Properties

Label 8015.2.a.l.1.10
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.17211 q^{2}\) \(+3.11306 q^{3}\) \(+2.71804 q^{4}\) \(-1.00000 q^{5}\) \(-6.76191 q^{6}\) \(-1.00000 q^{7}\) \(-1.55967 q^{8}\) \(+6.69117 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.17211 q^{2}\) \(+3.11306 q^{3}\) \(+2.71804 q^{4}\) \(-1.00000 q^{5}\) \(-6.76191 q^{6}\) \(-1.00000 q^{7}\) \(-1.55967 q^{8}\) \(+6.69117 q^{9}\) \(+2.17211 q^{10}\) \(-0.102826 q^{11}\) \(+8.46145 q^{12}\) \(+3.05479 q^{13}\) \(+2.17211 q^{14}\) \(-3.11306 q^{15}\) \(-2.04832 q^{16}\) \(+6.79945 q^{17}\) \(-14.5339 q^{18}\) \(+7.10673 q^{19}\) \(-2.71804 q^{20}\) \(-3.11306 q^{21}\) \(+0.223349 q^{22}\) \(-6.34050 q^{23}\) \(-4.85535 q^{24}\) \(+1.00000 q^{25}\) \(-6.63532 q^{26}\) \(+11.4909 q^{27}\) \(-2.71804 q^{28}\) \(+3.49304 q^{29}\) \(+6.76191 q^{30}\) \(-6.66081 q^{31}\) \(+7.56851 q^{32}\) \(-0.320104 q^{33}\) \(-14.7691 q^{34}\) \(+1.00000 q^{35}\) \(+18.1869 q^{36}\) \(+3.36922 q^{37}\) \(-15.4366 q^{38}\) \(+9.50975 q^{39}\) \(+1.55967 q^{40}\) \(+0.870493 q^{41}\) \(+6.76191 q^{42}\) \(-6.76435 q^{43}\) \(-0.279485 q^{44}\) \(-6.69117 q^{45}\) \(+13.7722 q^{46}\) \(-2.90931 q^{47}\) \(-6.37657 q^{48}\) \(+1.00000 q^{49}\) \(-2.17211 q^{50}\) \(+21.1671 q^{51}\) \(+8.30304 q^{52}\) \(+1.10328 q^{53}\) \(-24.9594 q^{54}\) \(+0.102826 q^{55}\) \(+1.55967 q^{56}\) \(+22.1237 q^{57}\) \(-7.58726 q^{58}\) \(-5.23203 q^{59}\) \(-8.46145 q^{60}\) \(+8.37943 q^{61}\) \(+14.4680 q^{62}\) \(-6.69117 q^{63}\) \(-12.3430 q^{64}\) \(-3.05479 q^{65}\) \(+0.695300 q^{66}\) \(+7.08104 q^{67}\) \(+18.4812 q^{68}\) \(-19.7384 q^{69}\) \(-2.17211 q^{70}\) \(-7.78159 q^{71}\) \(-10.4360 q^{72}\) \(+7.59574 q^{73}\) \(-7.31830 q^{74}\) \(+3.11306 q^{75}\) \(+19.3164 q^{76}\) \(+0.102826 q^{77}\) \(-20.6562 q^{78}\) \(+14.4279 q^{79}\) \(+2.04832 q^{80}\) \(+15.6983 q^{81}\) \(-1.89080 q^{82}\) \(+11.2735 q^{83}\) \(-8.46145 q^{84}\) \(-6.79945 q^{85}\) \(+14.6929 q^{86}\) \(+10.8741 q^{87}\) \(+0.160374 q^{88}\) \(+2.05982 q^{89}\) \(+14.5339 q^{90}\) \(-3.05479 q^{91}\) \(-17.2338 q^{92}\) \(-20.7355 q^{93}\) \(+6.31933 q^{94}\) \(-7.10673 q^{95}\) \(+23.5613 q^{96}\) \(+1.16378 q^{97}\) \(-2.17211 q^{98}\) \(-0.688026 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.17211 −1.53591 −0.767955 0.640503i \(-0.778726\pi\)
−0.767955 + 0.640503i \(0.778726\pi\)
\(3\) 3.11306 1.79733 0.898664 0.438637i \(-0.144539\pi\)
0.898664 + 0.438637i \(0.144539\pi\)
\(4\) 2.71804 1.35902
\(5\) −1.00000 −0.447214
\(6\) −6.76191 −2.76054
\(7\) −1.00000 −0.377964
\(8\) −1.55967 −0.551426
\(9\) 6.69117 2.23039
\(10\) 2.17211 0.686880
\(11\) −0.102826 −0.0310032 −0.0155016 0.999880i \(-0.504935\pi\)
−0.0155016 + 0.999880i \(0.504935\pi\)
\(12\) 8.46145 2.44261
\(13\) 3.05479 0.847245 0.423623 0.905839i \(-0.360758\pi\)
0.423623 + 0.905839i \(0.360758\pi\)
\(14\) 2.17211 0.580520
\(15\) −3.11306 −0.803790
\(16\) −2.04832 −0.512081
\(17\) 6.79945 1.64911 0.824555 0.565782i \(-0.191426\pi\)
0.824555 + 0.565782i \(0.191426\pi\)
\(18\) −14.5339 −3.42568
\(19\) 7.10673 1.63039 0.815197 0.579183i \(-0.196628\pi\)
0.815197 + 0.579183i \(0.196628\pi\)
\(20\) −2.71804 −0.607773
\(21\) −3.11306 −0.679326
\(22\) 0.223349 0.0476181
\(23\) −6.34050 −1.32209 −0.661043 0.750348i \(-0.729886\pi\)
−0.661043 + 0.750348i \(0.729886\pi\)
\(24\) −4.85535 −0.991094
\(25\) 1.00000 0.200000
\(26\) −6.63532 −1.30129
\(27\) 11.4909 2.21142
\(28\) −2.71804 −0.513662
\(29\) 3.49304 0.648641 0.324321 0.945947i \(-0.394864\pi\)
0.324321 + 0.945947i \(0.394864\pi\)
\(30\) 6.76191 1.23455
\(31\) −6.66081 −1.19632 −0.598159 0.801378i \(-0.704101\pi\)
−0.598159 + 0.801378i \(0.704101\pi\)
\(32\) 7.56851 1.33794
\(33\) −0.320104 −0.0557229
\(34\) −14.7691 −2.53288
\(35\) 1.00000 0.169031
\(36\) 18.1869 3.03115
\(37\) 3.36922 0.553896 0.276948 0.960885i \(-0.410677\pi\)
0.276948 + 0.960885i \(0.410677\pi\)
\(38\) −15.4366 −2.50414
\(39\) 9.50975 1.52278
\(40\) 1.55967 0.246605
\(41\) 0.870493 0.135948 0.0679741 0.997687i \(-0.478346\pi\)
0.0679741 + 0.997687i \(0.478346\pi\)
\(42\) 6.76191 1.04338
\(43\) −6.76435 −1.03155 −0.515777 0.856723i \(-0.672497\pi\)
−0.515777 + 0.856723i \(0.672497\pi\)
\(44\) −0.279485 −0.0421340
\(45\) −6.69117 −0.997461
\(46\) 13.7722 2.03061
\(47\) −2.90931 −0.424366 −0.212183 0.977230i \(-0.568057\pi\)
−0.212183 + 0.977230i \(0.568057\pi\)
\(48\) −6.37657 −0.920378
\(49\) 1.00000 0.142857
\(50\) −2.17211 −0.307182
\(51\) 21.1671 2.96399
\(52\) 8.30304 1.15143
\(53\) 1.10328 0.151548 0.0757738 0.997125i \(-0.475857\pi\)
0.0757738 + 0.997125i \(0.475857\pi\)
\(54\) −24.9594 −3.39654
\(55\) 0.102826 0.0138650
\(56\) 1.55967 0.208419
\(57\) 22.1237 2.93036
\(58\) −7.58726 −0.996255
\(59\) −5.23203 −0.681152 −0.340576 0.940217i \(-0.610622\pi\)
−0.340576 + 0.940217i \(0.610622\pi\)
\(60\) −8.46145 −1.09237
\(61\) 8.37943 1.07288 0.536438 0.843940i \(-0.319769\pi\)
0.536438 + 0.843940i \(0.319769\pi\)
\(62\) 14.4680 1.83744
\(63\) −6.69117 −0.843009
\(64\) −12.3430 −1.54287
\(65\) −3.05479 −0.378900
\(66\) 0.695300 0.0855855
\(67\) 7.08104 0.865087 0.432544 0.901613i \(-0.357616\pi\)
0.432544 + 0.901613i \(0.357616\pi\)
\(68\) 18.4812 2.24118
\(69\) −19.7384 −2.37622
\(70\) −2.17211 −0.259616
\(71\) −7.78159 −0.923505 −0.461753 0.887009i \(-0.652779\pi\)
−0.461753 + 0.887009i \(0.652779\pi\)
\(72\) −10.4360 −1.22990
\(73\) 7.59574 0.889014 0.444507 0.895775i \(-0.353379\pi\)
0.444507 + 0.895775i \(0.353379\pi\)
\(74\) −7.31830 −0.850735
\(75\) 3.11306 0.359466
\(76\) 19.3164 2.21574
\(77\) 0.102826 0.0117181
\(78\) −20.6562 −2.33885
\(79\) 14.4279 1.62326 0.811631 0.584170i \(-0.198580\pi\)
0.811631 + 0.584170i \(0.198580\pi\)
\(80\) 2.04832 0.229010
\(81\) 15.6983 1.74425
\(82\) −1.89080 −0.208804
\(83\) 11.2735 1.23742 0.618712 0.785618i \(-0.287655\pi\)
0.618712 + 0.785618i \(0.287655\pi\)
\(84\) −8.46145 −0.923220
\(85\) −6.79945 −0.737504
\(86\) 14.6929 1.58437
\(87\) 10.8741 1.16582
\(88\) 0.160374 0.0170960
\(89\) 2.05982 0.218341 0.109170 0.994023i \(-0.465181\pi\)
0.109170 + 0.994023i \(0.465181\pi\)
\(90\) 14.5339 1.53201
\(91\) −3.05479 −0.320229
\(92\) −17.2338 −1.79674
\(93\) −20.7355 −2.15018
\(94\) 6.31933 0.651789
\(95\) −7.10673 −0.729135
\(96\) 23.5613 2.40471
\(97\) 1.16378 0.118164 0.0590820 0.998253i \(-0.481183\pi\)
0.0590820 + 0.998253i \(0.481183\pi\)
\(98\) −2.17211 −0.219416
\(99\) −0.688026 −0.0691492
\(100\) 2.71804 0.271804
\(101\) 13.6692 1.36014 0.680069 0.733148i \(-0.261950\pi\)
0.680069 + 0.733148i \(0.261950\pi\)
\(102\) −45.9773 −4.55243
\(103\) 4.87115 0.479968 0.239984 0.970777i \(-0.422858\pi\)
0.239984 + 0.970777i \(0.422858\pi\)
\(104\) −4.76445 −0.467193
\(105\) 3.11306 0.303804
\(106\) −2.39645 −0.232764
\(107\) −6.00710 −0.580729 −0.290364 0.956916i \(-0.593776\pi\)
−0.290364 + 0.956916i \(0.593776\pi\)
\(108\) 31.2327 3.00537
\(109\) 13.0643 1.25134 0.625669 0.780089i \(-0.284826\pi\)
0.625669 + 0.780089i \(0.284826\pi\)
\(110\) −0.223349 −0.0212955
\(111\) 10.4886 0.995534
\(112\) 2.04832 0.193548
\(113\) −7.16338 −0.673875 −0.336937 0.941527i \(-0.609391\pi\)
−0.336937 + 0.941527i \(0.609391\pi\)
\(114\) −48.0550 −4.50076
\(115\) 6.34050 0.591255
\(116\) 9.49424 0.881518
\(117\) 20.4401 1.88969
\(118\) 11.3645 1.04619
\(119\) −6.79945 −0.623305
\(120\) 4.85535 0.443231
\(121\) −10.9894 −0.999039
\(122\) −18.2010 −1.64784
\(123\) 2.70990 0.244343
\(124\) −18.1044 −1.62582
\(125\) −1.00000 −0.0894427
\(126\) 14.5339 1.29479
\(127\) −18.1476 −1.61034 −0.805170 0.593044i \(-0.797926\pi\)
−0.805170 + 0.593044i \(0.797926\pi\)
\(128\) 11.6732 1.03177
\(129\) −21.0578 −1.85404
\(130\) 6.63532 0.581956
\(131\) −12.3798 −1.08163 −0.540815 0.841141i \(-0.681884\pi\)
−0.540815 + 0.841141i \(0.681884\pi\)
\(132\) −0.870056 −0.0757287
\(133\) −7.10673 −0.616231
\(134\) −15.3808 −1.32870
\(135\) −11.4909 −0.988976
\(136\) −10.6049 −0.909362
\(137\) 19.7491 1.68728 0.843638 0.536912i \(-0.180409\pi\)
0.843638 + 0.536912i \(0.180409\pi\)
\(138\) 42.8739 3.64967
\(139\) 0.155070 0.0131529 0.00657644 0.999978i \(-0.497907\pi\)
0.00657644 + 0.999978i \(0.497907\pi\)
\(140\) 2.71804 0.229717
\(141\) −9.05687 −0.762726
\(142\) 16.9024 1.41842
\(143\) −0.314111 −0.0262673
\(144\) −13.7057 −1.14214
\(145\) −3.49304 −0.290081
\(146\) −16.4988 −1.36545
\(147\) 3.11306 0.256761
\(148\) 9.15769 0.752757
\(149\) 20.7529 1.70014 0.850070 0.526669i \(-0.176559\pi\)
0.850070 + 0.526669i \(0.176559\pi\)
\(150\) −6.76191 −0.552107
\(151\) −0.865117 −0.0704022 −0.0352011 0.999380i \(-0.511207\pi\)
−0.0352011 + 0.999380i \(0.511207\pi\)
\(152\) −11.0841 −0.899042
\(153\) 45.4963 3.67816
\(154\) −0.223349 −0.0179980
\(155\) 6.66081 0.535009
\(156\) 25.8479 2.06949
\(157\) −6.35164 −0.506916 −0.253458 0.967346i \(-0.581568\pi\)
−0.253458 + 0.967346i \(0.581568\pi\)
\(158\) −31.3389 −2.49319
\(159\) 3.43459 0.272381
\(160\) −7.56851 −0.598343
\(161\) 6.34050 0.499701
\(162\) −34.0983 −2.67902
\(163\) 12.5084 0.979733 0.489867 0.871797i \(-0.337045\pi\)
0.489867 + 0.871797i \(0.337045\pi\)
\(164\) 2.36604 0.184756
\(165\) 0.320104 0.0249201
\(166\) −24.4872 −1.90057
\(167\) −6.02749 −0.466421 −0.233210 0.972426i \(-0.574923\pi\)
−0.233210 + 0.972426i \(0.574923\pi\)
\(168\) 4.85535 0.374598
\(169\) −3.66828 −0.282175
\(170\) 14.7691 1.13274
\(171\) 47.5523 3.63642
\(172\) −18.3858 −1.40190
\(173\) −16.2595 −1.23619 −0.618093 0.786105i \(-0.712095\pi\)
−0.618093 + 0.786105i \(0.712095\pi\)
\(174\) −23.6196 −1.79060
\(175\) −1.00000 −0.0755929
\(176\) 0.210621 0.0158761
\(177\) −16.2876 −1.22425
\(178\) −4.47416 −0.335352
\(179\) −4.56853 −0.341468 −0.170734 0.985317i \(-0.554614\pi\)
−0.170734 + 0.985317i \(0.554614\pi\)
\(180\) −18.1869 −1.35557
\(181\) −6.49969 −0.483118 −0.241559 0.970386i \(-0.577659\pi\)
−0.241559 + 0.970386i \(0.577659\pi\)
\(182\) 6.63532 0.491843
\(183\) 26.0857 1.92831
\(184\) 9.88907 0.729032
\(185\) −3.36922 −0.247710
\(186\) 45.0398 3.30248
\(187\) −0.699160 −0.0511277
\(188\) −7.90763 −0.576723
\(189\) −11.4909 −0.835837
\(190\) 15.4366 1.11989
\(191\) −15.4783 −1.11997 −0.559985 0.828503i \(-0.689193\pi\)
−0.559985 + 0.828503i \(0.689193\pi\)
\(192\) −38.4244 −2.77305
\(193\) −2.52612 −0.181834 −0.0909169 0.995858i \(-0.528980\pi\)
−0.0909169 + 0.995858i \(0.528980\pi\)
\(194\) −2.52785 −0.181489
\(195\) −9.50975 −0.681007
\(196\) 2.71804 0.194146
\(197\) −25.4728 −1.81486 −0.907430 0.420203i \(-0.861959\pi\)
−0.907430 + 0.420203i \(0.861959\pi\)
\(198\) 1.49447 0.106207
\(199\) −18.7698 −1.33056 −0.665278 0.746596i \(-0.731687\pi\)
−0.665278 + 0.746596i \(0.731687\pi\)
\(200\) −1.55967 −0.110285
\(201\) 22.0437 1.55485
\(202\) −29.6910 −2.08905
\(203\) −3.49304 −0.245163
\(204\) 57.5332 4.02813
\(205\) −0.870493 −0.0607978
\(206\) −10.5806 −0.737188
\(207\) −42.4254 −2.94877
\(208\) −6.25719 −0.433858
\(209\) −0.730756 −0.0505474
\(210\) −6.76191 −0.466616
\(211\) −22.9860 −1.58242 −0.791210 0.611545i \(-0.790548\pi\)
−0.791210 + 0.611545i \(0.790548\pi\)
\(212\) 2.99877 0.205957
\(213\) −24.2246 −1.65984
\(214\) 13.0481 0.891947
\(215\) 6.76435 0.461325
\(216\) −17.9219 −1.21943
\(217\) 6.66081 0.452165
\(218\) −28.3771 −1.92194
\(219\) 23.6460 1.59785
\(220\) 0.279485 0.0188429
\(221\) 20.7709 1.39720
\(222\) −22.7823 −1.52905
\(223\) 9.69459 0.649198 0.324599 0.945852i \(-0.394771\pi\)
0.324599 + 0.945852i \(0.394771\pi\)
\(224\) −7.56851 −0.505693
\(225\) 6.69117 0.446078
\(226\) 15.5596 1.03501
\(227\) −14.7518 −0.979112 −0.489556 0.871972i \(-0.662841\pi\)
−0.489556 + 0.871972i \(0.662841\pi\)
\(228\) 60.1332 3.98242
\(229\) 1.00000 0.0660819
\(230\) −13.7722 −0.908114
\(231\) 0.320104 0.0210613
\(232\) −5.44799 −0.357678
\(233\) −1.68649 −0.110486 −0.0552428 0.998473i \(-0.517593\pi\)
−0.0552428 + 0.998473i \(0.517593\pi\)
\(234\) −44.3981 −2.90239
\(235\) 2.90931 0.189782
\(236\) −14.2209 −0.925700
\(237\) 44.9149 2.91754
\(238\) 14.7691 0.957340
\(239\) −8.41214 −0.544136 −0.272068 0.962278i \(-0.587708\pi\)
−0.272068 + 0.962278i \(0.587708\pi\)
\(240\) 6.37657 0.411606
\(241\) −0.905279 −0.0583142 −0.0291571 0.999575i \(-0.509282\pi\)
−0.0291571 + 0.999575i \(0.509282\pi\)
\(242\) 23.8702 1.53443
\(243\) 14.3972 0.923580
\(244\) 22.7757 1.45806
\(245\) −1.00000 −0.0638877
\(246\) −5.88619 −0.375290
\(247\) 21.7095 1.38134
\(248\) 10.3887 0.659680
\(249\) 35.0950 2.22406
\(250\) 2.17211 0.137376
\(251\) 2.81828 0.177888 0.0889441 0.996037i \(-0.471651\pi\)
0.0889441 + 0.996037i \(0.471651\pi\)
\(252\) −18.1869 −1.14567
\(253\) 0.651968 0.0409889
\(254\) 39.4185 2.47334
\(255\) −21.1671 −1.32554
\(256\) −0.669499 −0.0418437
\(257\) −2.69672 −0.168217 −0.0841084 0.996457i \(-0.526804\pi\)
−0.0841084 + 0.996457i \(0.526804\pi\)
\(258\) 45.7399 2.84764
\(259\) −3.36922 −0.209353
\(260\) −8.30304 −0.514933
\(261\) 23.3725 1.44672
\(262\) 26.8903 1.66129
\(263\) 6.66574 0.411027 0.205514 0.978654i \(-0.434114\pi\)
0.205514 + 0.978654i \(0.434114\pi\)
\(264\) 0.499256 0.0307271
\(265\) −1.10328 −0.0677742
\(266\) 15.4366 0.946476
\(267\) 6.41236 0.392430
\(268\) 19.2466 1.17567
\(269\) −19.7870 −1.20644 −0.603218 0.797576i \(-0.706115\pi\)
−0.603218 + 0.797576i \(0.706115\pi\)
\(270\) 24.9594 1.51898
\(271\) 0.884167 0.0537093 0.0268547 0.999639i \(-0.491451\pi\)
0.0268547 + 0.999639i \(0.491451\pi\)
\(272\) −13.9275 −0.844478
\(273\) −9.50975 −0.575556
\(274\) −42.8971 −2.59151
\(275\) −0.102826 −0.00620064
\(276\) −53.6498 −3.22934
\(277\) 5.24972 0.315425 0.157712 0.987485i \(-0.449588\pi\)
0.157712 + 0.987485i \(0.449588\pi\)
\(278\) −0.336829 −0.0202017
\(279\) −44.5687 −2.66826
\(280\) −1.55967 −0.0932080
\(281\) 23.7773 1.41844 0.709218 0.704990i \(-0.249048\pi\)
0.709218 + 0.704990i \(0.249048\pi\)
\(282\) 19.6725 1.17148
\(283\) 9.39880 0.558700 0.279350 0.960189i \(-0.409881\pi\)
0.279350 + 0.960189i \(0.409881\pi\)
\(284\) −21.1507 −1.25506
\(285\) −22.1237 −1.31049
\(286\) 0.682283 0.0403442
\(287\) −0.870493 −0.0513836
\(288\) 50.6422 2.98412
\(289\) 29.2325 1.71956
\(290\) 7.58726 0.445539
\(291\) 3.62292 0.212380
\(292\) 20.6456 1.20819
\(293\) 26.8567 1.56898 0.784492 0.620138i \(-0.212924\pi\)
0.784492 + 0.620138i \(0.212924\pi\)
\(294\) −6.76191 −0.394362
\(295\) 5.23203 0.304620
\(296\) −5.25486 −0.305433
\(297\) −1.18156 −0.0685610
\(298\) −45.0774 −2.61126
\(299\) −19.3689 −1.12013
\(300\) 8.46145 0.488522
\(301\) 6.76435 0.389890
\(302\) 1.87913 0.108132
\(303\) 42.5532 2.44462
\(304\) −14.5569 −0.834894
\(305\) −8.37943 −0.479805
\(306\) −98.8228 −5.64932
\(307\) 10.1752 0.580728 0.290364 0.956916i \(-0.406224\pi\)
0.290364 + 0.956916i \(0.406224\pi\)
\(308\) 0.279485 0.0159252
\(309\) 15.1642 0.862661
\(310\) −14.4680 −0.821727
\(311\) 0.908506 0.0515167 0.0257583 0.999668i \(-0.491800\pi\)
0.0257583 + 0.999668i \(0.491800\pi\)
\(312\) −14.8321 −0.839700
\(313\) 13.8325 0.781862 0.390931 0.920420i \(-0.372153\pi\)
0.390931 + 0.920420i \(0.372153\pi\)
\(314\) 13.7964 0.778578
\(315\) 6.69117 0.377005
\(316\) 39.2156 2.20605
\(317\) 26.4053 1.48307 0.741536 0.670913i \(-0.234098\pi\)
0.741536 + 0.670913i \(0.234098\pi\)
\(318\) −7.46030 −0.418353
\(319\) −0.359175 −0.0201100
\(320\) 12.3430 0.689993
\(321\) −18.7005 −1.04376
\(322\) −13.7722 −0.767497
\(323\) 48.3218 2.68870
\(324\) 42.6686 2.37048
\(325\) 3.05479 0.169449
\(326\) −27.1696 −1.50478
\(327\) 40.6702 2.24907
\(328\) −1.35768 −0.0749653
\(329\) 2.90931 0.160395
\(330\) −0.695300 −0.0382750
\(331\) 26.2852 1.44476 0.722381 0.691495i \(-0.243047\pi\)
0.722381 + 0.691495i \(0.243047\pi\)
\(332\) 30.6418 1.68169
\(333\) 22.5440 1.23541
\(334\) 13.0923 0.716381
\(335\) −7.08104 −0.386879
\(336\) 6.37657 0.347870
\(337\) 21.5380 1.17325 0.586625 0.809858i \(-0.300456\pi\)
0.586625 + 0.809858i \(0.300456\pi\)
\(338\) 7.96790 0.433396
\(339\) −22.3001 −1.21117
\(340\) −18.4812 −1.00228
\(341\) 0.684904 0.0370897
\(342\) −103.289 −5.58521
\(343\) −1.00000 −0.0539949
\(344\) 10.5501 0.568825
\(345\) 19.7384 1.06268
\(346\) 35.3174 1.89867
\(347\) −5.63445 −0.302473 −0.151237 0.988498i \(-0.548326\pi\)
−0.151237 + 0.988498i \(0.548326\pi\)
\(348\) 29.5562 1.58438
\(349\) 18.0715 0.967343 0.483671 0.875250i \(-0.339303\pi\)
0.483671 + 0.875250i \(0.339303\pi\)
\(350\) 2.17211 0.116104
\(351\) 35.1021 1.87361
\(352\) −0.778240 −0.0414803
\(353\) −16.8473 −0.896689 −0.448345 0.893861i \(-0.647986\pi\)
−0.448345 + 0.893861i \(0.647986\pi\)
\(354\) 35.3785 1.88034
\(355\) 7.78159 0.413004
\(356\) 5.59869 0.296730
\(357\) −21.1671 −1.12028
\(358\) 9.92333 0.524464
\(359\) 1.86585 0.0984756 0.0492378 0.998787i \(-0.484321\pi\)
0.0492378 + 0.998787i \(0.484321\pi\)
\(360\) 10.4360 0.550026
\(361\) 31.5055 1.65819
\(362\) 14.1180 0.742027
\(363\) −34.2108 −1.79560
\(364\) −8.30304 −0.435198
\(365\) −7.59574 −0.397579
\(366\) −56.6609 −2.96171
\(367\) 9.71776 0.507263 0.253632 0.967301i \(-0.418375\pi\)
0.253632 + 0.967301i \(0.418375\pi\)
\(368\) 12.9874 0.677015
\(369\) 5.82462 0.303217
\(370\) 7.31830 0.380460
\(371\) −1.10328 −0.0572796
\(372\) −56.3601 −2.92214
\(373\) 31.9200 1.65275 0.826376 0.563118i \(-0.190398\pi\)
0.826376 + 0.563118i \(0.190398\pi\)
\(374\) 1.51865 0.0785275
\(375\) −3.11306 −0.160758
\(376\) 4.53756 0.234007
\(377\) 10.6705 0.549558
\(378\) 24.9594 1.28377
\(379\) 20.4226 1.04904 0.524520 0.851398i \(-0.324245\pi\)
0.524520 + 0.851398i \(0.324245\pi\)
\(380\) −19.3164 −0.990910
\(381\) −56.4947 −2.89431
\(382\) 33.6205 1.72017
\(383\) −29.1053 −1.48721 −0.743606 0.668618i \(-0.766886\pi\)
−0.743606 + 0.668618i \(0.766886\pi\)
\(384\) 36.3394 1.85444
\(385\) −0.102826 −0.00524050
\(386\) 5.48699 0.279281
\(387\) −45.2614 −2.30077
\(388\) 3.16321 0.160587
\(389\) −27.8679 −1.41296 −0.706480 0.707733i \(-0.749718\pi\)
−0.706480 + 0.707733i \(0.749718\pi\)
\(390\) 20.6562 1.04597
\(391\) −43.1119 −2.18026
\(392\) −1.55967 −0.0787751
\(393\) −38.5392 −1.94405
\(394\) 55.3296 2.78746
\(395\) −14.4279 −0.725945
\(396\) −1.87009 −0.0939754
\(397\) 14.4731 0.726382 0.363191 0.931715i \(-0.381687\pi\)
0.363191 + 0.931715i \(0.381687\pi\)
\(398\) 40.7700 2.04362
\(399\) −22.1237 −1.10757
\(400\) −2.04832 −0.102416
\(401\) 26.6313 1.32990 0.664952 0.746886i \(-0.268452\pi\)
0.664952 + 0.746886i \(0.268452\pi\)
\(402\) −47.8814 −2.38810
\(403\) −20.3474 −1.01357
\(404\) 37.1535 1.84846
\(405\) −15.6983 −0.780054
\(406\) 7.58726 0.376549
\(407\) −0.346443 −0.0171726
\(408\) −33.0137 −1.63442
\(409\) 9.38514 0.464065 0.232033 0.972708i \(-0.425462\pi\)
0.232033 + 0.972708i \(0.425462\pi\)
\(410\) 1.89080 0.0933801
\(411\) 61.4801 3.03259
\(412\) 13.2400 0.652288
\(413\) 5.23203 0.257451
\(414\) 92.1524 4.52904
\(415\) −11.2735 −0.553393
\(416\) 23.1202 1.13356
\(417\) 0.482744 0.0236401
\(418\) 1.58728 0.0776364
\(419\) 1.30305 0.0636582 0.0318291 0.999493i \(-0.489867\pi\)
0.0318291 + 0.999493i \(0.489867\pi\)
\(420\) 8.46145 0.412876
\(421\) 10.5958 0.516406 0.258203 0.966091i \(-0.416870\pi\)
0.258203 + 0.966091i \(0.416870\pi\)
\(422\) 49.9280 2.43046
\(423\) −19.4667 −0.946503
\(424\) −1.72076 −0.0835673
\(425\) 6.79945 0.329822
\(426\) 52.6184 2.54937
\(427\) −8.37943 −0.405509
\(428\) −16.3276 −0.789223
\(429\) −0.977849 −0.0472110
\(430\) −14.6929 −0.708553
\(431\) −36.0449 −1.73622 −0.868110 0.496372i \(-0.834665\pi\)
−0.868110 + 0.496372i \(0.834665\pi\)
\(432\) −23.5370 −1.13242
\(433\) −17.6845 −0.849862 −0.424931 0.905226i \(-0.639702\pi\)
−0.424931 + 0.905226i \(0.639702\pi\)
\(434\) −14.4680 −0.694486
\(435\) −10.8741 −0.521371
\(436\) 35.5095 1.70060
\(437\) −45.0602 −2.15552
\(438\) −51.3617 −2.45416
\(439\) 31.1139 1.48498 0.742492 0.669855i \(-0.233644\pi\)
0.742492 + 0.669855i \(0.233644\pi\)
\(440\) −0.160374 −0.00764555
\(441\) 6.69117 0.318627
\(442\) −45.1165 −2.14597
\(443\) −0.415957 −0.0197627 −0.00988136 0.999951i \(-0.503145\pi\)
−0.00988136 + 0.999951i \(0.503145\pi\)
\(444\) 28.5085 1.35295
\(445\) −2.05982 −0.0976450
\(446\) −21.0577 −0.997110
\(447\) 64.6050 3.05571
\(448\) 12.3430 0.583150
\(449\) −0.304179 −0.0143551 −0.00717754 0.999974i \(-0.502285\pi\)
−0.00717754 + 0.999974i \(0.502285\pi\)
\(450\) −14.5339 −0.685136
\(451\) −0.0895092 −0.00421483
\(452\) −19.4704 −0.915810
\(453\) −2.69317 −0.126536
\(454\) 32.0425 1.50383
\(455\) 3.05479 0.143211
\(456\) −34.5056 −1.61587
\(457\) −28.6458 −1.33999 −0.669996 0.742365i \(-0.733704\pi\)
−0.669996 + 0.742365i \(0.733704\pi\)
\(458\) −2.17211 −0.101496
\(459\) 78.1316 3.64687
\(460\) 17.2338 0.803528
\(461\) 6.42458 0.299223 0.149611 0.988745i \(-0.452198\pi\)
0.149611 + 0.988745i \(0.452198\pi\)
\(462\) −0.695300 −0.0323483
\(463\) −5.70188 −0.264989 −0.132494 0.991184i \(-0.542299\pi\)
−0.132494 + 0.991184i \(0.542299\pi\)
\(464\) −7.15488 −0.332157
\(465\) 20.7355 0.961588
\(466\) 3.66323 0.169696
\(467\) 36.1469 1.67268 0.836340 0.548212i \(-0.184691\pi\)
0.836340 + 0.548212i \(0.184691\pi\)
\(468\) 55.5571 2.56813
\(469\) −7.08104 −0.326972
\(470\) −6.31933 −0.291489
\(471\) −19.7731 −0.911095
\(472\) 8.16023 0.375605
\(473\) 0.695550 0.0319814
\(474\) −97.5599 −4.48108
\(475\) 7.10673 0.326079
\(476\) −18.4812 −0.847085
\(477\) 7.38226 0.338010
\(478\) 18.2720 0.835744
\(479\) −30.4520 −1.39139 −0.695694 0.718338i \(-0.744903\pi\)
−0.695694 + 0.718338i \(0.744903\pi\)
\(480\) −23.5613 −1.07542
\(481\) 10.2922 0.469286
\(482\) 1.96636 0.0895654
\(483\) 19.7384 0.898128
\(484\) −29.8697 −1.35772
\(485\) −1.16378 −0.0528445
\(486\) −31.2722 −1.41854
\(487\) 14.7751 0.669524 0.334762 0.942303i \(-0.391344\pi\)
0.334762 + 0.942303i \(0.391344\pi\)
\(488\) −13.0691 −0.591612
\(489\) 38.9395 1.76090
\(490\) 2.17211 0.0981257
\(491\) −8.63189 −0.389552 −0.194776 0.980848i \(-0.562398\pi\)
−0.194776 + 0.980848i \(0.562398\pi\)
\(492\) 7.36563 0.332068
\(493\) 23.7508 1.06968
\(494\) −47.1554 −2.12162
\(495\) 0.688026 0.0309245
\(496\) 13.6435 0.612611
\(497\) 7.78159 0.349052
\(498\) −76.2301 −3.41595
\(499\) 12.8633 0.575840 0.287920 0.957655i \(-0.407036\pi\)
0.287920 + 0.957655i \(0.407036\pi\)
\(500\) −2.71804 −0.121555
\(501\) −18.7640 −0.838312
\(502\) −6.12160 −0.273221
\(503\) 14.7692 0.658525 0.329262 0.944238i \(-0.393200\pi\)
0.329262 + 0.944238i \(0.393200\pi\)
\(504\) 10.4360 0.464857
\(505\) −13.6692 −0.608272
\(506\) −1.41614 −0.0629552
\(507\) −11.4196 −0.507162
\(508\) −49.3260 −2.18849
\(509\) −28.1750 −1.24883 −0.624417 0.781091i \(-0.714663\pi\)
−0.624417 + 0.781091i \(0.714663\pi\)
\(510\) 45.9773 2.03591
\(511\) −7.59574 −0.336016
\(512\) −21.8922 −0.967507
\(513\) 81.6624 3.60548
\(514\) 5.85756 0.258366
\(515\) −4.87115 −0.214648
\(516\) −57.2362 −2.51968
\(517\) 0.299153 0.0131567
\(518\) 7.31830 0.321548
\(519\) −50.6169 −2.22183
\(520\) 4.76445 0.208935
\(521\) −1.92597 −0.0843782 −0.0421891 0.999110i \(-0.513433\pi\)
−0.0421891 + 0.999110i \(0.513433\pi\)
\(522\) −50.7676 −2.22204
\(523\) 30.7122 1.34295 0.671476 0.741026i \(-0.265661\pi\)
0.671476 + 0.741026i \(0.265661\pi\)
\(524\) −33.6489 −1.46996
\(525\) −3.11306 −0.135865
\(526\) −14.4787 −0.631301
\(527\) −45.2899 −1.97286
\(528\) 0.655676 0.0285347
\(529\) 17.2019 0.747910
\(530\) 2.39645 0.104095
\(531\) −35.0084 −1.51923
\(532\) −19.3164 −0.837472
\(533\) 2.65917 0.115181
\(534\) −13.9283 −0.602738
\(535\) 6.00710 0.259710
\(536\) −11.0441 −0.477031
\(537\) −14.2221 −0.613730
\(538\) 42.9795 1.85298
\(539\) −0.102826 −0.00442903
\(540\) −31.2327 −1.34404
\(541\) 11.6957 0.502839 0.251420 0.967878i \(-0.419103\pi\)
0.251420 + 0.967878i \(0.419103\pi\)
\(542\) −1.92050 −0.0824927
\(543\) −20.2340 −0.868323
\(544\) 51.4617 2.20640
\(545\) −13.0643 −0.559615
\(546\) 20.6562 0.884003
\(547\) 17.7354 0.758312 0.379156 0.925333i \(-0.376214\pi\)
0.379156 + 0.925333i \(0.376214\pi\)
\(548\) 53.6788 2.29305
\(549\) 56.0682 2.39293
\(550\) 0.223349 0.00952363
\(551\) 24.8241 1.05754
\(552\) 30.7853 1.31031
\(553\) −14.4279 −0.613535
\(554\) −11.4029 −0.484464
\(555\) −10.4886 −0.445216
\(556\) 0.421488 0.0178751
\(557\) −21.6871 −0.918910 −0.459455 0.888201i \(-0.651955\pi\)
−0.459455 + 0.888201i \(0.651955\pi\)
\(558\) 96.8078 4.09820
\(559\) −20.6636 −0.873978
\(560\) −2.04832 −0.0865575
\(561\) −2.17653 −0.0918932
\(562\) −51.6468 −2.17859
\(563\) 0.814825 0.0343408 0.0171704 0.999853i \(-0.494534\pi\)
0.0171704 + 0.999853i \(0.494534\pi\)
\(564\) −24.6170 −1.03656
\(565\) 7.16338 0.301366
\(566\) −20.4152 −0.858114
\(567\) −15.6983 −0.659266
\(568\) 12.1367 0.509245
\(569\) 11.5836 0.485610 0.242805 0.970075i \(-0.421933\pi\)
0.242805 + 0.970075i \(0.421933\pi\)
\(570\) 48.0550 2.01280
\(571\) −15.6604 −0.655366 −0.327683 0.944788i \(-0.606268\pi\)
−0.327683 + 0.944788i \(0.606268\pi\)
\(572\) −0.853768 −0.0356979
\(573\) −48.1849 −2.01295
\(574\) 1.89080 0.0789206
\(575\) −6.34050 −0.264417
\(576\) −82.5889 −3.44120
\(577\) 24.9148 1.03722 0.518609 0.855012i \(-0.326450\pi\)
0.518609 + 0.855012i \(0.326450\pi\)
\(578\) −63.4962 −2.64109
\(579\) −7.86397 −0.326815
\(580\) −9.49424 −0.394227
\(581\) −11.2735 −0.467702
\(582\) −7.86937 −0.326196
\(583\) −0.113446 −0.00469846
\(584\) −11.8468 −0.490226
\(585\) −20.4401 −0.845094
\(586\) −58.3356 −2.40982
\(587\) 17.2353 0.711377 0.355689 0.934605i \(-0.384246\pi\)
0.355689 + 0.934605i \(0.384246\pi\)
\(588\) 8.46145 0.348944
\(589\) −47.3366 −1.95047
\(590\) −11.3645 −0.467870
\(591\) −79.2984 −3.26190
\(592\) −6.90125 −0.283640
\(593\) 38.7192 1.59001 0.795003 0.606606i \(-0.207469\pi\)
0.795003 + 0.606606i \(0.207469\pi\)
\(594\) 2.56647 0.105304
\(595\) 6.79945 0.278750
\(596\) 56.4072 2.31053
\(597\) −58.4316 −2.39145
\(598\) 42.0712 1.72042
\(599\) −15.3411 −0.626819 −0.313410 0.949618i \(-0.601471\pi\)
−0.313410 + 0.949618i \(0.601471\pi\)
\(600\) −4.85535 −0.198219
\(601\) −14.0883 −0.574675 −0.287337 0.957829i \(-0.592770\pi\)
−0.287337 + 0.957829i \(0.592770\pi\)
\(602\) −14.6929 −0.598837
\(603\) 47.3805 1.92948
\(604\) −2.35143 −0.0956782
\(605\) 10.9894 0.446784
\(606\) −92.4300 −3.75471
\(607\) −40.8918 −1.65975 −0.829874 0.557951i \(-0.811588\pi\)
−0.829874 + 0.557951i \(0.811588\pi\)
\(608\) 53.7873 2.18136
\(609\) −10.8741 −0.440639
\(610\) 18.2010 0.736937
\(611\) −8.88732 −0.359542
\(612\) 123.661 4.99870
\(613\) 20.4871 0.827465 0.413733 0.910398i \(-0.364225\pi\)
0.413733 + 0.910398i \(0.364225\pi\)
\(614\) −22.1015 −0.891946
\(615\) −2.70990 −0.109274
\(616\) −0.160374 −0.00646167
\(617\) −0.665042 −0.0267736 −0.0133868 0.999910i \(-0.504261\pi\)
−0.0133868 + 0.999910i \(0.504261\pi\)
\(618\) −32.9382 −1.32497
\(619\) 18.5476 0.745491 0.372745 0.927934i \(-0.378417\pi\)
0.372745 + 0.927934i \(0.378417\pi\)
\(620\) 18.1044 0.727090
\(621\) −72.8578 −2.92368
\(622\) −1.97337 −0.0791250
\(623\) −2.05982 −0.0825251
\(624\) −19.4790 −0.779786
\(625\) 1.00000 0.0400000
\(626\) −30.0457 −1.20087
\(627\) −2.27489 −0.0908504
\(628\) −17.2640 −0.688910
\(629\) 22.9088 0.913436
\(630\) −14.5339 −0.579046
\(631\) 46.8659 1.86570 0.932851 0.360262i \(-0.117313\pi\)
0.932851 + 0.360262i \(0.117313\pi\)
\(632\) −22.5027 −0.895109
\(633\) −71.5568 −2.84413
\(634\) −57.3552 −2.27787
\(635\) 18.1476 0.720166
\(636\) 9.33538 0.370172
\(637\) 3.05479 0.121035
\(638\) 0.780167 0.0308871
\(639\) −52.0680 −2.05978
\(640\) −11.6732 −0.461424
\(641\) 42.7847 1.68989 0.844947 0.534850i \(-0.179632\pi\)
0.844947 + 0.534850i \(0.179632\pi\)
\(642\) 40.6195 1.60312
\(643\) −25.2775 −0.996846 −0.498423 0.866934i \(-0.666087\pi\)
−0.498423 + 0.866934i \(0.666087\pi\)
\(644\) 17.2338 0.679105
\(645\) 21.0578 0.829152
\(646\) −104.960 −4.12960
\(647\) −38.8002 −1.52539 −0.762696 0.646757i \(-0.776125\pi\)
−0.762696 + 0.646757i \(0.776125\pi\)
\(648\) −24.4841 −0.961827
\(649\) 0.537988 0.0211179
\(650\) −6.63532 −0.260259
\(651\) 20.7355 0.812690
\(652\) 33.9984 1.33148
\(653\) 10.7403 0.420299 0.210149 0.977669i \(-0.432605\pi\)
0.210149 + 0.977669i \(0.432605\pi\)
\(654\) −88.3399 −3.45436
\(655\) 12.3798 0.483720
\(656\) −1.78305 −0.0696164
\(657\) 50.8244 1.98285
\(658\) −6.31933 −0.246353
\(659\) −39.6316 −1.54383 −0.771914 0.635727i \(-0.780700\pi\)
−0.771914 + 0.635727i \(0.780700\pi\)
\(660\) 0.870056 0.0338669
\(661\) −4.50623 −0.175272 −0.0876361 0.996153i \(-0.527931\pi\)
−0.0876361 + 0.996153i \(0.527931\pi\)
\(662\) −57.0941 −2.21903
\(663\) 64.6611 2.51123
\(664\) −17.5829 −0.682347
\(665\) 7.10673 0.275587
\(666\) −48.9680 −1.89747
\(667\) −22.1476 −0.857559
\(668\) −16.3830 −0.633876
\(669\) 30.1799 1.16682
\(670\) 15.3808 0.594211
\(671\) −0.861623 −0.0332626
\(672\) −23.5613 −0.908896
\(673\) 36.4948 1.40677 0.703386 0.710808i \(-0.251670\pi\)
0.703386 + 0.710808i \(0.251670\pi\)
\(674\) −46.7829 −1.80201
\(675\) 11.4909 0.442284
\(676\) −9.97055 −0.383483
\(677\) 31.0800 1.19450 0.597251 0.802054i \(-0.296259\pi\)
0.597251 + 0.802054i \(0.296259\pi\)
\(678\) 48.4381 1.86026
\(679\) −1.16378 −0.0446618
\(680\) 10.6049 0.406679
\(681\) −45.9233 −1.75979
\(682\) −1.48768 −0.0569664
\(683\) −16.2894 −0.623296 −0.311648 0.950198i \(-0.600881\pi\)
−0.311648 + 0.950198i \(0.600881\pi\)
\(684\) 129.249 4.94197
\(685\) −19.7491 −0.754573
\(686\) 2.17211 0.0829314
\(687\) 3.11306 0.118771
\(688\) 13.8556 0.528239
\(689\) 3.37029 0.128398
\(690\) −42.8739 −1.63218
\(691\) −18.6256 −0.708550 −0.354275 0.935141i \(-0.615272\pi\)
−0.354275 + 0.935141i \(0.615272\pi\)
\(692\) −44.1940 −1.68001
\(693\) 0.688026 0.0261360
\(694\) 12.2386 0.464572
\(695\) −0.155070 −0.00588215
\(696\) −16.9599 −0.642865
\(697\) 5.91887 0.224193
\(698\) −39.2531 −1.48575
\(699\) −5.25015 −0.198579
\(700\) −2.71804 −0.102732
\(701\) 11.3230 0.427663 0.213832 0.976871i \(-0.431406\pi\)
0.213832 + 0.976871i \(0.431406\pi\)
\(702\) −76.2455 −2.87770
\(703\) 23.9441 0.903070
\(704\) 1.26918 0.0478339
\(705\) 9.05687 0.341101
\(706\) 36.5940 1.37723
\(707\) −13.6692 −0.514084
\(708\) −44.2705 −1.66379
\(709\) 10.8956 0.409191 0.204595 0.978847i \(-0.434412\pi\)
0.204595 + 0.978847i \(0.434412\pi\)
\(710\) −16.9024 −0.634337
\(711\) 96.5394 3.62051
\(712\) −3.21264 −0.120399
\(713\) 42.2329 1.58163
\(714\) 45.9773 1.72066
\(715\) 0.314111 0.0117471
\(716\) −12.4175 −0.464062
\(717\) −26.1875 −0.977991
\(718\) −4.05281 −0.151250
\(719\) −27.6644 −1.03171 −0.515854 0.856677i \(-0.672525\pi\)
−0.515854 + 0.856677i \(0.672525\pi\)
\(720\) 13.7057 0.510781
\(721\) −4.87115 −0.181411
\(722\) −68.4334 −2.54683
\(723\) −2.81819 −0.104810
\(724\) −17.6665 −0.656569
\(725\) 3.49304 0.129728
\(726\) 74.3095 2.75788
\(727\) −19.8207 −0.735110 −0.367555 0.930002i \(-0.619805\pi\)
−0.367555 + 0.930002i \(0.619805\pi\)
\(728\) 4.76445 0.176582
\(729\) −2.27548 −0.0842770
\(730\) 16.4988 0.610646
\(731\) −45.9938 −1.70114
\(732\) 70.9021 2.62062
\(733\) 15.8034 0.583712 0.291856 0.956462i \(-0.405727\pi\)
0.291856 + 0.956462i \(0.405727\pi\)
\(734\) −21.1080 −0.779111
\(735\) −3.11306 −0.114827
\(736\) −47.9881 −1.76887
\(737\) −0.728115 −0.0268205
\(738\) −12.6517 −0.465715
\(739\) 21.7168 0.798866 0.399433 0.916762i \(-0.369207\pi\)
0.399433 + 0.916762i \(0.369207\pi\)
\(740\) −9.15769 −0.336643
\(741\) 67.5832 2.48273
\(742\) 2.39645 0.0879764
\(743\) 32.0473 1.17570 0.587850 0.808970i \(-0.299975\pi\)
0.587850 + 0.808970i \(0.299975\pi\)
\(744\) 32.3406 1.18566
\(745\) −20.7529 −0.760326
\(746\) −69.3335 −2.53848
\(747\) 75.4327 2.75994
\(748\) −1.90035 −0.0694836
\(749\) 6.00710 0.219495
\(750\) 6.76191 0.246910
\(751\) −9.55970 −0.348838 −0.174419 0.984671i \(-0.555805\pi\)
−0.174419 + 0.984671i \(0.555805\pi\)
\(752\) 5.95921 0.217310
\(753\) 8.77349 0.319724
\(754\) −23.1774 −0.844073
\(755\) 0.865117 0.0314848
\(756\) −31.2327 −1.13592
\(757\) 31.5331 1.14609 0.573044 0.819525i \(-0.305762\pi\)
0.573044 + 0.819525i \(0.305762\pi\)
\(758\) −44.3601 −1.61123
\(759\) 2.02962 0.0736705
\(760\) 11.0841 0.402064
\(761\) −13.8681 −0.502718 −0.251359 0.967894i \(-0.580877\pi\)
−0.251359 + 0.967894i \(0.580877\pi\)
\(762\) 122.712 4.44540
\(763\) −13.0643 −0.472961
\(764\) −42.0706 −1.52206
\(765\) −45.4963 −1.64492
\(766\) 63.2198 2.28423
\(767\) −15.9827 −0.577103
\(768\) −2.08419 −0.0752068
\(769\) −2.12500 −0.0766293 −0.0383146 0.999266i \(-0.512199\pi\)
−0.0383146 + 0.999266i \(0.512199\pi\)
\(770\) 0.223349 0.00804893
\(771\) −8.39507 −0.302341
\(772\) −6.86610 −0.247116
\(773\) 33.5625 1.20716 0.603580 0.797302i \(-0.293740\pi\)
0.603580 + 0.797302i \(0.293740\pi\)
\(774\) 98.3126 3.53377
\(775\) −6.66081 −0.239263
\(776\) −1.81511 −0.0651587
\(777\) −10.4886 −0.376276
\(778\) 60.5321 2.17018
\(779\) 6.18635 0.221649
\(780\) −25.8479 −0.925504
\(781\) 0.800150 0.0286316
\(782\) 93.6436 3.34869
\(783\) 40.1381 1.43442
\(784\) −2.04832 −0.0731544
\(785\) 6.35164 0.226700
\(786\) 83.7112 2.98588
\(787\) −43.0409 −1.53424 −0.767121 0.641502i \(-0.778312\pi\)
−0.767121 + 0.641502i \(0.778312\pi\)
\(788\) −69.2361 −2.46644
\(789\) 20.7509 0.738751
\(790\) 31.3389 1.11499
\(791\) 7.16338 0.254701
\(792\) 1.07309 0.0381307
\(793\) 25.5974 0.908989
\(794\) −31.4370 −1.11566
\(795\) −3.43459 −0.121812
\(796\) −51.0172 −1.80826
\(797\) 7.88948 0.279460 0.139730 0.990190i \(-0.455377\pi\)
0.139730 + 0.990190i \(0.455377\pi\)
\(798\) 48.0550 1.70113
\(799\) −19.7817 −0.699827
\(800\) 7.56851 0.267587
\(801\) 13.7826 0.486986
\(802\) −57.8460 −2.04261
\(803\) −0.781039 −0.0275623
\(804\) 59.9159 2.11307
\(805\) −6.34050 −0.223473
\(806\) 44.1966 1.55676
\(807\) −61.5983 −2.16836
\(808\) −21.3195 −0.750016
\(809\) 10.5509 0.370949 0.185474 0.982649i \(-0.440618\pi\)
0.185474 + 0.982649i \(0.440618\pi\)
\(810\) 34.0983 1.19809
\(811\) −0.824190 −0.0289412 −0.0144706 0.999895i \(-0.504606\pi\)
−0.0144706 + 0.999895i \(0.504606\pi\)
\(812\) −9.49424 −0.333183
\(813\) 2.75247 0.0965333
\(814\) 0.752511 0.0263755
\(815\) −12.5084 −0.438150
\(816\) −43.3571 −1.51780
\(817\) −48.0723 −1.68184
\(818\) −20.3855 −0.712763
\(819\) −20.4401 −0.714235
\(820\) −2.36604 −0.0826256
\(821\) 26.5713 0.927345 0.463673 0.886007i \(-0.346531\pi\)
0.463673 + 0.886007i \(0.346531\pi\)
\(822\) −133.541 −4.65779
\(823\) −0.216709 −0.00755401 −0.00377701 0.999993i \(-0.501202\pi\)
−0.00377701 + 0.999993i \(0.501202\pi\)
\(824\) −7.59737 −0.264667
\(825\) −0.320104 −0.0111446
\(826\) −11.3645 −0.395422
\(827\) 30.6375 1.06537 0.532686 0.846313i \(-0.321183\pi\)
0.532686 + 0.846313i \(0.321183\pi\)
\(828\) −115.314 −4.00744
\(829\) −39.5044 −1.37204 −0.686022 0.727581i \(-0.740645\pi\)
−0.686022 + 0.727581i \(0.740645\pi\)
\(830\) 24.4872 0.849962
\(831\) 16.3427 0.566922
\(832\) −37.7051 −1.30719
\(833\) 6.79945 0.235587
\(834\) −1.04857 −0.0363090
\(835\) 6.02749 0.208590
\(836\) −1.98623 −0.0686951
\(837\) −76.5385 −2.64556
\(838\) −2.83037 −0.0977734
\(839\) −31.3649 −1.08284 −0.541419 0.840753i \(-0.682113\pi\)
−0.541419 + 0.840753i \(0.682113\pi\)
\(840\) −4.85535 −0.167525
\(841\) −16.7987 −0.579264
\(842\) −23.0151 −0.793154
\(843\) 74.0203 2.54939
\(844\) −62.4769 −2.15054
\(845\) 3.66828 0.126193
\(846\) 42.2837 1.45374
\(847\) 10.9894 0.377601
\(848\) −2.25988 −0.0776047
\(849\) 29.2591 1.00417
\(850\) −14.7691 −0.506577
\(851\) −21.3625 −0.732298
\(852\) −65.8436 −2.25576
\(853\) −25.5673 −0.875406 −0.437703 0.899120i \(-0.644208\pi\)
−0.437703 + 0.899120i \(0.644208\pi\)
\(854\) 18.2010 0.622826
\(855\) −47.5523 −1.62626
\(856\) 9.36909 0.320229
\(857\) −31.7674 −1.08515 −0.542576 0.840007i \(-0.682551\pi\)
−0.542576 + 0.840007i \(0.682551\pi\)
\(858\) 2.12399 0.0725119
\(859\) 46.8125 1.59722 0.798611 0.601847i \(-0.205568\pi\)
0.798611 + 0.601847i \(0.205568\pi\)
\(860\) 18.3858 0.626950
\(861\) −2.70990 −0.0923532
\(862\) 78.2932 2.66668
\(863\) −24.8390 −0.845530 −0.422765 0.906239i \(-0.638940\pi\)
−0.422765 + 0.906239i \(0.638940\pi\)
\(864\) 86.9687 2.95874
\(865\) 16.2595 0.552840
\(866\) 38.4126 1.30531
\(867\) 91.0028 3.09062
\(868\) 18.1044 0.614503
\(869\) −1.48356 −0.0503263
\(870\) 23.6196 0.800780
\(871\) 21.6311 0.732941
\(872\) −20.3760 −0.690020
\(873\) 7.78706 0.263552
\(874\) 97.8755 3.31069
\(875\) 1.00000 0.0338062
\(876\) 64.2710 2.17151
\(877\) −35.1169 −1.18581 −0.592907 0.805271i \(-0.702020\pi\)
−0.592907 + 0.805271i \(0.702020\pi\)
\(878\) −67.5826 −2.28080
\(879\) 83.6066 2.81998
\(880\) −0.210621 −0.00710003
\(881\) 7.06882 0.238155 0.119077 0.992885i \(-0.462006\pi\)
0.119077 + 0.992885i \(0.462006\pi\)
\(882\) −14.5339 −0.489383
\(883\) −1.32433 −0.0445673 −0.0222836 0.999752i \(-0.507094\pi\)
−0.0222836 + 0.999752i \(0.507094\pi\)
\(884\) 56.4561 1.89883
\(885\) 16.2876 0.547503
\(886\) 0.903503 0.0303538
\(887\) 40.2163 1.35033 0.675166 0.737666i \(-0.264072\pi\)
0.675166 + 0.737666i \(0.264072\pi\)
\(888\) −16.3587 −0.548963
\(889\) 18.1476 0.608652
\(890\) 4.47416 0.149974
\(891\) −1.61419 −0.0540774
\(892\) 26.3503 0.882274
\(893\) −20.6757 −0.691885
\(894\) −140.329 −4.69330
\(895\) 4.56853 0.152709
\(896\) −11.6732 −0.389974
\(897\) −60.2965 −2.01324
\(898\) 0.660709 0.0220481
\(899\) −23.2665 −0.775981
\(900\) 18.1869 0.606230
\(901\) 7.50172 0.249919
\(902\) 0.194424 0.00647360
\(903\) 21.0578 0.700761
\(904\) 11.1725 0.371592
\(905\) 6.49969 0.216057
\(906\) 5.84984 0.194348
\(907\) 56.1213 1.86348 0.931738 0.363132i \(-0.118292\pi\)
0.931738 + 0.363132i \(0.118292\pi\)
\(908\) −40.0961 −1.33063
\(909\) 91.4631 3.03364
\(910\) −6.63532 −0.219959
\(911\) −40.2959 −1.33506 −0.667531 0.744582i \(-0.732649\pi\)
−0.667531 + 0.744582i \(0.732649\pi\)
\(912\) −45.3165 −1.50058
\(913\) −1.15920 −0.0383641
\(914\) 62.2216 2.05811
\(915\) −26.0857 −0.862367
\(916\) 2.71804 0.0898067
\(917\) 12.3798 0.408818
\(918\) −169.710 −5.60127
\(919\) −52.3469 −1.72676 −0.863382 0.504550i \(-0.831658\pi\)
−0.863382 + 0.504550i \(0.831658\pi\)
\(920\) −9.88907 −0.326033
\(921\) 31.6760 1.04376
\(922\) −13.9549 −0.459579
\(923\) −23.7711 −0.782435
\(924\) 0.870056 0.0286228
\(925\) 3.36922 0.110779
\(926\) 12.3851 0.406999
\(927\) 32.5937 1.07052
\(928\) 26.4371 0.867841
\(929\) −41.1491 −1.35006 −0.675029 0.737791i \(-0.735869\pi\)
−0.675029 + 0.737791i \(0.735869\pi\)
\(930\) −45.0398 −1.47691
\(931\) 7.10673 0.232914
\(932\) −4.58395 −0.150152
\(933\) 2.82824 0.0925924
\(934\) −78.5149 −2.56909
\(935\) 0.699160 0.0228650
\(936\) −31.8798 −1.04202
\(937\) 3.79567 0.123999 0.0619996 0.998076i \(-0.480252\pi\)
0.0619996 + 0.998076i \(0.480252\pi\)
\(938\) 15.3808 0.502200
\(939\) 43.0616 1.40526
\(940\) 7.90763 0.257919
\(941\) 7.14817 0.233024 0.116512 0.993189i \(-0.462829\pi\)
0.116512 + 0.993189i \(0.462829\pi\)
\(942\) 42.9492 1.39936
\(943\) −5.51936 −0.179735
\(944\) 10.7169 0.348805
\(945\) 11.4909 0.373798
\(946\) −1.51081 −0.0491206
\(947\) −16.1204 −0.523841 −0.261921 0.965089i \(-0.584356\pi\)
−0.261921 + 0.965089i \(0.584356\pi\)
\(948\) 122.081 3.96500
\(949\) 23.2034 0.753213
\(950\) −15.4366 −0.500828
\(951\) 82.2015 2.66557
\(952\) 10.6049 0.343706
\(953\) 25.3401 0.820848 0.410424 0.911895i \(-0.365381\pi\)
0.410424 + 0.911895i \(0.365381\pi\)
\(954\) −16.0351 −0.519154
\(955\) 15.4783 0.500865
\(956\) −22.8646 −0.739493
\(957\) −1.11814 −0.0361442
\(958\) 66.1450 2.13705
\(959\) −19.7491 −0.637731
\(960\) 38.4244 1.24014
\(961\) 13.3664 0.431175
\(962\) −22.3558 −0.720781
\(963\) −40.1946 −1.29525
\(964\) −2.46059 −0.0792502
\(965\) 2.52612 0.0813186
\(966\) −42.8739 −1.37944
\(967\) 32.9138 1.05844 0.529218 0.848486i \(-0.322485\pi\)
0.529218 + 0.848486i \(0.322485\pi\)
\(968\) 17.1399 0.550896
\(969\) 150.429 4.83248
\(970\) 2.52785 0.0811645
\(971\) 52.1076 1.67221 0.836106 0.548567i \(-0.184827\pi\)
0.836106 + 0.548567i \(0.184827\pi\)
\(972\) 39.1322 1.25517
\(973\) −0.155070 −0.00497132
\(974\) −32.0931 −1.02833
\(975\) 9.50975 0.304556
\(976\) −17.1638 −0.549399
\(977\) 45.8499 1.46687 0.733435 0.679760i \(-0.237916\pi\)
0.733435 + 0.679760i \(0.237916\pi\)
\(978\) −84.5806 −2.70459
\(979\) −0.211803 −0.00676926
\(980\) −2.71804 −0.0868247
\(981\) 87.4158 2.79097
\(982\) 18.7494 0.598317
\(983\) −31.5397 −1.00596 −0.502980 0.864298i \(-0.667763\pi\)
−0.502980 + 0.864298i \(0.667763\pi\)
\(984\) −4.22655 −0.134737
\(985\) 25.4728 0.811630
\(986\) −51.5892 −1.64293
\(987\) 9.05687 0.288283
\(988\) 59.0075 1.87728
\(989\) 42.8893 1.36380
\(990\) −1.49447 −0.0474972
\(991\) 32.0784 1.01900 0.509502 0.860469i \(-0.329829\pi\)
0.509502 + 0.860469i \(0.329829\pi\)
\(992\) −50.4124 −1.60060
\(993\) 81.8274 2.59671
\(994\) −16.9024 −0.536113
\(995\) 18.7698 0.595043
\(996\) 95.3898 3.02254
\(997\) −30.6817 −0.971699 −0.485849 0.874043i \(-0.661490\pi\)
−0.485849 + 0.874043i \(0.661490\pi\)
\(998\) −27.9404 −0.884438
\(999\) 38.7152 1.22490
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 \(a_p\))