Properties

Label 8046.2.a.l.1.6
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.448758\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+0.448758 q^{5}\) \(-1.52942 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+0.448758 q^{5}\) \(-1.52942 q^{7}\) \(-1.00000 q^{8}\) \(-0.448758 q^{10}\) \(-0.412196 q^{11}\) \(+3.36442 q^{13}\) \(+1.52942 q^{14}\) \(+1.00000 q^{16}\) \(+3.96634 q^{17}\) \(-5.13026 q^{19}\) \(+0.448758 q^{20}\) \(+0.412196 q^{22}\) \(-2.63703 q^{23}\) \(-4.79862 q^{25}\) \(-3.36442 q^{26}\) \(-1.52942 q^{28}\) \(-2.15254 q^{29}\) \(-5.88764 q^{31}\) \(-1.00000 q^{32}\) \(-3.96634 q^{34}\) \(-0.686340 q^{35}\) \(+10.4747 q^{37}\) \(+5.13026 q^{38}\) \(-0.448758 q^{40}\) \(-5.89535 q^{41}\) \(+1.10493 q^{43}\) \(-0.412196 q^{44}\) \(+2.63703 q^{46}\) \(+5.78830 q^{47}\) \(-4.66087 q^{49}\) \(+4.79862 q^{50}\) \(+3.36442 q^{52}\) \(-1.69686 q^{53}\) \(-0.184976 q^{55}\) \(+1.52942 q^{56}\) \(+2.15254 q^{58}\) \(+11.9240 q^{59}\) \(+12.2236 q^{61}\) \(+5.88764 q^{62}\) \(+1.00000 q^{64}\) \(+1.50981 q^{65}\) \(-15.8063 q^{67}\) \(+3.96634 q^{68}\) \(+0.686340 q^{70}\) \(+12.3113 q^{71}\) \(+5.42784 q^{73}\) \(-10.4747 q^{74}\) \(-5.13026 q^{76}\) \(+0.630422 q^{77}\) \(+2.21050 q^{79}\) \(+0.448758 q^{80}\) \(+5.89535 q^{82}\) \(+11.7231 q^{83}\) \(+1.77993 q^{85}\) \(-1.10493 q^{86}\) \(+0.412196 q^{88}\) \(+0.410694 q^{89}\) \(-5.14562 q^{91}\) \(-2.63703 q^{92}\) \(-5.78830 q^{94}\) \(-2.30224 q^{95}\) \(+4.08503 q^{97}\) \(+4.66087 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0.448758 0.200691 0.100345 0.994953i \(-0.468005\pi\)
0.100345 + 0.994953i \(0.468005\pi\)
\(6\) 0 0
\(7\) −1.52942 −0.578067 −0.289033 0.957319i \(-0.593334\pi\)
−0.289033 + 0.957319i \(0.593334\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.448758 −0.141910
\(11\) −0.412196 −0.124282 −0.0621409 0.998067i \(-0.519793\pi\)
−0.0621409 + 0.998067i \(0.519793\pi\)
\(12\) 0 0
\(13\) 3.36442 0.933123 0.466561 0.884489i \(-0.345493\pi\)
0.466561 + 0.884489i \(0.345493\pi\)
\(14\) 1.52942 0.408755
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.96634 0.961979 0.480989 0.876726i \(-0.340278\pi\)
0.480989 + 0.876726i \(0.340278\pi\)
\(18\) 0 0
\(19\) −5.13026 −1.17696 −0.588481 0.808511i \(-0.700274\pi\)
−0.588481 + 0.808511i \(0.700274\pi\)
\(20\) 0.448758 0.100345
\(21\) 0 0
\(22\) 0.412196 0.0878805
\(23\) −2.63703 −0.549858 −0.274929 0.961465i \(-0.588654\pi\)
−0.274929 + 0.961465i \(0.588654\pi\)
\(24\) 0 0
\(25\) −4.79862 −0.959723
\(26\) −3.36442 −0.659817
\(27\) 0 0
\(28\) −1.52942 −0.289033
\(29\) −2.15254 −0.399717 −0.199858 0.979825i \(-0.564048\pi\)
−0.199858 + 0.979825i \(0.564048\pi\)
\(30\) 0 0
\(31\) −5.88764 −1.05745 −0.528726 0.848793i \(-0.677330\pi\)
−0.528726 + 0.848793i \(0.677330\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.96634 −0.680222
\(35\) −0.686340 −0.116013
\(36\) 0 0
\(37\) 10.4747 1.72203 0.861013 0.508583i \(-0.169830\pi\)
0.861013 + 0.508583i \(0.169830\pi\)
\(38\) 5.13026 0.832238
\(39\) 0 0
\(40\) −0.448758 −0.0709549
\(41\) −5.89535 −0.920700 −0.460350 0.887738i \(-0.652276\pi\)
−0.460350 + 0.887738i \(0.652276\pi\)
\(42\) 0 0
\(43\) 1.10493 0.168500 0.0842498 0.996445i \(-0.473151\pi\)
0.0842498 + 0.996445i \(0.473151\pi\)
\(44\) −0.412196 −0.0621409
\(45\) 0 0
\(46\) 2.63703 0.388808
\(47\) 5.78830 0.844310 0.422155 0.906524i \(-0.361274\pi\)
0.422155 + 0.906524i \(0.361274\pi\)
\(48\) 0 0
\(49\) −4.66087 −0.665839
\(50\) 4.79862 0.678627
\(51\) 0 0
\(52\) 3.36442 0.466561
\(53\) −1.69686 −0.233082 −0.116541 0.993186i \(-0.537181\pi\)
−0.116541 + 0.993186i \(0.537181\pi\)
\(54\) 0 0
\(55\) −0.184976 −0.0249422
\(56\) 1.52942 0.204378
\(57\) 0 0
\(58\) 2.15254 0.282642
\(59\) 11.9240 1.55237 0.776187 0.630503i \(-0.217151\pi\)
0.776187 + 0.630503i \(0.217151\pi\)
\(60\) 0 0
\(61\) 12.2236 1.56507 0.782533 0.622609i \(-0.213927\pi\)
0.782533 + 0.622609i \(0.213927\pi\)
\(62\) 5.88764 0.747731
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.50981 0.187269
\(66\) 0 0
\(67\) −15.8063 −1.93105 −0.965526 0.260307i \(-0.916176\pi\)
−0.965526 + 0.260307i \(0.916176\pi\)
\(68\) 3.96634 0.480989
\(69\) 0 0
\(70\) 0.686340 0.0820333
\(71\) 12.3113 1.46108 0.730541 0.682869i \(-0.239268\pi\)
0.730541 + 0.682869i \(0.239268\pi\)
\(72\) 0 0
\(73\) 5.42784 0.635280 0.317640 0.948211i \(-0.397110\pi\)
0.317640 + 0.948211i \(0.397110\pi\)
\(74\) −10.4747 −1.21766
\(75\) 0 0
\(76\) −5.13026 −0.588481
\(77\) 0.630422 0.0718432
\(78\) 0 0
\(79\) 2.21050 0.248701 0.124350 0.992238i \(-0.460315\pi\)
0.124350 + 0.992238i \(0.460315\pi\)
\(80\) 0.448758 0.0501727
\(81\) 0 0
\(82\) 5.89535 0.651033
\(83\) 11.7231 1.28678 0.643390 0.765538i \(-0.277527\pi\)
0.643390 + 0.765538i \(0.277527\pi\)
\(84\) 0 0
\(85\) 1.77993 0.193060
\(86\) −1.10493 −0.119147
\(87\) 0 0
\(88\) 0.412196 0.0439403
\(89\) 0.410694 0.0435335 0.0217667 0.999763i \(-0.493071\pi\)
0.0217667 + 0.999763i \(0.493071\pi\)
\(90\) 0 0
\(91\) −5.14562 −0.539407
\(92\) −2.63703 −0.274929
\(93\) 0 0
\(94\) −5.78830 −0.597018
\(95\) −2.30224 −0.236205
\(96\) 0 0
\(97\) 4.08503 0.414772 0.207386 0.978259i \(-0.433504\pi\)
0.207386 + 0.978259i \(0.433504\pi\)
\(98\) 4.66087 0.470819
\(99\) 0 0
\(100\) −4.79862 −0.479862
\(101\) 2.71317 0.269971 0.134985 0.990848i \(-0.456901\pi\)
0.134985 + 0.990848i \(0.456901\pi\)
\(102\) 0 0
\(103\) −8.11049 −0.799150 −0.399575 0.916700i \(-0.630842\pi\)
−0.399575 + 0.916700i \(0.630842\pi\)
\(104\) −3.36442 −0.329909
\(105\) 0 0
\(106\) 1.69686 0.164814
\(107\) 2.84336 0.274878 0.137439 0.990510i \(-0.456113\pi\)
0.137439 + 0.990510i \(0.456113\pi\)
\(108\) 0 0
\(109\) −7.54113 −0.722309 −0.361155 0.932506i \(-0.617617\pi\)
−0.361155 + 0.932506i \(0.617617\pi\)
\(110\) 0.184976 0.0176368
\(111\) 0 0
\(112\) −1.52942 −0.144517
\(113\) 13.2743 1.24874 0.624369 0.781130i \(-0.285356\pi\)
0.624369 + 0.781130i \(0.285356\pi\)
\(114\) 0 0
\(115\) −1.18339 −0.110351
\(116\) −2.15254 −0.199858
\(117\) 0 0
\(118\) −11.9240 −1.09769
\(119\) −6.06621 −0.556088
\(120\) 0 0
\(121\) −10.8301 −0.984554
\(122\) −12.2236 −1.10667
\(123\) 0 0
\(124\) −5.88764 −0.528726
\(125\) −4.39721 −0.393298
\(126\) 0 0
\(127\) 2.16121 0.191776 0.0958882 0.995392i \(-0.469431\pi\)
0.0958882 + 0.995392i \(0.469431\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −1.50981 −0.132419
\(131\) −8.82663 −0.771187 −0.385593 0.922669i \(-0.626003\pi\)
−0.385593 + 0.922669i \(0.626003\pi\)
\(132\) 0 0
\(133\) 7.84633 0.680363
\(134\) 15.8063 1.36546
\(135\) 0 0
\(136\) −3.96634 −0.340111
\(137\) 16.8659 1.44095 0.720477 0.693478i \(-0.243923\pi\)
0.720477 + 0.693478i \(0.243923\pi\)
\(138\) 0 0
\(139\) −6.15934 −0.522428 −0.261214 0.965281i \(-0.584123\pi\)
−0.261214 + 0.965281i \(0.584123\pi\)
\(140\) −0.686340 −0.0580063
\(141\) 0 0
\(142\) −12.3113 −1.03314
\(143\) −1.38680 −0.115970
\(144\) 0 0
\(145\) −0.965970 −0.0802194
\(146\) −5.42784 −0.449211
\(147\) 0 0
\(148\) 10.4747 0.861013
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) −3.51636 −0.286157 −0.143079 0.989711i \(-0.545700\pi\)
−0.143079 + 0.989711i \(0.545700\pi\)
\(152\) 5.13026 0.416119
\(153\) 0 0
\(154\) −0.630422 −0.0508008
\(155\) −2.64213 −0.212221
\(156\) 0 0
\(157\) 8.71888 0.695843 0.347921 0.937524i \(-0.386888\pi\)
0.347921 + 0.937524i \(0.386888\pi\)
\(158\) −2.21050 −0.175858
\(159\) 0 0
\(160\) −0.448758 −0.0354774
\(161\) 4.03312 0.317855
\(162\) 0 0
\(163\) −5.58812 −0.437696 −0.218848 0.975759i \(-0.570230\pi\)
−0.218848 + 0.975759i \(0.570230\pi\)
\(164\) −5.89535 −0.460350
\(165\) 0 0
\(166\) −11.7231 −0.909891
\(167\) −22.8936 −1.77156 −0.885778 0.464108i \(-0.846375\pi\)
−0.885778 + 0.464108i \(0.846375\pi\)
\(168\) 0 0
\(169\) −1.68067 −0.129282
\(170\) −1.77993 −0.136514
\(171\) 0 0
\(172\) 1.10493 0.0842498
\(173\) 19.4389 1.47791 0.738955 0.673754i \(-0.235319\pi\)
0.738955 + 0.673754i \(0.235319\pi\)
\(174\) 0 0
\(175\) 7.33911 0.554784
\(176\) −0.412196 −0.0310705
\(177\) 0 0
\(178\) −0.410694 −0.0307828
\(179\) 16.6171 1.24202 0.621011 0.783802i \(-0.286722\pi\)
0.621011 + 0.783802i \(0.286722\pi\)
\(180\) 0 0
\(181\) 0.435647 0.0323814 0.0161907 0.999869i \(-0.494846\pi\)
0.0161907 + 0.999869i \(0.494846\pi\)
\(182\) 5.14562 0.381419
\(183\) 0 0
\(184\) 2.63703 0.194404
\(185\) 4.70059 0.345595
\(186\) 0 0
\(187\) −1.63491 −0.119557
\(188\) 5.78830 0.422155
\(189\) 0 0
\(190\) 2.30224 0.167022
\(191\) −16.5232 −1.19557 −0.597787 0.801655i \(-0.703953\pi\)
−0.597787 + 0.801655i \(0.703953\pi\)
\(192\) 0 0
\(193\) −11.9297 −0.858716 −0.429358 0.903134i \(-0.641260\pi\)
−0.429358 + 0.903134i \(0.641260\pi\)
\(194\) −4.08503 −0.293288
\(195\) 0 0
\(196\) −4.66087 −0.332919
\(197\) −17.4448 −1.24289 −0.621447 0.783456i \(-0.713455\pi\)
−0.621447 + 0.783456i \(0.713455\pi\)
\(198\) 0 0
\(199\) 21.2904 1.50923 0.754617 0.656166i \(-0.227823\pi\)
0.754617 + 0.656166i \(0.227823\pi\)
\(200\) 4.79862 0.339313
\(201\) 0 0
\(202\) −2.71317 −0.190898
\(203\) 3.29214 0.231063
\(204\) 0 0
\(205\) −2.64559 −0.184776
\(206\) 8.11049 0.565085
\(207\) 0 0
\(208\) 3.36442 0.233281
\(209\) 2.11467 0.146275
\(210\) 0 0
\(211\) 15.0226 1.03420 0.517098 0.855926i \(-0.327012\pi\)
0.517098 + 0.855926i \(0.327012\pi\)
\(212\) −1.69686 −0.116541
\(213\) 0 0
\(214\) −2.84336 −0.194368
\(215\) 0.495844 0.0338163
\(216\) 0 0
\(217\) 9.00469 0.611278
\(218\) 7.54113 0.510750
\(219\) 0 0
\(220\) −0.184976 −0.0124711
\(221\) 13.3444 0.897644
\(222\) 0 0
\(223\) −14.0252 −0.939196 −0.469598 0.882880i \(-0.655601\pi\)
−0.469598 + 0.882880i \(0.655601\pi\)
\(224\) 1.52942 0.102189
\(225\) 0 0
\(226\) −13.2743 −0.882991
\(227\) −0.382438 −0.0253833 −0.0126917 0.999919i \(-0.504040\pi\)
−0.0126917 + 0.999919i \(0.504040\pi\)
\(228\) 0 0
\(229\) 20.5931 1.36083 0.680416 0.732826i \(-0.261799\pi\)
0.680416 + 0.732826i \(0.261799\pi\)
\(230\) 1.18339 0.0780302
\(231\) 0 0
\(232\) 2.15254 0.141321
\(233\) 10.0982 0.661553 0.330776 0.943709i \(-0.392689\pi\)
0.330776 + 0.943709i \(0.392689\pi\)
\(234\) 0 0
\(235\) 2.59755 0.169445
\(236\) 11.9240 0.776187
\(237\) 0 0
\(238\) 6.06621 0.393214
\(239\) −11.1356 −0.720300 −0.360150 0.932894i \(-0.617275\pi\)
−0.360150 + 0.932894i \(0.617275\pi\)
\(240\) 0 0
\(241\) 5.22345 0.336472 0.168236 0.985747i \(-0.446193\pi\)
0.168236 + 0.985747i \(0.446193\pi\)
\(242\) 10.8301 0.696185
\(243\) 0 0
\(244\) 12.2236 0.782533
\(245\) −2.09160 −0.133628
\(246\) 0 0
\(247\) −17.2604 −1.09825
\(248\) 5.88764 0.373866
\(249\) 0 0
\(250\) 4.39721 0.278104
\(251\) −13.7996 −0.871026 −0.435513 0.900183i \(-0.643433\pi\)
−0.435513 + 0.900183i \(0.643433\pi\)
\(252\) 0 0
\(253\) 1.08697 0.0683374
\(254\) −2.16121 −0.135606
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 15.4652 0.964690 0.482345 0.875981i \(-0.339785\pi\)
0.482345 + 0.875981i \(0.339785\pi\)
\(258\) 0 0
\(259\) −16.0202 −0.995446
\(260\) 1.50981 0.0936345
\(261\) 0 0
\(262\) 8.82663 0.545311
\(263\) 25.6673 1.58271 0.791356 0.611355i \(-0.209375\pi\)
0.791356 + 0.611355i \(0.209375\pi\)
\(264\) 0 0
\(265\) −0.761480 −0.0467773
\(266\) −7.84633 −0.481089
\(267\) 0 0
\(268\) −15.8063 −0.965526
\(269\) 17.3104 1.05544 0.527718 0.849420i \(-0.323048\pi\)
0.527718 + 0.849420i \(0.323048\pi\)
\(270\) 0 0
\(271\) −1.02623 −0.0623391 −0.0311696 0.999514i \(-0.509923\pi\)
−0.0311696 + 0.999514i \(0.509923\pi\)
\(272\) 3.96634 0.240495
\(273\) 0 0
\(274\) −16.8659 −1.01891
\(275\) 1.97797 0.119276
\(276\) 0 0
\(277\) 21.6609 1.30148 0.650739 0.759302i \(-0.274459\pi\)
0.650739 + 0.759302i \(0.274459\pi\)
\(278\) 6.15934 0.369412
\(279\) 0 0
\(280\) 0.686340 0.0410167
\(281\) 23.3056 1.39029 0.695147 0.718867i \(-0.255339\pi\)
0.695147 + 0.718867i \(0.255339\pi\)
\(282\) 0 0
\(283\) 15.4938 0.921014 0.460507 0.887656i \(-0.347668\pi\)
0.460507 + 0.887656i \(0.347668\pi\)
\(284\) 12.3113 0.730541
\(285\) 0 0
\(286\) 1.38680 0.0820033
\(287\) 9.01648 0.532226
\(288\) 0 0
\(289\) −1.26814 −0.0745964
\(290\) 0.965970 0.0567237
\(291\) 0 0
\(292\) 5.42784 0.317640
\(293\) 18.4933 1.08039 0.540196 0.841539i \(-0.318350\pi\)
0.540196 + 0.841539i \(0.318350\pi\)
\(294\) 0 0
\(295\) 5.35099 0.311547
\(296\) −10.4747 −0.608828
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −8.87207 −0.513085
\(300\) 0 0
\(301\) −1.68990 −0.0974041
\(302\) 3.51636 0.202344
\(303\) 0 0
\(304\) −5.13026 −0.294240
\(305\) 5.48542 0.314094
\(306\) 0 0
\(307\) 20.5286 1.17163 0.585814 0.810445i \(-0.300775\pi\)
0.585814 + 0.810445i \(0.300775\pi\)
\(308\) 0.630422 0.0359216
\(309\) 0 0
\(310\) 2.64213 0.150063
\(311\) 15.1347 0.858212 0.429106 0.903254i \(-0.358829\pi\)
0.429106 + 0.903254i \(0.358829\pi\)
\(312\) 0 0
\(313\) −27.6172 −1.56102 −0.780509 0.625145i \(-0.785040\pi\)
−0.780509 + 0.625145i \(0.785040\pi\)
\(314\) −8.71888 −0.492035
\(315\) 0 0
\(316\) 2.21050 0.124350
\(317\) 23.3262 1.31013 0.655064 0.755573i \(-0.272642\pi\)
0.655064 + 0.755573i \(0.272642\pi\)
\(318\) 0 0
\(319\) 0.887269 0.0496775
\(320\) 0.448758 0.0250863
\(321\) 0 0
\(322\) −4.03312 −0.224757
\(323\) −20.3484 −1.13221
\(324\) 0 0
\(325\) −16.1446 −0.895539
\(326\) 5.58812 0.309498
\(327\) 0 0
\(328\) 5.89535 0.325516
\(329\) −8.85275 −0.488068
\(330\) 0 0
\(331\) −31.3199 −1.72149 −0.860747 0.509032i \(-0.830003\pi\)
−0.860747 + 0.509032i \(0.830003\pi\)
\(332\) 11.7231 0.643390
\(333\) 0 0
\(334\) 22.8936 1.25268
\(335\) −7.09322 −0.387544
\(336\) 0 0
\(337\) −3.36124 −0.183099 −0.0915493 0.995801i \(-0.529182\pi\)
−0.0915493 + 0.995801i \(0.529182\pi\)
\(338\) 1.68067 0.0914163
\(339\) 0 0
\(340\) 1.77993 0.0965301
\(341\) 2.42686 0.131422
\(342\) 0 0
\(343\) 17.8344 0.962966
\(344\) −1.10493 −0.0595736
\(345\) 0 0
\(346\) −19.4389 −1.04504
\(347\) −11.2162 −0.602116 −0.301058 0.953606i \(-0.597340\pi\)
−0.301058 + 0.953606i \(0.597340\pi\)
\(348\) 0 0
\(349\) 13.4404 0.719448 0.359724 0.933059i \(-0.382871\pi\)
0.359724 + 0.933059i \(0.382871\pi\)
\(350\) −7.33911 −0.392292
\(351\) 0 0
\(352\) 0.412196 0.0219701
\(353\) −8.27345 −0.440351 −0.220176 0.975460i \(-0.570663\pi\)
−0.220176 + 0.975460i \(0.570663\pi\)
\(354\) 0 0
\(355\) 5.52479 0.293226
\(356\) 0.410694 0.0217667
\(357\) 0 0
\(358\) −16.6171 −0.878242
\(359\) 31.9960 1.68869 0.844343 0.535802i \(-0.179991\pi\)
0.844343 + 0.535802i \(0.179991\pi\)
\(360\) 0 0
\(361\) 7.31955 0.385239
\(362\) −0.435647 −0.0228971
\(363\) 0 0
\(364\) −5.14562 −0.269704
\(365\) 2.43578 0.127495
\(366\) 0 0
\(367\) −17.2289 −0.899342 −0.449671 0.893194i \(-0.648459\pi\)
−0.449671 + 0.893194i \(0.648459\pi\)
\(368\) −2.63703 −0.137465
\(369\) 0 0
\(370\) −4.70059 −0.244372
\(371\) 2.59522 0.134737
\(372\) 0 0
\(373\) −4.22649 −0.218839 −0.109420 0.993996i \(-0.534899\pi\)
−0.109420 + 0.993996i \(0.534899\pi\)
\(374\) 1.63491 0.0845392
\(375\) 0 0
\(376\) −5.78830 −0.298509
\(377\) −7.24205 −0.372985
\(378\) 0 0
\(379\) −4.84751 −0.249000 −0.124500 0.992220i \(-0.539733\pi\)
−0.124500 + 0.992220i \(0.539733\pi\)
\(380\) −2.30224 −0.118103
\(381\) 0 0
\(382\) 16.5232 0.845399
\(383\) 26.5621 1.35726 0.678629 0.734481i \(-0.262574\pi\)
0.678629 + 0.734481i \(0.262574\pi\)
\(384\) 0 0
\(385\) 0.282907 0.0144183
\(386\) 11.9297 0.607204
\(387\) 0 0
\(388\) 4.08503 0.207386
\(389\) 31.1841 1.58110 0.790548 0.612400i \(-0.209796\pi\)
0.790548 + 0.612400i \(0.209796\pi\)
\(390\) 0 0
\(391\) −10.4593 −0.528952
\(392\) 4.66087 0.235410
\(393\) 0 0
\(394\) 17.4448 0.878858
\(395\) 0.991979 0.0499119
\(396\) 0 0
\(397\) 38.9060 1.95264 0.976319 0.216335i \(-0.0694103\pi\)
0.976319 + 0.216335i \(0.0694103\pi\)
\(398\) −21.2904 −1.06719
\(399\) 0 0
\(400\) −4.79862 −0.239931
\(401\) −27.4187 −1.36923 −0.684613 0.728907i \(-0.740029\pi\)
−0.684613 + 0.728907i \(0.740029\pi\)
\(402\) 0 0
\(403\) −19.8085 −0.986732
\(404\) 2.71317 0.134985
\(405\) 0 0
\(406\) −3.29214 −0.163386
\(407\) −4.31762 −0.214017
\(408\) 0 0
\(409\) 13.5525 0.670129 0.335065 0.942195i \(-0.391242\pi\)
0.335065 + 0.942195i \(0.391242\pi\)
\(410\) 2.64559 0.130656
\(411\) 0 0
\(412\) −8.11049 −0.399575
\(413\) −18.2368 −0.897376
\(414\) 0 0
\(415\) 5.26085 0.258245
\(416\) −3.36442 −0.164954
\(417\) 0 0
\(418\) −2.11467 −0.103432
\(419\) −5.66966 −0.276981 −0.138490 0.990364i \(-0.544225\pi\)
−0.138490 + 0.990364i \(0.544225\pi\)
\(420\) 0 0
\(421\) 18.4788 0.900603 0.450301 0.892877i \(-0.351317\pi\)
0.450301 + 0.892877i \(0.351317\pi\)
\(422\) −15.0226 −0.731287
\(423\) 0 0
\(424\) 1.69686 0.0824069
\(425\) −19.0329 −0.923234
\(426\) 0 0
\(427\) −18.6950 −0.904713
\(428\) 2.84336 0.137439
\(429\) 0 0
\(430\) −0.495844 −0.0239117
\(431\) 13.9772 0.673260 0.336630 0.941637i \(-0.390713\pi\)
0.336630 + 0.941637i \(0.390713\pi\)
\(432\) 0 0
\(433\) −23.6058 −1.13442 −0.567211 0.823572i \(-0.691978\pi\)
−0.567211 + 0.823572i \(0.691978\pi\)
\(434\) −9.00469 −0.432239
\(435\) 0 0
\(436\) −7.54113 −0.361155
\(437\) 13.5286 0.647162
\(438\) 0 0
\(439\) −36.6939 −1.75130 −0.875651 0.482944i \(-0.839567\pi\)
−0.875651 + 0.482944i \(0.839567\pi\)
\(440\) 0.184976 0.00881840
\(441\) 0 0
\(442\) −13.3444 −0.634730
\(443\) 26.2648 1.24788 0.623939 0.781473i \(-0.285531\pi\)
0.623939 + 0.781473i \(0.285531\pi\)
\(444\) 0 0
\(445\) 0.184302 0.00873676
\(446\) 14.0252 0.664112
\(447\) 0 0
\(448\) −1.52942 −0.0722584
\(449\) 15.4702 0.730084 0.365042 0.930991i \(-0.381055\pi\)
0.365042 + 0.930991i \(0.381055\pi\)
\(450\) 0 0
\(451\) 2.43004 0.114426
\(452\) 13.2743 0.624369
\(453\) 0 0
\(454\) 0.382438 0.0179487
\(455\) −2.30914 −0.108254
\(456\) 0 0
\(457\) −34.4833 −1.61306 −0.806531 0.591192i \(-0.798657\pi\)
−0.806531 + 0.591192i \(0.798657\pi\)
\(458\) −20.5931 −0.962253
\(459\) 0 0
\(460\) −1.18339 −0.0551757
\(461\) −22.4975 −1.04781 −0.523906 0.851776i \(-0.675526\pi\)
−0.523906 + 0.851776i \(0.675526\pi\)
\(462\) 0 0
\(463\) 20.7183 0.962859 0.481430 0.876485i \(-0.340118\pi\)
0.481430 + 0.876485i \(0.340118\pi\)
\(464\) −2.15254 −0.0999292
\(465\) 0 0
\(466\) −10.0982 −0.467789
\(467\) 21.3417 0.987575 0.493787 0.869583i \(-0.335612\pi\)
0.493787 + 0.869583i \(0.335612\pi\)
\(468\) 0 0
\(469\) 24.1746 1.11628
\(470\) −2.59755 −0.119816
\(471\) 0 0
\(472\) −11.9240 −0.548847
\(473\) −0.455447 −0.0209415
\(474\) 0 0
\(475\) 24.6181 1.12956
\(476\) −6.06621 −0.278044
\(477\) 0 0
\(478\) 11.1356 0.509329
\(479\) −21.6025 −0.987043 −0.493521 0.869734i \(-0.664291\pi\)
−0.493521 + 0.869734i \(0.664291\pi\)
\(480\) 0 0
\(481\) 35.2412 1.60686
\(482\) −5.22345 −0.237921
\(483\) 0 0
\(484\) −10.8301 −0.492277
\(485\) 1.83319 0.0832409
\(486\) 0 0
\(487\) −24.2335 −1.09812 −0.549062 0.835782i \(-0.685015\pi\)
−0.549062 + 0.835782i \(0.685015\pi\)
\(488\) −12.2236 −0.553334
\(489\) 0 0
\(490\) 2.09160 0.0944890
\(491\) −18.0062 −0.812609 −0.406305 0.913738i \(-0.633183\pi\)
−0.406305 + 0.913738i \(0.633183\pi\)
\(492\) 0 0
\(493\) −8.53771 −0.384519
\(494\) 17.2604 0.776580
\(495\) 0 0
\(496\) −5.88764 −0.264363
\(497\) −18.8292 −0.844604
\(498\) 0 0
\(499\) −32.4315 −1.45183 −0.725916 0.687784i \(-0.758584\pi\)
−0.725916 + 0.687784i \(0.758584\pi\)
\(500\) −4.39721 −0.196649
\(501\) 0 0
\(502\) 13.7996 0.615908
\(503\) 39.8535 1.77698 0.888489 0.458897i \(-0.151755\pi\)
0.888489 + 0.458897i \(0.151755\pi\)
\(504\) 0 0
\(505\) 1.21756 0.0541806
\(506\) −1.08697 −0.0483218
\(507\) 0 0
\(508\) 2.16121 0.0958882
\(509\) −25.8808 −1.14715 −0.573573 0.819155i \(-0.694443\pi\)
−0.573573 + 0.819155i \(0.694443\pi\)
\(510\) 0 0
\(511\) −8.30145 −0.367234
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.4652 −0.682139
\(515\) −3.63965 −0.160382
\(516\) 0 0
\(517\) −2.38592 −0.104932
\(518\) 16.0202 0.703887
\(519\) 0 0
\(520\) −1.50981 −0.0662096
\(521\) 1.80800 0.0792098 0.0396049 0.999215i \(-0.487390\pi\)
0.0396049 + 0.999215i \(0.487390\pi\)
\(522\) 0 0
\(523\) 12.7444 0.557274 0.278637 0.960396i \(-0.410117\pi\)
0.278637 + 0.960396i \(0.410117\pi\)
\(524\) −8.82663 −0.385593
\(525\) 0 0
\(526\) −25.6673 −1.11915
\(527\) −23.3524 −1.01725
\(528\) 0 0
\(529\) −16.0461 −0.697656
\(530\) 0.761480 0.0330766
\(531\) 0 0
\(532\) 7.84633 0.340181
\(533\) −19.8345 −0.859126
\(534\) 0 0
\(535\) 1.27598 0.0551655
\(536\) 15.8063 0.682730
\(537\) 0 0
\(538\) −17.3104 −0.746306
\(539\) 1.92119 0.0827517
\(540\) 0 0
\(541\) −1.88791 −0.0811674 −0.0405837 0.999176i \(-0.512922\pi\)
−0.0405837 + 0.999176i \(0.512922\pi\)
\(542\) 1.02623 0.0440804
\(543\) 0 0
\(544\) −3.96634 −0.170055
\(545\) −3.38414 −0.144961
\(546\) 0 0
\(547\) 32.6811 1.39734 0.698671 0.715443i \(-0.253775\pi\)
0.698671 + 0.715443i \(0.253775\pi\)
\(548\) 16.8659 0.720477
\(549\) 0 0
\(550\) −1.97797 −0.0843410
\(551\) 11.0431 0.470451
\(552\) 0 0
\(553\) −3.38078 −0.143766
\(554\) −21.6609 −0.920283
\(555\) 0 0
\(556\) −6.15934 −0.261214
\(557\) −19.7850 −0.838316 −0.419158 0.907913i \(-0.637675\pi\)
−0.419158 + 0.907913i \(0.637675\pi\)
\(558\) 0 0
\(559\) 3.71744 0.157231
\(560\) −0.686340 −0.0290032
\(561\) 0 0
\(562\) −23.3056 −0.983087
\(563\) 0.579433 0.0244202 0.0122101 0.999925i \(-0.496113\pi\)
0.0122101 + 0.999925i \(0.496113\pi\)
\(564\) 0 0
\(565\) 5.95693 0.250610
\(566\) −15.4938 −0.651255
\(567\) 0 0
\(568\) −12.3113 −0.516571
\(569\) 37.1560 1.55766 0.778830 0.627235i \(-0.215814\pi\)
0.778830 + 0.627235i \(0.215814\pi\)
\(570\) 0 0
\(571\) 27.4696 1.14957 0.574784 0.818305i \(-0.305086\pi\)
0.574784 + 0.818305i \(0.305086\pi\)
\(572\) −1.38680 −0.0579851
\(573\) 0 0
\(574\) −9.01648 −0.376341
\(575\) 12.6541 0.527712
\(576\) 0 0
\(577\) 40.5999 1.69019 0.845097 0.534613i \(-0.179543\pi\)
0.845097 + 0.534613i \(0.179543\pi\)
\(578\) 1.26814 0.0527476
\(579\) 0 0
\(580\) −0.965970 −0.0401097
\(581\) −17.9296 −0.743845
\(582\) 0 0
\(583\) 0.699440 0.0289678
\(584\) −5.42784 −0.224605
\(585\) 0 0
\(586\) −18.4933 −0.763952
\(587\) 13.9395 0.575344 0.287672 0.957729i \(-0.407119\pi\)
0.287672 + 0.957729i \(0.407119\pi\)
\(588\) 0 0
\(589\) 30.2051 1.24458
\(590\) −5.35099 −0.220297
\(591\) 0 0
\(592\) 10.4747 0.430507
\(593\) −9.08991 −0.373278 −0.186639 0.982429i \(-0.559759\pi\)
−0.186639 + 0.982429i \(0.559759\pi\)
\(594\) 0 0
\(595\) −2.72226 −0.111602
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) 8.87207 0.362806
\(599\) −26.2211 −1.07136 −0.535682 0.844420i \(-0.679946\pi\)
−0.535682 + 0.844420i \(0.679946\pi\)
\(600\) 0 0
\(601\) 23.6914 0.966393 0.483196 0.875512i \(-0.339476\pi\)
0.483196 + 0.875512i \(0.339476\pi\)
\(602\) 1.68990 0.0688751
\(603\) 0 0
\(604\) −3.51636 −0.143079
\(605\) −4.86009 −0.197591
\(606\) 0 0
\(607\) 44.2134 1.79457 0.897283 0.441457i \(-0.145538\pi\)
0.897283 + 0.441457i \(0.145538\pi\)
\(608\) 5.13026 0.208059
\(609\) 0 0
\(610\) −5.48542 −0.222098
\(611\) 19.4743 0.787845
\(612\) 0 0
\(613\) −32.3437 −1.30635 −0.653174 0.757208i \(-0.726563\pi\)
−0.653174 + 0.757208i \(0.726563\pi\)
\(614\) −20.5286 −0.828466
\(615\) 0 0
\(616\) −0.630422 −0.0254004
\(617\) −35.5068 −1.42945 −0.714725 0.699406i \(-0.753448\pi\)
−0.714725 + 0.699406i \(0.753448\pi\)
\(618\) 0 0
\(619\) 21.5408 0.865800 0.432900 0.901442i \(-0.357490\pi\)
0.432900 + 0.901442i \(0.357490\pi\)
\(620\) −2.64213 −0.106110
\(621\) 0 0
\(622\) −15.1347 −0.606848
\(623\) −0.628124 −0.0251653
\(624\) 0 0
\(625\) 22.0198 0.880792
\(626\) 27.6172 1.10381
\(627\) 0 0
\(628\) 8.71888 0.347921
\(629\) 41.5461 1.65655
\(630\) 0 0
\(631\) 19.9049 0.792400 0.396200 0.918164i \(-0.370329\pi\)
0.396200 + 0.918164i \(0.370329\pi\)
\(632\) −2.21050 −0.0879289
\(633\) 0 0
\(634\) −23.3262 −0.926401
\(635\) 0.969861 0.0384877
\(636\) 0 0
\(637\) −15.6811 −0.621309
\(638\) −0.887269 −0.0351273
\(639\) 0 0
\(640\) −0.448758 −0.0177387
\(641\) 47.4766 1.87521 0.937606 0.347700i \(-0.113037\pi\)
0.937606 + 0.347700i \(0.113037\pi\)
\(642\) 0 0
\(643\) 15.1115 0.595938 0.297969 0.954576i \(-0.403691\pi\)
0.297969 + 0.954576i \(0.403691\pi\)
\(644\) 4.03312 0.158927
\(645\) 0 0
\(646\) 20.3484 0.800595
\(647\) 0.935043 0.0367603 0.0183802 0.999831i \(-0.494149\pi\)
0.0183802 + 0.999831i \(0.494149\pi\)
\(648\) 0 0
\(649\) −4.91503 −0.192932
\(650\) 16.1446 0.633242
\(651\) 0 0
\(652\) −5.58812 −0.218848
\(653\) −6.49482 −0.254162 −0.127081 0.991892i \(-0.540561\pi\)
−0.127081 + 0.991892i \(0.540561\pi\)
\(654\) 0 0
\(655\) −3.96102 −0.154770
\(656\) −5.89535 −0.230175
\(657\) 0 0
\(658\) 8.85275 0.345116
\(659\) −19.9197 −0.775962 −0.387981 0.921667i \(-0.626827\pi\)
−0.387981 + 0.921667i \(0.626827\pi\)
\(660\) 0 0
\(661\) 51.2734 1.99430 0.997152 0.0754194i \(-0.0240296\pi\)
0.997152 + 0.0754194i \(0.0240296\pi\)
\(662\) 31.3199 1.21728
\(663\) 0 0
\(664\) −11.7231 −0.454946
\(665\) 3.52110 0.136542
\(666\) 0 0
\(667\) 5.67631 0.219787
\(668\) −22.8936 −0.885778
\(669\) 0 0
\(670\) 7.09322 0.274035
\(671\) −5.03850 −0.194509
\(672\) 0 0
\(673\) 8.64483 0.333234 0.166617 0.986022i \(-0.446716\pi\)
0.166617 + 0.986022i \(0.446716\pi\)
\(674\) 3.36124 0.129470
\(675\) 0 0
\(676\) −1.68067 −0.0646411
\(677\) −20.6047 −0.791904 −0.395952 0.918271i \(-0.629585\pi\)
−0.395952 + 0.918271i \(0.629585\pi\)
\(678\) 0 0
\(679\) −6.24773 −0.239766
\(680\) −1.77993 −0.0682571
\(681\) 0 0
\(682\) −2.42686 −0.0929294
\(683\) 30.6010 1.17091 0.585457 0.810704i \(-0.300915\pi\)
0.585457 + 0.810704i \(0.300915\pi\)
\(684\) 0 0
\(685\) 7.56873 0.289186
\(686\) −17.8344 −0.680920
\(687\) 0 0
\(688\) 1.10493 0.0421249
\(689\) −5.70896 −0.217494
\(690\) 0 0
\(691\) 13.6881 0.520720 0.260360 0.965512i \(-0.416159\pi\)
0.260360 + 0.965512i \(0.416159\pi\)
\(692\) 19.4389 0.738955
\(693\) 0 0
\(694\) 11.2162 0.425760
\(695\) −2.76405 −0.104846
\(696\) 0 0
\(697\) −23.3830 −0.885694
\(698\) −13.4404 −0.508727
\(699\) 0 0
\(700\) 7.33911 0.277392
\(701\) −9.14812 −0.345520 −0.172760 0.984964i \(-0.555268\pi\)
−0.172760 + 0.984964i \(0.555268\pi\)
\(702\) 0 0
\(703\) −53.7378 −2.02676
\(704\) −0.412196 −0.0155352
\(705\) 0 0
\(706\) 8.27345 0.311375
\(707\) −4.14958 −0.156061
\(708\) 0 0
\(709\) 48.8099 1.83309 0.916546 0.399929i \(-0.130965\pi\)
0.916546 + 0.399929i \(0.130965\pi\)
\(710\) −5.52479 −0.207342
\(711\) 0 0
\(712\) −0.410694 −0.0153914
\(713\) 15.5259 0.581448
\(714\) 0 0
\(715\) −0.622338 −0.0232741
\(716\) 16.6171 0.621011
\(717\) 0 0
\(718\) −31.9960 −1.19408
\(719\) −37.9337 −1.41469 −0.707344 0.706870i \(-0.750107\pi\)
−0.707344 + 0.706870i \(0.750107\pi\)
\(720\) 0 0
\(721\) 12.4044 0.461962
\(722\) −7.31955 −0.272405
\(723\) 0 0
\(724\) 0.435647 0.0161907
\(725\) 10.3292 0.383617
\(726\) 0 0
\(727\) 30.6546 1.13692 0.568458 0.822712i \(-0.307540\pi\)
0.568458 + 0.822712i \(0.307540\pi\)
\(728\) 5.14562 0.190709
\(729\) 0 0
\(730\) −2.43578 −0.0901524
\(731\) 4.38251 0.162093
\(732\) 0 0
\(733\) 7.53505 0.278313 0.139157 0.990270i \(-0.455561\pi\)
0.139157 + 0.990270i \(0.455561\pi\)
\(734\) 17.2289 0.635931
\(735\) 0 0
\(736\) 2.63703 0.0972021
\(737\) 6.51531 0.239995
\(738\) 0 0
\(739\) −0.680768 −0.0250424 −0.0125212 0.999922i \(-0.503986\pi\)
−0.0125212 + 0.999922i \(0.503986\pi\)
\(740\) 4.70059 0.172797
\(741\) 0 0
\(742\) −2.59522 −0.0952734
\(743\) −8.32757 −0.305509 −0.152754 0.988264i \(-0.548814\pi\)
−0.152754 + 0.988264i \(0.548814\pi\)
\(744\) 0 0
\(745\) 0.448758 0.0164412
\(746\) 4.22649 0.154743
\(747\) 0 0
\(748\) −1.63491 −0.0597783
\(749\) −4.34870 −0.158898
\(750\) 0 0
\(751\) −31.8640 −1.16273 −0.581366 0.813642i \(-0.697482\pi\)
−0.581366 + 0.813642i \(0.697482\pi\)
\(752\) 5.78830 0.211078
\(753\) 0 0
\(754\) 7.24205 0.263740
\(755\) −1.57799 −0.0574291
\(756\) 0 0
\(757\) 35.9885 1.30802 0.654012 0.756484i \(-0.273085\pi\)
0.654012 + 0.756484i \(0.273085\pi\)
\(758\) 4.84751 0.176069
\(759\) 0 0
\(760\) 2.30224 0.0835112
\(761\) 26.6709 0.966821 0.483410 0.875394i \(-0.339398\pi\)
0.483410 + 0.875394i \(0.339398\pi\)
\(762\) 0 0
\(763\) 11.5336 0.417543
\(764\) −16.5232 −0.597787
\(765\) 0 0
\(766\) −26.5621 −0.959727
\(767\) 40.1174 1.44856
\(768\) 0 0
\(769\) 30.4187 1.09692 0.548462 0.836175i \(-0.315213\pi\)
0.548462 + 0.836175i \(0.315213\pi\)
\(770\) −0.282907 −0.0101953
\(771\) 0 0
\(772\) −11.9297 −0.429358
\(773\) 10.8028 0.388550 0.194275 0.980947i \(-0.437765\pi\)
0.194275 + 0.980947i \(0.437765\pi\)
\(774\) 0 0
\(775\) 28.2525 1.01486
\(776\) −4.08503 −0.146644
\(777\) 0 0
\(778\) −31.1841 −1.11800
\(779\) 30.2447 1.08363
\(780\) 0 0
\(781\) −5.07467 −0.181586
\(782\) 10.4593 0.374025
\(783\) 0 0
\(784\) −4.66087 −0.166460
\(785\) 3.91267 0.139649
\(786\) 0 0
\(787\) 8.92923 0.318293 0.159146 0.987255i \(-0.449126\pi\)
0.159146 + 0.987255i \(0.449126\pi\)
\(788\) −17.4448 −0.621447
\(789\) 0 0
\(790\) −0.991979 −0.0352930
\(791\) −20.3019 −0.721854
\(792\) 0 0
\(793\) 41.1252 1.46040
\(794\) −38.9060 −1.38072
\(795\) 0 0
\(796\) 21.2904 0.754617
\(797\) −23.7646 −0.841784 −0.420892 0.907111i \(-0.638283\pi\)
−0.420892 + 0.907111i \(0.638283\pi\)
\(798\) 0 0
\(799\) 22.9584 0.812209
\(800\) 4.79862 0.169657
\(801\) 0 0
\(802\) 27.4187 0.968189
\(803\) −2.23733 −0.0789538
\(804\) 0 0
\(805\) 1.80990 0.0637905
\(806\) 19.8085 0.697725
\(807\) 0 0
\(808\) −2.71317 −0.0954490
\(809\) −29.4039 −1.03379 −0.516893 0.856050i \(-0.672912\pi\)
−0.516893 + 0.856050i \(0.672912\pi\)
\(810\) 0 0
\(811\) 35.0491 1.23074 0.615371 0.788238i \(-0.289006\pi\)
0.615371 + 0.788238i \(0.289006\pi\)
\(812\) 3.29214 0.115532
\(813\) 0 0
\(814\) 4.31762 0.151333
\(815\) −2.50771 −0.0878414
\(816\) 0 0
\(817\) −5.66856 −0.198318
\(818\) −13.5525 −0.473853
\(819\) 0 0
\(820\) −2.64559 −0.0923879
\(821\) −17.4579 −0.609287 −0.304643 0.952467i \(-0.598537\pi\)
−0.304643 + 0.952467i \(0.598537\pi\)
\(822\) 0 0
\(823\) 16.2840 0.567624 0.283812 0.958880i \(-0.408401\pi\)
0.283812 + 0.958880i \(0.408401\pi\)
\(824\) 8.11049 0.282542
\(825\) 0 0
\(826\) 18.2368 0.634541
\(827\) 31.3272 1.08935 0.544676 0.838646i \(-0.316652\pi\)
0.544676 + 0.838646i \(0.316652\pi\)
\(828\) 0 0
\(829\) −3.39656 −0.117967 −0.0589837 0.998259i \(-0.518786\pi\)
−0.0589837 + 0.998259i \(0.518786\pi\)
\(830\) −5.26085 −0.182607
\(831\) 0 0
\(832\) 3.36442 0.116640
\(833\) −18.4866 −0.640523
\(834\) 0 0
\(835\) −10.2737 −0.355535
\(836\) 2.11467 0.0731375
\(837\) 0 0
\(838\) 5.66966 0.195855
\(839\) −12.2041 −0.421331 −0.210666 0.977558i \(-0.567563\pi\)
−0.210666 + 0.977558i \(0.567563\pi\)
\(840\) 0 0
\(841\) −24.3666 −0.840227
\(842\) −18.4788 −0.636822
\(843\) 0 0
\(844\) 15.0226 0.517098
\(845\) −0.754213 −0.0259457
\(846\) 0 0
\(847\) 16.5638 0.569138
\(848\) −1.69686 −0.0582705
\(849\) 0 0
\(850\) 19.0329 0.652825
\(851\) −27.6220 −0.946870
\(852\) 0 0
\(853\) −0.474093 −0.0162326 −0.00811632 0.999967i \(-0.502584\pi\)
−0.00811632 + 0.999967i \(0.502584\pi\)
\(854\) 18.6950 0.639729
\(855\) 0 0
\(856\) −2.84336 −0.0971841
\(857\) −29.7904 −1.01762 −0.508810 0.860879i \(-0.669914\pi\)
−0.508810 + 0.860879i \(0.669914\pi\)
\(858\) 0 0
\(859\) −4.72469 −0.161204 −0.0806021 0.996746i \(-0.525684\pi\)
−0.0806021 + 0.996746i \(0.525684\pi\)
\(860\) 0.495844 0.0169082
\(861\) 0 0
\(862\) −13.9772 −0.476067
\(863\) −33.2971 −1.13345 −0.566723 0.823908i \(-0.691789\pi\)
−0.566723 + 0.823908i \(0.691789\pi\)
\(864\) 0 0
\(865\) 8.72335 0.296603
\(866\) 23.6058 0.802158
\(867\) 0 0
\(868\) 9.00469 0.305639
\(869\) −0.911160 −0.0309090
\(870\) 0 0
\(871\) −53.1792 −1.80191
\(872\) 7.54113 0.255375
\(873\) 0 0
\(874\) −13.5286 −0.457613
\(875\) 6.72518 0.227353
\(876\) 0 0
\(877\) −31.5174 −1.06427 −0.532134 0.846660i \(-0.678610\pi\)
−0.532134 + 0.846660i \(0.678610\pi\)
\(878\) 36.6939 1.23836
\(879\) 0 0
\(880\) −0.184976 −0.00623555
\(881\) 17.5526 0.591363 0.295682 0.955287i \(-0.404453\pi\)
0.295682 + 0.955287i \(0.404453\pi\)
\(882\) 0 0
\(883\) −24.7111 −0.831594 −0.415797 0.909457i \(-0.636497\pi\)
−0.415797 + 0.909457i \(0.636497\pi\)
\(884\) 13.3444 0.448822
\(885\) 0 0
\(886\) −26.2648 −0.882384
\(887\) 7.55626 0.253715 0.126857 0.991921i \(-0.459511\pi\)
0.126857 + 0.991921i \(0.459511\pi\)
\(888\) 0 0
\(889\) −3.30540 −0.110860
\(890\) −0.184302 −0.00617782
\(891\) 0 0
\(892\) −14.0252 −0.469598
\(893\) −29.6955 −0.993721
\(894\) 0 0
\(895\) 7.45706 0.249262
\(896\) 1.52942 0.0510944
\(897\) 0 0
\(898\) −15.4702 −0.516247
\(899\) 12.6734 0.422681
\(900\) 0 0
\(901\) −6.73033 −0.224220
\(902\) −2.43004 −0.0809116
\(903\) 0 0
\(904\) −13.2743 −0.441496
\(905\) 0.195500 0.00649865
\(906\) 0 0
\(907\) −58.9226 −1.95649 −0.978246 0.207447i \(-0.933485\pi\)
−0.978246 + 0.207447i \(0.933485\pi\)
\(908\) −0.382438 −0.0126917
\(909\) 0 0
\(910\) 2.30914 0.0765471
\(911\) 41.7691 1.38387 0.691937 0.721958i \(-0.256758\pi\)
0.691937 + 0.721958i \(0.256758\pi\)
\(912\) 0 0
\(913\) −4.83223 −0.159923
\(914\) 34.4833 1.14061
\(915\) 0 0
\(916\) 20.5931 0.680416
\(917\) 13.4996 0.445797
\(918\) 0 0
\(919\) 49.9848 1.64885 0.824423 0.565974i \(-0.191500\pi\)
0.824423 + 0.565974i \(0.191500\pi\)
\(920\) 1.18339 0.0390151
\(921\) 0 0
\(922\) 22.4975 0.740916
\(923\) 41.4204 1.36337
\(924\) 0 0
\(925\) −50.2639 −1.65267
\(926\) −20.7183 −0.680844
\(927\) 0 0
\(928\) 2.15254 0.0706606
\(929\) 22.3752 0.734106 0.367053 0.930200i \(-0.380367\pi\)
0.367053 + 0.930200i \(0.380367\pi\)
\(930\) 0 0
\(931\) 23.9115 0.783667
\(932\) 10.0982 0.330776
\(933\) 0 0
\(934\) −21.3417 −0.698321
\(935\) −0.733679 −0.0239939
\(936\) 0 0
\(937\) 31.4257 1.02663 0.513316 0.858199i \(-0.328417\pi\)
0.513316 + 0.858199i \(0.328417\pi\)
\(938\) −24.1746 −0.789327
\(939\) 0 0
\(940\) 2.59755 0.0847226
\(941\) 7.47412 0.243649 0.121825 0.992552i \(-0.461125\pi\)
0.121825 + 0.992552i \(0.461125\pi\)
\(942\) 0 0
\(943\) 15.5462 0.506254
\(944\) 11.9240 0.388094
\(945\) 0 0
\(946\) 0.455447 0.0148078
\(947\) −48.7738 −1.58494 −0.792468 0.609914i \(-0.791204\pi\)
−0.792468 + 0.609914i \(0.791204\pi\)
\(948\) 0 0
\(949\) 18.2615 0.592794
\(950\) −24.6181 −0.798718
\(951\) 0 0
\(952\) 6.06621 0.196607
\(953\) 54.8068 1.77537 0.887683 0.460455i \(-0.152314\pi\)
0.887683 + 0.460455i \(0.152314\pi\)
\(954\) 0 0
\(955\) −7.41490 −0.239941
\(956\) −11.1356 −0.360150
\(957\) 0 0
\(958\) 21.6025 0.697945
\(959\) −25.7951 −0.832968
\(960\) 0 0
\(961\) 3.66434 0.118205
\(962\) −35.2412 −1.13622
\(963\) 0 0
\(964\) 5.22345 0.168236
\(965\) −5.35353 −0.172336
\(966\) 0 0
\(967\) 9.63016 0.309685 0.154843 0.987939i \(-0.450513\pi\)
0.154843 + 0.987939i \(0.450513\pi\)
\(968\) 10.8301 0.348092
\(969\) 0 0
\(970\) −1.83319 −0.0588602
\(971\) 16.8080 0.539395 0.269698 0.962945i \(-0.413076\pi\)
0.269698 + 0.962945i \(0.413076\pi\)
\(972\) 0 0
\(973\) 9.42022 0.301998
\(974\) 24.2335 0.776491
\(975\) 0 0
\(976\) 12.2236 0.391266
\(977\) −4.01585 −0.128478 −0.0642392 0.997935i \(-0.520462\pi\)
−0.0642392 + 0.997935i \(0.520462\pi\)
\(978\) 0 0
\(979\) −0.169287 −0.00541042
\(980\) −2.09160 −0.0668138
\(981\) 0 0
\(982\) 18.0062 0.574601
\(983\) −4.31416 −0.137600 −0.0688001 0.997630i \(-0.521917\pi\)
−0.0688001 + 0.997630i \(0.521917\pi\)
\(984\) 0 0
\(985\) −7.82851 −0.249437
\(986\) 8.53771 0.271896
\(987\) 0 0
\(988\) −17.2604 −0.549125
\(989\) −2.91372 −0.0926509
\(990\) 0 0
\(991\) 35.7058 1.13423 0.567116 0.823638i \(-0.308059\pi\)
0.567116 + 0.823638i \(0.308059\pi\)
\(992\) 5.88764 0.186933
\(993\) 0 0
\(994\) 18.8292 0.597225
\(995\) 9.55422 0.302889
\(996\) 0 0
\(997\) −32.4431 −1.02748 −0.513742 0.857944i \(-0.671741\pi\)
−0.513742 + 0.857944i \(0.671741\pi\)
\(998\) 32.4315 1.02660
\(999\) 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 \(a_p\))