Properties

Label 6047.2.a.a.1.12
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.57504 q^{2} +1.64822 q^{3} +4.63081 q^{4} -3.44910 q^{5} -4.24422 q^{6} -0.596125 q^{7} -6.77442 q^{8} -0.283374 q^{9} +O(q^{10})\) \(q-2.57504 q^{2} +1.64822 q^{3} +4.63081 q^{4} -3.44910 q^{5} -4.24422 q^{6} -0.596125 q^{7} -6.77442 q^{8} -0.283374 q^{9} +8.88154 q^{10} +5.70669 q^{11} +7.63258 q^{12} +1.47414 q^{13} +1.53504 q^{14} -5.68486 q^{15} +8.18275 q^{16} +1.39828 q^{17} +0.729699 q^{18} -4.14607 q^{19} -15.9721 q^{20} -0.982545 q^{21} -14.6949 q^{22} -2.33910 q^{23} -11.1657 q^{24} +6.89626 q^{25} -3.79597 q^{26} -5.41172 q^{27} -2.76054 q^{28} +8.25188 q^{29} +14.6387 q^{30} -0.594481 q^{31} -7.52204 q^{32} +9.40588 q^{33} -3.60062 q^{34} +2.05609 q^{35} -1.31225 q^{36} -2.68931 q^{37} +10.6763 q^{38} +2.42971 q^{39} +23.3656 q^{40} -0.691211 q^{41} +2.53009 q^{42} -8.85577 q^{43} +26.4266 q^{44} +0.977385 q^{45} +6.02326 q^{46} +4.31958 q^{47} +13.4870 q^{48} -6.64463 q^{49} -17.7581 q^{50} +2.30467 q^{51} +6.82647 q^{52} -2.55497 q^{53} +13.9354 q^{54} -19.6829 q^{55} +4.03840 q^{56} -6.83363 q^{57} -21.2489 q^{58} -2.50149 q^{59} -26.3255 q^{60} -1.09221 q^{61} +1.53081 q^{62} +0.168927 q^{63} +3.00401 q^{64} -5.08446 q^{65} -24.2205 q^{66} +5.66288 q^{67} +6.47516 q^{68} -3.85534 q^{69} -5.29451 q^{70} +1.96944 q^{71} +1.91970 q^{72} -7.01042 q^{73} +6.92508 q^{74} +11.3665 q^{75} -19.1997 q^{76} -3.40190 q^{77} -6.25659 q^{78} +5.98518 q^{79} -28.2231 q^{80} -8.06958 q^{81} +1.77989 q^{82} +0.0878307 q^{83} -4.54997 q^{84} -4.82280 q^{85} +22.8039 q^{86} +13.6009 q^{87} -38.6595 q^{88} +0.350973 q^{89} -2.51680 q^{90} -0.878774 q^{91} -10.8319 q^{92} -0.979835 q^{93} -11.1231 q^{94} +14.3002 q^{95} -12.3980 q^{96} +6.42779 q^{97} +17.1102 q^{98} -1.61713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57504 −1.82082 −0.910412 0.413702i \(-0.864236\pi\)
−0.910412 + 0.413702i \(0.864236\pi\)
\(3\) 1.64822 0.951600 0.475800 0.879554i \(-0.342159\pi\)
0.475800 + 0.879554i \(0.342159\pi\)
\(4\) 4.63081 2.31540
\(5\) −3.44910 −1.54248 −0.771241 0.636543i \(-0.780364\pi\)
−0.771241 + 0.636543i \(0.780364\pi\)
\(6\) −4.24422 −1.73270
\(7\) −0.596125 −0.225314 −0.112657 0.993634i \(-0.535936\pi\)
−0.112657 + 0.993634i \(0.535936\pi\)
\(8\) −6.77442 −2.39512
\(9\) −0.283374 −0.0944581
\(10\) 8.88154 2.80859
\(11\) 5.70669 1.72063 0.860316 0.509761i \(-0.170266\pi\)
0.860316 + 0.509761i \(0.170266\pi\)
\(12\) 7.63258 2.20334
\(13\) 1.47414 0.408854 0.204427 0.978882i \(-0.434467\pi\)
0.204427 + 0.978882i \(0.434467\pi\)
\(14\) 1.53504 0.410258
\(15\) −5.68486 −1.46783
\(16\) 8.18275 2.04569
\(17\) 1.39828 0.339133 0.169566 0.985519i \(-0.445763\pi\)
0.169566 + 0.985519i \(0.445763\pi\)
\(18\) 0.729699 0.171992
\(19\) −4.14607 −0.951174 −0.475587 0.879669i \(-0.657764\pi\)
−0.475587 + 0.879669i \(0.657764\pi\)
\(20\) −15.9721 −3.57147
\(21\) −0.982545 −0.214409
\(22\) −14.6949 −3.13297
\(23\) −2.33910 −0.487735 −0.243868 0.969809i \(-0.578416\pi\)
−0.243868 + 0.969809i \(0.578416\pi\)
\(24\) −11.1657 −2.27919
\(25\) 6.89626 1.37925
\(26\) −3.79597 −0.744451
\(27\) −5.41172 −1.04149
\(28\) −2.76054 −0.521693
\(29\) 8.25188 1.53234 0.766168 0.642641i \(-0.222161\pi\)
0.766168 + 0.642641i \(0.222161\pi\)
\(30\) 14.6387 2.67265
\(31\) −0.594481 −0.106772 −0.0533860 0.998574i \(-0.517001\pi\)
−0.0533860 + 0.998574i \(0.517001\pi\)
\(32\) −7.52204 −1.32972
\(33\) 9.40588 1.63735
\(34\) −3.60062 −0.617501
\(35\) 2.05609 0.347543
\(36\) −1.31225 −0.218709
\(37\) −2.68931 −0.442120 −0.221060 0.975260i \(-0.570952\pi\)
−0.221060 + 0.975260i \(0.570952\pi\)
\(38\) 10.6763 1.73192
\(39\) 2.42971 0.389065
\(40\) 23.3656 3.69443
\(41\) −0.691211 −0.107949 −0.0539745 0.998542i \(-0.517189\pi\)
−0.0539745 + 0.998542i \(0.517189\pi\)
\(42\) 2.53009 0.390401
\(43\) −8.85577 −1.35049 −0.675246 0.737592i \(-0.735963\pi\)
−0.675246 + 0.737592i \(0.735963\pi\)
\(44\) 26.4266 3.98396
\(45\) 0.977385 0.145700
\(46\) 6.02326 0.888081
\(47\) 4.31958 0.630076 0.315038 0.949079i \(-0.397983\pi\)
0.315038 + 0.949079i \(0.397983\pi\)
\(48\) 13.4870 1.94668
\(49\) −6.64463 −0.949234
\(50\) −17.7581 −2.51138
\(51\) 2.30467 0.322718
\(52\) 6.82647 0.946661
\(53\) −2.55497 −0.350952 −0.175476 0.984484i \(-0.556146\pi\)
−0.175476 + 0.984484i \(0.556146\pi\)
\(54\) 13.9354 1.89636
\(55\) −19.6829 −2.65404
\(56\) 4.03840 0.539654
\(57\) −6.83363 −0.905137
\(58\) −21.2489 −2.79011
\(59\) −2.50149 −0.325666 −0.162833 0.986654i \(-0.552063\pi\)
−0.162833 + 0.986654i \(0.552063\pi\)
\(60\) −26.3255 −3.39861
\(61\) −1.09221 −0.139843 −0.0699213 0.997553i \(-0.522275\pi\)
−0.0699213 + 0.997553i \(0.522275\pi\)
\(62\) 1.53081 0.194413
\(63\) 0.168927 0.0212828
\(64\) 3.00401 0.375501
\(65\) −5.08446 −0.630650
\(66\) −24.2205 −2.98133
\(67\) 5.66288 0.691831 0.345915 0.938266i \(-0.387568\pi\)
0.345915 + 0.938266i \(0.387568\pi\)
\(68\) 6.47516 0.785229
\(69\) −3.85534 −0.464129
\(70\) −5.29451 −0.632815
\(71\) 1.96944 0.233729 0.116865 0.993148i \(-0.462716\pi\)
0.116865 + 0.993148i \(0.462716\pi\)
\(72\) 1.91970 0.226238
\(73\) −7.01042 −0.820508 −0.410254 0.911971i \(-0.634560\pi\)
−0.410254 + 0.911971i \(0.634560\pi\)
\(74\) 6.92508 0.805024
\(75\) 11.3665 1.31250
\(76\) −19.1997 −2.20235
\(77\) −3.40190 −0.387683
\(78\) −6.25659 −0.708419
\(79\) 5.98518 0.673386 0.336693 0.941615i \(-0.390692\pi\)
0.336693 + 0.941615i \(0.390692\pi\)
\(80\) −28.2231 −3.15544
\(81\) −8.06958 −0.896620
\(82\) 1.77989 0.196556
\(83\) 0.0878307 0.00964067 0.00482034 0.999988i \(-0.498466\pi\)
0.00482034 + 0.999988i \(0.498466\pi\)
\(84\) −4.54997 −0.496443
\(85\) −4.82280 −0.523106
\(86\) 22.8039 2.45901
\(87\) 13.6009 1.45817
\(88\) −38.6595 −4.12112
\(89\) 0.350973 0.0372031 0.0186015 0.999827i \(-0.494079\pi\)
0.0186015 + 0.999827i \(0.494079\pi\)
\(90\) −2.51680 −0.265294
\(91\) −0.878774 −0.0921205
\(92\) −10.8319 −1.12930
\(93\) −0.979835 −0.101604
\(94\) −11.1231 −1.14726
\(95\) 14.3002 1.46717
\(96\) −12.3980 −1.26536
\(97\) 6.42779 0.652644 0.326322 0.945259i \(-0.394191\pi\)
0.326322 + 0.945259i \(0.394191\pi\)
\(98\) 17.1102 1.72839
\(99\) −1.61713 −0.162528
\(100\) 31.9352 3.19352
\(101\) 3.75050 0.373189 0.186594 0.982437i \(-0.440255\pi\)
0.186594 + 0.982437i \(0.440255\pi\)
\(102\) −5.93461 −0.587614
\(103\) 2.65885 0.261985 0.130992 0.991383i \(-0.458184\pi\)
0.130992 + 0.991383i \(0.458184\pi\)
\(104\) −9.98646 −0.979253
\(105\) 3.38889 0.330722
\(106\) 6.57914 0.639022
\(107\) −2.83515 −0.274084 −0.137042 0.990565i \(-0.543760\pi\)
−0.137042 + 0.990565i \(0.543760\pi\)
\(108\) −25.0606 −2.41146
\(109\) −8.78429 −0.841382 −0.420691 0.907204i \(-0.638212\pi\)
−0.420691 + 0.907204i \(0.638212\pi\)
\(110\) 50.6842 4.83255
\(111\) −4.43258 −0.420722
\(112\) −4.87794 −0.460922
\(113\) 18.5214 1.74235 0.871174 0.490975i \(-0.163359\pi\)
0.871174 + 0.490975i \(0.163359\pi\)
\(114\) 17.5968 1.64810
\(115\) 8.06777 0.752323
\(116\) 38.2128 3.54797
\(117\) −0.417735 −0.0386196
\(118\) 6.44141 0.592980
\(119\) −0.833550 −0.0764114
\(120\) 38.5116 3.51562
\(121\) 21.5663 1.96057
\(122\) 2.81247 0.254629
\(123\) −1.13927 −0.102724
\(124\) −2.75293 −0.247220
\(125\) −6.54039 −0.584990
\(126\) −0.434992 −0.0387522
\(127\) −6.86859 −0.609489 −0.304744 0.952434i \(-0.598571\pi\)
−0.304744 + 0.952434i \(0.598571\pi\)
\(128\) 7.30865 0.646000
\(129\) −14.5963 −1.28513
\(130\) 13.0927 1.14830
\(131\) 6.50421 0.568276 0.284138 0.958783i \(-0.408293\pi\)
0.284138 + 0.958783i \(0.408293\pi\)
\(132\) 43.5568 3.79113
\(133\) 2.47158 0.214313
\(134\) −14.5821 −1.25970
\(135\) 18.6655 1.60647
\(136\) −9.47253 −0.812263
\(137\) −9.06672 −0.774623 −0.387311 0.921949i \(-0.626596\pi\)
−0.387311 + 0.921949i \(0.626596\pi\)
\(138\) 9.92765 0.845097
\(139\) 9.80496 0.831646 0.415823 0.909446i \(-0.363494\pi\)
0.415823 + 0.909446i \(0.363494\pi\)
\(140\) 9.52137 0.804702
\(141\) 7.11962 0.599580
\(142\) −5.07137 −0.425580
\(143\) 8.41248 0.703487
\(144\) −2.31878 −0.193232
\(145\) −28.4615 −2.36360
\(146\) 18.0521 1.49400
\(147\) −10.9518 −0.903290
\(148\) −12.4537 −1.02369
\(149\) 14.2751 1.16946 0.584731 0.811227i \(-0.301200\pi\)
0.584731 + 0.811227i \(0.301200\pi\)
\(150\) −29.2693 −2.38983
\(151\) −6.20078 −0.504612 −0.252306 0.967647i \(-0.581189\pi\)
−0.252306 + 0.967647i \(0.581189\pi\)
\(152\) 28.0872 2.27817
\(153\) −0.396237 −0.0320338
\(154\) 8.76002 0.705902
\(155\) 2.05042 0.164694
\(156\) 11.2515 0.900843
\(157\) 7.85452 0.626859 0.313429 0.949612i \(-0.398522\pi\)
0.313429 + 0.949612i \(0.398522\pi\)
\(158\) −15.4121 −1.22612
\(159\) −4.21115 −0.333966
\(160\) 25.9442 2.05107
\(161\) 1.39439 0.109894
\(162\) 20.7794 1.63259
\(163\) 3.00643 0.235482 0.117741 0.993044i \(-0.462435\pi\)
0.117741 + 0.993044i \(0.462435\pi\)
\(164\) −3.20086 −0.249945
\(165\) −32.4418 −2.52559
\(166\) −0.226167 −0.0175540
\(167\) −13.5775 −1.05066 −0.525331 0.850898i \(-0.676058\pi\)
−0.525331 + 0.850898i \(0.676058\pi\)
\(168\) 6.65617 0.513535
\(169\) −10.8269 −0.832839
\(170\) 12.4189 0.952485
\(171\) 1.17489 0.0898461
\(172\) −41.0094 −3.12693
\(173\) −2.80389 −0.213176 −0.106588 0.994303i \(-0.533993\pi\)
−0.106588 + 0.994303i \(0.533993\pi\)
\(174\) −35.0228 −2.65507
\(175\) −4.11103 −0.310765
\(176\) 46.6964 3.51988
\(177\) −4.12300 −0.309903
\(178\) −0.903768 −0.0677403
\(179\) 2.89567 0.216432 0.108216 0.994127i \(-0.465486\pi\)
0.108216 + 0.994127i \(0.465486\pi\)
\(180\) 4.52608 0.337354
\(181\) −13.3467 −0.992056 −0.496028 0.868307i \(-0.665209\pi\)
−0.496028 + 0.868307i \(0.665209\pi\)
\(182\) 2.26287 0.167735
\(183\) −1.80019 −0.133074
\(184\) 15.8460 1.16818
\(185\) 9.27570 0.681963
\(186\) 2.52311 0.185003
\(187\) 7.97955 0.583522
\(188\) 20.0031 1.45888
\(189\) 3.22606 0.234661
\(190\) −36.8235 −2.67146
\(191\) 14.9228 1.07978 0.539889 0.841736i \(-0.318466\pi\)
0.539889 + 0.841736i \(0.318466\pi\)
\(192\) 4.95126 0.357326
\(193\) −13.9743 −1.00589 −0.502945 0.864318i \(-0.667750\pi\)
−0.502945 + 0.864318i \(0.667750\pi\)
\(194\) −16.5518 −1.18835
\(195\) −8.38031 −0.600126
\(196\) −30.7700 −2.19786
\(197\) −27.8026 −1.98085 −0.990425 0.138049i \(-0.955917\pi\)
−0.990425 + 0.138049i \(0.955917\pi\)
\(198\) 4.16417 0.295934
\(199\) 21.1328 1.49807 0.749033 0.662533i \(-0.230519\pi\)
0.749033 + 0.662533i \(0.230519\pi\)
\(200\) −46.7182 −3.30347
\(201\) 9.33366 0.658346
\(202\) −9.65768 −0.679512
\(203\) −4.91915 −0.345257
\(204\) 10.6725 0.747223
\(205\) 2.38405 0.166509
\(206\) −6.84664 −0.477028
\(207\) 0.662840 0.0460706
\(208\) 12.0625 0.836387
\(209\) −23.6604 −1.63662
\(210\) −8.72651 −0.602187
\(211\) −9.20582 −0.633755 −0.316877 0.948467i \(-0.602634\pi\)
−0.316877 + 0.948467i \(0.602634\pi\)
\(212\) −11.8316 −0.812595
\(213\) 3.24606 0.222417
\(214\) 7.30060 0.499059
\(215\) 30.5444 2.08311
\(216\) 36.6612 2.49448
\(217\) 0.354385 0.0240572
\(218\) 22.6198 1.53201
\(219\) −11.5547 −0.780795
\(220\) −91.1478 −6.14518
\(221\) 2.06126 0.138656
\(222\) 11.4140 0.766061
\(223\) −24.1241 −1.61547 −0.807734 0.589547i \(-0.799306\pi\)
−0.807734 + 0.589547i \(0.799306\pi\)
\(224\) 4.48408 0.299605
\(225\) −1.95422 −0.130282
\(226\) −47.6933 −3.17251
\(227\) −19.5944 −1.30053 −0.650264 0.759709i \(-0.725342\pi\)
−0.650264 + 0.759709i \(0.725342\pi\)
\(228\) −31.6452 −2.09576
\(229\) 4.14439 0.273869 0.136935 0.990580i \(-0.456275\pi\)
0.136935 + 0.990580i \(0.456275\pi\)
\(230\) −20.7748 −1.36985
\(231\) −5.60708 −0.368919
\(232\) −55.9017 −3.67012
\(233\) 0.742793 0.0486620 0.0243310 0.999704i \(-0.492254\pi\)
0.0243310 + 0.999704i \(0.492254\pi\)
\(234\) 1.07568 0.0703195
\(235\) −14.8987 −0.971881
\(236\) −11.5839 −0.754047
\(237\) 9.86489 0.640794
\(238\) 2.14642 0.139132
\(239\) −2.70125 −0.174730 −0.0873648 0.996176i \(-0.527845\pi\)
−0.0873648 + 0.996176i \(0.527845\pi\)
\(240\) −46.5178 −3.00271
\(241\) −15.7286 −1.01317 −0.506585 0.862190i \(-0.669092\pi\)
−0.506585 + 0.862190i \(0.669092\pi\)
\(242\) −55.5340 −3.56986
\(243\) 2.93473 0.188263
\(244\) −5.05779 −0.323792
\(245\) 22.9180 1.46418
\(246\) 2.93365 0.187043
\(247\) −6.11190 −0.388891
\(248\) 4.02726 0.255731
\(249\) 0.144764 0.00917406
\(250\) 16.8417 1.06516
\(251\) 3.69851 0.233448 0.116724 0.993164i \(-0.462761\pi\)
0.116724 + 0.993164i \(0.462761\pi\)
\(252\) 0.782266 0.0492781
\(253\) −13.3485 −0.839213
\(254\) 17.6869 1.10977
\(255\) −7.94903 −0.497788
\(256\) −24.8280 −1.55175
\(257\) 1.53829 0.0959560 0.0479780 0.998848i \(-0.484722\pi\)
0.0479780 + 0.998848i \(0.484722\pi\)
\(258\) 37.5859 2.33999
\(259\) 1.60317 0.0996160
\(260\) −23.5452 −1.46021
\(261\) −2.33837 −0.144742
\(262\) −16.7486 −1.03473
\(263\) −16.4249 −1.01280 −0.506400 0.862299i \(-0.669024\pi\)
−0.506400 + 0.862299i \(0.669024\pi\)
\(264\) −63.7193 −3.92165
\(265\) 8.81233 0.541337
\(266\) −6.36440 −0.390226
\(267\) 0.578481 0.0354024
\(268\) 26.2237 1.60187
\(269\) −6.75750 −0.412012 −0.206006 0.978551i \(-0.566047\pi\)
−0.206006 + 0.978551i \(0.566047\pi\)
\(270\) −48.0644 −2.92511
\(271\) −5.23698 −0.318124 −0.159062 0.987269i \(-0.550847\pi\)
−0.159062 + 0.987269i \(0.550847\pi\)
\(272\) 11.4418 0.693760
\(273\) −1.44841 −0.0876619
\(274\) 23.3471 1.41045
\(275\) 39.3548 2.37319
\(276\) −17.8533 −1.07465
\(277\) 5.71309 0.343266 0.171633 0.985161i \(-0.445096\pi\)
0.171633 + 0.985161i \(0.445096\pi\)
\(278\) −25.2481 −1.51428
\(279\) 0.168461 0.0100855
\(280\) −13.9288 −0.832407
\(281\) −13.4789 −0.804081 −0.402041 0.915622i \(-0.631699\pi\)
−0.402041 + 0.915622i \(0.631699\pi\)
\(282\) −18.3333 −1.09173
\(283\) −7.19329 −0.427597 −0.213798 0.976878i \(-0.568584\pi\)
−0.213798 + 0.976878i \(0.568584\pi\)
\(284\) 9.12008 0.541177
\(285\) 23.5699 1.39616
\(286\) −21.6624 −1.28093
\(287\) 0.412048 0.0243224
\(288\) 2.13155 0.125603
\(289\) −15.0448 −0.884989
\(290\) 73.2894 4.30370
\(291\) 10.5944 0.621055
\(292\) −32.4639 −1.89981
\(293\) 13.5705 0.792796 0.396398 0.918079i \(-0.370260\pi\)
0.396398 + 0.918079i \(0.370260\pi\)
\(294\) 28.2013 1.64473
\(295\) 8.62786 0.502334
\(296\) 18.2185 1.05893
\(297\) −30.8830 −1.79201
\(298\) −36.7589 −2.12939
\(299\) −3.44816 −0.199412
\(300\) 52.6363 3.03896
\(301\) 5.27915 0.304285
\(302\) 15.9672 0.918811
\(303\) 6.18165 0.355126
\(304\) −33.9263 −1.94581
\(305\) 3.76712 0.215705
\(306\) 1.02032 0.0583280
\(307\) 15.0543 0.859195 0.429598 0.903020i \(-0.358655\pi\)
0.429598 + 0.903020i \(0.358655\pi\)
\(308\) −15.7535 −0.897642
\(309\) 4.38237 0.249304
\(310\) −5.27991 −0.299879
\(311\) 33.5228 1.90090 0.950450 0.310876i \(-0.100622\pi\)
0.950450 + 0.310876i \(0.100622\pi\)
\(312\) −16.4599 −0.931857
\(313\) −33.3744 −1.88643 −0.943215 0.332182i \(-0.892215\pi\)
−0.943215 + 0.332182i \(0.892215\pi\)
\(314\) −20.2257 −1.14140
\(315\) −0.582644 −0.0328283
\(316\) 27.7162 1.55916
\(317\) −26.3395 −1.47937 −0.739686 0.672952i \(-0.765026\pi\)
−0.739686 + 0.672952i \(0.765026\pi\)
\(318\) 10.8439 0.608093
\(319\) 47.0909 2.63659
\(320\) −10.3611 −0.579203
\(321\) −4.67294 −0.260818
\(322\) −3.59061 −0.200097
\(323\) −5.79737 −0.322574
\(324\) −37.3686 −2.07604
\(325\) 10.1661 0.563913
\(326\) −7.74166 −0.428771
\(327\) −14.4784 −0.800659
\(328\) 4.68255 0.258551
\(329\) −2.57501 −0.141965
\(330\) 83.5387 4.59865
\(331\) 24.4725 1.34513 0.672564 0.740039i \(-0.265193\pi\)
0.672564 + 0.740039i \(0.265193\pi\)
\(332\) 0.406727 0.0223220
\(333\) 0.762083 0.0417619
\(334\) 34.9626 1.91307
\(335\) −19.5318 −1.06714
\(336\) −8.03992 −0.438614
\(337\) 12.5012 0.680981 0.340491 0.940248i \(-0.389407\pi\)
0.340491 + 0.940248i \(0.389407\pi\)
\(338\) 27.8797 1.51645
\(339\) 30.5273 1.65802
\(340\) −22.3335 −1.21120
\(341\) −3.39252 −0.183715
\(342\) −3.02538 −0.163594
\(343\) 8.13391 0.439190
\(344\) 59.9927 3.23459
\(345\) 13.2975 0.715911
\(346\) 7.22011 0.388156
\(347\) −24.4039 −1.31007 −0.655034 0.755599i \(-0.727346\pi\)
−0.655034 + 0.755599i \(0.727346\pi\)
\(348\) 62.9831 3.37625
\(349\) −6.42710 −0.344035 −0.172017 0.985094i \(-0.555029\pi\)
−0.172017 + 0.985094i \(0.555029\pi\)
\(350\) 10.5861 0.565849
\(351\) −7.97765 −0.425816
\(352\) −42.9259 −2.28796
\(353\) 15.7126 0.836295 0.418147 0.908379i \(-0.362680\pi\)
0.418147 + 0.908379i \(0.362680\pi\)
\(354\) 10.6169 0.564280
\(355\) −6.79278 −0.360523
\(356\) 1.62529 0.0861401
\(357\) −1.37387 −0.0727130
\(358\) −7.45644 −0.394085
\(359\) −26.1538 −1.38034 −0.690172 0.723645i \(-0.742465\pi\)
−0.690172 + 0.723645i \(0.742465\pi\)
\(360\) −6.62122 −0.348969
\(361\) −1.81009 −0.0952677
\(362\) 34.3683 1.80636
\(363\) 35.5460 1.86568
\(364\) −4.06943 −0.213296
\(365\) 24.1796 1.26562
\(366\) 4.63556 0.242305
\(367\) −18.7934 −0.981008 −0.490504 0.871439i \(-0.663187\pi\)
−0.490504 + 0.871439i \(0.663187\pi\)
\(368\) −19.1402 −0.997754
\(369\) 0.195871 0.0101967
\(370\) −23.8853 −1.24174
\(371\) 1.52308 0.0790745
\(372\) −4.53742 −0.235254
\(373\) −13.0160 −0.673942 −0.336971 0.941515i \(-0.609402\pi\)
−0.336971 + 0.941515i \(0.609402\pi\)
\(374\) −20.5476 −1.06249
\(375\) −10.7800 −0.556676
\(376\) −29.2627 −1.50911
\(377\) 12.1645 0.626501
\(378\) −8.30722 −0.427277
\(379\) −29.0960 −1.49456 −0.747280 0.664510i \(-0.768640\pi\)
−0.747280 + 0.664510i \(0.768640\pi\)
\(380\) 66.2214 3.39709
\(381\) −11.3209 −0.579989
\(382\) −38.4268 −1.96609
\(383\) 3.16350 0.161647 0.0808237 0.996728i \(-0.474245\pi\)
0.0808237 + 0.996728i \(0.474245\pi\)
\(384\) 12.0463 0.614733
\(385\) 11.7335 0.597994
\(386\) 35.9843 1.83155
\(387\) 2.50950 0.127565
\(388\) 29.7659 1.51113
\(389\) 13.1657 0.667528 0.333764 0.942657i \(-0.391681\pi\)
0.333764 + 0.942657i \(0.391681\pi\)
\(390\) 21.5796 1.09272
\(391\) −3.27071 −0.165407
\(392\) 45.0135 2.27353
\(393\) 10.7204 0.540771
\(394\) 71.5926 3.60678
\(395\) −20.6435 −1.03869
\(396\) −7.48862 −0.376317
\(397\) 0.472606 0.0237194 0.0118597 0.999930i \(-0.496225\pi\)
0.0118597 + 0.999930i \(0.496225\pi\)
\(398\) −54.4177 −2.72771
\(399\) 4.07370 0.203940
\(400\) 56.4304 2.82152
\(401\) −32.0576 −1.60088 −0.800439 0.599414i \(-0.795400\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(402\) −24.0345 −1.19873
\(403\) −0.876350 −0.0436541
\(404\) 17.3678 0.864083
\(405\) 27.8327 1.38302
\(406\) 12.6670 0.628652
\(407\) −15.3471 −0.760727
\(408\) −15.6128 −0.772949
\(409\) −10.1232 −0.500562 −0.250281 0.968173i \(-0.580523\pi\)
−0.250281 + 0.968173i \(0.580523\pi\)
\(410\) −6.13902 −0.303185
\(411\) −14.9439 −0.737131
\(412\) 12.3126 0.606600
\(413\) 1.49120 0.0733771
\(414\) −1.70684 −0.0838865
\(415\) −0.302937 −0.0148706
\(416\) −11.0886 −0.543661
\(417\) 16.1607 0.791394
\(418\) 60.9262 2.98000
\(419\) −30.1222 −1.47157 −0.735783 0.677218i \(-0.763185\pi\)
−0.735783 + 0.677218i \(0.763185\pi\)
\(420\) 15.6933 0.765754
\(421\) −31.2589 −1.52346 −0.761732 0.647892i \(-0.775651\pi\)
−0.761732 + 0.647892i \(0.775651\pi\)
\(422\) 23.7053 1.15396
\(423\) −1.22406 −0.0595158
\(424\) 17.3084 0.840572
\(425\) 9.64290 0.467749
\(426\) −8.35873 −0.404982
\(427\) 0.651091 0.0315085
\(428\) −13.1290 −0.634615
\(429\) 13.8656 0.669438
\(430\) −78.6529 −3.79298
\(431\) −0.774182 −0.0372910 −0.0186455 0.999826i \(-0.505935\pi\)
−0.0186455 + 0.999826i \(0.505935\pi\)
\(432\) −44.2828 −2.13056
\(433\) −3.97971 −0.191253 −0.0956264 0.995417i \(-0.530485\pi\)
−0.0956264 + 0.995417i \(0.530485\pi\)
\(434\) −0.912554 −0.0438040
\(435\) −46.9108 −2.24920
\(436\) −40.6783 −1.94814
\(437\) 9.69806 0.463921
\(438\) 29.7538 1.42169
\(439\) 18.5761 0.886589 0.443295 0.896376i \(-0.353810\pi\)
0.443295 + 0.896376i \(0.353810\pi\)
\(440\) 133.340 6.35675
\(441\) 1.88292 0.0896628
\(442\) −5.30783 −0.252468
\(443\) −34.6861 −1.64799 −0.823994 0.566598i \(-0.808259\pi\)
−0.823994 + 0.566598i \(0.808259\pi\)
\(444\) −20.5264 −0.974140
\(445\) −1.21054 −0.0573851
\(446\) 62.1204 2.94149
\(447\) 23.5285 1.11286
\(448\) −1.79076 −0.0846056
\(449\) 13.1766 0.621843 0.310922 0.950436i \(-0.399362\pi\)
0.310922 + 0.950436i \(0.399362\pi\)
\(450\) 5.03220 0.237220
\(451\) −3.94453 −0.185741
\(452\) 85.7690 4.03424
\(453\) −10.2202 −0.480189
\(454\) 50.4563 2.36803
\(455\) 3.03098 0.142094
\(456\) 46.2939 2.16791
\(457\) −0.690301 −0.0322909 −0.0161455 0.999870i \(-0.505139\pi\)
−0.0161455 + 0.999870i \(0.505139\pi\)
\(458\) −10.6720 −0.498668
\(459\) −7.56710 −0.353202
\(460\) 37.3603 1.74193
\(461\) 17.5289 0.816401 0.408200 0.912892i \(-0.366156\pi\)
0.408200 + 0.912892i \(0.366156\pi\)
\(462\) 14.4384 0.671736
\(463\) −2.16708 −0.100713 −0.0503563 0.998731i \(-0.516036\pi\)
−0.0503563 + 0.998731i \(0.516036\pi\)
\(464\) 67.5231 3.13468
\(465\) 3.37954 0.156723
\(466\) −1.91272 −0.0886049
\(467\) 21.8356 1.01043 0.505216 0.862993i \(-0.331413\pi\)
0.505216 + 0.862993i \(0.331413\pi\)
\(468\) −1.93445 −0.0894199
\(469\) −3.37578 −0.155879
\(470\) 38.3646 1.76963
\(471\) 12.9460 0.596519
\(472\) 16.9461 0.780008
\(473\) −50.5372 −2.32370
\(474\) −25.4024 −1.16677
\(475\) −28.5924 −1.31191
\(476\) −3.86001 −0.176923
\(477\) 0.724013 0.0331503
\(478\) 6.95582 0.318152
\(479\) −42.3867 −1.93670 −0.968349 0.249598i \(-0.919701\pi\)
−0.968349 + 0.249598i \(0.919701\pi\)
\(480\) 42.7618 1.95180
\(481\) −3.96443 −0.180763
\(482\) 40.5018 1.84480
\(483\) 2.29827 0.104575
\(484\) 99.8694 4.53952
\(485\) −22.1701 −1.00669
\(486\) −7.55704 −0.342794
\(487\) 19.6255 0.889318 0.444659 0.895700i \(-0.353325\pi\)
0.444659 + 0.895700i \(0.353325\pi\)
\(488\) 7.39905 0.334939
\(489\) 4.95525 0.224084
\(490\) −59.0146 −2.66601
\(491\) −25.0439 −1.13022 −0.565108 0.825017i \(-0.691166\pi\)
−0.565108 + 0.825017i \(0.691166\pi\)
\(492\) −5.27572 −0.237848
\(493\) 11.5384 0.519665
\(494\) 15.7384 0.708103
\(495\) 5.57764 0.250696
\(496\) −4.86449 −0.218422
\(497\) −1.17403 −0.0526625
\(498\) −0.372773 −0.0167044
\(499\) 21.6423 0.968841 0.484420 0.874835i \(-0.339031\pi\)
0.484420 + 0.874835i \(0.339031\pi\)
\(500\) −30.2873 −1.35449
\(501\) −22.3788 −0.999809
\(502\) −9.52380 −0.425068
\(503\) −9.17074 −0.408903 −0.204452 0.978877i \(-0.565541\pi\)
−0.204452 + 0.978877i \(0.565541\pi\)
\(504\) −1.14438 −0.0509747
\(505\) −12.9358 −0.575637
\(506\) 34.3729 1.52806
\(507\) −17.8451 −0.792529
\(508\) −31.8071 −1.41121
\(509\) 2.89978 0.128531 0.0642653 0.997933i \(-0.479530\pi\)
0.0642653 + 0.997933i \(0.479530\pi\)
\(510\) 20.4690 0.906384
\(511\) 4.17909 0.184872
\(512\) 49.3158 2.17947
\(513\) 22.4374 0.990635
\(514\) −3.96115 −0.174719
\(515\) −9.17064 −0.404107
\(516\) −67.5924 −2.97559
\(517\) 24.6505 1.08413
\(518\) −4.12821 −0.181383
\(519\) −4.62142 −0.202858
\(520\) 34.4443 1.51048
\(521\) 18.6154 0.815556 0.407778 0.913081i \(-0.366304\pi\)
0.407778 + 0.913081i \(0.366304\pi\)
\(522\) 6.02139 0.263549
\(523\) −31.2659 −1.36716 −0.683581 0.729875i \(-0.739578\pi\)
−0.683581 + 0.729875i \(0.739578\pi\)
\(524\) 30.1197 1.31579
\(525\) −6.77589 −0.295724
\(526\) 42.2946 1.84413
\(527\) −0.831251 −0.0362098
\(528\) 76.9659 3.34951
\(529\) −17.5286 −0.762114
\(530\) −22.6921 −0.985681
\(531\) 0.708857 0.0307618
\(532\) 11.4454 0.496221
\(533\) −1.01894 −0.0441354
\(534\) −1.48961 −0.0644617
\(535\) 9.77870 0.422770
\(536\) −38.3627 −1.65702
\(537\) 4.77269 0.205957
\(538\) 17.4008 0.750201
\(539\) −37.9189 −1.63328
\(540\) 86.4365 3.71963
\(541\) 8.67249 0.372859 0.186430 0.982468i \(-0.440308\pi\)
0.186430 + 0.982468i \(0.440308\pi\)
\(542\) 13.4854 0.579247
\(543\) −21.9984 −0.944040
\(544\) −10.5179 −0.450952
\(545\) 30.2978 1.29782
\(546\) 3.72971 0.159617
\(547\) −1.15709 −0.0494736 −0.0247368 0.999694i \(-0.507875\pi\)
−0.0247368 + 0.999694i \(0.507875\pi\)
\(548\) −41.9862 −1.79356
\(549\) 0.309503 0.0132093
\(550\) −101.340 −4.32116
\(551\) −34.2129 −1.45752
\(552\) 26.1177 1.11164
\(553\) −3.56792 −0.151723
\(554\) −14.7114 −0.625028
\(555\) 15.2884 0.648956
\(556\) 45.4049 1.92560
\(557\) 13.3171 0.564262 0.282131 0.959376i \(-0.408959\pi\)
0.282131 + 0.959376i \(0.408959\pi\)
\(558\) −0.433792 −0.0183639
\(559\) −13.0547 −0.552154
\(560\) 16.8245 0.710965
\(561\) 13.1520 0.555280
\(562\) 34.7085 1.46409
\(563\) 22.0813 0.930614 0.465307 0.885149i \(-0.345944\pi\)
0.465307 + 0.885149i \(0.345944\pi\)
\(564\) 32.9696 1.38827
\(565\) −63.8821 −2.68754
\(566\) 18.5230 0.778578
\(567\) 4.81048 0.202021
\(568\) −13.3418 −0.559809
\(569\) 10.9914 0.460784 0.230392 0.973098i \(-0.425999\pi\)
0.230392 + 0.973098i \(0.425999\pi\)
\(570\) −60.6932 −2.54216
\(571\) 20.5009 0.857935 0.428968 0.903320i \(-0.358877\pi\)
0.428968 + 0.903320i \(0.358877\pi\)
\(572\) 38.9566 1.62886
\(573\) 24.5961 1.02752
\(574\) −1.06104 −0.0442869
\(575\) −16.1310 −0.672710
\(576\) −0.851259 −0.0354691
\(577\) −27.1346 −1.12963 −0.564814 0.825218i \(-0.691052\pi\)
−0.564814 + 0.825218i \(0.691052\pi\)
\(578\) 38.7409 1.61141
\(579\) −23.0327 −0.957205
\(580\) −131.800 −5.47269
\(581\) −0.0523581 −0.00217218
\(582\) −27.2810 −1.13083
\(583\) −14.5804 −0.603859
\(584\) 47.4915 1.96521
\(585\) 1.44081 0.0595700
\(586\) −34.9445 −1.44354
\(587\) −19.6763 −0.812126 −0.406063 0.913845i \(-0.633099\pi\)
−0.406063 + 0.913845i \(0.633099\pi\)
\(588\) −50.7157 −2.09148
\(589\) 2.46476 0.101559
\(590\) −22.2171 −0.914662
\(591\) −45.8247 −1.88498
\(592\) −22.0060 −0.904441
\(593\) −1.81388 −0.0744870 −0.0372435 0.999306i \(-0.511858\pi\)
−0.0372435 + 0.999306i \(0.511858\pi\)
\(594\) 79.5248 3.26294
\(595\) 2.87499 0.117863
\(596\) 66.1052 2.70778
\(597\) 34.8315 1.42556
\(598\) 8.87914 0.363095
\(599\) −27.1871 −1.11083 −0.555417 0.831572i \(-0.687441\pi\)
−0.555417 + 0.831572i \(0.687441\pi\)
\(600\) −77.0017 −3.14358
\(601\) 16.0879 0.656241 0.328120 0.944636i \(-0.393585\pi\)
0.328120 + 0.944636i \(0.393585\pi\)
\(602\) −13.5940 −0.554050
\(603\) −1.60471 −0.0653490
\(604\) −28.7146 −1.16838
\(605\) −74.3843 −3.02415
\(606\) −15.9180 −0.646623
\(607\) 28.4670 1.15544 0.577720 0.816235i \(-0.303943\pi\)
0.577720 + 0.816235i \(0.303943\pi\)
\(608\) 31.1869 1.26480
\(609\) −8.10784 −0.328546
\(610\) −9.70047 −0.392760
\(611\) 6.36768 0.257609
\(612\) −1.83490 −0.0741712
\(613\) 15.5549 0.628257 0.314129 0.949380i \(-0.398288\pi\)
0.314129 + 0.949380i \(0.398288\pi\)
\(614\) −38.7654 −1.56444
\(615\) 3.92944 0.158450
\(616\) 23.0459 0.928546
\(617\) −38.5796 −1.55315 −0.776577 0.630022i \(-0.783046\pi\)
−0.776577 + 0.630022i \(0.783046\pi\)
\(618\) −11.2848 −0.453940
\(619\) −37.3709 −1.50206 −0.751031 0.660267i \(-0.770443\pi\)
−0.751031 + 0.660267i \(0.770443\pi\)
\(620\) 9.49510 0.381333
\(621\) 12.6585 0.507970
\(622\) −86.3223 −3.46121
\(623\) −0.209224 −0.00838238
\(624\) 19.8817 0.795906
\(625\) −11.9229 −0.476915
\(626\) 85.9402 3.43486
\(627\) −38.9974 −1.55741
\(628\) 36.3728 1.45143
\(629\) −3.76041 −0.149937
\(630\) 1.50033 0.0597745
\(631\) −37.8318 −1.50606 −0.753029 0.657987i \(-0.771408\pi\)
−0.753029 + 0.657987i \(0.771408\pi\)
\(632\) −40.5461 −1.61284
\(633\) −15.1732 −0.603081
\(634\) 67.8251 2.69368
\(635\) 23.6904 0.940126
\(636\) −19.5010 −0.773266
\(637\) −9.79514 −0.388098
\(638\) −121.261 −4.80076
\(639\) −0.558088 −0.0220776
\(640\) −25.2082 −0.996443
\(641\) 11.3189 0.447071 0.223535 0.974696i \(-0.428240\pi\)
0.223535 + 0.974696i \(0.428240\pi\)
\(642\) 12.0330 0.474904
\(643\) −22.9295 −0.904253 −0.452126 0.891954i \(-0.649334\pi\)
−0.452126 + 0.891954i \(0.649334\pi\)
\(644\) 6.45717 0.254448
\(645\) 50.3439 1.98229
\(646\) 14.9284 0.587351
\(647\) −2.82046 −0.110884 −0.0554420 0.998462i \(-0.517657\pi\)
−0.0554420 + 0.998462i \(0.517657\pi\)
\(648\) 54.6667 2.14751
\(649\) −14.2752 −0.560351
\(650\) −26.1780 −1.02679
\(651\) 0.584104 0.0228928
\(652\) 13.9222 0.545235
\(653\) 6.93574 0.271416 0.135708 0.990749i \(-0.456669\pi\)
0.135708 + 0.990749i \(0.456669\pi\)
\(654\) 37.2825 1.45786
\(655\) −22.4337 −0.876555
\(656\) −5.65601 −0.220830
\(657\) 1.98657 0.0775036
\(658\) 6.63075 0.258493
\(659\) 16.4945 0.642533 0.321266 0.946989i \(-0.395892\pi\)
0.321266 + 0.946989i \(0.395892\pi\)
\(660\) −150.232 −5.84775
\(661\) −15.8915 −0.618107 −0.309054 0.951045i \(-0.600012\pi\)
−0.309054 + 0.951045i \(0.600012\pi\)
\(662\) −63.0174 −2.44924
\(663\) 3.39742 0.131945
\(664\) −0.595002 −0.0230906
\(665\) −8.52471 −0.330574
\(666\) −1.96239 −0.0760411
\(667\) −19.3019 −0.747374
\(668\) −62.8749 −2.43270
\(669\) −39.7618 −1.53728
\(670\) 50.2951 1.94307
\(671\) −6.23288 −0.240618
\(672\) 7.39074 0.285104
\(673\) 47.3419 1.82490 0.912448 0.409192i \(-0.134189\pi\)
0.912448 + 0.409192i \(0.134189\pi\)
\(674\) −32.1909 −1.23995
\(675\) −37.3206 −1.43647
\(676\) −50.1373 −1.92836
\(677\) 4.09800 0.157499 0.0787495 0.996894i \(-0.474907\pi\)
0.0787495 + 0.996894i \(0.474907\pi\)
\(678\) −78.6090 −3.01896
\(679\) −3.83177 −0.147050
\(680\) 32.6717 1.25290
\(681\) −32.2959 −1.23758
\(682\) 8.73585 0.334513
\(683\) −31.3469 −1.19945 −0.599727 0.800205i \(-0.704724\pi\)
−0.599727 + 0.800205i \(0.704724\pi\)
\(684\) 5.44069 0.208030
\(685\) 31.2720 1.19484
\(686\) −20.9451 −0.799688
\(687\) 6.83087 0.260614
\(688\) −72.4646 −2.76269
\(689\) −3.76639 −0.143488
\(690\) −34.2414 −1.30355
\(691\) 4.15799 0.158177 0.0790887 0.996868i \(-0.474799\pi\)
0.0790887 + 0.996868i \(0.474799\pi\)
\(692\) −12.9843 −0.493588
\(693\) 0.964012 0.0366198
\(694\) 62.8408 2.38540
\(695\) −33.8182 −1.28280
\(696\) −92.1382 −3.49249
\(697\) −0.966506 −0.0366090
\(698\) 16.5500 0.626427
\(699\) 1.22429 0.0463067
\(700\) −19.0374 −0.719546
\(701\) 17.4032 0.657309 0.328654 0.944450i \(-0.393405\pi\)
0.328654 + 0.944450i \(0.393405\pi\)
\(702\) 20.5427 0.775335
\(703\) 11.1501 0.420534
\(704\) 17.1429 0.646099
\(705\) −24.5562 −0.924842
\(706\) −40.4604 −1.52275
\(707\) −2.23577 −0.0840847
\(708\) −19.0928 −0.717551
\(709\) 10.2146 0.383616 0.191808 0.981432i \(-0.438565\pi\)
0.191808 + 0.981432i \(0.438565\pi\)
\(710\) 17.4916 0.656450
\(711\) −1.69605 −0.0636068
\(712\) −2.37764 −0.0891058
\(713\) 1.39055 0.0520765
\(714\) 3.53777 0.132398
\(715\) −29.0155 −1.08512
\(716\) 13.4093 0.501128
\(717\) −4.45226 −0.166273
\(718\) 67.3470 2.51337
\(719\) −5.12340 −0.191071 −0.0955353 0.995426i \(-0.530456\pi\)
−0.0955353 + 0.995426i \(0.530456\pi\)
\(720\) 7.99770 0.298057
\(721\) −1.58501 −0.0590288
\(722\) 4.66104 0.173466
\(723\) −25.9242 −0.964132
\(724\) −61.8062 −2.29701
\(725\) 56.9071 2.11348
\(726\) −91.5322 −3.39708
\(727\) 24.7878 0.919328 0.459664 0.888093i \(-0.347970\pi\)
0.459664 + 0.888093i \(0.347970\pi\)
\(728\) 5.95318 0.220640
\(729\) 29.0458 1.07577
\(730\) −62.2634 −2.30447
\(731\) −12.3828 −0.457996
\(732\) −8.33634 −0.308120
\(733\) 9.02701 0.333420 0.166710 0.986006i \(-0.446686\pi\)
0.166710 + 0.986006i \(0.446686\pi\)
\(734\) 48.3937 1.78624
\(735\) 37.7739 1.39331
\(736\) 17.5948 0.648552
\(737\) 32.3163 1.19039
\(738\) −0.504376 −0.0185663
\(739\) −50.6705 −1.86394 −0.931971 0.362532i \(-0.881912\pi\)
−0.931971 + 0.362532i \(0.881912\pi\)
\(740\) 42.9540 1.57902
\(741\) −10.0738 −0.370069
\(742\) −3.92199 −0.143981
\(743\) 43.5453 1.59752 0.798760 0.601649i \(-0.205490\pi\)
0.798760 + 0.601649i \(0.205490\pi\)
\(744\) 6.63781 0.243354
\(745\) −49.2362 −1.80387
\(746\) 33.5166 1.22713
\(747\) −0.0248890 −0.000910640 0
\(748\) 36.9517 1.35109
\(749\) 1.69010 0.0617550
\(750\) 27.7589 1.01361
\(751\) 23.3637 0.852553 0.426277 0.904593i \(-0.359825\pi\)
0.426277 + 0.904593i \(0.359825\pi\)
\(752\) 35.3461 1.28894
\(753\) 6.09596 0.222149
\(754\) −31.3239 −1.14075
\(755\) 21.3871 0.778356
\(756\) 14.9393 0.543336
\(757\) −3.05270 −0.110952 −0.0554761 0.998460i \(-0.517668\pi\)
−0.0554761 + 0.998460i \(0.517668\pi\)
\(758\) 74.9231 2.72133
\(759\) −22.0013 −0.798595
\(760\) −96.8755 −3.51404
\(761\) −10.5278 −0.381632 −0.190816 0.981626i \(-0.561113\pi\)
−0.190816 + 0.981626i \(0.561113\pi\)
\(762\) 29.1518 1.05606
\(763\) 5.23653 0.189575
\(764\) 69.1048 2.50012
\(765\) 1.36666 0.0494116
\(766\) −8.14612 −0.294331
\(767\) −3.68755 −0.133150
\(768\) −40.9221 −1.47665
\(769\) 30.8341 1.11191 0.555953 0.831214i \(-0.312354\pi\)
0.555953 + 0.831214i \(0.312354\pi\)
\(770\) −30.2141 −1.08884
\(771\) 2.53544 0.0913117
\(772\) −64.7122 −2.32904
\(773\) 7.18857 0.258555 0.129278 0.991608i \(-0.458734\pi\)
0.129278 + 0.991608i \(0.458734\pi\)
\(774\) −6.46205 −0.232274
\(775\) −4.09970 −0.147265
\(776\) −43.5446 −1.56316
\(777\) 2.64237 0.0947945
\(778\) −33.9022 −1.21545
\(779\) 2.86581 0.102678
\(780\) −38.8076 −1.38953
\(781\) 11.2390 0.402162
\(782\) 8.42220 0.301177
\(783\) −44.6569 −1.59591
\(784\) −54.3714 −1.94184
\(785\) −27.0910 −0.966919
\(786\) −27.6053 −0.984649
\(787\) 5.95920 0.212423 0.106211 0.994344i \(-0.466128\pi\)
0.106211 + 0.994344i \(0.466128\pi\)
\(788\) −128.748 −4.58647
\(789\) −27.0718 −0.963780
\(790\) 53.1577 1.89126
\(791\) −11.0411 −0.392576
\(792\) 10.9551 0.389273
\(793\) −1.61007 −0.0571752
\(794\) −1.21698 −0.0431889
\(795\) 14.5247 0.515136
\(796\) 97.8620 3.46863
\(797\) −36.3653 −1.28813 −0.644063 0.764972i \(-0.722753\pi\)
−0.644063 + 0.764972i \(0.722753\pi\)
\(798\) −10.4899 −0.371339
\(799\) 6.03998 0.213679
\(800\) −51.8739 −1.83402
\(801\) −0.0994568 −0.00351413
\(802\) 82.5493 2.91492
\(803\) −40.0063 −1.41179
\(804\) 43.2224 1.52434
\(805\) −4.80940 −0.169509
\(806\) 2.25663 0.0794865
\(807\) −11.1378 −0.392070
\(808\) −25.4075 −0.893832
\(809\) 48.8529 1.71758 0.858788 0.512332i \(-0.171218\pi\)
0.858788 + 0.512332i \(0.171218\pi\)
\(810\) −71.6703 −2.51824
\(811\) 30.2522 1.06230 0.531149 0.847278i \(-0.321760\pi\)
0.531149 + 0.847278i \(0.321760\pi\)
\(812\) −22.7796 −0.799409
\(813\) −8.63168 −0.302726
\(814\) 39.5193 1.38515
\(815\) −10.3695 −0.363227
\(816\) 18.8586 0.660181
\(817\) 36.7167 1.28455
\(818\) 26.0677 0.911436
\(819\) 0.249022 0.00870153
\(820\) 11.0401 0.385536
\(821\) 3.20176 0.111742 0.0558711 0.998438i \(-0.482206\pi\)
0.0558711 + 0.998438i \(0.482206\pi\)
\(822\) 38.4812 1.34219
\(823\) −22.1016 −0.770413 −0.385207 0.922830i \(-0.625870\pi\)
−0.385207 + 0.922830i \(0.625870\pi\)
\(824\) −18.0122 −0.627484
\(825\) 64.8654 2.25832
\(826\) −3.83989 −0.133607
\(827\) −54.8297 −1.90661 −0.953307 0.302002i \(-0.902345\pi\)
−0.953307 + 0.302002i \(0.902345\pi\)
\(828\) 3.06948 0.106672
\(829\) 2.50117 0.0868693 0.0434346 0.999056i \(-0.486170\pi\)
0.0434346 + 0.999056i \(0.486170\pi\)
\(830\) 0.780072 0.0270767
\(831\) 9.41642 0.326652
\(832\) 4.42834 0.153525
\(833\) −9.29106 −0.321916
\(834\) −41.6144 −1.44099
\(835\) 46.8302 1.62063
\(836\) −109.566 −3.78944
\(837\) 3.21716 0.111201
\(838\) 77.5657 2.67946
\(839\) −26.7154 −0.922319 −0.461160 0.887317i \(-0.652566\pi\)
−0.461160 + 0.887317i \(0.652566\pi\)
\(840\) −22.9578 −0.792118
\(841\) 39.0935 1.34805
\(842\) 80.4927 2.77396
\(843\) −22.2161 −0.765163
\(844\) −42.6304 −1.46740
\(845\) 37.3430 1.28464
\(846\) 3.15200 0.108368
\(847\) −12.8562 −0.441745
\(848\) −20.9067 −0.717938
\(849\) −11.8561 −0.406901
\(850\) −24.8308 −0.851690
\(851\) 6.29057 0.215638
\(852\) 15.0319 0.514984
\(853\) −6.62208 −0.226736 −0.113368 0.993553i \(-0.536164\pi\)
−0.113368 + 0.993553i \(0.536164\pi\)
\(854\) −1.67658 −0.0573714
\(855\) −4.05231 −0.138586
\(856\) 19.2065 0.656464
\(857\) 21.4937 0.734212 0.367106 0.930179i \(-0.380349\pi\)
0.367106 + 0.930179i \(0.380349\pi\)
\(858\) −35.7044 −1.21893
\(859\) −16.1583 −0.551315 −0.275657 0.961256i \(-0.588896\pi\)
−0.275657 + 0.961256i \(0.588896\pi\)
\(860\) 141.445 4.82324
\(861\) 0.679146 0.0231452
\(862\) 1.99355 0.0679004
\(863\) 17.6699 0.601491 0.300746 0.953704i \(-0.402764\pi\)
0.300746 + 0.953704i \(0.402764\pi\)
\(864\) 40.7072 1.38489
\(865\) 9.67088 0.328820
\(866\) 10.2479 0.348238
\(867\) −24.7971 −0.842155
\(868\) 1.64109 0.0557022
\(869\) 34.1556 1.15865
\(870\) 120.797 4.09540
\(871\) 8.34789 0.282858
\(872\) 59.5084 2.01521
\(873\) −1.82147 −0.0616475
\(874\) −24.9729 −0.844719
\(875\) 3.89889 0.131807
\(876\) −53.5076 −1.80785
\(877\) −48.9439 −1.65272 −0.826359 0.563144i \(-0.809592\pi\)
−0.826359 + 0.563144i \(0.809592\pi\)
\(878\) −47.8341 −1.61432
\(879\) 22.3671 0.754424
\(880\) −161.060 −5.42935
\(881\) 16.2505 0.547493 0.273747 0.961802i \(-0.411737\pi\)
0.273747 + 0.961802i \(0.411737\pi\)
\(882\) −4.84858 −0.163260
\(883\) −45.7323 −1.53901 −0.769507 0.638638i \(-0.779498\pi\)
−0.769507 + 0.638638i \(0.779498\pi\)
\(884\) 9.54532 0.321044
\(885\) 14.2206 0.478020
\(886\) 89.3180 3.00070
\(887\) −43.9844 −1.47685 −0.738425 0.674335i \(-0.764430\pi\)
−0.738425 + 0.674335i \(0.764430\pi\)
\(888\) 30.0281 1.00768
\(889\) 4.09454 0.137326
\(890\) 3.11718 0.104488
\(891\) −46.0506 −1.54275
\(892\) −111.714 −3.74046
\(893\) −17.9093 −0.599312
\(894\) −60.5867 −2.02632
\(895\) −9.98743 −0.333843
\(896\) −4.35687 −0.145553
\(897\) −5.68333 −0.189761
\(898\) −33.9303 −1.13227
\(899\) −4.90558 −0.163610
\(900\) −9.04963 −0.301654
\(901\) −3.57256 −0.119019
\(902\) 10.1573 0.338201
\(903\) 8.70119 0.289558
\(904\) −125.472 −4.17313
\(905\) 46.0342 1.53023
\(906\) 26.3175 0.874340
\(907\) −28.2690 −0.938656 −0.469328 0.883024i \(-0.655504\pi\)
−0.469328 + 0.883024i \(0.655504\pi\)
\(908\) −90.7379 −3.01124
\(909\) −1.06280 −0.0352507
\(910\) −7.80487 −0.258729
\(911\) 1.83829 0.0609053 0.0304527 0.999536i \(-0.490305\pi\)
0.0304527 + 0.999536i \(0.490305\pi\)
\(912\) −55.9179 −1.85163
\(913\) 0.501223 0.0165881
\(914\) 1.77755 0.0587961
\(915\) 6.20904 0.205264
\(916\) 19.1919 0.634118
\(917\) −3.87733 −0.128041
\(918\) 19.4855 0.643119
\(919\) 25.9691 0.856643 0.428322 0.903626i \(-0.359105\pi\)
0.428322 + 0.903626i \(0.359105\pi\)
\(920\) −54.6544 −1.80190
\(921\) 24.8128 0.817610
\(922\) −45.1374 −1.48652
\(923\) 2.90323 0.0955611
\(924\) −25.9653 −0.854195
\(925\) −18.5462 −0.609796
\(926\) 5.58030 0.183380
\(927\) −0.753451 −0.0247466
\(928\) −62.0709 −2.03758
\(929\) −29.8617 −0.979730 −0.489865 0.871798i \(-0.662954\pi\)
−0.489865 + 0.871798i \(0.662954\pi\)
\(930\) −8.70244 −0.285364
\(931\) 27.5491 0.902886
\(932\) 3.43973 0.112672
\(933\) 55.2528 1.80890
\(934\) −56.2275 −1.83982
\(935\) −27.5222 −0.900073
\(936\) 2.82991 0.0924984
\(937\) −7.52610 −0.245867 −0.122934 0.992415i \(-0.539230\pi\)
−0.122934 + 0.992415i \(0.539230\pi\)
\(938\) 8.69276 0.283829
\(939\) −55.0083 −1.79513
\(940\) −68.9928 −2.25030
\(941\) 6.95149 0.226612 0.113306 0.993560i \(-0.463856\pi\)
0.113306 + 0.993560i \(0.463856\pi\)
\(942\) −33.3363 −1.08616
\(943\) 1.61681 0.0526506
\(944\) −20.4690 −0.666210
\(945\) −11.1270 −0.361961
\(946\) 130.135 4.23105
\(947\) −2.72279 −0.0884787 −0.0442394 0.999021i \(-0.514086\pi\)
−0.0442394 + 0.999021i \(0.514086\pi\)
\(948\) 45.6824 1.48370
\(949\) −10.3344 −0.335468
\(950\) 73.6264 2.38876
\(951\) −43.4132 −1.40777
\(952\) 5.64681 0.183014
\(953\) −42.3943 −1.37329 −0.686643 0.726995i \(-0.740916\pi\)
−0.686643 + 0.726995i \(0.740916\pi\)
\(954\) −1.86436 −0.0603608
\(955\) −51.4703 −1.66554
\(956\) −12.5090 −0.404569
\(957\) 77.6161 2.50897
\(958\) 109.147 3.52639
\(959\) 5.40490 0.174533
\(960\) −17.0774 −0.551170
\(961\) −30.6466 −0.988600
\(962\) 10.2086 0.329137
\(963\) 0.803408 0.0258895
\(964\) −72.8362 −2.34590
\(965\) 48.1986 1.55157
\(966\) −5.91812 −0.190412
\(967\) −47.1392 −1.51589 −0.757947 0.652316i \(-0.773797\pi\)
−0.757947 + 0.652316i \(0.773797\pi\)
\(968\) −146.099 −4.69581
\(969\) −9.55533 −0.306961
\(970\) 57.0887 1.83301
\(971\) 28.4220 0.912107 0.456053 0.889952i \(-0.349263\pi\)
0.456053 + 0.889952i \(0.349263\pi\)
\(972\) 13.5902 0.435905
\(973\) −5.84498 −0.187382
\(974\) −50.5365 −1.61929
\(975\) 16.7559 0.536619
\(976\) −8.93724 −0.286074
\(977\) −29.4580 −0.942446 −0.471223 0.882014i \(-0.656187\pi\)
−0.471223 + 0.882014i \(0.656187\pi\)
\(978\) −12.7600 −0.408018
\(979\) 2.00290 0.0640128
\(980\) 106.129 3.39016
\(981\) 2.48924 0.0794754
\(982\) 64.4890 2.05793
\(983\) 38.8897 1.24039 0.620194 0.784448i \(-0.287054\pi\)
0.620194 + 0.784448i \(0.287054\pi\)
\(984\) 7.71787 0.246037
\(985\) 95.8937 3.05543
\(986\) −29.7119 −0.946219
\(987\) −4.24418 −0.135094
\(988\) −28.3030 −0.900440
\(989\) 20.7145 0.658683
\(990\) −14.3626 −0.456474
\(991\) 17.3180 0.550125 0.275062 0.961426i \(-0.411301\pi\)
0.275062 + 0.961426i \(0.411301\pi\)
\(992\) 4.47171 0.141977
\(993\) 40.3360 1.28002
\(994\) 3.02317 0.0958892
\(995\) −72.8891 −2.31074
\(996\) 0.670375 0.0212417
\(997\) 45.2943 1.43449 0.717243 0.696823i \(-0.245404\pi\)
0.717243 + 0.696823i \(0.245404\pi\)
\(998\) −55.7296 −1.76409
\(999\) 14.5538 0.460462
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 \(a_p\))