Properties

Label 8046.2.a.l.1.10
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 1.10
Root \(1.99250\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.99250 q^{5}\) \(-0.0206178 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.99250 q^{5}\) \(-0.0206178 q^{7}\) \(-1.00000 q^{8}\) \(-1.99250 q^{10}\) \(+5.26122 q^{11}\) \(+1.30783 q^{13}\) \(+0.0206178 q^{14}\) \(+1.00000 q^{16}\) \(-4.05669 q^{17}\) \(+0.295188 q^{19}\) \(+1.99250 q^{20}\) \(-5.26122 q^{22}\) \(-1.64920 q^{23}\) \(-1.02995 q^{25}\) \(-1.30783 q^{26}\) \(-0.0206178 q^{28}\) \(-3.96430 q^{29}\) \(+8.69374 q^{31}\) \(-1.00000 q^{32}\) \(+4.05669 q^{34}\) \(-0.0410810 q^{35}\) \(-8.66851 q^{37}\) \(-0.295188 q^{38}\) \(-1.99250 q^{40}\) \(-0.291717 q^{41}\) \(-0.389669 q^{43}\) \(+5.26122 q^{44}\) \(+1.64920 q^{46}\) \(+4.57012 q^{47}\) \(-6.99957 q^{49}\) \(+1.02995 q^{50}\) \(+1.30783 q^{52}\) \(+7.77757 q^{53}\) \(+10.4830 q^{55}\) \(+0.0206178 q^{56}\) \(+3.96430 q^{58}\) \(+12.8606 q^{59}\) \(+7.40709 q^{61}\) \(-8.69374 q^{62}\) \(+1.00000 q^{64}\) \(+2.60584 q^{65}\) \(+5.96178 q^{67}\) \(-4.05669 q^{68}\) \(+0.0410810 q^{70}\) \(-10.2613 q^{71}\) \(+5.21734 q^{73}\) \(+8.66851 q^{74}\) \(+0.295188 q^{76}\) \(-0.108475 q^{77}\) \(+5.69527 q^{79}\) \(+1.99250 q^{80}\) \(+0.291717 q^{82}\) \(+11.8162 q^{83}\) \(-8.08295 q^{85}\) \(+0.389669 q^{86}\) \(-5.26122 q^{88}\) \(+11.4015 q^{89}\) \(-0.0269646 q^{91}\) \(-1.64920 q^{92}\) \(-4.57012 q^{94}\) \(+0.588161 q^{95}\) \(-0.168718 q^{97}\) \(+6.99957 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.99250 0.891073 0.445536 0.895264i \(-0.353013\pi\)
0.445536 + 0.895264i \(0.353013\pi\)
\(6\) 0 0
\(7\) −0.0206178 −0.00779281 −0.00389641 0.999992i \(-0.501240\pi\)
−0.00389641 + 0.999992i \(0.501240\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.99250 −0.630084
\(11\) 5.26122 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(12\) 0 0
\(13\) 1.30783 0.362726 0.181363 0.983416i \(-0.441949\pi\)
0.181363 + 0.983416i \(0.441949\pi\)
\(14\) 0.0206178 0.00551035
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.05669 −0.983892 −0.491946 0.870626i \(-0.663714\pi\)
−0.491946 + 0.870626i \(0.663714\pi\)
\(18\) 0 0
\(19\) 0.295188 0.0677207 0.0338604 0.999427i \(-0.489220\pi\)
0.0338604 + 0.999427i \(0.489220\pi\)
\(20\) 1.99250 0.445536
\(21\) 0 0
\(22\) −5.26122 −1.12170
\(23\) −1.64920 −0.343882 −0.171941 0.985107i \(-0.555004\pi\)
−0.171941 + 0.985107i \(0.555004\pi\)
\(24\) 0 0
\(25\) −1.02995 −0.205990
\(26\) −1.30783 −0.256486
\(27\) 0 0
\(28\) −0.0206178 −0.00389641
\(29\) −3.96430 −0.736153 −0.368076 0.929796i \(-0.619984\pi\)
−0.368076 + 0.929796i \(0.619984\pi\)
\(30\) 0 0
\(31\) 8.69374 1.56144 0.780721 0.624880i \(-0.214852\pi\)
0.780721 + 0.624880i \(0.214852\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.05669 0.695717
\(35\) −0.0410810 −0.00694396
\(36\) 0 0
\(37\) −8.66851 −1.42509 −0.712547 0.701624i \(-0.752459\pi\)
−0.712547 + 0.701624i \(0.752459\pi\)
\(38\) −0.295188 −0.0478858
\(39\) 0 0
\(40\) −1.99250 −0.315042
\(41\) −0.291717 −0.0455585 −0.0227793 0.999741i \(-0.507251\pi\)
−0.0227793 + 0.999741i \(0.507251\pi\)
\(42\) 0 0
\(43\) −0.389669 −0.0594240 −0.0297120 0.999559i \(-0.509459\pi\)
−0.0297120 + 0.999559i \(0.509459\pi\)
\(44\) 5.26122 0.793159
\(45\) 0 0
\(46\) 1.64920 0.243161
\(47\) 4.57012 0.666621 0.333310 0.942817i \(-0.391834\pi\)
0.333310 + 0.942817i \(0.391834\pi\)
\(48\) 0 0
\(49\) −6.99957 −0.999939
\(50\) 1.02995 0.145657
\(51\) 0 0
\(52\) 1.30783 0.181363
\(53\) 7.77757 1.06833 0.534166 0.845380i \(-0.320626\pi\)
0.534166 + 0.845380i \(0.320626\pi\)
\(54\) 0 0
\(55\) 10.4830 1.41352
\(56\) 0.0206178 0.00275517
\(57\) 0 0
\(58\) 3.96430 0.520539
\(59\) 12.8606 1.67430 0.837151 0.546972i \(-0.184219\pi\)
0.837151 + 0.546972i \(0.184219\pi\)
\(60\) 0 0
\(61\) 7.40709 0.948381 0.474190 0.880422i \(-0.342741\pi\)
0.474190 + 0.880422i \(0.342741\pi\)
\(62\) −8.69374 −1.10411
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.60584 0.323215
\(66\) 0 0
\(67\) 5.96178 0.728348 0.364174 0.931331i \(-0.381351\pi\)
0.364174 + 0.931331i \(0.381351\pi\)
\(68\) −4.05669 −0.491946
\(69\) 0 0
\(70\) 0.0410810 0.00491012
\(71\) −10.2613 −1.21779 −0.608895 0.793251i \(-0.708387\pi\)
−0.608895 + 0.793251i \(0.708387\pi\)
\(72\) 0 0
\(73\) 5.21734 0.610644 0.305322 0.952249i \(-0.401236\pi\)
0.305322 + 0.952249i \(0.401236\pi\)
\(74\) 8.66851 1.00769
\(75\) 0 0
\(76\) 0.295188 0.0338604
\(77\) −0.108475 −0.0123619
\(78\) 0 0
\(79\) 5.69527 0.640768 0.320384 0.947288i \(-0.396188\pi\)
0.320384 + 0.947288i \(0.396188\pi\)
\(80\) 1.99250 0.222768
\(81\) 0 0
\(82\) 0.291717 0.0322147
\(83\) 11.8162 1.29700 0.648499 0.761215i \(-0.275397\pi\)
0.648499 + 0.761215i \(0.275397\pi\)
\(84\) 0 0
\(85\) −8.08295 −0.876720
\(86\) 0.389669 0.0420191
\(87\) 0 0
\(88\) −5.26122 −0.560848
\(89\) 11.4015 1.20855 0.604277 0.796775i \(-0.293462\pi\)
0.604277 + 0.796775i \(0.293462\pi\)
\(90\) 0 0
\(91\) −0.0269646 −0.00282665
\(92\) −1.64920 −0.171941
\(93\) 0 0
\(94\) −4.57012 −0.471372
\(95\) 0.588161 0.0603441
\(96\) 0 0
\(97\) −0.168718 −0.0171308 −0.00856538 0.999963i \(-0.502726\pi\)
−0.00856538 + 0.999963i \(0.502726\pi\)
\(98\) 6.99957 0.707064
\(99\) 0 0
\(100\) −1.02995 −0.102995
\(101\) 15.0043 1.49298 0.746492 0.665395i \(-0.231737\pi\)
0.746492 + 0.665395i \(0.231737\pi\)
\(102\) 0 0
\(103\) −2.19991 −0.216763 −0.108382 0.994109i \(-0.534567\pi\)
−0.108382 + 0.994109i \(0.534567\pi\)
\(104\) −1.30783 −0.128243
\(105\) 0 0
\(106\) −7.77757 −0.755425
\(107\) −4.80921 −0.464924 −0.232462 0.972605i \(-0.574678\pi\)
−0.232462 + 0.972605i \(0.574678\pi\)
\(108\) 0 0
\(109\) −12.8433 −1.23016 −0.615081 0.788464i \(-0.710877\pi\)
−0.615081 + 0.788464i \(0.710877\pi\)
\(110\) −10.4830 −0.999513
\(111\) 0 0
\(112\) −0.0206178 −0.00194820
\(113\) −3.21231 −0.302189 −0.151094 0.988519i \(-0.548280\pi\)
−0.151094 + 0.988519i \(0.548280\pi\)
\(114\) 0 0
\(115\) −3.28603 −0.306424
\(116\) −3.96430 −0.368076
\(117\) 0 0
\(118\) −12.8606 −1.18391
\(119\) 0.0836402 0.00766729
\(120\) 0 0
\(121\) 16.6804 1.51640
\(122\) −7.40709 −0.670607
\(123\) 0 0
\(124\) 8.69374 0.780721
\(125\) −12.0147 −1.07462
\(126\) 0 0
\(127\) 14.1266 1.25354 0.626768 0.779206i \(-0.284377\pi\)
0.626768 + 0.779206i \(0.284377\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −2.60584 −0.228548
\(131\) 17.7947 1.55473 0.777364 0.629051i \(-0.216556\pi\)
0.777364 + 0.629051i \(0.216556\pi\)
\(132\) 0 0
\(133\) −0.00608613 −0.000527735 0
\(134\) −5.96178 −0.515020
\(135\) 0 0
\(136\) 4.05669 0.347858
\(137\) 3.79487 0.324217 0.162109 0.986773i \(-0.448170\pi\)
0.162109 + 0.986773i \(0.448170\pi\)
\(138\) 0 0
\(139\) −13.1582 −1.11607 −0.558034 0.829818i \(-0.688444\pi\)
−0.558034 + 0.829818i \(0.688444\pi\)
\(140\) −0.0410810 −0.00347198
\(141\) 0 0
\(142\) 10.2613 0.861108
\(143\) 6.88076 0.575398
\(144\) 0 0
\(145\) −7.89887 −0.655966
\(146\) −5.21734 −0.431790
\(147\) 0 0
\(148\) −8.66851 −0.712547
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) −13.5614 −1.10361 −0.551806 0.833972i \(-0.686061\pi\)
−0.551806 + 0.833972i \(0.686061\pi\)
\(152\) −0.295188 −0.0239429
\(153\) 0 0
\(154\) 0.108475 0.00874116
\(155\) 17.3223 1.39136
\(156\) 0 0
\(157\) −11.9231 −0.951564 −0.475782 0.879563i \(-0.657835\pi\)
−0.475782 + 0.879563i \(0.657835\pi\)
\(158\) −5.69527 −0.453091
\(159\) 0 0
\(160\) −1.99250 −0.157521
\(161\) 0.0340029 0.00267981
\(162\) 0 0
\(163\) −2.75467 −0.215763 −0.107881 0.994164i \(-0.534407\pi\)
−0.107881 + 0.994164i \(0.534407\pi\)
\(164\) −0.291717 −0.0227793
\(165\) 0 0
\(166\) −11.8162 −0.917116
\(167\) 21.6245 1.67336 0.836678 0.547695i \(-0.184495\pi\)
0.836678 + 0.547695i \(0.184495\pi\)
\(168\) 0 0
\(169\) −11.2896 −0.868430
\(170\) 8.08295 0.619934
\(171\) 0 0
\(172\) −0.389669 −0.0297120
\(173\) 17.8683 1.35850 0.679252 0.733905i \(-0.262304\pi\)
0.679252 + 0.733905i \(0.262304\pi\)
\(174\) 0 0
\(175\) 0.0212353 0.00160524
\(176\) 5.26122 0.396579
\(177\) 0 0
\(178\) −11.4015 −0.854576
\(179\) 14.6929 1.09820 0.549098 0.835758i \(-0.314971\pi\)
0.549098 + 0.835758i \(0.314971\pi\)
\(180\) 0 0
\(181\) 20.5258 1.52567 0.762834 0.646595i \(-0.223808\pi\)
0.762834 + 0.646595i \(0.223808\pi\)
\(182\) 0.0269646 0.00199875
\(183\) 0 0
\(184\) 1.64920 0.121581
\(185\) −17.2720 −1.26986
\(186\) 0 0
\(187\) −21.3432 −1.56077
\(188\) 4.57012 0.333310
\(189\) 0 0
\(190\) −0.588161 −0.0426697
\(191\) 16.1527 1.16877 0.584384 0.811477i \(-0.301336\pi\)
0.584384 + 0.811477i \(0.301336\pi\)
\(192\) 0 0
\(193\) 0.667178 0.0480245 0.0240123 0.999712i \(-0.492356\pi\)
0.0240123 + 0.999712i \(0.492356\pi\)
\(194\) 0.168718 0.0121133
\(195\) 0 0
\(196\) −6.99957 −0.499970
\(197\) 2.10056 0.149659 0.0748295 0.997196i \(-0.476159\pi\)
0.0748295 + 0.997196i \(0.476159\pi\)
\(198\) 0 0
\(199\) −17.4910 −1.23990 −0.619951 0.784641i \(-0.712848\pi\)
−0.619951 + 0.784641i \(0.712848\pi\)
\(200\) 1.02995 0.0728283
\(201\) 0 0
\(202\) −15.0043 −1.05570
\(203\) 0.0817354 0.00573670
\(204\) 0 0
\(205\) −0.581245 −0.0405959
\(206\) 2.19991 0.153275
\(207\) 0 0
\(208\) 1.30783 0.0906815
\(209\) 1.55305 0.107427
\(210\) 0 0
\(211\) −6.81415 −0.469105 −0.234553 0.972103i \(-0.575363\pi\)
−0.234553 + 0.972103i \(0.575363\pi\)
\(212\) 7.77757 0.534166
\(213\) 0 0
\(214\) 4.80921 0.328751
\(215\) −0.776416 −0.0529511
\(216\) 0 0
\(217\) −0.179246 −0.0121680
\(218\) 12.8433 0.869857
\(219\) 0 0
\(220\) 10.4830 0.706762
\(221\) −5.30545 −0.356883
\(222\) 0 0
\(223\) −19.9915 −1.33873 −0.669366 0.742933i \(-0.733434\pi\)
−0.669366 + 0.742933i \(0.733434\pi\)
\(224\) 0.0206178 0.00137759
\(225\) 0 0
\(226\) 3.21231 0.213680
\(227\) −13.5705 −0.900706 −0.450353 0.892851i \(-0.648702\pi\)
−0.450353 + 0.892851i \(0.648702\pi\)
\(228\) 0 0
\(229\) 27.0742 1.78912 0.894558 0.446952i \(-0.147491\pi\)
0.894558 + 0.446952i \(0.147491\pi\)
\(230\) 3.28603 0.216674
\(231\) 0 0
\(232\) 3.96430 0.260269
\(233\) 1.11238 0.0728743 0.0364371 0.999336i \(-0.488399\pi\)
0.0364371 + 0.999336i \(0.488399\pi\)
\(234\) 0 0
\(235\) 9.10596 0.594007
\(236\) 12.8606 0.837151
\(237\) 0 0
\(238\) −0.0836402 −0.00542159
\(239\) −21.3359 −1.38011 −0.690053 0.723759i \(-0.742413\pi\)
−0.690053 + 0.723759i \(0.742413\pi\)
\(240\) 0 0
\(241\) 7.94889 0.512033 0.256016 0.966672i \(-0.417590\pi\)
0.256016 + 0.966672i \(0.417590\pi\)
\(242\) −16.6804 −1.07226
\(243\) 0 0
\(244\) 7.40709 0.474190
\(245\) −13.9466 −0.891019
\(246\) 0 0
\(247\) 0.386054 0.0245640
\(248\) −8.69374 −0.552053
\(249\) 0 0
\(250\) 12.0147 0.759874
\(251\) 30.3459 1.91541 0.957707 0.287745i \(-0.0929056\pi\)
0.957707 + 0.287745i \(0.0929056\pi\)
\(252\) 0 0
\(253\) −8.67680 −0.545506
\(254\) −14.1266 −0.886383
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −11.3203 −0.706142 −0.353071 0.935596i \(-0.614863\pi\)
−0.353071 + 0.935596i \(0.614863\pi\)
\(258\) 0 0
\(259\) 0.178726 0.0111055
\(260\) 2.60584 0.161608
\(261\) 0 0
\(262\) −17.7947 −1.09936
\(263\) −0.0140866 −0.000868618 0 −0.000434309 1.00000i \(-0.500138\pi\)
−0.000434309 1.00000i \(0.500138\pi\)
\(264\) 0 0
\(265\) 15.4968 0.951961
\(266\) 0.00608613 0.000373165 0
\(267\) 0 0
\(268\) 5.96178 0.364174
\(269\) 13.4107 0.817663 0.408831 0.912610i \(-0.365936\pi\)
0.408831 + 0.912610i \(0.365936\pi\)
\(270\) 0 0
\(271\) 30.1331 1.83045 0.915227 0.402938i \(-0.132011\pi\)
0.915227 + 0.402938i \(0.132011\pi\)
\(272\) −4.05669 −0.245973
\(273\) 0 0
\(274\) −3.79487 −0.229256
\(275\) −5.41878 −0.326765
\(276\) 0 0
\(277\) −18.7209 −1.12483 −0.562414 0.826856i \(-0.690127\pi\)
−0.562414 + 0.826856i \(0.690127\pi\)
\(278\) 13.1582 0.789179
\(279\) 0 0
\(280\) 0.0410810 0.00245506
\(281\) 7.41800 0.442521 0.221260 0.975215i \(-0.428983\pi\)
0.221260 + 0.975215i \(0.428983\pi\)
\(282\) 0 0
\(283\) −21.1335 −1.25625 −0.628127 0.778111i \(-0.716178\pi\)
−0.628127 + 0.778111i \(0.716178\pi\)
\(284\) −10.2613 −0.608895
\(285\) 0 0
\(286\) −6.88076 −0.406868
\(287\) 0.00601457 0.000355029 0
\(288\) 0 0
\(289\) −0.543249 −0.0319558
\(290\) 7.89887 0.463838
\(291\) 0 0
\(292\) 5.21734 0.305322
\(293\) −5.04458 −0.294707 −0.147354 0.989084i \(-0.547076\pi\)
−0.147354 + 0.989084i \(0.547076\pi\)
\(294\) 0 0
\(295\) 25.6247 1.49192
\(296\) 8.66851 0.503847
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −2.15687 −0.124735
\(300\) 0 0
\(301\) 0.00803414 0.000463080 0
\(302\) 13.5614 0.780372
\(303\) 0 0
\(304\) 0.295188 0.0169302
\(305\) 14.7586 0.845076
\(306\) 0 0
\(307\) −4.06035 −0.231736 −0.115868 0.993265i \(-0.536965\pi\)
−0.115868 + 0.993265i \(0.536965\pi\)
\(308\) −0.108475 −0.00618094
\(309\) 0 0
\(310\) −17.3223 −0.983839
\(311\) −30.1221 −1.70807 −0.854033 0.520219i \(-0.825850\pi\)
−0.854033 + 0.520219i \(0.825850\pi\)
\(312\) 0 0
\(313\) 5.86146 0.331309 0.165655 0.986184i \(-0.447026\pi\)
0.165655 + 0.986184i \(0.447026\pi\)
\(314\) 11.9231 0.672857
\(315\) 0 0
\(316\) 5.69527 0.320384
\(317\) −13.0792 −0.734602 −0.367301 0.930102i \(-0.619718\pi\)
−0.367301 + 0.930102i \(0.619718\pi\)
\(318\) 0 0
\(319\) −20.8571 −1.16777
\(320\) 1.99250 0.111384
\(321\) 0 0
\(322\) −0.0340029 −0.00189491
\(323\) −1.19749 −0.0666299
\(324\) 0 0
\(325\) −1.34699 −0.0747177
\(326\) 2.75467 0.152567
\(327\) 0 0
\(328\) 0.291717 0.0161074
\(329\) −0.0942260 −0.00519485
\(330\) 0 0
\(331\) 11.3159 0.621977 0.310988 0.950414i \(-0.399340\pi\)
0.310988 + 0.950414i \(0.399340\pi\)
\(332\) 11.8162 0.648499
\(333\) 0 0
\(334\) −21.6245 −1.18324
\(335\) 11.8788 0.649011
\(336\) 0 0
\(337\) 3.41103 0.185810 0.0929052 0.995675i \(-0.470385\pi\)
0.0929052 + 0.995675i \(0.470385\pi\)
\(338\) 11.2896 0.614073
\(339\) 0 0
\(340\) −8.08295 −0.438360
\(341\) 45.7397 2.47694
\(342\) 0 0
\(343\) 0.288641 0.0155851
\(344\) 0.389669 0.0210096
\(345\) 0 0
\(346\) −17.8683 −0.960608
\(347\) 5.91948 0.317774 0.158887 0.987297i \(-0.449209\pi\)
0.158887 + 0.987297i \(0.449209\pi\)
\(348\) 0 0
\(349\) 11.2779 0.603692 0.301846 0.953357i \(-0.402397\pi\)
0.301846 + 0.953357i \(0.402397\pi\)
\(350\) −0.0212353 −0.00113507
\(351\) 0 0
\(352\) −5.26122 −0.280424
\(353\) 14.0935 0.750123 0.375061 0.927000i \(-0.377622\pi\)
0.375061 + 0.927000i \(0.377622\pi\)
\(354\) 0 0
\(355\) −20.4456 −1.08514
\(356\) 11.4015 0.604277
\(357\) 0 0
\(358\) −14.6929 −0.776542
\(359\) 3.81544 0.201371 0.100686 0.994918i \(-0.467896\pi\)
0.100686 + 0.994918i \(0.467896\pi\)
\(360\) 0 0
\(361\) −18.9129 −0.995414
\(362\) −20.5258 −1.07881
\(363\) 0 0
\(364\) −0.0269646 −0.00141333
\(365\) 10.3955 0.544128
\(366\) 0 0
\(367\) −16.4625 −0.859337 −0.429669 0.902987i \(-0.641370\pi\)
−0.429669 + 0.902987i \(0.641370\pi\)
\(368\) −1.64920 −0.0859704
\(369\) 0 0
\(370\) 17.2720 0.897928
\(371\) −0.160357 −0.00832531
\(372\) 0 0
\(373\) 20.1014 1.04081 0.520406 0.853919i \(-0.325781\pi\)
0.520406 + 0.853919i \(0.325781\pi\)
\(374\) 21.3432 1.10363
\(375\) 0 0
\(376\) −4.57012 −0.235686
\(377\) −5.18462 −0.267022
\(378\) 0 0
\(379\) −0.0507386 −0.00260627 −0.00130313 0.999999i \(-0.500415\pi\)
−0.00130313 + 0.999999i \(0.500415\pi\)
\(380\) 0.588161 0.0301720
\(381\) 0 0
\(382\) −16.1527 −0.826444
\(383\) −24.2127 −1.23721 −0.618605 0.785702i \(-0.712302\pi\)
−0.618605 + 0.785702i \(0.712302\pi\)
\(384\) 0 0
\(385\) −0.216136 −0.0110153
\(386\) −0.667178 −0.0339585
\(387\) 0 0
\(388\) −0.168718 −0.00856538
\(389\) −16.8468 −0.854168 −0.427084 0.904212i \(-0.640459\pi\)
−0.427084 + 0.904212i \(0.640459\pi\)
\(390\) 0 0
\(391\) 6.69029 0.338343
\(392\) 6.99957 0.353532
\(393\) 0 0
\(394\) −2.10056 −0.105825
\(395\) 11.3478 0.570971
\(396\) 0 0
\(397\) 25.7132 1.29051 0.645254 0.763968i \(-0.276752\pi\)
0.645254 + 0.763968i \(0.276752\pi\)
\(398\) 17.4910 0.876743
\(399\) 0 0
\(400\) −1.02995 −0.0514974
\(401\) −18.5979 −0.928733 −0.464366 0.885643i \(-0.653718\pi\)
−0.464366 + 0.885643i \(0.653718\pi\)
\(402\) 0 0
\(403\) 11.3699 0.566375
\(404\) 15.0043 0.746492
\(405\) 0 0
\(406\) −0.0817354 −0.00405646
\(407\) −45.6069 −2.26065
\(408\) 0 0
\(409\) 36.7789 1.81860 0.909300 0.416142i \(-0.136618\pi\)
0.909300 + 0.416142i \(0.136618\pi\)
\(410\) 0.581245 0.0287057
\(411\) 0 0
\(412\) −2.19991 −0.108382
\(413\) −0.265157 −0.0130475
\(414\) 0 0
\(415\) 23.5438 1.15572
\(416\) −1.30783 −0.0641215
\(417\) 0 0
\(418\) −1.55305 −0.0759620
\(419\) 9.76046 0.476830 0.238415 0.971163i \(-0.423372\pi\)
0.238415 + 0.971163i \(0.423372\pi\)
\(420\) 0 0
\(421\) −32.0064 −1.55990 −0.779949 0.625843i \(-0.784755\pi\)
−0.779949 + 0.625843i \(0.784755\pi\)
\(422\) 6.81415 0.331707
\(423\) 0 0
\(424\) −7.77757 −0.377712
\(425\) 4.17818 0.202672
\(426\) 0 0
\(427\) −0.152718 −0.00739055
\(428\) −4.80921 −0.232462
\(429\) 0 0
\(430\) 0.776416 0.0374421
\(431\) 33.5502 1.61605 0.808027 0.589145i \(-0.200535\pi\)
0.808027 + 0.589145i \(0.200535\pi\)
\(432\) 0 0
\(433\) 35.8412 1.72242 0.861208 0.508253i \(-0.169708\pi\)
0.861208 + 0.508253i \(0.169708\pi\)
\(434\) 0.179246 0.00860409
\(435\) 0 0
\(436\) −12.8433 −0.615081
\(437\) −0.486823 −0.0232879
\(438\) 0 0
\(439\) −4.89036 −0.233404 −0.116702 0.993167i \(-0.537232\pi\)
−0.116702 + 0.993167i \(0.537232\pi\)
\(440\) −10.4830 −0.499756
\(441\) 0 0
\(442\) 5.30545 0.252355
\(443\) −6.82947 −0.324478 −0.162239 0.986752i \(-0.551872\pi\)
−0.162239 + 0.986752i \(0.551872\pi\)
\(444\) 0 0
\(445\) 22.7174 1.07691
\(446\) 19.9915 0.946627
\(447\) 0 0
\(448\) −0.0206178 −0.000974101 0
\(449\) 29.7864 1.40571 0.702854 0.711334i \(-0.251909\pi\)
0.702854 + 0.711334i \(0.251909\pi\)
\(450\) 0 0
\(451\) −1.53479 −0.0722703
\(452\) −3.21231 −0.151094
\(453\) 0 0
\(454\) 13.5705 0.636895
\(455\) −0.0537269 −0.00251875
\(456\) 0 0
\(457\) 4.05153 0.189522 0.0947612 0.995500i \(-0.469791\pi\)
0.0947612 + 0.995500i \(0.469791\pi\)
\(458\) −27.0742 −1.26510
\(459\) 0 0
\(460\) −3.28603 −0.153212
\(461\) 39.8347 1.85529 0.927643 0.373468i \(-0.121832\pi\)
0.927643 + 0.373468i \(0.121832\pi\)
\(462\) 0 0
\(463\) −22.9167 −1.06503 −0.532515 0.846421i \(-0.678753\pi\)
−0.532515 + 0.846421i \(0.678753\pi\)
\(464\) −3.96430 −0.184038
\(465\) 0 0
\(466\) −1.11238 −0.0515299
\(467\) 1.53647 0.0710993 0.0355496 0.999368i \(-0.488682\pi\)
0.0355496 + 0.999368i \(0.488682\pi\)
\(468\) 0 0
\(469\) −0.122919 −0.00567588
\(470\) −9.10596 −0.420027
\(471\) 0 0
\(472\) −12.8606 −0.591955
\(473\) −2.05014 −0.0942654
\(474\) 0 0
\(475\) −0.304028 −0.0139498
\(476\) 0.0836402 0.00383364
\(477\) 0 0
\(478\) 21.3359 0.975882
\(479\) 22.1043 1.00997 0.504985 0.863128i \(-0.331498\pi\)
0.504985 + 0.863128i \(0.331498\pi\)
\(480\) 0 0
\(481\) −11.3369 −0.516918
\(482\) −7.94889 −0.362062
\(483\) 0 0
\(484\) 16.6804 0.758202
\(485\) −0.336171 −0.0152648
\(486\) 0 0
\(487\) −34.8299 −1.57829 −0.789147 0.614204i \(-0.789477\pi\)
−0.789147 + 0.614204i \(0.789477\pi\)
\(488\) −7.40709 −0.335303
\(489\) 0 0
\(490\) 13.9466 0.630045
\(491\) −12.6656 −0.571589 −0.285795 0.958291i \(-0.592257\pi\)
−0.285795 + 0.958291i \(0.592257\pi\)
\(492\) 0 0
\(493\) 16.0820 0.724295
\(494\) −0.386054 −0.0173694
\(495\) 0 0
\(496\) 8.69374 0.390360
\(497\) 0.211566 0.00949001
\(498\) 0 0
\(499\) 17.1306 0.766872 0.383436 0.923567i \(-0.374741\pi\)
0.383436 + 0.923567i \(0.374741\pi\)
\(500\) −12.0147 −0.537312
\(501\) 0 0
\(502\) −30.3459 −1.35440
\(503\) 8.08515 0.360499 0.180250 0.983621i \(-0.442309\pi\)
0.180250 + 0.983621i \(0.442309\pi\)
\(504\) 0 0
\(505\) 29.8960 1.33036
\(506\) 8.67680 0.385731
\(507\) 0 0
\(508\) 14.1266 0.626768
\(509\) −27.1112 −1.20168 −0.600842 0.799368i \(-0.705168\pi\)
−0.600842 + 0.799368i \(0.705168\pi\)
\(510\) 0 0
\(511\) −0.107570 −0.00475863
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 11.3203 0.499318
\(515\) −4.38331 −0.193152
\(516\) 0 0
\(517\) 24.0444 1.05747
\(518\) −0.178726 −0.00785277
\(519\) 0 0
\(520\) −2.60584 −0.114274
\(521\) −4.65077 −0.203754 −0.101877 0.994797i \(-0.532485\pi\)
−0.101877 + 0.994797i \(0.532485\pi\)
\(522\) 0 0
\(523\) −11.6457 −0.509232 −0.254616 0.967042i \(-0.581949\pi\)
−0.254616 + 0.967042i \(0.581949\pi\)
\(524\) 17.7947 0.777364
\(525\) 0 0
\(526\) 0.0140866 0.000614206 0
\(527\) −35.2678 −1.53629
\(528\) 0 0
\(529\) −20.2801 −0.881745
\(530\) −15.4968 −0.673138
\(531\) 0 0
\(532\) −0.00608613 −0.000263867 0
\(533\) −0.381515 −0.0165252
\(534\) 0 0
\(535\) −9.58235 −0.414281
\(536\) −5.96178 −0.257510
\(537\) 0 0
\(538\) −13.4107 −0.578175
\(539\) −36.8263 −1.58622
\(540\) 0 0
\(541\) −8.80776 −0.378675 −0.189338 0.981912i \(-0.560634\pi\)
−0.189338 + 0.981912i \(0.560634\pi\)
\(542\) −30.1331 −1.29433
\(543\) 0 0
\(544\) 4.05669 0.173929
\(545\) −25.5902 −1.09616
\(546\) 0 0
\(547\) −22.6940 −0.970325 −0.485162 0.874424i \(-0.661239\pi\)
−0.485162 + 0.874424i \(0.661239\pi\)
\(548\) 3.79487 0.162109
\(549\) 0 0
\(550\) 5.41878 0.231058
\(551\) −1.17021 −0.0498528
\(552\) 0 0
\(553\) −0.117424 −0.00499338
\(554\) 18.7209 0.795373
\(555\) 0 0
\(556\) −13.1582 −0.558034
\(557\) −20.2130 −0.856454 −0.428227 0.903671i \(-0.640862\pi\)
−0.428227 + 0.903671i \(0.640862\pi\)
\(558\) 0 0
\(559\) −0.509620 −0.0215546
\(560\) −0.0410810 −0.00173599
\(561\) 0 0
\(562\) −7.41800 −0.312909
\(563\) 3.95448 0.166662 0.0833308 0.996522i \(-0.473444\pi\)
0.0833308 + 0.996522i \(0.473444\pi\)
\(564\) 0 0
\(565\) −6.40052 −0.269272
\(566\) 21.1335 0.888305
\(567\) 0 0
\(568\) 10.2613 0.430554
\(569\) −17.7277 −0.743182 −0.371591 0.928396i \(-0.621188\pi\)
−0.371591 + 0.928396i \(0.621188\pi\)
\(570\) 0 0
\(571\) −4.10744 −0.171891 −0.0859455 0.996300i \(-0.527391\pi\)
−0.0859455 + 0.996300i \(0.527391\pi\)
\(572\) 6.88076 0.287699
\(573\) 0 0
\(574\) −0.00601457 −0.000251043 0
\(575\) 1.69859 0.0708361
\(576\) 0 0
\(577\) −38.2521 −1.59245 −0.796227 0.604998i \(-0.793174\pi\)
−0.796227 + 0.604998i \(0.793174\pi\)
\(578\) 0.543249 0.0225962
\(579\) 0 0
\(580\) −7.89887 −0.327983
\(581\) −0.243625 −0.0101073
\(582\) 0 0
\(583\) 40.9195 1.69471
\(584\) −5.21734 −0.215895
\(585\) 0 0
\(586\) 5.04458 0.208390
\(587\) 26.6533 1.10010 0.550050 0.835131i \(-0.314609\pi\)
0.550050 + 0.835131i \(0.314609\pi\)
\(588\) 0 0
\(589\) 2.56629 0.105742
\(590\) −25.6247 −1.05495
\(591\) 0 0
\(592\) −8.66851 −0.356274
\(593\) −32.6922 −1.34251 −0.671254 0.741228i \(-0.734244\pi\)
−0.671254 + 0.741228i \(0.734244\pi\)
\(594\) 0 0
\(595\) 0.166653 0.00683211
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) 2.15687 0.0882008
\(599\) −39.6511 −1.62010 −0.810050 0.586361i \(-0.800560\pi\)
−0.810050 + 0.586361i \(0.800560\pi\)
\(600\) 0 0
\(601\) −22.2768 −0.908688 −0.454344 0.890826i \(-0.650126\pi\)
−0.454344 + 0.890826i \(0.650126\pi\)
\(602\) −0.00803414 −0.000327447 0
\(603\) 0 0
\(604\) −13.5614 −0.551806
\(605\) 33.2358 1.35123
\(606\) 0 0
\(607\) −0.442899 −0.0179767 −0.00898836 0.999960i \(-0.502861\pi\)
−0.00898836 + 0.999960i \(0.502861\pi\)
\(608\) −0.295188 −0.0119714
\(609\) 0 0
\(610\) −14.7586 −0.597559
\(611\) 5.97693 0.241801
\(612\) 0 0
\(613\) 23.1291 0.934177 0.467089 0.884211i \(-0.345303\pi\)
0.467089 + 0.884211i \(0.345303\pi\)
\(614\) 4.06035 0.163862
\(615\) 0 0
\(616\) 0.108475 0.00437058
\(617\) 18.6553 0.751033 0.375517 0.926816i \(-0.377465\pi\)
0.375517 + 0.926816i \(0.377465\pi\)
\(618\) 0 0
\(619\) −17.4442 −0.701142 −0.350571 0.936536i \(-0.614012\pi\)
−0.350571 + 0.936536i \(0.614012\pi\)
\(620\) 17.3223 0.695679
\(621\) 0 0
\(622\) 30.1221 1.20778
\(623\) −0.235074 −0.00941803
\(624\) 0 0
\(625\) −18.7895 −0.751579
\(626\) −5.86146 −0.234271
\(627\) 0 0
\(628\) −11.9231 −0.475782
\(629\) 35.1655 1.40214
\(630\) 0 0
\(631\) 37.4513 1.49091 0.745456 0.666555i \(-0.232232\pi\)
0.745456 + 0.666555i \(0.232232\pi\)
\(632\) −5.69527 −0.226546
\(633\) 0 0
\(634\) 13.0792 0.519442
\(635\) 28.1473 1.11699
\(636\) 0 0
\(637\) −9.15423 −0.362704
\(638\) 20.8571 0.825740
\(639\) 0 0
\(640\) −1.99250 −0.0787604
\(641\) −5.73239 −0.226416 −0.113208 0.993571i \(-0.536113\pi\)
−0.113208 + 0.993571i \(0.536113\pi\)
\(642\) 0 0
\(643\) −5.32139 −0.209855 −0.104928 0.994480i \(-0.533461\pi\)
−0.104928 + 0.994480i \(0.533461\pi\)
\(644\) 0.0340029 0.00133990
\(645\) 0 0
\(646\) 1.19749 0.0471144
\(647\) 27.7330 1.09030 0.545148 0.838340i \(-0.316474\pi\)
0.545148 + 0.838340i \(0.316474\pi\)
\(648\) 0 0
\(649\) 67.6622 2.65598
\(650\) 1.34699 0.0528334
\(651\) 0 0
\(652\) −2.75467 −0.107881
\(653\) 10.3642 0.405584 0.202792 0.979222i \(-0.434998\pi\)
0.202792 + 0.979222i \(0.434998\pi\)
\(654\) 0 0
\(655\) 35.4559 1.38538
\(656\) −0.291717 −0.0113896
\(657\) 0 0
\(658\) 0.0942260 0.00367331
\(659\) −36.1988 −1.41011 −0.705053 0.709155i \(-0.749077\pi\)
−0.705053 + 0.709155i \(0.749077\pi\)
\(660\) 0 0
\(661\) 43.6839 1.69911 0.849553 0.527503i \(-0.176872\pi\)
0.849553 + 0.527503i \(0.176872\pi\)
\(662\) −11.3159 −0.439804
\(663\) 0 0
\(664\) −11.8162 −0.458558
\(665\) −0.0121266 −0.000470250 0
\(666\) 0 0
\(667\) 6.53793 0.253150
\(668\) 21.6245 0.836678
\(669\) 0 0
\(670\) −11.8788 −0.458920
\(671\) 38.9703 1.50443
\(672\) 0 0
\(673\) −40.3949 −1.55711 −0.778555 0.627576i \(-0.784047\pi\)
−0.778555 + 0.627576i \(0.784047\pi\)
\(674\) −3.41103 −0.131388
\(675\) 0 0
\(676\) −11.2896 −0.434215
\(677\) 14.3060 0.549823 0.274912 0.961469i \(-0.411351\pi\)
0.274912 + 0.961469i \(0.411351\pi\)
\(678\) 0 0
\(679\) 0.00347861 0.000133497 0
\(680\) 8.08295 0.309967
\(681\) 0 0
\(682\) −45.7397 −1.75146
\(683\) −2.76087 −0.105642 −0.0528209 0.998604i \(-0.516821\pi\)
−0.0528209 + 0.998604i \(0.516821\pi\)
\(684\) 0 0
\(685\) 7.56127 0.288901
\(686\) −0.288641 −0.0110204
\(687\) 0 0
\(688\) −0.389669 −0.0148560
\(689\) 10.1717 0.387512
\(690\) 0 0
\(691\) 1.81589 0.0690797 0.0345399 0.999403i \(-0.489003\pi\)
0.0345399 + 0.999403i \(0.489003\pi\)
\(692\) 17.8683 0.679252
\(693\) 0 0
\(694\) −5.91948 −0.224700
\(695\) −26.2178 −0.994497
\(696\) 0 0
\(697\) 1.18340 0.0448247
\(698\) −11.2779 −0.426875
\(699\) 0 0
\(700\) 0.0212353 0.000802619 0
\(701\) −44.8307 −1.69323 −0.846617 0.532203i \(-0.821364\pi\)
−0.846617 + 0.532203i \(0.821364\pi\)
\(702\) 0 0
\(703\) −2.55884 −0.0965084
\(704\) 5.26122 0.198290
\(705\) 0 0
\(706\) −14.0935 −0.530417
\(707\) −0.309356 −0.0116345
\(708\) 0 0
\(709\) 19.6903 0.739485 0.369742 0.929134i \(-0.379446\pi\)
0.369742 + 0.929134i \(0.379446\pi\)
\(710\) 20.4456 0.767310
\(711\) 0 0
\(712\) −11.4015 −0.427288
\(713\) −14.3377 −0.536951
\(714\) 0 0
\(715\) 13.7099 0.512722
\(716\) 14.6929 0.549098
\(717\) 0 0
\(718\) −3.81544 −0.142391
\(719\) 38.2650 1.42704 0.713522 0.700632i \(-0.247099\pi\)
0.713522 + 0.700632i \(0.247099\pi\)
\(720\) 0 0
\(721\) 0.0453573 0.00168920
\(722\) 18.9129 0.703864
\(723\) 0 0
\(724\) 20.5258 0.762834
\(725\) 4.08303 0.151640
\(726\) 0 0
\(727\) −27.4811 −1.01922 −0.509610 0.860406i \(-0.670210\pi\)
−0.509610 + 0.860406i \(0.670210\pi\)
\(728\) 0.0269646 0.000999373 0
\(729\) 0 0
\(730\) −10.3955 −0.384756
\(731\) 1.58077 0.0584668
\(732\) 0 0
\(733\) 10.4364 0.385477 0.192738 0.981250i \(-0.438263\pi\)
0.192738 + 0.981250i \(0.438263\pi\)
\(734\) 16.4625 0.607643
\(735\) 0 0
\(736\) 1.64920 0.0607903
\(737\) 31.3663 1.15539
\(738\) 0 0
\(739\) 27.0604 0.995432 0.497716 0.867340i \(-0.334172\pi\)
0.497716 + 0.867340i \(0.334172\pi\)
\(740\) −17.2720 −0.634931
\(741\) 0 0
\(742\) 0.160357 0.00588688
\(743\) −8.47771 −0.311017 −0.155508 0.987835i \(-0.549702\pi\)
−0.155508 + 0.987835i \(0.549702\pi\)
\(744\) 0 0
\(745\) 1.99250 0.0729995
\(746\) −20.1014 −0.735965
\(747\) 0 0
\(748\) −21.3432 −0.780383
\(749\) 0.0991556 0.00362307
\(750\) 0 0
\(751\) 0.633305 0.0231096 0.0115548 0.999933i \(-0.496322\pi\)
0.0115548 + 0.999933i \(0.496322\pi\)
\(752\) 4.57012 0.166655
\(753\) 0 0
\(754\) 5.18462 0.188813
\(755\) −27.0211 −0.983399
\(756\) 0 0
\(757\) −16.7917 −0.610304 −0.305152 0.952304i \(-0.598707\pi\)
−0.305152 + 0.952304i \(0.598707\pi\)
\(758\) 0.0507386 0.00184291
\(759\) 0 0
\(760\) −0.588161 −0.0213348
\(761\) 15.9360 0.577681 0.288841 0.957377i \(-0.406730\pi\)
0.288841 + 0.957377i \(0.406730\pi\)
\(762\) 0 0
\(763\) 0.264801 0.00958643
\(764\) 16.1527 0.584384
\(765\) 0 0
\(766\) 24.2127 0.874840
\(767\) 16.8194 0.607313
\(768\) 0 0
\(769\) 16.2867 0.587315 0.293657 0.955911i \(-0.405127\pi\)
0.293657 + 0.955911i \(0.405127\pi\)
\(770\) 0.216136 0.00778901
\(771\) 0 0
\(772\) 0.667178 0.0240123
\(773\) 47.5479 1.71018 0.855090 0.518480i \(-0.173502\pi\)
0.855090 + 0.518480i \(0.173502\pi\)
\(774\) 0 0
\(775\) −8.95410 −0.321641
\(776\) 0.168718 0.00605664
\(777\) 0 0
\(778\) 16.8468 0.603988
\(779\) −0.0861112 −0.00308525
\(780\) 0 0
\(781\) −53.9869 −1.93180
\(782\) −6.69029 −0.239244
\(783\) 0 0
\(784\) −6.99957 −0.249985
\(785\) −23.7567 −0.847912
\(786\) 0 0
\(787\) 49.1312 1.75134 0.875668 0.482913i \(-0.160421\pi\)
0.875668 + 0.482913i \(0.160421\pi\)
\(788\) 2.10056 0.0748295
\(789\) 0 0
\(790\) −11.3478 −0.403737
\(791\) 0.0662309 0.00235490
\(792\) 0 0
\(793\) 9.68719 0.344002
\(794\) −25.7132 −0.912527
\(795\) 0 0
\(796\) −17.4910 −0.619951
\(797\) 41.7653 1.47940 0.739701 0.672936i \(-0.234967\pi\)
0.739701 + 0.672936i \(0.234967\pi\)
\(798\) 0 0
\(799\) −18.5396 −0.655883
\(800\) 1.02995 0.0364142
\(801\) 0 0
\(802\) 18.5979 0.656713
\(803\) 27.4496 0.968675
\(804\) 0 0
\(805\) 0.0677508 0.00238790
\(806\) −11.3699 −0.400488
\(807\) 0 0
\(808\) −15.0043 −0.527849
\(809\) 33.4974 1.17771 0.588853 0.808240i \(-0.299580\pi\)
0.588853 + 0.808240i \(0.299580\pi\)
\(810\) 0 0
\(811\) 24.2531 0.851641 0.425821 0.904808i \(-0.359985\pi\)
0.425821 + 0.904808i \(0.359985\pi\)
\(812\) 0.0817354 0.00286835
\(813\) 0 0
\(814\) 45.6069 1.59852
\(815\) −5.48869 −0.192260
\(816\) 0 0
\(817\) −0.115026 −0.00402424
\(818\) −36.7789 −1.28594
\(819\) 0 0
\(820\) −0.581245 −0.0202980
\(821\) 32.0387 1.11816 0.559080 0.829114i \(-0.311154\pi\)
0.559080 + 0.829114i \(0.311154\pi\)
\(822\) 0 0
\(823\) 19.6719 0.685718 0.342859 0.939387i \(-0.388605\pi\)
0.342859 + 0.939387i \(0.388605\pi\)
\(824\) 2.19991 0.0766374
\(825\) 0 0
\(826\) 0.265157 0.00922599
\(827\) 31.4913 1.09506 0.547529 0.836786i \(-0.315568\pi\)
0.547529 + 0.836786i \(0.315568\pi\)
\(828\) 0 0
\(829\) 11.9019 0.413371 0.206686 0.978407i \(-0.433732\pi\)
0.206686 + 0.978407i \(0.433732\pi\)
\(830\) −23.5438 −0.817217
\(831\) 0 0
\(832\) 1.30783 0.0453407
\(833\) 28.3951 0.983833
\(834\) 0 0
\(835\) 43.0868 1.49108
\(836\) 1.55305 0.0537133
\(837\) 0 0
\(838\) −9.76046 −0.337170
\(839\) 12.7598 0.440517 0.220258 0.975442i \(-0.429310\pi\)
0.220258 + 0.975442i \(0.429310\pi\)
\(840\) 0 0
\(841\) −13.2843 −0.458079
\(842\) 32.0064 1.10301
\(843\) 0 0
\(844\) −6.81415 −0.234553
\(845\) −22.4945 −0.773834
\(846\) 0 0
\(847\) −0.343915 −0.0118170
\(848\) 7.77757 0.267083
\(849\) 0 0
\(850\) −4.17818 −0.143310
\(851\) 14.2961 0.490064
\(852\) 0 0
\(853\) 32.8050 1.12322 0.561612 0.827401i \(-0.310182\pi\)
0.561612 + 0.827401i \(0.310182\pi\)
\(854\) 0.152718 0.00522591
\(855\) 0 0
\(856\) 4.80921 0.164375
\(857\) −7.56418 −0.258388 −0.129194 0.991619i \(-0.541239\pi\)
−0.129194 + 0.991619i \(0.541239\pi\)
\(858\) 0 0
\(859\) −52.5155 −1.79181 −0.895904 0.444249i \(-0.853471\pi\)
−0.895904 + 0.444249i \(0.853471\pi\)
\(860\) −0.776416 −0.0264756
\(861\) 0 0
\(862\) −33.5502 −1.14272
\(863\) 35.4413 1.20644 0.603218 0.797576i \(-0.293885\pi\)
0.603218 + 0.797576i \(0.293885\pi\)
\(864\) 0 0
\(865\) 35.6026 1.21053
\(866\) −35.8412 −1.21793
\(867\) 0 0
\(868\) −0.179246 −0.00608401
\(869\) 29.9641 1.01646
\(870\) 0 0
\(871\) 7.79698 0.264191
\(872\) 12.8433 0.434928
\(873\) 0 0
\(874\) 0.486823 0.0164670
\(875\) 0.247716 0.00837434
\(876\) 0 0
\(877\) 36.4135 1.22960 0.614799 0.788684i \(-0.289237\pi\)
0.614799 + 0.788684i \(0.289237\pi\)
\(878\) 4.89036 0.165042
\(879\) 0 0
\(880\) 10.4830 0.353381
\(881\) −56.1916 −1.89314 −0.946572 0.322492i \(-0.895479\pi\)
−0.946572 + 0.322492i \(0.895479\pi\)
\(882\) 0 0
\(883\) 26.3628 0.887180 0.443590 0.896230i \(-0.353705\pi\)
0.443590 + 0.896230i \(0.353705\pi\)
\(884\) −5.30545 −0.178442
\(885\) 0 0
\(886\) 6.82947 0.229440
\(887\) −51.2228 −1.71989 −0.859947 0.510383i \(-0.829504\pi\)
−0.859947 + 0.510383i \(0.829504\pi\)
\(888\) 0 0
\(889\) −0.291261 −0.00976857
\(890\) −22.7174 −0.761489
\(891\) 0 0
\(892\) −19.9915 −0.669366
\(893\) 1.34904 0.0451440
\(894\) 0 0
\(895\) 29.2755 0.978573
\(896\) 0.0206178 0.000688794 0
\(897\) 0 0
\(898\) −29.7864 −0.993986
\(899\) −34.4646 −1.14946
\(900\) 0 0
\(901\) −31.5512 −1.05112
\(902\) 1.53479 0.0511028
\(903\) 0 0
\(904\) 3.21231 0.106840
\(905\) 40.8975 1.35948
\(906\) 0 0
\(907\) −12.8286 −0.425966 −0.212983 0.977056i \(-0.568318\pi\)
−0.212983 + 0.977056i \(0.568318\pi\)
\(908\) −13.5705 −0.450353
\(909\) 0 0
\(910\) 0.0537269 0.00178103
\(911\) 8.07943 0.267683 0.133842 0.991003i \(-0.457269\pi\)
0.133842 + 0.991003i \(0.457269\pi\)
\(912\) 0 0
\(913\) 62.1677 2.05745
\(914\) −4.05153 −0.134013
\(915\) 0 0
\(916\) 27.0742 0.894558
\(917\) −0.366888 −0.0121157
\(918\) 0 0
\(919\) −39.1276 −1.29070 −0.645350 0.763887i \(-0.723288\pi\)
−0.645350 + 0.763887i \(0.723288\pi\)
\(920\) 3.28603 0.108337
\(921\) 0 0
\(922\) −39.8347 −1.31189
\(923\) −13.4200 −0.441724
\(924\) 0 0
\(925\) 8.92811 0.293555
\(926\) 22.9167 0.753090
\(927\) 0 0
\(928\) 3.96430 0.130135
\(929\) 27.9350 0.916518 0.458259 0.888819i \(-0.348473\pi\)
0.458259 + 0.888819i \(0.348473\pi\)
\(930\) 0 0
\(931\) −2.06619 −0.0677166
\(932\) 1.11238 0.0364371
\(933\) 0 0
\(934\) −1.53647 −0.0502748
\(935\) −42.5262 −1.39076
\(936\) 0 0
\(937\) −13.7977 −0.450751 −0.225375 0.974272i \(-0.572361\pi\)
−0.225375 + 0.974272i \(0.572361\pi\)
\(938\) 0.122919 0.00401345
\(939\) 0 0
\(940\) 9.10596 0.297004
\(941\) 40.3166 1.31428 0.657142 0.753767i \(-0.271765\pi\)
0.657142 + 0.753767i \(0.271765\pi\)
\(942\) 0 0
\(943\) 0.481099 0.0156667
\(944\) 12.8606 0.418576
\(945\) 0 0
\(946\) 2.05014 0.0666557
\(947\) 5.20950 0.169286 0.0846431 0.996411i \(-0.473025\pi\)
0.0846431 + 0.996411i \(0.473025\pi\)
\(948\) 0 0
\(949\) 6.82338 0.221496
\(950\) 0.304028 0.00986397
\(951\) 0 0
\(952\) −0.0836402 −0.00271080
\(953\) 13.5440 0.438733 0.219367 0.975642i \(-0.429601\pi\)
0.219367 + 0.975642i \(0.429601\pi\)
\(954\) 0 0
\(955\) 32.1843 1.04146
\(956\) −21.3359 −0.690053
\(957\) 0 0
\(958\) −22.1043 −0.714157
\(959\) −0.0782419 −0.00252656
\(960\) 0 0
\(961\) 44.5811 1.43810
\(962\) 11.3369 0.365517
\(963\) 0 0
\(964\) 7.94889 0.256016
\(965\) 1.32935 0.0427933
\(966\) 0 0
\(967\) −29.4315 −0.946452 −0.473226 0.880941i \(-0.656911\pi\)
−0.473226 + 0.880941i \(0.656911\pi\)
\(968\) −16.6804 −0.536130
\(969\) 0 0
\(970\) 0.336171 0.0107938
\(971\) −37.1081 −1.19086 −0.595428 0.803409i \(-0.703017\pi\)
−0.595428 + 0.803409i \(0.703017\pi\)
\(972\) 0 0
\(973\) 0.271294 0.00869730
\(974\) 34.8299 1.11602
\(975\) 0 0
\(976\) 7.40709 0.237095
\(977\) −44.0988 −1.41084 −0.705422 0.708787i \(-0.749243\pi\)
−0.705422 + 0.708787i \(0.749243\pi\)
\(978\) 0 0
\(979\) 59.9856 1.91715
\(980\) −13.9466 −0.445509
\(981\) 0 0
\(982\) 12.6656 0.404175
\(983\) −57.9838 −1.84940 −0.924699 0.380700i \(-0.875683\pi\)
−0.924699 + 0.380700i \(0.875683\pi\)
\(984\) 0 0
\(985\) 4.18537 0.133357
\(986\) −16.0820 −0.512154
\(987\) 0 0
\(988\) 0.386054 0.0122820
\(989\) 0.642642 0.0204348
\(990\) 0 0
\(991\) −0.591718 −0.0187965 −0.00939827 0.999956i \(-0.502992\pi\)
−0.00939827 + 0.999956i \(0.502992\pi\)
\(992\) −8.69374 −0.276027
\(993\) 0 0
\(994\) −0.211566 −0.00671045
\(995\) −34.8507 −1.10484
\(996\) 0 0
\(997\) 9.30402 0.294661 0.147331 0.989087i \(-0.452932\pi\)
0.147331 + 0.989087i \(0.452932\pi\)
\(998\) −17.1306 −0.542260
\(999\) 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 \(a_p\))