Properties

Label 8001.2.a.o.1.2
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.29288\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.29288 q^{2}\) \(+3.25728 q^{4}\) \(+0.132682 q^{5}\) \(+1.00000 q^{7}\) \(-2.88278 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.29288 q^{2}\) \(+3.25728 q^{4}\) \(+0.132682 q^{5}\) \(+1.00000 q^{7}\) \(-2.88278 q^{8}\) \(-0.304223 q^{10}\) \(+1.38028 q^{11}\) \(+3.00012 q^{13}\) \(-2.29288 q^{14}\) \(+0.0952967 q^{16}\) \(-4.60865 q^{17}\) \(-1.78380 q^{19}\) \(+0.432182 q^{20}\) \(-3.16481 q^{22}\) \(-6.02678 q^{23}\) \(-4.98240 q^{25}\) \(-6.87890 q^{26}\) \(+3.25728 q^{28}\) \(-2.00225 q^{29}\) \(+9.54114 q^{31}\) \(+5.54705 q^{32}\) \(+10.5670 q^{34}\) \(+0.132682 q^{35}\) \(+2.84160 q^{37}\) \(+4.09003 q^{38}\) \(-0.382493 q^{40}\) \(-2.18268 q^{41}\) \(+9.51578 q^{43}\) \(+4.49595 q^{44}\) \(+13.8187 q^{46}\) \(-2.52668 q^{47}\) \(+1.00000 q^{49}\) \(+11.4240 q^{50}\) \(+9.77222 q^{52}\) \(+8.38962 q^{53}\) \(+0.183138 q^{55}\) \(-2.88278 q^{56}\) \(+4.59090 q^{58}\) \(-7.78977 q^{59}\) \(+3.77711 q^{61}\) \(-21.8766 q^{62}\) \(-12.9093 q^{64}\) \(+0.398062 q^{65}\) \(-10.1772 q^{67}\) \(-15.0116 q^{68}\) \(-0.304223 q^{70}\) \(+2.19559 q^{71}\) \(+1.19059 q^{73}\) \(-6.51543 q^{74}\) \(-5.81033 q^{76}\) \(+1.38028 q^{77}\) \(-10.3605 q^{79}\) \(+0.0126442 q^{80}\) \(+5.00462 q^{82}\) \(-1.81059 q^{83}\) \(-0.611485 q^{85}\) \(-21.8185 q^{86}\) \(-3.97904 q^{88}\) \(+7.25065 q^{89}\) \(+3.00012 q^{91}\) \(-19.6309 q^{92}\) \(+5.79337 q^{94}\) \(-0.236678 q^{95}\) \(+2.14183 q^{97}\) \(-2.29288 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29288 −1.62131 −0.810654 0.585526i \(-0.800888\pi\)
−0.810654 + 0.585526i \(0.800888\pi\)
\(3\) 0 0
\(4\) 3.25728 1.62864
\(5\) 0.132682 0.0593372 0.0296686 0.999560i \(-0.490555\pi\)
0.0296686 + 0.999560i \(0.490555\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.88278 −1.01922
\(9\) 0 0
\(10\) −0.304223 −0.0962039
\(11\) 1.38028 0.416170 0.208085 0.978111i \(-0.433277\pi\)
0.208085 + 0.978111i \(0.433277\pi\)
\(12\) 0 0
\(13\) 3.00012 0.832083 0.416042 0.909346i \(-0.363417\pi\)
0.416042 + 0.909346i \(0.363417\pi\)
\(14\) −2.29288 −0.612797
\(15\) 0 0
\(16\) 0.0952967 0.0238242
\(17\) −4.60865 −1.11776 −0.558880 0.829248i \(-0.688769\pi\)
−0.558880 + 0.829248i \(0.688769\pi\)
\(18\) 0 0
\(19\) −1.78380 −0.409232 −0.204616 0.978842i \(-0.565595\pi\)
−0.204616 + 0.978842i \(0.565595\pi\)
\(20\) 0.432182 0.0966388
\(21\) 0 0
\(22\) −3.16481 −0.674739
\(23\) −6.02678 −1.25667 −0.628336 0.777942i \(-0.716264\pi\)
−0.628336 + 0.777942i \(0.716264\pi\)
\(24\) 0 0
\(25\) −4.98240 −0.996479
\(26\) −6.87890 −1.34906
\(27\) 0 0
\(28\) 3.25728 0.615567
\(29\) −2.00225 −0.371808 −0.185904 0.982568i \(-0.559521\pi\)
−0.185904 + 0.982568i \(0.559521\pi\)
\(30\) 0 0
\(31\) 9.54114 1.71364 0.856820 0.515616i \(-0.172437\pi\)
0.856820 + 0.515616i \(0.172437\pi\)
\(32\) 5.54705 0.980590
\(33\) 0 0
\(34\) 10.5670 1.81223
\(35\) 0.132682 0.0224274
\(36\) 0 0
\(37\) 2.84160 0.467156 0.233578 0.972338i \(-0.424957\pi\)
0.233578 + 0.972338i \(0.424957\pi\)
\(38\) 4.09003 0.663491
\(39\) 0 0
\(40\) −0.382493 −0.0604774
\(41\) −2.18268 −0.340878 −0.170439 0.985368i \(-0.554519\pi\)
−0.170439 + 0.985368i \(0.554519\pi\)
\(42\) 0 0
\(43\) 9.51578 1.45114 0.725571 0.688147i \(-0.241576\pi\)
0.725571 + 0.688147i \(0.241576\pi\)
\(44\) 4.49595 0.677790
\(45\) 0 0
\(46\) 13.8187 2.03745
\(47\) −2.52668 −0.368554 −0.184277 0.982874i \(-0.558994\pi\)
−0.184277 + 0.982874i \(0.558994\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 11.4240 1.61560
\(51\) 0 0
\(52\) 9.77222 1.35516
\(53\) 8.38962 1.15240 0.576202 0.817308i \(-0.304534\pi\)
0.576202 + 0.817308i \(0.304534\pi\)
\(54\) 0 0
\(55\) 0.183138 0.0246944
\(56\) −2.88278 −0.385227
\(57\) 0 0
\(58\) 4.59090 0.602815
\(59\) −7.78977 −1.01414 −0.507071 0.861904i \(-0.669272\pi\)
−0.507071 + 0.861904i \(0.669272\pi\)
\(60\) 0 0
\(61\) 3.77711 0.483609 0.241804 0.970325i \(-0.422261\pi\)
0.241804 + 0.970325i \(0.422261\pi\)
\(62\) −21.8766 −2.77834
\(63\) 0 0
\(64\) −12.9093 −1.61366
\(65\) 0.398062 0.0493735
\(66\) 0 0
\(67\) −10.1772 −1.24334 −0.621670 0.783280i \(-0.713545\pi\)
−0.621670 + 0.783280i \(0.713545\pi\)
\(68\) −15.0116 −1.82043
\(69\) 0 0
\(70\) −0.304223 −0.0363616
\(71\) 2.19559 0.260569 0.130284 0.991477i \(-0.458411\pi\)
0.130284 + 0.991477i \(0.458411\pi\)
\(72\) 0 0
\(73\) 1.19059 0.139348 0.0696738 0.997570i \(-0.477804\pi\)
0.0696738 + 0.997570i \(0.477804\pi\)
\(74\) −6.51543 −0.757403
\(75\) 0 0
\(76\) −5.81033 −0.666491
\(77\) 1.38028 0.157297
\(78\) 0 0
\(79\) −10.3605 −1.16565 −0.582826 0.812597i \(-0.698053\pi\)
−0.582826 + 0.812597i \(0.698053\pi\)
\(80\) 0.0126442 0.00141366
\(81\) 0 0
\(82\) 5.00462 0.552668
\(83\) −1.81059 −0.198738 −0.0993688 0.995051i \(-0.531682\pi\)
−0.0993688 + 0.995051i \(0.531682\pi\)
\(84\) 0 0
\(85\) −0.611485 −0.0663248
\(86\) −21.8185 −2.35275
\(87\) 0 0
\(88\) −3.97904 −0.424167
\(89\) 7.25065 0.768567 0.384284 0.923215i \(-0.374448\pi\)
0.384284 + 0.923215i \(0.374448\pi\)
\(90\) 0 0
\(91\) 3.00012 0.314498
\(92\) −19.6309 −2.04666
\(93\) 0 0
\(94\) 5.79337 0.597540
\(95\) −0.236678 −0.0242827
\(96\) 0 0
\(97\) 2.14183 0.217469 0.108735 0.994071i \(-0.465320\pi\)
0.108735 + 0.994071i \(0.465320\pi\)
\(98\) −2.29288 −0.231615
\(99\) 0 0
\(100\) −16.2290 −1.62290
\(101\) −16.2730 −1.61922 −0.809610 0.586969i \(-0.800321\pi\)
−0.809610 + 0.586969i \(0.800321\pi\)
\(102\) 0 0
\(103\) −12.7663 −1.25790 −0.628952 0.777444i \(-0.716516\pi\)
−0.628952 + 0.777444i \(0.716516\pi\)
\(104\) −8.64868 −0.848073
\(105\) 0 0
\(106\) −19.2364 −1.86840
\(107\) −1.40448 −0.135776 −0.0678880 0.997693i \(-0.521626\pi\)
−0.0678880 + 0.997693i \(0.521626\pi\)
\(108\) 0 0
\(109\) 11.1108 1.06422 0.532111 0.846674i \(-0.321399\pi\)
0.532111 + 0.846674i \(0.321399\pi\)
\(110\) −0.419913 −0.0400371
\(111\) 0 0
\(112\) 0.0952967 0.00900469
\(113\) −17.6560 −1.66094 −0.830469 0.557065i \(-0.811927\pi\)
−0.830469 + 0.557065i \(0.811927\pi\)
\(114\) 0 0
\(115\) −0.799646 −0.0745674
\(116\) −6.52187 −0.605540
\(117\) 0 0
\(118\) 17.8610 1.64424
\(119\) −4.60865 −0.422474
\(120\) 0 0
\(121\) −9.09483 −0.826803
\(122\) −8.66043 −0.784079
\(123\) 0 0
\(124\) 31.0781 2.79090
\(125\) −1.32448 −0.118466
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 18.5053 1.63565
\(129\) 0 0
\(130\) −0.912706 −0.0800497
\(131\) −5.73840 −0.501367 −0.250683 0.968069i \(-0.580655\pi\)
−0.250683 + 0.968069i \(0.580655\pi\)
\(132\) 0 0
\(133\) −1.78380 −0.154675
\(134\) 23.3350 2.01584
\(135\) 0 0
\(136\) 13.2857 1.13924
\(137\) 9.98542 0.853112 0.426556 0.904461i \(-0.359727\pi\)
0.426556 + 0.904461i \(0.359727\pi\)
\(138\) 0 0
\(139\) 7.44343 0.631344 0.315672 0.948868i \(-0.397770\pi\)
0.315672 + 0.948868i \(0.397770\pi\)
\(140\) 0.432182 0.0365261
\(141\) 0 0
\(142\) −5.03422 −0.422462
\(143\) 4.14100 0.346288
\(144\) 0 0
\(145\) −0.265662 −0.0220620
\(146\) −2.72987 −0.225925
\(147\) 0 0
\(148\) 9.25587 0.760828
\(149\) −8.64989 −0.708626 −0.354313 0.935127i \(-0.615285\pi\)
−0.354313 + 0.935127i \(0.615285\pi\)
\(150\) 0 0
\(151\) 0.112505 0.00915555 0.00457778 0.999990i \(-0.498543\pi\)
0.00457778 + 0.999990i \(0.498543\pi\)
\(152\) 5.14230 0.417096
\(153\) 0 0
\(154\) −3.16481 −0.255027
\(155\) 1.26594 0.101683
\(156\) 0 0
\(157\) 10.2079 0.814679 0.407340 0.913277i \(-0.366457\pi\)
0.407340 + 0.913277i \(0.366457\pi\)
\(158\) 23.7554 1.88988
\(159\) 0 0
\(160\) 0.735994 0.0581854
\(161\) −6.02678 −0.474977
\(162\) 0 0
\(163\) −12.2432 −0.958964 −0.479482 0.877552i \(-0.659175\pi\)
−0.479482 + 0.877552i \(0.659175\pi\)
\(164\) −7.10961 −0.555167
\(165\) 0 0
\(166\) 4.15145 0.322215
\(167\) 21.7101 1.67998 0.839990 0.542602i \(-0.182561\pi\)
0.839990 + 0.542602i \(0.182561\pi\)
\(168\) 0 0
\(169\) −3.99928 −0.307637
\(170\) 1.40206 0.107533
\(171\) 0 0
\(172\) 30.9955 2.36339
\(173\) 2.24784 0.170900 0.0854501 0.996342i \(-0.472767\pi\)
0.0854501 + 0.996342i \(0.472767\pi\)
\(174\) 0 0
\(175\) −4.98240 −0.376634
\(176\) 0.131536 0.00991490
\(177\) 0 0
\(178\) −16.6248 −1.24608
\(179\) 2.39212 0.178796 0.0893979 0.995996i \(-0.471506\pi\)
0.0893979 + 0.995996i \(0.471506\pi\)
\(180\) 0 0
\(181\) −20.6405 −1.53420 −0.767098 0.641530i \(-0.778300\pi\)
−0.767098 + 0.641530i \(0.778300\pi\)
\(182\) −6.87890 −0.509898
\(183\) 0 0
\(184\) 17.3739 1.28082
\(185\) 0.377029 0.0277197
\(186\) 0 0
\(187\) −6.36122 −0.465178
\(188\) −8.23010 −0.600242
\(189\) 0 0
\(190\) 0.542674 0.0393697
\(191\) 16.1222 1.16656 0.583279 0.812272i \(-0.301769\pi\)
0.583279 + 0.812272i \(0.301769\pi\)
\(192\) 0 0
\(193\) 8.63114 0.621283 0.310642 0.950527i \(-0.399456\pi\)
0.310642 + 0.950527i \(0.399456\pi\)
\(194\) −4.91094 −0.352585
\(195\) 0 0
\(196\) 3.25728 0.232663
\(197\) −0.747074 −0.0532268 −0.0266134 0.999646i \(-0.508472\pi\)
−0.0266134 + 0.999646i \(0.508472\pi\)
\(198\) 0 0
\(199\) −1.78469 −0.126513 −0.0632565 0.997997i \(-0.520149\pi\)
−0.0632565 + 0.997997i \(0.520149\pi\)
\(200\) 14.3631 1.01563
\(201\) 0 0
\(202\) 37.3118 2.62525
\(203\) −2.00225 −0.140530
\(204\) 0 0
\(205\) −0.289603 −0.0202268
\(206\) 29.2716 2.03945
\(207\) 0 0
\(208\) 0.285902 0.0198237
\(209\) −2.46214 −0.170310
\(210\) 0 0
\(211\) −13.0567 −0.898862 −0.449431 0.893315i \(-0.648373\pi\)
−0.449431 + 0.893315i \(0.648373\pi\)
\(212\) 27.3273 1.87685
\(213\) 0 0
\(214\) 3.22029 0.220135
\(215\) 1.26257 0.0861067
\(216\) 0 0
\(217\) 9.54114 0.647695
\(218\) −25.4757 −1.72543
\(219\) 0 0
\(220\) 0.596532 0.0402182
\(221\) −13.8265 −0.930070
\(222\) 0 0
\(223\) −9.47976 −0.634812 −0.317406 0.948290i \(-0.602812\pi\)
−0.317406 + 0.948290i \(0.602812\pi\)
\(224\) 5.54705 0.370628
\(225\) 0 0
\(226\) 40.4830 2.69289
\(227\) −3.99593 −0.265219 −0.132610 0.991168i \(-0.542336\pi\)
−0.132610 + 0.991168i \(0.542336\pi\)
\(228\) 0 0
\(229\) 5.69325 0.376220 0.188110 0.982148i \(-0.439764\pi\)
0.188110 + 0.982148i \(0.439764\pi\)
\(230\) 1.83349 0.120897
\(231\) 0 0
\(232\) 5.77203 0.378952
\(233\) 11.1279 0.729014 0.364507 0.931201i \(-0.381238\pi\)
0.364507 + 0.931201i \(0.381238\pi\)
\(234\) 0 0
\(235\) −0.335245 −0.0218690
\(236\) −25.3734 −1.65167
\(237\) 0 0
\(238\) 10.5670 0.684960
\(239\) 8.65428 0.559799 0.279900 0.960029i \(-0.409699\pi\)
0.279900 + 0.960029i \(0.409699\pi\)
\(240\) 0 0
\(241\) −26.5941 −1.71308 −0.856538 0.516083i \(-0.827390\pi\)
−0.856538 + 0.516083i \(0.827390\pi\)
\(242\) 20.8533 1.34050
\(243\) 0 0
\(244\) 12.3031 0.787624
\(245\) 0.132682 0.00847674
\(246\) 0 0
\(247\) −5.35162 −0.340515
\(248\) −27.5050 −1.74657
\(249\) 0 0
\(250\) 3.03688 0.192069
\(251\) 6.80462 0.429504 0.214752 0.976669i \(-0.431106\pi\)
0.214752 + 0.976669i \(0.431106\pi\)
\(252\) 0 0
\(253\) −8.31864 −0.522989
\(254\) 2.29288 0.143868
\(255\) 0 0
\(256\) −16.6117 −1.03823
\(257\) −25.0375 −1.56180 −0.780898 0.624658i \(-0.785238\pi\)
−0.780898 + 0.624658i \(0.785238\pi\)
\(258\) 0 0
\(259\) 2.84160 0.176568
\(260\) 1.29660 0.0804116
\(261\) 0 0
\(262\) 13.1574 0.812870
\(263\) 18.7441 1.15581 0.577905 0.816104i \(-0.303870\pi\)
0.577905 + 0.816104i \(0.303870\pi\)
\(264\) 0 0
\(265\) 1.11315 0.0683804
\(266\) 4.09003 0.250776
\(267\) 0 0
\(268\) −33.1499 −2.02495
\(269\) −11.3046 −0.689253 −0.344627 0.938740i \(-0.611995\pi\)
−0.344627 + 0.938740i \(0.611995\pi\)
\(270\) 0 0
\(271\) −19.6892 −1.19604 −0.598018 0.801483i \(-0.704045\pi\)
−0.598018 + 0.801483i \(0.704045\pi\)
\(272\) −0.439189 −0.0266297
\(273\) 0 0
\(274\) −22.8953 −1.38316
\(275\) −6.87710 −0.414704
\(276\) 0 0
\(277\) −19.1796 −1.15239 −0.576196 0.817311i \(-0.695464\pi\)
−0.576196 + 0.817311i \(0.695464\pi\)
\(278\) −17.0669 −1.02360
\(279\) 0 0
\(280\) −0.382493 −0.0228583
\(281\) 5.36195 0.319867 0.159934 0.987128i \(-0.448872\pi\)
0.159934 + 0.987128i \(0.448872\pi\)
\(282\) 0 0
\(283\) −25.2685 −1.50206 −0.751028 0.660271i \(-0.770442\pi\)
−0.751028 + 0.660271i \(0.770442\pi\)
\(284\) 7.15165 0.424372
\(285\) 0 0
\(286\) −9.49480 −0.561439
\(287\) −2.18268 −0.128840
\(288\) 0 0
\(289\) 4.23962 0.249389
\(290\) 0.609130 0.0357694
\(291\) 0 0
\(292\) 3.87807 0.226947
\(293\) −18.0751 −1.05596 −0.527980 0.849257i \(-0.677050\pi\)
−0.527980 + 0.849257i \(0.677050\pi\)
\(294\) 0 0
\(295\) −1.03356 −0.0601763
\(296\) −8.19169 −0.476132
\(297\) 0 0
\(298\) 19.8331 1.14890
\(299\) −18.0811 −1.04566
\(300\) 0 0
\(301\) 9.51578 0.548480
\(302\) −0.257961 −0.0148440
\(303\) 0 0
\(304\) −0.169990 −0.00974962
\(305\) 0.501154 0.0286960
\(306\) 0 0
\(307\) 19.0494 1.08721 0.543604 0.839342i \(-0.317059\pi\)
0.543604 + 0.839342i \(0.317059\pi\)
\(308\) 4.49595 0.256181
\(309\) 0 0
\(310\) −2.90264 −0.164859
\(311\) −4.75698 −0.269744 −0.134872 0.990863i \(-0.543062\pi\)
−0.134872 + 0.990863i \(0.543062\pi\)
\(312\) 0 0
\(313\) 1.35571 0.0766292 0.0383146 0.999266i \(-0.487801\pi\)
0.0383146 + 0.999266i \(0.487801\pi\)
\(314\) −23.4054 −1.32085
\(315\) 0 0
\(316\) −33.7472 −1.89843
\(317\) 13.3742 0.751173 0.375586 0.926787i \(-0.377441\pi\)
0.375586 + 0.926787i \(0.377441\pi\)
\(318\) 0 0
\(319\) −2.76366 −0.154735
\(320\) −1.71283 −0.0957502
\(321\) 0 0
\(322\) 13.8187 0.770084
\(323\) 8.22091 0.457424
\(324\) 0 0
\(325\) −14.9478 −0.829154
\(326\) 28.0722 1.55477
\(327\) 0 0
\(328\) 6.29219 0.347428
\(329\) −2.52668 −0.139300
\(330\) 0 0
\(331\) −11.6504 −0.640367 −0.320183 0.947356i \(-0.603744\pi\)
−0.320183 + 0.947356i \(0.603744\pi\)
\(332\) −5.89758 −0.323672
\(333\) 0 0
\(334\) −49.7786 −2.72376
\(335\) −1.35033 −0.0737763
\(336\) 0 0
\(337\) 16.5945 0.903962 0.451981 0.892028i \(-0.350718\pi\)
0.451981 + 0.892028i \(0.350718\pi\)
\(338\) 9.16985 0.498774
\(339\) 0 0
\(340\) −1.99177 −0.108019
\(341\) 13.1694 0.713165
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −27.4319 −1.47903
\(345\) 0 0
\(346\) −5.15402 −0.277082
\(347\) −1.74448 −0.0936485 −0.0468242 0.998903i \(-0.514910\pi\)
−0.0468242 + 0.998903i \(0.514910\pi\)
\(348\) 0 0
\(349\) 32.0356 1.71483 0.857413 0.514629i \(-0.172070\pi\)
0.857413 + 0.514629i \(0.172070\pi\)
\(350\) 11.4240 0.610639
\(351\) 0 0
\(352\) 7.65648 0.408092
\(353\) 15.9793 0.850494 0.425247 0.905077i \(-0.360187\pi\)
0.425247 + 0.905077i \(0.360187\pi\)
\(354\) 0 0
\(355\) 0.291316 0.0154614
\(356\) 23.6174 1.25172
\(357\) 0 0
\(358\) −5.48484 −0.289883
\(359\) 22.8017 1.20343 0.601713 0.798712i \(-0.294485\pi\)
0.601713 + 0.798712i \(0.294485\pi\)
\(360\) 0 0
\(361\) −15.8181 −0.832529
\(362\) 47.3261 2.48740
\(363\) 0 0
\(364\) 9.77222 0.512203
\(365\) 0.157969 0.00826850
\(366\) 0 0
\(367\) −2.46175 −0.128502 −0.0642511 0.997934i \(-0.520466\pi\)
−0.0642511 + 0.997934i \(0.520466\pi\)
\(368\) −0.574333 −0.0299392
\(369\) 0 0
\(370\) −0.864480 −0.0449422
\(371\) 8.38962 0.435567
\(372\) 0 0
\(373\) −25.6753 −1.32942 −0.664708 0.747103i \(-0.731444\pi\)
−0.664708 + 0.747103i \(0.731444\pi\)
\(374\) 14.5855 0.754197
\(375\) 0 0
\(376\) 7.28386 0.375637
\(377\) −6.00698 −0.309375
\(378\) 0 0
\(379\) 28.6117 1.46968 0.734842 0.678239i \(-0.237256\pi\)
0.734842 + 0.678239i \(0.237256\pi\)
\(380\) −0.770927 −0.0395477
\(381\) 0 0
\(382\) −36.9661 −1.89135
\(383\) 28.5878 1.46077 0.730385 0.683036i \(-0.239341\pi\)
0.730385 + 0.683036i \(0.239341\pi\)
\(384\) 0 0
\(385\) 0.183138 0.00933359
\(386\) −19.7901 −1.00729
\(387\) 0 0
\(388\) 6.97652 0.354179
\(389\) −17.3188 −0.878096 −0.439048 0.898464i \(-0.644684\pi\)
−0.439048 + 0.898464i \(0.644684\pi\)
\(390\) 0 0
\(391\) 27.7753 1.40466
\(392\) −2.88278 −0.145602
\(393\) 0 0
\(394\) 1.71295 0.0862970
\(395\) −1.37466 −0.0691666
\(396\) 0 0
\(397\) −15.8409 −0.795031 −0.397515 0.917595i \(-0.630127\pi\)
−0.397515 + 0.917595i \(0.630127\pi\)
\(398\) 4.09206 0.205116
\(399\) 0 0
\(400\) −0.474806 −0.0237403
\(401\) −25.1098 −1.25392 −0.626962 0.779050i \(-0.715702\pi\)
−0.626962 + 0.779050i \(0.715702\pi\)
\(402\) 0 0
\(403\) 28.6246 1.42589
\(404\) −53.0055 −2.63712
\(405\) 0 0
\(406\) 4.59090 0.227843
\(407\) 3.92220 0.194416
\(408\) 0 0
\(409\) 8.42996 0.416835 0.208417 0.978040i \(-0.433169\pi\)
0.208417 + 0.978040i \(0.433169\pi\)
\(410\) 0.664024 0.0327938
\(411\) 0 0
\(412\) −41.5835 −2.04867
\(413\) −7.78977 −0.383310
\(414\) 0 0
\(415\) −0.240232 −0.0117925
\(416\) 16.6418 0.815932
\(417\) 0 0
\(418\) 5.64539 0.276125
\(419\) 17.2527 0.842851 0.421425 0.906863i \(-0.361530\pi\)
0.421425 + 0.906863i \(0.361530\pi\)
\(420\) 0 0
\(421\) 27.9955 1.36442 0.682209 0.731157i \(-0.261019\pi\)
0.682209 + 0.731157i \(0.261019\pi\)
\(422\) 29.9375 1.45733
\(423\) 0 0
\(424\) −24.1854 −1.17455
\(425\) 22.9621 1.11383
\(426\) 0 0
\(427\) 3.77711 0.182787
\(428\) −4.57477 −0.221130
\(429\) 0 0
\(430\) −2.89492 −0.139605
\(431\) 12.7499 0.614142 0.307071 0.951687i \(-0.400651\pi\)
0.307071 + 0.951687i \(0.400651\pi\)
\(432\) 0 0
\(433\) 5.67855 0.272894 0.136447 0.990647i \(-0.456432\pi\)
0.136447 + 0.990647i \(0.456432\pi\)
\(434\) −21.8766 −1.05011
\(435\) 0 0
\(436\) 36.1910 1.73323
\(437\) 10.7506 0.514270
\(438\) 0 0
\(439\) −37.3733 −1.78373 −0.891865 0.452302i \(-0.850603\pi\)
−0.891865 + 0.452302i \(0.850603\pi\)
\(440\) −0.527947 −0.0251689
\(441\) 0 0
\(442\) 31.7024 1.50793
\(443\) −22.9515 −1.09046 −0.545230 0.838287i \(-0.683558\pi\)
−0.545230 + 0.838287i \(0.683558\pi\)
\(444\) 0 0
\(445\) 0.962031 0.0456046
\(446\) 21.7359 1.02922
\(447\) 0 0
\(448\) −12.9093 −0.609907
\(449\) −30.4308 −1.43612 −0.718059 0.695982i \(-0.754969\pi\)
−0.718059 + 0.695982i \(0.754969\pi\)
\(450\) 0 0
\(451\) −3.01271 −0.141863
\(452\) −57.5105 −2.70507
\(453\) 0 0
\(454\) 9.16216 0.430002
\(455\) 0.398062 0.0186614
\(456\) 0 0
\(457\) −32.1203 −1.50252 −0.751261 0.660005i \(-0.770554\pi\)
−0.751261 + 0.660005i \(0.770554\pi\)
\(458\) −13.0539 −0.609969
\(459\) 0 0
\(460\) −2.60467 −0.121443
\(461\) −11.1704 −0.520259 −0.260129 0.965574i \(-0.583765\pi\)
−0.260129 + 0.965574i \(0.583765\pi\)
\(462\) 0 0
\(463\) 25.3971 1.18030 0.590152 0.807292i \(-0.299068\pi\)
0.590152 + 0.807292i \(0.299068\pi\)
\(464\) −0.190807 −0.00885802
\(465\) 0 0
\(466\) −25.5149 −1.18196
\(467\) −37.9241 −1.75492 −0.877459 0.479652i \(-0.840763\pi\)
−0.877459 + 0.479652i \(0.840763\pi\)
\(468\) 0 0
\(469\) −10.1772 −0.469938
\(470\) 0.768676 0.0354564
\(471\) 0 0
\(472\) 22.4562 1.03363
\(473\) 13.1344 0.603921
\(474\) 0 0
\(475\) 8.88760 0.407791
\(476\) −15.0116 −0.688057
\(477\) 0 0
\(478\) −19.8432 −0.907606
\(479\) 9.94380 0.454344 0.227172 0.973855i \(-0.427052\pi\)
0.227172 + 0.973855i \(0.427052\pi\)
\(480\) 0 0
\(481\) 8.52513 0.388713
\(482\) 60.9770 2.77742
\(483\) 0 0
\(484\) −29.6244 −1.34656
\(485\) 0.284182 0.0129040
\(486\) 0 0
\(487\) −3.73337 −0.169175 −0.0845876 0.996416i \(-0.526957\pi\)
−0.0845876 + 0.996416i \(0.526957\pi\)
\(488\) −10.8886 −0.492902
\(489\) 0 0
\(490\) −0.304223 −0.0137434
\(491\) −37.0833 −1.67355 −0.836773 0.547550i \(-0.815561\pi\)
−0.836773 + 0.547550i \(0.815561\pi\)
\(492\) 0 0
\(493\) 9.22765 0.415592
\(494\) 12.2706 0.552080
\(495\) 0 0
\(496\) 0.909239 0.0408260
\(497\) 2.19559 0.0984858
\(498\) 0 0
\(499\) 24.7993 1.11017 0.555084 0.831795i \(-0.312686\pi\)
0.555084 + 0.831795i \(0.312686\pi\)
\(500\) −4.31421 −0.192937
\(501\) 0 0
\(502\) −15.6021 −0.696357
\(503\) 27.4762 1.22510 0.612551 0.790431i \(-0.290143\pi\)
0.612551 + 0.790431i \(0.290143\pi\)
\(504\) 0 0
\(505\) −2.15913 −0.0960800
\(506\) 19.0736 0.847925
\(507\) 0 0
\(508\) −3.25728 −0.144518
\(509\) −2.58766 −0.114696 −0.0573481 0.998354i \(-0.518264\pi\)
−0.0573481 + 0.998354i \(0.518264\pi\)
\(510\) 0 0
\(511\) 1.19059 0.0526684
\(512\) 1.07805 0.0476437
\(513\) 0 0
\(514\) 57.4079 2.53215
\(515\) −1.69386 −0.0746405
\(516\) 0 0
\(517\) −3.48753 −0.153381
\(518\) −6.51543 −0.286271
\(519\) 0 0
\(520\) −1.14752 −0.0503223
\(521\) 0.605284 0.0265180 0.0132590 0.999912i \(-0.495779\pi\)
0.0132590 + 0.999912i \(0.495779\pi\)
\(522\) 0 0
\(523\) −17.0952 −0.747522 −0.373761 0.927525i \(-0.621932\pi\)
−0.373761 + 0.927525i \(0.621932\pi\)
\(524\) −18.6916 −0.816545
\(525\) 0 0
\(526\) −42.9779 −1.87392
\(527\) −43.9717 −1.91544
\(528\) 0 0
\(529\) 13.3221 0.579223
\(530\) −2.55232 −0.110866
\(531\) 0 0
\(532\) −5.81033 −0.251910
\(533\) −6.54831 −0.283639
\(534\) 0 0
\(535\) −0.186349 −0.00805656
\(536\) 29.3385 1.26723
\(537\) 0 0
\(538\) 25.9200 1.11749
\(539\) 1.38028 0.0594528
\(540\) 0 0
\(541\) 3.19188 0.137230 0.0686149 0.997643i \(-0.478142\pi\)
0.0686149 + 0.997643i \(0.478142\pi\)
\(542\) 45.1449 1.93914
\(543\) 0 0
\(544\) −25.5644 −1.09606
\(545\) 1.47421 0.0631480
\(546\) 0 0
\(547\) −44.2108 −1.89032 −0.945159 0.326610i \(-0.894094\pi\)
−0.945159 + 0.326610i \(0.894094\pi\)
\(548\) 32.5253 1.38941
\(549\) 0 0
\(550\) 15.7683 0.672363
\(551\) 3.57161 0.152156
\(552\) 0 0
\(553\) −10.3605 −0.440575
\(554\) 43.9765 1.86838
\(555\) 0 0
\(556\) 24.2453 1.02823
\(557\) 35.3458 1.49765 0.748826 0.662767i \(-0.230618\pi\)
0.748826 + 0.662767i \(0.230618\pi\)
\(558\) 0 0
\(559\) 28.5485 1.20747
\(560\) 0.0126442 0.000534313 0
\(561\) 0 0
\(562\) −12.2943 −0.518603
\(563\) 18.2180 0.767798 0.383899 0.923375i \(-0.374581\pi\)
0.383899 + 0.923375i \(0.374581\pi\)
\(564\) 0 0
\(565\) −2.34264 −0.0985554
\(566\) 57.9375 2.43529
\(567\) 0 0
\(568\) −6.32941 −0.265576
\(569\) −30.8334 −1.29260 −0.646301 0.763083i \(-0.723685\pi\)
−0.646301 + 0.763083i \(0.723685\pi\)
\(570\) 0 0
\(571\) −19.1022 −0.799401 −0.399701 0.916646i \(-0.630886\pi\)
−0.399701 + 0.916646i \(0.630886\pi\)
\(572\) 13.4884 0.563978
\(573\) 0 0
\(574\) 5.00462 0.208889
\(575\) 30.0278 1.25225
\(576\) 0 0
\(577\) 19.0295 0.792207 0.396103 0.918206i \(-0.370362\pi\)
0.396103 + 0.918206i \(0.370362\pi\)
\(578\) −9.72091 −0.404337
\(579\) 0 0
\(580\) −0.865335 −0.0359311
\(581\) −1.81059 −0.0751158
\(582\) 0 0
\(583\) 11.5800 0.479595
\(584\) −3.43220 −0.142025
\(585\) 0 0
\(586\) 41.4440 1.71203
\(587\) −13.9522 −0.575868 −0.287934 0.957650i \(-0.592968\pi\)
−0.287934 + 0.957650i \(0.592968\pi\)
\(588\) 0 0
\(589\) −17.0195 −0.701276
\(590\) 2.36983 0.0975644
\(591\) 0 0
\(592\) 0.270795 0.0111296
\(593\) 11.3635 0.466642 0.233321 0.972400i \(-0.425041\pi\)
0.233321 + 0.972400i \(0.425041\pi\)
\(594\) 0 0
\(595\) −0.611485 −0.0250684
\(596\) −28.1751 −1.15410
\(597\) 0 0
\(598\) 41.4576 1.69533
\(599\) 7.97960 0.326037 0.163019 0.986623i \(-0.447877\pi\)
0.163019 + 0.986623i \(0.447877\pi\)
\(600\) 0 0
\(601\) −27.4921 −1.12143 −0.560713 0.828010i \(-0.689473\pi\)
−0.560713 + 0.828010i \(0.689473\pi\)
\(602\) −21.8185 −0.889255
\(603\) 0 0
\(604\) 0.366461 0.0149111
\(605\) −1.20672 −0.0490602
\(606\) 0 0
\(607\) −1.64188 −0.0666420 −0.0333210 0.999445i \(-0.510608\pi\)
−0.0333210 + 0.999445i \(0.510608\pi\)
\(608\) −9.89484 −0.401289
\(609\) 0 0
\(610\) −1.14908 −0.0465250
\(611\) −7.58035 −0.306668
\(612\) 0 0
\(613\) −21.9275 −0.885642 −0.442821 0.896610i \(-0.646022\pi\)
−0.442821 + 0.896610i \(0.646022\pi\)
\(614\) −43.6780 −1.76270
\(615\) 0 0
\(616\) −3.97904 −0.160320
\(617\) 28.4427 1.14506 0.572530 0.819883i \(-0.305962\pi\)
0.572530 + 0.819883i \(0.305962\pi\)
\(618\) 0 0
\(619\) 28.9635 1.16414 0.582071 0.813138i \(-0.302243\pi\)
0.582071 + 0.813138i \(0.302243\pi\)
\(620\) 4.12351 0.165604
\(621\) 0 0
\(622\) 10.9072 0.437338
\(623\) 7.25065 0.290491
\(624\) 0 0
\(625\) 24.7362 0.989450
\(626\) −3.10847 −0.124240
\(627\) 0 0
\(628\) 33.2499 1.32682
\(629\) −13.0959 −0.522168
\(630\) 0 0
\(631\) −26.5333 −1.05627 −0.528136 0.849160i \(-0.677109\pi\)
−0.528136 + 0.849160i \(0.677109\pi\)
\(632\) 29.8672 1.18805
\(633\) 0 0
\(634\) −30.6655 −1.21788
\(635\) −0.132682 −0.00526533
\(636\) 0 0
\(637\) 3.00012 0.118869
\(638\) 6.33672 0.250873
\(639\) 0 0
\(640\) 2.45532 0.0970550
\(641\) −25.6409 −1.01276 −0.506378 0.862312i \(-0.669016\pi\)
−0.506378 + 0.862312i \(0.669016\pi\)
\(642\) 0 0
\(643\) −43.4896 −1.71506 −0.857532 0.514431i \(-0.828003\pi\)
−0.857532 + 0.514431i \(0.828003\pi\)
\(644\) −19.6309 −0.773566
\(645\) 0 0
\(646\) −18.8495 −0.741624
\(647\) −7.81527 −0.307250 −0.153625 0.988129i \(-0.549095\pi\)
−0.153625 + 0.988129i \(0.549095\pi\)
\(648\) 0 0
\(649\) −10.7521 −0.422055
\(650\) 34.2734 1.34431
\(651\) 0 0
\(652\) −39.8796 −1.56180
\(653\) 20.2875 0.793912 0.396956 0.917838i \(-0.370067\pi\)
0.396956 + 0.917838i \(0.370067\pi\)
\(654\) 0 0
\(655\) −0.761383 −0.0297497
\(656\) −0.208003 −0.00812114
\(657\) 0 0
\(658\) 5.79337 0.225849
\(659\) −44.0567 −1.71620 −0.858102 0.513479i \(-0.828356\pi\)
−0.858102 + 0.513479i \(0.828356\pi\)
\(660\) 0 0
\(661\) −7.35149 −0.285940 −0.142970 0.989727i \(-0.545665\pi\)
−0.142970 + 0.989727i \(0.545665\pi\)
\(662\) 26.7130 1.03823
\(663\) 0 0
\(664\) 5.21952 0.202557
\(665\) −0.236678 −0.00917799
\(666\) 0 0
\(667\) 12.0671 0.467240
\(668\) 70.7159 2.73608
\(669\) 0 0
\(670\) 3.09613 0.119614
\(671\) 5.21346 0.201263
\(672\) 0 0
\(673\) 19.8435 0.764912 0.382456 0.923974i \(-0.375078\pi\)
0.382456 + 0.923974i \(0.375078\pi\)
\(674\) −38.0492 −1.46560
\(675\) 0 0
\(676\) −13.0268 −0.501030
\(677\) 13.3359 0.512539 0.256269 0.966605i \(-0.417507\pi\)
0.256269 + 0.966605i \(0.417507\pi\)
\(678\) 0 0
\(679\) 2.14183 0.0821957
\(680\) 1.76277 0.0675993
\(681\) 0 0
\(682\) −30.1959 −1.15626
\(683\) 15.1569 0.579962 0.289981 0.957032i \(-0.406351\pi\)
0.289981 + 0.957032i \(0.406351\pi\)
\(684\) 0 0
\(685\) 1.32489 0.0506213
\(686\) −2.29288 −0.0875424
\(687\) 0 0
\(688\) 0.906822 0.0345723
\(689\) 25.1699 0.958895
\(690\) 0 0
\(691\) −43.0546 −1.63788 −0.818938 0.573882i \(-0.805437\pi\)
−0.818938 + 0.573882i \(0.805437\pi\)
\(692\) 7.32184 0.278334
\(693\) 0 0
\(694\) 3.99987 0.151833
\(695\) 0.987610 0.0374622
\(696\) 0 0
\(697\) 10.0592 0.381020
\(698\) −73.4536 −2.78026
\(699\) 0 0
\(700\) −16.2290 −0.613400
\(701\) −30.1134 −1.13737 −0.568685 0.822556i \(-0.692547\pi\)
−0.568685 + 0.822556i \(0.692547\pi\)
\(702\) 0 0
\(703\) −5.06884 −0.191175
\(704\) −17.8184 −0.671557
\(705\) 0 0
\(706\) −36.6386 −1.37891
\(707\) −16.2730 −0.612007
\(708\) 0 0
\(709\) −23.1425 −0.869136 −0.434568 0.900639i \(-0.643099\pi\)
−0.434568 + 0.900639i \(0.643099\pi\)
\(710\) −0.667951 −0.0250677
\(711\) 0 0
\(712\) −20.9020 −0.783336
\(713\) −57.5024 −2.15348
\(714\) 0 0
\(715\) 0.549437 0.0205478
\(716\) 7.79181 0.291194
\(717\) 0 0
\(718\) −52.2814 −1.95112
\(719\) −6.88533 −0.256780 −0.128390 0.991724i \(-0.540981\pi\)
−0.128390 + 0.991724i \(0.540981\pi\)
\(720\) 0 0
\(721\) −12.7663 −0.475443
\(722\) 36.2688 1.34979
\(723\) 0 0
\(724\) −67.2318 −2.49865
\(725\) 9.97598 0.370499
\(726\) 0 0
\(727\) −3.64321 −0.135119 −0.0675596 0.997715i \(-0.521521\pi\)
−0.0675596 + 0.997715i \(0.521521\pi\)
\(728\) −8.64868 −0.320541
\(729\) 0 0
\(730\) −0.362204 −0.0134058
\(731\) −43.8548 −1.62203
\(732\) 0 0
\(733\) 27.4346 1.01332 0.506660 0.862146i \(-0.330880\pi\)
0.506660 + 0.862146i \(0.330880\pi\)
\(734\) 5.64448 0.208342
\(735\) 0 0
\(736\) −33.4309 −1.23228
\(737\) −14.0473 −0.517440
\(738\) 0 0
\(739\) −3.92099 −0.144236 −0.0721179 0.997396i \(-0.522976\pi\)
−0.0721179 + 0.997396i \(0.522976\pi\)
\(740\) 1.22809 0.0451454
\(741\) 0 0
\(742\) −19.2364 −0.706189
\(743\) −50.9410 −1.86885 −0.934423 0.356165i \(-0.884084\pi\)
−0.934423 + 0.356165i \(0.884084\pi\)
\(744\) 0 0
\(745\) −1.14768 −0.0420479
\(746\) 58.8703 2.15539
\(747\) 0 0
\(748\) −20.7202 −0.757607
\(749\) −1.40448 −0.0513185
\(750\) 0 0
\(751\) 3.73352 0.136238 0.0681191 0.997677i \(-0.478300\pi\)
0.0681191 + 0.997677i \(0.478300\pi\)
\(752\) −0.240784 −0.00878051
\(753\) 0 0
\(754\) 13.7733 0.501592
\(755\) 0.0149274 0.000543265 0
\(756\) 0 0
\(757\) −0.802306 −0.0291603 −0.0145802 0.999894i \(-0.504641\pi\)
−0.0145802 + 0.999894i \(0.504641\pi\)
\(758\) −65.6030 −2.38281
\(759\) 0 0
\(760\) 0.682291 0.0247493
\(761\) 28.3858 1.02899 0.514493 0.857495i \(-0.327980\pi\)
0.514493 + 0.857495i \(0.327980\pi\)
\(762\) 0 0
\(763\) 11.1108 0.402238
\(764\) 52.5143 1.89990
\(765\) 0 0
\(766\) −65.5483 −2.36836
\(767\) −23.3702 −0.843851
\(768\) 0 0
\(769\) 37.0161 1.33483 0.667417 0.744684i \(-0.267400\pi\)
0.667417 + 0.744684i \(0.267400\pi\)
\(770\) −0.419913 −0.0151326
\(771\) 0 0
\(772\) 28.1140 1.01185
\(773\) −13.8879 −0.499514 −0.249757 0.968309i \(-0.580351\pi\)
−0.249757 + 0.968309i \(0.580351\pi\)
\(774\) 0 0
\(775\) −47.5377 −1.70761
\(776\) −6.17441 −0.221648
\(777\) 0 0
\(778\) 39.7098 1.42366
\(779\) 3.89347 0.139498
\(780\) 0 0
\(781\) 3.03053 0.108441
\(782\) −63.6853 −2.27738
\(783\) 0 0
\(784\) 0.0952967 0.00340345
\(785\) 1.35440 0.0483408
\(786\) 0 0
\(787\) −4.72348 −0.168374 −0.0841869 0.996450i \(-0.526829\pi\)
−0.0841869 + 0.996450i \(0.526829\pi\)
\(788\) −2.43343 −0.0866872
\(789\) 0 0
\(790\) 3.15192 0.112140
\(791\) −17.6560 −0.627775
\(792\) 0 0
\(793\) 11.3318 0.402403
\(794\) 36.3212 1.28899
\(795\) 0 0
\(796\) −5.81321 −0.206044
\(797\) −7.11438 −0.252004 −0.126002 0.992030i \(-0.540215\pi\)
−0.126002 + 0.992030i \(0.540215\pi\)
\(798\) 0 0
\(799\) 11.6446 0.411956
\(800\) −27.6376 −0.977137
\(801\) 0 0
\(802\) 57.5736 2.03300
\(803\) 1.64334 0.0579923
\(804\) 0 0
\(805\) −0.799646 −0.0281838
\(806\) −65.6325 −2.31181
\(807\) 0 0
\(808\) 46.9113 1.65033
\(809\) 49.9190 1.75506 0.877529 0.479523i \(-0.159190\pi\)
0.877529 + 0.479523i \(0.159190\pi\)
\(810\) 0 0
\(811\) 24.6467 0.865464 0.432732 0.901523i \(-0.357550\pi\)
0.432732 + 0.901523i \(0.357550\pi\)
\(812\) −6.52187 −0.228873
\(813\) 0 0
\(814\) −8.99311 −0.315208
\(815\) −1.62446 −0.0569022
\(816\) 0 0
\(817\) −16.9743 −0.593854
\(818\) −19.3288 −0.675817
\(819\) 0 0
\(820\) −0.943317 −0.0329421
\(821\) −19.0309 −0.664183 −0.332092 0.943247i \(-0.607754\pi\)
−0.332092 + 0.943247i \(0.607754\pi\)
\(822\) 0 0
\(823\) 20.8785 0.727780 0.363890 0.931442i \(-0.381448\pi\)
0.363890 + 0.931442i \(0.381448\pi\)
\(824\) 36.8025 1.28208
\(825\) 0 0
\(826\) 17.8610 0.621463
\(827\) −30.7068 −1.06778 −0.533890 0.845554i \(-0.679270\pi\)
−0.533890 + 0.845554i \(0.679270\pi\)
\(828\) 0 0
\(829\) 9.14687 0.317684 0.158842 0.987304i \(-0.449224\pi\)
0.158842 + 0.987304i \(0.449224\pi\)
\(830\) 0.550822 0.0191193
\(831\) 0 0
\(832\) −38.7294 −1.34270
\(833\) −4.60865 −0.159680
\(834\) 0 0
\(835\) 2.88054 0.0996853
\(836\) −8.01988 −0.277373
\(837\) 0 0
\(838\) −39.5583 −1.36652
\(839\) −48.3089 −1.66781 −0.833904 0.551909i \(-0.813899\pi\)
−0.833904 + 0.551909i \(0.813899\pi\)
\(840\) 0 0
\(841\) −24.9910 −0.861759
\(842\) −64.1902 −2.21214
\(843\) 0 0
\(844\) −42.5294 −1.46392
\(845\) −0.530633 −0.0182543
\(846\) 0 0
\(847\) −9.09483 −0.312502
\(848\) 0.799503 0.0274551
\(849\) 0 0
\(850\) −52.6492 −1.80585
\(851\) −17.1257 −0.587061
\(852\) 0 0
\(853\) 1.91745 0.0656523 0.0328261 0.999461i \(-0.489549\pi\)
0.0328261 + 0.999461i \(0.489549\pi\)
\(854\) −8.66043 −0.296354
\(855\) 0 0
\(856\) 4.04880 0.138385
\(857\) −42.3948 −1.44818 −0.724090 0.689705i \(-0.757740\pi\)
−0.724090 + 0.689705i \(0.757740\pi\)
\(858\) 0 0
\(859\) −12.3574 −0.421629 −0.210815 0.977526i \(-0.567612\pi\)
−0.210815 + 0.977526i \(0.567612\pi\)
\(860\) 4.11255 0.140237
\(861\) 0 0
\(862\) −29.2340 −0.995714
\(863\) 6.84551 0.233024 0.116512 0.993189i \(-0.462829\pi\)
0.116512 + 0.993189i \(0.462829\pi\)
\(864\) 0 0
\(865\) 0.298248 0.0101407
\(866\) −13.0202 −0.442445
\(867\) 0 0
\(868\) 31.0781 1.05486
\(869\) −14.3004 −0.485109
\(870\) 0 0
\(871\) −30.5327 −1.03456
\(872\) −32.0300 −1.08467
\(873\) 0 0
\(874\) −24.6497 −0.833790
\(875\) −1.32448 −0.0447758
\(876\) 0 0
\(877\) 24.0490 0.812077 0.406038 0.913856i \(-0.366910\pi\)
0.406038 + 0.913856i \(0.366910\pi\)
\(878\) 85.6923 2.89197
\(879\) 0 0
\(880\) 0.0174525 0.000588323 0
\(881\) 13.2032 0.444826 0.222413 0.974953i \(-0.428607\pi\)
0.222413 + 0.974953i \(0.428607\pi\)
\(882\) 0 0
\(883\) 13.8993 0.467749 0.233874 0.972267i \(-0.424860\pi\)
0.233874 + 0.972267i \(0.424860\pi\)
\(884\) −45.0367 −1.51475
\(885\) 0 0
\(886\) 52.6250 1.76797
\(887\) −19.1216 −0.642041 −0.321020 0.947072i \(-0.604026\pi\)
−0.321020 + 0.947072i \(0.604026\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) −2.20582 −0.0739391
\(891\) 0 0
\(892\) −30.8782 −1.03388
\(893\) 4.50710 0.150824
\(894\) 0 0
\(895\) 0.317392 0.0106092
\(896\) 18.5053 0.618218
\(897\) 0 0
\(898\) 69.7741 2.32839
\(899\) −19.1037 −0.637145
\(900\) 0 0
\(901\) −38.6648 −1.28811
\(902\) 6.90778 0.230004
\(903\) 0 0
\(904\) 50.8983 1.69285
\(905\) −2.73862 −0.0910349
\(906\) 0 0
\(907\) −4.48188 −0.148818 −0.0744091 0.997228i \(-0.523707\pi\)
−0.0744091 + 0.997228i \(0.523707\pi\)
\(908\) −13.0158 −0.431946
\(909\) 0 0
\(910\) −0.912706 −0.0302559
\(911\) −10.0337 −0.332430 −0.166215 0.986090i \(-0.553155\pi\)
−0.166215 + 0.986090i \(0.553155\pi\)
\(912\) 0 0
\(913\) −2.49911 −0.0827086
\(914\) 73.6477 2.43605
\(915\) 0 0
\(916\) 18.5445 0.612727
\(917\) −5.73840 −0.189499
\(918\) 0 0
\(919\) 14.4554 0.476839 0.238419 0.971162i \(-0.423371\pi\)
0.238419 + 0.971162i \(0.423371\pi\)
\(920\) 2.30520 0.0760003
\(921\) 0 0
\(922\) 25.6124 0.843500
\(923\) 6.58704 0.216815
\(924\) 0 0
\(925\) −14.1580 −0.465511
\(926\) −58.2324 −1.91364
\(927\) 0 0
\(928\) −11.1066 −0.364591
\(929\) −53.1010 −1.74219 −0.871093 0.491117i \(-0.836589\pi\)
−0.871093 + 0.491117i \(0.836589\pi\)
\(930\) 0 0
\(931\) −1.78380 −0.0584617
\(932\) 36.2467 1.18730
\(933\) 0 0
\(934\) 86.9552 2.84526
\(935\) −0.844019 −0.0276024
\(936\) 0 0
\(937\) −0.659156 −0.0215337 −0.0107668 0.999942i \(-0.503427\pi\)
−0.0107668 + 0.999942i \(0.503427\pi\)
\(938\) 23.3350 0.761914
\(939\) 0 0
\(940\) −1.09199 −0.0356167
\(941\) 59.8621 1.95145 0.975724 0.219006i \(-0.0702814\pi\)
0.975724 + 0.219006i \(0.0702814\pi\)
\(942\) 0 0
\(943\) 13.1546 0.428372
\(944\) −0.742339 −0.0241611
\(945\) 0 0
\(946\) −30.1156 −0.979142
\(947\) −40.1186 −1.30368 −0.651840 0.758357i \(-0.726002\pi\)
−0.651840 + 0.758357i \(0.726002\pi\)
\(948\) 0 0
\(949\) 3.57190 0.115949
\(950\) −20.3782 −0.661155
\(951\) 0 0
\(952\) 13.2857 0.430592
\(953\) −24.9277 −0.807487 −0.403744 0.914872i \(-0.632291\pi\)
−0.403744 + 0.914872i \(0.632291\pi\)
\(954\) 0 0
\(955\) 2.13912 0.0692203
\(956\) 28.1894 0.911710
\(957\) 0 0
\(958\) −22.7999 −0.736631
\(959\) 9.98542 0.322446
\(960\) 0 0
\(961\) 60.0334 1.93656
\(962\) −19.5471 −0.630223
\(963\) 0 0
\(964\) −86.6244 −2.78998
\(965\) 1.14520 0.0368652
\(966\) 0 0
\(967\) 26.4870 0.851764 0.425882 0.904779i \(-0.359964\pi\)
0.425882 + 0.904779i \(0.359964\pi\)
\(968\) 26.2184 0.842690
\(969\) 0 0
\(970\) −0.651594 −0.0209214
\(971\) −5.35158 −0.171740 −0.0858702 0.996306i \(-0.527367\pi\)
−0.0858702 + 0.996306i \(0.527367\pi\)
\(972\) 0 0
\(973\) 7.44343 0.238625
\(974\) 8.56016 0.274285
\(975\) 0 0
\(976\) 0.359946 0.0115216
\(977\) 34.3412 1.09867 0.549336 0.835602i \(-0.314881\pi\)
0.549336 + 0.835602i \(0.314881\pi\)
\(978\) 0 0
\(979\) 10.0079 0.319854
\(980\) 0.432182 0.0138055
\(981\) 0 0
\(982\) 85.0274 2.71333
\(983\) 29.9723 0.955968 0.477984 0.878369i \(-0.341368\pi\)
0.477984 + 0.878369i \(0.341368\pi\)
\(984\) 0 0
\(985\) −0.0991233 −0.00315833
\(986\) −21.1578 −0.673803
\(987\) 0 0
\(988\) −17.4317 −0.554576
\(989\) −57.3495 −1.82361
\(990\) 0 0
\(991\) 27.5987 0.876703 0.438351 0.898804i \(-0.355563\pi\)
0.438351 + 0.898804i \(0.355563\pi\)
\(992\) 52.9252 1.68038
\(993\) 0 0
\(994\) −5.03422 −0.159676
\(995\) −0.236796 −0.00750693
\(996\) 0 0
\(997\) 53.8873 1.70663 0.853314 0.521397i \(-0.174589\pi\)
0.853314 + 0.521397i \(0.174589\pi\)
\(998\) −56.8616 −1.79992
\(999\) 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 \(a_p\))