Properties

Label 6039.2.a.j.1.14
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(2.63401\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.63401 q^{2}\) \(+4.93799 q^{4}\) \(-2.62502 q^{5}\) \(+5.18852 q^{7}\) \(+7.73867 q^{8}\) \(+O(q^{10})\) \(q\)\(+2.63401 q^{2}\) \(+4.93799 q^{4}\) \(-2.62502 q^{5}\) \(+5.18852 q^{7}\) \(+7.73867 q^{8}\) \(-6.91432 q^{10}\) \(+1.00000 q^{11}\) \(-3.47280 q^{13}\) \(+13.6666 q^{14}\) \(+10.5077 q^{16}\) \(-1.94870 q^{17}\) \(-0.343156 q^{19}\) \(-12.9623 q^{20}\) \(+2.63401 q^{22}\) \(+4.48645 q^{23}\) \(+1.89073 q^{25}\) \(-9.14738 q^{26}\) \(+25.6208 q^{28}\) \(+5.47498 q^{29}\) \(+2.40756 q^{31}\) \(+12.2001 q^{32}\) \(-5.13290 q^{34}\) \(-13.6200 q^{35}\) \(+10.3461 q^{37}\) \(-0.903876 q^{38}\) \(-20.3142 q^{40}\) \(+0.436542 q^{41}\) \(+6.40802 q^{43}\) \(+4.93799 q^{44}\) \(+11.8173 q^{46}\) \(-4.42685 q^{47}\) \(+19.9207 q^{49}\) \(+4.98019 q^{50}\) \(-17.1487 q^{52}\) \(-2.47102 q^{53}\) \(-2.62502 q^{55}\) \(+40.1522 q^{56}\) \(+14.4211 q^{58}\) \(-13.7469 q^{59}\) \(+1.00000 q^{61}\) \(+6.34152 q^{62}\) \(+11.1197 q^{64}\) \(+9.11617 q^{65}\) \(+2.76619 q^{67}\) \(-9.62267 q^{68}\) \(-35.8750 q^{70}\) \(+16.0977 q^{71}\) \(-3.11724 q^{73}\) \(+27.2517 q^{74}\) \(-1.69450 q^{76}\) \(+5.18852 q^{77}\) \(-5.15429 q^{79}\) \(-27.5830 q^{80}\) \(+1.14985 q^{82}\) \(-2.12536 q^{83}\) \(+5.11538 q^{85}\) \(+16.8788 q^{86}\) \(+7.73867 q^{88}\) \(-3.14440 q^{89}\) \(-18.0187 q^{91}\) \(+22.1540 q^{92}\) \(-11.6604 q^{94}\) \(+0.900792 q^{95}\) \(+6.51443 q^{97}\) \(+52.4712 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.63401 1.86252 0.931262 0.364351i \(-0.118709\pi\)
0.931262 + 0.364351i \(0.118709\pi\)
\(3\) 0 0
\(4\) 4.93799 2.46899
\(5\) −2.62502 −1.17394 −0.586972 0.809607i \(-0.699680\pi\)
−0.586972 + 0.809607i \(0.699680\pi\)
\(6\) 0 0
\(7\) 5.18852 1.96107 0.980537 0.196333i \(-0.0629034\pi\)
0.980537 + 0.196333i \(0.0629034\pi\)
\(8\) 7.73867 2.73603
\(9\) 0 0
\(10\) −6.91432 −2.18650
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −3.47280 −0.963182 −0.481591 0.876396i \(-0.659941\pi\)
−0.481591 + 0.876396i \(0.659941\pi\)
\(14\) 13.6666 3.65255
\(15\) 0 0
\(16\) 10.5077 2.62694
\(17\) −1.94870 −0.472630 −0.236315 0.971677i \(-0.575940\pi\)
−0.236315 + 0.971677i \(0.575940\pi\)
\(18\) 0 0
\(19\) −0.343156 −0.0787255 −0.0393627 0.999225i \(-0.512533\pi\)
−0.0393627 + 0.999225i \(0.512533\pi\)
\(20\) −12.9623 −2.89846
\(21\) 0 0
\(22\) 2.63401 0.561572
\(23\) 4.48645 0.935489 0.467744 0.883864i \(-0.345067\pi\)
0.467744 + 0.883864i \(0.345067\pi\)
\(24\) 0 0
\(25\) 1.89073 0.378146
\(26\) −9.14738 −1.79395
\(27\) 0 0
\(28\) 25.6208 4.84188
\(29\) 5.47498 1.01668 0.508339 0.861157i \(-0.330260\pi\)
0.508339 + 0.861157i \(0.330260\pi\)
\(30\) 0 0
\(31\) 2.40756 0.432410 0.216205 0.976348i \(-0.430632\pi\)
0.216205 + 0.976348i \(0.430632\pi\)
\(32\) 12.2001 2.15669
\(33\) 0 0
\(34\) −5.13290 −0.880284
\(35\) −13.6200 −2.30219
\(36\) 0 0
\(37\) 10.3461 1.70089 0.850444 0.526065i \(-0.176333\pi\)
0.850444 + 0.526065i \(0.176333\pi\)
\(38\) −0.903876 −0.146628
\(39\) 0 0
\(40\) −20.3142 −3.21195
\(41\) 0.436542 0.0681764 0.0340882 0.999419i \(-0.489147\pi\)
0.0340882 + 0.999419i \(0.489147\pi\)
\(42\) 0 0
\(43\) 6.40802 0.977214 0.488607 0.872504i \(-0.337505\pi\)
0.488607 + 0.872504i \(0.337505\pi\)
\(44\) 4.93799 0.744430
\(45\) 0 0
\(46\) 11.8173 1.74237
\(47\) −4.42685 −0.645723 −0.322861 0.946446i \(-0.604645\pi\)
−0.322861 + 0.946446i \(0.604645\pi\)
\(48\) 0 0
\(49\) 19.9207 2.84581
\(50\) 4.98019 0.704306
\(51\) 0 0
\(52\) −17.1487 −2.37809
\(53\) −2.47102 −0.339420 −0.169710 0.985494i \(-0.554283\pi\)
−0.169710 + 0.985494i \(0.554283\pi\)
\(54\) 0 0
\(55\) −2.62502 −0.353958
\(56\) 40.1522 5.36557
\(57\) 0 0
\(58\) 14.4211 1.89359
\(59\) −13.7469 −1.78970 −0.894849 0.446369i \(-0.852717\pi\)
−0.894849 + 0.446369i \(0.852717\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 6.34152 0.805374
\(63\) 0 0
\(64\) 11.1197 1.38996
\(65\) 9.11617 1.13072
\(66\) 0 0
\(67\) 2.76619 0.337944 0.168972 0.985621i \(-0.445955\pi\)
0.168972 + 0.985621i \(0.445955\pi\)
\(68\) −9.62267 −1.16692
\(69\) 0 0
\(70\) −35.8750 −4.28789
\(71\) 16.0977 1.91045 0.955225 0.295881i \(-0.0956130\pi\)
0.955225 + 0.295881i \(0.0956130\pi\)
\(72\) 0 0
\(73\) −3.11724 −0.364845 −0.182422 0.983220i \(-0.558394\pi\)
−0.182422 + 0.983220i \(0.558394\pi\)
\(74\) 27.2517 3.16794
\(75\) 0 0
\(76\) −1.69450 −0.194373
\(77\) 5.18852 0.591286
\(78\) 0 0
\(79\) −5.15429 −0.579903 −0.289952 0.957041i \(-0.593639\pi\)
−0.289952 + 0.957041i \(0.593639\pi\)
\(80\) −27.5830 −3.08388
\(81\) 0 0
\(82\) 1.14985 0.126980
\(83\) −2.12536 −0.233289 −0.116644 0.993174i \(-0.537214\pi\)
−0.116644 + 0.993174i \(0.537214\pi\)
\(84\) 0 0
\(85\) 5.11538 0.554841
\(86\) 16.8788 1.82008
\(87\) 0 0
\(88\) 7.73867 0.824946
\(89\) −3.14440 −0.333305 −0.166653 0.986016i \(-0.553296\pi\)
−0.166653 + 0.986016i \(0.553296\pi\)
\(90\) 0 0
\(91\) −18.0187 −1.88887
\(92\) 22.1540 2.30972
\(93\) 0 0
\(94\) −11.6604 −1.20267
\(95\) 0.900792 0.0924193
\(96\) 0 0
\(97\) 6.51443 0.661440 0.330720 0.943729i \(-0.392708\pi\)
0.330720 + 0.943729i \(0.392708\pi\)
\(98\) 52.4712 5.30039
\(99\) 0 0
\(100\) 9.33640 0.933640
\(101\) −11.1124 −1.10572 −0.552862 0.833273i \(-0.686464\pi\)
−0.552862 + 0.833273i \(0.686464\pi\)
\(102\) 0 0
\(103\) −0.504742 −0.0497337 −0.0248668 0.999691i \(-0.507916\pi\)
−0.0248668 + 0.999691i \(0.507916\pi\)
\(104\) −26.8749 −2.63530
\(105\) 0 0
\(106\) −6.50868 −0.632178
\(107\) −7.83003 −0.756957 −0.378479 0.925610i \(-0.623553\pi\)
−0.378479 + 0.925610i \(0.623553\pi\)
\(108\) 0 0
\(109\) −5.69464 −0.545448 −0.272724 0.962092i \(-0.587925\pi\)
−0.272724 + 0.962092i \(0.587925\pi\)
\(110\) −6.91432 −0.659254
\(111\) 0 0
\(112\) 54.5196 5.15162
\(113\) −16.5161 −1.55370 −0.776850 0.629686i \(-0.783184\pi\)
−0.776850 + 0.629686i \(0.783184\pi\)
\(114\) 0 0
\(115\) −11.7770 −1.09821
\(116\) 27.0354 2.51017
\(117\) 0 0
\(118\) −36.2095 −3.33335
\(119\) −10.1109 −0.926862
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 2.63401 0.238472
\(123\) 0 0
\(124\) 11.8885 1.06762
\(125\) 8.16190 0.730022
\(126\) 0 0
\(127\) 15.2576 1.35390 0.676948 0.736031i \(-0.263302\pi\)
0.676948 + 0.736031i \(0.263302\pi\)
\(128\) 4.88904 0.432134
\(129\) 0 0
\(130\) 24.0121 2.10600
\(131\) 2.57715 0.225167 0.112583 0.993642i \(-0.464087\pi\)
0.112583 + 0.993642i \(0.464087\pi\)
\(132\) 0 0
\(133\) −1.78047 −0.154387
\(134\) 7.28616 0.629428
\(135\) 0 0
\(136\) −15.0804 −1.29313
\(137\) −14.4185 −1.23185 −0.615926 0.787804i \(-0.711218\pi\)
−0.615926 + 0.787804i \(0.711218\pi\)
\(138\) 0 0
\(139\) 11.3125 0.959516 0.479758 0.877401i \(-0.340724\pi\)
0.479758 + 0.877401i \(0.340724\pi\)
\(140\) −67.2552 −5.68410
\(141\) 0 0
\(142\) 42.4015 3.55826
\(143\) −3.47280 −0.290410
\(144\) 0 0
\(145\) −14.3719 −1.19352
\(146\) −8.21082 −0.679532
\(147\) 0 0
\(148\) 51.0889 4.19948
\(149\) 4.30768 0.352899 0.176449 0.984310i \(-0.443539\pi\)
0.176449 + 0.984310i \(0.443539\pi\)
\(150\) 0 0
\(151\) −12.6896 −1.03267 −0.516334 0.856387i \(-0.672704\pi\)
−0.516334 + 0.856387i \(0.672704\pi\)
\(152\) −2.65558 −0.215396
\(153\) 0 0
\(154\) 13.6666 1.10128
\(155\) −6.31989 −0.507626
\(156\) 0 0
\(157\) 10.8043 0.862274 0.431137 0.902286i \(-0.358113\pi\)
0.431137 + 0.902286i \(0.358113\pi\)
\(158\) −13.5764 −1.08008
\(159\) 0 0
\(160\) −32.0255 −2.53184
\(161\) 23.2780 1.83456
\(162\) 0 0
\(163\) 25.0214 1.95983 0.979913 0.199427i \(-0.0639080\pi\)
0.979913 + 0.199427i \(0.0639080\pi\)
\(164\) 2.15564 0.168327
\(165\) 0 0
\(166\) −5.59821 −0.434506
\(167\) 21.9141 1.69576 0.847882 0.530185i \(-0.177877\pi\)
0.847882 + 0.530185i \(0.177877\pi\)
\(168\) 0 0
\(169\) −0.939647 −0.0722805
\(170\) 13.4740 1.03340
\(171\) 0 0
\(172\) 31.6427 2.41273
\(173\) 19.3446 1.47075 0.735373 0.677663i \(-0.237007\pi\)
0.735373 + 0.677663i \(0.237007\pi\)
\(174\) 0 0
\(175\) 9.81008 0.741572
\(176\) 10.5077 0.792051
\(177\) 0 0
\(178\) −8.28236 −0.620789
\(179\) −20.9873 −1.56866 −0.784331 0.620343i \(-0.786993\pi\)
−0.784331 + 0.620343i \(0.786993\pi\)
\(180\) 0 0
\(181\) −26.3913 −1.96165 −0.980826 0.194886i \(-0.937566\pi\)
−0.980826 + 0.194886i \(0.937566\pi\)
\(182\) −47.4613 −3.51807
\(183\) 0 0
\(184\) 34.7191 2.55953
\(185\) −27.1587 −1.99675
\(186\) 0 0
\(187\) −1.94870 −0.142503
\(188\) −21.8597 −1.59429
\(189\) 0 0
\(190\) 2.37269 0.172133
\(191\) −20.2002 −1.46164 −0.730818 0.682572i \(-0.760861\pi\)
−0.730818 + 0.682572i \(0.760861\pi\)
\(192\) 0 0
\(193\) −16.2353 −1.16864 −0.584321 0.811523i \(-0.698639\pi\)
−0.584321 + 0.811523i \(0.698639\pi\)
\(194\) 17.1591 1.23195
\(195\) 0 0
\(196\) 98.3681 7.02629
\(197\) −10.8231 −0.771112 −0.385556 0.922685i \(-0.625990\pi\)
−0.385556 + 0.922685i \(0.625990\pi\)
\(198\) 0 0
\(199\) 17.1207 1.21366 0.606828 0.794833i \(-0.292442\pi\)
0.606828 + 0.794833i \(0.292442\pi\)
\(200\) 14.6317 1.03462
\(201\) 0 0
\(202\) −29.2701 −2.05944
\(203\) 28.4070 1.99378
\(204\) 0 0
\(205\) −1.14593 −0.0800353
\(206\) −1.32949 −0.0926301
\(207\) 0 0
\(208\) −36.4913 −2.53022
\(209\) −0.343156 −0.0237366
\(210\) 0 0
\(211\) 6.07527 0.418239 0.209119 0.977890i \(-0.432940\pi\)
0.209119 + 0.977890i \(0.432940\pi\)
\(212\) −12.2019 −0.838027
\(213\) 0 0
\(214\) −20.6243 −1.40985
\(215\) −16.8212 −1.14719
\(216\) 0 0
\(217\) 12.4917 0.847989
\(218\) −14.9997 −1.01591
\(219\) 0 0
\(220\) −12.9623 −0.873919
\(221\) 6.76746 0.455229
\(222\) 0 0
\(223\) −24.7908 −1.66011 −0.830057 0.557679i \(-0.811692\pi\)
−0.830057 + 0.557679i \(0.811692\pi\)
\(224\) 63.3004 4.22944
\(225\) 0 0
\(226\) −43.5034 −2.89380
\(227\) −25.6959 −1.70549 −0.852747 0.522324i \(-0.825065\pi\)
−0.852747 + 0.522324i \(0.825065\pi\)
\(228\) 0 0
\(229\) −1.69139 −0.111770 −0.0558852 0.998437i \(-0.517798\pi\)
−0.0558852 + 0.998437i \(0.517798\pi\)
\(230\) −31.0207 −2.04545
\(231\) 0 0
\(232\) 42.3691 2.78167
\(233\) 8.61616 0.564463 0.282232 0.959346i \(-0.408925\pi\)
0.282232 + 0.959346i \(0.408925\pi\)
\(234\) 0 0
\(235\) 11.6206 0.758043
\(236\) −67.8822 −4.41875
\(237\) 0 0
\(238\) −26.6321 −1.72630
\(239\) 13.2629 0.857905 0.428953 0.903327i \(-0.358883\pi\)
0.428953 + 0.903327i \(0.358883\pi\)
\(240\) 0 0
\(241\) 2.12784 0.137066 0.0685332 0.997649i \(-0.478168\pi\)
0.0685332 + 0.997649i \(0.478168\pi\)
\(242\) 2.63401 0.169320
\(243\) 0 0
\(244\) 4.93799 0.316122
\(245\) −52.2922 −3.34083
\(246\) 0 0
\(247\) 1.19171 0.0758270
\(248\) 18.6313 1.18309
\(249\) 0 0
\(250\) 21.4985 1.35968
\(251\) −1.21883 −0.0769321 −0.0384661 0.999260i \(-0.512247\pi\)
−0.0384661 + 0.999260i \(0.512247\pi\)
\(252\) 0 0
\(253\) 4.48645 0.282060
\(254\) 40.1887 2.52166
\(255\) 0 0
\(256\) −9.36155 −0.585097
\(257\) 10.0350 0.625964 0.312982 0.949759i \(-0.398672\pi\)
0.312982 + 0.949759i \(0.398672\pi\)
\(258\) 0 0
\(259\) 53.6809 3.33557
\(260\) 45.0155 2.79175
\(261\) 0 0
\(262\) 6.78823 0.419378
\(263\) 15.4701 0.953925 0.476963 0.878924i \(-0.341738\pi\)
0.476963 + 0.878924i \(0.341738\pi\)
\(264\) 0 0
\(265\) 6.48647 0.398461
\(266\) −4.68977 −0.287549
\(267\) 0 0
\(268\) 13.6594 0.834381
\(269\) 11.4654 0.699059 0.349530 0.936925i \(-0.386341\pi\)
0.349530 + 0.936925i \(0.386341\pi\)
\(270\) 0 0
\(271\) −10.6925 −0.649521 −0.324760 0.945796i \(-0.605284\pi\)
−0.324760 + 0.945796i \(0.605284\pi\)
\(272\) −20.4765 −1.24157
\(273\) 0 0
\(274\) −37.9783 −2.29435
\(275\) 1.89073 0.114015
\(276\) 0 0
\(277\) −31.4466 −1.88944 −0.944720 0.327877i \(-0.893667\pi\)
−0.944720 + 0.327877i \(0.893667\pi\)
\(278\) 29.7973 1.78712
\(279\) 0 0
\(280\) −105.400 −6.29888
\(281\) −15.8197 −0.943723 −0.471861 0.881673i \(-0.656418\pi\)
−0.471861 + 0.881673i \(0.656418\pi\)
\(282\) 0 0
\(283\) −17.7131 −1.05293 −0.526467 0.850196i \(-0.676484\pi\)
−0.526467 + 0.850196i \(0.676484\pi\)
\(284\) 79.4904 4.71689
\(285\) 0 0
\(286\) −9.14738 −0.540896
\(287\) 2.26500 0.133699
\(288\) 0 0
\(289\) −13.2026 −0.776621
\(290\) −37.8557 −2.22296
\(291\) 0 0
\(292\) −15.3929 −0.900799
\(293\) 6.92077 0.404316 0.202158 0.979353i \(-0.435205\pi\)
0.202158 + 0.979353i \(0.435205\pi\)
\(294\) 0 0
\(295\) 36.0860 2.10101
\(296\) 80.0651 4.65369
\(297\) 0 0
\(298\) 11.3465 0.657282
\(299\) −15.5805 −0.901046
\(300\) 0 0
\(301\) 33.2481 1.91639
\(302\) −33.4246 −1.92337
\(303\) 0 0
\(304\) −3.60580 −0.206807
\(305\) −2.62502 −0.150308
\(306\) 0 0
\(307\) 15.9515 0.910401 0.455201 0.890389i \(-0.349568\pi\)
0.455201 + 0.890389i \(0.349568\pi\)
\(308\) 25.6208 1.45988
\(309\) 0 0
\(310\) −16.6466 −0.945465
\(311\) 13.8655 0.786239 0.393119 0.919487i \(-0.371396\pi\)
0.393119 + 0.919487i \(0.371396\pi\)
\(312\) 0 0
\(313\) 18.1128 1.02380 0.511898 0.859046i \(-0.328943\pi\)
0.511898 + 0.859046i \(0.328943\pi\)
\(314\) 28.4585 1.60601
\(315\) 0 0
\(316\) −25.4518 −1.43178
\(317\) −22.4082 −1.25857 −0.629286 0.777174i \(-0.716652\pi\)
−0.629286 + 0.777174i \(0.716652\pi\)
\(318\) 0 0
\(319\) 5.47498 0.306540
\(320\) −29.1893 −1.63173
\(321\) 0 0
\(322\) 61.3144 3.41692
\(323\) 0.668710 0.0372080
\(324\) 0 0
\(325\) −6.56613 −0.364223
\(326\) 65.9065 3.65022
\(327\) 0 0
\(328\) 3.37826 0.186533
\(329\) −22.9688 −1.26631
\(330\) 0 0
\(331\) −1.51172 −0.0830916 −0.0415458 0.999137i \(-0.513228\pi\)
−0.0415458 + 0.999137i \(0.513228\pi\)
\(332\) −10.4950 −0.575988
\(333\) 0 0
\(334\) 57.7219 3.15840
\(335\) −7.26130 −0.396727
\(336\) 0 0
\(337\) −2.97052 −0.161815 −0.0809074 0.996722i \(-0.525782\pi\)
−0.0809074 + 0.996722i \(0.525782\pi\)
\(338\) −2.47503 −0.134624
\(339\) 0 0
\(340\) 25.2597 1.36990
\(341\) 2.40756 0.130377
\(342\) 0 0
\(343\) 67.0392 3.61978
\(344\) 49.5896 2.67369
\(345\) 0 0
\(346\) 50.9539 2.73930
\(347\) −34.9082 −1.87397 −0.936985 0.349369i \(-0.886396\pi\)
−0.936985 + 0.349369i \(0.886396\pi\)
\(348\) 0 0
\(349\) −7.36747 −0.394371 −0.197186 0.980366i \(-0.563180\pi\)
−0.197186 + 0.980366i \(0.563180\pi\)
\(350\) 25.8398 1.38120
\(351\) 0 0
\(352\) 12.2001 0.650268
\(353\) −30.1994 −1.60735 −0.803675 0.595068i \(-0.797125\pi\)
−0.803675 + 0.595068i \(0.797125\pi\)
\(354\) 0 0
\(355\) −42.2569 −2.24276
\(356\) −15.5270 −0.822929
\(357\) 0 0
\(358\) −55.2806 −2.92167
\(359\) 28.2798 1.49255 0.746274 0.665639i \(-0.231841\pi\)
0.746274 + 0.665639i \(0.231841\pi\)
\(360\) 0 0
\(361\) −18.8822 −0.993802
\(362\) −69.5149 −3.65362
\(363\) 0 0
\(364\) −88.9760 −4.66361
\(365\) 8.18281 0.428308
\(366\) 0 0
\(367\) 9.06316 0.473093 0.236547 0.971620i \(-0.423984\pi\)
0.236547 + 0.971620i \(0.423984\pi\)
\(368\) 47.1424 2.45747
\(369\) 0 0
\(370\) −71.5362 −3.71899
\(371\) −12.8209 −0.665629
\(372\) 0 0
\(373\) 4.76411 0.246676 0.123338 0.992365i \(-0.460640\pi\)
0.123338 + 0.992365i \(0.460640\pi\)
\(374\) −5.13290 −0.265416
\(375\) 0 0
\(376\) −34.2580 −1.76672
\(377\) −19.0135 −0.979245
\(378\) 0 0
\(379\) 24.6033 1.26379 0.631893 0.775056i \(-0.282278\pi\)
0.631893 + 0.775056i \(0.282278\pi\)
\(380\) 4.44810 0.228183
\(381\) 0 0
\(382\) −53.2075 −2.72233
\(383\) −1.16351 −0.0594524 −0.0297262 0.999558i \(-0.509464\pi\)
−0.0297262 + 0.999558i \(0.509464\pi\)
\(384\) 0 0
\(385\) −13.6200 −0.694137
\(386\) −42.7638 −2.17662
\(387\) 0 0
\(388\) 32.1682 1.63309
\(389\) −4.68535 −0.237557 −0.118778 0.992921i \(-0.537898\pi\)
−0.118778 + 0.992921i \(0.537898\pi\)
\(390\) 0 0
\(391\) −8.74275 −0.442140
\(392\) 154.160 7.78624
\(393\) 0 0
\(394\) −28.5080 −1.43621
\(395\) 13.5301 0.680774
\(396\) 0 0
\(397\) −32.1659 −1.61436 −0.807180 0.590306i \(-0.799007\pi\)
−0.807180 + 0.590306i \(0.799007\pi\)
\(398\) 45.0961 2.26046
\(399\) 0 0
\(400\) 19.8673 0.993365
\(401\) 37.0986 1.85262 0.926309 0.376765i \(-0.122964\pi\)
0.926309 + 0.376765i \(0.122964\pi\)
\(402\) 0 0
\(403\) −8.36097 −0.416490
\(404\) −54.8729 −2.73003
\(405\) 0 0
\(406\) 74.8242 3.71346
\(407\) 10.3461 0.512837
\(408\) 0 0
\(409\) −22.4268 −1.10893 −0.554467 0.832206i \(-0.687078\pi\)
−0.554467 + 0.832206i \(0.687078\pi\)
\(410\) −3.01839 −0.149068
\(411\) 0 0
\(412\) −2.49241 −0.122792
\(413\) −71.3262 −3.50973
\(414\) 0 0
\(415\) 5.57912 0.273868
\(416\) −42.3685 −2.07729
\(417\) 0 0
\(418\) −0.903876 −0.0442100
\(419\) 8.94385 0.436936 0.218468 0.975844i \(-0.429894\pi\)
0.218468 + 0.975844i \(0.429894\pi\)
\(420\) 0 0
\(421\) −40.0168 −1.95030 −0.975151 0.221543i \(-0.928891\pi\)
−0.975151 + 0.221543i \(0.928891\pi\)
\(422\) 16.0023 0.778980
\(423\) 0 0
\(424\) −19.1224 −0.928666
\(425\) −3.68447 −0.178723
\(426\) 0 0
\(427\) 5.18852 0.251090
\(428\) −38.6646 −1.86892
\(429\) 0 0
\(430\) −44.3071 −2.13668
\(431\) 1.04053 0.0501205 0.0250603 0.999686i \(-0.492022\pi\)
0.0250603 + 0.999686i \(0.492022\pi\)
\(432\) 0 0
\(433\) −15.4980 −0.744785 −0.372393 0.928075i \(-0.621463\pi\)
−0.372393 + 0.928075i \(0.621463\pi\)
\(434\) 32.9031 1.57940
\(435\) 0 0
\(436\) −28.1201 −1.34671
\(437\) −1.53955 −0.0736468
\(438\) 0 0
\(439\) 22.0242 1.05116 0.525579 0.850745i \(-0.323849\pi\)
0.525579 + 0.850745i \(0.323849\pi\)
\(440\) −20.3142 −0.968440
\(441\) 0 0
\(442\) 17.8255 0.847874
\(443\) −27.4427 −1.30384 −0.651921 0.758287i \(-0.726036\pi\)
−0.651921 + 0.758287i \(0.726036\pi\)
\(444\) 0 0
\(445\) 8.25410 0.391282
\(446\) −65.2991 −3.09200
\(447\) 0 0
\(448\) 57.6945 2.72581
\(449\) 31.7031 1.49616 0.748081 0.663607i \(-0.230975\pi\)
0.748081 + 0.663607i \(0.230975\pi\)
\(450\) 0 0
\(451\) 0.436542 0.0205560
\(452\) −81.5561 −3.83607
\(453\) 0 0
\(454\) −67.6830 −3.17652
\(455\) 47.2994 2.21743
\(456\) 0 0
\(457\) −6.80691 −0.318414 −0.159207 0.987245i \(-0.550894\pi\)
−0.159207 + 0.987245i \(0.550894\pi\)
\(458\) −4.45514 −0.208175
\(459\) 0 0
\(460\) −58.1547 −2.71148
\(461\) −3.68797 −0.171766 −0.0858830 0.996305i \(-0.527371\pi\)
−0.0858830 + 0.996305i \(0.527371\pi\)
\(462\) 0 0
\(463\) 6.47116 0.300740 0.150370 0.988630i \(-0.451953\pi\)
0.150370 + 0.988630i \(0.451953\pi\)
\(464\) 57.5296 2.67075
\(465\) 0 0
\(466\) 22.6950 1.05133
\(467\) 14.4505 0.668692 0.334346 0.942450i \(-0.391485\pi\)
0.334346 + 0.942450i \(0.391485\pi\)
\(468\) 0 0
\(469\) 14.3524 0.662733
\(470\) 30.6087 1.41187
\(471\) 0 0
\(472\) −106.383 −4.89668
\(473\) 6.40802 0.294641
\(474\) 0 0
\(475\) −0.648816 −0.0297697
\(476\) −49.9274 −2.28842
\(477\) 0 0
\(478\) 34.9345 1.59787
\(479\) 26.3992 1.20621 0.603106 0.797661i \(-0.293930\pi\)
0.603106 + 0.797661i \(0.293930\pi\)
\(480\) 0 0
\(481\) −35.9300 −1.63827
\(482\) 5.60475 0.255289
\(483\) 0 0
\(484\) 4.93799 0.224454
\(485\) −17.1005 −0.776494
\(486\) 0 0
\(487\) 1.02748 0.0465596 0.0232798 0.999729i \(-0.492589\pi\)
0.0232798 + 0.999729i \(0.492589\pi\)
\(488\) 7.73867 0.350313
\(489\) 0 0
\(490\) −137.738 −6.22237
\(491\) −26.4321 −1.19286 −0.596432 0.802664i \(-0.703416\pi\)
−0.596432 + 0.802664i \(0.703416\pi\)
\(492\) 0 0
\(493\) −10.6691 −0.480512
\(494\) 3.13898 0.141229
\(495\) 0 0
\(496\) 25.2980 1.13591
\(497\) 83.5234 3.74653
\(498\) 0 0
\(499\) −21.5904 −0.966520 −0.483260 0.875477i \(-0.660547\pi\)
−0.483260 + 0.875477i \(0.660547\pi\)
\(500\) 40.3033 1.80242
\(501\) 0 0
\(502\) −3.21042 −0.143288
\(503\) 21.8467 0.974095 0.487048 0.873375i \(-0.338074\pi\)
0.487048 + 0.873375i \(0.338074\pi\)
\(504\) 0 0
\(505\) 29.1703 1.29806
\(506\) 11.8173 0.525344
\(507\) 0 0
\(508\) 75.3420 3.34276
\(509\) −39.4287 −1.74765 −0.873823 0.486245i \(-0.838366\pi\)
−0.873823 + 0.486245i \(0.838366\pi\)
\(510\) 0 0
\(511\) −16.1738 −0.715488
\(512\) −34.4365 −1.52189
\(513\) 0 0
\(514\) 26.4322 1.16587
\(515\) 1.32496 0.0583846
\(516\) 0 0
\(517\) −4.42685 −0.194693
\(518\) 141.396 6.21258
\(519\) 0 0
\(520\) 70.5471 3.09370
\(521\) −4.56305 −0.199911 −0.0999555 0.994992i \(-0.531870\pi\)
−0.0999555 + 0.994992i \(0.531870\pi\)
\(522\) 0 0
\(523\) 6.29112 0.275092 0.137546 0.990495i \(-0.456079\pi\)
0.137546 + 0.990495i \(0.456079\pi\)
\(524\) 12.7259 0.555935
\(525\) 0 0
\(526\) 40.7482 1.77671
\(527\) −4.69162 −0.204370
\(528\) 0 0
\(529\) −2.87181 −0.124861
\(530\) 17.0854 0.742143
\(531\) 0 0
\(532\) −8.79195 −0.381179
\(533\) −1.51602 −0.0656663
\(534\) 0 0
\(535\) 20.5540 0.888626
\(536\) 21.4066 0.924626
\(537\) 0 0
\(538\) 30.2000 1.30201
\(539\) 19.9207 0.858045
\(540\) 0 0
\(541\) 14.4263 0.620233 0.310117 0.950699i \(-0.399632\pi\)
0.310117 + 0.950699i \(0.399632\pi\)
\(542\) −28.1640 −1.20975
\(543\) 0 0
\(544\) −23.7744 −1.01932
\(545\) 14.9486 0.640326
\(546\) 0 0
\(547\) 9.30055 0.397663 0.198831 0.980034i \(-0.436285\pi\)
0.198831 + 0.980034i \(0.436285\pi\)
\(548\) −71.1982 −3.04144
\(549\) 0 0
\(550\) 4.98019 0.212356
\(551\) −1.87877 −0.0800384
\(552\) 0 0
\(553\) −26.7431 −1.13723
\(554\) −82.8304 −3.51913
\(555\) 0 0
\(556\) 55.8611 2.36904
\(557\) 4.86880 0.206298 0.103149 0.994666i \(-0.467108\pi\)
0.103149 + 0.994666i \(0.467108\pi\)
\(558\) 0 0
\(559\) −22.2538 −0.941235
\(560\) −143.115 −6.04771
\(561\) 0 0
\(562\) −41.6691 −1.75771
\(563\) −14.5434 −0.612929 −0.306465 0.951882i \(-0.599146\pi\)
−0.306465 + 0.951882i \(0.599146\pi\)
\(564\) 0 0
\(565\) 43.3550 1.82396
\(566\) −46.6564 −1.96111
\(567\) 0 0
\(568\) 124.575 5.22706
\(569\) −25.4145 −1.06543 −0.532717 0.846294i \(-0.678829\pi\)
−0.532717 + 0.846294i \(0.678829\pi\)
\(570\) 0 0
\(571\) 3.21902 0.134712 0.0673560 0.997729i \(-0.478544\pi\)
0.0673560 + 0.997729i \(0.478544\pi\)
\(572\) −17.1487 −0.717021
\(573\) 0 0
\(574\) 5.96603 0.249017
\(575\) 8.48266 0.353751
\(576\) 0 0
\(577\) 16.5724 0.689918 0.344959 0.938618i \(-0.387893\pi\)
0.344959 + 0.938618i \(0.387893\pi\)
\(578\) −34.7756 −1.44647
\(579\) 0 0
\(580\) −70.9684 −2.94680
\(581\) −11.0275 −0.457497
\(582\) 0 0
\(583\) −2.47102 −0.102339
\(584\) −24.1233 −0.998228
\(585\) 0 0
\(586\) 18.2294 0.753048
\(587\) −7.08569 −0.292458 −0.146229 0.989251i \(-0.546714\pi\)
−0.146229 + 0.989251i \(0.546714\pi\)
\(588\) 0 0
\(589\) −0.826169 −0.0340417
\(590\) 95.0507 3.91317
\(591\) 0 0
\(592\) 108.714 4.46812
\(593\) 10.7052 0.439612 0.219806 0.975544i \(-0.429458\pi\)
0.219806 + 0.975544i \(0.429458\pi\)
\(594\) 0 0
\(595\) 26.5412 1.08809
\(596\) 21.2713 0.871305
\(597\) 0 0
\(598\) −41.0392 −1.67822
\(599\) 15.1212 0.617836 0.308918 0.951089i \(-0.400033\pi\)
0.308918 + 0.951089i \(0.400033\pi\)
\(600\) 0 0
\(601\) −0.515149 −0.0210134 −0.0105067 0.999945i \(-0.503344\pi\)
−0.0105067 + 0.999945i \(0.503344\pi\)
\(602\) 87.5757 3.56932
\(603\) 0 0
\(604\) −62.6613 −2.54965
\(605\) −2.62502 −0.106722
\(606\) 0 0
\(607\) 33.0600 1.34186 0.670932 0.741519i \(-0.265894\pi\)
0.670932 + 0.741519i \(0.265894\pi\)
\(608\) −4.18654 −0.169787
\(609\) 0 0
\(610\) −6.91432 −0.279953
\(611\) 15.3736 0.621949
\(612\) 0 0
\(613\) 10.2485 0.413933 0.206966 0.978348i \(-0.433641\pi\)
0.206966 + 0.978348i \(0.433641\pi\)
\(614\) 42.0164 1.69564
\(615\) 0 0
\(616\) 40.1522 1.61778
\(617\) −29.1352 −1.17294 −0.586469 0.809971i \(-0.699483\pi\)
−0.586469 + 0.809971i \(0.699483\pi\)
\(618\) 0 0
\(619\) −13.3947 −0.538377 −0.269188 0.963088i \(-0.586755\pi\)
−0.269188 + 0.963088i \(0.586755\pi\)
\(620\) −31.2075 −1.25332
\(621\) 0 0
\(622\) 36.5217 1.46439
\(623\) −16.3147 −0.653636
\(624\) 0 0
\(625\) −30.8788 −1.23515
\(626\) 47.7092 1.90684
\(627\) 0 0
\(628\) 53.3513 2.12895
\(629\) −20.1615 −0.803891
\(630\) 0 0
\(631\) −24.1306 −0.960622 −0.480311 0.877098i \(-0.659476\pi\)
−0.480311 + 0.877098i \(0.659476\pi\)
\(632\) −39.8874 −1.58664
\(633\) 0 0
\(634\) −59.0234 −2.34412
\(635\) −40.0516 −1.58940
\(636\) 0 0
\(637\) −69.1806 −2.74104
\(638\) 14.4211 0.570938
\(639\) 0 0
\(640\) −12.8338 −0.507302
\(641\) −31.1854 −1.23175 −0.615874 0.787845i \(-0.711197\pi\)
−0.615874 + 0.787845i \(0.711197\pi\)
\(642\) 0 0
\(643\) 31.3001 1.23436 0.617178 0.786824i \(-0.288276\pi\)
0.617178 + 0.786824i \(0.288276\pi\)
\(644\) 114.946 4.52952
\(645\) 0 0
\(646\) 1.76139 0.0693008
\(647\) 25.8036 1.01445 0.507223 0.861815i \(-0.330672\pi\)
0.507223 + 0.861815i \(0.330672\pi\)
\(648\) 0 0
\(649\) −13.7469 −0.539614
\(650\) −17.2952 −0.678375
\(651\) 0 0
\(652\) 123.555 4.83880
\(653\) 39.3780 1.54098 0.770491 0.637451i \(-0.220011\pi\)
0.770491 + 0.637451i \(0.220011\pi\)
\(654\) 0 0
\(655\) −6.76507 −0.264333
\(656\) 4.58707 0.179095
\(657\) 0 0
\(658\) −60.4999 −2.35853
\(659\) 17.3863 0.677275 0.338637 0.940917i \(-0.390034\pi\)
0.338637 + 0.940917i \(0.390034\pi\)
\(660\) 0 0
\(661\) 10.6188 0.413025 0.206512 0.978444i \(-0.433789\pi\)
0.206512 + 0.978444i \(0.433789\pi\)
\(662\) −3.98188 −0.154760
\(663\) 0 0
\(664\) −16.4475 −0.638286
\(665\) 4.67377 0.181241
\(666\) 0 0
\(667\) 24.5632 0.951090
\(668\) 108.212 4.18683
\(669\) 0 0
\(670\) −19.1263 −0.738914
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −25.4524 −0.981117 −0.490559 0.871408i \(-0.663207\pi\)
−0.490559 + 0.871408i \(0.663207\pi\)
\(674\) −7.82438 −0.301384
\(675\) 0 0
\(676\) −4.63996 −0.178460
\(677\) −29.4870 −1.13328 −0.566638 0.823967i \(-0.691756\pi\)
−0.566638 + 0.823967i \(0.691756\pi\)
\(678\) 0 0
\(679\) 33.8002 1.29713
\(680\) 39.5863 1.51807
\(681\) 0 0
\(682\) 6.34152 0.242829
\(683\) −10.3877 −0.397475 −0.198737 0.980053i \(-0.563684\pi\)
−0.198737 + 0.980053i \(0.563684\pi\)
\(684\) 0 0
\(685\) 37.8487 1.44613
\(686\) 176.582 6.74192
\(687\) 0 0
\(688\) 67.3338 2.56708
\(689\) 8.58136 0.326924
\(690\) 0 0
\(691\) −8.92858 −0.339659 −0.169830 0.985473i \(-0.554322\pi\)
−0.169830 + 0.985473i \(0.554322\pi\)
\(692\) 95.5236 3.63126
\(693\) 0 0
\(694\) −91.9484 −3.49031
\(695\) −29.6956 −1.12642
\(696\) 0 0
\(697\) −0.850690 −0.0322222
\(698\) −19.4059 −0.734526
\(699\) 0 0
\(700\) 48.4420 1.83094
\(701\) −45.5207 −1.71929 −0.859646 0.510891i \(-0.829316\pi\)
−0.859646 + 0.510891i \(0.829316\pi\)
\(702\) 0 0
\(703\) −3.55033 −0.133903
\(704\) 11.1197 0.419088
\(705\) 0 0
\(706\) −79.5453 −2.99373
\(707\) −57.6568 −2.16841
\(708\) 0 0
\(709\) 16.4201 0.616670 0.308335 0.951278i \(-0.400228\pi\)
0.308335 + 0.951278i \(0.400228\pi\)
\(710\) −111.305 −4.17720
\(711\) 0 0
\(712\) −24.3335 −0.911935
\(713\) 10.8014 0.404515
\(714\) 0 0
\(715\) 9.11617 0.340926
\(716\) −103.635 −3.87301
\(717\) 0 0
\(718\) 74.4890 2.77991
\(719\) −17.6047 −0.656545 −0.328273 0.944583i \(-0.606466\pi\)
−0.328273 + 0.944583i \(0.606466\pi\)
\(720\) 0 0
\(721\) −2.61886 −0.0975314
\(722\) −49.7359 −1.85098
\(723\) 0 0
\(724\) −130.320 −4.84331
\(725\) 10.3517 0.384452
\(726\) 0 0
\(727\) 26.0709 0.966914 0.483457 0.875368i \(-0.339381\pi\)
0.483457 + 0.875368i \(0.339381\pi\)
\(728\) −139.441 −5.16802
\(729\) 0 0
\(730\) 21.5536 0.797733
\(731\) −12.4873 −0.461860
\(732\) 0 0
\(733\) −30.5781 −1.12943 −0.564715 0.825286i \(-0.691014\pi\)
−0.564715 + 0.825286i \(0.691014\pi\)
\(734\) 23.8724 0.881147
\(735\) 0 0
\(736\) 54.7351 2.01756
\(737\) 2.76619 0.101894
\(738\) 0 0
\(739\) −50.2330 −1.84785 −0.923926 0.382571i \(-0.875039\pi\)
−0.923926 + 0.382571i \(0.875039\pi\)
\(740\) −134.109 −4.92996
\(741\) 0 0
\(742\) −33.7704 −1.23975
\(743\) −31.2350 −1.14590 −0.572950 0.819590i \(-0.694201\pi\)
−0.572950 + 0.819590i \(0.694201\pi\)
\(744\) 0 0
\(745\) −11.3077 −0.414284
\(746\) 12.5487 0.459440
\(747\) 0 0
\(748\) −9.62267 −0.351840
\(749\) −40.6262 −1.48445
\(750\) 0 0
\(751\) −6.93821 −0.253179 −0.126590 0.991955i \(-0.540403\pi\)
−0.126590 + 0.991955i \(0.540403\pi\)
\(752\) −46.5162 −1.69627
\(753\) 0 0
\(754\) −50.0817 −1.82387
\(755\) 33.3105 1.21229
\(756\) 0 0
\(757\) −42.3758 −1.54017 −0.770086 0.637939i \(-0.779787\pi\)
−0.770086 + 0.637939i \(0.779787\pi\)
\(758\) 64.8052 2.35383
\(759\) 0 0
\(760\) 6.97094 0.252863
\(761\) 38.5976 1.39916 0.699582 0.714553i \(-0.253370\pi\)
0.699582 + 0.714553i \(0.253370\pi\)
\(762\) 0 0
\(763\) −29.5467 −1.06966
\(764\) −99.7484 −3.60877
\(765\) 0 0
\(766\) −3.06468 −0.110731
\(767\) 47.7404 1.72381
\(768\) 0 0
\(769\) −8.52482 −0.307413 −0.153706 0.988117i \(-0.549121\pi\)
−0.153706 + 0.988117i \(0.549121\pi\)
\(770\) −35.8750 −1.29285
\(771\) 0 0
\(772\) −80.1696 −2.88537
\(773\) 44.8848 1.61439 0.807197 0.590283i \(-0.200984\pi\)
0.807197 + 0.590283i \(0.200984\pi\)
\(774\) 0 0
\(775\) 4.55204 0.163514
\(776\) 50.4131 1.80972
\(777\) 0 0
\(778\) −12.3412 −0.442455
\(779\) −0.149802 −0.00536722
\(780\) 0 0
\(781\) 16.0977 0.576022
\(782\) −23.0285 −0.823496
\(783\) 0 0
\(784\) 209.321 7.47577
\(785\) −28.3614 −1.01226
\(786\) 0 0
\(787\) −13.9456 −0.497106 −0.248553 0.968618i \(-0.579955\pi\)
−0.248553 + 0.968618i \(0.579955\pi\)
\(788\) −53.4442 −1.90387
\(789\) 0 0
\(790\) 35.6384 1.26796
\(791\) −85.6938 −3.04692
\(792\) 0 0
\(793\) −3.47280 −0.123323
\(794\) −84.7251 −3.00678
\(795\) 0 0
\(796\) 84.5420 2.99651
\(797\) −23.5528 −0.834282 −0.417141 0.908842i \(-0.636968\pi\)
−0.417141 + 0.908842i \(0.636968\pi\)
\(798\) 0 0
\(799\) 8.62662 0.305188
\(800\) 23.0671 0.815545
\(801\) 0 0
\(802\) 97.7180 3.45054
\(803\) −3.11724 −0.110005
\(804\) 0 0
\(805\) −61.1052 −2.15367
\(806\) −22.0229 −0.775722
\(807\) 0 0
\(808\) −85.9952 −3.02530
\(809\) 32.6289 1.14717 0.573586 0.819145i \(-0.305552\pi\)
0.573586 + 0.819145i \(0.305552\pi\)
\(810\) 0 0
\(811\) 8.24758 0.289612 0.144806 0.989460i \(-0.453744\pi\)
0.144806 + 0.989460i \(0.453744\pi\)
\(812\) 140.273 4.92263
\(813\) 0 0
\(814\) 27.2517 0.955171
\(815\) −65.6816 −2.30073
\(816\) 0 0
\(817\) −2.19895 −0.0769316
\(818\) −59.0723 −2.06542
\(819\) 0 0
\(820\) −5.65859 −0.197607
\(821\) −53.7676 −1.87650 −0.938251 0.345954i \(-0.887555\pi\)
−0.938251 + 0.345954i \(0.887555\pi\)
\(822\) 0 0
\(823\) −8.85638 −0.308714 −0.154357 0.988015i \(-0.549331\pi\)
−0.154357 + 0.988015i \(0.549331\pi\)
\(824\) −3.90603 −0.136073
\(825\) 0 0
\(826\) −187.874 −6.53696
\(827\) 1.91639 0.0666395 0.0333198 0.999445i \(-0.489392\pi\)
0.0333198 + 0.999445i \(0.489392\pi\)
\(828\) 0 0
\(829\) −35.4299 −1.23053 −0.615266 0.788320i \(-0.710951\pi\)
−0.615266 + 0.788320i \(0.710951\pi\)
\(830\) 14.6954 0.510086
\(831\) 0 0
\(832\) −38.6164 −1.33878
\(833\) −38.8195 −1.34502
\(834\) 0 0
\(835\) −57.5250 −1.99073
\(836\) −1.69450 −0.0586056
\(837\) 0 0
\(838\) 23.5582 0.813803
\(839\) 11.2612 0.388781 0.194391 0.980924i \(-0.437727\pi\)
0.194391 + 0.980924i \(0.437727\pi\)
\(840\) 0 0
\(841\) 0.975363 0.0336332
\(842\) −105.405 −3.63248
\(843\) 0 0
\(844\) 29.9996 1.03263
\(845\) 2.46659 0.0848533
\(846\) 0 0
\(847\) 5.18852 0.178279
\(848\) −25.9648 −0.891635
\(849\) 0 0
\(850\) −9.70492 −0.332876
\(851\) 46.4172 1.59116
\(852\) 0 0
\(853\) 5.79874 0.198545 0.0992725 0.995060i \(-0.468348\pi\)
0.0992725 + 0.995060i \(0.468348\pi\)
\(854\) 13.6666 0.467661
\(855\) 0 0
\(856\) −60.5940 −2.07106
\(857\) −40.4860 −1.38298 −0.691488 0.722388i \(-0.743044\pi\)
−0.691488 + 0.722388i \(0.743044\pi\)
\(858\) 0 0
\(859\) 19.1302 0.652715 0.326357 0.945246i \(-0.394179\pi\)
0.326357 + 0.945246i \(0.394179\pi\)
\(860\) −83.0627 −2.83242
\(861\) 0 0
\(862\) 2.74076 0.0933506
\(863\) −25.2855 −0.860727 −0.430364 0.902656i \(-0.641615\pi\)
−0.430364 + 0.902656i \(0.641615\pi\)
\(864\) 0 0
\(865\) −50.7801 −1.72657
\(866\) −40.8218 −1.38718
\(867\) 0 0
\(868\) 61.6836 2.09368
\(869\) −5.15429 −0.174847
\(870\) 0 0
\(871\) −9.60643 −0.325501
\(872\) −44.0690 −1.49236
\(873\) 0 0
\(874\) −4.05519 −0.137169
\(875\) 42.3481 1.43163
\(876\) 0 0
\(877\) −31.4779 −1.06293 −0.531466 0.847080i \(-0.678359\pi\)
−0.531466 + 0.847080i \(0.678359\pi\)
\(878\) 58.0119 1.95781
\(879\) 0 0
\(880\) −27.5830 −0.929824
\(881\) 7.07691 0.238427 0.119214 0.992869i \(-0.461963\pi\)
0.119214 + 0.992869i \(0.461963\pi\)
\(882\) 0 0
\(883\) 39.1958 1.31904 0.659521 0.751686i \(-0.270759\pi\)
0.659521 + 0.751686i \(0.270759\pi\)
\(884\) 33.4176 1.12396
\(885\) 0 0
\(886\) −72.2842 −2.42843
\(887\) 33.0652 1.11022 0.555111 0.831776i \(-0.312676\pi\)
0.555111 + 0.831776i \(0.312676\pi\)
\(888\) 0 0
\(889\) 79.1645 2.65509
\(890\) 21.7414 0.728772
\(891\) 0 0
\(892\) −122.417 −4.09881
\(893\) 1.51910 0.0508348
\(894\) 0 0
\(895\) 55.0920 1.84152
\(896\) 25.3669 0.847448
\(897\) 0 0
\(898\) 83.5062 2.78664
\(899\) 13.1813 0.439622
\(900\) 0 0
\(901\) 4.81528 0.160420
\(902\) 1.14985 0.0382859
\(903\) 0 0
\(904\) −127.812 −4.25098
\(905\) 69.2778 2.30287
\(906\) 0 0
\(907\) −49.4081 −1.64057 −0.820285 0.571955i \(-0.806185\pi\)
−0.820285 + 0.571955i \(0.806185\pi\)
\(908\) −126.886 −4.21085
\(909\) 0 0
\(910\) 124.587 4.13002
\(911\) −11.0990 −0.367725 −0.183863 0.982952i \(-0.558860\pi\)
−0.183863 + 0.982952i \(0.558860\pi\)
\(912\) 0 0
\(913\) −2.12536 −0.0703392
\(914\) −17.9294 −0.593053
\(915\) 0 0
\(916\) −8.35207 −0.275960
\(917\) 13.3716 0.441569
\(918\) 0 0
\(919\) 9.02754 0.297791 0.148895 0.988853i \(-0.452428\pi\)
0.148895 + 0.988853i \(0.452428\pi\)
\(920\) −91.1384 −3.00475
\(921\) 0 0
\(922\) −9.71414 −0.319918
\(923\) −55.9043 −1.84011
\(924\) 0 0
\(925\) 19.5617 0.643184
\(926\) 17.0451 0.560136
\(927\) 0 0
\(928\) 66.7953 2.19266
\(929\) 22.1504 0.726732 0.363366 0.931646i \(-0.381627\pi\)
0.363366 + 0.931646i \(0.381627\pi\)
\(930\) 0 0
\(931\) −6.83591 −0.224038
\(932\) 42.5465 1.39366
\(933\) 0 0
\(934\) 38.0628 1.24545
\(935\) 5.11538 0.167291
\(936\) 0 0
\(937\) −32.4015 −1.05851 −0.529255 0.848463i \(-0.677529\pi\)
−0.529255 + 0.848463i \(0.677529\pi\)
\(938\) 37.8044 1.23436
\(939\) 0 0
\(940\) 57.3822 1.87160
\(941\) 23.0935 0.752826 0.376413 0.926452i \(-0.377157\pi\)
0.376413 + 0.926452i \(0.377157\pi\)
\(942\) 0 0
\(943\) 1.95852 0.0637782
\(944\) −144.449 −4.70142
\(945\) 0 0
\(946\) 16.8788 0.548776
\(947\) 19.1527 0.622378 0.311189 0.950348i \(-0.399273\pi\)
0.311189 + 0.950348i \(0.399273\pi\)
\(948\) 0 0
\(949\) 10.8255 0.351412
\(950\) −1.70899 −0.0554468
\(951\) 0 0
\(952\) −78.2448 −2.53593
\(953\) 18.1232 0.587067 0.293534 0.955949i \(-0.405169\pi\)
0.293534 + 0.955949i \(0.405169\pi\)
\(954\) 0 0
\(955\) 53.0260 1.71588
\(956\) 65.4920 2.11816
\(957\) 0 0
\(958\) 69.5358 2.24660
\(959\) −74.8104 −2.41575
\(960\) 0 0
\(961\) −25.2037 −0.813021
\(962\) −94.6397 −3.05131
\(963\) 0 0
\(964\) 10.5073 0.338416
\(965\) 42.6180 1.37192
\(966\) 0 0
\(967\) −40.9282 −1.31616 −0.658082 0.752947i \(-0.728632\pi\)
−0.658082 + 0.752947i \(0.728632\pi\)
\(968\) 7.73867 0.248730
\(969\) 0 0
\(970\) −45.0429 −1.44624
\(971\) −13.7378 −0.440866 −0.220433 0.975402i \(-0.570747\pi\)
−0.220433 + 0.975402i \(0.570747\pi\)
\(972\) 0 0
\(973\) 58.6952 1.88168
\(974\) 2.70639 0.0867183
\(975\) 0 0
\(976\) 10.5077 0.336345
\(977\) 25.1855 0.805755 0.402878 0.915254i \(-0.368010\pi\)
0.402878 + 0.915254i \(0.368010\pi\)
\(978\) 0 0
\(979\) −3.14440 −0.100495
\(980\) −258.218 −8.24848
\(981\) 0 0
\(982\) −69.6223 −2.22174
\(983\) −0.0437437 −0.00139521 −0.000697604 1.00000i \(-0.500222\pi\)
−0.000697604 1.00000i \(0.500222\pi\)
\(984\) 0 0
\(985\) 28.4108 0.905242
\(986\) −28.1025 −0.894965
\(987\) 0 0
\(988\) 5.88467 0.187216
\(989\) 28.7492 0.914172
\(990\) 0 0
\(991\) 12.7220 0.404126 0.202063 0.979373i \(-0.435235\pi\)
0.202063 + 0.979373i \(0.435235\pi\)
\(992\) 29.3725 0.932576
\(993\) 0 0
\(994\) 220.001 6.97801
\(995\) −44.9423 −1.42477
\(996\) 0 0
\(997\) −56.0727 −1.77584 −0.887920 0.459997i \(-0.847850\pi\)
−0.887920 + 0.459997i \(0.847850\pi\)
\(998\) −56.8693 −1.80017
\(999\) 0 0
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 \(a_p\))