Properties

Label 6019.2.a.c.1.8
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.59599 q^{2}\) \(+1.19783 q^{3}\) \(+4.73919 q^{4}\) \(-2.90334 q^{5}\) \(-3.10956 q^{6}\) \(-3.26881 q^{7}\) \(-7.11092 q^{8}\) \(-1.56520 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.59599 q^{2}\) \(+1.19783 q^{3}\) \(+4.73919 q^{4}\) \(-2.90334 q^{5}\) \(-3.10956 q^{6}\) \(-3.26881 q^{7}\) \(-7.11092 q^{8}\) \(-1.56520 q^{9}\) \(+7.53704 q^{10}\) \(-4.60151 q^{11}\) \(+5.67675 q^{12}\) \(-1.00000 q^{13}\) \(+8.48582 q^{14}\) \(-3.47771 q^{15}\) \(+8.98153 q^{16}\) \(-1.24562 q^{17}\) \(+4.06325 q^{18}\) \(+6.66984 q^{19}\) \(-13.7595 q^{20}\) \(-3.91549 q^{21}\) \(+11.9455 q^{22}\) \(+4.30073 q^{23}\) \(-8.51768 q^{24}\) \(+3.42936 q^{25}\) \(+2.59599 q^{26}\) \(-5.46834 q^{27}\) \(-15.4915 q^{28}\) \(+1.29367 q^{29}\) \(+9.02811 q^{30}\) \(+7.84670 q^{31}\) \(-9.09417 q^{32}\) \(-5.51183 q^{33}\) \(+3.23363 q^{34}\) \(+9.49046 q^{35}\) \(-7.41778 q^{36}\) \(+0.108301 q^{37}\) \(-17.3149 q^{38}\) \(-1.19783 q^{39}\) \(+20.6454 q^{40}\) \(-0.176638 q^{41}\) \(+10.1646 q^{42}\) \(+9.16147 q^{43}\) \(-21.8074 q^{44}\) \(+4.54430 q^{45}\) \(-11.1647 q^{46}\) \(-13.3444 q^{47}\) \(+10.7584 q^{48}\) \(+3.68514 q^{49}\) \(-8.90259 q^{50}\) \(-1.49205 q^{51}\) \(-4.73919 q^{52}\) \(+10.4074 q^{53}\) \(+14.1958 q^{54}\) \(+13.3597 q^{55}\) \(+23.2443 q^{56}\) \(+7.98935 q^{57}\) \(-3.35836 q^{58}\) \(-7.18999 q^{59}\) \(-16.4815 q^{60}\) \(-1.97518 q^{61}\) \(-20.3700 q^{62}\) \(+5.11635 q^{63}\) \(+5.64535 q^{64}\) \(+2.90334 q^{65}\) \(+14.3087 q^{66}\) \(+13.3805 q^{67}\) \(-5.90324 q^{68}\) \(+5.15155 q^{69}\) \(-24.6372 q^{70}\) \(-4.22652 q^{71}\) \(+11.1300 q^{72}\) \(-8.85875 q^{73}\) \(-0.281148 q^{74}\) \(+4.10779 q^{75}\) \(+31.6096 q^{76}\) \(+15.0415 q^{77}\) \(+3.10956 q^{78}\) \(+1.58575 q^{79}\) \(-26.0764 q^{80}\) \(-1.85455 q^{81}\) \(+0.458553 q^{82}\) \(+9.08708 q^{83}\) \(-18.5562 q^{84}\) \(+3.61646 q^{85}\) \(-23.7831 q^{86}\) \(+1.54960 q^{87}\) \(+32.7210 q^{88}\) \(-8.90530 q^{89}\) \(-11.7970 q^{90}\) \(+3.26881 q^{91}\) \(+20.3820 q^{92}\) \(+9.39903 q^{93}\) \(+34.6419 q^{94}\) \(-19.3648 q^{95}\) \(-10.8933 q^{96}\) \(+11.8648 q^{97}\) \(-9.56661 q^{98}\) \(+7.20228 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59599 −1.83565 −0.917823 0.396991i \(-0.870055\pi\)
−0.917823 + 0.396991i \(0.870055\pi\)
\(3\) 1.19783 0.691568 0.345784 0.938314i \(-0.387613\pi\)
0.345784 + 0.938314i \(0.387613\pi\)
\(4\) 4.73919 2.36959
\(5\) −2.90334 −1.29841 −0.649206 0.760613i \(-0.724898\pi\)
−0.649206 + 0.760613i \(0.724898\pi\)
\(6\) −3.10956 −1.26947
\(7\) −3.26881 −1.23550 −0.617748 0.786376i \(-0.711955\pi\)
−0.617748 + 0.786376i \(0.711955\pi\)
\(8\) −7.11092 −2.51409
\(9\) −1.56520 −0.521733
\(10\) 7.53704 2.38342
\(11\) −4.60151 −1.38741 −0.693704 0.720260i \(-0.744022\pi\)
−0.693704 + 0.720260i \(0.744022\pi\)
\(12\) 5.67675 1.63874
\(13\) −1.00000 −0.277350
\(14\) 8.48582 2.26793
\(15\) −3.47771 −0.897940
\(16\) 8.98153 2.24538
\(17\) −1.24562 −0.302108 −0.151054 0.988526i \(-0.548267\pi\)
−0.151054 + 0.988526i \(0.548267\pi\)
\(18\) 4.06325 0.957717
\(19\) 6.66984 1.53017 0.765084 0.643931i \(-0.222698\pi\)
0.765084 + 0.643931i \(0.222698\pi\)
\(20\) −13.7595 −3.07671
\(21\) −3.91549 −0.854430
\(22\) 11.9455 2.54679
\(23\) 4.30073 0.896764 0.448382 0.893842i \(-0.352000\pi\)
0.448382 + 0.893842i \(0.352000\pi\)
\(24\) −8.51768 −1.73866
\(25\) 3.42936 0.685871
\(26\) 2.59599 0.509116
\(27\) −5.46834 −1.05238
\(28\) −15.4915 −2.92762
\(29\) 1.29367 0.240228 0.120114 0.992760i \(-0.461674\pi\)
0.120114 + 0.992760i \(0.461674\pi\)
\(30\) 9.02811 1.64830
\(31\) 7.84670 1.40931 0.704655 0.709550i \(-0.251102\pi\)
0.704655 + 0.709550i \(0.251102\pi\)
\(32\) −9.09417 −1.60764
\(33\) −5.51183 −0.959487
\(34\) 3.23363 0.554563
\(35\) 9.49046 1.60418
\(36\) −7.41778 −1.23630
\(37\) 0.108301 0.0178045 0.00890225 0.999960i \(-0.497166\pi\)
0.00890225 + 0.999960i \(0.497166\pi\)
\(38\) −17.3149 −2.80884
\(39\) −1.19783 −0.191807
\(40\) 20.6454 3.26432
\(41\) −0.176638 −0.0275863 −0.0137931 0.999905i \(-0.504391\pi\)
−0.0137931 + 0.999905i \(0.504391\pi\)
\(42\) 10.1646 1.56843
\(43\) 9.16147 1.39711 0.698556 0.715556i \(-0.253826\pi\)
0.698556 + 0.715556i \(0.253826\pi\)
\(44\) −21.8074 −3.28759
\(45\) 4.54430 0.677424
\(46\) −11.1647 −1.64614
\(47\) −13.3444 −1.94647 −0.973237 0.229803i \(-0.926192\pi\)
−0.973237 + 0.229803i \(0.926192\pi\)
\(48\) 10.7584 1.55284
\(49\) 3.68514 0.526449
\(50\) −8.90259 −1.25902
\(51\) −1.49205 −0.208928
\(52\) −4.73919 −0.657207
\(53\) 10.4074 1.42957 0.714785 0.699344i \(-0.246524\pi\)
0.714785 + 0.699344i \(0.246524\pi\)
\(54\) 14.1958 1.93180
\(55\) 13.3597 1.80143
\(56\) 23.2443 3.10615
\(57\) 7.98935 1.05822
\(58\) −3.35836 −0.440974
\(59\) −7.18999 −0.936057 −0.468028 0.883713i \(-0.655036\pi\)
−0.468028 + 0.883713i \(0.655036\pi\)
\(60\) −16.4815 −2.12775
\(61\) −1.97518 −0.252896 −0.126448 0.991973i \(-0.540358\pi\)
−0.126448 + 0.991973i \(0.540358\pi\)
\(62\) −20.3700 −2.58699
\(63\) 5.11635 0.644599
\(64\) 5.64535 0.705668
\(65\) 2.90334 0.360114
\(66\) 14.3087 1.76128
\(67\) 13.3805 1.63469 0.817347 0.576146i \(-0.195444\pi\)
0.817347 + 0.576146i \(0.195444\pi\)
\(68\) −5.90324 −0.715873
\(69\) 5.15155 0.620174
\(70\) −24.6372 −2.94471
\(71\) −4.22652 −0.501596 −0.250798 0.968039i \(-0.580693\pi\)
−0.250798 + 0.968039i \(0.580693\pi\)
\(72\) 11.1300 1.31168
\(73\) −8.85875 −1.03684 −0.518419 0.855127i \(-0.673479\pi\)
−0.518419 + 0.855127i \(0.673479\pi\)
\(74\) −0.281148 −0.0326828
\(75\) 4.10779 0.474327
\(76\) 31.6096 3.62588
\(77\) 15.0415 1.71414
\(78\) 3.10956 0.352089
\(79\) 1.58575 0.178411 0.0892054 0.996013i \(-0.471567\pi\)
0.0892054 + 0.996013i \(0.471567\pi\)
\(80\) −26.0764 −2.91543
\(81\) −1.85455 −0.206061
\(82\) 0.458553 0.0506387
\(83\) 9.08708 0.997437 0.498718 0.866764i \(-0.333804\pi\)
0.498718 + 0.866764i \(0.333804\pi\)
\(84\) −18.5562 −2.02465
\(85\) 3.61646 0.392260
\(86\) −23.7831 −2.56460
\(87\) 1.54960 0.166134
\(88\) 32.7210 3.48807
\(89\) −8.90530 −0.943960 −0.471980 0.881609i \(-0.656460\pi\)
−0.471980 + 0.881609i \(0.656460\pi\)
\(90\) −11.7970 −1.24351
\(91\) 3.26881 0.342665
\(92\) 20.3820 2.12497
\(93\) 9.39903 0.974634
\(94\) 34.6419 3.57304
\(95\) −19.3648 −1.98679
\(96\) −10.8933 −1.11179
\(97\) 11.8648 1.20469 0.602345 0.798236i \(-0.294233\pi\)
0.602345 + 0.798236i \(0.294233\pi\)
\(98\) −9.56661 −0.966373
\(99\) 7.20228 0.723857
\(100\) 16.2524 1.62524
\(101\) 5.10951 0.508415 0.254207 0.967150i \(-0.418185\pi\)
0.254207 + 0.967150i \(0.418185\pi\)
\(102\) 3.87334 0.383518
\(103\) 13.4851 1.32873 0.664363 0.747410i \(-0.268703\pi\)
0.664363 + 0.747410i \(0.268703\pi\)
\(104\) 7.11092 0.697283
\(105\) 11.3680 1.10940
\(106\) −27.0176 −2.62418
\(107\) 15.9391 1.54089 0.770444 0.637508i \(-0.220035\pi\)
0.770444 + 0.637508i \(0.220035\pi\)
\(108\) −25.9155 −2.49372
\(109\) −7.42141 −0.710842 −0.355421 0.934706i \(-0.615662\pi\)
−0.355421 + 0.934706i \(0.615662\pi\)
\(110\) −34.6818 −3.30678
\(111\) 0.129726 0.0123130
\(112\) −29.3589 −2.77416
\(113\) 7.53667 0.708990 0.354495 0.935058i \(-0.384653\pi\)
0.354495 + 0.935058i \(0.384653\pi\)
\(114\) −20.7403 −1.94251
\(115\) −12.4865 −1.16437
\(116\) 6.13094 0.569244
\(117\) 1.56520 0.144703
\(118\) 18.6652 1.71827
\(119\) 4.07171 0.373253
\(120\) 24.7297 2.25750
\(121\) 10.1739 0.924900
\(122\) 5.12756 0.464227
\(123\) −0.211583 −0.0190778
\(124\) 37.1870 3.33949
\(125\) 4.56011 0.407868
\(126\) −13.2820 −1.18326
\(127\) −21.4707 −1.90521 −0.952606 0.304207i \(-0.901609\pi\)
−0.952606 + 0.304207i \(0.901609\pi\)
\(128\) 3.53304 0.312280
\(129\) 10.9739 0.966198
\(130\) −7.53704 −0.661042
\(131\) −3.09293 −0.270231 −0.135115 0.990830i \(-0.543140\pi\)
−0.135115 + 0.990830i \(0.543140\pi\)
\(132\) −26.1216 −2.27360
\(133\) −21.8025 −1.89051
\(134\) −34.7358 −3.00072
\(135\) 15.8764 1.36643
\(136\) 8.85752 0.759526
\(137\) 5.54114 0.473412 0.236706 0.971581i \(-0.423932\pi\)
0.236706 + 0.971581i \(0.423932\pi\)
\(138\) −13.3734 −1.13842
\(139\) −17.5232 −1.48630 −0.743149 0.669126i \(-0.766669\pi\)
−0.743149 + 0.669126i \(0.766669\pi\)
\(140\) 44.9771 3.80126
\(141\) −15.9843 −1.34612
\(142\) 10.9720 0.920753
\(143\) 4.60151 0.384798
\(144\) −14.0579 −1.17149
\(145\) −3.75596 −0.311915
\(146\) 22.9973 1.90327
\(147\) 4.41418 0.364075
\(148\) 0.513257 0.0421895
\(149\) 20.3849 1.67000 0.834998 0.550254i \(-0.185469\pi\)
0.834998 + 0.550254i \(0.185469\pi\)
\(150\) −10.6638 −0.870696
\(151\) 3.41286 0.277735 0.138867 0.990311i \(-0.455654\pi\)
0.138867 + 0.990311i \(0.455654\pi\)
\(152\) −47.4287 −3.84698
\(153\) 1.94965 0.157620
\(154\) −39.0476 −3.14655
\(155\) −22.7816 −1.82986
\(156\) −5.67675 −0.454504
\(157\) 4.87947 0.389424 0.194712 0.980860i \(-0.437623\pi\)
0.194712 + 0.980860i \(0.437623\pi\)
\(158\) −4.11660 −0.327499
\(159\) 12.4663 0.988646
\(160\) 26.4034 2.08737
\(161\) −14.0583 −1.10795
\(162\) 4.81441 0.378255
\(163\) −19.6785 −1.54134 −0.770670 0.637234i \(-0.780078\pi\)
−0.770670 + 0.637234i \(0.780078\pi\)
\(164\) −0.837123 −0.0653683
\(165\) 16.0027 1.24581
\(166\) −23.5900 −1.83094
\(167\) −8.13433 −0.629453 −0.314727 0.949182i \(-0.601913\pi\)
−0.314727 + 0.949182i \(0.601913\pi\)
\(168\) 27.8427 2.14811
\(169\) 1.00000 0.0769231
\(170\) −9.38831 −0.720051
\(171\) −10.4396 −0.798339
\(172\) 43.4179 3.31059
\(173\) 18.8623 1.43408 0.717039 0.697033i \(-0.245497\pi\)
0.717039 + 0.697033i \(0.245497\pi\)
\(174\) −4.02275 −0.304964
\(175\) −11.2099 −0.847391
\(176\) −41.3286 −3.11526
\(177\) −8.61240 −0.647347
\(178\) 23.1181 1.73278
\(179\) −7.53282 −0.563030 −0.281515 0.959557i \(-0.590837\pi\)
−0.281515 + 0.959557i \(0.590837\pi\)
\(180\) 21.5363 1.60522
\(181\) −20.3889 −1.51550 −0.757749 0.652546i \(-0.773701\pi\)
−0.757749 + 0.652546i \(0.773701\pi\)
\(182\) −8.48582 −0.629011
\(183\) −2.36593 −0.174895
\(184\) −30.5821 −2.25454
\(185\) −0.314433 −0.0231176
\(186\) −24.3998 −1.78908
\(187\) 5.73175 0.419147
\(188\) −63.2414 −4.61235
\(189\) 17.8750 1.30021
\(190\) 50.2709 3.64703
\(191\) −20.9114 −1.51309 −0.756547 0.653939i \(-0.773115\pi\)
−0.756547 + 0.653939i \(0.773115\pi\)
\(192\) 6.76217 0.488018
\(193\) −12.8488 −0.924876 −0.462438 0.886652i \(-0.653025\pi\)
−0.462438 + 0.886652i \(0.653025\pi\)
\(194\) −30.8010 −2.21138
\(195\) 3.47771 0.249044
\(196\) 17.4646 1.24747
\(197\) −0.469627 −0.0334595 −0.0167298 0.999860i \(-0.505325\pi\)
−0.0167298 + 0.999860i \(0.505325\pi\)
\(198\) −18.6971 −1.32874
\(199\) 5.12260 0.363131 0.181566 0.983379i \(-0.441883\pi\)
0.181566 + 0.983379i \(0.441883\pi\)
\(200\) −24.3859 −1.72434
\(201\) 16.0276 1.13050
\(202\) −13.2643 −0.933270
\(203\) −4.22876 −0.296801
\(204\) −7.07109 −0.495075
\(205\) 0.512841 0.0358184
\(206\) −35.0072 −2.43907
\(207\) −6.73150 −0.467872
\(208\) −8.98153 −0.622757
\(209\) −30.6914 −2.12297
\(210\) −29.5112 −2.03647
\(211\) 6.48606 0.446519 0.223259 0.974759i \(-0.428330\pi\)
0.223259 + 0.974759i \(0.428330\pi\)
\(212\) 49.3228 3.38750
\(213\) −5.06266 −0.346888
\(214\) −41.3777 −2.82852
\(215\) −26.5988 −1.81402
\(216\) 38.8849 2.64578
\(217\) −25.6494 −1.74120
\(218\) 19.2659 1.30485
\(219\) −10.6113 −0.717045
\(220\) 63.3143 4.26865
\(221\) 1.24562 0.0837897
\(222\) −0.336768 −0.0226024
\(223\) −3.13541 −0.209963 −0.104981 0.994474i \(-0.533478\pi\)
−0.104981 + 0.994474i \(0.533478\pi\)
\(224\) 29.7271 1.98623
\(225\) −5.36763 −0.357842
\(226\) −19.5651 −1.30145
\(227\) 10.7982 0.716703 0.358352 0.933587i \(-0.383339\pi\)
0.358352 + 0.933587i \(0.383339\pi\)
\(228\) 37.8630 2.50754
\(229\) 21.4214 1.41557 0.707784 0.706429i \(-0.249695\pi\)
0.707784 + 0.706429i \(0.249695\pi\)
\(230\) 32.4148 2.13737
\(231\) 18.0172 1.18544
\(232\) −9.19918 −0.603956
\(233\) −11.5668 −0.757766 −0.378883 0.925445i \(-0.623692\pi\)
−0.378883 + 0.925445i \(0.623692\pi\)
\(234\) −4.06325 −0.265623
\(235\) 38.7431 2.52732
\(236\) −34.0747 −2.21807
\(237\) 1.89946 0.123383
\(238\) −10.5701 −0.685160
\(239\) −14.4770 −0.936439 −0.468220 0.883612i \(-0.655104\pi\)
−0.468220 + 0.883612i \(0.655104\pi\)
\(240\) −31.2351 −2.01622
\(241\) 0.0718574 0.00462874 0.00231437 0.999997i \(-0.499263\pi\)
0.00231437 + 0.999997i \(0.499263\pi\)
\(242\) −26.4114 −1.69779
\(243\) 14.1836 0.909877
\(244\) −9.36076 −0.599261
\(245\) −10.6992 −0.683547
\(246\) 0.549269 0.0350201
\(247\) −6.66984 −0.424392
\(248\) −55.7973 −3.54313
\(249\) 10.8848 0.689796
\(250\) −11.8380 −0.748702
\(251\) −17.6859 −1.11632 −0.558161 0.829733i \(-0.688493\pi\)
−0.558161 + 0.829733i \(0.688493\pi\)
\(252\) 24.2473 1.52744
\(253\) −19.7898 −1.24418
\(254\) 55.7377 3.49729
\(255\) 4.33191 0.271275
\(256\) −20.4624 −1.27890
\(257\) 25.7299 1.60499 0.802493 0.596662i \(-0.203507\pi\)
0.802493 + 0.596662i \(0.203507\pi\)
\(258\) −28.4882 −1.77360
\(259\) −0.354014 −0.0219974
\(260\) 13.7595 0.853325
\(261\) −2.02485 −0.125335
\(262\) 8.02923 0.496048
\(263\) −17.1987 −1.06051 −0.530257 0.847837i \(-0.677905\pi\)
−0.530257 + 0.847837i \(0.677905\pi\)
\(264\) 39.1942 2.41224
\(265\) −30.2163 −1.85617
\(266\) 56.5991 3.47031
\(267\) −10.6670 −0.652813
\(268\) 63.4129 3.87356
\(269\) −12.2811 −0.748791 −0.374396 0.927269i \(-0.622150\pi\)
−0.374396 + 0.927269i \(0.622150\pi\)
\(270\) −41.2151 −2.50827
\(271\) 1.62404 0.0986537 0.0493269 0.998783i \(-0.484292\pi\)
0.0493269 + 0.998783i \(0.484292\pi\)
\(272\) −11.1876 −0.678348
\(273\) 3.91549 0.236976
\(274\) −14.3848 −0.869016
\(275\) −15.7802 −0.951583
\(276\) 24.4142 1.46956
\(277\) 3.36031 0.201902 0.100951 0.994891i \(-0.467812\pi\)
0.100951 + 0.994891i \(0.467812\pi\)
\(278\) 45.4901 2.72832
\(279\) −12.2817 −0.735284
\(280\) −67.4859 −4.03305
\(281\) −2.10298 −0.125453 −0.0627267 0.998031i \(-0.519980\pi\)
−0.0627267 + 0.998031i \(0.519980\pi\)
\(282\) 41.4951 2.47100
\(283\) −0.873881 −0.0519468 −0.0259734 0.999663i \(-0.508269\pi\)
−0.0259734 + 0.999663i \(0.508269\pi\)
\(284\) −20.0303 −1.18858
\(285\) −23.1958 −1.37400
\(286\) −11.9455 −0.706352
\(287\) 0.577398 0.0340827
\(288\) 14.2342 0.838757
\(289\) −15.4484 −0.908731
\(290\) 9.75044 0.572566
\(291\) 14.2121 0.833126
\(292\) −41.9833 −2.45689
\(293\) −12.4057 −0.724749 −0.362374 0.932033i \(-0.618034\pi\)
−0.362374 + 0.932033i \(0.618034\pi\)
\(294\) −11.4592 −0.668313
\(295\) 20.8749 1.21539
\(296\) −0.770117 −0.0447621
\(297\) 25.1626 1.46008
\(298\) −52.9191 −3.06552
\(299\) −4.30073 −0.248718
\(300\) 19.4676 1.12396
\(301\) −29.9471 −1.72612
\(302\) −8.85977 −0.509823
\(303\) 6.12033 0.351604
\(304\) 59.9054 3.43581
\(305\) 5.73461 0.328363
\(306\) −5.06128 −0.289334
\(307\) −1.12674 −0.0643064 −0.0321532 0.999483i \(-0.510236\pi\)
−0.0321532 + 0.999483i \(0.510236\pi\)
\(308\) 71.2844 4.06181
\(309\) 16.1529 0.918905
\(310\) 59.1409 3.35898
\(311\) −12.5210 −0.710002 −0.355001 0.934866i \(-0.615520\pi\)
−0.355001 + 0.934866i \(0.615520\pi\)
\(312\) 8.51768 0.482219
\(313\) 16.2691 0.919585 0.459793 0.888026i \(-0.347924\pi\)
0.459793 + 0.888026i \(0.347924\pi\)
\(314\) −12.6671 −0.714844
\(315\) −14.8545 −0.836954
\(316\) 7.51516 0.422761
\(317\) 0.00967991 0.000543678 0 0.000271839 1.00000i \(-0.499913\pi\)
0.000271839 1.00000i \(0.499913\pi\)
\(318\) −32.3626 −1.81480
\(319\) −5.95283 −0.333295
\(320\) −16.3903 −0.916248
\(321\) 19.0923 1.06563
\(322\) 36.4952 2.03380
\(323\) −8.30811 −0.462276
\(324\) −8.78907 −0.488282
\(325\) −3.42936 −0.190226
\(326\) 51.0853 2.82935
\(327\) −8.88960 −0.491596
\(328\) 1.25606 0.0693544
\(329\) 43.6202 2.40486
\(330\) −41.5429 −2.28686
\(331\) 7.65841 0.420944 0.210472 0.977600i \(-0.432500\pi\)
0.210472 + 0.977600i \(0.432500\pi\)
\(332\) 43.0654 2.36352
\(333\) −0.169512 −0.00928920
\(334\) 21.1167 1.15545
\(335\) −38.8482 −2.12250
\(336\) −35.1671 −1.91852
\(337\) −23.0458 −1.25538 −0.627692 0.778462i \(-0.716000\pi\)
−0.627692 + 0.778462i \(0.716000\pi\)
\(338\) −2.59599 −0.141203
\(339\) 9.02766 0.490315
\(340\) 17.1391 0.929498
\(341\) −36.1067 −1.95529
\(342\) 27.1012 1.46547
\(343\) 10.8357 0.585070
\(344\) −65.1465 −3.51246
\(345\) −14.9567 −0.805240
\(346\) −48.9666 −2.63246
\(347\) −25.1132 −1.34815 −0.674073 0.738665i \(-0.735457\pi\)
−0.674073 + 0.738665i \(0.735457\pi\)
\(348\) 7.34384 0.393671
\(349\) −1.29585 −0.0693652 −0.0346826 0.999398i \(-0.511042\pi\)
−0.0346826 + 0.999398i \(0.511042\pi\)
\(350\) 29.1009 1.55551
\(351\) 5.46834 0.291878
\(352\) 41.8469 2.23045
\(353\) −33.9466 −1.80679 −0.903397 0.428806i \(-0.858934\pi\)
−0.903397 + 0.428806i \(0.858934\pi\)
\(354\) 22.3577 1.18830
\(355\) 12.2710 0.651278
\(356\) −42.2039 −2.23680
\(357\) 4.87722 0.258130
\(358\) 19.5552 1.03352
\(359\) 2.79617 0.147576 0.0737882 0.997274i \(-0.476491\pi\)
0.0737882 + 0.997274i \(0.476491\pi\)
\(360\) −32.3141 −1.70310
\(361\) 25.4868 1.34141
\(362\) 52.9296 2.78192
\(363\) 12.1866 0.639632
\(364\) 15.4915 0.811976
\(365\) 25.7199 1.34624
\(366\) 6.14195 0.321045
\(367\) 34.9582 1.82480 0.912401 0.409297i \(-0.134226\pi\)
0.912401 + 0.409297i \(0.134226\pi\)
\(368\) 38.6271 2.01358
\(369\) 0.276475 0.0143927
\(370\) 0.816266 0.0424357
\(371\) −34.0200 −1.76623
\(372\) 44.5438 2.30949
\(373\) −9.69247 −0.501857 −0.250929 0.968006i \(-0.580736\pi\)
−0.250929 + 0.968006i \(0.580736\pi\)
\(374\) −14.8796 −0.769405
\(375\) 5.46224 0.282069
\(376\) 94.8906 4.89361
\(377\) −1.29367 −0.0666274
\(378\) −46.4034 −2.38673
\(379\) 38.7486 1.99038 0.995191 0.0979547i \(-0.0312300\pi\)
0.995191 + 0.0979547i \(0.0312300\pi\)
\(380\) −91.7734 −4.70788
\(381\) −25.7182 −1.31758
\(382\) 54.2858 2.77750
\(383\) −5.50089 −0.281083 −0.140541 0.990075i \(-0.544884\pi\)
−0.140541 + 0.990075i \(0.544884\pi\)
\(384\) 4.23199 0.215963
\(385\) −43.6705 −2.22565
\(386\) 33.3554 1.69774
\(387\) −14.3395 −0.728919
\(388\) 56.2296 2.85463
\(389\) −31.3870 −1.59138 −0.795691 0.605703i \(-0.792892\pi\)
−0.795691 + 0.605703i \(0.792892\pi\)
\(390\) −9.02811 −0.457156
\(391\) −5.35709 −0.270919
\(392\) −26.2047 −1.32354
\(393\) −3.70481 −0.186883
\(394\) 1.21915 0.0614198
\(395\) −4.60396 −0.231650
\(396\) 34.1330 1.71525
\(397\) 32.1944 1.61579 0.807896 0.589325i \(-0.200606\pi\)
0.807896 + 0.589325i \(0.200606\pi\)
\(398\) −13.2982 −0.666581
\(399\) −26.1157 −1.30742
\(400\) 30.8009 1.54004
\(401\) −24.3503 −1.21600 −0.607998 0.793938i \(-0.708027\pi\)
−0.607998 + 0.793938i \(0.708027\pi\)
\(402\) −41.6077 −2.07520
\(403\) −7.84670 −0.390872
\(404\) 24.2149 1.20474
\(405\) 5.38438 0.267552
\(406\) 10.9778 0.544822
\(407\) −0.498346 −0.0247021
\(408\) 10.6098 0.525264
\(409\) 39.3367 1.94507 0.972537 0.232748i \(-0.0747719\pi\)
0.972537 + 0.232748i \(0.0747719\pi\)
\(410\) −1.33133 −0.0657498
\(411\) 6.63735 0.327396
\(412\) 63.9084 3.14854
\(413\) 23.5027 1.15649
\(414\) 17.4749 0.858846
\(415\) −26.3828 −1.29508
\(416\) 9.09417 0.445878
\(417\) −20.9898 −1.02788
\(418\) 79.6746 3.89701
\(419\) 21.7238 1.06128 0.530638 0.847599i \(-0.321952\pi\)
0.530638 + 0.847599i \(0.321952\pi\)
\(420\) 53.8750 2.62883
\(421\) −12.0042 −0.585050 −0.292525 0.956258i \(-0.594496\pi\)
−0.292525 + 0.956258i \(0.594496\pi\)
\(422\) −16.8378 −0.819650
\(423\) 20.8866 1.01554
\(424\) −74.0064 −3.59407
\(425\) −4.27168 −0.207207
\(426\) 13.1426 0.636763
\(427\) 6.45650 0.312452
\(428\) 75.5383 3.65128
\(429\) 5.51183 0.266114
\(430\) 69.0504 3.32991
\(431\) −10.5962 −0.510403 −0.255202 0.966888i \(-0.582142\pi\)
−0.255202 + 0.966888i \(0.582142\pi\)
\(432\) −49.1141 −2.36300
\(433\) 1.09459 0.0526025 0.0263012 0.999654i \(-0.491627\pi\)
0.0263012 + 0.999654i \(0.491627\pi\)
\(434\) 66.5857 3.19622
\(435\) −4.49900 −0.215711
\(436\) −35.1714 −1.68441
\(437\) 28.6852 1.37220
\(438\) 27.5469 1.31624
\(439\) 0.612459 0.0292311 0.0146155 0.999893i \(-0.495348\pi\)
0.0146155 + 0.999893i \(0.495348\pi\)
\(440\) −94.9999 −4.52894
\(441\) −5.76798 −0.274666
\(442\) −3.23363 −0.153808
\(443\) 21.4424 1.01876 0.509378 0.860543i \(-0.329875\pi\)
0.509378 + 0.860543i \(0.329875\pi\)
\(444\) 0.614795 0.0291769
\(445\) 25.8551 1.22565
\(446\) 8.13951 0.385417
\(447\) 24.4177 1.15492
\(448\) −18.4536 −0.871850
\(449\) 31.9339 1.50705 0.753527 0.657417i \(-0.228351\pi\)
0.753527 + 0.657417i \(0.228351\pi\)
\(450\) 13.9343 0.656871
\(451\) 0.812804 0.0382734
\(452\) 35.7177 1.68002
\(453\) 4.08803 0.192073
\(454\) −28.0321 −1.31561
\(455\) −9.49046 −0.444920
\(456\) −56.8116 −2.66045
\(457\) 21.7988 1.01971 0.509853 0.860261i \(-0.329700\pi\)
0.509853 + 0.860261i \(0.329700\pi\)
\(458\) −55.6099 −2.59848
\(459\) 6.81149 0.317933
\(460\) −59.1757 −2.75908
\(461\) −1.11998 −0.0521626 −0.0260813 0.999660i \(-0.508303\pi\)
−0.0260813 + 0.999660i \(0.508303\pi\)
\(462\) −46.7725 −2.17605
\(463\) −1.00000 −0.0464739
\(464\) 11.6191 0.539405
\(465\) −27.2885 −1.26548
\(466\) 30.0273 1.39099
\(467\) 2.01749 0.0933583 0.0466791 0.998910i \(-0.485136\pi\)
0.0466791 + 0.998910i \(0.485136\pi\)
\(468\) 7.41778 0.342887
\(469\) −43.7385 −2.01966
\(470\) −100.577 −4.63927
\(471\) 5.84478 0.269313
\(472\) 51.1274 2.35333
\(473\) −42.1566 −1.93836
\(474\) −4.93099 −0.226488
\(475\) 22.8733 1.04950
\(476\) 19.2966 0.884458
\(477\) −16.2897 −0.745854
\(478\) 37.5822 1.71897
\(479\) −4.31473 −0.197145 −0.0985726 0.995130i \(-0.531428\pi\)
−0.0985726 + 0.995130i \(0.531428\pi\)
\(480\) 31.6268 1.44356
\(481\) −0.108301 −0.00493808
\(482\) −0.186541 −0.00849673
\(483\) −16.8395 −0.766222
\(484\) 48.2160 2.19164
\(485\) −34.4476 −1.56418
\(486\) −36.8205 −1.67021
\(487\) −19.1205 −0.866434 −0.433217 0.901290i \(-0.642622\pi\)
−0.433217 + 0.901290i \(0.642622\pi\)
\(488\) 14.0454 0.635803
\(489\) −23.5715 −1.06594
\(490\) 27.7751 1.25475
\(491\) 22.3271 1.00761 0.503805 0.863818i \(-0.331933\pi\)
0.503805 + 0.863818i \(0.331933\pi\)
\(492\) −1.00273 −0.0452067
\(493\) −1.61142 −0.0725749
\(494\) 17.3149 0.779033
\(495\) −20.9106 −0.939863
\(496\) 70.4754 3.16444
\(497\) 13.8157 0.619720
\(498\) −28.2569 −1.26622
\(499\) −12.7580 −0.571128 −0.285564 0.958360i \(-0.592181\pi\)
−0.285564 + 0.958360i \(0.592181\pi\)
\(500\) 21.6112 0.966482
\(501\) −9.74356 −0.435310
\(502\) 45.9124 2.04917
\(503\) −5.67650 −0.253102 −0.126551 0.991960i \(-0.540391\pi\)
−0.126551 + 0.991960i \(0.540391\pi\)
\(504\) −36.3819 −1.62058
\(505\) −14.8346 −0.660132
\(506\) 51.3743 2.28387
\(507\) 1.19783 0.0531976
\(508\) −101.753 −4.51458
\(509\) −16.7761 −0.743589 −0.371795 0.928315i \(-0.621257\pi\)
−0.371795 + 0.928315i \(0.621257\pi\)
\(510\) −11.2456 −0.497964
\(511\) 28.9576 1.28101
\(512\) 46.0543 2.03533
\(513\) −36.4730 −1.61032
\(514\) −66.7946 −2.94618
\(515\) −39.1518 −1.72523
\(516\) 52.0074 2.28950
\(517\) 61.4042 2.70055
\(518\) 0.919020 0.0403794
\(519\) 22.5939 0.991763
\(520\) −20.6454 −0.905360
\(521\) −19.8684 −0.870448 −0.435224 0.900322i \(-0.643331\pi\)
−0.435224 + 0.900322i \(0.643331\pi\)
\(522\) 5.25650 0.230071
\(523\) −24.6750 −1.07896 −0.539482 0.841997i \(-0.681380\pi\)
−0.539482 + 0.841997i \(0.681380\pi\)
\(524\) −14.6580 −0.640337
\(525\) −13.4276 −0.586029
\(526\) 44.6476 1.94673
\(527\) −9.77403 −0.425764
\(528\) −49.5047 −2.15442
\(529\) −4.50373 −0.195814
\(530\) 78.4413 3.40727
\(531\) 11.2538 0.488372
\(532\) −103.326 −4.47975
\(533\) 0.176638 0.00765106
\(534\) 27.6916 1.19833
\(535\) −46.2765 −2.00071
\(536\) −95.1480 −4.10977
\(537\) −9.02306 −0.389374
\(538\) 31.8816 1.37451
\(539\) −16.9572 −0.730399
\(540\) 75.2414 3.23787
\(541\) 37.1034 1.59520 0.797601 0.603186i \(-0.206102\pi\)
0.797601 + 0.603186i \(0.206102\pi\)
\(542\) −4.21601 −0.181093
\(543\) −24.4225 −1.04807
\(544\) 11.3279 0.485680
\(545\) 21.5468 0.922965
\(546\) −10.1646 −0.435004
\(547\) 31.4731 1.34569 0.672847 0.739782i \(-0.265071\pi\)
0.672847 + 0.739782i \(0.265071\pi\)
\(548\) 26.2605 1.12179
\(549\) 3.09155 0.131944
\(550\) 40.9654 1.74677
\(551\) 8.62857 0.367590
\(552\) −36.6322 −1.55917
\(553\) −5.18352 −0.220426
\(554\) −8.72335 −0.370620
\(555\) −0.376638 −0.0159874
\(556\) −83.0457 −3.52192
\(557\) 13.2351 0.560787 0.280394 0.959885i \(-0.409535\pi\)
0.280394 + 0.959885i \(0.409535\pi\)
\(558\) 31.8831 1.34972
\(559\) −9.16147 −0.387489
\(560\) 85.2389 3.60200
\(561\) 6.86567 0.289869
\(562\) 5.45933 0.230288
\(563\) 6.59233 0.277834 0.138917 0.990304i \(-0.455638\pi\)
0.138917 + 0.990304i \(0.455638\pi\)
\(564\) −75.7526 −3.18976
\(565\) −21.8815 −0.920561
\(566\) 2.26859 0.0953560
\(567\) 6.06218 0.254588
\(568\) 30.0545 1.26106
\(569\) 34.8028 1.45901 0.729504 0.683977i \(-0.239751\pi\)
0.729504 + 0.683977i \(0.239751\pi\)
\(570\) 60.2161 2.52217
\(571\) 3.16335 0.132382 0.0661910 0.997807i \(-0.478915\pi\)
0.0661910 + 0.997807i \(0.478915\pi\)
\(572\) 21.8074 0.911814
\(573\) −25.0483 −1.04641
\(574\) −1.49892 −0.0625638
\(575\) 14.7487 0.615065
\(576\) −8.83609 −0.368171
\(577\) −26.6635 −1.11002 −0.555009 0.831844i \(-0.687285\pi\)
−0.555009 + 0.831844i \(0.687285\pi\)
\(578\) 40.1040 1.66811
\(579\) −15.3907 −0.639615
\(580\) −17.8002 −0.739112
\(581\) −29.7040 −1.23233
\(582\) −36.8944 −1.52932
\(583\) −47.8899 −1.98340
\(584\) 62.9939 2.60670
\(585\) −4.54430 −0.187884
\(586\) 32.2051 1.33038
\(587\) 0.0274605 0.00113342 0.000566708 1.00000i \(-0.499820\pi\)
0.000566708 1.00000i \(0.499820\pi\)
\(588\) 20.9196 0.862711
\(589\) 52.3363 2.15648
\(590\) −54.1913 −2.23102
\(591\) −0.562534 −0.0231395
\(592\) 0.972705 0.0399779
\(593\) −33.2014 −1.36342 −0.681710 0.731623i \(-0.738763\pi\)
−0.681710 + 0.731623i \(0.738763\pi\)
\(594\) −65.3220 −2.68020
\(595\) −11.8215 −0.484636
\(596\) 96.6078 3.95721
\(597\) 6.13601 0.251130
\(598\) 11.1647 0.456557
\(599\) −31.5585 −1.28944 −0.644722 0.764417i \(-0.723027\pi\)
−0.644722 + 0.764417i \(0.723027\pi\)
\(600\) −29.2102 −1.19250
\(601\) 36.7472 1.49895 0.749475 0.662033i \(-0.230306\pi\)
0.749475 + 0.662033i \(0.230306\pi\)
\(602\) 77.7426 3.16855
\(603\) −20.9432 −0.852874
\(604\) 16.1742 0.658119
\(605\) −29.5382 −1.20090
\(606\) −15.8883 −0.645420
\(607\) −25.9084 −1.05159 −0.525794 0.850612i \(-0.676232\pi\)
−0.525794 + 0.850612i \(0.676232\pi\)
\(608\) −60.6567 −2.45995
\(609\) −5.06535 −0.205258
\(610\) −14.8870 −0.602758
\(611\) 13.3444 0.539855
\(612\) 9.23975 0.373495
\(613\) −21.9901 −0.888172 −0.444086 0.895984i \(-0.646472\pi\)
−0.444086 + 0.895984i \(0.646472\pi\)
\(614\) 2.92501 0.118044
\(615\) 0.614297 0.0247708
\(616\) −106.959 −4.30949
\(617\) 11.6709 0.469853 0.234927 0.972013i \(-0.424515\pi\)
0.234927 + 0.972013i \(0.424515\pi\)
\(618\) −41.9328 −1.68678
\(619\) 1.95607 0.0786211 0.0393106 0.999227i \(-0.487484\pi\)
0.0393106 + 0.999227i \(0.487484\pi\)
\(620\) −107.966 −4.33603
\(621\) −23.5178 −0.943739
\(622\) 32.5045 1.30331
\(623\) 29.1098 1.16626
\(624\) −10.7584 −0.430679
\(625\) −30.3863 −1.21545
\(626\) −42.2346 −1.68803
\(627\) −36.7631 −1.46818
\(628\) 23.1247 0.922777
\(629\) −0.134902 −0.00537888
\(630\) 38.5621 1.53635
\(631\) −37.9288 −1.50992 −0.754961 0.655769i \(-0.772344\pi\)
−0.754961 + 0.655769i \(0.772344\pi\)
\(632\) −11.2761 −0.448541
\(633\) 7.76921 0.308798
\(634\) −0.0251290 −0.000997999 0
\(635\) 62.3365 2.47375
\(636\) 59.0804 2.34269
\(637\) −3.68514 −0.146011
\(638\) 15.4535 0.611811
\(639\) 6.61535 0.261699
\(640\) −10.2576 −0.405467
\(641\) −10.6835 −0.421971 −0.210986 0.977489i \(-0.567667\pi\)
−0.210986 + 0.977489i \(0.567667\pi\)
\(642\) −49.5636 −1.95612
\(643\) −35.1803 −1.38738 −0.693688 0.720276i \(-0.744015\pi\)
−0.693688 + 0.720276i \(0.744015\pi\)
\(644\) −66.6248 −2.62539
\(645\) −31.8609 −1.25452
\(646\) 21.5678 0.848574
\(647\) −37.6032 −1.47833 −0.739166 0.673523i \(-0.764780\pi\)
−0.739166 + 0.673523i \(0.764780\pi\)
\(648\) 13.1876 0.518056
\(649\) 33.0848 1.29869
\(650\) 8.90259 0.349188
\(651\) −30.7237 −1.20416
\(652\) −93.2602 −3.65235
\(653\) −4.58942 −0.179598 −0.0897989 0.995960i \(-0.528622\pi\)
−0.0897989 + 0.995960i \(0.528622\pi\)
\(654\) 23.0773 0.902396
\(655\) 8.97982 0.350870
\(656\) −1.58648 −0.0619418
\(657\) 13.8657 0.540953
\(658\) −113.238 −4.41447
\(659\) 3.63735 0.141691 0.0708456 0.997487i \(-0.477430\pi\)
0.0708456 + 0.997487i \(0.477430\pi\)
\(660\) 75.8398 2.95206
\(661\) −18.6143 −0.724011 −0.362006 0.932176i \(-0.617908\pi\)
−0.362006 + 0.932176i \(0.617908\pi\)
\(662\) −19.8812 −0.772704
\(663\) 1.49205 0.0579463
\(664\) −64.6175 −2.50765
\(665\) 63.2999 2.45466
\(666\) 0.440052 0.0170517
\(667\) 5.56372 0.215428
\(668\) −38.5501 −1.49155
\(669\) −3.75569 −0.145203
\(670\) 100.850 3.89617
\(671\) 9.08882 0.350870
\(672\) 35.6081 1.37361
\(673\) −28.2604 −1.08936 −0.544678 0.838645i \(-0.683348\pi\)
−0.544678 + 0.838645i \(0.683348\pi\)
\(674\) 59.8267 2.30444
\(675\) −18.7529 −0.721799
\(676\) 4.73919 0.182276
\(677\) 18.1421 0.697257 0.348628 0.937261i \(-0.386648\pi\)
0.348628 + 0.937261i \(0.386648\pi\)
\(678\) −23.4358 −0.900045
\(679\) −38.7839 −1.48839
\(680\) −25.7164 −0.986177
\(681\) 12.9345 0.495649
\(682\) 93.7328 3.58921
\(683\) −21.8870 −0.837482 −0.418741 0.908106i \(-0.637528\pi\)
−0.418741 + 0.908106i \(0.637528\pi\)
\(684\) −49.4754 −1.89174
\(685\) −16.0878 −0.614683
\(686\) −28.1293 −1.07398
\(687\) 25.6593 0.978961
\(688\) 82.2840 3.13705
\(689\) −10.4074 −0.396492
\(690\) 38.8274 1.47814
\(691\) 26.4461 1.00606 0.503029 0.864269i \(-0.332219\pi\)
0.503029 + 0.864269i \(0.332219\pi\)
\(692\) 89.3922 3.39818
\(693\) −23.5429 −0.894322
\(694\) 65.1936 2.47472
\(695\) 50.8757 1.92983
\(696\) −11.0191 −0.417677
\(697\) 0.220025 0.00833404
\(698\) 3.36402 0.127330
\(699\) −13.8551 −0.524047
\(700\) −53.1259 −2.00797
\(701\) −8.16197 −0.308273 −0.154137 0.988050i \(-0.549260\pi\)
−0.154137 + 0.988050i \(0.549260\pi\)
\(702\) −14.1958 −0.535785
\(703\) 0.722348 0.0272439
\(704\) −25.9771 −0.979050
\(705\) 46.4078 1.74782
\(706\) 88.1251 3.31663
\(707\) −16.7020 −0.628144
\(708\) −40.8158 −1.53395
\(709\) −28.4035 −1.06672 −0.533358 0.845890i \(-0.679070\pi\)
−0.533358 + 0.845890i \(0.679070\pi\)
\(710\) −31.8555 −1.19552
\(711\) −2.48201 −0.0930828
\(712\) 63.3248 2.37320
\(713\) 33.7465 1.26382
\(714\) −12.6612 −0.473835
\(715\) −13.3597 −0.499626
\(716\) −35.6995 −1.33415
\(717\) −17.3410 −0.647612
\(718\) −7.25885 −0.270898
\(719\) −0.0521446 −0.00194467 −0.000972333 1.00000i \(-0.500310\pi\)
−0.000972333 1.00000i \(0.500310\pi\)
\(720\) 40.8148 1.52108
\(721\) −44.0803 −1.64163
\(722\) −66.1636 −2.46236
\(723\) 0.0860730 0.00320109
\(724\) −96.6270 −3.59112
\(725\) 4.43645 0.164766
\(726\) −31.6364 −1.17414
\(727\) −26.5609 −0.985091 −0.492545 0.870287i \(-0.663933\pi\)
−0.492545 + 0.870287i \(0.663933\pi\)
\(728\) −23.2443 −0.861490
\(729\) 22.5532 0.835303
\(730\) −66.7688 −2.47122
\(731\) −11.4117 −0.422078
\(732\) −11.2126 −0.414430
\(733\) −18.3348 −0.677213 −0.338606 0.940928i \(-0.609955\pi\)
−0.338606 + 0.940928i \(0.609955\pi\)
\(734\) −90.7512 −3.34969
\(735\) −12.8158 −0.472719
\(736\) −39.1115 −1.44167
\(737\) −61.5707 −2.26799
\(738\) −0.717726 −0.0264199
\(739\) 38.9057 1.43117 0.715584 0.698527i \(-0.246161\pi\)
0.715584 + 0.698527i \(0.246161\pi\)
\(740\) −1.49016 −0.0547793
\(741\) −7.98935 −0.293496
\(742\) 88.3156 3.24217
\(743\) 18.4919 0.678403 0.339202 0.940714i \(-0.389843\pi\)
0.339202 + 0.940714i \(0.389843\pi\)
\(744\) −66.8357 −2.45032
\(745\) −59.1842 −2.16834
\(746\) 25.1616 0.921232
\(747\) −14.2231 −0.520396
\(748\) 27.1638 0.993208
\(749\) −52.1018 −1.90376
\(750\) −14.1799 −0.517778
\(751\) −12.4821 −0.455478 −0.227739 0.973722i \(-0.573133\pi\)
−0.227739 + 0.973722i \(0.573133\pi\)
\(752\) −119.853 −4.37058
\(753\) −21.1847 −0.772013
\(754\) 3.35836 0.122304
\(755\) −9.90868 −0.360614
\(756\) 84.7129 3.08098
\(757\) 24.4333 0.888042 0.444021 0.896016i \(-0.353552\pi\)
0.444021 + 0.896016i \(0.353552\pi\)
\(758\) −100.591 −3.65364
\(759\) −23.7049 −0.860434
\(760\) 137.701 4.99496
\(761\) −7.10635 −0.257605 −0.128803 0.991670i \(-0.541113\pi\)
−0.128803 + 0.991670i \(0.541113\pi\)
\(762\) 66.7644 2.41862
\(763\) 24.2592 0.878242
\(764\) −99.1029 −3.58542
\(765\) −5.66048 −0.204655
\(766\) 14.2803 0.515968
\(767\) 7.18999 0.259615
\(768\) −24.5106 −0.884449
\(769\) −10.1591 −0.366345 −0.183172 0.983081i \(-0.558637\pi\)
−0.183172 + 0.983081i \(0.558637\pi\)
\(770\) 113.368 4.08551
\(771\) 30.8201 1.10996
\(772\) −60.8928 −2.19158
\(773\) 34.6072 1.24474 0.622368 0.782725i \(-0.286171\pi\)
0.622368 + 0.782725i \(0.286171\pi\)
\(774\) 37.2253 1.33804
\(775\) 26.9091 0.966605
\(776\) −84.3698 −3.02870
\(777\) −0.424050 −0.0152127
\(778\) 81.4804 2.92121
\(779\) −1.17815 −0.0422116
\(780\) 16.4815 0.590133
\(781\) 19.4484 0.695918
\(782\) 13.9070 0.497312
\(783\) −7.07422 −0.252812
\(784\) 33.0982 1.18208
\(785\) −14.1667 −0.505632
\(786\) 9.61767 0.343051
\(787\) 16.8127 0.599308 0.299654 0.954048i \(-0.403129\pi\)
0.299654 + 0.954048i \(0.403129\pi\)
\(788\) −2.22565 −0.0792855
\(789\) −20.6011 −0.733419
\(790\) 11.9519 0.425228
\(791\) −24.6360 −0.875954
\(792\) −51.2148 −1.81984
\(793\) 1.97518 0.0701407
\(794\) −83.5766 −2.96602
\(795\) −36.1940 −1.28367
\(796\) 24.2770 0.860474
\(797\) −35.4398 −1.25534 −0.627671 0.778479i \(-0.715992\pi\)
−0.627671 + 0.778479i \(0.715992\pi\)
\(798\) 67.7962 2.39996
\(799\) 16.6220 0.588045
\(800\) −31.1871 −1.10263
\(801\) 13.9386 0.492495
\(802\) 63.2133 2.23214
\(803\) 40.7636 1.43852
\(804\) 75.9580 2.67883
\(805\) 40.8159 1.43857
\(806\) 20.3700 0.717503
\(807\) −14.7107 −0.517840
\(808\) −36.3333 −1.27820
\(809\) 10.2835 0.361548 0.180774 0.983525i \(-0.442140\pi\)
0.180774 + 0.983525i \(0.442140\pi\)
\(810\) −13.9778 −0.491131
\(811\) −24.0961 −0.846130 −0.423065 0.906099i \(-0.639046\pi\)
−0.423065 + 0.906099i \(0.639046\pi\)
\(812\) −20.0409 −0.703298
\(813\) 1.94533 0.0682258
\(814\) 1.29370 0.0453443
\(815\) 57.1333 2.00129
\(816\) −13.4009 −0.469124
\(817\) 61.1056 2.13781
\(818\) −102.118 −3.57047
\(819\) −5.11635 −0.178780
\(820\) 2.43045 0.0848750
\(821\) −34.8312 −1.21562 −0.607809 0.794083i \(-0.707951\pi\)
−0.607809 + 0.794083i \(0.707951\pi\)
\(822\) −17.2305 −0.600984
\(823\) 5.04681 0.175921 0.0879603 0.996124i \(-0.471965\pi\)
0.0879603 + 0.996124i \(0.471965\pi\)
\(824\) −95.8914 −3.34054
\(825\) −18.9020 −0.658085
\(826\) −61.0130 −2.12291
\(827\) 49.3935 1.71758 0.858790 0.512328i \(-0.171217\pi\)
0.858790 + 0.512328i \(0.171217\pi\)
\(828\) −31.9018 −1.10867
\(829\) −51.4141 −1.78569 −0.892843 0.450368i \(-0.851293\pi\)
−0.892843 + 0.450368i \(0.851293\pi\)
\(830\) 68.4897 2.37731
\(831\) 4.02509 0.139629
\(832\) −5.64535 −0.195717
\(833\) −4.59030 −0.159044
\(834\) 54.4895 1.88682
\(835\) 23.6167 0.817289
\(836\) −145.452 −5.03057
\(837\) −42.9084 −1.48313
\(838\) −56.3948 −1.94813
\(839\) −32.8652 −1.13463 −0.567316 0.823500i \(-0.692018\pi\)
−0.567316 + 0.823500i \(0.692018\pi\)
\(840\) −80.8367 −2.78913
\(841\) −27.3264 −0.942290
\(842\) 31.1629 1.07395
\(843\) −2.51902 −0.0867596
\(844\) 30.7387 1.05807
\(845\) −2.90334 −0.0998778
\(846\) −54.2215 −1.86417
\(847\) −33.2566 −1.14271
\(848\) 93.4747 3.20993
\(849\) −1.04676 −0.0359248
\(850\) 11.0893 0.380359
\(851\) 0.465771 0.0159664
\(852\) −23.9929 −0.821984
\(853\) 28.6955 0.982517 0.491258 0.871014i \(-0.336537\pi\)
0.491258 + 0.871014i \(0.336537\pi\)
\(854\) −16.7610 −0.573551
\(855\) 30.3098 1.03657
\(856\) −113.341 −3.87393
\(857\) 30.4299 1.03947 0.519733 0.854329i \(-0.326031\pi\)
0.519733 + 0.854329i \(0.326031\pi\)
\(858\) −14.3087 −0.488491
\(859\) −8.60599 −0.293632 −0.146816 0.989164i \(-0.546903\pi\)
−0.146816 + 0.989164i \(0.546903\pi\)
\(860\) −126.057 −4.29850
\(861\) 0.691626 0.0235705
\(862\) 27.5078 0.936919
\(863\) 30.3056 1.03161 0.515807 0.856705i \(-0.327492\pi\)
0.515807 + 0.856705i \(0.327492\pi\)
\(864\) 49.7300 1.69185
\(865\) −54.7637 −1.86202
\(866\) −2.84154 −0.0965595
\(867\) −18.5046 −0.628449
\(868\) −121.557 −4.12593
\(869\) −7.29684 −0.247528
\(870\) 11.6794 0.395968
\(871\) −13.3805 −0.453383
\(872\) 52.7730 1.78712
\(873\) −18.5708 −0.628527
\(874\) −74.4666 −2.51887
\(875\) −14.9061 −0.503919
\(876\) −50.2889 −1.69910
\(877\) −39.1307 −1.32135 −0.660676 0.750671i \(-0.729730\pi\)
−0.660676 + 0.750671i \(0.729730\pi\)
\(878\) −1.58994 −0.0536579
\(879\) −14.8599 −0.501213
\(880\) 119.991 4.04489
\(881\) 58.3121 1.96458 0.982291 0.187359i \(-0.0599929\pi\)
0.982291 + 0.187359i \(0.0599929\pi\)
\(882\) 14.9737 0.504189
\(883\) −44.5609 −1.49959 −0.749797 0.661668i \(-0.769849\pi\)
−0.749797 + 0.661668i \(0.769849\pi\)
\(884\) 5.90324 0.198548
\(885\) 25.0047 0.840523
\(886\) −55.6642 −1.87008
\(887\) 22.5831 0.758265 0.379133 0.925342i \(-0.376222\pi\)
0.379133 + 0.925342i \(0.376222\pi\)
\(888\) −0.922470 −0.0309561
\(889\) 70.1836 2.35388
\(890\) −67.1196 −2.24985
\(891\) 8.53374 0.285891
\(892\) −14.8593 −0.497526
\(893\) −89.0048 −2.97843
\(894\) −63.3881 −2.12002
\(895\) 21.8703 0.731044
\(896\) −11.5489 −0.385820
\(897\) −5.15155 −0.172005
\(898\) −82.9002 −2.76642
\(899\) 10.1510 0.338556
\(900\) −25.4382 −0.847940
\(901\) −12.9637 −0.431885
\(902\) −2.11003 −0.0702565
\(903\) −35.8716 −1.19373
\(904\) −53.5926 −1.78246
\(905\) 59.1959 1.96774
\(906\) −10.6125 −0.352577
\(907\) −10.2604 −0.340689 −0.170345 0.985385i \(-0.554488\pi\)
−0.170345 + 0.985385i \(0.554488\pi\)
\(908\) 51.1748 1.69830
\(909\) −7.99740 −0.265257
\(910\) 24.6372 0.816715
\(911\) 1.36032 0.0450694 0.0225347 0.999746i \(-0.492826\pi\)
0.0225347 + 0.999746i \(0.492826\pi\)
\(912\) 71.7566 2.37610
\(913\) −41.8143 −1.38385
\(914\) −56.5897 −1.87182
\(915\) 6.86910 0.227085
\(916\) 101.520 3.35432
\(917\) 10.1102 0.333869
\(918\) −17.6826 −0.583612
\(919\) 32.9722 1.08765 0.543826 0.839198i \(-0.316975\pi\)
0.543826 + 0.839198i \(0.316975\pi\)
\(920\) 88.7902 2.92733
\(921\) −1.34964 −0.0444723
\(922\) 2.90746 0.0957520
\(923\) 4.22652 0.139118
\(924\) 85.3867 2.80902
\(925\) 0.371401 0.0122116
\(926\) 2.59599 0.0853097
\(927\) −21.1069 −0.693240
\(928\) −11.7648 −0.386200
\(929\) 12.6825 0.416098 0.208049 0.978118i \(-0.433289\pi\)
0.208049 + 0.978118i \(0.433289\pi\)
\(930\) 70.8409 2.32296
\(931\) 24.5793 0.805555
\(932\) −54.8172 −1.79560
\(933\) −14.9981 −0.491015
\(934\) −5.23739 −0.171373
\(935\) −16.6412 −0.544225
\(936\) −11.1300 −0.363796
\(937\) −0.329127 −0.0107521 −0.00537605 0.999986i \(-0.501711\pi\)
−0.00537605 + 0.999986i \(0.501711\pi\)
\(938\) 113.545 3.70737
\(939\) 19.4877 0.635956
\(940\) 183.611 5.98873
\(941\) 17.6086 0.574025 0.287013 0.957927i \(-0.407338\pi\)
0.287013 + 0.957927i \(0.407338\pi\)
\(942\) −15.1730 −0.494364
\(943\) −0.759674 −0.0247384
\(944\) −64.5771 −2.10181
\(945\) −51.8971 −1.68821
\(946\) 109.438 3.55815
\(947\) 36.8187 1.19645 0.598223 0.801330i \(-0.295874\pi\)
0.598223 + 0.801330i \(0.295874\pi\)
\(948\) 9.00190 0.292368
\(949\) 8.85875 0.287567
\(950\) −59.3789 −1.92651
\(951\) 0.0115949 0.000375990 0
\(952\) −28.9536 −0.938391
\(953\) 10.5860 0.342914 0.171457 0.985192i \(-0.445153\pi\)
0.171457 + 0.985192i \(0.445153\pi\)
\(954\) 42.2880 1.36912
\(955\) 60.7127 1.96462
\(956\) −68.6092 −2.21898
\(957\) −7.13049 −0.230496
\(958\) 11.2010 0.361889
\(959\) −18.1130 −0.584898
\(960\) −19.6329 −0.633648
\(961\) 30.5708 0.986154
\(962\) 0.281148 0.00906457
\(963\) −24.9478 −0.803932
\(964\) 0.340546 0.0109682
\(965\) 37.3043 1.20087
\(966\) 43.7151 1.40651
\(967\) 46.7024 1.50185 0.750924 0.660389i \(-0.229609\pi\)
0.750924 + 0.660389i \(0.229609\pi\)
\(968\) −72.3458 −2.32528
\(969\) −9.95172 −0.319695
\(970\) 89.4257 2.87129
\(971\) −50.4489 −1.61898 −0.809491 0.587132i \(-0.800257\pi\)
−0.809491 + 0.587132i \(0.800257\pi\)
\(972\) 67.2187 2.15604
\(973\) 57.2801 1.83631
\(974\) 49.6368 1.59046
\(975\) −4.10779 −0.131555
\(976\) −17.7401 −0.567848
\(977\) −29.3294 −0.938330 −0.469165 0.883111i \(-0.655445\pi\)
−0.469165 + 0.883111i \(0.655445\pi\)
\(978\) 61.1916 1.95669
\(979\) 40.9778 1.30966
\(980\) −50.7055 −1.61973
\(981\) 11.6160 0.370870
\(982\) −57.9611 −1.84961
\(983\) 11.4122 0.363992 0.181996 0.983299i \(-0.441744\pi\)
0.181996 + 0.983299i \(0.441744\pi\)
\(984\) 1.50455 0.0479633
\(985\) 1.36348 0.0434442
\(986\) 4.18325 0.133222
\(987\) 52.2497 1.66313
\(988\) −31.6096 −1.00564
\(989\) 39.4010 1.25288
\(990\) 54.2839 1.72526
\(991\) −14.9053 −0.473483 −0.236742 0.971573i \(-0.576079\pi\)
−0.236742 + 0.971573i \(0.576079\pi\)
\(992\) −71.3592 −2.26566
\(993\) 9.17348 0.291112
\(994\) −35.8655 −1.13759
\(995\) −14.8726 −0.471494
\(996\) 51.5851 1.63454
\(997\) −3.76399 −0.119207 −0.0596034 0.998222i \(-0.518984\pi\)
−0.0596034 + 0.998222i \(0.518984\pi\)
\(998\) 33.1198 1.04839
\(999\) −0.592224 −0.0187372
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 \(a_p\))