Properties

Label 8013.2.a.d.1.12
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.41705 q^{2}\) \(+1.00000 q^{3}\) \(+3.84214 q^{4}\) \(-2.77464 q^{5}\) \(-2.41705 q^{6}\) \(+0.900586 q^{7}\) \(-4.45255 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.41705 q^{2}\) \(+1.00000 q^{3}\) \(+3.84214 q^{4}\) \(-2.77464 q^{5}\) \(-2.41705 q^{6}\) \(+0.900586 q^{7}\) \(-4.45255 q^{8}\) \(+1.00000 q^{9}\) \(+6.70646 q^{10}\) \(-1.27387 q^{11}\) \(+3.84214 q^{12}\) \(-5.58494 q^{13}\) \(-2.17676 q^{14}\) \(-2.77464 q^{15}\) \(+3.07777 q^{16}\) \(-2.93223 q^{17}\) \(-2.41705 q^{18}\) \(-1.37714 q^{19}\) \(-10.6606 q^{20}\) \(+0.900586 q^{21}\) \(+3.07901 q^{22}\) \(-9.43206 q^{23}\) \(-4.45255 q^{24}\) \(+2.69865 q^{25}\) \(+13.4991 q^{26}\) \(+1.00000 q^{27}\) \(+3.46018 q^{28}\) \(-1.09717 q^{29}\) \(+6.70646 q^{30}\) \(+1.22262 q^{31}\) \(+1.46598 q^{32}\) \(-1.27387 q^{33}\) \(+7.08736 q^{34}\) \(-2.49881 q^{35}\) \(+3.84214 q^{36}\) \(+0.111472 q^{37}\) \(+3.32861 q^{38}\) \(-5.58494 q^{39}\) \(+12.3542 q^{40}\) \(-6.36057 q^{41}\) \(-2.17676 q^{42}\) \(+8.45869 q^{43}\) \(-4.89439 q^{44}\) \(-2.77464 q^{45}\) \(+22.7978 q^{46}\) \(-9.34739 q^{47}\) \(+3.07777 q^{48}\) \(-6.18894 q^{49}\) \(-6.52278 q^{50}\) \(-2.93223 q^{51}\) \(-21.4581 q^{52}\) \(-0.694746 q^{53}\) \(-2.41705 q^{54}\) \(+3.53454 q^{55}\) \(-4.00991 q^{56}\) \(-1.37714 q^{57}\) \(+2.65191 q^{58}\) \(-13.1818 q^{59}\) \(-10.6606 q^{60}\) \(-4.89206 q^{61}\) \(-2.95514 q^{62}\) \(+0.900586 q^{63}\) \(-9.69888 q^{64}\) \(+15.4962 q^{65}\) \(+3.07901 q^{66}\) \(-2.71553 q^{67}\) \(-11.2661 q^{68}\) \(-9.43206 q^{69}\) \(+6.03974 q^{70}\) \(+2.87878 q^{71}\) \(-4.45255 q^{72}\) \(-8.94958 q^{73}\) \(-0.269434 q^{74}\) \(+2.69865 q^{75}\) \(-5.29116 q^{76}\) \(-1.14723 q^{77}\) \(+13.4991 q^{78}\) \(+8.01421 q^{79}\) \(-8.53971 q^{80}\) \(+1.00000 q^{81}\) \(+15.3738 q^{82}\) \(-0.206750 q^{83}\) \(+3.46018 q^{84}\) \(+8.13590 q^{85}\) \(-20.4451 q^{86}\) \(-1.09717 q^{87}\) \(+5.67197 q^{88}\) \(+13.6189 q^{89}\) \(+6.70646 q^{90}\) \(-5.02972 q^{91}\) \(-36.2393 q^{92}\) \(+1.22262 q^{93}\) \(+22.5931 q^{94}\) \(+3.82107 q^{95}\) \(+1.46598 q^{96}\) \(+3.46030 q^{97}\) \(+14.9590 q^{98}\) \(-1.27387 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41705 −1.70911 −0.854557 0.519358i \(-0.826171\pi\)
−0.854557 + 0.519358i \(0.826171\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.84214 1.92107
\(5\) −2.77464 −1.24086 −0.620429 0.784262i \(-0.713042\pi\)
−0.620429 + 0.784262i \(0.713042\pi\)
\(6\) −2.41705 −0.986757
\(7\) 0.900586 0.340390 0.170195 0.985410i \(-0.445560\pi\)
0.170195 + 0.985410i \(0.445560\pi\)
\(8\) −4.45255 −1.57421
\(9\) 1.00000 0.333333
\(10\) 6.70646 2.12077
\(11\) −1.27387 −0.384086 −0.192043 0.981386i \(-0.561511\pi\)
−0.192043 + 0.981386i \(0.561511\pi\)
\(12\) 3.84214 1.10913
\(13\) −5.58494 −1.54898 −0.774491 0.632585i \(-0.781994\pi\)
−0.774491 + 0.632585i \(0.781994\pi\)
\(14\) −2.17676 −0.581764
\(15\) −2.77464 −0.716410
\(16\) 3.07777 0.769442
\(17\) −2.93223 −0.711171 −0.355585 0.934644i \(-0.615718\pi\)
−0.355585 + 0.934644i \(0.615718\pi\)
\(18\) −2.41705 −0.569705
\(19\) −1.37714 −0.315937 −0.157968 0.987444i \(-0.550494\pi\)
−0.157968 + 0.987444i \(0.550494\pi\)
\(20\) −10.6606 −2.38378
\(21\) 0.900586 0.196524
\(22\) 3.07901 0.656447
\(23\) −9.43206 −1.96672 −0.983361 0.181665i \(-0.941852\pi\)
−0.983361 + 0.181665i \(0.941852\pi\)
\(24\) −4.45255 −0.908873
\(25\) 2.69865 0.539730
\(26\) 13.4991 2.64739
\(27\) 1.00000 0.192450
\(28\) 3.46018 0.653912
\(29\) −1.09717 −0.203738 −0.101869 0.994798i \(-0.532482\pi\)
−0.101869 + 0.994798i \(0.532482\pi\)
\(30\) 6.70646 1.22443
\(31\) 1.22262 0.219589 0.109794 0.993954i \(-0.464981\pi\)
0.109794 + 0.993954i \(0.464981\pi\)
\(32\) 1.46598 0.259151
\(33\) −1.27387 −0.221752
\(34\) 7.08736 1.21547
\(35\) −2.49881 −0.422375
\(36\) 3.84214 0.640357
\(37\) 0.111472 0.0183259 0.00916296 0.999958i \(-0.497083\pi\)
0.00916296 + 0.999958i \(0.497083\pi\)
\(38\) 3.32861 0.539972
\(39\) −5.58494 −0.894305
\(40\) 12.3542 1.95338
\(41\) −6.36057 −0.993353 −0.496677 0.867936i \(-0.665447\pi\)
−0.496677 + 0.867936i \(0.665447\pi\)
\(42\) −2.17676 −0.335882
\(43\) 8.45869 1.28994 0.644969 0.764209i \(-0.276870\pi\)
0.644969 + 0.764209i \(0.276870\pi\)
\(44\) −4.89439 −0.737857
\(45\) −2.77464 −0.413620
\(46\) 22.7978 3.36135
\(47\) −9.34739 −1.36346 −0.681729 0.731605i \(-0.738771\pi\)
−0.681729 + 0.731605i \(0.738771\pi\)
\(48\) 3.07777 0.444237
\(49\) −6.18894 −0.884135
\(50\) −6.52278 −0.922461
\(51\) −2.93223 −0.410595
\(52\) −21.4581 −2.97570
\(53\) −0.694746 −0.0954307 −0.0477153 0.998861i \(-0.515194\pi\)
−0.0477153 + 0.998861i \(0.515194\pi\)
\(54\) −2.41705 −0.328919
\(55\) 3.53454 0.476597
\(56\) −4.00991 −0.535846
\(57\) −1.37714 −0.182406
\(58\) 2.65191 0.348212
\(59\) −13.1818 −1.71613 −0.858064 0.513543i \(-0.828333\pi\)
−0.858064 + 0.513543i \(0.828333\pi\)
\(60\) −10.6606 −1.37627
\(61\) −4.89206 −0.626364 −0.313182 0.949693i \(-0.601395\pi\)
−0.313182 + 0.949693i \(0.601395\pi\)
\(62\) −2.95514 −0.375303
\(63\) 0.900586 0.113463
\(64\) −9.69888 −1.21236
\(65\) 15.4962 1.92207
\(66\) 3.07901 0.379000
\(67\) −2.71553 −0.331755 −0.165878 0.986146i \(-0.553046\pi\)
−0.165878 + 0.986146i \(0.553046\pi\)
\(68\) −11.2661 −1.36621
\(69\) −9.43206 −1.13549
\(70\) 6.03974 0.721888
\(71\) 2.87878 0.341648 0.170824 0.985302i \(-0.445357\pi\)
0.170824 + 0.985302i \(0.445357\pi\)
\(72\) −4.45255 −0.524738
\(73\) −8.94958 −1.04747 −0.523734 0.851882i \(-0.675462\pi\)
−0.523734 + 0.851882i \(0.675462\pi\)
\(74\) −0.269434 −0.0313211
\(75\) 2.69865 0.311614
\(76\) −5.29116 −0.606937
\(77\) −1.14723 −0.130739
\(78\) 13.4991 1.52847
\(79\) 8.01421 0.901669 0.450835 0.892607i \(-0.351126\pi\)
0.450835 + 0.892607i \(0.351126\pi\)
\(80\) −8.53971 −0.954769
\(81\) 1.00000 0.111111
\(82\) 15.3738 1.69775
\(83\) −0.206750 −0.0226938 −0.0113469 0.999936i \(-0.503612\pi\)
−0.0113469 + 0.999936i \(0.503612\pi\)
\(84\) 3.46018 0.377536
\(85\) 8.13590 0.882462
\(86\) −20.4451 −2.20465
\(87\) −1.09717 −0.117628
\(88\) 5.67197 0.604634
\(89\) 13.6189 1.44360 0.721801 0.692101i \(-0.243315\pi\)
0.721801 + 0.692101i \(0.243315\pi\)
\(90\) 6.70646 0.706923
\(91\) −5.02972 −0.527257
\(92\) −36.2393 −3.77821
\(93\) 1.22262 0.126780
\(94\) 22.5931 2.33030
\(95\) 3.82107 0.392033
\(96\) 1.46598 0.149621
\(97\) 3.46030 0.351340 0.175670 0.984449i \(-0.443791\pi\)
0.175670 + 0.984449i \(0.443791\pi\)
\(98\) 14.9590 1.51109
\(99\) −1.27387 −0.128029
\(100\) 10.3686 1.03686
\(101\) −8.67687 −0.863381 −0.431690 0.902022i \(-0.642083\pi\)
−0.431690 + 0.902022i \(0.642083\pi\)
\(102\) 7.08736 0.701753
\(103\) 7.66574 0.755328 0.377664 0.925943i \(-0.376727\pi\)
0.377664 + 0.925943i \(0.376727\pi\)
\(104\) 24.8672 2.43843
\(105\) −2.49881 −0.243859
\(106\) 1.67924 0.163102
\(107\) 2.63298 0.254539 0.127270 0.991868i \(-0.459379\pi\)
0.127270 + 0.991868i \(0.459379\pi\)
\(108\) 3.84214 0.369710
\(109\) −11.3577 −1.08787 −0.543934 0.839128i \(-0.683066\pi\)
−0.543934 + 0.839128i \(0.683066\pi\)
\(110\) −8.54316 −0.814558
\(111\) 0.111472 0.0105805
\(112\) 2.77179 0.261910
\(113\) 5.64352 0.530897 0.265449 0.964125i \(-0.414480\pi\)
0.265449 + 0.964125i \(0.414480\pi\)
\(114\) 3.32861 0.311753
\(115\) 26.1706 2.44042
\(116\) −4.21546 −0.391396
\(117\) −5.58494 −0.516328
\(118\) 31.8612 2.93306
\(119\) −2.64073 −0.242075
\(120\) 12.3542 1.12778
\(121\) −9.37726 −0.852478
\(122\) 11.8244 1.07053
\(123\) −6.36057 −0.573513
\(124\) 4.69748 0.421846
\(125\) 6.38542 0.571129
\(126\) −2.17676 −0.193921
\(127\) 10.7700 0.955682 0.477841 0.878446i \(-0.341419\pi\)
0.477841 + 0.878446i \(0.341419\pi\)
\(128\) 20.5107 1.81291
\(129\) 8.45869 0.744746
\(130\) −37.4552 −3.28503
\(131\) −13.3198 −1.16375 −0.581876 0.813277i \(-0.697681\pi\)
−0.581876 + 0.813277i \(0.697681\pi\)
\(132\) −4.89439 −0.426002
\(133\) −1.24023 −0.107542
\(134\) 6.56359 0.567008
\(135\) −2.77464 −0.238803
\(136\) 13.0559 1.11954
\(137\) −3.15516 −0.269564 −0.134782 0.990875i \(-0.543033\pi\)
−0.134782 + 0.990875i \(0.543033\pi\)
\(138\) 22.7978 1.94068
\(139\) −11.1880 −0.948952 −0.474476 0.880268i \(-0.657363\pi\)
−0.474476 + 0.880268i \(0.657363\pi\)
\(140\) −9.60077 −0.811413
\(141\) −9.34739 −0.787192
\(142\) −6.95816 −0.583916
\(143\) 7.11448 0.594943
\(144\) 3.07777 0.256481
\(145\) 3.04424 0.252811
\(146\) 21.6316 1.79024
\(147\) −6.18894 −0.510456
\(148\) 0.428292 0.0352054
\(149\) 23.2434 1.90418 0.952088 0.305824i \(-0.0989318\pi\)
0.952088 + 0.305824i \(0.0989318\pi\)
\(150\) −6.52278 −0.532583
\(151\) 14.3304 1.16619 0.583096 0.812403i \(-0.301841\pi\)
0.583096 + 0.812403i \(0.301841\pi\)
\(152\) 6.13177 0.497353
\(153\) −2.93223 −0.237057
\(154\) 2.77291 0.223448
\(155\) −3.39233 −0.272479
\(156\) −21.4581 −1.71802
\(157\) 17.0943 1.36428 0.682138 0.731224i \(-0.261050\pi\)
0.682138 + 0.731224i \(0.261050\pi\)
\(158\) −19.3708 −1.54106
\(159\) −0.694746 −0.0550969
\(160\) −4.06757 −0.321570
\(161\) −8.49438 −0.669451
\(162\) −2.41705 −0.189902
\(163\) 15.9899 1.25243 0.626214 0.779651i \(-0.284604\pi\)
0.626214 + 0.779651i \(0.284604\pi\)
\(164\) −24.4382 −1.90830
\(165\) 3.53454 0.275163
\(166\) 0.499726 0.0387862
\(167\) −17.1243 −1.32512 −0.662560 0.749009i \(-0.730530\pi\)
−0.662560 + 0.749009i \(0.730530\pi\)
\(168\) −4.00991 −0.309371
\(169\) 18.1915 1.39935
\(170\) −19.6649 −1.50823
\(171\) −1.37714 −0.105312
\(172\) 32.4995 2.47806
\(173\) 4.42061 0.336092 0.168046 0.985779i \(-0.446254\pi\)
0.168046 + 0.985779i \(0.446254\pi\)
\(174\) 2.65191 0.201040
\(175\) 2.43037 0.183719
\(176\) −3.92068 −0.295532
\(177\) −13.1818 −0.990807
\(178\) −32.9176 −2.46728
\(179\) 6.66218 0.497954 0.248977 0.968509i \(-0.419906\pi\)
0.248977 + 0.968509i \(0.419906\pi\)
\(180\) −10.6606 −0.794592
\(181\) −12.3817 −0.920323 −0.460162 0.887835i \(-0.652209\pi\)
−0.460162 + 0.887835i \(0.652209\pi\)
\(182\) 12.1571 0.901143
\(183\) −4.89206 −0.361632
\(184\) 41.9968 3.09604
\(185\) −0.309296 −0.0227399
\(186\) −2.95514 −0.216681
\(187\) 3.73528 0.273151
\(188\) −35.9140 −2.61930
\(189\) 0.900586 0.0655080
\(190\) −9.23572 −0.670029
\(191\) −26.5656 −1.92222 −0.961111 0.276162i \(-0.910938\pi\)
−0.961111 + 0.276162i \(0.910938\pi\)
\(192\) −9.69888 −0.699957
\(193\) 14.1004 1.01497 0.507486 0.861660i \(-0.330575\pi\)
0.507486 + 0.861660i \(0.330575\pi\)
\(194\) −8.36372 −0.600480
\(195\) 15.4962 1.10971
\(196\) −23.7788 −1.69849
\(197\) 7.60149 0.541584 0.270792 0.962638i \(-0.412714\pi\)
0.270792 + 0.962638i \(0.412714\pi\)
\(198\) 3.07901 0.218816
\(199\) −17.7245 −1.25646 −0.628229 0.778029i \(-0.716220\pi\)
−0.628229 + 0.778029i \(0.716220\pi\)
\(200\) −12.0159 −0.849652
\(201\) −2.71553 −0.191539
\(202\) 20.9725 1.47562
\(203\) −0.988091 −0.0693504
\(204\) −11.2661 −0.788781
\(205\) 17.6483 1.23261
\(206\) −18.5285 −1.29094
\(207\) −9.43206 −0.655574
\(208\) −17.1891 −1.19185
\(209\) 1.75429 0.121347
\(210\) 6.03974 0.416782
\(211\) −23.1567 −1.59418 −0.797088 0.603863i \(-0.793627\pi\)
−0.797088 + 0.603863i \(0.793627\pi\)
\(212\) −2.66931 −0.183329
\(213\) 2.87878 0.197251
\(214\) −6.36404 −0.435037
\(215\) −23.4699 −1.60063
\(216\) −4.45255 −0.302958
\(217\) 1.10107 0.0747458
\(218\) 27.4521 1.85929
\(219\) −8.94958 −0.604756
\(220\) 13.5802 0.915576
\(221\) 16.3763 1.10159
\(222\) −0.269434 −0.0180832
\(223\) 23.9637 1.60473 0.802365 0.596833i \(-0.203575\pi\)
0.802365 + 0.596833i \(0.203575\pi\)
\(224\) 1.32024 0.0882123
\(225\) 2.69865 0.179910
\(226\) −13.6407 −0.907364
\(227\) 10.1059 0.670755 0.335377 0.942084i \(-0.391136\pi\)
0.335377 + 0.942084i \(0.391136\pi\)
\(228\) −5.29116 −0.350415
\(229\) −26.9013 −1.77769 −0.888844 0.458211i \(-0.848490\pi\)
−0.888844 + 0.458211i \(0.848490\pi\)
\(230\) −63.2558 −4.17096
\(231\) −1.14723 −0.0754821
\(232\) 4.88518 0.320728
\(233\) −2.47081 −0.161868 −0.0809340 0.996719i \(-0.525790\pi\)
−0.0809340 + 0.996719i \(0.525790\pi\)
\(234\) 13.4991 0.882463
\(235\) 25.9357 1.69186
\(236\) −50.6464 −3.29680
\(237\) 8.01421 0.520579
\(238\) 6.38278 0.413734
\(239\) −2.94597 −0.190559 −0.0952793 0.995451i \(-0.530374\pi\)
−0.0952793 + 0.995451i \(0.530374\pi\)
\(240\) −8.53971 −0.551236
\(241\) −5.51845 −0.355475 −0.177737 0.984078i \(-0.556878\pi\)
−0.177737 + 0.984078i \(0.556878\pi\)
\(242\) 22.6653 1.45698
\(243\) 1.00000 0.0641500
\(244\) −18.7960 −1.20329
\(245\) 17.1721 1.09709
\(246\) 15.3738 0.980199
\(247\) 7.69122 0.489381
\(248\) −5.44378 −0.345680
\(249\) −0.206750 −0.0131023
\(250\) −15.4339 −0.976125
\(251\) 13.9211 0.878691 0.439345 0.898318i \(-0.355210\pi\)
0.439345 + 0.898318i \(0.355210\pi\)
\(252\) 3.46018 0.217971
\(253\) 12.0152 0.755390
\(254\) −26.0316 −1.63337
\(255\) 8.13590 0.509490
\(256\) −30.1778 −1.88611
\(257\) 15.5978 0.972964 0.486482 0.873691i \(-0.338280\pi\)
0.486482 + 0.873691i \(0.338280\pi\)
\(258\) −20.4451 −1.27286
\(259\) 0.100390 0.00623795
\(260\) 59.5386 3.69243
\(261\) −1.09717 −0.0679128
\(262\) 32.1946 1.98899
\(263\) −24.4979 −1.51060 −0.755302 0.655377i \(-0.772510\pi\)
−0.755302 + 0.655377i \(0.772510\pi\)
\(264\) 5.67197 0.349086
\(265\) 1.92767 0.118416
\(266\) 2.99770 0.183801
\(267\) 13.6189 0.833464
\(268\) −10.4335 −0.637325
\(269\) −3.34574 −0.203993 −0.101997 0.994785i \(-0.532523\pi\)
−0.101997 + 0.994785i \(0.532523\pi\)
\(270\) 6.70646 0.408142
\(271\) 9.27925 0.563674 0.281837 0.959462i \(-0.409056\pi\)
0.281837 + 0.959462i \(0.409056\pi\)
\(272\) −9.02473 −0.547205
\(273\) −5.02972 −0.304412
\(274\) 7.62619 0.460715
\(275\) −3.43773 −0.207303
\(276\) −36.2393 −2.18135
\(277\) −25.6603 −1.54178 −0.770890 0.636968i \(-0.780188\pi\)
−0.770890 + 0.636968i \(0.780188\pi\)
\(278\) 27.0419 1.62187
\(279\) 1.22262 0.0731963
\(280\) 11.1261 0.664909
\(281\) −14.7166 −0.877920 −0.438960 0.898507i \(-0.644653\pi\)
−0.438960 + 0.898507i \(0.644653\pi\)
\(282\) 22.5931 1.34540
\(283\) 1.36979 0.0814254 0.0407127 0.999171i \(-0.487037\pi\)
0.0407127 + 0.999171i \(0.487037\pi\)
\(284\) 11.0607 0.656331
\(285\) 3.82107 0.226340
\(286\) −17.1961 −1.01683
\(287\) −5.72824 −0.338127
\(288\) 1.46598 0.0863836
\(289\) −8.40201 −0.494236
\(290\) −7.35809 −0.432082
\(291\) 3.46030 0.202846
\(292\) −34.3855 −2.01226
\(293\) −33.2586 −1.94299 −0.971494 0.237063i \(-0.923815\pi\)
−0.971494 + 0.237063i \(0.923815\pi\)
\(294\) 14.9590 0.872427
\(295\) 36.5749 2.12947
\(296\) −0.496336 −0.0288489
\(297\) −1.27387 −0.0739174
\(298\) −56.1806 −3.25445
\(299\) 52.6775 3.04642
\(300\) 10.3686 0.598632
\(301\) 7.61778 0.439081
\(302\) −34.6373 −1.99316
\(303\) −8.67687 −0.498473
\(304\) −4.23851 −0.243095
\(305\) 13.5737 0.777230
\(306\) 7.08736 0.405157
\(307\) 26.7870 1.52881 0.764407 0.644734i \(-0.223032\pi\)
0.764407 + 0.644734i \(0.223032\pi\)
\(308\) −4.40782 −0.251159
\(309\) 7.66574 0.436089
\(310\) 8.19945 0.465697
\(311\) 31.7867 1.80246 0.901229 0.433344i \(-0.142666\pi\)
0.901229 + 0.433344i \(0.142666\pi\)
\(312\) 24.8672 1.40783
\(313\) 29.8834 1.68911 0.844555 0.535469i \(-0.179865\pi\)
0.844555 + 0.535469i \(0.179865\pi\)
\(314\) −41.3179 −2.33170
\(315\) −2.49881 −0.140792
\(316\) 30.7917 1.73217
\(317\) 6.29224 0.353408 0.176704 0.984264i \(-0.443457\pi\)
0.176704 + 0.984264i \(0.443457\pi\)
\(318\) 1.67924 0.0941669
\(319\) 1.39765 0.0782531
\(320\) 26.9110 1.50437
\(321\) 2.63298 0.146958
\(322\) 20.5314 1.14417
\(323\) 4.03809 0.224685
\(324\) 3.84214 0.213452
\(325\) −15.0718 −0.836033
\(326\) −38.6485 −2.14054
\(327\) −11.3577 −0.628080
\(328\) 28.3207 1.56375
\(329\) −8.41813 −0.464106
\(330\) −8.54316 −0.470285
\(331\) 17.7939 0.978042 0.489021 0.872272i \(-0.337354\pi\)
0.489021 + 0.872272i \(0.337354\pi\)
\(332\) −0.794363 −0.0435963
\(333\) 0.111472 0.00610864
\(334\) 41.3904 2.26478
\(335\) 7.53464 0.411661
\(336\) 2.77179 0.151214
\(337\) 34.8773 1.89989 0.949944 0.312420i \(-0.101140\pi\)
0.949944 + 0.312420i \(0.101140\pi\)
\(338\) −43.9698 −2.39164
\(339\) 5.64352 0.306514
\(340\) 31.2593 1.69527
\(341\) −1.55746 −0.0843411
\(342\) 3.32861 0.179991
\(343\) −11.8778 −0.641340
\(344\) −37.6627 −2.03064
\(345\) 26.1706 1.40898
\(346\) −10.6848 −0.574420
\(347\) −23.5893 −1.26634 −0.633171 0.774012i \(-0.718247\pi\)
−0.633171 + 0.774012i \(0.718247\pi\)
\(348\) −4.21546 −0.225973
\(349\) 13.8322 0.740421 0.370211 0.928948i \(-0.379286\pi\)
0.370211 + 0.928948i \(0.379286\pi\)
\(350\) −5.87433 −0.313996
\(351\) −5.58494 −0.298102
\(352\) −1.86747 −0.0995363
\(353\) −30.7694 −1.63769 −0.818844 0.574016i \(-0.805385\pi\)
−0.818844 + 0.574016i \(0.805385\pi\)
\(354\) 31.8612 1.69340
\(355\) −7.98759 −0.423937
\(356\) 52.3258 2.77326
\(357\) −2.64073 −0.139762
\(358\) −16.1028 −0.851061
\(359\) 18.8217 0.993373 0.496686 0.867930i \(-0.334550\pi\)
0.496686 + 0.867930i \(0.334550\pi\)
\(360\) 12.3542 0.651126
\(361\) −17.1035 −0.900184
\(362\) 29.9272 1.57294
\(363\) −9.37726 −0.492178
\(364\) −19.3249 −1.01290
\(365\) 24.8319 1.29976
\(366\) 11.8244 0.618070
\(367\) −16.7292 −0.873255 −0.436628 0.899642i \(-0.643827\pi\)
−0.436628 + 0.899642i \(0.643827\pi\)
\(368\) −29.0297 −1.51328
\(369\) −6.36057 −0.331118
\(370\) 0.747584 0.0388650
\(371\) −0.625678 −0.0324836
\(372\) 4.69748 0.243553
\(373\) 11.2213 0.581015 0.290508 0.956873i \(-0.406176\pi\)
0.290508 + 0.956873i \(0.406176\pi\)
\(374\) −9.02837 −0.466846
\(375\) 6.38542 0.329742
\(376\) 41.6197 2.14637
\(377\) 6.12760 0.315587
\(378\) −2.17676 −0.111961
\(379\) 6.04118 0.310314 0.155157 0.987890i \(-0.450412\pi\)
0.155157 + 0.987890i \(0.450412\pi\)
\(380\) 14.6811 0.753123
\(381\) 10.7700 0.551763
\(382\) 64.2105 3.28530
\(383\) −21.9862 −1.12344 −0.561721 0.827327i \(-0.689860\pi\)
−0.561721 + 0.827327i \(0.689860\pi\)
\(384\) 20.5107 1.04668
\(385\) 3.18315 0.162229
\(386\) −34.0815 −1.73470
\(387\) 8.45869 0.429979
\(388\) 13.2950 0.674949
\(389\) −13.0933 −0.663854 −0.331927 0.943305i \(-0.607699\pi\)
−0.331927 + 0.943305i \(0.607699\pi\)
\(390\) −37.4552 −1.89662
\(391\) 27.6570 1.39867
\(392\) 27.5566 1.39182
\(393\) −13.3198 −0.671893
\(394\) −18.3732 −0.925628
\(395\) −22.2366 −1.11884
\(396\) −4.89439 −0.245952
\(397\) 29.2781 1.46942 0.734712 0.678379i \(-0.237317\pi\)
0.734712 + 0.678379i \(0.237317\pi\)
\(398\) 42.8411 2.14743
\(399\) −1.24023 −0.0620892
\(400\) 8.30582 0.415291
\(401\) −31.7755 −1.58680 −0.793398 0.608704i \(-0.791690\pi\)
−0.793398 + 0.608704i \(0.791690\pi\)
\(402\) 6.56359 0.327362
\(403\) −6.82825 −0.340139
\(404\) −33.3378 −1.65862
\(405\) −2.77464 −0.137873
\(406\) 2.38827 0.118528
\(407\) −0.142001 −0.00703873
\(408\) 13.0559 0.646364
\(409\) −21.9147 −1.08361 −0.541805 0.840504i \(-0.682259\pi\)
−0.541805 + 0.840504i \(0.682259\pi\)
\(410\) −42.6569 −2.10667
\(411\) −3.15516 −0.155633
\(412\) 29.4529 1.45104
\(413\) −11.8714 −0.584152
\(414\) 22.7978 1.12045
\(415\) 0.573658 0.0281598
\(416\) −8.18740 −0.401420
\(417\) −11.1880 −0.547878
\(418\) −4.24022 −0.207396
\(419\) −18.7123 −0.914158 −0.457079 0.889426i \(-0.651104\pi\)
−0.457079 + 0.889426i \(0.651104\pi\)
\(420\) −9.60077 −0.468469
\(421\) −11.0842 −0.540211 −0.270106 0.962831i \(-0.587059\pi\)
−0.270106 + 0.962831i \(0.587059\pi\)
\(422\) 55.9711 2.72463
\(423\) −9.34739 −0.454486
\(424\) 3.09339 0.150228
\(425\) −7.91308 −0.383841
\(426\) −6.95816 −0.337124
\(427\) −4.40572 −0.213208
\(428\) 10.1163 0.488988
\(429\) 7.11448 0.343490
\(430\) 56.7279 2.73566
\(431\) 2.06580 0.0995060 0.0497530 0.998762i \(-0.484157\pi\)
0.0497530 + 0.998762i \(0.484157\pi\)
\(432\) 3.07777 0.148079
\(433\) −15.8105 −0.759805 −0.379903 0.925027i \(-0.624042\pi\)
−0.379903 + 0.925027i \(0.624042\pi\)
\(434\) −2.66135 −0.127749
\(435\) 3.04424 0.145960
\(436\) −43.6378 −2.08987
\(437\) 12.9892 0.621360
\(438\) 21.6316 1.03360
\(439\) −1.71192 −0.0817056 −0.0408528 0.999165i \(-0.513007\pi\)
−0.0408528 + 0.999165i \(0.513007\pi\)
\(440\) −15.7377 −0.750266
\(441\) −6.18894 −0.294712
\(442\) −39.5824 −1.88274
\(443\) 14.4599 0.687009 0.343505 0.939151i \(-0.388386\pi\)
0.343505 + 0.939151i \(0.388386\pi\)
\(444\) 0.428292 0.0203258
\(445\) −37.7877 −1.79131
\(446\) −57.9216 −2.74267
\(447\) 23.2434 1.09938
\(448\) −8.73468 −0.412675
\(449\) 39.5760 1.86771 0.933854 0.357654i \(-0.116423\pi\)
0.933854 + 0.357654i \(0.116423\pi\)
\(450\) −6.52278 −0.307487
\(451\) 8.10253 0.381533
\(452\) 21.6832 1.01989
\(453\) 14.3304 0.673301
\(454\) −24.4266 −1.14640
\(455\) 13.9557 0.654252
\(456\) 6.13177 0.287147
\(457\) −37.8797 −1.77194 −0.885968 0.463746i \(-0.846505\pi\)
−0.885968 + 0.463746i \(0.846505\pi\)
\(458\) 65.0218 3.03827
\(459\) −2.93223 −0.136865
\(460\) 100.551 4.68823
\(461\) 10.6913 0.497942 0.248971 0.968511i \(-0.419908\pi\)
0.248971 + 0.968511i \(0.419908\pi\)
\(462\) 2.77291 0.129008
\(463\) 0.454352 0.0211155 0.0105578 0.999944i \(-0.496639\pi\)
0.0105578 + 0.999944i \(0.496639\pi\)
\(464\) −3.37682 −0.156765
\(465\) −3.39233 −0.157316
\(466\) 5.97207 0.276651
\(467\) 15.7674 0.729627 0.364814 0.931081i \(-0.381133\pi\)
0.364814 + 0.931081i \(0.381133\pi\)
\(468\) −21.4581 −0.991902
\(469\) −2.44557 −0.112926
\(470\) −62.6879 −2.89158
\(471\) 17.0943 0.787665
\(472\) 58.6928 2.70155
\(473\) −10.7753 −0.495447
\(474\) −19.3708 −0.889729
\(475\) −3.71641 −0.170521
\(476\) −10.1460 −0.465043
\(477\) −0.694746 −0.0318102
\(478\) 7.12055 0.325686
\(479\) −8.14081 −0.371963 −0.185981 0.982553i \(-0.559546\pi\)
−0.185981 + 0.982553i \(0.559546\pi\)
\(480\) −4.06757 −0.185658
\(481\) −0.622565 −0.0283865
\(482\) 13.3384 0.607547
\(483\) −8.49438 −0.386508
\(484\) −36.0287 −1.63767
\(485\) −9.60110 −0.435963
\(486\) −2.41705 −0.109640
\(487\) −9.11338 −0.412966 −0.206483 0.978450i \(-0.566202\pi\)
−0.206483 + 0.978450i \(0.566202\pi\)
\(488\) 21.7822 0.986032
\(489\) 15.9899 0.723090
\(490\) −41.5059 −1.87505
\(491\) 36.7897 1.66030 0.830149 0.557542i \(-0.188255\pi\)
0.830149 + 0.557542i \(0.188255\pi\)
\(492\) −24.4382 −1.10176
\(493\) 3.21714 0.144893
\(494\) −18.5901 −0.836408
\(495\) 3.53454 0.158866
\(496\) 3.76294 0.168961
\(497\) 2.59259 0.116294
\(498\) 0.499726 0.0223933
\(499\) −15.3142 −0.685558 −0.342779 0.939416i \(-0.611368\pi\)
−0.342779 + 0.939416i \(0.611368\pi\)
\(500\) 24.5337 1.09718
\(501\) −17.1243 −0.765058
\(502\) −33.6480 −1.50178
\(503\) −36.2116 −1.61460 −0.807298 0.590144i \(-0.799071\pi\)
−0.807298 + 0.590144i \(0.799071\pi\)
\(504\) −4.00991 −0.178615
\(505\) 24.0752 1.07133
\(506\) −29.0414 −1.29105
\(507\) 18.1915 0.807913
\(508\) 41.3798 1.83593
\(509\) 27.6719 1.22654 0.613268 0.789875i \(-0.289855\pi\)
0.613268 + 0.789875i \(0.289855\pi\)
\(510\) −19.6649 −0.870776
\(511\) −8.05986 −0.356547
\(512\) 31.9198 1.41067
\(513\) −1.37714 −0.0608021
\(514\) −37.7007 −1.66291
\(515\) −21.2697 −0.937256
\(516\) 32.4995 1.43071
\(517\) 11.9074 0.523685
\(518\) −0.242649 −0.0106614
\(519\) 4.42061 0.194043
\(520\) −68.9977 −3.02575
\(521\) 25.5272 1.11837 0.559184 0.829044i \(-0.311115\pi\)
0.559184 + 0.829044i \(0.311115\pi\)
\(522\) 2.65191 0.116071
\(523\) −21.8509 −0.955475 −0.477737 0.878503i \(-0.658543\pi\)
−0.477737 + 0.878503i \(0.658543\pi\)
\(524\) −51.1764 −2.23565
\(525\) 2.43037 0.106070
\(526\) 59.2127 2.58179
\(527\) −3.58500 −0.156165
\(528\) −3.92068 −0.170625
\(529\) 65.9638 2.86799
\(530\) −4.65928 −0.202386
\(531\) −13.1818 −0.572043
\(532\) −4.76514 −0.206595
\(533\) 35.5233 1.53869
\(534\) −32.9176 −1.42449
\(535\) −7.30557 −0.315848
\(536\) 12.0911 0.522254
\(537\) 6.66218 0.287494
\(538\) 8.08683 0.348648
\(539\) 7.88391 0.339584
\(540\) −10.6606 −0.458758
\(541\) −26.4902 −1.13890 −0.569451 0.822026i \(-0.692844\pi\)
−0.569451 + 0.822026i \(0.692844\pi\)
\(542\) −22.4284 −0.963383
\(543\) −12.3817 −0.531349
\(544\) −4.29859 −0.184301
\(545\) 31.5135 1.34989
\(546\) 12.1571 0.520275
\(547\) 36.2723 1.55089 0.775447 0.631413i \(-0.217525\pi\)
0.775447 + 0.631413i \(0.217525\pi\)
\(548\) −12.1226 −0.517851
\(549\) −4.89206 −0.208788
\(550\) 8.30918 0.354305
\(551\) 1.51095 0.0643685
\(552\) 41.9968 1.78750
\(553\) 7.21749 0.306919
\(554\) 62.0224 2.63508
\(555\) −0.309296 −0.0131289
\(556\) −42.9858 −1.82300
\(557\) −2.94719 −0.124877 −0.0624383 0.998049i \(-0.519888\pi\)
−0.0624383 + 0.998049i \(0.519888\pi\)
\(558\) −2.95514 −0.125101
\(559\) −47.2412 −1.99809
\(560\) −7.69074 −0.324993
\(561\) 3.73528 0.157704
\(562\) 35.5709 1.50047
\(563\) 21.5956 0.910146 0.455073 0.890454i \(-0.349613\pi\)
0.455073 + 0.890454i \(0.349613\pi\)
\(564\) −35.9140 −1.51225
\(565\) −15.6588 −0.658769
\(566\) −3.31085 −0.139165
\(567\) 0.900586 0.0378211
\(568\) −12.8179 −0.537828
\(569\) 3.86761 0.162139 0.0810694 0.996708i \(-0.474166\pi\)
0.0810694 + 0.996708i \(0.474166\pi\)
\(570\) −9.23572 −0.386842
\(571\) −39.9902 −1.67354 −0.836768 0.547557i \(-0.815558\pi\)
−0.836768 + 0.547557i \(0.815558\pi\)
\(572\) 27.3348 1.14293
\(573\) −26.5656 −1.10980
\(574\) 13.8454 0.577898
\(575\) −25.4539 −1.06150
\(576\) −9.69888 −0.404120
\(577\) −32.9209 −1.37051 −0.685257 0.728301i \(-0.740310\pi\)
−0.685257 + 0.728301i \(0.740310\pi\)
\(578\) 20.3081 0.844706
\(579\) 14.1004 0.585994
\(580\) 11.6964 0.485667
\(581\) −0.186196 −0.00772472
\(582\) −8.36372 −0.346687
\(583\) 0.885016 0.0366536
\(584\) 39.8485 1.64894
\(585\) 15.4962 0.640690
\(586\) 80.3878 3.32079
\(587\) 16.2240 0.669636 0.334818 0.942283i \(-0.391325\pi\)
0.334818 + 0.942283i \(0.391325\pi\)
\(588\) −23.7788 −0.980621
\(589\) −1.68371 −0.0693763
\(590\) −88.4034 −3.63951
\(591\) 7.60149 0.312684
\(592\) 0.343085 0.0141007
\(593\) 5.43644 0.223248 0.111624 0.993751i \(-0.464395\pi\)
0.111624 + 0.993751i \(0.464395\pi\)
\(594\) 3.07901 0.126333
\(595\) 7.32708 0.300381
\(596\) 89.3046 3.65806
\(597\) −17.7245 −0.725416
\(598\) −127.324 −5.20667
\(599\) −4.42338 −0.180735 −0.0903673 0.995909i \(-0.528804\pi\)
−0.0903673 + 0.995909i \(0.528804\pi\)
\(600\) −12.0159 −0.490547
\(601\) 16.8558 0.687563 0.343781 0.939050i \(-0.388292\pi\)
0.343781 + 0.939050i \(0.388292\pi\)
\(602\) −18.4126 −0.750440
\(603\) −2.71553 −0.110585
\(604\) 55.0595 2.24034
\(605\) 26.0186 1.05780
\(606\) 20.9725 0.851948
\(607\) −35.6191 −1.44573 −0.722867 0.690987i \(-0.757176\pi\)
−0.722867 + 0.690987i \(0.757176\pi\)
\(608\) −2.01885 −0.0818754
\(609\) −0.988091 −0.0400395
\(610\) −32.8084 −1.32837
\(611\) 52.2046 2.11197
\(612\) −11.2661 −0.455403
\(613\) 0.854413 0.0345094 0.0172547 0.999851i \(-0.494507\pi\)
0.0172547 + 0.999851i \(0.494507\pi\)
\(614\) −64.7456 −2.61292
\(615\) 17.6483 0.711648
\(616\) 5.10810 0.205811
\(617\) 31.4495 1.26611 0.633054 0.774108i \(-0.281801\pi\)
0.633054 + 0.774108i \(0.281801\pi\)
\(618\) −18.5285 −0.745326
\(619\) −2.60090 −0.104539 −0.0522695 0.998633i \(-0.516645\pi\)
−0.0522695 + 0.998633i \(0.516645\pi\)
\(620\) −13.0338 −0.523451
\(621\) −9.43206 −0.378496
\(622\) −76.8301 −3.08060
\(623\) 12.2650 0.491387
\(624\) −17.1891 −0.688116
\(625\) −31.2105 −1.24842
\(626\) −72.2298 −2.88688
\(627\) 1.75429 0.0700597
\(628\) 65.6788 2.62087
\(629\) −0.326862 −0.0130329
\(630\) 6.03974 0.240629
\(631\) −42.8437 −1.70558 −0.852791 0.522252i \(-0.825092\pi\)
−0.852791 + 0.522252i \(0.825092\pi\)
\(632\) −35.6837 −1.41942
\(633\) −23.1567 −0.920398
\(634\) −15.2087 −0.604014
\(635\) −29.8829 −1.18587
\(636\) −2.66931 −0.105845
\(637\) 34.5649 1.36951
\(638\) −3.37818 −0.133744
\(639\) 2.87878 0.113883
\(640\) −56.9100 −2.24957
\(641\) 21.1118 0.833864 0.416932 0.908938i \(-0.363105\pi\)
0.416932 + 0.908938i \(0.363105\pi\)
\(642\) −6.36404 −0.251169
\(643\) −32.8031 −1.29363 −0.646815 0.762647i \(-0.723899\pi\)
−0.646815 + 0.762647i \(0.723899\pi\)
\(644\) −32.6366 −1.28606
\(645\) −23.4699 −0.924125
\(646\) −9.76026 −0.384012
\(647\) −43.1095 −1.69481 −0.847405 0.530948i \(-0.821836\pi\)
−0.847405 + 0.530948i \(0.821836\pi\)
\(648\) −4.45255 −0.174913
\(649\) 16.7919 0.659141
\(650\) 36.4293 1.42888
\(651\) 1.10107 0.0431545
\(652\) 61.4356 2.40600
\(653\) 12.0881 0.473044 0.236522 0.971626i \(-0.423993\pi\)
0.236522 + 0.971626i \(0.423993\pi\)
\(654\) 27.4521 1.07346
\(655\) 36.9576 1.44405
\(656\) −19.5763 −0.764328
\(657\) −8.94958 −0.349156
\(658\) 20.3471 0.793211
\(659\) 9.65204 0.375990 0.187995 0.982170i \(-0.439801\pi\)
0.187995 + 0.982170i \(0.439801\pi\)
\(660\) 13.5802 0.528608
\(661\) 19.4018 0.754642 0.377321 0.926083i \(-0.376845\pi\)
0.377321 + 0.926083i \(0.376845\pi\)
\(662\) −43.0088 −1.67159
\(663\) 16.3763 0.636004
\(664\) 0.920566 0.0357249
\(665\) 3.44120 0.133444
\(666\) −0.269434 −0.0104404
\(667\) 10.3485 0.400697
\(668\) −65.7941 −2.54565
\(669\) 23.9637 0.926492
\(670\) −18.2116 −0.703576
\(671\) 6.23185 0.240578
\(672\) 1.32024 0.0509294
\(673\) −3.16594 −0.122038 −0.0610190 0.998137i \(-0.519435\pi\)
−0.0610190 + 0.998137i \(0.519435\pi\)
\(674\) −84.3003 −3.24713
\(675\) 2.69865 0.103871
\(676\) 69.8943 2.68824
\(677\) 8.07463 0.310333 0.155167 0.987888i \(-0.450409\pi\)
0.155167 + 0.987888i \(0.450409\pi\)
\(678\) −13.6407 −0.523867
\(679\) 3.11630 0.119592
\(680\) −36.2255 −1.38919
\(681\) 10.1059 0.387261
\(682\) 3.76446 0.144149
\(683\) 38.5680 1.47576 0.737882 0.674929i \(-0.235826\pi\)
0.737882 + 0.674929i \(0.235826\pi\)
\(684\) −5.29116 −0.202312
\(685\) 8.75445 0.334490
\(686\) 28.7092 1.09612
\(687\) −26.9013 −1.02635
\(688\) 26.0339 0.992532
\(689\) 3.88011 0.147820
\(690\) −63.2558 −2.40811
\(691\) −19.4440 −0.739684 −0.369842 0.929095i \(-0.620588\pi\)
−0.369842 + 0.929095i \(0.620588\pi\)
\(692\) 16.9846 0.645657
\(693\) −1.14723 −0.0435796
\(694\) 57.0167 2.16432
\(695\) 31.0427 1.17752
\(696\) 4.88518 0.185172
\(697\) 18.6507 0.706444
\(698\) −33.4332 −1.26546
\(699\) −2.47081 −0.0934545
\(700\) 9.33782 0.352936
\(701\) −23.3470 −0.881804 −0.440902 0.897555i \(-0.645341\pi\)
−0.440902 + 0.897555i \(0.645341\pi\)
\(702\) 13.4991 0.509490
\(703\) −0.153512 −0.00578983
\(704\) 12.3551 0.465651
\(705\) 25.9357 0.976794
\(706\) 74.3712 2.79900
\(707\) −7.81427 −0.293886
\(708\) −50.6464 −1.90341
\(709\) 20.8957 0.784753 0.392376 0.919805i \(-0.371653\pi\)
0.392376 + 0.919805i \(0.371653\pi\)
\(710\) 19.3064 0.724557
\(711\) 8.01421 0.300556
\(712\) −60.6389 −2.27254
\(713\) −11.5318 −0.431870
\(714\) 6.38278 0.238869
\(715\) −19.7402 −0.738240
\(716\) 25.5970 0.956606
\(717\) −2.94597 −0.110019
\(718\) −45.4931 −1.69779
\(719\) −28.9783 −1.08071 −0.540354 0.841438i \(-0.681710\pi\)
−0.540354 + 0.841438i \(0.681710\pi\)
\(720\) −8.53971 −0.318256
\(721\) 6.90366 0.257106
\(722\) 41.3400 1.53852
\(723\) −5.51845 −0.205233
\(724\) −47.5722 −1.76801
\(725\) −2.96087 −0.109964
\(726\) 22.6653 0.841189
\(727\) −23.3937 −0.867623 −0.433812 0.901004i \(-0.642832\pi\)
−0.433812 + 0.901004i \(0.642832\pi\)
\(728\) 22.3951 0.830016
\(729\) 1.00000 0.0370370
\(730\) −60.0200 −2.22144
\(731\) −24.8028 −0.917366
\(732\) −18.7960 −0.694720
\(733\) 47.0403 1.73747 0.868737 0.495274i \(-0.164932\pi\)
0.868737 + 0.495274i \(0.164932\pi\)
\(734\) 40.4353 1.49249
\(735\) 17.1721 0.633403
\(736\) −13.8272 −0.509678
\(737\) 3.45924 0.127423
\(738\) 15.3738 0.565918
\(739\) 23.5752 0.867228 0.433614 0.901099i \(-0.357238\pi\)
0.433614 + 0.901099i \(0.357238\pi\)
\(740\) −1.18836 −0.0436849
\(741\) 7.69122 0.282544
\(742\) 1.51230 0.0555182
\(743\) 16.0587 0.589135 0.294568 0.955631i \(-0.404824\pi\)
0.294568 + 0.955631i \(0.404824\pi\)
\(744\) −5.44378 −0.199579
\(745\) −64.4923 −2.36281
\(746\) −27.1224 −0.993021
\(747\) −0.206750 −0.00756459
\(748\) 14.3515 0.524742
\(749\) 2.37122 0.0866426
\(750\) −15.4339 −0.563566
\(751\) −16.1071 −0.587758 −0.293879 0.955843i \(-0.594946\pi\)
−0.293879 + 0.955843i \(0.594946\pi\)
\(752\) −28.7691 −1.04910
\(753\) 13.9211 0.507312
\(754\) −14.8107 −0.539375
\(755\) −39.7618 −1.44708
\(756\) 3.46018 0.125845
\(757\) 35.9703 1.30736 0.653682 0.756770i \(-0.273223\pi\)
0.653682 + 0.756770i \(0.273223\pi\)
\(758\) −14.6018 −0.530363
\(759\) 12.0152 0.436125
\(760\) −17.0135 −0.617144
\(761\) 7.22549 0.261924 0.130962 0.991387i \(-0.458193\pi\)
0.130962 + 0.991387i \(0.458193\pi\)
\(762\) −26.0316 −0.943027
\(763\) −10.2286 −0.370299
\(764\) −102.069 −3.69273
\(765\) 8.13590 0.294154
\(766\) 53.1417 1.92009
\(767\) 73.6197 2.65825
\(768\) −30.1778 −1.08895
\(769\) 31.5572 1.13798 0.568991 0.822344i \(-0.307334\pi\)
0.568991 + 0.822344i \(0.307334\pi\)
\(770\) −7.69385 −0.277267
\(771\) 15.5978 0.561741
\(772\) 54.1758 1.94983
\(773\) −2.13546 −0.0768071 −0.0384036 0.999262i \(-0.512227\pi\)
−0.0384036 + 0.999262i \(0.512227\pi\)
\(774\) −20.4451 −0.734884
\(775\) 3.29943 0.118519
\(776\) −15.4072 −0.553085
\(777\) 0.100390 0.00360148
\(778\) 31.6471 1.13460
\(779\) 8.75937 0.313837
\(780\) 59.5386 2.13183
\(781\) −3.66719 −0.131222
\(782\) −66.8484 −2.39049
\(783\) −1.09717 −0.0392095
\(784\) −19.0481 −0.680290
\(785\) −47.4307 −1.69287
\(786\) 32.1946 1.14834
\(787\) 6.15143 0.219275 0.109637 0.993972i \(-0.465031\pi\)
0.109637 + 0.993972i \(0.465031\pi\)
\(788\) 29.2060 1.04042
\(789\) −24.4979 −0.872148
\(790\) 53.7470 1.91223
\(791\) 5.08247 0.180712
\(792\) 5.67197 0.201545
\(793\) 27.3218 0.970227
\(794\) −70.7666 −2.51141
\(795\) 1.92767 0.0683675
\(796\) −68.1001 −2.41374
\(797\) 26.6589 0.944306 0.472153 0.881517i \(-0.343477\pi\)
0.472153 + 0.881517i \(0.343477\pi\)
\(798\) 2.99770 0.106117
\(799\) 27.4087 0.969651
\(800\) 3.95617 0.139872
\(801\) 13.6189 0.481201
\(802\) 76.8032 2.71201
\(803\) 11.4006 0.402318
\(804\) −10.4335 −0.367960
\(805\) 23.5689 0.830694
\(806\) 16.5042 0.581337
\(807\) −3.34574 −0.117776
\(808\) 38.6342 1.35915
\(809\) 8.64714 0.304017 0.152009 0.988379i \(-0.451426\pi\)
0.152009 + 0.988379i \(0.451426\pi\)
\(810\) 6.70646 0.235641
\(811\) −4.91950 −0.172747 −0.0863735 0.996263i \(-0.527528\pi\)
−0.0863735 + 0.996263i \(0.527528\pi\)
\(812\) −3.79639 −0.133227
\(813\) 9.27925 0.325437
\(814\) 0.343224 0.0120300
\(815\) −44.3664 −1.55409
\(816\) −9.02473 −0.315929
\(817\) −11.6488 −0.407539
\(818\) 52.9689 1.85201
\(819\) −5.02972 −0.175752
\(820\) 67.8073 2.36793
\(821\) 46.7485 1.63154 0.815768 0.578380i \(-0.196315\pi\)
0.815768 + 0.578380i \(0.196315\pi\)
\(822\) 7.62619 0.265994
\(823\) 8.46325 0.295010 0.147505 0.989061i \(-0.452876\pi\)
0.147505 + 0.989061i \(0.452876\pi\)
\(824\) −34.1321 −1.18905
\(825\) −3.43773 −0.119686
\(826\) 28.6937 0.998382
\(827\) 0.780966 0.0271569 0.0135784 0.999908i \(-0.495678\pi\)
0.0135784 + 0.999908i \(0.495678\pi\)
\(828\) −36.2393 −1.25940
\(829\) −10.9042 −0.378718 −0.189359 0.981908i \(-0.560641\pi\)
−0.189359 + 0.981908i \(0.560641\pi\)
\(830\) −1.38656 −0.0481283
\(831\) −25.6603 −0.890147
\(832\) 54.1676 1.87792
\(833\) 18.1474 0.628771
\(834\) 27.0419 0.936386
\(835\) 47.5139 1.64429
\(836\) 6.74024 0.233116
\(837\) 1.22262 0.0422599
\(838\) 45.2287 1.56240
\(839\) −21.3276 −0.736311 −0.368155 0.929764i \(-0.620011\pi\)
−0.368155 + 0.929764i \(0.620011\pi\)
\(840\) 11.1261 0.383886
\(841\) −27.7962 −0.958491
\(842\) 26.7911 0.923282
\(843\) −14.7166 −0.506868
\(844\) −88.9715 −3.06252
\(845\) −50.4750 −1.73639
\(846\) 22.5931 0.776768
\(847\) −8.44503 −0.290174
\(848\) −2.13827 −0.0734283
\(849\) 1.36979 0.0470109
\(850\) 19.1263 0.656027
\(851\) −1.05141 −0.0360420
\(852\) 11.0607 0.378933
\(853\) −4.60845 −0.157790 −0.0788952 0.996883i \(-0.525139\pi\)
−0.0788952 + 0.996883i \(0.525139\pi\)
\(854\) 10.6489 0.364396
\(855\) 3.82107 0.130678
\(856\) −11.7235 −0.400700
\(857\) 28.9169 0.987784 0.493892 0.869523i \(-0.335574\pi\)
0.493892 + 0.869523i \(0.335574\pi\)
\(858\) −17.1961 −0.587064
\(859\) −6.03136 −0.205787 −0.102894 0.994692i \(-0.532810\pi\)
−0.102894 + 0.994692i \(0.532810\pi\)
\(860\) −90.1745 −3.07492
\(861\) −5.72824 −0.195218
\(862\) −4.99314 −0.170067
\(863\) 30.9864 1.05479 0.527395 0.849621i \(-0.323169\pi\)
0.527395 + 0.849621i \(0.323169\pi\)
\(864\) 1.46598 0.0498736
\(865\) −12.2656 −0.417043
\(866\) 38.2149 1.29859
\(867\) −8.40201 −0.285347
\(868\) 4.23048 0.143592
\(869\) −10.2091 −0.346319
\(870\) −7.35809 −0.249463
\(871\) 15.1661 0.513883
\(872\) 50.5706 1.71254
\(873\) 3.46030 0.117113
\(874\) −31.3957 −1.06197
\(875\) 5.75062 0.194406
\(876\) −34.3855 −1.16178
\(877\) −35.2579 −1.19057 −0.595287 0.803513i \(-0.702962\pi\)
−0.595287 + 0.803513i \(0.702962\pi\)
\(878\) 4.13781 0.139644
\(879\) −33.2586 −1.12178
\(880\) 10.8785 0.366713
\(881\) 21.0519 0.709256 0.354628 0.935007i \(-0.384607\pi\)
0.354628 + 0.935007i \(0.384607\pi\)
\(882\) 14.9590 0.503696
\(883\) 55.5594 1.86972 0.934861 0.355014i \(-0.115524\pi\)
0.934861 + 0.355014i \(0.115524\pi\)
\(884\) 62.9202 2.11623
\(885\) 36.5749 1.22945
\(886\) −34.9503 −1.17418
\(887\) 26.6500 0.894818 0.447409 0.894329i \(-0.352347\pi\)
0.447409 + 0.894329i \(0.352347\pi\)
\(888\) −0.496336 −0.0166559
\(889\) 9.69931 0.325304
\(890\) 91.3347 3.06155
\(891\) −1.27387 −0.0426762
\(892\) 92.0721 3.08280
\(893\) 12.8726 0.430766
\(894\) −56.1806 −1.87896
\(895\) −18.4852 −0.617891
\(896\) 18.4717 0.617096
\(897\) 52.6775 1.75885
\(898\) −95.6573 −3.19213
\(899\) −1.34142 −0.0447387
\(900\) 10.3686 0.345620
\(901\) 2.03716 0.0678675
\(902\) −19.5842 −0.652084
\(903\) 7.61778 0.253504
\(904\) −25.1281 −0.835747
\(905\) 34.3548 1.14199
\(906\) −34.6373 −1.15075
\(907\) −19.2661 −0.639720 −0.319860 0.947465i \(-0.603636\pi\)
−0.319860 + 0.947465i \(0.603636\pi\)
\(908\) 38.8285 1.28857
\(909\) −8.67687 −0.287794
\(910\) −33.7316 −1.11819
\(911\) 28.5841 0.947035 0.473517 0.880784i \(-0.342984\pi\)
0.473517 + 0.880784i \(0.342984\pi\)
\(912\) −4.23851 −0.140351
\(913\) 0.263373 0.00871637
\(914\) 91.5572 3.02844
\(915\) 13.5737 0.448734
\(916\) −103.359 −3.41506
\(917\) −11.9956 −0.396129
\(918\) 7.08736 0.233918
\(919\) −39.7266 −1.31046 −0.655229 0.755430i \(-0.727428\pi\)
−0.655229 + 0.755430i \(0.727428\pi\)
\(920\) −116.526 −3.84175
\(921\) 26.7870 0.882662
\(922\) −25.8414 −0.851040
\(923\) −16.0778 −0.529207
\(924\) −4.40782 −0.145007
\(925\) 0.300825 0.00989105
\(926\) −1.09819 −0.0360888
\(927\) 7.66574 0.251776
\(928\) −1.60842 −0.0527990
\(929\) 24.1331 0.791782 0.395891 0.918298i \(-0.370436\pi\)
0.395891 + 0.918298i \(0.370436\pi\)
\(930\) 8.19945 0.268871
\(931\) 8.52303 0.279331
\(932\) −9.49319 −0.310960
\(933\) 31.7867 1.04065
\(934\) −38.1106 −1.24702
\(935\) −10.3641 −0.338942
\(936\) 24.8672 0.812810
\(937\) 30.2673 0.988788 0.494394 0.869238i \(-0.335390\pi\)
0.494394 + 0.869238i \(0.335390\pi\)
\(938\) 5.91108 0.193003
\(939\) 29.8834 0.975208
\(940\) 99.6486 3.25018
\(941\) −24.3518 −0.793847 −0.396924 0.917852i \(-0.629922\pi\)
−0.396924 + 0.917852i \(0.629922\pi\)
\(942\) −41.3179 −1.34621
\(943\) 59.9933 1.95365
\(944\) −40.5706 −1.32046
\(945\) −2.49881 −0.0812862
\(946\) 26.0444 0.846776
\(947\) 24.2958 0.789509 0.394754 0.918787i \(-0.370830\pi\)
0.394754 + 0.918787i \(0.370830\pi\)
\(948\) 30.7917 1.00007
\(949\) 49.9828 1.62251
\(950\) 8.98277 0.291439
\(951\) 6.29224 0.204040
\(952\) 11.7580 0.381078
\(953\) 47.7775 1.54766 0.773832 0.633391i \(-0.218337\pi\)
0.773832 + 0.633391i \(0.218337\pi\)
\(954\) 1.67924 0.0543673
\(955\) 73.7102 2.38521
\(956\) −11.3188 −0.366077
\(957\) 1.39765 0.0451795
\(958\) 19.6768 0.635727
\(959\) −2.84149 −0.0917566
\(960\) 26.9110 0.868547
\(961\) −29.5052 −0.951781
\(962\) 1.50477 0.0485158
\(963\) 2.63298 0.0848465
\(964\) −21.2027 −0.682892
\(965\) −39.1237 −1.25944
\(966\) 20.5314 0.660586
\(967\) 19.5303 0.628053 0.314026 0.949414i \(-0.398322\pi\)
0.314026 + 0.949414i \(0.398322\pi\)
\(968\) 41.7527 1.34198
\(969\) 4.03809 0.129722
\(970\) 23.2063 0.745111
\(971\) −11.2206 −0.360087 −0.180044 0.983659i \(-0.557624\pi\)
−0.180044 + 0.983659i \(0.557624\pi\)
\(972\) 3.84214 0.123237
\(973\) −10.0757 −0.323013
\(974\) 22.0275 0.705807
\(975\) −15.0718 −0.482684
\(976\) −15.0566 −0.481951
\(977\) −16.9933 −0.543665 −0.271832 0.962345i \(-0.587630\pi\)
−0.271832 + 0.962345i \(0.587630\pi\)
\(978\) −38.6485 −1.23584
\(979\) −17.3487 −0.554468
\(980\) 65.9777 2.10758
\(981\) −11.3577 −0.362622
\(982\) −88.9227 −2.83764
\(983\) −10.9037 −0.347775 −0.173887 0.984766i \(-0.555633\pi\)
−0.173887 + 0.984766i \(0.555633\pi\)
\(984\) 28.3207 0.902832
\(985\) −21.0914 −0.672029
\(986\) −7.77600 −0.247638
\(987\) −8.41813 −0.267952
\(988\) 29.5508 0.940135
\(989\) −79.7829 −2.53695
\(990\) −8.54316 −0.271519
\(991\) 20.2693 0.643876 0.321938 0.946761i \(-0.395666\pi\)
0.321938 + 0.946761i \(0.395666\pi\)
\(992\) 1.79233 0.0569067
\(993\) 17.7939 0.564673
\(994\) −6.26642 −0.198759
\(995\) 49.1792 1.55909
\(996\) −0.794363 −0.0251704
\(997\) −10.7616 −0.340822 −0.170411 0.985373i \(-0.554510\pi\)
−0.170411 + 0.985373i \(0.554510\pi\)
\(998\) 37.0152 1.17170
\(999\) 0.111472 0.00352682
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 \(a_p\))