Properties

Label 4015.2.a.h.1.6
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.99859 q^{2}\) \(+2.62046 q^{3}\) \(+1.99434 q^{4}\) \(+1.00000 q^{5}\) \(-5.23721 q^{6}\) \(+2.62346 q^{7}\) \(+0.0113035 q^{8}\) \(+3.86680 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.99859 q^{2}\) \(+2.62046 q^{3}\) \(+1.99434 q^{4}\) \(+1.00000 q^{5}\) \(-5.23721 q^{6}\) \(+2.62346 q^{7}\) \(+0.0113035 q^{8}\) \(+3.86680 q^{9}\) \(-1.99859 q^{10}\) \(+1.00000 q^{11}\) \(+5.22609 q^{12}\) \(-1.22641 q^{13}\) \(-5.24320 q^{14}\) \(+2.62046 q^{15}\) \(-4.01128 q^{16}\) \(-6.75860 q^{17}\) \(-7.72812 q^{18}\) \(+5.20995 q^{19}\) \(+1.99434 q^{20}\) \(+6.87466 q^{21}\) \(-1.99859 q^{22}\) \(-0.411436 q^{23}\) \(+0.0296204 q^{24}\) \(+1.00000 q^{25}\) \(+2.45109 q^{26}\) \(+2.27140 q^{27}\) \(+5.23208 q^{28}\) \(+2.08179 q^{29}\) \(-5.23721 q^{30}\) \(-5.35960 q^{31}\) \(+7.99428 q^{32}\) \(+2.62046 q^{33}\) \(+13.5076 q^{34}\) \(+2.62346 q^{35}\) \(+7.71172 q^{36}\) \(-8.62271 q^{37}\) \(-10.4125 q^{38}\) \(-3.21376 q^{39}\) \(+0.0113035 q^{40}\) \(+4.78486 q^{41}\) \(-13.7396 q^{42}\) \(+7.01675 q^{43}\) \(+1.99434 q^{44}\) \(+3.86680 q^{45}\) \(+0.822290 q^{46}\) \(+9.82038 q^{47}\) \(-10.5114 q^{48}\) \(-0.117475 q^{49}\) \(-1.99859 q^{50}\) \(-17.7106 q^{51}\) \(-2.44589 q^{52}\) \(+10.9519 q^{53}\) \(-4.53959 q^{54}\) \(+1.00000 q^{55}\) \(+0.0296543 q^{56}\) \(+13.6525 q^{57}\) \(-4.16064 q^{58}\) \(+5.13101 q^{59}\) \(+5.22609 q^{60}\) \(+13.4387 q^{61}\) \(+10.7116 q^{62}\) \(+10.1444 q^{63}\) \(-7.95469 q^{64}\) \(-1.22641 q^{65}\) \(-5.23721 q^{66}\) \(-0.917153 q^{67}\) \(-13.4790 q^{68}\) \(-1.07815 q^{69}\) \(-5.24320 q^{70}\) \(+2.96839 q^{71}\) \(+0.0437084 q^{72}\) \(+1.00000 q^{73}\) \(+17.2332 q^{74}\) \(+2.62046 q^{75}\) \(+10.3904 q^{76}\) \(+2.62346 q^{77}\) \(+6.42297 q^{78}\) \(+7.46040 q^{79}\) \(-4.01128 q^{80}\) \(-5.64828 q^{81}\) \(-9.56296 q^{82}\) \(+11.6845 q^{83}\) \(+13.7104 q^{84}\) \(-6.75860 q^{85}\) \(-14.0236 q^{86}\) \(+5.45524 q^{87}\) \(+0.0113035 q^{88}\) \(+11.3988 q^{89}\) \(-7.72812 q^{90}\) \(-3.21744 q^{91}\) \(-0.820545 q^{92}\) \(-14.0446 q^{93}\) \(-19.6269 q^{94}\) \(+5.20995 q^{95}\) \(+20.9487 q^{96}\) \(-4.28912 q^{97}\) \(+0.234784 q^{98}\) \(+3.86680 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99859 −1.41321 −0.706607 0.707607i \(-0.749775\pi\)
−0.706607 + 0.707607i \(0.749775\pi\)
\(3\) 2.62046 1.51292 0.756461 0.654039i \(-0.226927\pi\)
0.756461 + 0.654039i \(0.226927\pi\)
\(4\) 1.99434 0.997172
\(5\) 1.00000 0.447214
\(6\) −5.23721 −2.13808
\(7\) 2.62346 0.991573 0.495787 0.868444i \(-0.334880\pi\)
0.495787 + 0.868444i \(0.334880\pi\)
\(8\) 0.0113035 0.00399639
\(9\) 3.86680 1.28893
\(10\) −1.99859 −0.632008
\(11\) 1.00000 0.301511
\(12\) 5.22609 1.50864
\(13\) −1.22641 −0.340145 −0.170073 0.985432i \(-0.554400\pi\)
−0.170073 + 0.985432i \(0.554400\pi\)
\(14\) −5.24320 −1.40130
\(15\) 2.62046 0.676599
\(16\) −4.01128 −1.00282
\(17\) −6.75860 −1.63920 −0.819600 0.572936i \(-0.805804\pi\)
−0.819600 + 0.572936i \(0.805804\pi\)
\(18\) −7.72812 −1.82154
\(19\) 5.20995 1.19525 0.597623 0.801777i \(-0.296112\pi\)
0.597623 + 0.801777i \(0.296112\pi\)
\(20\) 1.99434 0.445949
\(21\) 6.87466 1.50017
\(22\) −1.99859 −0.426100
\(23\) −0.411436 −0.0857904 −0.0428952 0.999080i \(-0.513658\pi\)
−0.0428952 + 0.999080i \(0.513658\pi\)
\(24\) 0.0296204 0.00604623
\(25\) 1.00000 0.200000
\(26\) 2.45109 0.480698
\(27\) 2.27140 0.437131
\(28\) 5.23208 0.988769
\(29\) 2.08179 0.386579 0.193289 0.981142i \(-0.438084\pi\)
0.193289 + 0.981142i \(0.438084\pi\)
\(30\) −5.23721 −0.956179
\(31\) −5.35960 −0.962613 −0.481307 0.876552i \(-0.659838\pi\)
−0.481307 + 0.876552i \(0.659838\pi\)
\(32\) 7.99428 1.41320
\(33\) 2.62046 0.456163
\(34\) 13.5076 2.31654
\(35\) 2.62346 0.443445
\(36\) 7.71172 1.28529
\(37\) −8.62271 −1.41757 −0.708783 0.705427i \(-0.750755\pi\)
−0.708783 + 0.705427i \(0.750755\pi\)
\(38\) −10.4125 −1.68914
\(39\) −3.21376 −0.514613
\(40\) 0.0113035 0.00178724
\(41\) 4.78486 0.747270 0.373635 0.927576i \(-0.378111\pi\)
0.373635 + 0.927576i \(0.378111\pi\)
\(42\) −13.7396 −2.12006
\(43\) 7.01675 1.07004 0.535022 0.844838i \(-0.320303\pi\)
0.535022 + 0.844838i \(0.320303\pi\)
\(44\) 1.99434 0.300659
\(45\) 3.86680 0.576428
\(46\) 0.822290 0.121240
\(47\) 9.82038 1.43245 0.716225 0.697870i \(-0.245869\pi\)
0.716225 + 0.697870i \(0.245869\pi\)
\(48\) −10.5114 −1.51719
\(49\) −0.117475 −0.0167821
\(50\) −1.99859 −0.282643
\(51\) −17.7106 −2.47998
\(52\) −2.44589 −0.339184
\(53\) 10.9519 1.50435 0.752177 0.658961i \(-0.229004\pi\)
0.752177 + 0.658961i \(0.229004\pi\)
\(54\) −4.53959 −0.617760
\(55\) 1.00000 0.134840
\(56\) 0.0296543 0.00396272
\(57\) 13.6525 1.80831
\(58\) −4.16064 −0.546319
\(59\) 5.13101 0.668001 0.334000 0.942573i \(-0.391601\pi\)
0.334000 + 0.942573i \(0.391601\pi\)
\(60\) 5.22609 0.674686
\(61\) 13.4387 1.72065 0.860324 0.509748i \(-0.170261\pi\)
0.860324 + 0.509748i \(0.170261\pi\)
\(62\) 10.7116 1.36038
\(63\) 10.1444 1.27807
\(64\) −7.95469 −0.994336
\(65\) −1.22641 −0.152118
\(66\) −5.23721 −0.644656
\(67\) −0.917153 −0.112048 −0.0560240 0.998429i \(-0.517842\pi\)
−0.0560240 + 0.998429i \(0.517842\pi\)
\(68\) −13.4790 −1.63457
\(69\) −1.07815 −0.129794
\(70\) −5.24320 −0.626683
\(71\) 2.96839 0.352284 0.176142 0.984365i \(-0.443638\pi\)
0.176142 + 0.984365i \(0.443638\pi\)
\(72\) 0.0437084 0.00515108
\(73\) 1.00000 0.117041
\(74\) 17.2332 2.00332
\(75\) 2.62046 0.302584
\(76\) 10.3904 1.19187
\(77\) 2.62346 0.298971
\(78\) 6.42297 0.727259
\(79\) 7.46040 0.839360 0.419680 0.907672i \(-0.362142\pi\)
0.419680 + 0.907672i \(0.362142\pi\)
\(80\) −4.01128 −0.448475
\(81\) −5.64828 −0.627587
\(82\) −9.56296 −1.05605
\(83\) 11.6845 1.28254 0.641269 0.767316i \(-0.278408\pi\)
0.641269 + 0.767316i \(0.278408\pi\)
\(84\) 13.7104 1.49593
\(85\) −6.75860 −0.733073
\(86\) −14.0236 −1.51220
\(87\) 5.45524 0.584864
\(88\) 0.0113035 0.00120496
\(89\) 11.3988 1.20827 0.604135 0.796882i \(-0.293519\pi\)
0.604135 + 0.796882i \(0.293519\pi\)
\(90\) −7.72812 −0.814616
\(91\) −3.21744 −0.337279
\(92\) −0.820545 −0.0855478
\(93\) −14.0446 −1.45636
\(94\) −19.6269 −2.02436
\(95\) 5.20995 0.534530
\(96\) 20.9487 2.13806
\(97\) −4.28912 −0.435494 −0.217747 0.976005i \(-0.569871\pi\)
−0.217747 + 0.976005i \(0.569871\pi\)
\(98\) 0.234784 0.0237167
\(99\) 3.86680 0.388628
\(100\) 1.99434 0.199434
\(101\) 1.36798 0.136120 0.0680598 0.997681i \(-0.478319\pi\)
0.0680598 + 0.997681i \(0.478319\pi\)
\(102\) 35.3962 3.50474
\(103\) −5.68073 −0.559739 −0.279870 0.960038i \(-0.590291\pi\)
−0.279870 + 0.960038i \(0.590291\pi\)
\(104\) −0.0138628 −0.00135936
\(105\) 6.87466 0.670898
\(106\) −21.8882 −2.12597
\(107\) 6.96733 0.673557 0.336778 0.941584i \(-0.390663\pi\)
0.336778 + 0.941584i \(0.390663\pi\)
\(108\) 4.52995 0.435895
\(109\) 0.552609 0.0529303 0.0264652 0.999650i \(-0.491575\pi\)
0.0264652 + 0.999650i \(0.491575\pi\)
\(110\) −1.99859 −0.190558
\(111\) −22.5955 −2.14467
\(112\) −10.5234 −0.994370
\(113\) 2.91171 0.273911 0.136955 0.990577i \(-0.456268\pi\)
0.136955 + 0.990577i \(0.456268\pi\)
\(114\) −27.2856 −2.55553
\(115\) −0.411436 −0.0383666
\(116\) 4.15181 0.385486
\(117\) −4.74228 −0.438424
\(118\) −10.2548 −0.944027
\(119\) −17.7309 −1.62539
\(120\) 0.0296204 0.00270396
\(121\) 1.00000 0.0909091
\(122\) −26.8584 −2.43164
\(123\) 12.5385 1.13056
\(124\) −10.6889 −0.959891
\(125\) 1.00000 0.0894427
\(126\) −20.2744 −1.80619
\(127\) 19.7891 1.75599 0.877997 0.478666i \(-0.158879\pi\)
0.877997 + 0.478666i \(0.158879\pi\)
\(128\) −0.0904277 −0.00799276
\(129\) 18.3871 1.61889
\(130\) 2.45109 0.214975
\(131\) −10.6278 −0.928558 −0.464279 0.885689i \(-0.653686\pi\)
−0.464279 + 0.885689i \(0.653686\pi\)
\(132\) 5.22609 0.454873
\(133\) 13.6681 1.18517
\(134\) 1.83301 0.158348
\(135\) 2.27140 0.195491
\(136\) −0.0763959 −0.00655089
\(137\) 2.11478 0.180678 0.0903388 0.995911i \(-0.471205\pi\)
0.0903388 + 0.995911i \(0.471205\pi\)
\(138\) 2.15478 0.183427
\(139\) 21.2705 1.80414 0.902071 0.431588i \(-0.142046\pi\)
0.902071 + 0.431588i \(0.142046\pi\)
\(140\) 5.23208 0.442191
\(141\) 25.7339 2.16718
\(142\) −5.93259 −0.497852
\(143\) −1.22641 −0.102558
\(144\) −15.5108 −1.29257
\(145\) 2.08179 0.172883
\(146\) −1.99859 −0.165404
\(147\) −0.307838 −0.0253901
\(148\) −17.1967 −1.41356
\(149\) −14.5755 −1.19407 −0.597035 0.802215i \(-0.703655\pi\)
−0.597035 + 0.802215i \(0.703655\pi\)
\(150\) −5.23721 −0.427616
\(151\) −19.3490 −1.57460 −0.787298 0.616572i \(-0.788521\pi\)
−0.787298 + 0.616572i \(0.788521\pi\)
\(152\) 0.0588908 0.00477667
\(153\) −26.1341 −2.11282
\(154\) −5.24320 −0.422509
\(155\) −5.35960 −0.430494
\(156\) −6.40934 −0.513158
\(157\) −4.96387 −0.396160 −0.198080 0.980186i \(-0.563471\pi\)
−0.198080 + 0.980186i \(0.563471\pi\)
\(158\) −14.9102 −1.18620
\(159\) 28.6989 2.27597
\(160\) 7.99428 0.632003
\(161\) −1.07938 −0.0850675
\(162\) 11.2886 0.886914
\(163\) −10.2786 −0.805079 −0.402539 0.915403i \(-0.631872\pi\)
−0.402539 + 0.915403i \(0.631872\pi\)
\(164\) 9.54267 0.745157
\(165\) 2.62046 0.204002
\(166\) −23.3524 −1.81250
\(167\) 11.3997 0.882132 0.441066 0.897475i \(-0.354600\pi\)
0.441066 + 0.897475i \(0.354600\pi\)
\(168\) 0.0777077 0.00599528
\(169\) −11.4959 −0.884301
\(170\) 13.5076 1.03599
\(171\) 20.1458 1.54059
\(172\) 13.9938 1.06702
\(173\) 7.45096 0.566486 0.283243 0.959048i \(-0.408590\pi\)
0.283243 + 0.959048i \(0.408590\pi\)
\(174\) −10.9028 −0.826537
\(175\) 2.62346 0.198315
\(176\) −4.01128 −0.302362
\(177\) 13.4456 1.01063
\(178\) −22.7815 −1.70754
\(179\) 18.6247 1.39207 0.696037 0.718006i \(-0.254945\pi\)
0.696037 + 0.718006i \(0.254945\pi\)
\(180\) 7.71172 0.574798
\(181\) 5.28582 0.392892 0.196446 0.980515i \(-0.437060\pi\)
0.196446 + 0.980515i \(0.437060\pi\)
\(182\) 6.43033 0.476647
\(183\) 35.2155 2.60320
\(184\) −0.00465067 −0.000342852 0
\(185\) −8.62271 −0.633955
\(186\) 28.0694 2.05814
\(187\) −6.75860 −0.494238
\(188\) 19.5852 1.42840
\(189\) 5.95892 0.433448
\(190\) −10.4125 −0.755405
\(191\) −7.42434 −0.537207 −0.268603 0.963251i \(-0.586562\pi\)
−0.268603 + 0.963251i \(0.586562\pi\)
\(192\) −20.8449 −1.50435
\(193\) −9.18309 −0.661013 −0.330507 0.943804i \(-0.607220\pi\)
−0.330507 + 0.943804i \(0.607220\pi\)
\(194\) 8.57216 0.615446
\(195\) −3.21376 −0.230142
\(196\) −0.234286 −0.0167347
\(197\) −4.63996 −0.330584 −0.165292 0.986245i \(-0.552857\pi\)
−0.165292 + 0.986245i \(0.552857\pi\)
\(198\) −7.72812 −0.549214
\(199\) 9.71917 0.688974 0.344487 0.938791i \(-0.388053\pi\)
0.344487 + 0.938791i \(0.388053\pi\)
\(200\) 0.0113035 0.000799279 0
\(201\) −2.40336 −0.169520
\(202\) −2.73403 −0.192366
\(203\) 5.46149 0.383321
\(204\) −35.3211 −2.47297
\(205\) 4.78486 0.334189
\(206\) 11.3534 0.791031
\(207\) −1.59094 −0.110578
\(208\) 4.91948 0.341105
\(209\) 5.20995 0.360380
\(210\) −13.7396 −0.948122
\(211\) 5.83305 0.401563 0.200782 0.979636i \(-0.435652\pi\)
0.200782 + 0.979636i \(0.435652\pi\)
\(212\) 21.8418 1.50010
\(213\) 7.77855 0.532977
\(214\) −13.9248 −0.951880
\(215\) 7.01675 0.478538
\(216\) 0.0256748 0.00174695
\(217\) −14.0607 −0.954502
\(218\) −1.10444 −0.0748018
\(219\) 2.62046 0.177074
\(220\) 1.99434 0.134459
\(221\) 8.28882 0.557567
\(222\) 45.1589 3.03087
\(223\) −8.56703 −0.573691 −0.286845 0.957977i \(-0.592607\pi\)
−0.286845 + 0.957977i \(0.592607\pi\)
\(224\) 20.9726 1.40129
\(225\) 3.86680 0.257786
\(226\) −5.81931 −0.387095
\(227\) 25.2766 1.67767 0.838834 0.544387i \(-0.183238\pi\)
0.838834 + 0.544387i \(0.183238\pi\)
\(228\) 27.2277 1.80320
\(229\) −19.6282 −1.29707 −0.648533 0.761187i \(-0.724617\pi\)
−0.648533 + 0.761187i \(0.724617\pi\)
\(230\) 0.822290 0.0542202
\(231\) 6.87466 0.452319
\(232\) 0.0235316 0.00154492
\(233\) −20.7670 −1.36049 −0.680245 0.732985i \(-0.738127\pi\)
−0.680245 + 0.732985i \(0.738127\pi\)
\(234\) 9.47786 0.619587
\(235\) 9.82038 0.640611
\(236\) 10.2330 0.666112
\(237\) 19.5497 1.26989
\(238\) 35.4367 2.29702
\(239\) 3.04598 0.197028 0.0985140 0.995136i \(-0.468591\pi\)
0.0985140 + 0.995136i \(0.468591\pi\)
\(240\) −10.5114 −0.678507
\(241\) −17.7298 −1.14207 −0.571037 0.820924i \(-0.693459\pi\)
−0.571037 + 0.820924i \(0.693459\pi\)
\(242\) −1.99859 −0.128474
\(243\) −21.6153 −1.38662
\(244\) 26.8014 1.71578
\(245\) −0.117475 −0.00750520
\(246\) −25.0593 −1.59772
\(247\) −6.38955 −0.406557
\(248\) −0.0605823 −0.00384698
\(249\) 30.6187 1.94038
\(250\) −1.99859 −0.126402
\(251\) −18.1516 −1.14572 −0.572859 0.819654i \(-0.694166\pi\)
−0.572859 + 0.819654i \(0.694166\pi\)
\(252\) 20.2314 1.27446
\(253\) −0.411436 −0.0258668
\(254\) −39.5501 −2.48160
\(255\) −17.7106 −1.10908
\(256\) 16.0901 1.00563
\(257\) −27.1482 −1.69346 −0.846731 0.532022i \(-0.821432\pi\)
−0.846731 + 0.532022i \(0.821432\pi\)
\(258\) −36.7482 −2.28784
\(259\) −22.6213 −1.40562
\(260\) −2.44589 −0.151688
\(261\) 8.04986 0.498274
\(262\) 21.2406 1.31225
\(263\) −23.6698 −1.45954 −0.729770 0.683692i \(-0.760373\pi\)
−0.729770 + 0.683692i \(0.760373\pi\)
\(264\) 0.0296204 0.00182301
\(265\) 10.9519 0.672768
\(266\) −27.3168 −1.67490
\(267\) 29.8701 1.82802
\(268\) −1.82912 −0.111731
\(269\) −30.7845 −1.87696 −0.938481 0.345331i \(-0.887767\pi\)
−0.938481 + 0.345331i \(0.887767\pi\)
\(270\) −4.53959 −0.276270
\(271\) 28.0750 1.70543 0.852716 0.522374i \(-0.174954\pi\)
0.852716 + 0.522374i \(0.174954\pi\)
\(272\) 27.1106 1.64382
\(273\) −8.43116 −0.510277
\(274\) −4.22656 −0.255336
\(275\) 1.00000 0.0603023
\(276\) −2.15020 −0.129427
\(277\) −32.0371 −1.92492 −0.962461 0.271419i \(-0.912507\pi\)
−0.962461 + 0.271419i \(0.912507\pi\)
\(278\) −42.5110 −2.54964
\(279\) −20.7245 −1.24074
\(280\) 0.0296543 0.00177218
\(281\) −2.84913 −0.169965 −0.0849824 0.996382i \(-0.527083\pi\)
−0.0849824 + 0.996382i \(0.527083\pi\)
\(282\) −51.4314 −3.06269
\(283\) −2.64800 −0.157407 −0.0787037 0.996898i \(-0.525078\pi\)
−0.0787037 + 0.996898i \(0.525078\pi\)
\(284\) 5.92000 0.351287
\(285\) 13.6525 0.808702
\(286\) 2.45109 0.144936
\(287\) 12.5529 0.740973
\(288\) 30.9122 1.82152
\(289\) 28.6786 1.68698
\(290\) −4.16064 −0.244321
\(291\) −11.2394 −0.658868
\(292\) 1.99434 0.116710
\(293\) −33.4740 −1.95557 −0.977786 0.209607i \(-0.932781\pi\)
−0.977786 + 0.209607i \(0.932781\pi\)
\(294\) 0.615241 0.0358816
\(295\) 5.13101 0.298739
\(296\) −0.0974669 −0.00566515
\(297\) 2.27140 0.131800
\(298\) 29.1304 1.68748
\(299\) 0.504590 0.0291812
\(300\) 5.22609 0.301729
\(301\) 18.4081 1.06103
\(302\) 38.6706 2.22524
\(303\) 3.58474 0.205938
\(304\) −20.8986 −1.19862
\(305\) 13.4387 0.769497
\(306\) 52.2313 2.98586
\(307\) −12.1957 −0.696045 −0.348023 0.937486i \(-0.613147\pi\)
−0.348023 + 0.937486i \(0.613147\pi\)
\(308\) 5.23208 0.298125
\(309\) −14.8861 −0.846841
\(310\) 10.7116 0.608379
\(311\) 2.77001 0.157073 0.0785365 0.996911i \(-0.474975\pi\)
0.0785365 + 0.996911i \(0.474975\pi\)
\(312\) −0.0363268 −0.00205660
\(313\) 17.1827 0.971226 0.485613 0.874174i \(-0.338596\pi\)
0.485613 + 0.874174i \(0.338596\pi\)
\(314\) 9.92071 0.559858
\(315\) 10.1444 0.571571
\(316\) 14.8786 0.836987
\(317\) 21.4701 1.20588 0.602940 0.797787i \(-0.293996\pi\)
0.602940 + 0.797787i \(0.293996\pi\)
\(318\) −57.3572 −3.21643
\(319\) 2.08179 0.116558
\(320\) −7.95469 −0.444681
\(321\) 18.2576 1.01904
\(322\) 2.15724 0.120218
\(323\) −35.2120 −1.95925
\(324\) −11.2646 −0.625812
\(325\) −1.22641 −0.0680291
\(326\) 20.5426 1.13775
\(327\) 1.44809 0.0800794
\(328\) 0.0540858 0.00298639
\(329\) 25.7633 1.42038
\(330\) −5.23721 −0.288299
\(331\) −7.23522 −0.397684 −0.198842 0.980032i \(-0.563718\pi\)
−0.198842 + 0.980032i \(0.563718\pi\)
\(332\) 23.3029 1.27891
\(333\) −33.3423 −1.82715
\(334\) −22.7832 −1.24664
\(335\) −0.917153 −0.0501094
\(336\) −27.5762 −1.50440
\(337\) −26.9370 −1.46735 −0.733675 0.679501i \(-0.762196\pi\)
−0.733675 + 0.679501i \(0.762196\pi\)
\(338\) 22.9756 1.24971
\(339\) 7.63002 0.414406
\(340\) −13.4790 −0.731000
\(341\) −5.35960 −0.290239
\(342\) −40.2632 −2.17718
\(343\) −18.6724 −1.00821
\(344\) 0.0793139 0.00427632
\(345\) −1.07815 −0.0580457
\(346\) −14.8914 −0.800566
\(347\) 22.5590 1.21103 0.605515 0.795834i \(-0.292967\pi\)
0.605515 + 0.795834i \(0.292967\pi\)
\(348\) 10.8796 0.583210
\(349\) 0.498528 0.0266856 0.0133428 0.999911i \(-0.495753\pi\)
0.0133428 + 0.999911i \(0.495753\pi\)
\(350\) −5.24320 −0.280261
\(351\) −2.78567 −0.148688
\(352\) 7.99428 0.426096
\(353\) −5.77983 −0.307629 −0.153815 0.988100i \(-0.549156\pi\)
−0.153815 + 0.988100i \(0.549156\pi\)
\(354\) −26.8722 −1.42824
\(355\) 2.96839 0.157546
\(356\) 22.7331 1.20485
\(357\) −46.4630 −2.45908
\(358\) −37.2230 −1.96730
\(359\) 24.6654 1.30179 0.650895 0.759167i \(-0.274394\pi\)
0.650895 + 0.759167i \(0.274394\pi\)
\(360\) 0.0437084 0.00230363
\(361\) 8.14362 0.428612
\(362\) −10.5642 −0.555241
\(363\) 2.62046 0.137538
\(364\) −6.41668 −0.336325
\(365\) 1.00000 0.0523424
\(366\) −70.3812 −3.67888
\(367\) −19.6725 −1.02690 −0.513449 0.858120i \(-0.671632\pi\)
−0.513449 + 0.858120i \(0.671632\pi\)
\(368\) 1.65039 0.0860323
\(369\) 18.5021 0.963180
\(370\) 17.2332 0.895913
\(371\) 28.7317 1.49168
\(372\) −28.0098 −1.45224
\(373\) −10.6054 −0.549127 −0.274564 0.961569i \(-0.588533\pi\)
−0.274564 + 0.961569i \(0.588533\pi\)
\(374\) 13.5076 0.698463
\(375\) 2.62046 0.135320
\(376\) 0.111005 0.00572463
\(377\) −2.55313 −0.131493
\(378\) −11.9094 −0.612554
\(379\) −24.4129 −1.25401 −0.627004 0.779016i \(-0.715719\pi\)
−0.627004 + 0.779016i \(0.715719\pi\)
\(380\) 10.3904 0.533018
\(381\) 51.8564 2.65668
\(382\) 14.8382 0.759188
\(383\) −34.1520 −1.74509 −0.872543 0.488538i \(-0.837530\pi\)
−0.872543 + 0.488538i \(0.837530\pi\)
\(384\) −0.236962 −0.0120924
\(385\) 2.62346 0.133704
\(386\) 18.3532 0.934153
\(387\) 27.1323 1.37921
\(388\) −8.55397 −0.434262
\(389\) 23.6171 1.19744 0.598718 0.800960i \(-0.295677\pi\)
0.598718 + 0.800960i \(0.295677\pi\)
\(390\) 6.42297 0.325240
\(391\) 2.78073 0.140628
\(392\) −0.00132788 −6.70681e−5 0
\(393\) −27.8498 −1.40484
\(394\) 9.27336 0.467185
\(395\) 7.46040 0.375373
\(396\) 7.71172 0.387529
\(397\) −11.2353 −0.563884 −0.281942 0.959431i \(-0.590979\pi\)
−0.281942 + 0.959431i \(0.590979\pi\)
\(398\) −19.4246 −0.973667
\(399\) 35.8166 1.79307
\(400\) −4.01128 −0.200564
\(401\) −1.42302 −0.0710621 −0.0355311 0.999369i \(-0.511312\pi\)
−0.0355311 + 0.999369i \(0.511312\pi\)
\(402\) 4.80332 0.239568
\(403\) 6.57308 0.327428
\(404\) 2.72823 0.135735
\(405\) −5.64828 −0.280665
\(406\) −10.9153 −0.541715
\(407\) −8.62271 −0.427412
\(408\) −0.200192 −0.00991099
\(409\) 6.81810 0.337133 0.168567 0.985690i \(-0.446086\pi\)
0.168567 + 0.985690i \(0.446086\pi\)
\(410\) −9.56296 −0.472281
\(411\) 5.54168 0.273351
\(412\) −11.3293 −0.558156
\(413\) 13.4610 0.662372
\(414\) 3.17963 0.156270
\(415\) 11.6845 0.573569
\(416\) −9.80428 −0.480694
\(417\) 55.7385 2.72953
\(418\) −10.4125 −0.509294
\(419\) 6.57583 0.321250 0.160625 0.987015i \(-0.448649\pi\)
0.160625 + 0.987015i \(0.448649\pi\)
\(420\) 13.7104 0.669000
\(421\) 20.3330 0.990969 0.495484 0.868617i \(-0.334991\pi\)
0.495484 + 0.868617i \(0.334991\pi\)
\(422\) −11.6578 −0.567495
\(423\) 37.9734 1.84633
\(424\) 0.123795 0.00601199
\(425\) −6.75860 −0.327840
\(426\) −15.5461 −0.753211
\(427\) 35.2558 1.70615
\(428\) 13.8952 0.671652
\(429\) −3.21376 −0.155162
\(430\) −14.0236 −0.676277
\(431\) 30.1939 1.45439 0.727194 0.686432i \(-0.240824\pi\)
0.727194 + 0.686432i \(0.240824\pi\)
\(432\) −9.11122 −0.438364
\(433\) −37.5707 −1.80553 −0.902767 0.430131i \(-0.858467\pi\)
−0.902767 + 0.430131i \(0.858467\pi\)
\(434\) 28.1015 1.34891
\(435\) 5.45524 0.261559
\(436\) 1.10209 0.0527806
\(437\) −2.14356 −0.102541
\(438\) −5.23721 −0.250243
\(439\) −23.8925 −1.14033 −0.570163 0.821532i \(-0.693120\pi\)
−0.570163 + 0.821532i \(0.693120\pi\)
\(440\) 0.0113035 0.000538874 0
\(441\) −0.454252 −0.0216310
\(442\) −16.5659 −0.787961
\(443\) 38.1447 1.81231 0.906154 0.422948i \(-0.139005\pi\)
0.906154 + 0.422948i \(0.139005\pi\)
\(444\) −45.0631 −2.13860
\(445\) 11.3988 0.540355
\(446\) 17.1219 0.810748
\(447\) −38.1944 −1.80654
\(448\) −20.8688 −0.985957
\(449\) −19.8517 −0.936862 −0.468431 0.883500i \(-0.655180\pi\)
−0.468431 + 0.883500i \(0.655180\pi\)
\(450\) −7.72812 −0.364307
\(451\) 4.78486 0.225310
\(452\) 5.80696 0.273136
\(453\) −50.7031 −2.38224
\(454\) −50.5175 −2.37090
\(455\) −3.21744 −0.150836
\(456\) 0.154321 0.00722673
\(457\) −20.8215 −0.973986 −0.486993 0.873406i \(-0.661906\pi\)
−0.486993 + 0.873406i \(0.661906\pi\)
\(458\) 39.2286 1.83303
\(459\) −15.3515 −0.716546
\(460\) −0.820545 −0.0382581
\(461\) 13.4533 0.626582 0.313291 0.949657i \(-0.398569\pi\)
0.313291 + 0.949657i \(0.398569\pi\)
\(462\) −13.7396 −0.639223
\(463\) −8.56951 −0.398259 −0.199129 0.979973i \(-0.563811\pi\)
−0.199129 + 0.979973i \(0.563811\pi\)
\(464\) −8.35065 −0.387669
\(465\) −14.0446 −0.651303
\(466\) 41.5046 1.92266
\(467\) 12.8520 0.594719 0.297359 0.954766i \(-0.403894\pi\)
0.297359 + 0.954766i \(0.403894\pi\)
\(468\) −9.45775 −0.437184
\(469\) −2.40611 −0.111104
\(470\) −19.6269 −0.905320
\(471\) −13.0076 −0.599359
\(472\) 0.0579984 0.00266959
\(473\) 7.01675 0.322630
\(474\) −39.0717 −1.79462
\(475\) 5.20995 0.239049
\(476\) −35.3615 −1.62079
\(477\) 42.3486 1.93901
\(478\) −6.08765 −0.278443
\(479\) 10.3567 0.473210 0.236605 0.971606i \(-0.423965\pi\)
0.236605 + 0.971606i \(0.423965\pi\)
\(480\) 20.9487 0.956171
\(481\) 10.5750 0.482178
\(482\) 35.4344 1.61399
\(483\) −2.82848 −0.128700
\(484\) 1.99434 0.0906520
\(485\) −4.28912 −0.194759
\(486\) 43.2000 1.95959
\(487\) −2.71602 −0.123075 −0.0615373 0.998105i \(-0.519600\pi\)
−0.0615373 + 0.998105i \(0.519600\pi\)
\(488\) 0.151904 0.00687639
\(489\) −26.9345 −1.21802
\(490\) 0.234784 0.0106065
\(491\) 2.15605 0.0973012 0.0486506 0.998816i \(-0.484508\pi\)
0.0486506 + 0.998816i \(0.484508\pi\)
\(492\) 25.0061 1.12736
\(493\) −14.0700 −0.633680
\(494\) 12.7701 0.574552
\(495\) 3.86680 0.173800
\(496\) 21.4989 0.965328
\(497\) 7.78745 0.349315
\(498\) −61.1941 −2.74217
\(499\) 22.5530 1.00961 0.504805 0.863233i \(-0.331564\pi\)
0.504805 + 0.863233i \(0.331564\pi\)
\(500\) 1.99434 0.0891898
\(501\) 29.8723 1.33460
\(502\) 36.2775 1.61914
\(503\) 24.6173 1.09763 0.548816 0.835943i \(-0.315079\pi\)
0.548816 + 0.835943i \(0.315079\pi\)
\(504\) 0.114667 0.00510767
\(505\) 1.36798 0.0608745
\(506\) 0.822290 0.0365553
\(507\) −30.1245 −1.33788
\(508\) 39.4662 1.75103
\(509\) −18.2615 −0.809429 −0.404714 0.914443i \(-0.632629\pi\)
−0.404714 + 0.914443i \(0.632629\pi\)
\(510\) 35.3962 1.56737
\(511\) 2.62346 0.116055
\(512\) −31.9766 −1.41318
\(513\) 11.8339 0.522479
\(514\) 54.2581 2.39322
\(515\) −5.68073 −0.250323
\(516\) 36.6702 1.61431
\(517\) 9.82038 0.431900
\(518\) 45.2106 1.98644
\(519\) 19.5249 0.857049
\(520\) −0.0138628 −0.000607922 0
\(521\) 23.9877 1.05092 0.525461 0.850818i \(-0.323893\pi\)
0.525461 + 0.850818i \(0.323893\pi\)
\(522\) −16.0883 −0.704167
\(523\) 27.2475 1.19145 0.595726 0.803188i \(-0.296865\pi\)
0.595726 + 0.803188i \(0.296865\pi\)
\(524\) −21.1955 −0.925932
\(525\) 6.87466 0.300035
\(526\) 47.3061 2.06264
\(527\) 36.2234 1.57792
\(528\) −10.5114 −0.457449
\(529\) −22.8307 −0.992640
\(530\) −21.8882 −0.950764
\(531\) 19.8406 0.861007
\(532\) 27.2589 1.18182
\(533\) −5.86821 −0.254181
\(534\) −59.6979 −2.58338
\(535\) 6.96733 0.301224
\(536\) −0.0103670 −0.000447788 0
\(537\) 48.8052 2.10610
\(538\) 61.5254 2.65255
\(539\) −0.117475 −0.00506001
\(540\) 4.52995 0.194938
\(541\) 2.72379 0.117105 0.0585525 0.998284i \(-0.481351\pi\)
0.0585525 + 0.998284i \(0.481351\pi\)
\(542\) −56.1102 −2.41014
\(543\) 13.8513 0.594415
\(544\) −54.0301 −2.31652
\(545\) 0.552609 0.0236712
\(546\) 16.8504 0.721130
\(547\) 8.33868 0.356536 0.178268 0.983982i \(-0.442951\pi\)
0.178268 + 0.983982i \(0.442951\pi\)
\(548\) 4.21759 0.180167
\(549\) 51.9646 2.21780
\(550\) −1.99859 −0.0852200
\(551\) 10.8460 0.462057
\(552\) −0.0121869 −0.000518708 0
\(553\) 19.5720 0.832287
\(554\) 64.0289 2.72033
\(555\) −22.5955 −0.959124
\(556\) 42.4207 1.79904
\(557\) −18.5301 −0.785146 −0.392573 0.919721i \(-0.628415\pi\)
−0.392573 + 0.919721i \(0.628415\pi\)
\(558\) 41.4197 1.75343
\(559\) −8.60542 −0.363971
\(560\) −10.5234 −0.444696
\(561\) −17.7106 −0.747743
\(562\) 5.69423 0.240197
\(563\) −7.77217 −0.327558 −0.163779 0.986497i \(-0.552368\pi\)
−0.163779 + 0.986497i \(0.552368\pi\)
\(564\) 51.3222 2.16106
\(565\) 2.91171 0.122497
\(566\) 5.29226 0.222450
\(567\) −14.8180 −0.622298
\(568\) 0.0335533 0.00140786
\(569\) 34.6487 1.45255 0.726275 0.687404i \(-0.241250\pi\)
0.726275 + 0.687404i \(0.241250\pi\)
\(570\) −27.2856 −1.14287
\(571\) 18.8747 0.789880 0.394940 0.918707i \(-0.370765\pi\)
0.394940 + 0.918707i \(0.370765\pi\)
\(572\) −2.44589 −0.102268
\(573\) −19.4552 −0.812751
\(574\) −25.0880 −1.04715
\(575\) −0.411436 −0.0171581
\(576\) −30.7592 −1.28163
\(577\) 9.64512 0.401532 0.200766 0.979639i \(-0.435657\pi\)
0.200766 + 0.979639i \(0.435657\pi\)
\(578\) −57.3167 −2.38406
\(579\) −24.0639 −1.00006
\(580\) 4.15181 0.172394
\(581\) 30.6537 1.27173
\(582\) 22.4630 0.931121
\(583\) 10.9519 0.453580
\(584\) 0.0113035 0.000467743 0
\(585\) −4.74228 −0.196069
\(586\) 66.9006 2.76364
\(587\) −5.43089 −0.224157 −0.112078 0.993699i \(-0.535751\pi\)
−0.112078 + 0.993699i \(0.535751\pi\)
\(588\) −0.613935 −0.0253183
\(589\) −27.9233 −1.15056
\(590\) −10.2548 −0.422182
\(591\) −12.1588 −0.500147
\(592\) 34.5881 1.42156
\(593\) 0.679684 0.0279113 0.0139556 0.999903i \(-0.495558\pi\)
0.0139556 + 0.999903i \(0.495558\pi\)
\(594\) −4.53959 −0.186262
\(595\) −17.7309 −0.726896
\(596\) −29.0685 −1.19069
\(597\) 25.4687 1.04236
\(598\) −1.00847 −0.0412393
\(599\) 24.7597 1.01165 0.505826 0.862635i \(-0.331188\pi\)
0.505826 + 0.862635i \(0.331188\pi\)
\(600\) 0.0296204 0.00120925
\(601\) −28.5268 −1.16363 −0.581817 0.813320i \(-0.697658\pi\)
−0.581817 + 0.813320i \(0.697658\pi\)
\(602\) −36.7902 −1.49946
\(603\) −3.54644 −0.144422
\(604\) −38.5885 −1.57014
\(605\) 1.00000 0.0406558
\(606\) −7.16442 −0.291035
\(607\) −22.1726 −0.899959 −0.449979 0.893039i \(-0.648569\pi\)
−0.449979 + 0.893039i \(0.648569\pi\)
\(608\) 41.6498 1.68912
\(609\) 14.3116 0.579935
\(610\) −26.8584 −1.08746
\(611\) −12.0438 −0.487241
\(612\) −52.1204 −2.10684
\(613\) −9.78775 −0.395323 −0.197662 0.980270i \(-0.563335\pi\)
−0.197662 + 0.980270i \(0.563335\pi\)
\(614\) 24.3741 0.983660
\(615\) 12.5385 0.505602
\(616\) 0.0296543 0.00119480
\(617\) −23.7038 −0.954280 −0.477140 0.878827i \(-0.658327\pi\)
−0.477140 + 0.878827i \(0.658327\pi\)
\(618\) 29.7512 1.19677
\(619\) −18.9929 −0.763388 −0.381694 0.924289i \(-0.624659\pi\)
−0.381694 + 0.924289i \(0.624659\pi\)
\(620\) −10.6889 −0.429276
\(621\) −0.934536 −0.0375016
\(622\) −5.53611 −0.221978
\(623\) 29.9043 1.19809
\(624\) 12.8913 0.516065
\(625\) 1.00000 0.0400000
\(626\) −34.3412 −1.37255
\(627\) 13.6525 0.545227
\(628\) −9.89966 −0.395039
\(629\) 58.2775 2.32367
\(630\) −20.2744 −0.807751
\(631\) 4.92498 0.196060 0.0980301 0.995183i \(-0.468746\pi\)
0.0980301 + 0.995183i \(0.468746\pi\)
\(632\) 0.0843287 0.00335442
\(633\) 15.2852 0.607534
\(634\) −42.9098 −1.70417
\(635\) 19.7891 0.785305
\(636\) 57.2355 2.26953
\(637\) 0.144073 0.00570837
\(638\) −4.16064 −0.164721
\(639\) 11.4782 0.454069
\(640\) −0.0904277 −0.00357447
\(641\) −34.4888 −1.36222 −0.681112 0.732179i \(-0.738503\pi\)
−0.681112 + 0.732179i \(0.738503\pi\)
\(642\) −36.4893 −1.44012
\(643\) −20.4666 −0.807126 −0.403563 0.914952i \(-0.632228\pi\)
−0.403563 + 0.914952i \(0.632228\pi\)
\(644\) −2.15267 −0.0848269
\(645\) 18.3871 0.723991
\(646\) 70.3742 2.76883
\(647\) −24.6827 −0.970376 −0.485188 0.874410i \(-0.661249\pi\)
−0.485188 + 0.874410i \(0.661249\pi\)
\(648\) −0.0638454 −0.00250808
\(649\) 5.13101 0.201410
\(650\) 2.45109 0.0961396
\(651\) −36.8454 −1.44409
\(652\) −20.4990 −0.802802
\(653\) 0.216924 0.00848890 0.00424445 0.999991i \(-0.498649\pi\)
0.00424445 + 0.999991i \(0.498649\pi\)
\(654\) −2.89413 −0.113169
\(655\) −10.6278 −0.415264
\(656\) −19.1934 −0.749377
\(657\) 3.86680 0.150858
\(658\) −51.4902 −2.00730
\(659\) 10.5633 0.411489 0.205745 0.978606i \(-0.434038\pi\)
0.205745 + 0.978606i \(0.434038\pi\)
\(660\) 5.22609 0.203425
\(661\) 14.6463 0.569674 0.284837 0.958576i \(-0.408061\pi\)
0.284837 + 0.958576i \(0.408061\pi\)
\(662\) 14.4602 0.562012
\(663\) 21.7205 0.843555
\(664\) 0.132076 0.00512553
\(665\) 13.6681 0.530026
\(666\) 66.6374 2.58215
\(667\) −0.856524 −0.0331648
\(668\) 22.7348 0.879637
\(669\) −22.4495 −0.867949
\(670\) 1.83301 0.0708153
\(671\) 13.4387 0.518795
\(672\) 54.9579 2.12005
\(673\) −0.298628 −0.0115113 −0.00575563 0.999983i \(-0.501832\pi\)
−0.00575563 + 0.999983i \(0.501832\pi\)
\(674\) 53.8358 2.07368
\(675\) 2.27140 0.0874262
\(676\) −22.9268 −0.881800
\(677\) −14.4113 −0.553872 −0.276936 0.960888i \(-0.589319\pi\)
−0.276936 + 0.960888i \(0.589319\pi\)
\(678\) −15.2492 −0.585644
\(679\) −11.2523 −0.431824
\(680\) −0.0763959 −0.00292965
\(681\) 66.2363 2.53818
\(682\) 10.7116 0.410169
\(683\) 15.9312 0.609591 0.304795 0.952418i \(-0.401412\pi\)
0.304795 + 0.952418i \(0.401412\pi\)
\(684\) 40.1777 1.53623
\(685\) 2.11478 0.0808015
\(686\) 37.3184 1.42482
\(687\) −51.4348 −1.96236
\(688\) −28.1461 −1.07306
\(689\) −13.4315 −0.511699
\(690\) 2.15478 0.0820309
\(691\) 23.0094 0.875317 0.437659 0.899141i \(-0.355808\pi\)
0.437659 + 0.899141i \(0.355808\pi\)
\(692\) 14.8598 0.564884
\(693\) 10.1444 0.385353
\(694\) −45.0861 −1.71144
\(695\) 21.2705 0.806837
\(696\) 0.0616634 0.00233735
\(697\) −32.3390 −1.22493
\(698\) −0.996350 −0.0377124
\(699\) −54.4190 −2.05831
\(700\) 5.23208 0.197754
\(701\) 50.3427 1.90142 0.950708 0.310087i \(-0.100358\pi\)
0.950708 + 0.310087i \(0.100358\pi\)
\(702\) 5.56740 0.210128
\(703\) −44.9239 −1.69434
\(704\) −7.95469 −0.299804
\(705\) 25.7339 0.969194
\(706\) 11.5515 0.434746
\(707\) 3.58885 0.134972
\(708\) 26.8151 1.00777
\(709\) 22.0214 0.827031 0.413515 0.910497i \(-0.364301\pi\)
0.413515 + 0.910497i \(0.364301\pi\)
\(710\) −5.93259 −0.222646
\(711\) 28.8478 1.08188
\(712\) 0.128846 0.00482872
\(713\) 2.20513 0.0825829
\(714\) 92.8603 3.47521
\(715\) −1.22641 −0.0458652
\(716\) 37.1440 1.38814
\(717\) 7.98186 0.298088
\(718\) −49.2959 −1.83971
\(719\) −34.7955 −1.29765 −0.648827 0.760936i \(-0.724740\pi\)
−0.648827 + 0.760936i \(0.724740\pi\)
\(720\) −15.5108 −0.578053
\(721\) −14.9032 −0.555022
\(722\) −16.2757 −0.605720
\(723\) −46.4601 −1.72787
\(724\) 10.5418 0.391781
\(725\) 2.08179 0.0773158
\(726\) −5.23721 −0.194371
\(727\) −6.87342 −0.254921 −0.127461 0.991844i \(-0.540683\pi\)
−0.127461 + 0.991844i \(0.540683\pi\)
\(728\) −0.0363684 −0.00134790
\(729\) −39.6971 −1.47026
\(730\) −1.99859 −0.0739710
\(731\) −47.4234 −1.75402
\(732\) 70.2318 2.59584
\(733\) −38.2079 −1.41124 −0.705621 0.708590i \(-0.749332\pi\)
−0.705621 + 0.708590i \(0.749332\pi\)
\(734\) 39.3172 1.45122
\(735\) −0.307838 −0.0113548
\(736\) −3.28914 −0.121239
\(737\) −0.917153 −0.0337838
\(738\) −36.9780 −1.36118
\(739\) −27.3184 −1.00493 −0.502463 0.864599i \(-0.667573\pi\)
−0.502463 + 0.864599i \(0.667573\pi\)
\(740\) −17.1967 −0.632162
\(741\) −16.7435 −0.615089
\(742\) −57.4228 −2.10806
\(743\) −35.6716 −1.30867 −0.654333 0.756207i \(-0.727050\pi\)
−0.654333 + 0.756207i \(0.727050\pi\)
\(744\) −0.158753 −0.00582018
\(745\) −14.5755 −0.534005
\(746\) 21.1958 0.776034
\(747\) 45.1815 1.65311
\(748\) −13.4790 −0.492840
\(749\) 18.2785 0.667881
\(750\) −5.23721 −0.191236
\(751\) −3.93690 −0.143659 −0.0718297 0.997417i \(-0.522884\pi\)
−0.0718297 + 0.997417i \(0.522884\pi\)
\(752\) −39.3923 −1.43649
\(753\) −47.5654 −1.73338
\(754\) 5.10266 0.185828
\(755\) −19.3490 −0.704181
\(756\) 11.8841 0.432222
\(757\) 37.3787 1.35855 0.679275 0.733884i \(-0.262294\pi\)
0.679275 + 0.733884i \(0.262294\pi\)
\(758\) 48.7914 1.77218
\(759\) −1.07815 −0.0391344
\(760\) 0.0588908 0.00213619
\(761\) −9.97039 −0.361427 −0.180713 0.983536i \(-0.557841\pi\)
−0.180713 + 0.983536i \(0.557841\pi\)
\(762\) −103.639 −3.75446
\(763\) 1.44975 0.0524843
\(764\) −14.8067 −0.535687
\(765\) −26.1341 −0.944881
\(766\) 68.2557 2.46618
\(767\) −6.29273 −0.227217
\(768\) 42.1634 1.52144
\(769\) −16.7703 −0.604753 −0.302377 0.953189i \(-0.597780\pi\)
−0.302377 + 0.953189i \(0.597780\pi\)
\(770\) −5.24320 −0.188952
\(771\) −71.1408 −2.56207
\(772\) −18.3142 −0.659144
\(773\) −42.7338 −1.53703 −0.768515 0.639832i \(-0.779004\pi\)
−0.768515 + 0.639832i \(0.779004\pi\)
\(774\) −54.2263 −1.94912
\(775\) −5.35960 −0.192523
\(776\) −0.0484821 −0.00174040
\(777\) −59.2782 −2.12659
\(778\) −47.2008 −1.69223
\(779\) 24.9289 0.893171
\(780\) −6.40934 −0.229491
\(781\) 2.96839 0.106217
\(782\) −5.55753 −0.198737
\(783\) 4.72858 0.168986
\(784\) 0.471225 0.0168295
\(785\) −4.96387 −0.177168
\(786\) 55.6601 1.98533
\(787\) 24.0922 0.858793 0.429396 0.903116i \(-0.358726\pi\)
0.429396 + 0.903116i \(0.358726\pi\)
\(788\) −9.25368 −0.329649
\(789\) −62.0256 −2.20817
\(790\) −14.9102 −0.530483
\(791\) 7.63875 0.271603
\(792\) 0.0437084 0.00155311
\(793\) −16.4814 −0.585270
\(794\) 22.4547 0.796888
\(795\) 28.6989 1.01784
\(796\) 19.3834 0.687025
\(797\) 50.3800 1.78455 0.892276 0.451491i \(-0.149108\pi\)
0.892276 + 0.451491i \(0.149108\pi\)
\(798\) −71.5826 −2.53400
\(799\) −66.3720 −2.34807
\(800\) 7.99428 0.282640
\(801\) 44.0768 1.55738
\(802\) 2.84402 0.100426
\(803\) 1.00000 0.0352892
\(804\) −4.79313 −0.169041
\(805\) −1.07938 −0.0380433
\(806\) −13.1369 −0.462726
\(807\) −80.6694 −2.83970
\(808\) 0.0154630 0.000543987 0
\(809\) −21.7283 −0.763927 −0.381964 0.924177i \(-0.624752\pi\)
−0.381964 + 0.924177i \(0.624752\pi\)
\(810\) 11.2886 0.396640
\(811\) −9.27741 −0.325774 −0.162887 0.986645i \(-0.552081\pi\)
−0.162887 + 0.986645i \(0.552081\pi\)
\(812\) 10.8921 0.382237
\(813\) 73.5692 2.58019
\(814\) 17.2332 0.604024
\(815\) −10.2786 −0.360042
\(816\) 71.0422 2.48698
\(817\) 36.5569 1.27897
\(818\) −13.6265 −0.476441
\(819\) −12.4412 −0.434730
\(820\) 9.54267 0.333244
\(821\) −5.01148 −0.174902 −0.0874509 0.996169i \(-0.527872\pi\)
−0.0874509 + 0.996169i \(0.527872\pi\)
\(822\) −11.0755 −0.386303
\(823\) −17.6243 −0.614345 −0.307172 0.951654i \(-0.599383\pi\)
−0.307172 + 0.951654i \(0.599383\pi\)
\(824\) −0.0642122 −0.00223694
\(825\) 2.62046 0.0912326
\(826\) −26.9029 −0.936073
\(827\) −25.0585 −0.871370 −0.435685 0.900099i \(-0.643494\pi\)
−0.435685 + 0.900099i \(0.643494\pi\)
\(828\) −3.17288 −0.110265
\(829\) −1.96838 −0.0683647 −0.0341824 0.999416i \(-0.510883\pi\)
−0.0341824 + 0.999416i \(0.510883\pi\)
\(830\) −23.3524 −0.810575
\(831\) −83.9518 −2.91226
\(832\) 9.75573 0.338219
\(833\) 0.793966 0.0275093
\(834\) −111.398 −3.85740
\(835\) 11.3997 0.394501
\(836\) 10.3904 0.359361
\(837\) −12.1738 −0.420788
\(838\) −13.1424 −0.453995
\(839\) 49.9876 1.72576 0.862882 0.505405i \(-0.168657\pi\)
0.862882 + 0.505405i \(0.168657\pi\)
\(840\) 0.0777077 0.00268117
\(841\) −24.6661 −0.850557
\(842\) −40.6372 −1.40045
\(843\) −7.46602 −0.257143
\(844\) 11.6331 0.400428
\(845\) −11.4959 −0.395471
\(846\) −75.8931 −2.60926
\(847\) 2.62346 0.0901430
\(848\) −43.9310 −1.50860
\(849\) −6.93897 −0.238145
\(850\) 13.5076 0.463308
\(851\) 3.54770 0.121613
\(852\) 15.5131 0.531470
\(853\) 8.48391 0.290484 0.145242 0.989396i \(-0.453604\pi\)
0.145242 + 0.989396i \(0.453604\pi\)
\(854\) −70.4618 −2.41115
\(855\) 20.1458 0.688973
\(856\) 0.0787552 0.00269180
\(857\) 15.8496 0.541412 0.270706 0.962662i \(-0.412743\pi\)
0.270706 + 0.962662i \(0.412743\pi\)
\(858\) 6.42297 0.219277
\(859\) 51.2662 1.74918 0.874590 0.484864i \(-0.161131\pi\)
0.874590 + 0.484864i \(0.161131\pi\)
\(860\) 13.9938 0.477185
\(861\) 32.8943 1.12103
\(862\) −60.3451 −2.05536
\(863\) −9.53741 −0.324657 −0.162329 0.986737i \(-0.551900\pi\)
−0.162329 + 0.986737i \(0.551900\pi\)
\(864\) 18.1582 0.617755
\(865\) 7.45096 0.253340
\(866\) 75.0883 2.55160
\(867\) 75.1512 2.55227
\(868\) −28.0418 −0.951802
\(869\) 7.46040 0.253077
\(870\) −10.9028 −0.369639
\(871\) 1.12481 0.0381126
\(872\) 0.00624642 0.000211530 0
\(873\) −16.5851 −0.561322
\(874\) 4.28410 0.144912
\(875\) 2.62346 0.0886890
\(876\) 5.22609 0.176573
\(877\) 42.5714 1.43753 0.718767 0.695251i \(-0.244707\pi\)
0.718767 + 0.695251i \(0.244707\pi\)
\(878\) 47.7511 1.61152
\(879\) −87.7171 −2.95863
\(880\) −4.01128 −0.135220
\(881\) −17.6254 −0.593813 −0.296907 0.954906i \(-0.595955\pi\)
−0.296907 + 0.954906i \(0.595955\pi\)
\(882\) 0.907861 0.0305693
\(883\) 38.3531 1.29069 0.645343 0.763893i \(-0.276714\pi\)
0.645343 + 0.763893i \(0.276714\pi\)
\(884\) 16.5308 0.555990
\(885\) 13.4456 0.451969
\(886\) −76.2354 −2.56118
\(887\) −15.4545 −0.518911 −0.259456 0.965755i \(-0.583543\pi\)
−0.259456 + 0.965755i \(0.583543\pi\)
\(888\) −0.255408 −0.00857093
\(889\) 51.9157 1.74120
\(890\) −22.7815 −0.763637
\(891\) −5.64828 −0.189224
\(892\) −17.0856 −0.572069
\(893\) 51.1637 1.71213
\(894\) 76.3349 2.55302
\(895\) 18.6247 0.622554
\(896\) −0.237233 −0.00792541
\(897\) 1.32226 0.0441489
\(898\) 39.6754 1.32399
\(899\) −11.1576 −0.372126
\(900\) 7.71172 0.257057
\(901\) −74.0192 −2.46594
\(902\) −9.56296 −0.318412
\(903\) 48.2377 1.60525
\(904\) 0.0329126 0.00109466
\(905\) 5.28582 0.175707
\(906\) 101.335 3.36662
\(907\) −49.1781 −1.63293 −0.816467 0.577393i \(-0.804070\pi\)
−0.816467 + 0.577393i \(0.804070\pi\)
\(908\) 50.4103 1.67292
\(909\) 5.28971 0.175449
\(910\) 6.43033 0.213163
\(911\) −10.4727 −0.346976 −0.173488 0.984836i \(-0.555504\pi\)
−0.173488 + 0.984836i \(0.555504\pi\)
\(912\) −54.7638 −1.81341
\(913\) 11.6845 0.386700
\(914\) 41.6135 1.37645
\(915\) 35.2155 1.16419
\(916\) −39.1453 −1.29340
\(917\) −27.8816 −0.920733
\(918\) 30.6812 1.01263
\(919\) −45.9107 −1.51445 −0.757227 0.653152i \(-0.773446\pi\)
−0.757227 + 0.653152i \(0.773446\pi\)
\(920\) −0.00465067 −0.000153328 0
\(921\) −31.9583 −1.05306
\(922\) −26.8875 −0.885493
\(923\) −3.64047 −0.119828
\(924\) 13.7104 0.451040
\(925\) −8.62271 −0.283513
\(926\) 17.1269 0.562825
\(927\) −21.9662 −0.721465
\(928\) 16.6424 0.546314
\(929\) 42.5041 1.39451 0.697257 0.716821i \(-0.254404\pi\)
0.697257 + 0.716821i \(0.254404\pi\)
\(930\) 28.0694 0.920430
\(931\) −0.612039 −0.0200588
\(932\) −41.4165 −1.35664
\(933\) 7.25870 0.237639
\(934\) −25.6858 −0.840464
\(935\) −6.75860 −0.221030
\(936\) −0.0536045 −0.00175212
\(937\) −30.8978 −1.00939 −0.504693 0.863299i \(-0.668394\pi\)
−0.504693 + 0.863299i \(0.668394\pi\)
\(938\) 4.80882 0.157013
\(939\) 45.0266 1.46939
\(940\) 19.5852 0.638799
\(941\) −21.2158 −0.691615 −0.345808 0.938305i \(-0.612395\pi\)
−0.345808 + 0.938305i \(0.612395\pi\)
\(942\) 25.9968 0.847022
\(943\) −1.96867 −0.0641086
\(944\) −20.5819 −0.669884
\(945\) 5.95892 0.193844
\(946\) −14.0236 −0.455946
\(947\) −9.88968 −0.321372 −0.160686 0.987006i \(-0.551371\pi\)
−0.160686 + 0.987006i \(0.551371\pi\)
\(948\) 38.9887 1.26630
\(949\) −1.22641 −0.0398110
\(950\) −10.4125 −0.337827
\(951\) 56.2614 1.82440
\(952\) −0.200421 −0.00649569
\(953\) 44.8956 1.45431 0.727155 0.686473i \(-0.240842\pi\)
0.727155 + 0.686473i \(0.240842\pi\)
\(954\) −84.6373 −2.74024
\(955\) −7.42434 −0.240246
\(956\) 6.07473 0.196471
\(957\) 5.45524 0.176343
\(958\) −20.6988 −0.668747
\(959\) 5.54803 0.179155
\(960\) −20.8449 −0.672767
\(961\) −2.27465 −0.0733760
\(962\) −21.1350 −0.681421
\(963\) 26.9412 0.868169
\(964\) −35.3593 −1.13884
\(965\) −9.18309 −0.295614
\(966\) 5.65296 0.181881
\(967\) −7.79733 −0.250745 −0.125373 0.992110i \(-0.540013\pi\)
−0.125373 + 0.992110i \(0.540013\pi\)
\(968\) 0.0113035 0.000363309 0
\(969\) −92.2715 −2.96419
\(970\) 8.57216 0.275236
\(971\) 42.2902 1.35716 0.678579 0.734527i \(-0.262596\pi\)
0.678579 + 0.734527i \(0.262596\pi\)
\(972\) −43.1083 −1.38270
\(973\) 55.8023 1.78894
\(974\) 5.42820 0.173931
\(975\) −3.21376 −0.102923
\(976\) −53.9063 −1.72550
\(977\) 31.1327 0.996022 0.498011 0.867171i \(-0.334064\pi\)
0.498011 + 0.867171i \(0.334064\pi\)
\(978\) 53.8309 1.72132
\(979\) 11.3988 0.364307
\(980\) −0.234286 −0.00748398
\(981\) 2.13682 0.0682236
\(982\) −4.30905 −0.137507
\(983\) 17.8492 0.569300 0.284650 0.958632i \(-0.408123\pi\)
0.284650 + 0.958632i \(0.408123\pi\)
\(984\) 0.141729 0.00451817
\(985\) −4.63996 −0.147842
\(986\) 28.1201 0.895526
\(987\) 67.5117 2.14892
\(988\) −12.7430 −0.405408
\(989\) −2.88694 −0.0917995
\(990\) −7.72812 −0.245616
\(991\) 35.6820 1.13348 0.566738 0.823898i \(-0.308205\pi\)
0.566738 + 0.823898i \(0.308205\pi\)
\(992\) −42.8462 −1.36037
\(993\) −18.9596 −0.601664
\(994\) −15.5639 −0.493657
\(995\) 9.71917 0.308118
\(996\) 61.0642 1.93489
\(997\) 6.34846 0.201058 0.100529 0.994934i \(-0.467947\pi\)
0.100529 + 0.994934i \(0.467947\pi\)
\(998\) −45.0741 −1.42679
\(999\) −19.5856 −0.619662
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 \(a_p\))