0.625548i \(0.784875\pi\)
\(600\) −46.5462 −1.90024
\(601\) 33.5784 1.36969 0.684845 0.728689i \(-0.259870\pi\)
0.684845 + 0.728689i \(0.259870\pi\)
\(602\) −29.2044 −1.19028
\(603\) −3.55984 −0.144968
\(604\) 65.7804 2.67656
\(605\) 9.40343 0.382304
\(606\) 76.9629 3.12640
\(607\) 21.4948 0.872448 0.436224 0.899838i \(-0.356316\pi\)
0.436224 + 0.899838i \(0.356316\pi\)
\(608\) −7.45117 −0.302185
\(609\) 8.28947 0.335906
\(610\) −12.3064 −0.498271
\(611\) −4.64729 −0.188009
\(612\) −7.33651 −0.296561
\(613\) −4.55578 −0.184006 −0.0920031 0.995759i \(-0.529327\pi\)
−0.0920031 + 0.995759i \(0.529327\pi\)
\(614\) −9.67364 −0.390396
\(615\) −18.0590 −0.728208
\(616\) 12.3014 0.495638
\(617\) 32.5855 1.31184 0.655921 0.754829i \(-0.272280\pi\)
0.655921 + 0.754829i \(0.272280\pi\)
\(618\) −42.1699 −1.69632
\(619\) 19.2418 0.773391 0.386696 0.922207i \(-0.373616\pi\)
0.386696 + 0.922207i \(0.373616\pi\)
\(620\) −37.5410 −1.50768
\(621\) 2.40585 0.0965433
\(622\) 22.9159 0.918843
\(623\) −0.0154226 −0.000617892 0
\(624\) 8.40649 0.336529
\(625\) 11.1018 0.444072
\(626\) −14.1066 −0.563814
\(627\) 17.1679 0.685622
\(628\) 39.7565 1.58646
\(629\) −0.554762 −0.0221198
\(630\) 8.87052 0.353410
\(631\) −22.4410 −0.893361 −0.446680 0.894694i \(-0.647394\pi\)
−0.446680 + 0.894694i \(0.647394\pi\)
\(632\) −59.5452 −2.36858
\(633\) 40.0806 1.59306
\(634\) 42.8447 1.70158
\(635\) −13.7294 −0.544836
\(636\) 38.4116 1.52312
\(637\) 2.78220 0.110235
\(638\) −6.14253 −0.243185
\(639\) 3.48497 0.137863
\(640\) −18.3377 −0.724860
\(641\) 28.4505 1.12373 0.561864 0.827229i \(-0.310084\pi\)
0.561864 + 0.827229i \(0.310084\pi\)
\(642\) 61.5410 2.42883
\(643\) 45.8015 1.80624 0.903118 0.429392i \(-0.141272\pi\)
0.903118 + 0.429392i \(0.141272\pi\)
\(644\) 7.74309 0.305121
\(645\) 13.8663 0.545984
\(646\) 14.2710 0.561487
\(647\) −13.0083 −0.511410 −0.255705 0.966755i \(-0.582308\pi\)
−0.255705 + 0.966755i \(0.582308\pi\)
\(648\) 58.0341 2.27979
\(649\) 6.81425 0.267483
\(650\) −7.96110 −0.312260
\(651\) −38.1516 −1.49528
\(652\) 17.1622 0.672124
\(653\) 20.2771 0.793506 0.396753 0.917925i \(-0.370137\pi\)
0.396753 + 0.917925i \(0.370137\pi\)
\(654\) −19.3310 −0.755903
\(655\) −4.19599 −0.163951
\(656\) −38.6144 −1.50764
\(657\) 19.4593 0.759179
\(658\) −26.9137 −1.04921
\(659\) −8.00052 −0.311656 −0.155828 0.987784i \(-0.549805\pi\)
−0.155828 + 0.987784i \(0.549805\pi\)
\(660\) −11.3561 −0.442036
\(661\) 21.4404 0.833936 0.416968 0.908921i \(-0.363093\pi\)
0.416968 + 0.908921i \(0.363093\pi\)
\(662\) −2.29147 −0.0890606
\(663\) −1.65653 −0.0643343
\(664\) −55.5726 −2.15664
\(665\) −11.6142 −0.450381
\(666\) −2.82387 −0.109423
\(667\) −1.98858 −0.0769981
\(668\) −76.1777 −2.94740
\(669\) −3.15462 −0.121965
\(670\) −4.58045 −0.176958
\(671\) 6.23783 0.240809
\(672\) 5.00890 0.193223
\(673\) −20.8839 −0.805016 −0.402508 0.915416i \(-0.631861\pi\)
−0.402508 + 0.915416i \(0.631861\pi\)
\(674\) −28.8190 −1.11006
\(675\) −9.64222 −0.371129
\(676\) −50.8778 −1.95684
\(677\) −0.643454 −0.0247299 −0.0123650 0.999924i \(-0.503936\pi\)
−0.0123650 + 0.999924i \(0.503936\pi\)
\(678\) −55.1518 −2.11809
\(679\) 6.27210 0.240701
\(680\) −4.85516 −0.186187
\(681\) 4.48736 0.171956
\(682\) 28.2705 1.08253
\(683\) −12.6589 −0.484380 −0.242190 0.970229i \(-0.577866\pi\)
−0.242190 + 0.970229i \(0.577866\pi\)
\(684\) 48.8955 1.86957
\(685\) 4.94869 0.189080
\(686\) 48.6687 1.85818
\(687\) −16.6715 −0.636059
\(688\) 29.6494 1.13037
\(689\) 3.37899 0.128729
\(690\) −5.46198 −0.207934
\(691\) 40.4132 1.53739 0.768695 0.639616i \(-0.220907\pi\)
0.768695 + 0.639616i \(0.220907\pi\)
\(692\) −11.0355 −0.419508
\(693\) −4.49626 −0.170799
\(694\) −22.7182 −0.862372
\(695\) −12.0825 −0.458317
\(696\) −23.0950 −0.875415
\(697\) 7.60910 0.288215
\(698\) 2.47345 0.0936216
\(699\) −4.47790 −0.169370
\(700\) −31.0330 −1.17294
\(701\) 12.3709 0.467244 0.233622 0.972328i \(-0.424942\pi\)
0.233622 + 0.972328i \(0.424942\pi\)
\(702\) 4.77894 0.180370
\(703\) 3.69731 0.139447
\(704\) 8.08160 0.304587
\(705\) 12.7787 0.481272
\(706\) −3.16230 −0.119015
\(707\) 26.3911 0.992538
\(708\) 49.8142 1.87213
\(709\) −4.78560 −0.179727 −0.0898635 0.995954i \(-0.528643\pi\)
−0.0898635 + 0.995954i \(0.528643\pi\)
\(710\) 4.48412 0.168286
\(711\) 21.7642 0.816223
\(712\) 0.0429684 0.00161031
\(713\) 9.15227 0.342755
\(714\) −9.59343 −0.359025
\(715\) −0.998975 −0.0373595
\(716\) −4.94137 −0.184668
\(717\) −6.54396 −0.244389
\(718\) 30.3339 1.13205
\(719\) −1.10112 −0.0410648 −0.0205324 0.999789i \(-0.506536\pi\)
−0.0205324 + 0.999789i \(0.506536\pi\)
\(720\) −9.00567 −0.335621
\(721\) −14.4603 −0.538530
\(722\) −48.1163 −1.79070
\(723\) 14.6042 0.543136
\(724\) −9.57698 −0.355926
\(725\) 7.96988 0.295994
\(726\) −51.7665 −1.92123
\(727\) 43.1755 1.60129 0.800645 0.599140i \(-0.204491\pi\)
0.800645 + 0.599140i \(0.204491\pi\)
\(728\) 7.91070 0.293190
\(729\) −5.21111 −0.193004
\(730\) 25.0383 0.926708
\(731\) −5.84252 −0.216093
\(732\) 45.6004 1.68544
\(733\) −34.1276 −1.26053 −0.630266 0.776379i \(-0.717054\pi\)
−0.630266 + 0.776379i \(0.717054\pi\)
\(734\) −13.8477 −0.511126
\(735\) −7.65023 −0.282183
\(736\) −1.20160 −0.0442915
\(737\) 2.32173 0.0855219
\(738\) 38.7321 1.42575
\(739\) 37.6423 1.38470 0.692348 0.721564i \(-0.256576\pi\)
0.692348 + 0.721564i \(0.256576\pi\)
\(740\) −2.44567 −0.0899046
\(741\) 11.0402 0.405573
\(742\) 19.5687 0.718390
\(743\) −12.0911 −0.443580 −0.221790 0.975094i \(-0.571190\pi\)
−0.221790 + 0.975094i \(0.571190\pi\)
\(744\) 106.293 3.89689
\(745\) 11.4523 0.419582
\(746\) −76.8971 −2.81540
\(747\) 20.3122 0.743185
\(748\) 4.78487 0.174952
\(749\) 21.1028 0.771079
\(750\) 49.2005 1.79655
\(751\) −6.55647 −0.239249 −0.119624 0.992819i \(-0.538169\pi\)
−0.119624 + 0.992819i \(0.538169\pi\)
\(752\) 27.3238 0.996396
\(753\) 53.9674 1.96668
\(754\) −3.95009 −0.143854
\(755\) −15.9113 −0.579073
\(756\) 18.6287 0.677519
\(757\) −9.99695 −0.363345 −0.181673 0.983359i \(-0.558151\pi\)
−0.181673 + 0.983359i \(0.558151\pi\)
\(758\) 78.2334 2.84157
\(759\) 2.76855 0.100492
\(760\) 32.3581 1.17375
\(761\) −33.1512 −1.20173 −0.600864 0.799351i \(-0.705177\pi\)
−0.600864 + 0.799351i \(0.705177\pi\)
\(762\) 75.5814 2.73803
\(763\) −6.62873 −0.239976
\(764\) 41.4070 1.49805
\(765\) 1.77460 0.0641608
\(766\) 60.1346 2.17275
\(767\) 4.38206 0.158227
\(768\) 72.2568 2.60734
\(769\) −14.8882 −0.536883 −0.268442 0.963296i \(-0.586509\pi\)
−0.268442 + 0.963296i \(0.586509\pi\)
\(770\) −5.78534 −0.208489
\(771\) −61.9462 −2.23094
\(772\) 45.6242 1.64205
\(773\) −26.2647 −0.944675 −0.472337 0.881418i \(-0.656590\pi\)
−0.472337 + 0.881418i \(0.656590\pi\)
\(774\) −29.7397 −1.06897
\(775\) −36.6807 −1.31761
\(776\) −17.4745 −0.627298
\(777\) −2.48544 −0.0891648
\(778\) 20.9211 0.750056
\(779\) −50.7122 −1.81695
\(780\) −7.30280 −0.261482
\(781\) −2.27290 −0.0813306
\(782\) 2.30139 0.0822975
\(783\) −4.78422 −0.170974
\(784\) −16.3580 −0.584215
\(785\) −9.61654 −0.343229
\(786\) 23.0992 0.823921
\(787\) 43.2697 1.54240 0.771199 0.636595i \(-0.219658\pi\)
0.771199 + 0.636595i \(0.219658\pi\)
\(788\) −70.2163 −2.50135
\(789\) −17.8608 −0.635862
\(790\) 28.0041 0.996340
\(791\) −18.9119 −0.672429
\(792\) 12.5269 0.445124
\(793\) 4.01138 0.142448
\(794\) 47.6453 1.69087
\(795\) −9.29123 −0.329526
\(796\) −50.6472 −1.79514
\(797\) 37.8635 1.34119 0.670596 0.741822i \(-0.266038\pi\)
0.670596 + 0.741822i \(0.266038\pi\)
\(798\) 63.9371 2.26335
\(799\) −5.38426 −0.190481
\(800\) 4.81579 0.170264
\(801\) −0.0157053 −0.000554919 0
\(802\) 62.5048 2.20712
\(803\) −12.6913 −0.447867
\(804\) 16.9725 0.598574
\(805\) −1.87295 −0.0660126
\(806\) 18.1800 0.640361
\(807\) 10.1537 0.357426
\(808\) −73.5274 −2.58668
\(809\) −19.5049 −0.685756 −0.342878 0.939380i \(-0.611402\pi\)
−0.342878 + 0.939380i \(0.611402\pi\)
\(810\) −27.2934 −0.958991
\(811\) 26.6080 0.934332 0.467166 0.884170i \(-0.345275\pi\)
0.467166 + 0.884170i \(0.345275\pi\)
\(812\) −15.3978 −0.540355
\(813\) 57.8925 2.03038
\(814\) 1.84172 0.0645524
\(815\) −4.15129 −0.145414
\(816\) 9.73959 0.340954
\(817\) 38.9385 1.36229
\(818\) 28.2528 0.987835
\(819\) −2.89142 −0.101035
\(820\) 33.5447 1.17143
\(821\) −16.0876 −0.561461 −0.280730 0.959787i \(-0.590577\pi\)
−0.280730 + 0.959787i \(0.590577\pi\)
\(822\) −27.2428 −0.950203
\(823\) 19.2338 0.670450 0.335225 0.942138i \(-0.391188\pi\)
0.335225 + 0.942138i \(0.391188\pi\)
\(824\) 40.2874 1.40348
\(825\) −11.0959 −0.386309
\(826\) 25.3777 0.883004
\(827\) 55.7430 1.93837 0.969186 0.246329i \(-0.0792244\pi\)
0.969186 + 0.246329i \(0.0792244\pi\)
\(828\) 7.88503 0.274024
\(829\) 11.7010 0.406392 0.203196 0.979138i \(-0.434867\pi\)
0.203196 + 0.979138i \(0.434867\pi\)
\(830\) 26.1357 0.907185
\(831\) −4.39116 −0.152328
\(832\) 5.19705 0.180175
\(833\) 3.22341 0.111684
\(834\) 66.5151 2.30323
\(835\) 18.4263 0.637669
\(836\) −31.8896 −1.10293
\(837\) 22.0190 0.761086
\(838\) −52.1702 −1.80219
\(839\) −43.1397 −1.48935 −0.744674 0.667429i \(-0.767395\pi\)
−0.744674 + 0.667429i \(0.767395\pi\)
\(840\) −21.7521 −0.750518
\(841\) −25.0456 −0.863640
\(842\) 25.2658 0.870716
\(843\) −27.3328 −0.941392
\(844\) −74.4500 −2.56268
\(845\) 12.3066 0.423360
\(846\) −27.4071 −0.942275
\(847\) −17.7510 −0.609933
\(848\) −19.8668 −0.682230
\(849\) 19.8270 0.680460
\(850\) −9.22357 −0.316366
\(851\) 0.596239 0.0204388
\(852\) −16.6156 −0.569239
\(853\) −30.3211 −1.03817 −0.519087 0.854722i \(-0.673728\pi\)
−0.519087 + 0.854722i \(0.673728\pi\)
\(854\) 23.2310 0.794949
\(855\) −11.8271 −0.404479
\(856\) −58.7938 −2.00953
\(857\) 11.1027 0.379262 0.189631 0.981855i \(-0.439271\pi\)
0.189631 + 0.981855i \(0.439271\pi\)
\(858\) 5.49942 0.187747
\(859\) 57.8849 1.97501 0.987504 0.157596i \(-0.0503742\pi\)
0.987504 + 0.157596i \(0.0503742\pi\)
\(860\) −25.7567 −0.878297
\(861\) 34.0903 1.16179
\(862\) −42.8122 −1.45819
\(863\) 9.66847 0.329118 0.164559 0.986367i \(-0.447380\pi\)
0.164559 + 0.986367i \(0.447380\pi\)
\(864\) −2.89086 −0.0983490
\(865\) 2.66934 0.0907602
\(866\) −7.50424 −0.255005
\(867\) 35.7686 1.21477
\(868\) 70.8669 2.40538
\(869\) −14.1946 −0.481520
\(870\) 10.8616 0.368242
\(871\) 1.49304 0.0505897
\(872\) 18.4681 0.625409
\(873\) 6.38707 0.216169
\(874\) −15.3380 −0.518816
\(875\) 16.8712 0.570350
\(876\) −92.7774 −3.13466
\(877\) 2.94980 0.0996075 0.0498038 0.998759i \(-0.484140\pi\)
0.0498038 + 0.998759i \(0.484140\pi\)
\(878\) −45.3601 −1.53083
\(879\) 11.1499 0.376077
\(880\) 5.87349 0.197995
\(881\) 1.11750 0.0376495 0.0188248 0.999823i \(-0.494008\pi\)
0.0188248 + 0.999823i \(0.494008\pi\)
\(882\) 16.4079 0.552482
\(883\) 27.5305 0.926475 0.463238 0.886234i \(-0.346688\pi\)
0.463238 + 0.886234i \(0.346688\pi\)
\(884\) 3.07702 0.103491
\(885\) −12.0494 −0.405035
\(886\) −7.10300 −0.238630
\(887\) −22.6434 −0.760291 −0.380146 0.924927i \(-0.624126\pi\)
−0.380146 + 0.924927i \(0.624126\pi\)
\(888\) 6.92463 0.232375
\(889\) 25.9173 0.869240
\(890\) −0.0202080 −0.000677373 0
\(891\) 13.8344 0.463469
\(892\) 5.85974 0.196199
\(893\) 35.8843 1.20082
\(894\) −63.0459 −2.10857
\(895\) 1.19525 0.0399528
\(896\) 34.6164 1.15645
\(897\) 1.78038 0.0594451
\(898\) −11.9935 −0.400228
\(899\) −18.2000 −0.607004
\(900\) −31.6018 −1.05339
\(901\) 3.91484 0.130422
\(902\) −25.2610 −0.841100
\(903\) −26.1756 −0.871070
\(904\) 52.6899 1.75244
\(905\) 2.31654 0.0770043
\(906\) 87.5929 2.91008
\(907\) −5.54157 −0.184005 −0.0920024 0.995759i \(-0.529327\pi\)
−0.0920024 + 0.995759i \(0.529327\pi\)
\(908\) −8.33532 −0.276617
\(909\) 26.8748 0.891382
\(910\) −3.72040 −0.123330
\(911\) 31.3445 1.03849 0.519245 0.854626i \(-0.326213\pi\)
0.519245 + 0.854626i \(0.326213\pi\)
\(912\) −64.9112 −2.14943
\(913\) −13.2476 −0.438432
\(914\) 75.2115 2.48777
\(915\) −11.0301 −0.364644
\(916\) 30.9675 1.02320
\(917\) 7.92086 0.261570
\(918\) 5.53679 0.182741
\(919\) −24.5040 −0.808312 −0.404156 0.914690i \(-0.632435\pi\)
−0.404156 + 0.914690i \(0.632435\pi\)
\(920\) 5.21816 0.172038
\(921\) −8.67039 −0.285699
\(922\) −60.0806 −1.97865
\(923\) −1.46164 −0.0481104
\(924\) 21.4372 0.705231
\(925\) −2.38962 −0.0785703
\(926\) −33.0333 −1.08554
\(927\) −14.7254 −0.483645
\(928\) 2.38947 0.0784383
\(929\) −45.8559 −1.50448 −0.752242 0.658887i \(-0.771027\pi\)
−0.752242 + 0.658887i \(0.771027\pi\)
\(930\) −49.9895 −1.63922
\(931\) −21.4830 −0.704076
\(932\) 8.31773 0.272456
\(933\) 20.5393 0.672426
\(934\) 42.3797 1.38671
\(935\) −1.15739 −0.0378508
\(936\) 8.05571 0.263309
\(937\) −45.3678 −1.48210 −0.741051 0.671449i \(-0.765672\pi\)
−0.741051 + 0.671449i \(0.765672\pi\)
\(938\) 8.64661 0.282322
\(939\) −12.6436 −0.412609
\(940\) −23.7365 −0.774198
\(941\) 45.2869 1.47631 0.738155 0.674631i \(-0.235697\pi\)
0.738155 + 0.674631i \(0.235697\pi\)
\(942\) 52.9396 1.72487
\(943\) −8.17800 −0.266312
\(944\) −25.7644 −0.838559
\(945\) −4.50602 −0.146581
\(946\) 19.3962 0.630626
\(947\) −18.0556 −0.586727 −0.293364 0.956001i \(-0.594775\pi\)
−0.293364 + 0.956001i \(0.594775\pi\)
\(948\) −103.767 −3.37019
\(949\) −8.16145 −0.264932
\(950\) 61.4721 1.99442
\(951\) 38.4013 1.24525
\(952\) 9.16519 0.297045
\(953\) 20.1576 0.652969 0.326484 0.945203i \(-0.394136\pi\)
0.326484 + 0.945203i \(0.394136\pi\)
\(954\) 19.9274 0.645174
\(955\) −10.0158 −0.324103
\(956\) 12.1555 0.393136
\(957\) −5.50549 −0.177967
\(958\) −11.8238 −0.382011
\(959\) −9.34174 −0.301660
\(960\) −14.2904 −0.461219
\(961\) 52.7640 1.70206
\(962\) 1.18436 0.0381854
\(963\) 21.4896 0.692493
\(964\) −27.1274 −0.873715
\(965\) −11.0359 −0.355257
\(966\) 10.3107 0.331741
\(967\) 0.828369 0.0266385 0.0133193 0.999911i \(-0.495760\pi\)
0.0133193 + 0.999911i \(0.495760\pi\)
\(968\) 49.4557 1.58956
\(969\) 12.7910 0.410906
\(970\) 8.21824 0.263872
\(971\) −16.0775 −0.515952 −0.257976 0.966151i \(-0.583056\pi\)
−0.257976 + 0.966151i \(0.583056\pi\)
\(972\) 71.4119 2.29054
\(973\) 22.8084 0.731205
\(974\) 49.8994 1.59888
\(975\) −7.13545 −0.228517
\(976\) −23.5850 −0.754936
\(977\) 14.2178 0.454869 0.227434 0.973793i \(-0.426966\pi\)
0.227434 + 0.973793i \(0.426966\pi\)
\(978\) 22.8531 0.730762
\(979\) 0.0102430 0.000327367 0
\(980\) 14.2104 0.453934
\(981\) −6.75024 −0.215519
\(982\) 20.4205 0.651644
\(983\) 52.5542 1.67622 0.838109 0.545502i \(-0.183661\pi\)
0.838109 + 0.545502i \(0.183661\pi\)
\(984\) −94.9779 −3.02779
\(985\) 16.9843 0.541166
\(986\) −4.57650 −0.145745
\(987\) −24.1225 −0.767828
\(988\) −20.5073 −0.652425
\(989\) 6.27933 0.199671
\(990\) −5.89139 −0.187241
\(991\) −6.47337 −0.205633 −0.102817 0.994700i \(-0.532786\pi\)
−0.102817 + 0.994700i \(0.532786\pi\)
\(992\) −10.9973 −0.349166
\(993\) −2.05382 −0.0651761
\(994\) −8.46475 −0.268486
\(995\) 12.2508 0.388378
\(996\) −96.8440 −3.06862
\(997\) 29.4835 0.933752 0.466876 0.884323i \(-0.345379\pi\)
0.466876 + 0.884323i \(0.345379\pi\)
\(998\) −30.3301 −0.960083
\(999\) 1.43446 0.0453843
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 \(a_p\))