Properties

Label 6023.2.a.b.1.16
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.15033 q^{2}\) \(-0.758271 q^{3}\) \(+2.62390 q^{4}\) \(-3.61423 q^{5}\) \(+1.63053 q^{6}\) \(-3.46519 q^{7}\) \(-1.34159 q^{8}\) \(-2.42502 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.15033 q^{2}\) \(-0.758271 q^{3}\) \(+2.62390 q^{4}\) \(-3.61423 q^{5}\) \(+1.63053 q^{6}\) \(-3.46519 q^{7}\) \(-1.34159 q^{8}\) \(-2.42502 q^{9}\) \(+7.77178 q^{10}\) \(-2.36321 q^{11}\) \(-1.98963 q^{12}\) \(-5.83434 q^{13}\) \(+7.45128 q^{14}\) \(+2.74057 q^{15}\) \(-2.36294 q^{16}\) \(-1.13828 q^{17}\) \(+5.21459 q^{18}\) \(-1.00000 q^{19}\) \(-9.48339 q^{20}\) \(+2.62755 q^{21}\) \(+5.08167 q^{22}\) \(-8.30329 q^{23}\) \(+1.01729 q^{24}\) \(+8.06268 q^{25}\) \(+12.5457 q^{26}\) \(+4.11364 q^{27}\) \(-9.09231 q^{28}\) \(-0.468033 q^{29}\) \(-5.89312 q^{30}\) \(+5.31029 q^{31}\) \(+7.76428 q^{32}\) \(+1.79195 q^{33}\) \(+2.44768 q^{34}\) \(+12.5240 q^{35}\) \(-6.36302 q^{36}\) \(-8.64931 q^{37}\) \(+2.15033 q^{38}\) \(+4.42401 q^{39}\) \(+4.84882 q^{40}\) \(+0.0804774 q^{41}\) \(-5.65009 q^{42}\) \(+3.27407 q^{43}\) \(-6.20082 q^{44}\) \(+8.76460 q^{45}\) \(+17.8548 q^{46}\) \(+6.11975 q^{47}\) \(+1.79175 q^{48}\) \(+5.00751 q^{49}\) \(-17.3374 q^{50}\) \(+0.863126 q^{51}\) \(-15.3087 q^{52}\) \(+5.60205 q^{53}\) \(-8.84567 q^{54}\) \(+8.54119 q^{55}\) \(+4.64886 q^{56}\) \(+0.758271 q^{57}\) \(+1.00642 q^{58}\) \(-2.48579 q^{59}\) \(+7.19098 q^{60}\) \(+3.79889 q^{61}\) \(-11.4189 q^{62}\) \(+8.40316 q^{63}\) \(-11.9698 q^{64}\) \(+21.0867 q^{65}\) \(-3.85328 q^{66}\) \(-7.78246 q^{67}\) \(-2.98674 q^{68}\) \(+6.29615 q^{69}\) \(-26.9307 q^{70}\) \(+8.94185 q^{71}\) \(+3.25339 q^{72}\) \(-3.10520 q^{73}\) \(+18.5988 q^{74}\) \(-6.11370 q^{75}\) \(-2.62390 q^{76}\) \(+8.18896 q^{77}\) \(-9.51306 q^{78}\) \(-8.07936 q^{79}\) \(+8.54023 q^{80}\) \(+4.15582 q^{81}\) \(-0.173053 q^{82}\) \(+4.70994 q^{83}\) \(+6.89444 q^{84}\) \(+4.11401 q^{85}\) \(-7.04032 q^{86}\) \(+0.354896 q^{87}\) \(+3.17046 q^{88}\) \(-8.02104 q^{89}\) \(-18.8468 q^{90}\) \(+20.2171 q^{91}\) \(-21.7870 q^{92}\) \(-4.02664 q^{93}\) \(-13.1595 q^{94}\) \(+3.61423 q^{95}\) \(-5.88743 q^{96}\) \(+4.78710 q^{97}\) \(-10.7678 q^{98}\) \(+5.73084 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15033 −1.52051 −0.760255 0.649625i \(-0.774926\pi\)
−0.760255 + 0.649625i \(0.774926\pi\)
\(3\) −0.758271 −0.437788 −0.218894 0.975749i \(-0.570245\pi\)
−0.218894 + 0.975749i \(0.570245\pi\)
\(4\) 2.62390 1.31195
\(5\) −3.61423 −1.61633 −0.808167 0.588953i \(-0.799540\pi\)
−0.808167 + 0.588953i \(0.799540\pi\)
\(6\) 1.63053 0.665661
\(7\) −3.46519 −1.30972 −0.654859 0.755751i \(-0.727272\pi\)
−0.654859 + 0.755751i \(0.727272\pi\)
\(8\) −1.34159 −0.474324
\(9\) −2.42502 −0.808342
\(10\) 7.77178 2.45765
\(11\) −2.36321 −0.712534 −0.356267 0.934384i \(-0.615951\pi\)
−0.356267 + 0.934384i \(0.615951\pi\)
\(12\) −1.98963 −0.574356
\(13\) −5.83434 −1.61815 −0.809077 0.587703i \(-0.800032\pi\)
−0.809077 + 0.587703i \(0.800032\pi\)
\(14\) 7.45128 1.99144
\(15\) 2.74057 0.707612
\(16\) −2.36294 −0.590736
\(17\) −1.13828 −0.276074 −0.138037 0.990427i \(-0.544079\pi\)
−0.138037 + 0.990427i \(0.544079\pi\)
\(18\) 5.21459 1.22909
\(19\) −1.00000 −0.229416
\(20\) −9.48339 −2.12055
\(21\) 2.62755 0.573379
\(22\) 5.08167 1.08342
\(23\) −8.30329 −1.73136 −0.865678 0.500601i \(-0.833112\pi\)
−0.865678 + 0.500601i \(0.833112\pi\)
\(24\) 1.01729 0.207653
\(25\) 8.06268 1.61254
\(26\) 12.5457 2.46042
\(27\) 4.11364 0.791671
\(28\) −9.09231 −1.71828
\(29\) −0.468033 −0.0869116 −0.0434558 0.999055i \(-0.513837\pi\)
−0.0434558 + 0.999055i \(0.513837\pi\)
\(30\) −5.89312 −1.07593
\(31\) 5.31029 0.953757 0.476879 0.878969i \(-0.341768\pi\)
0.476879 + 0.878969i \(0.341768\pi\)
\(32\) 7.76428 1.37254
\(33\) 1.79195 0.311939
\(34\) 2.44768 0.419773
\(35\) 12.5240 2.11694
\(36\) −6.36302 −1.06050
\(37\) −8.64931 −1.42194 −0.710969 0.703224i \(-0.751743\pi\)
−0.710969 + 0.703224i \(0.751743\pi\)
\(38\) 2.15033 0.348829
\(39\) 4.42401 0.708409
\(40\) 4.84882 0.766666
\(41\) 0.0804774 0.0125685 0.00628423 0.999980i \(-0.498000\pi\)
0.00628423 + 0.999980i \(0.498000\pi\)
\(42\) −5.65009 −0.871828
\(43\) 3.27407 0.499291 0.249646 0.968337i \(-0.419686\pi\)
0.249646 + 0.968337i \(0.419686\pi\)
\(44\) −6.20082 −0.934809
\(45\) 8.76460 1.30655
\(46\) 17.8548 2.63254
\(47\) 6.11975 0.892657 0.446329 0.894869i \(-0.352731\pi\)
0.446329 + 0.894869i \(0.352731\pi\)
\(48\) 1.79175 0.258617
\(49\) 5.00751 0.715359
\(50\) −17.3374 −2.45188
\(51\) 0.863126 0.120862
\(52\) −15.3087 −2.12294
\(53\) 5.60205 0.769500 0.384750 0.923021i \(-0.374288\pi\)
0.384750 + 0.923021i \(0.374288\pi\)
\(54\) −8.84567 −1.20374
\(55\) 8.54119 1.15169
\(56\) 4.64886 0.621230
\(57\) 0.758271 0.100435
\(58\) 1.00642 0.132150
\(59\) −2.48579 −0.323623 −0.161811 0.986822i \(-0.551734\pi\)
−0.161811 + 0.986822i \(0.551734\pi\)
\(60\) 7.19098 0.928352
\(61\) 3.79889 0.486399 0.243199 0.969976i \(-0.421803\pi\)
0.243199 + 0.969976i \(0.421803\pi\)
\(62\) −11.4189 −1.45020
\(63\) 8.40316 1.05870
\(64\) −11.9698 −1.49623
\(65\) 21.0867 2.61548
\(66\) −3.85328 −0.474306
\(67\) −7.78246 −0.950779 −0.475390 0.879775i \(-0.657693\pi\)
−0.475390 + 0.879775i \(0.657693\pi\)
\(68\) −2.98674 −0.362195
\(69\) 6.29615 0.757967
\(70\) −26.9307 −3.21883
\(71\) 8.94185 1.06120 0.530601 0.847622i \(-0.321966\pi\)
0.530601 + 0.847622i \(0.321966\pi\)
\(72\) 3.25339 0.383416
\(73\) −3.10520 −0.363436 −0.181718 0.983351i \(-0.558166\pi\)
−0.181718 + 0.983351i \(0.558166\pi\)
\(74\) 18.5988 2.16207
\(75\) −6.11370 −0.705950
\(76\) −2.62390 −0.300982
\(77\) 8.18896 0.933218
\(78\) −9.51306 −1.07714
\(79\) −8.07936 −0.908999 −0.454500 0.890747i \(-0.650182\pi\)
−0.454500 + 0.890747i \(0.650182\pi\)
\(80\) 8.54023 0.954827
\(81\) 4.15582 0.461757
\(82\) −0.173053 −0.0191105
\(83\) 4.70994 0.516983 0.258492 0.966014i \(-0.416775\pi\)
0.258492 + 0.966014i \(0.416775\pi\)
\(84\) 6.89444 0.752245
\(85\) 4.11401 0.446227
\(86\) −7.04032 −0.759177
\(87\) 0.354896 0.0380489
\(88\) 3.17046 0.337972
\(89\) −8.02104 −0.850229 −0.425114 0.905140i \(-0.639766\pi\)
−0.425114 + 0.905140i \(0.639766\pi\)
\(90\) −18.8468 −1.98662
\(91\) 20.2171 2.11932
\(92\) −21.7870 −2.27145
\(93\) −4.02664 −0.417544
\(94\) −13.1595 −1.35729
\(95\) 3.61423 0.370813
\(96\) −5.88743 −0.600884
\(97\) 4.78710 0.486056 0.243028 0.970019i \(-0.421859\pi\)
0.243028 + 0.970019i \(0.421859\pi\)
\(98\) −10.7678 −1.08771
\(99\) 5.73084 0.575971
\(100\) 21.1557 2.11557
\(101\) 5.92423 0.589483 0.294741 0.955577i \(-0.404767\pi\)
0.294741 + 0.955577i \(0.404767\pi\)
\(102\) −1.85600 −0.183772
\(103\) −9.60535 −0.946443 −0.473221 0.880943i \(-0.656909\pi\)
−0.473221 + 0.880943i \(0.656909\pi\)
\(104\) 7.82729 0.767529
\(105\) −9.49658 −0.926772
\(106\) −12.0462 −1.17003
\(107\) −8.76418 −0.847265 −0.423633 0.905834i \(-0.639245\pi\)
−0.423633 + 0.905834i \(0.639245\pi\)
\(108\) 10.7938 1.03863
\(109\) 4.75916 0.455845 0.227923 0.973679i \(-0.426807\pi\)
0.227923 + 0.973679i \(0.426807\pi\)
\(110\) −18.3663 −1.75116
\(111\) 6.55852 0.622507
\(112\) 8.18804 0.773697
\(113\) 1.20485 0.113343 0.0566713 0.998393i \(-0.481951\pi\)
0.0566713 + 0.998393i \(0.481951\pi\)
\(114\) −1.63053 −0.152713
\(115\) 30.0100 2.79845
\(116\) −1.22807 −0.114024
\(117\) 14.1484 1.30802
\(118\) 5.34527 0.492072
\(119\) 3.94436 0.361578
\(120\) −3.67672 −0.335637
\(121\) −5.41525 −0.492295
\(122\) −8.16886 −0.739574
\(123\) −0.0610237 −0.00550232
\(124\) 13.9337 1.25128
\(125\) −11.0693 −0.990064
\(126\) −18.0695 −1.60976
\(127\) 12.3801 1.09856 0.549279 0.835639i \(-0.314902\pi\)
0.549279 + 0.835639i \(0.314902\pi\)
\(128\) 10.2105 0.902490
\(129\) −2.48263 −0.218584
\(130\) −45.3432 −3.97686
\(131\) 4.57409 0.399640 0.199820 0.979833i \(-0.435964\pi\)
0.199820 + 0.979833i \(0.435964\pi\)
\(132\) 4.70191 0.409249
\(133\) 3.46519 0.300470
\(134\) 16.7348 1.44567
\(135\) −14.8677 −1.27960
\(136\) 1.52711 0.130948
\(137\) 12.7303 1.08762 0.543809 0.839209i \(-0.316981\pi\)
0.543809 + 0.839209i \(0.316981\pi\)
\(138\) −13.5388 −1.15250
\(139\) −20.5528 −1.74327 −0.871634 0.490158i \(-0.836939\pi\)
−0.871634 + 0.490158i \(0.836939\pi\)
\(140\) 32.8617 2.77732
\(141\) −4.64043 −0.390795
\(142\) −19.2279 −1.61357
\(143\) 13.7878 1.15299
\(144\) 5.73020 0.477517
\(145\) 1.69158 0.140478
\(146\) 6.67719 0.552608
\(147\) −3.79705 −0.313176
\(148\) −22.6949 −1.86551
\(149\) 12.2221 1.00127 0.500635 0.865658i \(-0.333100\pi\)
0.500635 + 0.865658i \(0.333100\pi\)
\(150\) 13.1465 1.07340
\(151\) 4.74717 0.386320 0.193160 0.981167i \(-0.438126\pi\)
0.193160 + 0.981167i \(0.438126\pi\)
\(152\) 1.34159 0.108817
\(153\) 2.76036 0.223162
\(154\) −17.6089 −1.41897
\(155\) −19.1926 −1.54159
\(156\) 11.6082 0.929397
\(157\) 10.7757 0.859991 0.429996 0.902831i \(-0.358515\pi\)
0.429996 + 0.902831i \(0.358515\pi\)
\(158\) 17.3733 1.38214
\(159\) −4.24787 −0.336878
\(160\) −28.0619 −2.21849
\(161\) 28.7724 2.26759
\(162\) −8.93636 −0.702107
\(163\) −20.1957 −1.58185 −0.790925 0.611913i \(-0.790400\pi\)
−0.790925 + 0.611913i \(0.790400\pi\)
\(164\) 0.211165 0.0164892
\(165\) −6.47654 −0.504198
\(166\) −10.1279 −0.786078
\(167\) −10.7629 −0.832860 −0.416430 0.909168i \(-0.636719\pi\)
−0.416430 + 0.909168i \(0.636719\pi\)
\(168\) −3.52510 −0.271967
\(169\) 21.0395 1.61842
\(170\) −8.84647 −0.678493
\(171\) 2.42502 0.185446
\(172\) 8.59084 0.655045
\(173\) −10.9655 −0.833694 −0.416847 0.908977i \(-0.636865\pi\)
−0.416847 + 0.908977i \(0.636865\pi\)
\(174\) −0.763143 −0.0578537
\(175\) −27.9387 −2.11197
\(176\) 5.58413 0.420920
\(177\) 1.88491 0.141678
\(178\) 17.2479 1.29278
\(179\) 6.23241 0.465832 0.232916 0.972497i \(-0.425173\pi\)
0.232916 + 0.972497i \(0.425173\pi\)
\(180\) 22.9975 1.71413
\(181\) 7.73278 0.574773 0.287387 0.957815i \(-0.407214\pi\)
0.287387 + 0.957815i \(0.407214\pi\)
\(182\) −43.4733 −3.22245
\(183\) −2.88059 −0.212940
\(184\) 11.1396 0.821224
\(185\) 31.2606 2.29833
\(186\) 8.65860 0.634879
\(187\) 2.69000 0.196712
\(188\) 16.0576 1.17112
\(189\) −14.2545 −1.03686
\(190\) −7.77178 −0.563824
\(191\) −0.228860 −0.0165597 −0.00827986 0.999966i \(-0.502636\pi\)
−0.00827986 + 0.999966i \(0.502636\pi\)
\(192\) 9.07639 0.655032
\(193\) −16.2349 −1.16861 −0.584306 0.811534i \(-0.698633\pi\)
−0.584306 + 0.811534i \(0.698633\pi\)
\(194\) −10.2938 −0.739054
\(195\) −15.9894 −1.14503
\(196\) 13.1392 0.938516
\(197\) 19.6254 1.39825 0.699126 0.714998i \(-0.253572\pi\)
0.699126 + 0.714998i \(0.253572\pi\)
\(198\) −12.3232 −0.875769
\(199\) −6.74121 −0.477872 −0.238936 0.971035i \(-0.576799\pi\)
−0.238936 + 0.971035i \(0.576799\pi\)
\(200\) −10.8168 −0.764865
\(201\) 5.90122 0.416240
\(202\) −12.7390 −0.896314
\(203\) 1.62182 0.113830
\(204\) 2.26476 0.158565
\(205\) −0.290864 −0.0203148
\(206\) 20.6546 1.43908
\(207\) 20.1357 1.39953
\(208\) 13.7862 0.955902
\(209\) 2.36321 0.163467
\(210\) 20.4207 1.40917
\(211\) 27.6002 1.90008 0.950039 0.312130i \(-0.101042\pi\)
0.950039 + 0.312130i \(0.101042\pi\)
\(212\) 14.6992 1.00955
\(213\) −6.78035 −0.464582
\(214\) 18.8458 1.28827
\(215\) −11.8333 −0.807021
\(216\) −5.51882 −0.375508
\(217\) −18.4012 −1.24915
\(218\) −10.2338 −0.693117
\(219\) 2.35458 0.159108
\(220\) 22.4112 1.51096
\(221\) 6.64111 0.446730
\(222\) −14.1030 −0.946529
\(223\) −21.6754 −1.45149 −0.725747 0.687962i \(-0.758506\pi\)
−0.725747 + 0.687962i \(0.758506\pi\)
\(224\) −26.9047 −1.79764
\(225\) −19.5522 −1.30348
\(226\) −2.59082 −0.172339
\(227\) −5.48628 −0.364137 −0.182069 0.983286i \(-0.558279\pi\)
−0.182069 + 0.983286i \(0.558279\pi\)
\(228\) 1.98963 0.131766
\(229\) 15.0026 0.991398 0.495699 0.868494i \(-0.334912\pi\)
0.495699 + 0.868494i \(0.334912\pi\)
\(230\) −64.5314 −4.25507
\(231\) −6.20945 −0.408552
\(232\) 0.627909 0.0412243
\(233\) −28.5124 −1.86791 −0.933955 0.357392i \(-0.883666\pi\)
−0.933955 + 0.357392i \(0.883666\pi\)
\(234\) −30.4237 −1.98886
\(235\) −22.1182 −1.44283
\(236\) −6.52248 −0.424577
\(237\) 6.12635 0.397949
\(238\) −8.48165 −0.549784
\(239\) 20.4845 1.32503 0.662516 0.749048i \(-0.269489\pi\)
0.662516 + 0.749048i \(0.269489\pi\)
\(240\) −6.47582 −0.418012
\(241\) −17.7303 −1.14211 −0.571054 0.820912i \(-0.693465\pi\)
−0.571054 + 0.820912i \(0.693465\pi\)
\(242\) 11.6445 0.748540
\(243\) −15.4922 −0.993823
\(244\) 9.96792 0.638131
\(245\) −18.0983 −1.15626
\(246\) 0.131221 0.00836633
\(247\) 5.83434 0.371230
\(248\) −7.12424 −0.452390
\(249\) −3.57141 −0.226329
\(250\) 23.8025 1.50540
\(251\) 16.7542 1.05752 0.528758 0.848773i \(-0.322658\pi\)
0.528758 + 0.848773i \(0.322658\pi\)
\(252\) 22.0491 1.38896
\(253\) 19.6224 1.23365
\(254\) −26.6213 −1.67037
\(255\) −3.11954 −0.195353
\(256\) 1.98378 0.123986
\(257\) −13.2088 −0.823940 −0.411970 0.911197i \(-0.635159\pi\)
−0.411970 + 0.911197i \(0.635159\pi\)
\(258\) 5.33847 0.332359
\(259\) 29.9715 1.86234
\(260\) 55.3293 3.43138
\(261\) 1.13499 0.0702543
\(262\) −9.83579 −0.607657
\(263\) 24.0246 1.48142 0.740709 0.671826i \(-0.234490\pi\)
0.740709 + 0.671826i \(0.234490\pi\)
\(264\) −2.40407 −0.147960
\(265\) −20.2471 −1.24377
\(266\) −7.45128 −0.456867
\(267\) 6.08213 0.372220
\(268\) −20.4204 −1.24738
\(269\) 21.4987 1.31080 0.655398 0.755283i \(-0.272501\pi\)
0.655398 + 0.755283i \(0.272501\pi\)
\(270\) 31.9703 1.94565
\(271\) −3.54406 −0.215286 −0.107643 0.994190i \(-0.534330\pi\)
−0.107643 + 0.994190i \(0.534330\pi\)
\(272\) 2.68970 0.163087
\(273\) −15.3300 −0.927815
\(274\) −27.3742 −1.65374
\(275\) −19.0538 −1.14899
\(276\) 16.5205 0.994416
\(277\) −10.1076 −0.607306 −0.303653 0.952783i \(-0.598206\pi\)
−0.303653 + 0.952783i \(0.598206\pi\)
\(278\) 44.1953 2.65066
\(279\) −12.8776 −0.770961
\(280\) −16.8021 −1.00412
\(281\) −16.4244 −0.979799 −0.489900 0.871779i \(-0.662967\pi\)
−0.489900 + 0.871779i \(0.662967\pi\)
\(282\) 9.97844 0.594208
\(283\) −12.1933 −0.724815 −0.362408 0.932020i \(-0.618045\pi\)
−0.362408 + 0.932020i \(0.618045\pi\)
\(284\) 23.4625 1.39224
\(285\) −2.74057 −0.162337
\(286\) −29.6482 −1.75313
\(287\) −0.278869 −0.0164611
\(288\) −18.8286 −1.10948
\(289\) −15.7043 −0.923783
\(290\) −3.63745 −0.213599
\(291\) −3.62992 −0.212790
\(292\) −8.14774 −0.476810
\(293\) −0.684535 −0.0399910 −0.0199955 0.999800i \(-0.506365\pi\)
−0.0199955 + 0.999800i \(0.506365\pi\)
\(294\) 8.16490 0.476187
\(295\) 8.98424 0.523083
\(296\) 11.6038 0.674459
\(297\) −9.72139 −0.564092
\(298\) −26.2814 −1.52244
\(299\) 48.4442 2.80160
\(300\) −16.0418 −0.926171
\(301\) −11.3453 −0.653930
\(302\) −10.2080 −0.587403
\(303\) −4.49217 −0.258069
\(304\) 2.36294 0.135524
\(305\) −13.7301 −0.786183
\(306\) −5.93567 −0.339320
\(307\) 24.1375 1.37760 0.688800 0.724952i \(-0.258138\pi\)
0.688800 + 0.724952i \(0.258138\pi\)
\(308\) 21.4870 1.22434
\(309\) 7.28346 0.414342
\(310\) 41.2704 2.34400
\(311\) −23.0170 −1.30517 −0.652587 0.757714i \(-0.726316\pi\)
−0.652587 + 0.757714i \(0.726316\pi\)
\(312\) −5.93521 −0.336015
\(313\) 7.33966 0.414862 0.207431 0.978250i \(-0.433490\pi\)
0.207431 + 0.978250i \(0.433490\pi\)
\(314\) −23.1712 −1.30763
\(315\) −30.3710 −1.71121
\(316\) −21.1994 −1.19256
\(317\) −1.00000 −0.0561656
\(318\) 9.13431 0.512227
\(319\) 1.10606 0.0619275
\(320\) 43.2618 2.41841
\(321\) 6.64563 0.370923
\(322\) −61.8701 −3.44789
\(323\) 1.13828 0.0633357
\(324\) 10.9045 0.605803
\(325\) −47.0404 −2.60933
\(326\) 43.4273 2.40522
\(327\) −3.60874 −0.199564
\(328\) −0.107968 −0.00596152
\(329\) −21.2061 −1.16913
\(330\) 13.9267 0.766638
\(331\) −1.89396 −0.104102 −0.0520508 0.998644i \(-0.516576\pi\)
−0.0520508 + 0.998644i \(0.516576\pi\)
\(332\) 12.3584 0.678256
\(333\) 20.9748 1.14941
\(334\) 23.1438 1.26637
\(335\) 28.1276 1.53678
\(336\) −6.20876 −0.338716
\(337\) 7.38817 0.402459 0.201230 0.979544i \(-0.435506\pi\)
0.201230 + 0.979544i \(0.435506\pi\)
\(338\) −45.2417 −2.46083
\(339\) −0.913602 −0.0496201
\(340\) 10.7948 0.585428
\(341\) −12.5493 −0.679584
\(342\) −5.21459 −0.281973
\(343\) 6.90434 0.372799
\(344\) −4.39246 −0.236826
\(345\) −22.7558 −1.22513
\(346\) 23.5795 1.26764
\(347\) −20.0658 −1.07719 −0.538593 0.842566i \(-0.681044\pi\)
−0.538593 + 0.842566i \(0.681044\pi\)
\(348\) 0.931213 0.0499182
\(349\) 19.8296 1.06145 0.530727 0.847543i \(-0.321919\pi\)
0.530727 + 0.847543i \(0.321919\pi\)
\(350\) 60.0773 3.21127
\(351\) −24.0004 −1.28104
\(352\) −18.3486 −0.977985
\(353\) 25.3562 1.34957 0.674787 0.738012i \(-0.264235\pi\)
0.674787 + 0.738012i \(0.264235\pi\)
\(354\) −4.05316 −0.215423
\(355\) −32.3179 −1.71526
\(356\) −21.0464 −1.11546
\(357\) −2.99089 −0.158295
\(358\) −13.4017 −0.708302
\(359\) 25.8296 1.36324 0.681618 0.731708i \(-0.261277\pi\)
0.681618 + 0.731708i \(0.261277\pi\)
\(360\) −11.7585 −0.619728
\(361\) 1.00000 0.0526316
\(362\) −16.6280 −0.873948
\(363\) 4.10623 0.215521
\(364\) 53.0476 2.78045
\(365\) 11.2229 0.587434
\(366\) 6.19421 0.323777
\(367\) −15.3089 −0.799119 −0.399559 0.916707i \(-0.630837\pi\)
−0.399559 + 0.916707i \(0.630837\pi\)
\(368\) 19.6202 1.02277
\(369\) −0.195160 −0.0101596
\(370\) −67.2205 −3.49463
\(371\) −19.4121 −1.00783
\(372\) −10.5655 −0.547797
\(373\) 25.1146 1.30039 0.650193 0.759769i \(-0.274688\pi\)
0.650193 + 0.759769i \(0.274688\pi\)
\(374\) −5.78437 −0.299102
\(375\) 8.39350 0.433438
\(376\) −8.21020 −0.423409
\(377\) 2.73066 0.140636
\(378\) 30.6519 1.57656
\(379\) 21.9503 1.12751 0.563754 0.825942i \(-0.309356\pi\)
0.563754 + 0.825942i \(0.309356\pi\)
\(380\) 9.48339 0.486488
\(381\) −9.38750 −0.480936
\(382\) 0.492123 0.0251792
\(383\) 9.37501 0.479041 0.239520 0.970891i \(-0.423010\pi\)
0.239520 + 0.970891i \(0.423010\pi\)
\(384\) −7.74234 −0.395099
\(385\) −29.5968 −1.50839
\(386\) 34.9103 1.77689
\(387\) −7.93970 −0.403598
\(388\) 12.5609 0.637682
\(389\) −4.17034 −0.211445 −0.105722 0.994396i \(-0.533715\pi\)
−0.105722 + 0.994396i \(0.533715\pi\)
\(390\) 34.3824 1.74102
\(391\) 9.45148 0.477982
\(392\) −6.71803 −0.339312
\(393\) −3.46840 −0.174958
\(394\) −42.2010 −2.12606
\(395\) 29.2007 1.46925
\(396\) 15.0372 0.755645
\(397\) −10.6613 −0.535077 −0.267539 0.963547i \(-0.586210\pi\)
−0.267539 + 0.963547i \(0.586210\pi\)
\(398\) 14.4958 0.726609
\(399\) −2.62755 −0.131542
\(400\) −19.0517 −0.952584
\(401\) −3.02541 −0.151082 −0.0755408 0.997143i \(-0.524068\pi\)
−0.0755408 + 0.997143i \(0.524068\pi\)
\(402\) −12.6895 −0.632897
\(403\) −30.9820 −1.54333
\(404\) 15.5446 0.773372
\(405\) −15.0201 −0.746354
\(406\) −3.48745 −0.173079
\(407\) 20.4401 1.01318
\(408\) −1.15796 −0.0573277
\(409\) −23.5038 −1.16219 −0.581094 0.813836i \(-0.697375\pi\)
−0.581094 + 0.813836i \(0.697375\pi\)
\(410\) 0.625452 0.0308889
\(411\) −9.65299 −0.476147
\(412\) −25.2035 −1.24169
\(413\) 8.61374 0.423854
\(414\) −43.2983 −2.12799
\(415\) −17.0228 −0.835617
\(416\) −45.2994 −2.22099
\(417\) 15.5846 0.763182
\(418\) −5.08167 −0.248552
\(419\) 24.2611 1.18523 0.592617 0.805485i \(-0.298095\pi\)
0.592617 + 0.805485i \(0.298095\pi\)
\(420\) −24.9181 −1.21588
\(421\) 18.6543 0.909156 0.454578 0.890707i \(-0.349790\pi\)
0.454578 + 0.890707i \(0.349790\pi\)
\(422\) −59.3495 −2.88909
\(423\) −14.8405 −0.721572
\(424\) −7.51566 −0.364993
\(425\) −9.17760 −0.445179
\(426\) 14.5800 0.706401
\(427\) −13.1639 −0.637044
\(428\) −22.9963 −1.11157
\(429\) −10.4549 −0.504765
\(430\) 25.4454 1.22708
\(431\) −8.20581 −0.395260 −0.197630 0.980277i \(-0.563324\pi\)
−0.197630 + 0.980277i \(0.563324\pi\)
\(432\) −9.72031 −0.467668
\(433\) −0.0290442 −0.00139578 −0.000697888 1.00000i \(-0.500222\pi\)
−0.000697888 1.00000i \(0.500222\pi\)
\(434\) 39.5685 1.89935
\(435\) −1.28268 −0.0614997
\(436\) 12.4876 0.598046
\(437\) 8.30329 0.397200
\(438\) −5.06312 −0.241925
\(439\) 4.22968 0.201872 0.100936 0.994893i \(-0.467816\pi\)
0.100936 + 0.994893i \(0.467816\pi\)
\(440\) −11.4588 −0.546276
\(441\) −12.1433 −0.578254
\(442\) −14.2806 −0.679257
\(443\) 10.2463 0.486817 0.243409 0.969924i \(-0.421734\pi\)
0.243409 + 0.969924i \(0.421734\pi\)
\(444\) 17.2089 0.816699
\(445\) 28.9899 1.37425
\(446\) 46.6092 2.20701
\(447\) −9.26764 −0.438344
\(448\) 41.4778 1.95964
\(449\) −14.4468 −0.681787 −0.340893 0.940102i \(-0.610730\pi\)
−0.340893 + 0.940102i \(0.610730\pi\)
\(450\) 42.0436 1.98195
\(451\) −0.190185 −0.00895545
\(452\) 3.16140 0.148700
\(453\) −3.59965 −0.169126
\(454\) 11.7973 0.553675
\(455\) −73.0692 −3.42554
\(456\) −1.01729 −0.0476390
\(457\) 13.3265 0.623386 0.311693 0.950183i \(-0.399104\pi\)
0.311693 + 0.950183i \(0.399104\pi\)
\(458\) −32.2604 −1.50743
\(459\) −4.68248 −0.218559
\(460\) 78.7434 3.67143
\(461\) −9.56243 −0.445367 −0.222683 0.974891i \(-0.571482\pi\)
−0.222683 + 0.974891i \(0.571482\pi\)
\(462\) 13.3523 0.621207
\(463\) 1.93850 0.0900898 0.0450449 0.998985i \(-0.485657\pi\)
0.0450449 + 0.998985i \(0.485657\pi\)
\(464\) 1.10594 0.0513418
\(465\) 14.5532 0.674890
\(466\) 61.3109 2.84017
\(467\) −9.09582 −0.420904 −0.210452 0.977604i \(-0.567494\pi\)
−0.210452 + 0.977604i \(0.567494\pi\)
\(468\) 37.1240 1.71606
\(469\) 26.9677 1.24525
\(470\) 47.5614 2.19384
\(471\) −8.17087 −0.376494
\(472\) 3.33492 0.153502
\(473\) −7.73731 −0.355762
\(474\) −13.1736 −0.605086
\(475\) −8.06268 −0.369941
\(476\) 10.3496 0.474373
\(477\) −13.5851 −0.622019
\(478\) −44.0483 −2.01472
\(479\) 12.3698 0.565191 0.282595 0.959239i \(-0.408805\pi\)
0.282595 + 0.959239i \(0.408805\pi\)
\(480\) 21.2786 0.971229
\(481\) 50.4630 2.30091
\(482\) 38.1259 1.73659
\(483\) −21.8173 −0.992723
\(484\) −14.2091 −0.645867
\(485\) −17.3017 −0.785630
\(486\) 33.3132 1.51112
\(487\) 27.7348 1.25678 0.628391 0.777898i \(-0.283714\pi\)
0.628391 + 0.777898i \(0.283714\pi\)
\(488\) −5.09656 −0.230710
\(489\) 15.3138 0.692515
\(490\) 38.9173 1.75810
\(491\) 1.58105 0.0713520 0.0356760 0.999363i \(-0.488642\pi\)
0.0356760 + 0.999363i \(0.488642\pi\)
\(492\) −0.160120 −0.00721877
\(493\) 0.532754 0.0239940
\(494\) −12.5457 −0.564459
\(495\) −20.7126 −0.930961
\(496\) −12.5479 −0.563419
\(497\) −30.9852 −1.38987
\(498\) 7.67970 0.344136
\(499\) −43.2795 −1.93746 −0.968728 0.248125i \(-0.920186\pi\)
−0.968728 + 0.248125i \(0.920186\pi\)
\(500\) −29.0446 −1.29892
\(501\) 8.16122 0.364616
\(502\) −36.0270 −1.60796
\(503\) −26.8724 −1.19818 −0.599090 0.800682i \(-0.704471\pi\)
−0.599090 + 0.800682i \(0.704471\pi\)
\(504\) −11.2736 −0.502166
\(505\) −21.4115 −0.952801
\(506\) −42.1946 −1.87578
\(507\) −15.9536 −0.708526
\(508\) 32.4842 1.44125
\(509\) −3.59201 −0.159213 −0.0796066 0.996826i \(-0.525366\pi\)
−0.0796066 + 0.996826i \(0.525366\pi\)
\(510\) 6.70802 0.297036
\(511\) 10.7601 0.475999
\(512\) −24.6868 −1.09101
\(513\) −4.11364 −0.181622
\(514\) 28.4031 1.25281
\(515\) 34.7160 1.52977
\(516\) −6.51419 −0.286771
\(517\) −14.4622 −0.636049
\(518\) −64.4484 −2.83170
\(519\) 8.31485 0.364982
\(520\) −28.2897 −1.24058
\(521\) 8.48645 0.371798 0.185899 0.982569i \(-0.440480\pi\)
0.185899 + 0.982569i \(0.440480\pi\)
\(522\) −2.44060 −0.106822
\(523\) −38.5797 −1.68697 −0.843486 0.537151i \(-0.819501\pi\)
−0.843486 + 0.537151i \(0.819501\pi\)
\(524\) 12.0020 0.524308
\(525\) 21.1851 0.924594
\(526\) −51.6606 −2.25251
\(527\) −6.04461 −0.263307
\(528\) −4.23429 −0.184274
\(529\) 45.9447 1.99759
\(530\) 43.5379 1.89116
\(531\) 6.02811 0.261598
\(532\) 9.09231 0.394201
\(533\) −0.469532 −0.0203377
\(534\) −13.0786 −0.565964
\(535\) 31.6758 1.36946
\(536\) 10.4409 0.450977
\(537\) −4.72586 −0.203936
\(538\) −46.2291 −1.99308
\(539\) −11.8338 −0.509718
\(540\) −39.0113 −1.67878
\(541\) 10.3721 0.445933 0.222966 0.974826i \(-0.428426\pi\)
0.222966 + 0.974826i \(0.428426\pi\)
\(542\) 7.62088 0.327345
\(543\) −5.86355 −0.251629
\(544\) −8.83794 −0.378923
\(545\) −17.2007 −0.736798
\(546\) 32.9645 1.41075
\(547\) −14.0713 −0.601647 −0.300824 0.953680i \(-0.597262\pi\)
−0.300824 + 0.953680i \(0.597262\pi\)
\(548\) 33.4029 1.42690
\(549\) −9.21241 −0.393176
\(550\) 40.9719 1.74705
\(551\) 0.468033 0.0199389
\(552\) −8.44686 −0.359522
\(553\) 27.9965 1.19053
\(554\) 21.7346 0.923415
\(555\) −23.7040 −1.00618
\(556\) −53.9286 −2.28708
\(557\) −37.5748 −1.59209 −0.796047 0.605235i \(-0.793079\pi\)
−0.796047 + 0.605235i \(0.793079\pi\)
\(558\) 27.6910 1.17225
\(559\) −19.1020 −0.807930
\(560\) −29.5935 −1.25055
\(561\) −2.03975 −0.0861182
\(562\) 35.3179 1.48979
\(563\) 21.8906 0.922578 0.461289 0.887250i \(-0.347387\pi\)
0.461289 + 0.887250i \(0.347387\pi\)
\(564\) −12.1760 −0.512704
\(565\) −4.35460 −0.183200
\(566\) 26.2195 1.10209
\(567\) −14.4007 −0.604772
\(568\) −11.9963 −0.503354
\(569\) 15.9919 0.670416 0.335208 0.942144i \(-0.391193\pi\)
0.335208 + 0.942144i \(0.391193\pi\)
\(570\) 5.89312 0.246836
\(571\) −8.06717 −0.337601 −0.168800 0.985650i \(-0.553989\pi\)
−0.168800 + 0.985650i \(0.553989\pi\)
\(572\) 36.1777 1.51267
\(573\) 0.173538 0.00724965
\(574\) 0.599659 0.0250293
\(575\) −66.9468 −2.79188
\(576\) 29.0272 1.20947
\(577\) 6.69031 0.278521 0.139261 0.990256i \(-0.455527\pi\)
0.139261 + 0.990256i \(0.455527\pi\)
\(578\) 33.7694 1.40462
\(579\) 12.3104 0.511604
\(580\) 4.43854 0.184300
\(581\) −16.3208 −0.677102
\(582\) 7.80551 0.323549
\(583\) −13.2388 −0.548295
\(584\) 4.16591 0.172386
\(585\) −51.1357 −2.11420
\(586\) 1.47197 0.0608066
\(587\) 35.8224 1.47855 0.739275 0.673404i \(-0.235168\pi\)
0.739275 + 0.673404i \(0.235168\pi\)
\(588\) −9.96309 −0.410871
\(589\) −5.31029 −0.218807
\(590\) −19.3190 −0.795352
\(591\) −14.8814 −0.612139
\(592\) 20.4378 0.839990
\(593\) 3.06515 0.125871 0.0629354 0.998018i \(-0.479954\pi\)
0.0629354 + 0.998018i \(0.479954\pi\)
\(594\) 20.9042 0.857708
\(595\) −14.2558 −0.584432
\(596\) 32.0695 1.31362
\(597\) 5.11167 0.209207
\(598\) −104.171 −4.25986
\(599\) 28.4937 1.16422 0.582111 0.813109i \(-0.302227\pi\)
0.582111 + 0.813109i \(0.302227\pi\)
\(600\) 8.20209 0.334849
\(601\) −40.3516 −1.64597 −0.822987 0.568060i \(-0.807694\pi\)
−0.822987 + 0.568060i \(0.807694\pi\)
\(602\) 24.3960 0.994307
\(603\) 18.8727 0.768554
\(604\) 12.4561 0.506832
\(605\) 19.5720 0.795714
\(606\) 9.65963 0.392396
\(607\) 15.3266 0.622086 0.311043 0.950396i \(-0.399322\pi\)
0.311043 + 0.950396i \(0.399322\pi\)
\(608\) −7.76428 −0.314883
\(609\) −1.22978 −0.0498333
\(610\) 29.5242 1.19540
\(611\) −35.7047 −1.44446
\(612\) 7.24291 0.292777
\(613\) −34.7133 −1.40206 −0.701028 0.713133i \(-0.747275\pi\)
−0.701028 + 0.713133i \(0.747275\pi\)
\(614\) −51.9035 −2.09465
\(615\) 0.220554 0.00889359
\(616\) −10.9862 −0.442648
\(617\) 9.27524 0.373407 0.186704 0.982416i \(-0.440220\pi\)
0.186704 + 0.982416i \(0.440220\pi\)
\(618\) −15.6618 −0.630010
\(619\) −20.5227 −0.824875 −0.412438 0.910986i \(-0.635322\pi\)
−0.412438 + 0.910986i \(0.635322\pi\)
\(620\) −50.3596 −2.02249
\(621\) −34.1568 −1.37066
\(622\) 49.4940 1.98453
\(623\) 27.7944 1.11356
\(624\) −10.4537 −0.418483
\(625\) −0.306549 −0.0122620
\(626\) −15.7827 −0.630802
\(627\) −1.79195 −0.0715637
\(628\) 28.2743 1.12827
\(629\) 9.84534 0.392559
\(630\) 65.3075 2.60191
\(631\) −35.1992 −1.40126 −0.700629 0.713526i \(-0.747097\pi\)
−0.700629 + 0.713526i \(0.747097\pi\)
\(632\) 10.8392 0.431160
\(633\) −20.9285 −0.831832
\(634\) 2.15033 0.0854003
\(635\) −44.7447 −1.77564
\(636\) −11.1460 −0.441968
\(637\) −29.2155 −1.15756
\(638\) −2.37839 −0.0941614
\(639\) −21.6842 −0.857814
\(640\) −36.9032 −1.45873
\(641\) −21.7477 −0.858982 −0.429491 0.903071i \(-0.641307\pi\)
−0.429491 + 0.903071i \(0.641307\pi\)
\(642\) −14.2903 −0.563992
\(643\) 24.6227 0.971025 0.485512 0.874230i \(-0.338633\pi\)
0.485512 + 0.874230i \(0.338633\pi\)
\(644\) 75.4961 2.97496
\(645\) 8.97282 0.353304
\(646\) −2.44768 −0.0963025
\(647\) −23.1956 −0.911915 −0.455957 0.890002i \(-0.650703\pi\)
−0.455957 + 0.890002i \(0.650703\pi\)
\(648\) −5.57541 −0.219023
\(649\) 5.87445 0.230592
\(650\) 101.152 3.96752
\(651\) 13.9531 0.546864
\(652\) −52.9915 −2.07531
\(653\) 3.65615 0.143076 0.0715380 0.997438i \(-0.477209\pi\)
0.0715380 + 0.997438i \(0.477209\pi\)
\(654\) 7.75996 0.303438
\(655\) −16.5318 −0.645952
\(656\) −0.190164 −0.00742464
\(657\) 7.53019 0.293781
\(658\) 45.6000 1.77767
\(659\) 25.1423 0.979403 0.489702 0.871890i \(-0.337106\pi\)
0.489702 + 0.871890i \(0.337106\pi\)
\(660\) −16.9938 −0.661483
\(661\) −48.5827 −1.88965 −0.944824 0.327580i \(-0.893767\pi\)
−0.944824 + 0.327580i \(0.893767\pi\)
\(662\) 4.07264 0.158287
\(663\) −5.03577 −0.195573
\(664\) −6.31881 −0.245217
\(665\) −12.5240 −0.485660
\(666\) −45.1026 −1.74769
\(667\) 3.88622 0.150475
\(668\) −28.2408 −1.09267
\(669\) 16.4359 0.635447
\(670\) −60.4836 −2.33669
\(671\) −8.97758 −0.346576
\(672\) 20.4011 0.786988
\(673\) −51.6039 −1.98918 −0.994592 0.103863i \(-0.966880\pi\)
−0.994592 + 0.103863i \(0.966880\pi\)
\(674\) −15.8870 −0.611944
\(675\) 33.1670 1.27660
\(676\) 55.2055 2.12329
\(677\) 47.2366 1.81545 0.907725 0.419565i \(-0.137818\pi\)
0.907725 + 0.419565i \(0.137818\pi\)
\(678\) 1.96454 0.0754478
\(679\) −16.5882 −0.636596
\(680\) −5.51932 −0.211656
\(681\) 4.16009 0.159415
\(682\) 26.9852 1.03331
\(683\) −11.5833 −0.443223 −0.221611 0.975135i \(-0.571132\pi\)
−0.221611 + 0.975135i \(0.571132\pi\)
\(684\) 6.36302 0.243296
\(685\) −46.0101 −1.75796
\(686\) −14.8466 −0.566845
\(687\) −11.3760 −0.434022
\(688\) −7.73645 −0.294949
\(689\) −32.6842 −1.24517
\(690\) 48.9323 1.86282
\(691\) 11.4576 0.435867 0.217933 0.975964i \(-0.430068\pi\)
0.217933 + 0.975964i \(0.430068\pi\)
\(692\) −28.7725 −1.09377
\(693\) −19.8584 −0.754359
\(694\) 43.1479 1.63787
\(695\) 74.2827 2.81770
\(696\) −0.476126 −0.0180475
\(697\) −0.0916059 −0.00346982
\(698\) −42.6401 −1.61395
\(699\) 21.6201 0.817749
\(700\) −73.3084 −2.77080
\(701\) 1.52904 0.0577512 0.0288756 0.999583i \(-0.490807\pi\)
0.0288756 + 0.999583i \(0.490807\pi\)
\(702\) 51.6086 1.94784
\(703\) 8.64931 0.326215
\(704\) 28.2872 1.06612
\(705\) 16.7716 0.631655
\(706\) −54.5241 −2.05204
\(707\) −20.5285 −0.772056
\(708\) 4.94581 0.185875
\(709\) −2.00829 −0.0754230 −0.0377115 0.999289i \(-0.512007\pi\)
−0.0377115 + 0.999289i \(0.512007\pi\)
\(710\) 69.4941 2.60807
\(711\) 19.5927 0.734782
\(712\) 10.7610 0.403284
\(713\) −44.0929 −1.65129
\(714\) 6.43139 0.240689
\(715\) −49.8321 −1.86362
\(716\) 16.3532 0.611148
\(717\) −15.5328 −0.580083
\(718\) −55.5421 −2.07281
\(719\) 6.73336 0.251112 0.125556 0.992087i \(-0.459929\pi\)
0.125556 + 0.992087i \(0.459929\pi\)
\(720\) −20.7103 −0.771826
\(721\) 33.2843 1.23957
\(722\) −2.15033 −0.0800268
\(723\) 13.4444 0.500002
\(724\) 20.2901 0.754074
\(725\) −3.77361 −0.140148
\(726\) −8.82973 −0.327702
\(727\) −48.5715 −1.80142 −0.900708 0.434426i \(-0.856951\pi\)
−0.900708 + 0.434426i \(0.856951\pi\)
\(728\) −27.1230 −1.00525
\(729\) −0.720190 −0.0266737
\(730\) −24.1329 −0.893200
\(731\) −3.72681 −0.137841
\(732\) −7.55839 −0.279366
\(733\) 46.6878 1.72445 0.862226 0.506523i \(-0.169070\pi\)
0.862226 + 0.506523i \(0.169070\pi\)
\(734\) 32.9191 1.21507
\(735\) 13.7234 0.506197
\(736\) −64.4691 −2.37636
\(737\) 18.3916 0.677463
\(738\) 0.419657 0.0154478
\(739\) 21.3621 0.785818 0.392909 0.919577i \(-0.371469\pi\)
0.392909 + 0.919577i \(0.371469\pi\)
\(740\) 82.0248 3.01529
\(741\) −4.42401 −0.162520
\(742\) 41.7424 1.53241
\(743\) −25.4167 −0.932447 −0.466223 0.884667i \(-0.654386\pi\)
−0.466223 + 0.884667i \(0.654386\pi\)
\(744\) 5.40211 0.198051
\(745\) −44.1734 −1.61839
\(746\) −54.0046 −1.97725
\(747\) −11.4217 −0.417899
\(748\) 7.05828 0.258076
\(749\) 30.3695 1.10968
\(750\) −18.0488 −0.659047
\(751\) −34.0142 −1.24120 −0.620599 0.784128i \(-0.713110\pi\)
−0.620599 + 0.784128i \(0.713110\pi\)
\(752\) −14.4606 −0.527325
\(753\) −12.7042 −0.462968
\(754\) −5.87182 −0.213839
\(755\) −17.1574 −0.624422
\(756\) −37.4025 −1.36032
\(757\) −32.3114 −1.17438 −0.587188 0.809450i \(-0.699765\pi\)
−0.587188 + 0.809450i \(0.699765\pi\)
\(758\) −47.2002 −1.71439
\(759\) −14.8791 −0.540077
\(760\) −4.84882 −0.175885
\(761\) −21.5197 −0.780088 −0.390044 0.920796i \(-0.627540\pi\)
−0.390044 + 0.920796i \(0.627540\pi\)
\(762\) 20.1862 0.731268
\(763\) −16.4914 −0.597028
\(764\) −0.600506 −0.0217255
\(765\) −9.97658 −0.360704
\(766\) −20.1593 −0.728386
\(767\) 14.5030 0.523671
\(768\) −1.50424 −0.0542796
\(769\) −10.9627 −0.395325 −0.197663 0.980270i \(-0.563335\pi\)
−0.197663 + 0.980270i \(0.563335\pi\)
\(770\) 63.6428 2.29353
\(771\) 10.0158 0.360711
\(772\) −42.5987 −1.53316
\(773\) 35.2590 1.26818 0.634090 0.773259i \(-0.281375\pi\)
0.634090 + 0.773259i \(0.281375\pi\)
\(774\) 17.0729 0.613674
\(775\) 42.8152 1.53797
\(776\) −6.42233 −0.230548
\(777\) −22.7265 −0.815309
\(778\) 8.96760 0.321504
\(779\) −0.0804774 −0.00288340
\(780\) −41.9546 −1.50222
\(781\) −21.1314 −0.756143
\(782\) −20.3238 −0.726776
\(783\) −1.92532 −0.0688054
\(784\) −11.8325 −0.422588
\(785\) −38.9457 −1.39003
\(786\) 7.45820 0.266025
\(787\) −46.7499 −1.66646 −0.833228 0.552930i \(-0.813510\pi\)
−0.833228 + 0.552930i \(0.813510\pi\)
\(788\) 51.4951 1.83444
\(789\) −18.2171 −0.648547
\(790\) −62.7910 −2.23400
\(791\) −4.17502 −0.148447
\(792\) −7.68844 −0.273197
\(793\) −22.1640 −0.787068
\(794\) 22.9253 0.813590
\(795\) 15.3528 0.544508
\(796\) −17.6883 −0.626944
\(797\) 38.6354 1.36854 0.684269 0.729230i \(-0.260122\pi\)
0.684269 + 0.729230i \(0.260122\pi\)
\(798\) 5.65009 0.200011
\(799\) −6.96600 −0.246439
\(800\) 62.6010 2.21328
\(801\) 19.4512 0.687275
\(802\) 6.50561 0.229721
\(803\) 7.33823 0.258961
\(804\) 15.4842 0.546086
\(805\) −103.990 −3.66518
\(806\) 66.6215 2.34664
\(807\) −16.3018 −0.573851
\(808\) −7.94789 −0.279606
\(809\) 12.4315 0.437070 0.218535 0.975829i \(-0.429872\pi\)
0.218535 + 0.975829i \(0.429872\pi\)
\(810\) 32.2981 1.13484
\(811\) −19.9461 −0.700403 −0.350201 0.936674i \(-0.613887\pi\)
−0.350201 + 0.936674i \(0.613887\pi\)
\(812\) 4.25550 0.149339
\(813\) 2.68736 0.0942498
\(814\) −43.9529 −1.54055
\(815\) 72.9920 2.55680
\(816\) −2.03952 −0.0713974
\(817\) −3.27407 −0.114545
\(818\) 50.5408 1.76712
\(819\) −49.0269 −1.71314
\(820\) −0.763198 −0.0266520
\(821\) 31.0579 1.08393 0.541964 0.840402i \(-0.317681\pi\)
0.541964 + 0.840402i \(0.317681\pi\)
\(822\) 20.7571 0.723986
\(823\) 22.2263 0.774761 0.387381 0.921920i \(-0.373380\pi\)
0.387381 + 0.921920i \(0.373380\pi\)
\(824\) 12.8864 0.448921
\(825\) 14.4480 0.503013
\(826\) −18.5223 −0.644475
\(827\) −12.4274 −0.432145 −0.216072 0.976377i \(-0.569325\pi\)
−0.216072 + 0.976377i \(0.569325\pi\)
\(828\) 52.8341 1.83611
\(829\) −43.7789 −1.52050 −0.760252 0.649629i \(-0.774924\pi\)
−0.760252 + 0.649629i \(0.774924\pi\)
\(830\) 36.6046 1.27056
\(831\) 7.66429 0.265871
\(832\) 69.8361 2.42113
\(833\) −5.69996 −0.197492
\(834\) −33.5120 −1.16043
\(835\) 38.8997 1.34618
\(836\) 6.20082 0.214460
\(837\) 21.8446 0.755061
\(838\) −52.1693 −1.80216
\(839\) 1.26369 0.0436276 0.0218138 0.999762i \(-0.493056\pi\)
0.0218138 + 0.999762i \(0.493056\pi\)
\(840\) 12.7405 0.439590
\(841\) −28.7809 −0.992446
\(842\) −40.1129 −1.38238
\(843\) 12.4542 0.428945
\(844\) 72.4203 2.49281
\(845\) −76.0416 −2.61591
\(846\) 31.9120 1.09716
\(847\) 18.7648 0.644767
\(848\) −13.2373 −0.454572
\(849\) 9.24582 0.317316
\(850\) 19.7348 0.676899
\(851\) 71.8177 2.46188
\(852\) −17.7910 −0.609508
\(853\) 15.6806 0.536894 0.268447 0.963295i \(-0.413490\pi\)
0.268447 + 0.963295i \(0.413490\pi\)
\(854\) 28.3066 0.968632
\(855\) −8.76460 −0.299743
\(856\) 11.7579 0.401878
\(857\) 56.2918 1.92289 0.961446 0.274994i \(-0.0886760\pi\)
0.961446 + 0.274994i \(0.0886760\pi\)
\(858\) 22.4813 0.767501
\(859\) −15.3109 −0.522402 −0.261201 0.965284i \(-0.584119\pi\)
−0.261201 + 0.965284i \(0.584119\pi\)
\(860\) −31.0493 −1.05877
\(861\) 0.211458 0.00720648
\(862\) 17.6452 0.600997
\(863\) 33.5179 1.14096 0.570482 0.821310i \(-0.306757\pi\)
0.570482 + 0.821310i \(0.306757\pi\)
\(864\) 31.9395 1.08660
\(865\) 39.6320 1.34753
\(866\) 0.0624545 0.00212229
\(867\) 11.9081 0.404421
\(868\) −48.2828 −1.63883
\(869\) 19.0932 0.647693
\(870\) 2.75818 0.0935109
\(871\) 45.4055 1.53851
\(872\) −6.38485 −0.216218
\(873\) −11.6088 −0.392900
\(874\) −17.8548 −0.603947
\(875\) 38.3570 1.29670
\(876\) 6.17820 0.208742
\(877\) 21.9876 0.742469 0.371234 0.928539i \(-0.378935\pi\)
0.371234 + 0.928539i \(0.378935\pi\)
\(878\) −9.09520 −0.306948
\(879\) 0.519063 0.0175076
\(880\) −20.1824 −0.680347
\(881\) 9.04553 0.304752 0.152376 0.988323i \(-0.451308\pi\)
0.152376 + 0.988323i \(0.451308\pi\)
\(882\) 26.1121 0.879242
\(883\) −20.7042 −0.696752 −0.348376 0.937355i \(-0.613267\pi\)
−0.348376 + 0.937355i \(0.613267\pi\)
\(884\) 17.4256 0.586087
\(885\) −6.81249 −0.228999
\(886\) −22.0329 −0.740210
\(887\) −3.71329 −0.124680 −0.0623400 0.998055i \(-0.519856\pi\)
−0.0623400 + 0.998055i \(0.519856\pi\)
\(888\) −8.79885 −0.295270
\(889\) −42.8994 −1.43880
\(890\) −62.3378 −2.08957
\(891\) −9.82106 −0.329018
\(892\) −56.8742 −1.90429
\(893\) −6.11975 −0.204790
\(894\) 19.9285 0.666507
\(895\) −22.5254 −0.752940
\(896\) −35.3813 −1.18201
\(897\) −36.7338 −1.22651
\(898\) 31.0653 1.03666
\(899\) −2.48539 −0.0828926
\(900\) −51.3031 −1.71010
\(901\) −6.37670 −0.212439
\(902\) 0.408959 0.0136169
\(903\) 8.60279 0.286283
\(904\) −1.61641 −0.0537611
\(905\) −27.9481 −0.929026
\(906\) 7.74041 0.257158
\(907\) 1.21719 0.0404162 0.0202081 0.999796i \(-0.493567\pi\)
0.0202081 + 0.999796i \(0.493567\pi\)
\(908\) −14.3955 −0.477730
\(909\) −14.3664 −0.476503
\(910\) 157.123 5.20856
\(911\) 58.4949 1.93802 0.969012 0.247015i \(-0.0794498\pi\)
0.969012 + 0.247015i \(0.0794498\pi\)
\(912\) −1.79175 −0.0593309
\(913\) −11.1306 −0.368368
\(914\) −28.6562 −0.947864
\(915\) 10.4111 0.344181
\(916\) 39.3653 1.30066
\(917\) −15.8501 −0.523416
\(918\) 10.0689 0.332322
\(919\) 21.3438 0.704066 0.352033 0.935987i \(-0.385490\pi\)
0.352033 + 0.935987i \(0.385490\pi\)
\(920\) −40.2612 −1.32737
\(921\) −18.3028 −0.603097
\(922\) 20.5623 0.677185
\(923\) −52.1697 −1.71719
\(924\) −16.2930 −0.536000
\(925\) −69.7366 −2.29293
\(926\) −4.16841 −0.136982
\(927\) 23.2932 0.765049
\(928\) −3.63394 −0.119290
\(929\) 2.60236 0.0853806 0.0426903 0.999088i \(-0.486407\pi\)
0.0426903 + 0.999088i \(0.486407\pi\)
\(930\) −31.2942 −1.02618
\(931\) −5.00751 −0.164115
\(932\) −74.8137 −2.45060
\(933\) 17.4531 0.571389
\(934\) 19.5590 0.639989
\(935\) −9.72227 −0.317952
\(936\) −18.9814 −0.620426
\(937\) −24.3756 −0.796317 −0.398158 0.917317i \(-0.630351\pi\)
−0.398158 + 0.917317i \(0.630351\pi\)
\(938\) −57.9893 −1.89342
\(939\) −5.56546 −0.181622
\(940\) −58.0360 −1.89293
\(941\) 26.8171 0.874212 0.437106 0.899410i \(-0.356003\pi\)
0.437106 + 0.899410i \(0.356003\pi\)
\(942\) 17.5700 0.572463
\(943\) −0.668227 −0.0217605
\(944\) 5.87379 0.191176
\(945\) 51.5192 1.67592
\(946\) 16.6377 0.540940
\(947\) 6.66067 0.216443 0.108221 0.994127i \(-0.465485\pi\)
0.108221 + 0.994127i \(0.465485\pi\)
\(948\) 16.0749 0.522090
\(949\) 18.1168 0.588096
\(950\) 17.3374 0.562499
\(951\) 0.758271 0.0245886
\(952\) −5.29171 −0.171505
\(953\) 3.23814 0.104894 0.0524468 0.998624i \(-0.483298\pi\)
0.0524468 + 0.998624i \(0.483298\pi\)
\(954\) 29.2124 0.945786
\(955\) 0.827153 0.0267660
\(956\) 53.7493 1.73838
\(957\) −0.838694 −0.0271111
\(958\) −26.5991 −0.859378
\(959\) −44.1127 −1.42447
\(960\) −32.8042 −1.05875
\(961\) −2.80077 −0.0903476
\(962\) −108.512 −3.49856
\(963\) 21.2533 0.684880
\(964\) −46.5225 −1.49839
\(965\) 58.6766 1.88887
\(966\) 46.9144 1.50944
\(967\) 23.7419 0.763487 0.381743 0.924268i \(-0.375324\pi\)
0.381743 + 0.924268i \(0.375324\pi\)
\(968\) 7.26505 0.233507
\(969\) −0.863126 −0.0277276
\(970\) 37.2043 1.19456
\(971\) −43.3690 −1.39178 −0.695890 0.718149i \(-0.744990\pi\)
−0.695890 + 0.718149i \(0.744990\pi\)
\(972\) −40.6499 −1.30385
\(973\) 71.2193 2.28319
\(974\) −59.6388 −1.91095
\(975\) 35.6694 1.14233
\(976\) −8.97658 −0.287333
\(977\) 17.6134 0.563504 0.281752 0.959487i \(-0.409084\pi\)
0.281752 + 0.959487i \(0.409084\pi\)
\(978\) −32.9297 −1.05298
\(979\) 18.9554 0.605817
\(980\) −47.4882 −1.51696
\(981\) −11.5411 −0.368479
\(982\) −3.39978 −0.108491
\(983\) −7.98009 −0.254525 −0.127263 0.991869i \(-0.540619\pi\)
−0.127263 + 0.991869i \(0.540619\pi\)
\(984\) 0.0818688 0.00260988
\(985\) −70.9308 −2.26004
\(986\) −1.14559 −0.0364831
\(987\) 16.0800 0.511831
\(988\) 15.3087 0.487035
\(989\) −27.1856 −0.864451
\(990\) 44.5388 1.41554
\(991\) 42.2817 1.34312 0.671561 0.740949i \(-0.265624\pi\)
0.671561 + 0.740949i \(0.265624\pi\)
\(992\) 41.2306 1.30907
\(993\) 1.43614 0.0455744
\(994\) 66.6282 2.11332
\(995\) 24.3643 0.772400
\(996\) −9.37103 −0.296933
\(997\) 30.4877 0.965554 0.482777 0.875743i \(-0.339628\pi\)
0.482777 + 0.875743i \(0.339628\pi\)
\(998\) 93.0650 2.94592
\(999\) −35.5801 −1.12571
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 \(a_p\))