Properties

Label 8001.2.a.v.1.10
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(0.395540\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.395540 q^{2}\) \(-1.84355 q^{4}\) \(-1.95228 q^{5}\) \(+1.00000 q^{7}\) \(+1.52028 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.395540 q^{2}\) \(-1.84355 q^{4}\) \(-1.95228 q^{5}\) \(+1.00000 q^{7}\) \(+1.52028 q^{8}\) \(+0.772204 q^{10}\) \(+5.34735 q^{11}\) \(+6.49250 q^{13}\) \(-0.395540 q^{14}\) \(+3.08577 q^{16}\) \(-7.92778 q^{17}\) \(-5.50935 q^{19}\) \(+3.59912 q^{20}\) \(-2.11509 q^{22}\) \(+3.09814 q^{23}\) \(-1.18861 q^{25}\) \(-2.56804 q^{26}\) \(-1.84355 q^{28}\) \(+3.39563 q^{29}\) \(+10.2114 q^{31}\) \(-4.26110 q^{32}\) \(+3.13575 q^{34}\) \(-1.95228 q^{35}\) \(+7.25011 q^{37}\) \(+2.17917 q^{38}\) \(-2.96800 q^{40}\) \(+10.1950 q^{41}\) \(+12.7584 q^{43}\) \(-9.85809 q^{44}\) \(-1.22544 q^{46}\) \(+1.66284 q^{47}\) \(+1.00000 q^{49}\) \(+0.470144 q^{50}\) \(-11.9692 q^{52}\) \(-9.51844 q^{53}\) \(-10.4395 q^{55}\) \(+1.52028 q^{56}\) \(-1.34311 q^{58}\) \(+5.51303 q^{59}\) \(+0.0570727 q^{61}\) \(-4.03903 q^{62}\) \(-4.48610 q^{64}\) \(-12.6752 q^{65}\) \(-10.0453 q^{67}\) \(+14.6152 q^{68}\) \(+0.772204 q^{70}\) \(-7.73577 q^{71}\) \(+1.79288 q^{73}\) \(-2.86771 q^{74}\) \(+10.1568 q^{76}\) \(+5.34735 q^{77}\) \(+1.81852 q^{79}\) \(-6.02427 q^{80}\) \(-4.03252 q^{82}\) \(-6.90635 q^{83}\) \(+15.4772 q^{85}\) \(-5.04644 q^{86}\) \(+8.12944 q^{88}\) \(-17.5417 q^{89}\) \(+6.49250 q^{91}\) \(-5.71157 q^{92}\) \(-0.657719 q^{94}\) \(+10.7558 q^{95}\) \(+4.44649 q^{97}\) \(-0.395540 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.395540 −0.279689 −0.139844 0.990173i \(-0.544660\pi\)
−0.139844 + 0.990173i \(0.544660\pi\)
\(3\) 0 0
\(4\) −1.84355 −0.921774
\(5\) −1.95228 −0.873085 −0.436543 0.899684i \(-0.643797\pi\)
−0.436543 + 0.899684i \(0.643797\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.52028 0.537499
\(9\) 0 0
\(10\) 0.772204 0.244192
\(11\) 5.34735 1.61229 0.806143 0.591721i \(-0.201551\pi\)
0.806143 + 0.591721i \(0.201551\pi\)
\(12\) 0 0
\(13\) 6.49250 1.80070 0.900348 0.435170i \(-0.143312\pi\)
0.900348 + 0.435170i \(0.143312\pi\)
\(14\) −0.395540 −0.105712
\(15\) 0 0
\(16\) 3.08577 0.771442
\(17\) −7.92778 −1.92277 −0.961385 0.275208i \(-0.911253\pi\)
−0.961385 + 0.275208i \(0.911253\pi\)
\(18\) 0 0
\(19\) −5.50935 −1.26393 −0.631966 0.774996i \(-0.717752\pi\)
−0.631966 + 0.774996i \(0.717752\pi\)
\(20\) 3.59912 0.804787
\(21\) 0 0
\(22\) −2.11509 −0.450938
\(23\) 3.09814 0.646006 0.323003 0.946398i \(-0.395308\pi\)
0.323003 + 0.946398i \(0.395308\pi\)
\(24\) 0 0
\(25\) −1.18861 −0.237723
\(26\) −2.56804 −0.503635
\(27\) 0 0
\(28\) −1.84355 −0.348398
\(29\) 3.39563 0.630552 0.315276 0.949000i \(-0.397903\pi\)
0.315276 + 0.949000i \(0.397903\pi\)
\(30\) 0 0
\(31\) 10.2114 1.83403 0.917014 0.398855i \(-0.130592\pi\)
0.917014 + 0.398855i \(0.130592\pi\)
\(32\) −4.26110 −0.753263
\(33\) 0 0
\(34\) 3.13575 0.537777
\(35\) −1.95228 −0.329995
\(36\) 0 0
\(37\) 7.25011 1.19191 0.595955 0.803018i \(-0.296774\pi\)
0.595955 + 0.803018i \(0.296774\pi\)
\(38\) 2.17917 0.353508
\(39\) 0 0
\(40\) −2.96800 −0.469282
\(41\) 10.1950 1.59219 0.796093 0.605174i \(-0.206896\pi\)
0.796093 + 0.605174i \(0.206896\pi\)
\(42\) 0 0
\(43\) 12.7584 1.94563 0.972816 0.231581i \(-0.0743899\pi\)
0.972816 + 0.231581i \(0.0743899\pi\)
\(44\) −9.85809 −1.48616
\(45\) 0 0
\(46\) −1.22544 −0.180681
\(47\) 1.66284 0.242550 0.121275 0.992619i \(-0.461302\pi\)
0.121275 + 0.992619i \(0.461302\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0.470144 0.0664884
\(51\) 0 0
\(52\) −11.9692 −1.65984
\(53\) −9.51844 −1.30746 −0.653729 0.756729i \(-0.726796\pi\)
−0.653729 + 0.756729i \(0.726796\pi\)
\(54\) 0 0
\(55\) −10.4395 −1.40766
\(56\) 1.52028 0.203156
\(57\) 0 0
\(58\) −1.34311 −0.176358
\(59\) 5.51303 0.717735 0.358868 0.933388i \(-0.383163\pi\)
0.358868 + 0.933388i \(0.383163\pi\)
\(60\) 0 0
\(61\) 0.0570727 0.00730741 0.00365370 0.999993i \(-0.498837\pi\)
0.00365370 + 0.999993i \(0.498837\pi\)
\(62\) −4.03903 −0.512957
\(63\) 0 0
\(64\) −4.48610 −0.560762
\(65\) −12.6752 −1.57216
\(66\) 0 0
\(67\) −10.0453 −1.22723 −0.613617 0.789604i \(-0.710286\pi\)
−0.613617 + 0.789604i \(0.710286\pi\)
\(68\) 14.6152 1.77236
\(69\) 0 0
\(70\) 0.772204 0.0922960
\(71\) −7.73577 −0.918067 −0.459033 0.888419i \(-0.651804\pi\)
−0.459033 + 0.888419i \(0.651804\pi\)
\(72\) 0 0
\(73\) 1.79288 0.209841 0.104921 0.994481i \(-0.466541\pi\)
0.104921 + 0.994481i \(0.466541\pi\)
\(74\) −2.86771 −0.333364
\(75\) 0 0
\(76\) 10.1568 1.16506
\(77\) 5.34735 0.609387
\(78\) 0 0
\(79\) 1.81852 0.204600 0.102300 0.994754i \(-0.467380\pi\)
0.102300 + 0.994754i \(0.467380\pi\)
\(80\) −6.02427 −0.673534
\(81\) 0 0
\(82\) −4.03252 −0.445317
\(83\) −6.90635 −0.758070 −0.379035 0.925382i \(-0.623744\pi\)
−0.379035 + 0.925382i \(0.623744\pi\)
\(84\) 0 0
\(85\) 15.4772 1.67874
\(86\) −5.04644 −0.544171
\(87\) 0 0
\(88\) 8.12944 0.866602
\(89\) −17.5417 −1.85941 −0.929706 0.368303i \(-0.879939\pi\)
−0.929706 + 0.368303i \(0.879939\pi\)
\(90\) 0 0
\(91\) 6.49250 0.680599
\(92\) −5.71157 −0.595472
\(93\) 0 0
\(94\) −0.657719 −0.0678385
\(95\) 10.7558 1.10352
\(96\) 0 0
\(97\) 4.44649 0.451473 0.225736 0.974188i \(-0.427521\pi\)
0.225736 + 0.974188i \(0.427521\pi\)
\(98\) −0.395540 −0.0399556
\(99\) 0 0
\(100\) 2.19127 0.219127
\(101\) 4.31554 0.429412 0.214706 0.976679i \(-0.431121\pi\)
0.214706 + 0.976679i \(0.431121\pi\)
\(102\) 0 0
\(103\) −3.54414 −0.349214 −0.174607 0.984638i \(-0.555866\pi\)
−0.174607 + 0.984638i \(0.555866\pi\)
\(104\) 9.87040 0.967872
\(105\) 0 0
\(106\) 3.76492 0.365682
\(107\) −12.4575 −1.20431 −0.602155 0.798379i \(-0.705691\pi\)
−0.602155 + 0.798379i \(0.705691\pi\)
\(108\) 0 0
\(109\) 4.55460 0.436251 0.218126 0.975921i \(-0.430006\pi\)
0.218126 + 0.975921i \(0.430006\pi\)
\(110\) 4.12924 0.393707
\(111\) 0 0
\(112\) 3.08577 0.291578
\(113\) 0.943880 0.0887928 0.0443964 0.999014i \(-0.485864\pi\)
0.0443964 + 0.999014i \(0.485864\pi\)
\(114\) 0 0
\(115\) −6.04843 −0.564019
\(116\) −6.26000 −0.581227
\(117\) 0 0
\(118\) −2.18062 −0.200743
\(119\) −7.92778 −0.726739
\(120\) 0 0
\(121\) 17.5941 1.59946
\(122\) −0.0225745 −0.00204380
\(123\) 0 0
\(124\) −18.8253 −1.69056
\(125\) 12.0819 1.08064
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 10.2966 0.910102
\(129\) 0 0
\(130\) 5.01353 0.439716
\(131\) −4.18883 −0.365980 −0.182990 0.983115i \(-0.558578\pi\)
−0.182990 + 0.983115i \(0.558578\pi\)
\(132\) 0 0
\(133\) −5.50935 −0.477721
\(134\) 3.97333 0.343244
\(135\) 0 0
\(136\) −12.0524 −1.03349
\(137\) −4.87863 −0.416809 −0.208405 0.978043i \(-0.566827\pi\)
−0.208405 + 0.978043i \(0.566827\pi\)
\(138\) 0 0
\(139\) 3.61685 0.306777 0.153389 0.988166i \(-0.450981\pi\)
0.153389 + 0.988166i \(0.450981\pi\)
\(140\) 3.59912 0.304181
\(141\) 0 0
\(142\) 3.05980 0.256773
\(143\) 34.7177 2.90324
\(144\) 0 0
\(145\) −6.62921 −0.550526
\(146\) −0.709157 −0.0586903
\(147\) 0 0
\(148\) −13.3659 −1.09867
\(149\) 5.32520 0.436257 0.218129 0.975920i \(-0.430005\pi\)
0.218129 + 0.975920i \(0.430005\pi\)
\(150\) 0 0
\(151\) −11.1323 −0.905935 −0.452967 0.891527i \(-0.649635\pi\)
−0.452967 + 0.891527i \(0.649635\pi\)
\(152\) −8.37574 −0.679362
\(153\) 0 0
\(154\) −2.11509 −0.170439
\(155\) −19.9356 −1.60126
\(156\) 0 0
\(157\) −21.8326 −1.74243 −0.871214 0.490903i \(-0.836667\pi\)
−0.871214 + 0.490903i \(0.836667\pi\)
\(158\) −0.719298 −0.0572243
\(159\) 0 0
\(160\) 8.31884 0.657662
\(161\) 3.09814 0.244168
\(162\) 0 0
\(163\) 21.6255 1.69384 0.846921 0.531719i \(-0.178454\pi\)
0.846921 + 0.531719i \(0.178454\pi\)
\(164\) −18.7949 −1.46764
\(165\) 0 0
\(166\) 2.73174 0.212024
\(167\) −6.90780 −0.534542 −0.267271 0.963621i \(-0.586122\pi\)
−0.267271 + 0.963621i \(0.586122\pi\)
\(168\) 0 0
\(169\) 29.1526 2.24251
\(170\) −6.12186 −0.469525
\(171\) 0 0
\(172\) −23.5206 −1.79343
\(173\) −19.7315 −1.50016 −0.750080 0.661347i \(-0.769985\pi\)
−0.750080 + 0.661347i \(0.769985\pi\)
\(174\) 0 0
\(175\) −1.18861 −0.0898507
\(176\) 16.5007 1.24378
\(177\) 0 0
\(178\) 6.93843 0.520057
\(179\) 23.0568 1.72334 0.861672 0.507465i \(-0.169417\pi\)
0.861672 + 0.507465i \(0.169417\pi\)
\(180\) 0 0
\(181\) 1.92103 0.142789 0.0713946 0.997448i \(-0.477255\pi\)
0.0713946 + 0.997448i \(0.477255\pi\)
\(182\) −2.56804 −0.190356
\(183\) 0 0
\(184\) 4.71003 0.347228
\(185\) −14.1542 −1.04064
\(186\) 0 0
\(187\) −42.3926 −3.10005
\(188\) −3.06552 −0.223576
\(189\) 0 0
\(190\) −4.25434 −0.308642
\(191\) 5.70825 0.413034 0.206517 0.978443i \(-0.433787\pi\)
0.206517 + 0.978443i \(0.433787\pi\)
\(192\) 0 0
\(193\) −15.2985 −1.10121 −0.550606 0.834765i \(-0.685603\pi\)
−0.550606 + 0.834765i \(0.685603\pi\)
\(194\) −1.75877 −0.126272
\(195\) 0 0
\(196\) −1.84355 −0.131682
\(197\) −2.27770 −0.162279 −0.0811396 0.996703i \(-0.525856\pi\)
−0.0811396 + 0.996703i \(0.525856\pi\)
\(198\) 0 0
\(199\) −24.2047 −1.71583 −0.857913 0.513794i \(-0.828240\pi\)
−0.857913 + 0.513794i \(0.828240\pi\)
\(200\) −1.80702 −0.127776
\(201\) 0 0
\(202\) −1.70697 −0.120102
\(203\) 3.39563 0.238326
\(204\) 0 0
\(205\) −19.9034 −1.39011
\(206\) 1.40185 0.0976714
\(207\) 0 0
\(208\) 20.0343 1.38913
\(209\) −29.4604 −2.03782
\(210\) 0 0
\(211\) 3.91191 0.269307 0.134654 0.990893i \(-0.457008\pi\)
0.134654 + 0.990893i \(0.457008\pi\)
\(212\) 17.5477 1.20518
\(213\) 0 0
\(214\) 4.92743 0.336832
\(215\) −24.9079 −1.69870
\(216\) 0 0
\(217\) 10.2114 0.693197
\(218\) −1.80152 −0.122015
\(219\) 0 0
\(220\) 19.2457 1.29755
\(221\) −51.4712 −3.46232
\(222\) 0 0
\(223\) −2.42028 −0.162074 −0.0810371 0.996711i \(-0.525823\pi\)
−0.0810371 + 0.996711i \(0.525823\pi\)
\(224\) −4.26110 −0.284707
\(225\) 0 0
\(226\) −0.373342 −0.0248344
\(227\) 10.9159 0.724512 0.362256 0.932079i \(-0.382007\pi\)
0.362256 + 0.932079i \(0.382007\pi\)
\(228\) 0 0
\(229\) 8.16418 0.539504 0.269752 0.962930i \(-0.413058\pi\)
0.269752 + 0.962930i \(0.413058\pi\)
\(230\) 2.39239 0.157750
\(231\) 0 0
\(232\) 5.16229 0.338921
\(233\) 20.3575 1.33366 0.666831 0.745209i \(-0.267650\pi\)
0.666831 + 0.745209i \(0.267650\pi\)
\(234\) 0 0
\(235\) −3.24632 −0.211767
\(236\) −10.1635 −0.661590
\(237\) 0 0
\(238\) 3.13575 0.203261
\(239\) 9.63093 0.622973 0.311486 0.950251i \(-0.399173\pi\)
0.311486 + 0.950251i \(0.399173\pi\)
\(240\) 0 0
\(241\) 28.2537 1.81998 0.909992 0.414626i \(-0.136088\pi\)
0.909992 + 0.414626i \(0.136088\pi\)
\(242\) −6.95917 −0.447352
\(243\) 0 0
\(244\) −0.105216 −0.00673578
\(245\) −1.95228 −0.124726
\(246\) 0 0
\(247\) −35.7695 −2.27596
\(248\) 15.5242 0.985788
\(249\) 0 0
\(250\) −4.77887 −0.302242
\(251\) 5.81771 0.367210 0.183605 0.983000i \(-0.441223\pi\)
0.183605 + 0.983000i \(0.441223\pi\)
\(252\) 0 0
\(253\) 16.5668 1.04155
\(254\) −0.395540 −0.0248184
\(255\) 0 0
\(256\) 4.89947 0.306217
\(257\) 9.99962 0.623759 0.311880 0.950122i \(-0.399041\pi\)
0.311880 + 0.950122i \(0.399041\pi\)
\(258\) 0 0
\(259\) 7.25011 0.450500
\(260\) 23.3673 1.44918
\(261\) 0 0
\(262\) 1.65685 0.102360
\(263\) 6.44764 0.397579 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(264\) 0 0
\(265\) 18.5826 1.14152
\(266\) 2.17917 0.133613
\(267\) 0 0
\(268\) 18.5191 1.13123
\(269\) 0.309677 0.0188814 0.00944068 0.999955i \(-0.496995\pi\)
0.00944068 + 0.999955i \(0.496995\pi\)
\(270\) 0 0
\(271\) −8.35899 −0.507772 −0.253886 0.967234i \(-0.581709\pi\)
−0.253886 + 0.967234i \(0.581709\pi\)
\(272\) −24.4633 −1.48330
\(273\) 0 0
\(274\) 1.92969 0.116577
\(275\) −6.35592 −0.383277
\(276\) 0 0
\(277\) 19.4246 1.16711 0.583554 0.812074i \(-0.301662\pi\)
0.583554 + 0.812074i \(0.301662\pi\)
\(278\) −1.43061 −0.0858022
\(279\) 0 0
\(280\) −2.96800 −0.177372
\(281\) −6.46823 −0.385862 −0.192931 0.981212i \(-0.561799\pi\)
−0.192931 + 0.981212i \(0.561799\pi\)
\(282\) 0 0
\(283\) −14.6422 −0.870390 −0.435195 0.900336i \(-0.643321\pi\)
−0.435195 + 0.900336i \(0.643321\pi\)
\(284\) 14.2613 0.846250
\(285\) 0 0
\(286\) −13.7322 −0.812003
\(287\) 10.1950 0.601790
\(288\) 0 0
\(289\) 45.8497 2.69704
\(290\) 2.62212 0.153976
\(291\) 0 0
\(292\) −3.30527 −0.193426
\(293\) 4.71917 0.275697 0.137848 0.990453i \(-0.455981\pi\)
0.137848 + 0.990453i \(0.455981\pi\)
\(294\) 0 0
\(295\) −10.7630 −0.626644
\(296\) 11.0222 0.640651
\(297\) 0 0
\(298\) −2.10633 −0.122016
\(299\) 20.1147 1.16326
\(300\) 0 0
\(301\) 12.7584 0.735379
\(302\) 4.40327 0.253380
\(303\) 0 0
\(304\) −17.0006 −0.975049
\(305\) −0.111422 −0.00637999
\(306\) 0 0
\(307\) −6.36282 −0.363145 −0.181573 0.983378i \(-0.558119\pi\)
−0.181573 + 0.983378i \(0.558119\pi\)
\(308\) −9.85809 −0.561717
\(309\) 0 0
\(310\) 7.88531 0.447855
\(311\) −0.442606 −0.0250979 −0.0125489 0.999921i \(-0.503995\pi\)
−0.0125489 + 0.999921i \(0.503995\pi\)
\(312\) 0 0
\(313\) 27.8781 1.57576 0.787881 0.615827i \(-0.211178\pi\)
0.787881 + 0.615827i \(0.211178\pi\)
\(314\) 8.63565 0.487338
\(315\) 0 0
\(316\) −3.35253 −0.188595
\(317\) 27.0519 1.51938 0.759692 0.650283i \(-0.225350\pi\)
0.759692 + 0.650283i \(0.225350\pi\)
\(318\) 0 0
\(319\) 18.1576 1.01663
\(320\) 8.75811 0.489593
\(321\) 0 0
\(322\) −1.22544 −0.0682909
\(323\) 43.6769 2.43025
\(324\) 0 0
\(325\) −7.71707 −0.428066
\(326\) −8.55376 −0.473749
\(327\) 0 0
\(328\) 15.4992 0.855799
\(329\) 1.66284 0.0916753
\(330\) 0 0
\(331\) 25.1442 1.38205 0.691026 0.722830i \(-0.257159\pi\)
0.691026 + 0.722830i \(0.257159\pi\)
\(332\) 12.7322 0.698770
\(333\) 0 0
\(334\) 2.73231 0.149505
\(335\) 19.6113 1.07148
\(336\) 0 0
\(337\) −0.0529758 −0.00288578 −0.00144289 0.999999i \(-0.500459\pi\)
−0.00144289 + 0.999999i \(0.500459\pi\)
\(338\) −11.5310 −0.627204
\(339\) 0 0
\(340\) −28.5330 −1.54742
\(341\) 54.6041 2.95698
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 19.3962 1.04577
\(345\) 0 0
\(346\) 7.80461 0.419578
\(347\) 19.4800 1.04574 0.522870 0.852412i \(-0.324861\pi\)
0.522870 + 0.852412i \(0.324861\pi\)
\(348\) 0 0
\(349\) 0.0195389 0.00104589 0.000522947 1.00000i \(-0.499834\pi\)
0.000522947 1.00000i \(0.499834\pi\)
\(350\) 0.470144 0.0251302
\(351\) 0 0
\(352\) −22.7856 −1.21447
\(353\) 22.1141 1.17701 0.588507 0.808492i \(-0.299716\pi\)
0.588507 + 0.808492i \(0.299716\pi\)
\(354\) 0 0
\(355\) 15.1024 0.801550
\(356\) 32.3389 1.71396
\(357\) 0 0
\(358\) −9.11988 −0.482000
\(359\) −2.17615 −0.114853 −0.0574264 0.998350i \(-0.518289\pi\)
−0.0574264 + 0.998350i \(0.518289\pi\)
\(360\) 0 0
\(361\) 11.3529 0.597523
\(362\) −0.759844 −0.0399365
\(363\) 0 0
\(364\) −11.9692 −0.627359
\(365\) −3.50021 −0.183209
\(366\) 0 0
\(367\) −12.6682 −0.661276 −0.330638 0.943758i \(-0.607264\pi\)
−0.330638 + 0.943758i \(0.607264\pi\)
\(368\) 9.56013 0.498356
\(369\) 0 0
\(370\) 5.59856 0.291055
\(371\) −9.51844 −0.494173
\(372\) 0 0
\(373\) −31.9234 −1.65293 −0.826466 0.562987i \(-0.809652\pi\)
−0.826466 + 0.562987i \(0.809652\pi\)
\(374\) 16.7680 0.867051
\(375\) 0 0
\(376\) 2.52797 0.130370
\(377\) 22.0461 1.13543
\(378\) 0 0
\(379\) 6.66072 0.342138 0.171069 0.985259i \(-0.445278\pi\)
0.171069 + 0.985259i \(0.445278\pi\)
\(380\) −19.8288 −1.01720
\(381\) 0 0
\(382\) −2.25784 −0.115521
\(383\) 16.8149 0.859203 0.429602 0.903019i \(-0.358654\pi\)
0.429602 + 0.903019i \(0.358654\pi\)
\(384\) 0 0
\(385\) −10.4395 −0.532046
\(386\) 6.05118 0.307997
\(387\) 0 0
\(388\) −8.19732 −0.416156
\(389\) 1.76018 0.0892446 0.0446223 0.999004i \(-0.485792\pi\)
0.0446223 + 0.999004i \(0.485792\pi\)
\(390\) 0 0
\(391\) −24.5614 −1.24212
\(392\) 1.52028 0.0767856
\(393\) 0 0
\(394\) 0.900920 0.0453877
\(395\) −3.55026 −0.178633
\(396\) 0 0
\(397\) 12.5865 0.631698 0.315849 0.948809i \(-0.397711\pi\)
0.315849 + 0.948809i \(0.397711\pi\)
\(398\) 9.57393 0.479898
\(399\) 0 0
\(400\) −3.66778 −0.183389
\(401\) 8.90988 0.444938 0.222469 0.974940i \(-0.428588\pi\)
0.222469 + 0.974940i \(0.428588\pi\)
\(402\) 0 0
\(403\) 66.2978 3.30253
\(404\) −7.95590 −0.395821
\(405\) 0 0
\(406\) −1.34311 −0.0666572
\(407\) 38.7688 1.92170
\(408\) 0 0
\(409\) −30.6626 −1.51617 −0.758084 0.652157i \(-0.773864\pi\)
−0.758084 + 0.652157i \(0.773864\pi\)
\(410\) 7.87259 0.388800
\(411\) 0 0
\(412\) 6.53379 0.321897
\(413\) 5.51303 0.271278
\(414\) 0 0
\(415\) 13.4831 0.661860
\(416\) −27.6652 −1.35640
\(417\) 0 0
\(418\) 11.6528 0.569955
\(419\) −3.03425 −0.148233 −0.0741163 0.997250i \(-0.523614\pi\)
−0.0741163 + 0.997250i \(0.523614\pi\)
\(420\) 0 0
\(421\) 5.88620 0.286876 0.143438 0.989659i \(-0.454184\pi\)
0.143438 + 0.989659i \(0.454184\pi\)
\(422\) −1.54732 −0.0753222
\(423\) 0 0
\(424\) −14.4707 −0.702757
\(425\) 9.42306 0.457086
\(426\) 0 0
\(427\) 0.0570727 0.00276194
\(428\) 22.9660 1.11010
\(429\) 0 0
\(430\) 9.85205 0.475108
\(431\) −20.9852 −1.01082 −0.505412 0.862878i \(-0.668659\pi\)
−0.505412 + 0.862878i \(0.668659\pi\)
\(432\) 0 0
\(433\) −9.07998 −0.436356 −0.218178 0.975909i \(-0.570011\pi\)
−0.218178 + 0.975909i \(0.570011\pi\)
\(434\) −4.03903 −0.193880
\(435\) 0 0
\(436\) −8.39662 −0.402125
\(437\) −17.0687 −0.816508
\(438\) 0 0
\(439\) −16.3936 −0.782425 −0.391212 0.920300i \(-0.627944\pi\)
−0.391212 + 0.920300i \(0.627944\pi\)
\(440\) −15.8709 −0.756617
\(441\) 0 0
\(442\) 20.3589 0.968374
\(443\) −24.2993 −1.15449 −0.577247 0.816570i \(-0.695873\pi\)
−0.577247 + 0.816570i \(0.695873\pi\)
\(444\) 0 0
\(445\) 34.2462 1.62342
\(446\) 0.957318 0.0453303
\(447\) 0 0
\(448\) −4.48610 −0.211948
\(449\) −22.0774 −1.04190 −0.520948 0.853588i \(-0.674421\pi\)
−0.520948 + 0.853588i \(0.674421\pi\)
\(450\) 0 0
\(451\) 54.5160 2.56706
\(452\) −1.74009 −0.0818469
\(453\) 0 0
\(454\) −4.31766 −0.202638
\(455\) −12.6752 −0.594221
\(456\) 0 0
\(457\) 14.4817 0.677423 0.338712 0.940890i \(-0.390009\pi\)
0.338712 + 0.940890i \(0.390009\pi\)
\(458\) −3.22926 −0.150893
\(459\) 0 0
\(460\) 11.1506 0.519898
\(461\) 32.1184 1.49590 0.747951 0.663754i \(-0.231038\pi\)
0.747951 + 0.663754i \(0.231038\pi\)
\(462\) 0 0
\(463\) −15.8911 −0.738523 −0.369261 0.929326i \(-0.620389\pi\)
−0.369261 + 0.929326i \(0.620389\pi\)
\(464\) 10.4781 0.486434
\(465\) 0 0
\(466\) −8.05219 −0.373010
\(467\) 1.85900 0.0860242 0.0430121 0.999075i \(-0.486305\pi\)
0.0430121 + 0.999075i \(0.486305\pi\)
\(468\) 0 0
\(469\) −10.0453 −0.463851
\(470\) 1.28405 0.0592288
\(471\) 0 0
\(472\) 8.38133 0.385782
\(473\) 68.2233 3.13691
\(474\) 0 0
\(475\) 6.54848 0.300465
\(476\) 14.6152 0.669889
\(477\) 0 0
\(478\) −3.80942 −0.174239
\(479\) 21.7411 0.993376 0.496688 0.867929i \(-0.334549\pi\)
0.496688 + 0.867929i \(0.334549\pi\)
\(480\) 0 0
\(481\) 47.0714 2.14627
\(482\) −11.1755 −0.509029
\(483\) 0 0
\(484\) −32.4356 −1.47434
\(485\) −8.68079 −0.394174
\(486\) 0 0
\(487\) −33.5681 −1.52112 −0.760558 0.649270i \(-0.775074\pi\)
−0.760558 + 0.649270i \(0.775074\pi\)
\(488\) 0.0867663 0.00392772
\(489\) 0 0
\(490\) 0.772204 0.0348846
\(491\) 18.1365 0.818490 0.409245 0.912425i \(-0.365792\pi\)
0.409245 + 0.912425i \(0.365792\pi\)
\(492\) 0 0
\(493\) −26.9198 −1.21241
\(494\) 14.1483 0.636560
\(495\) 0 0
\(496\) 31.5101 1.41485
\(497\) −7.73577 −0.346997
\(498\) 0 0
\(499\) −22.7742 −1.01951 −0.509757 0.860318i \(-0.670265\pi\)
−0.509757 + 0.860318i \(0.670265\pi\)
\(500\) −22.2735 −0.996103
\(501\) 0 0
\(502\) −2.30113 −0.102705
\(503\) −30.7610 −1.37157 −0.685784 0.727805i \(-0.740540\pi\)
−0.685784 + 0.727805i \(0.740540\pi\)
\(504\) 0 0
\(505\) −8.42513 −0.374913
\(506\) −6.55284 −0.291309
\(507\) 0 0
\(508\) −1.84355 −0.0817942
\(509\) 7.29123 0.323178 0.161589 0.986858i \(-0.448338\pi\)
0.161589 + 0.986858i \(0.448338\pi\)
\(510\) 0 0
\(511\) 1.79288 0.0793125
\(512\) −22.5312 −0.995747
\(513\) 0 0
\(514\) −3.95525 −0.174459
\(515\) 6.91914 0.304894
\(516\) 0 0
\(517\) 8.89177 0.391060
\(518\) −2.86771 −0.126000
\(519\) 0 0
\(520\) −19.2698 −0.845035
\(521\) 14.8186 0.649213 0.324606 0.945849i \(-0.394768\pi\)
0.324606 + 0.945849i \(0.394768\pi\)
\(522\) 0 0
\(523\) −29.2907 −1.28079 −0.640396 0.768045i \(-0.721230\pi\)
−0.640396 + 0.768045i \(0.721230\pi\)
\(524\) 7.72231 0.337351
\(525\) 0 0
\(526\) −2.55030 −0.111198
\(527\) −80.9540 −3.52641
\(528\) 0 0
\(529\) −13.4015 −0.582676
\(530\) −7.35017 −0.319271
\(531\) 0 0
\(532\) 10.1568 0.440351
\(533\) 66.1909 2.86705
\(534\) 0 0
\(535\) 24.3205 1.05147
\(536\) −15.2717 −0.659637
\(537\) 0 0
\(538\) −0.122490 −0.00528091
\(539\) 5.34735 0.230326
\(540\) 0 0
\(541\) 43.0311 1.85005 0.925026 0.379903i \(-0.124043\pi\)
0.925026 + 0.379903i \(0.124043\pi\)
\(542\) 3.30631 0.142018
\(543\) 0 0
\(544\) 33.7810 1.44835
\(545\) −8.89184 −0.380884
\(546\) 0 0
\(547\) 28.9462 1.23765 0.618826 0.785528i \(-0.287609\pi\)
0.618826 + 0.785528i \(0.287609\pi\)
\(548\) 8.99398 0.384204
\(549\) 0 0
\(550\) 2.51402 0.107198
\(551\) −18.7077 −0.796975
\(552\) 0 0
\(553\) 1.81852 0.0773314
\(554\) −7.68319 −0.326427
\(555\) 0 0
\(556\) −6.66784 −0.282779
\(557\) 30.0717 1.27418 0.637089 0.770791i \(-0.280139\pi\)
0.637089 + 0.770791i \(0.280139\pi\)
\(558\) 0 0
\(559\) 82.8337 3.50349
\(560\) −6.02427 −0.254572
\(561\) 0 0
\(562\) 2.55844 0.107921
\(563\) 15.2506 0.642738 0.321369 0.946954i \(-0.395857\pi\)
0.321369 + 0.946954i \(0.395857\pi\)
\(564\) 0 0
\(565\) −1.84272 −0.0775236
\(566\) 5.79158 0.243438
\(567\) 0 0
\(568\) −11.7605 −0.493460
\(569\) 24.0976 1.01022 0.505112 0.863054i \(-0.331451\pi\)
0.505112 + 0.863054i \(0.331451\pi\)
\(570\) 0 0
\(571\) 3.54378 0.148302 0.0741512 0.997247i \(-0.476375\pi\)
0.0741512 + 0.997247i \(0.476375\pi\)
\(572\) −64.0037 −2.67613
\(573\) 0 0
\(574\) −4.03252 −0.168314
\(575\) −3.68249 −0.153570
\(576\) 0 0
\(577\) −34.4496 −1.43415 −0.717077 0.696994i \(-0.754520\pi\)
−0.717077 + 0.696994i \(0.754520\pi\)
\(578\) −18.1354 −0.754333
\(579\) 0 0
\(580\) 12.2213 0.507460
\(581\) −6.90635 −0.286524
\(582\) 0 0
\(583\) −50.8984 −2.10800
\(584\) 2.72568 0.112789
\(585\) 0 0
\(586\) −1.86662 −0.0771093
\(587\) −5.82459 −0.240407 −0.120203 0.992749i \(-0.538355\pi\)
−0.120203 + 0.992749i \(0.538355\pi\)
\(588\) 0 0
\(589\) −56.2584 −2.31809
\(590\) 4.25718 0.175265
\(591\) 0 0
\(592\) 22.3721 0.919489
\(593\) 17.5879 0.722250 0.361125 0.932517i \(-0.382393\pi\)
0.361125 + 0.932517i \(0.382393\pi\)
\(594\) 0 0
\(595\) 15.4772 0.634505
\(596\) −9.81726 −0.402131
\(597\) 0 0
\(598\) −7.95615 −0.325351
\(599\) 33.7610 1.37944 0.689718 0.724078i \(-0.257734\pi\)
0.689718 + 0.724078i \(0.257734\pi\)
\(600\) 0 0
\(601\) −34.6238 −1.41233 −0.706167 0.708045i \(-0.749577\pi\)
−0.706167 + 0.708045i \(0.749577\pi\)
\(602\) −5.04644 −0.205677
\(603\) 0 0
\(604\) 20.5230 0.835067
\(605\) −34.3486 −1.39647
\(606\) 0 0
\(607\) 2.20615 0.0895450 0.0447725 0.998997i \(-0.485744\pi\)
0.0447725 + 0.998997i \(0.485744\pi\)
\(608\) 23.4759 0.952072
\(609\) 0 0
\(610\) 0.0440717 0.00178441
\(611\) 10.7960 0.436759
\(612\) 0 0
\(613\) 18.7651 0.757914 0.378957 0.925414i \(-0.376283\pi\)
0.378957 + 0.925414i \(0.376283\pi\)
\(614\) 2.51675 0.101568
\(615\) 0 0
\(616\) 8.12944 0.327545
\(617\) −19.8323 −0.798419 −0.399209 0.916860i \(-0.630715\pi\)
−0.399209 + 0.916860i \(0.630715\pi\)
\(618\) 0 0
\(619\) 9.77604 0.392932 0.196466 0.980511i \(-0.437053\pi\)
0.196466 + 0.980511i \(0.437053\pi\)
\(620\) 36.7522 1.47600
\(621\) 0 0
\(622\) 0.175068 0.00701960
\(623\) −17.5417 −0.702792
\(624\) 0 0
\(625\) −17.6441 −0.705765
\(626\) −11.0269 −0.440723
\(627\) 0 0
\(628\) 40.2494 1.60613
\(629\) −57.4773 −2.29177
\(630\) 0 0
\(631\) −7.95483 −0.316677 −0.158338 0.987385i \(-0.550614\pi\)
−0.158338 + 0.987385i \(0.550614\pi\)
\(632\) 2.76466 0.109972
\(633\) 0 0
\(634\) −10.7001 −0.424955
\(635\) −1.95228 −0.0774738
\(636\) 0 0
\(637\) 6.49250 0.257242
\(638\) −7.18205 −0.284340
\(639\) 0 0
\(640\) −20.1019 −0.794596
\(641\) 34.9817 1.38169 0.690847 0.723001i \(-0.257238\pi\)
0.690847 + 0.723001i \(0.257238\pi\)
\(642\) 0 0
\(643\) 15.8737 0.625999 0.312999 0.949753i \(-0.398666\pi\)
0.312999 + 0.949753i \(0.398666\pi\)
\(644\) −5.71157 −0.225067
\(645\) 0 0
\(646\) −17.2760 −0.679714
\(647\) 21.9320 0.862234 0.431117 0.902296i \(-0.358120\pi\)
0.431117 + 0.902296i \(0.358120\pi\)
\(648\) 0 0
\(649\) 29.4801 1.15719
\(650\) 3.05241 0.119725
\(651\) 0 0
\(652\) −39.8677 −1.56134
\(653\) 1.16252 0.0454928 0.0227464 0.999741i \(-0.492759\pi\)
0.0227464 + 0.999741i \(0.492759\pi\)
\(654\) 0 0
\(655\) 8.17776 0.319531
\(656\) 31.4593 1.22828
\(657\) 0 0
\(658\) −0.657719 −0.0256406
\(659\) 45.3968 1.76841 0.884205 0.467099i \(-0.154701\pi\)
0.884205 + 0.467099i \(0.154701\pi\)
\(660\) 0 0
\(661\) 7.35732 0.286167 0.143083 0.989711i \(-0.454298\pi\)
0.143083 + 0.989711i \(0.454298\pi\)
\(662\) −9.94555 −0.386545
\(663\) 0 0
\(664\) −10.4996 −0.407462
\(665\) 10.7558 0.417091
\(666\) 0 0
\(667\) 10.5201 0.407341
\(668\) 12.7349 0.492727
\(669\) 0 0
\(670\) −7.75705 −0.299681
\(671\) 0.305187 0.0117816
\(672\) 0 0
\(673\) −38.8530 −1.49767 −0.748837 0.662755i \(-0.769387\pi\)
−0.748837 + 0.662755i \(0.769387\pi\)
\(674\) 0.0209540 0.000807120 0
\(675\) 0 0
\(676\) −53.7442 −2.06709
\(677\) −39.7794 −1.52885 −0.764424 0.644714i \(-0.776977\pi\)
−0.764424 + 0.644714i \(0.776977\pi\)
\(678\) 0 0
\(679\) 4.44649 0.170641
\(680\) 23.5297 0.902322
\(681\) 0 0
\(682\) −21.5981 −0.827034
\(683\) 22.0096 0.842176 0.421088 0.907020i \(-0.361648\pi\)
0.421088 + 0.907020i \(0.361648\pi\)
\(684\) 0 0
\(685\) 9.52443 0.363910
\(686\) −0.395540 −0.0151018
\(687\) 0 0
\(688\) 39.3693 1.50094
\(689\) −61.7985 −2.35434
\(690\) 0 0
\(691\) −9.52843 −0.362479 −0.181239 0.983439i \(-0.558011\pi\)
−0.181239 + 0.983439i \(0.558011\pi\)
\(692\) 36.3760 1.38281
\(693\) 0 0
\(694\) −7.70511 −0.292482
\(695\) −7.06110 −0.267843
\(696\) 0 0
\(697\) −80.8235 −3.06141
\(698\) −0.00772841 −0.000292525 0
\(699\) 0 0
\(700\) 2.19127 0.0828220
\(701\) 21.9732 0.829915 0.414957 0.909841i \(-0.363796\pi\)
0.414957 + 0.909841i \(0.363796\pi\)
\(702\) 0 0
\(703\) −39.9434 −1.50649
\(704\) −23.9887 −0.904109
\(705\) 0 0
\(706\) −8.74700 −0.329198
\(707\) 4.31554 0.162303
\(708\) 0 0
\(709\) −28.0969 −1.05520 −0.527600 0.849493i \(-0.676908\pi\)
−0.527600 + 0.849493i \(0.676908\pi\)
\(710\) −5.97359 −0.224185
\(711\) 0 0
\(712\) −26.6682 −0.999432
\(713\) 31.6364 1.18479
\(714\) 0 0
\(715\) −67.7785 −2.53477
\(716\) −42.5063 −1.58853
\(717\) 0 0
\(718\) 0.860755 0.0321231
\(719\) 25.8815 0.965218 0.482609 0.875836i \(-0.339689\pi\)
0.482609 + 0.875836i \(0.339689\pi\)
\(720\) 0 0
\(721\) −3.54414 −0.131991
\(722\) −4.49054 −0.167121
\(723\) 0 0
\(724\) −3.54151 −0.131619
\(725\) −4.03609 −0.149896
\(726\) 0 0
\(727\) 4.62598 0.171568 0.0857841 0.996314i \(-0.472660\pi\)
0.0857841 + 0.996314i \(0.472660\pi\)
\(728\) 9.87040 0.365821
\(729\) 0 0
\(730\) 1.38447 0.0512416
\(731\) −101.145 −3.74100
\(732\) 0 0
\(733\) −3.75379 −0.138649 −0.0693247 0.997594i \(-0.522084\pi\)
−0.0693247 + 0.997594i \(0.522084\pi\)
\(734\) 5.01079 0.184952
\(735\) 0 0
\(736\) −13.2015 −0.486613
\(737\) −53.7159 −1.97865
\(738\) 0 0
\(739\) −4.26601 −0.156928 −0.0784638 0.996917i \(-0.525002\pi\)
−0.0784638 + 0.996917i \(0.525002\pi\)
\(740\) 26.0940 0.959234
\(741\) 0 0
\(742\) 3.76492 0.138215
\(743\) 5.16502 0.189486 0.0947431 0.995502i \(-0.469797\pi\)
0.0947431 + 0.995502i \(0.469797\pi\)
\(744\) 0 0
\(745\) −10.3963 −0.380890
\(746\) 12.6270 0.462307
\(747\) 0 0
\(748\) 78.1528 2.85755
\(749\) −12.4575 −0.455187
\(750\) 0 0
\(751\) 22.8108 0.832377 0.416189 0.909278i \(-0.363366\pi\)
0.416189 + 0.909278i \(0.363366\pi\)
\(752\) 5.13113 0.187113
\(753\) 0 0
\(754\) −8.72012 −0.317568
\(755\) 21.7334 0.790958
\(756\) 0 0
\(757\) 7.90395 0.287274 0.143637 0.989630i \(-0.454120\pi\)
0.143637 + 0.989630i \(0.454120\pi\)
\(758\) −2.63458 −0.0956922
\(759\) 0 0
\(760\) 16.3518 0.593141
\(761\) −1.19183 −0.0432039 −0.0216020 0.999767i \(-0.506877\pi\)
−0.0216020 + 0.999767i \(0.506877\pi\)
\(762\) 0 0
\(763\) 4.55460 0.164887
\(764\) −10.5234 −0.380724
\(765\) 0 0
\(766\) −6.65098 −0.240310
\(767\) 35.7934 1.29242
\(768\) 0 0
\(769\) −1.86185 −0.0671400 −0.0335700 0.999436i \(-0.510688\pi\)
−0.0335700 + 0.999436i \(0.510688\pi\)
\(770\) 4.12924 0.148807
\(771\) 0 0
\(772\) 28.2036 1.01507
\(773\) −33.4527 −1.20321 −0.601604 0.798794i \(-0.705472\pi\)
−0.601604 + 0.798794i \(0.705472\pi\)
\(774\) 0 0
\(775\) −12.1374 −0.435990
\(776\) 6.75990 0.242666
\(777\) 0 0
\(778\) −0.696221 −0.0249607
\(779\) −56.1677 −2.01242
\(780\) 0 0
\(781\) −41.3658 −1.48019
\(782\) 9.71500 0.347408
\(783\) 0 0
\(784\) 3.08577 0.110206
\(785\) 42.6232 1.52129
\(786\) 0 0
\(787\) 20.8078 0.741718 0.370859 0.928689i \(-0.379063\pi\)
0.370859 + 0.928689i \(0.379063\pi\)
\(788\) 4.19904 0.149585
\(789\) 0 0
\(790\) 1.40427 0.0499617
\(791\) 0.943880 0.0335605
\(792\) 0 0
\(793\) 0.370545 0.0131584
\(794\) −4.97846 −0.176679
\(795\) 0 0
\(796\) 44.6226 1.58160
\(797\) 34.8605 1.23482 0.617410 0.786641i \(-0.288182\pi\)
0.617410 + 0.786641i \(0.288182\pi\)
\(798\) 0 0
\(799\) −13.1826 −0.466368
\(800\) 5.06479 0.179068
\(801\) 0 0
\(802\) −3.52421 −0.124444
\(803\) 9.58717 0.338324
\(804\) 0 0
\(805\) −6.04843 −0.213179
\(806\) −26.2234 −0.923680
\(807\) 0 0
\(808\) 6.56081 0.230809
\(809\) −2.21699 −0.0779452 −0.0389726 0.999240i \(-0.512409\pi\)
−0.0389726 + 0.999240i \(0.512409\pi\)
\(810\) 0 0
\(811\) 10.5287 0.369712 0.184856 0.982766i \(-0.440818\pi\)
0.184856 + 0.982766i \(0.440818\pi\)
\(812\) −6.26000 −0.219683
\(813\) 0 0
\(814\) −15.3346 −0.537478
\(815\) −42.2190 −1.47887
\(816\) 0 0
\(817\) −70.2903 −2.45914
\(818\) 12.1283 0.424056
\(819\) 0 0
\(820\) 36.6929 1.28137
\(821\) 3.61333 0.126106 0.0630530 0.998010i \(-0.479916\pi\)
0.0630530 + 0.998010i \(0.479916\pi\)
\(822\) 0 0
\(823\) 10.2088 0.355857 0.177928 0.984043i \(-0.443060\pi\)
0.177928 + 0.984043i \(0.443060\pi\)
\(824\) −5.38807 −0.187702
\(825\) 0 0
\(826\) −2.18062 −0.0758736
\(827\) 15.0646 0.523849 0.261924 0.965088i \(-0.415643\pi\)
0.261924 + 0.965088i \(0.415643\pi\)
\(828\) 0 0
\(829\) 26.0848 0.905962 0.452981 0.891520i \(-0.350361\pi\)
0.452981 + 0.891520i \(0.350361\pi\)
\(830\) −5.33311 −0.185115
\(831\) 0 0
\(832\) −29.1260 −1.00976
\(833\) −7.92778 −0.274681
\(834\) 0 0
\(835\) 13.4859 0.466700
\(836\) 54.3117 1.87841
\(837\) 0 0
\(838\) 1.20017 0.0414590
\(839\) −15.8729 −0.547993 −0.273996 0.961731i \(-0.588346\pi\)
−0.273996 + 0.961731i \(0.588346\pi\)
\(840\) 0 0
\(841\) −17.4697 −0.602404
\(842\) −2.32823 −0.0802360
\(843\) 0 0
\(844\) −7.21180 −0.248240
\(845\) −56.9140 −1.95790
\(846\) 0 0
\(847\) 17.5941 0.604540
\(848\) −29.3717 −1.00863
\(849\) 0 0
\(850\) −3.72720 −0.127842
\(851\) 22.4618 0.769982
\(852\) 0 0
\(853\) 36.2530 1.24128 0.620639 0.784096i \(-0.286873\pi\)
0.620639 + 0.784096i \(0.286873\pi\)
\(854\) −0.0225745 −0.000772484 0
\(855\) 0 0
\(856\) −18.9388 −0.647316
\(857\) −0.282539 −0.00965134 −0.00482567 0.999988i \(-0.501536\pi\)
−0.00482567 + 0.999988i \(0.501536\pi\)
\(858\) 0 0
\(859\) 21.8107 0.744172 0.372086 0.928198i \(-0.378643\pi\)
0.372086 + 0.928198i \(0.378643\pi\)
\(860\) 45.9188 1.56582
\(861\) 0 0
\(862\) 8.30050 0.282716
\(863\) −49.3581 −1.68017 −0.840084 0.542456i \(-0.817494\pi\)
−0.840084 + 0.542456i \(0.817494\pi\)
\(864\) 0 0
\(865\) 38.5214 1.30977
\(866\) 3.59150 0.122044
\(867\) 0 0
\(868\) −18.8253 −0.638971
\(869\) 9.72427 0.329873
\(870\) 0 0
\(871\) −65.2194 −2.20987
\(872\) 6.92425 0.234485
\(873\) 0 0
\(874\) 6.75136 0.228368
\(875\) 12.0819 0.408442
\(876\) 0 0
\(877\) 3.95664 0.133606 0.0668032 0.997766i \(-0.478720\pi\)
0.0668032 + 0.997766i \(0.478720\pi\)
\(878\) 6.48433 0.218836
\(879\) 0 0
\(880\) −32.2139 −1.08593
\(881\) −3.54601 −0.119468 −0.0597341 0.998214i \(-0.519025\pi\)
−0.0597341 + 0.998214i \(0.519025\pi\)
\(882\) 0 0
\(883\) 49.6627 1.67128 0.835642 0.549274i \(-0.185096\pi\)
0.835642 + 0.549274i \(0.185096\pi\)
\(884\) 94.8895 3.19148
\(885\) 0 0
\(886\) 9.61133 0.322899
\(887\) 55.3611 1.85884 0.929421 0.369021i \(-0.120307\pi\)
0.929421 + 0.369021i \(0.120307\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −13.5457 −0.454054
\(891\) 0 0
\(892\) 4.46191 0.149396
\(893\) −9.16116 −0.306567
\(894\) 0 0
\(895\) −45.0132 −1.50463
\(896\) 10.2966 0.343986
\(897\) 0 0
\(898\) 8.73248 0.291407
\(899\) 34.6742 1.15645
\(900\) 0 0
\(901\) 75.4601 2.51394
\(902\) −21.5633 −0.717978
\(903\) 0 0
\(904\) 1.43496 0.0477260
\(905\) −3.75039 −0.124667
\(906\) 0 0
\(907\) −14.0958 −0.468042 −0.234021 0.972231i \(-0.575189\pi\)
−0.234021 + 0.972231i \(0.575189\pi\)
\(908\) −20.1239 −0.667836
\(909\) 0 0
\(910\) 5.01353 0.166197
\(911\) −53.7470 −1.78072 −0.890359 0.455259i \(-0.849547\pi\)
−0.890359 + 0.455259i \(0.849547\pi\)
\(912\) 0 0
\(913\) −36.9306 −1.22223
\(914\) −5.72807 −0.189468
\(915\) 0 0
\(916\) −15.0511 −0.497301
\(917\) −4.18883 −0.138327
\(918\) 0 0
\(919\) −16.6028 −0.547675 −0.273837 0.961776i \(-0.588293\pi\)
−0.273837 + 0.961776i \(0.588293\pi\)
\(920\) −9.19528 −0.303159
\(921\) 0 0
\(922\) −12.7041 −0.418387
\(923\) −50.2245 −1.65316
\(924\) 0 0
\(925\) −8.61757 −0.283344
\(926\) 6.28557 0.206557
\(927\) 0 0
\(928\) −14.4691 −0.474971
\(929\) −47.3772 −1.55440 −0.777198 0.629256i \(-0.783360\pi\)
−0.777198 + 0.629256i \(0.783360\pi\)
\(930\) 0 0
\(931\) −5.50935 −0.180562
\(932\) −37.5300 −1.22933
\(933\) 0 0
\(934\) −0.735308 −0.0240600
\(935\) 82.7621 2.70661
\(936\) 0 0
\(937\) 20.7488 0.677832 0.338916 0.940817i \(-0.389940\pi\)
0.338916 + 0.940817i \(0.389940\pi\)
\(938\) 3.97333 0.129734
\(939\) 0 0
\(940\) 5.98475 0.195201
\(941\) −43.3850 −1.41431 −0.707155 0.707059i \(-0.750022\pi\)
−0.707155 + 0.707059i \(0.750022\pi\)
\(942\) 0 0
\(943\) 31.5854 1.02856
\(944\) 17.0119 0.553691
\(945\) 0 0
\(946\) −26.9850 −0.877360
\(947\) −17.1077 −0.555924 −0.277962 0.960592i \(-0.589659\pi\)
−0.277962 + 0.960592i \(0.589659\pi\)
\(948\) 0 0
\(949\) 11.6403 0.377860
\(950\) −2.59019 −0.0840368
\(951\) 0 0
\(952\) −12.0524 −0.390621
\(953\) −10.4394 −0.338165 −0.169082 0.985602i \(-0.554080\pi\)
−0.169082 + 0.985602i \(0.554080\pi\)
\(954\) 0 0
\(955\) −11.1441 −0.360614
\(956\) −17.7551 −0.574240
\(957\) 0 0
\(958\) −8.59947 −0.277836
\(959\) −4.87863 −0.157539
\(960\) 0 0
\(961\) 73.2734 2.36366
\(962\) −18.6186 −0.600288
\(963\) 0 0
\(964\) −52.0871 −1.67761
\(965\) 29.8670 0.961452
\(966\) 0 0
\(967\) 13.6829 0.440013 0.220007 0.975498i \(-0.429392\pi\)
0.220007 + 0.975498i \(0.429392\pi\)
\(968\) 26.7479 0.859710
\(969\) 0 0
\(970\) 3.43360 0.110246
\(971\) −47.4849 −1.52386 −0.761931 0.647658i \(-0.775749\pi\)
−0.761931 + 0.647658i \(0.775749\pi\)
\(972\) 0 0
\(973\) 3.61685 0.115951
\(974\) 13.2775 0.425439
\(975\) 0 0
\(976\) 0.176113 0.00563724
\(977\) 35.7720 1.14445 0.572223 0.820098i \(-0.306081\pi\)
0.572223 + 0.820098i \(0.306081\pi\)
\(978\) 0 0
\(979\) −93.8013 −2.99790
\(980\) 3.59912 0.114970
\(981\) 0 0
\(982\) −7.17372 −0.228922
\(983\) 4.08379 0.130253 0.0651263 0.997877i \(-0.479255\pi\)
0.0651263 + 0.997877i \(0.479255\pi\)
\(984\) 0 0
\(985\) 4.44670 0.141683
\(986\) 10.6479 0.339097
\(987\) 0 0
\(988\) 65.9427 2.09792
\(989\) 39.5272 1.25689
\(990\) 0 0
\(991\) 7.24609 0.230180 0.115090 0.993355i \(-0.463284\pi\)
0.115090 + 0.993355i \(0.463284\pi\)
\(992\) −43.5119 −1.38150
\(993\) 0 0
\(994\) 3.05980 0.0970511
\(995\) 47.2543 1.49806
\(996\) 0 0
\(997\) 4.41907 0.139953 0.0699767 0.997549i \(-0.477708\pi\)
0.0699767 + 0.997549i \(0.477708\pi\)
\(998\) 9.00812 0.285147
\(999\) 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 \(a_p\))