Properties

Label 6039.2.a.j.1.6
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 1.6
Root \(-0.231279\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.231279 q^{2}\) \(-1.94651 q^{4}\) \(-3.70694 q^{5}\) \(-0.911108 q^{7}\) \(+0.912746 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.231279 q^{2}\) \(-1.94651 q^{4}\) \(-3.70694 q^{5}\) \(-0.911108 q^{7}\) \(+0.912746 q^{8}\) \(+0.857338 q^{10}\) \(+1.00000 q^{11}\) \(-1.28993 q^{13}\) \(+0.210720 q^{14}\) \(+3.68192 q^{16}\) \(+7.36730 q^{17}\) \(+5.91624 q^{19}\) \(+7.21559 q^{20}\) \(-0.231279 q^{22}\) \(-6.40611 q^{23}\) \(+8.74139 q^{25}\) \(+0.298334 q^{26}\) \(+1.77348 q^{28}\) \(-9.58456 q^{29}\) \(-8.65847 q^{31}\) \(-2.67705 q^{32}\) \(-1.70390 q^{34}\) \(+3.37742 q^{35}\) \(-8.74406 q^{37}\) \(-1.36830 q^{38}\) \(-3.38349 q^{40}\) \(-6.54649 q^{41}\) \(+9.59278 q^{43}\) \(-1.94651 q^{44}\) \(+1.48160 q^{46}\) \(-5.82694 q^{47}\) \(-6.16988 q^{49}\) \(-2.02170 q^{50}\) \(+2.51086 q^{52}\) \(+5.01034 q^{53}\) \(-3.70694 q^{55}\) \(-0.831610 q^{56}\) \(+2.21671 q^{58}\) \(-1.55369 q^{59}\) \(+1.00000 q^{61}\) \(+2.00252 q^{62}\) \(-6.74470 q^{64}\) \(+4.78168 q^{65}\) \(+12.7209 q^{67}\) \(-14.3405 q^{68}\) \(-0.781128 q^{70}\) \(+0.506871 q^{71}\) \(-3.71011 q^{73}\) \(+2.02232 q^{74}\) \(-11.5160 q^{76}\) \(-0.911108 q^{77}\) \(-5.28303 q^{79}\) \(-13.6486 q^{80}\) \(+1.51407 q^{82}\) \(-7.43641 q^{83}\) \(-27.3101 q^{85}\) \(-2.21861 q^{86}\) \(+0.912746 q^{88}\) \(-12.7615 q^{89}\) \(+1.17526 q^{91}\) \(+12.4695 q^{92}\) \(+1.34765 q^{94}\) \(-21.9311 q^{95}\) \(+19.0085 q^{97}\) \(+1.42697 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.231279 −0.163539 −0.0817696 0.996651i \(-0.526057\pi\)
−0.0817696 + 0.996651i \(0.526057\pi\)
\(3\) 0 0
\(4\) −1.94651 −0.973255
\(5\) −3.70694 −1.65779 −0.828896 0.559402i \(-0.811031\pi\)
−0.828896 + 0.559402i \(0.811031\pi\)
\(6\) 0 0
\(7\) −0.911108 −0.344366 −0.172183 0.985065i \(-0.555082\pi\)
−0.172183 + 0.985065i \(0.555082\pi\)
\(8\) 0.912746 0.322705
\(9\) 0 0
\(10\) 0.857338 0.271114
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.28993 −0.357761 −0.178881 0.983871i \(-0.557248\pi\)
−0.178881 + 0.983871i \(0.557248\pi\)
\(14\) 0.210720 0.0563174
\(15\) 0 0
\(16\) 3.68192 0.920480
\(17\) 7.36730 1.78683 0.893416 0.449230i \(-0.148301\pi\)
0.893416 + 0.449230i \(0.148301\pi\)
\(18\) 0 0
\(19\) 5.91624 1.35728 0.678640 0.734472i \(-0.262570\pi\)
0.678640 + 0.734472i \(0.262570\pi\)
\(20\) 7.21559 1.61346
\(21\) 0 0
\(22\) −0.231279 −0.0493089
\(23\) −6.40611 −1.33577 −0.667883 0.744267i \(-0.732799\pi\)
−0.667883 + 0.744267i \(0.732799\pi\)
\(24\) 0 0
\(25\) 8.74139 1.74828
\(26\) 0.298334 0.0585080
\(27\) 0 0
\(28\) 1.77348 0.335156
\(29\) −9.58456 −1.77981 −0.889904 0.456147i \(-0.849229\pi\)
−0.889904 + 0.456147i \(0.849229\pi\)
\(30\) 0 0
\(31\) −8.65847 −1.55511 −0.777553 0.628817i \(-0.783539\pi\)
−0.777553 + 0.628817i \(0.783539\pi\)
\(32\) −2.67705 −0.473239
\(33\) 0 0
\(34\) −1.70390 −0.292217
\(35\) 3.37742 0.570888
\(36\) 0 0
\(37\) −8.74406 −1.43751 −0.718757 0.695261i \(-0.755289\pi\)
−0.718757 + 0.695261i \(0.755289\pi\)
\(38\) −1.36830 −0.221968
\(39\) 0 0
\(40\) −3.38349 −0.534977
\(41\) −6.54649 −1.02239 −0.511195 0.859465i \(-0.670797\pi\)
−0.511195 + 0.859465i \(0.670797\pi\)
\(42\) 0 0
\(43\) 9.59278 1.46289 0.731443 0.681903i \(-0.238847\pi\)
0.731443 + 0.681903i \(0.238847\pi\)
\(44\) −1.94651 −0.293447
\(45\) 0 0
\(46\) 1.48160 0.218450
\(47\) −5.82694 −0.849946 −0.424973 0.905206i \(-0.639716\pi\)
−0.424973 + 0.905206i \(0.639716\pi\)
\(48\) 0 0
\(49\) −6.16988 −0.881412
\(50\) −2.02170 −0.285912
\(51\) 0 0
\(52\) 2.51086 0.348193
\(53\) 5.01034 0.688223 0.344111 0.938929i \(-0.388180\pi\)
0.344111 + 0.938929i \(0.388180\pi\)
\(54\) 0 0
\(55\) −3.70694 −0.499843
\(56\) −0.831610 −0.111129
\(57\) 0 0
\(58\) 2.21671 0.291069
\(59\) −1.55369 −0.202273 −0.101137 0.994873i \(-0.532248\pi\)
−0.101137 + 0.994873i \(0.532248\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 2.00252 0.254321
\(63\) 0 0
\(64\) −6.74470 −0.843087
\(65\) 4.78168 0.593094
\(66\) 0 0
\(67\) 12.7209 1.55410 0.777052 0.629436i \(-0.216714\pi\)
0.777052 + 0.629436i \(0.216714\pi\)
\(68\) −14.3405 −1.73904
\(69\) 0 0
\(70\) −0.781128 −0.0933626
\(71\) 0.506871 0.0601545 0.0300773 0.999548i \(-0.490425\pi\)
0.0300773 + 0.999548i \(0.490425\pi\)
\(72\) 0 0
\(73\) −3.71011 −0.434236 −0.217118 0.976145i \(-0.569666\pi\)
−0.217118 + 0.976145i \(0.569666\pi\)
\(74\) 2.02232 0.235090
\(75\) 0 0
\(76\) −11.5160 −1.32098
\(77\) −0.911108 −0.103830
\(78\) 0 0
\(79\) −5.28303 −0.594387 −0.297194 0.954817i \(-0.596051\pi\)
−0.297194 + 0.954817i \(0.596051\pi\)
\(80\) −13.6486 −1.52597
\(81\) 0 0
\(82\) 1.51407 0.167201
\(83\) −7.43641 −0.816252 −0.408126 0.912926i \(-0.633818\pi\)
−0.408126 + 0.912926i \(0.633818\pi\)
\(84\) 0 0
\(85\) −27.3101 −2.96220
\(86\) −2.21861 −0.239239
\(87\) 0 0
\(88\) 0.912746 0.0972991
\(89\) −12.7615 −1.35272 −0.676360 0.736571i \(-0.736444\pi\)
−0.676360 + 0.736571i \(0.736444\pi\)
\(90\) 0 0
\(91\) 1.17526 0.123201
\(92\) 12.4695 1.30004
\(93\) 0 0
\(94\) 1.34765 0.139000
\(95\) −21.9311 −2.25009
\(96\) 0 0
\(97\) 19.0085 1.93002 0.965012 0.262207i \(-0.0844504\pi\)
0.965012 + 0.262207i \(0.0844504\pi\)
\(98\) 1.42697 0.144145
\(99\) 0 0
\(100\) −17.0152 −1.70152
\(101\) 5.60028 0.557249 0.278624 0.960400i \(-0.410122\pi\)
0.278624 + 0.960400i \(0.410122\pi\)
\(102\) 0 0
\(103\) 16.0507 1.58153 0.790763 0.612122i \(-0.209684\pi\)
0.790763 + 0.612122i \(0.209684\pi\)
\(104\) −1.17738 −0.115451
\(105\) 0 0
\(106\) −1.15879 −0.112551
\(107\) −16.1333 −1.55966 −0.779830 0.625991i \(-0.784695\pi\)
−0.779830 + 0.625991i \(0.784695\pi\)
\(108\) 0 0
\(109\) −15.2826 −1.46381 −0.731905 0.681407i \(-0.761369\pi\)
−0.731905 + 0.681407i \(0.761369\pi\)
\(110\) 0.857338 0.0817440
\(111\) 0 0
\(112\) −3.35463 −0.316982
\(113\) −13.4720 −1.26734 −0.633668 0.773605i \(-0.718451\pi\)
−0.633668 + 0.773605i \(0.718451\pi\)
\(114\) 0 0
\(115\) 23.7470 2.21442
\(116\) 18.6564 1.73221
\(117\) 0 0
\(118\) 0.359337 0.0330796
\(119\) −6.71240 −0.615325
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −0.231279 −0.0209391
\(123\) 0 0
\(124\) 16.8538 1.51352
\(125\) −13.8691 −1.24049
\(126\) 0 0
\(127\) 14.9118 1.32321 0.661605 0.749852i \(-0.269875\pi\)
0.661605 + 0.749852i \(0.269875\pi\)
\(128\) 6.91400 0.611117
\(129\) 0 0
\(130\) −1.10590 −0.0969942
\(131\) −1.52367 −0.133123 −0.0665617 0.997782i \(-0.521203\pi\)
−0.0665617 + 0.997782i \(0.521203\pi\)
\(132\) 0 0
\(133\) −5.39033 −0.467401
\(134\) −2.94208 −0.254157
\(135\) 0 0
\(136\) 6.72448 0.576619
\(137\) −3.70337 −0.316400 −0.158200 0.987407i \(-0.550569\pi\)
−0.158200 + 0.987407i \(0.550569\pi\)
\(138\) 0 0
\(139\) 6.10661 0.517956 0.258978 0.965883i \(-0.416614\pi\)
0.258978 + 0.965883i \(0.416614\pi\)
\(140\) −6.57418 −0.555620
\(141\) 0 0
\(142\) −0.117229 −0.00983762
\(143\) −1.28993 −0.107869
\(144\) 0 0
\(145\) 35.5294 2.95055
\(146\) 0.858073 0.0710146
\(147\) 0 0
\(148\) 17.0204 1.39907
\(149\) 13.5246 1.10797 0.553987 0.832525i \(-0.313106\pi\)
0.553987 + 0.832525i \(0.313106\pi\)
\(150\) 0 0
\(151\) −1.09346 −0.0889849 −0.0444924 0.999010i \(-0.514167\pi\)
−0.0444924 + 0.999010i \(0.514167\pi\)
\(152\) 5.40003 0.438000
\(153\) 0 0
\(154\) 0.210720 0.0169803
\(155\) 32.0964 2.57804
\(156\) 0 0
\(157\) 14.4608 1.15410 0.577049 0.816709i \(-0.304204\pi\)
0.577049 + 0.816709i \(0.304204\pi\)
\(158\) 1.22186 0.0972057
\(159\) 0 0
\(160\) 9.92364 0.784533
\(161\) 5.83665 0.459993
\(162\) 0 0
\(163\) 1.40734 0.110231 0.0551155 0.998480i \(-0.482447\pi\)
0.0551155 + 0.998480i \(0.482447\pi\)
\(164\) 12.7428 0.995046
\(165\) 0 0
\(166\) 1.71989 0.133489
\(167\) 14.0105 1.08416 0.542082 0.840326i \(-0.317636\pi\)
0.542082 + 0.840326i \(0.317636\pi\)
\(168\) 0 0
\(169\) −11.3361 −0.872007
\(170\) 6.31627 0.484436
\(171\) 0 0
\(172\) −18.6724 −1.42376
\(173\) −2.67772 −0.203584 −0.101792 0.994806i \(-0.532458\pi\)
−0.101792 + 0.994806i \(0.532458\pi\)
\(174\) 0 0
\(175\) −7.96434 −0.602048
\(176\) 3.68192 0.277535
\(177\) 0 0
\(178\) 2.95148 0.221223
\(179\) −2.14059 −0.159995 −0.0799977 0.996795i \(-0.525491\pi\)
−0.0799977 + 0.996795i \(0.525491\pi\)
\(180\) 0 0
\(181\) 10.4522 0.776903 0.388451 0.921469i \(-0.373010\pi\)
0.388451 + 0.921469i \(0.373010\pi\)
\(182\) −0.271814 −0.0201482
\(183\) 0 0
\(184\) −5.84715 −0.431058
\(185\) 32.4137 2.38310
\(186\) 0 0
\(187\) 7.36730 0.538750
\(188\) 11.3422 0.827214
\(189\) 0 0
\(190\) 5.07222 0.367978
\(191\) −6.90631 −0.499723 −0.249862 0.968282i \(-0.580385\pi\)
−0.249862 + 0.968282i \(0.580385\pi\)
\(192\) 0 0
\(193\) 13.5215 0.973300 0.486650 0.873597i \(-0.338219\pi\)
0.486650 + 0.873597i \(0.338219\pi\)
\(194\) −4.39628 −0.315634
\(195\) 0 0
\(196\) 12.0097 0.857838
\(197\) 12.6509 0.901342 0.450671 0.892690i \(-0.351185\pi\)
0.450671 + 0.892690i \(0.351185\pi\)
\(198\) 0 0
\(199\) 3.63188 0.257457 0.128728 0.991680i \(-0.458910\pi\)
0.128728 + 0.991680i \(0.458910\pi\)
\(200\) 7.97867 0.564177
\(201\) 0 0
\(202\) −1.29523 −0.0911320
\(203\) 8.73257 0.612906
\(204\) 0 0
\(205\) 24.2674 1.69491
\(206\) −3.71220 −0.258642
\(207\) 0 0
\(208\) −4.74941 −0.329312
\(209\) 5.91624 0.409235
\(210\) 0 0
\(211\) −18.3470 −1.26306 −0.631530 0.775352i \(-0.717573\pi\)
−0.631530 + 0.775352i \(0.717573\pi\)
\(212\) −9.75267 −0.669816
\(213\) 0 0
\(214\) 3.73129 0.255066
\(215\) −35.5598 −2.42516
\(216\) 0 0
\(217\) 7.88880 0.535526
\(218\) 3.53456 0.239390
\(219\) 0 0
\(220\) 7.21559 0.486475
\(221\) −9.50328 −0.639260
\(222\) 0 0
\(223\) 6.99961 0.468729 0.234364 0.972149i \(-0.424699\pi\)
0.234364 + 0.972149i \(0.424699\pi\)
\(224\) 2.43908 0.162968
\(225\) 0 0
\(226\) 3.11579 0.207259
\(227\) −6.85426 −0.454933 −0.227467 0.973786i \(-0.573044\pi\)
−0.227467 + 0.973786i \(0.573044\pi\)
\(228\) 0 0
\(229\) −2.15050 −0.142109 −0.0710544 0.997472i \(-0.522636\pi\)
−0.0710544 + 0.997472i \(0.522636\pi\)
\(230\) −5.49220 −0.362145
\(231\) 0 0
\(232\) −8.74827 −0.574352
\(233\) 0.0878610 0.00575597 0.00287798 0.999996i \(-0.499084\pi\)
0.00287798 + 0.999996i \(0.499084\pi\)
\(234\) 0 0
\(235\) 21.6001 1.40903
\(236\) 3.02428 0.196864
\(237\) 0 0
\(238\) 1.55244 0.100630
\(239\) 1.34617 0.0870763 0.0435382 0.999052i \(-0.486137\pi\)
0.0435382 + 0.999052i \(0.486137\pi\)
\(240\) 0 0
\(241\) 4.54006 0.292451 0.146225 0.989251i \(-0.453288\pi\)
0.146225 + 0.989251i \(0.453288\pi\)
\(242\) −0.231279 −0.0148672
\(243\) 0 0
\(244\) −1.94651 −0.124613
\(245\) 22.8714 1.46120
\(246\) 0 0
\(247\) −7.63152 −0.485582
\(248\) −7.90298 −0.501840
\(249\) 0 0
\(250\) 3.20763 0.202869
\(251\) 5.83748 0.368458 0.184229 0.982883i \(-0.441021\pi\)
0.184229 + 0.982883i \(0.441021\pi\)
\(252\) 0 0
\(253\) −6.40611 −0.402748
\(254\) −3.44880 −0.216397
\(255\) 0 0
\(256\) 11.8903 0.743145
\(257\) −19.2484 −1.20068 −0.600341 0.799744i \(-0.704968\pi\)
−0.600341 + 0.799744i \(0.704968\pi\)
\(258\) 0 0
\(259\) 7.96678 0.495032
\(260\) −9.30759 −0.577232
\(261\) 0 0
\(262\) 0.352393 0.0217709
\(263\) 12.4662 0.768698 0.384349 0.923188i \(-0.374426\pi\)
0.384349 + 0.923188i \(0.374426\pi\)
\(264\) 0 0
\(265\) −18.5730 −1.14093
\(266\) 1.24667 0.0764384
\(267\) 0 0
\(268\) −24.7614 −1.51254
\(269\) 10.9441 0.667276 0.333638 0.942701i \(-0.391724\pi\)
0.333638 + 0.942701i \(0.391724\pi\)
\(270\) 0 0
\(271\) −17.9716 −1.09169 −0.545847 0.837885i \(-0.683792\pi\)
−0.545847 + 0.837885i \(0.683792\pi\)
\(272\) 27.1258 1.64474
\(273\) 0 0
\(274\) 0.856514 0.0517439
\(275\) 8.74139 0.527125
\(276\) 0 0
\(277\) −5.74306 −0.345067 −0.172534 0.985004i \(-0.555195\pi\)
−0.172534 + 0.985004i \(0.555195\pi\)
\(278\) −1.41233 −0.0847061
\(279\) 0 0
\(280\) 3.08273 0.184228
\(281\) 31.3802 1.87199 0.935993 0.352019i \(-0.114505\pi\)
0.935993 + 0.352019i \(0.114505\pi\)
\(282\) 0 0
\(283\) −22.4497 −1.33450 −0.667248 0.744835i \(-0.732528\pi\)
−0.667248 + 0.744835i \(0.732528\pi\)
\(284\) −0.986629 −0.0585457
\(285\) 0 0
\(286\) 0.298334 0.0176408
\(287\) 5.96456 0.352077
\(288\) 0 0
\(289\) 37.2771 2.19277
\(290\) −8.21721 −0.482531
\(291\) 0 0
\(292\) 7.22177 0.422622
\(293\) 15.8824 0.927861 0.463931 0.885872i \(-0.346439\pi\)
0.463931 + 0.885872i \(0.346439\pi\)
\(294\) 0 0
\(295\) 5.75944 0.335327
\(296\) −7.98111 −0.463893
\(297\) 0 0
\(298\) −3.12795 −0.181197
\(299\) 8.26341 0.477885
\(300\) 0 0
\(301\) −8.74006 −0.503769
\(302\) 0.252896 0.0145525
\(303\) 0 0
\(304\) 21.7831 1.24935
\(305\) −3.70694 −0.212259
\(306\) 0 0
\(307\) 13.2053 0.753665 0.376832 0.926281i \(-0.377013\pi\)
0.376832 + 0.926281i \(0.377013\pi\)
\(308\) 1.77348 0.101053
\(309\) 0 0
\(310\) −7.42323 −0.421611
\(311\) −7.86121 −0.445768 −0.222884 0.974845i \(-0.571547\pi\)
−0.222884 + 0.974845i \(0.571547\pi\)
\(312\) 0 0
\(313\) −17.6385 −0.996988 −0.498494 0.866893i \(-0.666113\pi\)
−0.498494 + 0.866893i \(0.666113\pi\)
\(314\) −3.34449 −0.188740
\(315\) 0 0
\(316\) 10.2835 0.578490
\(317\) −10.5734 −0.593859 −0.296930 0.954899i \(-0.595963\pi\)
−0.296930 + 0.954899i \(0.595963\pi\)
\(318\) 0 0
\(319\) −9.58456 −0.536632
\(320\) 25.0022 1.39766
\(321\) 0 0
\(322\) −1.34990 −0.0752268
\(323\) 43.5867 2.42523
\(324\) 0 0
\(325\) −11.2758 −0.625466
\(326\) −0.325488 −0.0180271
\(327\) 0 0
\(328\) −5.97528 −0.329930
\(329\) 5.30897 0.292693
\(330\) 0 0
\(331\) −25.7221 −1.41381 −0.706906 0.707307i \(-0.749910\pi\)
−0.706906 + 0.707307i \(0.749910\pi\)
\(332\) 14.4750 0.794421
\(333\) 0 0
\(334\) −3.24034 −0.177303
\(335\) −47.1556 −2.57638
\(336\) 0 0
\(337\) −22.1471 −1.20643 −0.603216 0.797578i \(-0.706114\pi\)
−0.603216 + 0.797578i \(0.706114\pi\)
\(338\) 2.62180 0.142607
\(339\) 0 0
\(340\) 53.1594 2.88297
\(341\) −8.65847 −0.468882
\(342\) 0 0
\(343\) 11.9992 0.647895
\(344\) 8.75578 0.472080
\(345\) 0 0
\(346\) 0.619303 0.0332939
\(347\) −16.8724 −0.905757 −0.452879 0.891572i \(-0.649603\pi\)
−0.452879 + 0.891572i \(0.649603\pi\)
\(348\) 0 0
\(349\) −36.7014 −1.96458 −0.982291 0.187362i \(-0.940006\pi\)
−0.982291 + 0.187362i \(0.940006\pi\)
\(350\) 1.84199 0.0984584
\(351\) 0 0
\(352\) −2.67705 −0.142687
\(353\) −0.505931 −0.0269280 −0.0134640 0.999909i \(-0.504286\pi\)
−0.0134640 + 0.999909i \(0.504286\pi\)
\(354\) 0 0
\(355\) −1.87894 −0.0997237
\(356\) 24.8405 1.31654
\(357\) 0 0
\(358\) 0.495075 0.0261655
\(359\) −6.62258 −0.349527 −0.174763 0.984610i \(-0.555916\pi\)
−0.174763 + 0.984610i \(0.555916\pi\)
\(360\) 0 0
\(361\) 16.0019 0.842206
\(362\) −2.41737 −0.127054
\(363\) 0 0
\(364\) −2.28766 −0.119906
\(365\) 13.7532 0.719873
\(366\) 0 0
\(367\) 19.2989 1.00739 0.503696 0.863881i \(-0.331973\pi\)
0.503696 + 0.863881i \(0.331973\pi\)
\(368\) −23.5868 −1.22955
\(369\) 0 0
\(370\) −7.49662 −0.389731
\(371\) −4.56496 −0.237001
\(372\) 0 0
\(373\) −33.3340 −1.72597 −0.862985 0.505229i \(-0.831408\pi\)
−0.862985 + 0.505229i \(0.831408\pi\)
\(374\) −1.70390 −0.0881068
\(375\) 0 0
\(376\) −5.31852 −0.274282
\(377\) 12.3634 0.636747
\(378\) 0 0
\(379\) 38.6940 1.98757 0.993787 0.111294i \(-0.0354997\pi\)
0.993787 + 0.111294i \(0.0354997\pi\)
\(380\) 42.6892 2.18991
\(381\) 0 0
\(382\) 1.59729 0.0817244
\(383\) 9.35020 0.477773 0.238886 0.971048i \(-0.423218\pi\)
0.238886 + 0.971048i \(0.423218\pi\)
\(384\) 0 0
\(385\) 3.37742 0.172129
\(386\) −3.12725 −0.159173
\(387\) 0 0
\(388\) −37.0003 −1.87840
\(389\) −22.9294 −1.16257 −0.581283 0.813701i \(-0.697449\pi\)
−0.581283 + 0.813701i \(0.697449\pi\)
\(390\) 0 0
\(391\) −47.1957 −2.38679
\(392\) −5.63154 −0.284436
\(393\) 0 0
\(394\) −2.92590 −0.147405
\(395\) 19.5839 0.985371
\(396\) 0 0
\(397\) 17.2747 0.866993 0.433496 0.901155i \(-0.357280\pi\)
0.433496 + 0.901155i \(0.357280\pi\)
\(398\) −0.839978 −0.0421043
\(399\) 0 0
\(400\) 32.1851 1.60925
\(401\) 31.6046 1.57826 0.789129 0.614228i \(-0.210532\pi\)
0.789129 + 0.614228i \(0.210532\pi\)
\(402\) 0 0
\(403\) 11.1688 0.556357
\(404\) −10.9010 −0.542345
\(405\) 0 0
\(406\) −2.01966 −0.100234
\(407\) −8.74406 −0.433427
\(408\) 0 0
\(409\) 20.8224 1.02960 0.514800 0.857310i \(-0.327866\pi\)
0.514800 + 0.857310i \(0.327866\pi\)
\(410\) −5.61255 −0.277184
\(411\) 0 0
\(412\) −31.2429 −1.53923
\(413\) 1.41558 0.0696561
\(414\) 0 0
\(415\) 27.5663 1.35318
\(416\) 3.45319 0.169307
\(417\) 0 0
\(418\) −1.36830 −0.0669260
\(419\) 12.4302 0.607256 0.303628 0.952791i \(-0.401802\pi\)
0.303628 + 0.952791i \(0.401802\pi\)
\(420\) 0 0
\(421\) −9.53980 −0.464942 −0.232471 0.972603i \(-0.574681\pi\)
−0.232471 + 0.972603i \(0.574681\pi\)
\(422\) 4.24328 0.206560
\(423\) 0 0
\(424\) 4.57317 0.222093
\(425\) 64.4004 3.12388
\(426\) 0 0
\(427\) −0.911108 −0.0440916
\(428\) 31.4035 1.51795
\(429\) 0 0
\(430\) 8.22426 0.396609
\(431\) 12.5341 0.603745 0.301872 0.953348i \(-0.402388\pi\)
0.301872 + 0.953348i \(0.402388\pi\)
\(432\) 0 0
\(433\) −18.0140 −0.865696 −0.432848 0.901467i \(-0.642491\pi\)
−0.432848 + 0.901467i \(0.642491\pi\)
\(434\) −1.82452 −0.0875796
\(435\) 0 0
\(436\) 29.7478 1.42466
\(437\) −37.9001 −1.81301
\(438\) 0 0
\(439\) −4.17247 −0.199141 −0.0995707 0.995030i \(-0.531747\pi\)
−0.0995707 + 0.995030i \(0.531747\pi\)
\(440\) −3.38349 −0.161302
\(441\) 0 0
\(442\) 2.19791 0.104544
\(443\) 31.4449 1.49399 0.746995 0.664830i \(-0.231496\pi\)
0.746995 + 0.664830i \(0.231496\pi\)
\(444\) 0 0
\(445\) 47.3062 2.24253
\(446\) −1.61887 −0.0766556
\(447\) 0 0
\(448\) 6.14514 0.290331
\(449\) −13.4654 −0.635471 −0.317735 0.948179i \(-0.602922\pi\)
−0.317735 + 0.948179i \(0.602922\pi\)
\(450\) 0 0
\(451\) −6.54649 −0.308262
\(452\) 26.2233 1.23344
\(453\) 0 0
\(454\) 1.58525 0.0743994
\(455\) −4.35663 −0.204242
\(456\) 0 0
\(457\) 16.0392 0.750280 0.375140 0.926968i \(-0.377595\pi\)
0.375140 + 0.926968i \(0.377595\pi\)
\(458\) 0.497365 0.0232404
\(459\) 0 0
\(460\) −46.2238 −2.15520
\(461\) 2.07719 0.0967444 0.0483722 0.998829i \(-0.484597\pi\)
0.0483722 + 0.998829i \(0.484597\pi\)
\(462\) 0 0
\(463\) 22.3955 1.04081 0.520404 0.853920i \(-0.325781\pi\)
0.520404 + 0.853920i \(0.325781\pi\)
\(464\) −35.2896 −1.63828
\(465\) 0 0
\(466\) −0.0203204 −0.000941327 0
\(467\) −7.84551 −0.363047 −0.181523 0.983387i \(-0.558103\pi\)
−0.181523 + 0.983387i \(0.558103\pi\)
\(468\) 0 0
\(469\) −11.5901 −0.535181
\(470\) −4.99566 −0.230432
\(471\) 0 0
\(472\) −1.41813 −0.0652745
\(473\) 9.59278 0.441077
\(474\) 0 0
\(475\) 51.7162 2.37290
\(476\) 13.0658 0.598868
\(477\) 0 0
\(478\) −0.311341 −0.0142404
\(479\) 23.9318 1.09347 0.546736 0.837305i \(-0.315870\pi\)
0.546736 + 0.837305i \(0.315870\pi\)
\(480\) 0 0
\(481\) 11.2792 0.514287
\(482\) −1.05002 −0.0478272
\(483\) 0 0
\(484\) −1.94651 −0.0884777
\(485\) −70.4634 −3.19958
\(486\) 0 0
\(487\) 25.8238 1.17019 0.585094 0.810965i \(-0.301058\pi\)
0.585094 + 0.810965i \(0.301058\pi\)
\(488\) 0.912746 0.0413181
\(489\) 0 0
\(490\) −5.28968 −0.238963
\(491\) 31.3212 1.41351 0.706754 0.707459i \(-0.250159\pi\)
0.706754 + 0.707459i \(0.250159\pi\)
\(492\) 0 0
\(493\) −70.6123 −3.18022
\(494\) 1.76501 0.0794117
\(495\) 0 0
\(496\) −31.8798 −1.43144
\(497\) −0.461814 −0.0207152
\(498\) 0 0
\(499\) 24.5909 1.10084 0.550420 0.834888i \(-0.314467\pi\)
0.550420 + 0.834888i \(0.314467\pi\)
\(500\) 26.9963 1.20731
\(501\) 0 0
\(502\) −1.35009 −0.0602574
\(503\) 2.31095 0.103040 0.0515200 0.998672i \(-0.483593\pi\)
0.0515200 + 0.998672i \(0.483593\pi\)
\(504\) 0 0
\(505\) −20.7599 −0.923803
\(506\) 1.48160 0.0658652
\(507\) 0 0
\(508\) −29.0260 −1.28782
\(509\) 29.9915 1.32935 0.664676 0.747132i \(-0.268570\pi\)
0.664676 + 0.747132i \(0.268570\pi\)
\(510\) 0 0
\(511\) 3.38031 0.149536
\(512\) −16.5780 −0.732650
\(513\) 0 0
\(514\) 4.45176 0.196359
\(515\) −59.4991 −2.62184
\(516\) 0 0
\(517\) −5.82694 −0.256268
\(518\) −1.84255 −0.0809571
\(519\) 0 0
\(520\) 4.36446 0.191394
\(521\) 17.7422 0.777300 0.388650 0.921385i \(-0.372942\pi\)
0.388650 + 0.921385i \(0.372942\pi\)
\(522\) 0 0
\(523\) −16.2858 −0.712129 −0.356064 0.934461i \(-0.615882\pi\)
−0.356064 + 0.934461i \(0.615882\pi\)
\(524\) 2.96583 0.129563
\(525\) 0 0
\(526\) −2.88317 −0.125712
\(527\) −63.7895 −2.77872
\(528\) 0 0
\(529\) 18.0382 0.784269
\(530\) 4.29555 0.186587
\(531\) 0 0
\(532\) 10.4923 0.454901
\(533\) 8.44449 0.365772
\(534\) 0 0
\(535\) 59.8050 2.58559
\(536\) 11.6110 0.501517
\(537\) 0 0
\(538\) −2.53115 −0.109126
\(539\) −6.16988 −0.265756
\(540\) 0 0
\(541\) −4.81097 −0.206840 −0.103420 0.994638i \(-0.532979\pi\)
−0.103420 + 0.994638i \(0.532979\pi\)
\(542\) 4.15645 0.178535
\(543\) 0 0
\(544\) −19.7226 −0.845599
\(545\) 56.6517 2.42669
\(546\) 0 0
\(547\) 12.5709 0.537491 0.268745 0.963211i \(-0.413391\pi\)
0.268745 + 0.963211i \(0.413391\pi\)
\(548\) 7.20865 0.307938
\(549\) 0 0
\(550\) −2.02170 −0.0862057
\(551\) −56.7046 −2.41570
\(552\) 0 0
\(553\) 4.81341 0.204687
\(554\) 1.32825 0.0564320
\(555\) 0 0
\(556\) −11.8866 −0.504103
\(557\) 31.8497 1.34951 0.674757 0.738040i \(-0.264248\pi\)
0.674757 + 0.738040i \(0.264248\pi\)
\(558\) 0 0
\(559\) −12.3740 −0.523364
\(560\) 12.4354 0.525491
\(561\) 0 0
\(562\) −7.25759 −0.306143
\(563\) −37.6429 −1.58646 −0.793229 0.608923i \(-0.791602\pi\)
−0.793229 + 0.608923i \(0.791602\pi\)
\(564\) 0 0
\(565\) 49.9397 2.10098
\(566\) 5.19216 0.218243
\(567\) 0 0
\(568\) 0.462645 0.0194121
\(569\) 3.93199 0.164838 0.0824189 0.996598i \(-0.473735\pi\)
0.0824189 + 0.996598i \(0.473735\pi\)
\(570\) 0 0
\(571\) 18.8819 0.790185 0.395092 0.918641i \(-0.370713\pi\)
0.395092 + 0.918641i \(0.370713\pi\)
\(572\) 2.51086 0.104984
\(573\) 0 0
\(574\) −1.37948 −0.0575783
\(575\) −55.9982 −2.33529
\(576\) 0 0
\(577\) 34.1619 1.42218 0.711088 0.703103i \(-0.248203\pi\)
0.711088 + 0.703103i \(0.248203\pi\)
\(578\) −8.62143 −0.358604
\(579\) 0 0
\(580\) −69.1583 −2.87164
\(581\) 6.77537 0.281090
\(582\) 0 0
\(583\) 5.01034 0.207507
\(584\) −3.38639 −0.140130
\(585\) 0 0
\(586\) −3.67328 −0.151742
\(587\) 4.92186 0.203147 0.101573 0.994828i \(-0.467612\pi\)
0.101573 + 0.994828i \(0.467612\pi\)
\(588\) 0 0
\(589\) −51.2256 −2.11071
\(590\) −1.33204 −0.0548392
\(591\) 0 0
\(592\) −32.1949 −1.32320
\(593\) −38.0886 −1.56411 −0.782056 0.623208i \(-0.785829\pi\)
−0.782056 + 0.623208i \(0.785829\pi\)
\(594\) 0 0
\(595\) 24.8825 1.02008
\(596\) −26.3257 −1.07834
\(597\) 0 0
\(598\) −1.91116 −0.0781530
\(599\) 35.5566 1.45280 0.726401 0.687271i \(-0.241191\pi\)
0.726401 + 0.687271i \(0.241191\pi\)
\(600\) 0 0
\(601\) −3.34841 −0.136584 −0.0682922 0.997665i \(-0.521755\pi\)
−0.0682922 + 0.997665i \(0.521755\pi\)
\(602\) 2.02140 0.0823859
\(603\) 0 0
\(604\) 2.12844 0.0866050
\(605\) −3.70694 −0.150708
\(606\) 0 0
\(607\) −24.1878 −0.981753 −0.490877 0.871229i \(-0.663323\pi\)
−0.490877 + 0.871229i \(0.663323\pi\)
\(608\) −15.8380 −0.642318
\(609\) 0 0
\(610\) 0.857338 0.0347126
\(611\) 7.51633 0.304078
\(612\) 0 0
\(613\) −19.1329 −0.772769 −0.386384 0.922338i \(-0.626276\pi\)
−0.386384 + 0.922338i \(0.626276\pi\)
\(614\) −3.05411 −0.123254
\(615\) 0 0
\(616\) −0.831610 −0.0335065
\(617\) −22.2994 −0.897741 −0.448870 0.893597i \(-0.648173\pi\)
−0.448870 + 0.893597i \(0.648173\pi\)
\(618\) 0 0
\(619\) 31.9197 1.28296 0.641480 0.767140i \(-0.278321\pi\)
0.641480 + 0.767140i \(0.278321\pi\)
\(620\) −62.4759 −2.50909
\(621\) 0 0
\(622\) 1.81814 0.0729006
\(623\) 11.6271 0.465831
\(624\) 0 0
\(625\) 7.70489 0.308196
\(626\) 4.07943 0.163047
\(627\) 0 0
\(628\) −28.1481 −1.12323
\(629\) −64.4201 −2.56860
\(630\) 0 0
\(631\) 0.258718 0.0102994 0.00514971 0.999987i \(-0.498361\pi\)
0.00514971 + 0.999987i \(0.498361\pi\)
\(632\) −4.82207 −0.191812
\(633\) 0 0
\(634\) 2.44540 0.0971193
\(635\) −55.2772 −2.19361
\(636\) 0 0
\(637\) 7.95870 0.315335
\(638\) 2.21671 0.0877605
\(639\) 0 0
\(640\) −25.6298 −1.01311
\(641\) 26.1212 1.03173 0.515863 0.856671i \(-0.327471\pi\)
0.515863 + 0.856671i \(0.327471\pi\)
\(642\) 0 0
\(643\) 7.45790 0.294111 0.147056 0.989128i \(-0.453020\pi\)
0.147056 + 0.989128i \(0.453020\pi\)
\(644\) −11.3611 −0.447690
\(645\) 0 0
\(646\) −10.0807 −0.396620
\(647\) 44.3581 1.74390 0.871949 0.489597i \(-0.162856\pi\)
0.871949 + 0.489597i \(0.162856\pi\)
\(648\) 0 0
\(649\) −1.55369 −0.0609877
\(650\) 2.60785 0.102288
\(651\) 0 0
\(652\) −2.73939 −0.107283
\(653\) 6.14521 0.240481 0.120240 0.992745i \(-0.461633\pi\)
0.120240 + 0.992745i \(0.461633\pi\)
\(654\) 0 0
\(655\) 5.64814 0.220691
\(656\) −24.1036 −0.941089
\(657\) 0 0
\(658\) −1.22785 −0.0478668
\(659\) −27.8267 −1.08398 −0.541988 0.840387i \(-0.682328\pi\)
−0.541988 + 0.840387i \(0.682328\pi\)
\(660\) 0 0
\(661\) 41.3110 1.60681 0.803406 0.595431i \(-0.203019\pi\)
0.803406 + 0.595431i \(0.203019\pi\)
\(662\) 5.94898 0.231214
\(663\) 0 0
\(664\) −6.78756 −0.263408
\(665\) 19.9816 0.774854
\(666\) 0 0
\(667\) 61.3997 2.37741
\(668\) −27.2716 −1.05517
\(669\) 0 0
\(670\) 10.9061 0.421340
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −19.1769 −0.739214 −0.369607 0.929188i \(-0.620508\pi\)
−0.369607 + 0.929188i \(0.620508\pi\)
\(674\) 5.12218 0.197299
\(675\) 0 0
\(676\) 22.0658 0.848685
\(677\) 6.49815 0.249744 0.124872 0.992173i \(-0.460148\pi\)
0.124872 + 0.992173i \(0.460148\pi\)
\(678\) 0 0
\(679\) −17.3188 −0.664635
\(680\) −24.9272 −0.955915
\(681\) 0 0
\(682\) 2.00252 0.0766806
\(683\) 30.5994 1.17085 0.585426 0.810726i \(-0.300927\pi\)
0.585426 + 0.810726i \(0.300927\pi\)
\(684\) 0 0
\(685\) 13.7282 0.524526
\(686\) −2.77516 −0.105956
\(687\) 0 0
\(688\) 35.3199 1.34656
\(689\) −6.46297 −0.246220
\(690\) 0 0
\(691\) 21.3756 0.813166 0.406583 0.913614i \(-0.366720\pi\)
0.406583 + 0.913614i \(0.366720\pi\)
\(692\) 5.21222 0.198139
\(693\) 0 0
\(694\) 3.90224 0.148127
\(695\) −22.6368 −0.858663
\(696\) 0 0
\(697\) −48.2299 −1.82684
\(698\) 8.48828 0.321286
\(699\) 0 0
\(700\) 15.5027 0.585946
\(701\) 13.7805 0.520483 0.260241 0.965544i \(-0.416198\pi\)
0.260241 + 0.965544i \(0.416198\pi\)
\(702\) 0 0
\(703\) −51.7320 −1.95111
\(704\) −6.74470 −0.254200
\(705\) 0 0
\(706\) 0.117012 0.00440379
\(707\) −5.10246 −0.191898
\(708\) 0 0
\(709\) 19.3933 0.728332 0.364166 0.931334i \(-0.381354\pi\)
0.364166 + 0.931334i \(0.381354\pi\)
\(710\) 0.434560 0.0163087
\(711\) 0 0
\(712\) −11.6480 −0.436529
\(713\) 55.4671 2.07726
\(714\) 0 0
\(715\) 4.78168 0.178825
\(716\) 4.16669 0.155716
\(717\) 0 0
\(718\) 1.53167 0.0571613
\(719\) −6.37432 −0.237722 −0.118861 0.992911i \(-0.537924\pi\)
−0.118861 + 0.992911i \(0.537924\pi\)
\(720\) 0 0
\(721\) −14.6240 −0.544624
\(722\) −3.70091 −0.137734
\(723\) 0 0
\(724\) −20.3452 −0.756124
\(725\) −83.7824 −3.11160
\(726\) 0 0
\(727\) −21.3988 −0.793637 −0.396819 0.917897i \(-0.629886\pi\)
−0.396819 + 0.917897i \(0.629886\pi\)
\(728\) 1.07272 0.0397575
\(729\) 0 0
\(730\) −3.18082 −0.117728
\(731\) 70.6729 2.61393
\(732\) 0 0
\(733\) 23.1610 0.855470 0.427735 0.903904i \(-0.359312\pi\)
0.427735 + 0.903904i \(0.359312\pi\)
\(734\) −4.46343 −0.164748
\(735\) 0 0
\(736\) 17.1494 0.632137
\(737\) 12.7209 0.468580
\(738\) 0 0
\(739\) −31.1840 −1.14712 −0.573561 0.819163i \(-0.694439\pi\)
−0.573561 + 0.819163i \(0.694439\pi\)
\(740\) −63.0936 −2.31937
\(741\) 0 0
\(742\) 1.05578 0.0387589
\(743\) 11.7663 0.431663 0.215831 0.976431i \(-0.430754\pi\)
0.215831 + 0.976431i \(0.430754\pi\)
\(744\) 0 0
\(745\) −50.1347 −1.83679
\(746\) 7.70947 0.282264
\(747\) 0 0
\(748\) −14.3405 −0.524341
\(749\) 14.6991 0.537095
\(750\) 0 0
\(751\) −0.685367 −0.0250094 −0.0125047 0.999922i \(-0.503980\pi\)
−0.0125047 + 0.999922i \(0.503980\pi\)
\(752\) −21.4543 −0.782359
\(753\) 0 0
\(754\) −2.85940 −0.104133
\(755\) 4.05341 0.147519
\(756\) 0 0
\(757\) −32.9419 −1.19730 −0.598648 0.801013i \(-0.704295\pi\)
−0.598648 + 0.801013i \(0.704295\pi\)
\(758\) −8.94911 −0.325046
\(759\) 0 0
\(760\) −20.0176 −0.726114
\(761\) −24.4080 −0.884791 −0.442396 0.896820i \(-0.645871\pi\)
−0.442396 + 0.896820i \(0.645871\pi\)
\(762\) 0 0
\(763\) 13.9241 0.504087
\(764\) 13.4432 0.486358
\(765\) 0 0
\(766\) −2.16251 −0.0781346
\(767\) 2.00415 0.0723656
\(768\) 0 0
\(769\) −0.979264 −0.0353132 −0.0176566 0.999844i \(-0.505621\pi\)
−0.0176566 + 0.999844i \(0.505621\pi\)
\(770\) −0.781128 −0.0281499
\(771\) 0 0
\(772\) −26.3198 −0.947269
\(773\) 47.3585 1.70337 0.851683 0.524057i \(-0.175582\pi\)
0.851683 + 0.524057i \(0.175582\pi\)
\(774\) 0 0
\(775\) −75.6870 −2.71876
\(776\) 17.3500 0.622827
\(777\) 0 0
\(778\) 5.30310 0.190125
\(779\) −38.7306 −1.38767
\(780\) 0 0
\(781\) 0.506871 0.0181373
\(782\) 10.9154 0.390334
\(783\) 0 0
\(784\) −22.7170 −0.811322
\(785\) −53.6053 −1.91326
\(786\) 0 0
\(787\) −21.9000 −0.780651 −0.390326 0.920677i \(-0.627638\pi\)
−0.390326 + 0.920677i \(0.627638\pi\)
\(788\) −24.6252 −0.877235
\(789\) 0 0
\(790\) −4.52934 −0.161147
\(791\) 12.2744 0.436428
\(792\) 0 0
\(793\) −1.28993 −0.0458067
\(794\) −3.99528 −0.141787
\(795\) 0 0
\(796\) −7.06948 −0.250571
\(797\) −16.0797 −0.569571 −0.284785 0.958591i \(-0.591922\pi\)
−0.284785 + 0.958591i \(0.591922\pi\)
\(798\) 0 0
\(799\) −42.9288 −1.51871
\(800\) −23.4011 −0.827353
\(801\) 0 0
\(802\) −7.30949 −0.258107
\(803\) −3.71011 −0.130927
\(804\) 0 0
\(805\) −21.6361 −0.762573
\(806\) −2.58311 −0.0909862
\(807\) 0 0
\(808\) 5.11164 0.179827
\(809\) 11.8133 0.415333 0.207667 0.978200i \(-0.433413\pi\)
0.207667 + 0.978200i \(0.433413\pi\)
\(810\) 0 0
\(811\) 29.4126 1.03281 0.516407 0.856343i \(-0.327269\pi\)
0.516407 + 0.856343i \(0.327269\pi\)
\(812\) −16.9980 −0.596514
\(813\) 0 0
\(814\) 2.02232 0.0708823
\(815\) −5.21691 −0.182740
\(816\) 0 0
\(817\) 56.7532 1.98554
\(818\) −4.81579 −0.168380
\(819\) 0 0
\(820\) −47.2368 −1.64958
\(821\) 30.6948 1.07125 0.535627 0.844454i \(-0.320075\pi\)
0.535627 + 0.844454i \(0.320075\pi\)
\(822\) 0 0
\(823\) 31.6432 1.10301 0.551505 0.834171i \(-0.314054\pi\)
0.551505 + 0.834171i \(0.314054\pi\)
\(824\) 14.6503 0.510366
\(825\) 0 0
\(826\) −0.327394 −0.0113915
\(827\) 13.0222 0.452825 0.226413 0.974031i \(-0.427300\pi\)
0.226413 + 0.974031i \(0.427300\pi\)
\(828\) 0 0
\(829\) 47.5998 1.65321 0.826604 0.562783i \(-0.190269\pi\)
0.826604 + 0.562783i \(0.190269\pi\)
\(830\) −6.37552 −0.221298
\(831\) 0 0
\(832\) 8.70017 0.301624
\(833\) −45.4554 −1.57494
\(834\) 0 0
\(835\) −51.9360 −1.79732
\(836\) −11.5160 −0.398290
\(837\) 0 0
\(838\) −2.87485 −0.0993102
\(839\) 2.77869 0.0959309 0.0479655 0.998849i \(-0.484726\pi\)
0.0479655 + 0.998849i \(0.484726\pi\)
\(840\) 0 0
\(841\) 62.8638 2.16772
\(842\) 2.20636 0.0760362
\(843\) 0 0
\(844\) 35.7126 1.22928
\(845\) 42.0222 1.44561
\(846\) 0 0
\(847\) −0.911108 −0.0313060
\(848\) 18.4477 0.633495
\(849\) 0 0
\(850\) −14.8945 −0.510877
\(851\) 56.0154 1.92018
\(852\) 0 0
\(853\) 19.4760 0.666845 0.333423 0.942777i \(-0.391796\pi\)
0.333423 + 0.942777i \(0.391796\pi\)
\(854\) 0.210720 0.00721071
\(855\) 0 0
\(856\) −14.7256 −0.503310
\(857\) 34.8220 1.18950 0.594749 0.803912i \(-0.297252\pi\)
0.594749 + 0.803912i \(0.297252\pi\)
\(858\) 0 0
\(859\) −8.18830 −0.279381 −0.139691 0.990195i \(-0.544611\pi\)
−0.139691 + 0.990195i \(0.544611\pi\)
\(860\) 69.2176 2.36030
\(861\) 0 0
\(862\) −2.89887 −0.0987359
\(863\) −34.4697 −1.17336 −0.586681 0.809818i \(-0.699566\pi\)
−0.586681 + 0.809818i \(0.699566\pi\)
\(864\) 0 0
\(865\) 9.92616 0.337500
\(866\) 4.16626 0.141575
\(867\) 0 0
\(868\) −15.3556 −0.521204
\(869\) −5.28303 −0.179215
\(870\) 0 0
\(871\) −16.4090 −0.555999
\(872\) −13.9492 −0.472378
\(873\) 0 0
\(874\) 8.76551 0.296498
\(875\) 12.6362 0.427182
\(876\) 0 0
\(877\) 22.6206 0.763845 0.381922 0.924194i \(-0.375262\pi\)
0.381922 + 0.924194i \(0.375262\pi\)
\(878\) 0.965007 0.0325674
\(879\) 0 0
\(880\) −13.6486 −0.460096
\(881\) −20.0360 −0.675029 −0.337514 0.941320i \(-0.609586\pi\)
−0.337514 + 0.941320i \(0.609586\pi\)
\(882\) 0 0
\(883\) −16.1716 −0.544217 −0.272108 0.962267i \(-0.587721\pi\)
−0.272108 + 0.962267i \(0.587721\pi\)
\(884\) 18.4982 0.622163
\(885\) 0 0
\(886\) −7.27255 −0.244326
\(887\) 14.1009 0.473460 0.236730 0.971575i \(-0.423924\pi\)
0.236730 + 0.971575i \(0.423924\pi\)
\(888\) 0 0
\(889\) −13.5863 −0.455669
\(890\) −10.9410 −0.366742
\(891\) 0 0
\(892\) −13.6248 −0.456193
\(893\) −34.4736 −1.15361
\(894\) 0 0
\(895\) 7.93504 0.265239
\(896\) −6.29940 −0.210448
\(897\) 0 0
\(898\) 3.11427 0.103924
\(899\) 82.9876 2.76779
\(900\) 0 0
\(901\) 36.9127 1.22974
\(902\) 1.51407 0.0504129
\(903\) 0 0
\(904\) −12.2965 −0.408975
\(905\) −38.7455 −1.28794
\(906\) 0 0
\(907\) −36.0807 −1.19804 −0.599019 0.800735i \(-0.704443\pi\)
−0.599019 + 0.800735i \(0.704443\pi\)
\(908\) 13.3419 0.442766
\(909\) 0 0
\(910\) 1.00760 0.0334015
\(911\) 20.4544 0.677684 0.338842 0.940843i \(-0.389965\pi\)
0.338842 + 0.940843i \(0.389965\pi\)
\(912\) 0 0
\(913\) −7.43641 −0.246109
\(914\) −3.70953 −0.122700
\(915\) 0 0
\(916\) 4.18596 0.138308
\(917\) 1.38823 0.0458432
\(918\) 0 0
\(919\) 43.7171 1.44209 0.721046 0.692887i \(-0.243662\pi\)
0.721046 + 0.692887i \(0.243662\pi\)
\(920\) 21.6750 0.714604
\(921\) 0 0
\(922\) −0.480411 −0.0158215
\(923\) −0.653827 −0.0215210
\(924\) 0 0
\(925\) −76.4352 −2.51317
\(926\) −5.17962 −0.170213
\(927\) 0 0
\(928\) 25.6583 0.842275
\(929\) 34.9056 1.14521 0.572607 0.819830i \(-0.305932\pi\)
0.572607 + 0.819830i \(0.305932\pi\)
\(930\) 0 0
\(931\) −36.5025 −1.19632
\(932\) −0.171022 −0.00560202
\(933\) 0 0
\(934\) 1.81451 0.0593724
\(935\) −27.3101 −0.893136
\(936\) 0 0
\(937\) 27.5062 0.898589 0.449294 0.893384i \(-0.351675\pi\)
0.449294 + 0.893384i \(0.351675\pi\)
\(938\) 2.68055 0.0875232
\(939\) 0 0
\(940\) −42.0448 −1.37135
\(941\) −35.8790 −1.16962 −0.584811 0.811170i \(-0.698831\pi\)
−0.584811 + 0.811170i \(0.698831\pi\)
\(942\) 0 0
\(943\) 41.9375 1.36567
\(944\) −5.72057 −0.186189
\(945\) 0 0
\(946\) −2.21861 −0.0721333
\(947\) 11.3161 0.367724 0.183862 0.982952i \(-0.441140\pi\)
0.183862 + 0.982952i \(0.441140\pi\)
\(948\) 0 0
\(949\) 4.78578 0.155353
\(950\) −11.9609 −0.388062
\(951\) 0 0
\(952\) −6.12672 −0.198568
\(953\) 2.13994 0.0693195 0.0346598 0.999399i \(-0.488965\pi\)
0.0346598 + 0.999399i \(0.488965\pi\)
\(954\) 0 0
\(955\) 25.6013 0.828438
\(956\) −2.62033 −0.0847475
\(957\) 0 0
\(958\) −5.53493 −0.178826
\(959\) 3.37417 0.108958
\(960\) 0 0
\(961\) 43.9690 1.41836
\(962\) −2.60865 −0.0841062
\(963\) 0 0
\(964\) −8.83727 −0.284629
\(965\) −50.1234 −1.61353
\(966\) 0 0
\(967\) 28.0975 0.903555 0.451778 0.892131i \(-0.350790\pi\)
0.451778 + 0.892131i \(0.350790\pi\)
\(968\) 0.912746 0.0293368
\(969\) 0 0
\(970\) 16.2967 0.523257
\(971\) 50.8194 1.63087 0.815436 0.578847i \(-0.196497\pi\)
0.815436 + 0.578847i \(0.196497\pi\)
\(972\) 0 0
\(973\) −5.56378 −0.178366
\(974\) −5.97251 −0.191372
\(975\) 0 0
\(976\) 3.68192 0.117855
\(977\) 27.5896 0.882670 0.441335 0.897342i \(-0.354505\pi\)
0.441335 + 0.897342i \(0.354505\pi\)
\(978\) 0 0
\(979\) −12.7615 −0.407860
\(980\) −44.5193 −1.42212
\(981\) 0 0
\(982\) −7.24396 −0.231164
\(983\) −28.6548 −0.913945 −0.456973 0.889481i \(-0.651066\pi\)
−0.456973 + 0.889481i \(0.651066\pi\)
\(984\) 0 0
\(985\) −46.8962 −1.49424
\(986\) 16.3312 0.520091
\(987\) 0 0
\(988\) 14.8548 0.472595
\(989\) −61.4524 −1.95407
\(990\) 0 0
\(991\) 19.1844 0.609412 0.304706 0.952447i \(-0.401442\pi\)
0.304706 + 0.952447i \(0.401442\pi\)
\(992\) 23.1791 0.735937
\(993\) 0 0
\(994\) 0.106808 0.00338775
\(995\) −13.4631 −0.426810
\(996\) 0 0
\(997\) −4.14208 −0.131181 −0.0655905 0.997847i \(-0.520893\pi\)
−0.0655905 + 0.997847i \(0.520893\pi\)
\(998\) −5.68737 −0.180031
\(999\) 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 \(a_p\))