Properties

Label 8046.2.a.l.1.2
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 1.2
Root \(-2.26764\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-2.26764 q^{5}\) \(-0.397853 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-2.26764 q^{5}\) \(-0.397853 q^{7}\) \(-1.00000 q^{8}\) \(+2.26764 q^{10}\) \(+3.96969 q^{11}\) \(+0.823528 q^{13}\) \(+0.397853 q^{14}\) \(+1.00000 q^{16}\) \(-6.85300 q^{17}\) \(-8.38692 q^{19}\) \(-2.26764 q^{20}\) \(-3.96969 q^{22}\) \(+8.28167 q^{23}\) \(+0.142177 q^{25}\) \(-0.823528 q^{26}\) \(-0.397853 q^{28}\) \(+8.78572 q^{29}\) \(+4.00807 q^{31}\) \(-1.00000 q^{32}\) \(+6.85300 q^{34}\) \(+0.902187 q^{35}\) \(+0.694576 q^{37}\) \(+8.38692 q^{38}\) \(+2.26764 q^{40}\) \(+9.11675 q^{41}\) \(-8.24158 q^{43}\) \(+3.96969 q^{44}\) \(-8.28167 q^{46}\) \(+1.58117 q^{47}\) \(-6.84171 q^{49}\) \(-0.142177 q^{50}\) \(+0.823528 q^{52}\) \(-7.80173 q^{53}\) \(-9.00181 q^{55}\) \(+0.397853 q^{56}\) \(-8.78572 q^{58}\) \(-10.9286 q^{59}\) \(-8.40891 q^{61}\) \(-4.00807 q^{62}\) \(+1.00000 q^{64}\) \(-1.86746 q^{65}\) \(-11.4002 q^{67}\) \(-6.85300 q^{68}\) \(-0.902187 q^{70}\) \(+14.7645 q^{71}\) \(+6.27672 q^{73}\) \(-0.694576 q^{74}\) \(-8.38692 q^{76}\) \(-1.57935 q^{77}\) \(+9.64978 q^{79}\) \(-2.26764 q^{80}\) \(-9.11675 q^{82}\) \(+8.76097 q^{83}\) \(+15.5401 q^{85}\) \(+8.24158 q^{86}\) \(-3.96969 q^{88}\) \(-9.24953 q^{89}\) \(-0.327643 q^{91}\) \(+8.28167 q^{92}\) \(-1.58117 q^{94}\) \(+19.0185 q^{95}\) \(-8.05434 q^{97}\) \(+6.84171 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −2.26764 −1.01412 −0.507059 0.861911i \(-0.669267\pi\)
−0.507059 + 0.861911i \(0.669267\pi\)
\(6\) 0 0
\(7\) −0.397853 −0.150374 −0.0751872 0.997169i \(-0.523955\pi\)
−0.0751872 + 0.997169i \(0.523955\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 2.26764 0.717090
\(11\) 3.96969 1.19691 0.598453 0.801158i \(-0.295782\pi\)
0.598453 + 0.801158i \(0.295782\pi\)
\(12\) 0 0
\(13\) 0.823528 0.228406 0.114203 0.993457i \(-0.463569\pi\)
0.114203 + 0.993457i \(0.463569\pi\)
\(14\) 0.397853 0.106331
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.85300 −1.66210 −0.831049 0.556200i \(-0.812259\pi\)
−0.831049 + 0.556200i \(0.812259\pi\)
\(18\) 0 0
\(19\) −8.38692 −1.92409 −0.962045 0.272890i \(-0.912020\pi\)
−0.962045 + 0.272890i \(0.912020\pi\)
\(20\) −2.26764 −0.507059
\(21\) 0 0
\(22\) −3.96969 −0.846340
\(23\) 8.28167 1.72685 0.863424 0.504479i \(-0.168315\pi\)
0.863424 + 0.504479i \(0.168315\pi\)
\(24\) 0 0
\(25\) 0.142177 0.0284355
\(26\) −0.823528 −0.161507
\(27\) 0 0
\(28\) −0.397853 −0.0751872
\(29\) 8.78572 1.63147 0.815734 0.578428i \(-0.196333\pi\)
0.815734 + 0.578428i \(0.196333\pi\)
\(30\) 0 0
\(31\) 4.00807 0.719871 0.359936 0.932977i \(-0.382799\pi\)
0.359936 + 0.932977i \(0.382799\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 6.85300 1.17528
\(35\) 0.902187 0.152497
\(36\) 0 0
\(37\) 0.694576 0.114188 0.0570938 0.998369i \(-0.481817\pi\)
0.0570938 + 0.998369i \(0.481817\pi\)
\(38\) 8.38692 1.36054
\(39\) 0 0
\(40\) 2.26764 0.358545
\(41\) 9.11675 1.42380 0.711899 0.702282i \(-0.247836\pi\)
0.711899 + 0.702282i \(0.247836\pi\)
\(42\) 0 0
\(43\) −8.24158 −1.25683 −0.628414 0.777879i \(-0.716296\pi\)
−0.628414 + 0.777879i \(0.716296\pi\)
\(44\) 3.96969 0.598453
\(45\) 0 0
\(46\) −8.28167 −1.22107
\(47\) 1.58117 0.230638 0.115319 0.993329i \(-0.463211\pi\)
0.115319 + 0.993329i \(0.463211\pi\)
\(48\) 0 0
\(49\) −6.84171 −0.977388
\(50\) −0.142177 −0.0201069
\(51\) 0 0
\(52\) 0.823528 0.114203
\(53\) −7.80173 −1.07165 −0.535825 0.844329i \(-0.679999\pi\)
−0.535825 + 0.844329i \(0.679999\pi\)
\(54\) 0 0
\(55\) −9.00181 −1.21380
\(56\) 0.397853 0.0531654
\(57\) 0 0
\(58\) −8.78572 −1.15362
\(59\) −10.9286 −1.42278 −0.711390 0.702797i \(-0.751934\pi\)
−0.711390 + 0.702797i \(0.751934\pi\)
\(60\) 0 0
\(61\) −8.40891 −1.07665 −0.538325 0.842737i \(-0.680943\pi\)
−0.538325 + 0.842737i \(0.680943\pi\)
\(62\) −4.00807 −0.509026
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.86746 −0.231630
\(66\) 0 0
\(67\) −11.4002 −1.39276 −0.696379 0.717674i \(-0.745207\pi\)
−0.696379 + 0.717674i \(0.745207\pi\)
\(68\) −6.85300 −0.831049
\(69\) 0 0
\(70\) −0.902187 −0.107832
\(71\) 14.7645 1.75223 0.876113 0.482105i \(-0.160128\pi\)
0.876113 + 0.482105i \(0.160128\pi\)
\(72\) 0 0
\(73\) 6.27672 0.734635 0.367317 0.930096i \(-0.380276\pi\)
0.367317 + 0.930096i \(0.380276\pi\)
\(74\) −0.694576 −0.0807428
\(75\) 0 0
\(76\) −8.38692 −0.962045
\(77\) −1.57935 −0.179984
\(78\) 0 0
\(79\) 9.64978 1.08569 0.542843 0.839834i \(-0.317348\pi\)
0.542843 + 0.839834i \(0.317348\pi\)
\(80\) −2.26764 −0.253530
\(81\) 0 0
\(82\) −9.11675 −1.00678
\(83\) 8.76097 0.961641 0.480820 0.876819i \(-0.340339\pi\)
0.480820 + 0.876819i \(0.340339\pi\)
\(84\) 0 0
\(85\) 15.5401 1.68556
\(86\) 8.24158 0.888712
\(87\) 0 0
\(88\) −3.96969 −0.423170
\(89\) −9.24953 −0.980448 −0.490224 0.871596i \(-0.663085\pi\)
−0.490224 + 0.871596i \(0.663085\pi\)
\(90\) 0 0
\(91\) −0.327643 −0.0343464
\(92\) 8.28167 0.863424
\(93\) 0 0
\(94\) −1.58117 −0.163086
\(95\) 19.0185 1.95125
\(96\) 0 0
\(97\) −8.05434 −0.817794 −0.408897 0.912580i \(-0.634087\pi\)
−0.408897 + 0.912580i \(0.634087\pi\)
\(98\) 6.84171 0.691117
\(99\) 0 0
\(100\) 0.142177 0.0142177
\(101\) −9.77230 −0.972380 −0.486190 0.873853i \(-0.661614\pi\)
−0.486190 + 0.873853i \(0.661614\pi\)
\(102\) 0 0
\(103\) 2.13814 0.210678 0.105339 0.994436i \(-0.466407\pi\)
0.105339 + 0.994436i \(0.466407\pi\)
\(104\) −0.823528 −0.0807536
\(105\) 0 0
\(106\) 7.80173 0.757771
\(107\) −9.52464 −0.920782 −0.460391 0.887716i \(-0.652291\pi\)
−0.460391 + 0.887716i \(0.652291\pi\)
\(108\) 0 0
\(109\) 17.2092 1.64834 0.824170 0.566343i \(-0.191642\pi\)
0.824170 + 0.566343i \(0.191642\pi\)
\(110\) 9.00181 0.858288
\(111\) 0 0
\(112\) −0.397853 −0.0375936
\(113\) −0.853149 −0.0802575 −0.0401288 0.999195i \(-0.512777\pi\)
−0.0401288 + 0.999195i \(0.512777\pi\)
\(114\) 0 0
\(115\) −18.7798 −1.75123
\(116\) 8.78572 0.815734
\(117\) 0 0
\(118\) 10.9286 1.00606
\(119\) 2.72649 0.249937
\(120\) 0 0
\(121\) 4.75840 0.432582
\(122\) 8.40891 0.761307
\(123\) 0 0
\(124\) 4.00807 0.359936
\(125\) 11.0158 0.985281
\(126\) 0 0
\(127\) 10.3267 0.916349 0.458175 0.888862i \(-0.348503\pi\)
0.458175 + 0.888862i \(0.348503\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 1.86746 0.163787
\(131\) 7.41831 0.648141 0.324070 0.946033i \(-0.394949\pi\)
0.324070 + 0.946033i \(0.394949\pi\)
\(132\) 0 0
\(133\) 3.33676 0.289334
\(134\) 11.4002 0.984829
\(135\) 0 0
\(136\) 6.85300 0.587640
\(137\) 15.1282 1.29249 0.646245 0.763130i \(-0.276338\pi\)
0.646245 + 0.763130i \(0.276338\pi\)
\(138\) 0 0
\(139\) −13.7814 −1.16892 −0.584460 0.811423i \(-0.698694\pi\)
−0.584460 + 0.811423i \(0.698694\pi\)
\(140\) 0.902187 0.0762487
\(141\) 0 0
\(142\) −14.7645 −1.23901
\(143\) 3.26915 0.273380
\(144\) 0 0
\(145\) −19.9228 −1.65450
\(146\) −6.27672 −0.519465
\(147\) 0 0
\(148\) 0.694576 0.0570938
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) 16.9871 1.38239 0.691197 0.722666i \(-0.257084\pi\)
0.691197 + 0.722666i \(0.257084\pi\)
\(152\) 8.38692 0.680269
\(153\) 0 0
\(154\) 1.57935 0.127268
\(155\) −9.08885 −0.730034
\(156\) 0 0
\(157\) 1.17392 0.0936891 0.0468445 0.998902i \(-0.485083\pi\)
0.0468445 + 0.998902i \(0.485083\pi\)
\(158\) −9.64978 −0.767695
\(159\) 0 0
\(160\) 2.26764 0.179272
\(161\) −3.29489 −0.259674
\(162\) 0 0
\(163\) 17.5592 1.37534 0.687670 0.726023i \(-0.258633\pi\)
0.687670 + 0.726023i \(0.258633\pi\)
\(164\) 9.11675 0.711899
\(165\) 0 0
\(166\) −8.76097 −0.679983
\(167\) 4.50119 0.348312 0.174156 0.984718i \(-0.444280\pi\)
0.174156 + 0.984718i \(0.444280\pi\)
\(168\) 0 0
\(169\) −12.3218 −0.947831
\(170\) −15.5401 −1.19187
\(171\) 0 0
\(172\) −8.24158 −0.628414
\(173\) −6.31389 −0.480036 −0.240018 0.970768i \(-0.577153\pi\)
−0.240018 + 0.970768i \(0.577153\pi\)
\(174\) 0 0
\(175\) −0.0565658 −0.00427597
\(176\) 3.96969 0.299226
\(177\) 0 0
\(178\) 9.24953 0.693282
\(179\) 7.46421 0.557901 0.278951 0.960305i \(-0.410013\pi\)
0.278951 + 0.960305i \(0.410013\pi\)
\(180\) 0 0
\(181\) 15.8449 1.17774 0.588872 0.808226i \(-0.299572\pi\)
0.588872 + 0.808226i \(0.299572\pi\)
\(182\) 0.327643 0.0242865
\(183\) 0 0
\(184\) −8.28167 −0.610533
\(185\) −1.57505 −0.115800
\(186\) 0 0
\(187\) −27.2043 −1.98937
\(188\) 1.58117 0.115319
\(189\) 0 0
\(190\) −19.0185 −1.37975
\(191\) −16.6457 −1.20444 −0.602221 0.798330i \(-0.705717\pi\)
−0.602221 + 0.798330i \(0.705717\pi\)
\(192\) 0 0
\(193\) −9.73110 −0.700460 −0.350230 0.936664i \(-0.613897\pi\)
−0.350230 + 0.936664i \(0.613897\pi\)
\(194\) 8.05434 0.578268
\(195\) 0 0
\(196\) −6.84171 −0.488694
\(197\) 2.03744 0.145161 0.0725806 0.997363i \(-0.476877\pi\)
0.0725806 + 0.997363i \(0.476877\pi\)
\(198\) 0 0
\(199\) −20.4304 −1.44827 −0.724137 0.689656i \(-0.757762\pi\)
−0.724137 + 0.689656i \(0.757762\pi\)
\(200\) −0.142177 −0.0100535
\(201\) 0 0
\(202\) 9.77230 0.687577
\(203\) −3.49543 −0.245331
\(204\) 0 0
\(205\) −20.6735 −1.44390
\(206\) −2.13814 −0.148972
\(207\) 0 0
\(208\) 0.823528 0.0571014
\(209\) −33.2934 −2.30295
\(210\) 0 0
\(211\) 14.9296 1.02780 0.513898 0.857851i \(-0.328201\pi\)
0.513898 + 0.857851i \(0.328201\pi\)
\(212\) −7.80173 −0.535825
\(213\) 0 0
\(214\) 9.52464 0.651091
\(215\) 18.6889 1.27457
\(216\) 0 0
\(217\) −1.59463 −0.108250
\(218\) −17.2092 −1.16555
\(219\) 0 0
\(220\) −9.00181 −0.606902
\(221\) −5.64364 −0.379632
\(222\) 0 0
\(223\) −16.1349 −1.08047 −0.540235 0.841514i \(-0.681665\pi\)
−0.540235 + 0.841514i \(0.681665\pi\)
\(224\) 0.397853 0.0265827
\(225\) 0 0
\(226\) 0.853149 0.0567506
\(227\) −19.4983 −1.29415 −0.647074 0.762427i \(-0.724008\pi\)
−0.647074 + 0.762427i \(0.724008\pi\)
\(228\) 0 0
\(229\) −11.0086 −0.727467 −0.363734 0.931503i \(-0.618498\pi\)
−0.363734 + 0.931503i \(0.618498\pi\)
\(230\) 18.7798 1.23830
\(231\) 0 0
\(232\) −8.78572 −0.576811
\(233\) −28.0188 −1.83558 −0.917788 0.397071i \(-0.870027\pi\)
−0.917788 + 0.397071i \(0.870027\pi\)
\(234\) 0 0
\(235\) −3.58553 −0.233894
\(236\) −10.9286 −0.711390
\(237\) 0 0
\(238\) −2.72649 −0.176732
\(239\) 23.4730 1.51834 0.759172 0.650890i \(-0.225604\pi\)
0.759172 + 0.650890i \(0.225604\pi\)
\(240\) 0 0
\(241\) 16.6148 1.07025 0.535126 0.844772i \(-0.320264\pi\)
0.535126 + 0.844772i \(0.320264\pi\)
\(242\) −4.75840 −0.305882
\(243\) 0 0
\(244\) −8.40891 −0.538325
\(245\) 15.5145 0.991186
\(246\) 0 0
\(247\) −6.90686 −0.439473
\(248\) −4.00807 −0.254513
\(249\) 0 0
\(250\) −11.0158 −0.696699
\(251\) 21.7503 1.37287 0.686434 0.727193i \(-0.259175\pi\)
0.686434 + 0.727193i \(0.259175\pi\)
\(252\) 0 0
\(253\) 32.8756 2.06687
\(254\) −10.3267 −0.647957
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 25.0548 1.56288 0.781438 0.623983i \(-0.214486\pi\)
0.781438 + 0.623983i \(0.214486\pi\)
\(258\) 0 0
\(259\) −0.276339 −0.0171709
\(260\) −1.86746 −0.115815
\(261\) 0 0
\(262\) −7.41831 −0.458305
\(263\) −1.10598 −0.0681979 −0.0340989 0.999418i \(-0.510856\pi\)
−0.0340989 + 0.999418i \(0.510856\pi\)
\(264\) 0 0
\(265\) 17.6915 1.08678
\(266\) −3.33676 −0.204590
\(267\) 0 0
\(268\) −11.4002 −0.696379
\(269\) −14.9971 −0.914389 −0.457195 0.889367i \(-0.651146\pi\)
−0.457195 + 0.889367i \(0.651146\pi\)
\(270\) 0 0
\(271\) 25.6135 1.55591 0.777955 0.628320i \(-0.216257\pi\)
0.777955 + 0.628320i \(0.216257\pi\)
\(272\) −6.85300 −0.415524
\(273\) 0 0
\(274\) −15.1282 −0.913929
\(275\) 0.564399 0.0340346
\(276\) 0 0
\(277\) −17.2735 −1.03786 −0.518932 0.854815i \(-0.673670\pi\)
−0.518932 + 0.854815i \(0.673670\pi\)
\(278\) 13.7814 0.826551
\(279\) 0 0
\(280\) −0.902187 −0.0539160
\(281\) 3.74260 0.223265 0.111632 0.993750i \(-0.464392\pi\)
0.111632 + 0.993750i \(0.464392\pi\)
\(282\) 0 0
\(283\) −7.91599 −0.470557 −0.235278 0.971928i \(-0.575600\pi\)
−0.235278 + 0.971928i \(0.575600\pi\)
\(284\) 14.7645 0.876113
\(285\) 0 0
\(286\) −3.26915 −0.193309
\(287\) −3.62713 −0.214103
\(288\) 0 0
\(289\) 29.9636 1.76257
\(290\) 19.9228 1.16991
\(291\) 0 0
\(292\) 6.27672 0.367317
\(293\) −26.0968 −1.52459 −0.762295 0.647230i \(-0.775927\pi\)
−0.762295 + 0.647230i \(0.775927\pi\)
\(294\) 0 0
\(295\) 24.7821 1.44287
\(296\) −0.694576 −0.0403714
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 6.82019 0.394422
\(300\) 0 0
\(301\) 3.27894 0.188995
\(302\) −16.9871 −0.977500
\(303\) 0 0
\(304\) −8.38692 −0.481023
\(305\) 19.0684 1.09185
\(306\) 0 0
\(307\) 8.74645 0.499186 0.249593 0.968351i \(-0.419703\pi\)
0.249593 + 0.968351i \(0.419703\pi\)
\(308\) −1.57935 −0.0899920
\(309\) 0 0
\(310\) 9.08885 0.516212
\(311\) 11.6816 0.662403 0.331201 0.943560i \(-0.392546\pi\)
0.331201 + 0.943560i \(0.392546\pi\)
\(312\) 0 0
\(313\) 23.9981 1.35645 0.678226 0.734854i \(-0.262749\pi\)
0.678226 + 0.734854i \(0.262749\pi\)
\(314\) −1.17392 −0.0662482
\(315\) 0 0
\(316\) 9.64978 0.542843
\(317\) 30.2788 1.70063 0.850314 0.526276i \(-0.176412\pi\)
0.850314 + 0.526276i \(0.176412\pi\)
\(318\) 0 0
\(319\) 34.8765 1.95271
\(320\) −2.26764 −0.126765
\(321\) 0 0
\(322\) 3.29489 0.183617
\(323\) 57.4755 3.19803
\(324\) 0 0
\(325\) 0.117087 0.00649482
\(326\) −17.5592 −0.972513
\(327\) 0 0
\(328\) −9.11675 −0.503388
\(329\) −0.629075 −0.0346820
\(330\) 0 0
\(331\) 4.27876 0.235182 0.117591 0.993062i \(-0.462483\pi\)
0.117591 + 0.993062i \(0.462483\pi\)
\(332\) 8.76097 0.480820
\(333\) 0 0
\(334\) −4.50119 −0.246294
\(335\) 25.8516 1.41242
\(336\) 0 0
\(337\) −22.8901 −1.24690 −0.623450 0.781863i \(-0.714270\pi\)
−0.623450 + 0.781863i \(0.714270\pi\)
\(338\) 12.3218 0.670218
\(339\) 0 0
\(340\) 15.5401 0.842781
\(341\) 15.9108 0.861618
\(342\) 0 0
\(343\) 5.50697 0.297349
\(344\) 8.24158 0.444356
\(345\) 0 0
\(346\) 6.31389 0.339437
\(347\) 17.5781 0.943645 0.471822 0.881694i \(-0.343596\pi\)
0.471822 + 0.881694i \(0.343596\pi\)
\(348\) 0 0
\(349\) −6.75698 −0.361693 −0.180846 0.983511i \(-0.557884\pi\)
−0.180846 + 0.983511i \(0.557884\pi\)
\(350\) 0.0565658 0.00302357
\(351\) 0 0
\(352\) −3.96969 −0.211585
\(353\) 3.34841 0.178218 0.0891090 0.996022i \(-0.471598\pi\)
0.0891090 + 0.996022i \(0.471598\pi\)
\(354\) 0 0
\(355\) −33.4806 −1.77696
\(356\) −9.24953 −0.490224
\(357\) 0 0
\(358\) −7.46421 −0.394496
\(359\) 19.7588 1.04283 0.521415 0.853304i \(-0.325405\pi\)
0.521415 + 0.853304i \(0.325405\pi\)
\(360\) 0 0
\(361\) 51.3403 2.70212
\(362\) −15.8449 −0.832791
\(363\) 0 0
\(364\) −0.327643 −0.0171732
\(365\) −14.2333 −0.745006
\(366\) 0 0
\(367\) 5.61191 0.292939 0.146470 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(368\) 8.28167 0.431712
\(369\) 0 0
\(370\) 1.57505 0.0818827
\(371\) 3.10394 0.161149
\(372\) 0 0
\(373\) 6.40480 0.331628 0.165814 0.986157i \(-0.446975\pi\)
0.165814 + 0.986157i \(0.446975\pi\)
\(374\) 27.2043 1.40670
\(375\) 0 0
\(376\) −1.58117 −0.0815428
\(377\) 7.23529 0.372636
\(378\) 0 0
\(379\) −17.1296 −0.879891 −0.439945 0.898025i \(-0.645002\pi\)
−0.439945 + 0.898025i \(0.645002\pi\)
\(380\) 19.0185 0.975627
\(381\) 0 0
\(382\) 16.6457 0.851669
\(383\) 22.0618 1.12730 0.563652 0.826012i \(-0.309396\pi\)
0.563652 + 0.826012i \(0.309396\pi\)
\(384\) 0 0
\(385\) 3.58140 0.182525
\(386\) 9.73110 0.495300
\(387\) 0 0
\(388\) −8.05434 −0.408897
\(389\) −15.0190 −0.761494 −0.380747 0.924679i \(-0.624333\pi\)
−0.380747 + 0.924679i \(0.624333\pi\)
\(390\) 0 0
\(391\) −56.7543 −2.87019
\(392\) 6.84171 0.345559
\(393\) 0 0
\(394\) −2.03744 −0.102645
\(395\) −21.8822 −1.10101
\(396\) 0 0
\(397\) −9.26395 −0.464944 −0.232472 0.972603i \(-0.574681\pi\)
−0.232472 + 0.972603i \(0.574681\pi\)
\(398\) 20.4304 1.02408
\(399\) 0 0
\(400\) 0.142177 0.00710887
\(401\) −12.8908 −0.643733 −0.321867 0.946785i \(-0.604310\pi\)
−0.321867 + 0.946785i \(0.604310\pi\)
\(402\) 0 0
\(403\) 3.30076 0.164423
\(404\) −9.77230 −0.486190
\(405\) 0 0
\(406\) 3.49543 0.173475
\(407\) 2.75725 0.136672
\(408\) 0 0
\(409\) −9.86517 −0.487801 −0.243901 0.969800i \(-0.578427\pi\)
−0.243901 + 0.969800i \(0.578427\pi\)
\(410\) 20.6735 1.02099
\(411\) 0 0
\(412\) 2.13814 0.105339
\(413\) 4.34797 0.213950
\(414\) 0 0
\(415\) −19.8667 −0.975218
\(416\) −0.823528 −0.0403768
\(417\) 0 0
\(418\) 33.2934 1.62843
\(419\) 16.8632 0.823823 0.411912 0.911224i \(-0.364861\pi\)
0.411912 + 0.911224i \(0.364861\pi\)
\(420\) 0 0
\(421\) 16.7035 0.814078 0.407039 0.913411i \(-0.366561\pi\)
0.407039 + 0.913411i \(0.366561\pi\)
\(422\) −14.9296 −0.726762
\(423\) 0 0
\(424\) 7.80173 0.378885
\(425\) −0.974342 −0.0472625
\(426\) 0 0
\(427\) 3.34551 0.161901
\(428\) −9.52464 −0.460391
\(429\) 0 0
\(430\) −18.6889 −0.901259
\(431\) −3.42714 −0.165079 −0.0825397 0.996588i \(-0.526303\pi\)
−0.0825397 + 0.996588i \(0.526303\pi\)
\(432\) 0 0
\(433\) 9.04647 0.434746 0.217373 0.976089i \(-0.430251\pi\)
0.217373 + 0.976089i \(0.430251\pi\)
\(434\) 1.59463 0.0765445
\(435\) 0 0
\(436\) 17.2092 0.824170
\(437\) −69.4577 −3.32261
\(438\) 0 0
\(439\) 15.9907 0.763193 0.381597 0.924329i \(-0.375374\pi\)
0.381597 + 0.924329i \(0.375374\pi\)
\(440\) 9.00181 0.429144
\(441\) 0 0
\(442\) 5.64364 0.268441
\(443\) −2.78120 −0.132139 −0.0660693 0.997815i \(-0.521046\pi\)
−0.0660693 + 0.997815i \(0.521046\pi\)
\(444\) 0 0
\(445\) 20.9746 0.994290
\(446\) 16.1349 0.764008
\(447\) 0 0
\(448\) −0.397853 −0.0187968
\(449\) −22.6866 −1.07065 −0.535324 0.844647i \(-0.679810\pi\)
−0.535324 + 0.844647i \(0.679810\pi\)
\(450\) 0 0
\(451\) 36.1906 1.70415
\(452\) −0.853149 −0.0401288
\(453\) 0 0
\(454\) 19.4983 0.915101
\(455\) 0.742976 0.0348313
\(456\) 0 0
\(457\) 6.54589 0.306204 0.153102 0.988210i \(-0.451074\pi\)
0.153102 + 0.988210i \(0.451074\pi\)
\(458\) 11.0086 0.514397
\(459\) 0 0
\(460\) −18.7798 −0.875614
\(461\) 8.49455 0.395631 0.197815 0.980239i \(-0.436615\pi\)
0.197815 + 0.980239i \(0.436615\pi\)
\(462\) 0 0
\(463\) 29.4676 1.36947 0.684737 0.728790i \(-0.259917\pi\)
0.684737 + 0.728790i \(0.259917\pi\)
\(464\) 8.78572 0.407867
\(465\) 0 0
\(466\) 28.0188 1.29795
\(467\) 26.8493 1.24244 0.621218 0.783638i \(-0.286638\pi\)
0.621218 + 0.783638i \(0.286638\pi\)
\(468\) 0 0
\(469\) 4.53562 0.209435
\(470\) 3.58553 0.165388
\(471\) 0 0
\(472\) 10.9286 0.503029
\(473\) −32.7165 −1.50430
\(474\) 0 0
\(475\) −1.19243 −0.0547124
\(476\) 2.72649 0.124968
\(477\) 0 0
\(478\) −23.4730 −1.07363
\(479\) 17.1551 0.783837 0.391919 0.920000i \(-0.371811\pi\)
0.391919 + 0.920000i \(0.371811\pi\)
\(480\) 0 0
\(481\) 0.572003 0.0260811
\(482\) −16.6148 −0.756782
\(483\) 0 0
\(484\) 4.75840 0.216291
\(485\) 18.2643 0.829340
\(486\) 0 0
\(487\) 14.0684 0.637501 0.318750 0.947839i \(-0.396737\pi\)
0.318750 + 0.947839i \(0.396737\pi\)
\(488\) 8.40891 0.380654
\(489\) 0 0
\(490\) −15.5145 −0.700875
\(491\) −6.74375 −0.304341 −0.152171 0.988354i \(-0.548626\pi\)
−0.152171 + 0.988354i \(0.548626\pi\)
\(492\) 0 0
\(493\) −60.2086 −2.71166
\(494\) 6.90686 0.310754
\(495\) 0 0
\(496\) 4.00807 0.179968
\(497\) −5.87412 −0.263490
\(498\) 0 0
\(499\) 4.81728 0.215651 0.107825 0.994170i \(-0.465611\pi\)
0.107825 + 0.994170i \(0.465611\pi\)
\(500\) 11.0158 0.492641
\(501\) 0 0
\(502\) −21.7503 −0.970764
\(503\) 36.1200 1.61051 0.805255 0.592929i \(-0.202028\pi\)
0.805255 + 0.592929i \(0.202028\pi\)
\(504\) 0 0
\(505\) 22.1600 0.986108
\(506\) −32.8756 −1.46150
\(507\) 0 0
\(508\) 10.3267 0.458175
\(509\) 27.1181 1.20199 0.600994 0.799254i \(-0.294772\pi\)
0.600994 + 0.799254i \(0.294772\pi\)
\(510\) 0 0
\(511\) −2.49721 −0.110470
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −25.0548 −1.10512
\(515\) −4.84853 −0.213652
\(516\) 0 0
\(517\) 6.27676 0.276052
\(518\) 0.276339 0.0121417
\(519\) 0 0
\(520\) 1.86746 0.0818937
\(521\) 3.14188 0.137648 0.0688240 0.997629i \(-0.478075\pi\)
0.0688240 + 0.997629i \(0.478075\pi\)
\(522\) 0 0
\(523\) −27.3922 −1.19778 −0.598888 0.800833i \(-0.704390\pi\)
−0.598888 + 0.800833i \(0.704390\pi\)
\(524\) 7.41831 0.324070
\(525\) 0 0
\(526\) 1.10598 0.0482232
\(527\) −27.4673 −1.19650
\(528\) 0 0
\(529\) 45.5861 1.98200
\(530\) −17.6915 −0.768469
\(531\) 0 0
\(532\) 3.33676 0.144667
\(533\) 7.50790 0.325203
\(534\) 0 0
\(535\) 21.5984 0.933781
\(536\) 11.4002 0.492415
\(537\) 0 0
\(538\) 14.9971 0.646571
\(539\) −27.1594 −1.16984
\(540\) 0 0
\(541\) 13.0959 0.563036 0.281518 0.959556i \(-0.409162\pi\)
0.281518 + 0.959556i \(0.409162\pi\)
\(542\) −25.6135 −1.10019
\(543\) 0 0
\(544\) 6.85300 0.293820
\(545\) −39.0241 −1.67161
\(546\) 0 0
\(547\) −10.4468 −0.446674 −0.223337 0.974741i \(-0.571695\pi\)
−0.223337 + 0.974741i \(0.571695\pi\)
\(548\) 15.1282 0.646245
\(549\) 0 0
\(550\) −0.564399 −0.0240661
\(551\) −73.6851 −3.13909
\(552\) 0 0
\(553\) −3.83920 −0.163259
\(554\) 17.2735 0.733881
\(555\) 0 0
\(556\) −13.7814 −0.584460
\(557\) 23.7259 1.00530 0.502650 0.864490i \(-0.332358\pi\)
0.502650 + 0.864490i \(0.332358\pi\)
\(558\) 0 0
\(559\) −6.78717 −0.287067
\(560\) 0.902187 0.0381244
\(561\) 0 0
\(562\) −3.74260 −0.157872
\(563\) 15.4966 0.653106 0.326553 0.945179i \(-0.394113\pi\)
0.326553 + 0.945179i \(0.394113\pi\)
\(564\) 0 0
\(565\) 1.93463 0.0813906
\(566\) 7.91599 0.332734
\(567\) 0 0
\(568\) −14.7645 −0.619506
\(569\) 9.61882 0.403242 0.201621 0.979464i \(-0.435379\pi\)
0.201621 + 0.979464i \(0.435379\pi\)
\(570\) 0 0
\(571\) 34.8896 1.46008 0.730042 0.683402i \(-0.239500\pi\)
0.730042 + 0.683402i \(0.239500\pi\)
\(572\) 3.26915 0.136690
\(573\) 0 0
\(574\) 3.62713 0.151393
\(575\) 1.17747 0.0491037
\(576\) 0 0
\(577\) 5.66430 0.235808 0.117904 0.993025i \(-0.462382\pi\)
0.117904 + 0.993025i \(0.462382\pi\)
\(578\) −29.9636 −1.24632
\(579\) 0 0
\(580\) −19.9228 −0.827250
\(581\) −3.48558 −0.144606
\(582\) 0 0
\(583\) −30.9704 −1.28266
\(584\) −6.27672 −0.259733
\(585\) 0 0
\(586\) 26.0968 1.07805
\(587\) 13.8612 0.572112 0.286056 0.958213i \(-0.407656\pi\)
0.286056 + 0.958213i \(0.407656\pi\)
\(588\) 0 0
\(589\) −33.6154 −1.38510
\(590\) −24.7821 −1.02026
\(591\) 0 0
\(592\) 0.694576 0.0285469
\(593\) 42.2000 1.73295 0.866474 0.499222i \(-0.166381\pi\)
0.866474 + 0.499222i \(0.166381\pi\)
\(594\) 0 0
\(595\) −6.18269 −0.253466
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) −6.82019 −0.278898
\(599\) −40.0156 −1.63499 −0.817497 0.575933i \(-0.804639\pi\)
−0.817497 + 0.575933i \(0.804639\pi\)
\(600\) 0 0
\(601\) 12.4610 0.508296 0.254148 0.967165i \(-0.418205\pi\)
0.254148 + 0.967165i \(0.418205\pi\)
\(602\) −3.27894 −0.133640
\(603\) 0 0
\(604\) 16.9871 0.691197
\(605\) −10.7903 −0.438689
\(606\) 0 0
\(607\) 28.2278 1.14573 0.572865 0.819650i \(-0.305832\pi\)
0.572865 + 0.819650i \(0.305832\pi\)
\(608\) 8.38692 0.340134
\(609\) 0 0
\(610\) −19.0684 −0.772055
\(611\) 1.30214 0.0526790
\(612\) 0 0
\(613\) 9.70098 0.391819 0.195909 0.980622i \(-0.437234\pi\)
0.195909 + 0.980622i \(0.437234\pi\)
\(614\) −8.74645 −0.352978
\(615\) 0 0
\(616\) 1.57935 0.0636339
\(617\) −20.3190 −0.818012 −0.409006 0.912532i \(-0.634124\pi\)
−0.409006 + 0.912532i \(0.634124\pi\)
\(618\) 0 0
\(619\) 15.6405 0.628645 0.314323 0.949316i \(-0.398223\pi\)
0.314323 + 0.949316i \(0.398223\pi\)
\(620\) −9.08885 −0.365017
\(621\) 0 0
\(622\) −11.6816 −0.468389
\(623\) 3.67996 0.147434
\(624\) 0 0
\(625\) −25.6907 −1.02763
\(626\) −23.9981 −0.959156
\(627\) 0 0
\(628\) 1.17392 0.0468445
\(629\) −4.75993 −0.189791
\(630\) 0 0
\(631\) 4.45340 0.177287 0.0886436 0.996063i \(-0.471747\pi\)
0.0886436 + 0.996063i \(0.471747\pi\)
\(632\) −9.64978 −0.383848
\(633\) 0 0
\(634\) −30.2788 −1.20253
\(635\) −23.4173 −0.929287
\(636\) 0 0
\(637\) −5.63434 −0.223241
\(638\) −34.8765 −1.38078
\(639\) 0 0
\(640\) 2.26764 0.0896362
\(641\) 42.1227 1.66375 0.831874 0.554964i \(-0.187268\pi\)
0.831874 + 0.554964i \(0.187268\pi\)
\(642\) 0 0
\(643\) 10.4065 0.410392 0.205196 0.978721i \(-0.434217\pi\)
0.205196 + 0.978721i \(0.434217\pi\)
\(644\) −3.29489 −0.129837
\(645\) 0 0
\(646\) −57.4755 −2.26135
\(647\) −32.4987 −1.27765 −0.638827 0.769350i \(-0.720580\pi\)
−0.638827 + 0.769350i \(0.720580\pi\)
\(648\) 0 0
\(649\) −43.3830 −1.70293
\(650\) −0.117087 −0.00459253
\(651\) 0 0
\(652\) 17.5592 0.687670
\(653\) 42.1198 1.64827 0.824137 0.566391i \(-0.191661\pi\)
0.824137 + 0.566391i \(0.191661\pi\)
\(654\) 0 0
\(655\) −16.8220 −0.657291
\(656\) 9.11675 0.355949
\(657\) 0 0
\(658\) 0.629075 0.0245239
\(659\) 38.1964 1.48792 0.743960 0.668224i \(-0.232945\pi\)
0.743960 + 0.668224i \(0.232945\pi\)
\(660\) 0 0
\(661\) 34.9691 1.36014 0.680070 0.733147i \(-0.261949\pi\)
0.680070 + 0.733147i \(0.261949\pi\)
\(662\) −4.27876 −0.166299
\(663\) 0 0
\(664\) −8.76097 −0.339991
\(665\) −7.56657 −0.293419
\(666\) 0 0
\(667\) 72.7605 2.81730
\(668\) 4.50119 0.174156
\(669\) 0 0
\(670\) −25.8516 −0.998733
\(671\) −33.3807 −1.28865
\(672\) 0 0
\(673\) 9.28107 0.357759 0.178880 0.983871i \(-0.442753\pi\)
0.178880 + 0.983871i \(0.442753\pi\)
\(674\) 22.8901 0.881692
\(675\) 0 0
\(676\) −12.3218 −0.473915
\(677\) 43.5582 1.67408 0.837039 0.547143i \(-0.184285\pi\)
0.837039 + 0.547143i \(0.184285\pi\)
\(678\) 0 0
\(679\) 3.20445 0.122975
\(680\) −15.5401 −0.595936
\(681\) 0 0
\(682\) −15.9108 −0.609256
\(683\) 10.2891 0.393702 0.196851 0.980433i \(-0.436929\pi\)
0.196851 + 0.980433i \(0.436929\pi\)
\(684\) 0 0
\(685\) −34.3053 −1.31074
\(686\) −5.50697 −0.210257
\(687\) 0 0
\(688\) −8.24158 −0.314207
\(689\) −6.42494 −0.244771
\(690\) 0 0
\(691\) −19.7310 −0.750603 −0.375302 0.926903i \(-0.622461\pi\)
−0.375302 + 0.926903i \(0.622461\pi\)
\(692\) −6.31389 −0.240018
\(693\) 0 0
\(694\) −17.5781 −0.667257
\(695\) 31.2511 1.18542
\(696\) 0 0
\(697\) −62.4771 −2.36649
\(698\) 6.75698 0.255755
\(699\) 0 0
\(700\) −0.0565658 −0.00213798
\(701\) 44.6961 1.68815 0.844073 0.536228i \(-0.180151\pi\)
0.844073 + 0.536228i \(0.180151\pi\)
\(702\) 0 0
\(703\) −5.82535 −0.219707
\(704\) 3.96969 0.149613
\(705\) 0 0
\(706\) −3.34841 −0.126019
\(707\) 3.88794 0.146221
\(708\) 0 0
\(709\) 6.66685 0.250379 0.125189 0.992133i \(-0.460046\pi\)
0.125189 + 0.992133i \(0.460046\pi\)
\(710\) 33.4806 1.25650
\(711\) 0 0
\(712\) 9.24953 0.346641
\(713\) 33.1935 1.24311
\(714\) 0 0
\(715\) −7.41324 −0.277239
\(716\) 7.46421 0.278951
\(717\) 0 0
\(718\) −19.7588 −0.737391
\(719\) 21.3307 0.795502 0.397751 0.917493i \(-0.369791\pi\)
0.397751 + 0.917493i \(0.369791\pi\)
\(720\) 0 0
\(721\) −0.850668 −0.0316805
\(722\) −51.3403 −1.91069
\(723\) 0 0
\(724\) 15.8449 0.588872
\(725\) 1.24913 0.0463916
\(726\) 0 0
\(727\) −28.2804 −1.04886 −0.524430 0.851453i \(-0.675722\pi\)
−0.524430 + 0.851453i \(0.675722\pi\)
\(728\) 0.327643 0.0121433
\(729\) 0 0
\(730\) 14.2333 0.526799
\(731\) 56.4795 2.08897
\(732\) 0 0
\(733\) 6.79861 0.251112 0.125556 0.992087i \(-0.459928\pi\)
0.125556 + 0.992087i \(0.459928\pi\)
\(734\) −5.61191 −0.207139
\(735\) 0 0
\(736\) −8.28167 −0.305266
\(737\) −45.2553 −1.66700
\(738\) 0 0
\(739\) −18.8897 −0.694870 −0.347435 0.937704i \(-0.612947\pi\)
−0.347435 + 0.937704i \(0.612947\pi\)
\(740\) −1.57505 −0.0578998
\(741\) 0 0
\(742\) −3.10394 −0.113949
\(743\) −19.5087 −0.715704 −0.357852 0.933778i \(-0.616491\pi\)
−0.357852 + 0.933778i \(0.616491\pi\)
\(744\) 0 0
\(745\) −2.26764 −0.0830798
\(746\) −6.40480 −0.234496
\(747\) 0 0
\(748\) −27.2043 −0.994686
\(749\) 3.78941 0.138462
\(750\) 0 0
\(751\) 13.1392 0.479458 0.239729 0.970840i \(-0.422941\pi\)
0.239729 + 0.970840i \(0.422941\pi\)
\(752\) 1.58117 0.0576594
\(753\) 0 0
\(754\) −7.23529 −0.263494
\(755\) −38.5207 −1.40191
\(756\) 0 0
\(757\) −22.5014 −0.817827 −0.408913 0.912573i \(-0.634092\pi\)
−0.408913 + 0.912573i \(0.634092\pi\)
\(758\) 17.1296 0.622177
\(759\) 0 0
\(760\) −19.0185 −0.689873
\(761\) −4.15691 −0.150688 −0.0753440 0.997158i \(-0.524005\pi\)
−0.0753440 + 0.997158i \(0.524005\pi\)
\(762\) 0 0
\(763\) −6.84672 −0.247868
\(764\) −16.6457 −0.602221
\(765\) 0 0
\(766\) −22.0618 −0.797125
\(767\) −8.99999 −0.324971
\(768\) 0 0
\(769\) −17.5274 −0.632055 −0.316028 0.948750i \(-0.602349\pi\)
−0.316028 + 0.948750i \(0.602349\pi\)
\(770\) −3.58140 −0.129065
\(771\) 0 0
\(772\) −9.73110 −0.350230
\(773\) 5.94560 0.213849 0.106924 0.994267i \(-0.465900\pi\)
0.106924 + 0.994267i \(0.465900\pi\)
\(774\) 0 0
\(775\) 0.569857 0.0204699
\(776\) 8.05434 0.289134
\(777\) 0 0
\(778\) 15.0190 0.538458
\(779\) −76.4614 −2.73951
\(780\) 0 0
\(781\) 58.6105 2.09725
\(782\) 56.7543 2.02953
\(783\) 0 0
\(784\) −6.84171 −0.244347
\(785\) −2.66203 −0.0950118
\(786\) 0 0
\(787\) −31.7311 −1.13109 −0.565545 0.824717i \(-0.691334\pi\)
−0.565545 + 0.824717i \(0.691334\pi\)
\(788\) 2.03744 0.0725806
\(789\) 0 0
\(790\) 21.8822 0.778534
\(791\) 0.339428 0.0120687
\(792\) 0 0
\(793\) −6.92498 −0.245913
\(794\) 9.26395 0.328765
\(795\) 0 0
\(796\) −20.4304 −0.724137
\(797\) 21.1583 0.749466 0.374733 0.927133i \(-0.377734\pi\)
0.374733 + 0.927133i \(0.377734\pi\)
\(798\) 0 0
\(799\) −10.8358 −0.383342
\(800\) −0.142177 −0.00502673
\(801\) 0 0
\(802\) 12.8908 0.455188
\(803\) 24.9166 0.879288
\(804\) 0 0
\(805\) 7.47162 0.263340
\(806\) −3.30076 −0.116264
\(807\) 0 0
\(808\) 9.77230 0.343788
\(809\) 18.8833 0.663900 0.331950 0.943297i \(-0.392293\pi\)
0.331950 + 0.943297i \(0.392293\pi\)
\(810\) 0 0
\(811\) −21.7651 −0.764275 −0.382137 0.924105i \(-0.624812\pi\)
−0.382137 + 0.924105i \(0.624812\pi\)
\(812\) −3.49543 −0.122665
\(813\) 0 0
\(814\) −2.75725 −0.0966415
\(815\) −39.8178 −1.39476
\(816\) 0 0
\(817\) 69.1214 2.41825
\(818\) 9.86517 0.344928
\(819\) 0 0
\(820\) −20.6735 −0.721949
\(821\) 12.5288 0.437259 0.218630 0.975808i \(-0.429841\pi\)
0.218630 + 0.975808i \(0.429841\pi\)
\(822\) 0 0
\(823\) 2.12788 0.0741733 0.0370867 0.999312i \(-0.488192\pi\)
0.0370867 + 0.999312i \(0.488192\pi\)
\(824\) −2.13814 −0.0744858
\(825\) 0 0
\(826\) −4.34797 −0.151285
\(827\) −14.0345 −0.488026 −0.244013 0.969772i \(-0.578464\pi\)
−0.244013 + 0.969772i \(0.578464\pi\)
\(828\) 0 0
\(829\) −4.43826 −0.154147 −0.0770735 0.997025i \(-0.524558\pi\)
−0.0770735 + 0.997025i \(0.524558\pi\)
\(830\) 19.8667 0.689583
\(831\) 0 0
\(832\) 0.823528 0.0285507
\(833\) 46.8863 1.62451
\(834\) 0 0
\(835\) −10.2071 −0.353230
\(836\) −33.2934 −1.15148
\(837\) 0 0
\(838\) −16.8632 −0.582531
\(839\) 6.15626 0.212538 0.106269 0.994337i \(-0.466110\pi\)
0.106269 + 0.994337i \(0.466110\pi\)
\(840\) 0 0
\(841\) 48.1889 1.66169
\(842\) −16.7035 −0.575640
\(843\) 0 0
\(844\) 14.9296 0.513898
\(845\) 27.9414 0.961212
\(846\) 0 0
\(847\) −1.89315 −0.0650493
\(848\) −7.80173 −0.267912
\(849\) 0 0
\(850\) 0.974342 0.0334197
\(851\) 5.75225 0.197185
\(852\) 0 0
\(853\) 9.14473 0.313110 0.156555 0.987669i \(-0.449961\pi\)
0.156555 + 0.987669i \(0.449961\pi\)
\(854\) −3.34551 −0.114481
\(855\) 0 0
\(856\) 9.52464 0.325546
\(857\) 25.6375 0.875762 0.437881 0.899033i \(-0.355729\pi\)
0.437881 + 0.899033i \(0.355729\pi\)
\(858\) 0 0
\(859\) −5.45085 −0.185981 −0.0929903 0.995667i \(-0.529643\pi\)
−0.0929903 + 0.995667i \(0.529643\pi\)
\(860\) 18.6889 0.637286
\(861\) 0 0
\(862\) 3.42714 0.116729
\(863\) −15.4896 −0.527272 −0.263636 0.964622i \(-0.584922\pi\)
−0.263636 + 0.964622i \(0.584922\pi\)
\(864\) 0 0
\(865\) 14.3176 0.486814
\(866\) −9.04647 −0.307412
\(867\) 0 0
\(868\) −1.59463 −0.0541251
\(869\) 38.3066 1.29946
\(870\) 0 0
\(871\) −9.38840 −0.318114
\(872\) −17.2092 −0.582776
\(873\) 0 0
\(874\) 69.4577 2.34944
\(875\) −4.38266 −0.148161
\(876\) 0 0
\(877\) −2.33464 −0.0788353 −0.0394177 0.999223i \(-0.512550\pi\)
−0.0394177 + 0.999223i \(0.512550\pi\)
\(878\) −15.9907 −0.539659
\(879\) 0 0
\(880\) −9.00181 −0.303451
\(881\) 57.6543 1.94242 0.971211 0.238220i \(-0.0765640\pi\)
0.971211 + 0.238220i \(0.0765640\pi\)
\(882\) 0 0
\(883\) 25.7235 0.865663 0.432832 0.901475i \(-0.357514\pi\)
0.432832 + 0.901475i \(0.357514\pi\)
\(884\) −5.64364 −0.189816
\(885\) 0 0
\(886\) 2.78120 0.0934361
\(887\) 46.8090 1.57169 0.785846 0.618422i \(-0.212228\pi\)
0.785846 + 0.618422i \(0.212228\pi\)
\(888\) 0 0
\(889\) −4.10853 −0.137796
\(890\) −20.9746 −0.703069
\(891\) 0 0
\(892\) −16.1349 −0.540235
\(893\) −13.2612 −0.443768
\(894\) 0 0
\(895\) −16.9261 −0.565778
\(896\) 0.397853 0.0132913
\(897\) 0 0
\(898\) 22.6866 0.757062
\(899\) 35.2138 1.17445
\(900\) 0 0
\(901\) 53.4653 1.78119
\(902\) −36.1906 −1.20502
\(903\) 0 0
\(904\) 0.853149 0.0283753
\(905\) −35.9305 −1.19437
\(906\) 0 0
\(907\) −34.4229 −1.14299 −0.571497 0.820604i \(-0.693637\pi\)
−0.571497 + 0.820604i \(0.693637\pi\)
\(908\) −19.4983 −0.647074
\(909\) 0 0
\(910\) −0.742976 −0.0246294
\(911\) −6.77761 −0.224552 −0.112276 0.993677i \(-0.535814\pi\)
−0.112276 + 0.993677i \(0.535814\pi\)
\(912\) 0 0
\(913\) 34.7783 1.15099
\(914\) −6.54589 −0.216519
\(915\) 0 0
\(916\) −11.0086 −0.363734
\(917\) −2.95140 −0.0974638
\(918\) 0 0
\(919\) 36.3820 1.20013 0.600066 0.799950i \(-0.295141\pi\)
0.600066 + 0.799950i \(0.295141\pi\)
\(920\) 18.7798 0.619152
\(921\) 0 0
\(922\) −8.49455 −0.279753
\(923\) 12.1590 0.400218
\(924\) 0 0
\(925\) 0.0987530 0.00324698
\(926\) −29.4676 −0.968365
\(927\) 0 0
\(928\) −8.78572 −0.288405
\(929\) −49.3214 −1.61818 −0.809091 0.587683i \(-0.800040\pi\)
−0.809091 + 0.587683i \(0.800040\pi\)
\(930\) 0 0
\(931\) 57.3809 1.88058
\(932\) −28.0188 −0.917788
\(933\) 0 0
\(934\) −26.8493 −0.878535
\(935\) 61.6894 2.01746
\(936\) 0 0
\(937\) 22.8573 0.746717 0.373358 0.927687i \(-0.378206\pi\)
0.373358 + 0.927687i \(0.378206\pi\)
\(938\) −4.53562 −0.148093
\(939\) 0 0
\(940\) −3.58553 −0.116947
\(941\) −33.8585 −1.10375 −0.551877 0.833925i \(-0.686088\pi\)
−0.551877 + 0.833925i \(0.686088\pi\)
\(942\) 0 0
\(943\) 75.5019 2.45868
\(944\) −10.9286 −0.355695
\(945\) 0 0
\(946\) 32.7165 1.06370
\(947\) 0.515622 0.0167555 0.00837774 0.999965i \(-0.497333\pi\)
0.00837774 + 0.999965i \(0.497333\pi\)
\(948\) 0 0
\(949\) 5.16906 0.167795
\(950\) 1.19243 0.0386875
\(951\) 0 0
\(952\) −2.72649 −0.0883661
\(953\) 5.49709 0.178068 0.0890341 0.996029i \(-0.471622\pi\)
0.0890341 + 0.996029i \(0.471622\pi\)
\(954\) 0 0
\(955\) 37.7464 1.22145
\(956\) 23.4730 0.759172
\(957\) 0 0
\(958\) −17.1551 −0.554257
\(959\) −6.01881 −0.194357
\(960\) 0 0
\(961\) −14.9353 −0.481785
\(962\) −0.572003 −0.0184421
\(963\) 0 0
\(964\) 16.6148 0.535126
\(965\) 22.0666 0.710349
\(966\) 0 0
\(967\) 10.6176 0.341440 0.170720 0.985320i \(-0.445391\pi\)
0.170720 + 0.985320i \(0.445391\pi\)
\(968\) −4.75840 −0.152941
\(969\) 0 0
\(970\) −18.2643 −0.586432
\(971\) −51.8122 −1.66273 −0.831366 0.555725i \(-0.812441\pi\)
−0.831366 + 0.555725i \(0.812441\pi\)
\(972\) 0 0
\(973\) 5.48296 0.175776
\(974\) −14.0684 −0.450781
\(975\) 0 0
\(976\) −8.40891 −0.269163
\(977\) −33.6732 −1.07730 −0.538651 0.842529i \(-0.681066\pi\)
−0.538651 + 0.842529i \(0.681066\pi\)
\(978\) 0 0
\(979\) −36.7177 −1.17350
\(980\) 15.5145 0.495593
\(981\) 0 0
\(982\) 6.74375 0.215202
\(983\) −51.2822 −1.63565 −0.817823 0.575469i \(-0.804819\pi\)
−0.817823 + 0.575469i \(0.804819\pi\)
\(984\) 0 0
\(985\) −4.62016 −0.147211
\(986\) 60.2086 1.91743
\(987\) 0 0
\(988\) −6.90686 −0.219737
\(989\) −68.2540 −2.17035
\(990\) 0 0
\(991\) 6.69020 0.212521 0.106261 0.994338i \(-0.466112\pi\)
0.106261 + 0.994338i \(0.466112\pi\)
\(992\) −4.00807 −0.127256
\(993\) 0 0
\(994\) 5.87412 0.186316
\(995\) 46.3288 1.46872
\(996\) 0 0
\(997\) 10.3841 0.328869 0.164435 0.986388i \(-0.447420\pi\)
0.164435 + 0.986388i \(0.447420\pi\)
\(998\) −4.81728 −0.152488
\(999\) 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 \(a_p\))