Properties

Label 4015.2.a.h.1.1
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70375 q^{2}\) \(-1.27224 q^{3}\) \(+5.31028 q^{4}\) \(+1.00000 q^{5}\) \(+3.43983 q^{6}\) \(-0.968765 q^{7}\) \(-8.95019 q^{8}\) \(-1.38140 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70375 q^{2}\) \(-1.27224 q^{3}\) \(+5.31028 q^{4}\) \(+1.00000 q^{5}\) \(+3.43983 q^{6}\) \(-0.968765 q^{7}\) \(-8.95019 q^{8}\) \(-1.38140 q^{9}\) \(-2.70375 q^{10}\) \(+1.00000 q^{11}\) \(-6.75597 q^{12}\) \(+1.17856 q^{13}\) \(+2.61930 q^{14}\) \(-1.27224 q^{15}\) \(+13.5785 q^{16}\) \(-1.19285 q^{17}\) \(+3.73495 q^{18}\) \(+4.63111 q^{19}\) \(+5.31028 q^{20}\) \(+1.23250 q^{21}\) \(-2.70375 q^{22}\) \(+3.13145 q^{23}\) \(+11.3868 q^{24}\) \(+1.00000 q^{25}\) \(-3.18655 q^{26}\) \(+5.57420 q^{27}\) \(-5.14441 q^{28}\) \(+9.52697 q^{29}\) \(+3.43983 q^{30}\) \(-7.86250 q^{31}\) \(-18.8126 q^{32}\) \(-1.27224 q^{33}\) \(+3.22517 q^{34}\) \(-0.968765 q^{35}\) \(-7.33560 q^{36}\) \(-4.17187 q^{37}\) \(-12.5214 q^{38}\) \(-1.49942 q^{39}\) \(-8.95019 q^{40}\) \(+2.33996 q^{41}\) \(-3.33239 q^{42}\) \(-5.79300 q^{43}\) \(+5.31028 q^{44}\) \(-1.38140 q^{45}\) \(-8.46666 q^{46}\) \(+3.18307 q^{47}\) \(-17.2752 q^{48}\) \(-6.06150 q^{49}\) \(-2.70375 q^{50}\) \(+1.51759 q^{51}\) \(+6.25851 q^{52}\) \(-2.16838 q^{53}\) \(-15.0713 q^{54}\) \(+1.00000 q^{55}\) \(+8.67062 q^{56}\) \(-5.89191 q^{57}\) \(-25.7586 q^{58}\) \(+9.54460 q^{59}\) \(-6.75597 q^{60}\) \(+2.24895 q^{61}\) \(+21.2583 q^{62}\) \(+1.33825 q^{63}\) \(+23.7076 q^{64}\) \(+1.17856 q^{65}\) \(+3.43983 q^{66}\) \(-10.7576 q^{67}\) \(-6.33436 q^{68}\) \(-3.98397 q^{69}\) \(+2.61930 q^{70}\) \(+9.15992 q^{71}\) \(+12.3637 q^{72}\) \(+1.00000 q^{73}\) \(+11.2797 q^{74}\) \(-1.27224 q^{75}\) \(+24.5925 q^{76}\) \(-0.968765 q^{77}\) \(+4.05406 q^{78}\) \(+5.23984 q^{79}\) \(+13.5785 q^{80}\) \(-2.94756 q^{81}\) \(-6.32667 q^{82}\) \(+6.06424 q^{83}\) \(+6.54495 q^{84}\) \(-1.19285 q^{85}\) \(+15.6628 q^{86}\) \(-12.1206 q^{87}\) \(-8.95019 q^{88}\) \(-14.1945 q^{89}\) \(+3.73495 q^{90}\) \(-1.14175 q^{91}\) \(+16.6289 q^{92}\) \(+10.0030 q^{93}\) \(-8.60624 q^{94}\) \(+4.63111 q^{95}\) \(+23.9342 q^{96}\) \(-2.72029 q^{97}\) \(+16.3888 q^{98}\) \(-1.38140 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70375 −1.91184 −0.955921 0.293624i \(-0.905139\pi\)
−0.955921 + 0.293624i \(0.905139\pi\)
\(3\) −1.27224 −0.734530 −0.367265 0.930116i \(-0.619706\pi\)
−0.367265 + 0.930116i \(0.619706\pi\)
\(4\) 5.31028 2.65514
\(5\) 1.00000 0.447214
\(6\) 3.43983 1.40431
\(7\) −0.968765 −0.366159 −0.183079 0.983098i \(-0.558607\pi\)
−0.183079 + 0.983098i \(0.558607\pi\)
\(8\) −8.95019 −3.16437
\(9\) −1.38140 −0.460465
\(10\) −2.70375 −0.855002
\(11\) 1.00000 0.301511
\(12\) −6.75597 −1.95028
\(13\) 1.17856 0.326875 0.163437 0.986554i \(-0.447742\pi\)
0.163437 + 0.986554i \(0.447742\pi\)
\(14\) 2.61930 0.700038
\(15\) −1.27224 −0.328492
\(16\) 13.5785 3.39463
\(17\) −1.19285 −0.289308 −0.144654 0.989482i \(-0.546207\pi\)
−0.144654 + 0.989482i \(0.546207\pi\)
\(18\) 3.73495 0.880337
\(19\) 4.63111 1.06245 0.531225 0.847231i \(-0.321732\pi\)
0.531225 + 0.847231i \(0.321732\pi\)
\(20\) 5.31028 1.18742
\(21\) 1.23250 0.268955
\(22\) −2.70375 −0.576442
\(23\) 3.13145 0.652952 0.326476 0.945205i \(-0.394139\pi\)
0.326476 + 0.945205i \(0.394139\pi\)
\(24\) 11.3868 2.32432
\(25\) 1.00000 0.200000
\(26\) −3.18655 −0.624933
\(27\) 5.57420 1.07276
\(28\) −5.14441 −0.972203
\(29\) 9.52697 1.76911 0.884557 0.466432i \(-0.154461\pi\)
0.884557 + 0.466432i \(0.154461\pi\)
\(30\) 3.43983 0.628025
\(31\) −7.86250 −1.41215 −0.706074 0.708138i \(-0.749535\pi\)
−0.706074 + 0.708138i \(0.749535\pi\)
\(32\) −18.8126 −3.32563
\(33\) −1.27224 −0.221469
\(34\) 3.22517 0.553112
\(35\) −0.968765 −0.163751
\(36\) −7.33560 −1.22260
\(37\) −4.17187 −0.685851 −0.342925 0.939363i \(-0.611418\pi\)
−0.342925 + 0.939363i \(0.611418\pi\)
\(38\) −12.5214 −2.03124
\(39\) −1.49942 −0.240099
\(40\) −8.95019 −1.41515
\(41\) 2.33996 0.365440 0.182720 0.983165i \(-0.441510\pi\)
0.182720 + 0.983165i \(0.441510\pi\)
\(42\) −3.33239 −0.514199
\(43\) −5.79300 −0.883424 −0.441712 0.897157i \(-0.645629\pi\)
−0.441712 + 0.897157i \(0.645629\pi\)
\(44\) 5.31028 0.800555
\(45\) −1.38140 −0.205926
\(46\) −8.46666 −1.24834
\(47\) 3.18307 0.464299 0.232149 0.972680i \(-0.425424\pi\)
0.232149 + 0.972680i \(0.425424\pi\)
\(48\) −17.2752 −2.49346
\(49\) −6.06150 −0.865928
\(50\) −2.70375 −0.382368
\(51\) 1.51759 0.212506
\(52\) 6.25851 0.867899
\(53\) −2.16838 −0.297850 −0.148925 0.988849i \(-0.547581\pi\)
−0.148925 + 0.988849i \(0.547581\pi\)
\(54\) −15.0713 −2.05094
\(55\) 1.00000 0.134840
\(56\) 8.67062 1.15866
\(57\) −5.89191 −0.780402
\(58\) −25.7586 −3.38227
\(59\) 9.54460 1.24260 0.621300 0.783573i \(-0.286605\pi\)
0.621300 + 0.783573i \(0.286605\pi\)
\(60\) −6.75597 −0.872192
\(61\) 2.24895 0.287948 0.143974 0.989581i \(-0.454012\pi\)
0.143974 + 0.989581i \(0.454012\pi\)
\(62\) 21.2583 2.69980
\(63\) 1.33825 0.168603
\(64\) 23.7076 2.96345
\(65\) 1.17856 0.146183
\(66\) 3.43983 0.423414
\(67\) −10.7576 −1.31425 −0.657126 0.753781i \(-0.728228\pi\)
−0.657126 + 0.753781i \(0.728228\pi\)
\(68\) −6.33436 −0.768154
\(69\) −3.98397 −0.479613
\(70\) 2.61930 0.313066
\(71\) 9.15992 1.08708 0.543541 0.839382i \(-0.317083\pi\)
0.543541 + 0.839382i \(0.317083\pi\)
\(72\) 12.3637 1.45708
\(73\) 1.00000 0.117041
\(74\) 11.2797 1.31124
\(75\) −1.27224 −0.146906
\(76\) 24.5925 2.82096
\(77\) −0.968765 −0.110401
\(78\) 4.05406 0.459032
\(79\) 5.23984 0.589528 0.294764 0.955570i \(-0.404759\pi\)
0.294764 + 0.955570i \(0.404759\pi\)
\(80\) 13.5785 1.51813
\(81\) −2.94756 −0.327507
\(82\) −6.32667 −0.698664
\(83\) 6.06424 0.665637 0.332818 0.942991i \(-0.392000\pi\)
0.332818 + 0.942991i \(0.392000\pi\)
\(84\) 6.54495 0.714112
\(85\) −1.19285 −0.129383
\(86\) 15.6628 1.68897
\(87\) −12.1206 −1.29947
\(88\) −8.95019 −0.954093
\(89\) −14.1945 −1.50461 −0.752306 0.658814i \(-0.771058\pi\)
−0.752306 + 0.658814i \(0.771058\pi\)
\(90\) 3.73495 0.393699
\(91\) −1.14175 −0.119688
\(92\) 16.6289 1.73368
\(93\) 10.0030 1.03727
\(94\) −8.60624 −0.887666
\(95\) 4.63111 0.475142
\(96\) 23.9342 2.44278
\(97\) −2.72029 −0.276204 −0.138102 0.990418i \(-0.544100\pi\)
−0.138102 + 0.990418i \(0.544100\pi\)
\(98\) 16.3888 1.65552
\(99\) −1.38140 −0.138835
\(100\) 5.31028 0.531028
\(101\) 17.5380 1.74509 0.872547 0.488531i \(-0.162467\pi\)
0.872547 + 0.488531i \(0.162467\pi\)
\(102\) −4.10320 −0.406277
\(103\) 3.49675 0.344545 0.172273 0.985049i \(-0.444889\pi\)
0.172273 + 0.985049i \(0.444889\pi\)
\(104\) −10.5484 −1.03435
\(105\) 1.23250 0.120280
\(106\) 5.86276 0.569441
\(107\) −15.6762 −1.51548 −0.757739 0.652558i \(-0.773696\pi\)
−0.757739 + 0.652558i \(0.773696\pi\)
\(108\) 29.6006 2.84832
\(109\) 8.59662 0.823407 0.411703 0.911318i \(-0.364934\pi\)
0.411703 + 0.911318i \(0.364934\pi\)
\(110\) −2.70375 −0.257793
\(111\) 5.30763 0.503778
\(112\) −13.1544 −1.24297
\(113\) −8.64672 −0.813415 −0.406708 0.913558i \(-0.633323\pi\)
−0.406708 + 0.913558i \(0.633323\pi\)
\(114\) 15.9303 1.49201
\(115\) 3.13145 0.292009
\(116\) 50.5909 4.69725
\(117\) −1.62806 −0.150514
\(118\) −25.8062 −2.37566
\(119\) 1.15559 0.105933
\(120\) 11.3868 1.03947
\(121\) 1.00000 0.0909091
\(122\) −6.08060 −0.550512
\(123\) −2.97700 −0.268427
\(124\) −41.7521 −3.74945
\(125\) 1.00000 0.0894427
\(126\) −3.61829 −0.322343
\(127\) 16.7348 1.48497 0.742487 0.669861i \(-0.233646\pi\)
0.742487 + 0.669861i \(0.233646\pi\)
\(128\) −26.4743 −2.34002
\(129\) 7.37011 0.648902
\(130\) −3.18655 −0.279479
\(131\) −21.5488 −1.88273 −0.941365 0.337389i \(-0.890456\pi\)
−0.941365 + 0.337389i \(0.890456\pi\)
\(132\) −6.75597 −0.588032
\(133\) −4.48646 −0.389025
\(134\) 29.0859 2.51264
\(135\) 5.57420 0.479751
\(136\) 10.6762 0.915477
\(137\) −8.20987 −0.701417 −0.350708 0.936485i \(-0.614059\pi\)
−0.350708 + 0.936485i \(0.614059\pi\)
\(138\) 10.7717 0.916945
\(139\) −15.2511 −1.29358 −0.646789 0.762669i \(-0.723888\pi\)
−0.646789 + 0.762669i \(0.723888\pi\)
\(140\) −5.14441 −0.434782
\(141\) −4.04964 −0.341041
\(142\) −24.7662 −2.07833
\(143\) 1.17856 0.0985565
\(144\) −18.7573 −1.56311
\(145\) 9.52697 0.791172
\(146\) −2.70375 −0.223764
\(147\) 7.71170 0.636050
\(148\) −22.1538 −1.82103
\(149\) 18.5819 1.52229 0.761144 0.648583i \(-0.224638\pi\)
0.761144 + 0.648583i \(0.224638\pi\)
\(150\) 3.43983 0.280861
\(151\) −5.47867 −0.445848 −0.222924 0.974836i \(-0.571560\pi\)
−0.222924 + 0.974836i \(0.571560\pi\)
\(152\) −41.4493 −3.36198
\(153\) 1.64779 0.133216
\(154\) 2.61930 0.211069
\(155\) −7.86250 −0.631532
\(156\) −7.96235 −0.637498
\(157\) 8.18386 0.653143 0.326571 0.945173i \(-0.394107\pi\)
0.326571 + 0.945173i \(0.394107\pi\)
\(158\) −14.1672 −1.12708
\(159\) 2.75871 0.218780
\(160\) −18.8126 −1.48727
\(161\) −3.03364 −0.239084
\(162\) 7.96947 0.626141
\(163\) 2.24631 0.175945 0.0879724 0.996123i \(-0.471961\pi\)
0.0879724 + 0.996123i \(0.471961\pi\)
\(164\) 12.4258 0.970295
\(165\) −1.27224 −0.0990440
\(166\) −16.3962 −1.27259
\(167\) 9.48520 0.733987 0.366993 0.930224i \(-0.380387\pi\)
0.366993 + 0.930224i \(0.380387\pi\)
\(168\) −11.0311 −0.851071
\(169\) −11.6110 −0.893153
\(170\) 3.22517 0.247359
\(171\) −6.39740 −0.489221
\(172\) −30.7625 −2.34562
\(173\) 3.11794 0.237053 0.118526 0.992951i \(-0.462183\pi\)
0.118526 + 0.992951i \(0.462183\pi\)
\(174\) 32.7712 2.48438
\(175\) −0.968765 −0.0732317
\(176\) 13.5785 1.02352
\(177\) −12.1431 −0.912728
\(178\) 38.3784 2.87658
\(179\) 13.6553 1.02064 0.510321 0.859984i \(-0.329527\pi\)
0.510321 + 0.859984i \(0.329527\pi\)
\(180\) −7.33560 −0.546763
\(181\) 2.15937 0.160505 0.0802525 0.996775i \(-0.474427\pi\)
0.0802525 + 0.996775i \(0.474427\pi\)
\(182\) 3.08701 0.228825
\(183\) −2.86121 −0.211507
\(184\) −28.0270 −2.06618
\(185\) −4.17187 −0.306722
\(186\) −27.0457 −1.98309
\(187\) −1.19285 −0.0872297
\(188\) 16.9030 1.23278
\(189\) −5.40009 −0.392799
\(190\) −12.5214 −0.908397
\(191\) 9.47771 0.685783 0.342892 0.939375i \(-0.388594\pi\)
0.342892 + 0.939375i \(0.388594\pi\)
\(192\) −30.1619 −2.17675
\(193\) −13.6330 −0.981323 −0.490661 0.871350i \(-0.663245\pi\)
−0.490661 + 0.871350i \(0.663245\pi\)
\(194\) 7.35501 0.528059
\(195\) −1.49942 −0.107376
\(196\) −32.1882 −2.29916
\(197\) 21.7011 1.54614 0.773069 0.634322i \(-0.218721\pi\)
0.773069 + 0.634322i \(0.218721\pi\)
\(198\) 3.73495 0.265432
\(199\) −20.2297 −1.43404 −0.717022 0.697051i \(-0.754495\pi\)
−0.717022 + 0.697051i \(0.754495\pi\)
\(200\) −8.95019 −0.632874
\(201\) 13.6863 0.965358
\(202\) −47.4184 −3.33634
\(203\) −9.22939 −0.647776
\(204\) 8.05885 0.564232
\(205\) 2.33996 0.163430
\(206\) −9.45436 −0.658716
\(207\) −4.32577 −0.300662
\(208\) 16.0032 1.10962
\(209\) 4.63111 0.320341
\(210\) −3.33239 −0.229957
\(211\) −9.81658 −0.675801 −0.337901 0.941182i \(-0.609717\pi\)
−0.337901 + 0.941182i \(0.609717\pi\)
\(212\) −11.5147 −0.790833
\(213\) −11.6537 −0.798495
\(214\) 42.3846 2.89735
\(215\) −5.79300 −0.395079
\(216\) −49.8902 −3.39460
\(217\) 7.61692 0.517070
\(218\) −23.2431 −1.57422
\(219\) −1.27224 −0.0859703
\(220\) 5.31028 0.358019
\(221\) −1.40585 −0.0945675
\(222\) −14.3505 −0.963144
\(223\) −3.61113 −0.241819 −0.120910 0.992664i \(-0.538581\pi\)
−0.120910 + 0.992664i \(0.538581\pi\)
\(224\) 18.2250 1.21771
\(225\) −1.38140 −0.0920930
\(226\) 23.3786 1.55512
\(227\) 14.9233 0.990495 0.495247 0.868752i \(-0.335077\pi\)
0.495247 + 0.868752i \(0.335077\pi\)
\(228\) −31.2877 −2.07208
\(229\) 23.6020 1.55966 0.779832 0.625989i \(-0.215305\pi\)
0.779832 + 0.625989i \(0.215305\pi\)
\(230\) −8.46666 −0.558275
\(231\) 1.23250 0.0810929
\(232\) −85.2681 −5.59813
\(233\) 10.9690 0.718604 0.359302 0.933221i \(-0.383015\pi\)
0.359302 + 0.933221i \(0.383015\pi\)
\(234\) 4.40188 0.287760
\(235\) 3.18307 0.207641
\(236\) 50.6845 3.29928
\(237\) −6.66635 −0.433026
\(238\) −3.12443 −0.202527
\(239\) −23.1920 −1.50016 −0.750082 0.661345i \(-0.769986\pi\)
−0.750082 + 0.661345i \(0.769986\pi\)
\(240\) −17.2752 −1.11511
\(241\) 4.16361 0.268202 0.134101 0.990968i \(-0.457185\pi\)
0.134101 + 0.990968i \(0.457185\pi\)
\(242\) −2.70375 −0.173804
\(243\) −12.9726 −0.832192
\(244\) 11.9425 0.764543
\(245\) −6.06150 −0.387255
\(246\) 8.04907 0.513190
\(247\) 5.45806 0.347288
\(248\) 70.3709 4.46855
\(249\) −7.71519 −0.488930
\(250\) −2.70375 −0.171000
\(251\) −18.2743 −1.15347 −0.576733 0.816933i \(-0.695673\pi\)
−0.576733 + 0.816933i \(0.695673\pi\)
\(252\) 7.10647 0.447666
\(253\) 3.13145 0.196872
\(254\) −45.2468 −2.83903
\(255\) 1.51759 0.0950354
\(256\) 24.1648 1.51030
\(257\) 14.5172 0.905561 0.452780 0.891622i \(-0.350432\pi\)
0.452780 + 0.891622i \(0.350432\pi\)
\(258\) −19.9269 −1.24060
\(259\) 4.04156 0.251130
\(260\) 6.25851 0.388136
\(261\) −13.1605 −0.814615
\(262\) 58.2627 3.59948
\(263\) −12.2954 −0.758168 −0.379084 0.925362i \(-0.623761\pi\)
−0.379084 + 0.925362i \(0.623761\pi\)
\(264\) 11.3868 0.700810
\(265\) −2.16838 −0.133202
\(266\) 12.1303 0.743755
\(267\) 18.0588 1.10518
\(268\) −57.1260 −3.48952
\(269\) −5.35815 −0.326692 −0.163346 0.986569i \(-0.552229\pi\)
−0.163346 + 0.986569i \(0.552229\pi\)
\(270\) −15.0713 −0.917208
\(271\) −14.2061 −0.862957 −0.431478 0.902123i \(-0.642008\pi\)
−0.431478 + 0.902123i \(0.642008\pi\)
\(272\) −16.1971 −0.982095
\(273\) 1.45259 0.0879145
\(274\) 22.1975 1.34100
\(275\) 1.00000 0.0603023
\(276\) −21.1560 −1.27344
\(277\) 20.3216 1.22101 0.610504 0.792013i \(-0.290967\pi\)
0.610504 + 0.792013i \(0.290967\pi\)
\(278\) 41.2351 2.47312
\(279\) 10.8612 0.650245
\(280\) 8.67062 0.518169
\(281\) 10.0021 0.596674 0.298337 0.954461i \(-0.403568\pi\)
0.298337 + 0.954461i \(0.403568\pi\)
\(282\) 10.9492 0.652018
\(283\) 15.4115 0.916120 0.458060 0.888921i \(-0.348544\pi\)
0.458060 + 0.888921i \(0.348544\pi\)
\(284\) 48.6418 2.88636
\(285\) −5.89191 −0.349006
\(286\) −3.18655 −0.188424
\(287\) −2.26687 −0.133809
\(288\) 25.9877 1.53134
\(289\) −15.5771 −0.916301
\(290\) −25.7586 −1.51260
\(291\) 3.46088 0.202880
\(292\) 5.31028 0.310761
\(293\) 0.927528 0.0541868 0.0270934 0.999633i \(-0.491375\pi\)
0.0270934 + 0.999633i \(0.491375\pi\)
\(294\) −20.8505 −1.21603
\(295\) 9.54460 0.555708
\(296\) 37.3390 2.17028
\(297\) 5.57420 0.323448
\(298\) −50.2409 −2.91037
\(299\) 3.69061 0.213434
\(300\) −6.75597 −0.390056
\(301\) 5.61205 0.323473
\(302\) 14.8130 0.852391
\(303\) −22.3126 −1.28182
\(304\) 62.8837 3.60663
\(305\) 2.24895 0.128774
\(306\) −4.45523 −0.254689
\(307\) 14.4001 0.821857 0.410929 0.911668i \(-0.365205\pi\)
0.410929 + 0.911668i \(0.365205\pi\)
\(308\) −5.14441 −0.293130
\(309\) −4.44872 −0.253079
\(310\) 21.2583 1.20739
\(311\) −11.4706 −0.650440 −0.325220 0.945638i \(-0.605438\pi\)
−0.325220 + 0.945638i \(0.605438\pi\)
\(312\) 13.4201 0.759763
\(313\) −27.3078 −1.54353 −0.771763 0.635910i \(-0.780625\pi\)
−0.771763 + 0.635910i \(0.780625\pi\)
\(314\) −22.1271 −1.24871
\(315\) 1.33825 0.0754017
\(316\) 27.8250 1.56528
\(317\) 3.27303 0.183832 0.0919158 0.995767i \(-0.470701\pi\)
0.0919158 + 0.995767i \(0.470701\pi\)
\(318\) −7.45886 −0.418272
\(319\) 9.52697 0.533408
\(320\) 23.7076 1.32530
\(321\) 19.9440 1.11316
\(322\) 8.20221 0.457091
\(323\) −5.52422 −0.307376
\(324\) −15.6524 −0.869576
\(325\) 1.17856 0.0653750
\(326\) −6.07347 −0.336379
\(327\) −10.9370 −0.604817
\(328\) −20.9431 −1.15639
\(329\) −3.08365 −0.170007
\(330\) 3.43983 0.189357
\(331\) 31.4299 1.72754 0.863771 0.503884i \(-0.168096\pi\)
0.863771 + 0.503884i \(0.168096\pi\)
\(332\) 32.2028 1.76736
\(333\) 5.76300 0.315810
\(334\) −25.6456 −1.40327
\(335\) −10.7576 −0.587751
\(336\) 16.7356 0.913002
\(337\) 18.6135 1.01394 0.506970 0.861964i \(-0.330765\pi\)
0.506970 + 0.861964i \(0.330765\pi\)
\(338\) 31.3932 1.70757
\(339\) 11.0007 0.597478
\(340\) −6.33436 −0.343529
\(341\) −7.86250 −0.425778
\(342\) 17.2970 0.935314
\(343\) 12.6535 0.683226
\(344\) 51.8484 2.79548
\(345\) −3.98397 −0.214490
\(346\) −8.43015 −0.453208
\(347\) 19.6533 1.05504 0.527521 0.849542i \(-0.323122\pi\)
0.527521 + 0.849542i \(0.323122\pi\)
\(348\) −64.3640 −3.45027
\(349\) −2.60085 −0.139221 −0.0696103 0.997574i \(-0.522176\pi\)
−0.0696103 + 0.997574i \(0.522176\pi\)
\(350\) 2.61930 0.140008
\(351\) 6.56956 0.350657
\(352\) −18.8126 −1.00272
\(353\) −4.56840 −0.243152 −0.121576 0.992582i \(-0.538795\pi\)
−0.121576 + 0.992582i \(0.538795\pi\)
\(354\) 32.8318 1.74499
\(355\) 9.15992 0.486158
\(356\) −75.3767 −3.99496
\(357\) −1.47019 −0.0778108
\(358\) −36.9205 −1.95131
\(359\) −15.8842 −0.838336 −0.419168 0.907909i \(-0.637678\pi\)
−0.419168 + 0.907909i \(0.637678\pi\)
\(360\) 12.3637 0.651627
\(361\) 2.44722 0.128801
\(362\) −5.83841 −0.306860
\(363\) −1.27224 −0.0667755
\(364\) −6.06302 −0.317789
\(365\) 1.00000 0.0523424
\(366\) 7.73600 0.404367
\(367\) 1.58307 0.0826354 0.0413177 0.999146i \(-0.486844\pi\)
0.0413177 + 0.999146i \(0.486844\pi\)
\(368\) 42.5205 2.21653
\(369\) −3.23241 −0.168272
\(370\) 11.2797 0.586404
\(371\) 2.10065 0.109060
\(372\) 53.1189 2.75409
\(373\) 32.1045 1.66231 0.831154 0.556042i \(-0.187681\pi\)
0.831154 + 0.556042i \(0.187681\pi\)
\(374\) 3.22517 0.166769
\(375\) −1.27224 −0.0656984
\(376\) −28.4891 −1.46921
\(377\) 11.2281 0.578279
\(378\) 14.6005 0.750969
\(379\) 26.9082 1.38218 0.691092 0.722767i \(-0.257130\pi\)
0.691092 + 0.722767i \(0.257130\pi\)
\(380\) 24.5925 1.26157
\(381\) −21.2907 −1.09076
\(382\) −25.6254 −1.31111
\(383\) −13.2905 −0.679114 −0.339557 0.940586i \(-0.610277\pi\)
−0.339557 + 0.940586i \(0.610277\pi\)
\(384\) 33.6818 1.71882
\(385\) −0.968765 −0.0493728
\(386\) 36.8602 1.87613
\(387\) 8.00242 0.406786
\(388\) −14.4455 −0.733361
\(389\) −1.28597 −0.0652011 −0.0326006 0.999468i \(-0.510379\pi\)
−0.0326006 + 0.999468i \(0.510379\pi\)
\(390\) 4.05406 0.205286
\(391\) −3.73534 −0.188904
\(392\) 54.2515 2.74011
\(393\) 27.4154 1.38292
\(394\) −58.6743 −2.95597
\(395\) 5.23984 0.263645
\(396\) −7.33560 −0.368628
\(397\) 31.9071 1.60137 0.800685 0.599086i \(-0.204469\pi\)
0.800685 + 0.599086i \(0.204469\pi\)
\(398\) 54.6961 2.74167
\(399\) 5.70787 0.285751
\(400\) 13.5785 0.678926
\(401\) 38.1822 1.90673 0.953364 0.301823i \(-0.0975952\pi\)
0.953364 + 0.301823i \(0.0975952\pi\)
\(402\) −37.0044 −1.84561
\(403\) −9.26646 −0.461595
\(404\) 93.1316 4.63347
\(405\) −2.94756 −0.146465
\(406\) 24.9540 1.23845
\(407\) −4.17187 −0.206792
\(408\) −13.5827 −0.672446
\(409\) 0.912283 0.0451095 0.0225547 0.999746i \(-0.492820\pi\)
0.0225547 + 0.999746i \(0.492820\pi\)
\(410\) −6.32667 −0.312452
\(411\) 10.4450 0.515212
\(412\) 18.5687 0.914816
\(413\) −9.24647 −0.454989
\(414\) 11.6958 0.574818
\(415\) 6.06424 0.297682
\(416\) −22.1719 −1.08707
\(417\) 19.4031 0.950172
\(418\) −12.5214 −0.612441
\(419\) 5.50500 0.268937 0.134469 0.990918i \(-0.457067\pi\)
0.134469 + 0.990918i \(0.457067\pi\)
\(420\) 6.54495 0.319361
\(421\) −8.04720 −0.392197 −0.196098 0.980584i \(-0.562827\pi\)
−0.196098 + 0.980584i \(0.562827\pi\)
\(422\) 26.5416 1.29203
\(423\) −4.39708 −0.213793
\(424\) 19.4074 0.942506
\(425\) −1.19285 −0.0578616
\(426\) 31.5086 1.52660
\(427\) −2.17870 −0.105435
\(428\) −83.2451 −4.02381
\(429\) −1.49942 −0.0723927
\(430\) 15.6628 0.755329
\(431\) −11.9665 −0.576408 −0.288204 0.957569i \(-0.593058\pi\)
−0.288204 + 0.957569i \(0.593058\pi\)
\(432\) 75.6895 3.64161
\(433\) 29.5566 1.42040 0.710201 0.703999i \(-0.248604\pi\)
0.710201 + 0.703999i \(0.248604\pi\)
\(434\) −20.5943 −0.988556
\(435\) −12.1206 −0.581140
\(436\) 45.6505 2.18626
\(437\) 14.5021 0.693729
\(438\) 3.43983 0.164362
\(439\) 17.3711 0.829075 0.414538 0.910032i \(-0.363943\pi\)
0.414538 + 0.910032i \(0.363943\pi\)
\(440\) −8.95019 −0.426683
\(441\) 8.37332 0.398730
\(442\) 3.80107 0.180798
\(443\) 19.2798 0.916012 0.458006 0.888949i \(-0.348564\pi\)
0.458006 + 0.888949i \(0.348564\pi\)
\(444\) 28.1850 1.33760
\(445\) −14.1945 −0.672883
\(446\) 9.76361 0.462320
\(447\) −23.6407 −1.11817
\(448\) −22.9671 −1.08509
\(449\) 6.51781 0.307595 0.153797 0.988102i \(-0.450850\pi\)
0.153797 + 0.988102i \(0.450850\pi\)
\(450\) 3.73495 0.176067
\(451\) 2.33996 0.110184
\(452\) −45.9165 −2.15973
\(453\) 6.97020 0.327489
\(454\) −40.3489 −1.89367
\(455\) −1.14175 −0.0535261
\(456\) 52.7337 2.46948
\(457\) −12.7406 −0.595981 −0.297991 0.954569i \(-0.596316\pi\)
−0.297991 + 0.954569i \(0.596316\pi\)
\(458\) −63.8140 −2.98183
\(459\) −6.64918 −0.310357
\(460\) 16.6289 0.775325
\(461\) 31.1508 1.45084 0.725419 0.688308i \(-0.241646\pi\)
0.725419 + 0.688308i \(0.241646\pi\)
\(462\) −3.33239 −0.155037
\(463\) 9.72995 0.452189 0.226095 0.974105i \(-0.427404\pi\)
0.226095 + 0.974105i \(0.427404\pi\)
\(464\) 129.362 6.00549
\(465\) 10.0030 0.463879
\(466\) −29.6575 −1.37386
\(467\) 4.23935 0.196174 0.0980868 0.995178i \(-0.468728\pi\)
0.0980868 + 0.995178i \(0.468728\pi\)
\(468\) −8.64547 −0.399637
\(469\) 10.4216 0.481225
\(470\) −8.60624 −0.396976
\(471\) −10.4119 −0.479753
\(472\) −85.4259 −3.93205
\(473\) −5.79300 −0.266362
\(474\) 18.0242 0.827877
\(475\) 4.63111 0.212490
\(476\) 6.13650 0.281266
\(477\) 2.99539 0.137149
\(478\) 62.7054 2.86808
\(479\) 31.7379 1.45014 0.725071 0.688674i \(-0.241807\pi\)
0.725071 + 0.688674i \(0.241807\pi\)
\(480\) 23.9342 1.09244
\(481\) −4.91681 −0.224187
\(482\) −11.2574 −0.512760
\(483\) 3.85953 0.175614
\(484\) 5.31028 0.241376
\(485\) −2.72029 −0.123522
\(486\) 35.0747 1.59102
\(487\) −6.48491 −0.293859 −0.146930 0.989147i \(-0.546939\pi\)
−0.146930 + 0.989147i \(0.546939\pi\)
\(488\) −20.1285 −0.911174
\(489\) −2.85786 −0.129237
\(490\) 16.3888 0.740370
\(491\) 21.3615 0.964031 0.482016 0.876163i \(-0.339905\pi\)
0.482016 + 0.876163i \(0.339905\pi\)
\(492\) −15.8087 −0.712711
\(493\) −11.3642 −0.511819
\(494\) −14.7573 −0.663961
\(495\) −1.38140 −0.0620891
\(496\) −106.761 −4.79372
\(497\) −8.87381 −0.398045
\(498\) 20.8600 0.934758
\(499\) 15.1949 0.680218 0.340109 0.940386i \(-0.389536\pi\)
0.340109 + 0.940386i \(0.389536\pi\)
\(500\) 5.31028 0.237483
\(501\) −12.0675 −0.539135
\(502\) 49.4093 2.20524
\(503\) −16.8224 −0.750076 −0.375038 0.927010i \(-0.622370\pi\)
−0.375038 + 0.927010i \(0.622370\pi\)
\(504\) −11.9776 −0.533523
\(505\) 17.5380 0.780430
\(506\) −8.46666 −0.376389
\(507\) 14.7720 0.656048
\(508\) 88.8665 3.94281
\(509\) 2.31853 0.102767 0.0513835 0.998679i \(-0.483637\pi\)
0.0513835 + 0.998679i \(0.483637\pi\)
\(510\) −4.10320 −0.181693
\(511\) −0.968765 −0.0428556
\(512\) −12.3870 −0.547435
\(513\) 25.8148 1.13975
\(514\) −39.2510 −1.73129
\(515\) 3.49675 0.154085
\(516\) 39.1373 1.72293
\(517\) 3.18307 0.139991
\(518\) −10.9274 −0.480121
\(519\) −3.96679 −0.174123
\(520\) −10.5484 −0.462576
\(521\) 4.39367 0.192490 0.0962450 0.995358i \(-0.469317\pi\)
0.0962450 + 0.995358i \(0.469317\pi\)
\(522\) 35.5828 1.55742
\(523\) 8.83180 0.386188 0.193094 0.981180i \(-0.438148\pi\)
0.193094 + 0.981180i \(0.438148\pi\)
\(524\) −114.430 −4.99892
\(525\) 1.23250 0.0537909
\(526\) 33.2438 1.44950
\(527\) 9.37877 0.408546
\(528\) −17.2752 −0.751807
\(529\) −13.1940 −0.573653
\(530\) 5.86276 0.254662
\(531\) −13.1849 −0.572174
\(532\) −23.8244 −1.03292
\(533\) 2.75779 0.119453
\(534\) −48.8266 −2.11293
\(535\) −15.6762 −0.677742
\(536\) 96.2826 4.15878
\(537\) −17.3728 −0.749693
\(538\) 14.4871 0.624584
\(539\) −6.06150 −0.261087
\(540\) 29.6006 1.27381
\(541\) 25.4462 1.09402 0.547009 0.837127i \(-0.315766\pi\)
0.547009 + 0.837127i \(0.315766\pi\)
\(542\) 38.4097 1.64984
\(543\) −2.74725 −0.117896
\(544\) 22.4406 0.962133
\(545\) 8.59662 0.368239
\(546\) −3.92743 −0.168079
\(547\) 20.8447 0.891255 0.445627 0.895219i \(-0.352981\pi\)
0.445627 + 0.895219i \(0.352981\pi\)
\(548\) −43.5967 −1.86236
\(549\) −3.10669 −0.132590
\(550\) −2.70375 −0.115288
\(551\) 44.1205 1.87960
\(552\) 35.6572 1.51767
\(553\) −5.07617 −0.215861
\(554\) −54.9447 −2.33437
\(555\) 5.30763 0.225296
\(556\) −80.9874 −3.43463
\(557\) 18.1884 0.770666 0.385333 0.922778i \(-0.374087\pi\)
0.385333 + 0.922778i \(0.374087\pi\)
\(558\) −29.3661 −1.24317
\(559\) −6.82742 −0.288769
\(560\) −13.1544 −0.555875
\(561\) 1.51759 0.0640728
\(562\) −27.0431 −1.14075
\(563\) 41.9655 1.76864 0.884318 0.466886i \(-0.154624\pi\)
0.884318 + 0.466886i \(0.154624\pi\)
\(564\) −21.5047 −0.905513
\(565\) −8.64672 −0.363770
\(566\) −41.6690 −1.75148
\(567\) 2.85549 0.119919
\(568\) −81.9830 −3.43993
\(569\) −4.03365 −0.169099 −0.0845496 0.996419i \(-0.526945\pi\)
−0.0845496 + 0.996419i \(0.526945\pi\)
\(570\) 15.9303 0.667245
\(571\) −39.9132 −1.67032 −0.835158 0.550010i \(-0.814624\pi\)
−0.835158 + 0.550010i \(0.814624\pi\)
\(572\) 6.25851 0.261681
\(573\) −12.0580 −0.503728
\(574\) 6.12906 0.255822
\(575\) 3.13145 0.130590
\(576\) −32.7496 −1.36457
\(577\) −21.4729 −0.893929 −0.446965 0.894552i \(-0.647495\pi\)
−0.446965 + 0.894552i \(0.647495\pi\)
\(578\) 42.1167 1.75182
\(579\) 17.3445 0.720811
\(580\) 50.5909 2.10067
\(581\) −5.87482 −0.243729
\(582\) −9.35736 −0.387875
\(583\) −2.16838 −0.0898050
\(584\) −8.95019 −0.370361
\(585\) −1.62806 −0.0673121
\(586\) −2.50781 −0.103597
\(587\) 8.50628 0.351092 0.175546 0.984471i \(-0.443831\pi\)
0.175546 + 0.984471i \(0.443831\pi\)
\(588\) 40.9513 1.68880
\(589\) −36.4122 −1.50034
\(590\) −25.8062 −1.06243
\(591\) −27.6091 −1.13568
\(592\) −56.6478 −2.32821
\(593\) −31.7932 −1.30559 −0.652795 0.757535i \(-0.726404\pi\)
−0.652795 + 0.757535i \(0.726404\pi\)
\(594\) −15.0713 −0.618382
\(595\) 1.15559 0.0473745
\(596\) 98.6751 4.04189
\(597\) 25.7371 1.05335
\(598\) −9.97851 −0.408051
\(599\) −48.4679 −1.98034 −0.990172 0.139852i \(-0.955337\pi\)
−0.990172 + 0.139852i \(0.955337\pi\)
\(600\) 11.3868 0.464865
\(601\) −33.4695 −1.36525 −0.682625 0.730769i \(-0.739162\pi\)
−0.682625 + 0.730769i \(0.739162\pi\)
\(602\) −15.1736 −0.618430
\(603\) 14.8605 0.605167
\(604\) −29.0933 −1.18379
\(605\) 1.00000 0.0406558
\(606\) 60.3277 2.45065
\(607\) 2.67486 0.108569 0.0542845 0.998526i \(-0.482712\pi\)
0.0542845 + 0.998526i \(0.482712\pi\)
\(608\) −87.1234 −3.53332
\(609\) 11.7420 0.475811
\(610\) −6.08060 −0.246196
\(611\) 3.75145 0.151768
\(612\) 8.75026 0.353708
\(613\) −47.9182 −1.93540 −0.967699 0.252107i \(-0.918877\pi\)
−0.967699 + 0.252107i \(0.918877\pi\)
\(614\) −38.9343 −1.57126
\(615\) −2.97700 −0.120044
\(616\) 8.67062 0.349349
\(617\) 26.8831 1.08227 0.541137 0.840935i \(-0.317994\pi\)
0.541137 + 0.840935i \(0.317994\pi\)
\(618\) 12.0282 0.483847
\(619\) 23.1893 0.932056 0.466028 0.884770i \(-0.345685\pi\)
0.466028 + 0.884770i \(0.345685\pi\)
\(620\) −41.7521 −1.67681
\(621\) 17.4553 0.700458
\(622\) 31.0138 1.24354
\(623\) 13.7511 0.550926
\(624\) −20.3599 −0.815049
\(625\) 1.00000 0.0400000
\(626\) 73.8334 2.95098
\(627\) −5.89191 −0.235300
\(628\) 43.4586 1.73419
\(629\) 4.97640 0.198422
\(630\) −3.61829 −0.144156
\(631\) 23.5589 0.937865 0.468932 0.883234i \(-0.344639\pi\)
0.468932 + 0.883234i \(0.344639\pi\)
\(632\) −46.8975 −1.86548
\(633\) 12.4891 0.496396
\(634\) −8.84946 −0.351457
\(635\) 16.7348 0.664100
\(636\) 14.6495 0.580891
\(637\) −7.14386 −0.283050
\(638\) −25.7586 −1.01979
\(639\) −12.6535 −0.500564
\(640\) −26.4743 −1.04649
\(641\) −4.55225 −0.179803 −0.0899016 0.995951i \(-0.528655\pi\)
−0.0899016 + 0.995951i \(0.528655\pi\)
\(642\) −53.9236 −2.12819
\(643\) −9.85269 −0.388552 −0.194276 0.980947i \(-0.562236\pi\)
−0.194276 + 0.980947i \(0.562236\pi\)
\(644\) −16.1095 −0.634802
\(645\) 7.37011 0.290198
\(646\) 14.9361 0.587654
\(647\) −2.14227 −0.0842213 −0.0421107 0.999113i \(-0.513408\pi\)
−0.0421107 + 0.999113i \(0.513408\pi\)
\(648\) 26.3812 1.03635
\(649\) 9.54460 0.374658
\(650\) −3.18655 −0.124987
\(651\) −9.69057 −0.379804
\(652\) 11.9285 0.467158
\(653\) 30.1085 1.17824 0.589119 0.808046i \(-0.299475\pi\)
0.589119 + 0.808046i \(0.299475\pi\)
\(654\) 29.5709 1.15632
\(655\) −21.5488 −0.841983
\(656\) 31.7732 1.24054
\(657\) −1.38140 −0.0538934
\(658\) 8.33742 0.325027
\(659\) −15.5244 −0.604747 −0.302373 0.953190i \(-0.597779\pi\)
−0.302373 + 0.953190i \(0.597779\pi\)
\(660\) −6.75597 −0.262976
\(661\) 2.42023 0.0941358 0.0470679 0.998892i \(-0.485012\pi\)
0.0470679 + 0.998892i \(0.485012\pi\)
\(662\) −84.9787 −3.30279
\(663\) 1.78858 0.0694627
\(664\) −54.2761 −2.10632
\(665\) −4.48646 −0.173977
\(666\) −15.5817 −0.603780
\(667\) 29.8332 1.15515
\(668\) 50.3691 1.94884
\(669\) 4.59424 0.177624
\(670\) 29.0859 1.12369
\(671\) 2.24895 0.0868197
\(672\) −23.1866 −0.894444
\(673\) −0.133513 −0.00514655 −0.00257327 0.999997i \(-0.500819\pi\)
−0.00257327 + 0.999997i \(0.500819\pi\)
\(674\) −50.3262 −1.93849
\(675\) 5.57420 0.214551
\(676\) −61.6576 −2.37145
\(677\) 24.7677 0.951898 0.475949 0.879473i \(-0.342105\pi\)
0.475949 + 0.879473i \(0.342105\pi\)
\(678\) −29.7433 −1.14228
\(679\) 2.63533 0.101135
\(680\) 10.6762 0.409414
\(681\) −18.9861 −0.727548
\(682\) 21.2583 0.814021
\(683\) −0.262116 −0.0100296 −0.00501480 0.999987i \(-0.501596\pi\)
−0.00501480 + 0.999987i \(0.501596\pi\)
\(684\) −33.9720 −1.29895
\(685\) −8.20987 −0.313683
\(686\) −34.2120 −1.30622
\(687\) −30.0275 −1.14562
\(688\) −78.6604 −2.99890
\(689\) −2.55557 −0.0973595
\(690\) 10.7717 0.410070
\(691\) −37.6806 −1.43344 −0.716720 0.697361i \(-0.754357\pi\)
−0.716720 + 0.697361i \(0.754357\pi\)
\(692\) 16.5572 0.629409
\(693\) 1.33825 0.0508358
\(694\) −53.1376 −2.01707
\(695\) −15.2511 −0.578505
\(696\) 108.482 4.11199
\(697\) −2.79122 −0.105725
\(698\) 7.03207 0.266168
\(699\) −13.9553 −0.527836
\(700\) −5.14441 −0.194441
\(701\) 38.7705 1.46434 0.732172 0.681120i \(-0.238507\pi\)
0.732172 + 0.681120i \(0.238507\pi\)
\(702\) −17.7625 −0.670401
\(703\) −19.3204 −0.728682
\(704\) 23.7076 0.893515
\(705\) −4.04964 −0.152518
\(706\) 12.3518 0.464867
\(707\) −16.9902 −0.638981
\(708\) −64.4830 −2.42342
\(709\) 14.4160 0.541403 0.270702 0.962663i \(-0.412744\pi\)
0.270702 + 0.962663i \(0.412744\pi\)
\(710\) −24.7662 −0.929458
\(711\) −7.23829 −0.271457
\(712\) 127.043 4.76114
\(713\) −24.6210 −0.922065
\(714\) 3.97503 0.148762
\(715\) 1.17856 0.0440758
\(716\) 72.5133 2.70995
\(717\) 29.5058 1.10192
\(718\) 42.9470 1.60277
\(719\) 51.7436 1.92971 0.964855 0.262783i \(-0.0846402\pi\)
0.964855 + 0.262783i \(0.0846402\pi\)
\(720\) −18.7573 −0.699044
\(721\) −3.38753 −0.126158
\(722\) −6.61668 −0.246247
\(723\) −5.29713 −0.197002
\(724\) 11.4669 0.426163
\(725\) 9.52697 0.353823
\(726\) 3.43983 0.127664
\(727\) −12.5070 −0.463859 −0.231930 0.972733i \(-0.574504\pi\)
−0.231930 + 0.972733i \(0.574504\pi\)
\(728\) 10.2189 0.378737
\(729\) 25.3470 0.938777
\(730\) −2.70375 −0.100070
\(731\) 6.91017 0.255582
\(732\) −15.1938 −0.561580
\(733\) −30.8493 −1.13944 −0.569722 0.821837i \(-0.692949\pi\)
−0.569722 + 0.821837i \(0.692949\pi\)
\(734\) −4.28022 −0.157986
\(735\) 7.71170 0.284450
\(736\) −58.9108 −2.17148
\(737\) −10.7576 −0.396262
\(738\) 8.73964 0.321710
\(739\) −40.7402 −1.49865 −0.749327 0.662201i \(-0.769623\pi\)
−0.749327 + 0.662201i \(0.769623\pi\)
\(740\) −22.1538 −0.814390
\(741\) −6.94399 −0.255094
\(742\) −5.67963 −0.208506
\(743\) −4.29466 −0.157556 −0.0787780 0.996892i \(-0.525102\pi\)
−0.0787780 + 0.996892i \(0.525102\pi\)
\(744\) −89.5289 −3.28229
\(745\) 18.5819 0.680788
\(746\) −86.8027 −3.17807
\(747\) −8.37712 −0.306503
\(748\) −6.33436 −0.231607
\(749\) 15.1866 0.554905
\(750\) 3.43983 0.125605
\(751\) 14.8650 0.542430 0.271215 0.962519i \(-0.412575\pi\)
0.271215 + 0.962519i \(0.412575\pi\)
\(752\) 43.2214 1.57612
\(753\) 23.2494 0.847255
\(754\) −30.3581 −1.10558
\(755\) −5.47867 −0.199389
\(756\) −28.6760 −1.04294
\(757\) 52.1803 1.89652 0.948262 0.317489i \(-0.102840\pi\)
0.948262 + 0.317489i \(0.102840\pi\)
\(758\) −72.7532 −2.64252
\(759\) −3.98397 −0.144609
\(760\) −41.4493 −1.50353
\(761\) 41.7563 1.51367 0.756833 0.653608i \(-0.226746\pi\)
0.756833 + 0.653608i \(0.226746\pi\)
\(762\) 57.5649 2.08536
\(763\) −8.32810 −0.301498
\(764\) 50.3293 1.82085
\(765\) 1.64779 0.0595762
\(766\) 35.9343 1.29836
\(767\) 11.2489 0.406175
\(768\) −30.7435 −1.10936
\(769\) 35.0611 1.26434 0.632168 0.774832i \(-0.282165\pi\)
0.632168 + 0.774832i \(0.282165\pi\)
\(770\) 2.61930 0.0943930
\(771\) −18.4695 −0.665162
\(772\) −72.3949 −2.60555
\(773\) 13.8158 0.496919 0.248459 0.968642i \(-0.420076\pi\)
0.248459 + 0.968642i \(0.420076\pi\)
\(774\) −21.6366 −0.777711
\(775\) −7.86250 −0.282429
\(776\) 24.3471 0.874011
\(777\) −5.14185 −0.184463
\(778\) 3.47694 0.124654
\(779\) 10.8366 0.388262
\(780\) −7.96235 −0.285098
\(781\) 9.15992 0.327768
\(782\) 10.0994 0.361155
\(783\) 53.1053 1.89783
\(784\) −82.3062 −2.93951
\(785\) 8.18386 0.292094
\(786\) −74.1244 −2.64393
\(787\) −14.1305 −0.503697 −0.251849 0.967767i \(-0.581038\pi\)
−0.251849 + 0.967767i \(0.581038\pi\)
\(788\) 115.239 4.10521
\(789\) 15.6428 0.556897
\(790\) −14.1672 −0.504047
\(791\) 8.37664 0.297839
\(792\) 12.3637 0.439327
\(793\) 2.65053 0.0941230
\(794\) −86.2688 −3.06157
\(795\) 2.75871 0.0978412
\(796\) −107.425 −3.80759
\(797\) −30.9703 −1.09702 −0.548512 0.836143i \(-0.684805\pi\)
−0.548512 + 0.836143i \(0.684805\pi\)
\(798\) −15.4327 −0.546311
\(799\) −3.79692 −0.134325
\(800\) −18.8126 −0.665127
\(801\) 19.6082 0.692821
\(802\) −103.235 −3.64536
\(803\) 1.00000 0.0352892
\(804\) 72.6781 2.56316
\(805\) −3.03364 −0.106922
\(806\) 25.0542 0.882498
\(807\) 6.81688 0.239965
\(808\) −156.968 −5.52212
\(809\) 12.8226 0.450818 0.225409 0.974264i \(-0.427628\pi\)
0.225409 + 0.974264i \(0.427628\pi\)
\(810\) 7.96947 0.280019
\(811\) 30.7422 1.07950 0.539751 0.841824i \(-0.318518\pi\)
0.539751 + 0.841824i \(0.318518\pi\)
\(812\) −49.0107 −1.71994
\(813\) 18.0736 0.633868
\(814\) 11.2797 0.395353
\(815\) 2.24631 0.0786849
\(816\) 20.6067 0.721378
\(817\) −26.8280 −0.938594
\(818\) −2.46659 −0.0862422
\(819\) 1.57721 0.0551122
\(820\) 12.4258 0.433929
\(821\) −6.36417 −0.222111 −0.111056 0.993814i \(-0.535423\pi\)
−0.111056 + 0.993814i \(0.535423\pi\)
\(822\) −28.2406 −0.985004
\(823\) −10.9711 −0.382430 −0.191215 0.981548i \(-0.561243\pi\)
−0.191215 + 0.981548i \(0.561243\pi\)
\(824\) −31.2966 −1.09027
\(825\) −1.27224 −0.0442938
\(826\) 25.0002 0.869867
\(827\) 19.4525 0.676431 0.338216 0.941069i \(-0.390177\pi\)
0.338216 + 0.941069i \(0.390177\pi\)
\(828\) −22.9711 −0.798299
\(829\) 30.2928 1.05211 0.526057 0.850449i \(-0.323670\pi\)
0.526057 + 0.850449i \(0.323670\pi\)
\(830\) −16.3962 −0.569121
\(831\) −25.8541 −0.896867
\(832\) 27.9410 0.968679
\(833\) 7.23044 0.250520
\(834\) −52.4611 −1.81658
\(835\) 9.48520 0.328249
\(836\) 24.5925 0.850550
\(837\) −43.8272 −1.51489
\(838\) −14.8842 −0.514165
\(839\) −36.1185 −1.24695 −0.623474 0.781844i \(-0.714279\pi\)
−0.623474 + 0.781844i \(0.714279\pi\)
\(840\) −11.0311 −0.380611
\(841\) 61.7632 2.12976
\(842\) 21.7577 0.749818
\(843\) −12.7251 −0.438275
\(844\) −52.1288 −1.79435
\(845\) −11.6110 −0.399430
\(846\) 11.8886 0.408739
\(847\) −0.968765 −0.0332871
\(848\) −29.4434 −1.01109
\(849\) −19.6072 −0.672918
\(850\) 3.22517 0.110622
\(851\) −13.0640 −0.447828
\(852\) −61.8842 −2.12012
\(853\) 3.33345 0.114135 0.0570676 0.998370i \(-0.481825\pi\)
0.0570676 + 0.998370i \(0.481825\pi\)
\(854\) 5.89067 0.201575
\(855\) −6.39740 −0.218786
\(856\) 140.305 4.79553
\(857\) 17.4481 0.596017 0.298008 0.954563i \(-0.403678\pi\)
0.298008 + 0.954563i \(0.403678\pi\)
\(858\) 4.05406 0.138403
\(859\) −26.8695 −0.916774 −0.458387 0.888753i \(-0.651573\pi\)
−0.458387 + 0.888753i \(0.651573\pi\)
\(860\) −30.7625 −1.04899
\(861\) 2.88401 0.0982868
\(862\) 32.3546 1.10200
\(863\) −39.2400 −1.33575 −0.667873 0.744275i \(-0.732795\pi\)
−0.667873 + 0.744275i \(0.732795\pi\)
\(864\) −104.865 −3.56759
\(865\) 3.11794 0.106013
\(866\) −79.9139 −2.71558
\(867\) 19.8179 0.673051
\(868\) 40.4480 1.37289
\(869\) 5.23984 0.177749
\(870\) 32.7712 1.11105
\(871\) −12.6785 −0.429596
\(872\) −76.9414 −2.60556
\(873\) 3.75780 0.127182
\(874\) −39.2101 −1.32630
\(875\) −0.968765 −0.0327502
\(876\) −6.75597 −0.228263
\(877\) 45.1170 1.52349 0.761747 0.647875i \(-0.224342\pi\)
0.761747 + 0.647875i \(0.224342\pi\)
\(878\) −46.9671 −1.58506
\(879\) −1.18004 −0.0398018
\(880\) 13.5785 0.457732
\(881\) −12.2355 −0.412223 −0.206112 0.978528i \(-0.566081\pi\)
−0.206112 + 0.978528i \(0.566081\pi\)
\(882\) −22.6394 −0.762308
\(883\) 17.6401 0.593637 0.296819 0.954934i \(-0.404074\pi\)
0.296819 + 0.954934i \(0.404074\pi\)
\(884\) −7.46545 −0.251090
\(885\) −12.1431 −0.408184
\(886\) −52.1279 −1.75127
\(887\) 42.8795 1.43975 0.719876 0.694103i \(-0.244199\pi\)
0.719876 + 0.694103i \(0.244199\pi\)
\(888\) −47.5043 −1.59414
\(889\) −16.2121 −0.543736
\(890\) 38.3784 1.28645
\(891\) −2.94756 −0.0987470
\(892\) −19.1761 −0.642064
\(893\) 14.7412 0.493294
\(894\) 63.9186 2.13776
\(895\) 13.6553 0.456445
\(896\) 25.6474 0.856820
\(897\) −4.69536 −0.156773
\(898\) −17.6226 −0.588072
\(899\) −74.9058 −2.49825
\(900\) −7.33560 −0.244520
\(901\) 2.58655 0.0861703
\(902\) −6.32667 −0.210655
\(903\) −7.13990 −0.237601
\(904\) 77.3898 2.57395
\(905\) 2.15937 0.0717800
\(906\) −18.8457 −0.626107
\(907\) −35.6009 −1.18211 −0.591054 0.806632i \(-0.701288\pi\)
−0.591054 + 0.806632i \(0.701288\pi\)
\(908\) 79.2470 2.62990
\(909\) −24.2269 −0.803555
\(910\) 3.08701 0.102334
\(911\) 2.04185 0.0676495 0.0338247 0.999428i \(-0.489231\pi\)
0.0338247 + 0.999428i \(0.489231\pi\)
\(912\) −80.0034 −2.64918
\(913\) 6.06424 0.200697
\(914\) 34.4475 1.13942
\(915\) −2.86121 −0.0945887
\(916\) 125.333 4.14113
\(917\) 20.8758 0.689378
\(918\) 17.9777 0.593354
\(919\) −20.3660 −0.671812 −0.335906 0.941896i \(-0.609042\pi\)
−0.335906 + 0.941896i \(0.609042\pi\)
\(920\) −28.0270 −0.924024
\(921\) −18.3204 −0.603679
\(922\) −84.2241 −2.77377
\(923\) 10.7956 0.355340
\(924\) 6.54495 0.215313
\(925\) −4.17187 −0.137170
\(926\) −26.3074 −0.864515
\(927\) −4.83040 −0.158651
\(928\) −179.227 −5.88342
\(929\) 37.9505 1.24512 0.622558 0.782574i \(-0.286094\pi\)
0.622558 + 0.782574i \(0.286094\pi\)
\(930\) −27.0457 −0.886864
\(931\) −28.0715 −0.920005
\(932\) 58.2486 1.90799
\(933\) 14.5935 0.477768
\(934\) −11.4621 −0.375053
\(935\) −1.19285 −0.0390103
\(936\) 14.5715 0.476283
\(937\) 58.8257 1.92175 0.960875 0.276981i \(-0.0893339\pi\)
0.960875 + 0.276981i \(0.0893339\pi\)
\(938\) −28.1774 −0.920025
\(939\) 34.7421 1.13377
\(940\) 16.9030 0.551315
\(941\) 31.8352 1.03780 0.518899 0.854836i \(-0.326342\pi\)
0.518899 + 0.854836i \(0.326342\pi\)
\(942\) 28.1511 0.917212
\(943\) 7.32746 0.238615
\(944\) 129.602 4.21817
\(945\) −5.40009 −0.175665
\(946\) 15.6628 0.509243
\(947\) −0.796045 −0.0258680 −0.0129340 0.999916i \(-0.504117\pi\)
−0.0129340 + 0.999916i \(0.504117\pi\)
\(948\) −35.4002 −1.14975
\(949\) 1.17856 0.0382578
\(950\) −12.5214 −0.406248
\(951\) −4.16409 −0.135030
\(952\) −10.3427 −0.335210
\(953\) −36.0714 −1.16847 −0.584233 0.811586i \(-0.698605\pi\)
−0.584233 + 0.811586i \(0.698605\pi\)
\(954\) −8.09879 −0.262208
\(955\) 9.47771 0.306692
\(956\) −123.156 −3.98315
\(957\) −12.1206 −0.391804
\(958\) −85.8114 −2.77244
\(959\) 7.95343 0.256830
\(960\) −30.1619 −0.973471
\(961\) 30.8190 0.994160
\(962\) 13.2938 0.428611
\(963\) 21.6551 0.697825
\(964\) 22.1100 0.712114
\(965\) −13.6330 −0.438861
\(966\) −10.4352 −0.335747
\(967\) 23.9237 0.769335 0.384668 0.923055i \(-0.374316\pi\)
0.384668 + 0.923055i \(0.374316\pi\)
\(968\) −8.95019 −0.287670
\(969\) 7.02815 0.225777
\(970\) 7.35501 0.236155
\(971\) −18.8358 −0.604469 −0.302234 0.953234i \(-0.597732\pi\)
−0.302234 + 0.953234i \(0.597732\pi\)
\(972\) −68.8881 −2.20959
\(973\) 14.7747 0.473655
\(974\) 17.5336 0.561813
\(975\) −1.49942 −0.0480199
\(976\) 30.5374 0.977478
\(977\) 35.2631 1.12817 0.564083 0.825718i \(-0.309230\pi\)
0.564083 + 0.825718i \(0.309230\pi\)
\(978\) 7.72694 0.247080
\(979\) −14.1945 −0.453657
\(980\) −32.1882 −1.02822
\(981\) −11.8753 −0.379150
\(982\) −57.7563 −1.84308
\(983\) 10.1781 0.324631 0.162315 0.986739i \(-0.448104\pi\)
0.162315 + 0.986739i \(0.448104\pi\)
\(984\) 26.6447 0.849402
\(985\) 21.7011 0.691454
\(986\) 30.7261 0.978517
\(987\) 3.92315 0.124875
\(988\) 28.9839 0.922099
\(989\) −18.1405 −0.576834
\(990\) 3.73495 0.118705
\(991\) 32.2748 1.02524 0.512621 0.858615i \(-0.328675\pi\)
0.512621 + 0.858615i \(0.328675\pi\)
\(992\) 147.914 4.69628
\(993\) −39.9865 −1.26893
\(994\) 23.9926 0.760999
\(995\) −20.2297 −0.641324
\(996\) −40.9698 −1.29818
\(997\) −22.7855 −0.721624 −0.360812 0.932639i \(-0.617500\pi\)
−0.360812 + 0.932639i \(0.617500\pi\)
\(998\) −41.0833 −1.30047
\(999\) −23.2548 −0.735750
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 \(a_p\))