Properties

Label 8001.2.a.u.1.9
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
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: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(0.0366427\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.0366427 q^{2}\) \(-1.99866 q^{4}\) \(-1.02187 q^{5}\) \(+1.00000 q^{7}\) \(-0.146522 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.0366427 q^{2}\) \(-1.99866 q^{4}\) \(-1.02187 q^{5}\) \(+1.00000 q^{7}\) \(-0.146522 q^{8}\) \(-0.0374440 q^{10}\) \(+4.36561 q^{11}\) \(-3.87219 q^{13}\) \(+0.0366427 q^{14}\) \(+3.99195 q^{16}\) \(-6.07872 q^{17}\) \(+6.90344 q^{19}\) \(+2.04236 q^{20}\) \(+0.159968 q^{22}\) \(+5.17354 q^{23}\) \(-3.95579 q^{25}\) \(-0.141888 q^{26}\) \(-1.99866 q^{28}\) \(+1.01222 q^{29}\) \(+8.54462 q^{31}\) \(+0.439319 q^{32}\) \(-0.222741 q^{34}\) \(-1.02187 q^{35}\) \(-8.38368 q^{37}\) \(+0.252961 q^{38}\) \(+0.149726 q^{40}\) \(-1.56657 q^{41}\) \(-6.37089 q^{43}\) \(-8.72536 q^{44}\) \(+0.189573 q^{46}\) \(-4.23682 q^{47}\) \(+1.00000 q^{49}\) \(-0.144951 q^{50}\) \(+7.73918 q^{52}\) \(+5.22125 q^{53}\) \(-4.46107 q^{55}\) \(-0.146522 q^{56}\) \(+0.0370905 q^{58}\) \(+7.49969 q^{59}\) \(+14.3692 q^{61}\) \(+0.313098 q^{62}\) \(-7.96779 q^{64}\) \(+3.95686 q^{65}\) \(+7.55792 q^{67}\) \(+12.1493 q^{68}\) \(-0.0374440 q^{70}\) \(-15.2047 q^{71}\) \(-1.99435 q^{73}\) \(-0.307201 q^{74}\) \(-13.7976 q^{76}\) \(+4.36561 q^{77}\) \(-14.9551 q^{79}\) \(-4.07924 q^{80}\) \(-0.0574035 q^{82}\) \(+15.0270 q^{83}\) \(+6.21164 q^{85}\) \(-0.233447 q^{86}\) \(-0.639657 q^{88}\) \(+3.14237 q^{89}\) \(-3.87219 q^{91}\) \(-10.3401 q^{92}\) \(-0.155249 q^{94}\) \(-7.05440 q^{95}\) \(-16.4469 q^{97}\) \(+0.0366427 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0366427 0.0259103 0.0129552 0.999916i \(-0.495876\pi\)
0.0129552 + 0.999916i \(0.495876\pi\)
\(3\) 0 0
\(4\) −1.99866 −0.999329
\(5\) −1.02187 −0.456993 −0.228497 0.973545i \(-0.573381\pi\)
−0.228497 + 0.973545i \(0.573381\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −0.146522 −0.0518033
\(9\) 0 0
\(10\) −0.0374440 −0.0118408
\(11\) 4.36561 1.31628 0.658140 0.752895i \(-0.271343\pi\)
0.658140 + 0.752895i \(0.271343\pi\)
\(12\) 0 0
\(13\) −3.87219 −1.07395 −0.536976 0.843598i \(-0.680433\pi\)
−0.536976 + 0.843598i \(0.680433\pi\)
\(14\) 0.0366427 0.00979319
\(15\) 0 0
\(16\) 3.99195 0.997986
\(17\) −6.07872 −1.47431 −0.737153 0.675726i \(-0.763830\pi\)
−0.737153 + 0.675726i \(0.763830\pi\)
\(18\) 0 0
\(19\) 6.90344 1.58376 0.791879 0.610678i \(-0.209103\pi\)
0.791879 + 0.610678i \(0.209103\pi\)
\(20\) 2.04236 0.456686
\(21\) 0 0
\(22\) 0.159968 0.0341053
\(23\) 5.17354 1.07876 0.539379 0.842063i \(-0.318659\pi\)
0.539379 + 0.842063i \(0.318659\pi\)
\(24\) 0 0
\(25\) −3.95579 −0.791157
\(26\) −0.141888 −0.0278265
\(27\) 0 0
\(28\) −1.99866 −0.377711
\(29\) 1.01222 0.187965 0.0939823 0.995574i \(-0.470040\pi\)
0.0939823 + 0.995574i \(0.470040\pi\)
\(30\) 0 0
\(31\) 8.54462 1.53466 0.767329 0.641253i \(-0.221585\pi\)
0.767329 + 0.641253i \(0.221585\pi\)
\(32\) 0.439319 0.0776614
\(33\) 0 0
\(34\) −0.222741 −0.0381997
\(35\) −1.02187 −0.172727
\(36\) 0 0
\(37\) −8.38368 −1.37827 −0.689134 0.724634i \(-0.742009\pi\)
−0.689134 + 0.724634i \(0.742009\pi\)
\(38\) 0.252961 0.0410357
\(39\) 0 0
\(40\) 0.149726 0.0236737
\(41\) −1.56657 −0.244657 −0.122329 0.992490i \(-0.539036\pi\)
−0.122329 + 0.992490i \(0.539036\pi\)
\(42\) 0 0
\(43\) −6.37089 −0.971552 −0.485776 0.874083i \(-0.661463\pi\)
−0.485776 + 0.874083i \(0.661463\pi\)
\(44\) −8.72536 −1.31540
\(45\) 0 0
\(46\) 0.189573 0.0279510
\(47\) −4.23682 −0.618003 −0.309002 0.951062i \(-0.599995\pi\)
−0.309002 + 0.951062i \(0.599995\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −0.144951 −0.0204992
\(51\) 0 0
\(52\) 7.73918 1.07323
\(53\) 5.22125 0.717194 0.358597 0.933492i \(-0.383255\pi\)
0.358597 + 0.933492i \(0.383255\pi\)
\(54\) 0 0
\(55\) −4.46107 −0.601531
\(56\) −0.146522 −0.0195798
\(57\) 0 0
\(58\) 0.0370905 0.00487022
\(59\) 7.49969 0.976377 0.488188 0.872738i \(-0.337658\pi\)
0.488188 + 0.872738i \(0.337658\pi\)
\(60\) 0 0
\(61\) 14.3692 1.83979 0.919895 0.392165i \(-0.128274\pi\)
0.919895 + 0.392165i \(0.128274\pi\)
\(62\) 0.313098 0.0397635
\(63\) 0 0
\(64\) −7.96779 −0.995974
\(65\) 3.95686 0.490789
\(66\) 0 0
\(67\) 7.55792 0.923346 0.461673 0.887050i \(-0.347249\pi\)
0.461673 + 0.887050i \(0.347249\pi\)
\(68\) 12.1493 1.47332
\(69\) 0 0
\(70\) −0.0374440 −0.00447542
\(71\) −15.2047 −1.80447 −0.902233 0.431248i \(-0.858073\pi\)
−0.902233 + 0.431248i \(0.858073\pi\)
\(72\) 0 0
\(73\) −1.99435 −0.233421 −0.116711 0.993166i \(-0.537235\pi\)
−0.116711 + 0.993166i \(0.537235\pi\)
\(74\) −0.307201 −0.0357114
\(75\) 0 0
\(76\) −13.7976 −1.58269
\(77\) 4.36561 0.497507
\(78\) 0 0
\(79\) −14.9551 −1.68258 −0.841288 0.540587i \(-0.818202\pi\)
−0.841288 + 0.540587i \(0.818202\pi\)
\(80\) −4.07924 −0.456073
\(81\) 0 0
\(82\) −0.0574035 −0.00633916
\(83\) 15.0270 1.64943 0.824717 0.565546i \(-0.191335\pi\)
0.824717 + 0.565546i \(0.191335\pi\)
\(84\) 0 0
\(85\) 6.21164 0.673747
\(86\) −0.233447 −0.0251732
\(87\) 0 0
\(88\) −0.639657 −0.0681876
\(89\) 3.14237 0.333090 0.166545 0.986034i \(-0.446739\pi\)
0.166545 + 0.986034i \(0.446739\pi\)
\(90\) 0 0
\(91\) −3.87219 −0.405916
\(92\) −10.3401 −1.07803
\(93\) 0 0
\(94\) −0.155249 −0.0160127
\(95\) −7.05440 −0.723767
\(96\) 0 0
\(97\) −16.4469 −1.66993 −0.834966 0.550301i \(-0.814513\pi\)
−0.834966 + 0.550301i \(0.814513\pi\)
\(98\) 0.0366427 0.00370148
\(99\) 0 0
\(100\) 7.90626 0.790626
\(101\) −2.20148 −0.219055 −0.109528 0.993984i \(-0.534934\pi\)
−0.109528 + 0.993984i \(0.534934\pi\)
\(102\) 0 0
\(103\) −12.2962 −1.21158 −0.605789 0.795625i \(-0.707142\pi\)
−0.605789 + 0.795625i \(0.707142\pi\)
\(104\) 0.567360 0.0556342
\(105\) 0 0
\(106\) 0.191321 0.0185827
\(107\) −2.63179 −0.254424 −0.127212 0.991876i \(-0.540603\pi\)
−0.127212 + 0.991876i \(0.540603\pi\)
\(108\) 0 0
\(109\) 0.425217 0.0407284 0.0203642 0.999793i \(-0.493517\pi\)
0.0203642 + 0.999793i \(0.493517\pi\)
\(110\) −0.163466 −0.0155859
\(111\) 0 0
\(112\) 3.99195 0.377203
\(113\) 17.2777 1.62535 0.812674 0.582719i \(-0.198011\pi\)
0.812674 + 0.582719i \(0.198011\pi\)
\(114\) 0 0
\(115\) −5.28667 −0.492985
\(116\) −2.02308 −0.187838
\(117\) 0 0
\(118\) 0.274809 0.0252983
\(119\) −6.07872 −0.557235
\(120\) 0 0
\(121\) 8.05854 0.732595
\(122\) 0.526528 0.0476696
\(123\) 0 0
\(124\) −17.0778 −1.53363
\(125\) 9.15163 0.818547
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −1.17060 −0.103467
\(129\) 0 0
\(130\) 0.144990 0.0127165
\(131\) −2.45915 −0.214857 −0.107428 0.994213i \(-0.534262\pi\)
−0.107428 + 0.994213i \(0.534262\pi\)
\(132\) 0 0
\(133\) 6.90344 0.598604
\(134\) 0.276943 0.0239242
\(135\) 0 0
\(136\) 0.890665 0.0763739
\(137\) −3.53859 −0.302322 −0.151161 0.988509i \(-0.548301\pi\)
−0.151161 + 0.988509i \(0.548301\pi\)
\(138\) 0 0
\(139\) −7.30754 −0.619817 −0.309909 0.950766i \(-0.600298\pi\)
−0.309909 + 0.950766i \(0.600298\pi\)
\(140\) 2.04236 0.172611
\(141\) 0 0
\(142\) −0.557142 −0.0467543
\(143\) −16.9045 −1.41362
\(144\) 0 0
\(145\) −1.03435 −0.0858985
\(146\) −0.0730785 −0.00604802
\(147\) 0 0
\(148\) 16.7561 1.37734
\(149\) 14.4377 1.18278 0.591390 0.806386i \(-0.298579\pi\)
0.591390 + 0.806386i \(0.298579\pi\)
\(150\) 0 0
\(151\) 1.71468 0.139539 0.0697693 0.997563i \(-0.477774\pi\)
0.0697693 + 0.997563i \(0.477774\pi\)
\(152\) −1.01150 −0.0820439
\(153\) 0 0
\(154\) 0.159968 0.0128906
\(155\) −8.73147 −0.701329
\(156\) 0 0
\(157\) −13.0418 −1.04085 −0.520426 0.853907i \(-0.674227\pi\)
−0.520426 + 0.853907i \(0.674227\pi\)
\(158\) −0.547995 −0.0435961
\(159\) 0 0
\(160\) −0.448926 −0.0354907
\(161\) 5.17354 0.407732
\(162\) 0 0
\(163\) −2.54240 −0.199136 −0.0995679 0.995031i \(-0.531746\pi\)
−0.0995679 + 0.995031i \(0.531746\pi\)
\(164\) 3.13104 0.244493
\(165\) 0 0
\(166\) 0.550632 0.0427374
\(167\) −2.11145 −0.163389 −0.0816943 0.996657i \(-0.526033\pi\)
−0.0816943 + 0.996657i \(0.526033\pi\)
\(168\) 0 0
\(169\) 1.99384 0.153372
\(170\) 0.227612 0.0174570
\(171\) 0 0
\(172\) 12.7332 0.970900
\(173\) 1.36849 0.104045 0.0520224 0.998646i \(-0.483433\pi\)
0.0520224 + 0.998646i \(0.483433\pi\)
\(174\) 0 0
\(175\) −3.95579 −0.299029
\(176\) 17.4273 1.31363
\(177\) 0 0
\(178\) 0.115145 0.00863048
\(179\) 22.1352 1.65446 0.827231 0.561862i \(-0.189915\pi\)
0.827231 + 0.561862i \(0.189915\pi\)
\(180\) 0 0
\(181\) 9.74075 0.724024 0.362012 0.932173i \(-0.382090\pi\)
0.362012 + 0.932173i \(0.382090\pi\)
\(182\) −0.141888 −0.0105174
\(183\) 0 0
\(184\) −0.758036 −0.0558832
\(185\) 8.56701 0.629859
\(186\) 0 0
\(187\) −26.5373 −1.94060
\(188\) 8.46794 0.617588
\(189\) 0 0
\(190\) −0.258493 −0.0187530
\(191\) 14.6153 1.05752 0.528762 0.848770i \(-0.322657\pi\)
0.528762 + 0.848770i \(0.322657\pi\)
\(192\) 0 0
\(193\) 13.9523 1.00431 0.502154 0.864778i \(-0.332541\pi\)
0.502154 + 0.864778i \(0.332541\pi\)
\(194\) −0.602661 −0.0432685
\(195\) 0 0
\(196\) −1.99866 −0.142761
\(197\) 24.5804 1.75128 0.875639 0.482966i \(-0.160440\pi\)
0.875639 + 0.482966i \(0.160440\pi\)
\(198\) 0 0
\(199\) 19.8486 1.40703 0.703515 0.710681i \(-0.251613\pi\)
0.703515 + 0.710681i \(0.251613\pi\)
\(200\) 0.579609 0.0409845
\(201\) 0 0
\(202\) −0.0806681 −0.00567579
\(203\) 1.01222 0.0710439
\(204\) 0 0
\(205\) 1.60083 0.111807
\(206\) −0.450566 −0.0313924
\(207\) 0 0
\(208\) −15.4576 −1.07179
\(209\) 30.1377 2.08467
\(210\) 0 0
\(211\) −15.9995 −1.10145 −0.550725 0.834687i \(-0.685649\pi\)
−0.550725 + 0.834687i \(0.685649\pi\)
\(212\) −10.4355 −0.716713
\(213\) 0 0
\(214\) −0.0964359 −0.00659222
\(215\) 6.51021 0.443993
\(216\) 0 0
\(217\) 8.54462 0.580047
\(218\) 0.0155811 0.00105529
\(219\) 0 0
\(220\) 8.91616 0.601127
\(221\) 23.5379 1.58333
\(222\) 0 0
\(223\) 13.5951 0.910394 0.455197 0.890391i \(-0.349569\pi\)
0.455197 + 0.890391i \(0.349569\pi\)
\(224\) 0.439319 0.0293533
\(225\) 0 0
\(226\) 0.633102 0.0421133
\(227\) 4.86970 0.323214 0.161607 0.986855i \(-0.448332\pi\)
0.161607 + 0.986855i \(0.448332\pi\)
\(228\) 0 0
\(229\) −23.0172 −1.52102 −0.760509 0.649328i \(-0.775050\pi\)
−0.760509 + 0.649328i \(0.775050\pi\)
\(230\) −0.193718 −0.0127734
\(231\) 0 0
\(232\) −0.148312 −0.00973718
\(233\) 18.3244 1.20047 0.600237 0.799822i \(-0.295073\pi\)
0.600237 + 0.799822i \(0.295073\pi\)
\(234\) 0 0
\(235\) 4.32947 0.282423
\(236\) −14.9893 −0.975721
\(237\) 0 0
\(238\) −0.222741 −0.0144381
\(239\) 16.8820 1.09201 0.546003 0.837783i \(-0.316149\pi\)
0.546003 + 0.837783i \(0.316149\pi\)
\(240\) 0 0
\(241\) −19.2430 −1.23955 −0.619776 0.784779i \(-0.712777\pi\)
−0.619776 + 0.784779i \(0.712777\pi\)
\(242\) 0.295287 0.0189818
\(243\) 0 0
\(244\) −28.7191 −1.83855
\(245\) −1.02187 −0.0652847
\(246\) 0 0
\(247\) −26.7314 −1.70088
\(248\) −1.25197 −0.0795004
\(249\) 0 0
\(250\) 0.335341 0.0212088
\(251\) −14.0644 −0.887736 −0.443868 0.896092i \(-0.646394\pi\)
−0.443868 + 0.896092i \(0.646394\pi\)
\(252\) 0 0
\(253\) 22.5856 1.41995
\(254\) 0.0366427 0.00229917
\(255\) 0 0
\(256\) 15.8927 0.993293
\(257\) −3.70073 −0.230845 −0.115422 0.993316i \(-0.536822\pi\)
−0.115422 + 0.993316i \(0.536822\pi\)
\(258\) 0 0
\(259\) −8.38368 −0.520936
\(260\) −7.90841 −0.490459
\(261\) 0 0
\(262\) −0.0901100 −0.00556701
\(263\) 0.927045 0.0571641 0.0285820 0.999591i \(-0.490901\pi\)
0.0285820 + 0.999591i \(0.490901\pi\)
\(264\) 0 0
\(265\) −5.33543 −0.327753
\(266\) 0.252961 0.0155100
\(267\) 0 0
\(268\) −15.1057 −0.922726
\(269\) 22.9177 1.39732 0.698659 0.715455i \(-0.253781\pi\)
0.698659 + 0.715455i \(0.253781\pi\)
\(270\) 0 0
\(271\) 4.10911 0.249610 0.124805 0.992181i \(-0.460169\pi\)
0.124805 + 0.992181i \(0.460169\pi\)
\(272\) −24.2659 −1.47134
\(273\) 0 0
\(274\) −0.129664 −0.00783327
\(275\) −17.2694 −1.04138
\(276\) 0 0
\(277\) −2.61597 −0.157179 −0.0785893 0.996907i \(-0.525042\pi\)
−0.0785893 + 0.996907i \(0.525042\pi\)
\(278\) −0.267768 −0.0160597
\(279\) 0 0
\(280\) 0.149726 0.00894783
\(281\) 2.34509 0.139896 0.0699482 0.997551i \(-0.477717\pi\)
0.0699482 + 0.997551i \(0.477717\pi\)
\(282\) 0 0
\(283\) −8.87213 −0.527393 −0.263697 0.964606i \(-0.584942\pi\)
−0.263697 + 0.964606i \(0.584942\pi\)
\(284\) 30.3890 1.80325
\(285\) 0 0
\(286\) −0.619426 −0.0366274
\(287\) −1.56657 −0.0924718
\(288\) 0 0
\(289\) 19.9508 1.17358
\(290\) −0.0379016 −0.00222566
\(291\) 0 0
\(292\) 3.98602 0.233264
\(293\) 12.1220 0.708176 0.354088 0.935212i \(-0.384791\pi\)
0.354088 + 0.935212i \(0.384791\pi\)
\(294\) 0 0
\(295\) −7.66369 −0.446198
\(296\) 1.22839 0.0713988
\(297\) 0 0
\(298\) 0.529036 0.0306462
\(299\) −20.0329 −1.15853
\(300\) 0 0
\(301\) −6.37089 −0.367212
\(302\) 0.0628306 0.00361549
\(303\) 0 0
\(304\) 27.5582 1.58057
\(305\) −14.6834 −0.840771
\(306\) 0 0
\(307\) 24.8259 1.41689 0.708443 0.705768i \(-0.249398\pi\)
0.708443 + 0.705768i \(0.249398\pi\)
\(308\) −8.72536 −0.497173
\(309\) 0 0
\(310\) −0.319945 −0.0181717
\(311\) −28.3900 −1.60985 −0.804926 0.593375i \(-0.797795\pi\)
−0.804926 + 0.593375i \(0.797795\pi\)
\(312\) 0 0
\(313\) −24.0947 −1.36191 −0.680957 0.732323i \(-0.738436\pi\)
−0.680957 + 0.732323i \(0.738436\pi\)
\(314\) −0.477889 −0.0269688
\(315\) 0 0
\(316\) 29.8901 1.68145
\(317\) 26.5259 1.48984 0.744921 0.667153i \(-0.232487\pi\)
0.744921 + 0.667153i \(0.232487\pi\)
\(318\) 0 0
\(319\) 4.41896 0.247414
\(320\) 8.14203 0.455153
\(321\) 0 0
\(322\) 0.189573 0.0105645
\(323\) −41.9641 −2.33494
\(324\) 0 0
\(325\) 15.3175 0.849665
\(326\) −0.0931604 −0.00515968
\(327\) 0 0
\(328\) 0.229537 0.0126741
\(329\) −4.23682 −0.233583
\(330\) 0 0
\(331\) 18.8041 1.03357 0.516783 0.856116i \(-0.327129\pi\)
0.516783 + 0.856116i \(0.327129\pi\)
\(332\) −30.0339 −1.64833
\(333\) 0 0
\(334\) −0.0773692 −0.00423345
\(335\) −7.72319 −0.421963
\(336\) 0 0
\(337\) 22.4878 1.22499 0.612494 0.790475i \(-0.290166\pi\)
0.612494 + 0.790475i \(0.290166\pi\)
\(338\) 0.0730598 0.00397393
\(339\) 0 0
\(340\) −12.4149 −0.673295
\(341\) 37.3025 2.02004
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.933475 0.0503296
\(345\) 0 0
\(346\) 0.0501454 0.00269583
\(347\) −17.8599 −0.958772 −0.479386 0.877604i \(-0.659141\pi\)
−0.479386 + 0.877604i \(0.659141\pi\)
\(348\) 0 0
\(349\) 30.3258 1.62330 0.811652 0.584141i \(-0.198569\pi\)
0.811652 + 0.584141i \(0.198569\pi\)
\(350\) −0.144951 −0.00774795
\(351\) 0 0
\(352\) 1.91790 0.102224
\(353\) −23.4387 −1.24752 −0.623759 0.781617i \(-0.714395\pi\)
−0.623759 + 0.781617i \(0.714395\pi\)
\(354\) 0 0
\(355\) 15.5372 0.824629
\(356\) −6.28051 −0.332867
\(357\) 0 0
\(358\) 0.811094 0.0428676
\(359\) −33.4031 −1.76295 −0.881473 0.472234i \(-0.843448\pi\)
−0.881473 + 0.472234i \(0.843448\pi\)
\(360\) 0 0
\(361\) 28.6575 1.50829
\(362\) 0.356928 0.0187597
\(363\) 0 0
\(364\) 7.73918 0.405643
\(365\) 2.03796 0.106672
\(366\) 0 0
\(367\) 5.05854 0.264054 0.132027 0.991246i \(-0.457852\pi\)
0.132027 + 0.991246i \(0.457852\pi\)
\(368\) 20.6525 1.07659
\(369\) 0 0
\(370\) 0.313919 0.0163199
\(371\) 5.22125 0.271074
\(372\) 0 0
\(373\) 19.5903 1.01435 0.507173 0.861844i \(-0.330690\pi\)
0.507173 + 0.861844i \(0.330690\pi\)
\(374\) −0.972400 −0.0502816
\(375\) 0 0
\(376\) 0.620786 0.0320146
\(377\) −3.91951 −0.201865
\(378\) 0 0
\(379\) 33.1031 1.70039 0.850195 0.526467i \(-0.176484\pi\)
0.850195 + 0.526467i \(0.176484\pi\)
\(380\) 14.0993 0.723281
\(381\) 0 0
\(382\) 0.535543 0.0274008
\(383\) 29.4067 1.50261 0.751307 0.659953i \(-0.229424\pi\)
0.751307 + 0.659953i \(0.229424\pi\)
\(384\) 0 0
\(385\) −4.46107 −0.227357
\(386\) 0.511251 0.0260220
\(387\) 0 0
\(388\) 32.8718 1.66881
\(389\) 22.2547 1.12836 0.564178 0.825653i \(-0.309193\pi\)
0.564178 + 0.825653i \(0.309193\pi\)
\(390\) 0 0
\(391\) −31.4485 −1.59042
\(392\) −0.146522 −0.00740047
\(393\) 0 0
\(394\) 0.900692 0.0453762
\(395\) 15.2821 0.768926
\(396\) 0 0
\(397\) 15.2378 0.764765 0.382383 0.924004i \(-0.375104\pi\)
0.382383 + 0.924004i \(0.375104\pi\)
\(398\) 0.727307 0.0364566
\(399\) 0 0
\(400\) −15.7913 −0.789564
\(401\) 7.18602 0.358853 0.179426 0.983771i \(-0.442576\pi\)
0.179426 + 0.983771i \(0.442576\pi\)
\(402\) 0 0
\(403\) −33.0864 −1.64815
\(404\) 4.40000 0.218908
\(405\) 0 0
\(406\) 0.0370905 0.00184077
\(407\) −36.5999 −1.81419
\(408\) 0 0
\(409\) 13.1266 0.649067 0.324534 0.945874i \(-0.394793\pi\)
0.324534 + 0.945874i \(0.394793\pi\)
\(410\) 0.0586588 0.00289695
\(411\) 0 0
\(412\) 24.5758 1.21076
\(413\) 7.49969 0.369036
\(414\) 0 0
\(415\) −15.3557 −0.753780
\(416\) −1.70113 −0.0834046
\(417\) 0 0
\(418\) 1.10433 0.0540145
\(419\) 23.9348 1.16929 0.584645 0.811289i \(-0.301234\pi\)
0.584645 + 0.811289i \(0.301234\pi\)
\(420\) 0 0
\(421\) −3.33899 −0.162732 −0.0813662 0.996684i \(-0.525928\pi\)
−0.0813662 + 0.996684i \(0.525928\pi\)
\(422\) −0.586265 −0.0285389
\(423\) 0 0
\(424\) −0.765027 −0.0371530
\(425\) 24.0461 1.16641
\(426\) 0 0
\(427\) 14.3692 0.695375
\(428\) 5.26004 0.254254
\(429\) 0 0
\(430\) 0.238552 0.0115040
\(431\) 18.6000 0.895932 0.447966 0.894051i \(-0.352149\pi\)
0.447966 + 0.894051i \(0.352149\pi\)
\(432\) 0 0
\(433\) −10.1711 −0.488792 −0.244396 0.969676i \(-0.578590\pi\)
−0.244396 + 0.969676i \(0.578590\pi\)
\(434\) 0.313098 0.0150292
\(435\) 0 0
\(436\) −0.849862 −0.0407010
\(437\) 35.7152 1.70849
\(438\) 0 0
\(439\) 5.54172 0.264492 0.132246 0.991217i \(-0.457781\pi\)
0.132246 + 0.991217i \(0.457781\pi\)
\(440\) 0.653645 0.0311613
\(441\) 0 0
\(442\) 0.862495 0.0410247
\(443\) 11.7233 0.556989 0.278495 0.960438i \(-0.410165\pi\)
0.278495 + 0.960438i \(0.410165\pi\)
\(444\) 0 0
\(445\) −3.21108 −0.152220
\(446\) 0.498161 0.0235886
\(447\) 0 0
\(448\) −7.96779 −0.376443
\(449\) 26.5397 1.25249 0.626243 0.779628i \(-0.284592\pi\)
0.626243 + 0.779628i \(0.284592\pi\)
\(450\) 0 0
\(451\) −6.83904 −0.322038
\(452\) −34.5322 −1.62426
\(453\) 0 0
\(454\) 0.178439 0.00837457
\(455\) 3.95686 0.185501
\(456\) 0 0
\(457\) 9.91495 0.463802 0.231901 0.972739i \(-0.425505\pi\)
0.231901 + 0.972739i \(0.425505\pi\)
\(458\) −0.843412 −0.0394101
\(459\) 0 0
\(460\) 10.5662 0.492654
\(461\) 1.17683 0.0548107 0.0274053 0.999624i \(-0.491276\pi\)
0.0274053 + 0.999624i \(0.491276\pi\)
\(462\) 0 0
\(463\) 19.2312 0.893751 0.446875 0.894596i \(-0.352537\pi\)
0.446875 + 0.894596i \(0.352537\pi\)
\(464\) 4.04073 0.187586
\(465\) 0 0
\(466\) 0.671458 0.0311047
\(467\) −22.2523 −1.02972 −0.514858 0.857276i \(-0.672155\pi\)
−0.514858 + 0.857276i \(0.672155\pi\)
\(468\) 0 0
\(469\) 7.55792 0.348992
\(470\) 0.158644 0.00731768
\(471\) 0 0
\(472\) −1.09887 −0.0505795
\(473\) −27.8128 −1.27883
\(474\) 0 0
\(475\) −27.3085 −1.25300
\(476\) 12.1493 0.556861
\(477\) 0 0
\(478\) 0.618603 0.0282943
\(479\) −5.63308 −0.257382 −0.128691 0.991685i \(-0.541078\pi\)
−0.128691 + 0.991685i \(0.541078\pi\)
\(480\) 0 0
\(481\) 32.4632 1.48019
\(482\) −0.705117 −0.0321172
\(483\) 0 0
\(484\) −16.1063 −0.732103
\(485\) 16.8066 0.763148
\(486\) 0 0
\(487\) 25.9817 1.17734 0.588672 0.808372i \(-0.299651\pi\)
0.588672 + 0.808372i \(0.299651\pi\)
\(488\) −2.10540 −0.0953071
\(489\) 0 0
\(490\) −0.0374440 −0.00169155
\(491\) 25.7518 1.16216 0.581081 0.813846i \(-0.302630\pi\)
0.581081 + 0.813846i \(0.302630\pi\)
\(492\) 0 0
\(493\) −6.15300 −0.277117
\(494\) −0.979513 −0.0440704
\(495\) 0 0
\(496\) 34.1097 1.53157
\(497\) −15.2047 −0.682024
\(498\) 0 0
\(499\) 29.1717 1.30591 0.652953 0.757398i \(-0.273530\pi\)
0.652953 + 0.757398i \(0.273530\pi\)
\(500\) −18.2910 −0.817997
\(501\) 0 0
\(502\) −0.515358 −0.0230015
\(503\) 13.8331 0.616787 0.308393 0.951259i \(-0.400209\pi\)
0.308393 + 0.951259i \(0.400209\pi\)
\(504\) 0 0
\(505\) 2.24962 0.100107
\(506\) 0.827600 0.0367913
\(507\) 0 0
\(508\) −1.99866 −0.0886761
\(509\) −6.56616 −0.291040 −0.145520 0.989355i \(-0.546485\pi\)
−0.145520 + 0.989355i \(0.546485\pi\)
\(510\) 0 0
\(511\) −1.99435 −0.0882249
\(512\) 2.92355 0.129204
\(513\) 0 0
\(514\) −0.135605 −0.00598127
\(515\) 12.5651 0.553683
\(516\) 0 0
\(517\) −18.4963 −0.813466
\(518\) −0.307201 −0.0134976
\(519\) 0 0
\(520\) −0.579767 −0.0254245
\(521\) 5.05524 0.221474 0.110737 0.993850i \(-0.464679\pi\)
0.110737 + 0.993850i \(0.464679\pi\)
\(522\) 0 0
\(523\) 11.1440 0.487292 0.243646 0.969864i \(-0.421656\pi\)
0.243646 + 0.969864i \(0.421656\pi\)
\(524\) 4.91500 0.214713
\(525\) 0 0
\(526\) 0.0339695 0.00148114
\(527\) −51.9403 −2.26256
\(528\) 0 0
\(529\) 3.76551 0.163718
\(530\) −0.195505 −0.00849219
\(531\) 0 0
\(532\) −13.7976 −0.598202
\(533\) 6.06606 0.262750
\(534\) 0 0
\(535\) 2.68934 0.116270
\(536\) −1.10740 −0.0478324
\(537\) 0 0
\(538\) 0.839768 0.0362050
\(539\) 4.36561 0.188040
\(540\) 0 0
\(541\) −10.6947 −0.459801 −0.229901 0.973214i \(-0.573840\pi\)
−0.229901 + 0.973214i \(0.573840\pi\)
\(542\) 0.150569 0.00646749
\(543\) 0 0
\(544\) −2.67050 −0.114497
\(545\) −0.434515 −0.0186126
\(546\) 0 0
\(547\) −34.1696 −1.46099 −0.730494 0.682919i \(-0.760710\pi\)
−0.730494 + 0.682919i \(0.760710\pi\)
\(548\) 7.07243 0.302119
\(549\) 0 0
\(550\) −0.632799 −0.0269826
\(551\) 6.98780 0.297690
\(552\) 0 0
\(553\) −14.9551 −0.635954
\(554\) −0.0958564 −0.00407255
\(555\) 0 0
\(556\) 14.6053 0.619401
\(557\) −41.7086 −1.76725 −0.883625 0.468195i \(-0.844904\pi\)
−0.883625 + 0.468195i \(0.844904\pi\)
\(558\) 0 0
\(559\) 24.6693 1.04340
\(560\) −4.07924 −0.172379
\(561\) 0 0
\(562\) 0.0859306 0.00362476
\(563\) −21.3267 −0.898814 −0.449407 0.893327i \(-0.648365\pi\)
−0.449407 + 0.893327i \(0.648365\pi\)
\(564\) 0 0
\(565\) −17.6555 −0.742773
\(566\) −0.325099 −0.0136649
\(567\) 0 0
\(568\) 2.22782 0.0934773
\(569\) −28.0181 −1.17458 −0.587290 0.809377i \(-0.699805\pi\)
−0.587290 + 0.809377i \(0.699805\pi\)
\(570\) 0 0
\(571\) 40.4176 1.69143 0.845713 0.533638i \(-0.179176\pi\)
0.845713 + 0.533638i \(0.179176\pi\)
\(572\) 33.7862 1.41267
\(573\) 0 0
\(574\) −0.0574035 −0.00239598
\(575\) −20.4654 −0.853467
\(576\) 0 0
\(577\) −19.8471 −0.826244 −0.413122 0.910676i \(-0.635562\pi\)
−0.413122 + 0.910676i \(0.635562\pi\)
\(578\) 0.731052 0.0304078
\(579\) 0 0
\(580\) 2.06732 0.0858408
\(581\) 15.0270 0.623427
\(582\) 0 0
\(583\) 22.7940 0.944029
\(584\) 0.292216 0.0120920
\(585\) 0 0
\(586\) 0.444184 0.0183491
\(587\) 19.8820 0.820616 0.410308 0.911947i \(-0.365421\pi\)
0.410308 + 0.911947i \(0.365421\pi\)
\(588\) 0 0
\(589\) 58.9873 2.43053
\(590\) −0.280819 −0.0115611
\(591\) 0 0
\(592\) −33.4672 −1.37549
\(593\) −29.7636 −1.22225 −0.611123 0.791536i \(-0.709282\pi\)
−0.611123 + 0.791536i \(0.709282\pi\)
\(594\) 0 0
\(595\) 6.21164 0.254653
\(596\) −28.8560 −1.18199
\(597\) 0 0
\(598\) −0.734061 −0.0300180
\(599\) 39.5210 1.61478 0.807392 0.590016i \(-0.200878\pi\)
0.807392 + 0.590016i \(0.200878\pi\)
\(600\) 0 0
\(601\) −8.39771 −0.342550 −0.171275 0.985223i \(-0.554789\pi\)
−0.171275 + 0.985223i \(0.554789\pi\)
\(602\) −0.233447 −0.00951459
\(603\) 0 0
\(604\) −3.42706 −0.139445
\(605\) −8.23476 −0.334791
\(606\) 0 0
\(607\) −8.95531 −0.363485 −0.181742 0.983346i \(-0.558174\pi\)
−0.181742 + 0.983346i \(0.558174\pi\)
\(608\) 3.03282 0.122997
\(609\) 0 0
\(610\) −0.538041 −0.0217847
\(611\) 16.4058 0.663706
\(612\) 0 0
\(613\) −20.6982 −0.835991 −0.417995 0.908449i \(-0.637267\pi\)
−0.417995 + 0.908449i \(0.637267\pi\)
\(614\) 0.909688 0.0367120
\(615\) 0 0
\(616\) −0.639657 −0.0257725
\(617\) −5.71815 −0.230204 −0.115102 0.993354i \(-0.536720\pi\)
−0.115102 + 0.993354i \(0.536720\pi\)
\(618\) 0 0
\(619\) −41.8747 −1.68309 −0.841544 0.540189i \(-0.818353\pi\)
−0.841544 + 0.540189i \(0.818353\pi\)
\(620\) 17.4512 0.700858
\(621\) 0 0
\(622\) −1.04029 −0.0417118
\(623\) 3.14237 0.125896
\(624\) 0 0
\(625\) 10.4272 0.417087
\(626\) −0.882897 −0.0352876
\(627\) 0 0
\(628\) 26.0662 1.04015
\(629\) 50.9620 2.03199
\(630\) 0 0
\(631\) −0.116518 −0.00463852 −0.00231926 0.999997i \(-0.500738\pi\)
−0.00231926 + 0.999997i \(0.500738\pi\)
\(632\) 2.19124 0.0871630
\(633\) 0 0
\(634\) 0.971981 0.0386023
\(635\) −1.02187 −0.0405516
\(636\) 0 0
\(637\) −3.87219 −0.153422
\(638\) 0.161923 0.00641058
\(639\) 0 0
\(640\) 1.19620 0.0472839
\(641\) 12.7160 0.502250 0.251125 0.967955i \(-0.419199\pi\)
0.251125 + 0.967955i \(0.419199\pi\)
\(642\) 0 0
\(643\) 5.87970 0.231873 0.115936 0.993257i \(-0.463013\pi\)
0.115936 + 0.993257i \(0.463013\pi\)
\(644\) −10.3401 −0.407458
\(645\) 0 0
\(646\) −1.53768 −0.0604992
\(647\) −24.5196 −0.963966 −0.481983 0.876181i \(-0.660083\pi\)
−0.481983 + 0.876181i \(0.660083\pi\)
\(648\) 0 0
\(649\) 32.7407 1.28519
\(650\) 0.561277 0.0220151
\(651\) 0 0
\(652\) 5.08138 0.199002
\(653\) 26.9393 1.05421 0.527107 0.849799i \(-0.323277\pi\)
0.527107 + 0.849799i \(0.323277\pi\)
\(654\) 0 0
\(655\) 2.51292 0.0981881
\(656\) −6.25367 −0.244165
\(657\) 0 0
\(658\) −0.155249 −0.00605222
\(659\) −25.2200 −0.982432 −0.491216 0.871038i \(-0.663447\pi\)
−0.491216 + 0.871038i \(0.663447\pi\)
\(660\) 0 0
\(661\) −18.6507 −0.725429 −0.362714 0.931900i \(-0.618150\pi\)
−0.362714 + 0.931900i \(0.618150\pi\)
\(662\) 0.689034 0.0267801
\(663\) 0 0
\(664\) −2.20179 −0.0854460
\(665\) −7.05440 −0.273558
\(666\) 0 0
\(667\) 5.23676 0.202768
\(668\) 4.22006 0.163279
\(669\) 0 0
\(670\) −0.282999 −0.0109332
\(671\) 62.7304 2.42168
\(672\) 0 0
\(673\) 17.2225 0.663879 0.331939 0.943301i \(-0.392297\pi\)
0.331939 + 0.943301i \(0.392297\pi\)
\(674\) 0.824015 0.0317399
\(675\) 0 0
\(676\) −3.98501 −0.153269
\(677\) 14.8363 0.570207 0.285104 0.958497i \(-0.407972\pi\)
0.285104 + 0.958497i \(0.407972\pi\)
\(678\) 0 0
\(679\) −16.4469 −0.631175
\(680\) −0.910141 −0.0349023
\(681\) 0 0
\(682\) 1.36686 0.0523400
\(683\) 6.22360 0.238139 0.119070 0.992886i \(-0.462009\pi\)
0.119070 + 0.992886i \(0.462009\pi\)
\(684\) 0 0
\(685\) 3.61597 0.138159
\(686\) 0.0366427 0.00139903
\(687\) 0 0
\(688\) −25.4323 −0.969596
\(689\) −20.2177 −0.770232
\(690\) 0 0
\(691\) −16.4440 −0.625561 −0.312780 0.949825i \(-0.601260\pi\)
−0.312780 + 0.949825i \(0.601260\pi\)
\(692\) −2.73515 −0.103975
\(693\) 0 0
\(694\) −0.654437 −0.0248421
\(695\) 7.46733 0.283252
\(696\) 0 0
\(697\) 9.52275 0.360700
\(698\) 1.11122 0.0420604
\(699\) 0 0
\(700\) 7.90626 0.298829
\(701\) 33.7827 1.27595 0.637977 0.770055i \(-0.279771\pi\)
0.637977 + 0.770055i \(0.279771\pi\)
\(702\) 0 0
\(703\) −57.8762 −2.18284
\(704\) −34.7843 −1.31098
\(705\) 0 0
\(706\) −0.858859 −0.0323236
\(707\) −2.20148 −0.0827950
\(708\) 0 0
\(709\) 49.4454 1.85696 0.928481 0.371380i \(-0.121115\pi\)
0.928481 + 0.371380i \(0.121115\pi\)
\(710\) 0.569326 0.0213664
\(711\) 0 0
\(712\) −0.460425 −0.0172552
\(713\) 44.2059 1.65552
\(714\) 0 0
\(715\) 17.2741 0.646015
\(716\) −44.2406 −1.65335
\(717\) 0 0
\(718\) −1.22398 −0.0456785
\(719\) 39.8435 1.48591 0.742955 0.669341i \(-0.233424\pi\)
0.742955 + 0.669341i \(0.233424\pi\)
\(720\) 0 0
\(721\) −12.2962 −0.457933
\(722\) 1.05009 0.0390803
\(723\) 0 0
\(724\) −19.4684 −0.723538
\(725\) −4.00413 −0.148709
\(726\) 0 0
\(727\) −15.6229 −0.579421 −0.289710 0.957114i \(-0.593559\pi\)
−0.289710 + 0.957114i \(0.593559\pi\)
\(728\) 0.567360 0.0210278
\(729\) 0 0
\(730\) 0.0746766 0.00276390
\(731\) 38.7269 1.43236
\(732\) 0 0
\(733\) 37.9306 1.40100 0.700499 0.713653i \(-0.252961\pi\)
0.700499 + 0.713653i \(0.252961\pi\)
\(734\) 0.185359 0.00684171
\(735\) 0 0
\(736\) 2.27284 0.0837779
\(737\) 32.9949 1.21538
\(738\) 0 0
\(739\) 24.3400 0.895362 0.447681 0.894193i \(-0.352250\pi\)
0.447681 + 0.894193i \(0.352250\pi\)
\(740\) −17.1225 −0.629436
\(741\) 0 0
\(742\) 0.191321 0.00702362
\(743\) −29.3253 −1.07584 −0.537920 0.842996i \(-0.680790\pi\)
−0.537920 + 0.842996i \(0.680790\pi\)
\(744\) 0 0
\(745\) −14.7534 −0.540522
\(746\) 0.717842 0.0262821
\(747\) 0 0
\(748\) 53.0390 1.93930
\(749\) −2.63179 −0.0961634
\(750\) 0 0
\(751\) −1.30594 −0.0476543 −0.0238272 0.999716i \(-0.507585\pi\)
−0.0238272 + 0.999716i \(0.507585\pi\)
\(752\) −16.9131 −0.616759
\(753\) 0 0
\(754\) −0.143621 −0.00523039
\(755\) −1.75218 −0.0637682
\(756\) 0 0
\(757\) −16.6342 −0.604580 −0.302290 0.953216i \(-0.597751\pi\)
−0.302290 + 0.953216i \(0.597751\pi\)
\(758\) 1.21299 0.0440577
\(759\) 0 0
\(760\) 1.03362 0.0374935
\(761\) −20.4601 −0.741677 −0.370838 0.928697i \(-0.620930\pi\)
−0.370838 + 0.928697i \(0.620930\pi\)
\(762\) 0 0
\(763\) 0.425217 0.0153939
\(764\) −29.2109 −1.05681
\(765\) 0 0
\(766\) 1.07754 0.0389332
\(767\) −29.0402 −1.04858
\(768\) 0 0
\(769\) 37.8309 1.36422 0.682108 0.731251i \(-0.261063\pi\)
0.682108 + 0.731251i \(0.261063\pi\)
\(770\) −0.163466 −0.00589091
\(771\) 0 0
\(772\) −27.8859 −1.00363
\(773\) −23.3436 −0.839613 −0.419806 0.907614i \(-0.637902\pi\)
−0.419806 + 0.907614i \(0.637902\pi\)
\(774\) 0 0
\(775\) −33.8007 −1.21416
\(776\) 2.40983 0.0865080
\(777\) 0 0
\(778\) 0.815472 0.0292361
\(779\) −10.8147 −0.387478
\(780\) 0 0
\(781\) −66.3778 −2.37518
\(782\) −1.15236 −0.0412083
\(783\) 0 0
\(784\) 3.99195 0.142569
\(785\) 13.3270 0.475662
\(786\) 0 0
\(787\) 11.4350 0.407613 0.203806 0.979011i \(-0.434669\pi\)
0.203806 + 0.979011i \(0.434669\pi\)
\(788\) −49.1277 −1.75010
\(789\) 0 0
\(790\) 0.559978 0.0199231
\(791\) 17.2777 0.614324
\(792\) 0 0
\(793\) −55.6403 −1.97585
\(794\) 0.558356 0.0198153
\(795\) 0 0
\(796\) −39.6705 −1.40609
\(797\) 46.3966 1.64345 0.821726 0.569883i \(-0.193012\pi\)
0.821726 + 0.569883i \(0.193012\pi\)
\(798\) 0 0
\(799\) 25.7544 0.911126
\(800\) −1.73785 −0.0614424
\(801\) 0 0
\(802\) 0.263316 0.00929800
\(803\) −8.70656 −0.307248
\(804\) 0 0
\(805\) −5.28667 −0.186331
\(806\) −1.21238 −0.0427041
\(807\) 0 0
\(808\) 0.322564 0.0113478
\(809\) 38.6606 1.35923 0.679617 0.733567i \(-0.262146\pi\)
0.679617 + 0.733567i \(0.262146\pi\)
\(810\) 0 0
\(811\) 18.9107 0.664043 0.332021 0.943272i \(-0.392269\pi\)
0.332021 + 0.943272i \(0.392269\pi\)
\(812\) −2.02308 −0.0709962
\(813\) 0 0
\(814\) −1.34112 −0.0470062
\(815\) 2.59799 0.0910037
\(816\) 0 0
\(817\) −43.9811 −1.53870
\(818\) 0.480994 0.0168175
\(819\) 0 0
\(820\) −3.19951 −0.111732
\(821\) 41.0661 1.43322 0.716608 0.697477i \(-0.245694\pi\)
0.716608 + 0.697477i \(0.245694\pi\)
\(822\) 0 0
\(823\) −10.9130 −0.380402 −0.190201 0.981745i \(-0.560914\pi\)
−0.190201 + 0.981745i \(0.560914\pi\)
\(824\) 1.80166 0.0627637
\(825\) 0 0
\(826\) 0.274809 0.00956184
\(827\) 16.0479 0.558041 0.279021 0.960285i \(-0.409990\pi\)
0.279021 + 0.960285i \(0.409990\pi\)
\(828\) 0 0
\(829\) −48.1452 −1.67215 −0.836076 0.548614i \(-0.815156\pi\)
−0.836076 + 0.548614i \(0.815156\pi\)
\(830\) −0.562673 −0.0195307
\(831\) 0 0
\(832\) 30.8528 1.06963
\(833\) −6.07872 −0.210615
\(834\) 0 0
\(835\) 2.15762 0.0746675
\(836\) −60.2350 −2.08327
\(837\) 0 0
\(838\) 0.877036 0.0302967
\(839\) 28.2575 0.975558 0.487779 0.872967i \(-0.337807\pi\)
0.487779 + 0.872967i \(0.337807\pi\)
\(840\) 0 0
\(841\) −27.9754 −0.964669
\(842\) −0.122350 −0.00421645
\(843\) 0 0
\(844\) 31.9775 1.10071
\(845\) −2.03744 −0.0700901
\(846\) 0 0
\(847\) 8.05854 0.276895
\(848\) 20.8430 0.715750
\(849\) 0 0
\(850\) 0.881115 0.0302220
\(851\) −43.3733 −1.48682
\(852\) 0 0
\(853\) −8.89198 −0.304456 −0.152228 0.988345i \(-0.548645\pi\)
−0.152228 + 0.988345i \(0.548645\pi\)
\(854\) 0.526528 0.0180174
\(855\) 0 0
\(856\) 0.385614 0.0131800
\(857\) −6.16814 −0.210700 −0.105350 0.994435i \(-0.533596\pi\)
−0.105350 + 0.994435i \(0.533596\pi\)
\(858\) 0 0
\(859\) −13.4714 −0.459640 −0.229820 0.973233i \(-0.573814\pi\)
−0.229820 + 0.973233i \(0.573814\pi\)
\(860\) −13.0117 −0.443694
\(861\) 0 0
\(862\) 0.681556 0.0232139
\(863\) −8.88588 −0.302479 −0.151239 0.988497i \(-0.548326\pi\)
−0.151239 + 0.988497i \(0.548326\pi\)
\(864\) 0 0
\(865\) −1.39842 −0.0475477
\(866\) −0.372697 −0.0126648
\(867\) 0 0
\(868\) −17.0778 −0.579657
\(869\) −65.2880 −2.21474
\(870\) 0 0
\(871\) −29.2657 −0.991629
\(872\) −0.0623035 −0.00210986
\(873\) 0 0
\(874\) 1.30870 0.0442676
\(875\) 9.15163 0.309382
\(876\) 0 0
\(877\) −41.0939 −1.38764 −0.693821 0.720148i \(-0.744074\pi\)
−0.693821 + 0.720148i \(0.744074\pi\)
\(878\) 0.203064 0.00685307
\(879\) 0 0
\(880\) −17.8084 −0.600320
\(881\) −48.4814 −1.63338 −0.816690 0.577076i \(-0.804194\pi\)
−0.816690 + 0.577076i \(0.804194\pi\)
\(882\) 0 0
\(883\) −14.3235 −0.482025 −0.241012 0.970522i \(-0.577479\pi\)
−0.241012 + 0.970522i \(0.577479\pi\)
\(884\) −47.0443 −1.58227
\(885\) 0 0
\(886\) 0.429573 0.0144318
\(887\) −16.4012 −0.550700 −0.275350 0.961344i \(-0.588794\pi\)
−0.275350 + 0.961344i \(0.588794\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −0.117663 −0.00394407
\(891\) 0 0
\(892\) −27.1719 −0.909783
\(893\) −29.2486 −0.978768
\(894\) 0 0
\(895\) −22.6192 −0.756077
\(896\) −1.17060 −0.0391070
\(897\) 0 0
\(898\) 0.972488 0.0324523
\(899\) 8.64903 0.288461
\(900\) 0 0
\(901\) −31.7385 −1.05736
\(902\) −0.250601 −0.00834411
\(903\) 0 0
\(904\) −2.53156 −0.0841983
\(905\) −9.95376 −0.330874
\(906\) 0 0
\(907\) 3.75725 0.124757 0.0623787 0.998053i \(-0.480131\pi\)
0.0623787 + 0.998053i \(0.480131\pi\)
\(908\) −9.73287 −0.322997
\(909\) 0 0
\(910\) 0.144990 0.00480638
\(911\) 36.8735 1.22167 0.610837 0.791756i \(-0.290833\pi\)
0.610837 + 0.791756i \(0.290833\pi\)
\(912\) 0 0
\(913\) 65.6022 2.17112
\(914\) 0.363311 0.0120173
\(915\) 0 0
\(916\) 46.0034 1.52000
\(917\) −2.45915 −0.0812083
\(918\) 0 0
\(919\) 23.2231 0.766060 0.383030 0.923736i \(-0.374881\pi\)
0.383030 + 0.923736i \(0.374881\pi\)
\(920\) 0.774613 0.0255382
\(921\) 0 0
\(922\) 0.0431225 0.00142016
\(923\) 58.8755 1.93791
\(924\) 0 0
\(925\) 33.1640 1.09043
\(926\) 0.704685 0.0231574
\(927\) 0 0
\(928\) 0.444688 0.0145976
\(929\) −46.8936 −1.53853 −0.769265 0.638930i \(-0.779377\pi\)
−0.769265 + 0.638930i \(0.779377\pi\)
\(930\) 0 0
\(931\) 6.90344 0.226251
\(932\) −36.6243 −1.19967
\(933\) 0 0
\(934\) −0.815387 −0.0266803
\(935\) 27.1176 0.886841
\(936\) 0 0
\(937\) −6.16009 −0.201241 −0.100621 0.994925i \(-0.532083\pi\)
−0.100621 + 0.994925i \(0.532083\pi\)
\(938\) 0.276943 0.00904250
\(939\) 0 0
\(940\) −8.65312 −0.282234
\(941\) −40.2409 −1.31182 −0.655908 0.754841i \(-0.727714\pi\)
−0.655908 + 0.754841i \(0.727714\pi\)
\(942\) 0 0
\(943\) −8.10472 −0.263926
\(944\) 29.9384 0.974411
\(945\) 0 0
\(946\) −1.01914 −0.0331350
\(947\) −0.731230 −0.0237618 −0.0118809 0.999929i \(-0.503782\pi\)
−0.0118809 + 0.999929i \(0.503782\pi\)
\(948\) 0 0
\(949\) 7.72250 0.250683
\(950\) −1.00066 −0.0324657
\(951\) 0 0
\(952\) 0.890665 0.0288666
\(953\) −2.38255 −0.0771785 −0.0385892 0.999255i \(-0.512286\pi\)
−0.0385892 + 0.999255i \(0.512286\pi\)
\(954\) 0 0
\(955\) −14.9349 −0.483281
\(956\) −33.7414 −1.09127
\(957\) 0 0
\(958\) −0.206412 −0.00666885
\(959\) −3.53859 −0.114267
\(960\) 0 0
\(961\) 42.0105 1.35518
\(962\) 1.18954 0.0383523
\(963\) 0 0
\(964\) 38.4602 1.23872
\(965\) −14.2574 −0.458962
\(966\) 0 0
\(967\) −53.9701 −1.73556 −0.867781 0.496948i \(-0.834454\pi\)
−0.867781 + 0.496948i \(0.834454\pi\)
\(968\) −1.18075 −0.0379508
\(969\) 0 0
\(970\) 0.615839 0.0197734
\(971\) 31.0823 0.997477 0.498739 0.866752i \(-0.333797\pi\)
0.498739 + 0.866752i \(0.333797\pi\)
\(972\) 0 0
\(973\) −7.30754 −0.234269
\(974\) 0.952041 0.0305054
\(975\) 0 0
\(976\) 57.3611 1.83608
\(977\) 12.7232 0.407051 0.203526 0.979070i \(-0.434760\pi\)
0.203526 + 0.979070i \(0.434760\pi\)
\(978\) 0 0
\(979\) 13.7183 0.438440
\(980\) 2.04236 0.0652409
\(981\) 0 0
\(982\) 0.943617 0.0301120
\(983\) −49.5307 −1.57978 −0.789892 0.613246i \(-0.789863\pi\)
−0.789892 + 0.613246i \(0.789863\pi\)
\(984\) 0 0
\(985\) −25.1179 −0.800322
\(986\) −0.225463 −0.00718020
\(987\) 0 0
\(988\) 53.4270 1.69974
\(989\) −32.9601 −1.04807
\(990\) 0 0
\(991\) 38.0811 1.20969 0.604843 0.796345i \(-0.293236\pi\)
0.604843 + 0.796345i \(0.293236\pi\)
\(992\) 3.75382 0.119184
\(993\) 0 0
\(994\) −0.557142 −0.0176715
\(995\) −20.2826 −0.643003
\(996\) 0 0
\(997\) 11.9772 0.379320 0.189660 0.981850i \(-0.439261\pi\)
0.189660 + 0.981850i \(0.439261\pi\)
\(998\) 1.06893 0.0338365
\(999\) 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 \(a_p\))