Properties

Label 8011.2.a.b.1.14
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61809 q^{2}\) \(-3.37147 q^{3}\) \(+4.85437 q^{4}\) \(+3.62871 q^{5}\) \(+8.82680 q^{6}\) \(-2.17662 q^{7}\) \(-7.47299 q^{8}\) \(+8.36681 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61809 q^{2}\) \(-3.37147 q^{3}\) \(+4.85437 q^{4}\) \(+3.62871 q^{5}\) \(+8.82680 q^{6}\) \(-2.17662 q^{7}\) \(-7.47299 q^{8}\) \(+8.36681 q^{9}\) \(-9.50027 q^{10}\) \(-5.68339 q^{11}\) \(-16.3664 q^{12}\) \(-3.89143 q^{13}\) \(+5.69858 q^{14}\) \(-12.2341 q^{15}\) \(+9.85618 q^{16}\) \(-4.90540 q^{17}\) \(-21.9050 q^{18}\) \(+3.00670 q^{19}\) \(+17.6151 q^{20}\) \(+7.33841 q^{21}\) \(+14.8796 q^{22}\) \(+1.00449 q^{23}\) \(+25.1950 q^{24}\) \(+8.16751 q^{25}\) \(+10.1881 q^{26}\) \(-18.0940 q^{27}\) \(-10.5661 q^{28}\) \(+3.18572 q^{29}\) \(+32.0299 q^{30}\) \(-4.93247 q^{31}\) \(-10.8584 q^{32}\) \(+19.1614 q^{33}\) \(+12.8428 q^{34}\) \(-7.89832 q^{35}\) \(+40.6156 q^{36}\) \(-9.30560 q^{37}\) \(-7.87180 q^{38}\) \(+13.1198 q^{39}\) \(-27.1173 q^{40}\) \(-1.24511 q^{41}\) \(-19.2126 q^{42}\) \(-5.29208 q^{43}\) \(-27.5893 q^{44}\) \(+30.3607 q^{45}\) \(-2.62985 q^{46}\) \(-0.229215 q^{47}\) \(-33.2298 q^{48}\) \(-2.26232 q^{49}\) \(-21.3833 q^{50}\) \(+16.5384 q^{51}\) \(-18.8905 q^{52}\) \(-8.56333 q^{53}\) \(+47.3717 q^{54}\) \(-20.6234 q^{55}\) \(+16.2659 q^{56}\) \(-10.1370 q^{57}\) \(-8.34048 q^{58}\) \(-9.35565 q^{59}\) \(-59.3888 q^{60}\) \(+1.01390 q^{61}\) \(+12.9136 q^{62}\) \(-18.2114 q^{63}\) \(+8.71573 q^{64}\) \(-14.1209 q^{65}\) \(-50.1662 q^{66}\) \(-4.22483 q^{67}\) \(-23.8126 q^{68}\) \(-3.38662 q^{69}\) \(+20.6785 q^{70}\) \(-4.82623 q^{71}\) \(-62.5251 q^{72}\) \(+10.1842 q^{73}\) \(+24.3628 q^{74}\) \(-27.5365 q^{75}\) \(+14.5956 q^{76}\) \(+12.3706 q^{77}\) \(-34.3489 q^{78}\) \(-14.8509 q^{79}\) \(+35.7652 q^{80}\) \(+35.9030 q^{81}\) \(+3.25981 q^{82}\) \(-1.48956 q^{83}\) \(+35.6234 q^{84}\) \(-17.8003 q^{85}\) \(+13.8551 q^{86}\) \(-10.7406 q^{87}\) \(+42.4719 q^{88}\) \(+0.582583 q^{89}\) \(-79.4869 q^{90}\) \(+8.47017 q^{91}\) \(+4.87618 q^{92}\) \(+16.6297 q^{93}\) \(+0.600104 q^{94}\) \(+10.9104 q^{95}\) \(+36.6086 q^{96}\) \(-8.11866 q^{97}\) \(+5.92295 q^{98}\) \(-47.5519 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61809 −1.85127 −0.925633 0.378422i \(-0.876467\pi\)
−0.925633 + 0.378422i \(0.876467\pi\)
\(3\) −3.37147 −1.94652 −0.973259 0.229709i \(-0.926223\pi\)
−0.973259 + 0.229709i \(0.926223\pi\)
\(4\) 4.85437 2.42719
\(5\) 3.62871 1.62281 0.811404 0.584486i \(-0.198704\pi\)
0.811404 + 0.584486i \(0.198704\pi\)
\(6\) 8.82680 3.60352
\(7\) −2.17662 −0.822685 −0.411343 0.911481i \(-0.634940\pi\)
−0.411343 + 0.911481i \(0.634940\pi\)
\(8\) −7.47299 −2.64210
\(9\) 8.36681 2.78894
\(10\) −9.50027 −3.00425
\(11\) −5.68339 −1.71361 −0.856804 0.515642i \(-0.827553\pi\)
−0.856804 + 0.515642i \(0.827553\pi\)
\(12\) −16.3664 −4.72456
\(13\) −3.89143 −1.07929 −0.539645 0.841893i \(-0.681441\pi\)
−0.539645 + 0.841893i \(0.681441\pi\)
\(14\) 5.69858 1.52301
\(15\) −12.2341 −3.15882
\(16\) 9.85618 2.46405
\(17\) −4.90540 −1.18973 −0.594867 0.803824i \(-0.702795\pi\)
−0.594867 + 0.803824i \(0.702795\pi\)
\(18\) −21.9050 −5.16306
\(19\) 3.00670 0.689784 0.344892 0.938642i \(-0.387916\pi\)
0.344892 + 0.938642i \(0.387916\pi\)
\(20\) 17.6151 3.93885
\(21\) 7.33841 1.60137
\(22\) 14.8796 3.17234
\(23\) 1.00449 0.209451 0.104726 0.994501i \(-0.466604\pi\)
0.104726 + 0.994501i \(0.466604\pi\)
\(24\) 25.1950 5.14290
\(25\) 8.16751 1.63350
\(26\) 10.1881 1.99805
\(27\) −18.0940 −3.48220
\(28\) −10.5661 −1.99681
\(29\) 3.18572 0.591573 0.295786 0.955254i \(-0.404418\pi\)
0.295786 + 0.955254i \(0.404418\pi\)
\(30\) 32.0299 5.84782
\(31\) −4.93247 −0.885898 −0.442949 0.896547i \(-0.646068\pi\)
−0.442949 + 0.896547i \(0.646068\pi\)
\(32\) −10.8584 −1.91950
\(33\) 19.1614 3.33557
\(34\) 12.8428 2.20252
\(35\) −7.89832 −1.33506
\(36\) 40.6156 6.76927
\(37\) −9.30560 −1.52983 −0.764915 0.644131i \(-0.777219\pi\)
−0.764915 + 0.644131i \(0.777219\pi\)
\(38\) −7.87180 −1.27697
\(39\) 13.1198 2.10086
\(40\) −27.1173 −4.28762
\(41\) −1.24511 −0.194454 −0.0972271 0.995262i \(-0.530997\pi\)
−0.0972271 + 0.995262i \(0.530997\pi\)
\(42\) −19.2126 −2.96457
\(43\) −5.29208 −0.807035 −0.403518 0.914972i \(-0.632213\pi\)
−0.403518 + 0.914972i \(0.632213\pi\)
\(44\) −27.5893 −4.15924
\(45\) 30.3607 4.52590
\(46\) −2.62985 −0.387750
\(47\) −0.229215 −0.0334344 −0.0167172 0.999860i \(-0.505322\pi\)
−0.0167172 + 0.999860i \(0.505322\pi\)
\(48\) −33.2298 −4.79631
\(49\) −2.26232 −0.323189
\(50\) −21.3833 −3.02405
\(51\) 16.5384 2.31584
\(52\) −18.8905 −2.61964
\(53\) −8.56333 −1.17626 −0.588132 0.808765i \(-0.700136\pi\)
−0.588132 + 0.808765i \(0.700136\pi\)
\(54\) 47.3717 6.44647
\(55\) −20.6234 −2.78085
\(56\) 16.2659 2.17362
\(57\) −10.1370 −1.34268
\(58\) −8.34048 −1.09516
\(59\) −9.35565 −1.21800 −0.609001 0.793170i \(-0.708429\pi\)
−0.609001 + 0.793170i \(0.708429\pi\)
\(60\) −59.3888 −7.66706
\(61\) 1.01390 0.129816 0.0649082 0.997891i \(-0.479325\pi\)
0.0649082 + 0.997891i \(0.479325\pi\)
\(62\) 12.9136 1.64003
\(63\) −18.2114 −2.29442
\(64\) 8.71573 1.08947
\(65\) −14.1209 −1.75148
\(66\) −50.1662 −6.17503
\(67\) −4.22483 −0.516145 −0.258072 0.966126i \(-0.583087\pi\)
−0.258072 + 0.966126i \(0.583087\pi\)
\(68\) −23.8126 −2.88771
\(69\) −3.38662 −0.407701
\(70\) 20.6785 2.47155
\(71\) −4.82623 −0.572768 −0.286384 0.958115i \(-0.592453\pi\)
−0.286384 + 0.958115i \(0.592453\pi\)
\(72\) −62.5251 −7.36865
\(73\) 10.1842 1.19197 0.595984 0.802996i \(-0.296762\pi\)
0.595984 + 0.802996i \(0.296762\pi\)
\(74\) 24.3628 2.83212
\(75\) −27.5365 −3.17964
\(76\) 14.5956 1.67423
\(77\) 12.3706 1.40976
\(78\) −34.3489 −3.88925
\(79\) −14.8509 −1.67086 −0.835430 0.549596i \(-0.814782\pi\)
−0.835430 + 0.549596i \(0.814782\pi\)
\(80\) 35.7652 3.99867
\(81\) 35.9030 3.98923
\(82\) 3.25981 0.359986
\(83\) −1.48956 −0.163500 −0.0817502 0.996653i \(-0.526051\pi\)
−0.0817502 + 0.996653i \(0.526051\pi\)
\(84\) 35.6234 3.88683
\(85\) −17.8003 −1.93071
\(86\) 13.8551 1.49404
\(87\) −10.7406 −1.15151
\(88\) 42.4719 4.52753
\(89\) 0.582583 0.0617537 0.0308769 0.999523i \(-0.490170\pi\)
0.0308769 + 0.999523i \(0.490170\pi\)
\(90\) −79.4869 −8.37865
\(91\) 8.47017 0.887915
\(92\) 4.87618 0.508377
\(93\) 16.6297 1.72442
\(94\) 0.600104 0.0618960
\(95\) 10.9104 1.11939
\(96\) 36.6086 3.73635
\(97\) −8.11866 −0.824325 −0.412162 0.911110i \(-0.635226\pi\)
−0.412162 + 0.911110i \(0.635226\pi\)
\(98\) 5.92295 0.598309
\(99\) −47.5519 −4.77914
\(100\) 39.6482 3.96482
\(101\) 18.4015 1.83102 0.915509 0.402298i \(-0.131788\pi\)
0.915509 + 0.402298i \(0.131788\pi\)
\(102\) −43.2990 −4.28724
\(103\) 9.25067 0.911496 0.455748 0.890109i \(-0.349372\pi\)
0.455748 + 0.890109i \(0.349372\pi\)
\(104\) 29.0806 2.85159
\(105\) 26.6289 2.59872
\(106\) 22.4195 2.17758
\(107\) 6.29314 0.608381 0.304190 0.952611i \(-0.401614\pi\)
0.304190 + 0.952611i \(0.401614\pi\)
\(108\) −87.8352 −8.45194
\(109\) −12.3273 −1.18074 −0.590370 0.807133i \(-0.701018\pi\)
−0.590370 + 0.807133i \(0.701018\pi\)
\(110\) 53.9937 5.14810
\(111\) 31.3735 2.97784
\(112\) −21.4532 −2.02713
\(113\) 0.723465 0.0680579 0.0340289 0.999421i \(-0.489166\pi\)
0.0340289 + 0.999421i \(0.489166\pi\)
\(114\) 26.5395 2.48565
\(115\) 3.64501 0.339899
\(116\) 15.4647 1.43586
\(117\) −32.5589 −3.01007
\(118\) 24.4939 2.25484
\(119\) 10.6772 0.978777
\(120\) 91.4251 8.34593
\(121\) 21.3010 1.93645
\(122\) −2.65447 −0.240325
\(123\) 4.19786 0.378509
\(124\) −23.9441 −2.15024
\(125\) 11.4940 1.02805
\(126\) 47.6789 4.24758
\(127\) 12.9576 1.14980 0.574901 0.818223i \(-0.305041\pi\)
0.574901 + 0.818223i \(0.305041\pi\)
\(128\) −1.10182 −0.0973882
\(129\) 17.8421 1.57091
\(130\) 36.9696 3.24245
\(131\) −22.0159 −1.92354 −0.961769 0.273861i \(-0.911699\pi\)
−0.961769 + 0.273861i \(0.911699\pi\)
\(132\) 93.0165 8.09605
\(133\) −6.54444 −0.567475
\(134\) 11.0610 0.955521
\(135\) −65.6579 −5.65094
\(136\) 36.6580 3.14340
\(137\) −19.1958 −1.64001 −0.820004 0.572357i \(-0.806029\pi\)
−0.820004 + 0.572357i \(0.806029\pi\)
\(138\) 8.86645 0.754763
\(139\) 3.97676 0.337305 0.168652 0.985676i \(-0.446058\pi\)
0.168652 + 0.985676i \(0.446058\pi\)
\(140\) −38.3414 −3.24044
\(141\) 0.772791 0.0650807
\(142\) 12.6355 1.06035
\(143\) 22.1165 1.84948
\(144\) 82.4648 6.87207
\(145\) 11.5600 0.960009
\(146\) −26.6631 −2.20665
\(147\) 7.62735 0.629093
\(148\) −45.1728 −3.71318
\(149\) −5.11471 −0.419013 −0.209507 0.977807i \(-0.567186\pi\)
−0.209507 + 0.977807i \(0.567186\pi\)
\(150\) 72.0930 5.88637
\(151\) −23.5475 −1.91626 −0.958132 0.286326i \(-0.907566\pi\)
−0.958132 + 0.286326i \(0.907566\pi\)
\(152\) −22.4690 −1.82248
\(153\) −41.0426 −3.31809
\(154\) −32.3873 −2.60984
\(155\) −17.8985 −1.43764
\(156\) 63.6886 5.09917
\(157\) −8.61895 −0.687867 −0.343934 0.938994i \(-0.611760\pi\)
−0.343934 + 0.938994i \(0.611760\pi\)
\(158\) 38.8810 3.09321
\(159\) 28.8710 2.28962
\(160\) −39.4018 −3.11498
\(161\) −2.18640 −0.172312
\(162\) −93.9973 −7.38512
\(163\) −9.04156 −0.708190 −0.354095 0.935210i \(-0.615211\pi\)
−0.354095 + 0.935210i \(0.615211\pi\)
\(164\) −6.04425 −0.471976
\(165\) 69.5311 5.41299
\(166\) 3.89979 0.302683
\(167\) −20.6179 −1.59546 −0.797730 0.603015i \(-0.793966\pi\)
−0.797730 + 0.603015i \(0.793966\pi\)
\(168\) −54.8399 −4.23099
\(169\) 2.14325 0.164865
\(170\) 46.6026 3.57426
\(171\) 25.1565 1.92376
\(172\) −25.6897 −1.95882
\(173\) 12.1203 0.921488 0.460744 0.887533i \(-0.347583\pi\)
0.460744 + 0.887533i \(0.347583\pi\)
\(174\) 28.1197 2.13175
\(175\) −17.7776 −1.34386
\(176\) −56.0166 −4.22241
\(177\) 31.5423 2.37086
\(178\) −1.52525 −0.114323
\(179\) 9.02400 0.674486 0.337243 0.941418i \(-0.390506\pi\)
0.337243 + 0.941418i \(0.390506\pi\)
\(180\) 147.382 10.9852
\(181\) 6.14583 0.456816 0.228408 0.973566i \(-0.426648\pi\)
0.228408 + 0.973566i \(0.426648\pi\)
\(182\) −22.1756 −1.64377
\(183\) −3.41833 −0.252690
\(184\) −7.50656 −0.553391
\(185\) −33.7673 −2.48262
\(186\) −43.5379 −3.19236
\(187\) 27.8793 2.03874
\(188\) −1.11269 −0.0811516
\(189\) 39.3838 2.86475
\(190\) −28.5644 −2.07228
\(191\) −6.22183 −0.450196 −0.225098 0.974336i \(-0.572270\pi\)
−0.225098 + 0.974336i \(0.572270\pi\)
\(192\) −29.3848 −2.12067
\(193\) −15.9712 −1.14964 −0.574818 0.818282i \(-0.694927\pi\)
−0.574818 + 0.818282i \(0.694927\pi\)
\(194\) 21.2553 1.52604
\(195\) 47.6081 3.40929
\(196\) −10.9822 −0.784439
\(197\) 16.8874 1.20318 0.601590 0.798805i \(-0.294534\pi\)
0.601590 + 0.798805i \(0.294534\pi\)
\(198\) 124.495 8.84746
\(199\) −0.997807 −0.0707327 −0.0353663 0.999374i \(-0.511260\pi\)
−0.0353663 + 0.999374i \(0.511260\pi\)
\(200\) −61.0358 −4.31588
\(201\) 14.2439 1.00469
\(202\) −48.1767 −3.38970
\(203\) −6.93410 −0.486678
\(204\) 80.2836 5.62098
\(205\) −4.51815 −0.315562
\(206\) −24.2190 −1.68742
\(207\) 8.40440 0.584146
\(208\) −38.3547 −2.65942
\(209\) −17.0883 −1.18202
\(210\) −69.7169 −4.81092
\(211\) 14.4529 0.994982 0.497491 0.867469i \(-0.334255\pi\)
0.497491 + 0.867469i \(0.334255\pi\)
\(212\) −41.5696 −2.85501
\(213\) 16.2715 1.11490
\(214\) −16.4760 −1.12627
\(215\) −19.2034 −1.30966
\(216\) 135.217 9.20032
\(217\) 10.7361 0.728815
\(218\) 32.2739 2.18586
\(219\) −34.3357 −2.32019
\(220\) −100.114 −6.74965
\(221\) 19.0890 1.28407
\(222\) −82.1386 −5.51278
\(223\) −21.4093 −1.43368 −0.716838 0.697240i \(-0.754411\pi\)
−0.716838 + 0.697240i \(0.754411\pi\)
\(224\) 23.6345 1.57915
\(225\) 68.3360 4.55573
\(226\) −1.89409 −0.125993
\(227\) 18.7585 1.24505 0.622524 0.782601i \(-0.286107\pi\)
0.622524 + 0.782601i \(0.286107\pi\)
\(228\) −49.2087 −3.25893
\(229\) 3.54506 0.234264 0.117132 0.993116i \(-0.462630\pi\)
0.117132 + 0.993116i \(0.462630\pi\)
\(230\) −9.54295 −0.629243
\(231\) −41.7071 −2.74412
\(232\) −23.8068 −1.56300
\(233\) −8.91016 −0.583724 −0.291862 0.956460i \(-0.594275\pi\)
−0.291862 + 0.956460i \(0.594275\pi\)
\(234\) 85.2419 5.57244
\(235\) −0.831753 −0.0542576
\(236\) −45.4158 −2.95632
\(237\) 50.0695 3.25236
\(238\) −27.9538 −1.81198
\(239\) −0.324371 −0.0209818 −0.0104909 0.999945i \(-0.503339\pi\)
−0.0104909 + 0.999945i \(0.503339\pi\)
\(240\) −120.581 −7.78349
\(241\) 17.1949 1.10762 0.553810 0.832643i \(-0.313174\pi\)
0.553810 + 0.832643i \(0.313174\pi\)
\(242\) −55.7678 −3.58489
\(243\) −66.7640 −4.28291
\(244\) 4.92184 0.315089
\(245\) −8.20930 −0.524473
\(246\) −10.9904 −0.700720
\(247\) −11.7004 −0.744477
\(248\) 36.8603 2.34063
\(249\) 5.02200 0.318257
\(250\) −30.0922 −1.90320
\(251\) 22.1029 1.39512 0.697561 0.716525i \(-0.254268\pi\)
0.697561 + 0.716525i \(0.254268\pi\)
\(252\) −88.4048 −5.56898
\(253\) −5.70893 −0.358917
\(254\) −33.9241 −2.12859
\(255\) 60.0131 3.75816
\(256\) −14.5468 −0.909175
\(257\) 26.8063 1.67213 0.836066 0.548628i \(-0.184850\pi\)
0.836066 + 0.548628i \(0.184850\pi\)
\(258\) −46.7121 −2.90817
\(259\) 20.2548 1.25857
\(260\) −68.5480 −4.25116
\(261\) 26.6543 1.64986
\(262\) 57.6395 3.56098
\(263\) 23.7722 1.46586 0.732928 0.680306i \(-0.238153\pi\)
0.732928 + 0.680306i \(0.238153\pi\)
\(264\) −143.193 −8.81291
\(265\) −31.0738 −1.90885
\(266\) 17.1339 1.05055
\(267\) −1.96416 −0.120205
\(268\) −20.5089 −1.25278
\(269\) 12.3870 0.755249 0.377625 0.925959i \(-0.376741\pi\)
0.377625 + 0.925959i \(0.376741\pi\)
\(270\) 171.898 10.4614
\(271\) −29.7418 −1.80669 −0.903344 0.428917i \(-0.858895\pi\)
−0.903344 + 0.428917i \(0.858895\pi\)
\(272\) −48.3485 −2.93156
\(273\) −28.5569 −1.72834
\(274\) 50.2563 3.03609
\(275\) −46.4192 −2.79918
\(276\) −16.4399 −0.989566
\(277\) 27.2473 1.63713 0.818565 0.574413i \(-0.194770\pi\)
0.818565 + 0.574413i \(0.194770\pi\)
\(278\) −10.4115 −0.624441
\(279\) −41.2690 −2.47071
\(280\) 59.0241 3.52736
\(281\) −30.6829 −1.83039 −0.915195 0.403012i \(-0.867963\pi\)
−0.915195 + 0.403012i \(0.867963\pi\)
\(282\) −2.02323 −0.120482
\(283\) 15.7351 0.935357 0.467679 0.883899i \(-0.345090\pi\)
0.467679 + 0.883899i \(0.345090\pi\)
\(284\) −23.4283 −1.39021
\(285\) −36.7842 −2.17891
\(286\) −57.9030 −3.42388
\(287\) 2.71014 0.159975
\(288\) −90.8498 −5.35337
\(289\) 7.06297 0.415469
\(290\) −30.2652 −1.77723
\(291\) 27.3718 1.60456
\(292\) 49.4378 2.89313
\(293\) 9.33066 0.545103 0.272552 0.962141i \(-0.412132\pi\)
0.272552 + 0.962141i \(0.412132\pi\)
\(294\) −19.9691 −1.16462
\(295\) −33.9489 −1.97658
\(296\) 69.5406 4.04197
\(297\) 102.835 5.96712
\(298\) 13.3907 0.775705
\(299\) −3.90892 −0.226058
\(300\) −133.673 −7.71759
\(301\) 11.5189 0.663936
\(302\) 61.6492 3.54752
\(303\) −62.0401 −3.56411
\(304\) 29.6346 1.69966
\(305\) 3.67914 0.210667
\(306\) 107.453 6.14267
\(307\) 22.8399 1.30354 0.651772 0.758415i \(-0.274026\pi\)
0.651772 + 0.758415i \(0.274026\pi\)
\(308\) 60.0515 3.42175
\(309\) −31.1884 −1.77424
\(310\) 46.8598 2.66146
\(311\) −22.5780 −1.28028 −0.640141 0.768257i \(-0.721124\pi\)
−0.640141 + 0.768257i \(0.721124\pi\)
\(312\) −98.0445 −5.55068
\(313\) −21.5233 −1.21657 −0.608285 0.793719i \(-0.708142\pi\)
−0.608285 + 0.793719i \(0.708142\pi\)
\(314\) 22.5652 1.27343
\(315\) −66.0837 −3.72340
\(316\) −72.0920 −4.05549
\(317\) −26.1263 −1.46740 −0.733699 0.679474i \(-0.762208\pi\)
−0.733699 + 0.679474i \(0.762208\pi\)
\(318\) −75.5868 −4.23870
\(319\) −18.1057 −1.01372
\(320\) 31.6268 1.76799
\(321\) −21.2171 −1.18422
\(322\) 5.72418 0.318996
\(323\) −14.7491 −0.820660
\(324\) 174.287 9.68260
\(325\) −31.7833 −1.76302
\(326\) 23.6716 1.31105
\(327\) 41.5611 2.29833
\(328\) 9.30472 0.513767
\(329\) 0.498914 0.0275060
\(330\) −182.038 −10.0209
\(331\) −25.6465 −1.40966 −0.704831 0.709375i \(-0.748977\pi\)
−0.704831 + 0.709375i \(0.748977\pi\)
\(332\) −7.23088 −0.396846
\(333\) −77.8581 −4.26660
\(334\) 53.9794 2.95362
\(335\) −15.3307 −0.837603
\(336\) 72.3287 3.94586
\(337\) −3.88890 −0.211842 −0.105921 0.994375i \(-0.533779\pi\)
−0.105921 + 0.994375i \(0.533779\pi\)
\(338\) −5.61121 −0.305210
\(339\) −2.43914 −0.132476
\(340\) −86.4091 −4.68619
\(341\) 28.0332 1.51808
\(342\) −65.8618 −3.56140
\(343\) 20.1606 1.08857
\(344\) 39.5477 2.13227
\(345\) −12.2890 −0.661620
\(346\) −31.7319 −1.70592
\(347\) 11.4154 0.612810 0.306405 0.951901i \(-0.400874\pi\)
0.306405 + 0.951901i \(0.400874\pi\)
\(348\) −52.1386 −2.79492
\(349\) 17.0860 0.914591 0.457296 0.889315i \(-0.348818\pi\)
0.457296 + 0.889315i \(0.348818\pi\)
\(350\) 46.5432 2.48784
\(351\) 70.4117 3.75830
\(352\) 61.7123 3.28928
\(353\) 1.36994 0.0729146 0.0364573 0.999335i \(-0.488393\pi\)
0.0364573 + 0.999335i \(0.488393\pi\)
\(354\) −82.5804 −4.38910
\(355\) −17.5130 −0.929492
\(356\) 2.82808 0.149888
\(357\) −35.9979 −1.90521
\(358\) −23.6256 −1.24865
\(359\) 3.68956 0.194728 0.0973638 0.995249i \(-0.468959\pi\)
0.0973638 + 0.995249i \(0.468959\pi\)
\(360\) −226.885 −11.9579
\(361\) −9.95976 −0.524198
\(362\) −16.0903 −0.845687
\(363\) −71.8156 −3.76934
\(364\) 41.1174 2.15514
\(365\) 36.9554 1.93434
\(366\) 8.94948 0.467797
\(367\) −11.1288 −0.580920 −0.290460 0.956887i \(-0.593808\pi\)
−0.290460 + 0.956887i \(0.593808\pi\)
\(368\) 9.90047 0.516097
\(369\) −10.4176 −0.542320
\(370\) 88.4056 4.59599
\(371\) 18.6391 0.967695
\(372\) 80.7266 4.18548
\(373\) −6.28098 −0.325217 −0.162608 0.986691i \(-0.551991\pi\)
−0.162608 + 0.986691i \(0.551991\pi\)
\(374\) −72.9905 −3.77425
\(375\) −38.7516 −2.00112
\(376\) 1.71292 0.0883371
\(377\) −12.3970 −0.638478
\(378\) −103.110 −5.30342
\(379\) 9.69666 0.498084 0.249042 0.968493i \(-0.419884\pi\)
0.249042 + 0.968493i \(0.419884\pi\)
\(380\) 52.9633 2.71696
\(381\) −43.6862 −2.23811
\(382\) 16.2893 0.833433
\(383\) −28.7181 −1.46743 −0.733714 0.679459i \(-0.762215\pi\)
−0.733714 + 0.679459i \(0.762215\pi\)
\(384\) 3.71476 0.189568
\(385\) 44.8893 2.28777
\(386\) 41.8141 2.12828
\(387\) −44.2778 −2.25077
\(388\) −39.4110 −2.00079
\(389\) 4.91637 0.249270 0.124635 0.992203i \(-0.460224\pi\)
0.124635 + 0.992203i \(0.460224\pi\)
\(390\) −124.642 −6.31150
\(391\) −4.92744 −0.249191
\(392\) 16.9063 0.853898
\(393\) 74.2260 3.74420
\(394\) −44.2127 −2.22740
\(395\) −53.8897 −2.71148
\(396\) −230.834 −11.5999
\(397\) −18.7084 −0.938947 −0.469473 0.882947i \(-0.655556\pi\)
−0.469473 + 0.882947i \(0.655556\pi\)
\(398\) 2.61234 0.130945
\(399\) 22.0644 1.10460
\(400\) 80.5005 4.02503
\(401\) 2.59028 0.129352 0.0646762 0.997906i \(-0.479399\pi\)
0.0646762 + 0.997906i \(0.479399\pi\)
\(402\) −37.2917 −1.85994
\(403\) 19.1944 0.956140
\(404\) 89.3277 4.44422
\(405\) 130.282 6.47375
\(406\) 18.1541 0.900971
\(407\) 52.8874 2.62153
\(408\) −123.591 −6.11869
\(409\) 10.9505 0.541466 0.270733 0.962654i \(-0.412734\pi\)
0.270733 + 0.962654i \(0.412734\pi\)
\(410\) 11.8289 0.584188
\(411\) 64.7181 3.19231
\(412\) 44.9062 2.21237
\(413\) 20.3637 1.00203
\(414\) −22.0034 −1.08141
\(415\) −5.40517 −0.265330
\(416\) 42.2546 2.07170
\(417\) −13.4075 −0.656570
\(418\) 44.7385 2.18823
\(419\) −8.89545 −0.434571 −0.217286 0.976108i \(-0.569720\pi\)
−0.217286 + 0.976108i \(0.569720\pi\)
\(420\) 129.267 6.30757
\(421\) −40.1677 −1.95766 −0.978828 0.204686i \(-0.934383\pi\)
−0.978828 + 0.204686i \(0.934383\pi\)
\(422\) −37.8390 −1.84198
\(423\) −1.91780 −0.0932465
\(424\) 63.9937 3.10781
\(425\) −40.0649 −1.94343
\(426\) −42.6001 −2.06398
\(427\) −2.20687 −0.106798
\(428\) 30.5492 1.47665
\(429\) −74.5653 −3.60004
\(430\) 50.2762 2.42453
\(431\) 13.4589 0.648290 0.324145 0.946007i \(-0.394923\pi\)
0.324145 + 0.946007i \(0.394923\pi\)
\(432\) −178.338 −8.58030
\(433\) −15.5724 −0.748360 −0.374180 0.927356i \(-0.622076\pi\)
−0.374180 + 0.927356i \(0.622076\pi\)
\(434\) −28.1081 −1.34923
\(435\) −38.9743 −1.86868
\(436\) −59.8412 −2.86588
\(437\) 3.02021 0.144476
\(438\) 89.8937 4.29529
\(439\) 35.0255 1.67168 0.835839 0.548975i \(-0.184982\pi\)
0.835839 + 0.548975i \(0.184982\pi\)
\(440\) 154.118 7.34730
\(441\) −18.9284 −0.901353
\(442\) −49.9767 −2.37715
\(443\) 23.5558 1.11917 0.559585 0.828773i \(-0.310961\pi\)
0.559585 + 0.828773i \(0.310961\pi\)
\(444\) 152.299 7.22778
\(445\) 2.11402 0.100214
\(446\) 56.0515 2.65412
\(447\) 17.2441 0.815617
\(448\) −18.9708 −0.896288
\(449\) −2.33777 −0.110326 −0.0551632 0.998477i \(-0.517568\pi\)
−0.0551632 + 0.998477i \(0.517568\pi\)
\(450\) −178.910 −8.43388
\(451\) 7.07647 0.333218
\(452\) 3.51197 0.165189
\(453\) 79.3895 3.73004
\(454\) −49.1115 −2.30491
\(455\) 30.7358 1.44092
\(456\) 75.7537 3.54749
\(457\) −16.6574 −0.779199 −0.389600 0.920984i \(-0.627387\pi\)
−0.389600 + 0.920984i \(0.627387\pi\)
\(458\) −9.28128 −0.433686
\(459\) 88.7585 4.14289
\(460\) 17.6942 0.824998
\(461\) −28.9584 −1.34873 −0.674363 0.738400i \(-0.735582\pi\)
−0.674363 + 0.738400i \(0.735582\pi\)
\(462\) 109.193 5.08010
\(463\) −0.195048 −0.00906467 −0.00453234 0.999990i \(-0.501443\pi\)
−0.00453234 + 0.999990i \(0.501443\pi\)
\(464\) 31.3990 1.45766
\(465\) 60.3442 2.79840
\(466\) 23.3276 1.08063
\(467\) −0.436989 −0.0202215 −0.0101107 0.999949i \(-0.503218\pi\)
−0.0101107 + 0.999949i \(0.503218\pi\)
\(468\) −158.053 −7.30600
\(469\) 9.19585 0.424625
\(470\) 2.17760 0.100445
\(471\) 29.0585 1.33895
\(472\) 69.9147 3.21808
\(473\) 30.0770 1.38294
\(474\) −131.086 −6.02099
\(475\) 24.5573 1.12676
\(476\) 51.8311 2.37567
\(477\) −71.6477 −3.28052
\(478\) 0.849231 0.0388429
\(479\) −26.9684 −1.23222 −0.616108 0.787662i \(-0.711291\pi\)
−0.616108 + 0.787662i \(0.711291\pi\)
\(480\) 132.842 6.06338
\(481\) 36.2121 1.65113
\(482\) −45.0177 −2.05050
\(483\) 7.37138 0.335409
\(484\) 103.403 4.70013
\(485\) −29.4602 −1.33772
\(486\) 174.794 7.92881
\(487\) 15.0000 0.679715 0.339858 0.940477i \(-0.389621\pi\)
0.339858 + 0.940477i \(0.389621\pi\)
\(488\) −7.57685 −0.342988
\(489\) 30.4833 1.37850
\(490\) 21.4927 0.970939
\(491\) −7.32141 −0.330411 −0.165205 0.986259i \(-0.552829\pi\)
−0.165205 + 0.986259i \(0.552829\pi\)
\(492\) 20.3780 0.918711
\(493\) −15.6272 −0.703815
\(494\) 30.6326 1.37822
\(495\) −172.552 −7.75563
\(496\) −48.6153 −2.18289
\(497\) 10.5049 0.471208
\(498\) −13.1480 −0.589178
\(499\) −34.6430 −1.55083 −0.775416 0.631451i \(-0.782460\pi\)
−0.775416 + 0.631451i \(0.782460\pi\)
\(500\) 55.7961 2.49528
\(501\) 69.5126 3.10559
\(502\) −57.8673 −2.58274
\(503\) −14.4771 −0.645500 −0.322750 0.946484i \(-0.604607\pi\)
−0.322750 + 0.946484i \(0.604607\pi\)
\(504\) 136.093 6.06208
\(505\) 66.7736 2.97139
\(506\) 14.9465 0.664451
\(507\) −7.22590 −0.320914
\(508\) 62.9011 2.79078
\(509\) 5.00509 0.221847 0.110923 0.993829i \(-0.464619\pi\)
0.110923 + 0.993829i \(0.464619\pi\)
\(510\) −157.119 −6.95736
\(511\) −22.1671 −0.980615
\(512\) 40.2884 1.78051
\(513\) −54.4033 −2.40196
\(514\) −70.1813 −3.09556
\(515\) 33.5680 1.47918
\(516\) 86.6122 3.81289
\(517\) 1.30272 0.0572935
\(518\) −53.0287 −2.32995
\(519\) −40.8632 −1.79369
\(520\) 105.525 4.62758
\(521\) 13.7342 0.601708 0.300854 0.953670i \(-0.402728\pi\)
0.300854 + 0.953670i \(0.402728\pi\)
\(522\) −69.7832 −3.05433
\(523\) −35.6959 −1.56087 −0.780437 0.625235i \(-0.785003\pi\)
−0.780437 + 0.625235i \(0.785003\pi\)
\(524\) −106.873 −4.66879
\(525\) 59.9366 2.61585
\(526\) −62.2376 −2.71369
\(527\) 24.1958 1.05398
\(528\) 188.858 8.21900
\(529\) −21.9910 −0.956130
\(530\) 81.3539 3.53379
\(531\) −78.2769 −3.39693
\(532\) −31.7692 −1.37737
\(533\) 4.84528 0.209872
\(534\) 5.14234 0.222531
\(535\) 22.8360 0.987285
\(536\) 31.5721 1.36371
\(537\) −30.4241 −1.31290
\(538\) −32.4302 −1.39817
\(539\) 12.8577 0.553819
\(540\) −318.728 −13.7159
\(541\) 3.02386 0.130006 0.0650029 0.997885i \(-0.479294\pi\)
0.0650029 + 0.997885i \(0.479294\pi\)
\(542\) 77.8667 3.34466
\(543\) −20.7205 −0.889200
\(544\) 53.2646 2.28370
\(545\) −44.7321 −1.91611
\(546\) 74.7645 3.19963
\(547\) 7.00312 0.299432 0.149716 0.988729i \(-0.452164\pi\)
0.149716 + 0.988729i \(0.452164\pi\)
\(548\) −93.1836 −3.98061
\(549\) 8.48309 0.362050
\(550\) 121.529 5.18203
\(551\) 9.57849 0.408058
\(552\) 25.3082 1.07719
\(553\) 32.3249 1.37459
\(554\) −71.3357 −3.03076
\(555\) 113.845 4.83247
\(556\) 19.3047 0.818701
\(557\) 4.87347 0.206495 0.103248 0.994656i \(-0.467077\pi\)
0.103248 + 0.994656i \(0.467077\pi\)
\(558\) 108.046 4.57395
\(559\) 20.5938 0.871024
\(560\) −77.8473 −3.28965
\(561\) −93.9943 −3.96844
\(562\) 80.3305 3.38854
\(563\) −10.2589 −0.432362 −0.216181 0.976353i \(-0.569360\pi\)
−0.216181 + 0.976353i \(0.569360\pi\)
\(564\) 3.75141 0.157963
\(565\) 2.62524 0.110445
\(566\) −41.1959 −1.73159
\(567\) −78.1473 −3.28188
\(568\) 36.0664 1.51331
\(569\) −44.9732 −1.88537 −0.942687 0.333678i \(-0.891710\pi\)
−0.942687 + 0.333678i \(0.891710\pi\)
\(570\) 96.3041 4.03374
\(571\) −2.23429 −0.0935022 −0.0467511 0.998907i \(-0.514887\pi\)
−0.0467511 + 0.998907i \(0.514887\pi\)
\(572\) 107.362 4.48903
\(573\) 20.9767 0.876315
\(574\) −7.09538 −0.296155
\(575\) 8.20421 0.342139
\(576\) 72.9228 3.03845
\(577\) 9.18651 0.382439 0.191220 0.981547i \(-0.438756\pi\)
0.191220 + 0.981547i \(0.438756\pi\)
\(578\) −18.4914 −0.769143
\(579\) 53.8466 2.23779
\(580\) 56.1167 2.33012
\(581\) 3.24221 0.134509
\(582\) −71.6617 −2.97047
\(583\) 48.6688 2.01565
\(584\) −76.1063 −3.14930
\(585\) −118.147 −4.88476
\(586\) −24.4285 −1.00913
\(587\) −24.9695 −1.03060 −0.515300 0.857010i \(-0.672320\pi\)
−0.515300 + 0.857010i \(0.672320\pi\)
\(588\) 37.0260 1.52693
\(589\) −14.8305 −0.611078
\(590\) 88.8811 3.65918
\(591\) −56.9354 −2.34201
\(592\) −91.7177 −3.76957
\(593\) −23.2337 −0.954094 −0.477047 0.878878i \(-0.658293\pi\)
−0.477047 + 0.878878i \(0.658293\pi\)
\(594\) −269.232 −11.0467
\(595\) 38.7444 1.58837
\(596\) −24.8287 −1.01702
\(597\) 3.36408 0.137682
\(598\) 10.2339 0.418494
\(599\) 43.7371 1.78705 0.893524 0.449016i \(-0.148225\pi\)
0.893524 + 0.449016i \(0.148225\pi\)
\(600\) 205.780 8.40094
\(601\) −5.55625 −0.226644 −0.113322 0.993558i \(-0.536149\pi\)
−0.113322 + 0.993558i \(0.536149\pi\)
\(602\) −30.1574 −1.22912
\(603\) −35.3483 −1.43949
\(604\) −114.308 −4.65113
\(605\) 77.2950 3.14249
\(606\) 162.426 6.59812
\(607\) 3.78453 0.153609 0.0768046 0.997046i \(-0.475528\pi\)
0.0768046 + 0.997046i \(0.475528\pi\)
\(608\) −32.6478 −1.32404
\(609\) 23.3781 0.947329
\(610\) −9.63231 −0.390001
\(611\) 0.891974 0.0360854
\(612\) −199.236 −8.05363
\(613\) 11.6003 0.468533 0.234266 0.972172i \(-0.424731\pi\)
0.234266 + 0.972172i \(0.424731\pi\)
\(614\) −59.7969 −2.41321
\(615\) 15.2328 0.614246
\(616\) −92.4453 −3.72473
\(617\) 27.7427 1.11688 0.558440 0.829545i \(-0.311400\pi\)
0.558440 + 0.829545i \(0.311400\pi\)
\(618\) 81.6538 3.28460
\(619\) −28.0199 −1.12622 −0.563108 0.826383i \(-0.690394\pi\)
−0.563108 + 0.826383i \(0.690394\pi\)
\(620\) −86.8859 −3.48942
\(621\) −18.1753 −0.729351
\(622\) 59.1112 2.37014
\(623\) −1.26806 −0.0508039
\(624\) 129.312 5.17661
\(625\) 0.870715 0.0348286
\(626\) 56.3499 2.25219
\(627\) 57.6125 2.30082
\(628\) −41.8396 −1.66958
\(629\) 45.6477 1.82009
\(630\) 173.013 6.89300
\(631\) −29.0374 −1.15596 −0.577980 0.816051i \(-0.696159\pi\)
−0.577980 + 0.816051i \(0.696159\pi\)
\(632\) 110.981 4.41458
\(633\) −48.7277 −1.93675
\(634\) 68.4009 2.71655
\(635\) 47.0194 1.86591
\(636\) 140.151 5.55733
\(637\) 8.80367 0.348814
\(638\) 47.4022 1.87667
\(639\) −40.3801 −1.59741
\(640\) −3.99819 −0.158042
\(641\) 16.6843 0.658989 0.329495 0.944157i \(-0.393122\pi\)
0.329495 + 0.944157i \(0.393122\pi\)
\(642\) 55.5483 2.19232
\(643\) −8.56361 −0.337716 −0.168858 0.985640i \(-0.554008\pi\)
−0.168858 + 0.985640i \(0.554008\pi\)
\(644\) −10.6136 −0.418234
\(645\) 64.7437 2.54928
\(646\) 38.6143 1.51926
\(647\) 48.2731 1.89781 0.948906 0.315558i \(-0.102192\pi\)
0.948906 + 0.315558i \(0.102192\pi\)
\(648\) −268.303 −10.5399
\(649\) 53.1718 2.08718
\(650\) 83.2115 3.26382
\(651\) −36.1965 −1.41865
\(652\) −43.8911 −1.71891
\(653\) −21.5108 −0.841784 −0.420892 0.907111i \(-0.638283\pi\)
−0.420892 + 0.907111i \(0.638283\pi\)
\(654\) −108.810 −4.25483
\(655\) −79.8893 −3.12153
\(656\) −12.2721 −0.479144
\(657\) 85.2091 3.32432
\(658\) −1.30620 −0.0509209
\(659\) 38.6137 1.50418 0.752089 0.659062i \(-0.229047\pi\)
0.752089 + 0.659062i \(0.229047\pi\)
\(660\) 337.530 13.1383
\(661\) 20.2078 0.785993 0.392997 0.919540i \(-0.371438\pi\)
0.392997 + 0.919540i \(0.371438\pi\)
\(662\) 67.1448 2.60966
\(663\) −64.3581 −2.49946
\(664\) 11.1315 0.431985
\(665\) −23.7479 −0.920903
\(666\) 203.839 7.89861
\(667\) 3.20003 0.123906
\(668\) −100.087 −3.87248
\(669\) 72.1810 2.79068
\(670\) 40.1370 1.55063
\(671\) −5.76239 −0.222454
\(672\) −79.6831 −3.07384
\(673\) −44.4790 −1.71454 −0.857270 0.514867i \(-0.827841\pi\)
−0.857270 + 0.514867i \(0.827841\pi\)
\(674\) 10.1815 0.392176
\(675\) −147.783 −5.68818
\(676\) 10.4041 0.400159
\(677\) −36.6478 −1.40849 −0.704245 0.709957i \(-0.748714\pi\)
−0.704245 + 0.709957i \(0.748714\pi\)
\(678\) 6.38588 0.245248
\(679\) 17.6712 0.678160
\(680\) 133.021 5.10113
\(681\) −63.2438 −2.42351
\(682\) −73.3933 −2.81037
\(683\) 52.1166 1.99419 0.997093 0.0761997i \(-0.0242787\pi\)
0.997093 + 0.0761997i \(0.0242787\pi\)
\(684\) 122.119 4.66933
\(685\) −69.6560 −2.66142
\(686\) −52.7821 −2.01523
\(687\) −11.9521 −0.456000
\(688\) −52.1598 −1.98857
\(689\) 33.3236 1.26953
\(690\) 32.1738 1.22483
\(691\) −42.4202 −1.61374 −0.806871 0.590728i \(-0.798841\pi\)
−0.806871 + 0.590728i \(0.798841\pi\)
\(692\) 58.8364 2.23662
\(693\) 103.502 3.93173
\(694\) −29.8865 −1.13447
\(695\) 14.4305 0.547380
\(696\) 80.2640 3.04240
\(697\) 6.10778 0.231349
\(698\) −44.7325 −1.69315
\(699\) 30.0403 1.13623
\(700\) −86.2990 −3.26180
\(701\) 27.2622 1.02968 0.514839 0.857287i \(-0.327852\pi\)
0.514839 + 0.857287i \(0.327852\pi\)
\(702\) −184.344 −6.95761
\(703\) −27.9791 −1.05525
\(704\) −49.5349 −1.86692
\(705\) 2.80423 0.105613
\(706\) −3.58662 −0.134984
\(707\) −40.0531 −1.50635
\(708\) 153.118 5.75453
\(709\) −5.14111 −0.193078 −0.0965391 0.995329i \(-0.530777\pi\)
−0.0965391 + 0.995329i \(0.530777\pi\)
\(710\) 45.8505 1.72074
\(711\) −124.255 −4.65992
\(712\) −4.35364 −0.163160
\(713\) −4.95463 −0.185552
\(714\) 94.2455 3.52705
\(715\) 80.2545 3.00135
\(716\) 43.8059 1.63710
\(717\) 1.09361 0.0408415
\(718\) −9.65958 −0.360492
\(719\) 48.4957 1.80858 0.904292 0.426914i \(-0.140399\pi\)
0.904292 + 0.426914i \(0.140399\pi\)
\(720\) 299.241 11.1520
\(721\) −20.1352 −0.749874
\(722\) 26.0755 0.970430
\(723\) −57.9720 −2.15600
\(724\) 29.8341 1.10878
\(725\) 26.0194 0.966336
\(726\) 188.019 6.97805
\(727\) 13.9737 0.518258 0.259129 0.965843i \(-0.416565\pi\)
0.259129 + 0.965843i \(0.416565\pi\)
\(728\) −63.2975 −2.34596
\(729\) 117.383 4.34754
\(730\) −96.7525 −3.58097
\(731\) 25.9598 0.960158
\(732\) −16.5938 −0.613326
\(733\) −15.0944 −0.557525 −0.278763 0.960360i \(-0.589924\pi\)
−0.278763 + 0.960360i \(0.589924\pi\)
\(734\) 29.1362 1.07544
\(735\) 27.6774 1.02090
\(736\) −10.9071 −0.402042
\(737\) 24.0114 0.884470
\(738\) 27.2742 1.00398
\(739\) 39.3054 1.44587 0.722937 0.690914i \(-0.242792\pi\)
0.722937 + 0.690914i \(0.242792\pi\)
\(740\) −163.919 −6.02578
\(741\) 39.4474 1.44914
\(742\) −48.7988 −1.79146
\(743\) −32.8300 −1.20441 −0.602207 0.798340i \(-0.705712\pi\)
−0.602207 + 0.798340i \(0.705712\pi\)
\(744\) −124.273 −4.55608
\(745\) −18.5598 −0.679978
\(746\) 16.4441 0.602063
\(747\) −12.4629 −0.455992
\(748\) 135.337 4.94840
\(749\) −13.6978 −0.500506
\(750\) 101.455 3.70461
\(751\) 33.2676 1.21395 0.606976 0.794720i \(-0.292382\pi\)
0.606976 + 0.794720i \(0.292382\pi\)
\(752\) −2.25918 −0.0823840
\(753\) −74.5193 −2.71563
\(754\) 32.4564 1.18199
\(755\) −85.4468 −3.10973
\(756\) 191.184 6.95329
\(757\) 3.38338 0.122971 0.0614855 0.998108i \(-0.480416\pi\)
0.0614855 + 0.998108i \(0.480416\pi\)
\(758\) −25.3867 −0.922086
\(759\) 19.2475 0.698639
\(760\) −81.5335 −2.95753
\(761\) 36.2469 1.31395 0.656975 0.753912i \(-0.271836\pi\)
0.656975 + 0.753912i \(0.271836\pi\)
\(762\) 114.374 4.14334
\(763\) 26.8318 0.971377
\(764\) −30.2031 −1.09271
\(765\) −148.931 −5.38463
\(766\) 75.1865 2.71660
\(767\) 36.4069 1.31458
\(768\) 49.0441 1.76973
\(769\) 5.33480 0.192378 0.0961888 0.995363i \(-0.469335\pi\)
0.0961888 + 0.995363i \(0.469335\pi\)
\(770\) −117.524 −4.23527
\(771\) −90.3767 −3.25484
\(772\) −77.5303 −2.79038
\(773\) 37.0231 1.33163 0.665814 0.746118i \(-0.268085\pi\)
0.665814 + 0.746118i \(0.268085\pi\)
\(774\) 115.923 4.16677
\(775\) −40.2860 −1.44712
\(776\) 60.6707 2.17795
\(777\) −68.2883 −2.44983
\(778\) −12.8715 −0.461465
\(779\) −3.74368 −0.134131
\(780\) 231.107 8.27497
\(781\) 27.4294 0.981500
\(782\) 12.9005 0.461320
\(783\) −57.6425 −2.05997
\(784\) −22.2979 −0.796352
\(785\) −31.2756 −1.11628
\(786\) −194.330 −6.93152
\(787\) 9.00298 0.320922 0.160461 0.987042i \(-0.448702\pi\)
0.160461 + 0.987042i \(0.448702\pi\)
\(788\) 81.9778 2.92034
\(789\) −80.1472 −2.85332
\(790\) 141.088 5.01968
\(791\) −1.57471 −0.0559902
\(792\) 355.355 12.6270
\(793\) −3.94552 −0.140109
\(794\) 48.9802 1.73824
\(795\) 104.764 3.71561
\(796\) −4.84373 −0.171681
\(797\) −39.0230 −1.38227 −0.691133 0.722727i \(-0.742888\pi\)
−0.691133 + 0.722727i \(0.742888\pi\)
\(798\) −57.7665 −2.04491
\(799\) 1.12439 0.0397781
\(800\) −88.6858 −3.13552
\(801\) 4.87436 0.172227
\(802\) −6.78158 −0.239466
\(803\) −57.8807 −2.04257
\(804\) 69.1451 2.43856
\(805\) −7.93380 −0.279630
\(806\) −50.2525 −1.77007
\(807\) −41.7624 −1.47011
\(808\) −137.514 −4.83773
\(809\) −2.59145 −0.0911106 −0.0455553 0.998962i \(-0.514506\pi\)
−0.0455553 + 0.998962i \(0.514506\pi\)
\(810\) −341.088 −11.9846
\(811\) −37.8238 −1.32817 −0.664086 0.747656i \(-0.731179\pi\)
−0.664086 + 0.747656i \(0.731179\pi\)
\(812\) −33.6607 −1.18126
\(813\) 100.274 3.51675
\(814\) −138.464 −4.85315
\(815\) −32.8092 −1.14925
\(816\) 163.006 5.70634
\(817\) −15.9117 −0.556680
\(818\) −28.6693 −1.00240
\(819\) 70.8683 2.47634
\(820\) −21.9328 −0.765927
\(821\) 43.8766 1.53130 0.765652 0.643255i \(-0.222417\pi\)
0.765652 + 0.643255i \(0.222417\pi\)
\(822\) −169.438 −5.90981
\(823\) 34.4813 1.20194 0.600972 0.799270i \(-0.294780\pi\)
0.600972 + 0.799270i \(0.294780\pi\)
\(824\) −69.1302 −2.40826
\(825\) 156.501 5.44866
\(826\) −53.3139 −1.85503
\(827\) 40.2493 1.39961 0.699803 0.714336i \(-0.253271\pi\)
0.699803 + 0.714336i \(0.253271\pi\)
\(828\) 40.7981 1.41783
\(829\) −31.7610 −1.10311 −0.551553 0.834140i \(-0.685965\pi\)
−0.551553 + 0.834140i \(0.685965\pi\)
\(830\) 14.1512 0.491196
\(831\) −91.8634 −3.18671
\(832\) −33.9167 −1.17585
\(833\) 11.0976 0.384509
\(834\) 35.1021 1.21549
\(835\) −74.8163 −2.58912
\(836\) −82.9527 −2.86898
\(837\) 89.2483 3.08487
\(838\) 23.2891 0.804507
\(839\) −1.35259 −0.0466964 −0.0233482 0.999727i \(-0.507433\pi\)
−0.0233482 + 0.999727i \(0.507433\pi\)
\(840\) −198.998 −6.86608
\(841\) −18.8512 −0.650041
\(842\) 105.163 3.62414
\(843\) 103.447 3.56289
\(844\) 70.1600 2.41501
\(845\) 7.77723 0.267545
\(846\) 5.02096 0.172624
\(847\) −46.3641 −1.59309
\(848\) −84.4018 −2.89837
\(849\) −53.0506 −1.82069
\(850\) 104.893 3.59782
\(851\) −9.34740 −0.320425
\(852\) 78.9878 2.70608
\(853\) −31.3775 −1.07435 −0.537173 0.843472i \(-0.680508\pi\)
−0.537173 + 0.843472i \(0.680508\pi\)
\(854\) 5.77778 0.197712
\(855\) 91.2855 3.12190
\(856\) −47.0286 −1.60740
\(857\) −18.9530 −0.647421 −0.323711 0.946156i \(-0.604930\pi\)
−0.323711 + 0.946156i \(0.604930\pi\)
\(858\) 195.218 6.66464
\(859\) 5.15902 0.176024 0.0880118 0.996119i \(-0.471949\pi\)
0.0880118 + 0.996119i \(0.471949\pi\)
\(860\) −93.2205 −3.17879
\(861\) −9.13716 −0.311394
\(862\) −35.2364 −1.20016
\(863\) −29.4534 −1.00261 −0.501303 0.865272i \(-0.667146\pi\)
−0.501303 + 0.865272i \(0.667146\pi\)
\(864\) 196.471 6.68409
\(865\) 43.9810 1.49540
\(866\) 40.7698 1.38541
\(867\) −23.8126 −0.808717
\(868\) 52.1171 1.76897
\(869\) 84.4037 2.86320
\(870\) 102.038 3.45941
\(871\) 16.4406 0.557069
\(872\) 92.1217 3.11963
\(873\) −67.9273 −2.29899
\(874\) −7.90716 −0.267464
\(875\) −25.0180 −0.845764
\(876\) −166.678 −5.63153
\(877\) −30.5542 −1.03174 −0.515871 0.856666i \(-0.672532\pi\)
−0.515871 + 0.856666i \(0.672532\pi\)
\(878\) −91.6998 −3.09472
\(879\) −31.4581 −1.06105
\(880\) −203.268 −6.85215
\(881\) 8.45654 0.284908 0.142454 0.989801i \(-0.454501\pi\)
0.142454 + 0.989801i \(0.454501\pi\)
\(882\) 49.5562 1.66864
\(883\) 9.13229 0.307326 0.153663 0.988123i \(-0.450893\pi\)
0.153663 + 0.988123i \(0.450893\pi\)
\(884\) 92.6653 3.11667
\(885\) 114.458 3.84745
\(886\) −61.6711 −2.07188
\(887\) −27.7218 −0.930808 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(888\) −234.454 −7.86777
\(889\) −28.2038 −0.945925
\(890\) −5.53470 −0.185523
\(891\) −204.051 −6.83597
\(892\) −103.929 −3.47980
\(893\) −0.689180 −0.0230625
\(894\) −45.1465 −1.50992
\(895\) 32.7455 1.09456
\(896\) 2.39825 0.0801199
\(897\) 13.1788 0.440027
\(898\) 6.12049 0.204243
\(899\) −15.7135 −0.524073
\(900\) 331.728 11.0576
\(901\) 42.0066 1.39944
\(902\) −18.5268 −0.616875
\(903\) −38.8355 −1.29236
\(904\) −5.40645 −0.179816
\(905\) 22.3014 0.741324
\(906\) −207.849 −6.90531
\(907\) −16.8880 −0.560758 −0.280379 0.959889i \(-0.590460\pi\)
−0.280379 + 0.959889i \(0.590460\pi\)
\(908\) 91.0609 3.02196
\(909\) 153.962 5.10659
\(910\) −80.4689 −2.66752
\(911\) −42.7644 −1.41685 −0.708424 0.705787i \(-0.750593\pi\)
−0.708424 + 0.705787i \(0.750593\pi\)
\(912\) −99.9121 −3.30842
\(913\) 8.46575 0.280176
\(914\) 43.6104 1.44251
\(915\) −12.4041 −0.410067
\(916\) 17.2091 0.568603
\(917\) 47.9203 1.58247
\(918\) −232.377 −7.66959
\(919\) −39.3199 −1.29704 −0.648521 0.761197i \(-0.724612\pi\)
−0.648521 + 0.761197i \(0.724612\pi\)
\(920\) −27.2391 −0.898047
\(921\) −77.0042 −2.53737
\(922\) 75.8155 2.49685
\(923\) 18.7809 0.618182
\(924\) −202.462 −6.66050
\(925\) −76.0036 −2.49898
\(926\) 0.510654 0.0167811
\(927\) 77.3986 2.54210
\(928\) −34.5917 −1.13553
\(929\) −12.5528 −0.411843 −0.205922 0.978568i \(-0.566019\pi\)
−0.205922 + 0.978568i \(0.566019\pi\)
\(930\) −157.986 −5.18058
\(931\) −6.80212 −0.222931
\(932\) −43.2532 −1.41681
\(933\) 76.1212 2.49209
\(934\) 1.14408 0.0374353
\(935\) 101.166 3.30848
\(936\) 243.312 7.95291
\(937\) 30.0404 0.981376 0.490688 0.871335i \(-0.336746\pi\)
0.490688 + 0.871335i \(0.336746\pi\)
\(938\) −24.0755 −0.786093
\(939\) 72.5652 2.36808
\(940\) −4.03764 −0.131693
\(941\) 42.7095 1.39229 0.696146 0.717900i \(-0.254897\pi\)
0.696146 + 0.717900i \(0.254897\pi\)
\(942\) −76.0777 −2.47875
\(943\) −1.25071 −0.0407287
\(944\) −92.2110 −3.00121
\(945\) 142.912 4.64894
\(946\) −78.7441 −2.56019
\(947\) −19.0392 −0.618691 −0.309345 0.950950i \(-0.600110\pi\)
−0.309345 + 0.950950i \(0.600110\pi\)
\(948\) 243.056 7.89409
\(949\) −39.6311 −1.28648
\(950\) −64.2930 −2.08594
\(951\) 88.0840 2.85632
\(952\) −79.7906 −2.58603
\(953\) −3.48043 −0.112742 −0.0563710 0.998410i \(-0.517953\pi\)
−0.0563710 + 0.998410i \(0.517953\pi\)
\(954\) 187.580 6.07312
\(955\) −22.5772 −0.730581
\(956\) −1.57462 −0.0509268
\(957\) 61.0428 1.97323
\(958\) 70.6055 2.28116
\(959\) 41.7820 1.34921
\(960\) −106.629 −3.44143
\(961\) −6.67073 −0.215185
\(962\) −94.8064 −3.05668
\(963\) 52.6535 1.69674
\(964\) 83.4703 2.68840
\(965\) −57.9550 −1.86564
\(966\) −19.2989 −0.620932
\(967\) −21.7410 −0.699142 −0.349571 0.936910i \(-0.613673\pi\)
−0.349571 + 0.936910i \(0.613673\pi\)
\(968\) −159.182 −5.11630
\(969\) 49.7260 1.59743
\(970\) 77.1294 2.47648
\(971\) 42.3396 1.35874 0.679371 0.733795i \(-0.262253\pi\)
0.679371 + 0.733795i \(0.262253\pi\)
\(972\) −324.097 −10.3954
\(973\) −8.65591 −0.277496
\(974\) −39.2713 −1.25833
\(975\) 107.157 3.43176
\(976\) 9.99317 0.319874
\(977\) 49.8498 1.59484 0.797418 0.603427i \(-0.206199\pi\)
0.797418 + 0.603427i \(0.206199\pi\)
\(978\) −79.8080 −2.55198
\(979\) −3.31105 −0.105822
\(980\) −39.8510 −1.27299
\(981\) −103.140 −3.29301
\(982\) 19.1681 0.611678
\(983\) 16.8279 0.536727 0.268364 0.963318i \(-0.413517\pi\)
0.268364 + 0.963318i \(0.413517\pi\)
\(984\) −31.3706 −1.00006
\(985\) 61.2795 1.95253
\(986\) 40.9134 1.30295
\(987\) −1.68207 −0.0535410
\(988\) −56.7979 −1.80698
\(989\) −5.31586 −0.169034
\(990\) 451.755 14.3577
\(991\) 31.1482 0.989455 0.494728 0.869048i \(-0.335268\pi\)
0.494728 + 0.869048i \(0.335268\pi\)
\(992\) 53.5585 1.70048
\(993\) 86.4665 2.74393
\(994\) −27.5026 −0.872331
\(995\) −3.62075 −0.114785
\(996\) 24.3787 0.772468
\(997\) 17.0965 0.541451 0.270726 0.962657i \(-0.412736\pi\)
0.270726 + 0.962657i \(0.412736\pi\)
\(998\) 90.6983 2.87100
\(999\) 168.376 5.32717
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 \(a_p\))