Properties

Label 6019.2.a.c.1.12
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 1.12
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.34535 q^{2}\) \(-1.65067 q^{3}\) \(+3.50065 q^{4}\) \(-1.17678 q^{5}\) \(+3.87140 q^{6}\) \(+2.05341 q^{7}\) \(-3.51955 q^{8}\) \(-0.275278 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.34535 q^{2}\) \(-1.65067 q^{3}\) \(+3.50065 q^{4}\) \(-1.17678 q^{5}\) \(+3.87140 q^{6}\) \(+2.05341 q^{7}\) \(-3.51955 q^{8}\) \(-0.275278 q^{9}\) \(+2.75996 q^{10}\) \(+3.35882 q^{11}\) \(-5.77843 q^{12}\) \(-1.00000 q^{13}\) \(-4.81595 q^{14}\) \(+1.94248 q^{15}\) \(+1.25326 q^{16}\) \(+4.47018 q^{17}\) \(+0.645622 q^{18}\) \(+7.77434 q^{19}\) \(-4.11949 q^{20}\) \(-3.38950 q^{21}\) \(-7.87759 q^{22}\) \(-7.71657 q^{23}\) \(+5.80962 q^{24}\) \(-3.61519 q^{25}\) \(+2.34535 q^{26}\) \(+5.40641 q^{27}\) \(+7.18826 q^{28}\) \(+1.46185 q^{29}\) \(-4.55578 q^{30}\) \(-3.68184 q^{31}\) \(+4.09977 q^{32}\) \(-5.54431 q^{33}\) \(-10.4841 q^{34}\) \(-2.41640 q^{35}\) \(-0.963653 q^{36}\) \(+6.86030 q^{37}\) \(-18.2335 q^{38}\) \(+1.65067 q^{39}\) \(+4.14173 q^{40}\) \(-4.73919 q^{41}\) \(+7.94956 q^{42}\) \(+4.69953 q^{43}\) \(+11.7581 q^{44}\) \(+0.323941 q^{45}\) \(+18.0980 q^{46}\) \(-9.86429 q^{47}\) \(-2.06872 q^{48}\) \(-2.78353 q^{49}\) \(+8.47888 q^{50}\) \(-7.37880 q^{51}\) \(-3.50065 q^{52}\) \(-4.33860 q^{53}\) \(-12.6799 q^{54}\) \(-3.95259 q^{55}\) \(-7.22706 q^{56}\) \(-12.8329 q^{57}\) \(-3.42855 q^{58}\) \(+0.235407 q^{59}\) \(+6.79994 q^{60}\) \(-0.187165 q^{61}\) \(+8.63518 q^{62}\) \(-0.565257 q^{63}\) \(-12.1219 q^{64}\) \(+1.17678 q^{65}\) \(+13.0033 q^{66}\) \(+1.31340 q^{67}\) \(+15.6485 q^{68}\) \(+12.7375 q^{69}\) \(+5.66731 q^{70}\) \(-7.95224 q^{71}\) \(+0.968855 q^{72}\) \(-1.12431 q^{73}\) \(-16.0898 q^{74}\) \(+5.96750 q^{75}\) \(+27.2153 q^{76}\) \(+6.89702 q^{77}\) \(-3.87140 q^{78}\) \(-8.42207 q^{79}\) \(-1.47481 q^{80}\) \(-8.09839 q^{81}\) \(+11.1150 q^{82}\) \(+16.3277 q^{83}\) \(-11.8655 q^{84}\) \(-5.26041 q^{85}\) \(-11.0220 q^{86}\) \(-2.41304 q^{87}\) \(-11.8215 q^{88}\) \(-13.9408 q^{89}\) \(-0.759755 q^{90}\) \(-2.05341 q^{91}\) \(-27.0130 q^{92}\) \(+6.07751 q^{93}\) \(+23.1352 q^{94}\) \(-9.14868 q^{95}\) \(-6.76738 q^{96}\) \(+14.7783 q^{97}\) \(+6.52833 q^{98}\) \(-0.924609 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34535 −1.65841 −0.829205 0.558944i \(-0.811207\pi\)
−0.829205 + 0.558944i \(0.811207\pi\)
\(3\) −1.65067 −0.953017 −0.476508 0.879170i \(-0.658098\pi\)
−0.476508 + 0.879170i \(0.658098\pi\)
\(4\) 3.50065 1.75033
\(5\) −1.17678 −0.526272 −0.263136 0.964759i \(-0.584757\pi\)
−0.263136 + 0.964759i \(0.584757\pi\)
\(6\) 3.87140 1.58049
\(7\) 2.05341 0.776114 0.388057 0.921635i \(-0.373146\pi\)
0.388057 + 0.921635i \(0.373146\pi\)
\(8\) −3.51955 −1.24435
\(9\) −0.275278 −0.0917593
\(10\) 2.75996 0.872774
\(11\) 3.35882 1.01272 0.506361 0.862322i \(-0.330990\pi\)
0.506361 + 0.862322i \(0.330990\pi\)
\(12\) −5.77843 −1.66809
\(13\) −1.00000 −0.277350
\(14\) −4.81595 −1.28712
\(15\) 1.94248 0.501546
\(16\) 1.25326 0.313315
\(17\) 4.47018 1.08418 0.542089 0.840321i \(-0.317634\pi\)
0.542089 + 0.840321i \(0.317634\pi\)
\(18\) 0.645622 0.152175
\(19\) 7.77434 1.78356 0.891778 0.452474i \(-0.149458\pi\)
0.891778 + 0.452474i \(0.149458\pi\)
\(20\) −4.11949 −0.921147
\(21\) −3.38950 −0.739650
\(22\) −7.87759 −1.67951
\(23\) −7.71657 −1.60902 −0.804508 0.593942i \(-0.797571\pi\)
−0.804508 + 0.593942i \(0.797571\pi\)
\(24\) 5.80962 1.18588
\(25\) −3.61519 −0.723038
\(26\) 2.34535 0.459960
\(27\) 5.40641 1.04046
\(28\) 7.18826 1.35845
\(29\) 1.46185 0.271459 0.135730 0.990746i \(-0.456662\pi\)
0.135730 + 0.990746i \(0.456662\pi\)
\(30\) −4.55578 −0.831769
\(31\) −3.68184 −0.661277 −0.330639 0.943757i \(-0.607264\pi\)
−0.330639 + 0.943757i \(0.607264\pi\)
\(32\) 4.09977 0.724744
\(33\) −5.54431 −0.965141
\(34\) −10.4841 −1.79801
\(35\) −2.41640 −0.408447
\(36\) −0.963653 −0.160609
\(37\) 6.86030 1.12783 0.563913 0.825834i \(-0.309295\pi\)
0.563913 + 0.825834i \(0.309295\pi\)
\(38\) −18.2335 −2.95787
\(39\) 1.65067 0.264319
\(40\) 4.14173 0.654865
\(41\) −4.73919 −0.740136 −0.370068 0.929005i \(-0.620666\pi\)
−0.370068 + 0.929005i \(0.620666\pi\)
\(42\) 7.94956 1.22664
\(43\) 4.69953 0.716671 0.358335 0.933593i \(-0.383344\pi\)
0.358335 + 0.933593i \(0.383344\pi\)
\(44\) 11.7581 1.77259
\(45\) 0.323941 0.0482903
\(46\) 18.0980 2.66841
\(47\) −9.86429 −1.43885 −0.719427 0.694568i \(-0.755596\pi\)
−0.719427 + 0.694568i \(0.755596\pi\)
\(48\) −2.06872 −0.298594
\(49\) −2.78353 −0.397646
\(50\) 8.47888 1.19909
\(51\) −7.37880 −1.03324
\(52\) −3.50065 −0.485453
\(53\) −4.33860 −0.595952 −0.297976 0.954573i \(-0.596312\pi\)
−0.297976 + 0.954573i \(0.596312\pi\)
\(54\) −12.6799 −1.72552
\(55\) −3.95259 −0.532967
\(56\) −7.22706 −0.965757
\(57\) −12.8329 −1.69976
\(58\) −3.42855 −0.450191
\(59\) 0.235407 0.0306474 0.0153237 0.999883i \(-0.495122\pi\)
0.0153237 + 0.999883i \(0.495122\pi\)
\(60\) 6.79994 0.877868
\(61\) −0.187165 −0.0239640 −0.0119820 0.999928i \(-0.503814\pi\)
−0.0119820 + 0.999928i \(0.503814\pi\)
\(62\) 8.63518 1.09667
\(63\) −0.565257 −0.0712157
\(64\) −12.1219 −1.51524
\(65\) 1.17678 0.145961
\(66\) 13.0033 1.60060
\(67\) 1.31340 0.160458 0.0802289 0.996776i \(-0.474435\pi\)
0.0802289 + 0.996776i \(0.474435\pi\)
\(68\) 15.6485 1.89766
\(69\) 12.7375 1.53342
\(70\) 5.66731 0.677373
\(71\) −7.95224 −0.943758 −0.471879 0.881663i \(-0.656424\pi\)
−0.471879 + 0.881663i \(0.656424\pi\)
\(72\) 0.968855 0.114181
\(73\) −1.12431 −0.131590 −0.0657950 0.997833i \(-0.520958\pi\)
−0.0657950 + 0.997833i \(0.520958\pi\)
\(74\) −16.0898 −1.87040
\(75\) 5.96750 0.689067
\(76\) 27.2153 3.12180
\(77\) 6.89702 0.785988
\(78\) −3.87140 −0.438350
\(79\) −8.42207 −0.947556 −0.473778 0.880644i \(-0.657110\pi\)
−0.473778 + 0.880644i \(0.657110\pi\)
\(80\) −1.47481 −0.164889
\(81\) −8.09839 −0.899821
\(82\) 11.1150 1.22745
\(83\) 16.3277 1.79220 0.896100 0.443853i \(-0.146389\pi\)
0.896100 + 0.443853i \(0.146389\pi\)
\(84\) −11.8655 −1.29463
\(85\) −5.26041 −0.570572
\(86\) −11.0220 −1.18853
\(87\) −2.41304 −0.258705
\(88\) −11.8215 −1.26018
\(89\) −13.9408 −1.47772 −0.738860 0.673859i \(-0.764636\pi\)
−0.738860 + 0.673859i \(0.764636\pi\)
\(90\) −0.759755 −0.0800852
\(91\) −2.05341 −0.215255
\(92\) −27.0130 −2.81630
\(93\) 6.07751 0.630208
\(94\) 23.1352 2.38621
\(95\) −9.14868 −0.938635
\(96\) −6.76738 −0.690693
\(97\) 14.7783 1.50051 0.750257 0.661147i \(-0.229930\pi\)
0.750257 + 0.661147i \(0.229930\pi\)
\(98\) 6.52833 0.659461
\(99\) −0.924609 −0.0929267
\(100\) −12.6555 −1.26555
\(101\) −18.8061 −1.87128 −0.935640 0.352957i \(-0.885176\pi\)
−0.935640 + 0.352957i \(0.885176\pi\)
\(102\) 17.3059 1.71353
\(103\) −16.7076 −1.64625 −0.823124 0.567862i \(-0.807771\pi\)
−0.823124 + 0.567862i \(0.807771\pi\)
\(104\) 3.51955 0.345120
\(105\) 3.98869 0.389257
\(106\) 10.1755 0.988334
\(107\) −8.30921 −0.803282 −0.401641 0.915797i \(-0.631560\pi\)
−0.401641 + 0.915797i \(0.631560\pi\)
\(108\) 18.9260 1.82115
\(109\) 9.20099 0.881295 0.440648 0.897680i \(-0.354749\pi\)
0.440648 + 0.897680i \(0.354749\pi\)
\(110\) 9.27019 0.883878
\(111\) −11.3241 −1.07484
\(112\) 2.57345 0.243168
\(113\) 11.6455 1.09551 0.547757 0.836638i \(-0.315482\pi\)
0.547757 + 0.836638i \(0.315482\pi\)
\(114\) 30.0976 2.81890
\(115\) 9.08069 0.846779
\(116\) 5.11744 0.475142
\(117\) 0.275278 0.0254495
\(118\) −0.552111 −0.0508259
\(119\) 9.17909 0.841446
\(120\) −6.83664 −0.624097
\(121\) 0.281657 0.0256052
\(122\) 0.438967 0.0397422
\(123\) 7.82285 0.705362
\(124\) −12.8888 −1.15745
\(125\) 10.1382 0.906786
\(126\) 1.32572 0.118105
\(127\) −4.31315 −0.382730 −0.191365 0.981519i \(-0.561291\pi\)
−0.191365 + 0.981519i \(0.561291\pi\)
\(128\) 20.2305 1.78814
\(129\) −7.75738 −0.682999
\(130\) −2.75996 −0.242064
\(131\) −8.61452 −0.752654 −0.376327 0.926487i \(-0.622813\pi\)
−0.376327 + 0.926487i \(0.622813\pi\)
\(132\) −19.4087 −1.68931
\(133\) 15.9639 1.38424
\(134\) −3.08039 −0.266105
\(135\) −6.36215 −0.547567
\(136\) −15.7330 −1.34909
\(137\) −7.75851 −0.662854 −0.331427 0.943481i \(-0.607530\pi\)
−0.331427 + 0.943481i \(0.607530\pi\)
\(138\) −29.8739 −2.54304
\(139\) 15.5249 1.31681 0.658404 0.752665i \(-0.271232\pi\)
0.658404 + 0.752665i \(0.271232\pi\)
\(140\) −8.45899 −0.714915
\(141\) 16.2827 1.37125
\(142\) 18.6508 1.56514
\(143\) −3.35882 −0.280878
\(144\) −0.344995 −0.0287496
\(145\) −1.72028 −0.142861
\(146\) 2.63689 0.218230
\(147\) 4.59469 0.378964
\(148\) 24.0155 1.97406
\(149\) 4.85569 0.397794 0.198897 0.980020i \(-0.436264\pi\)
0.198897 + 0.980020i \(0.436264\pi\)
\(150\) −13.9959 −1.14276
\(151\) −16.5480 −1.34666 −0.673330 0.739342i \(-0.735136\pi\)
−0.673330 + 0.739342i \(0.735136\pi\)
\(152\) −27.3622 −2.21936
\(153\) −1.23054 −0.0994834
\(154\) −16.1759 −1.30349
\(155\) 4.33271 0.348012
\(156\) 5.77843 0.462645
\(157\) −20.7001 −1.65205 −0.826023 0.563636i \(-0.809402\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(158\) 19.7527 1.57144
\(159\) 7.16161 0.567953
\(160\) −4.82452 −0.381412
\(161\) −15.8452 −1.24878
\(162\) 18.9935 1.49227
\(163\) 6.13774 0.480745 0.240372 0.970681i \(-0.422730\pi\)
0.240372 + 0.970681i \(0.422730\pi\)
\(164\) −16.5902 −1.29548
\(165\) 6.52443 0.507926
\(166\) −38.2942 −2.97220
\(167\) −16.8358 −1.30279 −0.651396 0.758738i \(-0.725816\pi\)
−0.651396 + 0.758738i \(0.725816\pi\)
\(168\) 11.9295 0.920382
\(169\) 1.00000 0.0769231
\(170\) 12.3375 0.946242
\(171\) −2.14010 −0.163658
\(172\) 16.4514 1.25441
\(173\) 19.0864 1.45111 0.725556 0.688164i \(-0.241583\pi\)
0.725556 + 0.688164i \(0.241583\pi\)
\(174\) 5.65942 0.429039
\(175\) −7.42345 −0.561160
\(176\) 4.20947 0.317301
\(177\) −0.388580 −0.0292074
\(178\) 32.6960 2.45067
\(179\) −10.3164 −0.771082 −0.385541 0.922691i \(-0.625985\pi\)
−0.385541 + 0.922691i \(0.625985\pi\)
\(180\) 1.13401 0.0845238
\(181\) 10.3258 0.767509 0.383755 0.923435i \(-0.374631\pi\)
0.383755 + 0.923435i \(0.374631\pi\)
\(182\) 4.81595 0.356982
\(183\) 0.308949 0.0228381
\(184\) 27.1588 2.00218
\(185\) −8.07306 −0.593543
\(186\) −14.2539 −1.04514
\(187\) 15.0145 1.09797
\(188\) −34.5314 −2.51846
\(189\) 11.1016 0.807520
\(190\) 21.4568 1.55664
\(191\) 22.4150 1.62190 0.810948 0.585118i \(-0.198952\pi\)
0.810948 + 0.585118i \(0.198952\pi\)
\(192\) 20.0093 1.44405
\(193\) 18.3953 1.32412 0.662061 0.749450i \(-0.269682\pi\)
0.662061 + 0.749450i \(0.269682\pi\)
\(194\) −34.6603 −2.48847
\(195\) −1.94248 −0.139104
\(196\) −9.74415 −0.696011
\(197\) −0.515714 −0.0367431 −0.0183715 0.999831i \(-0.505848\pi\)
−0.0183715 + 0.999831i \(0.505848\pi\)
\(198\) 2.16853 0.154111
\(199\) 0.637140 0.0451656 0.0225828 0.999745i \(-0.492811\pi\)
0.0225828 + 0.999745i \(0.492811\pi\)
\(200\) 12.7238 0.899711
\(201\) −2.16800 −0.152919
\(202\) 44.1069 3.10335
\(203\) 3.00178 0.210683
\(204\) −25.8306 −1.80851
\(205\) 5.57697 0.389513
\(206\) 39.1851 2.73016
\(207\) 2.12420 0.147642
\(208\) −1.25326 −0.0868979
\(209\) 26.1126 1.80625
\(210\) −9.35487 −0.645547
\(211\) −5.19925 −0.357931 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(212\) −15.1879 −1.04311
\(213\) 13.1266 0.899417
\(214\) 19.4880 1.33217
\(215\) −5.53030 −0.377164
\(216\) −19.0281 −1.29470
\(217\) −7.56030 −0.513227
\(218\) −21.5795 −1.46155
\(219\) 1.85586 0.125407
\(220\) −13.8366 −0.932865
\(221\) −4.47018 −0.300697
\(222\) 26.5590 1.78252
\(223\) 10.0622 0.673811 0.336906 0.941538i \(-0.390620\pi\)
0.336906 + 0.941538i \(0.390620\pi\)
\(224\) 8.41849 0.562484
\(225\) 0.995183 0.0663455
\(226\) −27.3127 −1.81681
\(227\) −4.70794 −0.312477 −0.156239 0.987719i \(-0.549937\pi\)
−0.156239 + 0.987719i \(0.549937\pi\)
\(228\) −44.9235 −2.97513
\(229\) 20.1233 1.32978 0.664891 0.746940i \(-0.268478\pi\)
0.664891 + 0.746940i \(0.268478\pi\)
\(230\) −21.2974 −1.40431
\(231\) −11.3847 −0.749059
\(232\) −5.14506 −0.337790
\(233\) 2.30660 0.151110 0.0755551 0.997142i \(-0.475927\pi\)
0.0755551 + 0.997142i \(0.475927\pi\)
\(234\) −0.645622 −0.0422057
\(235\) 11.6081 0.757228
\(236\) 0.824078 0.0536429
\(237\) 13.9021 0.903037
\(238\) −21.5281 −1.39546
\(239\) 1.72415 0.111526 0.0557630 0.998444i \(-0.482241\pi\)
0.0557630 + 0.998444i \(0.482241\pi\)
\(240\) 2.43443 0.157142
\(241\) −11.0609 −0.712495 −0.356247 0.934392i \(-0.615944\pi\)
−0.356247 + 0.934392i \(0.615944\pi\)
\(242\) −0.660584 −0.0424640
\(243\) −2.85145 −0.182921
\(244\) −0.655200 −0.0419449
\(245\) 3.27559 0.209270
\(246\) −18.3473 −1.16978
\(247\) −7.77434 −0.494669
\(248\) 12.9584 0.822860
\(249\) −26.9517 −1.70800
\(250\) −23.7775 −1.50382
\(251\) −7.59593 −0.479451 −0.239725 0.970841i \(-0.577057\pi\)
−0.239725 + 0.970841i \(0.577057\pi\)
\(252\) −1.97877 −0.124651
\(253\) −25.9185 −1.62948
\(254\) 10.1158 0.634724
\(255\) 8.68322 0.543764
\(256\) −23.2038 −1.45024
\(257\) 5.40333 0.337050 0.168525 0.985697i \(-0.446100\pi\)
0.168525 + 0.985697i \(0.446100\pi\)
\(258\) 18.1937 1.13269
\(259\) 14.0870 0.875322
\(260\) 4.11949 0.255480
\(261\) −0.402416 −0.0249089
\(262\) 20.2040 1.24821
\(263\) −8.13411 −0.501570 −0.250785 0.968043i \(-0.580689\pi\)
−0.250785 + 0.968043i \(0.580689\pi\)
\(264\) 19.5135 1.20097
\(265\) 5.10557 0.313633
\(266\) −37.4408 −2.29564
\(267\) 23.0117 1.40829
\(268\) 4.59777 0.280854
\(269\) −15.9763 −0.974095 −0.487048 0.873375i \(-0.661926\pi\)
−0.487048 + 0.873375i \(0.661926\pi\)
\(270\) 14.9215 0.908091
\(271\) 21.1591 1.28532 0.642662 0.766150i \(-0.277830\pi\)
0.642662 + 0.766150i \(0.277830\pi\)
\(272\) 5.60229 0.339689
\(273\) 3.38950 0.205142
\(274\) 18.1964 1.09928
\(275\) −12.1428 −0.732236
\(276\) 44.5896 2.68398
\(277\) 1.47859 0.0888399 0.0444199 0.999013i \(-0.485856\pi\)
0.0444199 + 0.999013i \(0.485856\pi\)
\(278\) −36.4114 −2.18381
\(279\) 1.01353 0.0606784
\(280\) 8.50465 0.508250
\(281\) 18.4673 1.10167 0.550834 0.834615i \(-0.314310\pi\)
0.550834 + 0.834615i \(0.314310\pi\)
\(282\) −38.1886 −2.27410
\(283\) −5.32122 −0.316314 −0.158157 0.987414i \(-0.550555\pi\)
−0.158157 + 0.987414i \(0.550555\pi\)
\(284\) −27.8380 −1.65188
\(285\) 15.1015 0.894534
\(286\) 7.87759 0.465812
\(287\) −9.73147 −0.574430
\(288\) −1.12858 −0.0665020
\(289\) 2.98249 0.175441
\(290\) 4.03465 0.236923
\(291\) −24.3942 −1.43001
\(292\) −3.93580 −0.230325
\(293\) −7.40227 −0.432445 −0.216223 0.976344i \(-0.569374\pi\)
−0.216223 + 0.976344i \(0.569374\pi\)
\(294\) −10.7761 −0.628477
\(295\) −0.277022 −0.0161288
\(296\) −24.1452 −1.40341
\(297\) 18.1592 1.05370
\(298\) −11.3883 −0.659705
\(299\) 7.71657 0.446260
\(300\) 20.8901 1.20609
\(301\) 9.65003 0.556219
\(302\) 38.8109 2.23331
\(303\) 31.0428 1.78336
\(304\) 9.74326 0.558814
\(305\) 0.220252 0.0126116
\(306\) 2.88605 0.164984
\(307\) 12.9999 0.741943 0.370971 0.928644i \(-0.379025\pi\)
0.370971 + 0.928644i \(0.379025\pi\)
\(308\) 24.1440 1.37573
\(309\) 27.5788 1.56890
\(310\) −10.1617 −0.577146
\(311\) −20.4378 −1.15892 −0.579460 0.815001i \(-0.696736\pi\)
−0.579460 + 0.815001i \(0.696736\pi\)
\(312\) −5.80962 −0.328905
\(313\) −3.72032 −0.210285 −0.105142 0.994457i \(-0.533530\pi\)
−0.105142 + 0.994457i \(0.533530\pi\)
\(314\) 48.5489 2.73977
\(315\) 0.665183 0.0374788
\(316\) −29.4827 −1.65853
\(317\) −0.799939 −0.0449291 −0.0224645 0.999748i \(-0.507151\pi\)
−0.0224645 + 0.999748i \(0.507151\pi\)
\(318\) −16.7965 −0.941898
\(319\) 4.91010 0.274913
\(320\) 14.2648 0.797427
\(321\) 13.7158 0.765541
\(322\) 37.1626 2.07099
\(323\) 34.7527 1.93369
\(324\) −28.3496 −1.57498
\(325\) 3.61519 0.200535
\(326\) −14.3951 −0.797273
\(327\) −15.1878 −0.839889
\(328\) 16.6798 0.920988
\(329\) −20.2554 −1.11672
\(330\) −15.3020 −0.842350
\(331\) 8.15231 0.448092 0.224046 0.974579i \(-0.428073\pi\)
0.224046 + 0.974579i \(0.428073\pi\)
\(332\) 57.1576 3.13693
\(333\) −1.88849 −0.103489
\(334\) 39.4857 2.16056
\(335\) −1.54559 −0.0844444
\(336\) −4.24792 −0.231743
\(337\) 27.5642 1.50152 0.750758 0.660577i \(-0.229688\pi\)
0.750758 + 0.660577i \(0.229688\pi\)
\(338\) −2.34535 −0.127570
\(339\) −19.2229 −1.04404
\(340\) −18.4149 −0.998687
\(341\) −12.3666 −0.669690
\(342\) 5.01929 0.271412
\(343\) −20.0895 −1.08473
\(344\) −16.5402 −0.891788
\(345\) −14.9893 −0.806994
\(346\) −44.7642 −2.40654
\(347\) −7.70956 −0.413871 −0.206935 0.978355i \(-0.566349\pi\)
−0.206935 + 0.978355i \(0.566349\pi\)
\(348\) −8.44722 −0.452818
\(349\) −10.2107 −0.546565 −0.273283 0.961934i \(-0.588109\pi\)
−0.273283 + 0.961934i \(0.588109\pi\)
\(350\) 17.4106 0.930634
\(351\) −5.40641 −0.288573
\(352\) 13.7704 0.733964
\(353\) 30.0421 1.59898 0.799491 0.600678i \(-0.205103\pi\)
0.799491 + 0.600678i \(0.205103\pi\)
\(354\) 0.911354 0.0484379
\(355\) 9.35803 0.496673
\(356\) −48.8018 −2.58649
\(357\) −15.1517 −0.801912
\(358\) 24.1955 1.27877
\(359\) 20.9090 1.10353 0.551767 0.833999i \(-0.313954\pi\)
0.551767 + 0.833999i \(0.313954\pi\)
\(360\) −1.14013 −0.0600900
\(361\) 41.4403 2.18107
\(362\) −24.2175 −1.27285
\(363\) −0.464924 −0.0244022
\(364\) −7.18826 −0.376767
\(365\) 1.32306 0.0692521
\(366\) −0.724592 −0.0378750
\(367\) 22.4231 1.17048 0.585238 0.810862i \(-0.301001\pi\)
0.585238 + 0.810862i \(0.301001\pi\)
\(368\) −9.67086 −0.504128
\(369\) 1.30459 0.0679144
\(370\) 18.9341 0.984338
\(371\) −8.90890 −0.462527
\(372\) 21.2752 1.10307
\(373\) 17.8447 0.923963 0.461981 0.886890i \(-0.347139\pi\)
0.461981 + 0.886890i \(0.347139\pi\)
\(374\) −35.2142 −1.82089
\(375\) −16.7348 −0.864182
\(376\) 34.7179 1.79044
\(377\) −1.46185 −0.0752892
\(378\) −26.0370 −1.33920
\(379\) 20.2510 1.04023 0.520113 0.854098i \(-0.325890\pi\)
0.520113 + 0.854098i \(0.325890\pi\)
\(380\) −32.0263 −1.64292
\(381\) 7.11960 0.364748
\(382\) −52.5711 −2.68977
\(383\) −30.1757 −1.54191 −0.770954 0.636891i \(-0.780220\pi\)
−0.770954 + 0.636891i \(0.780220\pi\)
\(384\) −33.3940 −1.70413
\(385\) −8.11626 −0.413643
\(386\) −43.1433 −2.19594
\(387\) −1.29368 −0.0657613
\(388\) 51.7338 2.62639
\(389\) −12.7978 −0.648875 −0.324438 0.945907i \(-0.605175\pi\)
−0.324438 + 0.945907i \(0.605175\pi\)
\(390\) 4.55578 0.230691
\(391\) −34.4944 −1.74446
\(392\) 9.79675 0.494811
\(393\) 14.2198 0.717292
\(394\) 1.20953 0.0609351
\(395\) 9.91091 0.498672
\(396\) −3.23673 −0.162652
\(397\) −6.97484 −0.350057 −0.175029 0.984563i \(-0.556002\pi\)
−0.175029 + 0.984563i \(0.556002\pi\)
\(398\) −1.49431 −0.0749032
\(399\) −26.3511 −1.31921
\(400\) −4.53077 −0.226539
\(401\) −32.7327 −1.63459 −0.817296 0.576218i \(-0.804528\pi\)
−0.817296 + 0.576218i \(0.804528\pi\)
\(402\) 5.08471 0.253602
\(403\) 3.68184 0.183405
\(404\) −65.8337 −3.27535
\(405\) 9.53001 0.473550
\(406\) −7.04021 −0.349400
\(407\) 23.0425 1.14217
\(408\) 25.9701 1.28571
\(409\) −34.1250 −1.68737 −0.843686 0.536837i \(-0.819619\pi\)
−0.843686 + 0.536837i \(0.819619\pi\)
\(410\) −13.0799 −0.645972
\(411\) 12.8068 0.631711
\(412\) −58.4875 −2.88147
\(413\) 0.483386 0.0237859
\(414\) −4.98199 −0.244851
\(415\) −19.2141 −0.943184
\(416\) −4.09977 −0.201008
\(417\) −25.6266 −1.25494
\(418\) −61.2431 −2.99550
\(419\) −7.87824 −0.384877 −0.192439 0.981309i \(-0.561640\pi\)
−0.192439 + 0.981309i \(0.561640\pi\)
\(420\) 13.9630 0.681326
\(421\) −10.3585 −0.504841 −0.252421 0.967618i \(-0.581227\pi\)
−0.252421 + 0.967618i \(0.581227\pi\)
\(422\) 12.1940 0.593597
\(423\) 2.71542 0.132028
\(424\) 15.2699 0.741572
\(425\) −16.1605 −0.783902
\(426\) −30.7863 −1.49160
\(427\) −0.384326 −0.0185988
\(428\) −29.0877 −1.40600
\(429\) 5.54431 0.267682
\(430\) 12.9705 0.625492
\(431\) −40.9375 −1.97189 −0.985946 0.167066i \(-0.946571\pi\)
−0.985946 + 0.167066i \(0.946571\pi\)
\(432\) 6.77564 0.325993
\(433\) −2.56626 −0.123326 −0.0616632 0.998097i \(-0.519640\pi\)
−0.0616632 + 0.998097i \(0.519640\pi\)
\(434\) 17.7315 0.851141
\(435\) 2.83962 0.136149
\(436\) 32.2095 1.54255
\(437\) −59.9912 −2.86977
\(438\) −4.35264 −0.207977
\(439\) 11.4464 0.546307 0.273154 0.961970i \(-0.411933\pi\)
0.273154 + 0.961970i \(0.411933\pi\)
\(440\) 13.9113 0.663196
\(441\) 0.766243 0.0364878
\(442\) 10.4841 0.498679
\(443\) 38.6806 1.83777 0.918885 0.394525i \(-0.129091\pi\)
0.918885 + 0.394525i \(0.129091\pi\)
\(444\) −39.6418 −1.88131
\(445\) 16.4052 0.777682
\(446\) −23.5992 −1.11746
\(447\) −8.01516 −0.379104
\(448\) −24.8912 −1.17600
\(449\) −32.4700 −1.53236 −0.766178 0.642629i \(-0.777844\pi\)
−0.766178 + 0.642629i \(0.777844\pi\)
\(450\) −2.33405 −0.110028
\(451\) −15.9181 −0.749552
\(452\) 40.7667 1.91751
\(453\) 27.3154 1.28339
\(454\) 11.0418 0.518215
\(455\) 2.41640 0.113283
\(456\) 45.1660 2.11509
\(457\) −27.5969 −1.29093 −0.645465 0.763790i \(-0.723336\pi\)
−0.645465 + 0.763790i \(0.723336\pi\)
\(458\) −47.1960 −2.20533
\(459\) 24.1676 1.12805
\(460\) 31.7883 1.48214
\(461\) −7.76824 −0.361803 −0.180902 0.983501i \(-0.557902\pi\)
−0.180902 + 0.983501i \(0.557902\pi\)
\(462\) 26.7011 1.24225
\(463\) −1.00000 −0.0464739
\(464\) 1.83208 0.0850522
\(465\) −7.15189 −0.331661
\(466\) −5.40977 −0.250603
\(467\) 3.51723 0.162758 0.0813789 0.996683i \(-0.474068\pi\)
0.0813789 + 0.996683i \(0.474068\pi\)
\(468\) 0.963653 0.0445449
\(469\) 2.69695 0.124534
\(470\) −27.2250 −1.25580
\(471\) 34.1691 1.57443
\(472\) −0.828526 −0.0381360
\(473\) 15.7848 0.725788
\(474\) −32.6052 −1.49761
\(475\) −28.1057 −1.28958
\(476\) 32.1328 1.47280
\(477\) 1.19432 0.0546842
\(478\) −4.04373 −0.184956
\(479\) −20.8676 −0.953463 −0.476731 0.879049i \(-0.658179\pi\)
−0.476731 + 0.879049i \(0.658179\pi\)
\(480\) 7.96371 0.363492
\(481\) −6.86030 −0.312803
\(482\) 25.9416 1.18161
\(483\) 26.1553 1.19011
\(484\) 0.985985 0.0448175
\(485\) −17.3908 −0.789678
\(486\) 6.68764 0.303357
\(487\) −10.6513 −0.482656 −0.241328 0.970444i \(-0.577583\pi\)
−0.241328 + 0.970444i \(0.577583\pi\)
\(488\) 0.658737 0.0298196
\(489\) −10.1314 −0.458158
\(490\) −7.68240 −0.347056
\(491\) −21.4034 −0.965921 −0.482960 0.875642i \(-0.660438\pi\)
−0.482960 + 0.875642i \(0.660438\pi\)
\(492\) 27.3851 1.23461
\(493\) 6.53474 0.294310
\(494\) 18.2335 0.820365
\(495\) 1.08806 0.0489047
\(496\) −4.61430 −0.207188
\(497\) −16.3292 −0.732464
\(498\) 63.2111 2.83256
\(499\) −16.1760 −0.724139 −0.362070 0.932151i \(-0.617930\pi\)
−0.362070 + 0.932151i \(0.617930\pi\)
\(500\) 35.4902 1.58717
\(501\) 27.7904 1.24158
\(502\) 17.8151 0.795126
\(503\) −36.7061 −1.63664 −0.818321 0.574761i \(-0.805095\pi\)
−0.818321 + 0.574761i \(0.805095\pi\)
\(504\) 1.98945 0.0886172
\(505\) 22.1307 0.984801
\(506\) 60.7880 2.70235
\(507\) −1.65067 −0.0733090
\(508\) −15.0988 −0.669902
\(509\) 10.0322 0.444670 0.222335 0.974970i \(-0.428632\pi\)
0.222335 + 0.974970i \(0.428632\pi\)
\(510\) −20.3652 −0.901785
\(511\) −2.30866 −0.102129
\(512\) 13.9599 0.616946
\(513\) 42.0313 1.85573
\(514\) −12.6727 −0.558968
\(515\) 19.6611 0.866374
\(516\) −27.1559 −1.19547
\(517\) −33.1324 −1.45716
\(518\) −33.0388 −1.45164
\(519\) −31.5054 −1.38293
\(520\) −4.14173 −0.181627
\(521\) −39.8464 −1.74570 −0.872851 0.487988i \(-0.837731\pi\)
−0.872851 + 0.487988i \(0.837731\pi\)
\(522\) 0.943805 0.0413092
\(523\) 4.33379 0.189503 0.0947516 0.995501i \(-0.469794\pi\)
0.0947516 + 0.995501i \(0.469794\pi\)
\(524\) −30.1564 −1.31739
\(525\) 12.2537 0.534795
\(526\) 19.0773 0.831810
\(527\) −16.4585 −0.716942
\(528\) −6.94846 −0.302393
\(529\) 36.5454 1.58893
\(530\) −11.9743 −0.520132
\(531\) −0.0648023 −0.00281218
\(532\) 55.8840 2.42288
\(533\) 4.73919 0.205277
\(534\) −53.9704 −2.33553
\(535\) 9.77811 0.422744
\(536\) −4.62259 −0.199665
\(537\) 17.0290 0.734854
\(538\) 37.4701 1.61545
\(539\) −9.34935 −0.402705
\(540\) −22.2717 −0.958421
\(541\) −34.5042 −1.48345 −0.741726 0.670703i \(-0.765993\pi\)
−0.741726 + 0.670703i \(0.765993\pi\)
\(542\) −49.6254 −2.13159
\(543\) −17.0445 −0.731449
\(544\) 18.3267 0.785751
\(545\) −10.8275 −0.463801
\(546\) −7.94956 −0.340210
\(547\) 15.2149 0.650542 0.325271 0.945621i \(-0.394545\pi\)
0.325271 + 0.945621i \(0.394545\pi\)
\(548\) −27.1598 −1.16021
\(549\) 0.0515225 0.00219893
\(550\) 28.4790 1.21435
\(551\) 11.3649 0.484163
\(552\) −44.8304 −1.90811
\(553\) −17.2939 −0.735412
\(554\) −3.46781 −0.147333
\(555\) 13.3260 0.565656
\(556\) 54.3474 2.30484
\(557\) −11.6392 −0.493170 −0.246585 0.969121i \(-0.579308\pi\)
−0.246585 + 0.969121i \(0.579308\pi\)
\(558\) −2.37708 −0.100630
\(559\) −4.69953 −0.198769
\(560\) −3.02838 −0.127972
\(561\) −24.7841 −1.04638
\(562\) −43.3123 −1.82702
\(563\) −5.24610 −0.221097 −0.110548 0.993871i \(-0.535261\pi\)
−0.110548 + 0.993871i \(0.535261\pi\)
\(564\) 57.0001 2.40014
\(565\) −13.7041 −0.576538
\(566\) 12.4801 0.524578
\(567\) −16.6293 −0.698364
\(568\) 27.9883 1.17436
\(569\) 30.3721 1.27326 0.636632 0.771168i \(-0.280327\pi\)
0.636632 + 0.771168i \(0.280327\pi\)
\(570\) −35.4182 −1.48351
\(571\) 8.55417 0.357981 0.178990 0.983851i \(-0.442717\pi\)
0.178990 + 0.983851i \(0.442717\pi\)
\(572\) −11.7581 −0.491629
\(573\) −36.9999 −1.54569
\(574\) 22.8237 0.952642
\(575\) 27.8969 1.16338
\(576\) 3.33689 0.139037
\(577\) −16.3414 −0.680301 −0.340150 0.940371i \(-0.610478\pi\)
−0.340150 + 0.940371i \(0.610478\pi\)
\(578\) −6.99498 −0.290953
\(579\) −30.3646 −1.26191
\(580\) −6.02209 −0.250054
\(581\) 33.5274 1.39095
\(582\) 57.2129 2.37155
\(583\) −14.5726 −0.603534
\(584\) 3.95705 0.163744
\(585\) −0.323941 −0.0133933
\(586\) 17.3609 0.717172
\(587\) 6.71206 0.277036 0.138518 0.990360i \(-0.455766\pi\)
0.138518 + 0.990360i \(0.455766\pi\)
\(588\) 16.0844 0.663310
\(589\) −28.6238 −1.17943
\(590\) 0.649712 0.0267482
\(591\) 0.851275 0.0350168
\(592\) 8.59773 0.353365
\(593\) 34.6077 1.42117 0.710584 0.703612i \(-0.248431\pi\)
0.710584 + 0.703612i \(0.248431\pi\)
\(594\) −42.5895 −1.74747
\(595\) −10.8018 −0.442829
\(596\) 16.9981 0.696268
\(597\) −1.05171 −0.0430436
\(598\) −18.0980 −0.740083
\(599\) −23.5561 −0.962476 −0.481238 0.876590i \(-0.659813\pi\)
−0.481238 + 0.876590i \(0.659813\pi\)
\(600\) −21.0029 −0.857440
\(601\) −3.39434 −0.138458 −0.0692289 0.997601i \(-0.522054\pi\)
−0.0692289 + 0.997601i \(0.522054\pi\)
\(602\) −22.6327 −0.922439
\(603\) −0.361551 −0.0147235
\(604\) −57.9289 −2.35709
\(605\) −0.331449 −0.0134753
\(606\) −72.8060 −2.95754
\(607\) −13.2356 −0.537217 −0.268608 0.963249i \(-0.586564\pi\)
−0.268608 + 0.963249i \(0.586564\pi\)
\(608\) 31.8730 1.29262
\(609\) −4.95495 −0.200785
\(610\) −0.516568 −0.0209152
\(611\) 9.86429 0.399066
\(612\) −4.30770 −0.174128
\(613\) −40.9304 −1.65316 −0.826581 0.562818i \(-0.809717\pi\)
−0.826581 + 0.562818i \(0.809717\pi\)
\(614\) −30.4892 −1.23045
\(615\) −9.20576 −0.371212
\(616\) −24.2744 −0.978043
\(617\) −36.9601 −1.48796 −0.743978 0.668204i \(-0.767063\pi\)
−0.743978 + 0.668204i \(0.767063\pi\)
\(618\) −64.6818 −2.60188
\(619\) −43.7376 −1.75796 −0.878982 0.476855i \(-0.841777\pi\)
−0.878982 + 0.476855i \(0.841777\pi\)
\(620\) 15.1673 0.609134
\(621\) −41.7189 −1.67412
\(622\) 47.9337 1.92196
\(623\) −28.6261 −1.14688
\(624\) 2.06872 0.0828151
\(625\) 6.14556 0.245822
\(626\) 8.72544 0.348739
\(627\) −43.1033 −1.72138
\(628\) −72.4638 −2.89162
\(629\) 30.6668 1.22276
\(630\) −1.56009 −0.0621553
\(631\) 38.5065 1.53292 0.766460 0.642292i \(-0.222016\pi\)
0.766460 + 0.642292i \(0.222016\pi\)
\(632\) 29.6419 1.17909
\(633\) 8.58226 0.341114
\(634\) 1.87614 0.0745108
\(635\) 5.07562 0.201420
\(636\) 25.0703 0.994102
\(637\) 2.78353 0.110287
\(638\) −11.5159 −0.455918
\(639\) 2.18908 0.0865986
\(640\) −23.8069 −0.941049
\(641\) 33.1894 1.31090 0.655451 0.755238i \(-0.272479\pi\)
0.655451 + 0.755238i \(0.272479\pi\)
\(642\) −32.1683 −1.26958
\(643\) 7.86750 0.310264 0.155132 0.987894i \(-0.450420\pi\)
0.155132 + 0.987894i \(0.450420\pi\)
\(644\) −55.4687 −2.18577
\(645\) 9.12872 0.359443
\(646\) −81.5071 −3.20685
\(647\) 14.9166 0.586430 0.293215 0.956046i \(-0.405275\pi\)
0.293215 + 0.956046i \(0.405275\pi\)
\(648\) 28.5027 1.11969
\(649\) 0.790689 0.0310373
\(650\) −8.47888 −0.332569
\(651\) 12.4796 0.489114
\(652\) 21.4861 0.841460
\(653\) 1.58211 0.0619126 0.0309563 0.999521i \(-0.490145\pi\)
0.0309563 + 0.999521i \(0.490145\pi\)
\(654\) 35.6207 1.39288
\(655\) 10.1374 0.396100
\(656\) −5.93943 −0.231896
\(657\) 0.309497 0.0120746
\(658\) 47.5059 1.85197
\(659\) −29.6557 −1.15522 −0.577612 0.816312i \(-0.696015\pi\)
−0.577612 + 0.816312i \(0.696015\pi\)
\(660\) 22.8398 0.889036
\(661\) 3.01285 0.117186 0.0585932 0.998282i \(-0.481339\pi\)
0.0585932 + 0.998282i \(0.481339\pi\)
\(662\) −19.1200 −0.743120
\(663\) 7.37880 0.286569
\(664\) −57.4662 −2.23012
\(665\) −18.7859 −0.728488
\(666\) 4.42916 0.171627
\(667\) −11.2805 −0.436782
\(668\) −58.9362 −2.28031
\(669\) −16.6093 −0.642153
\(670\) 3.62494 0.140043
\(671\) −0.628654 −0.0242689
\(672\) −13.8962 −0.536057
\(673\) 30.3291 1.16910 0.584551 0.811357i \(-0.301271\pi\)
0.584551 + 0.811357i \(0.301271\pi\)
\(674\) −64.6476 −2.49013
\(675\) −19.5452 −0.752296
\(676\) 3.50065 0.134640
\(677\) −23.5122 −0.903649 −0.451825 0.892107i \(-0.649227\pi\)
−0.451825 + 0.892107i \(0.649227\pi\)
\(678\) 45.0843 1.73145
\(679\) 30.3459 1.16457
\(680\) 18.5143 0.709990
\(681\) 7.77127 0.297796
\(682\) 29.0040 1.11062
\(683\) −26.7500 −1.02356 −0.511781 0.859116i \(-0.671014\pi\)
−0.511781 + 0.859116i \(0.671014\pi\)
\(684\) −7.49176 −0.286455
\(685\) 9.13005 0.348841
\(686\) 47.1170 1.79893
\(687\) −33.2169 −1.26731
\(688\) 5.88972 0.224544
\(689\) 4.33860 0.165287
\(690\) 35.1550 1.33833
\(691\) −4.32225 −0.164426 −0.0822131 0.996615i \(-0.526199\pi\)
−0.0822131 + 0.996615i \(0.526199\pi\)
\(692\) 66.8148 2.53992
\(693\) −1.89860 −0.0721217
\(694\) 18.0816 0.686368
\(695\) −18.2694 −0.692999
\(696\) 8.49282 0.321919
\(697\) −21.1850 −0.802439
\(698\) 23.9476 0.906430
\(699\) −3.80744 −0.144011
\(700\) −25.9869 −0.982213
\(701\) 6.69840 0.252995 0.126498 0.991967i \(-0.459626\pi\)
0.126498 + 0.991967i \(0.459626\pi\)
\(702\) 12.6799 0.478573
\(703\) 53.3343 2.01154
\(704\) −40.7153 −1.53451
\(705\) −19.1612 −0.721651
\(706\) −70.4592 −2.65177
\(707\) −38.6166 −1.45233
\(708\) −1.36028 −0.0511226
\(709\) 4.31526 0.162063 0.0810315 0.996712i \(-0.474179\pi\)
0.0810315 + 0.996712i \(0.474179\pi\)
\(710\) −21.9478 −0.823688
\(711\) 2.31841 0.0869472
\(712\) 49.0653 1.83880
\(713\) 28.4111 1.06401
\(714\) 35.5359 1.32990
\(715\) 3.95259 0.147818
\(716\) −36.1140 −1.34964
\(717\) −2.84601 −0.106286
\(718\) −49.0388 −1.83011
\(719\) 2.76799 0.103229 0.0516144 0.998667i \(-0.483563\pi\)
0.0516144 + 0.998667i \(0.483563\pi\)
\(720\) 0.405983 0.0151301
\(721\) −34.3075 −1.27768
\(722\) −97.1920 −3.61711
\(723\) 18.2579 0.679019
\(724\) 36.1470 1.34339
\(725\) −5.28488 −0.196275
\(726\) 1.09041 0.0404689
\(727\) 7.45861 0.276624 0.138312 0.990389i \(-0.455832\pi\)
0.138312 + 0.990389i \(0.455832\pi\)
\(728\) 7.22706 0.267853
\(729\) 29.0020 1.07415
\(730\) −3.10303 −0.114848
\(731\) 21.0077 0.776998
\(732\) 1.08152 0.0399742
\(733\) −16.9100 −0.624585 −0.312292 0.949986i \(-0.601097\pi\)
−0.312292 + 0.949986i \(0.601097\pi\)
\(734\) −52.5899 −1.94113
\(735\) −5.40694 −0.199438
\(736\) −31.6361 −1.16612
\(737\) 4.41148 0.162499
\(738\) −3.05972 −0.112630
\(739\) −23.8035 −0.875627 −0.437814 0.899066i \(-0.644247\pi\)
−0.437814 + 0.899066i \(0.644247\pi\)
\(740\) −28.2610 −1.03889
\(741\) 12.8329 0.471428
\(742\) 20.8945 0.767060
\(743\) −37.3549 −1.37042 −0.685209 0.728347i \(-0.740289\pi\)
−0.685209 + 0.728347i \(0.740289\pi\)
\(744\) −21.3901 −0.784199
\(745\) −5.71407 −0.209347
\(746\) −41.8520 −1.53231
\(747\) −4.49466 −0.164451
\(748\) 52.5606 1.92181
\(749\) −17.0622 −0.623439
\(750\) 39.2489 1.43317
\(751\) 35.7899 1.30599 0.652995 0.757362i \(-0.273512\pi\)
0.652995 + 0.757362i \(0.273512\pi\)
\(752\) −12.3625 −0.450814
\(753\) 12.5384 0.456924
\(754\) 3.42855 0.124860
\(755\) 19.4734 0.708708
\(756\) 38.8627 1.41342
\(757\) 5.64469 0.205160 0.102580 0.994725i \(-0.467290\pi\)
0.102580 + 0.994725i \(0.467290\pi\)
\(758\) −47.4957 −1.72512
\(759\) 42.7830 1.55293
\(760\) 32.1992 1.16799
\(761\) −22.2716 −0.807343 −0.403672 0.914904i \(-0.632266\pi\)
−0.403672 + 0.914904i \(0.632266\pi\)
\(762\) −16.6979 −0.604902
\(763\) 18.8934 0.683986
\(764\) 78.4673 2.83885
\(765\) 1.44808 0.0523553
\(766\) 70.7726 2.55712
\(767\) −0.235407 −0.00850005
\(768\) 38.3019 1.38210
\(769\) −32.3340 −1.16600 −0.582998 0.812474i \(-0.698120\pi\)
−0.582998 + 0.812474i \(0.698120\pi\)
\(770\) 19.0355 0.685990
\(771\) −8.91913 −0.321215
\(772\) 64.3955 2.31765
\(773\) −24.4466 −0.879283 −0.439642 0.898173i \(-0.644895\pi\)
−0.439642 + 0.898173i \(0.644895\pi\)
\(774\) 3.03412 0.109059
\(775\) 13.3105 0.478129
\(776\) −52.0131 −1.86716
\(777\) −23.2530 −0.834196
\(778\) 30.0153 1.07610
\(779\) −36.8440 −1.32007
\(780\) −6.79994 −0.243477
\(781\) −26.7101 −0.955764
\(782\) 80.9014 2.89303
\(783\) 7.90338 0.282444
\(784\) −3.48848 −0.124589
\(785\) 24.3594 0.869425
\(786\) −33.3503 −1.18956
\(787\) −13.4491 −0.479410 −0.239705 0.970846i \(-0.577051\pi\)
−0.239705 + 0.970846i \(0.577051\pi\)
\(788\) −1.80533 −0.0643123
\(789\) 13.4268 0.478005
\(790\) −23.2445 −0.827003
\(791\) 23.9129 0.850244
\(792\) 3.25421 0.115633
\(793\) 0.187165 0.00664643
\(794\) 16.3584 0.580538
\(795\) −8.42763 −0.298897
\(796\) 2.23040 0.0790546
\(797\) 35.6487 1.26274 0.631370 0.775481i \(-0.282493\pi\)
0.631370 + 0.775481i \(0.282493\pi\)
\(798\) 61.8025 2.18779
\(799\) −44.0951 −1.55997
\(800\) −14.8215 −0.524017
\(801\) 3.83759 0.135595
\(802\) 76.7695 2.71083
\(803\) −3.77634 −0.133264
\(804\) −7.58942 −0.267658
\(805\) 18.6463 0.657197
\(806\) −8.63518 −0.304161
\(807\) 26.3717 0.928329
\(808\) 66.1891 2.32852
\(809\) −25.3556 −0.891455 −0.445728 0.895169i \(-0.647055\pi\)
−0.445728 + 0.895169i \(0.647055\pi\)
\(810\) −22.3512 −0.785341
\(811\) 42.3734 1.48793 0.743966 0.668217i \(-0.232942\pi\)
0.743966 + 0.668217i \(0.232942\pi\)
\(812\) 10.5082 0.368765
\(813\) −34.9268 −1.22494
\(814\) −54.0426 −1.89419
\(815\) −7.22276 −0.253002
\(816\) −9.24755 −0.323729
\(817\) 36.5357 1.27822
\(818\) 80.0349 2.79836
\(819\) 0.565257 0.0197517
\(820\) 19.5230 0.681774
\(821\) −34.9901 −1.22116 −0.610582 0.791953i \(-0.709065\pi\)
−0.610582 + 0.791953i \(0.709065\pi\)
\(822\) −30.0363 −1.04764
\(823\) 26.2436 0.914794 0.457397 0.889263i \(-0.348782\pi\)
0.457397 + 0.889263i \(0.348782\pi\)
\(824\) 58.8032 2.04851
\(825\) 20.0437 0.697834
\(826\) −1.13371 −0.0394467
\(827\) 35.8718 1.24739 0.623693 0.781670i \(-0.285632\pi\)
0.623693 + 0.781670i \(0.285632\pi\)
\(828\) 7.43609 0.258422
\(829\) 22.3899 0.777634 0.388817 0.921315i \(-0.372884\pi\)
0.388817 + 0.921315i \(0.372884\pi\)
\(830\) 45.0638 1.56419
\(831\) −2.44067 −0.0846659
\(832\) 12.1219 0.420251
\(833\) −12.4429 −0.431119
\(834\) 60.1033 2.08121
\(835\) 19.8120 0.685622
\(836\) 91.4111 3.16152
\(837\) −19.9055 −0.688036
\(838\) 18.4772 0.638285
\(839\) −9.31199 −0.321485 −0.160743 0.986996i \(-0.551389\pi\)
−0.160743 + 0.986996i \(0.551389\pi\)
\(840\) −14.0384 −0.484371
\(841\) −26.8630 −0.926310
\(842\) 24.2942 0.837234
\(843\) −30.4835 −1.04991
\(844\) −18.2008 −0.626496
\(845\) −1.17678 −0.0404824
\(846\) −6.36861 −0.218957
\(847\) 0.578357 0.0198726
\(848\) −5.43739 −0.186721
\(849\) 8.78360 0.301452
\(850\) 37.9021 1.30003
\(851\) −52.9379 −1.81469
\(852\) 45.9515 1.57427
\(853\) −25.6209 −0.877243 −0.438621 0.898672i \(-0.644533\pi\)
−0.438621 + 0.898672i \(0.644533\pi\)
\(854\) 0.901378 0.0308445
\(855\) 2.51843 0.0861285
\(856\) 29.2447 0.999562
\(857\) 7.85009 0.268154 0.134077 0.990971i \(-0.457193\pi\)
0.134077 + 0.990971i \(0.457193\pi\)
\(858\) −13.0033 −0.443926
\(859\) −18.5076 −0.631470 −0.315735 0.948847i \(-0.602251\pi\)
−0.315735 + 0.948847i \(0.602251\pi\)
\(860\) −19.3597 −0.660159
\(861\) 16.0635 0.547442
\(862\) 96.0127 3.27021
\(863\) 5.32755 0.181352 0.0906759 0.995880i \(-0.471097\pi\)
0.0906759 + 0.995880i \(0.471097\pi\)
\(864\) 22.1651 0.754070
\(865\) −22.4605 −0.763679
\(866\) 6.01876 0.204526
\(867\) −4.92312 −0.167198
\(868\) −26.4660 −0.898314
\(869\) −28.2882 −0.959611
\(870\) −6.65988 −0.225791
\(871\) −1.31340 −0.0445030
\(872\) −32.3833 −1.09664
\(873\) −4.06815 −0.137686
\(874\) 140.700 4.75925
\(875\) 20.8178 0.703770
\(876\) 6.49672 0.219504
\(877\) −2.07870 −0.0701926 −0.0350963 0.999384i \(-0.511174\pi\)
−0.0350963 + 0.999384i \(0.511174\pi\)
\(878\) −26.8458 −0.906002
\(879\) 12.2187 0.412128
\(880\) −4.95362 −0.166986
\(881\) 11.5668 0.389695 0.194847 0.980834i \(-0.437579\pi\)
0.194847 + 0.980834i \(0.437579\pi\)
\(882\) −1.79711 −0.0605117
\(883\) −11.2769 −0.379498 −0.189749 0.981833i \(-0.560767\pi\)
−0.189749 + 0.981833i \(0.560767\pi\)
\(884\) −15.6485 −0.526317
\(885\) 0.457273 0.0153711
\(886\) −90.7194 −3.04778
\(887\) −55.4726 −1.86259 −0.931294 0.364269i \(-0.881319\pi\)
−0.931294 + 0.364269i \(0.881319\pi\)
\(888\) 39.8558 1.33747
\(889\) −8.85664 −0.297042
\(890\) −38.4759 −1.28972
\(891\) −27.2010 −0.911268
\(892\) 35.2241 1.17939
\(893\) −76.6883 −2.56628
\(894\) 18.7983 0.628710
\(895\) 12.1401 0.405798
\(896\) 41.5415 1.38780
\(897\) −12.7375 −0.425294
\(898\) 76.1535 2.54127
\(899\) −5.38230 −0.179510
\(900\) 3.48379 0.116126
\(901\) −19.3943 −0.646118
\(902\) 37.3334 1.24307
\(903\) −15.9290 −0.530086
\(904\) −40.9868 −1.36320
\(905\) −12.1512 −0.403918
\(906\) −64.0640 −2.12839
\(907\) −31.6157 −1.04978 −0.524892 0.851169i \(-0.675894\pi\)
−0.524892 + 0.851169i \(0.675894\pi\)
\(908\) −16.4809 −0.546937
\(909\) 5.17691 0.171707
\(910\) −5.66731 −0.187869
\(911\) 7.69749 0.255029 0.127515 0.991837i \(-0.459300\pi\)
0.127515 + 0.991837i \(0.459300\pi\)
\(912\) −16.0829 −0.532559
\(913\) 54.8418 1.81500
\(914\) 64.7244 2.14089
\(915\) −0.363564 −0.0120191
\(916\) 70.4445 2.32755
\(917\) −17.6891 −0.584146
\(918\) −56.6815 −1.87077
\(919\) −15.7089 −0.518190 −0.259095 0.965852i \(-0.583424\pi\)
−0.259095 + 0.965852i \(0.583424\pi\)
\(920\) −31.9599 −1.05369
\(921\) −21.4586 −0.707084
\(922\) 18.2192 0.600018
\(923\) 7.95224 0.261751
\(924\) −39.8539 −1.31110
\(925\) −24.8013 −0.815461
\(926\) 2.34535 0.0770729
\(927\) 4.59923 0.151059
\(928\) 5.99326 0.196738
\(929\) −26.0229 −0.853784 −0.426892 0.904303i \(-0.640392\pi\)
−0.426892 + 0.904303i \(0.640392\pi\)
\(930\) 16.7737 0.550030
\(931\) −21.6401 −0.709225
\(932\) 8.07459 0.264492
\(933\) 33.7361 1.10447
\(934\) −8.24912 −0.269919
\(935\) −17.6688 −0.577830
\(936\) −0.968855 −0.0316680
\(937\) −10.9730 −0.358472 −0.179236 0.983806i \(-0.557363\pi\)
−0.179236 + 0.983806i \(0.557363\pi\)
\(938\) −6.32529 −0.206528
\(939\) 6.14103 0.200405
\(940\) 40.6359 1.32540
\(941\) 9.68440 0.315702 0.157851 0.987463i \(-0.449543\pi\)
0.157851 + 0.987463i \(0.449543\pi\)
\(942\) −80.1383 −2.61105
\(943\) 36.5702 1.19089
\(944\) 0.295026 0.00960227
\(945\) −13.0641 −0.424975
\(946\) −37.0209 −1.20365
\(947\) 29.3611 0.954106 0.477053 0.878874i \(-0.341705\pi\)
0.477053 + 0.878874i \(0.341705\pi\)
\(948\) 48.6663 1.58061
\(949\) 1.12431 0.0364965
\(950\) 65.9177 2.13865
\(951\) 1.32044 0.0428181
\(952\) −32.3063 −1.04705
\(953\) 32.0233 1.03734 0.518668 0.854976i \(-0.326428\pi\)
0.518668 + 0.854976i \(0.326428\pi\)
\(954\) −2.80110 −0.0906889
\(955\) −26.3776 −0.853558
\(956\) 6.03565 0.195207
\(957\) −8.10496 −0.261996
\(958\) 48.9416 1.58123
\(959\) −15.9314 −0.514450
\(960\) −23.5465 −0.759961
\(961\) −17.4441 −0.562712
\(962\) 16.0898 0.518755
\(963\) 2.28734 0.0737086
\(964\) −38.7203 −1.24710
\(965\) −21.6472 −0.696848
\(966\) −61.3433 −1.97369
\(967\) −17.7899 −0.572084 −0.286042 0.958217i \(-0.592340\pi\)
−0.286042 + 0.958217i \(0.592340\pi\)
\(968\) −0.991307 −0.0318618
\(969\) −57.3653 −1.84284
\(970\) 40.7876 1.30961
\(971\) −4.79097 −0.153749 −0.0768747 0.997041i \(-0.524494\pi\)
−0.0768747 + 0.997041i \(0.524494\pi\)
\(972\) −9.98193 −0.320171
\(973\) 31.8790 1.02199
\(974\) 24.9809 0.800441
\(975\) −5.96750 −0.191113
\(976\) −0.234567 −0.00750829
\(977\) −60.0639 −1.92161 −0.960807 0.277218i \(-0.910588\pi\)
−0.960807 + 0.277218i \(0.910588\pi\)
\(978\) 23.7617 0.759814
\(979\) −46.8246 −1.49652
\(980\) 11.4667 0.366291
\(981\) −2.53283 −0.0808671
\(982\) 50.1983 1.60189
\(983\) −17.7583 −0.566403 −0.283202 0.959060i \(-0.591397\pi\)
−0.283202 + 0.959060i \(0.591397\pi\)
\(984\) −27.5329 −0.877716
\(985\) 0.606881 0.0193368
\(986\) −15.3262 −0.488087
\(987\) 33.4350 1.06425
\(988\) −27.2153 −0.865833
\(989\) −36.2642 −1.15313
\(990\) −2.55188 −0.0811040
\(991\) −24.5801 −0.780813 −0.390407 0.920643i \(-0.627666\pi\)
−0.390407 + 0.920643i \(0.627666\pi\)
\(992\) −15.0947 −0.479257
\(993\) −13.4568 −0.427039
\(994\) 38.2976 1.21473
\(995\) −0.749773 −0.0237694
\(996\) −94.3486 −2.98955
\(997\) −29.0419 −0.919767 −0.459884 0.887979i \(-0.652109\pi\)
−0.459884 + 0.887979i \(0.652109\pi\)
\(998\) 37.9384 1.20092
\(999\) 37.0896 1.17346
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 \(a_p\))