Properties

Label 6026.2.a.i.1.13
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.0412722 q^{3}\) \(+1.00000 q^{4}\) \(-3.47552 q^{5}\) \(+0.0412722 q^{6}\) \(-4.67489 q^{7}\) \(-1.00000 q^{8}\) \(-2.99830 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.0412722 q^{3}\) \(+1.00000 q^{4}\) \(-3.47552 q^{5}\) \(+0.0412722 q^{6}\) \(-4.67489 q^{7}\) \(-1.00000 q^{8}\) \(-2.99830 q^{9}\) \(+3.47552 q^{10}\) \(-0.864604 q^{11}\) \(-0.0412722 q^{12}\) \(+1.77625 q^{13}\) \(+4.67489 q^{14}\) \(+0.143443 q^{15}\) \(+1.00000 q^{16}\) \(+0.0423660 q^{17}\) \(+2.99830 q^{18}\) \(-0.190142 q^{19}\) \(-3.47552 q^{20}\) \(+0.192943 q^{21}\) \(+0.864604 q^{22}\) \(+1.00000 q^{23}\) \(+0.0412722 q^{24}\) \(+7.07925 q^{25}\) \(-1.77625 q^{26}\) \(+0.247563 q^{27}\) \(-4.67489 q^{28}\) \(+8.29029 q^{29}\) \(-0.143443 q^{30}\) \(-5.15683 q^{31}\) \(-1.00000 q^{32}\) \(+0.0356842 q^{33}\) \(-0.0423660 q^{34}\) \(+16.2477 q^{35}\) \(-2.99830 q^{36}\) \(+3.01004 q^{37}\) \(+0.190142 q^{38}\) \(-0.0733097 q^{39}\) \(+3.47552 q^{40}\) \(+5.50915 q^{41}\) \(-0.192943 q^{42}\) \(+1.97222 q^{43}\) \(-0.864604 q^{44}\) \(+10.4206 q^{45}\) \(-1.00000 q^{46}\) \(-6.19777 q^{47}\) \(-0.0412722 q^{48}\) \(+14.8546 q^{49}\) \(-7.07925 q^{50}\) \(-0.00174854 q^{51}\) \(+1.77625 q^{52}\) \(+12.3238 q^{53}\) \(-0.247563 q^{54}\) \(+3.00495 q^{55}\) \(+4.67489 q^{56}\) \(+0.00784760 q^{57}\) \(-8.29029 q^{58}\) \(-12.5038 q^{59}\) \(+0.143443 q^{60}\) \(-1.83577 q^{61}\) \(+5.15683 q^{62}\) \(+14.0167 q^{63}\) \(+1.00000 q^{64}\) \(-6.17339 q^{65}\) \(-0.0356842 q^{66}\) \(-8.37015 q^{67}\) \(+0.0423660 q^{68}\) \(-0.0412722 q^{69}\) \(-16.2477 q^{70}\) \(-8.15822 q^{71}\) \(+2.99830 q^{72}\) \(-1.53021 q^{73}\) \(-3.01004 q^{74}\) \(-0.292176 q^{75}\) \(-0.190142 q^{76}\) \(+4.04194 q^{77}\) \(+0.0733097 q^{78}\) \(+7.35334 q^{79}\) \(-3.47552 q^{80}\) \(+8.98467 q^{81}\) \(-5.50915 q^{82}\) \(+14.9726 q^{83}\) \(+0.192943 q^{84}\) \(-0.147244 q^{85}\) \(-1.97222 q^{86}\) \(-0.342159 q^{87}\) \(+0.864604 q^{88}\) \(-3.01022 q^{89}\) \(-10.4206 q^{90}\) \(-8.30377 q^{91}\) \(+1.00000 q^{92}\) \(+0.212834 q^{93}\) \(+6.19777 q^{94}\) \(+0.660844 q^{95}\) \(+0.0412722 q^{96}\) \(+9.58972 q^{97}\) \(-14.8546 q^{98}\) \(+2.59234 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.0412722 −0.0238285 −0.0119143 0.999929i \(-0.503793\pi\)
−0.0119143 + 0.999929i \(0.503793\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.47552 −1.55430 −0.777150 0.629315i \(-0.783335\pi\)
−0.777150 + 0.629315i \(0.783335\pi\)
\(6\) 0.0412722 0.0168493
\(7\) −4.67489 −1.76694 −0.883472 0.468484i \(-0.844800\pi\)
−0.883472 + 0.468484i \(0.844800\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.99830 −0.999432
\(10\) 3.47552 1.09906
\(11\) −0.864604 −0.260688 −0.130344 0.991469i \(-0.541608\pi\)
−0.130344 + 0.991469i \(0.541608\pi\)
\(12\) −0.0412722 −0.0119143
\(13\) 1.77625 0.492642 0.246321 0.969188i \(-0.420778\pi\)
0.246321 + 0.969188i \(0.420778\pi\)
\(14\) 4.67489 1.24942
\(15\) 0.143443 0.0370367
\(16\) 1.00000 0.250000
\(17\) 0.0423660 0.0102753 0.00513764 0.999987i \(-0.498365\pi\)
0.00513764 + 0.999987i \(0.498365\pi\)
\(18\) 2.99830 0.706705
\(19\) −0.190142 −0.0436216 −0.0218108 0.999762i \(-0.506943\pi\)
−0.0218108 + 0.999762i \(0.506943\pi\)
\(20\) −3.47552 −0.777150
\(21\) 0.192943 0.0421037
\(22\) 0.864604 0.184334
\(23\) 1.00000 0.208514
\(24\) 0.0412722 0.00842466
\(25\) 7.07925 1.41585
\(26\) −1.77625 −0.348351
\(27\) 0.247563 0.0476436
\(28\) −4.67489 −0.883472
\(29\) 8.29029 1.53947 0.769734 0.638365i \(-0.220389\pi\)
0.769734 + 0.638365i \(0.220389\pi\)
\(30\) −0.143443 −0.0261889
\(31\) −5.15683 −0.926194 −0.463097 0.886308i \(-0.653262\pi\)
−0.463097 + 0.886308i \(0.653262\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.0356842 0.00621182
\(34\) −0.0423660 −0.00726571
\(35\) 16.2477 2.74636
\(36\) −2.99830 −0.499716
\(37\) 3.01004 0.494847 0.247424 0.968907i \(-0.420416\pi\)
0.247424 + 0.968907i \(0.420416\pi\)
\(38\) 0.190142 0.0308452
\(39\) −0.0733097 −0.0117390
\(40\) 3.47552 0.549528
\(41\) 5.50915 0.860384 0.430192 0.902737i \(-0.358446\pi\)
0.430192 + 0.902737i \(0.358446\pi\)
\(42\) −0.192943 −0.0297718
\(43\) 1.97222 0.300761 0.150381 0.988628i \(-0.451950\pi\)
0.150381 + 0.988628i \(0.451950\pi\)
\(44\) −0.864604 −0.130344
\(45\) 10.4206 1.55342
\(46\) −1.00000 −0.147442
\(47\) −6.19777 −0.904037 −0.452019 0.892009i \(-0.649296\pi\)
−0.452019 + 0.892009i \(0.649296\pi\)
\(48\) −0.0412722 −0.00595714
\(49\) 14.8546 2.12209
\(50\) −7.07925 −1.00116
\(51\) −0.00174854 −0.000244845 0
\(52\) 1.77625 0.246321
\(53\) 12.3238 1.69281 0.846404 0.532541i \(-0.178763\pi\)
0.846404 + 0.532541i \(0.178763\pi\)
\(54\) −0.247563 −0.0336891
\(55\) 3.00495 0.405188
\(56\) 4.67489 0.624709
\(57\) 0.00784760 0.00103944
\(58\) −8.29029 −1.08857
\(59\) −12.5038 −1.62785 −0.813926 0.580968i \(-0.802674\pi\)
−0.813926 + 0.580968i \(0.802674\pi\)
\(60\) 0.143443 0.0185184
\(61\) −1.83577 −0.235047 −0.117523 0.993070i \(-0.537495\pi\)
−0.117523 + 0.993070i \(0.537495\pi\)
\(62\) 5.15683 0.654918
\(63\) 14.0167 1.76594
\(64\) 1.00000 0.125000
\(65\) −6.17339 −0.765714
\(66\) −0.0356842 −0.00439242
\(67\) −8.37015 −1.02258 −0.511288 0.859409i \(-0.670832\pi\)
−0.511288 + 0.859409i \(0.670832\pi\)
\(68\) 0.0423660 0.00513764
\(69\) −0.0412722 −0.00496859
\(70\) −16.2477 −1.94197
\(71\) −8.15822 −0.968203 −0.484102 0.875012i \(-0.660853\pi\)
−0.484102 + 0.875012i \(0.660853\pi\)
\(72\) 2.99830 0.353353
\(73\) −1.53021 −0.179097 −0.0895487 0.995982i \(-0.528542\pi\)
−0.0895487 + 0.995982i \(0.528542\pi\)
\(74\) −3.01004 −0.349910
\(75\) −0.292176 −0.0337376
\(76\) −0.190142 −0.0218108
\(77\) 4.04194 0.460621
\(78\) 0.0733097 0.00830069
\(79\) 7.35334 0.827315 0.413657 0.910433i \(-0.364251\pi\)
0.413657 + 0.910433i \(0.364251\pi\)
\(80\) −3.47552 −0.388575
\(81\) 8.98467 0.998297
\(82\) −5.50915 −0.608383
\(83\) 14.9726 1.64346 0.821730 0.569878i \(-0.193009\pi\)
0.821730 + 0.569878i \(0.193009\pi\)
\(84\) 0.192943 0.0210519
\(85\) −0.147244 −0.0159709
\(86\) −1.97222 −0.212670
\(87\) −0.342159 −0.0366833
\(88\) 0.864604 0.0921671
\(89\) −3.01022 −0.319083 −0.159542 0.987191i \(-0.551002\pi\)
−0.159542 + 0.987191i \(0.551002\pi\)
\(90\) −10.4206 −1.09843
\(91\) −8.30377 −0.870472
\(92\) 1.00000 0.104257
\(93\) 0.212834 0.0220698
\(94\) 6.19777 0.639251
\(95\) 0.660844 0.0678011
\(96\) 0.0412722 0.00421233
\(97\) 9.58972 0.973688 0.486844 0.873489i \(-0.338148\pi\)
0.486844 + 0.873489i \(0.338148\pi\)
\(98\) −14.8546 −1.50055
\(99\) 2.59234 0.260540
\(100\) 7.07925 0.707925
\(101\) 1.84549 0.183634 0.0918168 0.995776i \(-0.470733\pi\)
0.0918168 + 0.995776i \(0.470733\pi\)
\(102\) 0.00174854 0.000173131 0
\(103\) 3.17903 0.313239 0.156619 0.987659i \(-0.449940\pi\)
0.156619 + 0.987659i \(0.449940\pi\)
\(104\) −1.77625 −0.174175
\(105\) −0.670579 −0.0654418
\(106\) −12.3238 −1.19700
\(107\) 8.94815 0.865050 0.432525 0.901622i \(-0.357623\pi\)
0.432525 + 0.901622i \(0.357623\pi\)
\(108\) 0.247563 0.0238218
\(109\) 13.9356 1.33479 0.667396 0.744703i \(-0.267409\pi\)
0.667396 + 0.744703i \(0.267409\pi\)
\(110\) −3.00495 −0.286511
\(111\) −0.124231 −0.0117915
\(112\) −4.67489 −0.441736
\(113\) 0.872199 0.0820496 0.0410248 0.999158i \(-0.486938\pi\)
0.0410248 + 0.999158i \(0.486938\pi\)
\(114\) −0.00784760 −0.000734995 0
\(115\) −3.47552 −0.324094
\(116\) 8.29029 0.769734
\(117\) −5.32572 −0.492363
\(118\) 12.5038 1.15107
\(119\) −0.198057 −0.0181558
\(120\) −0.143443 −0.0130945
\(121\) −10.2525 −0.932042
\(122\) 1.83577 0.166203
\(123\) −0.227375 −0.0205017
\(124\) −5.15683 −0.463097
\(125\) −7.22647 −0.646355
\(126\) −14.0167 −1.24871
\(127\) −9.06565 −0.804446 −0.402223 0.915542i \(-0.631762\pi\)
−0.402223 + 0.915542i \(0.631762\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.0813981 −0.00716671
\(130\) 6.17339 0.541442
\(131\) 1.00000 0.0873704
\(132\) 0.0356842 0.00310591
\(133\) 0.888896 0.0770770
\(134\) 8.37015 0.723071
\(135\) −0.860411 −0.0740524
\(136\) −0.0423660 −0.00363286
\(137\) −20.6634 −1.76540 −0.882698 0.469940i \(-0.844276\pi\)
−0.882698 + 0.469940i \(0.844276\pi\)
\(138\) 0.0412722 0.00351333
\(139\) 18.6588 1.58262 0.791311 0.611414i \(-0.209399\pi\)
0.791311 + 0.611414i \(0.209399\pi\)
\(140\) 16.2477 1.37318
\(141\) 0.255796 0.0215419
\(142\) 8.15822 0.684623
\(143\) −1.53575 −0.128426
\(144\) −2.99830 −0.249858
\(145\) −28.8131 −2.39279
\(146\) 1.53021 0.126641
\(147\) −0.613084 −0.0505664
\(148\) 3.01004 0.247424
\(149\) 19.9068 1.63083 0.815416 0.578876i \(-0.196508\pi\)
0.815416 + 0.578876i \(0.196508\pi\)
\(150\) 0.292176 0.0238561
\(151\) −6.46915 −0.526452 −0.263226 0.964734i \(-0.584786\pi\)
−0.263226 + 0.964734i \(0.584786\pi\)
\(152\) 0.190142 0.0154226
\(153\) −0.127026 −0.0102694
\(154\) −4.04194 −0.325708
\(155\) 17.9227 1.43958
\(156\) −0.0733097 −0.00586948
\(157\) 9.16519 0.731461 0.365731 0.930721i \(-0.380819\pi\)
0.365731 + 0.930721i \(0.380819\pi\)
\(158\) −7.35334 −0.585000
\(159\) −0.508632 −0.0403372
\(160\) 3.47552 0.274764
\(161\) −4.67489 −0.368433
\(162\) −8.98467 −0.705903
\(163\) −14.0111 −1.09744 −0.548718 0.836007i \(-0.684884\pi\)
−0.548718 + 0.836007i \(0.684884\pi\)
\(164\) 5.50915 0.430192
\(165\) −0.124021 −0.00965503
\(166\) −14.9726 −1.16210
\(167\) −12.2410 −0.947238 −0.473619 0.880730i \(-0.657053\pi\)
−0.473619 + 0.880730i \(0.657053\pi\)
\(168\) −0.192943 −0.0148859
\(169\) −9.84494 −0.757303
\(170\) 0.147244 0.0112931
\(171\) 0.570103 0.0435969
\(172\) 1.97222 0.150381
\(173\) 14.5343 1.10502 0.552512 0.833505i \(-0.313669\pi\)
0.552512 + 0.833505i \(0.313669\pi\)
\(174\) 0.342159 0.0259390
\(175\) −33.0947 −2.50173
\(176\) −0.864604 −0.0651720
\(177\) 0.516059 0.0387894
\(178\) 3.01022 0.225626
\(179\) −13.8315 −1.03382 −0.516908 0.856041i \(-0.672917\pi\)
−0.516908 + 0.856041i \(0.672917\pi\)
\(180\) 10.4206 0.776709
\(181\) −15.1875 −1.12888 −0.564440 0.825474i \(-0.690908\pi\)
−0.564440 + 0.825474i \(0.690908\pi\)
\(182\) 8.30377 0.615516
\(183\) 0.0757664 0.00560082
\(184\) −1.00000 −0.0737210
\(185\) −10.4615 −0.769141
\(186\) −0.212834 −0.0156057
\(187\) −0.0366299 −0.00267864
\(188\) −6.19777 −0.452019
\(189\) −1.15733 −0.0841835
\(190\) −0.660844 −0.0479426
\(191\) −6.00261 −0.434333 −0.217167 0.976135i \(-0.569682\pi\)
−0.217167 + 0.976135i \(0.569682\pi\)
\(192\) −0.0412722 −0.00297857
\(193\) −22.5349 −1.62210 −0.811050 0.584977i \(-0.801103\pi\)
−0.811050 + 0.584977i \(0.801103\pi\)
\(194\) −9.58972 −0.688502
\(195\) 0.254790 0.0182459
\(196\) 14.8546 1.06105
\(197\) −14.9776 −1.06711 −0.533554 0.845766i \(-0.679144\pi\)
−0.533554 + 0.845766i \(0.679144\pi\)
\(198\) −2.59234 −0.184230
\(199\) −15.4970 −1.09855 −0.549277 0.835640i \(-0.685097\pi\)
−0.549277 + 0.835640i \(0.685097\pi\)
\(200\) −7.07925 −0.500578
\(201\) 0.345455 0.0243665
\(202\) −1.84549 −0.129849
\(203\) −38.7562 −2.72015
\(204\) −0.00174854 −0.000122422 0
\(205\) −19.1472 −1.33730
\(206\) −3.17903 −0.221493
\(207\) −2.99830 −0.208396
\(208\) 1.77625 0.123161
\(209\) 0.164398 0.0113716
\(210\) 0.670579 0.0462743
\(211\) −11.1133 −0.765071 −0.382536 0.923941i \(-0.624949\pi\)
−0.382536 + 0.923941i \(0.624949\pi\)
\(212\) 12.3238 0.846404
\(213\) 0.336708 0.0230709
\(214\) −8.94815 −0.611683
\(215\) −6.85451 −0.467474
\(216\) −0.247563 −0.0168445
\(217\) 24.1076 1.63653
\(218\) −13.9356 −0.943840
\(219\) 0.0631552 0.00426763
\(220\) 3.00495 0.202594
\(221\) 0.0752526 0.00506203
\(222\) 0.124231 0.00833784
\(223\) 26.3115 1.76195 0.880973 0.473167i \(-0.156889\pi\)
0.880973 + 0.473167i \(0.156889\pi\)
\(224\) 4.67489 0.312355
\(225\) −21.2257 −1.41505
\(226\) −0.872199 −0.0580178
\(227\) 2.83976 0.188482 0.0942408 0.995549i \(-0.469958\pi\)
0.0942408 + 0.995549i \(0.469958\pi\)
\(228\) 0.00784760 0.000519720 0
\(229\) −25.6328 −1.69386 −0.846932 0.531702i \(-0.821553\pi\)
−0.846932 + 0.531702i \(0.821553\pi\)
\(230\) 3.47552 0.229169
\(231\) −0.166820 −0.0109759
\(232\) −8.29029 −0.544284
\(233\) 8.73343 0.572146 0.286073 0.958208i \(-0.407650\pi\)
0.286073 + 0.958208i \(0.407650\pi\)
\(234\) 5.32572 0.348153
\(235\) 21.5405 1.40515
\(236\) −12.5038 −0.813926
\(237\) −0.303489 −0.0197137
\(238\) 0.198057 0.0128381
\(239\) 7.12982 0.461190 0.230595 0.973050i \(-0.425933\pi\)
0.230595 + 0.973050i \(0.425933\pi\)
\(240\) 0.143443 0.00925918
\(241\) 15.4202 0.993303 0.496651 0.867950i \(-0.334563\pi\)
0.496651 + 0.867950i \(0.334563\pi\)
\(242\) 10.2525 0.659053
\(243\) −1.11351 −0.0714315
\(244\) −1.83577 −0.117523
\(245\) −51.6276 −3.29837
\(246\) 0.227375 0.0144969
\(247\) −0.337740 −0.0214899
\(248\) 5.15683 0.327459
\(249\) −0.617954 −0.0391612
\(250\) 7.22647 0.457042
\(251\) 7.09374 0.447753 0.223876 0.974618i \(-0.428129\pi\)
0.223876 + 0.974618i \(0.428129\pi\)
\(252\) 14.0167 0.882970
\(253\) −0.864604 −0.0543572
\(254\) 9.06565 0.568829
\(255\) 0.00607709 0.000380562 0
\(256\) 1.00000 0.0625000
\(257\) 11.0409 0.688710 0.344355 0.938839i \(-0.388098\pi\)
0.344355 + 0.938839i \(0.388098\pi\)
\(258\) 0.0813981 0.00506763
\(259\) −14.0716 −0.874368
\(260\) −6.17339 −0.382857
\(261\) −24.8567 −1.53859
\(262\) −1.00000 −0.0617802
\(263\) 3.30817 0.203990 0.101995 0.994785i \(-0.467477\pi\)
0.101995 + 0.994785i \(0.467477\pi\)
\(264\) −0.0356842 −0.00219621
\(265\) −42.8317 −2.63113
\(266\) −0.888896 −0.0545017
\(267\) 0.124239 0.00760328
\(268\) −8.37015 −0.511288
\(269\) 7.18955 0.438354 0.219177 0.975685i \(-0.429663\pi\)
0.219177 + 0.975685i \(0.429663\pi\)
\(270\) 0.860411 0.0523629
\(271\) 17.3708 1.05520 0.527600 0.849493i \(-0.323092\pi\)
0.527600 + 0.849493i \(0.323092\pi\)
\(272\) 0.0423660 0.00256882
\(273\) 0.342715 0.0207421
\(274\) 20.6634 1.24832
\(275\) −6.12075 −0.369095
\(276\) −0.0412722 −0.00248430
\(277\) −28.3063 −1.70076 −0.850381 0.526167i \(-0.823629\pi\)
−0.850381 + 0.526167i \(0.823629\pi\)
\(278\) −18.6588 −1.11908
\(279\) 15.4617 0.925668
\(280\) −16.2477 −0.970986
\(281\) 6.39709 0.381618 0.190809 0.981627i \(-0.438889\pi\)
0.190809 + 0.981627i \(0.438889\pi\)
\(282\) −0.255796 −0.0152324
\(283\) 16.7184 0.993808 0.496904 0.867805i \(-0.334470\pi\)
0.496904 + 0.867805i \(0.334470\pi\)
\(284\) −8.15822 −0.484102
\(285\) −0.0272745 −0.00161560
\(286\) 1.53575 0.0908109
\(287\) −25.7547 −1.52025
\(288\) 2.99830 0.176676
\(289\) −16.9982 −0.999894
\(290\) 28.8131 1.69196
\(291\) −0.395789 −0.0232016
\(292\) −1.53021 −0.0895487
\(293\) 31.8350 1.85982 0.929911 0.367784i \(-0.119883\pi\)
0.929911 + 0.367784i \(0.119883\pi\)
\(294\) 0.613084 0.0357558
\(295\) 43.4571 2.53017
\(296\) −3.01004 −0.174955
\(297\) −0.214044 −0.0124201
\(298\) −19.9068 −1.15317
\(299\) 1.77625 0.102723
\(300\) −0.292176 −0.0168688
\(301\) −9.21994 −0.531429
\(302\) 6.46915 0.372258
\(303\) −0.0761677 −0.00437572
\(304\) −0.190142 −0.0109054
\(305\) 6.38027 0.365333
\(306\) 0.127026 0.00726159
\(307\) 5.80297 0.331193 0.165596 0.986194i \(-0.447045\pi\)
0.165596 + 0.986194i \(0.447045\pi\)
\(308\) 4.04194 0.230311
\(309\) −0.131206 −0.00746403
\(310\) −17.9227 −1.01794
\(311\) 7.37807 0.418372 0.209186 0.977876i \(-0.432919\pi\)
0.209186 + 0.977876i \(0.432919\pi\)
\(312\) 0.0733097 0.00415035
\(313\) −24.4896 −1.38424 −0.692118 0.721784i \(-0.743322\pi\)
−0.692118 + 0.721784i \(0.743322\pi\)
\(314\) −9.16519 −0.517221
\(315\) −48.7154 −2.74480
\(316\) 7.35334 0.413657
\(317\) 10.2462 0.575484 0.287742 0.957708i \(-0.407095\pi\)
0.287742 + 0.957708i \(0.407095\pi\)
\(318\) 0.508632 0.0285227
\(319\) −7.16782 −0.401321
\(320\) −3.47552 −0.194288
\(321\) −0.369310 −0.0206129
\(322\) 4.67489 0.260522
\(323\) −0.00805558 −0.000448224 0
\(324\) 8.98467 0.499148
\(325\) 12.5745 0.697508
\(326\) 14.0111 0.776005
\(327\) −0.575155 −0.0318061
\(328\) −5.50915 −0.304192
\(329\) 28.9739 1.59738
\(330\) 0.124021 0.00682714
\(331\) −23.1127 −1.27039 −0.635195 0.772352i \(-0.719080\pi\)
−0.635195 + 0.772352i \(0.719080\pi\)
\(332\) 14.9726 0.821730
\(333\) −9.02499 −0.494566
\(334\) 12.2410 0.669798
\(335\) 29.0906 1.58939
\(336\) 0.192943 0.0105259
\(337\) −5.86119 −0.319279 −0.159640 0.987175i \(-0.551033\pi\)
−0.159640 + 0.987175i \(0.551033\pi\)
\(338\) 9.84494 0.535494
\(339\) −0.0359976 −0.00195512
\(340\) −0.147244 −0.00798543
\(341\) 4.45862 0.241448
\(342\) −0.570103 −0.0308276
\(343\) −36.7196 −1.98267
\(344\) −1.97222 −0.106335
\(345\) 0.143443 0.00772269
\(346\) −14.5343 −0.781370
\(347\) 3.30471 0.177406 0.0887030 0.996058i \(-0.471728\pi\)
0.0887030 + 0.996058i \(0.471728\pi\)
\(348\) −0.342159 −0.0183416
\(349\) −33.0618 −1.76976 −0.884880 0.465819i \(-0.845760\pi\)
−0.884880 + 0.465819i \(0.845760\pi\)
\(350\) 33.0947 1.76899
\(351\) 0.439734 0.0234712
\(352\) 0.864604 0.0460836
\(353\) 30.6985 1.63392 0.816959 0.576696i \(-0.195658\pi\)
0.816959 + 0.576696i \(0.195658\pi\)
\(354\) −0.516059 −0.0274282
\(355\) 28.3541 1.50488
\(356\) −3.01022 −0.159542
\(357\) 0.00817425 0.000432627 0
\(358\) 13.8315 0.731018
\(359\) −18.5718 −0.980180 −0.490090 0.871672i \(-0.663036\pi\)
−0.490090 + 0.871672i \(0.663036\pi\)
\(360\) −10.4206 −0.549216
\(361\) −18.9638 −0.998097
\(362\) 15.1875 0.798239
\(363\) 0.423142 0.0222092
\(364\) −8.30377 −0.435236
\(365\) 5.31827 0.278371
\(366\) −0.0757664 −0.00396038
\(367\) 1.80375 0.0941548 0.0470774 0.998891i \(-0.485009\pi\)
0.0470774 + 0.998891i \(0.485009\pi\)
\(368\) 1.00000 0.0521286
\(369\) −16.5181 −0.859895
\(370\) 10.4615 0.543865
\(371\) −57.6126 −2.99110
\(372\) 0.212834 0.0110349
\(373\) 33.0923 1.71345 0.856727 0.515771i \(-0.172494\pi\)
0.856727 + 0.515771i \(0.172494\pi\)
\(374\) 0.0366299 0.00189408
\(375\) 0.298253 0.0154017
\(376\) 6.19777 0.319625
\(377\) 14.7256 0.758407
\(378\) 1.15733 0.0595267
\(379\) −18.7938 −0.965371 −0.482686 0.875794i \(-0.660339\pi\)
−0.482686 + 0.875794i \(0.660339\pi\)
\(380\) 0.660844 0.0339006
\(381\) 0.374160 0.0191688
\(382\) 6.00261 0.307120
\(383\) −9.84527 −0.503070 −0.251535 0.967848i \(-0.580935\pi\)
−0.251535 + 0.967848i \(0.580935\pi\)
\(384\) 0.0412722 0.00210617
\(385\) −14.0478 −0.715944
\(386\) 22.5349 1.14700
\(387\) −5.91331 −0.300591
\(388\) 9.58972 0.486844
\(389\) 23.5844 1.19577 0.597887 0.801580i \(-0.296007\pi\)
0.597887 + 0.801580i \(0.296007\pi\)
\(390\) −0.254790 −0.0129018
\(391\) 0.0423660 0.00214254
\(392\) −14.8546 −0.750273
\(393\) −0.0412722 −0.00208191
\(394\) 14.9776 0.754560
\(395\) −25.5567 −1.28590
\(396\) 2.59234 0.130270
\(397\) −18.0989 −0.908356 −0.454178 0.890911i \(-0.650067\pi\)
−0.454178 + 0.890911i \(0.650067\pi\)
\(398\) 15.4970 0.776795
\(399\) −0.0366867 −0.00183663
\(400\) 7.07925 0.353962
\(401\) 18.9159 0.944617 0.472308 0.881433i \(-0.343421\pi\)
0.472308 + 0.881433i \(0.343421\pi\)
\(402\) −0.345455 −0.0172297
\(403\) −9.15980 −0.456282
\(404\) 1.84549 0.0918168
\(405\) −31.2264 −1.55165
\(406\) 38.7562 1.92344
\(407\) −2.60249 −0.129001
\(408\) 0.00174854 8.65657e−5 0
\(409\) −17.9680 −0.888462 −0.444231 0.895912i \(-0.646523\pi\)
−0.444231 + 0.895912i \(0.646523\pi\)
\(410\) 19.1472 0.945610
\(411\) 0.852827 0.0420668
\(412\) 3.17903 0.156619
\(413\) 58.4538 2.87632
\(414\) 2.99830 0.147358
\(415\) −52.0377 −2.55443
\(416\) −1.77625 −0.0870877
\(417\) −0.770092 −0.0377116
\(418\) −0.164398 −0.00804097
\(419\) 32.6997 1.59748 0.798742 0.601674i \(-0.205499\pi\)
0.798742 + 0.601674i \(0.205499\pi\)
\(420\) −0.670579 −0.0327209
\(421\) 33.4154 1.62857 0.814283 0.580469i \(-0.197131\pi\)
0.814283 + 0.580469i \(0.197131\pi\)
\(422\) 11.1133 0.540987
\(423\) 18.5827 0.903524
\(424\) −12.3238 −0.598498
\(425\) 0.299920 0.0145482
\(426\) −0.336708 −0.0163136
\(427\) 8.58204 0.415314
\(428\) 8.94815 0.432525
\(429\) 0.0633839 0.00306020
\(430\) 6.85451 0.330554
\(431\) −6.27017 −0.302023 −0.151012 0.988532i \(-0.548253\pi\)
−0.151012 + 0.988532i \(0.548253\pi\)
\(432\) 0.247563 0.0119109
\(433\) −20.6938 −0.994481 −0.497240 0.867613i \(-0.665653\pi\)
−0.497240 + 0.867613i \(0.665653\pi\)
\(434\) −24.1076 −1.15720
\(435\) 1.18918 0.0570168
\(436\) 13.9356 0.667396
\(437\) −0.190142 −0.00909574
\(438\) −0.0631552 −0.00301767
\(439\) 24.4058 1.16482 0.582412 0.812894i \(-0.302109\pi\)
0.582412 + 0.812894i \(0.302109\pi\)
\(440\) −3.00495 −0.143255
\(441\) −44.5386 −2.12089
\(442\) −0.0752526 −0.00357940
\(443\) −31.8722 −1.51429 −0.757147 0.653244i \(-0.773407\pi\)
−0.757147 + 0.653244i \(0.773407\pi\)
\(444\) −0.124231 −0.00589575
\(445\) 10.4621 0.495951
\(446\) −26.3115 −1.24588
\(447\) −0.821600 −0.0388603
\(448\) −4.67489 −0.220868
\(449\) −25.2156 −1.19000 −0.595000 0.803726i \(-0.702848\pi\)
−0.595000 + 0.803726i \(0.702848\pi\)
\(450\) 21.2257 1.00059
\(451\) −4.76323 −0.224292
\(452\) 0.872199 0.0410248
\(453\) 0.266996 0.0125446
\(454\) −2.83976 −0.133277
\(455\) 28.8599 1.35297
\(456\) −0.00784760 −0.000367498 0
\(457\) 34.6630 1.62147 0.810733 0.585416i \(-0.199069\pi\)
0.810733 + 0.585416i \(0.199069\pi\)
\(458\) 25.6328 1.19774
\(459\) 0.0104883 0.000489550 0
\(460\) −3.47552 −0.162047
\(461\) 22.9197 1.06748 0.533738 0.845650i \(-0.320787\pi\)
0.533738 + 0.845650i \(0.320787\pi\)
\(462\) 0.166820 0.00776116
\(463\) 24.2266 1.12590 0.562952 0.826489i \(-0.309665\pi\)
0.562952 + 0.826489i \(0.309665\pi\)
\(464\) 8.29029 0.384867
\(465\) −0.739709 −0.0343032
\(466\) −8.73343 −0.404568
\(467\) 8.44872 0.390960 0.195480 0.980708i \(-0.437373\pi\)
0.195480 + 0.980708i \(0.437373\pi\)
\(468\) −5.32572 −0.246181
\(469\) 39.1296 1.80684
\(470\) −21.5405 −0.993588
\(471\) −0.378268 −0.0174297
\(472\) 12.5038 0.575533
\(473\) −1.70519 −0.0784049
\(474\) 0.303489 0.0139397
\(475\) −1.34606 −0.0617617
\(476\) −0.198057 −0.00907791
\(477\) −36.9505 −1.69185
\(478\) −7.12982 −0.326110
\(479\) −15.6448 −0.714829 −0.357415 0.933946i \(-0.616342\pi\)
−0.357415 + 0.933946i \(0.616342\pi\)
\(480\) −0.143443 −0.00654723
\(481\) 5.34658 0.243783
\(482\) −15.4202 −0.702371
\(483\) 0.192943 0.00877923
\(484\) −10.2525 −0.466021
\(485\) −33.3293 −1.51340
\(486\) 1.11351 0.0505097
\(487\) 23.5517 1.06723 0.533615 0.845728i \(-0.320833\pi\)
0.533615 + 0.845728i \(0.320833\pi\)
\(488\) 1.83577 0.0831015
\(489\) 0.578271 0.0261503
\(490\) 51.6276 2.33230
\(491\) −9.07759 −0.409666 −0.204833 0.978797i \(-0.565665\pi\)
−0.204833 + 0.978797i \(0.565665\pi\)
\(492\) −0.227375 −0.0102508
\(493\) 0.351226 0.0158184
\(494\) 0.337740 0.0151956
\(495\) −9.00973 −0.404957
\(496\) −5.15683 −0.231548
\(497\) 38.1388 1.71076
\(498\) 0.617954 0.0276912
\(499\) 1.08724 0.0486713 0.0243357 0.999704i \(-0.492253\pi\)
0.0243357 + 0.999704i \(0.492253\pi\)
\(500\) −7.22647 −0.323177
\(501\) 0.505214 0.0225713
\(502\) −7.09374 −0.316609
\(503\) 33.7707 1.50576 0.752881 0.658157i \(-0.228664\pi\)
0.752881 + 0.658157i \(0.228664\pi\)
\(504\) −14.0167 −0.624354
\(505\) −6.41406 −0.285422
\(506\) 0.864604 0.0384364
\(507\) 0.406323 0.0180454
\(508\) −9.06565 −0.402223
\(509\) 13.9629 0.618893 0.309447 0.950917i \(-0.399856\pi\)
0.309447 + 0.950917i \(0.399856\pi\)
\(510\) −0.00607709 −0.000269098 0
\(511\) 7.15357 0.316455
\(512\) −1.00000 −0.0441942
\(513\) −0.0470722 −0.00207829
\(514\) −11.0409 −0.486992
\(515\) −11.0488 −0.486867
\(516\) −0.0813981 −0.00358335
\(517\) 5.35862 0.235672
\(518\) 14.0716 0.618271
\(519\) −0.599864 −0.0263311
\(520\) 6.17339 0.270721
\(521\) −20.3616 −0.892060 −0.446030 0.895018i \(-0.647163\pi\)
−0.446030 + 0.895018i \(0.647163\pi\)
\(522\) 24.8567 1.08795
\(523\) −15.9682 −0.698242 −0.349121 0.937078i \(-0.613520\pi\)
−0.349121 + 0.937078i \(0.613520\pi\)
\(524\) 1.00000 0.0436852
\(525\) 1.36589 0.0596125
\(526\) −3.30817 −0.144243
\(527\) −0.218474 −0.00951689
\(528\) 0.0356842 0.00155295
\(529\) 1.00000 0.0434783
\(530\) 42.8317 1.86049
\(531\) 37.4900 1.62693
\(532\) 0.888896 0.0385385
\(533\) 9.78561 0.423862
\(534\) −0.124239 −0.00537633
\(535\) −31.0995 −1.34455
\(536\) 8.37015 0.361535
\(537\) 0.570857 0.0246343
\(538\) −7.18955 −0.309963
\(539\) −12.8434 −0.553204
\(540\) −0.860411 −0.0370262
\(541\) −0.119484 −0.00513703 −0.00256852 0.999997i \(-0.500818\pi\)
−0.00256852 + 0.999997i \(0.500818\pi\)
\(542\) −17.3708 −0.746138
\(543\) 0.626823 0.0268996
\(544\) −0.0423660 −0.00181643
\(545\) −48.4336 −2.07467
\(546\) −0.342715 −0.0146669
\(547\) 20.1739 0.862575 0.431287 0.902215i \(-0.358059\pi\)
0.431287 + 0.902215i \(0.358059\pi\)
\(548\) −20.6634 −0.882698
\(549\) 5.50419 0.234913
\(550\) 6.12075 0.260990
\(551\) −1.57633 −0.0671541
\(552\) 0.0412722 0.00175666
\(553\) −34.3761 −1.46182
\(554\) 28.3063 1.20262
\(555\) 0.431768 0.0183275
\(556\) 18.6588 0.791311
\(557\) 24.4050 1.03407 0.517037 0.855963i \(-0.327035\pi\)
0.517037 + 0.855963i \(0.327035\pi\)
\(558\) −15.4617 −0.654546
\(559\) 3.50316 0.148168
\(560\) 16.2477 0.686590
\(561\) 0.00151180 6.38281e−5 0
\(562\) −6.39709 −0.269845
\(563\) 7.23851 0.305067 0.152533 0.988298i \(-0.451257\pi\)
0.152533 + 0.988298i \(0.451257\pi\)
\(564\) 0.255796 0.0107709
\(565\) −3.03135 −0.127530
\(566\) −16.7184 −0.702729
\(567\) −42.0024 −1.76393
\(568\) 8.15822 0.342311
\(569\) −23.5696 −0.988088 −0.494044 0.869437i \(-0.664482\pi\)
−0.494044 + 0.869437i \(0.664482\pi\)
\(570\) 0.0272745 0.00114240
\(571\) −37.5303 −1.57059 −0.785297 0.619119i \(-0.787490\pi\)
−0.785297 + 0.619119i \(0.787490\pi\)
\(572\) −1.53575 −0.0642130
\(573\) 0.247741 0.0103495
\(574\) 25.7547 1.07498
\(575\) 7.07925 0.295225
\(576\) −2.99830 −0.124929
\(577\) −32.8755 −1.36863 −0.684313 0.729188i \(-0.739898\pi\)
−0.684313 + 0.729188i \(0.739898\pi\)
\(578\) 16.9982 0.707032
\(579\) 0.930067 0.0386523
\(580\) −28.8131 −1.19640
\(581\) −69.9955 −2.90390
\(582\) 0.395789 0.0164060
\(583\) −10.6552 −0.441295
\(584\) 1.53021 0.0633205
\(585\) 18.5096 0.765280
\(586\) −31.8350 −1.31509
\(587\) −26.5449 −1.09562 −0.547812 0.836601i \(-0.684539\pi\)
−0.547812 + 0.836601i \(0.684539\pi\)
\(588\) −0.613084 −0.0252832
\(589\) 0.980531 0.0404021
\(590\) −43.4571 −1.78910
\(591\) 0.618159 0.0254276
\(592\) 3.01004 0.123712
\(593\) −15.5165 −0.637185 −0.318592 0.947892i \(-0.603210\pi\)
−0.318592 + 0.947892i \(0.603210\pi\)
\(594\) 0.214044 0.00878234
\(595\) 0.688350 0.0282196
\(596\) 19.9068 0.815416
\(597\) 0.639597 0.0261769
\(598\) −1.77625 −0.0726362
\(599\) 41.7557 1.70609 0.853046 0.521836i \(-0.174753\pi\)
0.853046 + 0.521836i \(0.174753\pi\)
\(600\) 0.292176 0.0119281
\(601\) 16.3294 0.666091 0.333046 0.942911i \(-0.391924\pi\)
0.333046 + 0.942911i \(0.391924\pi\)
\(602\) 9.21994 0.375777
\(603\) 25.0962 1.02200
\(604\) −6.46915 −0.263226
\(605\) 35.6326 1.44867
\(606\) 0.0761677 0.00309410
\(607\) −26.9070 −1.09212 −0.546060 0.837746i \(-0.683873\pi\)
−0.546060 + 0.837746i \(0.683873\pi\)
\(608\) 0.190142 0.00771129
\(609\) 1.59956 0.0648173
\(610\) −6.38027 −0.258329
\(611\) −11.0088 −0.445367
\(612\) −0.127026 −0.00513472
\(613\) −22.6280 −0.913935 −0.456968 0.889483i \(-0.651065\pi\)
−0.456968 + 0.889483i \(0.651065\pi\)
\(614\) −5.80297 −0.234189
\(615\) 0.790246 0.0318658
\(616\) −4.04194 −0.162854
\(617\) 35.4013 1.42520 0.712602 0.701569i \(-0.247517\pi\)
0.712602 + 0.701569i \(0.247517\pi\)
\(618\) 0.131206 0.00527786
\(619\) 20.4815 0.823221 0.411611 0.911360i \(-0.364966\pi\)
0.411611 + 0.911360i \(0.364966\pi\)
\(620\) 17.9227 0.719791
\(621\) 0.247563 0.00993437
\(622\) −7.37807 −0.295834
\(623\) 14.0725 0.563802
\(624\) −0.0733097 −0.00293474
\(625\) −10.2805 −0.411220
\(626\) 24.4896 0.978803
\(627\) −0.00678507 −0.000270970 0
\(628\) 9.16519 0.365731
\(629\) 0.127523 0.00508469
\(630\) 48.7154 1.94087
\(631\) −42.6326 −1.69718 −0.848588 0.529054i \(-0.822547\pi\)
−0.848588 + 0.529054i \(0.822547\pi\)
\(632\) −7.35334 −0.292500
\(633\) 0.458671 0.0182305
\(634\) −10.2462 −0.406929
\(635\) 31.5079 1.25035
\(636\) −0.508632 −0.0201686
\(637\) 26.3855 1.04543
\(638\) 7.16782 0.283777
\(639\) 24.4608 0.967653
\(640\) 3.47552 0.137382
\(641\) −17.9556 −0.709203 −0.354602 0.935018i \(-0.615383\pi\)
−0.354602 + 0.935018i \(0.615383\pi\)
\(642\) 0.369310 0.0145755
\(643\) 25.2299 0.994971 0.497486 0.867472i \(-0.334257\pi\)
0.497486 + 0.867472i \(0.334257\pi\)
\(644\) −4.67489 −0.184217
\(645\) 0.282901 0.0111392
\(646\) 0.00805558 0.000316942 0
\(647\) −19.3390 −0.760294 −0.380147 0.924926i \(-0.624127\pi\)
−0.380147 + 0.924926i \(0.624127\pi\)
\(648\) −8.98467 −0.352951
\(649\) 10.8108 0.424362
\(650\) −12.5745 −0.493212
\(651\) −0.994976 −0.0389962
\(652\) −14.0111 −0.548718
\(653\) −37.3477 −1.46153 −0.730764 0.682630i \(-0.760836\pi\)
−0.730764 + 0.682630i \(0.760836\pi\)
\(654\) 0.575155 0.0224903
\(655\) −3.47552 −0.135800
\(656\) 5.50915 0.215096
\(657\) 4.58802 0.178996
\(658\) −28.9739 −1.12952
\(659\) 25.0911 0.977410 0.488705 0.872449i \(-0.337469\pi\)
0.488705 + 0.872449i \(0.337469\pi\)
\(660\) −0.124021 −0.00482751
\(661\) −16.2810 −0.633257 −0.316629 0.948550i \(-0.602551\pi\)
−0.316629 + 0.948550i \(0.602551\pi\)
\(662\) 23.1127 0.898301
\(663\) −0.00310584 −0.000120621 0
\(664\) −14.9726 −0.581051
\(665\) −3.08938 −0.119801
\(666\) 9.02499 0.349711
\(667\) 8.29029 0.321001
\(668\) −12.2410 −0.473619
\(669\) −1.08593 −0.0419846
\(670\) −29.0906 −1.12387
\(671\) 1.58722 0.0612738
\(672\) −0.192943 −0.00744295
\(673\) 35.4722 1.36735 0.683677 0.729785i \(-0.260380\pi\)
0.683677 + 0.729785i \(0.260380\pi\)
\(674\) 5.86119 0.225765
\(675\) 1.75256 0.0674561
\(676\) −9.84494 −0.378652
\(677\) 22.1996 0.853199 0.426599 0.904441i \(-0.359711\pi\)
0.426599 + 0.904441i \(0.359711\pi\)
\(678\) 0.0359976 0.00138248
\(679\) −44.8309 −1.72045
\(680\) 0.147244 0.00564655
\(681\) −0.117203 −0.00449124
\(682\) −4.45862 −0.170729
\(683\) −38.8502 −1.48656 −0.743281 0.668980i \(-0.766731\pi\)
−0.743281 + 0.668980i \(0.766731\pi\)
\(684\) 0.570103 0.0217984
\(685\) 71.8162 2.74396
\(686\) 36.7196 1.40196
\(687\) 1.05792 0.0403623
\(688\) 1.97222 0.0751904
\(689\) 21.8902 0.833949
\(690\) −0.143443 −0.00546077
\(691\) 13.4523 0.511751 0.255876 0.966710i \(-0.417636\pi\)
0.255876 + 0.966710i \(0.417636\pi\)
\(692\) 14.5343 0.552512
\(693\) −12.1189 −0.460360
\(694\) −3.30471 −0.125445
\(695\) −64.8492 −2.45987
\(696\) 0.342159 0.0129695
\(697\) 0.233401 0.00884068
\(698\) 33.0618 1.25141
\(699\) −0.360448 −0.0136334
\(700\) −33.0947 −1.25086
\(701\) −20.6030 −0.778164 −0.389082 0.921203i \(-0.627208\pi\)
−0.389082 + 0.921203i \(0.627208\pi\)
\(702\) −0.439734 −0.0165967
\(703\) −0.572336 −0.0215861
\(704\) −0.864604 −0.0325860
\(705\) −0.889024 −0.0334826
\(706\) −30.6985 −1.15535
\(707\) −8.62749 −0.324470
\(708\) 0.516059 0.0193947
\(709\) 0.381165 0.0143149 0.00715747 0.999974i \(-0.497722\pi\)
0.00715747 + 0.999974i \(0.497722\pi\)
\(710\) −28.3541 −1.06411
\(711\) −22.0475 −0.826845
\(712\) 3.01022 0.112813
\(713\) −5.15683 −0.193125
\(714\) −0.00817425 −0.000305913 0
\(715\) 5.33754 0.199613
\(716\) −13.8315 −0.516908
\(717\) −0.294264 −0.0109895
\(718\) 18.5718 0.693092
\(719\) −10.4968 −0.391466 −0.195733 0.980657i \(-0.562709\pi\)
−0.195733 + 0.980657i \(0.562709\pi\)
\(720\) 10.4206 0.388354
\(721\) −14.8616 −0.553476
\(722\) 18.9638 0.705761
\(723\) −0.636426 −0.0236690
\(724\) −15.1875 −0.564440
\(725\) 58.6890 2.17965
\(726\) −0.423142 −0.0157043
\(727\) −39.2239 −1.45474 −0.727368 0.686248i \(-0.759257\pi\)
−0.727368 + 0.686248i \(0.759257\pi\)
\(728\) 8.30377 0.307758
\(729\) −26.9081 −0.996595
\(730\) −5.31827 −0.196838
\(731\) 0.0835553 0.00309040
\(732\) 0.0757664 0.00280041
\(733\) 27.9896 1.03382 0.516909 0.856040i \(-0.327083\pi\)
0.516909 + 0.856040i \(0.327083\pi\)
\(734\) −1.80375 −0.0665775
\(735\) 2.13079 0.0785953
\(736\) −1.00000 −0.0368605
\(737\) 7.23687 0.266574
\(738\) 16.5181 0.608038
\(739\) 6.90180 0.253887 0.126943 0.991910i \(-0.459483\pi\)
0.126943 + 0.991910i \(0.459483\pi\)
\(740\) −10.4615 −0.384571
\(741\) 0.0139393 0.000512072 0
\(742\) 57.6126 2.11503
\(743\) 15.6206 0.573066 0.286533 0.958070i \(-0.407497\pi\)
0.286533 + 0.958070i \(0.407497\pi\)
\(744\) −0.212834 −0.00780287
\(745\) −69.1866 −2.53480
\(746\) −33.0923 −1.21159
\(747\) −44.8924 −1.64253
\(748\) −0.0366299 −0.00133932
\(749\) −41.8316 −1.52849
\(750\) −0.298253 −0.0108906
\(751\) −35.5230 −1.29625 −0.648127 0.761533i \(-0.724447\pi\)
−0.648127 + 0.761533i \(0.724447\pi\)
\(752\) −6.19777 −0.226009
\(753\) −0.292775 −0.0106693
\(754\) −14.7256 −0.536275
\(755\) 22.4837 0.818264
\(756\) −1.15733 −0.0420918
\(757\) 31.5217 1.14568 0.572838 0.819668i \(-0.305842\pi\)
0.572838 + 0.819668i \(0.305842\pi\)
\(758\) 18.7938 0.682621
\(759\) 0.0356842 0.00129525
\(760\) −0.660844 −0.0239713
\(761\) −12.1218 −0.439414 −0.219707 0.975566i \(-0.570510\pi\)
−0.219707 + 0.975566i \(0.570510\pi\)
\(762\) −0.374160 −0.0135544
\(763\) −65.1476 −2.35850
\(764\) −6.00261 −0.217167
\(765\) 0.441481 0.0159618
\(766\) 9.84527 0.355724
\(767\) −22.2098 −0.801949
\(768\) −0.0412722 −0.00148928
\(769\) −34.9286 −1.25956 −0.629779 0.776774i \(-0.716855\pi\)
−0.629779 + 0.776774i \(0.716855\pi\)
\(770\) 14.0478 0.506249
\(771\) −0.455681 −0.0164110
\(772\) −22.5349 −0.811050
\(773\) 32.8442 1.18132 0.590662 0.806919i \(-0.298867\pi\)
0.590662 + 0.806919i \(0.298867\pi\)
\(774\) 5.91331 0.212550
\(775\) −36.5065 −1.31135
\(776\) −9.58972 −0.344251
\(777\) 0.580767 0.0208349
\(778\) −23.5844 −0.845541
\(779\) −1.04752 −0.0375314
\(780\) 0.254790 0.00912293
\(781\) 7.05364 0.252399
\(782\) −0.0423660 −0.00151501
\(783\) 2.05237 0.0733457
\(784\) 14.8546 0.530523
\(785\) −31.8538 −1.13691
\(786\) 0.0412722 0.00147213
\(787\) 1.64417 0.0586082 0.0293041 0.999571i \(-0.490671\pi\)
0.0293041 + 0.999571i \(0.490671\pi\)
\(788\) −14.9776 −0.533554
\(789\) −0.136535 −0.00486079
\(790\) 25.5567 0.909266
\(791\) −4.07744 −0.144977
\(792\) −2.59234 −0.0921148
\(793\) −3.26079 −0.115794
\(794\) 18.0989 0.642304
\(795\) 1.76776 0.0626960
\(796\) −15.4970 −0.549277
\(797\) −25.8675 −0.916275 −0.458137 0.888881i \(-0.651483\pi\)
−0.458137 + 0.888881i \(0.651483\pi\)
\(798\) 0.0366867 0.00129870
\(799\) −0.262575 −0.00928923
\(800\) −7.07925 −0.250289
\(801\) 9.02554 0.318902
\(802\) −18.9159 −0.667945
\(803\) 1.32303 0.0466886
\(804\) 0.345455 0.0121833
\(805\) 16.2477 0.572656
\(806\) 9.15980 0.322640
\(807\) −0.296729 −0.0104453
\(808\) −1.84549 −0.0649243
\(809\) −32.6307 −1.14723 −0.573616 0.819124i \(-0.694460\pi\)
−0.573616 + 0.819124i \(0.694460\pi\)
\(810\) 31.2264 1.09718
\(811\) 26.3040 0.923658 0.461829 0.886969i \(-0.347193\pi\)
0.461829 + 0.886969i \(0.347193\pi\)
\(812\) −38.7562 −1.36008
\(813\) −0.716931 −0.0251439
\(814\) 2.60249 0.0912173
\(815\) 48.6960 1.70575
\(816\) −0.00174854 −6.12112e−5 0
\(817\) −0.375003 −0.0131197
\(818\) 17.9680 0.628237
\(819\) 24.8972 0.869978
\(820\) −19.1472 −0.668648
\(821\) −27.3627 −0.954965 −0.477483 0.878641i \(-0.658451\pi\)
−0.477483 + 0.878641i \(0.658451\pi\)
\(822\) −0.852827 −0.0297457
\(823\) 27.5890 0.961691 0.480845 0.876805i \(-0.340330\pi\)
0.480845 + 0.876805i \(0.340330\pi\)
\(824\) −3.17903 −0.110747
\(825\) 0.252617 0.00879500
\(826\) −58.4538 −2.03387
\(827\) 1.06654 0.0370873 0.0185437 0.999828i \(-0.494097\pi\)
0.0185437 + 0.999828i \(0.494097\pi\)
\(828\) −2.99830 −0.104198
\(829\) −3.53135 −0.122649 −0.0613245 0.998118i \(-0.519532\pi\)
−0.0613245 + 0.998118i \(0.519532\pi\)
\(830\) 52.0377 1.80625
\(831\) 1.16827 0.0405267
\(832\) 1.77625 0.0615803
\(833\) 0.629332 0.0218051
\(834\) 0.770092 0.0266661
\(835\) 42.5439 1.47229
\(836\) 0.164398 0.00568582
\(837\) −1.27664 −0.0441272
\(838\) −32.6997 −1.12959
\(839\) −23.8880 −0.824706 −0.412353 0.911024i \(-0.635293\pi\)
−0.412353 + 0.911024i \(0.635293\pi\)
\(840\) 0.670579 0.0231372
\(841\) 39.7288 1.36996
\(842\) −33.4154 −1.15157
\(843\) −0.264022 −0.00909341
\(844\) −11.1133 −0.382536
\(845\) 34.2163 1.17708
\(846\) −18.5827 −0.638888
\(847\) 47.9292 1.64687
\(848\) 12.3238 0.423202
\(849\) −0.690008 −0.0236810
\(850\) −0.299920 −0.0102872
\(851\) 3.01004 0.103183
\(852\) 0.336708 0.0115354
\(853\) −51.2915 −1.75619 −0.878094 0.478487i \(-0.841185\pi\)
−0.878094 + 0.478487i \(0.841185\pi\)
\(854\) −8.58204 −0.293671
\(855\) −1.98141 −0.0677626
\(856\) −8.94815 −0.305841
\(857\) 10.4768 0.357882 0.178941 0.983860i \(-0.442733\pi\)
0.178941 + 0.983860i \(0.442733\pi\)
\(858\) −0.0633839 −0.00216389
\(859\) 10.9096 0.372232 0.186116 0.982528i \(-0.440410\pi\)
0.186116 + 0.982528i \(0.440410\pi\)
\(860\) −6.85451 −0.233737
\(861\) 1.06295 0.0362254
\(862\) 6.27017 0.213563
\(863\) 31.9340 1.08705 0.543524 0.839394i \(-0.317090\pi\)
0.543524 + 0.839394i \(0.317090\pi\)
\(864\) −0.247563 −0.00842227
\(865\) −50.5144 −1.71754
\(866\) 20.6938 0.703204
\(867\) 0.701554 0.0238260
\(868\) 24.1076 0.818266
\(869\) −6.35773 −0.215671
\(870\) −1.18918 −0.0403170
\(871\) −14.8675 −0.503765
\(872\) −13.9356 −0.471920
\(873\) −28.7528 −0.973135
\(874\) 0.190142 0.00643166
\(875\) 33.7830 1.14207
\(876\) 0.0631552 0.00213382
\(877\) 45.6266 1.54070 0.770350 0.637621i \(-0.220081\pi\)
0.770350 + 0.637621i \(0.220081\pi\)
\(878\) −24.4058 −0.823655
\(879\) −1.31390 −0.0443169
\(880\) 3.00495 0.101297
\(881\) 34.8012 1.17248 0.586242 0.810136i \(-0.300607\pi\)
0.586242 + 0.810136i \(0.300607\pi\)
\(882\) 44.5386 1.49969
\(883\) −41.6654 −1.40215 −0.701077 0.713086i \(-0.747297\pi\)
−0.701077 + 0.713086i \(0.747297\pi\)
\(884\) 0.0752526 0.00253102
\(885\) −1.79357 −0.0602903
\(886\) 31.8722 1.07077
\(887\) −17.6236 −0.591744 −0.295872 0.955228i \(-0.595610\pi\)
−0.295872 + 0.955228i \(0.595610\pi\)
\(888\) 0.124231 0.00416892
\(889\) 42.3810 1.42141
\(890\) −10.4621 −0.350690
\(891\) −7.76819 −0.260244
\(892\) 26.3115 0.880973
\(893\) 1.17846 0.0394356
\(894\) 0.821600 0.0274784
\(895\) 48.0717 1.60686
\(896\) 4.67489 0.156177
\(897\) −0.0733097 −0.00244774
\(898\) 25.2156 0.841457
\(899\) −42.7516 −1.42584
\(900\) −21.2257 −0.707523
\(901\) 0.522112 0.0173941
\(902\) 4.76323 0.158598
\(903\) 0.380528 0.0126632
\(904\) −0.872199 −0.0290089
\(905\) 52.7846 1.75462
\(906\) −0.266996 −0.00887036
\(907\) 19.0203 0.631558 0.315779 0.948833i \(-0.397734\pi\)
0.315779 + 0.948833i \(0.397734\pi\)
\(908\) 2.83976 0.0942408
\(909\) −5.53334 −0.183529
\(910\) −28.8599 −0.956697
\(911\) −15.7797 −0.522804 −0.261402 0.965230i \(-0.584185\pi\)
−0.261402 + 0.965230i \(0.584185\pi\)
\(912\) 0.00784760 0.000259860 0
\(913\) −12.9454 −0.428430
\(914\) −34.6630 −1.14655
\(915\) −0.263328 −0.00870535
\(916\) −25.6328 −0.846932
\(917\) −4.67489 −0.154379
\(918\) −0.0104883 −0.000346164 0
\(919\) −4.88291 −0.161072 −0.0805362 0.996752i \(-0.525663\pi\)
−0.0805362 + 0.996752i \(0.525663\pi\)
\(920\) 3.47552 0.114585
\(921\) −0.239502 −0.00789184
\(922\) −22.9197 −0.754819
\(923\) −14.4910 −0.476978
\(924\) −0.166820 −0.00548797
\(925\) 21.3088 0.700629
\(926\) −24.2266 −0.796135
\(927\) −9.53167 −0.313061
\(928\) −8.29029 −0.272142
\(929\) 35.6581 1.16991 0.584953 0.811067i \(-0.301113\pi\)
0.584953 + 0.811067i \(0.301113\pi\)
\(930\) 0.739709 0.0242560
\(931\) −2.82450 −0.0925691
\(932\) 8.73343 0.286073
\(933\) −0.304510 −0.00996920
\(934\) −8.44872 −0.276451
\(935\) 0.127308 0.00416341
\(936\) 5.32572 0.174077
\(937\) 32.6424 1.06638 0.533190 0.845996i \(-0.320993\pi\)
0.533190 + 0.845996i \(0.320993\pi\)
\(938\) −39.1296 −1.27763
\(939\) 1.01074 0.0329843
\(940\) 21.5405 0.702573
\(941\) −4.19759 −0.136838 −0.0684188 0.997657i \(-0.521795\pi\)
−0.0684188 + 0.997657i \(0.521795\pi\)
\(942\) 0.378268 0.0123246
\(943\) 5.50915 0.179402
\(944\) −12.5038 −0.406963
\(945\) 4.02233 0.130846
\(946\) 1.70519 0.0554406
\(947\) −4.51522 −0.146725 −0.0733624 0.997305i \(-0.523373\pi\)
−0.0733624 + 0.997305i \(0.523373\pi\)
\(948\) −0.303489 −0.00985686
\(949\) −2.71803 −0.0882310
\(950\) 1.34606 0.0436721
\(951\) −0.422884 −0.0137130
\(952\) 0.198057 0.00641906
\(953\) −25.9868 −0.841794 −0.420897 0.907108i \(-0.638285\pi\)
−0.420897 + 0.907108i \(0.638285\pi\)
\(954\) 36.9505 1.19632
\(955\) 20.8622 0.675085
\(956\) 7.12982 0.230595
\(957\) 0.295832 0.00956289
\(958\) 15.6448 0.505461
\(959\) 96.5994 3.11936
\(960\) 0.143443 0.00462959
\(961\) −4.40713 −0.142165
\(962\) −5.34658 −0.172381
\(963\) −26.8292 −0.864559
\(964\) 15.4202 0.496651
\(965\) 78.3206 2.52123
\(966\) −0.192943 −0.00620785
\(967\) 7.03394 0.226196 0.113098 0.993584i \(-0.463923\pi\)
0.113098 + 0.993584i \(0.463923\pi\)
\(968\) 10.2525 0.329527
\(969\) 0.000332472 0 1.06805e−5 0
\(970\) 33.3293 1.07014
\(971\) −9.26587 −0.297356 −0.148678 0.988886i \(-0.547502\pi\)
−0.148678 + 0.988886i \(0.547502\pi\)
\(972\) −1.11351 −0.0357158
\(973\) −87.2281 −2.79640
\(974\) −23.5517 −0.754645
\(975\) −0.518978 −0.0166206
\(976\) −1.83577 −0.0587616
\(977\) 12.1087 0.387393 0.193697 0.981061i \(-0.437952\pi\)
0.193697 + 0.981061i \(0.437952\pi\)
\(978\) −0.578271 −0.0184911
\(979\) 2.60265 0.0831811
\(980\) −51.6276 −1.64918
\(981\) −41.7832 −1.33403
\(982\) 9.07759 0.289678
\(983\) −14.0941 −0.449533 −0.224766 0.974413i \(-0.572162\pi\)
−0.224766 + 0.974413i \(0.572162\pi\)
\(984\) 0.227375 0.00724844
\(985\) 52.0549 1.65861
\(986\) −0.351226 −0.0111853
\(987\) −1.19582 −0.0380633
\(988\) −0.337740 −0.0107449
\(989\) 1.97222 0.0627131
\(990\) 9.00973 0.286348
\(991\) 36.5012 1.15950 0.579749 0.814795i \(-0.303151\pi\)
0.579749 + 0.814795i \(0.303151\pi\)
\(992\) 5.15683 0.163729
\(993\) 0.953913 0.0302715
\(994\) −38.1388 −1.20969
\(995\) 53.8602 1.70748
\(996\) −0.617954 −0.0195806
\(997\) 16.0618 0.508682 0.254341 0.967115i \(-0.418141\pi\)
0.254341 + 0.967115i \(0.418141\pi\)
\(998\) −1.08724 −0.0344158
\(999\) 0.745175 0.0235763
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 \(a_p\))