Properties

Label 8023.2.a.c.1.12
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.54938 q^{2}\) \(+0.0117245 q^{3}\) \(+4.49933 q^{4}\) \(+3.26987 q^{5}\) \(-0.0298901 q^{6}\) \(-0.929031 q^{7}\) \(-6.37175 q^{8}\) \(-2.99986 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.54938 q^{2}\) \(+0.0117245 q^{3}\) \(+4.49933 q^{4}\) \(+3.26987 q^{5}\) \(-0.0298901 q^{6}\) \(-0.929031 q^{7}\) \(-6.37175 q^{8}\) \(-2.99986 q^{9}\) \(-8.33615 q^{10}\) \(-5.56961 q^{11}\) \(+0.0527523 q^{12}\) \(+3.44304 q^{13}\) \(+2.36845 q^{14}\) \(+0.0383375 q^{15}\) \(+7.24534 q^{16}\) \(+1.70770 q^{17}\) \(+7.64779 q^{18}\) \(+5.28092 q^{19}\) \(+14.7123 q^{20}\) \(-0.0108924 q^{21}\) \(+14.1990 q^{22}\) \(-9.41041 q^{23}\) \(-0.0747054 q^{24}\) \(+5.69208 q^{25}\) \(-8.77761 q^{26}\) \(-0.0703452 q^{27}\) \(-4.18002 q^{28}\) \(+1.77199 q^{29}\) \(-0.0977369 q^{30}\) \(+9.57642 q^{31}\) \(-5.72761 q^{32}\) \(-0.0653007 q^{33}\) \(-4.35358 q^{34}\) \(-3.03781 q^{35}\) \(-13.4974 q^{36}\) \(-7.57145 q^{37}\) \(-13.4631 q^{38}\) \(+0.0403678 q^{39}\) \(-20.8348 q^{40}\) \(-8.48628 q^{41}\) \(+0.0277688 q^{42}\) \(+6.66532 q^{43}\) \(-25.0595 q^{44}\) \(-9.80917 q^{45}\) \(+23.9907 q^{46}\) \(+2.35175 q^{47}\) \(+0.0849477 q^{48}\) \(-6.13690 q^{49}\) \(-14.5113 q^{50}\) \(+0.0200219 q^{51}\) \(+15.4914 q^{52}\) \(-6.47642 q^{53}\) \(+0.179337 q^{54}\) \(-18.2119 q^{55}\) \(+5.91955 q^{56}\) \(+0.0619160 q^{57}\) \(-4.51747 q^{58}\) \(+6.35518 q^{59}\) \(+0.172493 q^{60}\) \(+9.96874 q^{61}\) \(-24.4139 q^{62}\) \(+2.78696 q^{63}\) \(+0.111184 q^{64}\) \(+11.2583 q^{65}\) \(+0.166476 q^{66}\) \(-3.80965 q^{67}\) \(+7.68353 q^{68}\) \(-0.110332 q^{69}\) \(+7.74454 q^{70}\) \(-1.00000 q^{71}\) \(+19.1144 q^{72}\) \(+3.10423 q^{73}\) \(+19.3025 q^{74}\) \(+0.0667366 q^{75}\) \(+23.7606 q^{76}\) \(+5.17434 q^{77}\) \(-0.102913 q^{78}\) \(+10.9911 q^{79}\) \(+23.6913 q^{80}\) \(+8.99876 q^{81}\) \(+21.6347 q^{82}\) \(-0.444810 q^{83}\) \(-0.0490085 q^{84}\) \(+5.58398 q^{85}\) \(-16.9924 q^{86}\) \(+0.0207756 q^{87}\) \(+35.4881 q^{88}\) \(-16.2834 q^{89}\) \(+25.0073 q^{90}\) \(-3.19869 q^{91}\) \(-42.3406 q^{92}\) \(+0.112278 q^{93}\) \(-5.99549 q^{94}\) \(+17.2679 q^{95}\) \(-0.0671532 q^{96}\) \(+1.42351 q^{97}\) \(+15.6453 q^{98}\) \(+16.7081 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54938 −1.80268 −0.901342 0.433109i \(-0.857417\pi\)
−0.901342 + 0.433109i \(0.857417\pi\)
\(3\) 0.0117245 0.00676912 0.00338456 0.999994i \(-0.498923\pi\)
0.00338456 + 0.999994i \(0.498923\pi\)
\(4\) 4.49933 2.24967
\(5\) 3.26987 1.46233 0.731166 0.682200i \(-0.238976\pi\)
0.731166 + 0.682200i \(0.238976\pi\)
\(6\) −0.0298901 −0.0122026
\(7\) −0.929031 −0.351141 −0.175570 0.984467i \(-0.556177\pi\)
−0.175570 + 0.984467i \(0.556177\pi\)
\(8\) −6.37175 −2.25275
\(9\) −2.99986 −0.999954
\(10\) −8.33615 −2.63612
\(11\) −5.56961 −1.67930 −0.839650 0.543128i \(-0.817240\pi\)
−0.839650 + 0.543128i \(0.817240\pi\)
\(12\) 0.0527523 0.0152283
\(13\) 3.44304 0.954927 0.477463 0.878652i \(-0.341556\pi\)
0.477463 + 0.878652i \(0.341556\pi\)
\(14\) 2.36845 0.632995
\(15\) 0.0383375 0.00989871
\(16\) 7.24534 1.81133
\(17\) 1.70770 0.414179 0.207090 0.978322i \(-0.433601\pi\)
0.207090 + 0.978322i \(0.433601\pi\)
\(18\) 7.64779 1.80260
\(19\) 5.28092 1.21153 0.605763 0.795645i \(-0.292868\pi\)
0.605763 + 0.795645i \(0.292868\pi\)
\(20\) 14.7123 3.28976
\(21\) −0.0108924 −0.00237691
\(22\) 14.1990 3.02725
\(23\) −9.41041 −1.96221 −0.981103 0.193487i \(-0.938020\pi\)
−0.981103 + 0.193487i \(0.938020\pi\)
\(24\) −0.0747054 −0.0152492
\(25\) 5.69208 1.13842
\(26\) −8.77761 −1.72143
\(27\) −0.0703452 −0.0135379
\(28\) −4.18002 −0.789949
\(29\) 1.77199 0.329050 0.164525 0.986373i \(-0.447391\pi\)
0.164525 + 0.986373i \(0.447391\pi\)
\(30\) −0.0977369 −0.0178442
\(31\) 9.57642 1.71998 0.859988 0.510314i \(-0.170471\pi\)
0.859988 + 0.510314i \(0.170471\pi\)
\(32\) −5.72761 −1.01251
\(33\) −0.0653007 −0.0113674
\(34\) −4.35358 −0.746634
\(35\) −3.03781 −0.513484
\(36\) −13.4974 −2.24956
\(37\) −7.57145 −1.24474 −0.622370 0.782723i \(-0.713830\pi\)
−0.622370 + 0.782723i \(0.713830\pi\)
\(38\) −13.4631 −2.18400
\(39\) 0.0403678 0.00646402
\(40\) −20.8348 −3.29427
\(41\) −8.48628 −1.32533 −0.662667 0.748914i \(-0.730576\pi\)
−0.662667 + 0.748914i \(0.730576\pi\)
\(42\) 0.0277688 0.00428482
\(43\) 6.66532 1.01645 0.508226 0.861224i \(-0.330302\pi\)
0.508226 + 0.861224i \(0.330302\pi\)
\(44\) −25.0595 −3.77787
\(45\) −9.80917 −1.46227
\(46\) 23.9907 3.53724
\(47\) 2.35175 0.343037 0.171519 0.985181i \(-0.445133\pi\)
0.171519 + 0.985181i \(0.445133\pi\)
\(48\) 0.0849477 0.0122611
\(49\) −6.13690 −0.876700
\(50\) −14.5113 −2.05220
\(51\) 0.0200219 0.00280363
\(52\) 15.4914 2.14827
\(53\) −6.47642 −0.889605 −0.444803 0.895629i \(-0.646726\pi\)
−0.444803 + 0.895629i \(0.646726\pi\)
\(54\) 0.179337 0.0244046
\(55\) −18.2119 −2.45569
\(56\) 5.91955 0.791033
\(57\) 0.0619160 0.00820097
\(58\) −4.51747 −0.593172
\(59\) 6.35518 0.827374 0.413687 0.910419i \(-0.364241\pi\)
0.413687 + 0.910419i \(0.364241\pi\)
\(60\) 0.172493 0.0222688
\(61\) 9.96874 1.27637 0.638183 0.769884i \(-0.279686\pi\)
0.638183 + 0.769884i \(0.279686\pi\)
\(62\) −24.4139 −3.10057
\(63\) 2.78696 0.351125
\(64\) 0.111184 0.0138980
\(65\) 11.2583 1.39642
\(66\) 0.166476 0.0204918
\(67\) −3.80965 −0.465423 −0.232712 0.972546i \(-0.574760\pi\)
−0.232712 + 0.972546i \(0.574760\pi\)
\(68\) 7.68353 0.931765
\(69\) −0.110332 −0.0132824
\(70\) 7.74454 0.925649
\(71\) −1.00000 −0.118678
\(72\) 19.1144 2.25265
\(73\) 3.10423 0.363322 0.181661 0.983361i \(-0.441853\pi\)
0.181661 + 0.983361i \(0.441853\pi\)
\(74\) 19.3025 2.24387
\(75\) 0.0667366 0.00770607
\(76\) 23.7606 2.72553
\(77\) 5.17434 0.589670
\(78\) −0.102913 −0.0116526
\(79\) 10.9911 1.23659 0.618295 0.785946i \(-0.287824\pi\)
0.618295 + 0.785946i \(0.287824\pi\)
\(80\) 23.6913 2.64877
\(81\) 8.99876 0.999863
\(82\) 21.6347 2.38916
\(83\) −0.444810 −0.0488242 −0.0244121 0.999702i \(-0.507771\pi\)
−0.0244121 + 0.999702i \(0.507771\pi\)
\(84\) −0.0490085 −0.00534727
\(85\) 5.58398 0.605667
\(86\) −16.9924 −1.83234
\(87\) 0.0207756 0.00222738
\(88\) 35.4881 3.78305
\(89\) −16.2834 −1.72604 −0.863021 0.505169i \(-0.831430\pi\)
−0.863021 + 0.505169i \(0.831430\pi\)
\(90\) 25.0073 2.63600
\(91\) −3.19869 −0.335314
\(92\) −42.3406 −4.41431
\(93\) 0.112278 0.0116427
\(94\) −5.99549 −0.618388
\(95\) 17.2679 1.77165
\(96\) −0.0671532 −0.00685380
\(97\) 1.42351 0.144536 0.0722678 0.997385i \(-0.476976\pi\)
0.0722678 + 0.997385i \(0.476976\pi\)
\(98\) 15.6453 1.58041
\(99\) 16.7081 1.67922
\(100\) 25.6106 2.56106
\(101\) 3.69311 0.367478 0.183739 0.982975i \(-0.441180\pi\)
0.183739 + 0.982975i \(0.441180\pi\)
\(102\) −0.0510435 −0.00505406
\(103\) −2.27534 −0.224196 −0.112098 0.993697i \(-0.535757\pi\)
−0.112098 + 0.993697i \(0.535757\pi\)
\(104\) −21.9382 −2.15121
\(105\) −0.0356167 −0.00347584
\(106\) 16.5109 1.60368
\(107\) 4.03121 0.389711 0.194856 0.980832i \(-0.437576\pi\)
0.194856 + 0.980832i \(0.437576\pi\)
\(108\) −0.316507 −0.0304559
\(109\) −11.8856 −1.13843 −0.569216 0.822188i \(-0.692753\pi\)
−0.569216 + 0.822188i \(0.692753\pi\)
\(110\) 46.4291 4.42684
\(111\) −0.0887713 −0.00842580
\(112\) −6.73114 −0.636033
\(113\) −1.00000 −0.0940721
\(114\) −0.157847 −0.0147837
\(115\) −30.7708 −2.86940
\(116\) 7.97276 0.740252
\(117\) −10.3286 −0.954883
\(118\) −16.2018 −1.49149
\(119\) −1.58651 −0.145435
\(120\) −0.244277 −0.0222994
\(121\) 20.0205 1.82005
\(122\) −25.4141 −2.30089
\(123\) −0.0994971 −0.00897135
\(124\) 43.0875 3.86937
\(125\) 2.26300 0.202409
\(126\) −7.10503 −0.632966
\(127\) 14.6142 1.29680 0.648400 0.761300i \(-0.275439\pi\)
0.648400 + 0.761300i \(0.275439\pi\)
\(128\) 11.1718 0.987455
\(129\) 0.0781473 0.00688048
\(130\) −28.7017 −2.51730
\(131\) −3.45705 −0.302044 −0.151022 0.988530i \(-0.548256\pi\)
−0.151022 + 0.988530i \(0.548256\pi\)
\(132\) −0.293810 −0.0255728
\(133\) −4.90614 −0.425416
\(134\) 9.71225 0.839010
\(135\) −0.230020 −0.0197970
\(136\) −10.8811 −0.933043
\(137\) 5.82743 0.497871 0.248936 0.968520i \(-0.419919\pi\)
0.248936 + 0.968520i \(0.419919\pi\)
\(138\) 0.281278 0.0239440
\(139\) −12.2602 −1.03990 −0.519948 0.854198i \(-0.674049\pi\)
−0.519948 + 0.854198i \(0.674049\pi\)
\(140\) −13.6681 −1.15517
\(141\) 0.0275730 0.00232206
\(142\) 2.54938 0.213939
\(143\) −19.1764 −1.60361
\(144\) −21.7350 −1.81125
\(145\) 5.79417 0.481180
\(146\) −7.91385 −0.654955
\(147\) −0.0719519 −0.00593449
\(148\) −34.0665 −2.80025
\(149\) −5.41982 −0.444009 −0.222004 0.975046i \(-0.571260\pi\)
−0.222004 + 0.975046i \(0.571260\pi\)
\(150\) −0.170137 −0.0138916
\(151\) −9.47806 −0.771314 −0.385657 0.922642i \(-0.626025\pi\)
−0.385657 + 0.922642i \(0.626025\pi\)
\(152\) −33.6487 −2.72927
\(153\) −5.12288 −0.414160
\(154\) −13.1913 −1.06299
\(155\) 31.3137 2.51518
\(156\) 0.181628 0.0145419
\(157\) −9.38842 −0.749277 −0.374639 0.927171i \(-0.622233\pi\)
−0.374639 + 0.927171i \(0.622233\pi\)
\(158\) −28.0204 −2.22918
\(159\) −0.0759326 −0.00602185
\(160\) −18.7286 −1.48062
\(161\) 8.74256 0.689010
\(162\) −22.9413 −1.80244
\(163\) 2.88184 0.225723 0.112862 0.993611i \(-0.463998\pi\)
0.112862 + 0.993611i \(0.463998\pi\)
\(164\) −38.1826 −2.98156
\(165\) −0.213525 −0.0166229
\(166\) 1.13399 0.0880146
\(167\) 0.473924 0.0366734 0.0183367 0.999832i \(-0.494163\pi\)
0.0183367 + 0.999832i \(0.494163\pi\)
\(168\) 0.0694036 0.00535460
\(169\) −1.14549 −0.0881148
\(170\) −14.2357 −1.09183
\(171\) −15.8420 −1.21147
\(172\) 29.9895 2.28668
\(173\) −3.24839 −0.246970 −0.123485 0.992346i \(-0.539407\pi\)
−0.123485 + 0.992346i \(0.539407\pi\)
\(174\) −0.0529649 −0.00401526
\(175\) −5.28811 −0.399744
\(176\) −40.3537 −3.04177
\(177\) 0.0745111 0.00560060
\(178\) 41.5127 3.11151
\(179\) 17.4771 1.30630 0.653150 0.757229i \(-0.273447\pi\)
0.653150 + 0.757229i \(0.273447\pi\)
\(180\) −44.1347 −3.28961
\(181\) 16.5353 1.22906 0.614530 0.788893i \(-0.289346\pi\)
0.614530 + 0.788893i \(0.289346\pi\)
\(182\) 8.15467 0.604464
\(183\) 0.116878 0.00863989
\(184\) 59.9608 4.42037
\(185\) −24.7577 −1.82022
\(186\) −0.286240 −0.0209882
\(187\) −9.51124 −0.695531
\(188\) 10.5813 0.771720
\(189\) 0.0653528 0.00475372
\(190\) −44.0225 −3.19373
\(191\) −25.2018 −1.82354 −0.911769 0.410704i \(-0.865283\pi\)
−0.911769 + 0.410704i \(0.865283\pi\)
\(192\) 0.00130358 9.40775e−5 0
\(193\) −18.7587 −1.35028 −0.675139 0.737691i \(-0.735916\pi\)
−0.675139 + 0.737691i \(0.735916\pi\)
\(194\) −3.62907 −0.260552
\(195\) 0.131998 0.00945254
\(196\) −27.6120 −1.97228
\(197\) −5.02044 −0.357692 −0.178846 0.983877i \(-0.557236\pi\)
−0.178846 + 0.983877i \(0.557236\pi\)
\(198\) −42.5952 −3.02711
\(199\) −25.4114 −1.80136 −0.900682 0.434478i \(-0.856933\pi\)
−0.900682 + 0.434478i \(0.856933\pi\)
\(200\) −36.2685 −2.56457
\(201\) −0.0446661 −0.00315051
\(202\) −9.41512 −0.662446
\(203\) −1.64623 −0.115543
\(204\) 0.0900853 0.00630723
\(205\) −27.7491 −1.93808
\(206\) 5.80071 0.404154
\(207\) 28.2299 1.96212
\(208\) 24.9460 1.72969
\(209\) −29.4126 −2.03452
\(210\) 0.0908006 0.00626584
\(211\) −9.95845 −0.685568 −0.342784 0.939414i \(-0.611370\pi\)
−0.342784 + 0.939414i \(0.611370\pi\)
\(212\) −29.1396 −2.00132
\(213\) −0.0117245 −0.000803347 0
\(214\) −10.2771 −0.702526
\(215\) 21.7947 1.48639
\(216\) 0.448222 0.0304976
\(217\) −8.89679 −0.603953
\(218\) 30.3008 2.05223
\(219\) 0.0363954 0.00245937
\(220\) −81.9415 −5.52449
\(221\) 5.87969 0.395511
\(222\) 0.226312 0.0151890
\(223\) 10.8374 0.725725 0.362862 0.931843i \(-0.381799\pi\)
0.362862 + 0.931843i \(0.381799\pi\)
\(224\) 5.32113 0.355533
\(225\) −17.0754 −1.13836
\(226\) 2.54938 0.169582
\(227\) −3.82878 −0.254125 −0.127063 0.991895i \(-0.540555\pi\)
−0.127063 + 0.991895i \(0.540555\pi\)
\(228\) 0.278581 0.0184494
\(229\) 4.40440 0.291051 0.145526 0.989354i \(-0.453513\pi\)
0.145526 + 0.989354i \(0.453513\pi\)
\(230\) 78.4466 5.17261
\(231\) 0.0606663 0.00399155
\(232\) −11.2907 −0.741268
\(233\) 6.40012 0.419286 0.209643 0.977778i \(-0.432770\pi\)
0.209643 + 0.977778i \(0.432770\pi\)
\(234\) 26.3316 1.72135
\(235\) 7.68991 0.501635
\(236\) 28.5941 1.86132
\(237\) 0.128864 0.00837063
\(238\) 4.04461 0.262173
\(239\) 16.0555 1.03855 0.519273 0.854609i \(-0.326203\pi\)
0.519273 + 0.854609i \(0.326203\pi\)
\(240\) 0.277768 0.0179299
\(241\) −28.5223 −1.83728 −0.918641 0.395094i \(-0.870712\pi\)
−0.918641 + 0.395094i \(0.870712\pi\)
\(242\) −51.0399 −3.28097
\(243\) 0.316541 0.0203061
\(244\) 44.8527 2.87140
\(245\) −20.0669 −1.28203
\(246\) 0.253656 0.0161725
\(247\) 18.1824 1.15692
\(248\) −61.0186 −3.87468
\(249\) −0.00521516 −0.000330497 0
\(250\) −5.76925 −0.364880
\(251\) 18.0735 1.14079 0.570395 0.821371i \(-0.306790\pi\)
0.570395 + 0.821371i \(0.306790\pi\)
\(252\) 12.5395 0.789913
\(253\) 52.4123 3.29513
\(254\) −37.2571 −2.33772
\(255\) 0.0654692 0.00409984
\(256\) −28.7035 −1.79397
\(257\) −28.2394 −1.76153 −0.880764 0.473556i \(-0.842970\pi\)
−0.880764 + 0.473556i \(0.842970\pi\)
\(258\) −0.199227 −0.0124033
\(259\) 7.03411 0.437079
\(260\) 50.6548 3.14148
\(261\) −5.31572 −0.329035
\(262\) 8.81334 0.544490
\(263\) −19.8293 −1.22273 −0.611364 0.791349i \(-0.709379\pi\)
−0.611364 + 0.791349i \(0.709379\pi\)
\(264\) 0.416080 0.0256079
\(265\) −21.1771 −1.30090
\(266\) 12.5076 0.766890
\(267\) −0.190915 −0.0116838
\(268\) −17.1409 −1.04705
\(269\) 12.9440 0.789212 0.394606 0.918851i \(-0.370881\pi\)
0.394606 + 0.918851i \(0.370881\pi\)
\(270\) 0.586408 0.0356877
\(271\) −19.2483 −1.16925 −0.584625 0.811303i \(-0.698758\pi\)
−0.584625 + 0.811303i \(0.698758\pi\)
\(272\) 12.3729 0.750217
\(273\) −0.0375029 −0.00226978
\(274\) −14.8563 −0.897504
\(275\) −31.7026 −1.91174
\(276\) −0.496421 −0.0298810
\(277\) −27.4561 −1.64967 −0.824837 0.565370i \(-0.808733\pi\)
−0.824837 + 0.565370i \(0.808733\pi\)
\(278\) 31.2559 1.87460
\(279\) −28.7279 −1.71990
\(280\) 19.3562 1.15675
\(281\) 2.25837 0.134723 0.0673616 0.997729i \(-0.478542\pi\)
0.0673616 + 0.997729i \(0.478542\pi\)
\(282\) −0.0702940 −0.00418594
\(283\) −1.49274 −0.0887343 −0.0443671 0.999015i \(-0.514127\pi\)
−0.0443671 + 0.999015i \(0.514127\pi\)
\(284\) −4.49933 −0.266986
\(285\) 0.202457 0.0119925
\(286\) 48.8878 2.89080
\(287\) 7.88401 0.465379
\(288\) 17.1821 1.01246
\(289\) −14.0837 −0.828456
\(290\) −14.7715 −0.867415
\(291\) 0.0166899 0.000978380 0
\(292\) 13.9670 0.817354
\(293\) 9.94664 0.581089 0.290544 0.956861i \(-0.406164\pi\)
0.290544 + 0.956861i \(0.406164\pi\)
\(294\) 0.183433 0.0106980
\(295\) 20.7806 1.20990
\(296\) 48.2434 2.80409
\(297\) 0.391795 0.0227343
\(298\) 13.8172 0.800407
\(299\) −32.4004 −1.87376
\(300\) 0.300270 0.0173361
\(301\) −6.19228 −0.356917
\(302\) 24.1632 1.39043
\(303\) 0.0432997 0.00248750
\(304\) 38.2620 2.19448
\(305\) 32.5965 1.86647
\(306\) 13.0602 0.746599
\(307\) −26.0517 −1.48685 −0.743425 0.668819i \(-0.766800\pi\)
−0.743425 + 0.668819i \(0.766800\pi\)
\(308\) 23.2811 1.32656
\(309\) −0.0266772 −0.00151761
\(310\) −79.8305 −4.53407
\(311\) 4.82082 0.273364 0.136682 0.990615i \(-0.456356\pi\)
0.136682 + 0.990615i \(0.456356\pi\)
\(312\) −0.257213 −0.0145618
\(313\) 9.44313 0.533757 0.266879 0.963730i \(-0.414008\pi\)
0.266879 + 0.963730i \(0.414008\pi\)
\(314\) 23.9346 1.35071
\(315\) 9.11302 0.513461
\(316\) 49.4524 2.78192
\(317\) 10.8513 0.609470 0.304735 0.952437i \(-0.401432\pi\)
0.304735 + 0.952437i \(0.401432\pi\)
\(318\) 0.193581 0.0108555
\(319\) −9.86927 −0.552573
\(320\) 0.363559 0.0203235
\(321\) 0.0472638 0.00263801
\(322\) −22.2881 −1.24207
\(323\) 9.01825 0.501789
\(324\) 40.4884 2.24936
\(325\) 19.5980 1.08710
\(326\) −7.34691 −0.406908
\(327\) −0.139352 −0.00770619
\(328\) 54.0724 2.98565
\(329\) −2.18484 −0.120454
\(330\) 0.544356 0.0299658
\(331\) 9.31371 0.511928 0.255964 0.966686i \(-0.417607\pi\)
0.255964 + 0.966686i \(0.417607\pi\)
\(332\) −2.00135 −0.109838
\(333\) 22.7133 1.24468
\(334\) −1.20821 −0.0661104
\(335\) −12.4571 −0.680603
\(336\) −0.0789191 −0.00430539
\(337\) 28.4746 1.55111 0.775556 0.631279i \(-0.217470\pi\)
0.775556 + 0.631279i \(0.217470\pi\)
\(338\) 2.92029 0.158843
\(339\) −0.0117245 −0.000636786 0
\(340\) 25.1242 1.36255
\(341\) −53.3369 −2.88836
\(342\) 40.3873 2.18390
\(343\) 12.2046 0.658986
\(344\) −42.4697 −2.28981
\(345\) −0.360772 −0.0194233
\(346\) 8.28137 0.445209
\(347\) −32.7256 −1.75680 −0.878401 0.477924i \(-0.841389\pi\)
−0.878401 + 0.477924i \(0.841389\pi\)
\(348\) 0.0934763 0.00501086
\(349\) −26.3566 −1.41084 −0.705418 0.708792i \(-0.749241\pi\)
−0.705418 + 0.708792i \(0.749241\pi\)
\(350\) 13.4814 0.720612
\(351\) −0.242201 −0.0129277
\(352\) 31.9006 1.70031
\(353\) −19.1170 −1.01749 −0.508747 0.860916i \(-0.669891\pi\)
−0.508747 + 0.860916i \(0.669891\pi\)
\(354\) −0.189957 −0.0100961
\(355\) −3.26987 −0.173547
\(356\) −73.2646 −3.88302
\(357\) −0.0186010 −0.000984468 0
\(358\) −44.5557 −2.35484
\(359\) −3.22116 −0.170006 −0.0850031 0.996381i \(-0.527090\pi\)
−0.0850031 + 0.996381i \(0.527090\pi\)
\(360\) 62.5016 3.29412
\(361\) 8.88810 0.467795
\(362\) −42.1548 −2.21561
\(363\) 0.234730 0.0123201
\(364\) −14.3920 −0.754344
\(365\) 10.1504 0.531298
\(366\) −0.297967 −0.0155750
\(367\) −17.0879 −0.891979 −0.445990 0.895038i \(-0.647148\pi\)
−0.445990 + 0.895038i \(0.647148\pi\)
\(368\) −68.1816 −3.55421
\(369\) 25.4577 1.32527
\(370\) 63.1168 3.28128
\(371\) 6.01680 0.312377
\(372\) 0.505178 0.0261923
\(373\) 7.94138 0.411189 0.205595 0.978637i \(-0.434087\pi\)
0.205595 + 0.978637i \(0.434087\pi\)
\(374\) 24.2478 1.25382
\(375\) 0.0265325 0.00137013
\(376\) −14.9847 −0.772779
\(377\) 6.10102 0.314218
\(378\) −0.166609 −0.00856945
\(379\) 25.9919 1.33511 0.667557 0.744559i \(-0.267340\pi\)
0.667557 + 0.744559i \(0.267340\pi\)
\(380\) 77.6942 3.98563
\(381\) 0.171344 0.00877820
\(382\) 64.2489 3.28726
\(383\) 4.18043 0.213610 0.106805 0.994280i \(-0.465938\pi\)
0.106805 + 0.994280i \(0.465938\pi\)
\(384\) 0.130983 0.00668421
\(385\) 16.9194 0.862294
\(386\) 47.8229 2.43412
\(387\) −19.9950 −1.01640
\(388\) 6.40485 0.325157
\(389\) −3.59198 −0.182121 −0.0910603 0.995845i \(-0.529026\pi\)
−0.0910603 + 0.995845i \(0.529026\pi\)
\(390\) −0.336512 −0.0170399
\(391\) −16.0702 −0.812704
\(392\) 39.1028 1.97499
\(393\) −0.0405321 −0.00204457
\(394\) 12.7990 0.644805
\(395\) 35.9394 1.80831
\(396\) 75.1751 3.77769
\(397\) 10.3509 0.519499 0.259749 0.965676i \(-0.416360\pi\)
0.259749 + 0.965676i \(0.416360\pi\)
\(398\) 64.7832 3.24729
\(399\) −0.0575218 −0.00287969
\(400\) 41.2410 2.06205
\(401\) 31.4248 1.56928 0.784640 0.619951i \(-0.212848\pi\)
0.784640 + 0.619951i \(0.212848\pi\)
\(402\) 0.113871 0.00567937
\(403\) 32.9720 1.64245
\(404\) 16.6165 0.826702
\(405\) 29.4248 1.46213
\(406\) 4.19686 0.208287
\(407\) 42.1700 2.09029
\(408\) −0.127575 −0.00631589
\(409\) −8.92108 −0.441119 −0.220560 0.975374i \(-0.570788\pi\)
−0.220560 + 0.975374i \(0.570788\pi\)
\(410\) 70.7429 3.49374
\(411\) 0.0683235 0.00337015
\(412\) −10.2375 −0.504366
\(413\) −5.90416 −0.290525
\(414\) −71.9688 −3.53707
\(415\) −1.45447 −0.0713972
\(416\) −19.7204 −0.966872
\(417\) −0.143744 −0.00703919
\(418\) 74.9840 3.66759
\(419\) 5.05826 0.247112 0.123556 0.992338i \(-0.460570\pi\)
0.123556 + 0.992338i \(0.460570\pi\)
\(420\) −0.160252 −0.00781948
\(421\) −37.4612 −1.82575 −0.912873 0.408244i \(-0.866141\pi\)
−0.912873 + 0.408244i \(0.866141\pi\)
\(422\) 25.3879 1.23586
\(423\) −7.05492 −0.343022
\(424\) 41.2662 2.00406
\(425\) 9.72038 0.471508
\(426\) 0.0298901 0.00144818
\(427\) −9.26127 −0.448184
\(428\) 18.1377 0.876721
\(429\) −0.224833 −0.0108550
\(430\) −55.5631 −2.67949
\(431\) 24.5304 1.18159 0.590793 0.806823i \(-0.298815\pi\)
0.590793 + 0.806823i \(0.298815\pi\)
\(432\) −0.509675 −0.0245217
\(433\) −12.0374 −0.578479 −0.289239 0.957257i \(-0.593402\pi\)
−0.289239 + 0.957257i \(0.593402\pi\)
\(434\) 22.6813 1.08874
\(435\) 0.0679336 0.00325717
\(436\) −53.4772 −2.56109
\(437\) −49.6956 −2.37726
\(438\) −0.0927857 −0.00443347
\(439\) 28.2367 1.34766 0.673831 0.738885i \(-0.264648\pi\)
0.673831 + 0.738885i \(0.264648\pi\)
\(440\) 116.042 5.53207
\(441\) 18.4099 0.876660
\(442\) −14.9896 −0.712980
\(443\) 12.1710 0.578260 0.289130 0.957290i \(-0.406634\pi\)
0.289130 + 0.957290i \(0.406634\pi\)
\(444\) −0.399412 −0.0189552
\(445\) −53.2448 −2.52405
\(446\) −27.6286 −1.30825
\(447\) −0.0635445 −0.00300555
\(448\) −0.103294 −0.00488016
\(449\) 7.93731 0.374585 0.187292 0.982304i \(-0.440029\pi\)
0.187292 + 0.982304i \(0.440029\pi\)
\(450\) 43.5318 2.05211
\(451\) 47.2652 2.22563
\(452\) −4.49933 −0.211631
\(453\) −0.111125 −0.00522112
\(454\) 9.76102 0.458107
\(455\) −10.4593 −0.490340
\(456\) −0.394513 −0.0184748
\(457\) −19.2744 −0.901618 −0.450809 0.892620i \(-0.648864\pi\)
−0.450809 + 0.892620i \(0.648864\pi\)
\(458\) −11.2285 −0.524673
\(459\) −0.120129 −0.00560713
\(460\) −138.448 −6.45519
\(461\) −14.5004 −0.675352 −0.337676 0.941262i \(-0.609641\pi\)
−0.337676 + 0.941262i \(0.609641\pi\)
\(462\) −0.154662 −0.00719550
\(463\) −16.9131 −0.786019 −0.393010 0.919534i \(-0.628566\pi\)
−0.393010 + 0.919534i \(0.628566\pi\)
\(464\) 12.8386 0.596019
\(465\) 0.367136 0.0170255
\(466\) −16.3163 −0.755839
\(467\) 1.91976 0.0888360 0.0444180 0.999013i \(-0.485857\pi\)
0.0444180 + 0.999013i \(0.485857\pi\)
\(468\) −46.4720 −2.14817
\(469\) 3.53928 0.163429
\(470\) −19.6045 −0.904289
\(471\) −0.110074 −0.00507195
\(472\) −40.4936 −1.86387
\(473\) −37.1232 −1.70693
\(474\) −0.328524 −0.0150896
\(475\) 30.0594 1.37922
\(476\) −7.13824 −0.327181
\(477\) 19.4284 0.889565
\(478\) −40.9316 −1.87217
\(479\) 4.59034 0.209738 0.104869 0.994486i \(-0.466558\pi\)
0.104869 + 0.994486i \(0.466558\pi\)
\(480\) −0.219583 −0.0100225
\(481\) −26.0688 −1.18863
\(482\) 72.7141 3.31204
\(483\) 0.102502 0.00466399
\(484\) 90.0790 4.09450
\(485\) 4.65470 0.211359
\(486\) −0.806984 −0.0366055
\(487\) 22.7328 1.03012 0.515060 0.857154i \(-0.327769\pi\)
0.515060 + 0.857154i \(0.327769\pi\)
\(488\) −63.5183 −2.87534
\(489\) 0.0337881 0.00152795
\(490\) 51.1581 2.31109
\(491\) −16.4531 −0.742520 −0.371260 0.928529i \(-0.621074\pi\)
−0.371260 + 0.928529i \(0.621074\pi\)
\(492\) −0.447671 −0.0201826
\(493\) 3.02603 0.136285
\(494\) −46.3538 −2.08556
\(495\) 54.6332 2.45558
\(496\) 69.3844 3.11545
\(497\) 0.929031 0.0416727
\(498\) 0.0132954 0.000595782 0
\(499\) −19.5547 −0.875390 −0.437695 0.899124i \(-0.644205\pi\)
−0.437695 + 0.899124i \(0.644205\pi\)
\(500\) 10.1820 0.455353
\(501\) 0.00555651 0.000248246 0
\(502\) −46.0762 −2.05648
\(503\) −34.7915 −1.55128 −0.775638 0.631178i \(-0.782572\pi\)
−0.775638 + 0.631178i \(0.782572\pi\)
\(504\) −17.7578 −0.790997
\(505\) 12.0760 0.537374
\(506\) −133.619 −5.94008
\(507\) −0.0134303 −0.000596460 0
\(508\) 65.7541 2.91737
\(509\) −11.1044 −0.492193 −0.246097 0.969245i \(-0.579148\pi\)
−0.246097 + 0.969245i \(0.579148\pi\)
\(510\) −0.166906 −0.00739071
\(511\) −2.88392 −0.127577
\(512\) 50.8325 2.24650
\(513\) −0.371487 −0.0164016
\(514\) 71.9930 3.17548
\(515\) −7.44008 −0.327849
\(516\) 0.351611 0.0154788
\(517\) −13.0983 −0.576063
\(518\) −17.9326 −0.787914
\(519\) −0.0380856 −0.00167177
\(520\) −71.7351 −3.14579
\(521\) −40.2936 −1.76530 −0.882648 0.470035i \(-0.844241\pi\)
−0.882648 + 0.470035i \(0.844241\pi\)
\(522\) 13.5518 0.593145
\(523\) −25.2861 −1.10568 −0.552841 0.833286i \(-0.686456\pi\)
−0.552841 + 0.833286i \(0.686456\pi\)
\(524\) −15.5544 −0.679498
\(525\) −0.0620003 −0.00270592
\(526\) 50.5524 2.20419
\(527\) 16.3537 0.712378
\(528\) −0.473126 −0.0205901
\(529\) 65.5558 2.85025
\(530\) 53.9884 2.34511
\(531\) −19.0647 −0.827336
\(532\) −22.0743 −0.957044
\(533\) −29.2186 −1.26560
\(534\) 0.486714 0.0210622
\(535\) 13.1815 0.569888
\(536\) 24.2741 1.04848
\(537\) 0.204910 0.00884250
\(538\) −32.9992 −1.42270
\(539\) 34.1801 1.47224
\(540\) −1.03494 −0.0445366
\(541\) −5.32773 −0.229057 −0.114529 0.993420i \(-0.536536\pi\)
−0.114529 + 0.993420i \(0.536536\pi\)
\(542\) 49.0712 2.10779
\(543\) 0.193868 0.00831966
\(544\) −9.78107 −0.419360
\(545\) −38.8643 −1.66477
\(546\) 0.0956091 0.00409169
\(547\) −16.1736 −0.691532 −0.345766 0.938321i \(-0.612381\pi\)
−0.345766 + 0.938321i \(0.612381\pi\)
\(548\) 26.2196 1.12004
\(549\) −29.9049 −1.27631
\(550\) 80.8220 3.44626
\(551\) 9.35772 0.398652
\(552\) 0.703008 0.0299220
\(553\) −10.2110 −0.434217
\(554\) 69.9959 2.97384
\(555\) −0.290271 −0.0123213
\(556\) −55.1627 −2.33942
\(557\) 5.62127 0.238181 0.119090 0.992883i \(-0.462002\pi\)
0.119090 + 0.992883i \(0.462002\pi\)
\(558\) 73.2384 3.10043
\(559\) 22.9489 0.970636
\(560\) −22.0100 −0.930092
\(561\) −0.111514 −0.00470813
\(562\) −5.75745 −0.242863
\(563\) −19.2079 −0.809516 −0.404758 0.914424i \(-0.632644\pi\)
−0.404758 + 0.914424i \(0.632644\pi\)
\(564\) 0.124060 0.00522387
\(565\) −3.26987 −0.137565
\(566\) 3.80557 0.159960
\(567\) −8.36013 −0.351092
\(568\) 6.37175 0.267353
\(569\) −19.5553 −0.819801 −0.409900 0.912130i \(-0.634437\pi\)
−0.409900 + 0.912130i \(0.634437\pi\)
\(570\) −0.516141 −0.0216188
\(571\) −18.4863 −0.773626 −0.386813 0.922158i \(-0.626424\pi\)
−0.386813 + 0.922158i \(0.626424\pi\)
\(572\) −86.2809 −3.60759
\(573\) −0.295477 −0.0123437
\(574\) −20.0993 −0.838930
\(575\) −53.5648 −2.23380
\(576\) −0.333537 −0.0138974
\(577\) −14.8524 −0.618315 −0.309158 0.951011i \(-0.600047\pi\)
−0.309158 + 0.951011i \(0.600047\pi\)
\(578\) 35.9048 1.49344
\(579\) −0.219935 −0.00914020
\(580\) 26.0699 1.08249
\(581\) 0.413242 0.0171442
\(582\) −0.0425489 −0.00176371
\(583\) 36.0711 1.49391
\(584\) −19.7794 −0.818476
\(585\) −33.7734 −1.39636
\(586\) −25.3578 −1.04752
\(587\) −25.0986 −1.03593 −0.517965 0.855402i \(-0.673310\pi\)
−0.517965 + 0.855402i \(0.673310\pi\)
\(588\) −0.323736 −0.0133506
\(589\) 50.5723 2.08380
\(590\) −52.9777 −2.18106
\(591\) −0.0588620 −0.00242126
\(592\) −54.8577 −2.25464
\(593\) −47.3392 −1.94399 −0.971995 0.235003i \(-0.924490\pi\)
−0.971995 + 0.235003i \(0.924490\pi\)
\(594\) −0.998834 −0.0409827
\(595\) −5.18769 −0.212674
\(596\) −24.3856 −0.998872
\(597\) −0.297935 −0.0121937
\(598\) 82.6009 3.37780
\(599\) 27.0511 1.10528 0.552639 0.833421i \(-0.313621\pi\)
0.552639 + 0.833421i \(0.313621\pi\)
\(600\) −0.425229 −0.0173599
\(601\) 31.3381 1.27831 0.639154 0.769079i \(-0.279285\pi\)
0.639154 + 0.769079i \(0.279285\pi\)
\(602\) 15.7865 0.643409
\(603\) 11.4284 0.465402
\(604\) −42.6450 −1.73520
\(605\) 65.4646 2.66151
\(606\) −0.110387 −0.00448418
\(607\) 16.9699 0.688788 0.344394 0.938825i \(-0.388084\pi\)
0.344394 + 0.938825i \(0.388084\pi\)
\(608\) −30.2471 −1.22668
\(609\) −0.0193012 −0.000782123 0
\(610\) −83.1009 −3.36466
\(611\) 8.09715 0.327576
\(612\) −23.0495 −0.931722
\(613\) −19.7055 −0.795898 −0.397949 0.917407i \(-0.630278\pi\)
−0.397949 + 0.917407i \(0.630278\pi\)
\(614\) 66.4157 2.68032
\(615\) −0.325343 −0.0131191
\(616\) −32.9696 −1.32838
\(617\) −43.7337 −1.76065 −0.880327 0.474368i \(-0.842677\pi\)
−0.880327 + 0.474368i \(0.842677\pi\)
\(618\) 0.0680102 0.00273577
\(619\) 43.5685 1.75117 0.875583 0.483068i \(-0.160478\pi\)
0.875583 + 0.483068i \(0.160478\pi\)
\(620\) 140.891 5.65831
\(621\) 0.661977 0.0265642
\(622\) −12.2901 −0.492788
\(623\) 15.1278 0.606083
\(624\) 0.292478 0.0117085
\(625\) −21.0606 −0.842426
\(626\) −24.0741 −0.962195
\(627\) −0.344848 −0.0137719
\(628\) −42.2416 −1.68562
\(629\) −12.9298 −0.515545
\(630\) −23.2326 −0.925607
\(631\) 42.0877 1.67548 0.837742 0.546067i \(-0.183875\pi\)
0.837742 + 0.546067i \(0.183875\pi\)
\(632\) −70.0322 −2.78573
\(633\) −0.116757 −0.00464069
\(634\) −27.6641 −1.09868
\(635\) 47.7866 1.89635
\(636\) −0.341646 −0.0135472
\(637\) −21.1296 −0.837185
\(638\) 25.1605 0.996114
\(639\) 2.99986 0.118673
\(640\) 36.5303 1.44399
\(641\) −45.8246 −1.80996 −0.904982 0.425450i \(-0.860116\pi\)
−0.904982 + 0.425450i \(0.860116\pi\)
\(642\) −0.120493 −0.00475549
\(643\) 20.1937 0.796362 0.398181 0.917307i \(-0.369642\pi\)
0.398181 + 0.917307i \(0.369642\pi\)
\(644\) 39.3357 1.55004
\(645\) 0.255532 0.0100616
\(646\) −22.9909 −0.904566
\(647\) 6.77909 0.266514 0.133257 0.991082i \(-0.457456\pi\)
0.133257 + 0.991082i \(0.457456\pi\)
\(648\) −57.3379 −2.25244
\(649\) −35.3959 −1.38941
\(650\) −49.9628 −1.95970
\(651\) −0.104310 −0.00408824
\(652\) 12.9664 0.507802
\(653\) −38.1200 −1.49175 −0.745875 0.666086i \(-0.767968\pi\)
−0.745875 + 0.666086i \(0.767968\pi\)
\(654\) 0.355261 0.0138918
\(655\) −11.3041 −0.441689
\(656\) −61.4860 −2.40062
\(657\) −9.31226 −0.363306
\(658\) 5.57000 0.217141
\(659\) 19.2408 0.749515 0.374758 0.927123i \(-0.377726\pi\)
0.374758 + 0.927123i \(0.377726\pi\)
\(660\) −0.960720 −0.0373960
\(661\) 9.01691 0.350717 0.175359 0.984505i \(-0.443892\pi\)
0.175359 + 0.984505i \(0.443892\pi\)
\(662\) −23.7442 −0.922844
\(663\) 0.0689362 0.00267726
\(664\) 2.83422 0.109989
\(665\) −16.0424 −0.622099
\(666\) −57.9049 −2.24377
\(667\) −16.6751 −0.645663
\(668\) 2.13234 0.0825028
\(669\) 0.127063 0.00491252
\(670\) 31.7578 1.22691
\(671\) −55.5220 −2.14340
\(672\) 0.0623874 0.00240665
\(673\) −46.1469 −1.77883 −0.889417 0.457097i \(-0.848889\pi\)
−0.889417 + 0.457097i \(0.848889\pi\)
\(674\) −72.5926 −2.79616
\(675\) −0.400410 −0.0154118
\(676\) −5.15395 −0.198229
\(677\) 36.0355 1.38496 0.692478 0.721439i \(-0.256519\pi\)
0.692478 + 0.721439i \(0.256519\pi\)
\(678\) 0.0298901 0.00114792
\(679\) −1.32249 −0.0507524
\(680\) −35.5797 −1.36442
\(681\) −0.0448904 −0.00172021
\(682\) 135.976 5.20679
\(683\) 9.62920 0.368451 0.184226 0.982884i \(-0.441022\pi\)
0.184226 + 0.982884i \(0.441022\pi\)
\(684\) −71.2786 −2.72540
\(685\) 19.0550 0.728053
\(686\) −31.1141 −1.18794
\(687\) 0.0516393 0.00197016
\(688\) 48.2925 1.84113
\(689\) −22.2986 −0.849508
\(690\) 0.919744 0.0350141
\(691\) 15.2620 0.580592 0.290296 0.956937i \(-0.406246\pi\)
0.290296 + 0.956937i \(0.406246\pi\)
\(692\) −14.6156 −0.555601
\(693\) −15.5223 −0.589643
\(694\) 83.4299 3.16696
\(695\) −40.0893 −1.52067
\(696\) −0.132377 −0.00501773
\(697\) −14.4921 −0.548926
\(698\) 67.1929 2.54329
\(699\) 0.0750380 0.00283820
\(700\) −23.7930 −0.899291
\(701\) 36.9246 1.39462 0.697312 0.716767i \(-0.254379\pi\)
0.697312 + 0.716767i \(0.254379\pi\)
\(702\) 0.617463 0.0233046
\(703\) −39.9842 −1.50803
\(704\) −0.619253 −0.0233390
\(705\) 0.0901602 0.00339563
\(706\) 48.7364 1.83422
\(707\) −3.43101 −0.129036
\(708\) 0.335250 0.0125995
\(709\) −24.3982 −0.916293 −0.458146 0.888877i \(-0.651486\pi\)
−0.458146 + 0.888877i \(0.651486\pi\)
\(710\) 8.33615 0.312850
\(711\) −32.9716 −1.23653
\(712\) 103.754 3.88835
\(713\) −90.1180 −3.37495
\(714\) 0.0474209 0.00177468
\(715\) −62.7043 −2.34501
\(716\) 78.6353 2.93874
\(717\) 0.188242 0.00703004
\(718\) 8.21196 0.306467
\(719\) 5.08613 0.189680 0.0948402 0.995493i \(-0.469766\pi\)
0.0948402 + 0.995493i \(0.469766\pi\)
\(720\) −71.0708 −2.64865
\(721\) 2.11386 0.0787243
\(722\) −22.6591 −0.843286
\(723\) −0.334408 −0.0124368
\(724\) 74.3979 2.76498
\(725\) 10.0863 0.374595
\(726\) −0.598416 −0.0222093
\(727\) −27.8236 −1.03192 −0.515960 0.856613i \(-0.672565\pi\)
−0.515960 + 0.856613i \(0.672565\pi\)
\(728\) 20.3812 0.755379
\(729\) −26.9926 −0.999725
\(730\) −25.8773 −0.957762
\(731\) 11.3824 0.420993
\(732\) 0.525874 0.0194369
\(733\) −37.2228 −1.37486 −0.687428 0.726253i \(-0.741260\pi\)
−0.687428 + 0.726253i \(0.741260\pi\)
\(734\) 43.5635 1.60796
\(735\) −0.235274 −0.00867820
\(736\) 53.8992 1.98675
\(737\) 21.2183 0.781585
\(738\) −64.9012 −2.38905
\(739\) 27.7877 1.02219 0.511093 0.859526i \(-0.329241\pi\)
0.511093 + 0.859526i \(0.329241\pi\)
\(740\) −111.393 −4.09489
\(741\) 0.213179 0.00783132
\(742\) −15.3391 −0.563116
\(743\) −1.49616 −0.0548888 −0.0274444 0.999623i \(-0.508737\pi\)
−0.0274444 + 0.999623i \(0.508737\pi\)
\(744\) −0.715410 −0.0262282
\(745\) −17.7221 −0.649288
\(746\) −20.2456 −0.741244
\(747\) 1.33437 0.0488220
\(748\) −42.7943 −1.56471
\(749\) −3.74511 −0.136844
\(750\) −0.0676414 −0.00246992
\(751\) 9.83820 0.359001 0.179500 0.983758i \(-0.442552\pi\)
0.179500 + 0.983758i \(0.442552\pi\)
\(752\) 17.0392 0.621356
\(753\) 0.211902 0.00772215
\(754\) −15.5538 −0.566436
\(755\) −30.9921 −1.12792
\(756\) 0.294044 0.0106943
\(757\) −41.0354 −1.49146 −0.745728 0.666250i \(-0.767898\pi\)
−0.745728 + 0.666250i \(0.767898\pi\)
\(758\) −66.2632 −2.40679
\(759\) 0.614506 0.0223052
\(760\) −110.027 −3.99110
\(761\) 11.8831 0.430762 0.215381 0.976530i \(-0.430901\pi\)
0.215381 + 0.976530i \(0.430901\pi\)
\(762\) −0.436820 −0.0158243
\(763\) 11.0421 0.399750
\(764\) −113.391 −4.10235
\(765\) −16.7512 −0.605640
\(766\) −10.6575 −0.385071
\(767\) 21.8811 0.790082
\(768\) −0.336533 −0.0121436
\(769\) 45.9250 1.65610 0.828049 0.560656i \(-0.189451\pi\)
0.828049 + 0.560656i \(0.189451\pi\)
\(770\) −43.1340 −1.55444
\(771\) −0.331092 −0.0119240
\(772\) −84.4015 −3.03768
\(773\) −0.796653 −0.0286536 −0.0143268 0.999897i \(-0.504561\pi\)
−0.0143268 + 0.999897i \(0.504561\pi\)
\(774\) 50.9749 1.83226
\(775\) 54.5097 1.95805
\(776\) −9.07026 −0.325603
\(777\) 0.0824712 0.00295864
\(778\) 9.15732 0.328306
\(779\) −44.8153 −1.60568
\(780\) 0.593901 0.0212651
\(781\) 5.56961 0.199296
\(782\) 40.9690 1.46505
\(783\) −0.124651 −0.00445465
\(784\) −44.4639 −1.58800
\(785\) −30.6989 −1.09569
\(786\) 0.103332 0.00368572
\(787\) −37.3664 −1.33197 −0.665983 0.745967i \(-0.731988\pi\)
−0.665983 + 0.745967i \(0.731988\pi\)
\(788\) −22.5886 −0.804687
\(789\) −0.232488 −0.00827680
\(790\) −91.6230 −3.25980
\(791\) 0.929031 0.0330325
\(792\) −106.460 −3.78288
\(793\) 34.3228 1.21884
\(794\) −26.3885 −0.936491
\(795\) −0.248290 −0.00880594
\(796\) −114.334 −4.05247
\(797\) −7.82125 −0.277043 −0.138521 0.990359i \(-0.544235\pi\)
−0.138521 + 0.990359i \(0.544235\pi\)
\(798\) 0.146645 0.00519117
\(799\) 4.01609 0.142079
\(800\) −32.6020 −1.15266
\(801\) 48.8481 1.72596
\(802\) −80.1138 −2.82892
\(803\) −17.2893 −0.610127
\(804\) −0.200968 −0.00708759
\(805\) 28.5871 1.00756
\(806\) −84.0581 −2.96082
\(807\) 0.151762 0.00534227
\(808\) −23.5315 −0.827837
\(809\) 13.3569 0.469603 0.234802 0.972043i \(-0.424556\pi\)
0.234802 + 0.972043i \(0.424556\pi\)
\(810\) −75.0150 −2.63576
\(811\) −32.3923 −1.13745 −0.568723 0.822529i \(-0.692562\pi\)
−0.568723 + 0.822529i \(0.692562\pi\)
\(812\) −7.40694 −0.259933
\(813\) −0.225676 −0.00791480
\(814\) −107.507 −3.76813
\(815\) 9.42326 0.330082
\(816\) 0.145066 0.00507831
\(817\) 35.1990 1.23146
\(818\) 22.7432 0.795198
\(819\) 9.59562 0.335298
\(820\) −124.852 −4.36003
\(821\) −19.9575 −0.696522 −0.348261 0.937398i \(-0.613228\pi\)
−0.348261 + 0.937398i \(0.613228\pi\)
\(822\) −0.174183 −0.00607532
\(823\) 2.45284 0.0855008 0.0427504 0.999086i \(-0.486388\pi\)
0.0427504 + 0.999086i \(0.486388\pi\)
\(824\) 14.4979 0.505058
\(825\) −0.371696 −0.0129408
\(826\) 15.0519 0.523724
\(827\) 10.5398 0.366506 0.183253 0.983066i \(-0.441337\pi\)
0.183253 + 0.983066i \(0.441337\pi\)
\(828\) 127.016 4.41411
\(829\) 46.3162 1.60863 0.804314 0.594204i \(-0.202533\pi\)
0.804314 + 0.594204i \(0.202533\pi\)
\(830\) 3.70800 0.128707
\(831\) −0.321908 −0.0111669
\(832\) 0.382812 0.0132716
\(833\) −10.4800 −0.363111
\(834\) 0.366459 0.0126894
\(835\) 1.54967 0.0536286
\(836\) −132.337 −4.57698
\(837\) −0.673655 −0.0232849
\(838\) −12.8954 −0.445465
\(839\) 12.9920 0.448534 0.224267 0.974528i \(-0.428001\pi\)
0.224267 + 0.974528i \(0.428001\pi\)
\(840\) 0.226941 0.00783021
\(841\) −25.8601 −0.891726
\(842\) 95.5027 3.29124
\(843\) 0.0264782 0.000911959 0
\(844\) −44.8064 −1.54230
\(845\) −3.74562 −0.128853
\(846\) 17.9857 0.618360
\(847\) −18.5997 −0.639093
\(848\) −46.9239 −1.61137
\(849\) −0.0175016 −0.000600653 0
\(850\) −24.7809 −0.849979
\(851\) 71.2505 2.44243
\(852\) −0.0527523 −0.00180726
\(853\) 38.1029 1.30462 0.652310 0.757953i \(-0.273800\pi\)
0.652310 + 0.757953i \(0.273800\pi\)
\(854\) 23.6105 0.807934
\(855\) −51.8014 −1.77157
\(856\) −25.6858 −0.877924
\(857\) 24.7332 0.844871 0.422435 0.906393i \(-0.361175\pi\)
0.422435 + 0.906393i \(0.361175\pi\)
\(858\) 0.573184 0.0195682
\(859\) 21.1804 0.722666 0.361333 0.932437i \(-0.382322\pi\)
0.361333 + 0.932437i \(0.382322\pi\)
\(860\) 98.0618 3.34388
\(861\) 0.0924359 0.00315021
\(862\) −62.5372 −2.13003
\(863\) 32.9643 1.12212 0.561059 0.827776i \(-0.310394\pi\)
0.561059 + 0.827776i \(0.310394\pi\)
\(864\) 0.402910 0.0137073
\(865\) −10.6218 −0.361152
\(866\) 30.6878 1.04281
\(867\) −0.165124 −0.00560792
\(868\) −40.0296 −1.35869
\(869\) −61.2158 −2.07661
\(870\) −0.173188 −0.00587164
\(871\) −13.1168 −0.444445
\(872\) 75.7319 2.56461
\(873\) −4.27034 −0.144529
\(874\) 126.693 4.28545
\(875\) −2.10240 −0.0710741
\(876\) 0.163755 0.00553277
\(877\) −12.3822 −0.418116 −0.209058 0.977903i \(-0.567040\pi\)
−0.209058 + 0.977903i \(0.567040\pi\)
\(878\) −71.9859 −2.42941
\(879\) 0.116619 0.00393346
\(880\) −131.951 −4.44808
\(881\) 22.6066 0.761636 0.380818 0.924650i \(-0.375642\pi\)
0.380818 + 0.924650i \(0.375642\pi\)
\(882\) −46.9337 −1.58034
\(883\) 11.6576 0.392309 0.196154 0.980573i \(-0.437155\pi\)
0.196154 + 0.980573i \(0.437155\pi\)
\(884\) 26.4547 0.889767
\(885\) 0.243642 0.00818993
\(886\) −31.0284 −1.04242
\(887\) −24.9958 −0.839275 −0.419638 0.907692i \(-0.637843\pi\)
−0.419638 + 0.907692i \(0.637843\pi\)
\(888\) 0.565628 0.0189812
\(889\) −13.5770 −0.455359
\(890\) 135.741 4.55005
\(891\) −50.1196 −1.67907
\(892\) 48.7610 1.63264
\(893\) 12.4194 0.415599
\(894\) 0.161999 0.00541806
\(895\) 57.1479 1.91024
\(896\) −10.3789 −0.346736
\(897\) −0.379877 −0.0126837
\(898\) −20.2352 −0.675258
\(899\) 16.9693 0.565957
\(900\) −76.8281 −2.56094
\(901\) −11.0598 −0.368456
\(902\) −120.497 −4.01211
\(903\) −0.0726012 −0.00241602
\(904\) 6.37175 0.211921
\(905\) 54.0684 1.79729
\(906\) 0.283300 0.00941202
\(907\) −53.5941 −1.77956 −0.889782 0.456387i \(-0.849143\pi\)
−0.889782 + 0.456387i \(0.849143\pi\)
\(908\) −17.2270 −0.571697
\(909\) −11.0788 −0.367461
\(910\) 26.6647 0.883927
\(911\) −28.0838 −0.930457 −0.465228 0.885191i \(-0.654028\pi\)
−0.465228 + 0.885191i \(0.654028\pi\)
\(912\) 0.448602 0.0148547
\(913\) 2.47742 0.0819905
\(914\) 49.1377 1.62533
\(915\) 0.382177 0.0126344
\(916\) 19.8169 0.654768
\(917\) 3.21171 0.106060
\(918\) 0.306254 0.0101079
\(919\) −14.5367 −0.479520 −0.239760 0.970832i \(-0.577069\pi\)
−0.239760 + 0.970832i \(0.577069\pi\)
\(920\) 196.064 6.46404
\(921\) −0.305443 −0.0100647
\(922\) 36.9671 1.21745
\(923\) −3.44304 −0.113329
\(924\) 0.272958 0.00897966
\(925\) −43.0973 −1.41703
\(926\) 43.1180 1.41694
\(927\) 6.82571 0.224186
\(928\) −10.1493 −0.333166
\(929\) 49.7393 1.63189 0.815947 0.578126i \(-0.196216\pi\)
0.815947 + 0.578126i \(0.196216\pi\)
\(930\) −0.935970 −0.0306917
\(931\) −32.4085 −1.06214
\(932\) 28.7963 0.943253
\(933\) 0.0565216 0.00185043
\(934\) −4.89420 −0.160143
\(935\) −31.1006 −1.01710
\(936\) 65.8115 2.15112
\(937\) 1.98083 0.0647108 0.0323554 0.999476i \(-0.489699\pi\)
0.0323554 + 0.999476i \(0.489699\pi\)
\(938\) −9.02298 −0.294611
\(939\) 0.110716 0.00361307
\(940\) 34.5995 1.12851
\(941\) 17.7936 0.580054 0.290027 0.957019i \(-0.406336\pi\)
0.290027 + 0.957019i \(0.406336\pi\)
\(942\) 0.280621 0.00914312
\(943\) 79.8593 2.60058
\(944\) 46.0454 1.49865
\(945\) 0.213696 0.00695152
\(946\) 94.6411 3.07705
\(947\) −17.6855 −0.574700 −0.287350 0.957826i \(-0.592774\pi\)
−0.287350 + 0.957826i \(0.592774\pi\)
\(948\) 0.579803 0.0188311
\(949\) 10.6880 0.346946
\(950\) −76.6328 −2.48630
\(951\) 0.127226 0.00412558
\(952\) 10.1088 0.327629
\(953\) 33.7874 1.09448 0.547241 0.836975i \(-0.315678\pi\)
0.547241 + 0.836975i \(0.315678\pi\)
\(954\) −49.5303 −1.60360
\(955\) −82.4067 −2.66662
\(956\) 72.2392 2.33638
\(957\) −0.115712 −0.00374044
\(958\) −11.7025 −0.378091
\(959\) −5.41386 −0.174823
\(960\) 0.00426253 0.000137573 0
\(961\) 60.7078 1.95832
\(962\) 66.4593 2.14273
\(963\) −12.0931 −0.389694
\(964\) −128.331 −4.13327
\(965\) −61.3385 −1.97456
\(966\) −0.261316 −0.00840771
\(967\) 47.5889 1.53036 0.765178 0.643818i \(-0.222651\pi\)
0.765178 + 0.643818i \(0.222651\pi\)
\(968\) −127.566 −4.10012
\(969\) 0.105734 0.00339667
\(970\) −11.8666 −0.381014
\(971\) −9.79537 −0.314349 −0.157174 0.987571i \(-0.550238\pi\)
−0.157174 + 0.987571i \(0.550238\pi\)
\(972\) 1.42422 0.0456820
\(973\) 11.3901 0.365150
\(974\) −57.9545 −1.85698
\(975\) 0.229777 0.00735874
\(976\) 72.2269 2.31193
\(977\) 2.58502 0.0827022 0.0413511 0.999145i \(-0.486834\pi\)
0.0413511 + 0.999145i \(0.486834\pi\)
\(978\) −0.0861386 −0.00275441
\(979\) 90.6924 2.89854
\(980\) −90.2877 −2.88413
\(981\) 35.6551 1.13838
\(982\) 41.9453 1.33853
\(983\) −28.4543 −0.907550 −0.453775 0.891116i \(-0.649923\pi\)
−0.453775 + 0.891116i \(0.649923\pi\)
\(984\) 0.633971 0.0202102
\(985\) −16.4162 −0.523064
\(986\) −7.71449 −0.245680
\(987\) −0.0256161 −0.000815371 0
\(988\) 81.8087 2.60268
\(989\) −62.7233 −1.99449
\(990\) −139.281 −4.42664
\(991\) 48.4296 1.53842 0.769208 0.638999i \(-0.220651\pi\)
0.769208 + 0.638999i \(0.220651\pi\)
\(992\) −54.8500 −1.74149
\(993\) 0.109198 0.00346530
\(994\) −2.36845 −0.0751227
\(995\) −83.0920 −2.63419
\(996\) −0.0234647 −0.000743509 0
\(997\) −24.0452 −0.761520 −0.380760 0.924674i \(-0.624338\pi\)
−0.380760 + 0.924674i \(0.624338\pi\)
\(998\) 49.8524 1.57805
\(999\) 0.532615 0.0168512
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 \(a_p\))