Properties

Label 8018.2.a.d.1.9
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.51420 q^{3}\) \(+1.00000 q^{4}\) \(-2.91196 q^{5}\) \(-1.51420 q^{6}\) \(-3.75064 q^{7}\) \(+1.00000 q^{8}\) \(-0.707195 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.51420 q^{3}\) \(+1.00000 q^{4}\) \(-2.91196 q^{5}\) \(-1.51420 q^{6}\) \(-3.75064 q^{7}\) \(+1.00000 q^{8}\) \(-0.707195 q^{9}\) \(-2.91196 q^{10}\) \(-1.07783 q^{11}\) \(-1.51420 q^{12}\) \(+3.84825 q^{13}\) \(-3.75064 q^{14}\) \(+4.40929 q^{15}\) \(+1.00000 q^{16}\) \(+1.46263 q^{17}\) \(-0.707195 q^{18}\) \(+1.00000 q^{19}\) \(-2.91196 q^{20}\) \(+5.67922 q^{21}\) \(-1.07783 q^{22}\) \(-1.57188 q^{23}\) \(-1.51420 q^{24}\) \(+3.47950 q^{25}\) \(+3.84825 q^{26}\) \(+5.61344 q^{27}\) \(-3.75064 q^{28}\) \(+2.48697 q^{29}\) \(+4.40929 q^{30}\) \(-5.80679 q^{31}\) \(+1.00000 q^{32}\) \(+1.63205 q^{33}\) \(+1.46263 q^{34}\) \(+10.9217 q^{35}\) \(-0.707195 q^{36}\) \(+8.92851 q^{37}\) \(+1.00000 q^{38}\) \(-5.82702 q^{39}\) \(-2.91196 q^{40}\) \(-3.70538 q^{41}\) \(+5.67922 q^{42}\) \(+2.26373 q^{43}\) \(-1.07783 q^{44}\) \(+2.05932 q^{45}\) \(-1.57188 q^{46}\) \(+3.11736 q^{47}\) \(-1.51420 q^{48}\) \(+7.06728 q^{49}\) \(+3.47950 q^{50}\) \(-2.21472 q^{51}\) \(+3.84825 q^{52}\) \(-4.03335 q^{53}\) \(+5.61344 q^{54}\) \(+3.13859 q^{55}\) \(-3.75064 q^{56}\) \(-1.51420 q^{57}\) \(+2.48697 q^{58}\) \(+15.0431 q^{59}\) \(+4.40929 q^{60}\) \(+6.86485 q^{61}\) \(-5.80679 q^{62}\) \(+2.65243 q^{63}\) \(+1.00000 q^{64}\) \(-11.2059 q^{65}\) \(+1.63205 q^{66}\) \(+7.13230 q^{67}\) \(+1.46263 q^{68}\) \(+2.38015 q^{69}\) \(+10.9217 q^{70}\) \(+4.01635 q^{71}\) \(-0.707195 q^{72}\) \(-15.5522 q^{73}\) \(+8.92851 q^{74}\) \(-5.26867 q^{75}\) \(+1.00000 q^{76}\) \(+4.04254 q^{77}\) \(-5.82702 q^{78}\) \(-11.9353 q^{79}\) \(-2.91196 q^{80}\) \(-6.37829 q^{81}\) \(-3.70538 q^{82}\) \(-0.410968 q^{83}\) \(+5.67922 q^{84}\) \(-4.25913 q^{85}\) \(+2.26373 q^{86}\) \(-3.76577 q^{87}\) \(-1.07783 q^{88}\) \(-1.42947 q^{89}\) \(+2.05932 q^{90}\) \(-14.4334 q^{91}\) \(-1.57188 q^{92}\) \(+8.79265 q^{93}\) \(+3.11736 q^{94}\) \(-2.91196 q^{95}\) \(-1.51420 q^{96}\) \(-7.18019 q^{97}\) \(+7.06728 q^{98}\) \(+0.762233 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.51420 −0.874224 −0.437112 0.899407i \(-0.643999\pi\)
−0.437112 + 0.899407i \(0.643999\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.91196 −1.30227 −0.651134 0.758963i \(-0.725706\pi\)
−0.651134 + 0.758963i \(0.725706\pi\)
\(6\) −1.51420 −0.618170
\(7\) −3.75064 −1.41761 −0.708804 0.705406i \(-0.750765\pi\)
−0.708804 + 0.705406i \(0.750765\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.707195 −0.235732
\(10\) −2.91196 −0.920842
\(11\) −1.07783 −0.324977 −0.162488 0.986710i \(-0.551952\pi\)
−0.162488 + 0.986710i \(0.551952\pi\)
\(12\) −1.51420 −0.437112
\(13\) 3.84825 1.06731 0.533656 0.845702i \(-0.320818\pi\)
0.533656 + 0.845702i \(0.320818\pi\)
\(14\) −3.75064 −1.00240
\(15\) 4.40929 1.13847
\(16\) 1.00000 0.250000
\(17\) 1.46263 0.354741 0.177370 0.984144i \(-0.443241\pi\)
0.177370 + 0.984144i \(0.443241\pi\)
\(18\) −0.707195 −0.166687
\(19\) 1.00000 0.229416
\(20\) −2.91196 −0.651134
\(21\) 5.67922 1.23931
\(22\) −1.07783 −0.229793
\(23\) −1.57188 −0.327760 −0.163880 0.986480i \(-0.552401\pi\)
−0.163880 + 0.986480i \(0.552401\pi\)
\(24\) −1.51420 −0.309085
\(25\) 3.47950 0.695901
\(26\) 3.84825 0.754703
\(27\) 5.61344 1.08031
\(28\) −3.75064 −0.708804
\(29\) 2.48697 0.461818 0.230909 0.972975i \(-0.425830\pi\)
0.230909 + 0.972975i \(0.425830\pi\)
\(30\) 4.40929 0.805023
\(31\) −5.80679 −1.04293 −0.521465 0.853273i \(-0.674614\pi\)
−0.521465 + 0.853273i \(0.674614\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.63205 0.284103
\(34\) 1.46263 0.250840
\(35\) 10.9217 1.84610
\(36\) −0.707195 −0.117866
\(37\) 8.92851 1.46784 0.733919 0.679237i \(-0.237689\pi\)
0.733919 + 0.679237i \(0.237689\pi\)
\(38\) 1.00000 0.162221
\(39\) −5.82702 −0.933070
\(40\) −2.91196 −0.460421
\(41\) −3.70538 −0.578683 −0.289341 0.957226i \(-0.593436\pi\)
−0.289341 + 0.957226i \(0.593436\pi\)
\(42\) 5.67922 0.876322
\(43\) 2.26373 0.345216 0.172608 0.984991i \(-0.444781\pi\)
0.172608 + 0.984991i \(0.444781\pi\)
\(44\) −1.07783 −0.162488
\(45\) 2.05932 0.306986
\(46\) −1.57188 −0.231762
\(47\) 3.11736 0.454713 0.227357 0.973812i \(-0.426992\pi\)
0.227357 + 0.973812i \(0.426992\pi\)
\(48\) −1.51420 −0.218556
\(49\) 7.06728 1.00961
\(50\) 3.47950 0.492076
\(51\) −2.21472 −0.310123
\(52\) 3.84825 0.533656
\(53\) −4.03335 −0.554023 −0.277012 0.960867i \(-0.589344\pi\)
−0.277012 + 0.960867i \(0.589344\pi\)
\(54\) 5.61344 0.763892
\(55\) 3.13859 0.423207
\(56\) −3.75064 −0.501200
\(57\) −1.51420 −0.200561
\(58\) 2.48697 0.326555
\(59\) 15.0431 1.95844 0.979222 0.202791i \(-0.0650011\pi\)
0.979222 + 0.202791i \(0.0650011\pi\)
\(60\) 4.40929 0.569237
\(61\) 6.86485 0.878954 0.439477 0.898254i \(-0.355164\pi\)
0.439477 + 0.898254i \(0.355164\pi\)
\(62\) −5.80679 −0.737463
\(63\) 2.65243 0.334175
\(64\) 1.00000 0.125000
\(65\) −11.2059 −1.38992
\(66\) 1.63205 0.200891
\(67\) 7.13230 0.871349 0.435675 0.900104i \(-0.356510\pi\)
0.435675 + 0.900104i \(0.356510\pi\)
\(68\) 1.46263 0.177370
\(69\) 2.38015 0.286536
\(70\) 10.9217 1.30539
\(71\) 4.01635 0.476653 0.238326 0.971185i \(-0.423401\pi\)
0.238326 + 0.971185i \(0.423401\pi\)
\(72\) −0.707195 −0.0833437
\(73\) −15.5522 −1.82025 −0.910125 0.414333i \(-0.864015\pi\)
−0.910125 + 0.414333i \(0.864015\pi\)
\(74\) 8.92851 1.03792
\(75\) −5.26867 −0.608374
\(76\) 1.00000 0.114708
\(77\) 4.04254 0.460690
\(78\) −5.82702 −0.659780
\(79\) −11.9353 −1.34283 −0.671415 0.741081i \(-0.734313\pi\)
−0.671415 + 0.741081i \(0.734313\pi\)
\(80\) −2.91196 −0.325567
\(81\) −6.37829 −0.708699
\(82\) −3.70538 −0.409190
\(83\) −0.410968 −0.0451095 −0.0225548 0.999746i \(-0.507180\pi\)
−0.0225548 + 0.999746i \(0.507180\pi\)
\(84\) 5.67922 0.619654
\(85\) −4.25913 −0.461967
\(86\) 2.26373 0.244104
\(87\) −3.76577 −0.403733
\(88\) −1.07783 −0.114897
\(89\) −1.42947 −0.151523 −0.0757617 0.997126i \(-0.524139\pi\)
−0.0757617 + 0.997126i \(0.524139\pi\)
\(90\) 2.05932 0.217072
\(91\) −14.4334 −1.51303
\(92\) −1.57188 −0.163880
\(93\) 8.79265 0.911755
\(94\) 3.11736 0.321531
\(95\) −2.91196 −0.298761
\(96\) −1.51420 −0.154543
\(97\) −7.18019 −0.729038 −0.364519 0.931196i \(-0.618767\pi\)
−0.364519 + 0.931196i \(0.618767\pi\)
\(98\) 7.06728 0.713903
\(99\) 0.762233 0.0766073
\(100\) 3.47950 0.347950
\(101\) −15.3214 −1.52454 −0.762270 0.647260i \(-0.775915\pi\)
−0.762270 + 0.647260i \(0.775915\pi\)
\(102\) −2.21472 −0.219290
\(103\) 17.0428 1.67928 0.839640 0.543143i \(-0.182766\pi\)
0.839640 + 0.543143i \(0.182766\pi\)
\(104\) 3.84825 0.377352
\(105\) −16.5377 −1.61391
\(106\) −4.03335 −0.391754
\(107\) 5.51478 0.533134 0.266567 0.963816i \(-0.414111\pi\)
0.266567 + 0.963816i \(0.414111\pi\)
\(108\) 5.61344 0.540153
\(109\) 5.98523 0.573281 0.286641 0.958038i \(-0.407461\pi\)
0.286641 + 0.958038i \(0.407461\pi\)
\(110\) 3.13859 0.299252
\(111\) −13.5196 −1.28322
\(112\) −3.75064 −0.354402
\(113\) −12.7751 −1.20178 −0.600892 0.799331i \(-0.705188\pi\)
−0.600892 + 0.799331i \(0.705188\pi\)
\(114\) −1.51420 −0.141818
\(115\) 4.57726 0.426832
\(116\) 2.48697 0.230909
\(117\) −2.72146 −0.251599
\(118\) 15.0431 1.38483
\(119\) −5.48581 −0.502883
\(120\) 4.40929 0.402511
\(121\) −9.83829 −0.894390
\(122\) 6.86485 0.621514
\(123\) 5.61069 0.505899
\(124\) −5.80679 −0.521465
\(125\) 4.42762 0.396018
\(126\) 2.65243 0.236297
\(127\) 12.7818 1.13420 0.567100 0.823649i \(-0.308065\pi\)
0.567100 + 0.823649i \(0.308065\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.42775 −0.301796
\(130\) −11.2059 −0.982825
\(131\) 7.49553 0.654888 0.327444 0.944871i \(-0.393813\pi\)
0.327444 + 0.944871i \(0.393813\pi\)
\(132\) 1.63205 0.142051
\(133\) −3.75064 −0.325221
\(134\) 7.13230 0.616137
\(135\) −16.3461 −1.40685
\(136\) 1.46263 0.125420
\(137\) 13.2190 1.12937 0.564687 0.825305i \(-0.308997\pi\)
0.564687 + 0.825305i \(0.308997\pi\)
\(138\) 2.38015 0.202612
\(139\) 6.65074 0.564108 0.282054 0.959399i \(-0.408984\pi\)
0.282054 + 0.959399i \(0.408984\pi\)
\(140\) 10.9217 0.923052
\(141\) −4.72031 −0.397522
\(142\) 4.01635 0.337045
\(143\) −4.14774 −0.346852
\(144\) −0.707195 −0.0589329
\(145\) −7.24195 −0.601411
\(146\) −15.5522 −1.28711
\(147\) −10.7013 −0.882626
\(148\) 8.92851 0.733919
\(149\) 1.10176 0.0902598 0.0451299 0.998981i \(-0.485630\pi\)
0.0451299 + 0.998981i \(0.485630\pi\)
\(150\) −5.26867 −0.430185
\(151\) −18.1525 −1.47723 −0.738616 0.674126i \(-0.764520\pi\)
−0.738616 + 0.674126i \(0.764520\pi\)
\(152\) 1.00000 0.0811107
\(153\) −1.03437 −0.0836236
\(154\) 4.04254 0.325757
\(155\) 16.9091 1.35817
\(156\) −5.82702 −0.466535
\(157\) −12.2033 −0.973932 −0.486966 0.873421i \(-0.661896\pi\)
−0.486966 + 0.873421i \(0.661896\pi\)
\(158\) −11.9353 −0.949525
\(159\) 6.10731 0.484341
\(160\) −2.91196 −0.230211
\(161\) 5.89557 0.464636
\(162\) −6.37829 −0.501126
\(163\) −12.8855 −1.00927 −0.504634 0.863333i \(-0.668373\pi\)
−0.504634 + 0.863333i \(0.668373\pi\)
\(164\) −3.70538 −0.289341
\(165\) −4.75245 −0.369978
\(166\) −0.410968 −0.0318973
\(167\) 16.3595 1.26594 0.632968 0.774178i \(-0.281837\pi\)
0.632968 + 0.774178i \(0.281837\pi\)
\(168\) 5.67922 0.438161
\(169\) 1.80900 0.139153
\(170\) −4.25913 −0.326660
\(171\) −0.707195 −0.0540805
\(172\) 2.26373 0.172608
\(173\) 8.11338 0.616849 0.308424 0.951249i \(-0.400198\pi\)
0.308424 + 0.951249i \(0.400198\pi\)
\(174\) −3.76577 −0.285482
\(175\) −13.0504 −0.986514
\(176\) −1.07783 −0.0812442
\(177\) −22.7783 −1.71212
\(178\) −1.42947 −0.107143
\(179\) 15.2583 1.14046 0.570231 0.821484i \(-0.306854\pi\)
0.570231 + 0.821484i \(0.306854\pi\)
\(180\) 2.05932 0.153493
\(181\) −7.21792 −0.536504 −0.268252 0.963349i \(-0.586446\pi\)
−0.268252 + 0.963349i \(0.586446\pi\)
\(182\) −14.4334 −1.06987
\(183\) −10.3948 −0.768403
\(184\) −1.57188 −0.115881
\(185\) −25.9995 −1.91152
\(186\) 8.79265 0.644708
\(187\) −1.57646 −0.115283
\(188\) 3.11736 0.227357
\(189\) −21.0540 −1.53145
\(190\) −2.91196 −0.211256
\(191\) −8.88480 −0.642882 −0.321441 0.946930i \(-0.604167\pi\)
−0.321441 + 0.946930i \(0.604167\pi\)
\(192\) −1.51420 −0.109278
\(193\) −13.7683 −0.991065 −0.495533 0.868589i \(-0.665027\pi\)
−0.495533 + 0.868589i \(0.665027\pi\)
\(194\) −7.18019 −0.515508
\(195\) 16.9680 1.21511
\(196\) 7.06728 0.504805
\(197\) −22.4145 −1.59697 −0.798483 0.602017i \(-0.794364\pi\)
−0.798483 + 0.602017i \(0.794364\pi\)
\(198\) 0.762233 0.0541695
\(199\) −9.43267 −0.668664 −0.334332 0.942455i \(-0.608511\pi\)
−0.334332 + 0.942455i \(0.608511\pi\)
\(200\) 3.47950 0.246038
\(201\) −10.7997 −0.761755
\(202\) −15.3214 −1.07801
\(203\) −9.32771 −0.654677
\(204\) −2.21472 −0.155061
\(205\) 10.7899 0.753600
\(206\) 17.0428 1.18743
\(207\) 1.11163 0.0772635
\(208\) 3.84825 0.266828
\(209\) −1.07783 −0.0745548
\(210\) −16.5377 −1.14121
\(211\) −1.00000 −0.0688428
\(212\) −4.03335 −0.277012
\(213\) −6.08156 −0.416702
\(214\) 5.51478 0.376983
\(215\) −6.59189 −0.449563
\(216\) 5.61344 0.381946
\(217\) 21.7792 1.47847
\(218\) 5.98523 0.405371
\(219\) 23.5492 1.59131
\(220\) 3.13859 0.211603
\(221\) 5.62857 0.378619
\(222\) −13.5196 −0.907374
\(223\) −16.7954 −1.12470 −0.562352 0.826898i \(-0.690103\pi\)
−0.562352 + 0.826898i \(0.690103\pi\)
\(224\) −3.75064 −0.250600
\(225\) −2.46069 −0.164046
\(226\) −12.7751 −0.849789
\(227\) −20.7288 −1.37582 −0.687910 0.725796i \(-0.741472\pi\)
−0.687910 + 0.725796i \(0.741472\pi\)
\(228\) −1.51420 −0.100280
\(229\) 11.3130 0.747584 0.373792 0.927512i \(-0.378057\pi\)
0.373792 + 0.927512i \(0.378057\pi\)
\(230\) 4.57726 0.301816
\(231\) −6.12121 −0.402746
\(232\) 2.48697 0.163277
\(233\) −9.25379 −0.606236 −0.303118 0.952953i \(-0.598028\pi\)
−0.303118 + 0.952953i \(0.598028\pi\)
\(234\) −2.72146 −0.177907
\(235\) −9.07762 −0.592159
\(236\) 15.0431 0.979222
\(237\) 18.0725 1.17394
\(238\) −5.48581 −0.355592
\(239\) −17.7783 −1.14998 −0.574992 0.818159i \(-0.694995\pi\)
−0.574992 + 0.818159i \(0.694995\pi\)
\(240\) 4.40929 0.284619
\(241\) −26.5501 −1.71024 −0.855122 0.518427i \(-0.826518\pi\)
−0.855122 + 0.518427i \(0.826518\pi\)
\(242\) −9.83829 −0.632429
\(243\) −7.18230 −0.460745
\(244\) 6.86485 0.439477
\(245\) −20.5796 −1.31478
\(246\) 5.61069 0.357724
\(247\) 3.84825 0.244858
\(248\) −5.80679 −0.368732
\(249\) 0.622287 0.0394359
\(250\) 4.42762 0.280027
\(251\) −12.9230 −0.815693 −0.407846 0.913051i \(-0.633720\pi\)
−0.407846 + 0.913051i \(0.633720\pi\)
\(252\) 2.65243 0.167087
\(253\) 1.69422 0.106515
\(254\) 12.7818 0.802001
\(255\) 6.44918 0.403863
\(256\) 1.00000 0.0625000
\(257\) −8.73531 −0.544894 −0.272447 0.962171i \(-0.587833\pi\)
−0.272447 + 0.962171i \(0.587833\pi\)
\(258\) −3.42775 −0.213402
\(259\) −33.4876 −2.08082
\(260\) −11.2059 −0.694962
\(261\) −1.75877 −0.108865
\(262\) 7.49553 0.463075
\(263\) 3.79962 0.234295 0.117147 0.993115i \(-0.462625\pi\)
0.117147 + 0.993115i \(0.462625\pi\)
\(264\) 1.63205 0.100445
\(265\) 11.7450 0.721487
\(266\) −3.75064 −0.229966
\(267\) 2.16450 0.132465
\(268\) 7.13230 0.435675
\(269\) −25.0708 −1.52859 −0.764297 0.644865i \(-0.776914\pi\)
−0.764297 + 0.644865i \(0.776914\pi\)
\(270\) −16.3461 −0.994792
\(271\) 15.6996 0.953686 0.476843 0.878989i \(-0.341781\pi\)
0.476843 + 0.878989i \(0.341781\pi\)
\(272\) 1.46263 0.0886852
\(273\) 21.8550 1.32273
\(274\) 13.2190 0.798588
\(275\) −3.75030 −0.226152
\(276\) 2.38015 0.143268
\(277\) 3.43748 0.206538 0.103269 0.994653i \(-0.467070\pi\)
0.103269 + 0.994653i \(0.467070\pi\)
\(278\) 6.65074 0.398885
\(279\) 4.10653 0.245852
\(280\) 10.9217 0.652696
\(281\) 18.6736 1.11398 0.556988 0.830520i \(-0.311957\pi\)
0.556988 + 0.830520i \(0.311957\pi\)
\(282\) −4.72031 −0.281090
\(283\) 29.7132 1.76627 0.883133 0.469123i \(-0.155430\pi\)
0.883133 + 0.469123i \(0.155430\pi\)
\(284\) 4.01635 0.238326
\(285\) 4.40929 0.261184
\(286\) −4.14774 −0.245261
\(287\) 13.8975 0.820345
\(288\) −0.707195 −0.0416718
\(289\) −14.8607 −0.874159
\(290\) −7.24195 −0.425262
\(291\) 10.8723 0.637343
\(292\) −15.5522 −0.910125
\(293\) −16.6447 −0.972392 −0.486196 0.873850i \(-0.661616\pi\)
−0.486196 + 0.873850i \(0.661616\pi\)
\(294\) −10.7013 −0.624111
\(295\) −43.8049 −2.55042
\(296\) 8.92851 0.518959
\(297\) −6.05031 −0.351075
\(298\) 1.10176 0.0638233
\(299\) −6.04900 −0.349822
\(300\) −5.26867 −0.304187
\(301\) −8.49044 −0.489381
\(302\) −18.1525 −1.04456
\(303\) 23.1997 1.33279
\(304\) 1.00000 0.0573539
\(305\) −19.9902 −1.14463
\(306\) −1.03437 −0.0591308
\(307\) −21.8723 −1.24832 −0.624158 0.781298i \(-0.714558\pi\)
−0.624158 + 0.781298i \(0.714558\pi\)
\(308\) 4.04254 0.230345
\(309\) −25.8063 −1.46807
\(310\) 16.9091 0.960375
\(311\) 14.2577 0.808479 0.404239 0.914653i \(-0.367536\pi\)
0.404239 + 0.914653i \(0.367536\pi\)
\(312\) −5.82702 −0.329890
\(313\) 1.50800 0.0852373 0.0426187 0.999091i \(-0.486430\pi\)
0.0426187 + 0.999091i \(0.486430\pi\)
\(314\) −12.2033 −0.688674
\(315\) −7.72377 −0.435185
\(316\) −11.9353 −0.671415
\(317\) 7.27695 0.408714 0.204357 0.978896i \(-0.434490\pi\)
0.204357 + 0.978896i \(0.434490\pi\)
\(318\) 6.10731 0.342481
\(319\) −2.68052 −0.150080
\(320\) −2.91196 −0.162783
\(321\) −8.35049 −0.466079
\(322\) 5.89557 0.328547
\(323\) 1.46263 0.0813831
\(324\) −6.37829 −0.354350
\(325\) 13.3900 0.742743
\(326\) −12.8855 −0.713661
\(327\) −9.06285 −0.501177
\(328\) −3.70538 −0.204595
\(329\) −11.6921 −0.644605
\(330\) −4.75245 −0.261614
\(331\) 22.6267 1.24368 0.621838 0.783146i \(-0.286386\pi\)
0.621838 + 0.783146i \(0.286386\pi\)
\(332\) −0.410968 −0.0225548
\(333\) −6.31419 −0.346016
\(334\) 16.3595 0.895152
\(335\) −20.7690 −1.13473
\(336\) 5.67922 0.309827
\(337\) 0.650779 0.0354502 0.0177251 0.999843i \(-0.494358\pi\)
0.0177251 + 0.999843i \(0.494358\pi\)
\(338\) 1.80900 0.0983964
\(339\) 19.3441 1.05063
\(340\) −4.25913 −0.230984
\(341\) 6.25871 0.338928
\(342\) −0.707195 −0.0382407
\(343\) −0.252324 −0.0136242
\(344\) 2.26373 0.122052
\(345\) −6.93090 −0.373147
\(346\) 8.11338 0.436178
\(347\) 9.25992 0.497098 0.248549 0.968619i \(-0.420046\pi\)
0.248549 + 0.968619i \(0.420046\pi\)
\(348\) −3.76577 −0.201866
\(349\) −10.2506 −0.548704 −0.274352 0.961629i \(-0.588463\pi\)
−0.274352 + 0.961629i \(0.588463\pi\)
\(350\) −13.0504 −0.697571
\(351\) 21.6019 1.15302
\(352\) −1.07783 −0.0574483
\(353\) 16.8906 0.898993 0.449497 0.893282i \(-0.351603\pi\)
0.449497 + 0.893282i \(0.351603\pi\)
\(354\) −22.7783 −1.21065
\(355\) −11.6954 −0.620730
\(356\) −1.42947 −0.0757617
\(357\) 8.30661 0.439633
\(358\) 15.2583 0.806429
\(359\) −15.9866 −0.843743 −0.421872 0.906656i \(-0.638627\pi\)
−0.421872 + 0.906656i \(0.638627\pi\)
\(360\) 2.05932 0.108536
\(361\) 1.00000 0.0526316
\(362\) −7.21792 −0.379365
\(363\) 14.8972 0.781898
\(364\) −14.4334 −0.756514
\(365\) 45.2875 2.37045
\(366\) −10.3948 −0.543343
\(367\) −25.4157 −1.32669 −0.663346 0.748313i \(-0.730864\pi\)
−0.663346 + 0.748313i \(0.730864\pi\)
\(368\) −1.57188 −0.0819401
\(369\) 2.62042 0.136414
\(370\) −25.9995 −1.35165
\(371\) 15.1276 0.785388
\(372\) 8.79265 0.455878
\(373\) −8.15582 −0.422293 −0.211146 0.977454i \(-0.567720\pi\)
−0.211146 + 0.977454i \(0.567720\pi\)
\(374\) −1.57646 −0.0815171
\(375\) −6.70431 −0.346209
\(376\) 3.11736 0.160765
\(377\) 9.57046 0.492904
\(378\) −21.0540 −1.08290
\(379\) −25.6554 −1.31783 −0.658915 0.752217i \(-0.728984\pi\)
−0.658915 + 0.752217i \(0.728984\pi\)
\(380\) −2.91196 −0.149380
\(381\) −19.3542 −0.991546
\(382\) −8.88480 −0.454586
\(383\) −8.78453 −0.448869 −0.224434 0.974489i \(-0.572053\pi\)
−0.224434 + 0.974489i \(0.572053\pi\)
\(384\) −1.51420 −0.0772713
\(385\) −11.7717 −0.599941
\(386\) −13.7683 −0.700789
\(387\) −1.60090 −0.0813783
\(388\) −7.18019 −0.364519
\(389\) 18.6271 0.944429 0.472215 0.881484i \(-0.343455\pi\)
0.472215 + 0.881484i \(0.343455\pi\)
\(390\) 16.9680 0.859210
\(391\) −2.29909 −0.116270
\(392\) 7.06728 0.356951
\(393\) −11.3497 −0.572519
\(394\) −22.4145 −1.12923
\(395\) 34.7552 1.74872
\(396\) 0.762233 0.0383037
\(397\) 6.46399 0.324418 0.162209 0.986756i \(-0.448138\pi\)
0.162209 + 0.986756i \(0.448138\pi\)
\(398\) −9.43267 −0.472817
\(399\) 5.67922 0.284317
\(400\) 3.47950 0.173975
\(401\) −23.6505 −1.18105 −0.590524 0.807020i \(-0.701079\pi\)
−0.590524 + 0.807020i \(0.701079\pi\)
\(402\) −10.7997 −0.538642
\(403\) −22.3460 −1.11313
\(404\) −15.3214 −0.762270
\(405\) 18.5733 0.922916
\(406\) −9.32771 −0.462927
\(407\) −9.62338 −0.477013
\(408\) −2.21472 −0.109645
\(409\) 0.663992 0.0328323 0.0164161 0.999865i \(-0.494774\pi\)
0.0164161 + 0.999865i \(0.494774\pi\)
\(410\) 10.7899 0.532875
\(411\) −20.0162 −0.987326
\(412\) 17.0428 0.839640
\(413\) −56.4212 −2.77630
\(414\) 1.11163 0.0546335
\(415\) 1.19672 0.0587447
\(416\) 3.84825 0.188676
\(417\) −10.0706 −0.493157
\(418\) −1.07783 −0.0527182
\(419\) 29.2325 1.42810 0.714050 0.700095i \(-0.246859\pi\)
0.714050 + 0.700095i \(0.246859\pi\)
\(420\) −16.5377 −0.806955
\(421\) 12.7450 0.621154 0.310577 0.950548i \(-0.399478\pi\)
0.310577 + 0.950548i \(0.399478\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −2.20458 −0.107190
\(424\) −4.03335 −0.195877
\(425\) 5.08924 0.246864
\(426\) −6.08156 −0.294653
\(427\) −25.7476 −1.24601
\(428\) 5.51478 0.266567
\(429\) 6.28051 0.303226
\(430\) −6.59189 −0.317889
\(431\) 10.6344 0.512241 0.256121 0.966645i \(-0.417556\pi\)
0.256121 + 0.966645i \(0.417556\pi\)
\(432\) 5.61344 0.270077
\(433\) 34.3350 1.65004 0.825018 0.565107i \(-0.191165\pi\)
0.825018 + 0.565107i \(0.191165\pi\)
\(434\) 21.7792 1.04543
\(435\) 10.9658 0.525768
\(436\) 5.98523 0.286641
\(437\) −1.57188 −0.0751934
\(438\) 23.5492 1.12522
\(439\) 3.35608 0.160177 0.0800885 0.996788i \(-0.474480\pi\)
0.0800885 + 0.996788i \(0.474480\pi\)
\(440\) 3.13859 0.149626
\(441\) −4.99794 −0.237997
\(442\) 5.62857 0.267724
\(443\) 17.8153 0.846431 0.423216 0.906029i \(-0.360901\pi\)
0.423216 + 0.906029i \(0.360901\pi\)
\(444\) −13.5196 −0.641610
\(445\) 4.16255 0.197324
\(446\) −16.7954 −0.795285
\(447\) −1.66829 −0.0789073
\(448\) −3.75064 −0.177201
\(449\) 12.0352 0.567978 0.283989 0.958828i \(-0.408342\pi\)
0.283989 + 0.958828i \(0.408342\pi\)
\(450\) −2.46069 −0.115998
\(451\) 3.99375 0.188058
\(452\) −12.7751 −0.600892
\(453\) 27.4866 1.29143
\(454\) −20.7288 −0.972851
\(455\) 42.0294 1.97037
\(456\) −1.51420 −0.0709090
\(457\) −26.3704 −1.23355 −0.616777 0.787138i \(-0.711562\pi\)
−0.616777 + 0.787138i \(0.711562\pi\)
\(458\) 11.3130 0.528622
\(459\) 8.21040 0.383229
\(460\) 4.57726 0.213416
\(461\) 41.5856 1.93684 0.968418 0.249333i \(-0.0802112\pi\)
0.968418 + 0.249333i \(0.0802112\pi\)
\(462\) −6.12121 −0.284785
\(463\) −7.69812 −0.357762 −0.178881 0.983871i \(-0.557248\pi\)
−0.178881 + 0.983871i \(0.557248\pi\)
\(464\) 2.48697 0.115455
\(465\) −25.6038 −1.18735
\(466\) −9.25379 −0.428673
\(467\) −8.83687 −0.408922 −0.204461 0.978875i \(-0.565544\pi\)
−0.204461 + 0.978875i \(0.565544\pi\)
\(468\) −2.72146 −0.125799
\(469\) −26.7507 −1.23523
\(470\) −9.07762 −0.418719
\(471\) 18.4783 0.851435
\(472\) 15.0431 0.692415
\(473\) −2.43991 −0.112187
\(474\) 18.0725 0.830098
\(475\) 3.47950 0.159651
\(476\) −5.48581 −0.251441
\(477\) 2.85236 0.130601
\(478\) −17.7783 −0.813161
\(479\) 1.71555 0.0783854 0.0391927 0.999232i \(-0.487521\pi\)
0.0391927 + 0.999232i \(0.487521\pi\)
\(480\) 4.40929 0.201256
\(481\) 34.3591 1.56664
\(482\) −26.5501 −1.20932
\(483\) −8.92707 −0.406196
\(484\) −9.83829 −0.447195
\(485\) 20.9084 0.949403
\(486\) −7.18230 −0.325796
\(487\) 36.7555 1.66555 0.832775 0.553612i \(-0.186751\pi\)
0.832775 + 0.553612i \(0.186751\pi\)
\(488\) 6.86485 0.310757
\(489\) 19.5112 0.882327
\(490\) −20.5796 −0.929692
\(491\) −27.6658 −1.24854 −0.624270 0.781208i \(-0.714604\pi\)
−0.624270 + 0.781208i \(0.714604\pi\)
\(492\) 5.61069 0.252949
\(493\) 3.63752 0.163826
\(494\) 3.84825 0.173141
\(495\) −2.21959 −0.0997632
\(496\) −5.80679 −0.260733
\(497\) −15.0639 −0.675707
\(498\) 0.622287 0.0278854
\(499\) 10.8003 0.483489 0.241744 0.970340i \(-0.422280\pi\)
0.241744 + 0.970340i \(0.422280\pi\)
\(500\) 4.42762 0.198009
\(501\) −24.7716 −1.10671
\(502\) −12.9230 −0.576782
\(503\) 35.5294 1.58418 0.792090 0.610405i \(-0.208993\pi\)
0.792090 + 0.610405i \(0.208993\pi\)
\(504\) 2.65243 0.118149
\(505\) 44.6154 1.98536
\(506\) 1.69422 0.0753172
\(507\) −2.73918 −0.121651
\(508\) 12.7818 0.567100
\(509\) 12.3705 0.548313 0.274156 0.961685i \(-0.411601\pi\)
0.274156 + 0.961685i \(0.411601\pi\)
\(510\) 6.44918 0.285574
\(511\) 58.3308 2.58040
\(512\) 1.00000 0.0441942
\(513\) 5.61344 0.247839
\(514\) −8.73531 −0.385298
\(515\) −49.6280 −2.18687
\(516\) −3.42775 −0.150898
\(517\) −3.35997 −0.147771
\(518\) −33.4876 −1.47136
\(519\) −12.2853 −0.539264
\(520\) −11.2059 −0.491413
\(521\) 2.85190 0.124944 0.0624720 0.998047i \(-0.480102\pi\)
0.0624720 + 0.998047i \(0.480102\pi\)
\(522\) −1.75877 −0.0769793
\(523\) −38.7923 −1.69627 −0.848135 0.529780i \(-0.822274\pi\)
−0.848135 + 0.529780i \(0.822274\pi\)
\(524\) 7.49553 0.327444
\(525\) 19.7609 0.862435
\(526\) 3.79962 0.165671
\(527\) −8.49321 −0.369970
\(528\) 1.63205 0.0710257
\(529\) −20.5292 −0.892573
\(530\) 11.7450 0.510168
\(531\) −10.6384 −0.461667
\(532\) −3.75064 −0.162611
\(533\) −14.2592 −0.617634
\(534\) 2.16450 0.0936672
\(535\) −16.0588 −0.694283
\(536\) 7.13230 0.308068
\(537\) −23.1042 −0.997020
\(538\) −25.0708 −1.08088
\(539\) −7.61730 −0.328100
\(540\) −16.3461 −0.703424
\(541\) 12.1375 0.521832 0.260916 0.965362i \(-0.415975\pi\)
0.260916 + 0.965362i \(0.415975\pi\)
\(542\) 15.6996 0.674357
\(543\) 10.9294 0.469025
\(544\) 1.46263 0.0627099
\(545\) −17.4288 −0.746566
\(546\) 21.8550 0.935309
\(547\) −22.8269 −0.976008 −0.488004 0.872841i \(-0.662275\pi\)
−0.488004 + 0.872841i \(0.662275\pi\)
\(548\) 13.2190 0.564687
\(549\) −4.85478 −0.207197
\(550\) −3.75030 −0.159913
\(551\) 2.48697 0.105948
\(552\) 2.38015 0.101306
\(553\) 44.7651 1.90361
\(554\) 3.43748 0.146045
\(555\) 39.3684 1.67110
\(556\) 6.65074 0.282054
\(557\) −25.2863 −1.07142 −0.535708 0.844403i \(-0.679955\pi\)
−0.535708 + 0.844403i \(0.679955\pi\)
\(558\) 4.10653 0.173843
\(559\) 8.71140 0.368453
\(560\) 10.9217 0.461526
\(561\) 2.38708 0.100783
\(562\) 18.6736 0.787700
\(563\) −15.2668 −0.643419 −0.321709 0.946838i \(-0.604257\pi\)
−0.321709 + 0.946838i \(0.604257\pi\)
\(564\) −4.72031 −0.198761
\(565\) 37.2007 1.56504
\(566\) 29.7132 1.24894
\(567\) 23.9227 1.00466
\(568\) 4.01635 0.168522
\(569\) 10.3893 0.435542 0.217771 0.976000i \(-0.430121\pi\)
0.217771 + 0.976000i \(0.430121\pi\)
\(570\) 4.40929 0.184685
\(571\) 43.2802 1.81122 0.905610 0.424111i \(-0.139413\pi\)
0.905610 + 0.424111i \(0.139413\pi\)
\(572\) −4.14774 −0.173426
\(573\) 13.4534 0.562023
\(574\) 13.8975 0.580071
\(575\) −5.46938 −0.228089
\(576\) −0.707195 −0.0294664
\(577\) −0.0509341 −0.00212042 −0.00106021 0.999999i \(-0.500337\pi\)
−0.00106021 + 0.999999i \(0.500337\pi\)
\(578\) −14.8607 −0.618124
\(579\) 20.8480 0.866413
\(580\) −7.24195 −0.300705
\(581\) 1.54139 0.0639476
\(582\) 10.8723 0.450670
\(583\) 4.34725 0.180045
\(584\) −15.5522 −0.643556
\(585\) 7.92478 0.327649
\(586\) −16.6447 −0.687585
\(587\) 35.4468 1.46305 0.731523 0.681816i \(-0.238810\pi\)
0.731523 + 0.681816i \(0.238810\pi\)
\(588\) −10.7013 −0.441313
\(589\) −5.80679 −0.239265
\(590\) −43.8049 −1.80342
\(591\) 33.9401 1.39611
\(592\) 8.92851 0.366960
\(593\) 42.7870 1.75705 0.878527 0.477693i \(-0.158527\pi\)
0.878527 + 0.477693i \(0.158527\pi\)
\(594\) −6.05031 −0.248247
\(595\) 15.9744 0.654888
\(596\) 1.10176 0.0451299
\(597\) 14.2830 0.584562
\(598\) −6.04900 −0.247362
\(599\) −9.99719 −0.408474 −0.204237 0.978921i \(-0.565471\pi\)
−0.204237 + 0.978921i \(0.565471\pi\)
\(600\) −5.26867 −0.215093
\(601\) −33.2591 −1.35667 −0.678334 0.734754i \(-0.737298\pi\)
−0.678334 + 0.734754i \(0.737298\pi\)
\(602\) −8.49044 −0.346044
\(603\) −5.04392 −0.205404
\(604\) −18.1525 −0.738616
\(605\) 28.6487 1.16474
\(606\) 23.1997 0.942425
\(607\) −36.1194 −1.46604 −0.733020 0.680207i \(-0.761890\pi\)
−0.733020 + 0.680207i \(0.761890\pi\)
\(608\) 1.00000 0.0405554
\(609\) 14.1240 0.572335
\(610\) −19.9902 −0.809378
\(611\) 11.9964 0.485321
\(612\) −1.03437 −0.0418118
\(613\) −6.76126 −0.273085 −0.136542 0.990634i \(-0.543599\pi\)
−0.136542 + 0.990634i \(0.543599\pi\)
\(614\) −21.8723 −0.882693
\(615\) −16.3381 −0.658815
\(616\) 4.04254 0.162878
\(617\) 7.78351 0.313352 0.156676 0.987650i \(-0.449922\pi\)
0.156676 + 0.987650i \(0.449922\pi\)
\(618\) −25.8063 −1.03808
\(619\) −38.9974 −1.56744 −0.783718 0.621116i \(-0.786679\pi\)
−0.783718 + 0.621116i \(0.786679\pi\)
\(620\) 16.9091 0.679087
\(621\) −8.82368 −0.354082
\(622\) 14.2577 0.571681
\(623\) 5.36142 0.214801
\(624\) −5.82702 −0.233267
\(625\) −30.2906 −1.21162
\(626\) 1.50800 0.0602719
\(627\) 1.63205 0.0651776
\(628\) −12.2033 −0.486966
\(629\) 13.0591 0.520702
\(630\) −7.72377 −0.307722
\(631\) 4.37505 0.174168 0.0870840 0.996201i \(-0.472245\pi\)
0.0870840 + 0.996201i \(0.472245\pi\)
\(632\) −11.9353 −0.474762
\(633\) 1.51420 0.0601841
\(634\) 7.27695 0.289005
\(635\) −37.2200 −1.47703
\(636\) 6.10731 0.242170
\(637\) 27.1966 1.07757
\(638\) −2.68052 −0.106123
\(639\) −2.84034 −0.112362
\(640\) −2.91196 −0.115105
\(641\) −37.2885 −1.47281 −0.736403 0.676543i \(-0.763477\pi\)
−0.736403 + 0.676543i \(0.763477\pi\)
\(642\) −8.35049 −0.329567
\(643\) 8.12265 0.320326 0.160163 0.987091i \(-0.448798\pi\)
0.160163 + 0.987091i \(0.448798\pi\)
\(644\) 5.89557 0.232318
\(645\) 9.98145 0.393019
\(646\) 1.46263 0.0575465
\(647\) −11.0717 −0.435273 −0.217637 0.976030i \(-0.569835\pi\)
−0.217637 + 0.976030i \(0.569835\pi\)
\(648\) −6.37829 −0.250563
\(649\) −16.2138 −0.636449
\(650\) 13.3900 0.525199
\(651\) −32.9780 −1.29251
\(652\) −12.8855 −0.504634
\(653\) −18.4963 −0.723818 −0.361909 0.932213i \(-0.617875\pi\)
−0.361909 + 0.932213i \(0.617875\pi\)
\(654\) −9.06285 −0.354385
\(655\) −21.8267 −0.852839
\(656\) −3.70538 −0.144671
\(657\) 10.9985 0.429091
\(658\) −11.6921 −0.455805
\(659\) 5.55865 0.216534 0.108267 0.994122i \(-0.465470\pi\)
0.108267 + 0.994122i \(0.465470\pi\)
\(660\) −4.75245 −0.184989
\(661\) 31.7288 1.23411 0.617053 0.786921i \(-0.288326\pi\)
0.617053 + 0.786921i \(0.288326\pi\)
\(662\) 22.6267 0.879412
\(663\) −8.52279 −0.330998
\(664\) −0.410968 −0.0159486
\(665\) 10.9217 0.423525
\(666\) −6.31419 −0.244670
\(667\) −3.90922 −0.151366
\(668\) 16.3595 0.632968
\(669\) 25.4316 0.983243
\(670\) −20.7690 −0.802375
\(671\) −7.39912 −0.285640
\(672\) 5.67922 0.219081
\(673\) −9.09724 −0.350673 −0.175336 0.984509i \(-0.556101\pi\)
−0.175336 + 0.984509i \(0.556101\pi\)
\(674\) 0.650779 0.0250671
\(675\) 19.5320 0.751787
\(676\) 1.80900 0.0695767
\(677\) −22.6646 −0.871073 −0.435537 0.900171i \(-0.643441\pi\)
−0.435537 + 0.900171i \(0.643441\pi\)
\(678\) 19.3441 0.742906
\(679\) 26.9303 1.03349
\(680\) −4.25913 −0.163330
\(681\) 31.3876 1.20278
\(682\) 6.25871 0.239659
\(683\) −43.6585 −1.67055 −0.835273 0.549836i \(-0.814690\pi\)
−0.835273 + 0.549836i \(0.814690\pi\)
\(684\) −0.707195 −0.0270403
\(685\) −38.4931 −1.47075
\(686\) −0.252324 −0.00963379
\(687\) −17.1302 −0.653557
\(688\) 2.26373 0.0863040
\(689\) −15.5213 −0.591316
\(690\) −6.93090 −0.263855
\(691\) 11.2109 0.426481 0.213241 0.977000i \(-0.431598\pi\)
0.213241 + 0.977000i \(0.431598\pi\)
\(692\) 8.11338 0.308424
\(693\) −2.85886 −0.108599
\(694\) 9.25992 0.351502
\(695\) −19.3667 −0.734620
\(696\) −3.76577 −0.142741
\(697\) −5.41961 −0.205282
\(698\) −10.2506 −0.387992
\(699\) 14.0121 0.529986
\(700\) −13.0504 −0.493257
\(701\) −3.58061 −0.135238 −0.0676188 0.997711i \(-0.521540\pi\)
−0.0676188 + 0.997711i \(0.521540\pi\)
\(702\) 21.6019 0.815311
\(703\) 8.92851 0.336745
\(704\) −1.07783 −0.0406221
\(705\) 13.7453 0.517679
\(706\) 16.8906 0.635684
\(707\) 57.4651 2.16120
\(708\) −22.7783 −0.856060
\(709\) −2.67917 −0.100618 −0.0503091 0.998734i \(-0.516021\pi\)
−0.0503091 + 0.998734i \(0.516021\pi\)
\(710\) −11.6954 −0.438922
\(711\) 8.44061 0.316548
\(712\) −1.42947 −0.0535716
\(713\) 9.12760 0.341831
\(714\) 8.30661 0.310867
\(715\) 12.0781 0.451694
\(716\) 15.2583 0.570231
\(717\) 26.9199 1.00534
\(718\) −15.9866 −0.596616
\(719\) 14.8596 0.554170 0.277085 0.960845i \(-0.410632\pi\)
0.277085 + 0.960845i \(0.410632\pi\)
\(720\) 2.05932 0.0767464
\(721\) −63.9215 −2.38056
\(722\) 1.00000 0.0372161
\(723\) 40.2022 1.49514
\(724\) −7.21792 −0.268252
\(725\) 8.65341 0.321380
\(726\) 14.8972 0.552885
\(727\) 9.59031 0.355685 0.177842 0.984059i \(-0.443088\pi\)
0.177842 + 0.984059i \(0.443088\pi\)
\(728\) −14.4334 −0.534936
\(729\) 30.0103 1.11149
\(730\) 45.2875 1.67616
\(731\) 3.31101 0.122462
\(732\) −10.3948 −0.384201
\(733\) 23.0869 0.852733 0.426367 0.904550i \(-0.359793\pi\)
0.426367 + 0.904550i \(0.359793\pi\)
\(734\) −25.4157 −0.938112
\(735\) 31.1617 1.14942
\(736\) −1.57188 −0.0579404
\(737\) −7.68738 −0.283168
\(738\) 2.62042 0.0964591
\(739\) −13.6708 −0.502889 −0.251444 0.967872i \(-0.580906\pi\)
−0.251444 + 0.967872i \(0.580906\pi\)
\(740\) −25.9995 −0.955759
\(741\) −5.82702 −0.214061
\(742\) 15.1276 0.555353
\(743\) 33.5068 1.22925 0.614623 0.788821i \(-0.289308\pi\)
0.614623 + 0.788821i \(0.289308\pi\)
\(744\) 8.79265 0.322354
\(745\) −3.20828 −0.117542
\(746\) −8.15582 −0.298606
\(747\) 0.290634 0.0106337
\(748\) −1.57646 −0.0576413
\(749\) −20.6839 −0.755774
\(750\) −6.70431 −0.244807
\(751\) −41.6802 −1.52093 −0.760466 0.649377i \(-0.775030\pi\)
−0.760466 + 0.649377i \(0.775030\pi\)
\(752\) 3.11736 0.113678
\(753\) 19.5680 0.713098
\(754\) 9.57046 0.348536
\(755\) 52.8594 1.92375
\(756\) −21.0540 −0.765725
\(757\) −17.9851 −0.653678 −0.326839 0.945080i \(-0.605984\pi\)
−0.326839 + 0.945080i \(0.605984\pi\)
\(758\) −25.6554 −0.931846
\(759\) −2.56539 −0.0931177
\(760\) −2.91196 −0.105628
\(761\) −4.58948 −0.166369 −0.0831843 0.996534i \(-0.526509\pi\)
−0.0831843 + 0.996534i \(0.526509\pi\)
\(762\) −19.3542 −0.701129
\(763\) −22.4484 −0.812688
\(764\) −8.88480 −0.321441
\(765\) 3.01203 0.108900
\(766\) −8.78453 −0.317398
\(767\) 57.8895 2.09027
\(768\) −1.51420 −0.0546390
\(769\) 37.8200 1.36382 0.681911 0.731435i \(-0.261149\pi\)
0.681911 + 0.731435i \(0.261149\pi\)
\(770\) −11.7717 −0.424223
\(771\) 13.2270 0.476360
\(772\) −13.7683 −0.495533
\(773\) −28.6396 −1.03009 −0.515047 0.857162i \(-0.672226\pi\)
−0.515047 + 0.857162i \(0.672226\pi\)
\(774\) −1.60090 −0.0575431
\(775\) −20.2048 −0.725776
\(776\) −7.18019 −0.257754
\(777\) 50.7070 1.81910
\(778\) 18.6271 0.667812
\(779\) −3.70538 −0.132759
\(780\) 16.9680 0.607553
\(781\) −4.32893 −0.154901
\(782\) −2.29909 −0.0822153
\(783\) 13.9604 0.498905
\(784\) 7.06728 0.252403
\(785\) 35.5356 1.26832
\(786\) −11.3497 −0.404832
\(787\) 10.9807 0.391419 0.195710 0.980662i \(-0.437299\pi\)
0.195710 + 0.980662i \(0.437299\pi\)
\(788\) −22.4145 −0.798483
\(789\) −5.75339 −0.204826
\(790\) 34.7552 1.23654
\(791\) 47.9149 1.70366
\(792\) 0.762233 0.0270848
\(793\) 26.4176 0.938117
\(794\) 6.46399 0.229398
\(795\) −17.7842 −0.630741
\(796\) −9.43267 −0.334332
\(797\) −51.9536 −1.84029 −0.920145 0.391578i \(-0.871929\pi\)
−0.920145 + 0.391578i \(0.871929\pi\)
\(798\) 5.67922 0.201042
\(799\) 4.55955 0.161305
\(800\) 3.47950 0.123019
\(801\) 1.01091 0.0357188
\(802\) −23.6505 −0.835127
\(803\) 16.7626 0.591539
\(804\) −10.7997 −0.380877
\(805\) −17.1676 −0.605080
\(806\) −22.3460 −0.787103
\(807\) 37.9622 1.33633
\(808\) −15.3214 −0.539006
\(809\) −44.5391 −1.56591 −0.782955 0.622078i \(-0.786289\pi\)
−0.782955 + 0.622078i \(0.786289\pi\)
\(810\) 18.5733 0.652600
\(811\) −14.9982 −0.526657 −0.263329 0.964706i \(-0.584820\pi\)
−0.263329 + 0.964706i \(0.584820\pi\)
\(812\) −9.32771 −0.327338
\(813\) −23.7724 −0.833735
\(814\) −9.62338 −0.337299
\(815\) 37.5220 1.31434
\(816\) −2.21472 −0.0775307
\(817\) 2.26373 0.0791980
\(818\) 0.663992 0.0232159
\(819\) 10.2072 0.356669
\(820\) 10.7899 0.376800
\(821\) 2.08865 0.0728946 0.0364473 0.999336i \(-0.488396\pi\)
0.0364473 + 0.999336i \(0.488396\pi\)
\(822\) −20.0162 −0.698145
\(823\) −41.4810 −1.44594 −0.722969 0.690881i \(-0.757223\pi\)
−0.722969 + 0.690881i \(0.757223\pi\)
\(824\) 17.0428 0.593715
\(825\) 5.67871 0.197707
\(826\) −56.4212 −1.96314
\(827\) 8.40067 0.292120 0.146060 0.989276i \(-0.453341\pi\)
0.146060 + 0.989276i \(0.453341\pi\)
\(828\) 1.11163 0.0386317
\(829\) 19.8866 0.690690 0.345345 0.938476i \(-0.387762\pi\)
0.345345 + 0.938476i \(0.387762\pi\)
\(830\) 1.19672 0.0415388
\(831\) −5.20504 −0.180561
\(832\) 3.84825 0.133414
\(833\) 10.3368 0.358150
\(834\) −10.0706 −0.348715
\(835\) −47.6382 −1.64859
\(836\) −1.07783 −0.0372774
\(837\) −32.5961 −1.12668
\(838\) 29.2325 1.00982
\(839\) −11.3724 −0.392619 −0.196309 0.980542i \(-0.562896\pi\)
−0.196309 + 0.980542i \(0.562896\pi\)
\(840\) −16.5377 −0.570603
\(841\) −22.8150 −0.786724
\(842\) 12.7450 0.439222
\(843\) −28.2757 −0.973865
\(844\) −1.00000 −0.0344214
\(845\) −5.26772 −0.181215
\(846\) −2.20458 −0.0757950
\(847\) 36.8999 1.26789
\(848\) −4.03335 −0.138506
\(849\) −44.9917 −1.54411
\(850\) 5.08924 0.174559
\(851\) −14.0346 −0.481099
\(852\) −6.08156 −0.208351
\(853\) 41.3708 1.41651 0.708255 0.705957i \(-0.249483\pi\)
0.708255 + 0.705957i \(0.249483\pi\)
\(854\) −25.7476 −0.881063
\(855\) 2.05932 0.0704273
\(856\) 5.51478 0.188491
\(857\) −2.40091 −0.0820134 −0.0410067 0.999159i \(-0.513057\pi\)
−0.0410067 + 0.999159i \(0.513057\pi\)
\(858\) 6.28051 0.214413
\(859\) −26.9831 −0.920651 −0.460326 0.887750i \(-0.652267\pi\)
−0.460326 + 0.887750i \(0.652267\pi\)
\(860\) −6.59189 −0.224782
\(861\) −21.0436 −0.717165
\(862\) 10.6344 0.362209
\(863\) −30.0776 −1.02385 −0.511926 0.859029i \(-0.671068\pi\)
−0.511926 + 0.859029i \(0.671068\pi\)
\(864\) 5.61344 0.190973
\(865\) −23.6258 −0.803302
\(866\) 34.3350 1.16675
\(867\) 22.5021 0.764211
\(868\) 21.7792 0.739233
\(869\) 12.8642 0.436389
\(870\) 10.9658 0.371774
\(871\) 27.4468 0.930001
\(872\) 5.98523 0.202686
\(873\) 5.07779 0.171857
\(874\) −1.57188 −0.0531698
\(875\) −16.6064 −0.561398
\(876\) 23.5492 0.795654
\(877\) 34.9447 1.18000 0.589999 0.807404i \(-0.299128\pi\)
0.589999 + 0.807404i \(0.299128\pi\)
\(878\) 3.35608 0.113262
\(879\) 25.2034 0.850089
\(880\) 3.13859 0.105802
\(881\) −18.7866 −0.632936 −0.316468 0.948603i \(-0.602497\pi\)
−0.316468 + 0.948603i \(0.602497\pi\)
\(882\) −4.99794 −0.168289
\(883\) −7.55279 −0.254172 −0.127086 0.991892i \(-0.540562\pi\)
−0.127086 + 0.991892i \(0.540562\pi\)
\(884\) 5.62857 0.189309
\(885\) 66.3294 2.22964
\(886\) 17.8153 0.598517
\(887\) 50.9029 1.70915 0.854576 0.519327i \(-0.173817\pi\)
0.854576 + 0.519327i \(0.173817\pi\)
\(888\) −13.5196 −0.453687
\(889\) −47.9398 −1.60785
\(890\) 4.16255 0.139529
\(891\) 6.87469 0.230311
\(892\) −16.7954 −0.562352
\(893\) 3.11736 0.104318
\(894\) −1.66829 −0.0557959
\(895\) −44.4317 −1.48519
\(896\) −3.75064 −0.125300
\(897\) 9.15940 0.305823
\(898\) 12.0352 0.401621
\(899\) −14.4413 −0.481644
\(900\) −2.46069 −0.0820229
\(901\) −5.89931 −0.196535
\(902\) 3.99375 0.132977
\(903\) 12.8562 0.427828
\(904\) −12.7751 −0.424894
\(905\) 21.0183 0.698671
\(906\) 27.4866 0.913181
\(907\) −49.9273 −1.65781 −0.828904 0.559391i \(-0.811035\pi\)
−0.828904 + 0.559391i \(0.811035\pi\)
\(908\) −20.7288 −0.687910
\(909\) 10.8352 0.359382
\(910\) 42.0294 1.39326
\(911\) 17.5228 0.580557 0.290278 0.956942i \(-0.406252\pi\)
0.290278 + 0.956942i \(0.406252\pi\)
\(912\) −1.51420 −0.0501402
\(913\) 0.442952 0.0146596
\(914\) −26.3704 −0.872255
\(915\) 30.2691 1.00067
\(916\) 11.3130 0.373792
\(917\) −28.1130 −0.928373
\(918\) 8.21040 0.270984
\(919\) 45.3792 1.49692 0.748461 0.663179i \(-0.230793\pi\)
0.748461 + 0.663179i \(0.230793\pi\)
\(920\) 4.57726 0.150908
\(921\) 33.1190 1.09131
\(922\) 41.5856 1.36955
\(923\) 15.4559 0.508737
\(924\) −6.12121 −0.201373
\(925\) 31.0668 1.02147
\(926\) −7.69812 −0.252976
\(927\) −12.0526 −0.395859
\(928\) 2.48697 0.0816387
\(929\) −12.7024 −0.416753 −0.208376 0.978049i \(-0.566818\pi\)
−0.208376 + 0.978049i \(0.566818\pi\)
\(930\) −25.6038 −0.839583
\(931\) 7.06728 0.231621
\(932\) −9.25379 −0.303118
\(933\) −21.5890 −0.706792
\(934\) −8.83687 −0.289151
\(935\) 4.59060 0.150129
\(936\) −2.72146 −0.0889537
\(937\) −14.7613 −0.482230 −0.241115 0.970497i \(-0.577513\pi\)
−0.241115 + 0.970497i \(0.577513\pi\)
\(938\) −26.7507 −0.873440
\(939\) −2.28342 −0.0745166
\(940\) −9.07762 −0.296079
\(941\) −41.3244 −1.34714 −0.673569 0.739124i \(-0.735240\pi\)
−0.673569 + 0.739124i \(0.735240\pi\)
\(942\) 18.4783 0.602055
\(943\) 5.82442 0.189669
\(944\) 15.0431 0.489611
\(945\) 61.3083 1.99436
\(946\) −2.43991 −0.0793283
\(947\) −13.6375 −0.443161 −0.221580 0.975142i \(-0.571121\pi\)
−0.221580 + 0.975142i \(0.571121\pi\)
\(948\) 18.0725 0.586968
\(949\) −59.8488 −1.94277
\(950\) 3.47950 0.112890
\(951\) −11.0188 −0.357308
\(952\) −5.48581 −0.177796
\(953\) −36.7962 −1.19195 −0.595974 0.803004i \(-0.703234\pi\)
−0.595974 + 0.803004i \(0.703234\pi\)
\(954\) 2.85236 0.0923487
\(955\) 25.8722 0.837204
\(956\) −17.7783 −0.574992
\(957\) 4.05885 0.131204
\(958\) 1.71555 0.0554268
\(959\) −49.5796 −1.60101
\(960\) 4.40929 0.142309
\(961\) 2.71883 0.0877041
\(962\) 34.3591 1.10778
\(963\) −3.90002 −0.125676
\(964\) −26.5501 −0.855122
\(965\) 40.0928 1.29063
\(966\) −8.92707 −0.287224
\(967\) −58.2120 −1.87197 −0.935986 0.352037i \(-0.885489\pi\)
−0.935986 + 0.352037i \(0.885489\pi\)
\(968\) −9.83829 −0.316215
\(969\) −2.21472 −0.0711471
\(970\) 20.9084 0.671329
\(971\) 37.8708 1.21533 0.607666 0.794193i \(-0.292106\pi\)
0.607666 + 0.794193i \(0.292106\pi\)
\(972\) −7.18230 −0.230372
\(973\) −24.9445 −0.799684
\(974\) 36.7555 1.17772
\(975\) −20.2751 −0.649324
\(976\) 6.86485 0.219738
\(977\) −12.9466 −0.414197 −0.207099 0.978320i \(-0.566402\pi\)
−0.207099 + 0.978320i \(0.566402\pi\)
\(978\) 19.5112 0.623900
\(979\) 1.54072 0.0492416
\(980\) −20.5796 −0.657392
\(981\) −4.23273 −0.135141
\(982\) −27.6658 −0.882852
\(983\) 32.3229 1.03094 0.515471 0.856907i \(-0.327617\pi\)
0.515471 + 0.856907i \(0.327617\pi\)
\(984\) 5.61069 0.178862
\(985\) 65.2701 2.07968
\(986\) 3.63752 0.115842
\(987\) 17.7042 0.563530
\(988\) 3.84825 0.122429
\(989\) −3.55832 −0.113148
\(990\) −2.21959 −0.0705432
\(991\) −5.15566 −0.163775 −0.0818875 0.996642i \(-0.526095\pi\)
−0.0818875 + 0.996642i \(0.526095\pi\)
\(992\) −5.80679 −0.184366
\(993\) −34.2614 −1.08725
\(994\) −15.0639 −0.477797
\(995\) 27.4675 0.870779
\(996\) 0.622287 0.0197179
\(997\) 44.7018 1.41572 0.707861 0.706352i \(-0.249661\pi\)
0.707861 + 0.706352i \(0.249661\pi\)
\(998\) 10.8003 0.341878
\(999\) 50.1196 1.58572
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 \(a_p\))