Properties

Label 8013.2.a.d.1.15
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 1.15
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.27654 q^{2}\) \(+1.00000 q^{3}\) \(+3.18262 q^{4}\) \(-2.00184 q^{5}\) \(-2.27654 q^{6}\) \(+2.08885 q^{7}\) \(-2.69227 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.27654 q^{2}\) \(+1.00000 q^{3}\) \(+3.18262 q^{4}\) \(-2.00184 q^{5}\) \(-2.27654 q^{6}\) \(+2.08885 q^{7}\) \(-2.69227 q^{8}\) \(+1.00000 q^{9}\) \(+4.55727 q^{10}\) \(-1.88228 q^{11}\) \(+3.18262 q^{12}\) \(+2.84320 q^{13}\) \(-4.75535 q^{14}\) \(-2.00184 q^{15}\) \(-0.236176 q^{16}\) \(-6.19071 q^{17}\) \(-2.27654 q^{18}\) \(+3.03112 q^{19}\) \(-6.37110 q^{20}\) \(+2.08885 q^{21}\) \(+4.28508 q^{22}\) \(+0.0200996 q^{23}\) \(-2.69227 q^{24}\) \(-0.992628 q^{25}\) \(-6.47264 q^{26}\) \(+1.00000 q^{27}\) \(+6.64802 q^{28}\) \(+1.86310 q^{29}\) \(+4.55727 q^{30}\) \(+2.83716 q^{31}\) \(+5.92221 q^{32}\) \(-1.88228 q^{33}\) \(+14.0934 q^{34}\) \(-4.18156 q^{35}\) \(+3.18262 q^{36}\) \(-0.519885 q^{37}\) \(-6.90044 q^{38}\) \(+2.84320 q^{39}\) \(+5.38951 q^{40}\) \(-10.0911 q^{41}\) \(-4.75535 q^{42}\) \(+6.33966 q^{43}\) \(-5.99057 q^{44}\) \(-2.00184 q^{45}\) \(-0.0457574 q^{46}\) \(+7.21759 q^{47}\) \(-0.236176 q^{48}\) \(-2.63669 q^{49}\) \(+2.25975 q^{50}\) \(-6.19071 q^{51}\) \(+9.04881 q^{52}\) \(-4.87026 q^{53}\) \(-2.27654 q^{54}\) \(+3.76802 q^{55}\) \(-5.62377 q^{56}\) \(+3.03112 q^{57}\) \(-4.24142 q^{58}\) \(+2.44093 q^{59}\) \(-6.37110 q^{60}\) \(+2.77322 q^{61}\) \(-6.45891 q^{62}\) \(+2.08885 q^{63}\) \(-13.0098 q^{64}\) \(-5.69163 q^{65}\) \(+4.28508 q^{66}\) \(-6.84103 q^{67}\) \(-19.7027 q^{68}\) \(+0.0200996 q^{69}\) \(+9.51946 q^{70}\) \(+2.19829 q^{71}\) \(-2.69227 q^{72}\) \(+4.10705 q^{73}\) \(+1.18354 q^{74}\) \(-0.992628 q^{75}\) \(+9.64688 q^{76}\) \(-3.93180 q^{77}\) \(-6.47264 q^{78}\) \(-3.87452 q^{79}\) \(+0.472787 q^{80}\) \(+1.00000 q^{81}\) \(+22.9727 q^{82}\) \(-11.4382 q^{83}\) \(+6.64802 q^{84}\) \(+12.3928 q^{85}\) \(-14.4325 q^{86}\) \(+1.86310 q^{87}\) \(+5.06761 q^{88}\) \(+13.7392 q^{89}\) \(+4.55727 q^{90}\) \(+5.93902 q^{91}\) \(+0.0639692 q^{92}\) \(+2.83716 q^{93}\) \(-16.4311 q^{94}\) \(-6.06781 q^{95}\) \(+5.92221 q^{96}\) \(-13.2404 q^{97}\) \(+6.00252 q^{98}\) \(-1.88228 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27654 −1.60975 −0.804877 0.593441i \(-0.797769\pi\)
−0.804877 + 0.593441i \(0.797769\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.18262 1.59131
\(5\) −2.00184 −0.895251 −0.447626 0.894221i \(-0.647730\pi\)
−0.447626 + 0.894221i \(0.647730\pi\)
\(6\) −2.27654 −0.929392
\(7\) 2.08885 0.789512 0.394756 0.918786i \(-0.370829\pi\)
0.394756 + 0.918786i \(0.370829\pi\)
\(8\) −2.69227 −0.951863
\(9\) 1.00000 0.333333
\(10\) 4.55727 1.44113
\(11\) −1.88228 −0.567528 −0.283764 0.958894i \(-0.591583\pi\)
−0.283764 + 0.958894i \(0.591583\pi\)
\(12\) 3.18262 0.918743
\(13\) 2.84320 0.788561 0.394280 0.918990i \(-0.370994\pi\)
0.394280 + 0.918990i \(0.370994\pi\)
\(14\) −4.75535 −1.27092
\(15\) −2.00184 −0.516873
\(16\) −0.236176 −0.0590440
\(17\) −6.19071 −1.50147 −0.750734 0.660605i \(-0.770300\pi\)
−0.750734 + 0.660605i \(0.770300\pi\)
\(18\) −2.27654 −0.536585
\(19\) 3.03112 0.695385 0.347693 0.937609i \(-0.386965\pi\)
0.347693 + 0.937609i \(0.386965\pi\)
\(20\) −6.37110 −1.42462
\(21\) 2.08885 0.455825
\(22\) 4.28508 0.913581
\(23\) 0.0200996 0.00419105 0.00209552 0.999998i \(-0.499333\pi\)
0.00209552 + 0.999998i \(0.499333\pi\)
\(24\) −2.69227 −0.549558
\(25\) −0.992628 −0.198526
\(26\) −6.47264 −1.26939
\(27\) 1.00000 0.192450
\(28\) 6.64802 1.25636
\(29\) 1.86310 0.345969 0.172985 0.984925i \(-0.444659\pi\)
0.172985 + 0.984925i \(0.444659\pi\)
\(30\) 4.55727 0.832039
\(31\) 2.83716 0.509570 0.254785 0.966998i \(-0.417995\pi\)
0.254785 + 0.966998i \(0.417995\pi\)
\(32\) 5.92221 1.04691
\(33\) −1.88228 −0.327663
\(34\) 14.0934 2.41699
\(35\) −4.18156 −0.706812
\(36\) 3.18262 0.530436
\(37\) −0.519885 −0.0854685 −0.0427343 0.999086i \(-0.513607\pi\)
−0.0427343 + 0.999086i \(0.513607\pi\)
\(38\) −6.90044 −1.11940
\(39\) 2.84320 0.455276
\(40\) 5.38951 0.852156
\(41\) −10.0911 −1.57596 −0.787981 0.615699i \(-0.788874\pi\)
−0.787981 + 0.615699i \(0.788874\pi\)
\(42\) −4.75535 −0.733767
\(43\) 6.33966 0.966789 0.483394 0.875403i \(-0.339404\pi\)
0.483394 + 0.875403i \(0.339404\pi\)
\(44\) −5.99057 −0.903113
\(45\) −2.00184 −0.298417
\(46\) −0.0457574 −0.00674656
\(47\) 7.21759 1.05279 0.526397 0.850239i \(-0.323543\pi\)
0.526397 + 0.850239i \(0.323543\pi\)
\(48\) −0.236176 −0.0340890
\(49\) −2.63669 −0.376670
\(50\) 2.25975 0.319577
\(51\) −6.19071 −0.866873
\(52\) 9.04881 1.25484
\(53\) −4.87026 −0.668982 −0.334491 0.942399i \(-0.608564\pi\)
−0.334491 + 0.942399i \(0.608564\pi\)
\(54\) −2.27654 −0.309797
\(55\) 3.76802 0.508080
\(56\) −5.62377 −0.751507
\(57\) 3.03112 0.401481
\(58\) −4.24142 −0.556926
\(59\) 2.44093 0.317782 0.158891 0.987296i \(-0.449208\pi\)
0.158891 + 0.987296i \(0.449208\pi\)
\(60\) −6.37110 −0.822506
\(61\) 2.77322 0.355075 0.177537 0.984114i \(-0.443187\pi\)
0.177537 + 0.984114i \(0.443187\pi\)
\(62\) −6.45891 −0.820282
\(63\) 2.08885 0.263171
\(64\) −13.0098 −1.62622
\(65\) −5.69163 −0.705960
\(66\) 4.28508 0.527456
\(67\) −6.84103 −0.835765 −0.417882 0.908501i \(-0.637228\pi\)
−0.417882 + 0.908501i \(0.637228\pi\)
\(68\) −19.7027 −2.38930
\(69\) 0.0200996 0.00241970
\(70\) 9.51946 1.13779
\(71\) 2.19829 0.260889 0.130444 0.991456i \(-0.458360\pi\)
0.130444 + 0.991456i \(0.458360\pi\)
\(72\) −2.69227 −0.317288
\(73\) 4.10705 0.480694 0.240347 0.970687i \(-0.422739\pi\)
0.240347 + 0.970687i \(0.422739\pi\)
\(74\) 1.18354 0.137583
\(75\) −0.992628 −0.114619
\(76\) 9.64688 1.10657
\(77\) −3.93180 −0.448071
\(78\) −6.47264 −0.732882
\(79\) −3.87452 −0.435918 −0.217959 0.975958i \(-0.569940\pi\)
−0.217959 + 0.975958i \(0.569940\pi\)
\(80\) 0.472787 0.0528592
\(81\) 1.00000 0.111111
\(82\) 22.9727 2.53691
\(83\) −11.4382 −1.25550 −0.627752 0.778413i \(-0.716025\pi\)
−0.627752 + 0.778413i \(0.716025\pi\)
\(84\) 6.64802 0.725359
\(85\) 12.3928 1.34419
\(86\) −14.4325 −1.55629
\(87\) 1.86310 0.199746
\(88\) 5.06761 0.540209
\(89\) 13.7392 1.45635 0.728174 0.685393i \(-0.240369\pi\)
0.728174 + 0.685393i \(0.240369\pi\)
\(90\) 4.55727 0.480378
\(91\) 5.93902 0.622578
\(92\) 0.0639692 0.00666925
\(93\) 2.83716 0.294200
\(94\) −16.4311 −1.69474
\(95\) −6.06781 −0.622545
\(96\) 5.92221 0.604433
\(97\) −13.2404 −1.34436 −0.672181 0.740387i \(-0.734642\pi\)
−0.672181 + 0.740387i \(0.734642\pi\)
\(98\) 6.00252 0.606347
\(99\) −1.88228 −0.189176
\(100\) −3.15916 −0.315916
\(101\) 15.6887 1.56109 0.780544 0.625100i \(-0.214942\pi\)
0.780544 + 0.625100i \(0.214942\pi\)
\(102\) 14.0934 1.39545
\(103\) 7.15400 0.704905 0.352452 0.935830i \(-0.385348\pi\)
0.352452 + 0.935830i \(0.385348\pi\)
\(104\) −7.65466 −0.750601
\(105\) −4.18156 −0.408078
\(106\) 11.0873 1.07690
\(107\) −3.69482 −0.357191 −0.178596 0.983923i \(-0.557155\pi\)
−0.178596 + 0.983923i \(0.557155\pi\)
\(108\) 3.18262 0.306248
\(109\) 16.2075 1.55240 0.776199 0.630487i \(-0.217145\pi\)
0.776199 + 0.630487i \(0.217145\pi\)
\(110\) −8.57805 −0.817885
\(111\) −0.519885 −0.0493453
\(112\) −0.493337 −0.0466159
\(113\) 8.17145 0.768706 0.384353 0.923186i \(-0.374425\pi\)
0.384353 + 0.923186i \(0.374425\pi\)
\(114\) −6.90044 −0.646286
\(115\) −0.0402362 −0.00375204
\(116\) 5.92954 0.550544
\(117\) 2.84320 0.262854
\(118\) −5.55686 −0.511551
\(119\) −12.9315 −1.18543
\(120\) 5.38951 0.491993
\(121\) −7.45703 −0.677912
\(122\) −6.31335 −0.571583
\(123\) −10.0911 −0.909882
\(124\) 9.02961 0.810883
\(125\) 11.9963 1.07298
\(126\) −4.75535 −0.423640
\(127\) 14.5201 1.28845 0.644223 0.764838i \(-0.277181\pi\)
0.644223 + 0.764838i \(0.277181\pi\)
\(128\) 17.7728 1.57091
\(129\) 6.33966 0.558176
\(130\) 12.9572 1.13642
\(131\) 9.93534 0.868055 0.434027 0.900900i \(-0.357092\pi\)
0.434027 + 0.900900i \(0.357092\pi\)
\(132\) −5.99057 −0.521413
\(133\) 6.33155 0.549015
\(134\) 15.5739 1.34538
\(135\) −2.00184 −0.172291
\(136\) 16.6671 1.42919
\(137\) 12.6643 1.08198 0.540991 0.841028i \(-0.318049\pi\)
0.540991 + 0.841028i \(0.318049\pi\)
\(138\) −0.0457574 −0.00389513
\(139\) −3.97464 −0.337125 −0.168562 0.985691i \(-0.553912\pi\)
−0.168562 + 0.985691i \(0.553912\pi\)
\(140\) −13.3083 −1.12476
\(141\) 7.21759 0.607831
\(142\) −5.00448 −0.419967
\(143\) −5.35169 −0.447530
\(144\) −0.236176 −0.0196813
\(145\) −3.72964 −0.309730
\(146\) −9.34985 −0.773799
\(147\) −2.63669 −0.217471
\(148\) −1.65459 −0.136007
\(149\) −17.1073 −1.40148 −0.700740 0.713416i \(-0.747147\pi\)
−0.700740 + 0.713416i \(0.747147\pi\)
\(150\) 2.25975 0.184508
\(151\) −4.73113 −0.385014 −0.192507 0.981296i \(-0.561662\pi\)
−0.192507 + 0.981296i \(0.561662\pi\)
\(152\) −8.16059 −0.661912
\(153\) −6.19071 −0.500489
\(154\) 8.95089 0.721284
\(155\) −5.67956 −0.456193
\(156\) 9.04881 0.724484
\(157\) 23.2385 1.85464 0.927319 0.374272i \(-0.122108\pi\)
0.927319 + 0.374272i \(0.122108\pi\)
\(158\) 8.82049 0.701721
\(159\) −4.87026 −0.386237
\(160\) −11.8553 −0.937246
\(161\) 0.0419850 0.00330888
\(162\) −2.27654 −0.178862
\(163\) −23.1919 −1.81653 −0.908267 0.418392i \(-0.862594\pi\)
−0.908267 + 0.418392i \(0.862594\pi\)
\(164\) −32.1161 −2.50784
\(165\) 3.76802 0.293340
\(166\) 26.0395 2.02105
\(167\) 16.4185 1.27050 0.635249 0.772307i \(-0.280897\pi\)
0.635249 + 0.772307i \(0.280897\pi\)
\(168\) −5.62377 −0.433883
\(169\) −4.91624 −0.378172
\(170\) −28.2127 −2.16382
\(171\) 3.03112 0.231795
\(172\) 20.1767 1.53846
\(173\) −15.5457 −1.18192 −0.590960 0.806701i \(-0.701251\pi\)
−0.590960 + 0.806701i \(0.701251\pi\)
\(174\) −4.24142 −0.321541
\(175\) −2.07345 −0.156738
\(176\) 0.444549 0.0335091
\(177\) 2.44093 0.183471
\(178\) −31.2777 −2.34436
\(179\) −0.352055 −0.0263138 −0.0131569 0.999913i \(-0.504188\pi\)
−0.0131569 + 0.999913i \(0.504188\pi\)
\(180\) −6.37110 −0.474874
\(181\) 5.15127 0.382891 0.191445 0.981503i \(-0.438682\pi\)
0.191445 + 0.981503i \(0.438682\pi\)
\(182\) −13.5204 −1.00220
\(183\) 2.77322 0.205003
\(184\) −0.0541135 −0.00398930
\(185\) 1.04073 0.0765158
\(186\) −6.45891 −0.473590
\(187\) 11.6526 0.852125
\(188\) 22.9708 1.67532
\(189\) 2.08885 0.151942
\(190\) 13.8136 1.00214
\(191\) 17.5285 1.26832 0.634159 0.773202i \(-0.281346\pi\)
0.634159 + 0.773202i \(0.281346\pi\)
\(192\) −13.0098 −0.938900
\(193\) 16.9953 1.22335 0.611674 0.791110i \(-0.290496\pi\)
0.611674 + 0.791110i \(0.290496\pi\)
\(194\) 30.1423 2.16409
\(195\) −5.69163 −0.407586
\(196\) −8.39158 −0.599399
\(197\) −10.6530 −0.758998 −0.379499 0.925192i \(-0.623904\pi\)
−0.379499 + 0.925192i \(0.623904\pi\)
\(198\) 4.28508 0.304527
\(199\) 1.60011 0.113429 0.0567144 0.998390i \(-0.481938\pi\)
0.0567144 + 0.998390i \(0.481938\pi\)
\(200\) 2.67243 0.188969
\(201\) −6.84103 −0.482529
\(202\) −35.7160 −2.51297
\(203\) 3.89175 0.273147
\(204\) −19.7027 −1.37946
\(205\) 20.2008 1.41088
\(206\) −16.2863 −1.13472
\(207\) 0.0200996 0.00139702
\(208\) −0.671494 −0.0465597
\(209\) −5.70540 −0.394651
\(210\) 9.51946 0.656905
\(211\) 8.25886 0.568563 0.284282 0.958741i \(-0.408245\pi\)
0.284282 + 0.958741i \(0.408245\pi\)
\(212\) −15.5002 −1.06456
\(213\) 2.19829 0.150624
\(214\) 8.41139 0.574991
\(215\) −12.6910 −0.865519
\(216\) −2.69227 −0.183186
\(217\) 5.92642 0.402312
\(218\) −36.8970 −2.49898
\(219\) 4.10705 0.277529
\(220\) 11.9922 0.808513
\(221\) −17.6014 −1.18400
\(222\) 1.18354 0.0794338
\(223\) −4.75449 −0.318384 −0.159192 0.987248i \(-0.550889\pi\)
−0.159192 + 0.987248i \(0.550889\pi\)
\(224\) 12.3706 0.826548
\(225\) −0.992628 −0.0661752
\(226\) −18.6026 −1.23743
\(227\) −17.9008 −1.18812 −0.594058 0.804422i \(-0.702475\pi\)
−0.594058 + 0.804422i \(0.702475\pi\)
\(228\) 9.64688 0.638880
\(229\) −13.0277 −0.860897 −0.430449 0.902615i \(-0.641645\pi\)
−0.430449 + 0.902615i \(0.641645\pi\)
\(230\) 0.0915991 0.00603986
\(231\) −3.93180 −0.258694
\(232\) −5.01598 −0.329315
\(233\) −12.0850 −0.791713 −0.395857 0.918312i \(-0.629552\pi\)
−0.395857 + 0.918312i \(0.629552\pi\)
\(234\) −6.47264 −0.423130
\(235\) −14.4485 −0.942515
\(236\) 7.76854 0.505689
\(237\) −3.87452 −0.251677
\(238\) 29.4390 1.90825
\(239\) 5.80701 0.375624 0.187812 0.982205i \(-0.439860\pi\)
0.187812 + 0.982205i \(0.439860\pi\)
\(240\) 0.472787 0.0305183
\(241\) −9.59210 −0.617881 −0.308941 0.951081i \(-0.599974\pi\)
−0.308941 + 0.951081i \(0.599974\pi\)
\(242\) 16.9762 1.09127
\(243\) 1.00000 0.0641500
\(244\) 8.82611 0.565034
\(245\) 5.27824 0.337214
\(246\) 22.9727 1.46469
\(247\) 8.61805 0.548354
\(248\) −7.63843 −0.485040
\(249\) −11.4382 −0.724866
\(250\) −27.3100 −1.72724
\(251\) −12.3913 −0.782134 −0.391067 0.920362i \(-0.627894\pi\)
−0.391067 + 0.920362i \(0.627894\pi\)
\(252\) 6.64802 0.418786
\(253\) −0.0378330 −0.00237854
\(254\) −33.0554 −2.07408
\(255\) 12.3928 0.776069
\(256\) −14.4409 −0.902557
\(257\) 10.8895 0.679267 0.339633 0.940558i \(-0.389697\pi\)
0.339633 + 0.940558i \(0.389697\pi\)
\(258\) −14.4325 −0.898526
\(259\) −1.08596 −0.0674785
\(260\) −18.1143 −1.12340
\(261\) 1.86310 0.115323
\(262\) −22.6182 −1.39736
\(263\) 6.62175 0.408315 0.204157 0.978938i \(-0.434555\pi\)
0.204157 + 0.978938i \(0.434555\pi\)
\(264\) 5.06761 0.311890
\(265\) 9.74949 0.598907
\(266\) −14.4140 −0.883780
\(267\) 13.7392 0.840823
\(268\) −21.7724 −1.32996
\(269\) 18.4347 1.12398 0.561991 0.827144i \(-0.310036\pi\)
0.561991 + 0.827144i \(0.310036\pi\)
\(270\) 4.55727 0.277346
\(271\) 1.69508 0.102969 0.0514845 0.998674i \(-0.483605\pi\)
0.0514845 + 0.998674i \(0.483605\pi\)
\(272\) 1.46210 0.0886526
\(273\) 5.93902 0.359446
\(274\) −28.8307 −1.74173
\(275\) 1.86840 0.112669
\(276\) 0.0639692 0.00385050
\(277\) 24.0787 1.44675 0.723374 0.690457i \(-0.242590\pi\)
0.723374 + 0.690457i \(0.242590\pi\)
\(278\) 9.04842 0.542688
\(279\) 2.83716 0.169857
\(280\) 11.2579 0.672788
\(281\) 30.0179 1.79072 0.895360 0.445343i \(-0.146918\pi\)
0.895360 + 0.445343i \(0.146918\pi\)
\(282\) −16.4311 −0.978459
\(283\) 12.6432 0.751562 0.375781 0.926709i \(-0.377375\pi\)
0.375781 + 0.926709i \(0.377375\pi\)
\(284\) 6.99631 0.415155
\(285\) −6.06781 −0.359426
\(286\) 12.1833 0.720414
\(287\) −21.0788 −1.24424
\(288\) 5.92221 0.348970
\(289\) 21.3249 1.25440
\(290\) 8.49066 0.498588
\(291\) −13.2404 −0.776167
\(292\) 13.0712 0.764933
\(293\) 8.11743 0.474225 0.237113 0.971482i \(-0.423799\pi\)
0.237113 + 0.971482i \(0.423799\pi\)
\(294\) 6.00252 0.350074
\(295\) −4.88635 −0.284495
\(296\) 1.39967 0.0813543
\(297\) −1.88228 −0.109221
\(298\) 38.9453 2.25604
\(299\) 0.0571470 0.00330490
\(300\) −3.15916 −0.182394
\(301\) 13.2426 0.763292
\(302\) 10.7706 0.619778
\(303\) 15.6887 0.901295
\(304\) −0.715876 −0.0410583
\(305\) −5.55156 −0.317881
\(306\) 14.0934 0.805665
\(307\) −20.2784 −1.15735 −0.578675 0.815558i \(-0.696430\pi\)
−0.578675 + 0.815558i \(0.696430\pi\)
\(308\) −12.5134 −0.713019
\(309\) 7.15400 0.406977
\(310\) 12.9297 0.734358
\(311\) −0.789591 −0.0447736 −0.0223868 0.999749i \(-0.507127\pi\)
−0.0223868 + 0.999749i \(0.507127\pi\)
\(312\) −7.65466 −0.433360
\(313\) −5.99597 −0.338912 −0.169456 0.985538i \(-0.554201\pi\)
−0.169456 + 0.985538i \(0.554201\pi\)
\(314\) −52.9034 −2.98551
\(315\) −4.18156 −0.235604
\(316\) −12.3311 −0.693680
\(317\) 4.34365 0.243964 0.121982 0.992532i \(-0.461075\pi\)
0.121982 + 0.992532i \(0.461075\pi\)
\(318\) 11.0873 0.621746
\(319\) −3.50688 −0.196347
\(320\) 26.0435 1.45588
\(321\) −3.69482 −0.206225
\(322\) −0.0955805 −0.00532649
\(323\) −18.7648 −1.04410
\(324\) 3.18262 0.176812
\(325\) −2.82223 −0.156549
\(326\) 52.7973 2.92417
\(327\) 16.2075 0.896278
\(328\) 27.1680 1.50010
\(329\) 15.0765 0.831194
\(330\) −8.57805 −0.472206
\(331\) −14.2108 −0.781095 −0.390547 0.920583i \(-0.627714\pi\)
−0.390547 + 0.920583i \(0.627714\pi\)
\(332\) −36.4034 −1.99790
\(333\) −0.519885 −0.0284895
\(334\) −37.3772 −2.04519
\(335\) 13.6947 0.748219
\(336\) −0.493337 −0.0269137
\(337\) −12.0499 −0.656398 −0.328199 0.944609i \(-0.606442\pi\)
−0.328199 + 0.944609i \(0.606442\pi\)
\(338\) 11.1920 0.608765
\(339\) 8.17145 0.443812
\(340\) 39.4416 2.13902
\(341\) −5.34033 −0.289195
\(342\) −6.90044 −0.373133
\(343\) −20.1296 −1.08690
\(344\) −17.0681 −0.920250
\(345\) −0.0402362 −0.00216624
\(346\) 35.3904 1.90260
\(347\) −32.6064 −1.75040 −0.875202 0.483757i \(-0.839272\pi\)
−0.875202 + 0.483757i \(0.839272\pi\)
\(348\) 5.92954 0.317857
\(349\) 21.7208 1.16269 0.581344 0.813658i \(-0.302527\pi\)
0.581344 + 0.813658i \(0.302527\pi\)
\(350\) 4.72029 0.252310
\(351\) 2.84320 0.151759
\(352\) −11.1473 −0.594151
\(353\) 36.9662 1.96751 0.983757 0.179505i \(-0.0574496\pi\)
0.983757 + 0.179505i \(0.0574496\pi\)
\(354\) −5.55686 −0.295344
\(355\) −4.40063 −0.233561
\(356\) 43.7265 2.31750
\(357\) −12.9315 −0.684407
\(358\) 0.801467 0.0423588
\(359\) −1.88171 −0.0993127 −0.0496563 0.998766i \(-0.515813\pi\)
−0.0496563 + 0.998766i \(0.515813\pi\)
\(360\) 5.38951 0.284052
\(361\) −9.81234 −0.516439
\(362\) −11.7271 −0.616360
\(363\) −7.45703 −0.391392
\(364\) 18.9016 0.990715
\(365\) −8.22167 −0.430342
\(366\) −6.31335 −0.330004
\(367\) 7.38143 0.385308 0.192654 0.981267i \(-0.438291\pi\)
0.192654 + 0.981267i \(0.438291\pi\)
\(368\) −0.00474703 −0.000247456 0
\(369\) −10.0911 −0.525321
\(370\) −2.36925 −0.123172
\(371\) −10.1733 −0.528169
\(372\) 9.02961 0.468164
\(373\) 4.89911 0.253666 0.126833 0.991924i \(-0.459519\pi\)
0.126833 + 0.991924i \(0.459519\pi\)
\(374\) −26.5277 −1.37171
\(375\) 11.9963 0.619486
\(376\) −19.4317 −1.00212
\(377\) 5.29716 0.272818
\(378\) −4.75535 −0.244589
\(379\) 0.472635 0.0242776 0.0121388 0.999926i \(-0.496136\pi\)
0.0121388 + 0.999926i \(0.496136\pi\)
\(380\) −19.3115 −0.990661
\(381\) 14.5201 0.743885
\(382\) −39.9043 −2.04168
\(383\) −3.44047 −0.175800 −0.0878998 0.996129i \(-0.528016\pi\)
−0.0878998 + 0.996129i \(0.528016\pi\)
\(384\) 17.7728 0.906965
\(385\) 7.87085 0.401136
\(386\) −38.6904 −1.96929
\(387\) 6.33966 0.322263
\(388\) −42.1392 −2.13929
\(389\) −14.1601 −0.717947 −0.358973 0.933348i \(-0.616873\pi\)
−0.358973 + 0.933348i \(0.616873\pi\)
\(390\) 12.9572 0.656113
\(391\) −0.124431 −0.00629272
\(392\) 7.09870 0.358538
\(393\) 9.93534 0.501172
\(394\) 24.2520 1.22180
\(395\) 7.75618 0.390256
\(396\) −5.99057 −0.301038
\(397\) 24.4675 1.22799 0.613995 0.789310i \(-0.289562\pi\)
0.613995 + 0.789310i \(0.289562\pi\)
\(398\) −3.64271 −0.182592
\(399\) 6.33155 0.316974
\(400\) 0.234435 0.0117217
\(401\) 14.9397 0.746051 0.373026 0.927821i \(-0.378320\pi\)
0.373026 + 0.927821i \(0.378320\pi\)
\(402\) 15.5739 0.776753
\(403\) 8.06661 0.401827
\(404\) 49.9313 2.48418
\(405\) −2.00184 −0.0994723
\(406\) −8.85971 −0.439700
\(407\) 0.978568 0.0485058
\(408\) 16.6671 0.825144
\(409\) −27.6096 −1.36521 −0.682603 0.730789i \(-0.739152\pi\)
−0.682603 + 0.730789i \(0.739152\pi\)
\(410\) −45.9878 −2.27117
\(411\) 12.6643 0.624683
\(412\) 22.7685 1.12172
\(413\) 5.09874 0.250893
\(414\) −0.0457574 −0.00224885
\(415\) 22.8975 1.12399
\(416\) 16.8380 0.825551
\(417\) −3.97464 −0.194639
\(418\) 12.9886 0.635291
\(419\) 29.8856 1.46001 0.730003 0.683443i \(-0.239518\pi\)
0.730003 + 0.683443i \(0.239518\pi\)
\(420\) −13.3083 −0.649378
\(421\) 33.7353 1.64416 0.822079 0.569374i \(-0.192814\pi\)
0.822079 + 0.569374i \(0.192814\pi\)
\(422\) −18.8016 −0.915247
\(423\) 7.21759 0.350931
\(424\) 13.1121 0.636779
\(425\) 6.14507 0.298080
\(426\) −5.00448 −0.242468
\(427\) 5.79286 0.280336
\(428\) −11.7592 −0.568402
\(429\) −5.35169 −0.258382
\(430\) 28.8915 1.39327
\(431\) −20.6917 −0.996686 −0.498343 0.866980i \(-0.666058\pi\)
−0.498343 + 0.866980i \(0.666058\pi\)
\(432\) −0.236176 −0.0113630
\(433\) 26.1492 1.25665 0.628325 0.777951i \(-0.283741\pi\)
0.628325 + 0.777951i \(0.283741\pi\)
\(434\) −13.4917 −0.647623
\(435\) −3.72964 −0.178822
\(436\) 51.5824 2.47035
\(437\) 0.0609241 0.00291439
\(438\) −9.34985 −0.446753
\(439\) 11.9421 0.569967 0.284983 0.958532i \(-0.408012\pi\)
0.284983 + 0.958532i \(0.408012\pi\)
\(440\) −10.1446 −0.483623
\(441\) −2.63669 −0.125557
\(442\) 40.0702 1.90595
\(443\) 10.5654 0.501978 0.250989 0.967990i \(-0.419244\pi\)
0.250989 + 0.967990i \(0.419244\pi\)
\(444\) −1.65459 −0.0785236
\(445\) −27.5036 −1.30380
\(446\) 10.8238 0.512520
\(447\) −17.1073 −0.809145
\(448\) −27.1755 −1.28392
\(449\) −7.47543 −0.352787 −0.176394 0.984320i \(-0.556443\pi\)
−0.176394 + 0.984320i \(0.556443\pi\)
\(450\) 2.25975 0.106526
\(451\) 18.9942 0.894403
\(452\) 26.0066 1.22325
\(453\) −4.73113 −0.222288
\(454\) 40.7518 1.91258
\(455\) −11.8890 −0.557364
\(456\) −8.16059 −0.382155
\(457\) −4.33594 −0.202827 −0.101413 0.994844i \(-0.532336\pi\)
−0.101413 + 0.994844i \(0.532336\pi\)
\(458\) 29.6581 1.38583
\(459\) −6.19071 −0.288958
\(460\) −0.128056 −0.00597066
\(461\) 22.1666 1.03240 0.516201 0.856468i \(-0.327346\pi\)
0.516201 + 0.856468i \(0.327346\pi\)
\(462\) 8.95089 0.416433
\(463\) −20.5385 −0.954503 −0.477252 0.878767i \(-0.658367\pi\)
−0.477252 + 0.878767i \(0.658367\pi\)
\(464\) −0.440020 −0.0204274
\(465\) −5.67956 −0.263383
\(466\) 27.5119 1.27446
\(467\) −32.4992 −1.50388 −0.751941 0.659230i \(-0.770882\pi\)
−0.751941 + 0.659230i \(0.770882\pi\)
\(468\) 9.04881 0.418281
\(469\) −14.2899 −0.659847
\(470\) 32.8925 1.51722
\(471\) 23.2385 1.07078
\(472\) −6.57165 −0.302485
\(473\) −11.9330 −0.548680
\(474\) 8.82049 0.405139
\(475\) −3.00877 −0.138052
\(476\) −41.1560 −1.88638
\(477\) −4.87026 −0.222994
\(478\) −13.2199 −0.604663
\(479\) −8.30660 −0.379538 −0.189769 0.981829i \(-0.560774\pi\)
−0.189769 + 0.981829i \(0.560774\pi\)
\(480\) −11.8553 −0.541120
\(481\) −1.47813 −0.0673971
\(482\) 21.8368 0.994637
\(483\) 0.0419850 0.00191039
\(484\) −23.7329 −1.07877
\(485\) 26.5052 1.20354
\(486\) −2.27654 −0.103266
\(487\) 23.9835 1.08680 0.543398 0.839475i \(-0.317137\pi\)
0.543398 + 0.839475i \(0.317137\pi\)
\(488\) −7.46628 −0.337983
\(489\) −23.1919 −1.04878
\(490\) −12.0161 −0.542832
\(491\) 19.7496 0.891289 0.445644 0.895210i \(-0.352975\pi\)
0.445644 + 0.895210i \(0.352975\pi\)
\(492\) −32.1161 −1.44790
\(493\) −11.5339 −0.519462
\(494\) −19.6193 −0.882715
\(495\) 3.76802 0.169360
\(496\) −0.670070 −0.0300870
\(497\) 4.59190 0.205975
\(498\) 26.0395 1.16686
\(499\) 16.6971 0.747464 0.373732 0.927537i \(-0.378078\pi\)
0.373732 + 0.927537i \(0.378078\pi\)
\(500\) 38.1796 1.70745
\(501\) 16.4185 0.733523
\(502\) 28.2093 1.25904
\(503\) 27.3685 1.22030 0.610150 0.792286i \(-0.291109\pi\)
0.610150 + 0.792286i \(0.291109\pi\)
\(504\) −5.62377 −0.250502
\(505\) −31.4064 −1.39757
\(506\) 0.0861282 0.00382886
\(507\) −4.91624 −0.218338
\(508\) 46.2118 2.05032
\(509\) −25.6214 −1.13565 −0.567824 0.823150i \(-0.692215\pi\)
−0.567824 + 0.823150i \(0.692215\pi\)
\(510\) −28.2127 −1.24928
\(511\) 8.57903 0.379514
\(512\) −2.67038 −0.118015
\(513\) 3.03112 0.133827
\(514\) −24.7903 −1.09345
\(515\) −14.3212 −0.631067
\(516\) 20.1767 0.888230
\(517\) −13.5855 −0.597491
\(518\) 2.47223 0.108624
\(519\) −15.5457 −0.682381
\(520\) 15.3234 0.671977
\(521\) −3.94071 −0.172646 −0.0863228 0.996267i \(-0.527512\pi\)
−0.0863228 + 0.996267i \(0.527512\pi\)
\(522\) −4.24142 −0.185642
\(523\) 11.2202 0.490624 0.245312 0.969444i \(-0.421110\pi\)
0.245312 + 0.969444i \(0.421110\pi\)
\(524\) 31.6204 1.38134
\(525\) −2.07345 −0.0904929
\(526\) −15.0747 −0.657286
\(527\) −17.5641 −0.765102
\(528\) 0.444549 0.0193465
\(529\) −22.9996 −0.999982
\(530\) −22.1951 −0.964093
\(531\) 2.44093 0.105927
\(532\) 20.1509 0.873653
\(533\) −28.6909 −1.24274
\(534\) −31.2777 −1.35352
\(535\) 7.39644 0.319776
\(536\) 18.4179 0.795533
\(537\) −0.352055 −0.0151923
\(538\) −41.9672 −1.80933
\(539\) 4.96299 0.213771
\(540\) −6.37110 −0.274169
\(541\) 10.5730 0.454568 0.227284 0.973828i \(-0.427015\pi\)
0.227284 + 0.973828i \(0.427015\pi\)
\(542\) −3.85892 −0.165755
\(543\) 5.15127 0.221062
\(544\) −36.6627 −1.57190
\(545\) −32.4449 −1.38979
\(546\) −13.5204 −0.578619
\(547\) 8.35560 0.357259 0.178630 0.983916i \(-0.442834\pi\)
0.178630 + 0.983916i \(0.442834\pi\)
\(548\) 40.3056 1.72177
\(549\) 2.77322 0.118358
\(550\) −4.25348 −0.181369
\(551\) 5.64728 0.240582
\(552\) −0.0541135 −0.00230323
\(553\) −8.09331 −0.344162
\(554\) −54.8160 −2.32891
\(555\) 1.04073 0.0441764
\(556\) −12.6498 −0.536470
\(557\) −20.1752 −0.854851 −0.427425 0.904051i \(-0.640579\pi\)
−0.427425 + 0.904051i \(0.640579\pi\)
\(558\) −6.45891 −0.273427
\(559\) 18.0249 0.762371
\(560\) 0.987582 0.0417330
\(561\) 11.6526 0.491975
\(562\) −68.3369 −2.88262
\(563\) 9.58339 0.403892 0.201946 0.979397i \(-0.435273\pi\)
0.201946 + 0.979397i \(0.435273\pi\)
\(564\) 22.9708 0.967247
\(565\) −16.3580 −0.688185
\(566\) −28.7828 −1.20983
\(567\) 2.08885 0.0877236
\(568\) −5.91840 −0.248330
\(569\) −15.4584 −0.648051 −0.324025 0.946048i \(-0.605036\pi\)
−0.324025 + 0.946048i \(0.605036\pi\)
\(570\) 13.8136 0.578588
\(571\) 3.36194 0.140693 0.0703465 0.997523i \(-0.477590\pi\)
0.0703465 + 0.997523i \(0.477590\pi\)
\(572\) −17.0324 −0.712159
\(573\) 17.5285 0.732264
\(574\) 47.9866 2.00292
\(575\) −0.0199514 −0.000832030 0
\(576\) −13.0098 −0.542074
\(577\) 29.3415 1.22150 0.610751 0.791823i \(-0.290868\pi\)
0.610751 + 0.791823i \(0.290868\pi\)
\(578\) −48.5469 −2.01928
\(579\) 16.9953 0.706300
\(580\) −11.8700 −0.492875
\(581\) −23.8927 −0.991236
\(582\) 30.1423 1.24944
\(583\) 9.16719 0.379666
\(584\) −11.0573 −0.457555
\(585\) −5.69163 −0.235320
\(586\) −18.4796 −0.763386
\(587\) 26.9791 1.11355 0.556774 0.830664i \(-0.312039\pi\)
0.556774 + 0.830664i \(0.312039\pi\)
\(588\) −8.39158 −0.346063
\(589\) 8.59977 0.354347
\(590\) 11.1240 0.457966
\(591\) −10.6530 −0.438208
\(592\) 0.122784 0.00504640
\(593\) −5.78848 −0.237704 −0.118852 0.992912i \(-0.537921\pi\)
−0.118852 + 0.992912i \(0.537921\pi\)
\(594\) 4.28508 0.175819
\(595\) 25.8868 1.06125
\(596\) −54.4459 −2.23019
\(597\) 1.60011 0.0654881
\(598\) −0.130097 −0.00532007
\(599\) 22.5543 0.921543 0.460771 0.887519i \(-0.347573\pi\)
0.460771 + 0.887519i \(0.347573\pi\)
\(600\) 2.67243 0.109101
\(601\) 4.04594 0.165037 0.0825186 0.996590i \(-0.473704\pi\)
0.0825186 + 0.996590i \(0.473704\pi\)
\(602\) −30.1473 −1.22871
\(603\) −6.84103 −0.278588
\(604\) −15.0574 −0.612676
\(605\) 14.9278 0.606901
\(606\) −35.7160 −1.45086
\(607\) −8.17869 −0.331963 −0.165981 0.986129i \(-0.553079\pi\)
−0.165981 + 0.986129i \(0.553079\pi\)
\(608\) 17.9509 0.728005
\(609\) 3.89175 0.157702
\(610\) 12.6383 0.511711
\(611\) 20.5210 0.830192
\(612\) −19.7027 −0.796433
\(613\) −24.8265 −1.00273 −0.501366 0.865235i \(-0.667169\pi\)
−0.501366 + 0.865235i \(0.667169\pi\)
\(614\) 46.1646 1.86305
\(615\) 20.2008 0.814573
\(616\) 10.5855 0.426502
\(617\) 2.86256 0.115242 0.0576211 0.998339i \(-0.481648\pi\)
0.0576211 + 0.998339i \(0.481648\pi\)
\(618\) −16.2863 −0.655133
\(619\) −34.9486 −1.40470 −0.702351 0.711831i \(-0.747866\pi\)
−0.702351 + 0.711831i \(0.747866\pi\)
\(620\) −18.0759 −0.725944
\(621\) 0.0200996 0.000806568 0
\(622\) 1.79753 0.0720745
\(623\) 28.6991 1.14980
\(624\) −0.671494 −0.0268813
\(625\) −19.0516 −0.762062
\(626\) 13.6500 0.545565
\(627\) −5.70540 −0.227852
\(628\) 73.9594 2.95130
\(629\) 3.21846 0.128328
\(630\) 9.51946 0.379264
\(631\) 38.8495 1.54657 0.773286 0.634057i \(-0.218611\pi\)
0.773286 + 0.634057i \(0.218611\pi\)
\(632\) 10.4313 0.414934
\(633\) 8.25886 0.328260
\(634\) −9.88848 −0.392722
\(635\) −29.0669 −1.15348
\(636\) −15.5002 −0.614622
\(637\) −7.49663 −0.297027
\(638\) 7.98353 0.316071
\(639\) 2.19829 0.0869630
\(640\) −35.5784 −1.40636
\(641\) 40.9515 1.61749 0.808744 0.588161i \(-0.200148\pi\)
0.808744 + 0.588161i \(0.200148\pi\)
\(642\) 8.41139 0.331971
\(643\) −9.22090 −0.363637 −0.181818 0.983332i \(-0.558198\pi\)
−0.181818 + 0.983332i \(0.558198\pi\)
\(644\) 0.133622 0.00526546
\(645\) −12.6910 −0.499707
\(646\) 42.7186 1.68074
\(647\) −0.365141 −0.0143552 −0.00717758 0.999974i \(-0.502285\pi\)
−0.00717758 + 0.999974i \(0.502285\pi\)
\(648\) −2.69227 −0.105763
\(649\) −4.59451 −0.180350
\(650\) 6.42492 0.252006
\(651\) 5.92642 0.232275
\(652\) −73.8111 −2.89067
\(653\) −26.1813 −1.02455 −0.512277 0.858820i \(-0.671198\pi\)
−0.512277 + 0.858820i \(0.671198\pi\)
\(654\) −36.8970 −1.44279
\(655\) −19.8890 −0.777127
\(656\) 2.38327 0.0930510
\(657\) 4.10705 0.160231
\(658\) −34.3222 −1.33802
\(659\) 2.10505 0.0820013 0.0410006 0.999159i \(-0.486945\pi\)
0.0410006 + 0.999159i \(0.486945\pi\)
\(660\) 11.9922 0.466795
\(661\) −16.7419 −0.651186 −0.325593 0.945510i \(-0.605564\pi\)
−0.325593 + 0.945510i \(0.605564\pi\)
\(662\) 32.3513 1.25737
\(663\) −17.6014 −0.683582
\(664\) 30.7948 1.19507
\(665\) −12.6748 −0.491507
\(666\) 1.18354 0.0458611
\(667\) 0.0374475 0.00144997
\(668\) 52.2537 2.02176
\(669\) −4.75449 −0.183819
\(670\) −31.1764 −1.20445
\(671\) −5.21998 −0.201515
\(672\) 12.3706 0.477208
\(673\) −29.0045 −1.11804 −0.559021 0.829154i \(-0.688823\pi\)
−0.559021 + 0.829154i \(0.688823\pi\)
\(674\) 27.4320 1.05664
\(675\) −0.992628 −0.0382063
\(676\) −15.6465 −0.601789
\(677\) −13.4929 −0.518575 −0.259288 0.965800i \(-0.583488\pi\)
−0.259288 + 0.965800i \(0.583488\pi\)
\(678\) −18.6026 −0.714429
\(679\) −27.6573 −1.06139
\(680\) −33.3649 −1.27948
\(681\) −17.9008 −0.685959
\(682\) 12.1575 0.465533
\(683\) 27.2081 1.04109 0.520545 0.853834i \(-0.325729\pi\)
0.520545 + 0.853834i \(0.325729\pi\)
\(684\) 9.64688 0.368858
\(685\) −25.3519 −0.968646
\(686\) 45.8259 1.74964
\(687\) −13.0277 −0.497039
\(688\) −1.49727 −0.0570830
\(689\) −13.8471 −0.527533
\(690\) 0.0915991 0.00348712
\(691\) −24.9247 −0.948181 −0.474090 0.880476i \(-0.657223\pi\)
−0.474090 + 0.880476i \(0.657223\pi\)
\(692\) −49.4761 −1.88080
\(693\) −3.93180 −0.149357
\(694\) 74.2297 2.81772
\(695\) 7.95661 0.301811
\(696\) −5.01598 −0.190130
\(697\) 62.4709 2.36626
\(698\) −49.4482 −1.87164
\(699\) −12.0850 −0.457096
\(700\) −6.59901 −0.249419
\(701\) −30.6524 −1.15772 −0.578862 0.815425i \(-0.696503\pi\)
−0.578862 + 0.815425i \(0.696503\pi\)
\(702\) −6.47264 −0.244294
\(703\) −1.57583 −0.0594336
\(704\) 24.4880 0.922927
\(705\) −14.4485 −0.544161
\(706\) −84.1550 −3.16721
\(707\) 32.7715 1.23250
\(708\) 7.76854 0.291960
\(709\) 33.6592 1.26410 0.632049 0.774928i \(-0.282214\pi\)
0.632049 + 0.774928i \(0.282214\pi\)
\(710\) 10.0182 0.375976
\(711\) −3.87452 −0.145306
\(712\) −36.9896 −1.38624
\(713\) 0.0570258 0.00213563
\(714\) 29.4390 1.10173
\(715\) 10.7132 0.400652
\(716\) −1.12046 −0.0418735
\(717\) 5.80701 0.216867
\(718\) 4.28377 0.159869
\(719\) 18.6224 0.694500 0.347250 0.937773i \(-0.387116\pi\)
0.347250 + 0.937773i \(0.387116\pi\)
\(720\) 0.472787 0.0176197
\(721\) 14.9437 0.556531
\(722\) 22.3382 0.831340
\(723\) −9.59210 −0.356734
\(724\) 16.3945 0.609298
\(725\) −1.84937 −0.0686838
\(726\) 16.9762 0.630046
\(727\) 34.6145 1.28378 0.641890 0.766797i \(-0.278151\pi\)
0.641890 + 0.766797i \(0.278151\pi\)
\(728\) −15.9895 −0.592609
\(729\) 1.00000 0.0370370
\(730\) 18.7169 0.692745
\(731\) −39.2470 −1.45160
\(732\) 8.82611 0.326223
\(733\) 16.9759 0.627019 0.313510 0.949585i \(-0.398495\pi\)
0.313510 + 0.949585i \(0.398495\pi\)
\(734\) −16.8041 −0.620251
\(735\) 5.27824 0.194691
\(736\) 0.119034 0.00438765
\(737\) 12.8767 0.474320
\(738\) 22.9727 0.845637
\(739\) −14.1309 −0.519813 −0.259906 0.965634i \(-0.583692\pi\)
−0.259906 + 0.965634i \(0.583692\pi\)
\(740\) 3.31224 0.121760
\(741\) 8.61805 0.316592
\(742\) 23.1598 0.850223
\(743\) 18.8077 0.689987 0.344993 0.938605i \(-0.387881\pi\)
0.344993 + 0.938605i \(0.387881\pi\)
\(744\) −7.63843 −0.280038
\(745\) 34.2460 1.25468
\(746\) −11.1530 −0.408340
\(747\) −11.4382 −0.418502
\(748\) 37.0859 1.35599
\(749\) −7.71793 −0.282007
\(750\) −27.3100 −0.997220
\(751\) 26.9289 0.982651 0.491326 0.870976i \(-0.336513\pi\)
0.491326 + 0.870976i \(0.336513\pi\)
\(752\) −1.70462 −0.0621611
\(753\) −12.3913 −0.451565
\(754\) −12.0592 −0.439170
\(755\) 9.47097 0.344684
\(756\) 6.64802 0.241786
\(757\) 40.6574 1.47772 0.738860 0.673859i \(-0.235365\pi\)
0.738860 + 0.673859i \(0.235365\pi\)
\(758\) −1.07597 −0.0390810
\(759\) −0.0378330 −0.00137325
\(760\) 16.3362 0.592577
\(761\) 30.8254 1.11742 0.558710 0.829363i \(-0.311296\pi\)
0.558710 + 0.829363i \(0.311296\pi\)
\(762\) −33.0554 −1.19747
\(763\) 33.8551 1.22564
\(764\) 55.7866 2.01829
\(765\) 12.3928 0.448063
\(766\) 7.83235 0.282994
\(767\) 6.94004 0.250590
\(768\) −14.4409 −0.521091
\(769\) 8.95267 0.322841 0.161421 0.986886i \(-0.448392\pi\)
0.161421 + 0.986886i \(0.448392\pi\)
\(770\) −17.9183 −0.645730
\(771\) 10.8895 0.392175
\(772\) 54.0895 1.94673
\(773\) −5.76563 −0.207375 −0.103688 0.994610i \(-0.533064\pi\)
−0.103688 + 0.994610i \(0.533064\pi\)
\(774\) −14.4325 −0.518764
\(775\) −2.81625 −0.101163
\(776\) 35.6468 1.27965
\(777\) −1.08596 −0.0389587
\(778\) 32.2360 1.15572
\(779\) −30.5872 −1.09590
\(780\) −18.1143 −0.648595
\(781\) −4.13779 −0.148062
\(782\) 0.283271 0.0101297
\(783\) 1.86310 0.0665818
\(784\) 0.622723 0.0222401
\(785\) −46.5199 −1.66037
\(786\) −22.6182 −0.806763
\(787\) 31.1041 1.10874 0.554371 0.832270i \(-0.312959\pi\)
0.554371 + 0.832270i \(0.312959\pi\)
\(788\) −33.9046 −1.20780
\(789\) 6.62175 0.235741
\(790\) −17.6572 −0.628216
\(791\) 17.0690 0.606903
\(792\) 5.06761 0.180070
\(793\) 7.88482 0.279998
\(794\) −55.7012 −1.97676
\(795\) 9.74949 0.345779
\(796\) 5.09254 0.180500
\(797\) 31.7658 1.12520 0.562601 0.826729i \(-0.309801\pi\)
0.562601 + 0.826729i \(0.309801\pi\)
\(798\) −14.4140 −0.510251
\(799\) −44.6820 −1.58074
\(800\) −5.87855 −0.207838
\(801\) 13.7392 0.485449
\(802\) −34.0107 −1.20096
\(803\) −7.73061 −0.272807
\(804\) −21.7724 −0.767853
\(805\) −0.0840474 −0.00296228
\(806\) −18.3639 −0.646842
\(807\) 18.4347 0.648931
\(808\) −42.2384 −1.48594
\(809\) −18.4158 −0.647463 −0.323732 0.946149i \(-0.604938\pi\)
−0.323732 + 0.946149i \(0.604938\pi\)
\(810\) 4.55727 0.160126
\(811\) 31.7930 1.11640 0.558201 0.829706i \(-0.311492\pi\)
0.558201 + 0.829706i \(0.311492\pi\)
\(812\) 12.3859 0.434662
\(813\) 1.69508 0.0594492
\(814\) −2.22775 −0.0780824
\(815\) 46.4266 1.62625
\(816\) 1.46210 0.0511836
\(817\) 19.2162 0.672291
\(818\) 62.8543 2.19765
\(819\) 5.93902 0.207526
\(820\) 64.2913 2.24515
\(821\) 34.2396 1.19497 0.597484 0.801881i \(-0.296167\pi\)
0.597484 + 0.801881i \(0.296167\pi\)
\(822\) −28.8307 −1.00559
\(823\) 16.0400 0.559118 0.279559 0.960129i \(-0.409812\pi\)
0.279559 + 0.960129i \(0.409812\pi\)
\(824\) −19.2605 −0.670973
\(825\) 1.86840 0.0650494
\(826\) −11.6075 −0.403876
\(827\) 38.6322 1.34337 0.671687 0.740835i \(-0.265570\pi\)
0.671687 + 0.740835i \(0.265570\pi\)
\(828\) 0.0639692 0.00222308
\(829\) 13.6891 0.475441 0.237720 0.971334i \(-0.423600\pi\)
0.237720 + 0.971334i \(0.423600\pi\)
\(830\) −52.1269 −1.80935
\(831\) 24.0787 0.835280
\(832\) −36.9893 −1.28237
\(833\) 16.3230 0.565558
\(834\) 9.04842 0.313321
\(835\) −32.8672 −1.13742
\(836\) −18.1581 −0.628012
\(837\) 2.83716 0.0980667
\(838\) −68.0356 −2.35025
\(839\) −16.3010 −0.562773 −0.281386 0.959595i \(-0.590794\pi\)
−0.281386 + 0.959595i \(0.590794\pi\)
\(840\) 11.2579 0.388434
\(841\) −25.5288 −0.880305
\(842\) −76.7996 −2.64669
\(843\) 30.0179 1.03387
\(844\) 26.2848 0.904760
\(845\) 9.84154 0.338559
\(846\) −16.4311 −0.564913
\(847\) −15.5766 −0.535220
\(848\) 1.15024 0.0394993
\(849\) 12.6432 0.433914
\(850\) −13.9895 −0.479835
\(851\) −0.0104495 −0.000358203 0
\(852\) 6.99631 0.239690
\(853\) 39.0045 1.33549 0.667744 0.744391i \(-0.267260\pi\)
0.667744 + 0.744391i \(0.267260\pi\)
\(854\) −13.1877 −0.451272
\(855\) −6.06781 −0.207515
\(856\) 9.94746 0.339997
\(857\) 30.6658 1.04752 0.523761 0.851865i \(-0.324528\pi\)
0.523761 + 0.851865i \(0.324528\pi\)
\(858\) 12.1833 0.415931
\(859\) −14.1640 −0.483270 −0.241635 0.970367i \(-0.577684\pi\)
−0.241635 + 0.970367i \(0.577684\pi\)
\(860\) −40.3906 −1.37731
\(861\) −21.0788 −0.718363
\(862\) 47.1055 1.60442
\(863\) 15.5749 0.530174 0.265087 0.964224i \(-0.414599\pi\)
0.265087 + 0.964224i \(0.414599\pi\)
\(864\) 5.92221 0.201478
\(865\) 31.1201 1.05811
\(866\) −59.5296 −2.02290
\(867\) 21.3249 0.724231
\(868\) 18.8615 0.640202
\(869\) 7.29293 0.247396
\(870\) 8.49066 0.287860
\(871\) −19.4504 −0.659051
\(872\) −43.6351 −1.47767
\(873\) −13.2404 −0.448120
\(874\) −0.138696 −0.00469146
\(875\) 25.0585 0.847132
\(876\) 13.0712 0.441634
\(877\) 8.76628 0.296016 0.148008 0.988986i \(-0.452714\pi\)
0.148008 + 0.988986i \(0.452714\pi\)
\(878\) −27.1867 −0.917507
\(879\) 8.11743 0.273794
\(880\) −0.889916 −0.0299991
\(881\) −34.6399 −1.16705 −0.583525 0.812095i \(-0.698327\pi\)
−0.583525 + 0.812095i \(0.698327\pi\)
\(882\) 6.00252 0.202116
\(883\) 3.35391 0.112868 0.0564340 0.998406i \(-0.482027\pi\)
0.0564340 + 0.998406i \(0.482027\pi\)
\(884\) −56.0185 −1.88411
\(885\) −4.88635 −0.164253
\(886\) −24.0526 −0.808061
\(887\) 47.2528 1.58659 0.793296 0.608836i \(-0.208363\pi\)
0.793296 + 0.608836i \(0.208363\pi\)
\(888\) 1.39967 0.0469699
\(889\) 30.3303 1.01724
\(890\) 62.6130 2.09879
\(891\) −1.88228 −0.0630587
\(892\) −15.1317 −0.506648
\(893\) 21.8774 0.732098
\(894\) 38.9453 1.30253
\(895\) 0.704759 0.0235575
\(896\) 37.1248 1.24025
\(897\) 0.0571470 0.00190808
\(898\) 17.0181 0.567901
\(899\) 5.28593 0.176296
\(900\) −3.15916 −0.105305
\(901\) 30.1504 1.00445
\(902\) −43.2411 −1.43977
\(903\) 13.2426 0.440687
\(904\) −21.9998 −0.731702
\(905\) −10.3120 −0.342783
\(906\) 10.7706 0.357829
\(907\) 41.8576 1.38986 0.694930 0.719078i \(-0.255436\pi\)
0.694930 + 0.719078i \(0.255436\pi\)
\(908\) −56.9713 −1.89066
\(909\) 15.6887 0.520363
\(910\) 27.0657 0.897219
\(911\) −34.1655 −1.13195 −0.565976 0.824422i \(-0.691501\pi\)
−0.565976 + 0.824422i \(0.691501\pi\)
\(912\) −0.715876 −0.0237050
\(913\) 21.5299 0.712534
\(914\) 9.87092 0.326501
\(915\) −5.55156 −0.183529
\(916\) −41.4623 −1.36995
\(917\) 20.7535 0.685340
\(918\) 14.0934 0.465151
\(919\) 16.5383 0.545547 0.272773 0.962078i \(-0.412059\pi\)
0.272773 + 0.962078i \(0.412059\pi\)
\(920\) 0.108327 0.00357143
\(921\) −20.2784 −0.668197
\(922\) −50.4631 −1.66191
\(923\) 6.25016 0.205727
\(924\) −12.5134 −0.411662
\(925\) 0.516052 0.0169677
\(926\) 46.7566 1.53652
\(927\) 7.15400 0.234968
\(928\) 11.0337 0.362199
\(929\) 31.0774 1.01962 0.509808 0.860288i \(-0.329717\pi\)
0.509808 + 0.860288i \(0.329717\pi\)
\(930\) 12.9297 0.423982
\(931\) −7.99212 −0.261931
\(932\) −38.4619 −1.25986
\(933\) −0.789591 −0.0258500
\(934\) 73.9855 2.42088
\(935\) −23.3267 −0.762866
\(936\) −7.65466 −0.250200
\(937\) −45.2341 −1.47773 −0.738866 0.673852i \(-0.764639\pi\)
−0.738866 + 0.673852i \(0.764639\pi\)
\(938\) 32.5315 1.06219
\(939\) −5.99597 −0.195671
\(940\) −45.9840 −1.49983
\(941\) 40.5493 1.32187 0.660935 0.750443i \(-0.270160\pi\)
0.660935 + 0.750443i \(0.270160\pi\)
\(942\) −52.9034 −1.72369
\(943\) −0.202826 −0.00660493
\(944\) −0.576488 −0.0187631
\(945\) −4.18156 −0.136026
\(946\) 27.1659 0.883240
\(947\) −53.3125 −1.73242 −0.866211 0.499678i \(-0.833452\pi\)
−0.866211 + 0.499678i \(0.833452\pi\)
\(948\) −12.3311 −0.400496
\(949\) 11.6771 0.379056
\(950\) 6.84957 0.222229
\(951\) 4.34365 0.140852
\(952\) 34.8151 1.12836
\(953\) −13.9133 −0.450697 −0.225348 0.974278i \(-0.572352\pi\)
−0.225348 + 0.974278i \(0.572352\pi\)
\(954\) 11.0873 0.358965
\(955\) −35.0893 −1.13546
\(956\) 18.4815 0.597734
\(957\) −3.50688 −0.113361
\(958\) 18.9103 0.610964
\(959\) 26.4538 0.854239
\(960\) 26.0435 0.840551
\(961\) −22.9505 −0.740339
\(962\) 3.36503 0.108493
\(963\) −3.69482 −0.119064
\(964\) −30.5280 −0.983240
\(965\) −34.0219 −1.09520
\(966\) −0.0955805 −0.00307525
\(967\) 25.5656 0.822133 0.411066 0.911605i \(-0.365156\pi\)
0.411066 + 0.911605i \(0.365156\pi\)
\(968\) 20.0764 0.645279
\(969\) −18.7648 −0.602811
\(970\) −60.3401 −1.93741
\(971\) −1.47504 −0.0473364 −0.0236682 0.999720i \(-0.507535\pi\)
−0.0236682 + 0.999720i \(0.507535\pi\)
\(972\) 3.18262 0.102083
\(973\) −8.30244 −0.266164
\(974\) −54.5993 −1.74947
\(975\) −2.82223 −0.0903838
\(976\) −0.654968 −0.0209650
\(977\) 10.3406 0.330825 0.165413 0.986224i \(-0.447104\pi\)
0.165413 + 0.986224i \(0.447104\pi\)
\(978\) 52.7973 1.68827
\(979\) −25.8609 −0.826518
\(980\) 16.7986 0.536612
\(981\) 16.2075 0.517466
\(982\) −44.9608 −1.43476
\(983\) −19.3345 −0.616673 −0.308337 0.951277i \(-0.599772\pi\)
−0.308337 + 0.951277i \(0.599772\pi\)
\(984\) 27.1680 0.866083
\(985\) 21.3257 0.679494
\(986\) 26.2574 0.836206
\(987\) 15.0765 0.479890
\(988\) 27.4280 0.872600
\(989\) 0.127424 0.00405186
\(990\) −8.57805 −0.272628
\(991\) −45.7936 −1.45468 −0.727342 0.686276i \(-0.759244\pi\)
−0.727342 + 0.686276i \(0.759244\pi\)
\(992\) 16.8023 0.533473
\(993\) −14.2108 −0.450965
\(994\) −10.4536 −0.331569
\(995\) −3.20317 −0.101547
\(996\) −36.4034 −1.15349
\(997\) 19.3559 0.613007 0.306503 0.951870i \(-0.400841\pi\)
0.306503 + 0.951870i \(0.400841\pi\)
\(998\) −38.0115 −1.20323
\(999\) −0.519885 −0.0164484
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 \(a_p\))