Properties

Label 6041.2.a.f.1.14
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.47641 q^{2}\) \(+1.36965 q^{3}\) \(+4.13259 q^{4}\) \(-1.36117 q^{5}\) \(-3.39181 q^{6}\) \(+1.00000 q^{7}\) \(-5.28115 q^{8}\) \(-1.12406 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.47641 q^{2}\) \(+1.36965 q^{3}\) \(+4.13259 q^{4}\) \(-1.36117 q^{5}\) \(-3.39181 q^{6}\) \(+1.00000 q^{7}\) \(-5.28115 q^{8}\) \(-1.12406 q^{9}\) \(+3.37081 q^{10}\) \(-4.82681 q^{11}\) \(+5.66019 q^{12}\) \(-3.75983 q^{13}\) \(-2.47641 q^{14}\) \(-1.86433 q^{15}\) \(+4.81310 q^{16}\) \(-7.95365 q^{17}\) \(+2.78363 q^{18}\) \(+3.12881 q^{19}\) \(-5.62516 q^{20}\) \(+1.36965 q^{21}\) \(+11.9532 q^{22}\) \(-6.41972 q^{23}\) \(-7.23332 q^{24}\) \(-3.14721 q^{25}\) \(+9.31087 q^{26}\) \(-5.64852 q^{27}\) \(+4.13259 q^{28}\) \(+4.44520 q^{29}\) \(+4.61683 q^{30}\) \(+7.80206 q^{31}\) \(-1.35688 q^{32}\) \(-6.61104 q^{33}\) \(+19.6965 q^{34}\) \(-1.36117 q^{35}\) \(-4.64528 q^{36}\) \(-8.05339 q^{37}\) \(-7.74822 q^{38}\) \(-5.14965 q^{39}\) \(+7.18855 q^{40}\) \(-11.2949 q^{41}\) \(-3.39181 q^{42}\) \(+2.45552 q^{43}\) \(-19.9472 q^{44}\) \(+1.53004 q^{45}\) \(+15.8978 q^{46}\) \(+4.92588 q^{47}\) \(+6.59225 q^{48}\) \(+1.00000 q^{49}\) \(+7.79377 q^{50}\) \(-10.8937 q^{51}\) \(-15.5378 q^{52}\) \(-11.3662 q^{53}\) \(+13.9880 q^{54}\) \(+6.57012 q^{55}\) \(-5.28115 q^{56}\) \(+4.28538 q^{57}\) \(-11.0081 q^{58}\) \(+8.11169 q^{59}\) \(-7.70449 q^{60}\) \(+4.27979 q^{61}\) \(-19.3211 q^{62}\) \(-1.12406 q^{63}\) \(-6.26600 q^{64}\) \(+5.11778 q^{65}\) \(+16.3716 q^{66}\) \(-3.83017 q^{67}\) \(-32.8692 q^{68}\) \(-8.79276 q^{69}\) \(+3.37081 q^{70}\) \(-13.9578 q^{71}\) \(+5.93634 q^{72}\) \(+1.34885 q^{73}\) \(+19.9435 q^{74}\) \(-4.31057 q^{75}\) \(+12.9301 q^{76}\) \(-4.82681 q^{77}\) \(+12.7526 q^{78}\) \(+5.14082 q^{79}\) \(-6.55145 q^{80}\) \(-4.36430 q^{81}\) \(+27.9708 q^{82}\) \(+10.8767 q^{83}\) \(+5.66019 q^{84}\) \(+10.8263 q^{85}\) \(-6.08087 q^{86}\) \(+6.08837 q^{87}\) \(+25.4911 q^{88}\) \(+9.07796 q^{89}\) \(-3.78900 q^{90}\) \(-3.75983 q^{91}\) \(-26.5300 q^{92}\) \(+10.6861 q^{93}\) \(-12.1985 q^{94}\) \(-4.25886 q^{95}\) \(-1.85845 q^{96}\) \(-3.05324 q^{97}\) \(-2.47641 q^{98}\) \(+5.42564 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47641 −1.75108 −0.875542 0.483143i \(-0.839495\pi\)
−0.875542 + 0.483143i \(0.839495\pi\)
\(3\) 1.36965 0.790767 0.395384 0.918516i \(-0.370612\pi\)
0.395384 + 0.918516i \(0.370612\pi\)
\(4\) 4.13259 2.06629
\(5\) −1.36117 −0.608735 −0.304367 0.952555i \(-0.598445\pi\)
−0.304367 + 0.952555i \(0.598445\pi\)
\(6\) −3.39181 −1.38470
\(7\) 1.00000 0.377964
\(8\) −5.28115 −1.86717
\(9\) −1.12406 −0.374687
\(10\) 3.37081 1.06595
\(11\) −4.82681 −1.45534 −0.727670 0.685928i \(-0.759397\pi\)
−0.727670 + 0.685928i \(0.759397\pi\)
\(12\) 5.66019 1.63396
\(13\) −3.75983 −1.04279 −0.521395 0.853315i \(-0.674588\pi\)
−0.521395 + 0.853315i \(0.674588\pi\)
\(14\) −2.47641 −0.661847
\(15\) −1.86433 −0.481367
\(16\) 4.81310 1.20327
\(17\) −7.95365 −1.92904 −0.964522 0.264002i \(-0.914957\pi\)
−0.964522 + 0.264002i \(0.914957\pi\)
\(18\) 2.78363 0.656109
\(19\) 3.12881 0.717799 0.358900 0.933376i \(-0.383152\pi\)
0.358900 + 0.933376i \(0.383152\pi\)
\(20\) −5.62516 −1.25782
\(21\) 1.36965 0.298882
\(22\) 11.9532 2.54842
\(23\) −6.41972 −1.33860 −0.669302 0.742991i \(-0.733407\pi\)
−0.669302 + 0.742991i \(0.733407\pi\)
\(24\) −7.23332 −1.47650
\(25\) −3.14721 −0.629442
\(26\) 9.31087 1.82601
\(27\) −5.64852 −1.08706
\(28\) 4.13259 0.780985
\(29\) 4.44520 0.825454 0.412727 0.910855i \(-0.364576\pi\)
0.412727 + 0.910855i \(0.364576\pi\)
\(30\) 4.61683 0.842914
\(31\) 7.80206 1.40129 0.700646 0.713509i \(-0.252895\pi\)
0.700646 + 0.713509i \(0.252895\pi\)
\(32\) −1.35688 −0.239865
\(33\) −6.61104 −1.15083
\(34\) 19.6965 3.37792
\(35\) −1.36117 −0.230080
\(36\) −4.64528 −0.774214
\(37\) −8.05339 −1.32397 −0.661984 0.749518i \(-0.730285\pi\)
−0.661984 + 0.749518i \(0.730285\pi\)
\(38\) −7.74822 −1.25693
\(39\) −5.14965 −0.824604
\(40\) 7.18855 1.13661
\(41\) −11.2949 −1.76397 −0.881986 0.471275i \(-0.843794\pi\)
−0.881986 + 0.471275i \(0.843794\pi\)
\(42\) −3.39181 −0.523367
\(43\) 2.45552 0.374464 0.187232 0.982316i \(-0.440048\pi\)
0.187232 + 0.982316i \(0.440048\pi\)
\(44\) −19.9472 −3.00716
\(45\) 1.53004 0.228085
\(46\) 15.8978 2.34401
\(47\) 4.92588 0.718513 0.359257 0.933239i \(-0.383030\pi\)
0.359257 + 0.933239i \(0.383030\pi\)
\(48\) 6.59225 0.951510
\(49\) 1.00000 0.142857
\(50\) 7.79377 1.10221
\(51\) −10.8937 −1.52542
\(52\) −15.5378 −2.15471
\(53\) −11.3662 −1.56127 −0.780635 0.624988i \(-0.785104\pi\)
−0.780635 + 0.624988i \(0.785104\pi\)
\(54\) 13.9880 1.90353
\(55\) 6.57012 0.885915
\(56\) −5.28115 −0.705723
\(57\) 4.28538 0.567612
\(58\) −11.0081 −1.44544
\(59\) 8.11169 1.05605 0.528026 0.849228i \(-0.322932\pi\)
0.528026 + 0.849228i \(0.322932\pi\)
\(60\) −7.70449 −0.994646
\(61\) 4.27979 0.547971 0.273986 0.961734i \(-0.411658\pi\)
0.273986 + 0.961734i \(0.411658\pi\)
\(62\) −19.3211 −2.45378
\(63\) −1.12406 −0.141619
\(64\) −6.26600 −0.783250
\(65\) 5.11778 0.634783
\(66\) 16.3716 2.01521
\(67\) −3.83017 −0.467930 −0.233965 0.972245i \(-0.575170\pi\)
−0.233965 + 0.972245i \(0.575170\pi\)
\(68\) −32.8692 −3.98597
\(69\) −8.79276 −1.05852
\(70\) 3.37081 0.402889
\(71\) −13.9578 −1.65648 −0.828240 0.560373i \(-0.810658\pi\)
−0.828240 + 0.560373i \(0.810658\pi\)
\(72\) 5.93634 0.699604
\(73\) 1.34885 0.157871 0.0789355 0.996880i \(-0.474848\pi\)
0.0789355 + 0.996880i \(0.474848\pi\)
\(74\) 19.9435 2.31838
\(75\) −4.31057 −0.497742
\(76\) 12.9301 1.48318
\(77\) −4.82681 −0.550067
\(78\) 12.7526 1.44395
\(79\) 5.14082 0.578388 0.289194 0.957271i \(-0.406613\pi\)
0.289194 + 0.957271i \(0.406613\pi\)
\(80\) −6.55145 −0.732475
\(81\) −4.36430 −0.484922
\(82\) 27.9708 3.08886
\(83\) 10.8767 1.19388 0.596938 0.802288i \(-0.296384\pi\)
0.596938 + 0.802288i \(0.296384\pi\)
\(84\) 5.66019 0.617578
\(85\) 10.8263 1.17428
\(86\) −6.08087 −0.655717
\(87\) 6.08837 0.652742
\(88\) 25.4911 2.71736
\(89\) 9.07796 0.962262 0.481131 0.876649i \(-0.340226\pi\)
0.481131 + 0.876649i \(0.340226\pi\)
\(90\) −3.78900 −0.399396
\(91\) −3.75983 −0.394138
\(92\) −26.5300 −2.76595
\(93\) 10.6861 1.10810
\(94\) −12.1985 −1.25818
\(95\) −4.25886 −0.436949
\(96\) −1.85845 −0.189677
\(97\) −3.05324 −0.310009 −0.155005 0.987914i \(-0.549539\pi\)
−0.155005 + 0.987914i \(0.549539\pi\)
\(98\) −2.47641 −0.250155
\(99\) 5.42564 0.545297
\(100\) −13.0061 −1.30061
\(101\) 14.7297 1.46566 0.732830 0.680411i \(-0.238199\pi\)
0.732830 + 0.680411i \(0.238199\pi\)
\(102\) 26.9772 2.67115
\(103\) 1.07742 0.106162 0.0530808 0.998590i \(-0.483096\pi\)
0.0530808 + 0.998590i \(0.483096\pi\)
\(104\) 19.8562 1.94706
\(105\) −1.86433 −0.181940
\(106\) 28.1474 2.73391
\(107\) −17.4434 −1.68631 −0.843157 0.537668i \(-0.819305\pi\)
−0.843157 + 0.537668i \(0.819305\pi\)
\(108\) −23.3430 −2.24618
\(109\) 10.4483 1.00076 0.500382 0.865804i \(-0.333193\pi\)
0.500382 + 0.865804i \(0.333193\pi\)
\(110\) −16.2703 −1.55131
\(111\) −11.0303 −1.04695
\(112\) 4.81310 0.454795
\(113\) −4.60337 −0.433049 −0.216525 0.976277i \(-0.569472\pi\)
−0.216525 + 0.976277i \(0.569472\pi\)
\(114\) −10.6123 −0.993936
\(115\) 8.73834 0.814855
\(116\) 18.3702 1.70563
\(117\) 4.22629 0.390720
\(118\) −20.0878 −1.84924
\(119\) −7.95365 −0.729110
\(120\) 9.84579 0.898794
\(121\) 12.2981 1.11801
\(122\) −10.5985 −0.959544
\(123\) −15.4701 −1.39489
\(124\) 32.2427 2.89548
\(125\) 11.0898 0.991898
\(126\) 2.78363 0.247986
\(127\) −21.2790 −1.88821 −0.944103 0.329650i \(-0.893069\pi\)
−0.944103 + 0.329650i \(0.893069\pi\)
\(128\) 18.2309 1.61140
\(129\) 3.36320 0.296114
\(130\) −12.6737 −1.11156
\(131\) 6.16387 0.538540 0.269270 0.963065i \(-0.413218\pi\)
0.269270 + 0.963065i \(0.413218\pi\)
\(132\) −27.3207 −2.37796
\(133\) 3.12881 0.271303
\(134\) 9.48505 0.819384
\(135\) 7.68860 0.661730
\(136\) 42.0044 3.60185
\(137\) 7.65434 0.653954 0.326977 0.945032i \(-0.393970\pi\)
0.326977 + 0.945032i \(0.393970\pi\)
\(138\) 21.7744 1.85356
\(139\) 0.167412 0.0141997 0.00709983 0.999975i \(-0.497740\pi\)
0.00709983 + 0.999975i \(0.497740\pi\)
\(140\) −5.62516 −0.475413
\(141\) 6.74673 0.568177
\(142\) 34.5651 2.90064
\(143\) 18.1480 1.51761
\(144\) −5.41022 −0.450852
\(145\) −6.05069 −0.502482
\(146\) −3.34030 −0.276445
\(147\) 1.36965 0.112967
\(148\) −33.2813 −2.73571
\(149\) 22.7711 1.86548 0.932740 0.360550i \(-0.117411\pi\)
0.932740 + 0.360550i \(0.117411\pi\)
\(150\) 10.6747 0.871588
\(151\) −19.0935 −1.55381 −0.776905 0.629618i \(-0.783211\pi\)
−0.776905 + 0.629618i \(0.783211\pi\)
\(152\) −16.5237 −1.34025
\(153\) 8.94040 0.722788
\(154\) 11.9532 0.963212
\(155\) −10.6199 −0.853015
\(156\) −21.2814 −1.70387
\(157\) 7.22773 0.576836 0.288418 0.957505i \(-0.406871\pi\)
0.288418 + 0.957505i \(0.406871\pi\)
\(158\) −12.7308 −1.01281
\(159\) −15.5677 −1.23460
\(160\) 1.84695 0.146014
\(161\) −6.41972 −0.505945
\(162\) 10.8078 0.849139
\(163\) 0.0111351 0.000872170 0 0.000436085 1.00000i \(-0.499861\pi\)
0.000436085 1.00000i \(0.499861\pi\)
\(164\) −46.6773 −3.64488
\(165\) 8.99876 0.700553
\(166\) −26.9352 −2.09058
\(167\) −13.3635 −1.03410 −0.517048 0.855956i \(-0.672969\pi\)
−0.517048 + 0.855956i \(0.672969\pi\)
\(168\) −7.23332 −0.558063
\(169\) 1.13635 0.0874114
\(170\) −26.8103 −2.05626
\(171\) −3.51698 −0.268950
\(172\) 10.1477 0.773752
\(173\) 2.19027 0.166523 0.0832616 0.996528i \(-0.473466\pi\)
0.0832616 + 0.996528i \(0.473466\pi\)
\(174\) −15.0773 −1.14300
\(175\) −3.14721 −0.237907
\(176\) −23.2319 −1.75117
\(177\) 11.1102 0.835091
\(178\) −22.4807 −1.68500
\(179\) 11.3473 0.848133 0.424067 0.905631i \(-0.360602\pi\)
0.424067 + 0.905631i \(0.360602\pi\)
\(180\) 6.32303 0.471291
\(181\) 1.98524 0.147562 0.0737808 0.997274i \(-0.476493\pi\)
0.0737808 + 0.997274i \(0.476493\pi\)
\(182\) 9.31087 0.690168
\(183\) 5.86181 0.433318
\(184\) 33.9035 2.49940
\(185\) 10.9620 0.805946
\(186\) −26.4631 −1.94037
\(187\) 38.3908 2.80741
\(188\) 20.3566 1.48466
\(189\) −5.64852 −0.410869
\(190\) 10.5467 0.765135
\(191\) 16.8807 1.22144 0.610722 0.791845i \(-0.290879\pi\)
0.610722 + 0.791845i \(0.290879\pi\)
\(192\) −8.58222 −0.619369
\(193\) 19.1453 1.37811 0.689055 0.724709i \(-0.258026\pi\)
0.689055 + 0.724709i \(0.258026\pi\)
\(194\) 7.56105 0.542852
\(195\) 7.00956 0.501965
\(196\) 4.13259 0.295185
\(197\) 2.51493 0.179181 0.0895905 0.995979i \(-0.471444\pi\)
0.0895905 + 0.995979i \(0.471444\pi\)
\(198\) −13.4361 −0.954861
\(199\) 13.2545 0.939585 0.469793 0.882777i \(-0.344329\pi\)
0.469793 + 0.882777i \(0.344329\pi\)
\(200\) 16.6209 1.17527
\(201\) −5.24599 −0.370023
\(202\) −36.4767 −2.56649
\(203\) 4.44520 0.311992
\(204\) −45.0192 −3.15197
\(205\) 15.3744 1.07379
\(206\) −2.66814 −0.185898
\(207\) 7.21616 0.501558
\(208\) −18.0964 −1.25476
\(209\) −15.1022 −1.04464
\(210\) 4.61683 0.318592
\(211\) 17.0722 1.17530 0.587649 0.809116i \(-0.300054\pi\)
0.587649 + 0.809116i \(0.300054\pi\)
\(212\) −46.9719 −3.22604
\(213\) −19.1172 −1.30989
\(214\) 43.1968 2.95288
\(215\) −3.34239 −0.227949
\(216\) 29.8307 2.02972
\(217\) 7.80206 0.529638
\(218\) −25.8742 −1.75242
\(219\) 1.84745 0.124839
\(220\) 27.1516 1.83056
\(221\) 29.9044 2.01159
\(222\) 27.3155 1.83330
\(223\) −0.411557 −0.0275599 −0.0137800 0.999905i \(-0.504386\pi\)
−0.0137800 + 0.999905i \(0.504386\pi\)
\(224\) −1.35688 −0.0906605
\(225\) 3.53766 0.235844
\(226\) 11.3998 0.758305
\(227\) 20.4070 1.35446 0.677231 0.735770i \(-0.263180\pi\)
0.677231 + 0.735770i \(0.263180\pi\)
\(228\) 17.7097 1.17285
\(229\) −26.1155 −1.72576 −0.862881 0.505407i \(-0.831342\pi\)
−0.862881 + 0.505407i \(0.831342\pi\)
\(230\) −21.6397 −1.42688
\(231\) −6.61104 −0.434975
\(232\) −23.4758 −1.54126
\(233\) 4.09124 0.268026 0.134013 0.990980i \(-0.457214\pi\)
0.134013 + 0.990980i \(0.457214\pi\)
\(234\) −10.4660 −0.684184
\(235\) −6.70497 −0.437384
\(236\) 33.5223 2.18211
\(237\) 7.04112 0.457370
\(238\) 19.6965 1.27673
\(239\) −27.6539 −1.78878 −0.894391 0.447285i \(-0.852391\pi\)
−0.894391 + 0.447285i \(0.852391\pi\)
\(240\) −8.97319 −0.579217
\(241\) −14.8975 −0.959629 −0.479815 0.877370i \(-0.659296\pi\)
−0.479815 + 0.877370i \(0.659296\pi\)
\(242\) −30.4552 −1.95773
\(243\) 10.9680 0.703597
\(244\) 17.6866 1.13227
\(245\) −1.36117 −0.0869621
\(246\) 38.3102 2.44257
\(247\) −11.7638 −0.748514
\(248\) −41.2038 −2.61645
\(249\) 14.8973 0.944077
\(250\) −27.4627 −1.73690
\(251\) −10.6543 −0.672490 −0.336245 0.941774i \(-0.609157\pi\)
−0.336245 + 0.941774i \(0.609157\pi\)
\(252\) −4.64528 −0.292625
\(253\) 30.9868 1.94812
\(254\) 52.6955 3.30641
\(255\) 14.8282 0.928579
\(256\) −32.6152 −2.03845
\(257\) 18.9727 1.18348 0.591741 0.806128i \(-0.298441\pi\)
0.591741 + 0.806128i \(0.298441\pi\)
\(258\) −8.32866 −0.518519
\(259\) −8.05339 −0.500413
\(260\) 21.1497 1.31165
\(261\) −4.99668 −0.309287
\(262\) −15.2642 −0.943028
\(263\) −10.6016 −0.653721 −0.326861 0.945073i \(-0.605991\pi\)
−0.326861 + 0.945073i \(0.605991\pi\)
\(264\) 34.9139 2.14880
\(265\) 15.4714 0.950399
\(266\) −7.74822 −0.475074
\(267\) 12.4336 0.760925
\(268\) −15.8285 −0.966880
\(269\) −13.3866 −0.816193 −0.408097 0.912939i \(-0.633807\pi\)
−0.408097 + 0.912939i \(0.633807\pi\)
\(270\) −19.0401 −1.15874
\(271\) −2.05389 −0.124765 −0.0623825 0.998052i \(-0.519870\pi\)
−0.0623825 + 0.998052i \(0.519870\pi\)
\(272\) −38.2817 −2.32117
\(273\) −5.14965 −0.311671
\(274\) −18.9552 −1.14513
\(275\) 15.1910 0.916052
\(276\) −36.3368 −2.18722
\(277\) −20.8842 −1.25481 −0.627404 0.778694i \(-0.715883\pi\)
−0.627404 + 0.778694i \(0.715883\pi\)
\(278\) −0.414579 −0.0248648
\(279\) −8.77000 −0.525046
\(280\) 7.18855 0.429598
\(281\) −22.9131 −1.36688 −0.683439 0.730007i \(-0.739517\pi\)
−0.683439 + 0.730007i \(0.739517\pi\)
\(282\) −16.7076 −0.994925
\(283\) −9.87834 −0.587207 −0.293603 0.955927i \(-0.594854\pi\)
−0.293603 + 0.955927i \(0.594854\pi\)
\(284\) −57.6816 −3.42277
\(285\) −5.83314 −0.345525
\(286\) −44.9419 −2.65747
\(287\) −11.2949 −0.666719
\(288\) 1.52522 0.0898744
\(289\) 46.2606 2.72121
\(290\) 14.9840 0.879888
\(291\) −4.18186 −0.245145
\(292\) 5.57424 0.326208
\(293\) −22.2757 −1.30136 −0.650681 0.759351i \(-0.725517\pi\)
−0.650681 + 0.759351i \(0.725517\pi\)
\(294\) −3.39181 −0.197814
\(295\) −11.0414 −0.642855
\(296\) 42.5311 2.47207
\(297\) 27.2643 1.58204
\(298\) −56.3905 −3.26661
\(299\) 24.1371 1.39588
\(300\) −17.8138 −1.02848
\(301\) 2.45552 0.141534
\(302\) 47.2833 2.72085
\(303\) 20.1745 1.15900
\(304\) 15.0593 0.863709
\(305\) −5.82554 −0.333569
\(306\) −22.1401 −1.26566
\(307\) −1.62188 −0.0925658 −0.0462829 0.998928i \(-0.514738\pi\)
−0.0462829 + 0.998928i \(0.514738\pi\)
\(308\) −19.9472 −1.13660
\(309\) 1.47569 0.0839491
\(310\) 26.2993 1.49370
\(311\) −21.0344 −1.19275 −0.596377 0.802705i \(-0.703394\pi\)
−0.596377 + 0.802705i \(0.703394\pi\)
\(312\) 27.1961 1.53967
\(313\) 32.0980 1.81429 0.907144 0.420820i \(-0.138258\pi\)
0.907144 + 0.420820i \(0.138258\pi\)
\(314\) −17.8988 −1.01009
\(315\) 1.53004 0.0862081
\(316\) 21.2449 1.19512
\(317\) 10.5692 0.593627 0.296813 0.954935i \(-0.404076\pi\)
0.296813 + 0.954935i \(0.404076\pi\)
\(318\) 38.5520 2.16189
\(319\) −21.4562 −1.20132
\(320\) 8.52911 0.476792
\(321\) −23.8913 −1.33348
\(322\) 15.8978 0.885951
\(323\) −24.8855 −1.38467
\(324\) −18.0358 −1.00199
\(325\) 11.8330 0.656376
\(326\) −0.0275751 −0.00152724
\(327\) 14.3105 0.791372
\(328\) 59.6502 3.29363
\(329\) 4.92588 0.271573
\(330\) −22.2846 −1.22673
\(331\) −12.7553 −0.701097 −0.350548 0.936545i \(-0.614005\pi\)
−0.350548 + 0.936545i \(0.614005\pi\)
\(332\) 44.9490 2.46690
\(333\) 9.05251 0.496074
\(334\) 33.0934 1.81079
\(335\) 5.21352 0.284845
\(336\) 6.59225 0.359637
\(337\) −7.69435 −0.419138 −0.209569 0.977794i \(-0.567206\pi\)
−0.209569 + 0.977794i \(0.567206\pi\)
\(338\) −2.81406 −0.153065
\(339\) −6.30501 −0.342441
\(340\) 44.7406 2.42640
\(341\) −37.6591 −2.03935
\(342\) 8.70947 0.470954
\(343\) 1.00000 0.0539949
\(344\) −12.9680 −0.699187
\(345\) 11.9685 0.644360
\(346\) −5.42400 −0.291596
\(347\) 30.7882 1.65280 0.826400 0.563084i \(-0.190385\pi\)
0.826400 + 0.563084i \(0.190385\pi\)
\(348\) 25.1607 1.34876
\(349\) 33.9862 1.81924 0.909619 0.415444i \(-0.136374\pi\)
0.909619 + 0.415444i \(0.136374\pi\)
\(350\) 7.79377 0.416595
\(351\) 21.2375 1.13357
\(352\) 6.54942 0.349085
\(353\) 19.0638 1.01467 0.507333 0.861750i \(-0.330631\pi\)
0.507333 + 0.861750i \(0.330631\pi\)
\(354\) −27.5133 −1.46231
\(355\) 18.9989 1.00836
\(356\) 37.5155 1.98832
\(357\) −10.8937 −0.576556
\(358\) −28.1004 −1.48515
\(359\) 11.3040 0.596601 0.298300 0.954472i \(-0.403580\pi\)
0.298300 + 0.954472i \(0.403580\pi\)
\(360\) −8.08038 −0.425873
\(361\) −9.21052 −0.484764
\(362\) −4.91626 −0.258393
\(363\) 16.8441 0.884087
\(364\) −15.5378 −0.814404
\(365\) −1.83602 −0.0961016
\(366\) −14.5162 −0.758776
\(367\) −18.0988 −0.944751 −0.472375 0.881397i \(-0.656603\pi\)
−0.472375 + 0.881397i \(0.656603\pi\)
\(368\) −30.8987 −1.61071
\(369\) 12.6962 0.660938
\(370\) −27.1465 −1.41128
\(371\) −11.3662 −0.590104
\(372\) 44.1612 2.28965
\(373\) −3.56325 −0.184498 −0.0922491 0.995736i \(-0.529406\pi\)
−0.0922491 + 0.995736i \(0.529406\pi\)
\(374\) −95.0712 −4.91602
\(375\) 15.1891 0.784360
\(376\) −26.0143 −1.34159
\(377\) −16.7132 −0.860775
\(378\) 13.9880 0.719466
\(379\) 14.8926 0.764982 0.382491 0.923959i \(-0.375066\pi\)
0.382491 + 0.923959i \(0.375066\pi\)
\(380\) −17.6001 −0.902865
\(381\) −29.1448 −1.49313
\(382\) −41.8035 −2.13885
\(383\) −16.5812 −0.847260 −0.423630 0.905835i \(-0.639244\pi\)
−0.423630 + 0.905835i \(0.639244\pi\)
\(384\) 24.9700 1.27424
\(385\) 6.57012 0.334845
\(386\) −47.4116 −2.41319
\(387\) −2.76016 −0.140307
\(388\) −12.6178 −0.640570
\(389\) −21.7981 −1.10521 −0.552603 0.833445i \(-0.686365\pi\)
−0.552603 + 0.833445i \(0.686365\pi\)
\(390\) −17.3585 −0.878983
\(391\) 51.0602 2.58223
\(392\) −5.28115 −0.266738
\(393\) 8.44234 0.425860
\(394\) −6.22798 −0.313761
\(395\) −6.99755 −0.352085
\(396\) 22.4219 1.12674
\(397\) −24.8261 −1.24599 −0.622994 0.782226i \(-0.714084\pi\)
−0.622994 + 0.782226i \(0.714084\pi\)
\(398\) −32.8235 −1.64529
\(399\) 4.28538 0.214537
\(400\) −15.1478 −0.757391
\(401\) −15.6648 −0.782262 −0.391131 0.920335i \(-0.627916\pi\)
−0.391131 + 0.920335i \(0.627916\pi\)
\(402\) 12.9912 0.647942
\(403\) −29.3345 −1.46125
\(404\) 60.8718 3.02848
\(405\) 5.94056 0.295189
\(406\) −11.0081 −0.546324
\(407\) 38.8722 1.92682
\(408\) 57.5313 2.84822
\(409\) −13.3397 −0.659603 −0.329802 0.944050i \(-0.606982\pi\)
−0.329802 + 0.944050i \(0.606982\pi\)
\(410\) −38.0731 −1.88030
\(411\) 10.4838 0.517126
\(412\) 4.45254 0.219361
\(413\) 8.11169 0.399150
\(414\) −17.8701 −0.878270
\(415\) −14.8051 −0.726753
\(416\) 5.10165 0.250129
\(417\) 0.229295 0.0112286
\(418\) 37.3992 1.82925
\(419\) −3.53788 −0.172837 −0.0864184 0.996259i \(-0.527542\pi\)
−0.0864184 + 0.996259i \(0.527542\pi\)
\(420\) −7.70449 −0.375941
\(421\) −9.69546 −0.472528 −0.236264 0.971689i \(-0.575923\pi\)
−0.236264 + 0.971689i \(0.575923\pi\)
\(422\) −42.2777 −2.05804
\(423\) −5.53700 −0.269218
\(424\) 60.0267 2.91515
\(425\) 25.0318 1.21422
\(426\) 47.3420 2.29373
\(427\) 4.27979 0.207114
\(428\) −72.0862 −3.48442
\(429\) 24.8564 1.20008
\(430\) 8.27711 0.399158
\(431\) −3.83078 −0.184522 −0.0922610 0.995735i \(-0.529409\pi\)
−0.0922610 + 0.995735i \(0.529409\pi\)
\(432\) −27.1869 −1.30803
\(433\) −0.324199 −0.0155800 −0.00779001 0.999970i \(-0.502480\pi\)
−0.00779001 + 0.999970i \(0.502480\pi\)
\(434\) −19.3211 −0.927441
\(435\) −8.28732 −0.397346
\(436\) 43.1785 2.06787
\(437\) −20.0861 −0.960849
\(438\) −4.57504 −0.218604
\(439\) 8.19796 0.391267 0.195634 0.980677i \(-0.437324\pi\)
0.195634 + 0.980677i \(0.437324\pi\)
\(440\) −34.6978 −1.65415
\(441\) −1.12406 −0.0535268
\(442\) −74.0555 −3.52246
\(443\) −18.3580 −0.872215 −0.436107 0.899895i \(-0.643643\pi\)
−0.436107 + 0.899895i \(0.643643\pi\)
\(444\) −45.5837 −2.16331
\(445\) −12.3567 −0.585762
\(446\) 1.01918 0.0482597
\(447\) 31.1884 1.47516
\(448\) −6.26600 −0.296041
\(449\) 1.88116 0.0887775 0.0443888 0.999014i \(-0.485866\pi\)
0.0443888 + 0.999014i \(0.485866\pi\)
\(450\) −8.76068 −0.412983
\(451\) 54.5186 2.56718
\(452\) −19.0238 −0.894806
\(453\) −26.1514 −1.22870
\(454\) −50.5361 −2.37178
\(455\) 5.11778 0.239925
\(456\) −22.6317 −1.05983
\(457\) −27.0356 −1.26467 −0.632335 0.774695i \(-0.717904\pi\)
−0.632335 + 0.774695i \(0.717904\pi\)
\(458\) 64.6726 3.02195
\(459\) 44.9263 2.09698
\(460\) 36.1119 1.68373
\(461\) −28.7063 −1.33699 −0.668494 0.743718i \(-0.733061\pi\)
−0.668494 + 0.743718i \(0.733061\pi\)
\(462\) 16.3716 0.761677
\(463\) −26.1908 −1.21719 −0.608594 0.793482i \(-0.708266\pi\)
−0.608594 + 0.793482i \(0.708266\pi\)
\(464\) 21.3952 0.993247
\(465\) −14.5456 −0.674536
\(466\) −10.1316 −0.469336
\(467\) −14.0623 −0.650724 −0.325362 0.945590i \(-0.605486\pi\)
−0.325362 + 0.945590i \(0.605486\pi\)
\(468\) 17.4655 0.807343
\(469\) −3.83017 −0.176861
\(470\) 16.6042 0.765896
\(471\) 9.89946 0.456143
\(472\) −42.8390 −1.97183
\(473\) −11.8523 −0.544972
\(474\) −17.4367 −0.800893
\(475\) −9.84704 −0.451813
\(476\) −32.8692 −1.50656
\(477\) 12.7763 0.584988
\(478\) 68.4823 3.13231
\(479\) −9.09674 −0.415641 −0.207820 0.978167i \(-0.566637\pi\)
−0.207820 + 0.978167i \(0.566637\pi\)
\(480\) 2.52967 0.115463
\(481\) 30.2794 1.38062
\(482\) 36.8921 1.68039
\(483\) −8.79276 −0.400084
\(484\) 50.8231 2.31014
\(485\) 4.15598 0.188713
\(486\) −27.1612 −1.23206
\(487\) 32.8239 1.48739 0.743696 0.668518i \(-0.233071\pi\)
0.743696 + 0.668518i \(0.233071\pi\)
\(488\) −22.6022 −1.02315
\(489\) 0.0152512 0.000689683 0
\(490\) 3.37081 0.152278
\(491\) −8.93039 −0.403023 −0.201511 0.979486i \(-0.564585\pi\)
−0.201511 + 0.979486i \(0.564585\pi\)
\(492\) −63.9315 −2.88225
\(493\) −35.3556 −1.59234
\(494\) 29.1320 1.31071
\(495\) −7.38523 −0.331941
\(496\) 37.5521 1.68614
\(497\) −13.9578 −0.626091
\(498\) −36.8917 −1.65316
\(499\) 12.7399 0.570318 0.285159 0.958480i \(-0.407954\pi\)
0.285159 + 0.958480i \(0.407954\pi\)
\(500\) 45.8294 2.04955
\(501\) −18.3033 −0.817729
\(502\) 26.3842 1.17759
\(503\) −1.92167 −0.0856832 −0.0428416 0.999082i \(-0.513641\pi\)
−0.0428416 + 0.999082i \(0.513641\pi\)
\(504\) 5.93634 0.264426
\(505\) −20.0497 −0.892199
\(506\) −76.7359 −3.41133
\(507\) 1.55640 0.0691221
\(508\) −87.9373 −3.90159
\(509\) 20.0363 0.888092 0.444046 0.896004i \(-0.353543\pi\)
0.444046 + 0.896004i \(0.353543\pi\)
\(510\) −36.7207 −1.62602
\(511\) 1.34885 0.0596696
\(512\) 44.3066 1.95809
\(513\) −17.6732 −0.780289
\(514\) −46.9840 −2.07238
\(515\) −1.46656 −0.0646243
\(516\) 13.8987 0.611857
\(517\) −23.7763 −1.04568
\(518\) 19.9435 0.876265
\(519\) 2.99990 0.131681
\(520\) −27.0278 −1.18525
\(521\) −9.10947 −0.399093 −0.199547 0.979888i \(-0.563947\pi\)
−0.199547 + 0.979888i \(0.563947\pi\)
\(522\) 12.3738 0.541587
\(523\) 8.05802 0.352352 0.176176 0.984359i \(-0.443627\pi\)
0.176176 + 0.984359i \(0.443627\pi\)
\(524\) 25.4727 1.11278
\(525\) −4.31057 −0.188129
\(526\) 26.2538 1.14472
\(527\) −62.0549 −2.70315
\(528\) −31.8196 −1.38477
\(529\) 18.2128 0.791860
\(530\) −38.3134 −1.66423
\(531\) −9.11804 −0.395689
\(532\) 12.9301 0.560591
\(533\) 42.4671 1.83945
\(534\) −30.7907 −1.33244
\(535\) 23.7434 1.02652
\(536\) 20.2277 0.873703
\(537\) 15.5417 0.670676
\(538\) 33.1506 1.42922
\(539\) −4.82681 −0.207906
\(540\) 31.7738 1.36733
\(541\) −9.61212 −0.413257 −0.206629 0.978419i \(-0.566249\pi\)
−0.206629 + 0.978419i \(0.566249\pi\)
\(542\) 5.08627 0.218474
\(543\) 2.71908 0.116687
\(544\) 10.7922 0.462710
\(545\) −14.2219 −0.609200
\(546\) 12.7526 0.545762
\(547\) −40.6353 −1.73744 −0.868721 0.495302i \(-0.835057\pi\)
−0.868721 + 0.495302i \(0.835057\pi\)
\(548\) 31.6322 1.35126
\(549\) −4.81075 −0.205318
\(550\) −37.6191 −1.60408
\(551\) 13.9082 0.592510
\(552\) 46.4359 1.97644
\(553\) 5.14082 0.218610
\(554\) 51.7177 2.19727
\(555\) 15.0142 0.637315
\(556\) 0.691843 0.0293407
\(557\) −35.3734 −1.49882 −0.749410 0.662107i \(-0.769663\pi\)
−0.749410 + 0.662107i \(0.769663\pi\)
\(558\) 21.7181 0.919400
\(559\) −9.23235 −0.390487
\(560\) −6.55145 −0.276849
\(561\) 52.5819 2.22001
\(562\) 56.7420 2.39352
\(563\) 13.1714 0.555108 0.277554 0.960710i \(-0.410476\pi\)
0.277554 + 0.960710i \(0.410476\pi\)
\(564\) 27.8814 1.17402
\(565\) 6.26599 0.263612
\(566\) 24.4628 1.02825
\(567\) −4.36430 −0.183283
\(568\) 73.7130 3.09293
\(569\) 7.00486 0.293659 0.146830 0.989162i \(-0.453093\pi\)
0.146830 + 0.989162i \(0.453093\pi\)
\(570\) 14.4452 0.605043
\(571\) −12.5623 −0.525715 −0.262857 0.964835i \(-0.584665\pi\)
−0.262857 + 0.964835i \(0.584665\pi\)
\(572\) 74.9983 3.13583
\(573\) 23.1206 0.965878
\(574\) 27.9708 1.16748
\(575\) 20.2042 0.842574
\(576\) 7.04338 0.293474
\(577\) 27.8537 1.15957 0.579783 0.814771i \(-0.303137\pi\)
0.579783 + 0.814771i \(0.303137\pi\)
\(578\) −114.560 −4.76507
\(579\) 26.2224 1.08976
\(580\) −25.0050 −1.03828
\(581\) 10.8767 0.451242
\(582\) 10.3560 0.429269
\(583\) 54.8626 2.27218
\(584\) −7.12348 −0.294772
\(585\) −5.75270 −0.237845
\(586\) 55.1638 2.27879
\(587\) 26.0642 1.07579 0.537893 0.843013i \(-0.319220\pi\)
0.537893 + 0.843013i \(0.319220\pi\)
\(588\) 5.66019 0.233422
\(589\) 24.4112 1.00585
\(590\) 27.3430 1.12569
\(591\) 3.44456 0.141690
\(592\) −38.7617 −1.59310
\(593\) −1.52694 −0.0627037 −0.0313519 0.999508i \(-0.509981\pi\)
−0.0313519 + 0.999508i \(0.509981\pi\)
\(594\) −67.5176 −2.77028
\(595\) 10.8263 0.443835
\(596\) 94.1035 3.85463
\(597\) 18.1540 0.742993
\(598\) −59.7732 −2.44431
\(599\) 13.9309 0.569202 0.284601 0.958646i \(-0.408139\pi\)
0.284601 + 0.958646i \(0.408139\pi\)
\(600\) 22.7648 0.929368
\(601\) −18.4665 −0.753264 −0.376632 0.926363i \(-0.622918\pi\)
−0.376632 + 0.926363i \(0.622918\pi\)
\(602\) −6.08087 −0.247838
\(603\) 4.30535 0.175327
\(604\) −78.9057 −3.21063
\(605\) −16.7399 −0.680573
\(606\) −49.9603 −2.02950
\(607\) −6.98184 −0.283384 −0.141692 0.989911i \(-0.545254\pi\)
−0.141692 + 0.989911i \(0.545254\pi\)
\(608\) −4.24543 −0.172175
\(609\) 6.08837 0.246713
\(610\) 14.4264 0.584107
\(611\) −18.5205 −0.749259
\(612\) 36.9470 1.49349
\(613\) 18.1030 0.731174 0.365587 0.930777i \(-0.380868\pi\)
0.365587 + 0.930777i \(0.380868\pi\)
\(614\) 4.01644 0.162090
\(615\) 21.0575 0.849119
\(616\) 25.4911 1.02707
\(617\) 47.0623 1.89465 0.947327 0.320267i \(-0.103773\pi\)
0.947327 + 0.320267i \(0.103773\pi\)
\(618\) −3.65441 −0.147002
\(619\) −8.30274 −0.333715 −0.166858 0.985981i \(-0.553362\pi\)
−0.166858 + 0.985981i \(0.553362\pi\)
\(620\) −43.8878 −1.76258
\(621\) 36.2619 1.45514
\(622\) 52.0898 2.08861
\(623\) 9.07796 0.363701
\(624\) −24.7858 −0.992225
\(625\) 0.640988 0.0256395
\(626\) −79.4878 −3.17697
\(627\) −20.6847 −0.826068
\(628\) 29.8692 1.19191
\(629\) 64.0538 2.55399
\(630\) −3.78900 −0.150958
\(631\) 0.859319 0.0342090 0.0171045 0.999854i \(-0.494555\pi\)
0.0171045 + 0.999854i \(0.494555\pi\)
\(632\) −27.1495 −1.07995
\(633\) 23.3829 0.929387
\(634\) −26.1737 −1.03949
\(635\) 28.9644 1.14942
\(636\) −64.3349 −2.55105
\(637\) −3.75983 −0.148970
\(638\) 53.1342 2.10360
\(639\) 15.6894 0.620662
\(640\) −24.8154 −0.980916
\(641\) −31.5811 −1.24738 −0.623690 0.781672i \(-0.714367\pi\)
−0.623690 + 0.781672i \(0.714367\pi\)
\(642\) 59.1645 2.33504
\(643\) −31.3747 −1.23730 −0.618649 0.785667i \(-0.712320\pi\)
−0.618649 + 0.785667i \(0.712320\pi\)
\(644\) −26.5300 −1.04543
\(645\) −4.57790 −0.180255
\(646\) 61.6266 2.42467
\(647\) 22.9234 0.901213 0.450607 0.892723i \(-0.351208\pi\)
0.450607 + 0.892723i \(0.351208\pi\)
\(648\) 23.0485 0.905431
\(649\) −39.1536 −1.53691
\(650\) −29.3033 −1.14937
\(651\) 10.6861 0.418821
\(652\) 0.0460168 0.00180216
\(653\) 30.4719 1.19246 0.596228 0.802815i \(-0.296665\pi\)
0.596228 + 0.802815i \(0.296665\pi\)
\(654\) −35.4386 −1.38576
\(655\) −8.39009 −0.327828
\(656\) −54.3636 −2.12254
\(657\) −1.51619 −0.0591523
\(658\) −12.1985 −0.475546
\(659\) 12.8567 0.500827 0.250413 0.968139i \(-0.419433\pi\)
0.250413 + 0.968139i \(0.419433\pi\)
\(660\) 37.1882 1.44755
\(661\) 10.4601 0.406850 0.203425 0.979091i \(-0.434793\pi\)
0.203425 + 0.979091i \(0.434793\pi\)
\(662\) 31.5874 1.22768
\(663\) 40.9585 1.59070
\(664\) −57.4416 −2.22917
\(665\) −4.25886 −0.165151
\(666\) −22.4177 −0.868667
\(667\) −28.5370 −1.10496
\(668\) −55.2257 −2.13675
\(669\) −0.563689 −0.0217935
\(670\) −12.9108 −0.498787
\(671\) −20.6578 −0.797484
\(672\) −1.85845 −0.0716913
\(673\) 35.9617 1.38622 0.693111 0.720831i \(-0.256240\pi\)
0.693111 + 0.720831i \(0.256240\pi\)
\(674\) 19.0543 0.733946
\(675\) 17.7771 0.684240
\(676\) 4.69606 0.180618
\(677\) −8.64518 −0.332261 −0.166131 0.986104i \(-0.553127\pi\)
−0.166131 + 0.986104i \(0.553127\pi\)
\(678\) 15.6138 0.599643
\(679\) −3.05324 −0.117172
\(680\) −57.1752 −2.19257
\(681\) 27.9505 1.07106
\(682\) 93.2592 3.57108
\(683\) −21.4482 −0.820691 −0.410346 0.911930i \(-0.634592\pi\)
−0.410346 + 0.911930i \(0.634592\pi\)
\(684\) −14.5342 −0.555730
\(685\) −10.4189 −0.398085
\(686\) −2.47641 −0.0945496
\(687\) −35.7691 −1.36468
\(688\) 11.8187 0.450582
\(689\) 42.7351 1.62808
\(690\) −29.6388 −1.12833
\(691\) −10.0322 −0.381643 −0.190821 0.981625i \(-0.561115\pi\)
−0.190821 + 0.981625i \(0.561115\pi\)
\(692\) 9.05148 0.344086
\(693\) 5.42564 0.206103
\(694\) −76.2442 −2.89419
\(695\) −0.227876 −0.00864383
\(696\) −32.1536 −1.21878
\(697\) 89.8360 3.40278
\(698\) −84.1635 −3.18564
\(699\) 5.60356 0.211946
\(700\) −13.0061 −0.491585
\(701\) 24.9626 0.942826 0.471413 0.881913i \(-0.343744\pi\)
0.471413 + 0.881913i \(0.343744\pi\)
\(702\) −52.5926 −1.98498
\(703\) −25.1976 −0.950344
\(704\) 30.2448 1.13989
\(705\) −9.18346 −0.345869
\(706\) −47.2098 −1.77676
\(707\) 14.7297 0.553968
\(708\) 45.9137 1.72554
\(709\) 12.8574 0.482871 0.241435 0.970417i \(-0.422382\pi\)
0.241435 + 0.970417i \(0.422382\pi\)
\(710\) −47.0490 −1.76572
\(711\) −5.77861 −0.216715
\(712\) −47.9421 −1.79670
\(713\) −50.0870 −1.87577
\(714\) 26.9772 1.00960
\(715\) −24.7026 −0.923824
\(716\) 46.8935 1.75249
\(717\) −37.8761 −1.41451
\(718\) −27.9932 −1.04470
\(719\) 49.4280 1.84335 0.921677 0.387958i \(-0.126820\pi\)
0.921677 + 0.387958i \(0.126820\pi\)
\(720\) 7.36424 0.274449
\(721\) 1.07742 0.0401253
\(722\) 22.8090 0.848862
\(723\) −20.4043 −0.758843
\(724\) 8.20417 0.304906
\(725\) −13.9900 −0.519575
\(726\) −41.7129 −1.54811
\(727\) −3.07735 −0.114133 −0.0570664 0.998370i \(-0.518175\pi\)
−0.0570664 + 0.998370i \(0.518175\pi\)
\(728\) 19.8562 0.735921
\(729\) 28.1152 1.04130
\(730\) 4.54672 0.168282
\(731\) −19.5304 −0.722357
\(732\) 24.2245 0.895362
\(733\) 51.2910 1.89448 0.947238 0.320530i \(-0.103861\pi\)
0.947238 + 0.320530i \(0.103861\pi\)
\(734\) 44.8200 1.65434
\(735\) −1.86433 −0.0687668
\(736\) 8.71080 0.321084
\(737\) 18.4875 0.680996
\(738\) −31.4410 −1.15736
\(739\) 7.86046 0.289152 0.144576 0.989494i \(-0.453818\pi\)
0.144576 + 0.989494i \(0.453818\pi\)
\(740\) 45.3016 1.66532
\(741\) −16.1123 −0.591900
\(742\) 28.1474 1.03332
\(743\) 20.1813 0.740378 0.370189 0.928956i \(-0.379293\pi\)
0.370189 + 0.928956i \(0.379293\pi\)
\(744\) −56.4348 −2.06900
\(745\) −30.9954 −1.13558
\(746\) 8.82406 0.323072
\(747\) −12.2261 −0.447330
\(748\) 158.653 5.80094
\(749\) −17.4434 −0.637366
\(750\) −37.6143 −1.37348
\(751\) 24.8078 0.905251 0.452625 0.891701i \(-0.350488\pi\)
0.452625 + 0.891701i \(0.350488\pi\)
\(752\) 23.7087 0.864569
\(753\) −14.5926 −0.531783
\(754\) 41.3887 1.50729
\(755\) 25.9896 0.945858
\(756\) −23.3430 −0.848976
\(757\) 37.1368 1.34976 0.674880 0.737927i \(-0.264195\pi\)
0.674880 + 0.737927i \(0.264195\pi\)
\(758\) −36.8802 −1.33955
\(759\) 42.4410 1.54051
\(760\) 22.4916 0.815858
\(761\) 9.51244 0.344826 0.172413 0.985025i \(-0.444844\pi\)
0.172413 + 0.985025i \(0.444844\pi\)
\(762\) 72.1743 2.61460
\(763\) 10.4483 0.378254
\(764\) 69.7609 2.52386
\(765\) −12.1694 −0.439986
\(766\) 41.0618 1.48362
\(767\) −30.4986 −1.10124
\(768\) −44.6713 −1.61194
\(769\) 9.78969 0.353025 0.176513 0.984298i \(-0.443518\pi\)
0.176513 + 0.984298i \(0.443518\pi\)
\(770\) −16.2703 −0.586341
\(771\) 25.9859 0.935859
\(772\) 79.1197 2.84758
\(773\) 18.4164 0.662391 0.331196 0.943562i \(-0.392548\pi\)
0.331196 + 0.943562i \(0.392548\pi\)
\(774\) 6.83527 0.245689
\(775\) −24.5547 −0.882032
\(776\) 16.1246 0.578839
\(777\) −11.0303 −0.395710
\(778\) 53.9809 1.93531
\(779\) −35.3398 −1.26618
\(780\) 28.9676 1.03721
\(781\) 67.3715 2.41074
\(782\) −126.446 −4.52169
\(783\) −25.1088 −0.897316
\(784\) 4.81310 0.171896
\(785\) −9.83819 −0.351140
\(786\) −20.9067 −0.745716
\(787\) −47.8941 −1.70724 −0.853621 0.520895i \(-0.825598\pi\)
−0.853621 + 0.520895i \(0.825598\pi\)
\(788\) 10.3931 0.370240
\(789\) −14.5204 −0.516941
\(790\) 17.3288 0.616530
\(791\) −4.60337 −0.163677
\(792\) −28.6536 −1.01816
\(793\) −16.0913 −0.571419
\(794\) 61.4796 2.18183
\(795\) 21.1903 0.751544
\(796\) 54.7753 1.94146
\(797\) 42.9621 1.52180 0.760899 0.648871i \(-0.224758\pi\)
0.760899 + 0.648871i \(0.224758\pi\)
\(798\) −10.6123 −0.375673
\(799\) −39.1787 −1.38604
\(800\) 4.27039 0.150981
\(801\) −10.2042 −0.360547
\(802\) 38.7924 1.36981
\(803\) −6.51065 −0.229756
\(804\) −21.6795 −0.764577
\(805\) 8.73834 0.307986
\(806\) 72.6440 2.55878
\(807\) −18.3349 −0.645419
\(808\) −77.7898 −2.73664
\(809\) −28.9384 −1.01742 −0.508710 0.860938i \(-0.669878\pi\)
−0.508710 + 0.860938i \(0.669878\pi\)
\(810\) −14.7112 −0.516900
\(811\) −40.7765 −1.43186 −0.715928 0.698174i \(-0.753996\pi\)
−0.715928 + 0.698174i \(0.753996\pi\)
\(812\) 18.3702 0.644667
\(813\) −2.81311 −0.0986601
\(814\) −96.2633 −3.37403
\(815\) −0.0151568 −0.000530920 0
\(816\) −52.4325 −1.83550
\(817\) 7.68287 0.268790
\(818\) 33.0344 1.15502
\(819\) 4.22629 0.147678
\(820\) 63.5358 2.21877
\(821\) −17.9268 −0.625650 −0.312825 0.949811i \(-0.601275\pi\)
−0.312825 + 0.949811i \(0.601275\pi\)
\(822\) −25.9620 −0.905530
\(823\) 25.5250 0.889744 0.444872 0.895594i \(-0.353249\pi\)
0.444872 + 0.895594i \(0.353249\pi\)
\(824\) −5.69003 −0.198222
\(825\) 20.8063 0.724384
\(826\) −20.0878 −0.698945
\(827\) −17.1208 −0.595350 −0.297675 0.954667i \(-0.596211\pi\)
−0.297675 + 0.954667i \(0.596211\pi\)
\(828\) 29.8214 1.03637
\(829\) 38.2548 1.32864 0.664322 0.747447i \(-0.268721\pi\)
0.664322 + 0.747447i \(0.268721\pi\)
\(830\) 36.6634 1.27261
\(831\) −28.6040 −0.992261
\(832\) 23.5591 0.816766
\(833\) −7.95365 −0.275578
\(834\) −0.567828 −0.0196623
\(835\) 18.1900 0.629490
\(836\) −62.4112 −2.15854
\(837\) −44.0701 −1.52328
\(838\) 8.76123 0.302652
\(839\) −21.9804 −0.758847 −0.379424 0.925223i \(-0.623878\pi\)
−0.379424 + 0.925223i \(0.623878\pi\)
\(840\) 9.84579 0.339712
\(841\) −9.24016 −0.318626
\(842\) 24.0099 0.827435
\(843\) −31.3829 −1.08088
\(844\) 70.5523 2.42851
\(845\) −1.54677 −0.0532104
\(846\) 13.7118 0.471423
\(847\) 12.2981 0.422569
\(848\) −54.7067 −1.87863
\(849\) −13.5299 −0.464344
\(850\) −61.9889 −2.12620
\(851\) 51.7005 1.77227
\(852\) −79.0035 −2.70662
\(853\) −37.0349 −1.26805 −0.634025 0.773313i \(-0.718598\pi\)
−0.634025 + 0.773313i \(0.718598\pi\)
\(854\) −10.5985 −0.362673
\(855\) 4.78722 0.163719
\(856\) 92.1210 3.14863
\(857\) 53.6104 1.83130 0.915649 0.401979i \(-0.131677\pi\)
0.915649 + 0.401979i \(0.131677\pi\)
\(858\) −61.5546 −2.10144
\(859\) 20.9489 0.714769 0.357384 0.933957i \(-0.383669\pi\)
0.357384 + 0.933957i \(0.383669\pi\)
\(860\) −13.8127 −0.471009
\(861\) −15.4701 −0.527219
\(862\) 9.48656 0.323113
\(863\) −1.00000 −0.0340404
\(864\) 7.66437 0.260747
\(865\) −2.98133 −0.101368
\(866\) 0.802849 0.0272819
\(867\) 63.3608 2.15184
\(868\) 32.2427 1.09439
\(869\) −24.8138 −0.841751
\(870\) 20.5228 0.695787
\(871\) 14.4008 0.487952
\(872\) −55.1790 −1.86860
\(873\) 3.43203 0.116156
\(874\) 49.7414 1.68253
\(875\) 11.0898 0.374902
\(876\) 7.63475 0.257954
\(877\) 23.9128 0.807477 0.403739 0.914874i \(-0.367710\pi\)
0.403739 + 0.914874i \(0.367710\pi\)
\(878\) −20.3015 −0.685142
\(879\) −30.5099 −1.02907
\(880\) 31.6226 1.06600
\(881\) 43.4188 1.46282 0.731408 0.681940i \(-0.238864\pi\)
0.731408 + 0.681940i \(0.238864\pi\)
\(882\) 2.78363 0.0937298
\(883\) 10.7701 0.362444 0.181222 0.983442i \(-0.441995\pi\)
0.181222 + 0.983442i \(0.441995\pi\)
\(884\) 123.583 4.15653
\(885\) −15.1228 −0.508349
\(886\) 45.4618 1.52732
\(887\) −18.4272 −0.618725 −0.309362 0.950944i \(-0.600116\pi\)
−0.309362 + 0.950944i \(0.600116\pi\)
\(888\) 58.2527 1.95483
\(889\) −21.2790 −0.713675
\(890\) 30.6001 1.02572
\(891\) 21.0657 0.705726
\(892\) −1.70080 −0.0569469
\(893\) 15.4122 0.515749
\(894\) −77.2351 −2.58313
\(895\) −15.4456 −0.516288
\(896\) 18.2309 0.609053
\(897\) 33.0593 1.10382
\(898\) −4.65852 −0.155457
\(899\) 34.6817 1.15670
\(900\) 14.6197 0.487323
\(901\) 90.4029 3.01176
\(902\) −135.010 −4.49534
\(903\) 3.36320 0.111920
\(904\) 24.3111 0.808575
\(905\) −2.70225 −0.0898259
\(906\) 64.7616 2.15156
\(907\) 24.3751 0.809363 0.404681 0.914458i \(-0.367382\pi\)
0.404681 + 0.914458i \(0.367382\pi\)
\(908\) 84.3338 2.79872
\(909\) −16.5571 −0.549165
\(910\) −12.6737 −0.420129
\(911\) 6.28736 0.208310 0.104155 0.994561i \(-0.466786\pi\)
0.104155 + 0.994561i \(0.466786\pi\)
\(912\) 20.6259 0.682993
\(913\) −52.4999 −1.73749
\(914\) 66.9510 2.21454
\(915\) −7.97894 −0.263776
\(916\) −107.925 −3.56593
\(917\) 6.16387 0.203549
\(918\) −111.256 −3.67199
\(919\) 3.14648 0.103793 0.0518964 0.998652i \(-0.483473\pi\)
0.0518964 + 0.998652i \(0.483473\pi\)
\(920\) −46.1485 −1.52147
\(921\) −2.22141 −0.0731980
\(922\) 71.0885 2.34118
\(923\) 52.4788 1.72736
\(924\) −27.3207 −0.898785
\(925\) 25.3457 0.833362
\(926\) 64.8590 2.13140
\(927\) −1.21109 −0.0397774
\(928\) −6.03162 −0.197997
\(929\) 1.64684 0.0540311 0.0270156 0.999635i \(-0.491400\pi\)
0.0270156 + 0.999635i \(0.491400\pi\)
\(930\) 36.0208 1.18117
\(931\) 3.12881 0.102543
\(932\) 16.9074 0.553820
\(933\) −28.8098 −0.943190
\(934\) 34.8239 1.13947
\(935\) −52.2565 −1.70897
\(936\) −22.3196 −0.729540
\(937\) −5.35150 −0.174826 −0.0874130 0.996172i \(-0.527860\pi\)
−0.0874130 + 0.996172i \(0.527860\pi\)
\(938\) 9.48505 0.309698
\(939\) 43.9630 1.43468
\(940\) −27.7089 −0.903764
\(941\) −16.0695 −0.523850 −0.261925 0.965088i \(-0.584357\pi\)
−0.261925 + 0.965088i \(0.584357\pi\)
\(942\) −24.5151 −0.798744
\(943\) 72.5103 2.36126
\(944\) 39.0423 1.27072
\(945\) 7.68860 0.250110
\(946\) 29.3512 0.954291
\(947\) −38.7591 −1.25950 −0.629750 0.776798i \(-0.716843\pi\)
−0.629750 + 0.776798i \(0.716843\pi\)
\(948\) 29.0981 0.945061
\(949\) −5.07145 −0.164626
\(950\) 24.3853 0.791162
\(951\) 14.4761 0.469421
\(952\) 42.0044 1.36137
\(953\) −34.8226 −1.12801 −0.564007 0.825770i \(-0.690741\pi\)
−0.564007 + 0.825770i \(0.690741\pi\)
\(954\) −31.6394 −1.02436
\(955\) −22.9775 −0.743536
\(956\) −114.282 −3.69615
\(957\) −29.3874 −0.949960
\(958\) 22.5272 0.727822
\(959\) 7.65434 0.247171
\(960\) 11.6819 0.377031
\(961\) 29.8722 0.963618
\(962\) −74.9841 −2.41758
\(963\) 19.6074 0.631840
\(964\) −61.5650 −1.98288
\(965\) −26.0601 −0.838903
\(966\) 21.7744 0.700581
\(967\) −27.6286 −0.888474 −0.444237 0.895909i \(-0.646525\pi\)
−0.444237 + 0.895909i \(0.646525\pi\)
\(968\) −64.9483 −2.08752
\(969\) −34.0844 −1.09495
\(970\) −10.2919 −0.330453
\(971\) 3.58141 0.114933 0.0574665 0.998347i \(-0.481698\pi\)
0.0574665 + 0.998347i \(0.481698\pi\)
\(972\) 45.3262 1.45384
\(973\) 0.167412 0.00536697
\(974\) −81.2852 −2.60455
\(975\) 16.2070 0.519041
\(976\) 20.5991 0.659360
\(977\) −11.9512 −0.382354 −0.191177 0.981556i \(-0.561230\pi\)
−0.191177 + 0.981556i \(0.561230\pi\)
\(978\) −0.0377682 −0.00120769
\(979\) −43.8176 −1.40042
\(980\) −5.62516 −0.179689
\(981\) −11.7445 −0.374974
\(982\) 22.1153 0.705727
\(983\) −6.25902 −0.199632 −0.0998159 0.995006i \(-0.531825\pi\)
−0.0998159 + 0.995006i \(0.531825\pi\)
\(984\) 81.6999 2.60450
\(985\) −3.42325 −0.109074
\(986\) 87.5548 2.78831
\(987\) 6.74673 0.214751
\(988\) −48.6150 −1.54665
\(989\) −15.7638 −0.501258
\(990\) 18.2888 0.581257
\(991\) 41.8783 1.33031 0.665155 0.746706i \(-0.268366\pi\)
0.665155 + 0.746706i \(0.268366\pi\)
\(992\) −10.5865 −0.336121
\(993\) −17.4703 −0.554404
\(994\) 34.5651 1.09634
\(995\) −18.0416 −0.571958
\(996\) 61.5643 1.95074
\(997\) 12.3726 0.391845 0.195923 0.980619i \(-0.437230\pi\)
0.195923 + 0.980619i \(0.437230\pi\)
\(998\) −31.5493 −0.998674
\(999\) 45.4897 1.43923
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 \(a_p\))