Properties

Label 8043.2.a.t.1.2
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.71076 q^{2}\) \(-1.00000 q^{3}\) \(+5.34821 q^{4}\) \(+0.130231 q^{5}\) \(+2.71076 q^{6}\) \(+1.00000 q^{7}\) \(-9.07620 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.71076 q^{2}\) \(-1.00000 q^{3}\) \(+5.34821 q^{4}\) \(+0.130231 q^{5}\) \(+2.71076 q^{6}\) \(+1.00000 q^{7}\) \(-9.07620 q^{8}\) \(+1.00000 q^{9}\) \(-0.353025 q^{10}\) \(+3.25358 q^{11}\) \(-5.34821 q^{12}\) \(+1.11985 q^{13}\) \(-2.71076 q^{14}\) \(-0.130231 q^{15}\) \(+13.9070 q^{16}\) \(+0.0623671 q^{17}\) \(-2.71076 q^{18}\) \(+2.72595 q^{19}\) \(+0.696503 q^{20}\) \(-1.00000 q^{21}\) \(-8.81967 q^{22}\) \(+6.67141 q^{23}\) \(+9.07620 q^{24}\) \(-4.98304 q^{25}\) \(-3.03565 q^{26}\) \(-1.00000 q^{27}\) \(+5.34821 q^{28}\) \(-7.51601 q^{29}\) \(+0.353025 q^{30}\) \(+8.48682 q^{31}\) \(-19.5460 q^{32}\) \(-3.25358 q^{33}\) \(-0.169062 q^{34}\) \(+0.130231 q^{35}\) \(+5.34821 q^{36}\) \(+10.9966 q^{37}\) \(-7.38938 q^{38}\) \(-1.11985 q^{39}\) \(-1.18200 q^{40}\) \(-6.34625 q^{41}\) \(+2.71076 q^{42}\) \(+2.41223 q^{43}\) \(+17.4008 q^{44}\) \(+0.130231 q^{45}\) \(-18.0846 q^{46}\) \(+7.87767 q^{47}\) \(-13.9070 q^{48}\) \(+1.00000 q^{49}\) \(+13.5078 q^{50}\) \(-0.0623671 q^{51}\) \(+5.98922 q^{52}\) \(-6.90598 q^{53}\) \(+2.71076 q^{54}\) \(+0.423717 q^{55}\) \(-9.07620 q^{56}\) \(-2.72595 q^{57}\) \(+20.3741 q^{58}\) \(+9.66024 q^{59}\) \(-0.696503 q^{60}\) \(-3.59541 q^{61}\) \(-23.0057 q^{62}\) \(+1.00000 q^{63}\) \(+25.1706 q^{64}\) \(+0.145840 q^{65}\) \(+8.81967 q^{66}\) \(+12.8812 q^{67}\) \(+0.333553 q^{68}\) \(-6.67141 q^{69}\) \(-0.353025 q^{70}\) \(-3.03164 q^{71}\) \(-9.07620 q^{72}\) \(-0.955600 q^{73}\) \(-29.8091 q^{74}\) \(+4.98304 q^{75}\) \(+14.5789 q^{76}\) \(+3.25358 q^{77}\) \(+3.03565 q^{78}\) \(-9.46286 q^{79}\) \(+1.81112 q^{80}\) \(+1.00000 q^{81}\) \(+17.2032 q^{82}\) \(+0.768405 q^{83}\) \(-5.34821 q^{84}\) \(+0.00812213 q^{85}\) \(-6.53898 q^{86}\) \(+7.51601 q^{87}\) \(-29.5301 q^{88}\) \(+2.54138 q^{89}\) \(-0.353025 q^{90}\) \(+1.11985 q^{91}\) \(+35.6801 q^{92}\) \(-8.48682 q^{93}\) \(-21.3545 q^{94}\) \(+0.355003 q^{95}\) \(+19.5460 q^{96}\) \(+2.85023 q^{97}\) \(-2.71076 q^{98}\) \(+3.25358 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71076 −1.91680 −0.958398 0.285435i \(-0.907862\pi\)
−0.958398 + 0.285435i \(0.907862\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.34821 2.67411
\(5\) 0.130231 0.0582411 0.0291205 0.999576i \(-0.490729\pi\)
0.0291205 + 0.999576i \(0.490729\pi\)
\(6\) 2.71076 1.10666
\(7\) 1.00000 0.377964
\(8\) −9.07620 −3.20892
\(9\) 1.00000 0.333333
\(10\) −0.353025 −0.111636
\(11\) 3.25358 0.980991 0.490495 0.871444i \(-0.336816\pi\)
0.490495 + 0.871444i \(0.336816\pi\)
\(12\) −5.34821 −1.54390
\(13\) 1.11985 0.310591 0.155296 0.987868i \(-0.450367\pi\)
0.155296 + 0.987868i \(0.450367\pi\)
\(14\) −2.71076 −0.724481
\(15\) −0.130231 −0.0336255
\(16\) 13.9070 3.47674
\(17\) 0.0623671 0.0151262 0.00756312 0.999971i \(-0.497593\pi\)
0.00756312 + 0.999971i \(0.497593\pi\)
\(18\) −2.71076 −0.638932
\(19\) 2.72595 0.625375 0.312688 0.949856i \(-0.398771\pi\)
0.312688 + 0.949856i \(0.398771\pi\)
\(20\) 0.696503 0.155743
\(21\) −1.00000 −0.218218
\(22\) −8.81967 −1.88036
\(23\) 6.67141 1.39108 0.695542 0.718485i \(-0.255164\pi\)
0.695542 + 0.718485i \(0.255164\pi\)
\(24\) 9.07620 1.85267
\(25\) −4.98304 −0.996608
\(26\) −3.03565 −0.595340
\(27\) −1.00000 −0.192450
\(28\) 5.34821 1.01072
\(29\) −7.51601 −1.39569 −0.697844 0.716250i \(-0.745857\pi\)
−0.697844 + 0.716250i \(0.745857\pi\)
\(30\) 0.353025 0.0644532
\(31\) 8.48682 1.52428 0.762139 0.647414i \(-0.224149\pi\)
0.762139 + 0.647414i \(0.224149\pi\)
\(32\) −19.5460 −3.45528
\(33\) −3.25358 −0.566375
\(34\) −0.169062 −0.0289939
\(35\) 0.130231 0.0220131
\(36\) 5.34821 0.891369
\(37\) 10.9966 1.80783 0.903915 0.427712i \(-0.140680\pi\)
0.903915 + 0.427712i \(0.140680\pi\)
\(38\) −7.38938 −1.19872
\(39\) −1.11985 −0.179320
\(40\) −1.18200 −0.186891
\(41\) −6.34625 −0.991118 −0.495559 0.868574i \(-0.665037\pi\)
−0.495559 + 0.868574i \(0.665037\pi\)
\(42\) 2.71076 0.418279
\(43\) 2.41223 0.367862 0.183931 0.982939i \(-0.441118\pi\)
0.183931 + 0.982939i \(0.441118\pi\)
\(44\) 17.4008 2.62327
\(45\) 0.130231 0.0194137
\(46\) −18.0846 −2.66642
\(47\) 7.87767 1.14908 0.574538 0.818478i \(-0.305182\pi\)
0.574538 + 0.818478i \(0.305182\pi\)
\(48\) −13.9070 −2.00730
\(49\) 1.00000 0.142857
\(50\) 13.5078 1.91029
\(51\) −0.0623671 −0.00873314
\(52\) 5.98922 0.830555
\(53\) −6.90598 −0.948609 −0.474304 0.880361i \(-0.657300\pi\)
−0.474304 + 0.880361i \(0.657300\pi\)
\(54\) 2.71076 0.368888
\(55\) 0.423717 0.0571339
\(56\) −9.07620 −1.21286
\(57\) −2.72595 −0.361060
\(58\) 20.3741 2.67525
\(59\) 9.66024 1.25766 0.628828 0.777545i \(-0.283535\pi\)
0.628828 + 0.777545i \(0.283535\pi\)
\(60\) −0.696503 −0.0899182
\(61\) −3.59541 −0.460345 −0.230172 0.973150i \(-0.573929\pi\)
−0.230172 + 0.973150i \(0.573929\pi\)
\(62\) −23.0057 −2.92173
\(63\) 1.00000 0.125988
\(64\) 25.1706 3.14633
\(65\) 0.145840 0.0180892
\(66\) 8.81967 1.08563
\(67\) 12.8812 1.57369 0.786845 0.617151i \(-0.211713\pi\)
0.786845 + 0.617151i \(0.211713\pi\)
\(68\) 0.333553 0.0404492
\(69\) −6.67141 −0.803143
\(70\) −0.353025 −0.0421945
\(71\) −3.03164 −0.359790 −0.179895 0.983686i \(-0.557576\pi\)
−0.179895 + 0.983686i \(0.557576\pi\)
\(72\) −9.07620 −1.06964
\(73\) −0.955600 −0.111844 −0.0559222 0.998435i \(-0.517810\pi\)
−0.0559222 + 0.998435i \(0.517810\pi\)
\(74\) −29.8091 −3.46524
\(75\) 4.98304 0.575392
\(76\) 14.5789 1.67232
\(77\) 3.25358 0.370780
\(78\) 3.03565 0.343720
\(79\) −9.46286 −1.06465 −0.532327 0.846539i \(-0.678682\pi\)
−0.532327 + 0.846539i \(0.678682\pi\)
\(80\) 1.81112 0.202489
\(81\) 1.00000 0.111111
\(82\) 17.2032 1.89977
\(83\) 0.768405 0.0843434 0.0421717 0.999110i \(-0.486572\pi\)
0.0421717 + 0.999110i \(0.486572\pi\)
\(84\) −5.34821 −0.583538
\(85\) 0.00812213 0.000880968 0
\(86\) −6.53898 −0.705116
\(87\) 7.51601 0.805801
\(88\) −29.5301 −3.14792
\(89\) 2.54138 0.269386 0.134693 0.990887i \(-0.456995\pi\)
0.134693 + 0.990887i \(0.456995\pi\)
\(90\) −0.353025 −0.0372121
\(91\) 1.11985 0.117393
\(92\) 35.6801 3.71991
\(93\) −8.48682 −0.880042
\(94\) −21.3545 −2.20254
\(95\) 0.355003 0.0364225
\(96\) 19.5460 1.99491
\(97\) 2.85023 0.289397 0.144699 0.989476i \(-0.453779\pi\)
0.144699 + 0.989476i \(0.453779\pi\)
\(98\) −2.71076 −0.273828
\(99\) 3.25358 0.326997
\(100\) −26.6504 −2.66504
\(101\) −10.0545 −1.00046 −0.500231 0.865892i \(-0.666752\pi\)
−0.500231 + 0.865892i \(0.666752\pi\)
\(102\) 0.169062 0.0167396
\(103\) 9.36566 0.922826 0.461413 0.887185i \(-0.347343\pi\)
0.461413 + 0.887185i \(0.347343\pi\)
\(104\) −10.1640 −0.996664
\(105\) −0.130231 −0.0127092
\(106\) 18.7204 1.81829
\(107\) 11.7033 1.13140 0.565700 0.824611i \(-0.308606\pi\)
0.565700 + 0.824611i \(0.308606\pi\)
\(108\) −5.34821 −0.514632
\(109\) 5.17573 0.495745 0.247872 0.968793i \(-0.420269\pi\)
0.247872 + 0.968793i \(0.420269\pi\)
\(110\) −1.14859 −0.109514
\(111\) −10.9966 −1.04375
\(112\) 13.9070 1.31408
\(113\) 8.66917 0.815527 0.407764 0.913088i \(-0.366309\pi\)
0.407764 + 0.913088i \(0.366309\pi\)
\(114\) 7.38938 0.692079
\(115\) 0.868824 0.0810182
\(116\) −40.1972 −3.73222
\(117\) 1.11985 0.103530
\(118\) −26.1866 −2.41067
\(119\) 0.0623671 0.00571718
\(120\) 1.18200 0.107902
\(121\) −0.414226 −0.0376569
\(122\) 9.74628 0.882387
\(123\) 6.34625 0.572222
\(124\) 45.3893 4.07608
\(125\) −1.30010 −0.116285
\(126\) −2.71076 −0.241494
\(127\) −0.493993 −0.0438348 −0.0219174 0.999760i \(-0.506977\pi\)
−0.0219174 + 0.999760i \(0.506977\pi\)
\(128\) −29.1395 −2.57559
\(129\) −2.41223 −0.212385
\(130\) −0.395336 −0.0346733
\(131\) −18.9040 −1.65165 −0.825824 0.563927i \(-0.809290\pi\)
−0.825824 + 0.563927i \(0.809290\pi\)
\(132\) −17.4008 −1.51455
\(133\) 2.72595 0.236370
\(134\) −34.9179 −3.01644
\(135\) −0.130231 −0.0112085
\(136\) −0.566056 −0.0485389
\(137\) 13.6960 1.17013 0.585063 0.810988i \(-0.301070\pi\)
0.585063 + 0.810988i \(0.301070\pi\)
\(138\) 18.0846 1.53946
\(139\) 2.92684 0.248252 0.124126 0.992266i \(-0.460387\pi\)
0.124126 + 0.992266i \(0.460387\pi\)
\(140\) 0.696503 0.0588653
\(141\) −7.87767 −0.663419
\(142\) 8.21806 0.689644
\(143\) 3.64353 0.304687
\(144\) 13.9070 1.15891
\(145\) −0.978817 −0.0812863
\(146\) 2.59040 0.214383
\(147\) −1.00000 −0.0824786
\(148\) 58.8122 4.83433
\(149\) −21.5069 −1.76191 −0.880957 0.473197i \(-0.843100\pi\)
−0.880957 + 0.473197i \(0.843100\pi\)
\(150\) −13.5078 −1.10291
\(151\) 2.82899 0.230220 0.115110 0.993353i \(-0.463278\pi\)
0.115110 + 0.993353i \(0.463278\pi\)
\(152\) −24.7412 −2.00678
\(153\) 0.0623671 0.00504208
\(154\) −8.81967 −0.710709
\(155\) 1.10525 0.0887755
\(156\) −5.98922 −0.479521
\(157\) 7.59643 0.606261 0.303130 0.952949i \(-0.401968\pi\)
0.303130 + 0.952949i \(0.401968\pi\)
\(158\) 25.6515 2.04073
\(159\) 6.90598 0.547680
\(160\) −2.54550 −0.201239
\(161\) 6.67141 0.525780
\(162\) −2.71076 −0.212977
\(163\) 5.41853 0.424412 0.212206 0.977225i \(-0.431935\pi\)
0.212206 + 0.977225i \(0.431935\pi\)
\(164\) −33.9411 −2.65035
\(165\) −0.423717 −0.0329863
\(166\) −2.08296 −0.161669
\(167\) 12.8244 0.992382 0.496191 0.868214i \(-0.334732\pi\)
0.496191 + 0.868214i \(0.334732\pi\)
\(168\) 9.07620 0.700244
\(169\) −11.7459 −0.903533
\(170\) −0.0220171 −0.00168864
\(171\) 2.72595 0.208458
\(172\) 12.9011 0.983702
\(173\) −3.42175 −0.260151 −0.130076 0.991504i \(-0.541522\pi\)
−0.130076 + 0.991504i \(0.541522\pi\)
\(174\) −20.3741 −1.54456
\(175\) −4.98304 −0.376682
\(176\) 45.2474 3.41065
\(177\) −9.66024 −0.726108
\(178\) −6.88907 −0.516357
\(179\) 11.4708 0.857368 0.428684 0.903454i \(-0.358977\pi\)
0.428684 + 0.903454i \(0.358977\pi\)
\(180\) 0.696503 0.0519143
\(181\) −2.92554 −0.217454 −0.108727 0.994072i \(-0.534677\pi\)
−0.108727 + 0.994072i \(0.534677\pi\)
\(182\) −3.03565 −0.225018
\(183\) 3.59541 0.265780
\(184\) −60.5510 −4.46388
\(185\) 1.43210 0.105290
\(186\) 23.0057 1.68686
\(187\) 0.202916 0.0148387
\(188\) 42.1314 3.07275
\(189\) −1.00000 −0.0727393
\(190\) −0.962327 −0.0698145
\(191\) −11.3119 −0.818501 −0.409250 0.912422i \(-0.634210\pi\)
−0.409250 + 0.912422i \(0.634210\pi\)
\(192\) −25.1706 −1.81654
\(193\) 3.48149 0.250603 0.125302 0.992119i \(-0.460010\pi\)
0.125302 + 0.992119i \(0.460010\pi\)
\(194\) −7.72629 −0.554716
\(195\) −0.145840 −0.0104438
\(196\) 5.34821 0.382015
\(197\) 10.9479 0.780006 0.390003 0.920814i \(-0.372474\pi\)
0.390003 + 0.920814i \(0.372474\pi\)
\(198\) −8.81967 −0.626786
\(199\) 23.1722 1.64264 0.821318 0.570471i \(-0.193239\pi\)
0.821318 + 0.570471i \(0.193239\pi\)
\(200\) 45.2271 3.19804
\(201\) −12.8812 −0.908570
\(202\) 27.2554 1.91768
\(203\) −7.51601 −0.527520
\(204\) −0.333553 −0.0233534
\(205\) −0.826478 −0.0577237
\(206\) −25.3880 −1.76887
\(207\) 6.67141 0.463695
\(208\) 15.5738 1.07985
\(209\) 8.86908 0.613487
\(210\) 0.353025 0.0243610
\(211\) 20.3087 1.39811 0.699053 0.715070i \(-0.253605\pi\)
0.699053 + 0.715070i \(0.253605\pi\)
\(212\) −36.9346 −2.53668
\(213\) 3.03164 0.207725
\(214\) −31.7248 −2.16866
\(215\) 0.314147 0.0214247
\(216\) 9.07620 0.617557
\(217\) 8.48682 0.576123
\(218\) −14.0302 −0.950242
\(219\) 0.955600 0.0645734
\(220\) 2.26613 0.152782
\(221\) 0.0698420 0.00469808
\(222\) 29.8091 2.00066
\(223\) 27.4714 1.83962 0.919812 0.392360i \(-0.128341\pi\)
0.919812 + 0.392360i \(0.128341\pi\)
\(224\) −19.5460 −1.30597
\(225\) −4.98304 −0.332203
\(226\) −23.5000 −1.56320
\(227\) −20.5618 −1.36474 −0.682369 0.731008i \(-0.739050\pi\)
−0.682369 + 0.731008i \(0.739050\pi\)
\(228\) −14.5789 −0.965514
\(229\) 5.61860 0.371288 0.185644 0.982617i \(-0.440563\pi\)
0.185644 + 0.982617i \(0.440563\pi\)
\(230\) −2.35517 −0.155295
\(231\) −3.25358 −0.214070
\(232\) 68.2168 4.47865
\(233\) 7.80020 0.511008 0.255504 0.966808i \(-0.417759\pi\)
0.255504 + 0.966808i \(0.417759\pi\)
\(234\) −3.03565 −0.198447
\(235\) 1.02592 0.0669234
\(236\) 51.6650 3.36311
\(237\) 9.46286 0.614679
\(238\) −0.169062 −0.0109587
\(239\) 7.89339 0.510581 0.255290 0.966864i \(-0.417829\pi\)
0.255290 + 0.966864i \(0.417829\pi\)
\(240\) −1.81112 −0.116907
\(241\) −12.0448 −0.775872 −0.387936 0.921686i \(-0.626812\pi\)
−0.387936 + 0.921686i \(0.626812\pi\)
\(242\) 1.12287 0.0721806
\(243\) −1.00000 −0.0641500
\(244\) −19.2290 −1.23101
\(245\) 0.130231 0.00832015
\(246\) −17.2032 −1.09683
\(247\) 3.05266 0.194236
\(248\) −77.0281 −4.89129
\(249\) −0.768405 −0.0486957
\(250\) 3.52426 0.222894
\(251\) −6.39187 −0.403451 −0.201726 0.979442i \(-0.564655\pi\)
−0.201726 + 0.979442i \(0.564655\pi\)
\(252\) 5.34821 0.336906
\(253\) 21.7059 1.36464
\(254\) 1.33910 0.0840224
\(255\) −0.00812213 −0.000508627 0
\(256\) 28.6489 1.79055
\(257\) −26.8685 −1.67601 −0.838005 0.545662i \(-0.816278\pi\)
−0.838005 + 0.545662i \(0.816278\pi\)
\(258\) 6.53898 0.407099
\(259\) 10.9966 0.683296
\(260\) 0.779981 0.0483724
\(261\) −7.51601 −0.465229
\(262\) 51.2441 3.16587
\(263\) −18.2727 −1.12674 −0.563372 0.826204i \(-0.690496\pi\)
−0.563372 + 0.826204i \(0.690496\pi\)
\(264\) 29.5301 1.81745
\(265\) −0.899372 −0.0552480
\(266\) −7.38938 −0.453072
\(267\) −2.54138 −0.155530
\(268\) 68.8915 4.20822
\(269\) 20.5732 1.25437 0.627186 0.778869i \(-0.284207\pi\)
0.627186 + 0.778869i \(0.284207\pi\)
\(270\) 0.353025 0.0214844
\(271\) 1.99413 0.121135 0.0605674 0.998164i \(-0.480709\pi\)
0.0605674 + 0.998164i \(0.480709\pi\)
\(272\) 0.867337 0.0525900
\(273\) −1.11985 −0.0677766
\(274\) −37.1265 −2.24289
\(275\) −16.2127 −0.977663
\(276\) −35.6801 −2.14769
\(277\) −22.5582 −1.35539 −0.677697 0.735342i \(-0.737022\pi\)
−0.677697 + 0.735342i \(0.737022\pi\)
\(278\) −7.93397 −0.475848
\(279\) 8.48682 0.508092
\(280\) −1.18200 −0.0706382
\(281\) 1.42401 0.0849492 0.0424746 0.999098i \(-0.486476\pi\)
0.0424746 + 0.999098i \(0.486476\pi\)
\(282\) 21.3545 1.27164
\(283\) −5.41435 −0.321849 −0.160925 0.986967i \(-0.551448\pi\)
−0.160925 + 0.986967i \(0.551448\pi\)
\(284\) −16.2139 −0.962117
\(285\) −0.355003 −0.0210285
\(286\) −9.87673 −0.584023
\(287\) −6.34625 −0.374607
\(288\) −19.5460 −1.15176
\(289\) −16.9961 −0.999771
\(290\) 2.65334 0.155809
\(291\) −2.85023 −0.167084
\(292\) −5.11075 −0.299084
\(293\) 12.0874 0.706152 0.353076 0.935595i \(-0.385136\pi\)
0.353076 + 0.935595i \(0.385136\pi\)
\(294\) 2.71076 0.158095
\(295\) 1.25806 0.0732472
\(296\) −99.8074 −5.80119
\(297\) −3.25358 −0.188792
\(298\) 58.3000 3.37723
\(299\) 7.47099 0.432059
\(300\) 26.6504 1.53866
\(301\) 2.41223 0.139039
\(302\) −7.66870 −0.441284
\(303\) 10.0545 0.577617
\(304\) 37.9097 2.17427
\(305\) −0.468233 −0.0268110
\(306\) −0.169062 −0.00966464
\(307\) 3.96360 0.226215 0.113107 0.993583i \(-0.463920\pi\)
0.113107 + 0.993583i \(0.463920\pi\)
\(308\) 17.4008 0.991505
\(309\) −9.36566 −0.532794
\(310\) −2.99606 −0.170165
\(311\) −8.25019 −0.467825 −0.233913 0.972258i \(-0.575153\pi\)
−0.233913 + 0.972258i \(0.575153\pi\)
\(312\) 10.1640 0.575424
\(313\) −3.41258 −0.192890 −0.0964452 0.995338i \(-0.530747\pi\)
−0.0964452 + 0.995338i \(0.530747\pi\)
\(314\) −20.5921 −1.16208
\(315\) 0.130231 0.00733768
\(316\) −50.6094 −2.84700
\(317\) −1.19667 −0.0672116 −0.0336058 0.999435i \(-0.510699\pi\)
−0.0336058 + 0.999435i \(0.510699\pi\)
\(318\) −18.7204 −1.04979
\(319\) −24.4539 −1.36916
\(320\) 3.27800 0.183246
\(321\) −11.7033 −0.653215
\(322\) −18.0846 −1.00781
\(323\) 0.170009 0.00945957
\(324\) 5.34821 0.297123
\(325\) −5.58027 −0.309538
\(326\) −14.6883 −0.813511
\(327\) −5.17573 −0.286218
\(328\) 57.5998 3.18042
\(329\) 7.87767 0.434310
\(330\) 1.14859 0.0632280
\(331\) 0.820069 0.0450751 0.0225375 0.999746i \(-0.492825\pi\)
0.0225375 + 0.999746i \(0.492825\pi\)
\(332\) 4.10960 0.225543
\(333\) 10.9966 0.602610
\(334\) −34.7638 −1.90219
\(335\) 1.67753 0.0916534
\(336\) −13.9070 −0.758687
\(337\) −17.0703 −0.929878 −0.464939 0.885343i \(-0.653924\pi\)
−0.464939 + 0.885343i \(0.653924\pi\)
\(338\) 31.8404 1.73189
\(339\) −8.66917 −0.470845
\(340\) 0.0434389 0.00235580
\(341\) 27.6125 1.49530
\(342\) −7.38938 −0.399572
\(343\) 1.00000 0.0539949
\(344\) −21.8939 −1.18044
\(345\) −0.868824 −0.0467759
\(346\) 9.27555 0.498657
\(347\) −10.3864 −0.557570 −0.278785 0.960354i \(-0.589932\pi\)
−0.278785 + 0.960354i \(0.589932\pi\)
\(348\) 40.1972 2.15480
\(349\) −15.2538 −0.816516 −0.408258 0.912867i \(-0.633864\pi\)
−0.408258 + 0.912867i \(0.633864\pi\)
\(350\) 13.5078 0.722023
\(351\) −1.11985 −0.0597733
\(352\) −63.5946 −3.38960
\(353\) −23.6146 −1.25688 −0.628438 0.777859i \(-0.716306\pi\)
−0.628438 + 0.777859i \(0.716306\pi\)
\(354\) 26.1866 1.39180
\(355\) −0.394814 −0.0209546
\(356\) 13.5918 0.720366
\(357\) −0.0623671 −0.00330082
\(358\) −31.0946 −1.64340
\(359\) 0.529839 0.0279638 0.0139819 0.999902i \(-0.495549\pi\)
0.0139819 + 0.999902i \(0.495549\pi\)
\(360\) −1.18200 −0.0622970
\(361\) −11.5692 −0.608906
\(362\) 7.93044 0.416814
\(363\) 0.414226 0.0217412
\(364\) 5.98922 0.313920
\(365\) −0.124449 −0.00651394
\(366\) −9.74628 −0.509446
\(367\) −34.0933 −1.77966 −0.889829 0.456294i \(-0.849177\pi\)
−0.889829 + 0.456294i \(0.849177\pi\)
\(368\) 92.7790 4.83644
\(369\) −6.34625 −0.330373
\(370\) −3.88207 −0.201819
\(371\) −6.90598 −0.358540
\(372\) −45.3893 −2.35333
\(373\) −16.9473 −0.877497 −0.438749 0.898610i \(-0.644578\pi\)
−0.438749 + 0.898610i \(0.644578\pi\)
\(374\) −0.550057 −0.0284428
\(375\) 1.30010 0.0671369
\(376\) −71.4993 −3.68729
\(377\) −8.41683 −0.433489
\(378\) 2.71076 0.139426
\(379\) 25.2513 1.29707 0.648537 0.761183i \(-0.275381\pi\)
0.648537 + 0.761183i \(0.275381\pi\)
\(380\) 1.89863 0.0973977
\(381\) 0.493993 0.0253080
\(382\) 30.6638 1.56890
\(383\) −1.00000 −0.0510976
\(384\) 29.1395 1.48702
\(385\) 0.423717 0.0215946
\(386\) −9.43749 −0.480355
\(387\) 2.41223 0.122621
\(388\) 15.2437 0.773879
\(389\) 9.41733 0.477477 0.238739 0.971084i \(-0.423266\pi\)
0.238739 + 0.971084i \(0.423266\pi\)
\(390\) 0.395336 0.0200186
\(391\) 0.416076 0.0210419
\(392\) −9.07620 −0.458417
\(393\) 18.9040 0.953580
\(394\) −29.6771 −1.49511
\(395\) −1.23236 −0.0620066
\(396\) 17.4008 0.874425
\(397\) 20.0566 1.00661 0.503306 0.864108i \(-0.332117\pi\)
0.503306 + 0.864108i \(0.332117\pi\)
\(398\) −62.8143 −3.14860
\(399\) −2.72595 −0.136468
\(400\) −69.2990 −3.46495
\(401\) −1.89294 −0.0945290 −0.0472645 0.998882i \(-0.515050\pi\)
−0.0472645 + 0.998882i \(0.515050\pi\)
\(402\) 34.9179 1.74154
\(403\) 9.50399 0.473427
\(404\) −53.7737 −2.67534
\(405\) 0.130231 0.00647123
\(406\) 20.3741 1.01115
\(407\) 35.7783 1.77346
\(408\) 0.566056 0.0280240
\(409\) −8.73941 −0.432136 −0.216068 0.976378i \(-0.569323\pi\)
−0.216068 + 0.976378i \(0.569323\pi\)
\(410\) 2.24038 0.110645
\(411\) −13.6960 −0.675572
\(412\) 50.0896 2.46774
\(413\) 9.66024 0.475349
\(414\) −18.0846 −0.888808
\(415\) 0.100070 0.00491225
\(416\) −21.8887 −1.07318
\(417\) −2.92684 −0.143328
\(418\) −24.0419 −1.17593
\(419\) −15.8166 −0.772692 −0.386346 0.922354i \(-0.626263\pi\)
−0.386346 + 0.922354i \(0.626263\pi\)
\(420\) −0.696503 −0.0339859
\(421\) 0.369195 0.0179935 0.00899673 0.999960i \(-0.497136\pi\)
0.00899673 + 0.999960i \(0.497136\pi\)
\(422\) −55.0519 −2.67989
\(423\) 7.87767 0.383025
\(424\) 62.6800 3.04401
\(425\) −0.310778 −0.0150749
\(426\) −8.21806 −0.398166
\(427\) −3.59541 −0.173994
\(428\) 62.5918 3.02549
\(429\) −3.64353 −0.175911
\(430\) −0.851577 −0.0410667
\(431\) 35.1026 1.69083 0.845416 0.534109i \(-0.179353\pi\)
0.845416 + 0.534109i \(0.179353\pi\)
\(432\) −13.9070 −0.669099
\(433\) −13.6961 −0.658192 −0.329096 0.944297i \(-0.606744\pi\)
−0.329096 + 0.944297i \(0.606744\pi\)
\(434\) −23.0057 −1.10431
\(435\) 0.978817 0.0469307
\(436\) 27.6809 1.32568
\(437\) 18.1859 0.869949
\(438\) −2.59040 −0.123774
\(439\) −20.7546 −0.990563 −0.495281 0.868733i \(-0.664935\pi\)
−0.495281 + 0.868733i \(0.664935\pi\)
\(440\) −3.84574 −0.183338
\(441\) 1.00000 0.0476190
\(442\) −0.189325 −0.00900526
\(443\) −20.9446 −0.995106 −0.497553 0.867434i \(-0.665768\pi\)
−0.497553 + 0.867434i \(0.665768\pi\)
\(444\) −58.8122 −2.79110
\(445\) 0.330966 0.0156893
\(446\) −74.4685 −3.52618
\(447\) 21.5069 1.01724
\(448\) 25.1706 1.18920
\(449\) 30.2255 1.42643 0.713214 0.700946i \(-0.247239\pi\)
0.713214 + 0.700946i \(0.247239\pi\)
\(450\) 13.5078 0.636765
\(451\) −20.6480 −0.972277
\(452\) 46.3646 2.18081
\(453\) −2.82899 −0.132917
\(454\) 55.7382 2.61592
\(455\) 0.145840 0.00683706
\(456\) 24.7412 1.15861
\(457\) −17.0866 −0.799277 −0.399638 0.916673i \(-0.630864\pi\)
−0.399638 + 0.916673i \(0.630864\pi\)
\(458\) −15.2307 −0.711683
\(459\) −0.0623671 −0.00291105
\(460\) 4.64665 0.216651
\(461\) −29.9374 −1.39432 −0.697161 0.716914i \(-0.745554\pi\)
−0.697161 + 0.716914i \(0.745554\pi\)
\(462\) 8.81967 0.410328
\(463\) 16.4784 0.765815 0.382907 0.923787i \(-0.374923\pi\)
0.382907 + 0.923787i \(0.374923\pi\)
\(464\) −104.525 −4.85245
\(465\) −1.10525 −0.0512546
\(466\) −21.1445 −0.979499
\(467\) −25.0695 −1.16008 −0.580039 0.814589i \(-0.696963\pi\)
−0.580039 + 0.814589i \(0.696963\pi\)
\(468\) 5.98922 0.276852
\(469\) 12.8812 0.594799
\(470\) −2.78101 −0.128278
\(471\) −7.59643 −0.350025
\(472\) −87.6782 −4.03572
\(473\) 7.84838 0.360869
\(474\) −25.6515 −1.17821
\(475\) −13.5835 −0.623254
\(476\) 0.333553 0.0152884
\(477\) −6.90598 −0.316203
\(478\) −21.3971 −0.978679
\(479\) −37.6782 −1.72156 −0.860781 0.508976i \(-0.830024\pi\)
−0.860781 + 0.508976i \(0.830024\pi\)
\(480\) 2.54550 0.116186
\(481\) 12.3146 0.561497
\(482\) 32.6505 1.48719
\(483\) −6.67141 −0.303559
\(484\) −2.21537 −0.100699
\(485\) 0.371189 0.0168548
\(486\) 2.71076 0.122963
\(487\) −31.7521 −1.43882 −0.719412 0.694584i \(-0.755588\pi\)
−0.719412 + 0.694584i \(0.755588\pi\)
\(488\) 32.6326 1.47721
\(489\) −5.41853 −0.245034
\(490\) −0.353025 −0.0159480
\(491\) −22.7319 −1.02588 −0.512938 0.858425i \(-0.671443\pi\)
−0.512938 + 0.858425i \(0.671443\pi\)
\(492\) 33.9411 1.53018
\(493\) −0.468752 −0.0211115
\(494\) −8.27503 −0.372311
\(495\) 0.423717 0.0190446
\(496\) 118.026 5.29952
\(497\) −3.03164 −0.135988
\(498\) 2.08296 0.0933397
\(499\) 1.39611 0.0624983 0.0312492 0.999512i \(-0.490051\pi\)
0.0312492 + 0.999512i \(0.490051\pi\)
\(500\) −6.95322 −0.310957
\(501\) −12.8244 −0.572952
\(502\) 17.3268 0.773333
\(503\) 26.4249 1.17823 0.589114 0.808050i \(-0.299477\pi\)
0.589114 + 0.808050i \(0.299477\pi\)
\(504\) −9.07620 −0.404286
\(505\) −1.30941 −0.0582680
\(506\) −58.8396 −2.61574
\(507\) 11.7459 0.521655
\(508\) −2.64198 −0.117219
\(509\) 34.0757 1.51038 0.755189 0.655507i \(-0.227545\pi\)
0.755189 + 0.655507i \(0.227545\pi\)
\(510\) 0.0220171 0.000974935 0
\(511\) −0.955600 −0.0422732
\(512\) −19.3811 −0.856534
\(513\) −2.72595 −0.120353
\(514\) 72.8340 3.21257
\(515\) 1.21970 0.0537464
\(516\) −12.9011 −0.567941
\(517\) 25.6306 1.12723
\(518\) −29.8091 −1.30974
\(519\) 3.42175 0.150198
\(520\) −1.32367 −0.0580467
\(521\) −17.2741 −0.756792 −0.378396 0.925644i \(-0.623524\pi\)
−0.378396 + 0.925644i \(0.623524\pi\)
\(522\) 20.3741 0.891750
\(523\) 17.7980 0.778251 0.389126 0.921185i \(-0.372777\pi\)
0.389126 + 0.921185i \(0.372777\pi\)
\(524\) −101.103 −4.41669
\(525\) 4.98304 0.217478
\(526\) 49.5329 2.15974
\(527\) 0.529298 0.0230566
\(528\) −45.2474 −1.96914
\(529\) 21.5076 0.935115
\(530\) 2.43798 0.105899
\(531\) 9.66024 0.419218
\(532\) 14.5789 0.632078
\(533\) −7.10687 −0.307833
\(534\) 6.88907 0.298119
\(535\) 1.52413 0.0658940
\(536\) −116.912 −5.04985
\(537\) −11.4708 −0.495002
\(538\) −55.7691 −2.40438
\(539\) 3.25358 0.140142
\(540\) −0.696503 −0.0299727
\(541\) −6.78690 −0.291791 −0.145896 0.989300i \(-0.546606\pi\)
−0.145896 + 0.989300i \(0.546606\pi\)
\(542\) −5.40561 −0.232191
\(543\) 2.92554 0.125547
\(544\) −1.21903 −0.0522654
\(545\) 0.674040 0.0288727
\(546\) 3.03565 0.129914
\(547\) 19.6562 0.840439 0.420220 0.907422i \(-0.361953\pi\)
0.420220 + 0.907422i \(0.361953\pi\)
\(548\) 73.2490 3.12904
\(549\) −3.59541 −0.153448
\(550\) 43.9488 1.87398
\(551\) −20.4882 −0.872828
\(552\) 60.5510 2.57722
\(553\) −9.46286 −0.402402
\(554\) 61.1500 2.59801
\(555\) −1.43210 −0.0607892
\(556\) 15.6534 0.663852
\(557\) 24.2238 1.02640 0.513199 0.858270i \(-0.328460\pi\)
0.513199 + 0.858270i \(0.328460\pi\)
\(558\) −23.0057 −0.973909
\(559\) 2.70134 0.114255
\(560\) 1.81112 0.0765337
\(561\) −0.202916 −0.00856713
\(562\) −3.86014 −0.162830
\(563\) 16.6008 0.699641 0.349821 0.936817i \(-0.386243\pi\)
0.349821 + 0.936817i \(0.386243\pi\)
\(564\) −42.1314 −1.77405
\(565\) 1.12899 0.0474972
\(566\) 14.6770 0.616920
\(567\) 1.00000 0.0419961
\(568\) 27.5158 1.15454
\(569\) 27.7424 1.16302 0.581511 0.813539i \(-0.302462\pi\)
0.581511 + 0.813539i \(0.302462\pi\)
\(570\) 0.962327 0.0403074
\(571\) 24.3865 1.02054 0.510272 0.860013i \(-0.329545\pi\)
0.510272 + 0.860013i \(0.329545\pi\)
\(572\) 19.4864 0.814767
\(573\) 11.3119 0.472562
\(574\) 17.2032 0.718046
\(575\) −33.2439 −1.38637
\(576\) 25.1706 1.04878
\(577\) −23.9450 −0.996845 −0.498423 0.866934i \(-0.666087\pi\)
−0.498423 + 0.866934i \(0.666087\pi\)
\(578\) 46.0724 1.91636
\(579\) −3.48149 −0.144686
\(580\) −5.23492 −0.217368
\(581\) 0.768405 0.0318788
\(582\) 7.72629 0.320265
\(583\) −22.4691 −0.930577
\(584\) 8.67322 0.358900
\(585\) 0.145840 0.00602972
\(586\) −32.7659 −1.35355
\(587\) −33.8816 −1.39844 −0.699222 0.714905i \(-0.746470\pi\)
−0.699222 + 0.714905i \(0.746470\pi\)
\(588\) −5.34821 −0.220557
\(589\) 23.1346 0.953245
\(590\) −3.41030 −0.140400
\(591\) −10.9479 −0.450337
\(592\) 152.929 6.28536
\(593\) 46.5077 1.90984 0.954921 0.296860i \(-0.0959395\pi\)
0.954921 + 0.296860i \(0.0959395\pi\)
\(594\) 8.81967 0.361875
\(595\) 0.00812213 0.000332975 0
\(596\) −115.024 −4.71155
\(597\) −23.1722 −0.948376
\(598\) −20.2521 −0.828169
\(599\) 25.3698 1.03658 0.518291 0.855204i \(-0.326568\pi\)
0.518291 + 0.855204i \(0.326568\pi\)
\(600\) −45.2271 −1.84639
\(601\) 16.8004 0.685303 0.342651 0.939463i \(-0.388675\pi\)
0.342651 + 0.939463i \(0.388675\pi\)
\(602\) −6.53898 −0.266509
\(603\) 12.8812 0.524563
\(604\) 15.1300 0.615632
\(605\) −0.0539450 −0.00219318
\(606\) −27.2554 −1.10717
\(607\) −31.3882 −1.27401 −0.637004 0.770861i \(-0.719827\pi\)
−0.637004 + 0.770861i \(0.719827\pi\)
\(608\) −53.2814 −2.16085
\(609\) 7.51601 0.304564
\(610\) 1.26927 0.0513911
\(611\) 8.82183 0.356893
\(612\) 0.333553 0.0134831
\(613\) −44.4574 −1.79562 −0.897808 0.440387i \(-0.854841\pi\)
−0.897808 + 0.440387i \(0.854841\pi\)
\(614\) −10.7444 −0.433608
\(615\) 0.826478 0.0333268
\(616\) −29.5301 −1.18980
\(617\) 9.45031 0.380455 0.190228 0.981740i \(-0.439077\pi\)
0.190228 + 0.981740i \(0.439077\pi\)
\(618\) 25.3880 1.02126
\(619\) 18.3975 0.739457 0.369729 0.929140i \(-0.379451\pi\)
0.369729 + 0.929140i \(0.379451\pi\)
\(620\) 5.91109 0.237395
\(621\) −6.67141 −0.267714
\(622\) 22.3643 0.896726
\(623\) 2.54138 0.101818
\(624\) −15.5738 −0.623449
\(625\) 24.7459 0.989835
\(626\) 9.25068 0.369732
\(627\) −8.86908 −0.354197
\(628\) 40.6273 1.62121
\(629\) 0.685826 0.0273457
\(630\) −0.353025 −0.0140648
\(631\) −17.5690 −0.699409 −0.349705 0.936860i \(-0.613718\pi\)
−0.349705 + 0.936860i \(0.613718\pi\)
\(632\) 85.8868 3.41639
\(633\) −20.3087 −0.807197
\(634\) 3.24388 0.128831
\(635\) −0.0643332 −0.00255299
\(636\) 36.9346 1.46455
\(637\) 1.11985 0.0443702
\(638\) 66.2887 2.62439
\(639\) −3.03164 −0.119930
\(640\) −3.79486 −0.150005
\(641\) 22.8566 0.902782 0.451391 0.892326i \(-0.350928\pi\)
0.451391 + 0.892326i \(0.350928\pi\)
\(642\) 31.7248 1.25208
\(643\) −2.16724 −0.0854676 −0.0427338 0.999086i \(-0.513607\pi\)
−0.0427338 + 0.999086i \(0.513607\pi\)
\(644\) 35.6801 1.40599
\(645\) −0.314147 −0.0123695
\(646\) −0.460854 −0.0181321
\(647\) 35.0366 1.37743 0.688715 0.725033i \(-0.258175\pi\)
0.688715 + 0.725033i \(0.258175\pi\)
\(648\) −9.07620 −0.356547
\(649\) 31.4303 1.23375
\(650\) 15.1268 0.593321
\(651\) −8.48682 −0.332625
\(652\) 28.9795 1.13492
\(653\) −26.0011 −1.01750 −0.508752 0.860913i \(-0.669893\pi\)
−0.508752 + 0.860913i \(0.669893\pi\)
\(654\) 14.0302 0.548622
\(655\) −2.46188 −0.0961938
\(656\) −88.2571 −3.44586
\(657\) −0.955600 −0.0372815
\(658\) −21.3545 −0.832483
\(659\) 37.3860 1.45635 0.728175 0.685391i \(-0.240369\pi\)
0.728175 + 0.685391i \(0.240369\pi\)
\(660\) −2.26613 −0.0882089
\(661\) −34.3439 −1.33582 −0.667912 0.744240i \(-0.732812\pi\)
−0.667912 + 0.744240i \(0.732812\pi\)
\(662\) −2.22301 −0.0863998
\(663\) −0.0698420 −0.00271244
\(664\) −6.97420 −0.270651
\(665\) 0.355003 0.0137664
\(666\) −29.8091 −1.15508
\(667\) −50.1423 −1.94152
\(668\) 68.5876 2.65373
\(669\) −27.4714 −1.06211
\(670\) −4.54739 −0.175681
\(671\) −11.6979 −0.451594
\(672\) 19.5460 0.754005
\(673\) 35.1605 1.35534 0.677669 0.735367i \(-0.262990\pi\)
0.677669 + 0.735367i \(0.262990\pi\)
\(674\) 46.2735 1.78239
\(675\) 4.98304 0.191797
\(676\) −62.8197 −2.41614
\(677\) 13.2935 0.510911 0.255456 0.966821i \(-0.417775\pi\)
0.255456 + 0.966821i \(0.417775\pi\)
\(678\) 23.5000 0.902513
\(679\) 2.85023 0.109382
\(680\) −0.0737181 −0.00282696
\(681\) 20.5618 0.787932
\(682\) −74.8509 −2.86619
\(683\) 15.3320 0.586661 0.293331 0.956011i \(-0.405236\pi\)
0.293331 + 0.956011i \(0.405236\pi\)
\(684\) 14.5789 0.557440
\(685\) 1.78364 0.0681493
\(686\) −2.71076 −0.103497
\(687\) −5.61860 −0.214363
\(688\) 33.5468 1.27896
\(689\) −7.73368 −0.294630
\(690\) 2.35517 0.0896598
\(691\) −36.1856 −1.37657 −0.688283 0.725443i \(-0.741635\pi\)
−0.688283 + 0.725443i \(0.741635\pi\)
\(692\) −18.3003 −0.695672
\(693\) 3.25358 0.123593
\(694\) 28.1550 1.06875
\(695\) 0.381166 0.0144584
\(696\) −68.2168 −2.58575
\(697\) −0.395797 −0.0149919
\(698\) 41.3493 1.56509
\(699\) −7.80020 −0.295031
\(700\) −26.6504 −1.00729
\(701\) 37.9834 1.43461 0.717307 0.696757i \(-0.245374\pi\)
0.717307 + 0.696757i \(0.245374\pi\)
\(702\) 3.03565 0.114573
\(703\) 29.9761 1.13057
\(704\) 81.8947 3.08652
\(705\) −1.02592 −0.0386382
\(706\) 64.0134 2.40918
\(707\) −10.0545 −0.378139
\(708\) −51.6650 −1.94169
\(709\) −6.57688 −0.247000 −0.123500 0.992345i \(-0.539412\pi\)
−0.123500 + 0.992345i \(0.539412\pi\)
\(710\) 1.07025 0.0401656
\(711\) −9.46286 −0.354885
\(712\) −23.0661 −0.864438
\(713\) 56.6190 2.12040
\(714\) 0.169062 0.00632699
\(715\) 0.474501 0.0177453
\(716\) 61.3483 2.29269
\(717\) −7.89339 −0.294784
\(718\) −1.43626 −0.0536009
\(719\) 6.11475 0.228042 0.114021 0.993478i \(-0.463627\pi\)
0.114021 + 0.993478i \(0.463627\pi\)
\(720\) 1.81112 0.0674964
\(721\) 9.36566 0.348795
\(722\) 31.3614 1.16715
\(723\) 12.0448 0.447950
\(724\) −15.6464 −0.581495
\(725\) 37.4526 1.39095
\(726\) −1.12287 −0.0416735
\(727\) 2.46466 0.0914092 0.0457046 0.998955i \(-0.485447\pi\)
0.0457046 + 0.998955i \(0.485447\pi\)
\(728\) −10.1640 −0.376703
\(729\) 1.00000 0.0370370
\(730\) 0.337350 0.0124859
\(731\) 0.150444 0.00556437
\(732\) 19.2290 0.710724
\(733\) 3.34622 0.123595 0.0617977 0.998089i \(-0.480317\pi\)
0.0617977 + 0.998089i \(0.480317\pi\)
\(734\) 92.4188 3.41124
\(735\) −0.130231 −0.00480364
\(736\) −130.400 −4.80659
\(737\) 41.9100 1.54378
\(738\) 17.2032 0.633257
\(739\) −24.8920 −0.915666 −0.457833 0.889038i \(-0.651374\pi\)
−0.457833 + 0.889038i \(0.651374\pi\)
\(740\) 7.65917 0.281557
\(741\) −3.05266 −0.112142
\(742\) 18.7204 0.687249
\(743\) −5.19266 −0.190500 −0.0952501 0.995453i \(-0.530365\pi\)
−0.0952501 + 0.995453i \(0.530365\pi\)
\(744\) 77.0281 2.82399
\(745\) −2.80086 −0.102616
\(746\) 45.9400 1.68198
\(747\) 0.768405 0.0281145
\(748\) 1.08524 0.0396803
\(749\) 11.7033 0.427629
\(750\) −3.52426 −0.128688
\(751\) 24.9740 0.911315 0.455658 0.890155i \(-0.349404\pi\)
0.455658 + 0.890155i \(0.349404\pi\)
\(752\) 109.554 3.99504
\(753\) 6.39187 0.232933
\(754\) 22.8160 0.830909
\(755\) 0.368422 0.0134082
\(756\) −5.34821 −0.194513
\(757\) −26.0322 −0.946158 −0.473079 0.881020i \(-0.656857\pi\)
−0.473079 + 0.881020i \(0.656857\pi\)
\(758\) −68.4503 −2.48623
\(759\) −21.7059 −0.787876
\(760\) −3.22208 −0.116877
\(761\) 9.77322 0.354279 0.177139 0.984186i \(-0.443316\pi\)
0.177139 + 0.984186i \(0.443316\pi\)
\(762\) −1.33910 −0.0485104
\(763\) 5.17573 0.187374
\(764\) −60.4985 −2.18876
\(765\) 0.00812213 0.000293656 0
\(766\) 2.71076 0.0979437
\(767\) 10.8180 0.390617
\(768\) −28.6489 −1.03378
\(769\) 44.8402 1.61698 0.808490 0.588510i \(-0.200285\pi\)
0.808490 + 0.588510i \(0.200285\pi\)
\(770\) −1.14859 −0.0413924
\(771\) 26.8685 0.967645
\(772\) 18.6198 0.670140
\(773\) −15.1776 −0.545899 −0.272950 0.962028i \(-0.587999\pi\)
−0.272950 + 0.962028i \(0.587999\pi\)
\(774\) −6.53898 −0.235039
\(775\) −42.2901 −1.51911
\(776\) −25.8693 −0.928653
\(777\) −10.9966 −0.394501
\(778\) −25.5281 −0.915227
\(779\) −17.2995 −0.619820
\(780\) −0.779981 −0.0279278
\(781\) −9.86370 −0.352951
\(782\) −1.12788 −0.0403330
\(783\) 7.51601 0.268600
\(784\) 13.9070 0.496677
\(785\) 0.989290 0.0353093
\(786\) −51.2441 −1.82782
\(787\) −6.14414 −0.219015 −0.109507 0.993986i \(-0.534927\pi\)
−0.109507 + 0.993986i \(0.534927\pi\)
\(788\) 58.5518 2.08582
\(789\) 18.2727 0.650525
\(790\) 3.34062 0.118854
\(791\) 8.66917 0.308240
\(792\) −29.5301 −1.04931
\(793\) −4.02633 −0.142979
\(794\) −54.3686 −1.92947
\(795\) 0.899372 0.0318974
\(796\) 123.930 4.39258
\(797\) −30.1003 −1.06621 −0.533104 0.846050i \(-0.678975\pi\)
−0.533104 + 0.846050i \(0.678975\pi\)
\(798\) 7.38938 0.261581
\(799\) 0.491307 0.0173812
\(800\) 97.3987 3.44356
\(801\) 2.54138 0.0897952
\(802\) 5.13131 0.181193
\(803\) −3.10912 −0.109718
\(804\) −68.8915 −2.42961
\(805\) 0.868824 0.0306220
\(806\) −25.7630 −0.907464
\(807\) −20.5732 −0.724212
\(808\) 91.2569 3.21041
\(809\) 5.38338 0.189270 0.0946348 0.995512i \(-0.469832\pi\)
0.0946348 + 0.995512i \(0.469832\pi\)
\(810\) −0.353025 −0.0124040
\(811\) 0.721790 0.0253455 0.0126727 0.999920i \(-0.495966\pi\)
0.0126727 + 0.999920i \(0.495966\pi\)
\(812\) −40.1972 −1.41065
\(813\) −1.99413 −0.0699373
\(814\) −96.9864 −3.39937
\(815\) 0.705660 0.0247182
\(816\) −0.867337 −0.0303629
\(817\) 6.57561 0.230052
\(818\) 23.6904 0.828317
\(819\) 1.11985 0.0391308
\(820\) −4.42018 −0.154359
\(821\) 28.8889 1.00823 0.504115 0.863637i \(-0.331819\pi\)
0.504115 + 0.863637i \(0.331819\pi\)
\(822\) 37.1265 1.29493
\(823\) −6.54311 −0.228078 −0.114039 0.993476i \(-0.536379\pi\)
−0.114039 + 0.993476i \(0.536379\pi\)
\(824\) −85.0046 −2.96128
\(825\) 16.2127 0.564454
\(826\) −26.1866 −0.911147
\(827\) 39.3333 1.36775 0.683876 0.729599i \(-0.260293\pi\)
0.683876 + 0.729599i \(0.260293\pi\)
\(828\) 35.6801 1.23997
\(829\) 1.81794 0.0631396 0.0315698 0.999502i \(-0.489949\pi\)
0.0315698 + 0.999502i \(0.489949\pi\)
\(830\) −0.271266 −0.00941578
\(831\) 22.5582 0.782537
\(832\) 28.1874 0.977223
\(833\) 0.0623671 0.00216089
\(834\) 7.93397 0.274731
\(835\) 1.67013 0.0577974
\(836\) 47.4338 1.64053
\(837\) −8.48682 −0.293347
\(838\) 42.8750 1.48109
\(839\) 38.7823 1.33891 0.669457 0.742851i \(-0.266527\pi\)
0.669457 + 0.742851i \(0.266527\pi\)
\(840\) 1.18200 0.0407830
\(841\) 27.4904 0.947944
\(842\) −1.00080 −0.0344898
\(843\) −1.42401 −0.0490454
\(844\) 108.615 3.73869
\(845\) −1.52968 −0.0526227
\(846\) −21.3545 −0.734181
\(847\) −0.414226 −0.0142330
\(848\) −96.0412 −3.29807
\(849\) 5.41435 0.185820
\(850\) 0.842443 0.0288956
\(851\) 73.3628 2.51484
\(852\) 16.2139 0.555479
\(853\) 33.2662 1.13901 0.569506 0.821987i \(-0.307135\pi\)
0.569506 + 0.821987i \(0.307135\pi\)
\(854\) 9.74628 0.333511
\(855\) 0.355003 0.0121408
\(856\) −106.222 −3.63058
\(857\) 2.22266 0.0759245 0.0379622 0.999279i \(-0.487913\pi\)
0.0379622 + 0.999279i \(0.487913\pi\)
\(858\) 9.87673 0.337186
\(859\) 47.6152 1.62461 0.812305 0.583233i \(-0.198212\pi\)
0.812305 + 0.583233i \(0.198212\pi\)
\(860\) 1.68013 0.0572918
\(861\) 6.34625 0.216280
\(862\) −95.1546 −3.24098
\(863\) −2.91403 −0.0991948 −0.0495974 0.998769i \(-0.515794\pi\)
−0.0495974 + 0.998769i \(0.515794\pi\)
\(864\) 19.5460 0.664970
\(865\) −0.445618 −0.0151515
\(866\) 37.1268 1.26162
\(867\) 16.9961 0.577218
\(868\) 45.3893 1.54061
\(869\) −30.7882 −1.04442
\(870\) −2.65334 −0.0899566
\(871\) 14.4251 0.488775
\(872\) −46.9760 −1.59081
\(873\) 2.85023 0.0964658
\(874\) −49.2976 −1.66752
\(875\) −1.30010 −0.0439514
\(876\) 5.11075 0.172676
\(877\) 7.83945 0.264720 0.132360 0.991202i \(-0.457745\pi\)
0.132360 + 0.991202i \(0.457745\pi\)
\(878\) 56.2607 1.89871
\(879\) −12.0874 −0.407697
\(880\) 5.89261 0.198640
\(881\) −38.3717 −1.29278 −0.646389 0.763008i \(-0.723721\pi\)
−0.646389 + 0.763008i \(0.723721\pi\)
\(882\) −2.71076 −0.0912760
\(883\) 17.7826 0.598431 0.299216 0.954186i \(-0.403275\pi\)
0.299216 + 0.954186i \(0.403275\pi\)
\(884\) 0.373530 0.0125632
\(885\) −1.25806 −0.0422893
\(886\) 56.7756 1.90741
\(887\) 1.22071 0.0409875 0.0204938 0.999790i \(-0.493476\pi\)
0.0204938 + 0.999790i \(0.493476\pi\)
\(888\) 99.8074 3.34932
\(889\) −0.493993 −0.0165680
\(890\) −0.897170 −0.0300732
\(891\) 3.25358 0.108999
\(892\) 146.923 4.91935
\(893\) 21.4741 0.718603
\(894\) −58.3000 −1.94984
\(895\) 1.49385 0.0499340
\(896\) −29.1395 −0.973482
\(897\) −7.47099 −0.249449
\(898\) −81.9340 −2.73417
\(899\) −63.7870 −2.12741
\(900\) −26.6504 −0.888345
\(901\) −0.430706 −0.0143489
\(902\) 55.9718 1.86366
\(903\) −2.41223 −0.0802740
\(904\) −78.6831 −2.61696
\(905\) −0.380996 −0.0126647
\(906\) 7.66870 0.254776
\(907\) −22.1739 −0.736274 −0.368137 0.929772i \(-0.620004\pi\)
−0.368137 + 0.929772i \(0.620004\pi\)
\(908\) −109.969 −3.64945
\(909\) −10.0545 −0.333487
\(910\) −0.395336 −0.0131053
\(911\) −13.8113 −0.457588 −0.228794 0.973475i \(-0.573478\pi\)
−0.228794 + 0.973475i \(0.573478\pi\)
\(912\) −37.9097 −1.25531
\(913\) 2.50007 0.0827401
\(914\) 46.3176 1.53205
\(915\) 0.468233 0.0154793
\(916\) 30.0495 0.992863
\(917\) −18.9040 −0.624265
\(918\) 0.169062 0.00557988
\(919\) −54.5506 −1.79946 −0.899730 0.436448i \(-0.856236\pi\)
−0.899730 + 0.436448i \(0.856236\pi\)
\(920\) −7.88562 −0.259981
\(921\) −3.96360 −0.130605
\(922\) 81.1530 2.67263
\(923\) −3.39500 −0.111748
\(924\) −17.4008 −0.572445
\(925\) −54.7965 −1.80170
\(926\) −44.6689 −1.46791
\(927\) 9.36566 0.307609
\(928\) 146.908 4.82250
\(929\) 22.3940 0.734724 0.367362 0.930078i \(-0.380261\pi\)
0.367362 + 0.930078i \(0.380261\pi\)
\(930\) 2.99606 0.0982446
\(931\) 2.72595 0.0893393
\(932\) 41.7172 1.36649
\(933\) 8.25019 0.270099
\(934\) 67.9574 2.22363
\(935\) 0.0264260 0.000864222 0
\(936\) −10.1640 −0.332221
\(937\) −16.2670 −0.531419 −0.265710 0.964053i \(-0.585606\pi\)
−0.265710 + 0.964053i \(0.585606\pi\)
\(938\) −34.9179 −1.14011
\(939\) 3.41258 0.111365
\(940\) 5.48682 0.178960
\(941\) 42.6848 1.39149 0.695743 0.718291i \(-0.255075\pi\)
0.695743 + 0.718291i \(0.255075\pi\)
\(942\) 20.5921 0.670926
\(943\) −42.3384 −1.37873
\(944\) 134.345 4.37254
\(945\) −0.130231 −0.00423641
\(946\) −21.2751 −0.691712
\(947\) −2.02208 −0.0657088 −0.0328544 0.999460i \(-0.510460\pi\)
−0.0328544 + 0.999460i \(0.510460\pi\)
\(948\) 50.6094 1.64372
\(949\) −1.07013 −0.0347379
\(950\) 36.8216 1.19465
\(951\) 1.19667 0.0388047
\(952\) −0.566056 −0.0183460
\(953\) 44.7699 1.45024 0.725119 0.688624i \(-0.241785\pi\)
0.725119 + 0.688624i \(0.241785\pi\)
\(954\) 18.7204 0.606097
\(955\) −1.47316 −0.0476703
\(956\) 42.2155 1.36535
\(957\) 24.4539 0.790483
\(958\) 102.137 3.29988
\(959\) 13.6960 0.442266
\(960\) −3.27800 −0.105797
\(961\) 41.0260 1.32342
\(962\) −33.3819 −1.07627
\(963\) 11.7033 0.377134
\(964\) −64.4180 −2.07476
\(965\) 0.453398 0.0145954
\(966\) 18.0846 0.581862
\(967\) 22.2040 0.714032 0.357016 0.934098i \(-0.383794\pi\)
0.357016 + 0.934098i \(0.383794\pi\)
\(968\) 3.75960 0.120838
\(969\) −0.170009 −0.00546149
\(970\) −1.00620 −0.0323072
\(971\) 16.5395 0.530778 0.265389 0.964141i \(-0.414500\pi\)
0.265389 + 0.964141i \(0.414500\pi\)
\(972\) −5.34821 −0.171544
\(973\) 2.92684 0.0938303
\(974\) 86.0722 2.75793
\(975\) 5.58027 0.178712
\(976\) −50.0012 −1.60050
\(977\) 39.3154 1.25781 0.628906 0.777482i \(-0.283503\pi\)
0.628906 + 0.777482i \(0.283503\pi\)
\(978\) 14.6883 0.469681
\(979\) 8.26858 0.264265
\(980\) 0.696503 0.0222490
\(981\) 5.17573 0.165248
\(982\) 61.6207 1.96640
\(983\) 3.20276 0.102152 0.0510761 0.998695i \(-0.483735\pi\)
0.0510761 + 0.998695i \(0.483735\pi\)
\(984\) −57.5998 −1.83622
\(985\) 1.42576 0.0454284
\(986\) 1.27067 0.0404665
\(987\) −7.87767 −0.250749
\(988\) 16.3263 0.519408
\(989\) 16.0930 0.511727
\(990\) −1.14859 −0.0365047
\(991\) 19.0357 0.604689 0.302344 0.953199i \(-0.402231\pi\)
0.302344 + 0.953199i \(0.402231\pi\)
\(992\) −165.884 −5.26681
\(993\) −0.820069 −0.0260241
\(994\) 8.21806 0.260661
\(995\) 3.01774 0.0956689
\(996\) −4.10960 −0.130218
\(997\) 55.0507 1.74347 0.871736 0.489976i \(-0.162994\pi\)
0.871736 + 0.489976i \(0.162994\pi\)
\(998\) −3.78451 −0.119797
\(999\) −10.9966 −0.347917
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 \(a_p\))