Properties

Label 6039.2.a.j.1.10
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

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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 1.10
Root \(1.61392\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.61392 q^{2}\) \(+0.604750 q^{4}\) \(+3.65776 q^{5}\) \(+0.985739 q^{7}\) \(-2.25183 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.61392 q^{2}\) \(+0.604750 q^{4}\) \(+3.65776 q^{5}\) \(+0.985739 q^{7}\) \(-2.25183 q^{8}\) \(+5.90335 q^{10}\) \(+1.00000 q^{11}\) \(+2.65320 q^{13}\) \(+1.59091 q^{14}\) \(-4.84378 q^{16}\) \(+6.25317 q^{17}\) \(+1.35459 q^{19}\) \(+2.21203 q^{20}\) \(+1.61392 q^{22}\) \(-2.24451 q^{23}\) \(+8.37924 q^{25}\) \(+4.28207 q^{26}\) \(+0.596126 q^{28}\) \(+4.46976 q^{29}\) \(-4.00805 q^{31}\) \(-3.31383 q^{32}\) \(+10.0921 q^{34}\) \(+3.60560 q^{35}\) \(-1.24458 q^{37}\) \(+2.18620 q^{38}\) \(-8.23665 q^{40}\) \(-6.27870 q^{41}\) \(+0.305238 q^{43}\) \(+0.604750 q^{44}\) \(-3.62247 q^{46}\) \(+10.8096 q^{47}\) \(-6.02832 q^{49}\) \(+13.5235 q^{50}\) \(+1.60452 q^{52}\) \(+10.0242 q^{53}\) \(+3.65776 q^{55}\) \(-2.21971 q^{56}\) \(+7.21386 q^{58}\) \(-8.28564 q^{59}\) \(+1.00000 q^{61}\) \(-6.46869 q^{62}\) \(+4.33928 q^{64}\) \(+9.70479 q^{65}\) \(-15.5138 q^{67}\) \(+3.78160 q^{68}\) \(+5.81917 q^{70}\) \(+8.28871 q^{71}\) \(+8.53532 q^{73}\) \(-2.00866 q^{74}\) \(+0.819186 q^{76}\) \(+0.985739 q^{77}\) \(-13.4999 q^{79}\) \(-17.7174 q^{80}\) \(-10.1333 q^{82}\) \(-4.84293 q^{83}\) \(+22.8726 q^{85}\) \(+0.492631 q^{86}\) \(-2.25183 q^{88}\) \(+15.4360 q^{89}\) \(+2.61537 q^{91}\) \(-1.35737 q^{92}\) \(+17.4459 q^{94}\) \(+4.95476 q^{95}\) \(+10.8187 q^{97}\) \(-9.72925 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61392 1.14122 0.570608 0.821222i \(-0.306708\pi\)
0.570608 + 0.821222i \(0.306708\pi\)
\(3\) 0 0
\(4\) 0.604750 0.302375
\(5\) 3.65776 1.63580 0.817901 0.575359i \(-0.195138\pi\)
0.817901 + 0.575359i \(0.195138\pi\)
\(6\) 0 0
\(7\) 0.985739 0.372574 0.186287 0.982495i \(-0.440355\pi\)
0.186287 + 0.982495i \(0.440355\pi\)
\(8\) −2.25183 −0.796141
\(9\) 0 0
\(10\) 5.90335 1.86680
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 2.65320 0.735866 0.367933 0.929852i \(-0.380066\pi\)
0.367933 + 0.929852i \(0.380066\pi\)
\(14\) 1.59091 0.425188
\(15\) 0 0
\(16\) −4.84378 −1.21094
\(17\) 6.25317 1.51662 0.758308 0.651896i \(-0.226026\pi\)
0.758308 + 0.651896i \(0.226026\pi\)
\(18\) 0 0
\(19\) 1.35459 0.310763 0.155382 0.987855i \(-0.450339\pi\)
0.155382 + 0.987855i \(0.450339\pi\)
\(20\) 2.21203 0.494626
\(21\) 0 0
\(22\) 1.61392 0.344090
\(23\) −2.24451 −0.468012 −0.234006 0.972235i \(-0.575184\pi\)
−0.234006 + 0.972235i \(0.575184\pi\)
\(24\) 0 0
\(25\) 8.37924 1.67585
\(26\) 4.28207 0.839782
\(27\) 0 0
\(28\) 0.596126 0.112657
\(29\) 4.46976 0.830014 0.415007 0.909818i \(-0.363779\pi\)
0.415007 + 0.909818i \(0.363779\pi\)
\(30\) 0 0
\(31\) −4.00805 −0.719867 −0.359934 0.932978i \(-0.617201\pi\)
−0.359934 + 0.932978i \(0.617201\pi\)
\(32\) −3.31383 −0.585808
\(33\) 0 0
\(34\) 10.0921 1.73079
\(35\) 3.60560 0.609458
\(36\) 0 0
\(37\) −1.24458 −0.204608 −0.102304 0.994753i \(-0.532621\pi\)
−0.102304 + 0.994753i \(0.532621\pi\)
\(38\) 2.18620 0.354648
\(39\) 0 0
\(40\) −8.23665 −1.30233
\(41\) −6.27870 −0.980568 −0.490284 0.871563i \(-0.663107\pi\)
−0.490284 + 0.871563i \(0.663107\pi\)
\(42\) 0 0
\(43\) 0.305238 0.0465483 0.0232742 0.999729i \(-0.492591\pi\)
0.0232742 + 0.999729i \(0.492591\pi\)
\(44\) 0.604750 0.0911695
\(45\) 0 0
\(46\) −3.62247 −0.534103
\(47\) 10.8096 1.57675 0.788374 0.615197i \(-0.210923\pi\)
0.788374 + 0.615197i \(0.210923\pi\)
\(48\) 0 0
\(49\) −6.02832 −0.861188
\(50\) 13.5235 1.91251
\(51\) 0 0
\(52\) 1.60452 0.222507
\(53\) 10.0242 1.37693 0.688466 0.725269i \(-0.258285\pi\)
0.688466 + 0.725269i \(0.258285\pi\)
\(54\) 0 0
\(55\) 3.65776 0.493213
\(56\) −2.21971 −0.296622
\(57\) 0 0
\(58\) 7.21386 0.947226
\(59\) −8.28564 −1.07870 −0.539350 0.842082i \(-0.681330\pi\)
−0.539350 + 0.842082i \(0.681330\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) −6.46869 −0.821524
\(63\) 0 0
\(64\) 4.33928 0.542410
\(65\) 9.70479 1.20373
\(66\) 0 0
\(67\) −15.5138 −1.89531 −0.947654 0.319298i \(-0.896553\pi\)
−0.947654 + 0.319298i \(0.896553\pi\)
\(68\) 3.78160 0.458587
\(69\) 0 0
\(70\) 5.81917 0.695524
\(71\) 8.28871 0.983689 0.491845 0.870683i \(-0.336323\pi\)
0.491845 + 0.870683i \(0.336323\pi\)
\(72\) 0 0
\(73\) 8.53532 0.998984 0.499492 0.866319i \(-0.333520\pi\)
0.499492 + 0.866319i \(0.333520\pi\)
\(74\) −2.00866 −0.233502
\(75\) 0 0
\(76\) 0.819186 0.0939670
\(77\) 0.985739 0.112335
\(78\) 0 0
\(79\) −13.4999 −1.51886 −0.759429 0.650590i \(-0.774522\pi\)
−0.759429 + 0.650590i \(0.774522\pi\)
\(80\) −17.7174 −1.98087
\(81\) 0 0
\(82\) −10.1333 −1.11904
\(83\) −4.84293 −0.531581 −0.265790 0.964031i \(-0.585633\pi\)
−0.265790 + 0.964031i \(0.585633\pi\)
\(84\) 0 0
\(85\) 22.8726 2.48088
\(86\) 0.492631 0.0531217
\(87\) 0 0
\(88\) −2.25183 −0.240046
\(89\) 15.4360 1.63621 0.818105 0.575069i \(-0.195025\pi\)
0.818105 + 0.575069i \(0.195025\pi\)
\(90\) 0 0
\(91\) 2.61537 0.274165
\(92\) −1.35737 −0.141515
\(93\) 0 0
\(94\) 17.4459 1.79941
\(95\) 4.95476 0.508347
\(96\) 0 0
\(97\) 10.8187 1.09847 0.549235 0.835668i \(-0.314919\pi\)
0.549235 + 0.835668i \(0.314919\pi\)
\(98\) −9.72925 −0.982802
\(99\) 0 0
\(100\) 5.06735 0.506735
\(101\) −18.5401 −1.84481 −0.922406 0.386221i \(-0.873780\pi\)
−0.922406 + 0.386221i \(0.873780\pi\)
\(102\) 0 0
\(103\) 13.3353 1.31396 0.656982 0.753907i \(-0.271833\pi\)
0.656982 + 0.753907i \(0.271833\pi\)
\(104\) −5.97455 −0.585853
\(105\) 0 0
\(106\) 16.1783 1.57138
\(107\) −12.9262 −1.24962 −0.624811 0.780776i \(-0.714824\pi\)
−0.624811 + 0.780776i \(0.714824\pi\)
\(108\) 0 0
\(109\) 17.1301 1.64077 0.820384 0.571813i \(-0.193760\pi\)
0.820384 + 0.571813i \(0.193760\pi\)
\(110\) 5.90335 0.562863
\(111\) 0 0
\(112\) −4.77470 −0.451167
\(113\) −12.6163 −1.18685 −0.593423 0.804891i \(-0.702224\pi\)
−0.593423 + 0.804891i \(0.702224\pi\)
\(114\) 0 0
\(115\) −8.20988 −0.765576
\(116\) 2.70309 0.250976
\(117\) 0 0
\(118\) −13.3724 −1.23103
\(119\) 6.16399 0.565052
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 1.61392 0.146118
\(123\) 0 0
\(124\) −2.42387 −0.217670
\(125\) 12.3605 1.10555
\(126\) 0 0
\(127\) 14.7816 1.31166 0.655828 0.754910i \(-0.272320\pi\)
0.655828 + 0.754910i \(0.272320\pi\)
\(128\) 13.6309 1.20482
\(129\) 0 0
\(130\) 15.6628 1.37372
\(131\) −12.0226 −1.05042 −0.525210 0.850972i \(-0.676013\pi\)
−0.525210 + 0.850972i \(0.676013\pi\)
\(132\) 0 0
\(133\) 1.33527 0.115782
\(134\) −25.0380 −2.16296
\(135\) 0 0
\(136\) −14.0811 −1.20744
\(137\) 12.6310 1.07914 0.539568 0.841942i \(-0.318587\pi\)
0.539568 + 0.841942i \(0.318587\pi\)
\(138\) 0 0
\(139\) −16.6404 −1.41142 −0.705711 0.708500i \(-0.749372\pi\)
−0.705711 + 0.708500i \(0.749372\pi\)
\(140\) 2.18049 0.184285
\(141\) 0 0
\(142\) 13.3774 1.12260
\(143\) 2.65320 0.221872
\(144\) 0 0
\(145\) 16.3493 1.35774
\(146\) 13.7754 1.14006
\(147\) 0 0
\(148\) −0.752659 −0.0618682
\(149\) 3.29899 0.270264 0.135132 0.990828i \(-0.456854\pi\)
0.135132 + 0.990828i \(0.456854\pi\)
\(150\) 0 0
\(151\) 13.8467 1.12683 0.563413 0.826176i \(-0.309488\pi\)
0.563413 + 0.826176i \(0.309488\pi\)
\(152\) −3.05029 −0.247411
\(153\) 0 0
\(154\) 1.59091 0.128199
\(155\) −14.6605 −1.17756
\(156\) 0 0
\(157\) −5.10610 −0.407512 −0.203756 0.979022i \(-0.565315\pi\)
−0.203756 + 0.979022i \(0.565315\pi\)
\(158\) −21.7878 −1.73335
\(159\) 0 0
\(160\) −12.1212 −0.958267
\(161\) −2.21250 −0.174369
\(162\) 0 0
\(163\) 14.0106 1.09739 0.548696 0.836022i \(-0.315124\pi\)
0.548696 + 0.836022i \(0.315124\pi\)
\(164\) −3.79704 −0.296499
\(165\) 0 0
\(166\) −7.81612 −0.606648
\(167\) 19.1530 1.48210 0.741052 0.671448i \(-0.234327\pi\)
0.741052 + 0.671448i \(0.234327\pi\)
\(168\) 0 0
\(169\) −5.96052 −0.458502
\(170\) 36.9147 2.83123
\(171\) 0 0
\(172\) 0.184593 0.0140751
\(173\) 22.4432 1.70632 0.853161 0.521647i \(-0.174682\pi\)
0.853161 + 0.521647i \(0.174682\pi\)
\(174\) 0 0
\(175\) 8.25975 0.624378
\(176\) −4.84378 −0.365113
\(177\) 0 0
\(178\) 24.9125 1.86727
\(179\) −13.1373 −0.981927 −0.490964 0.871180i \(-0.663355\pi\)
−0.490964 + 0.871180i \(0.663355\pi\)
\(180\) 0 0
\(181\) 7.41628 0.551247 0.275624 0.961266i \(-0.411116\pi\)
0.275624 + 0.961266i \(0.411116\pi\)
\(182\) 4.22100 0.312881
\(183\) 0 0
\(184\) 5.05425 0.372604
\(185\) −4.55238 −0.334698
\(186\) 0 0
\(187\) 6.25317 0.457277
\(188\) 6.53713 0.476769
\(189\) 0 0
\(190\) 7.99660 0.580134
\(191\) 6.22085 0.450125 0.225063 0.974344i \(-0.427741\pi\)
0.225063 + 0.974344i \(0.427741\pi\)
\(192\) 0 0
\(193\) −1.95576 −0.140779 −0.0703893 0.997520i \(-0.522424\pi\)
−0.0703893 + 0.997520i \(0.522424\pi\)
\(194\) 17.4605 1.25359
\(195\) 0 0
\(196\) −3.64563 −0.260402
\(197\) −27.6283 −1.96843 −0.984217 0.176968i \(-0.943371\pi\)
−0.984217 + 0.176968i \(0.943371\pi\)
\(198\) 0 0
\(199\) −3.84659 −0.272678 −0.136339 0.990662i \(-0.543534\pi\)
−0.136339 + 0.990662i \(0.543534\pi\)
\(200\) −18.8686 −1.33421
\(201\) 0 0
\(202\) −29.9224 −2.10533
\(203\) 4.40602 0.309242
\(204\) 0 0
\(205\) −22.9660 −1.60402
\(206\) 21.5221 1.49952
\(207\) 0 0
\(208\) −12.8515 −0.891093
\(209\) 1.35459 0.0936987
\(210\) 0 0
\(211\) −11.4958 −0.791405 −0.395703 0.918379i \(-0.629499\pi\)
−0.395703 + 0.918379i \(0.629499\pi\)
\(212\) 6.06214 0.416350
\(213\) 0 0
\(214\) −20.8619 −1.42609
\(215\) 1.11649 0.0761439
\(216\) 0 0
\(217\) −3.95089 −0.268204
\(218\) 27.6467 1.87247
\(219\) 0 0
\(220\) 2.21203 0.149135
\(221\) 16.5909 1.11603
\(222\) 0 0
\(223\) 9.82324 0.657813 0.328906 0.944363i \(-0.393320\pi\)
0.328906 + 0.944363i \(0.393320\pi\)
\(224\) −3.26658 −0.218257
\(225\) 0 0
\(226\) −20.3618 −1.35445
\(227\) −12.7593 −0.846867 −0.423433 0.905927i \(-0.639175\pi\)
−0.423433 + 0.905927i \(0.639175\pi\)
\(228\) 0 0
\(229\) 10.6052 0.700808 0.350404 0.936599i \(-0.386044\pi\)
0.350404 + 0.936599i \(0.386044\pi\)
\(230\) −13.2501 −0.873688
\(231\) 0 0
\(232\) −10.0651 −0.660809
\(233\) −23.6060 −1.54648 −0.773239 0.634115i \(-0.781365\pi\)
−0.773239 + 0.634115i \(0.781365\pi\)
\(234\) 0 0
\(235\) 39.5391 2.57925
\(236\) −5.01074 −0.326172
\(237\) 0 0
\(238\) 9.94822 0.644847
\(239\) 7.79900 0.504476 0.252238 0.967665i \(-0.418833\pi\)
0.252238 + 0.967665i \(0.418833\pi\)
\(240\) 0 0
\(241\) −14.4302 −0.929531 −0.464766 0.885434i \(-0.653861\pi\)
−0.464766 + 0.885434i \(0.653861\pi\)
\(242\) 1.61392 0.103747
\(243\) 0 0
\(244\) 0.604750 0.0387151
\(245\) −22.0502 −1.40873
\(246\) 0 0
\(247\) 3.59399 0.228680
\(248\) 9.02544 0.573116
\(249\) 0 0
\(250\) 19.9489 1.26168
\(251\) −27.7902 −1.75410 −0.877050 0.480399i \(-0.840492\pi\)
−0.877050 + 0.480399i \(0.840492\pi\)
\(252\) 0 0
\(253\) −2.24451 −0.141111
\(254\) 23.8564 1.49688
\(255\) 0 0
\(256\) 13.3207 0.832545
\(257\) −1.48481 −0.0926199 −0.0463100 0.998927i \(-0.514746\pi\)
−0.0463100 + 0.998927i \(0.514746\pi\)
\(258\) 0 0
\(259\) −1.22683 −0.0762316
\(260\) 5.86897 0.363978
\(261\) 0 0
\(262\) −19.4036 −1.19876
\(263\) 1.16715 0.0719693 0.0359847 0.999352i \(-0.488543\pi\)
0.0359847 + 0.999352i \(0.488543\pi\)
\(264\) 0 0
\(265\) 36.6662 2.25239
\(266\) 2.15502 0.132133
\(267\) 0 0
\(268\) −9.38195 −0.573094
\(269\) −26.7060 −1.62829 −0.814147 0.580659i \(-0.802795\pi\)
−0.814147 + 0.580659i \(0.802795\pi\)
\(270\) 0 0
\(271\) 2.63024 0.159776 0.0798879 0.996804i \(-0.474544\pi\)
0.0798879 + 0.996804i \(0.474544\pi\)
\(272\) −30.2890 −1.83654
\(273\) 0 0
\(274\) 20.3854 1.23153
\(275\) 8.37924 0.505287
\(276\) 0 0
\(277\) −7.34527 −0.441335 −0.220667 0.975349i \(-0.570824\pi\)
−0.220667 + 0.975349i \(0.570824\pi\)
\(278\) −26.8564 −1.61074
\(279\) 0 0
\(280\) −8.11919 −0.485215
\(281\) −6.09887 −0.363828 −0.181914 0.983314i \(-0.558229\pi\)
−0.181914 + 0.983314i \(0.558229\pi\)
\(282\) 0 0
\(283\) 22.2465 1.32242 0.661209 0.750202i \(-0.270044\pi\)
0.661209 + 0.750202i \(0.270044\pi\)
\(284\) 5.01260 0.297443
\(285\) 0 0
\(286\) 4.28207 0.253204
\(287\) −6.18916 −0.365335
\(288\) 0 0
\(289\) 22.1021 1.30013
\(290\) 26.3866 1.54947
\(291\) 0 0
\(292\) 5.16173 0.302068
\(293\) 7.69309 0.449435 0.224718 0.974424i \(-0.427854\pi\)
0.224718 + 0.974424i \(0.427854\pi\)
\(294\) 0 0
\(295\) −30.3069 −1.76454
\(296\) 2.80258 0.162897
\(297\) 0 0
\(298\) 5.32431 0.308429
\(299\) −5.95513 −0.344394
\(300\) 0 0
\(301\) 0.300885 0.0173427
\(302\) 22.3475 1.28595
\(303\) 0 0
\(304\) −6.56131 −0.376317
\(305\) 3.65776 0.209443
\(306\) 0 0
\(307\) 10.6159 0.605879 0.302939 0.953010i \(-0.402032\pi\)
0.302939 + 0.953010i \(0.402032\pi\)
\(308\) 0.596126 0.0339674
\(309\) 0 0
\(310\) −23.6609 −1.34385
\(311\) 34.2582 1.94261 0.971303 0.237847i \(-0.0764417\pi\)
0.971303 + 0.237847i \(0.0764417\pi\)
\(312\) 0 0
\(313\) 6.50686 0.367789 0.183895 0.982946i \(-0.441129\pi\)
0.183895 + 0.982946i \(0.441129\pi\)
\(314\) −8.24086 −0.465059
\(315\) 0 0
\(316\) −8.16407 −0.459265
\(317\) −8.11911 −0.456015 −0.228007 0.973659i \(-0.573221\pi\)
−0.228007 + 0.973659i \(0.573221\pi\)
\(318\) 0 0
\(319\) 4.46976 0.250259
\(320\) 15.8721 0.887276
\(321\) 0 0
\(322\) −3.57081 −0.198993
\(323\) 8.47045 0.471309
\(324\) 0 0
\(325\) 22.2318 1.23320
\(326\) 22.6120 1.25236
\(327\) 0 0
\(328\) 14.1385 0.780671
\(329\) 10.6555 0.587456
\(330\) 0 0
\(331\) −31.4323 −1.72768 −0.863839 0.503768i \(-0.831947\pi\)
−0.863839 + 0.503768i \(0.831947\pi\)
\(332\) −2.92876 −0.160737
\(333\) 0 0
\(334\) 30.9115 1.69140
\(335\) −56.7457 −3.10035
\(336\) 0 0
\(337\) −18.6087 −1.01368 −0.506841 0.862040i \(-0.669187\pi\)
−0.506841 + 0.862040i \(0.669187\pi\)
\(338\) −9.61982 −0.523249
\(339\) 0 0
\(340\) 13.8322 0.750157
\(341\) −4.00805 −0.217048
\(342\) 0 0
\(343\) −12.8425 −0.693431
\(344\) −0.687343 −0.0370591
\(345\) 0 0
\(346\) 36.2216 1.94728
\(347\) 4.39085 0.235713 0.117856 0.993031i \(-0.462398\pi\)
0.117856 + 0.993031i \(0.462398\pi\)
\(348\) 0 0
\(349\) 20.5921 1.10227 0.551134 0.834417i \(-0.314195\pi\)
0.551134 + 0.834417i \(0.314195\pi\)
\(350\) 13.3306 0.712551
\(351\) 0 0
\(352\) −3.31383 −0.176628
\(353\) 8.31752 0.442697 0.221348 0.975195i \(-0.428954\pi\)
0.221348 + 0.975195i \(0.428954\pi\)
\(354\) 0 0
\(355\) 30.3182 1.60912
\(356\) 9.33490 0.494749
\(357\) 0 0
\(358\) −21.2026 −1.12059
\(359\) −15.5845 −0.822520 −0.411260 0.911518i \(-0.634911\pi\)
−0.411260 + 0.911518i \(0.634911\pi\)
\(360\) 0 0
\(361\) −17.1651 −0.903426
\(362\) 11.9693 0.629093
\(363\) 0 0
\(364\) 1.58164 0.0829006
\(365\) 31.2202 1.63414
\(366\) 0 0
\(367\) 10.5398 0.550175 0.275088 0.961419i \(-0.411293\pi\)
0.275088 + 0.961419i \(0.411293\pi\)
\(368\) 10.8719 0.566737
\(369\) 0 0
\(370\) −7.34719 −0.381962
\(371\) 9.88126 0.513009
\(372\) 0 0
\(373\) 19.3765 1.00328 0.501638 0.865078i \(-0.332731\pi\)
0.501638 + 0.865078i \(0.332731\pi\)
\(374\) 10.0921 0.521852
\(375\) 0 0
\(376\) −24.3414 −1.25531
\(377\) 11.8592 0.610779
\(378\) 0 0
\(379\) −6.66214 −0.342211 −0.171106 0.985253i \(-0.554734\pi\)
−0.171106 + 0.985253i \(0.554734\pi\)
\(380\) 2.99639 0.153711
\(381\) 0 0
\(382\) 10.0400 0.513690
\(383\) −18.7882 −0.960031 −0.480016 0.877260i \(-0.659369\pi\)
−0.480016 + 0.877260i \(0.659369\pi\)
\(384\) 0 0
\(385\) 3.60560 0.183759
\(386\) −3.15645 −0.160659
\(387\) 0 0
\(388\) 6.54259 0.332150
\(389\) 21.2173 1.07576 0.537880 0.843021i \(-0.319225\pi\)
0.537880 + 0.843021i \(0.319225\pi\)
\(390\) 0 0
\(391\) −14.0353 −0.709795
\(392\) 13.5747 0.685627
\(393\) 0 0
\(394\) −44.5899 −2.24641
\(395\) −49.3795 −2.48455
\(396\) 0 0
\(397\) −1.82400 −0.0915440 −0.0457720 0.998952i \(-0.514575\pi\)
−0.0457720 + 0.998952i \(0.514575\pi\)
\(398\) −6.20810 −0.311184
\(399\) 0 0
\(400\) −40.5872 −2.02936
\(401\) −18.6265 −0.930164 −0.465082 0.885268i \(-0.653975\pi\)
−0.465082 + 0.885268i \(0.653975\pi\)
\(402\) 0 0
\(403\) −10.6342 −0.529726
\(404\) −11.2121 −0.557825
\(405\) 0 0
\(406\) 7.11098 0.352912
\(407\) −1.24458 −0.0616915
\(408\) 0 0
\(409\) −28.3454 −1.40159 −0.700795 0.713362i \(-0.747171\pi\)
−0.700795 + 0.713362i \(0.747171\pi\)
\(410\) −37.0654 −1.83053
\(411\) 0 0
\(412\) 8.06450 0.397310
\(413\) −8.16749 −0.401896
\(414\) 0 0
\(415\) −17.7143 −0.869561
\(416\) −8.79227 −0.431076
\(417\) 0 0
\(418\) 2.18620 0.106930
\(419\) −14.0074 −0.684307 −0.342154 0.939644i \(-0.611156\pi\)
−0.342154 + 0.939644i \(0.611156\pi\)
\(420\) 0 0
\(421\) −0.242484 −0.0118180 −0.00590898 0.999983i \(-0.501881\pi\)
−0.00590898 + 0.999983i \(0.501881\pi\)
\(422\) −18.5534 −0.903165
\(423\) 0 0
\(424\) −22.5728 −1.09623
\(425\) 52.3968 2.54162
\(426\) 0 0
\(427\) 0.985739 0.0477033
\(428\) −7.81712 −0.377855
\(429\) 0 0
\(430\) 1.80193 0.0868967
\(431\) 20.9192 1.00764 0.503822 0.863807i \(-0.331927\pi\)
0.503822 + 0.863807i \(0.331927\pi\)
\(432\) 0 0
\(433\) 38.5719 1.85364 0.926822 0.375500i \(-0.122529\pi\)
0.926822 + 0.375500i \(0.122529\pi\)
\(434\) −6.37644 −0.306079
\(435\) 0 0
\(436\) 10.3594 0.496127
\(437\) −3.04038 −0.145441
\(438\) 0 0
\(439\) −7.54989 −0.360337 −0.180168 0.983636i \(-0.557664\pi\)
−0.180168 + 0.983636i \(0.557664\pi\)
\(440\) −8.23665 −0.392667
\(441\) 0 0
\(442\) 26.7765 1.27363
\(443\) 7.89709 0.375202 0.187601 0.982245i \(-0.439929\pi\)
0.187601 + 0.982245i \(0.439929\pi\)
\(444\) 0 0
\(445\) 56.4611 2.67651
\(446\) 15.8540 0.750707
\(447\) 0 0
\(448\) 4.27740 0.202088
\(449\) −21.7371 −1.02584 −0.512919 0.858437i \(-0.671436\pi\)
−0.512919 + 0.858437i \(0.671436\pi\)
\(450\) 0 0
\(451\) −6.27870 −0.295652
\(452\) −7.62973 −0.358872
\(453\) 0 0
\(454\) −20.5926 −0.966458
\(455\) 9.56639 0.448479
\(456\) 0 0
\(457\) −17.7422 −0.829943 −0.414972 0.909834i \(-0.636209\pi\)
−0.414972 + 0.909834i \(0.636209\pi\)
\(458\) 17.1159 0.799774
\(459\) 0 0
\(460\) −4.96493 −0.231491
\(461\) 5.74408 0.267529 0.133764 0.991013i \(-0.457294\pi\)
0.133764 + 0.991013i \(0.457294\pi\)
\(462\) 0 0
\(463\) 11.0072 0.511550 0.255775 0.966736i \(-0.417669\pi\)
0.255775 + 0.966736i \(0.417669\pi\)
\(464\) −21.6505 −1.00510
\(465\) 0 0
\(466\) −38.0982 −1.76487
\(467\) −20.3504 −0.941704 −0.470852 0.882212i \(-0.656053\pi\)
−0.470852 + 0.882212i \(0.656053\pi\)
\(468\) 0 0
\(469\) −15.2925 −0.706144
\(470\) 63.8131 2.94348
\(471\) 0 0
\(472\) 18.6578 0.858797
\(473\) 0.305238 0.0140349
\(474\) 0 0
\(475\) 11.3504 0.520792
\(476\) 3.72768 0.170858
\(477\) 0 0
\(478\) 12.5870 0.575716
\(479\) −18.4382 −0.842463 −0.421232 0.906953i \(-0.638402\pi\)
−0.421232 + 0.906953i \(0.638402\pi\)
\(480\) 0 0
\(481\) −3.30212 −0.150564
\(482\) −23.2892 −1.06080
\(483\) 0 0
\(484\) 0.604750 0.0274886
\(485\) 39.5721 1.79688
\(486\) 0 0
\(487\) 5.57853 0.252787 0.126394 0.991980i \(-0.459660\pi\)
0.126394 + 0.991980i \(0.459660\pi\)
\(488\) −2.25183 −0.101935
\(489\) 0 0
\(490\) −35.5873 −1.60767
\(491\) −18.1802 −0.820461 −0.410231 0.911982i \(-0.634552\pi\)
−0.410231 + 0.911982i \(0.634552\pi\)
\(492\) 0 0
\(493\) 27.9502 1.25881
\(494\) 5.80043 0.260973
\(495\) 0 0
\(496\) 19.4141 0.871719
\(497\) 8.17051 0.366498
\(498\) 0 0
\(499\) −10.6130 −0.475104 −0.237552 0.971375i \(-0.576345\pi\)
−0.237552 + 0.971375i \(0.576345\pi\)
\(500\) 7.47500 0.334292
\(501\) 0 0
\(502\) −44.8512 −2.00181
\(503\) −34.9625 −1.55890 −0.779449 0.626465i \(-0.784501\pi\)
−0.779449 + 0.626465i \(0.784501\pi\)
\(504\) 0 0
\(505\) −67.8155 −3.01775
\(506\) −3.62247 −0.161038
\(507\) 0 0
\(508\) 8.93918 0.396612
\(509\) −10.0360 −0.444838 −0.222419 0.974951i \(-0.571395\pi\)
−0.222419 + 0.974951i \(0.571395\pi\)
\(510\) 0 0
\(511\) 8.41360 0.372196
\(512\) −5.76323 −0.254701
\(513\) 0 0
\(514\) −2.39637 −0.105699
\(515\) 48.7773 2.14938
\(516\) 0 0
\(517\) 10.8096 0.475407
\(518\) −1.98001 −0.0869967
\(519\) 0 0
\(520\) −21.8535 −0.958340
\(521\) 34.0373 1.49120 0.745601 0.666393i \(-0.232163\pi\)
0.745601 + 0.666393i \(0.232163\pi\)
\(522\) 0 0
\(523\) −0.293817 −0.0128477 −0.00642386 0.999979i \(-0.502045\pi\)
−0.00642386 + 0.999979i \(0.502045\pi\)
\(524\) −7.27067 −0.317621
\(525\) 0 0
\(526\) 1.88369 0.0821326
\(527\) −25.0630 −1.09176
\(528\) 0 0
\(529\) −17.9622 −0.780964
\(530\) 59.1765 2.57046
\(531\) 0 0
\(532\) 0.807504 0.0350097
\(533\) −16.6587 −0.721567
\(534\) 0 0
\(535\) −47.2810 −2.04414
\(536\) 34.9343 1.50893
\(537\) 0 0
\(538\) −43.1014 −1.85824
\(539\) −6.02832 −0.259658
\(540\) 0 0
\(541\) −35.6219 −1.53151 −0.765753 0.643134i \(-0.777634\pi\)
−0.765753 + 0.643134i \(0.777634\pi\)
\(542\) 4.24501 0.182339
\(543\) 0 0
\(544\) −20.7220 −0.888447
\(545\) 62.6580 2.68397
\(546\) 0 0
\(547\) 43.3050 1.85159 0.925794 0.378029i \(-0.123398\pi\)
0.925794 + 0.378029i \(0.123398\pi\)
\(548\) 7.63858 0.326304
\(549\) 0 0
\(550\) 13.5235 0.576642
\(551\) 6.05468 0.257938
\(552\) 0 0
\(553\) −13.3074 −0.565888
\(554\) −11.8547 −0.503658
\(555\) 0 0
\(556\) −10.0633 −0.426779
\(557\) −23.9291 −1.01391 −0.506954 0.861973i \(-0.669229\pi\)
−0.506954 + 0.861973i \(0.669229\pi\)
\(558\) 0 0
\(559\) 0.809858 0.0342533
\(560\) −17.4647 −0.738020
\(561\) 0 0
\(562\) −9.84310 −0.415206
\(563\) −6.09496 −0.256872 −0.128436 0.991718i \(-0.540996\pi\)
−0.128436 + 0.991718i \(0.540996\pi\)
\(564\) 0 0
\(565\) −46.1476 −1.94144
\(566\) 35.9042 1.50917
\(567\) 0 0
\(568\) −18.6648 −0.783156
\(569\) 11.4324 0.479271 0.239635 0.970863i \(-0.422972\pi\)
0.239635 + 0.970863i \(0.422972\pi\)
\(570\) 0 0
\(571\) 4.26007 0.178278 0.0891392 0.996019i \(-0.471588\pi\)
0.0891392 + 0.996019i \(0.471588\pi\)
\(572\) 1.60452 0.0670885
\(573\) 0 0
\(574\) −9.98884 −0.416926
\(575\) −18.8073 −0.784318
\(576\) 0 0
\(577\) 31.0517 1.29270 0.646351 0.763041i \(-0.276294\pi\)
0.646351 + 0.763041i \(0.276294\pi\)
\(578\) 35.6711 1.48372
\(579\) 0 0
\(580\) 9.88726 0.410546
\(581\) −4.77387 −0.198053
\(582\) 0 0
\(583\) 10.0242 0.415160
\(584\) −19.2201 −0.795332
\(585\) 0 0
\(586\) 12.4161 0.512903
\(587\) −12.7689 −0.527030 −0.263515 0.964655i \(-0.584882\pi\)
−0.263515 + 0.964655i \(0.584882\pi\)
\(588\) 0 0
\(589\) −5.42925 −0.223708
\(590\) −48.9131 −2.01372
\(591\) 0 0
\(592\) 6.02847 0.247768
\(593\) 20.4992 0.841800 0.420900 0.907107i \(-0.361714\pi\)
0.420900 + 0.907107i \(0.361714\pi\)
\(594\) 0 0
\(595\) 22.5464 0.924314
\(596\) 1.99506 0.0817209
\(597\) 0 0
\(598\) −9.61113 −0.393028
\(599\) −4.42860 −0.180948 −0.0904739 0.995899i \(-0.528838\pi\)
−0.0904739 + 0.995899i \(0.528838\pi\)
\(600\) 0 0
\(601\) 1.08793 0.0443774 0.0221887 0.999754i \(-0.492937\pi\)
0.0221887 + 0.999754i \(0.492937\pi\)
\(602\) 0.485605 0.0197918
\(603\) 0 0
\(604\) 8.37377 0.340724
\(605\) 3.65776 0.148709
\(606\) 0 0
\(607\) 1.52522 0.0619067 0.0309534 0.999521i \(-0.490146\pi\)
0.0309534 + 0.999521i \(0.490146\pi\)
\(608\) −4.48887 −0.182048
\(609\) 0 0
\(610\) 5.90335 0.239020
\(611\) 28.6801 1.16027
\(612\) 0 0
\(613\) 23.3564 0.943356 0.471678 0.881771i \(-0.343648\pi\)
0.471678 + 0.881771i \(0.343648\pi\)
\(614\) 17.1332 0.691439
\(615\) 0 0
\(616\) −2.21971 −0.0894348
\(617\) −34.2890 −1.38042 −0.690211 0.723608i \(-0.742482\pi\)
−0.690211 + 0.723608i \(0.742482\pi\)
\(618\) 0 0
\(619\) −9.90023 −0.397924 −0.198962 0.980007i \(-0.563757\pi\)
−0.198962 + 0.980007i \(0.563757\pi\)
\(620\) −8.86594 −0.356065
\(621\) 0 0
\(622\) 55.2901 2.21693
\(623\) 15.2158 0.609610
\(624\) 0 0
\(625\) 3.31550 0.132620
\(626\) 10.5016 0.419727
\(627\) 0 0
\(628\) −3.08792 −0.123221
\(629\) −7.78257 −0.310311
\(630\) 0 0
\(631\) −12.6953 −0.505390 −0.252695 0.967546i \(-0.581317\pi\)
−0.252695 + 0.967546i \(0.581317\pi\)
\(632\) 30.3995 1.20923
\(633\) 0 0
\(634\) −13.1036 −0.520412
\(635\) 54.0677 2.14561
\(636\) 0 0
\(637\) −15.9943 −0.633719
\(638\) 7.21386 0.285599
\(639\) 0 0
\(640\) 49.8588 1.97084
\(641\) −14.9145 −0.589087 −0.294544 0.955638i \(-0.595168\pi\)
−0.294544 + 0.955638i \(0.595168\pi\)
\(642\) 0 0
\(643\) −20.7823 −0.819576 −0.409788 0.912181i \(-0.634397\pi\)
−0.409788 + 0.912181i \(0.634397\pi\)
\(644\) −1.33801 −0.0527250
\(645\) 0 0
\(646\) 13.6707 0.537865
\(647\) −2.22546 −0.0874919 −0.0437460 0.999043i \(-0.513929\pi\)
−0.0437460 + 0.999043i \(0.513929\pi\)
\(648\) 0 0
\(649\) −8.28564 −0.325240
\(650\) 35.8805 1.40735
\(651\) 0 0
\(652\) 8.47289 0.331824
\(653\) 11.3494 0.444135 0.222068 0.975031i \(-0.428719\pi\)
0.222068 + 0.975031i \(0.428719\pi\)
\(654\) 0 0
\(655\) −43.9759 −1.71828
\(656\) 30.4126 1.18741
\(657\) 0 0
\(658\) 17.1971 0.670414
\(659\) −1.23695 −0.0481847 −0.0240923 0.999710i \(-0.507670\pi\)
−0.0240923 + 0.999710i \(0.507670\pi\)
\(660\) 0 0
\(661\) 34.0520 1.32447 0.662234 0.749297i \(-0.269608\pi\)
0.662234 + 0.749297i \(0.269608\pi\)
\(662\) −50.7294 −1.97165
\(663\) 0 0
\(664\) 10.9054 0.423213
\(665\) 4.88410 0.189397
\(666\) 0 0
\(667\) −10.0324 −0.388457
\(668\) 11.5828 0.448151
\(669\) 0 0
\(670\) −91.5833 −3.53817
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) 17.1078 0.659456 0.329728 0.944076i \(-0.393043\pi\)
0.329728 + 0.944076i \(0.393043\pi\)
\(674\) −30.0331 −1.15683
\(675\) 0 0
\(676\) −3.60462 −0.138639
\(677\) −18.9338 −0.727687 −0.363843 0.931460i \(-0.618536\pi\)
−0.363843 + 0.931460i \(0.618536\pi\)
\(678\) 0 0
\(679\) 10.6644 0.409262
\(680\) −51.5052 −1.97513
\(681\) 0 0
\(682\) −6.46869 −0.247699
\(683\) −34.1390 −1.30629 −0.653146 0.757232i \(-0.726551\pi\)
−0.653146 + 0.757232i \(0.726551\pi\)
\(684\) 0 0
\(685\) 46.2011 1.76525
\(686\) −20.7269 −0.791355
\(687\) 0 0
\(688\) −1.47850 −0.0563675
\(689\) 26.5963 1.01324
\(690\) 0 0
\(691\) 4.19429 0.159558 0.0797792 0.996813i \(-0.474578\pi\)
0.0797792 + 0.996813i \(0.474578\pi\)
\(692\) 13.5725 0.515949
\(693\) 0 0
\(694\) 7.08649 0.268999
\(695\) −60.8668 −2.30881
\(696\) 0 0
\(697\) −39.2618 −1.48715
\(698\) 33.2340 1.25793
\(699\) 0 0
\(700\) 4.99508 0.188796
\(701\) 44.7848 1.69150 0.845749 0.533581i \(-0.179154\pi\)
0.845749 + 0.533581i \(0.179154\pi\)
\(702\) 0 0
\(703\) −1.68589 −0.0635845
\(704\) 4.33928 0.163543
\(705\) 0 0
\(706\) 13.4238 0.505213
\(707\) −18.2757 −0.687330
\(708\) 0 0
\(709\) −45.6124 −1.71301 −0.856504 0.516140i \(-0.827369\pi\)
−0.856504 + 0.516140i \(0.827369\pi\)
\(710\) 48.9312 1.83636
\(711\) 0 0
\(712\) −34.7591 −1.30265
\(713\) 8.99610 0.336907
\(714\) 0 0
\(715\) 9.70479 0.362939
\(716\) −7.94478 −0.296910
\(717\) 0 0
\(718\) −25.1523 −0.938674
\(719\) −27.9564 −1.04260 −0.521299 0.853374i \(-0.674552\pi\)
−0.521299 + 0.853374i \(0.674552\pi\)
\(720\) 0 0
\(721\) 13.1451 0.489549
\(722\) −27.7032 −1.03100
\(723\) 0 0
\(724\) 4.48499 0.166683
\(725\) 37.4532 1.39098
\(726\) 0 0
\(727\) 34.9140 1.29489 0.647445 0.762112i \(-0.275837\pi\)
0.647445 + 0.762112i \(0.275837\pi\)
\(728\) −5.88935 −0.218274
\(729\) 0 0
\(730\) 50.3870 1.86491
\(731\) 1.90870 0.0705960
\(732\) 0 0
\(733\) 27.5891 1.01903 0.509514 0.860462i \(-0.329825\pi\)
0.509514 + 0.860462i \(0.329825\pi\)
\(734\) 17.0105 0.627869
\(735\) 0 0
\(736\) 7.43793 0.274166
\(737\) −15.5138 −0.571457
\(738\) 0 0
\(739\) −35.9604 −1.32282 −0.661412 0.750023i \(-0.730042\pi\)
−0.661412 + 0.750023i \(0.730042\pi\)
\(740\) −2.75305 −0.101204
\(741\) 0 0
\(742\) 15.9476 0.585455
\(743\) −47.0587 −1.72642 −0.863208 0.504849i \(-0.831548\pi\)
−0.863208 + 0.504849i \(0.831548\pi\)
\(744\) 0 0
\(745\) 12.0669 0.442098
\(746\) 31.2722 1.14495
\(747\) 0 0
\(748\) 3.78160 0.138269
\(749\) −12.7419 −0.465577
\(750\) 0 0
\(751\) 3.48808 0.127282 0.0636410 0.997973i \(-0.479729\pi\)
0.0636410 + 0.997973i \(0.479729\pi\)
\(752\) −52.3595 −1.90935
\(753\) 0 0
\(754\) 19.1398 0.697031
\(755\) 50.6478 1.84326
\(756\) 0 0
\(757\) −20.7003 −0.752364 −0.376182 0.926546i \(-0.622763\pi\)
−0.376182 + 0.926546i \(0.622763\pi\)
\(758\) −10.7522 −0.390537
\(759\) 0 0
\(760\) −11.1573 −0.404716
\(761\) −19.3864 −0.702756 −0.351378 0.936234i \(-0.614287\pi\)
−0.351378 + 0.936234i \(0.614287\pi\)
\(762\) 0 0
\(763\) 16.8858 0.611308
\(764\) 3.76206 0.136107
\(765\) 0 0
\(766\) −30.3227 −1.09560
\(767\) −21.9835 −0.793778
\(768\) 0 0
\(769\) 42.9108 1.54740 0.773702 0.633549i \(-0.218403\pi\)
0.773702 + 0.633549i \(0.218403\pi\)
\(770\) 5.81917 0.209708
\(771\) 0 0
\(772\) −1.18275 −0.0425679
\(773\) 8.56024 0.307890 0.153945 0.988079i \(-0.450802\pi\)
0.153945 + 0.988079i \(0.450802\pi\)
\(774\) 0 0
\(775\) −33.5844 −1.20639
\(776\) −24.3618 −0.874537
\(777\) 0 0
\(778\) 34.2431 1.22768
\(779\) −8.50504 −0.304725
\(780\) 0 0
\(781\) 8.28871 0.296594
\(782\) −22.6519 −0.810030
\(783\) 0 0
\(784\) 29.1998 1.04285
\(785\) −18.6769 −0.666608
\(786\) 0 0
\(787\) 6.09934 0.217418 0.108709 0.994074i \(-0.465328\pi\)
0.108709 + 0.994074i \(0.465328\pi\)
\(788\) −16.7082 −0.595205
\(789\) 0 0
\(790\) −79.6947 −2.83541
\(791\) −12.4364 −0.442188
\(792\) 0 0
\(793\) 2.65320 0.0942180
\(794\) −2.94380 −0.104471
\(795\) 0 0
\(796\) −2.32623 −0.0824509
\(797\) −17.6881 −0.626546 −0.313273 0.949663i \(-0.601425\pi\)
−0.313273 + 0.949663i \(0.601425\pi\)
\(798\) 0 0
\(799\) 67.5945 2.39132
\(800\) −27.7674 −0.981726
\(801\) 0 0
\(802\) −30.0618 −1.06152
\(803\) 8.53532 0.301205
\(804\) 0 0
\(805\) −8.09281 −0.285234
\(806\) −17.1627 −0.604532
\(807\) 0 0
\(808\) 41.7492 1.46873
\(809\) 3.78295 0.133001 0.0665007 0.997786i \(-0.478817\pi\)
0.0665007 + 0.997786i \(0.478817\pi\)
\(810\) 0 0
\(811\) 48.6839 1.70952 0.854761 0.519021i \(-0.173703\pi\)
0.854761 + 0.519021i \(0.173703\pi\)
\(812\) 2.66454 0.0935071
\(813\) 0 0
\(814\) −2.00866 −0.0704034
\(815\) 51.2474 1.79512
\(816\) 0 0
\(817\) 0.413471 0.0144655
\(818\) −45.7473 −1.59952
\(819\) 0 0
\(820\) −13.8887 −0.485014
\(821\) 15.5709 0.543429 0.271714 0.962378i \(-0.412409\pi\)
0.271714 + 0.962378i \(0.412409\pi\)
\(822\) 0 0
\(823\) −23.6529 −0.824487 −0.412244 0.911074i \(-0.635255\pi\)
−0.412244 + 0.911074i \(0.635255\pi\)
\(824\) −30.0287 −1.04610
\(825\) 0 0
\(826\) −13.1817 −0.458650
\(827\) 24.0287 0.835560 0.417780 0.908548i \(-0.362808\pi\)
0.417780 + 0.908548i \(0.362808\pi\)
\(828\) 0 0
\(829\) −40.8171 −1.41764 −0.708818 0.705391i \(-0.750771\pi\)
−0.708818 + 0.705391i \(0.750771\pi\)
\(830\) −28.5895 −0.992357
\(831\) 0 0
\(832\) 11.5130 0.399141
\(833\) −37.6961 −1.30609
\(834\) 0 0
\(835\) 70.0572 2.42443
\(836\) 0.819186 0.0283321
\(837\) 0 0
\(838\) −22.6069 −0.780943
\(839\) −15.1758 −0.523927 −0.261963 0.965078i \(-0.584370\pi\)
−0.261963 + 0.965078i \(0.584370\pi\)
\(840\) 0 0
\(841\) −9.02121 −0.311076
\(842\) −0.391351 −0.0134868
\(843\) 0 0
\(844\) −6.95210 −0.239301
\(845\) −21.8022 −0.750018
\(846\) 0 0
\(847\) 0.985739 0.0338704
\(848\) −48.5551 −1.66739
\(849\) 0 0
\(850\) 84.5645 2.90054
\(851\) 2.79347 0.0957589
\(852\) 0 0
\(853\) 2.51030 0.0859511 0.0429756 0.999076i \(-0.486316\pi\)
0.0429756 + 0.999076i \(0.486316\pi\)
\(854\) 1.59091 0.0544398
\(855\) 0 0
\(856\) 29.1076 0.994876
\(857\) 30.5364 1.04310 0.521552 0.853219i \(-0.325353\pi\)
0.521552 + 0.853219i \(0.325353\pi\)
\(858\) 0 0
\(859\) 10.4340 0.356003 0.178001 0.984030i \(-0.443037\pi\)
0.178001 + 0.984030i \(0.443037\pi\)
\(860\) 0.675196 0.0230240
\(861\) 0 0
\(862\) 33.7621 1.14994
\(863\) −7.19925 −0.245065 −0.122533 0.992464i \(-0.539102\pi\)
−0.122533 + 0.992464i \(0.539102\pi\)
\(864\) 0 0
\(865\) 82.0918 2.79121
\(866\) 62.2520 2.11541
\(867\) 0 0
\(868\) −2.38930 −0.0810982
\(869\) −13.4999 −0.457953
\(870\) 0 0
\(871\) −41.1612 −1.39469
\(872\) −38.5741 −1.30628
\(873\) 0 0
\(874\) −4.90694 −0.165980
\(875\) 12.1842 0.411901
\(876\) 0 0
\(877\) −26.2304 −0.885738 −0.442869 0.896586i \(-0.646039\pi\)
−0.442869 + 0.896586i \(0.646039\pi\)
\(878\) −12.1849 −0.411222
\(879\) 0 0
\(880\) −17.7174 −0.597253
\(881\) −16.5850 −0.558764 −0.279382 0.960180i \(-0.590130\pi\)
−0.279382 + 0.960180i \(0.590130\pi\)
\(882\) 0 0
\(883\) −29.1642 −0.981452 −0.490726 0.871314i \(-0.663268\pi\)
−0.490726 + 0.871314i \(0.663268\pi\)
\(884\) 10.0334 0.337458
\(885\) 0 0
\(886\) 12.7453 0.428187
\(887\) 20.2621 0.680334 0.340167 0.940365i \(-0.389516\pi\)
0.340167 + 0.940365i \(0.389516\pi\)
\(888\) 0 0
\(889\) 14.5708 0.488689
\(890\) 91.1240 3.05448
\(891\) 0 0
\(892\) 5.94060 0.198906
\(893\) 14.6426 0.489995
\(894\) 0 0
\(895\) −48.0531 −1.60624
\(896\) 13.4365 0.448884
\(897\) 0 0
\(898\) −35.0820 −1.17070
\(899\) −17.9150 −0.597500
\(900\) 0 0
\(901\) 62.6831 2.08828
\(902\) −10.1333 −0.337403
\(903\) 0 0
\(904\) 28.4098 0.944896
\(905\) 27.1270 0.901732
\(906\) 0 0
\(907\) 34.5315 1.14660 0.573300 0.819345i \(-0.305663\pi\)
0.573300 + 0.819345i \(0.305663\pi\)
\(908\) −7.71621 −0.256071
\(909\) 0 0
\(910\) 15.4394 0.511812
\(911\) −5.96287 −0.197559 −0.0987794 0.995109i \(-0.531494\pi\)
−0.0987794 + 0.995109i \(0.531494\pi\)
\(912\) 0 0
\(913\) −4.84293 −0.160278
\(914\) −28.6345 −0.947145
\(915\) 0 0
\(916\) 6.41347 0.211907
\(917\) −11.8512 −0.391360
\(918\) 0 0
\(919\) 31.1321 1.02695 0.513476 0.858104i \(-0.328358\pi\)
0.513476 + 0.858104i \(0.328358\pi\)
\(920\) 18.4872 0.609506
\(921\) 0 0
\(922\) 9.27051 0.305308
\(923\) 21.9916 0.723863
\(924\) 0 0
\(925\) −10.4286 −0.342891
\(926\) 17.7648 0.583789
\(927\) 0 0
\(928\) −14.8121 −0.486229
\(929\) −16.4949 −0.541181 −0.270591 0.962695i \(-0.587219\pi\)
−0.270591 + 0.962695i \(0.587219\pi\)
\(930\) 0 0
\(931\) −8.16587 −0.267626
\(932\) −14.2757 −0.467616
\(933\) 0 0
\(934\) −32.8440 −1.07469
\(935\) 22.8726 0.748015
\(936\) 0 0
\(937\) −1.65979 −0.0542229 −0.0271114 0.999632i \(-0.508631\pi\)
−0.0271114 + 0.999632i \(0.508631\pi\)
\(938\) −24.6810 −0.805863
\(939\) 0 0
\(940\) 23.9113 0.779900
\(941\) −16.4332 −0.535707 −0.267853 0.963460i \(-0.586314\pi\)
−0.267853 + 0.963460i \(0.586314\pi\)
\(942\) 0 0
\(943\) 14.0926 0.458918
\(944\) 40.1338 1.30624
\(945\) 0 0
\(946\) 0.492631 0.0160168
\(947\) −7.61673 −0.247510 −0.123755 0.992313i \(-0.539494\pi\)
−0.123755 + 0.992313i \(0.539494\pi\)
\(948\) 0 0
\(949\) 22.6459 0.735118
\(950\) 18.3187 0.594337
\(951\) 0 0
\(952\) −13.8803 −0.449862
\(953\) 36.1956 1.17249 0.586246 0.810133i \(-0.300605\pi\)
0.586246 + 0.810133i \(0.300605\pi\)
\(954\) 0 0
\(955\) 22.7544 0.736316
\(956\) 4.71645 0.152541
\(957\) 0 0
\(958\) −29.7579 −0.961433
\(959\) 12.4508 0.402059
\(960\) 0 0
\(961\) −14.9355 −0.481791
\(962\) −5.32937 −0.171826
\(963\) 0 0
\(964\) −8.72666 −0.281067
\(965\) −7.15371 −0.230286
\(966\) 0 0
\(967\) −12.3745 −0.397936 −0.198968 0.980006i \(-0.563759\pi\)
−0.198968 + 0.980006i \(0.563759\pi\)
\(968\) −2.25183 −0.0723765
\(969\) 0 0
\(970\) 63.8664 2.05063
\(971\) −46.6524 −1.49715 −0.748574 0.663052i \(-0.769261\pi\)
−0.748574 + 0.663052i \(0.769261\pi\)
\(972\) 0 0
\(973\) −16.4031 −0.525860
\(974\) 9.00332 0.288485
\(975\) 0 0
\(976\) −4.84378 −0.155046
\(977\) −54.8844 −1.75591 −0.877953 0.478746i \(-0.841091\pi\)
−0.877953 + 0.478746i \(0.841091\pi\)
\(978\) 0 0
\(979\) 15.4360 0.493336
\(980\) −13.3348 −0.425966
\(981\) 0 0
\(982\) −29.3415 −0.936324
\(983\) −37.6301 −1.20021 −0.600107 0.799920i \(-0.704875\pi\)
−0.600107 + 0.799920i \(0.704875\pi\)
\(984\) 0 0
\(985\) −101.058 −3.21997
\(986\) 45.1095 1.43658
\(987\) 0 0
\(988\) 2.17346 0.0691471
\(989\) −0.685109 −0.0217852
\(990\) 0 0
\(991\) −54.0536 −1.71707 −0.858535 0.512755i \(-0.828625\pi\)
−0.858535 + 0.512755i \(0.828625\pi\)
\(992\) 13.2820 0.421704
\(993\) 0 0
\(994\) 13.1866 0.418253
\(995\) −14.0699 −0.446047
\(996\) 0 0
\(997\) 9.87216 0.312655 0.156327 0.987705i \(-0.450035\pi\)
0.156327 + 0.987705i \(0.450035\pi\)
\(998\) −17.1286 −0.542197
\(999\) 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 \(a_p\))