Properties

Label 8013.2.a.d.1.18
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.17979 q^{2}\) \(+1.00000 q^{3}\) \(+2.75150 q^{4}\) \(+1.63083 q^{5}\) \(-2.17979 q^{6}\) \(+4.53329 q^{7}\) \(-1.63812 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.17979 q^{2}\) \(+1.00000 q^{3}\) \(+2.75150 q^{4}\) \(+1.63083 q^{5}\) \(-2.17979 q^{6}\) \(+4.53329 q^{7}\) \(-1.63812 q^{8}\) \(+1.00000 q^{9}\) \(-3.55488 q^{10}\) \(-1.15452 q^{11}\) \(+2.75150 q^{12}\) \(+6.10389 q^{13}\) \(-9.88164 q^{14}\) \(+1.63083 q^{15}\) \(-1.93224 q^{16}\) \(+3.44362 q^{17}\) \(-2.17979 q^{18}\) \(+0.492911 q^{19}\) \(+4.48724 q^{20}\) \(+4.53329 q^{21}\) \(+2.51661 q^{22}\) \(+4.54798 q^{23}\) \(-1.63812 q^{24}\) \(-2.34039 q^{25}\) \(-13.3052 q^{26}\) \(+1.00000 q^{27}\) \(+12.4734 q^{28}\) \(-4.65430 q^{29}\) \(-3.55488 q^{30}\) \(-1.04901 q^{31}\) \(+7.48812 q^{32}\) \(-1.15452 q^{33}\) \(-7.50639 q^{34}\) \(+7.39303 q^{35}\) \(+2.75150 q^{36}\) \(+4.71618 q^{37}\) \(-1.07445 q^{38}\) \(+6.10389 q^{39}\) \(-2.67150 q^{40}\) \(-1.03650 q^{41}\) \(-9.88164 q^{42}\) \(-4.05914 q^{43}\) \(-3.17666 q^{44}\) \(+1.63083 q^{45}\) \(-9.91367 q^{46}\) \(-1.52099 q^{47}\) \(-1.93224 q^{48}\) \(+13.5507 q^{49}\) \(+5.10157 q^{50}\) \(+3.44362 q^{51}\) \(+16.7949 q^{52}\) \(-4.35516 q^{53}\) \(-2.17979 q^{54}\) \(-1.88282 q^{55}\) \(-7.42609 q^{56}\) \(+0.492911 q^{57}\) \(+10.1454 q^{58}\) \(-2.85187 q^{59}\) \(+4.48724 q^{60}\) \(+0.275253 q^{61}\) \(+2.28663 q^{62}\) \(+4.53329 q^{63}\) \(-12.4581 q^{64}\) \(+9.95441 q^{65}\) \(+2.51661 q^{66}\) \(+11.9975 q^{67}\) \(+9.47514 q^{68}\) \(+4.54798 q^{69}\) \(-16.1153 q^{70}\) \(-2.51334 q^{71}\) \(-1.63812 q^{72}\) \(-3.11857 q^{73}\) \(-10.2803 q^{74}\) \(-2.34039 q^{75}\) \(+1.35625 q^{76}\) \(-5.23377 q^{77}\) \(-13.3052 q^{78}\) \(+13.7720 q^{79}\) \(-3.15115 q^{80}\) \(+1.00000 q^{81}\) \(+2.25935 q^{82}\) \(-8.00702 q^{83}\) \(+12.4734 q^{84}\) \(+5.61597 q^{85}\) \(+8.84809 q^{86}\) \(-4.65430 q^{87}\) \(+1.89124 q^{88}\) \(-1.95903 q^{89}\) \(-3.55488 q^{90}\) \(+27.6707 q^{91}\) \(+12.5138 q^{92}\) \(-1.04901 q^{93}\) \(+3.31545 q^{94}\) \(+0.803855 q^{95}\) \(+7.48812 q^{96}\) \(+3.14557 q^{97}\) \(-29.5378 q^{98}\) \(-1.15452 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.17979 −1.54135 −0.770674 0.637230i \(-0.780080\pi\)
−0.770674 + 0.637230i \(0.780080\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.75150 1.37575
\(5\) 1.63083 0.729330 0.364665 0.931139i \(-0.381184\pi\)
0.364665 + 0.931139i \(0.381184\pi\)
\(6\) −2.17979 −0.889897
\(7\) 4.53329 1.71342 0.856712 0.515796i \(-0.172504\pi\)
0.856712 + 0.515796i \(0.172504\pi\)
\(8\) −1.63812 −0.579164
\(9\) 1.00000 0.333333
\(10\) −3.55488 −1.12415
\(11\) −1.15452 −0.348100 −0.174050 0.984737i \(-0.555685\pi\)
−0.174050 + 0.984737i \(0.555685\pi\)
\(12\) 2.75150 0.794291
\(13\) 6.10389 1.69291 0.846457 0.532457i \(-0.178731\pi\)
0.846457 + 0.532457i \(0.178731\pi\)
\(14\) −9.88164 −2.64098
\(15\) 1.63083 0.421079
\(16\) −1.93224 −0.483059
\(17\) 3.44362 0.835201 0.417601 0.908631i \(-0.362871\pi\)
0.417601 + 0.908631i \(0.362871\pi\)
\(18\) −2.17979 −0.513782
\(19\) 0.492911 0.113082 0.0565408 0.998400i \(-0.481993\pi\)
0.0565408 + 0.998400i \(0.481993\pi\)
\(20\) 4.48724 1.00338
\(21\) 4.53329 0.989245
\(22\) 2.51661 0.536543
\(23\) 4.54798 0.948320 0.474160 0.880439i \(-0.342752\pi\)
0.474160 + 0.880439i \(0.342752\pi\)
\(24\) −1.63812 −0.334380
\(25\) −2.34039 −0.468078
\(26\) −13.3052 −2.60937
\(27\) 1.00000 0.192450
\(28\) 12.4734 2.35724
\(29\) −4.65430 −0.864281 −0.432141 0.901806i \(-0.642242\pi\)
−0.432141 + 0.901806i \(0.642242\pi\)
\(30\) −3.55488 −0.649029
\(31\) −1.04901 −0.188408 −0.0942039 0.995553i \(-0.530031\pi\)
−0.0942039 + 0.995553i \(0.530031\pi\)
\(32\) 7.48812 1.32373
\(33\) −1.15452 −0.200976
\(34\) −7.50639 −1.28734
\(35\) 7.39303 1.24965
\(36\) 2.75150 0.458584
\(37\) 4.71618 0.775335 0.387667 0.921799i \(-0.373281\pi\)
0.387667 + 0.921799i \(0.373281\pi\)
\(38\) −1.07445 −0.174298
\(39\) 6.10389 0.977405
\(40\) −2.67150 −0.422401
\(41\) −1.03650 −0.161874 −0.0809368 0.996719i \(-0.525791\pi\)
−0.0809368 + 0.996719i \(0.525791\pi\)
\(42\) −9.88164 −1.52477
\(43\) −4.05914 −0.619013 −0.309507 0.950897i \(-0.600164\pi\)
−0.309507 + 0.950897i \(0.600164\pi\)
\(44\) −3.17666 −0.478899
\(45\) 1.63083 0.243110
\(46\) −9.91367 −1.46169
\(47\) −1.52099 −0.221860 −0.110930 0.993828i \(-0.535383\pi\)
−0.110930 + 0.993828i \(0.535383\pi\)
\(48\) −1.93224 −0.278894
\(49\) 13.5507 1.93582
\(50\) 5.10157 0.721471
\(51\) 3.44362 0.482204
\(52\) 16.7949 2.32903
\(53\) −4.35516 −0.598227 −0.299113 0.954218i \(-0.596691\pi\)
−0.299113 + 0.954218i \(0.596691\pi\)
\(54\) −2.17979 −0.296632
\(55\) −1.88282 −0.253880
\(56\) −7.42609 −0.992352
\(57\) 0.492911 0.0652877
\(58\) 10.1454 1.33216
\(59\) −2.85187 −0.371282 −0.185641 0.982618i \(-0.559436\pi\)
−0.185641 + 0.982618i \(0.559436\pi\)
\(60\) 4.48724 0.579300
\(61\) 0.275253 0.0352425 0.0176213 0.999845i \(-0.494391\pi\)
0.0176213 + 0.999845i \(0.494391\pi\)
\(62\) 2.28663 0.290402
\(63\) 4.53329 0.571141
\(64\) −12.4581 −1.55726
\(65\) 9.95441 1.23469
\(66\) 2.51661 0.309773
\(67\) 11.9975 1.46573 0.732867 0.680372i \(-0.238182\pi\)
0.732867 + 0.680372i \(0.238182\pi\)
\(68\) 9.47514 1.14903
\(69\) 4.54798 0.547513
\(70\) −16.1153 −1.92615
\(71\) −2.51334 −0.298279 −0.149140 0.988816i \(-0.547650\pi\)
−0.149140 + 0.988816i \(0.547650\pi\)
\(72\) −1.63812 −0.193055
\(73\) −3.11857 −0.365001 −0.182500 0.983206i \(-0.558419\pi\)
−0.182500 + 0.983206i \(0.558419\pi\)
\(74\) −10.2803 −1.19506
\(75\) −2.34039 −0.270245
\(76\) 1.35625 0.155572
\(77\) −5.23377 −0.596443
\(78\) −13.3052 −1.50652
\(79\) 13.7720 1.54947 0.774736 0.632285i \(-0.217883\pi\)
0.774736 + 0.632285i \(0.217883\pi\)
\(80\) −3.15115 −0.352309
\(81\) 1.00000 0.111111
\(82\) 2.25935 0.249504
\(83\) −8.00702 −0.878885 −0.439442 0.898271i \(-0.644824\pi\)
−0.439442 + 0.898271i \(0.644824\pi\)
\(84\) 12.4734 1.36096
\(85\) 5.61597 0.609137
\(86\) 8.84809 0.954114
\(87\) −4.65430 −0.498993
\(88\) 1.89124 0.201607
\(89\) −1.95903 −0.207656 −0.103828 0.994595i \(-0.533109\pi\)
−0.103828 + 0.994595i \(0.533109\pi\)
\(90\) −3.55488 −0.374717
\(91\) 27.6707 2.90068
\(92\) 12.5138 1.30465
\(93\) −1.04901 −0.108777
\(94\) 3.31545 0.341963
\(95\) 0.803855 0.0824738
\(96\) 7.48812 0.764253
\(97\) 3.14557 0.319384 0.159692 0.987167i \(-0.448950\pi\)
0.159692 + 0.987167i \(0.448950\pi\)
\(98\) −29.5378 −2.98377
\(99\) −1.15452 −0.116033
\(100\) −6.43959 −0.643959
\(101\) 4.69030 0.466702 0.233351 0.972393i \(-0.425031\pi\)
0.233351 + 0.972393i \(0.425031\pi\)
\(102\) −7.50639 −0.743243
\(103\) −7.82999 −0.771511 −0.385756 0.922601i \(-0.626059\pi\)
−0.385756 + 0.922601i \(0.626059\pi\)
\(104\) −9.99892 −0.980475
\(105\) 7.39303 0.721486
\(106\) 9.49334 0.922075
\(107\) −14.9438 −1.44467 −0.722335 0.691543i \(-0.756931\pi\)
−0.722335 + 0.691543i \(0.756931\pi\)
\(108\) 2.75150 0.264764
\(109\) 13.4912 1.29222 0.646110 0.763244i \(-0.276395\pi\)
0.646110 + 0.763244i \(0.276395\pi\)
\(110\) 4.10417 0.391317
\(111\) 4.71618 0.447640
\(112\) −8.75939 −0.827685
\(113\) −11.0642 −1.04083 −0.520415 0.853914i \(-0.674223\pi\)
−0.520415 + 0.853914i \(0.674223\pi\)
\(114\) −1.07445 −0.100631
\(115\) 7.41699 0.691638
\(116\) −12.8063 −1.18904
\(117\) 6.10389 0.564305
\(118\) 6.21649 0.572275
\(119\) 15.6109 1.43105
\(120\) −2.67150 −0.243874
\(121\) −9.66709 −0.878826
\(122\) −0.599995 −0.0543210
\(123\) −1.03650 −0.0934578
\(124\) −2.88636 −0.259202
\(125\) −11.9709 −1.07071
\(126\) −9.88164 −0.880327
\(127\) 2.00617 0.178019 0.0890094 0.996031i \(-0.471630\pi\)
0.0890094 + 0.996031i \(0.471630\pi\)
\(128\) 12.1798 1.07656
\(129\) −4.05914 −0.357387
\(130\) −21.6986 −1.90309
\(131\) 7.84744 0.685634 0.342817 0.939402i \(-0.388619\pi\)
0.342817 + 0.939402i \(0.388619\pi\)
\(132\) −3.17666 −0.276493
\(133\) 2.23451 0.193757
\(134\) −26.1522 −2.25920
\(135\) 1.63083 0.140360
\(136\) −5.64107 −0.483718
\(137\) 16.4274 1.40349 0.701743 0.712430i \(-0.252406\pi\)
0.701743 + 0.712430i \(0.252406\pi\)
\(138\) −9.91367 −0.843907
\(139\) 21.5126 1.82468 0.912338 0.409439i \(-0.134275\pi\)
0.912338 + 0.409439i \(0.134275\pi\)
\(140\) 20.3420 1.71921
\(141\) −1.52099 −0.128091
\(142\) 5.47857 0.459752
\(143\) −7.04705 −0.589304
\(144\) −1.93224 −0.161020
\(145\) −7.59037 −0.630346
\(146\) 6.79784 0.562593
\(147\) 13.5507 1.11765
\(148\) 12.9766 1.06667
\(149\) 14.5067 1.18844 0.594220 0.804303i \(-0.297461\pi\)
0.594220 + 0.804303i \(0.297461\pi\)
\(150\) 5.10157 0.416541
\(151\) −10.8123 −0.879896 −0.439948 0.898023i \(-0.645003\pi\)
−0.439948 + 0.898023i \(0.645003\pi\)
\(152\) −0.807449 −0.0654928
\(153\) 3.44362 0.278400
\(154\) 11.4085 0.919326
\(155\) −1.71076 −0.137411
\(156\) 16.7949 1.34467
\(157\) 12.3685 0.987114 0.493557 0.869714i \(-0.335697\pi\)
0.493557 + 0.869714i \(0.335697\pi\)
\(158\) −30.0201 −2.38827
\(159\) −4.35516 −0.345386
\(160\) 12.2119 0.965433
\(161\) 20.6173 1.62487
\(162\) −2.17979 −0.171261
\(163\) 6.71431 0.525906 0.262953 0.964809i \(-0.415304\pi\)
0.262953 + 0.964809i \(0.415304\pi\)
\(164\) −2.85193 −0.222698
\(165\) −1.88282 −0.146578
\(166\) 17.4537 1.35467
\(167\) −1.41567 −0.109548 −0.0547740 0.998499i \(-0.517444\pi\)
−0.0547740 + 0.998499i \(0.517444\pi\)
\(168\) −7.42609 −0.572935
\(169\) 24.2575 1.86596
\(170\) −12.2417 −0.938892
\(171\) 0.492911 0.0376939
\(172\) −11.1687 −0.851609
\(173\) −1.06716 −0.0811344 −0.0405672 0.999177i \(-0.512916\pi\)
−0.0405672 + 0.999177i \(0.512916\pi\)
\(174\) 10.1454 0.769122
\(175\) −10.6097 −0.802016
\(176\) 2.23080 0.168153
\(177\) −2.85187 −0.214360
\(178\) 4.27027 0.320071
\(179\) 4.04251 0.302152 0.151076 0.988522i \(-0.451726\pi\)
0.151076 + 0.988522i \(0.451726\pi\)
\(180\) 4.48724 0.334459
\(181\) 0.853466 0.0634376 0.0317188 0.999497i \(-0.489902\pi\)
0.0317188 + 0.999497i \(0.489902\pi\)
\(182\) −60.3165 −4.47095
\(183\) 0.275253 0.0203473
\(184\) −7.45015 −0.549232
\(185\) 7.69129 0.565475
\(186\) 2.28663 0.167664
\(187\) −3.97572 −0.290734
\(188\) −4.18502 −0.305224
\(189\) 4.53329 0.329748
\(190\) −1.75224 −0.127121
\(191\) 8.25710 0.597463 0.298731 0.954337i \(-0.403437\pi\)
0.298731 + 0.954337i \(0.403437\pi\)
\(192\) −12.4581 −0.899086
\(193\) −5.80293 −0.417704 −0.208852 0.977947i \(-0.566973\pi\)
−0.208852 + 0.977947i \(0.566973\pi\)
\(194\) −6.85670 −0.492282
\(195\) 9.95441 0.712850
\(196\) 37.2849 2.66321
\(197\) −15.0440 −1.07184 −0.535919 0.844269i \(-0.680035\pi\)
−0.535919 + 0.844269i \(0.680035\pi\)
\(198\) 2.51661 0.178848
\(199\) −9.37057 −0.664262 −0.332131 0.943233i \(-0.607768\pi\)
−0.332131 + 0.943233i \(0.607768\pi\)
\(200\) 3.83384 0.271094
\(201\) 11.9975 0.846241
\(202\) −10.2239 −0.719350
\(203\) −21.0993 −1.48088
\(204\) 9.47514 0.663392
\(205\) −1.69035 −0.118059
\(206\) 17.0678 1.18917
\(207\) 4.54798 0.316107
\(208\) −11.7942 −0.817778
\(209\) −0.569075 −0.0393637
\(210\) −16.1153 −1.11206
\(211\) −4.02616 −0.277173 −0.138586 0.990350i \(-0.544256\pi\)
−0.138586 + 0.990350i \(0.544256\pi\)
\(212\) −11.9832 −0.823011
\(213\) −2.51334 −0.172212
\(214\) 32.5744 2.22674
\(215\) −6.61977 −0.451465
\(216\) −1.63812 −0.111460
\(217\) −4.75547 −0.322822
\(218\) −29.4080 −1.99176
\(219\) −3.11857 −0.210733
\(220\) −5.18060 −0.349276
\(221\) 21.0195 1.41392
\(222\) −10.2803 −0.689968
\(223\) 25.4422 1.70374 0.851869 0.523755i \(-0.175469\pi\)
0.851869 + 0.523755i \(0.175469\pi\)
\(224\) 33.9458 2.26810
\(225\) −2.34039 −0.156026
\(226\) 24.1176 1.60428
\(227\) −26.6520 −1.76895 −0.884476 0.466585i \(-0.845484\pi\)
−0.884476 + 0.466585i \(0.845484\pi\)
\(228\) 1.35625 0.0898197
\(229\) −16.1440 −1.06683 −0.533414 0.845855i \(-0.679091\pi\)
−0.533414 + 0.845855i \(0.679091\pi\)
\(230\) −16.1675 −1.06605
\(231\) −5.23377 −0.344357
\(232\) 7.62431 0.500560
\(233\) −1.34141 −0.0878787 −0.0439393 0.999034i \(-0.513991\pi\)
−0.0439393 + 0.999034i \(0.513991\pi\)
\(234\) −13.3052 −0.869790
\(235\) −2.48048 −0.161809
\(236\) −7.84693 −0.510792
\(237\) 13.7720 0.894588
\(238\) −34.0287 −2.20575
\(239\) 23.7540 1.53652 0.768258 0.640140i \(-0.221124\pi\)
0.768258 + 0.640140i \(0.221124\pi\)
\(240\) −3.15115 −0.203406
\(241\) −4.96650 −0.319921 −0.159960 0.987123i \(-0.551137\pi\)
−0.159960 + 0.987123i \(0.551137\pi\)
\(242\) 21.0723 1.35458
\(243\) 1.00000 0.0641500
\(244\) 0.757359 0.0484850
\(245\) 22.0990 1.41185
\(246\) 2.25935 0.144051
\(247\) 3.00868 0.191438
\(248\) 1.71841 0.109119
\(249\) −8.00702 −0.507424
\(250\) 26.0942 1.65034
\(251\) 22.0859 1.39405 0.697026 0.717046i \(-0.254506\pi\)
0.697026 + 0.717046i \(0.254506\pi\)
\(252\) 12.4734 0.785748
\(253\) −5.25073 −0.330110
\(254\) −4.37304 −0.274389
\(255\) 5.61597 0.351685
\(256\) −1.63335 −0.102084
\(257\) −0.893955 −0.0557634 −0.0278817 0.999611i \(-0.508876\pi\)
−0.0278817 + 0.999611i \(0.508876\pi\)
\(258\) 8.84809 0.550858
\(259\) 21.3798 1.32848
\(260\) 27.3896 1.69863
\(261\) −4.65430 −0.288094
\(262\) −17.1058 −1.05680
\(263\) 3.24703 0.200220 0.100110 0.994976i \(-0.468080\pi\)
0.100110 + 0.994976i \(0.468080\pi\)
\(264\) 1.89124 0.116398
\(265\) −7.10252 −0.436305
\(266\) −4.87077 −0.298646
\(267\) −1.95903 −0.119890
\(268\) 33.0113 2.01648
\(269\) −15.7408 −0.959732 −0.479866 0.877342i \(-0.659315\pi\)
−0.479866 + 0.877342i \(0.659315\pi\)
\(270\) −3.55488 −0.216343
\(271\) −32.7396 −1.98879 −0.994395 0.105732i \(-0.966282\pi\)
−0.994395 + 0.105732i \(0.966282\pi\)
\(272\) −6.65389 −0.403452
\(273\) 27.6707 1.67471
\(274\) −35.8083 −2.16326
\(275\) 2.70202 0.162938
\(276\) 12.5138 0.753241
\(277\) −0.345505 −0.0207594 −0.0103797 0.999946i \(-0.503304\pi\)
−0.0103797 + 0.999946i \(0.503304\pi\)
\(278\) −46.8931 −2.81246
\(279\) −1.04901 −0.0628026
\(280\) −12.1107 −0.723752
\(281\) 0.308444 0.0184002 0.00920011 0.999958i \(-0.497071\pi\)
0.00920011 + 0.999958i \(0.497071\pi\)
\(282\) 3.31545 0.197432
\(283\) −26.2140 −1.55826 −0.779129 0.626863i \(-0.784338\pi\)
−0.779129 + 0.626863i \(0.784338\pi\)
\(284\) −6.91547 −0.410358
\(285\) 0.803855 0.0476163
\(286\) 15.3611 0.908322
\(287\) −4.69874 −0.277358
\(288\) 7.48812 0.441242
\(289\) −5.14146 −0.302439
\(290\) 16.5455 0.971583
\(291\) 3.14557 0.184397
\(292\) −8.58075 −0.502150
\(293\) −8.17898 −0.477821 −0.238910 0.971042i \(-0.576790\pi\)
−0.238910 + 0.971042i \(0.576790\pi\)
\(294\) −29.5378 −1.72268
\(295\) −4.65092 −0.270787
\(296\) −7.72567 −0.449046
\(297\) −1.15452 −0.0669919
\(298\) −31.6217 −1.83180
\(299\) 27.7604 1.60542
\(300\) −6.43959 −0.371790
\(301\) −18.4013 −1.06063
\(302\) 23.5687 1.35623
\(303\) 4.69030 0.269451
\(304\) −0.952422 −0.0546251
\(305\) 0.448891 0.0257034
\(306\) −7.50639 −0.429112
\(307\) 16.9485 0.967303 0.483652 0.875261i \(-0.339310\pi\)
0.483652 + 0.875261i \(0.339310\pi\)
\(308\) −14.4007 −0.820557
\(309\) −7.82999 −0.445432
\(310\) 3.72910 0.211799
\(311\) 11.8198 0.670238 0.335119 0.942176i \(-0.391223\pi\)
0.335119 + 0.942176i \(0.391223\pi\)
\(312\) −9.99892 −0.566077
\(313\) 27.5235 1.55572 0.777861 0.628436i \(-0.216305\pi\)
0.777861 + 0.628436i \(0.216305\pi\)
\(314\) −26.9608 −1.52148
\(315\) 7.39303 0.416550
\(316\) 37.8937 2.13169
\(317\) −34.7997 −1.95454 −0.977272 0.211990i \(-0.932006\pi\)
−0.977272 + 0.211990i \(0.932006\pi\)
\(318\) 9.49334 0.532360
\(319\) 5.37347 0.300857
\(320\) −20.3170 −1.13576
\(321\) −14.9438 −0.834080
\(322\) −44.9415 −2.50449
\(323\) 1.69740 0.0944459
\(324\) 2.75150 0.152861
\(325\) −14.2855 −0.792416
\(326\) −14.6358 −0.810603
\(327\) 13.4912 0.746064
\(328\) 1.69791 0.0937513
\(329\) −6.89511 −0.380140
\(330\) 4.10417 0.225927
\(331\) −22.9707 −1.26258 −0.631292 0.775545i \(-0.717475\pi\)
−0.631292 + 0.775545i \(0.717475\pi\)
\(332\) −22.0313 −1.20913
\(333\) 4.71618 0.258445
\(334\) 3.08587 0.168852
\(335\) 19.5660 1.06900
\(336\) −8.75939 −0.477864
\(337\) 17.0561 0.929103 0.464551 0.885546i \(-0.346216\pi\)
0.464551 + 0.885546i \(0.346216\pi\)
\(338\) −52.8763 −2.87609
\(339\) −11.0642 −0.600923
\(340\) 15.4524 0.838021
\(341\) 1.21110 0.0655848
\(342\) −1.07445 −0.0580994
\(343\) 29.6964 1.60345
\(344\) 6.64937 0.358510
\(345\) 7.41699 0.399317
\(346\) 2.32618 0.125056
\(347\) −19.6245 −1.05350 −0.526750 0.850020i \(-0.676590\pi\)
−0.526750 + 0.850020i \(0.676590\pi\)
\(348\) −12.8063 −0.686491
\(349\) 3.99745 0.213978 0.106989 0.994260i \(-0.465879\pi\)
0.106989 + 0.994260i \(0.465879\pi\)
\(350\) 23.1269 1.23618
\(351\) 6.10389 0.325802
\(352\) −8.64517 −0.460789
\(353\) −13.8631 −0.737860 −0.368930 0.929457i \(-0.620276\pi\)
−0.368930 + 0.929457i \(0.620276\pi\)
\(354\) 6.21649 0.330403
\(355\) −4.09884 −0.217544
\(356\) −5.39027 −0.285684
\(357\) 15.6109 0.826219
\(358\) −8.81185 −0.465721
\(359\) −12.4302 −0.656042 −0.328021 0.944670i \(-0.606382\pi\)
−0.328021 + 0.944670i \(0.606382\pi\)
\(360\) −2.67150 −0.140800
\(361\) −18.7570 −0.987213
\(362\) −1.86038 −0.0977794
\(363\) −9.66709 −0.507391
\(364\) 76.1361 3.99061
\(365\) −5.08586 −0.266206
\(366\) −0.599995 −0.0313622
\(367\) 6.43692 0.336004 0.168002 0.985787i \(-0.446268\pi\)
0.168002 + 0.985787i \(0.446268\pi\)
\(368\) −8.78778 −0.458095
\(369\) −1.03650 −0.0539579
\(370\) −16.7654 −0.871593
\(371\) −19.7432 −1.02502
\(372\) −2.88636 −0.149651
\(373\) 2.47213 0.128002 0.0640009 0.997950i \(-0.479614\pi\)
0.0640009 + 0.997950i \(0.479614\pi\)
\(374\) 8.66626 0.448122
\(375\) −11.9709 −0.618176
\(376\) 2.49157 0.128493
\(377\) −28.4093 −1.46315
\(378\) −9.88164 −0.508257
\(379\) −2.74509 −0.141006 −0.0705030 0.997512i \(-0.522460\pi\)
−0.0705030 + 0.997512i \(0.522460\pi\)
\(380\) 2.21181 0.113463
\(381\) 2.00617 0.102779
\(382\) −17.9988 −0.920898
\(383\) 16.1841 0.826970 0.413485 0.910511i \(-0.364311\pi\)
0.413485 + 0.910511i \(0.364311\pi\)
\(384\) 12.1798 0.621550
\(385\) −8.53539 −0.435004
\(386\) 12.6492 0.643827
\(387\) −4.05914 −0.206338
\(388\) 8.65505 0.439393
\(389\) 27.3775 1.38809 0.694047 0.719929i \(-0.255826\pi\)
0.694047 + 0.719929i \(0.255826\pi\)
\(390\) −21.6986 −1.09875
\(391\) 15.6615 0.792038
\(392\) −22.1978 −1.12116
\(393\) 7.84744 0.395851
\(394\) 32.7927 1.65207
\(395\) 22.4598 1.13008
\(396\) −3.17666 −0.159633
\(397\) 2.20323 0.110577 0.0552886 0.998470i \(-0.482392\pi\)
0.0552886 + 0.998470i \(0.482392\pi\)
\(398\) 20.4259 1.02386
\(399\) 2.23451 0.111865
\(400\) 4.52219 0.226109
\(401\) −15.5911 −0.778582 −0.389291 0.921115i \(-0.627280\pi\)
−0.389291 + 0.921115i \(0.627280\pi\)
\(402\) −26.1522 −1.30435
\(403\) −6.40304 −0.318958
\(404\) 12.9054 0.642066
\(405\) 1.63083 0.0810366
\(406\) 45.9921 2.28255
\(407\) −5.44491 −0.269894
\(408\) −5.64107 −0.279275
\(409\) 5.54101 0.273986 0.136993 0.990572i \(-0.456256\pi\)
0.136993 + 0.990572i \(0.456256\pi\)
\(410\) 3.68462 0.181970
\(411\) 16.4274 0.810303
\(412\) −21.5442 −1.06141
\(413\) −12.9284 −0.636163
\(414\) −9.91367 −0.487230
\(415\) −13.0581 −0.640997
\(416\) 45.7067 2.24095
\(417\) 21.5126 1.05348
\(418\) 1.24047 0.0606732
\(419\) −28.6015 −1.39728 −0.698638 0.715475i \(-0.746210\pi\)
−0.698638 + 0.715475i \(0.746210\pi\)
\(420\) 20.3420 0.992586
\(421\) 1.57986 0.0769976 0.0384988 0.999259i \(-0.487742\pi\)
0.0384988 + 0.999259i \(0.487742\pi\)
\(422\) 8.77621 0.427219
\(423\) −1.52099 −0.0739532
\(424\) 7.13428 0.346471
\(425\) −8.05942 −0.390939
\(426\) 5.47857 0.265438
\(427\) 1.24780 0.0603853
\(428\) −41.1179 −1.98751
\(429\) −7.04705 −0.340235
\(430\) 14.4297 0.695864
\(431\) 3.66565 0.176568 0.0882841 0.996095i \(-0.471862\pi\)
0.0882841 + 0.996095i \(0.471862\pi\)
\(432\) −1.93224 −0.0929648
\(433\) −16.2380 −0.780349 −0.390175 0.920741i \(-0.627585\pi\)
−0.390175 + 0.920741i \(0.627585\pi\)
\(434\) 10.3659 0.497581
\(435\) −7.59037 −0.363931
\(436\) 37.1210 1.77777
\(437\) 2.24175 0.107238
\(438\) 6.79784 0.324813
\(439\) −24.1196 −1.15116 −0.575582 0.817744i \(-0.695225\pi\)
−0.575582 + 0.817744i \(0.695225\pi\)
\(440\) 3.08430 0.147038
\(441\) 13.5507 0.645273
\(442\) −45.8182 −2.17935
\(443\) 17.3975 0.826580 0.413290 0.910599i \(-0.364380\pi\)
0.413290 + 0.910599i \(0.364380\pi\)
\(444\) 12.9766 0.615841
\(445\) −3.19484 −0.151450
\(446\) −55.4588 −2.62605
\(447\) 14.5067 0.686146
\(448\) −56.4762 −2.66825
\(449\) −20.4504 −0.965114 −0.482557 0.875865i \(-0.660292\pi\)
−0.482557 + 0.875865i \(0.660292\pi\)
\(450\) 5.10157 0.240490
\(451\) 1.19665 0.0563483
\(452\) −30.4431 −1.43192
\(453\) −10.8123 −0.508008
\(454\) 58.0958 2.72657
\(455\) 45.1263 2.11555
\(456\) −0.807449 −0.0378123
\(457\) −36.7314 −1.71822 −0.859110 0.511791i \(-0.828982\pi\)
−0.859110 + 0.511791i \(0.828982\pi\)
\(458\) 35.1907 1.64435
\(459\) 3.44362 0.160735
\(460\) 20.4079 0.951522
\(461\) −26.9436 −1.25489 −0.627444 0.778661i \(-0.715899\pi\)
−0.627444 + 0.778661i \(0.715899\pi\)
\(462\) 11.4085 0.530773
\(463\) −3.90576 −0.181516 −0.0907580 0.995873i \(-0.528929\pi\)
−0.0907580 + 0.995873i \(0.528929\pi\)
\(464\) 8.99321 0.417499
\(465\) −1.71076 −0.0793345
\(466\) 2.92400 0.135452
\(467\) 3.14731 0.145640 0.0728202 0.997345i \(-0.476800\pi\)
0.0728202 + 0.997345i \(0.476800\pi\)
\(468\) 16.7949 0.776343
\(469\) 54.3884 2.51142
\(470\) 5.40694 0.249404
\(471\) 12.3685 0.569910
\(472\) 4.67171 0.215033
\(473\) 4.68635 0.215479
\(474\) −30.0201 −1.37887
\(475\) −1.15360 −0.0529310
\(476\) 42.9536 1.96877
\(477\) −4.35516 −0.199409
\(478\) −51.7788 −2.36831
\(479\) 2.02660 0.0925977 0.0462989 0.998928i \(-0.485257\pi\)
0.0462989 + 0.998928i \(0.485257\pi\)
\(480\) 12.2119 0.557393
\(481\) 28.7870 1.31258
\(482\) 10.8260 0.493109
\(483\) 20.6173 0.938121
\(484\) −26.5990 −1.20905
\(485\) 5.12989 0.232937
\(486\) −2.17979 −0.0988775
\(487\) 5.13673 0.232767 0.116384 0.993204i \(-0.462870\pi\)
0.116384 + 0.993204i \(0.462870\pi\)
\(488\) −0.450898 −0.0204112
\(489\) 6.71431 0.303632
\(490\) −48.1712 −2.17615
\(491\) −20.8634 −0.941554 −0.470777 0.882252i \(-0.656026\pi\)
−0.470777 + 0.882252i \(0.656026\pi\)
\(492\) −2.85193 −0.128575
\(493\) −16.0276 −0.721849
\(494\) −6.55830 −0.295072
\(495\) −1.88282 −0.0846266
\(496\) 2.02694 0.0910121
\(497\) −11.3937 −0.511078
\(498\) 17.4537 0.782117
\(499\) 16.8504 0.754329 0.377164 0.926146i \(-0.376899\pi\)
0.377164 + 0.926146i \(0.376899\pi\)
\(500\) −32.9381 −1.47304
\(501\) −1.41567 −0.0632476
\(502\) −48.1428 −2.14872
\(503\) −33.3536 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(504\) −7.42609 −0.330784
\(505\) 7.64908 0.340380
\(506\) 11.4455 0.508815
\(507\) 24.2575 1.07731
\(508\) 5.51998 0.244910
\(509\) 1.42920 0.0633481 0.0316741 0.999498i \(-0.489916\pi\)
0.0316741 + 0.999498i \(0.489916\pi\)
\(510\) −12.2417 −0.542069
\(511\) −14.1374 −0.625401
\(512\) −20.7993 −0.919208
\(513\) 0.492911 0.0217626
\(514\) 1.94864 0.0859508
\(515\) −12.7694 −0.562686
\(516\) −11.1687 −0.491676
\(517\) 1.75601 0.0772294
\(518\) −46.6036 −2.04764
\(519\) −1.06716 −0.0468430
\(520\) −16.3065 −0.715089
\(521\) 6.51591 0.285467 0.142734 0.989761i \(-0.454411\pi\)
0.142734 + 0.989761i \(0.454411\pi\)
\(522\) 10.1454 0.444053
\(523\) −22.6740 −0.991465 −0.495733 0.868475i \(-0.665100\pi\)
−0.495733 + 0.868475i \(0.665100\pi\)
\(524\) 21.5923 0.943262
\(525\) −10.6097 −0.463044
\(526\) −7.07786 −0.308609
\(527\) −3.61240 −0.157358
\(528\) 2.23080 0.0970832
\(529\) −2.31586 −0.100690
\(530\) 15.4820 0.672497
\(531\) −2.85187 −0.123761
\(532\) 6.14826 0.266561
\(533\) −6.32667 −0.274038
\(534\) 4.27027 0.184793
\(535\) −24.3708 −1.05364
\(536\) −19.6534 −0.848899
\(537\) 4.04251 0.174447
\(538\) 34.3117 1.47928
\(539\) −15.6446 −0.673859
\(540\) 4.48724 0.193100
\(541\) 14.8620 0.638969 0.319485 0.947591i \(-0.396490\pi\)
0.319485 + 0.947591i \(0.396490\pi\)
\(542\) 71.3656 3.06542
\(543\) 0.853466 0.0366257
\(544\) 25.7863 1.10558
\(545\) 22.0018 0.942455
\(546\) −60.3165 −2.58131
\(547\) 44.3623 1.89680 0.948398 0.317083i \(-0.102703\pi\)
0.948398 + 0.317083i \(0.102703\pi\)
\(548\) 45.2000 1.93085
\(549\) 0.275253 0.0117475
\(550\) −5.88985 −0.251144
\(551\) −2.29416 −0.0977344
\(552\) −7.45015 −0.317099
\(553\) 62.4325 2.65490
\(554\) 0.753130 0.0319974
\(555\) 7.69129 0.326477
\(556\) 59.1920 2.51030
\(557\) −2.12701 −0.0901245 −0.0450622 0.998984i \(-0.514349\pi\)
−0.0450622 + 0.998984i \(0.514349\pi\)
\(558\) 2.28663 0.0968006
\(559\) −24.7766 −1.04794
\(560\) −14.2851 −0.603655
\(561\) −3.97572 −0.167855
\(562\) −0.672344 −0.0283611
\(563\) −6.43249 −0.271097 −0.135549 0.990771i \(-0.543280\pi\)
−0.135549 + 0.990771i \(0.543280\pi\)
\(564\) −4.18502 −0.176221
\(565\) −18.0438 −0.759108
\(566\) 57.1410 2.40182
\(567\) 4.53329 0.190380
\(568\) 4.11716 0.172752
\(569\) 4.61534 0.193485 0.0967426 0.995309i \(-0.469158\pi\)
0.0967426 + 0.995309i \(0.469158\pi\)
\(570\) −1.75224 −0.0733932
\(571\) 3.45289 0.144499 0.0722494 0.997387i \(-0.476982\pi\)
0.0722494 + 0.997387i \(0.476982\pi\)
\(572\) −19.3900 −0.810736
\(573\) 8.25710 0.344945
\(574\) 10.2423 0.427505
\(575\) −10.6441 −0.443888
\(576\) −12.4581 −0.519087
\(577\) −11.9006 −0.495430 −0.247715 0.968833i \(-0.579680\pi\)
−0.247715 + 0.968833i \(0.579680\pi\)
\(578\) 11.2073 0.466163
\(579\) −5.80293 −0.241162
\(580\) −20.8849 −0.867200
\(581\) −36.2982 −1.50590
\(582\) −6.85670 −0.284219
\(583\) 5.02811 0.208243
\(584\) 5.10860 0.211395
\(585\) 9.95441 0.411564
\(586\) 17.8285 0.736488
\(587\) −28.1860 −1.16336 −0.581680 0.813417i \(-0.697605\pi\)
−0.581680 + 0.813417i \(0.697605\pi\)
\(588\) 37.2849 1.53760
\(589\) −0.517069 −0.0213055
\(590\) 10.1381 0.417377
\(591\) −15.0440 −0.618826
\(592\) −9.11277 −0.374533
\(593\) 23.0557 0.946785 0.473392 0.880852i \(-0.343029\pi\)
0.473392 + 0.880852i \(0.343029\pi\)
\(594\) 2.51661 0.103258
\(595\) 25.4588 1.04371
\(596\) 39.9154 1.63500
\(597\) −9.37057 −0.383512
\(598\) −60.5119 −2.47452
\(599\) 2.66205 0.108769 0.0543843 0.998520i \(-0.482680\pi\)
0.0543843 + 0.998520i \(0.482680\pi\)
\(600\) 3.83384 0.156516
\(601\) −15.0959 −0.615776 −0.307888 0.951423i \(-0.599622\pi\)
−0.307888 + 0.951423i \(0.599622\pi\)
\(602\) 40.1110 1.63480
\(603\) 11.9975 0.488578
\(604\) −29.7502 −1.21052
\(605\) −15.7654 −0.640954
\(606\) −10.2239 −0.415317
\(607\) −8.67904 −0.352272 −0.176136 0.984366i \(-0.556360\pi\)
−0.176136 + 0.984366i \(0.556360\pi\)
\(608\) 3.69098 0.149689
\(609\) −21.0993 −0.854986
\(610\) −0.978490 −0.0396179
\(611\) −9.28398 −0.375590
\(612\) 9.47514 0.383010
\(613\) 17.3213 0.699602 0.349801 0.936824i \(-0.386249\pi\)
0.349801 + 0.936824i \(0.386249\pi\)
\(614\) −36.9443 −1.49095
\(615\) −1.69035 −0.0681616
\(616\) 8.57355 0.345438
\(617\) −8.91856 −0.359048 −0.179524 0.983754i \(-0.557456\pi\)
−0.179524 + 0.983754i \(0.557456\pi\)
\(618\) 17.0678 0.686566
\(619\) −22.3800 −0.899526 −0.449763 0.893148i \(-0.648492\pi\)
−0.449763 + 0.893148i \(0.648492\pi\)
\(620\) −4.70716 −0.189044
\(621\) 4.54798 0.182504
\(622\) −25.7647 −1.03307
\(623\) −8.88084 −0.355803
\(624\) −11.7942 −0.472144
\(625\) −7.82062 −0.312825
\(626\) −59.9957 −2.39791
\(627\) −0.569075 −0.0227267
\(628\) 34.0320 1.35802
\(629\) 16.2407 0.647560
\(630\) −16.1153 −0.642049
\(631\) 18.1087 0.720898 0.360449 0.932779i \(-0.382624\pi\)
0.360449 + 0.932779i \(0.382624\pi\)
\(632\) −22.5602 −0.897398
\(633\) −4.02616 −0.160026
\(634\) 75.8561 3.01263
\(635\) 3.27172 0.129834
\(636\) −11.9832 −0.475166
\(637\) 82.7122 3.27718
\(638\) −11.7131 −0.463725
\(639\) −2.51334 −0.0994264
\(640\) 19.8633 0.785164
\(641\) −43.6139 −1.72264 −0.861322 0.508059i \(-0.830363\pi\)
−0.861322 + 0.508059i \(0.830363\pi\)
\(642\) 32.5744 1.28561
\(643\) −14.7281 −0.580820 −0.290410 0.956902i \(-0.593792\pi\)
−0.290410 + 0.956902i \(0.593792\pi\)
\(644\) 56.7286 2.23542
\(645\) −6.61977 −0.260653
\(646\) −3.69998 −0.145574
\(647\) 11.9559 0.470035 0.235017 0.971991i \(-0.424485\pi\)
0.235017 + 0.971991i \(0.424485\pi\)
\(648\) −1.63812 −0.0643515
\(649\) 3.29254 0.129243
\(650\) 31.1394 1.22139
\(651\) −4.75547 −0.186382
\(652\) 18.4745 0.723515
\(653\) 47.9051 1.87467 0.937336 0.348428i \(-0.113284\pi\)
0.937336 + 0.348428i \(0.113284\pi\)
\(654\) −29.4080 −1.14994
\(655\) 12.7979 0.500053
\(656\) 2.00276 0.0781946
\(657\) −3.11857 −0.121667
\(658\) 15.0299 0.585927
\(659\) 12.2393 0.476774 0.238387 0.971170i \(-0.423381\pi\)
0.238387 + 0.971170i \(0.423381\pi\)
\(660\) −5.18060 −0.201654
\(661\) 29.4299 1.14469 0.572345 0.820013i \(-0.306034\pi\)
0.572345 + 0.820013i \(0.306034\pi\)
\(662\) 50.0714 1.94608
\(663\) 21.0195 0.816330
\(664\) 13.1165 0.509018
\(665\) 3.64411 0.141313
\(666\) −10.2803 −0.398353
\(667\) −21.1677 −0.819615
\(668\) −3.89523 −0.150711
\(669\) 25.4422 0.983654
\(670\) −42.6498 −1.64770
\(671\) −0.317784 −0.0122679
\(672\) 33.9458 1.30949
\(673\) −3.97781 −0.153333 −0.0766666 0.997057i \(-0.524428\pi\)
−0.0766666 + 0.997057i \(0.524428\pi\)
\(674\) −37.1787 −1.43207
\(675\) −2.34039 −0.0900817
\(676\) 66.7445 2.56710
\(677\) −8.74837 −0.336227 −0.168114 0.985768i \(-0.553768\pi\)
−0.168114 + 0.985768i \(0.553768\pi\)
\(678\) 24.1176 0.926231
\(679\) 14.2598 0.547240
\(680\) −9.19964 −0.352790
\(681\) −26.6520 −1.02131
\(682\) −2.63995 −0.101089
\(683\) 37.5479 1.43673 0.718365 0.695666i \(-0.244891\pi\)
0.718365 + 0.695666i \(0.244891\pi\)
\(684\) 1.35625 0.0518574
\(685\) 26.7903 1.02360
\(686\) −64.7320 −2.47148
\(687\) −16.1440 −0.615933
\(688\) 7.84322 0.299020
\(689\) −26.5834 −1.01275
\(690\) −16.1675 −0.615487
\(691\) 36.3728 1.38369 0.691843 0.722048i \(-0.256799\pi\)
0.691843 + 0.722048i \(0.256799\pi\)
\(692\) −2.93628 −0.111621
\(693\) −5.23377 −0.198814
\(694\) 42.7775 1.62381
\(695\) 35.0834 1.33079
\(696\) 7.62431 0.288999
\(697\) −3.56931 −0.135197
\(698\) −8.71361 −0.329815
\(699\) −1.34141 −0.0507368
\(700\) −29.1925 −1.10337
\(701\) 32.5890 1.23087 0.615436 0.788187i \(-0.288980\pi\)
0.615436 + 0.788187i \(0.288980\pi\)
\(702\) −13.3052 −0.502173
\(703\) 2.32466 0.0876761
\(704\) 14.3831 0.542083
\(705\) −2.48048 −0.0934204
\(706\) 30.2188 1.13730
\(707\) 21.2625 0.799658
\(708\) −7.84693 −0.294906
\(709\) 36.3783 1.36621 0.683107 0.730318i \(-0.260628\pi\)
0.683107 + 0.730318i \(0.260628\pi\)
\(710\) 8.93463 0.335311
\(711\) 13.7720 0.516491
\(712\) 3.20912 0.120267
\(713\) −4.77088 −0.178671
\(714\) −34.0287 −1.27349
\(715\) −11.4925 −0.429797
\(716\) 11.1230 0.415686
\(717\) 23.7540 0.887108
\(718\) 27.0953 1.01119
\(719\) 9.61553 0.358599 0.179299 0.983795i \(-0.442617\pi\)
0.179299 + 0.983795i \(0.442617\pi\)
\(720\) −3.15115 −0.117436
\(721\) −35.4956 −1.32193
\(722\) 40.8865 1.52164
\(723\) −4.96650 −0.184706
\(724\) 2.34831 0.0872744
\(725\) 10.8929 0.404551
\(726\) 21.0723 0.782065
\(727\) −2.49390 −0.0924936 −0.0462468 0.998930i \(-0.514726\pi\)
−0.0462468 + 0.998930i \(0.514726\pi\)
\(728\) −45.3280 −1.67997
\(729\) 1.00000 0.0370370
\(730\) 11.0861 0.410316
\(731\) −13.9782 −0.517001
\(732\) 0.757359 0.0279928
\(733\) −10.8910 −0.402269 −0.201135 0.979564i \(-0.564463\pi\)
−0.201135 + 0.979564i \(0.564463\pi\)
\(734\) −14.0312 −0.517900
\(735\) 22.0990 0.815132
\(736\) 34.0559 1.25532
\(737\) −13.8514 −0.510222
\(738\) 2.25935 0.0831678
\(739\) −3.47767 −0.127928 −0.0639641 0.997952i \(-0.520374\pi\)
−0.0639641 + 0.997952i \(0.520374\pi\)
\(740\) 21.1626 0.777953
\(741\) 3.00868 0.110527
\(742\) 43.0361 1.57990
\(743\) 44.5423 1.63410 0.817049 0.576568i \(-0.195608\pi\)
0.817049 + 0.576568i \(0.195608\pi\)
\(744\) 1.71841 0.0629999
\(745\) 23.6581 0.866764
\(746\) −5.38873 −0.197295
\(747\) −8.00702 −0.292962
\(748\) −10.9392 −0.399977
\(749\) −67.7445 −2.47533
\(750\) 26.0942 0.952825
\(751\) −0.0646940 −0.00236072 −0.00118036 0.999999i \(-0.500376\pi\)
−0.00118036 + 0.999999i \(0.500376\pi\)
\(752\) 2.93892 0.107171
\(753\) 22.0859 0.804856
\(754\) 61.9265 2.25523
\(755\) −17.6331 −0.641734
\(756\) 12.4734 0.453652
\(757\) 22.7616 0.827286 0.413643 0.910439i \(-0.364256\pi\)
0.413643 + 0.910439i \(0.364256\pi\)
\(758\) 5.98374 0.217339
\(759\) −5.25073 −0.190589
\(760\) −1.31681 −0.0477658
\(761\) −0.985556 −0.0357264 −0.0178632 0.999840i \(-0.505686\pi\)
−0.0178632 + 0.999840i \(0.505686\pi\)
\(762\) −4.37304 −0.158418
\(763\) 61.1594 2.21412
\(764\) 22.7194 0.821960
\(765\) 5.61597 0.203046
\(766\) −35.2781 −1.27465
\(767\) −17.4075 −0.628549
\(768\) −1.63335 −0.0589384
\(769\) −48.1988 −1.73809 −0.869046 0.494731i \(-0.835266\pi\)
−0.869046 + 0.494731i \(0.835266\pi\)
\(770\) 18.6054 0.670492
\(771\) −0.893955 −0.0321950
\(772\) −15.9668 −0.574657
\(773\) −21.7147 −0.781022 −0.390511 0.920598i \(-0.627702\pi\)
−0.390511 + 0.920598i \(0.627702\pi\)
\(774\) 8.84809 0.318038
\(775\) 2.45509 0.0881896
\(776\) −5.15283 −0.184976
\(777\) 21.3798 0.766996
\(778\) −59.6773 −2.13954
\(779\) −0.510901 −0.0183049
\(780\) 27.3896 0.980705
\(781\) 2.90170 0.103831
\(782\) −34.1389 −1.22081
\(783\) −4.65430 −0.166331
\(784\) −26.1832 −0.935115
\(785\) 20.1709 0.719931
\(786\) −17.1058 −0.610144
\(787\) 15.8704 0.565718 0.282859 0.959161i \(-0.408717\pi\)
0.282859 + 0.959161i \(0.408717\pi\)
\(788\) −41.3935 −1.47458
\(789\) 3.24703 0.115597
\(790\) −48.9578 −1.74184
\(791\) −50.1571 −1.78338
\(792\) 1.89124 0.0672023
\(793\) 1.68011 0.0596626
\(794\) −4.80260 −0.170438
\(795\) −7.10252 −0.251901
\(796\) −25.7832 −0.913860
\(797\) −32.6977 −1.15821 −0.579106 0.815252i \(-0.696598\pi\)
−0.579106 + 0.815252i \(0.696598\pi\)
\(798\) −4.87077 −0.172424
\(799\) −5.23773 −0.185297
\(800\) −17.5251 −0.619607
\(801\) −1.95903 −0.0692188
\(802\) 33.9854 1.20007
\(803\) 3.60044 0.127057
\(804\) 33.0113 1.16422
\(805\) 33.6234 1.18507
\(806\) 13.9573 0.491626
\(807\) −15.7408 −0.554102
\(808\) −7.68328 −0.270297
\(809\) −44.3864 −1.56054 −0.780271 0.625442i \(-0.784919\pi\)
−0.780271 + 0.625442i \(0.784919\pi\)
\(810\) −3.55488 −0.124906
\(811\) −37.2685 −1.30867 −0.654337 0.756203i \(-0.727052\pi\)
−0.654337 + 0.756203i \(0.727052\pi\)
\(812\) −58.0548 −2.03732
\(813\) −32.7396 −1.14823
\(814\) 11.8688 0.416001
\(815\) 10.9499 0.383559
\(816\) −6.65389 −0.232933
\(817\) −2.00080 −0.0699990
\(818\) −12.0783 −0.422307
\(819\) 27.6707 0.966893
\(820\) −4.65101 −0.162420
\(821\) 13.9394 0.486488 0.243244 0.969965i \(-0.421788\pi\)
0.243244 + 0.969965i \(0.421788\pi\)
\(822\) −35.8083 −1.24896
\(823\) 0.322759 0.0112507 0.00562533 0.999984i \(-0.498209\pi\)
0.00562533 + 0.999984i \(0.498209\pi\)
\(824\) 12.8265 0.446831
\(825\) 2.70202 0.0940723
\(826\) 28.1812 0.980549
\(827\) 10.9789 0.381775 0.190887 0.981612i \(-0.438863\pi\)
0.190887 + 0.981612i \(0.438863\pi\)
\(828\) 12.5138 0.434884
\(829\) −2.10954 −0.0732674 −0.0366337 0.999329i \(-0.511663\pi\)
−0.0366337 + 0.999329i \(0.511663\pi\)
\(830\) 28.4640 0.987999
\(831\) −0.345505 −0.0119854
\(832\) −76.0428 −2.63631
\(833\) 46.6636 1.61680
\(834\) −46.8931 −1.62377
\(835\) −2.30872 −0.0798966
\(836\) −1.56581 −0.0541547
\(837\) −1.04901 −0.0362591
\(838\) 62.3455 2.15369
\(839\) −57.2323 −1.97588 −0.987940 0.154839i \(-0.950514\pi\)
−0.987940 + 0.154839i \(0.950514\pi\)
\(840\) −12.1107 −0.417859
\(841\) −7.33751 −0.253018
\(842\) −3.44377 −0.118680
\(843\) 0.308444 0.0106234
\(844\) −11.0780 −0.381321
\(845\) 39.5598 1.36090
\(846\) 3.31545 0.113988
\(847\) −43.8237 −1.50580
\(848\) 8.41519 0.288979
\(849\) −26.2140 −0.899661
\(850\) 17.5679 0.602573
\(851\) 21.4491 0.735265
\(852\) −6.91547 −0.236920
\(853\) −33.3498 −1.14188 −0.570938 0.820993i \(-0.693420\pi\)
−0.570938 + 0.820993i \(0.693420\pi\)
\(854\) −2.71995 −0.0930748
\(855\) 0.803855 0.0274913
\(856\) 24.4797 0.836700
\(857\) 10.1400 0.346377 0.173189 0.984889i \(-0.444593\pi\)
0.173189 + 0.984889i \(0.444593\pi\)
\(858\) 15.3611 0.524420
\(859\) −15.3223 −0.522791 −0.261396 0.965232i \(-0.584183\pi\)
−0.261396 + 0.965232i \(0.584183\pi\)
\(860\) −18.2143 −0.621103
\(861\) −4.69874 −0.160133
\(862\) −7.99037 −0.272153
\(863\) 9.54726 0.324992 0.162496 0.986709i \(-0.448045\pi\)
0.162496 + 0.986709i \(0.448045\pi\)
\(864\) 7.48812 0.254751
\(865\) −1.74035 −0.0591737
\(866\) 35.3955 1.20279
\(867\) −5.14146 −0.174613
\(868\) −13.0847 −0.444123
\(869\) −15.9000 −0.539372
\(870\) 16.5455 0.560943
\(871\) 73.2317 2.48136
\(872\) −22.1002 −0.748407
\(873\) 3.14557 0.106461
\(874\) −4.88656 −0.165290
\(875\) −54.2677 −1.83458
\(876\) −8.58075 −0.289917
\(877\) 17.0313 0.575107 0.287554 0.957765i \(-0.407158\pi\)
0.287554 + 0.957765i \(0.407158\pi\)
\(878\) 52.5757 1.77434
\(879\) −8.17898 −0.275870
\(880\) 3.63806 0.122639
\(881\) 44.4861 1.49878 0.749388 0.662132i \(-0.230348\pi\)
0.749388 + 0.662132i \(0.230348\pi\)
\(882\) −29.5378 −0.994590
\(883\) −11.3791 −0.382937 −0.191468 0.981499i \(-0.561325\pi\)
−0.191468 + 0.981499i \(0.561325\pi\)
\(884\) 57.8352 1.94521
\(885\) −4.65092 −0.156339
\(886\) −37.9230 −1.27405
\(887\) 34.2017 1.14838 0.574191 0.818721i \(-0.305317\pi\)
0.574191 + 0.818721i \(0.305317\pi\)
\(888\) −7.72567 −0.259257
\(889\) 9.09456 0.305022
\(890\) 6.96410 0.233437
\(891\) −1.15452 −0.0386778
\(892\) 70.0044 2.34392
\(893\) −0.749715 −0.0250883
\(894\) −31.6217 −1.05759
\(895\) 6.59266 0.220368
\(896\) 55.2147 1.84460
\(897\) 27.7604 0.926892
\(898\) 44.5776 1.48758
\(899\) 4.88241 0.162837
\(900\) −6.43959 −0.214653
\(901\) −14.9975 −0.499640
\(902\) −2.60846 −0.0868522
\(903\) −18.4013 −0.612356
\(904\) 18.1245 0.602811
\(905\) 1.39186 0.0462669
\(906\) 23.5687 0.783017
\(907\) −9.62682 −0.319653 −0.159827 0.987145i \(-0.551094\pi\)
−0.159827 + 0.987145i \(0.551094\pi\)
\(908\) −73.3330 −2.43364
\(909\) 4.69030 0.155567
\(910\) −98.3660 −3.26080
\(911\) 44.1868 1.46397 0.731986 0.681319i \(-0.238593\pi\)
0.731986 + 0.681319i \(0.238593\pi\)
\(912\) −0.952422 −0.0315378
\(913\) 9.24425 0.305940
\(914\) 80.0668 2.64837
\(915\) 0.448891 0.0148399
\(916\) −44.4203 −1.46769
\(917\) 35.5747 1.17478
\(918\) −7.50639 −0.247748
\(919\) 32.6517 1.07708 0.538540 0.842600i \(-0.318976\pi\)
0.538540 + 0.842600i \(0.318976\pi\)
\(920\) −12.1499 −0.400572
\(921\) 16.9485 0.558473
\(922\) 58.7315 1.93422
\(923\) −15.3412 −0.504961
\(924\) −14.4007 −0.473749
\(925\) −11.0377 −0.362917
\(926\) 8.51375 0.279779
\(927\) −7.82999 −0.257170
\(928\) −34.8520 −1.14407
\(929\) −22.4039 −0.735048 −0.367524 0.930014i \(-0.619794\pi\)
−0.367524 + 0.930014i \(0.619794\pi\)
\(930\) 3.72910 0.122282
\(931\) 6.67931 0.218906
\(932\) −3.69089 −0.120899
\(933\) 11.8198 0.386962
\(934\) −6.86050 −0.224482
\(935\) −6.48373 −0.212041
\(936\) −9.99892 −0.326825
\(937\) −36.7918 −1.20194 −0.600968 0.799273i \(-0.705218\pi\)
−0.600968 + 0.799273i \(0.705218\pi\)
\(938\) −118.555 −3.87097
\(939\) 27.5235 0.898197
\(940\) −6.82506 −0.222609
\(941\) 11.2183 0.365707 0.182853 0.983140i \(-0.441467\pi\)
0.182853 + 0.983140i \(0.441467\pi\)
\(942\) −26.9608 −0.878430
\(943\) −4.71397 −0.153508
\(944\) 5.51049 0.179351
\(945\) 7.39303 0.240495
\(946\) −10.2153 −0.332128
\(947\) 19.6133 0.637345 0.318673 0.947865i \(-0.396763\pi\)
0.318673 + 0.947865i \(0.396763\pi\)
\(948\) 37.8937 1.23073
\(949\) −19.0354 −0.617915
\(950\) 2.51462 0.0815851
\(951\) −34.7997 −1.12846
\(952\) −25.5726 −0.828814
\(953\) −1.84865 −0.0598836 −0.0299418 0.999552i \(-0.509532\pi\)
−0.0299418 + 0.999552i \(0.509532\pi\)
\(954\) 9.49334 0.307358
\(955\) 13.4659 0.435747
\(956\) 65.3591 2.11386
\(957\) 5.37347 0.173700
\(958\) −4.41757 −0.142725
\(959\) 74.4701 2.40476
\(960\) −20.3170 −0.655730
\(961\) −29.8996 −0.964502
\(962\) −62.7498 −2.02313
\(963\) −14.9438 −0.481557
\(964\) −13.6653 −0.440131
\(965\) −9.46360 −0.304644
\(966\) −44.9415 −1.44597
\(967\) 41.0913 1.32141 0.660703 0.750647i \(-0.270258\pi\)
0.660703 + 0.750647i \(0.270258\pi\)
\(968\) 15.8359 0.508984
\(969\) 1.69740 0.0545284
\(970\) −11.1821 −0.359036
\(971\) 6.54666 0.210092 0.105046 0.994467i \(-0.466501\pi\)
0.105046 + 0.994467i \(0.466501\pi\)
\(972\) 2.75150 0.0882545
\(973\) 97.5229 3.12644
\(974\) −11.1970 −0.358775
\(975\) −14.2855 −0.457502
\(976\) −0.531854 −0.0170242
\(977\) 29.9459 0.958053 0.479027 0.877800i \(-0.340990\pi\)
0.479027 + 0.877800i \(0.340990\pi\)
\(978\) −14.6358 −0.468002
\(979\) 2.26173 0.0722852
\(980\) 60.8053 1.94236
\(981\) 13.4912 0.430740
\(982\) 45.4780 1.45126
\(983\) 25.4478 0.811659 0.405830 0.913949i \(-0.366983\pi\)
0.405830 + 0.913949i \(0.366983\pi\)
\(984\) 1.69791 0.0541274
\(985\) −24.5342 −0.781723
\(986\) 34.9370 1.11262
\(987\) −6.89511 −0.219474
\(988\) 8.27838 0.263370
\(989\) −18.4609 −0.587023
\(990\) 4.10417 0.130439
\(991\) −10.0203 −0.318304 −0.159152 0.987254i \(-0.550876\pi\)
−0.159152 + 0.987254i \(0.550876\pi\)
\(992\) −7.85512 −0.249400
\(993\) −22.9707 −0.728953
\(994\) 24.8360 0.787749
\(995\) −15.2818 −0.484466
\(996\) −22.0313 −0.698090
\(997\) −15.3886 −0.487361 −0.243681 0.969856i \(-0.578355\pi\)
−0.243681 + 0.969856i \(0.578355\pi\)
\(998\) −36.7305 −1.16268
\(999\) 4.71618 0.149213
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 \(a_p\))