Properties

Label 6013.2.a.e.1.13
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.18834 q^{2}\) \(+3.06167 q^{3}\) \(+2.78881 q^{4}\) \(-2.53450 q^{5}\) \(-6.69995 q^{6}\) \(+1.00000 q^{7}\) \(-1.72618 q^{8}\) \(+6.37380 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.18834 q^{2}\) \(+3.06167 q^{3}\) \(+2.78881 q^{4}\) \(-2.53450 q^{5}\) \(-6.69995 q^{6}\) \(+1.00000 q^{7}\) \(-1.72618 q^{8}\) \(+6.37380 q^{9}\) \(+5.54634 q^{10}\) \(+1.03269 q^{11}\) \(+8.53841 q^{12}\) \(-1.80328 q^{13}\) \(-2.18834 q^{14}\) \(-7.75980 q^{15}\) \(-1.80016 q^{16}\) \(+0.365608 q^{17}\) \(-13.9480 q^{18}\) \(+0.444175 q^{19}\) \(-7.06825 q^{20}\) \(+3.06167 q^{21}\) \(-2.25987 q^{22}\) \(+0.166616 q^{23}\) \(-5.28499 q^{24}\) \(+1.42370 q^{25}\) \(+3.94618 q^{26}\) \(+10.3294 q^{27}\) \(+2.78881 q^{28}\) \(+7.51023 q^{29}\) \(+16.9810 q^{30}\) \(+6.36658 q^{31}\) \(+7.39171 q^{32}\) \(+3.16176 q^{33}\) \(-0.800073 q^{34}\) \(-2.53450 q^{35}\) \(+17.7753 q^{36}\) \(-9.60062 q^{37}\) \(-0.972004 q^{38}\) \(-5.52104 q^{39}\) \(+4.37501 q^{40}\) \(+5.61678 q^{41}\) \(-6.69995 q^{42}\) \(-1.75757 q^{43}\) \(+2.87998 q^{44}\) \(-16.1544 q^{45}\) \(-0.364612 q^{46}\) \(-8.83237 q^{47}\) \(-5.51147 q^{48}\) \(+1.00000 q^{49}\) \(-3.11553 q^{50}\) \(+1.11937 q^{51}\) \(-5.02901 q^{52}\) \(-1.76674 q^{53}\) \(-22.6043 q^{54}\) \(-2.61736 q^{55}\) \(-1.72618 q^{56}\) \(+1.35992 q^{57}\) \(-16.4349 q^{58}\) \(+13.3903 q^{59}\) \(-21.6406 q^{60}\) \(-3.66072 q^{61}\) \(-13.9322 q^{62}\) \(+6.37380 q^{63}\) \(-12.5752 q^{64}\) \(+4.57041 q^{65}\) \(-6.91898 q^{66}\) \(+12.3839 q^{67}\) \(+1.01961 q^{68}\) \(+0.510123 q^{69}\) \(+5.54634 q^{70}\) \(-3.04550 q^{71}\) \(-11.0023 q^{72}\) \(+16.5322 q^{73}\) \(+21.0094 q^{74}\) \(+4.35889 q^{75}\) \(+1.23872 q^{76}\) \(+1.03269 q^{77}\) \(+12.0819 q^{78}\) \(-9.94489 q^{79}\) \(+4.56250 q^{80}\) \(+12.5039 q^{81}\) \(-12.2914 q^{82}\) \(-8.63706 q^{83}\) \(+8.53841 q^{84}\) \(-0.926634 q^{85}\) \(+3.84616 q^{86}\) \(+22.9938 q^{87}\) \(-1.78261 q^{88}\) \(+6.98103 q^{89}\) \(+35.3512 q^{90}\) \(-1.80328 q^{91}\) \(+0.464661 q^{92}\) \(+19.4923 q^{93}\) \(+19.3282 q^{94}\) \(-1.12576 q^{95}\) \(+22.6309 q^{96}\) \(+6.46081 q^{97}\) \(-2.18834 q^{98}\) \(+6.58216 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18834 −1.54739 −0.773693 0.633560i \(-0.781593\pi\)
−0.773693 + 0.633560i \(0.781593\pi\)
\(3\) 3.06167 1.76765 0.883827 0.467814i \(-0.154958\pi\)
0.883827 + 0.467814i \(0.154958\pi\)
\(4\) 2.78881 1.39441
\(5\) −2.53450 −1.13346 −0.566732 0.823902i \(-0.691792\pi\)
−0.566732 + 0.823902i \(0.691792\pi\)
\(6\) −6.69995 −2.73524
\(7\) 1.00000 0.377964
\(8\) −1.72618 −0.610298
\(9\) 6.37380 2.12460
\(10\) 5.54634 1.75391
\(11\) 1.03269 0.311368 0.155684 0.987807i \(-0.450242\pi\)
0.155684 + 0.987807i \(0.450242\pi\)
\(12\) 8.53841 2.46483
\(13\) −1.80328 −0.500140 −0.250070 0.968228i \(-0.580454\pi\)
−0.250070 + 0.968228i \(0.580454\pi\)
\(14\) −2.18834 −0.584857
\(15\) −7.75980 −2.00357
\(16\) −1.80016 −0.450039
\(17\) 0.365608 0.0886730 0.0443365 0.999017i \(-0.485883\pi\)
0.0443365 + 0.999017i \(0.485883\pi\)
\(18\) −13.9480 −3.28758
\(19\) 0.444175 0.101901 0.0509504 0.998701i \(-0.483775\pi\)
0.0509504 + 0.998701i \(0.483775\pi\)
\(20\) −7.06825 −1.58051
\(21\) 3.06167 0.668110
\(22\) −2.25987 −0.481807
\(23\) 0.166616 0.0347419 0.0173709 0.999849i \(-0.494470\pi\)
0.0173709 + 0.999849i \(0.494470\pi\)
\(24\) −5.28499 −1.07879
\(25\) 1.42370 0.284739
\(26\) 3.94618 0.773910
\(27\) 10.3294 1.98790
\(28\) 2.78881 0.527036
\(29\) 7.51023 1.39461 0.697307 0.716773i \(-0.254381\pi\)
0.697307 + 0.716773i \(0.254381\pi\)
\(30\) 16.9810 3.10030
\(31\) 6.36658 1.14347 0.571736 0.820438i \(-0.306270\pi\)
0.571736 + 0.820438i \(0.306270\pi\)
\(32\) 7.39171 1.30668
\(33\) 3.16176 0.550391
\(34\) −0.800073 −0.137211
\(35\) −2.53450 −0.428409
\(36\) 17.7753 2.96255
\(37\) −9.60062 −1.57833 −0.789166 0.614179i \(-0.789487\pi\)
−0.789166 + 0.614179i \(0.789487\pi\)
\(38\) −0.972004 −0.157680
\(39\) −5.52104 −0.884074
\(40\) 4.37501 0.691750
\(41\) 5.61678 0.877193 0.438597 0.898684i \(-0.355476\pi\)
0.438597 + 0.898684i \(0.355476\pi\)
\(42\) −6.69995 −1.03382
\(43\) −1.75757 −0.268027 −0.134014 0.990979i \(-0.542787\pi\)
−0.134014 + 0.990979i \(0.542787\pi\)
\(44\) 2.87998 0.434173
\(45\) −16.1544 −2.40816
\(46\) −0.364612 −0.0537591
\(47\) −8.83237 −1.28833 −0.644167 0.764885i \(-0.722796\pi\)
−0.644167 + 0.764885i \(0.722796\pi\)
\(48\) −5.51147 −0.795513
\(49\) 1.00000 0.142857
\(50\) −3.11553 −0.440602
\(51\) 1.11937 0.156743
\(52\) −5.02901 −0.697398
\(53\) −1.76674 −0.242681 −0.121340 0.992611i \(-0.538719\pi\)
−0.121340 + 0.992611i \(0.538719\pi\)
\(54\) −22.6043 −3.07605
\(55\) −2.61736 −0.352924
\(56\) −1.72618 −0.230671
\(57\) 1.35992 0.180125
\(58\) −16.4349 −2.15801
\(59\) 13.3903 1.74327 0.871633 0.490160i \(-0.163062\pi\)
0.871633 + 0.490160i \(0.163062\pi\)
\(60\) −21.6406 −2.79379
\(61\) −3.66072 −0.468707 −0.234353 0.972151i \(-0.575297\pi\)
−0.234353 + 0.972151i \(0.575297\pi\)
\(62\) −13.9322 −1.76939
\(63\) 6.37380 0.803023
\(64\) −12.5752 −1.57190
\(65\) 4.57041 0.566890
\(66\) −6.91898 −0.851668
\(67\) 12.3839 1.51294 0.756469 0.654029i \(-0.226923\pi\)
0.756469 + 0.654029i \(0.226923\pi\)
\(68\) 1.01961 0.123646
\(69\) 0.510123 0.0614116
\(70\) 5.54634 0.662914
\(71\) −3.04550 −0.361435 −0.180717 0.983535i \(-0.557842\pi\)
−0.180717 + 0.983535i \(0.557842\pi\)
\(72\) −11.0023 −1.29664
\(73\) 16.5322 1.93494 0.967471 0.252980i \(-0.0814107\pi\)
0.967471 + 0.252980i \(0.0814107\pi\)
\(74\) 21.0094 2.44229
\(75\) 4.35889 0.503321
\(76\) 1.23872 0.142091
\(77\) 1.03269 0.117686
\(78\) 12.0819 1.36800
\(79\) −9.94489 −1.11889 −0.559444 0.828868i \(-0.688985\pi\)
−0.559444 + 0.828868i \(0.688985\pi\)
\(80\) 4.56250 0.510103
\(81\) 12.5039 1.38932
\(82\) −12.2914 −1.35736
\(83\) −8.63706 −0.948041 −0.474020 0.880514i \(-0.657198\pi\)
−0.474020 + 0.880514i \(0.657198\pi\)
\(84\) 8.53841 0.931617
\(85\) −0.926634 −0.100508
\(86\) 3.84616 0.414742
\(87\) 22.9938 2.46519
\(88\) −1.78261 −0.190027
\(89\) 6.98103 0.739987 0.369994 0.929034i \(-0.379360\pi\)
0.369994 + 0.929034i \(0.379360\pi\)
\(90\) 35.3512 3.72635
\(91\) −1.80328 −0.189035
\(92\) 0.464661 0.0484443
\(93\) 19.4923 2.02126
\(94\) 19.3282 1.99355
\(95\) −1.12576 −0.115501
\(96\) 22.6309 2.30976
\(97\) 6.46081 0.655996 0.327998 0.944678i \(-0.393626\pi\)
0.327998 + 0.944678i \(0.393626\pi\)
\(98\) −2.18834 −0.221055
\(99\) 6.58216 0.661532
\(100\) 3.97042 0.397042
\(101\) −7.53537 −0.749798 −0.374899 0.927066i \(-0.622323\pi\)
−0.374899 + 0.927066i \(0.622323\pi\)
\(102\) −2.44956 −0.242542
\(103\) 16.4601 1.62186 0.810929 0.585144i \(-0.198962\pi\)
0.810929 + 0.585144i \(0.198962\pi\)
\(104\) 3.11279 0.305234
\(105\) −7.75980 −0.757279
\(106\) 3.86622 0.375521
\(107\) 16.8753 1.63140 0.815699 0.578477i \(-0.196353\pi\)
0.815699 + 0.578477i \(0.196353\pi\)
\(108\) 28.8069 2.77194
\(109\) −14.1956 −1.35969 −0.679846 0.733355i \(-0.737954\pi\)
−0.679846 + 0.733355i \(0.737954\pi\)
\(110\) 5.72766 0.546110
\(111\) −29.3939 −2.78995
\(112\) −1.80016 −0.170099
\(113\) 4.23224 0.398135 0.199068 0.979986i \(-0.436209\pi\)
0.199068 + 0.979986i \(0.436209\pi\)
\(114\) −2.97595 −0.278723
\(115\) −0.422289 −0.0393786
\(116\) 20.9446 1.94466
\(117\) −11.4937 −1.06260
\(118\) −29.3024 −2.69751
\(119\) 0.365608 0.0335152
\(120\) 13.3948 1.22277
\(121\) −9.93355 −0.903050
\(122\) 8.01087 0.725270
\(123\) 17.1967 1.55057
\(124\) 17.7552 1.59446
\(125\) 9.06414 0.810722
\(126\) −13.9480 −1.24259
\(127\) 6.49327 0.576185 0.288092 0.957603i \(-0.406979\pi\)
0.288092 + 0.957603i \(0.406979\pi\)
\(128\) 12.7354 1.12566
\(129\) −5.38110 −0.473779
\(130\) −10.0016 −0.877198
\(131\) −18.4094 −1.60844 −0.804220 0.594332i \(-0.797417\pi\)
−0.804220 + 0.594332i \(0.797417\pi\)
\(132\) 8.81754 0.767468
\(133\) 0.444175 0.0385149
\(134\) −27.1002 −2.34110
\(135\) −26.1800 −2.25321
\(136\) −0.631106 −0.0541169
\(137\) 5.67795 0.485100 0.242550 0.970139i \(-0.422016\pi\)
0.242550 + 0.970139i \(0.422016\pi\)
\(138\) −1.11632 −0.0950275
\(139\) −8.85010 −0.750656 −0.375328 0.926892i \(-0.622470\pi\)
−0.375328 + 0.926892i \(0.622470\pi\)
\(140\) −7.06825 −0.597376
\(141\) −27.0418 −2.27733
\(142\) 6.66458 0.559279
\(143\) −1.86223 −0.155728
\(144\) −11.4738 −0.956152
\(145\) −19.0347 −1.58074
\(146\) −36.1779 −2.99410
\(147\) 3.06167 0.252522
\(148\) −26.7743 −2.20084
\(149\) 23.8163 1.95111 0.975553 0.219764i \(-0.0705287\pi\)
0.975553 + 0.219764i \(0.0705287\pi\)
\(150\) −9.53870 −0.778832
\(151\) 9.30062 0.756874 0.378437 0.925627i \(-0.376462\pi\)
0.378437 + 0.925627i \(0.376462\pi\)
\(152\) −0.766727 −0.0621898
\(153\) 2.33031 0.188395
\(154\) −2.25987 −0.182106
\(155\) −16.1361 −1.29608
\(156\) −15.3971 −1.23276
\(157\) 3.05228 0.243599 0.121799 0.992555i \(-0.461134\pi\)
0.121799 + 0.992555i \(0.461134\pi\)
\(158\) 21.7628 1.73135
\(159\) −5.40917 −0.428975
\(160\) −18.7343 −1.48108
\(161\) 0.166616 0.0131312
\(162\) −27.3627 −2.14982
\(163\) 7.14776 0.559855 0.279928 0.960021i \(-0.409689\pi\)
0.279928 + 0.960021i \(0.409689\pi\)
\(164\) 15.6641 1.22316
\(165\) −8.01347 −0.623848
\(166\) 18.9008 1.46699
\(167\) −7.77020 −0.601276 −0.300638 0.953738i \(-0.597200\pi\)
−0.300638 + 0.953738i \(0.597200\pi\)
\(168\) −5.28499 −0.407746
\(169\) −9.74818 −0.749860
\(170\) 2.02779 0.155524
\(171\) 2.83108 0.216498
\(172\) −4.90153 −0.373739
\(173\) 18.3839 1.39770 0.698852 0.715267i \(-0.253695\pi\)
0.698852 + 0.715267i \(0.253695\pi\)
\(174\) −50.3182 −3.81461
\(175\) 1.42370 0.107621
\(176\) −1.85900 −0.140128
\(177\) 40.9965 3.08149
\(178\) −15.2768 −1.14505
\(179\) 2.96703 0.221766 0.110883 0.993833i \(-0.464632\pi\)
0.110883 + 0.993833i \(0.464632\pi\)
\(180\) −45.0516 −3.35795
\(181\) −17.9535 −1.33447 −0.667237 0.744846i \(-0.732523\pi\)
−0.667237 + 0.744846i \(0.732523\pi\)
\(182\) 3.94618 0.292510
\(183\) −11.2079 −0.828511
\(184\) −0.287610 −0.0212029
\(185\) 24.3328 1.78898
\(186\) −42.6558 −3.12767
\(187\) 0.377560 0.0276099
\(188\) −24.6318 −1.79646
\(189\) 10.3294 0.751356
\(190\) 2.46355 0.178724
\(191\) 14.3719 1.03992 0.519958 0.854192i \(-0.325948\pi\)
0.519958 + 0.854192i \(0.325948\pi\)
\(192\) −38.5011 −2.77858
\(193\) −15.5310 −1.11795 −0.558974 0.829185i \(-0.688805\pi\)
−0.558974 + 0.829185i \(0.688805\pi\)
\(194\) −14.1384 −1.01508
\(195\) 13.9931 1.00207
\(196\) 2.78881 0.199201
\(197\) 22.3532 1.59260 0.796298 0.604904i \(-0.206788\pi\)
0.796298 + 0.604904i \(0.206788\pi\)
\(198\) −14.4040 −1.02365
\(199\) 7.65149 0.542400 0.271200 0.962523i \(-0.412580\pi\)
0.271200 + 0.962523i \(0.412580\pi\)
\(200\) −2.45756 −0.173776
\(201\) 37.9155 2.67435
\(202\) 16.4899 1.16023
\(203\) 7.51023 0.527115
\(204\) 3.12171 0.218563
\(205\) −14.2357 −0.994267
\(206\) −36.0201 −2.50964
\(207\) 1.06198 0.0738125
\(208\) 3.24618 0.225082
\(209\) 0.458696 0.0317286
\(210\) 16.9810 1.17180
\(211\) 24.4197 1.68112 0.840560 0.541718i \(-0.182226\pi\)
0.840560 + 0.541718i \(0.182226\pi\)
\(212\) −4.92711 −0.338395
\(213\) −9.32432 −0.638892
\(214\) −36.9288 −2.52440
\(215\) 4.45457 0.303799
\(216\) −17.8305 −1.21321
\(217\) 6.36658 0.432192
\(218\) 31.0648 2.10397
\(219\) 50.6159 3.42031
\(220\) −7.29931 −0.492120
\(221\) −0.659294 −0.0443489
\(222\) 64.3237 4.31712
\(223\) −7.51341 −0.503135 −0.251567 0.967840i \(-0.580946\pi\)
−0.251567 + 0.967840i \(0.580946\pi\)
\(224\) 7.39171 0.493879
\(225\) 9.07436 0.604957
\(226\) −9.26155 −0.616069
\(227\) 7.03627 0.467013 0.233507 0.972355i \(-0.424980\pi\)
0.233507 + 0.972355i \(0.424980\pi\)
\(228\) 3.79255 0.251168
\(229\) −20.8190 −1.37576 −0.687881 0.725824i \(-0.741459\pi\)
−0.687881 + 0.725824i \(0.741459\pi\)
\(230\) 0.924110 0.0609340
\(231\) 3.16176 0.208028
\(232\) −12.9640 −0.851130
\(233\) 6.13998 0.402244 0.201122 0.979566i \(-0.435541\pi\)
0.201122 + 0.979566i \(0.435541\pi\)
\(234\) 25.1522 1.64425
\(235\) 22.3857 1.46028
\(236\) 37.3429 2.43082
\(237\) −30.4479 −1.97781
\(238\) −0.800073 −0.0518610
\(239\) −8.32850 −0.538726 −0.269363 0.963039i \(-0.586813\pi\)
−0.269363 + 0.963039i \(0.586813\pi\)
\(240\) 13.9688 0.901685
\(241\) 3.19307 0.205684 0.102842 0.994698i \(-0.467206\pi\)
0.102842 + 0.994698i \(0.467206\pi\)
\(242\) 21.7379 1.39737
\(243\) 7.29445 0.467939
\(244\) −10.2090 −0.653567
\(245\) −2.53450 −0.161923
\(246\) −37.6321 −2.39934
\(247\) −0.800972 −0.0509646
\(248\) −10.9899 −0.697858
\(249\) −26.4438 −1.67581
\(250\) −19.8354 −1.25450
\(251\) 11.1132 0.701459 0.350730 0.936477i \(-0.385934\pi\)
0.350730 + 0.936477i \(0.385934\pi\)
\(252\) 17.7753 1.11974
\(253\) 0.172063 0.0108175
\(254\) −14.2095 −0.891581
\(255\) −2.83704 −0.177663
\(256\) −2.71885 −0.169928
\(257\) 9.04607 0.564278 0.282139 0.959374i \(-0.408956\pi\)
0.282139 + 0.959374i \(0.408956\pi\)
\(258\) 11.7756 0.733120
\(259\) −9.60062 −0.596554
\(260\) 12.7460 0.790475
\(261\) 47.8687 2.96300
\(262\) 40.2860 2.48888
\(263\) −3.47466 −0.214256 −0.107128 0.994245i \(-0.534166\pi\)
−0.107128 + 0.994245i \(0.534166\pi\)
\(264\) −5.45777 −0.335902
\(265\) 4.47781 0.275070
\(266\) −0.972004 −0.0595974
\(267\) 21.3736 1.30804
\(268\) 34.5365 2.10965
\(269\) −9.80598 −0.597881 −0.298941 0.954272i \(-0.596633\pi\)
−0.298941 + 0.954272i \(0.596633\pi\)
\(270\) 57.2906 3.48659
\(271\) −22.9388 −1.39344 −0.696718 0.717345i \(-0.745357\pi\)
−0.696718 + 0.717345i \(0.745357\pi\)
\(272\) −0.658152 −0.0399063
\(273\) −5.52104 −0.334148
\(274\) −12.4253 −0.750637
\(275\) 1.47024 0.0886588
\(276\) 1.42264 0.0856327
\(277\) 3.07652 0.184850 0.0924251 0.995720i \(-0.470538\pi\)
0.0924251 + 0.995720i \(0.470538\pi\)
\(278\) 19.3670 1.16156
\(279\) 40.5793 2.42942
\(280\) 4.37501 0.261457
\(281\) 23.7113 1.41450 0.707249 0.706964i \(-0.249936\pi\)
0.707249 + 0.706964i \(0.249936\pi\)
\(282\) 59.1764 3.52391
\(283\) −3.97763 −0.236446 −0.118223 0.992987i \(-0.537720\pi\)
−0.118223 + 0.992987i \(0.537720\pi\)
\(284\) −8.49334 −0.503987
\(285\) −3.44671 −0.204165
\(286\) 4.07519 0.240971
\(287\) 5.61678 0.331548
\(288\) 47.1133 2.77618
\(289\) −16.8663 −0.992137
\(290\) 41.6543 2.44602
\(291\) 19.7809 1.15957
\(292\) 46.1051 2.69809
\(293\) 13.9114 0.812714 0.406357 0.913714i \(-0.366799\pi\)
0.406357 + 0.913714i \(0.366799\pi\)
\(294\) −6.69995 −0.390749
\(295\) −33.9377 −1.97593
\(296\) 16.5724 0.963253
\(297\) 10.6671 0.618969
\(298\) −52.1180 −3.01912
\(299\) −0.300455 −0.0173758
\(300\) 12.1561 0.701833
\(301\) −1.75757 −0.101305
\(302\) −20.3529 −1.17118
\(303\) −23.0708 −1.32538
\(304\) −0.799584 −0.0458593
\(305\) 9.27809 0.531262
\(306\) −5.09950 −0.291519
\(307\) −5.63628 −0.321679 −0.160840 0.986981i \(-0.551420\pi\)
−0.160840 + 0.986981i \(0.551420\pi\)
\(308\) 2.87998 0.164102
\(309\) 50.3952 2.86688
\(310\) 35.3112 2.00554
\(311\) −0.462987 −0.0262536 −0.0131268 0.999914i \(-0.504179\pi\)
−0.0131268 + 0.999914i \(0.504179\pi\)
\(312\) 9.53032 0.539548
\(313\) −11.2073 −0.633473 −0.316736 0.948514i \(-0.602587\pi\)
−0.316736 + 0.948514i \(0.602587\pi\)
\(314\) −6.67941 −0.376941
\(315\) −16.1544 −0.910197
\(316\) −27.7344 −1.56018
\(317\) 0.263746 0.0148135 0.00740673 0.999973i \(-0.497642\pi\)
0.00740673 + 0.999973i \(0.497642\pi\)
\(318\) 11.8371 0.663791
\(319\) 7.75575 0.434238
\(320\) 31.8719 1.78169
\(321\) 51.6666 2.88375
\(322\) −0.364612 −0.0203190
\(323\) 0.162394 0.00903584
\(324\) 34.8710 1.93728
\(325\) −2.56732 −0.142410
\(326\) −15.6417 −0.866313
\(327\) −43.4622 −2.40347
\(328\) −9.69558 −0.535349
\(329\) −8.83237 −0.486944
\(330\) 17.5362 0.965334
\(331\) 16.2122 0.891104 0.445552 0.895256i \(-0.353007\pi\)
0.445552 + 0.895256i \(0.353007\pi\)
\(332\) −24.0871 −1.32195
\(333\) −61.1924 −3.35332
\(334\) 17.0038 0.930407
\(335\) −31.3871 −1.71486
\(336\) −5.51147 −0.300676
\(337\) 10.7386 0.584966 0.292483 0.956271i \(-0.405518\pi\)
0.292483 + 0.956271i \(0.405518\pi\)
\(338\) 21.3323 1.16032
\(339\) 12.9577 0.703765
\(340\) −2.58421 −0.140148
\(341\) 6.57471 0.356040
\(342\) −6.19536 −0.335007
\(343\) 1.00000 0.0539949
\(344\) 3.03389 0.163576
\(345\) −1.29291 −0.0696078
\(346\) −40.2302 −2.16279
\(347\) 34.6582 1.86055 0.930276 0.366861i \(-0.119567\pi\)
0.930276 + 0.366861i \(0.119567\pi\)
\(348\) 64.1254 3.43748
\(349\) 23.3166 1.24811 0.624054 0.781382i \(-0.285485\pi\)
0.624054 + 0.781382i \(0.285485\pi\)
\(350\) −3.11553 −0.166532
\(351\) −18.6269 −0.994229
\(352\) 7.63335 0.406859
\(353\) −19.2085 −1.02236 −0.511182 0.859473i \(-0.670792\pi\)
−0.511182 + 0.859473i \(0.670792\pi\)
\(354\) −89.7142 −4.76825
\(355\) 7.71883 0.409673
\(356\) 19.4688 1.03184
\(357\) 1.11937 0.0592433
\(358\) −6.49286 −0.343158
\(359\) 20.6827 1.09159 0.545795 0.837919i \(-0.316228\pi\)
0.545795 + 0.837919i \(0.316228\pi\)
\(360\) 27.8854 1.46969
\(361\) −18.8027 −0.989616
\(362\) 39.2883 2.06495
\(363\) −30.4132 −1.59628
\(364\) −5.02901 −0.263592
\(365\) −41.9008 −2.19319
\(366\) 24.5266 1.28203
\(367\) 31.3653 1.63726 0.818628 0.574324i \(-0.194735\pi\)
0.818628 + 0.574324i \(0.194735\pi\)
\(368\) −0.299935 −0.0156352
\(369\) 35.8002 1.86368
\(370\) −53.2483 −2.76825
\(371\) −1.76674 −0.0917247
\(372\) 54.3604 2.81846
\(373\) −24.1120 −1.24847 −0.624235 0.781237i \(-0.714589\pi\)
−0.624235 + 0.781237i \(0.714589\pi\)
\(374\) −0.826228 −0.0427233
\(375\) 27.7514 1.43308
\(376\) 15.2463 0.786267
\(377\) −13.5430 −0.697502
\(378\) −22.6043 −1.16264
\(379\) 2.84242 0.146006 0.0730028 0.997332i \(-0.476742\pi\)
0.0730028 + 0.997332i \(0.476742\pi\)
\(380\) −3.13954 −0.161055
\(381\) 19.8802 1.01850
\(382\) −31.4506 −1.60915
\(383\) 23.2422 1.18762 0.593811 0.804604i \(-0.297622\pi\)
0.593811 + 0.804604i \(0.297622\pi\)
\(384\) 38.9915 1.98978
\(385\) −2.61736 −0.133393
\(386\) 33.9871 1.72990
\(387\) −11.2024 −0.569450
\(388\) 18.0180 0.914725
\(389\) 27.9317 1.41619 0.708096 0.706117i \(-0.249555\pi\)
0.708096 + 0.706117i \(0.249555\pi\)
\(390\) −30.6216 −1.55058
\(391\) 0.0609162 0.00308067
\(392\) −1.72618 −0.0871854
\(393\) −56.3635 −2.84316
\(394\) −48.9162 −2.46436
\(395\) 25.2053 1.26822
\(396\) 18.3564 0.922444
\(397\) 1.36301 0.0684074 0.0342037 0.999415i \(-0.489111\pi\)
0.0342037 + 0.999415i \(0.489111\pi\)
\(398\) −16.7440 −0.839302
\(399\) 1.35992 0.0680809
\(400\) −2.56288 −0.128144
\(401\) 9.92547 0.495655 0.247827 0.968804i \(-0.420283\pi\)
0.247827 + 0.968804i \(0.420283\pi\)
\(402\) −82.9718 −4.13826
\(403\) −11.4807 −0.571895
\(404\) −21.0147 −1.04552
\(405\) −31.6912 −1.57475
\(406\) −16.4349 −0.815650
\(407\) −9.91448 −0.491443
\(408\) −1.93224 −0.0956600
\(409\) 29.5333 1.46033 0.730164 0.683272i \(-0.239444\pi\)
0.730164 + 0.683272i \(0.239444\pi\)
\(410\) 31.1525 1.53851
\(411\) 17.3840 0.857488
\(412\) 45.9040 2.26153
\(413\) 13.3903 0.658892
\(414\) −2.32396 −0.114217
\(415\) 21.8906 1.07457
\(416\) −13.3293 −0.653524
\(417\) −27.0961 −1.32690
\(418\) −1.00378 −0.0490965
\(419\) −22.5660 −1.10242 −0.551210 0.834367i \(-0.685834\pi\)
−0.551210 + 0.834367i \(0.685834\pi\)
\(420\) −21.6406 −1.05595
\(421\) −16.5967 −0.808875 −0.404437 0.914566i \(-0.632533\pi\)
−0.404437 + 0.914566i \(0.632533\pi\)
\(422\) −53.4385 −2.60134
\(423\) −56.2957 −2.73719
\(424\) 3.04972 0.148107
\(425\) 0.520515 0.0252487
\(426\) 20.4047 0.988612
\(427\) −3.66072 −0.177154
\(428\) 47.0621 2.27483
\(429\) −5.70153 −0.275272
\(430\) −9.74809 −0.470095
\(431\) −7.94466 −0.382681 −0.191340 0.981524i \(-0.561283\pi\)
−0.191340 + 0.981524i \(0.561283\pi\)
\(432\) −18.5946 −0.894633
\(433\) −37.8928 −1.82101 −0.910506 0.413496i \(-0.864308\pi\)
−0.910506 + 0.413496i \(0.864308\pi\)
\(434\) −13.9322 −0.668767
\(435\) −58.2778 −2.79421
\(436\) −39.5889 −1.89596
\(437\) 0.0740067 0.00354022
\(438\) −110.765 −5.29254
\(439\) 0.284171 0.0135627 0.00678137 0.999977i \(-0.497841\pi\)
0.00678137 + 0.999977i \(0.497841\pi\)
\(440\) 4.51804 0.215389
\(441\) 6.37380 0.303514
\(442\) 1.44276 0.0686249
\(443\) 30.1382 1.43191 0.715955 0.698146i \(-0.245991\pi\)
0.715955 + 0.698146i \(0.245991\pi\)
\(444\) −81.9740 −3.89032
\(445\) −17.6934 −0.838748
\(446\) 16.4419 0.778544
\(447\) 72.9175 3.44888
\(448\) −12.5752 −0.594124
\(449\) −37.2252 −1.75677 −0.878384 0.477956i \(-0.841378\pi\)
−0.878384 + 0.477956i \(0.841378\pi\)
\(450\) −19.8577 −0.936103
\(451\) 5.80040 0.273130
\(452\) 11.8029 0.555162
\(453\) 28.4754 1.33789
\(454\) −15.3977 −0.722650
\(455\) 4.57041 0.214264
\(456\) −2.34746 −0.109930
\(457\) 0.906470 0.0424029 0.0212014 0.999775i \(-0.493251\pi\)
0.0212014 + 0.999775i \(0.493251\pi\)
\(458\) 45.5591 2.12883
\(459\) 3.77653 0.176273
\(460\) −1.17768 −0.0549098
\(461\) 39.1587 1.82380 0.911902 0.410409i \(-0.134614\pi\)
0.911902 + 0.410409i \(0.134614\pi\)
\(462\) −6.91898 −0.321900
\(463\) −5.71682 −0.265683 −0.132842 0.991137i \(-0.542410\pi\)
−0.132842 + 0.991137i \(0.542410\pi\)
\(464\) −13.5196 −0.627631
\(465\) −49.4034 −2.29103
\(466\) −13.4363 −0.622426
\(467\) −39.8097 −1.84217 −0.921087 0.389357i \(-0.872697\pi\)
−0.921087 + 0.389357i \(0.872697\pi\)
\(468\) −32.0539 −1.48169
\(469\) 12.3839 0.571837
\(470\) −48.9873 −2.25962
\(471\) 9.34506 0.430598
\(472\) −23.1141 −1.06391
\(473\) −1.81503 −0.0834551
\(474\) 66.6303 3.06043
\(475\) 0.632371 0.0290152
\(476\) 1.01961 0.0467338
\(477\) −11.2609 −0.515599
\(478\) 18.2255 0.833617
\(479\) −12.1014 −0.552928 −0.276464 0.961024i \(-0.589163\pi\)
−0.276464 + 0.961024i \(0.589163\pi\)
\(480\) −57.3582 −2.61803
\(481\) 17.3126 0.789387
\(482\) −6.98751 −0.318272
\(483\) 0.510123 0.0232114
\(484\) −27.7028 −1.25922
\(485\) −16.3749 −0.743548
\(486\) −15.9627 −0.724083
\(487\) 19.4701 0.882274 0.441137 0.897440i \(-0.354575\pi\)
0.441137 + 0.897440i \(0.354575\pi\)
\(488\) 6.31906 0.286051
\(489\) 21.8840 0.989630
\(490\) 5.54634 0.250558
\(491\) −23.3450 −1.05354 −0.526772 0.850007i \(-0.676598\pi\)
−0.526772 + 0.850007i \(0.676598\pi\)
\(492\) 47.9583 2.16213
\(493\) 2.74580 0.123665
\(494\) 1.75279 0.0788620
\(495\) −16.6825 −0.749823
\(496\) −11.4608 −0.514607
\(497\) −3.04550 −0.136610
\(498\) 57.8679 2.59312
\(499\) −1.39608 −0.0624971 −0.0312486 0.999512i \(-0.509948\pi\)
−0.0312486 + 0.999512i \(0.509948\pi\)
\(500\) 25.2782 1.13047
\(501\) −23.7898 −1.06285
\(502\) −24.3194 −1.08543
\(503\) −10.0032 −0.446020 −0.223010 0.974816i \(-0.571588\pi\)
−0.223010 + 0.974816i \(0.571588\pi\)
\(504\) −11.0023 −0.490083
\(505\) 19.0984 0.849868
\(506\) −0.376532 −0.0167389
\(507\) −29.8457 −1.32549
\(508\) 18.1085 0.803435
\(509\) 18.7664 0.831805 0.415902 0.909409i \(-0.363466\pi\)
0.415902 + 0.909409i \(0.363466\pi\)
\(510\) 6.20840 0.274913
\(511\) 16.5322 0.731340
\(512\) −19.5210 −0.862715
\(513\) 4.58808 0.202569
\(514\) −19.7958 −0.873156
\(515\) −41.7181 −1.83832
\(516\) −15.0069 −0.660640
\(517\) −9.12111 −0.401146
\(518\) 21.0094 0.923099
\(519\) 56.2854 2.47066
\(520\) −7.88937 −0.345972
\(521\) 42.8475 1.87718 0.938591 0.345032i \(-0.112132\pi\)
0.938591 + 0.345032i \(0.112132\pi\)
\(522\) −104.753 −4.58490
\(523\) −17.4782 −0.764268 −0.382134 0.924107i \(-0.624811\pi\)
−0.382134 + 0.924107i \(0.624811\pi\)
\(524\) −51.3404 −2.24282
\(525\) 4.35889 0.190237
\(526\) 7.60371 0.331538
\(527\) 2.32767 0.101395
\(528\) −5.69165 −0.247697
\(529\) −22.9722 −0.998793
\(530\) −9.79895 −0.425639
\(531\) 85.3469 3.70374
\(532\) 1.23872 0.0537053
\(533\) −10.1286 −0.438719
\(534\) −46.7725 −2.02405
\(535\) −42.7705 −1.84913
\(536\) −21.3769 −0.923343
\(537\) 9.08406 0.392006
\(538\) 21.4588 0.925153
\(539\) 1.03269 0.0444812
\(540\) −73.0110 −3.14189
\(541\) 24.6276 1.05882 0.529411 0.848365i \(-0.322413\pi\)
0.529411 + 0.848365i \(0.322413\pi\)
\(542\) 50.1979 2.15618
\(543\) −54.9676 −2.35889
\(544\) 2.70247 0.115867
\(545\) 35.9788 1.54116
\(546\) 12.0819 0.517057
\(547\) −9.94054 −0.425027 −0.212513 0.977158i \(-0.568165\pi\)
−0.212513 + 0.977158i \(0.568165\pi\)
\(548\) 15.8347 0.676426
\(549\) −23.3327 −0.995814
\(550\) −3.21738 −0.137189
\(551\) 3.33586 0.142112
\(552\) −0.880565 −0.0374794
\(553\) −9.94489 −0.422900
\(554\) −6.73246 −0.286035
\(555\) 74.4989 3.16230
\(556\) −24.6813 −1.04672
\(557\) 6.41990 0.272020 0.136010 0.990707i \(-0.456572\pi\)
0.136010 + 0.990707i \(0.456572\pi\)
\(558\) −88.8011 −3.75925
\(559\) 3.16939 0.134051
\(560\) 4.56250 0.192801
\(561\) 1.15596 0.0488048
\(562\) −51.8883 −2.18878
\(563\) −4.05629 −0.170952 −0.0854760 0.996340i \(-0.527241\pi\)
−0.0854760 + 0.996340i \(0.527241\pi\)
\(564\) −75.4144 −3.17552
\(565\) −10.7266 −0.451272
\(566\) 8.70440 0.365873
\(567\) 12.5039 0.525115
\(568\) 5.25710 0.220583
\(569\) −43.6796 −1.83114 −0.915572 0.402155i \(-0.868261\pi\)
−0.915572 + 0.402155i \(0.868261\pi\)
\(570\) 7.54255 0.315923
\(571\) −3.88786 −0.162702 −0.0813510 0.996686i \(-0.525923\pi\)
−0.0813510 + 0.996686i \(0.525923\pi\)
\(572\) −5.19341 −0.217147
\(573\) 44.0020 1.83821
\(574\) −12.2914 −0.513033
\(575\) 0.237211 0.00989238
\(576\) −80.1519 −3.33966
\(577\) 16.8119 0.699890 0.349945 0.936770i \(-0.386200\pi\)
0.349945 + 0.936770i \(0.386200\pi\)
\(578\) 36.9092 1.53522
\(579\) −47.5508 −1.97614
\(580\) −53.0841 −2.20420
\(581\) −8.63706 −0.358326
\(582\) −43.2871 −1.79431
\(583\) −1.82450 −0.0755630
\(584\) −28.5375 −1.18089
\(585\) 29.1309 1.20441
\(586\) −30.4429 −1.25758
\(587\) 45.5129 1.87852 0.939259 0.343210i \(-0.111514\pi\)
0.939259 + 0.343210i \(0.111514\pi\)
\(588\) 8.53841 0.352118
\(589\) 2.82788 0.116521
\(590\) 74.2670 3.05752
\(591\) 68.4379 2.81516
\(592\) 17.2826 0.710311
\(593\) −18.3137 −0.752054 −0.376027 0.926609i \(-0.622710\pi\)
−0.376027 + 0.926609i \(0.622710\pi\)
\(594\) −23.3432 −0.957785
\(595\) −0.926634 −0.0379883
\(596\) 66.4191 2.72063
\(597\) 23.4263 0.958775
\(598\) 0.657497 0.0268871
\(599\) −25.2463 −1.03154 −0.515769 0.856728i \(-0.672494\pi\)
−0.515769 + 0.856728i \(0.672494\pi\)
\(600\) −7.52423 −0.307176
\(601\) 15.0178 0.612590 0.306295 0.951937i \(-0.400911\pi\)
0.306295 + 0.951937i \(0.400911\pi\)
\(602\) 3.84616 0.156758
\(603\) 78.9327 3.21439
\(604\) 25.9377 1.05539
\(605\) 25.1766 1.02357
\(606\) 50.4866 2.05088
\(607\) −11.0999 −0.450529 −0.225265 0.974298i \(-0.572325\pi\)
−0.225265 + 0.974298i \(0.572325\pi\)
\(608\) 3.28321 0.133152
\(609\) 22.9938 0.931756
\(610\) −20.3036 −0.822068
\(611\) 15.9272 0.644347
\(612\) 6.49880 0.262698
\(613\) 19.9317 0.805034 0.402517 0.915412i \(-0.368135\pi\)
0.402517 + 0.915412i \(0.368135\pi\)
\(614\) 12.3341 0.497762
\(615\) −43.5850 −1.75752
\(616\) −1.78261 −0.0718235
\(617\) 23.1490 0.931946 0.465973 0.884799i \(-0.345704\pi\)
0.465973 + 0.884799i \(0.345704\pi\)
\(618\) −110.282 −4.43618
\(619\) 21.6806 0.871418 0.435709 0.900088i \(-0.356498\pi\)
0.435709 + 0.900088i \(0.356498\pi\)
\(620\) −45.0005 −1.80727
\(621\) 1.72105 0.0690634
\(622\) 1.01317 0.0406245
\(623\) 6.98103 0.279689
\(624\) 9.93873 0.397868
\(625\) −30.0916 −1.20366
\(626\) 24.5253 0.980228
\(627\) 1.40437 0.0560853
\(628\) 8.51223 0.339675
\(629\) −3.51007 −0.139956
\(630\) 35.3512 1.40843
\(631\) −12.7828 −0.508877 −0.254439 0.967089i \(-0.581891\pi\)
−0.254439 + 0.967089i \(0.581891\pi\)
\(632\) 17.1667 0.682855
\(633\) 74.7649 2.97164
\(634\) −0.577165 −0.0229222
\(635\) −16.4572 −0.653085
\(636\) −15.0852 −0.598165
\(637\) −1.80328 −0.0714485
\(638\) −16.9722 −0.671935
\(639\) −19.4114 −0.767904
\(640\) −32.2779 −1.27589
\(641\) 14.6413 0.578297 0.289148 0.957284i \(-0.406628\pi\)
0.289148 + 0.957284i \(0.406628\pi\)
\(642\) −113.064 −4.46227
\(643\) 45.4149 1.79099 0.895494 0.445074i \(-0.146823\pi\)
0.895494 + 0.445074i \(0.146823\pi\)
\(644\) 0.464661 0.0183102
\(645\) 13.6384 0.537011
\(646\) −0.355373 −0.0139819
\(647\) −22.9211 −0.901120 −0.450560 0.892746i \(-0.648776\pi\)
−0.450560 + 0.892746i \(0.648776\pi\)
\(648\) −21.5840 −0.847900
\(649\) 13.8280 0.542797
\(650\) 5.61817 0.220363
\(651\) 19.4923 0.763965
\(652\) 19.9337 0.780665
\(653\) −6.52087 −0.255181 −0.127591 0.991827i \(-0.540724\pi\)
−0.127591 + 0.991827i \(0.540724\pi\)
\(654\) 95.1099 3.71909
\(655\) 46.6587 1.82311
\(656\) −10.1111 −0.394771
\(657\) 105.373 4.11098
\(658\) 19.3282 0.753491
\(659\) 29.1233 1.13448 0.567242 0.823551i \(-0.308010\pi\)
0.567242 + 0.823551i \(0.308010\pi\)
\(660\) −22.3481 −0.869897
\(661\) −7.44150 −0.289441 −0.144720 0.989473i \(-0.546228\pi\)
−0.144720 + 0.989473i \(0.546228\pi\)
\(662\) −35.4778 −1.37888
\(663\) −2.01854 −0.0783935
\(664\) 14.9091 0.578587
\(665\) −1.12576 −0.0436552
\(666\) 133.910 5.18889
\(667\) 1.25133 0.0484515
\(668\) −21.6696 −0.838423
\(669\) −23.0035 −0.889368
\(670\) 68.6855 2.65355
\(671\) −3.78039 −0.145940
\(672\) 22.6309 0.873008
\(673\) 9.38404 0.361728 0.180864 0.983508i \(-0.442111\pi\)
0.180864 + 0.983508i \(0.442111\pi\)
\(674\) −23.4995 −0.905169
\(675\) 14.7060 0.566034
\(676\) −27.1858 −1.04561
\(677\) −26.4008 −1.01467 −0.507333 0.861750i \(-0.669369\pi\)
−0.507333 + 0.861750i \(0.669369\pi\)
\(678\) −28.3558 −1.08900
\(679\) 6.46081 0.247943
\(680\) 1.59954 0.0613396
\(681\) 21.5427 0.825518
\(682\) −14.3877 −0.550932
\(683\) 13.5006 0.516586 0.258293 0.966067i \(-0.416840\pi\)
0.258293 + 0.966067i \(0.416840\pi\)
\(684\) 7.89535 0.301886
\(685\) −14.3908 −0.549843
\(686\) −2.18834 −0.0835510
\(687\) −63.7410 −2.43187
\(688\) 3.16390 0.120623
\(689\) 3.18593 0.121374
\(690\) 2.82931 0.107710
\(691\) 32.6554 1.24227 0.621134 0.783704i \(-0.286672\pi\)
0.621134 + 0.783704i \(0.286672\pi\)
\(692\) 51.2693 1.94897
\(693\) 6.58216 0.250036
\(694\) −75.8438 −2.87899
\(695\) 22.4306 0.850841
\(696\) −39.6915 −1.50450
\(697\) 2.05354 0.0777834
\(698\) −51.0245 −1.93130
\(699\) 18.7986 0.711027
\(700\) 3.97042 0.150068
\(701\) −19.0983 −0.721334 −0.360667 0.932695i \(-0.617451\pi\)
−0.360667 + 0.932695i \(0.617451\pi\)
\(702\) 40.7618 1.53846
\(703\) −4.26436 −0.160833
\(704\) −12.9863 −0.489441
\(705\) 68.5374 2.58127
\(706\) 42.0346 1.58199
\(707\) −7.53537 −0.283397
\(708\) 114.332 4.29684
\(709\) −6.35006 −0.238482 −0.119241 0.992865i \(-0.538046\pi\)
−0.119241 + 0.992865i \(0.538046\pi\)
\(710\) −16.8914 −0.633923
\(711\) −63.3867 −2.37719
\(712\) −12.0505 −0.451612
\(713\) 1.06077 0.0397263
\(714\) −2.44956 −0.0916724
\(715\) 4.71983 0.176512
\(716\) 8.27449 0.309232
\(717\) −25.4991 −0.952280
\(718\) −45.2606 −1.68911
\(719\) 10.9266 0.407495 0.203748 0.979023i \(-0.434688\pi\)
0.203748 + 0.979023i \(0.434688\pi\)
\(720\) 29.0804 1.08376
\(721\) 16.4601 0.613005
\(722\) 41.1466 1.53132
\(723\) 9.77612 0.363578
\(724\) −50.0689 −1.86080
\(725\) 10.6923 0.397102
\(726\) 66.5543 2.47006
\(727\) 39.4177 1.46192 0.730961 0.682419i \(-0.239072\pi\)
0.730961 + 0.682419i \(0.239072\pi\)
\(728\) 3.11279 0.115368
\(729\) −15.1785 −0.562168
\(730\) 91.6930 3.39371
\(731\) −0.642582 −0.0237668
\(732\) −31.2567 −1.15528
\(733\) 26.9034 0.993699 0.496850 0.867837i \(-0.334490\pi\)
0.496850 + 0.867837i \(0.334490\pi\)
\(734\) −68.6379 −2.53347
\(735\) −7.75980 −0.286224
\(736\) 1.23158 0.0453966
\(737\) 12.7888 0.471081
\(738\) −78.3428 −2.88384
\(739\) −53.5467 −1.96975 −0.984873 0.173278i \(-0.944564\pi\)
−0.984873 + 0.173278i \(0.944564\pi\)
\(740\) 67.8596 2.49457
\(741\) −2.45231 −0.0900878
\(742\) 3.86622 0.141934
\(743\) −19.5540 −0.717366 −0.358683 0.933459i \(-0.616774\pi\)
−0.358683 + 0.933459i \(0.616774\pi\)
\(744\) −33.6473 −1.23357
\(745\) −60.3624 −2.21151
\(746\) 52.7651 1.93187
\(747\) −55.0509 −2.01421
\(748\) 1.05294 0.0384995
\(749\) 16.8753 0.616610
\(750\) −60.7293 −2.21752
\(751\) −17.6934 −0.645640 −0.322820 0.946460i \(-0.604631\pi\)
−0.322820 + 0.946460i \(0.604631\pi\)
\(752\) 15.8996 0.579800
\(753\) 34.0249 1.23994
\(754\) 29.6367 1.07931
\(755\) −23.5724 −0.857889
\(756\) 28.8069 1.04770
\(757\) 13.2039 0.479903 0.239952 0.970785i \(-0.422868\pi\)
0.239952 + 0.970785i \(0.422868\pi\)
\(758\) −6.22018 −0.225927
\(759\) 0.526800 0.0191216
\(760\) 1.94327 0.0704899
\(761\) −18.9993 −0.688724 −0.344362 0.938837i \(-0.611905\pi\)
−0.344362 + 0.938837i \(0.611905\pi\)
\(762\) −43.5046 −1.57601
\(763\) −14.1956 −0.513916
\(764\) 40.0806 1.45006
\(765\) −5.90618 −0.213538
\(766\) −50.8618 −1.83771
\(767\) −24.1464 −0.871876
\(768\) −8.32422 −0.300374
\(769\) 24.5604 0.885672 0.442836 0.896603i \(-0.353972\pi\)
0.442836 + 0.896603i \(0.353972\pi\)
\(770\) 5.72766 0.206410
\(771\) 27.6960 0.997448
\(772\) −43.3131 −1.55887
\(773\) −21.1364 −0.760223 −0.380111 0.924941i \(-0.624114\pi\)
−0.380111 + 0.924941i \(0.624114\pi\)
\(774\) 24.5146 0.881160
\(775\) 9.06408 0.325591
\(776\) −11.1525 −0.400353
\(777\) −29.3939 −1.05450
\(778\) −61.1238 −2.19140
\(779\) 2.49483 0.0893867
\(780\) 39.0241 1.39729
\(781\) −3.14507 −0.112539
\(782\) −0.133305 −0.00476698
\(783\) 77.5764 2.77236
\(784\) −1.80016 −0.0642913
\(785\) −7.73601 −0.276110
\(786\) 123.342 4.39947
\(787\) −36.1468 −1.28849 −0.644247 0.764817i \(-0.722829\pi\)
−0.644247 + 0.764817i \(0.722829\pi\)
\(788\) 62.3387 2.22073
\(789\) −10.6382 −0.378731
\(790\) −55.1577 −1.96242
\(791\) 4.23224 0.150481
\(792\) −11.3620 −0.403732
\(793\) 6.60129 0.234419
\(794\) −2.98272 −0.105853
\(795\) 13.7096 0.486228
\(796\) 21.3386 0.756325
\(797\) −27.1430 −0.961453 −0.480727 0.876871i \(-0.659627\pi\)
−0.480727 + 0.876871i \(0.659627\pi\)
\(798\) −2.97595 −0.105348
\(799\) −3.22919 −0.114240
\(800\) 10.5236 0.372064
\(801\) 44.4956 1.57218
\(802\) −21.7203 −0.766969
\(803\) 17.0726 0.602480
\(804\) 105.739 3.72913
\(805\) −0.422289 −0.0148837
\(806\) 25.1237 0.884943
\(807\) −30.0226 −1.05685
\(808\) 13.0074 0.457600
\(809\) −12.3761 −0.435121 −0.217561 0.976047i \(-0.569810\pi\)
−0.217561 + 0.976047i \(0.569810\pi\)
\(810\) 69.3509 2.43674
\(811\) −36.6159 −1.28576 −0.642879 0.765967i \(-0.722260\pi\)
−0.642879 + 0.765967i \(0.722260\pi\)
\(812\) 20.9446 0.735011
\(813\) −70.2311 −2.46311
\(814\) 21.6962 0.760452
\(815\) −18.1160 −0.634576
\(816\) −2.01504 −0.0705405
\(817\) −0.780670 −0.0273122
\(818\) −64.6288 −2.25969
\(819\) −11.4937 −0.401624
\(820\) −39.7008 −1.38641
\(821\) 16.7224 0.583617 0.291809 0.956477i \(-0.405743\pi\)
0.291809 + 0.956477i \(0.405743\pi\)
\(822\) −38.0420 −1.32687
\(823\) −19.5991 −0.683183 −0.341591 0.939849i \(-0.610966\pi\)
−0.341591 + 0.939849i \(0.610966\pi\)
\(824\) −28.4131 −0.989816
\(825\) 4.50138 0.156718
\(826\) −29.3024 −1.01956
\(827\) 6.90812 0.240219 0.120110 0.992761i \(-0.461675\pi\)
0.120110 + 0.992761i \(0.461675\pi\)
\(828\) 2.96165 0.102925
\(829\) 38.4627 1.33587 0.667933 0.744222i \(-0.267179\pi\)
0.667933 + 0.744222i \(0.267179\pi\)
\(830\) −47.9041 −1.66277
\(831\) 9.41928 0.326751
\(832\) 22.6766 0.786171
\(833\) 0.365608 0.0126676
\(834\) 59.2953 2.05323
\(835\) 19.6936 0.681525
\(836\) 1.27922 0.0442426
\(837\) 65.7632 2.27311
\(838\) 49.3819 1.70587
\(839\) 20.1537 0.695784 0.347892 0.937535i \(-0.386898\pi\)
0.347892 + 0.937535i \(0.386898\pi\)
\(840\) 13.3948 0.462165
\(841\) 27.4035 0.944949
\(842\) 36.3192 1.25164
\(843\) 72.5961 2.50034
\(844\) 68.1019 2.34416
\(845\) 24.7068 0.849939
\(846\) 123.194 4.23549
\(847\) −9.93355 −0.341321
\(848\) 3.18041 0.109216
\(849\) −12.1782 −0.417954
\(850\) −1.13906 −0.0390695
\(851\) −1.59962 −0.0548342
\(852\) −26.0038 −0.890874
\(853\) 11.7285 0.401575 0.200788 0.979635i \(-0.435650\pi\)
0.200788 + 0.979635i \(0.435650\pi\)
\(854\) 8.01087 0.274126
\(855\) −7.17538 −0.245393
\(856\) −29.1299 −0.995639
\(857\) −14.3190 −0.489129 −0.244564 0.969633i \(-0.578645\pi\)
−0.244564 + 0.969633i \(0.578645\pi\)
\(858\) 12.4769 0.425953
\(859\) −1.00000 −0.0341196
\(860\) 12.4229 0.423619
\(861\) 17.1967 0.586062
\(862\) 17.3856 0.592155
\(863\) 0.496892 0.0169144 0.00845720 0.999964i \(-0.497308\pi\)
0.00845720 + 0.999964i \(0.497308\pi\)
\(864\) 76.3522 2.59756
\(865\) −46.5941 −1.58425
\(866\) 82.9222 2.81781
\(867\) −51.6391 −1.75375
\(868\) 17.7552 0.602650
\(869\) −10.2700 −0.348386
\(870\) 127.531 4.32372
\(871\) −22.3317 −0.756681
\(872\) 24.5042 0.829817
\(873\) 41.1799 1.39373
\(874\) −0.161952 −0.00547809
\(875\) 9.06414 0.306424
\(876\) 141.158 4.76930
\(877\) −5.00805 −0.169110 −0.0845549 0.996419i \(-0.526947\pi\)
−0.0845549 + 0.996419i \(0.526947\pi\)
\(878\) −0.621861 −0.0209868
\(879\) 42.5921 1.43660
\(880\) 4.71165 0.158830
\(881\) 44.4434 1.49734 0.748668 0.662945i \(-0.230694\pi\)
0.748668 + 0.662945i \(0.230694\pi\)
\(882\) −13.9480 −0.469654
\(883\) 38.7823 1.30513 0.652564 0.757733i \(-0.273693\pi\)
0.652564 + 0.757733i \(0.273693\pi\)
\(884\) −1.83865 −0.0618403
\(885\) −103.906 −3.49276
\(886\) −65.9525 −2.21572
\(887\) 21.5559 0.723776 0.361888 0.932222i \(-0.382132\pi\)
0.361888 + 0.932222i \(0.382132\pi\)
\(888\) 50.7392 1.70270
\(889\) 6.49327 0.217777
\(890\) 38.7191 1.29787
\(891\) 12.9127 0.432591
\(892\) −20.9535 −0.701574
\(893\) −3.92312 −0.131282
\(894\) −159.568 −5.33675
\(895\) −7.51995 −0.251364
\(896\) 12.7354 0.425460
\(897\) −0.919894 −0.0307144
\(898\) 81.4613 2.71840
\(899\) 47.8144 1.59470
\(900\) 25.3067 0.843556
\(901\) −0.645935 −0.0215192
\(902\) −12.6932 −0.422638
\(903\) −5.38110 −0.179072
\(904\) −7.30561 −0.242981
\(905\) 45.5032 1.51258
\(906\) −62.3137 −2.07023
\(907\) −12.6792 −0.421007 −0.210503 0.977593i \(-0.567510\pi\)
−0.210503 + 0.977593i \(0.567510\pi\)
\(908\) 19.6228 0.651206
\(909\) −48.0290 −1.59302
\(910\) −10.0016 −0.331550
\(911\) −55.9229 −1.85281 −0.926404 0.376530i \(-0.877117\pi\)
−0.926404 + 0.376530i \(0.877117\pi\)
\(912\) −2.44806 −0.0810634
\(913\) −8.91942 −0.295190
\(914\) −1.98366 −0.0656136
\(915\) 28.4064 0.939087
\(916\) −58.0604 −1.91837
\(917\) −18.4094 −0.607933
\(918\) −8.26431 −0.272763
\(919\) −10.4143 −0.343535 −0.171767 0.985138i \(-0.554948\pi\)
−0.171767 + 0.985138i \(0.554948\pi\)
\(920\) 0.728948 0.0240327
\(921\) −17.2564 −0.568617
\(922\) −85.6924 −2.82213
\(923\) 5.49189 0.180768
\(924\) 8.81754 0.290076
\(925\) −13.6684 −0.449414
\(926\) 12.5103 0.411115
\(927\) 104.913 3.44580
\(928\) 55.5134 1.82232
\(929\) −13.5039 −0.443049 −0.221524 0.975155i \(-0.571103\pi\)
−0.221524 + 0.975155i \(0.571103\pi\)
\(930\) 108.111 3.54510
\(931\) 0.444175 0.0145573
\(932\) 17.1232 0.560891
\(933\) −1.41751 −0.0464073
\(934\) 87.1170 2.85056
\(935\) −0.956927 −0.0312949
\(936\) 19.8403 0.648500
\(937\) 19.3030 0.630601 0.315300 0.948992i \(-0.397895\pi\)
0.315300 + 0.948992i \(0.397895\pi\)
\(938\) −27.1002 −0.884853
\(939\) −34.3129 −1.11976
\(940\) 62.4293 2.03622
\(941\) −44.7842 −1.45992 −0.729962 0.683488i \(-0.760462\pi\)
−0.729962 + 0.683488i \(0.760462\pi\)
\(942\) −20.4501 −0.666301
\(943\) 0.935846 0.0304753
\(944\) −24.1046 −0.784537
\(945\) −26.1800 −0.851635
\(946\) 3.97189 0.129137
\(947\) 13.1630 0.427740 0.213870 0.976862i \(-0.431393\pi\)
0.213870 + 0.976862i \(0.431393\pi\)
\(948\) −84.9136 −2.75786
\(949\) −29.8121 −0.967742
\(950\) −1.38384 −0.0448977
\(951\) 0.807503 0.0261851
\(952\) −0.631106 −0.0204543
\(953\) 26.0629 0.844259 0.422129 0.906536i \(-0.361283\pi\)
0.422129 + 0.906536i \(0.361283\pi\)
\(954\) 24.6425 0.797831
\(955\) −36.4257 −1.17871
\(956\) −23.2266 −0.751202
\(957\) 23.7455 0.767583
\(958\) 26.4820 0.855594
\(959\) 5.67795 0.183350
\(960\) 97.5812 3.14942
\(961\) 9.53332 0.307527
\(962\) −37.8858 −1.22149
\(963\) 107.560 3.46607
\(964\) 8.90487 0.286807
\(965\) 39.3634 1.26715
\(966\) −1.11632 −0.0359170
\(967\) 17.8254 0.573225 0.286613 0.958047i \(-0.407471\pi\)
0.286613 + 0.958047i \(0.407471\pi\)
\(968\) 17.1471 0.551129
\(969\) 0.497196 0.0159722
\(970\) 35.8339 1.15056
\(971\) 35.0593 1.12511 0.562553 0.826761i \(-0.309819\pi\)
0.562553 + 0.826761i \(0.309819\pi\)
\(972\) 20.3428 0.652497
\(973\) −8.85010 −0.283721
\(974\) −42.6071 −1.36522
\(975\) −7.86029 −0.251731
\(976\) 6.58986 0.210936
\(977\) −3.24167 −0.103710 −0.0518551 0.998655i \(-0.516513\pi\)
−0.0518551 + 0.998655i \(0.516513\pi\)
\(978\) −47.8896 −1.53134
\(979\) 7.20924 0.230408
\(980\) −7.06825 −0.225787
\(981\) −90.4799 −2.88880
\(982\) 51.0866 1.63024
\(983\) 33.8836 1.08072 0.540359 0.841435i \(-0.318288\pi\)
0.540359 + 0.841435i \(0.318288\pi\)
\(984\) −29.6846 −0.946312
\(985\) −56.6541 −1.80515
\(986\) −6.00873 −0.191357
\(987\) −27.0418 −0.860749
\(988\) −2.23376 −0.0710653
\(989\) −0.292840 −0.00931176
\(990\) 36.5069 1.16027
\(991\) −5.01954 −0.159451 −0.0797254 0.996817i \(-0.525404\pi\)
−0.0797254 + 0.996817i \(0.525404\pi\)
\(992\) 47.0599 1.49415
\(993\) 49.6364 1.57516
\(994\) 6.66458 0.211388
\(995\) −19.3927 −0.614790
\(996\) −73.7467 −2.33675
\(997\) 13.6730 0.433029 0.216514 0.976279i \(-0.430531\pi\)
0.216514 + 0.976279i \(0.430531\pi\)
\(998\) 3.05509 0.0967072
\(999\) −99.1691 −3.13757
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 \(a_p\))