Properties

Label 4014.2.a.q.1.2
Level 4014
Weight 2
Character 4014.1
Self dual Yes
Analytic conductor 32.052
Analytic rank 1
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0519513713\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.10273.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.641043\)
Character \(\chi\) = 4014.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.64104 q^{5}\) \(-3.78585 q^{7}\) \(+1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.64104 q^{5}\) \(-3.78585 q^{7}\) \(+1.00000 q^{8}\) \(-1.64104 q^{10}\) \(+0.948021 q^{11}\) \(+2.09283 q^{13}\) \(-3.78585 q^{14}\) \(+1.00000 q^{16}\) \(+0.0270879 q^{17}\) \(+5.38464 q^{19}\) \(-1.64104 q^{20}\) \(+0.948021 q^{22}\) \(+3.61615 q^{23}\) \(-2.30698 q^{25}\) \(+2.09283 q^{26}\) \(-3.78585 q^{28}\) \(-3.17189 q^{29}\) \(-7.38464 q^{31}\) \(+1.00000 q^{32}\) \(+0.0270879 q^{34}\) \(+6.21274 q^{35}\) \(-2.49624 q^{37}\) \(+5.38464 q^{38}\) \(-1.64104 q^{40}\) \(+4.22247 q^{41}\) \(-6.30698 q^{43}\) \(+0.948021 q^{44}\) \(+3.61615 q^{46}\) \(-2.59879 q^{47}\) \(+7.33266 q^{49}\) \(-2.30698 q^{50}\) \(+2.09283 q^{52}\) \(-5.09502 q^{53}\) \(-1.55574 q^{55}\) \(-3.78585 q^{56}\) \(-3.17189 q^{58}\) \(-9.78444 q^{59}\) \(-2.50376 q^{61}\) \(-7.38464 q^{62}\) \(+1.00000 q^{64}\) \(-3.43442 q^{65}\) \(-4.35896 q^{67}\) \(+0.0270879 q^{68}\) \(+6.21274 q^{70}\) \(+8.97370 q^{71}\) \(-11.0083 q^{73}\) \(-2.49624 q^{74}\) \(+5.38464 q^{76}\) \(-3.58906 q^{77}\) \(-12.7361 q^{79}\) \(-1.64104 q^{80}\) \(+4.22247 q^{82}\) \(+8.87868 q^{83}\) \(-0.0444524 q^{85}\) \(-6.30698 q^{86}\) \(+0.948021 q^{88}\) \(+0.793377 q^{89}\) \(-7.92313 q^{91}\) \(+3.61615 q^{92}\) \(-2.59879 q^{94}\) \(-8.83642 q^{95}\) \(-8.13728 q^{97}\) \(+7.33266 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 5q^{28} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 5q^{56} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut -\mathstrut 3q^{73} \) \(\mathstrut -\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 7q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 22q^{86} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.64104 −0.733897 −0.366948 0.930241i \(-0.619597\pi\)
−0.366948 + 0.930241i \(0.619597\pi\)
\(6\) 0 0
\(7\) −3.78585 −1.43092 −0.715458 0.698655i \(-0.753782\pi\)
−0.715458 + 0.698655i \(0.753782\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.64104 −0.518943
\(11\) 0.948021 0.285839 0.142919 0.989734i \(-0.454351\pi\)
0.142919 + 0.989734i \(0.454351\pi\)
\(12\) 0 0
\(13\) 2.09283 0.580446 0.290223 0.956959i \(-0.406271\pi\)
0.290223 + 0.956959i \(0.406271\pi\)
\(14\) −3.78585 −1.01181
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.0270879 0.00656977 0.00328489 0.999995i \(-0.498954\pi\)
0.00328489 + 0.999995i \(0.498954\pi\)
\(18\) 0 0
\(19\) 5.38464 1.23532 0.617660 0.786445i \(-0.288081\pi\)
0.617660 + 0.786445i \(0.288081\pi\)
\(20\) −1.64104 −0.366948
\(21\) 0 0
\(22\) 0.948021 0.202119
\(23\) 3.61615 0.754020 0.377010 0.926209i \(-0.376952\pi\)
0.377010 + 0.926209i \(0.376952\pi\)
\(24\) 0 0
\(25\) −2.30698 −0.461396
\(26\) 2.09283 0.410437
\(27\) 0 0
\(28\) −3.78585 −0.715458
\(29\) −3.17189 −0.589006 −0.294503 0.955651i \(-0.595154\pi\)
−0.294503 + 0.955651i \(0.595154\pi\)
\(30\) 0 0
\(31\) −7.38464 −1.32632 −0.663160 0.748478i \(-0.730785\pi\)
−0.663160 + 0.748478i \(0.730785\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0.0270879 0.00464553
\(35\) 6.21274 1.05015
\(36\) 0 0
\(37\) −2.49624 −0.410379 −0.205189 0.978722i \(-0.565781\pi\)
−0.205189 + 0.978722i \(0.565781\pi\)
\(38\) 5.38464 0.873503
\(39\) 0 0
\(40\) −1.64104 −0.259472
\(41\) 4.22247 0.659438 0.329719 0.944079i \(-0.393046\pi\)
0.329719 + 0.944079i \(0.393046\pi\)
\(42\) 0 0
\(43\) −6.30698 −0.961805 −0.480903 0.876774i \(-0.659691\pi\)
−0.480903 + 0.876774i \(0.659691\pi\)
\(44\) 0.948021 0.142919
\(45\) 0 0
\(46\) 3.61615 0.533172
\(47\) −2.59879 −0.379072 −0.189536 0.981874i \(-0.560698\pi\)
−0.189536 + 0.981874i \(0.560698\pi\)
\(48\) 0 0
\(49\) 7.33266 1.04752
\(50\) −2.30698 −0.326256
\(51\) 0 0
\(52\) 2.09283 0.290223
\(53\) −5.09502 −0.699855 −0.349928 0.936777i \(-0.613794\pi\)
−0.349928 + 0.936777i \(0.613794\pi\)
\(54\) 0 0
\(55\) −1.55574 −0.209776
\(56\) −3.78585 −0.505905
\(57\) 0 0
\(58\) −3.17189 −0.416490
\(59\) −9.78444 −1.27383 −0.636913 0.770936i \(-0.719789\pi\)
−0.636913 + 0.770936i \(0.719789\pi\)
\(60\) 0 0
\(61\) −2.50376 −0.320574 −0.160287 0.987070i \(-0.551242\pi\)
−0.160287 + 0.987070i \(0.551242\pi\)
\(62\) −7.38464 −0.937850
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.43442 −0.425987
\(66\) 0 0
\(67\) −4.35896 −0.532531 −0.266266 0.963900i \(-0.585790\pi\)
−0.266266 + 0.963900i \(0.585790\pi\)
\(68\) 0.0270879 0.00328489
\(69\) 0 0
\(70\) 6.21274 0.742565
\(71\) 8.97370 1.06498 0.532491 0.846436i \(-0.321256\pi\)
0.532491 + 0.846436i \(0.321256\pi\)
\(72\) 0 0
\(73\) −11.0083 −1.28843 −0.644213 0.764846i \(-0.722815\pi\)
−0.644213 + 0.764846i \(0.722815\pi\)
\(74\) −2.49624 −0.290182
\(75\) 0 0
\(76\) 5.38464 0.617660
\(77\) −3.58906 −0.409012
\(78\) 0 0
\(79\) −12.7361 −1.43292 −0.716460 0.697628i \(-0.754239\pi\)
−0.716460 + 0.697628i \(0.754239\pi\)
\(80\) −1.64104 −0.183474
\(81\) 0 0
\(82\) 4.22247 0.466293
\(83\) 8.87868 0.974561 0.487281 0.873245i \(-0.337989\pi\)
0.487281 + 0.873245i \(0.337989\pi\)
\(84\) 0 0
\(85\) −0.0444524 −0.00482154
\(86\) −6.30698 −0.680099
\(87\) 0 0
\(88\) 0.948021 0.101059
\(89\) 0.793377 0.0840977 0.0420489 0.999116i \(-0.486611\pi\)
0.0420489 + 0.999116i \(0.486611\pi\)
\(90\) 0 0
\(91\) −7.92313 −0.830570
\(92\) 3.61615 0.377010
\(93\) 0 0
\(94\) −2.59879 −0.268044
\(95\) −8.83642 −0.906598
\(96\) 0 0
\(97\) −8.13728 −0.826216 −0.413108 0.910682i \(-0.635557\pi\)
−0.413108 + 0.910682i \(0.635557\pi\)
\(98\) 7.33266 0.740710
\(99\) 0 0
\(100\) −2.30698 −0.230698
\(101\) −14.2655 −1.41947 −0.709736 0.704468i \(-0.751186\pi\)
−0.709736 + 0.704468i \(0.751186\pi\)
\(102\) 0 0
\(103\) −2.92987 −0.288688 −0.144344 0.989528i \(-0.546107\pi\)
−0.144344 + 0.989528i \(0.546107\pi\)
\(104\) 2.09283 0.205219
\(105\) 0 0
\(106\) −5.09502 −0.494872
\(107\) 6.15233 0.594769 0.297384 0.954758i \(-0.403886\pi\)
0.297384 + 0.954758i \(0.403886\pi\)
\(108\) 0 0
\(109\) −1.92093 −0.183992 −0.0919960 0.995759i \(-0.529325\pi\)
−0.0919960 + 0.995759i \(0.529325\pi\)
\(110\) −1.55574 −0.148334
\(111\) 0 0
\(112\) −3.78585 −0.357729
\(113\) 12.3153 1.15853 0.579263 0.815141i \(-0.303341\pi\)
0.579263 + 0.815141i \(0.303341\pi\)
\(114\) 0 0
\(115\) −5.93426 −0.553373
\(116\) −3.17189 −0.294503
\(117\) 0 0
\(118\) −9.78444 −0.900731
\(119\) −0.102551 −0.00940080
\(120\) 0 0
\(121\) −10.1013 −0.918296
\(122\) −2.50376 −0.226680
\(123\) 0 0
\(124\) −7.38464 −0.663160
\(125\) 11.9911 1.07251
\(126\) 0 0
\(127\) −15.4851 −1.37408 −0.687040 0.726619i \(-0.741090\pi\)
−0.687040 + 0.726619i \(0.741090\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −3.43442 −0.301219
\(131\) −3.90357 −0.341056 −0.170528 0.985353i \(-0.554547\pi\)
−0.170528 + 0.985353i \(0.554547\pi\)
\(132\) 0 0
\(133\) −20.3854 −1.76764
\(134\) −4.35896 −0.376557
\(135\) 0 0
\(136\) 0.0270879 0.00232277
\(137\) −4.38464 −0.374605 −0.187302 0.982302i \(-0.559974\pi\)
−0.187302 + 0.982302i \(0.559974\pi\)
\(138\) 0 0
\(139\) −14.5565 −1.23467 −0.617334 0.786701i \(-0.711787\pi\)
−0.617334 + 0.786701i \(0.711787\pi\)
\(140\) 6.21274 0.525073
\(141\) 0 0
\(142\) 8.97370 0.753056
\(143\) 1.98404 0.165914
\(144\) 0 0
\(145\) 5.20522 0.432270
\(146\) −11.0083 −0.911055
\(147\) 0 0
\(148\) −2.49624 −0.205189
\(149\) −16.4783 −1.34995 −0.674976 0.737840i \(-0.735846\pi\)
−0.674976 + 0.737840i \(0.735846\pi\)
\(150\) 0 0
\(151\) −4.31450 −0.351109 −0.175555 0.984470i \(-0.556172\pi\)
−0.175555 + 0.984470i \(0.556172\pi\)
\(152\) 5.38464 0.436752
\(153\) 0 0
\(154\) −3.58906 −0.289215
\(155\) 12.1185 0.973382
\(156\) 0 0
\(157\) 7.51219 0.599538 0.299769 0.954012i \(-0.403090\pi\)
0.299769 + 0.954012i \(0.403090\pi\)
\(158\) −12.7361 −1.01323
\(159\) 0 0
\(160\) −1.64104 −0.129736
\(161\) −13.6902 −1.07894
\(162\) 0 0
\(163\) −5.94179 −0.465397 −0.232698 0.972549i \(-0.574755\pi\)
−0.232698 + 0.972549i \(0.574755\pi\)
\(164\) 4.22247 0.329719
\(165\) 0 0
\(166\) 8.87868 0.689119
\(167\) −3.87868 −0.300141 −0.150071 0.988675i \(-0.547950\pi\)
−0.150071 + 0.988675i \(0.547950\pi\)
\(168\) 0 0
\(169\) −8.62007 −0.663083
\(170\) −0.0444524 −0.00340934
\(171\) 0 0
\(172\) −6.30698 −0.480903
\(173\) 7.89244 0.600051 0.300025 0.953931i \(-0.403005\pi\)
0.300025 + 0.953931i \(0.403005\pi\)
\(174\) 0 0
\(175\) 8.73387 0.660219
\(176\) 0.948021 0.0714597
\(177\) 0 0
\(178\) 0.793377 0.0594661
\(179\) 4.44994 0.332604 0.166302 0.986075i \(-0.446817\pi\)
0.166302 + 0.986075i \(0.446817\pi\)
\(180\) 0 0
\(181\) 8.23972 0.612453 0.306227 0.951959i \(-0.400933\pi\)
0.306227 + 0.951959i \(0.400933\pi\)
\(182\) −7.92313 −0.587301
\(183\) 0 0
\(184\) 3.61615 0.266586
\(185\) 4.09643 0.301176
\(186\) 0 0
\(187\) 0.0256799 0.00187790
\(188\) −2.59879 −0.189536
\(189\) 0 0
\(190\) −8.83642 −0.641061
\(191\) 5.91408 0.427928 0.213964 0.976842i \(-0.431363\pi\)
0.213964 + 0.976842i \(0.431363\pi\)
\(192\) 0 0
\(193\) 16.7133 1.20305 0.601523 0.798855i \(-0.294561\pi\)
0.601523 + 0.798855i \(0.294561\pi\)
\(194\) −8.13728 −0.584223
\(195\) 0 0
\(196\) 7.33266 0.523761
\(197\) 6.95010 0.495174 0.247587 0.968866i \(-0.420362\pi\)
0.247587 + 0.968866i \(0.420362\pi\)
\(198\) 0 0
\(199\) −18.5053 −1.31181 −0.655904 0.754844i \(-0.727713\pi\)
−0.655904 + 0.754844i \(0.727713\pi\)
\(200\) −2.30698 −0.163128
\(201\) 0 0
\(202\) −14.2655 −1.00372
\(203\) 12.0083 0.842819
\(204\) 0 0
\(205\) −6.92925 −0.483960
\(206\) −2.92987 −0.204134
\(207\) 0 0
\(208\) 2.09283 0.145111
\(209\) 5.10475 0.353103
\(210\) 0 0
\(211\) 20.8892 1.43807 0.719036 0.694973i \(-0.244584\pi\)
0.719036 + 0.694973i \(0.244584\pi\)
\(212\) −5.09502 −0.349928
\(213\) 0 0
\(214\) 6.15233 0.420565
\(215\) 10.3500 0.705866
\(216\) 0 0
\(217\) 27.9571 1.89785
\(218\) −1.92093 −0.130102
\(219\) 0 0
\(220\) −1.55574 −0.104888
\(221\) 0.0566902 0.00381340
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) −3.78585 −0.252953
\(225\) 0 0
\(226\) 12.3153 0.819201
\(227\) −5.44959 −0.361702 −0.180851 0.983511i \(-0.557885\pi\)
−0.180851 + 0.983511i \(0.557885\pi\)
\(228\) 0 0
\(229\) 20.9369 1.38355 0.691774 0.722114i \(-0.256829\pi\)
0.691774 + 0.722114i \(0.256829\pi\)
\(230\) −5.93426 −0.391294
\(231\) 0 0
\(232\) −3.17189 −0.208245
\(233\) 27.0478 1.77196 0.885979 0.463726i \(-0.153488\pi\)
0.885979 + 0.463726i \(0.153488\pi\)
\(234\) 0 0
\(235\) 4.26472 0.278200
\(236\) −9.78444 −0.636913
\(237\) 0 0
\(238\) −0.102551 −0.00664737
\(239\) −30.6714 −1.98397 −0.991985 0.126355i \(-0.959672\pi\)
−0.991985 + 0.126355i \(0.959672\pi\)
\(240\) 0 0
\(241\) −9.66531 −0.622598 −0.311299 0.950312i \(-0.600764\pi\)
−0.311299 + 0.950312i \(0.600764\pi\)
\(242\) −10.1013 −0.649333
\(243\) 0 0
\(244\) −2.50376 −0.160287
\(245\) −12.0332 −0.768773
\(246\) 0 0
\(247\) 11.2691 0.717037
\(248\) −7.38464 −0.468925
\(249\) 0 0
\(250\) 11.9911 0.758382
\(251\) −14.8004 −0.934193 −0.467096 0.884206i \(-0.654700\pi\)
−0.467096 + 0.884206i \(0.654700\pi\)
\(252\) 0 0
\(253\) 3.42819 0.215528
\(254\) −15.4851 −0.971622
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −13.5800 −0.847098 −0.423549 0.905873i \(-0.639216\pi\)
−0.423549 + 0.905873i \(0.639216\pi\)
\(258\) 0 0
\(259\) 9.45038 0.587218
\(260\) −3.43442 −0.212994
\(261\) 0 0
\(262\) −3.90357 −0.241163
\(263\) −7.89420 −0.486777 −0.243389 0.969929i \(-0.578259\pi\)
−0.243389 + 0.969929i \(0.578259\pi\)
\(264\) 0 0
\(265\) 8.36115 0.513622
\(266\) −20.3854 −1.24991
\(267\) 0 0
\(268\) −4.35896 −0.266266
\(269\) 14.8946 0.908142 0.454071 0.890966i \(-0.349971\pi\)
0.454071 + 0.890966i \(0.349971\pi\)
\(270\) 0 0
\(271\) 3.27769 0.199106 0.0995528 0.995032i \(-0.468259\pi\)
0.0995528 + 0.995032i \(0.468259\pi\)
\(272\) 0.0270879 0.00164244
\(273\) 0 0
\(274\) −4.38464 −0.264886
\(275\) −2.18706 −0.131885
\(276\) 0 0
\(277\) −8.26018 −0.496306 −0.248153 0.968721i \(-0.579824\pi\)
−0.248153 + 0.968721i \(0.579824\pi\)
\(278\) −14.5565 −0.873043
\(279\) 0 0
\(280\) 6.21274 0.371282
\(281\) 14.6209 0.872208 0.436104 0.899896i \(-0.356358\pi\)
0.436104 + 0.899896i \(0.356358\pi\)
\(282\) 0 0
\(283\) 24.5961 1.46209 0.731043 0.682332i \(-0.239034\pi\)
0.731043 + 0.682332i \(0.239034\pi\)
\(284\) 8.97370 0.532491
\(285\) 0 0
\(286\) 1.98404 0.117319
\(287\) −15.9856 −0.943601
\(288\) 0 0
\(289\) −16.9993 −0.999957
\(290\) 5.20522 0.305661
\(291\) 0 0
\(292\) −11.0083 −0.644213
\(293\) 2.60282 0.152059 0.0760293 0.997106i \(-0.475776\pi\)
0.0760293 + 0.997106i \(0.475776\pi\)
\(294\) 0 0
\(295\) 16.0567 0.934857
\(296\) −2.49624 −0.145091
\(297\) 0 0
\(298\) −16.4783 −0.954560
\(299\) 7.56798 0.437668
\(300\) 0 0
\(301\) 23.8773 1.37626
\(302\) −4.31450 −0.248272
\(303\) 0 0
\(304\) 5.38464 0.308830
\(305\) 4.10878 0.235268
\(306\) 0 0
\(307\) −7.52944 −0.429728 −0.214864 0.976644i \(-0.568931\pi\)
−0.214864 + 0.976644i \(0.568931\pi\)
\(308\) −3.58906 −0.204506
\(309\) 0 0
\(310\) 12.1185 0.688285
\(311\) −17.8696 −1.01329 −0.506647 0.862154i \(-0.669115\pi\)
−0.506647 + 0.862154i \(0.669115\pi\)
\(312\) 0 0
\(313\) 6.41094 0.362368 0.181184 0.983449i \(-0.442007\pi\)
0.181184 + 0.983449i \(0.442007\pi\)
\(314\) 7.51219 0.423938
\(315\) 0 0
\(316\) −12.7361 −0.716460
\(317\) −1.66593 −0.0935682 −0.0467841 0.998905i \(-0.514897\pi\)
−0.0467841 + 0.998905i \(0.514897\pi\)
\(318\) 0 0
\(319\) −3.00702 −0.168361
\(320\) −1.64104 −0.0917371
\(321\) 0 0
\(322\) −13.6902 −0.762925
\(323\) 0.145858 0.00811578
\(324\) 0 0
\(325\) −4.82811 −0.267815
\(326\) −5.94179 −0.329085
\(327\) 0 0
\(328\) 4.22247 0.233147
\(329\) 9.83862 0.542421
\(330\) 0 0
\(331\) 19.0695 1.04816 0.524078 0.851671i \(-0.324410\pi\)
0.524078 + 0.851671i \(0.324410\pi\)
\(332\) 8.87868 0.487281
\(333\) 0 0
\(334\) −3.87868 −0.212232
\(335\) 7.15324 0.390823
\(336\) 0 0
\(337\) 26.7929 1.45950 0.729750 0.683714i \(-0.239636\pi\)
0.729750 + 0.683714i \(0.239636\pi\)
\(338\) −8.62007 −0.468870
\(339\) 0 0
\(340\) −0.0444524 −0.00241077
\(341\) −7.00079 −0.379114
\(342\) 0 0
\(343\) −1.25939 −0.0680007
\(344\) −6.30698 −0.340049
\(345\) 0 0
\(346\) 7.89244 0.424300
\(347\) 5.95645 0.319759 0.159880 0.987137i \(-0.448889\pi\)
0.159880 + 0.987137i \(0.448889\pi\)
\(348\) 0 0
\(349\) 20.4552 1.09494 0.547471 0.836825i \(-0.315591\pi\)
0.547471 + 0.836825i \(0.315591\pi\)
\(350\) 8.73387 0.466845
\(351\) 0 0
\(352\) 0.948021 0.0505297
\(353\) 18.0301 0.959644 0.479822 0.877366i \(-0.340701\pi\)
0.479822 + 0.877366i \(0.340701\pi\)
\(354\) 0 0
\(355\) −14.7262 −0.781587
\(356\) 0.793377 0.0420489
\(357\) 0 0
\(358\) 4.44994 0.235187
\(359\) −2.62901 −0.138754 −0.0693769 0.997591i \(-0.522101\pi\)
−0.0693769 + 0.997591i \(0.522101\pi\)
\(360\) 0 0
\(361\) 9.99431 0.526016
\(362\) 8.23972 0.433070
\(363\) 0 0
\(364\) −7.92313 −0.415285
\(365\) 18.0651 0.945572
\(366\) 0 0
\(367\) −12.3616 −0.645270 −0.322635 0.946524i \(-0.604569\pi\)
−0.322635 + 0.946524i \(0.604569\pi\)
\(368\) 3.61615 0.188505
\(369\) 0 0
\(370\) 4.09643 0.212963
\(371\) 19.2890 1.00143
\(372\) 0 0
\(373\) −7.62796 −0.394961 −0.197480 0.980307i \(-0.563276\pi\)
−0.197480 + 0.980307i \(0.563276\pi\)
\(374\) 0.0256799 0.00132787
\(375\) 0 0
\(376\) −2.59879 −0.134022
\(377\) −6.63823 −0.341886
\(378\) 0 0
\(379\) −13.1004 −0.672920 −0.336460 0.941698i \(-0.609230\pi\)
−0.336460 + 0.941698i \(0.609230\pi\)
\(380\) −8.83642 −0.453299
\(381\) 0 0
\(382\) 5.91408 0.302591
\(383\) −9.78260 −0.499868 −0.249934 0.968263i \(-0.580409\pi\)
−0.249934 + 0.968263i \(0.580409\pi\)
\(384\) 0 0
\(385\) 5.88981 0.300172
\(386\) 16.7133 0.850682
\(387\) 0 0
\(388\) −8.13728 −0.413108
\(389\) −11.6978 −0.593104 −0.296552 0.955017i \(-0.595837\pi\)
−0.296552 + 0.955017i \(0.595837\pi\)
\(390\) 0 0
\(391\) 0.0979539 0.00495374
\(392\) 7.33266 0.370355
\(393\) 0 0
\(394\) 6.95010 0.350141
\(395\) 20.9004 1.05161
\(396\) 0 0
\(397\) 12.8336 0.644100 0.322050 0.946723i \(-0.395628\pi\)
0.322050 + 0.946723i \(0.395628\pi\)
\(398\) −18.5053 −0.927589
\(399\) 0 0
\(400\) −2.30698 −0.115349
\(401\) 4.45606 0.222525 0.111263 0.993791i \(-0.464511\pi\)
0.111263 + 0.993791i \(0.464511\pi\)
\(402\) 0 0
\(403\) −15.4548 −0.769857
\(404\) −14.2655 −0.709736
\(405\) 0 0
\(406\) 12.0083 0.595963
\(407\) −2.36648 −0.117302
\(408\) 0 0
\(409\) 5.99236 0.296303 0.148152 0.988965i \(-0.452668\pi\)
0.148152 + 0.988965i \(0.452668\pi\)
\(410\) −6.92925 −0.342211
\(411\) 0 0
\(412\) −2.92987 −0.144344
\(413\) 37.0424 1.82274
\(414\) 0 0
\(415\) −14.5703 −0.715227
\(416\) 2.09283 0.102609
\(417\) 0 0
\(418\) 5.10475 0.249681
\(419\) 12.6376 0.617385 0.308692 0.951162i \(-0.400109\pi\)
0.308692 + 0.951162i \(0.400109\pi\)
\(420\) 0 0
\(421\) −16.3801 −0.798317 −0.399158 0.916882i \(-0.630698\pi\)
−0.399158 + 0.916882i \(0.630698\pi\)
\(422\) 20.8892 1.01687
\(423\) 0 0
\(424\) −5.09502 −0.247436
\(425\) −0.0624911 −0.00303126
\(426\) 0 0
\(427\) 9.47887 0.458715
\(428\) 6.15233 0.297384
\(429\) 0 0
\(430\) 10.3500 0.499122
\(431\) −28.8933 −1.39174 −0.695872 0.718166i \(-0.744982\pi\)
−0.695872 + 0.718166i \(0.744982\pi\)
\(432\) 0 0
\(433\) 24.1503 1.16059 0.580295 0.814406i \(-0.302937\pi\)
0.580295 + 0.814406i \(0.302937\pi\)
\(434\) 27.9571 1.34198
\(435\) 0 0
\(436\) −1.92093 −0.0919960
\(437\) 19.4717 0.931456
\(438\) 0 0
\(439\) 20.0038 0.954728 0.477364 0.878706i \(-0.341592\pi\)
0.477364 + 0.878706i \(0.341592\pi\)
\(440\) −1.55574 −0.0741671
\(441\) 0 0
\(442\) 0.0566902 0.00269648
\(443\) −41.2816 −1.96135 −0.980675 0.195645i \(-0.937320\pi\)
−0.980675 + 0.195645i \(0.937320\pi\)
\(444\) 0 0
\(445\) −1.30197 −0.0617191
\(446\) −1.00000 −0.0473514
\(447\) 0 0
\(448\) −3.78585 −0.178865
\(449\) 15.7414 0.742882 0.371441 0.928456i \(-0.378864\pi\)
0.371441 + 0.928456i \(0.378864\pi\)
\(450\) 0 0
\(451\) 4.00298 0.188493
\(452\) 12.3153 0.579263
\(453\) 0 0
\(454\) −5.44959 −0.255762
\(455\) 13.0022 0.609552
\(456\) 0 0
\(457\) −41.5156 −1.94202 −0.971009 0.239042i \(-0.923167\pi\)
−0.971009 + 0.239042i \(0.923167\pi\)
\(458\) 20.9369 0.978317
\(459\) 0 0
\(460\) −5.93426 −0.276686
\(461\) 12.7813 0.595285 0.297642 0.954677i \(-0.403800\pi\)
0.297642 + 0.954677i \(0.403800\pi\)
\(462\) 0 0
\(463\) −0.386833 −0.0179777 −0.00898883 0.999960i \(-0.502861\pi\)
−0.00898883 + 0.999960i \(0.502861\pi\)
\(464\) −3.17189 −0.147252
\(465\) 0 0
\(466\) 27.0478 1.25296
\(467\) 22.6179 1.04663 0.523315 0.852139i \(-0.324695\pi\)
0.523315 + 0.852139i \(0.324695\pi\)
\(468\) 0 0
\(469\) 16.5024 0.762008
\(470\) 4.26472 0.196717
\(471\) 0 0
\(472\) −9.78444 −0.450365
\(473\) −5.97915 −0.274921
\(474\) 0 0
\(475\) −12.4222 −0.569971
\(476\) −0.102551 −0.00470040
\(477\) 0 0
\(478\) −30.6714 −1.40288
\(479\) −5.46476 −0.249691 −0.124846 0.992176i \(-0.539844\pi\)
−0.124846 + 0.992176i \(0.539844\pi\)
\(480\) 0 0
\(481\) −5.22419 −0.238203
\(482\) −9.66531 −0.440243
\(483\) 0 0
\(484\) −10.1013 −0.459148
\(485\) 13.3536 0.606357
\(486\) 0 0
\(487\) 0.0270879 0.00122747 0.000613734 1.00000i \(-0.499805\pi\)
0.000613734 1.00000i \(0.499805\pi\)
\(488\) −2.50376 −0.113340
\(489\) 0 0
\(490\) −12.0332 −0.543605
\(491\) 20.0131 0.903180 0.451590 0.892225i \(-0.350857\pi\)
0.451590 + 0.892225i \(0.350857\pi\)
\(492\) 0 0
\(493\) −0.0859199 −0.00386964
\(494\) 11.2691 0.507021
\(495\) 0 0
\(496\) −7.38464 −0.331580
\(497\) −33.9731 −1.52390
\(498\) 0 0
\(499\) −36.4407 −1.63131 −0.815655 0.578539i \(-0.803623\pi\)
−0.815655 + 0.578539i \(0.803623\pi\)
\(500\) 11.9911 0.536257
\(501\) 0 0
\(502\) −14.8004 −0.660574
\(503\) 5.49325 0.244932 0.122466 0.992473i \(-0.460920\pi\)
0.122466 + 0.992473i \(0.460920\pi\)
\(504\) 0 0
\(505\) 23.4103 1.04175
\(506\) 3.42819 0.152401
\(507\) 0 0
\(508\) −15.4851 −0.687040
\(509\) −11.1585 −0.494590 −0.247295 0.968940i \(-0.579542\pi\)
−0.247295 + 0.968940i \(0.579542\pi\)
\(510\) 0 0
\(511\) 41.6758 1.84363
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −13.5800 −0.598989
\(515\) 4.80804 0.211868
\(516\) 0 0
\(517\) −2.46370 −0.108354
\(518\) 9.45038 0.415226
\(519\) 0 0
\(520\) −3.43442 −0.150609
\(521\) −24.6217 −1.07869 −0.539347 0.842084i \(-0.681329\pi\)
−0.539347 + 0.842084i \(0.681329\pi\)
\(522\) 0 0
\(523\) 7.45222 0.325863 0.162931 0.986637i \(-0.447905\pi\)
0.162931 + 0.986637i \(0.447905\pi\)
\(524\) −3.90357 −0.170528
\(525\) 0 0
\(526\) −7.89420 −0.344204
\(527\) −0.200034 −0.00871362
\(528\) 0 0
\(529\) −9.92345 −0.431454
\(530\) 8.36115 0.363185
\(531\) 0 0
\(532\) −20.3854 −0.883820
\(533\) 8.83689 0.382768
\(534\) 0 0
\(535\) −10.0962 −0.436499
\(536\) −4.35896 −0.188278
\(537\) 0 0
\(538\) 14.8946 0.642153
\(539\) 6.95151 0.299423
\(540\) 0 0
\(541\) 21.7032 0.933093 0.466546 0.884497i \(-0.345498\pi\)
0.466546 + 0.884497i \(0.345498\pi\)
\(542\) 3.27769 0.140789
\(543\) 0 0
\(544\) 0.0270879 0.00116138
\(545\) 3.15233 0.135031
\(546\) 0 0
\(547\) 11.0550 0.472676 0.236338 0.971671i \(-0.424053\pi\)
0.236338 + 0.971671i \(0.424053\pi\)
\(548\) −4.38464 −0.187302
\(549\) 0 0
\(550\) −2.18706 −0.0932567
\(551\) −17.0795 −0.727611
\(552\) 0 0
\(553\) 48.2168 2.05039
\(554\) −8.26018 −0.350941
\(555\) 0 0
\(556\) −14.5565 −0.617334
\(557\) −39.8283 −1.68758 −0.843789 0.536675i \(-0.819680\pi\)
−0.843789 + 0.536675i \(0.819680\pi\)
\(558\) 0 0
\(559\) −13.1994 −0.558276
\(560\) 6.21274 0.262536
\(561\) 0 0
\(562\) 14.6209 0.616744
\(563\) 4.41392 0.186025 0.0930123 0.995665i \(-0.470350\pi\)
0.0930123 + 0.995665i \(0.470350\pi\)
\(564\) 0 0
\(565\) −20.2099 −0.850238
\(566\) 24.5961 1.03385
\(567\) 0 0
\(568\) 8.97370 0.376528
\(569\) 4.68863 0.196558 0.0982788 0.995159i \(-0.468666\pi\)
0.0982788 + 0.995159i \(0.468666\pi\)
\(570\) 0 0
\(571\) 35.2974 1.47715 0.738576 0.674171i \(-0.235499\pi\)
0.738576 + 0.674171i \(0.235499\pi\)
\(572\) 1.98404 0.0829570
\(573\) 0 0
\(574\) −15.9856 −0.667227
\(575\) −8.34238 −0.347901
\(576\) 0 0
\(577\) 5.19146 0.216123 0.108062 0.994144i \(-0.465536\pi\)
0.108062 + 0.994144i \(0.465536\pi\)
\(578\) −16.9993 −0.707076
\(579\) 0 0
\(580\) 5.20522 0.216135
\(581\) −33.6133 −1.39452
\(582\) 0 0
\(583\) −4.83019 −0.200046
\(584\) −11.0083 −0.455527
\(585\) 0 0
\(586\) 2.60282 0.107522
\(587\) 15.1913 0.627014 0.313507 0.949586i \(-0.398496\pi\)
0.313507 + 0.949586i \(0.398496\pi\)
\(588\) 0 0
\(589\) −39.7636 −1.63843
\(590\) 16.0567 0.661043
\(591\) 0 0
\(592\) −2.49624 −0.102595
\(593\) −44.8330 −1.84107 −0.920535 0.390660i \(-0.872247\pi\)
−0.920535 + 0.390660i \(0.872247\pi\)
\(594\) 0 0
\(595\) 0.168290 0.00689922
\(596\) −16.4783 −0.674976
\(597\) 0 0
\(598\) 7.56798 0.309478
\(599\) −10.9904 −0.449055 −0.224528 0.974468i \(-0.572084\pi\)
−0.224528 + 0.974468i \(0.572084\pi\)
\(600\) 0 0
\(601\) 3.17471 0.129499 0.0647496 0.997902i \(-0.479375\pi\)
0.0647496 + 0.997902i \(0.479375\pi\)
\(602\) 23.8773 0.973165
\(603\) 0 0
\(604\) −4.31450 −0.175555
\(605\) 16.5766 0.673935
\(606\) 0 0
\(607\) −20.1193 −0.816617 −0.408309 0.912844i \(-0.633881\pi\)
−0.408309 + 0.912844i \(0.633881\pi\)
\(608\) 5.38464 0.218376
\(609\) 0 0
\(610\) 4.10878 0.166360
\(611\) −5.43881 −0.220031
\(612\) 0 0
\(613\) −28.4725 −1.14999 −0.574996 0.818156i \(-0.694996\pi\)
−0.574996 + 0.818156i \(0.694996\pi\)
\(614\) −7.52944 −0.303864
\(615\) 0 0
\(616\) −3.58906 −0.144608
\(617\) −24.7637 −0.996950 −0.498475 0.866904i \(-0.666106\pi\)
−0.498475 + 0.866904i \(0.666106\pi\)
\(618\) 0 0
\(619\) 20.6260 0.829031 0.414515 0.910042i \(-0.363951\pi\)
0.414515 + 0.910042i \(0.363951\pi\)
\(620\) 12.1185 0.486691
\(621\) 0 0
\(622\) −17.8696 −0.716507
\(623\) −3.00360 −0.120337
\(624\) 0 0
\(625\) −8.14297 −0.325719
\(626\) 6.41094 0.256233
\(627\) 0 0
\(628\) 7.51219 0.299769
\(629\) −0.0676177 −0.00269610
\(630\) 0 0
\(631\) −3.65060 −0.145328 −0.0726640 0.997356i \(-0.523150\pi\)
−0.0726640 + 0.997356i \(0.523150\pi\)
\(632\) −12.7361 −0.506614
\(633\) 0 0
\(634\) −1.66593 −0.0661627
\(635\) 25.4117 1.00843
\(636\) 0 0
\(637\) 15.3460 0.608030
\(638\) −3.00702 −0.119049
\(639\) 0 0
\(640\) −1.64104 −0.0648679
\(641\) 34.4091 1.35908 0.679538 0.733640i \(-0.262180\pi\)
0.679538 + 0.733640i \(0.262180\pi\)
\(642\) 0 0
\(643\) 28.6486 1.12979 0.564896 0.825162i \(-0.308916\pi\)
0.564896 + 0.825162i \(0.308916\pi\)
\(644\) −13.6902 −0.539470
\(645\) 0 0
\(646\) 0.145858 0.00573872
\(647\) −6.35045 −0.249662 −0.124831 0.992178i \(-0.539839\pi\)
−0.124831 + 0.992178i \(0.539839\pi\)
\(648\) 0 0
\(649\) −9.27585 −0.364109
\(650\) −4.82811 −0.189374
\(651\) 0 0
\(652\) −5.94179 −0.232698
\(653\) 12.1639 0.476010 0.238005 0.971264i \(-0.423507\pi\)
0.238005 + 0.971264i \(0.423507\pi\)
\(654\) 0 0
\(655\) 6.40592 0.250300
\(656\) 4.22247 0.164860
\(657\) 0 0
\(658\) 9.83862 0.383549
\(659\) −21.9037 −0.853248 −0.426624 0.904429i \(-0.640297\pi\)
−0.426624 + 0.904429i \(0.640297\pi\)
\(660\) 0 0
\(661\) −21.5772 −0.839256 −0.419628 0.907696i \(-0.637839\pi\)
−0.419628 + 0.907696i \(0.637839\pi\)
\(662\) 19.0695 0.741158
\(663\) 0 0
\(664\) 8.87868 0.344559
\(665\) 33.4534 1.29727
\(666\) 0 0
\(667\) −11.4701 −0.444122
\(668\) −3.87868 −0.150071
\(669\) 0 0
\(670\) 7.15324 0.276354
\(671\) −2.37362 −0.0916326
\(672\) 0 0
\(673\) 18.7512 0.722807 0.361403 0.932410i \(-0.382298\pi\)
0.361403 + 0.932410i \(0.382298\pi\)
\(674\) 26.7929 1.03202
\(675\) 0 0
\(676\) −8.62007 −0.331541
\(677\) 11.2434 0.432120 0.216060 0.976380i \(-0.430679\pi\)
0.216060 + 0.976380i \(0.430679\pi\)
\(678\) 0 0
\(679\) 30.8065 1.18225
\(680\) −0.0444524 −0.00170467
\(681\) 0 0
\(682\) −7.00079 −0.268074
\(683\) 19.5387 0.747626 0.373813 0.927504i \(-0.378050\pi\)
0.373813 + 0.927504i \(0.378050\pi\)
\(684\) 0 0
\(685\) 7.19538 0.274921
\(686\) −1.25939 −0.0480838
\(687\) 0 0
\(688\) −6.30698 −0.240451
\(689\) −10.6630 −0.406228
\(690\) 0 0
\(691\) −42.2422 −1.60697 −0.803484 0.595326i \(-0.797023\pi\)
−0.803484 + 0.595326i \(0.797023\pi\)
\(692\) 7.89244 0.300025
\(693\) 0 0
\(694\) 5.95645 0.226104
\(695\) 23.8879 0.906119
\(696\) 0 0
\(697\) 0.114378 0.00433236
\(698\) 20.4552 0.774241
\(699\) 0 0
\(700\) 8.73387 0.330109
\(701\) 20.5501 0.776165 0.388082 0.921625i \(-0.373138\pi\)
0.388082 + 0.921625i \(0.373138\pi\)
\(702\) 0 0
\(703\) −13.4413 −0.506949
\(704\) 0.948021 0.0357299
\(705\) 0 0
\(706\) 18.0301 0.678571
\(707\) 54.0071 2.03115
\(708\) 0 0
\(709\) −18.0271 −0.677021 −0.338511 0.940963i \(-0.609923\pi\)
−0.338511 + 0.940963i \(0.609923\pi\)
\(710\) −14.7262 −0.552666
\(711\) 0 0
\(712\) 0.793377 0.0297330
\(713\) −26.7040 −1.00007
\(714\) 0 0
\(715\) −3.25590 −0.121764
\(716\) 4.44994 0.166302
\(717\) 0 0
\(718\) −2.62901 −0.0981137
\(719\) 27.9105 1.04089 0.520443 0.853897i \(-0.325767\pi\)
0.520443 + 0.853897i \(0.325767\pi\)
\(720\) 0 0
\(721\) 11.0920 0.413089
\(722\) 9.99431 0.371950
\(723\) 0 0
\(724\) 8.23972 0.306227
\(725\) 7.31749 0.271765
\(726\) 0 0
\(727\) −46.4208 −1.72165 −0.860827 0.508898i \(-0.830053\pi\)
−0.860827 + 0.508898i \(0.830053\pi\)
\(728\) −7.92313 −0.293651
\(729\) 0 0
\(730\) 18.0651 0.668620
\(731\) −0.170843 −0.00631884
\(732\) 0 0
\(733\) 30.1465 1.11349 0.556743 0.830685i \(-0.312051\pi\)
0.556743 + 0.830685i \(0.312051\pi\)
\(734\) −12.3616 −0.456274
\(735\) 0 0
\(736\) 3.61615 0.133293
\(737\) −4.13238 −0.152218
\(738\) 0 0
\(739\) 22.4392 0.825441 0.412720 0.910858i \(-0.364579\pi\)
0.412720 + 0.910858i \(0.364579\pi\)
\(740\) 4.09643 0.150588
\(741\) 0 0
\(742\) 19.2890 0.708121
\(743\) 45.5002 1.66924 0.834620 0.550825i \(-0.185687\pi\)
0.834620 + 0.550825i \(0.185687\pi\)
\(744\) 0 0
\(745\) 27.0415 0.990725
\(746\) −7.62796 −0.279279
\(747\) 0 0
\(748\) 0.0256799 0.000938949 0
\(749\) −23.2918 −0.851064
\(750\) 0 0
\(751\) −14.7463 −0.538101 −0.269051 0.963126i \(-0.586710\pi\)
−0.269051 + 0.963126i \(0.586710\pi\)
\(752\) −2.59879 −0.0947680
\(753\) 0 0
\(754\) −6.63823 −0.241750
\(755\) 7.08029 0.257678
\(756\) 0 0
\(757\) −21.6569 −0.787133 −0.393566 0.919296i \(-0.628759\pi\)
−0.393566 + 0.919296i \(0.628759\pi\)
\(758\) −13.1004 −0.475826
\(759\) 0 0
\(760\) −8.83642 −0.320531
\(761\) 9.81348 0.355739 0.177869 0.984054i \(-0.443080\pi\)
0.177869 + 0.984054i \(0.443080\pi\)
\(762\) 0 0
\(763\) 7.27236 0.263277
\(764\) 5.91408 0.213964
\(765\) 0 0
\(766\) −9.78260 −0.353460
\(767\) −20.4771 −0.739387
\(768\) 0 0
\(769\) −6.83685 −0.246543 −0.123272 0.992373i \(-0.539339\pi\)
−0.123272 + 0.992373i \(0.539339\pi\)
\(770\) 5.88981 0.212254
\(771\) 0 0
\(772\) 16.7133 0.601523
\(773\) 49.2899 1.77283 0.886417 0.462887i \(-0.153187\pi\)
0.886417 + 0.462887i \(0.153187\pi\)
\(774\) 0 0
\(775\) 17.0362 0.611958
\(776\) −8.13728 −0.292111
\(777\) 0 0
\(778\) −11.6978 −0.419388
\(779\) 22.7364 0.814618
\(780\) 0 0
\(781\) 8.50725 0.304413
\(782\) 0.0979539 0.00350282
\(783\) 0 0
\(784\) 7.33266 0.261881
\(785\) −12.3278 −0.439999
\(786\) 0 0
\(787\) −46.6575 −1.66316 −0.831580 0.555405i \(-0.812563\pi\)
−0.831580 + 0.555405i \(0.812563\pi\)
\(788\) 6.95010 0.247587
\(789\) 0 0
\(790\) 20.9004 0.743604
\(791\) −46.6238 −1.65775
\(792\) 0 0
\(793\) −5.23994 −0.186076
\(794\) 12.8336 0.455448
\(795\) 0 0
\(796\) −18.5053 −0.655904
\(797\) 22.8186 0.808277 0.404139 0.914698i \(-0.367571\pi\)
0.404139 + 0.914698i \(0.367571\pi\)
\(798\) 0 0
\(799\) −0.0703956 −0.00249042
\(800\) −2.30698 −0.0815640
\(801\) 0 0
\(802\) 4.45606 0.157349
\(803\) −10.4361 −0.368282
\(804\) 0 0
\(805\) 22.4662 0.791830
\(806\) −15.4548 −0.544371
\(807\) 0 0
\(808\) −14.2655 −0.501859
\(809\) −21.3057 −0.749070 −0.374535 0.927213i \(-0.622198\pi\)
−0.374535 + 0.927213i \(0.622198\pi\)
\(810\) 0 0
\(811\) −4.37178 −0.153514 −0.0767570 0.997050i \(-0.524457\pi\)
−0.0767570 + 0.997050i \(0.524457\pi\)
\(812\) 12.0083 0.421409
\(813\) 0 0
\(814\) −2.36648 −0.0829452
\(815\) 9.75073 0.341553
\(816\) 0 0
\(817\) −33.9608 −1.18814
\(818\) 5.99236 0.209518
\(819\) 0 0
\(820\) −6.92925 −0.241980
\(821\) −48.6264 −1.69707 −0.848536 0.529138i \(-0.822515\pi\)
−0.848536 + 0.529138i \(0.822515\pi\)
\(822\) 0 0
\(823\) 23.9936 0.836364 0.418182 0.908363i \(-0.362667\pi\)
0.418182 + 0.908363i \(0.362667\pi\)
\(824\) −2.92987 −0.102067
\(825\) 0 0
\(826\) 37.0424 1.28887
\(827\) −43.1952 −1.50204 −0.751022 0.660277i \(-0.770439\pi\)
−0.751022 + 0.660277i \(0.770439\pi\)
\(828\) 0 0
\(829\) −27.2828 −0.947569 −0.473785 0.880641i \(-0.657113\pi\)
−0.473785 + 0.880641i \(0.657113\pi\)
\(830\) −14.5703 −0.505742
\(831\) 0 0
\(832\) 2.09283 0.0725557
\(833\) 0.198626 0.00688199
\(834\) 0 0
\(835\) 6.36508 0.220273
\(836\) 5.10475 0.176551
\(837\) 0 0
\(838\) 12.6376 0.436557
\(839\) 1.65139 0.0570122 0.0285061 0.999594i \(-0.490925\pi\)
0.0285061 + 0.999594i \(0.490925\pi\)
\(840\) 0 0
\(841\) −18.9391 −0.653072
\(842\) −16.3801 −0.564495
\(843\) 0 0
\(844\) 20.8892 0.719036
\(845\) 14.1459 0.486634
\(846\) 0 0
\(847\) 38.2418 1.31401
\(848\) −5.09502 −0.174964
\(849\) 0 0
\(850\) −0.0624911 −0.00214343
\(851\) −9.02677 −0.309434
\(852\) 0 0
\(853\) 6.90638 0.236470 0.118235 0.992986i \(-0.462276\pi\)
0.118235 + 0.992986i \(0.462276\pi\)
\(854\) 9.47887 0.324360
\(855\) 0 0
\(856\) 6.15233 0.210282
\(857\) 25.8488 0.882977 0.441489 0.897267i \(-0.354451\pi\)
0.441489 + 0.897267i \(0.354451\pi\)
\(858\) 0 0
\(859\) −33.9690 −1.15901 −0.579504 0.814969i \(-0.696754\pi\)
−0.579504 + 0.814969i \(0.696754\pi\)
\(860\) 10.3500 0.352933
\(861\) 0 0
\(862\) −28.8933 −0.984111
\(863\) 8.63729 0.294017 0.147008 0.989135i \(-0.453036\pi\)
0.147008 + 0.989135i \(0.453036\pi\)
\(864\) 0 0
\(865\) −12.9518 −0.440375
\(866\) 24.1503 0.820661
\(867\) 0 0
\(868\) 27.9571 0.948927
\(869\) −12.0741 −0.409584
\(870\) 0 0
\(871\) −9.12254 −0.309106
\(872\) −1.92093 −0.0650510
\(873\) 0 0
\(874\) 19.4717 0.658639
\(875\) −45.3964 −1.53468
\(876\) 0 0
\(877\) 30.1650 1.01860 0.509301 0.860589i \(-0.329904\pi\)
0.509301 + 0.860589i \(0.329904\pi\)
\(878\) 20.0038 0.675095
\(879\) 0 0
\(880\) −1.55574 −0.0524441
\(881\) −12.4248 −0.418603 −0.209301 0.977851i \(-0.567119\pi\)
−0.209301 + 0.977851i \(0.567119\pi\)
\(882\) 0 0
\(883\) 11.3493 0.381934 0.190967 0.981596i \(-0.438838\pi\)
0.190967 + 0.981596i \(0.438838\pi\)
\(884\) 0.0566902 0.00190670
\(885\) 0 0
\(886\) −41.2816 −1.38688
\(887\) 8.39412 0.281847 0.140923 0.990020i \(-0.454993\pi\)
0.140923 + 0.990020i \(0.454993\pi\)
\(888\) 0 0
\(889\) 58.6243 1.96620
\(890\) −1.30197 −0.0436420
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) −13.9935 −0.468275
\(894\) 0 0
\(895\) −7.30255 −0.244097
\(896\) −3.78585 −0.126476
\(897\) 0 0
\(898\) 15.7414 0.525297
\(899\) 23.4233 0.781210
\(900\) 0 0
\(901\) −0.138013 −0.00459789
\(902\) 4.00298 0.133285
\(903\) 0 0
\(904\) 12.3153 0.409601
\(905\) −13.5217 −0.449477
\(906\) 0 0
\(907\) 12.7461 0.423229 0.211614 0.977353i \(-0.432128\pi\)
0.211614 + 0.977353i \(0.432128\pi\)
\(908\) −5.44959 −0.180851
\(909\) 0 0
\(910\) 13.0022 0.431019
\(911\) −15.4866 −0.513095 −0.256547 0.966532i \(-0.582585\pi\)
−0.256547 + 0.966532i \(0.582585\pi\)
\(912\) 0 0
\(913\) 8.41717 0.278568
\(914\) −41.5156 −1.37321
\(915\) 0 0
\(916\) 20.9369 0.691774
\(917\) 14.7783 0.488023
\(918\) 0 0
\(919\) −1.68380 −0.0555436 −0.0277718 0.999614i \(-0.508841\pi\)
−0.0277718 + 0.999614i \(0.508841\pi\)
\(920\) −5.93426 −0.195647
\(921\) 0 0
\(922\) 12.7813 0.420930
\(923\) 18.7804 0.618165
\(924\) 0 0
\(925\) 5.75876 0.189347
\(926\) −0.386833 −0.0127121
\(927\) 0 0
\(928\) −3.17189 −0.104123
\(929\) 54.6754 1.79384 0.896921 0.442190i \(-0.145798\pi\)
0.896921 + 0.442190i \(0.145798\pi\)
\(930\) 0 0
\(931\) 39.4837 1.29403
\(932\) 27.0478 0.885979
\(933\) 0 0
\(934\) 22.6179 0.740080
\(935\) −0.0421418 −0.00137818
\(936\) 0 0
\(937\) −5.35265 −0.174863 −0.0874317 0.996171i \(-0.527866\pi\)
−0.0874317 + 0.996171i \(0.527866\pi\)
\(938\) 16.5024 0.538821
\(939\) 0 0
\(940\) 4.26472 0.139100
\(941\) −29.1362 −0.949811 −0.474906 0.880037i \(-0.657518\pi\)
−0.474906 + 0.880037i \(0.657518\pi\)
\(942\) 0 0
\(943\) 15.2691 0.497230
\(944\) −9.78444 −0.318456
\(945\) 0 0
\(946\) −5.97915 −0.194399
\(947\) 22.3852 0.727421 0.363711 0.931512i \(-0.381510\pi\)
0.363711 + 0.931512i \(0.381510\pi\)
\(948\) 0 0
\(949\) −23.0385 −0.747861
\(950\) −12.4222 −0.403031
\(951\) 0 0
\(952\) −0.102551 −0.00332368
\(953\) 32.7939 1.06230 0.531149 0.847278i \(-0.321760\pi\)
0.531149 + 0.847278i \(0.321760\pi\)
\(954\) 0 0
\(955\) −9.70526 −0.314055
\(956\) −30.6714 −0.991985
\(957\) 0 0
\(958\) −5.46476 −0.176558
\(959\) 16.5996 0.536028
\(960\) 0 0
\(961\) 23.5329 0.759125
\(962\) −5.22419 −0.168435
\(963\) 0 0
\(964\) −9.66531 −0.311299
\(965\) −27.4272 −0.882912
\(966\) 0 0
\(967\) −16.6658 −0.535936 −0.267968 0.963428i \(-0.586352\pi\)
−0.267968 + 0.963428i \(0.586352\pi\)
\(968\) −10.1013 −0.324667
\(969\) 0 0
\(970\) 13.3536 0.428759
\(971\) 54.9760 1.76426 0.882131 0.471004i \(-0.156108\pi\)
0.882131 + 0.471004i \(0.156108\pi\)
\(972\) 0 0
\(973\) 55.1088 1.76671
\(974\) 0.0270879 0.000867951 0
\(975\) 0 0
\(976\) −2.50376 −0.0801435
\(977\) 24.4672 0.782776 0.391388 0.920226i \(-0.371995\pi\)
0.391388 + 0.920226i \(0.371995\pi\)
\(978\) 0 0
\(979\) 0.752137 0.0240384
\(980\) −12.0332 −0.384387
\(981\) 0 0
\(982\) 20.0131 0.638645
\(983\) −3.46248 −0.110436 −0.0552180 0.998474i \(-0.517585\pi\)
−0.0552180 + 0.998474i \(0.517585\pi\)
\(984\) 0 0
\(985\) −11.4054 −0.363407
\(986\) −0.0859199 −0.00273625
\(987\) 0 0
\(988\) 11.2691 0.358518
\(989\) −22.8070 −0.725220
\(990\) 0 0
\(991\) −1.65963 −0.0527198 −0.0263599 0.999653i \(-0.508392\pi\)
−0.0263599 + 0.999653i \(0.508392\pi\)
\(992\) −7.38464 −0.234462
\(993\) 0 0
\(994\) −33.9731 −1.07756
\(995\) 30.3681 0.962732
\(996\) 0 0
\(997\) 46.9184 1.48592 0.742960 0.669335i \(-0.233421\pi\)
0.742960 + 0.669335i \(0.233421\pi\)
\(998\) −36.4407 −1.15351
\(999\) 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 \(a_p\))