Properties

Label 8018.2.a.j.1.9
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
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: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.19254 q^{3}\) \(+1.00000 q^{4}\) \(+1.33631 q^{5}\) \(-2.19254 q^{6}\) \(-4.99100 q^{7}\) \(+1.00000 q^{8}\) \(+1.80723 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.19254 q^{3}\) \(+1.00000 q^{4}\) \(+1.33631 q^{5}\) \(-2.19254 q^{6}\) \(-4.99100 q^{7}\) \(+1.00000 q^{8}\) \(+1.80723 q^{9}\) \(+1.33631 q^{10}\) \(+3.23517 q^{11}\) \(-2.19254 q^{12}\) \(+3.93273 q^{13}\) \(-4.99100 q^{14}\) \(-2.92992 q^{15}\) \(+1.00000 q^{16}\) \(+2.30236 q^{17}\) \(+1.80723 q^{18}\) \(-1.00000 q^{19}\) \(+1.33631 q^{20}\) \(+10.9430 q^{21}\) \(+3.23517 q^{22}\) \(+2.41135 q^{23}\) \(-2.19254 q^{24}\) \(-3.21427 q^{25}\) \(+3.93273 q^{26}\) \(+2.61520 q^{27}\) \(-4.99100 q^{28}\) \(+7.68845 q^{29}\) \(-2.92992 q^{30}\) \(-10.1826 q^{31}\) \(+1.00000 q^{32}\) \(-7.09323 q^{33}\) \(+2.30236 q^{34}\) \(-6.66954 q^{35}\) \(+1.80723 q^{36}\) \(+3.67800 q^{37}\) \(-1.00000 q^{38}\) \(-8.62266 q^{39}\) \(+1.33631 q^{40}\) \(-8.72443 q^{41}\) \(+10.9430 q^{42}\) \(+9.15875 q^{43}\) \(+3.23517 q^{44}\) \(+2.41502 q^{45}\) \(+2.41135 q^{46}\) \(-9.14506 q^{47}\) \(-2.19254 q^{48}\) \(+17.9101 q^{49}\) \(-3.21427 q^{50}\) \(-5.04802 q^{51}\) \(+3.93273 q^{52}\) \(+5.22097 q^{53}\) \(+2.61520 q^{54}\) \(+4.32320 q^{55}\) \(-4.99100 q^{56}\) \(+2.19254 q^{57}\) \(+7.68845 q^{58}\) \(-9.07487 q^{59}\) \(-2.92992 q^{60}\) \(-1.01640 q^{61}\) \(-10.1826 q^{62}\) \(-9.01987 q^{63}\) \(+1.00000 q^{64}\) \(+5.25536 q^{65}\) \(-7.09323 q^{66}\) \(-14.2825 q^{67}\) \(+2.30236 q^{68}\) \(-5.28697 q^{69}\) \(-6.66954 q^{70}\) \(-5.03857 q^{71}\) \(+1.80723 q^{72}\) \(+0.0673096 q^{73}\) \(+3.67800 q^{74}\) \(+7.04740 q^{75}\) \(-1.00000 q^{76}\) \(-16.1467 q^{77}\) \(-8.62266 q^{78}\) \(+17.2366 q^{79}\) \(+1.33631 q^{80}\) \(-11.1556 q^{81}\) \(-8.72443 q^{82}\) \(-7.67587 q^{83}\) \(+10.9430 q^{84}\) \(+3.07668 q^{85}\) \(+9.15875 q^{86}\) \(-16.8572 q^{87}\) \(+3.23517 q^{88}\) \(+16.3005 q^{89}\) \(+2.41502 q^{90}\) \(-19.6282 q^{91}\) \(+2.41135 q^{92}\) \(+22.3258 q^{93}\) \(-9.14506 q^{94}\) \(-1.33631 q^{95}\) \(-2.19254 q^{96}\) \(-11.3545 q^{97}\) \(+17.9101 q^{98}\) \(+5.84668 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.19254 −1.26586 −0.632932 0.774208i \(-0.718149\pi\)
−0.632932 + 0.774208i \(0.718149\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.33631 0.597618 0.298809 0.954313i \(-0.403411\pi\)
0.298809 + 0.954313i \(0.403411\pi\)
\(6\) −2.19254 −0.895100
\(7\) −4.99100 −1.88642 −0.943210 0.332198i \(-0.892210\pi\)
−0.943210 + 0.332198i \(0.892210\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.80723 0.602410
\(10\) 1.33631 0.422580
\(11\) 3.23517 0.975439 0.487719 0.873000i \(-0.337829\pi\)
0.487719 + 0.873000i \(0.337829\pi\)
\(12\) −2.19254 −0.632932
\(13\) 3.93273 1.09074 0.545371 0.838194i \(-0.316389\pi\)
0.545371 + 0.838194i \(0.316389\pi\)
\(14\) −4.99100 −1.33390
\(15\) −2.92992 −0.756502
\(16\) 1.00000 0.250000
\(17\) 2.30236 0.558405 0.279202 0.960232i \(-0.409930\pi\)
0.279202 + 0.960232i \(0.409930\pi\)
\(18\) 1.80723 0.425968
\(19\) −1.00000 −0.229416
\(20\) 1.33631 0.298809
\(21\) 10.9430 2.38795
\(22\) 3.23517 0.689739
\(23\) 2.41135 0.502800 0.251400 0.967883i \(-0.419109\pi\)
0.251400 + 0.967883i \(0.419109\pi\)
\(24\) −2.19254 −0.447550
\(25\) −3.21427 −0.642853
\(26\) 3.93273 0.771272
\(27\) 2.61520 0.503295
\(28\) −4.99100 −0.943210
\(29\) 7.68845 1.42771 0.713854 0.700294i \(-0.246948\pi\)
0.713854 + 0.700294i \(0.246948\pi\)
\(30\) −2.92992 −0.534928
\(31\) −10.1826 −1.82885 −0.914427 0.404751i \(-0.867358\pi\)
−0.914427 + 0.404751i \(0.867358\pi\)
\(32\) 1.00000 0.176777
\(33\) −7.09323 −1.23477
\(34\) 2.30236 0.394852
\(35\) −6.66954 −1.12736
\(36\) 1.80723 0.301205
\(37\) 3.67800 0.604659 0.302330 0.953203i \(-0.402236\pi\)
0.302330 + 0.953203i \(0.402236\pi\)
\(38\) −1.00000 −0.162221
\(39\) −8.62266 −1.38073
\(40\) 1.33631 0.211290
\(41\) −8.72443 −1.36253 −0.681264 0.732038i \(-0.738569\pi\)
−0.681264 + 0.732038i \(0.738569\pi\)
\(42\) 10.9430 1.68853
\(43\) 9.15875 1.39670 0.698348 0.715758i \(-0.253919\pi\)
0.698348 + 0.715758i \(0.253919\pi\)
\(44\) 3.23517 0.487719
\(45\) 2.41502 0.360011
\(46\) 2.41135 0.355533
\(47\) −9.14506 −1.33394 −0.666972 0.745083i \(-0.732410\pi\)
−0.666972 + 0.745083i \(0.732410\pi\)
\(48\) −2.19254 −0.316466
\(49\) 17.9101 2.55858
\(50\) −3.21427 −0.454566
\(51\) −5.04802 −0.706864
\(52\) 3.93273 0.545371
\(53\) 5.22097 0.717155 0.358577 0.933500i \(-0.383262\pi\)
0.358577 + 0.933500i \(0.383262\pi\)
\(54\) 2.61520 0.355883
\(55\) 4.32320 0.582940
\(56\) −4.99100 −0.666950
\(57\) 2.19254 0.290409
\(58\) 7.68845 1.00954
\(59\) −9.07487 −1.18145 −0.590724 0.806874i \(-0.701158\pi\)
−0.590724 + 0.806874i \(0.701158\pi\)
\(60\) −2.92992 −0.378251
\(61\) −1.01640 −0.130137 −0.0650686 0.997881i \(-0.520727\pi\)
−0.0650686 + 0.997881i \(0.520727\pi\)
\(62\) −10.1826 −1.29319
\(63\) −9.01987 −1.13640
\(64\) 1.00000 0.125000
\(65\) 5.25536 0.651847
\(66\) −7.09323 −0.873116
\(67\) −14.2825 −1.74488 −0.872440 0.488721i \(-0.837464\pi\)
−0.872440 + 0.488721i \(0.837464\pi\)
\(68\) 2.30236 0.279202
\(69\) −5.28697 −0.636476
\(70\) −6.66954 −0.797162
\(71\) −5.03857 −0.597968 −0.298984 0.954258i \(-0.596648\pi\)
−0.298984 + 0.954258i \(0.596648\pi\)
\(72\) 1.80723 0.212984
\(73\) 0.0673096 0.00787800 0.00393900 0.999992i \(-0.498746\pi\)
0.00393900 + 0.999992i \(0.498746\pi\)
\(74\) 3.67800 0.427559
\(75\) 7.04740 0.813764
\(76\) −1.00000 −0.114708
\(77\) −16.1467 −1.84009
\(78\) −8.62266 −0.976324
\(79\) 17.2366 1.93927 0.969634 0.244562i \(-0.0786441\pi\)
0.969634 + 0.244562i \(0.0786441\pi\)
\(80\) 1.33631 0.149404
\(81\) −11.1556 −1.23951
\(82\) −8.72443 −0.963453
\(83\) −7.67587 −0.842536 −0.421268 0.906936i \(-0.638415\pi\)
−0.421268 + 0.906936i \(0.638415\pi\)
\(84\) 10.9430 1.19397
\(85\) 3.07668 0.333713
\(86\) 9.15875 0.987613
\(87\) −16.8572 −1.80728
\(88\) 3.23517 0.344870
\(89\) 16.3005 1.72785 0.863926 0.503618i \(-0.167998\pi\)
0.863926 + 0.503618i \(0.167998\pi\)
\(90\) 2.41502 0.254566
\(91\) −19.6282 −2.05760
\(92\) 2.41135 0.251400
\(93\) 22.3258 2.31508
\(94\) −9.14506 −0.943240
\(95\) −1.33631 −0.137103
\(96\) −2.19254 −0.223775
\(97\) −11.3545 −1.15287 −0.576437 0.817142i \(-0.695557\pi\)
−0.576437 + 0.817142i \(0.695557\pi\)
\(98\) 17.9101 1.80919
\(99\) 5.84668 0.587614
\(100\) −3.21427 −0.321427
\(101\) 7.04416 0.700920 0.350460 0.936578i \(-0.386025\pi\)
0.350460 + 0.936578i \(0.386025\pi\)
\(102\) −5.04802 −0.499828
\(103\) 0.709413 0.0699006 0.0349503 0.999389i \(-0.488873\pi\)
0.0349503 + 0.999389i \(0.488873\pi\)
\(104\) 3.93273 0.385636
\(105\) 14.6232 1.42708
\(106\) 5.22097 0.507105
\(107\) −5.94411 −0.574639 −0.287319 0.957835i \(-0.592764\pi\)
−0.287319 + 0.957835i \(0.592764\pi\)
\(108\) 2.61520 0.251648
\(109\) 17.7690 1.70196 0.850982 0.525195i \(-0.176008\pi\)
0.850982 + 0.525195i \(0.176008\pi\)
\(110\) 4.32320 0.412201
\(111\) −8.06416 −0.765416
\(112\) −4.99100 −0.471605
\(113\) 3.00814 0.282982 0.141491 0.989940i \(-0.454810\pi\)
0.141491 + 0.989940i \(0.454810\pi\)
\(114\) 2.19254 0.205350
\(115\) 3.22231 0.300482
\(116\) 7.68845 0.713854
\(117\) 7.10734 0.657074
\(118\) −9.07487 −0.835410
\(119\) −11.4911 −1.05339
\(120\) −2.92992 −0.267464
\(121\) −0.533707 −0.0485188
\(122\) −1.01640 −0.0920210
\(123\) 19.1287 1.72477
\(124\) −10.1826 −0.914427
\(125\) −10.9768 −0.981798
\(126\) −9.01987 −0.803554
\(127\) 19.8593 1.76223 0.881114 0.472905i \(-0.156794\pi\)
0.881114 + 0.472905i \(0.156794\pi\)
\(128\) 1.00000 0.0883883
\(129\) −20.0809 −1.76803
\(130\) 5.25536 0.460926
\(131\) 18.9722 1.65761 0.828806 0.559536i \(-0.189021\pi\)
0.828806 + 0.559536i \(0.189021\pi\)
\(132\) −7.09323 −0.617386
\(133\) 4.99100 0.432774
\(134\) −14.2825 −1.23382
\(135\) 3.49472 0.300778
\(136\) 2.30236 0.197426
\(137\) 17.6422 1.50728 0.753638 0.657290i \(-0.228297\pi\)
0.753638 + 0.657290i \(0.228297\pi\)
\(138\) −5.28697 −0.450057
\(139\) −15.5679 −1.32045 −0.660227 0.751066i \(-0.729540\pi\)
−0.660227 + 0.751066i \(0.729540\pi\)
\(140\) −6.66954 −0.563679
\(141\) 20.0509 1.68859
\(142\) −5.03857 −0.422827
\(143\) 12.7230 1.06395
\(144\) 1.80723 0.150602
\(145\) 10.2742 0.853224
\(146\) 0.0673096 0.00557058
\(147\) −39.2685 −3.23881
\(148\) 3.67800 0.302330
\(149\) −4.97748 −0.407771 −0.203886 0.978995i \(-0.565357\pi\)
−0.203886 + 0.978995i \(0.565357\pi\)
\(150\) 7.04740 0.575418
\(151\) −3.25853 −0.265175 −0.132588 0.991171i \(-0.542329\pi\)
−0.132588 + 0.991171i \(0.542329\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 4.16090 0.336388
\(154\) −16.1467 −1.30114
\(155\) −13.6072 −1.09296
\(156\) −8.62266 −0.690366
\(157\) −8.55713 −0.682933 −0.341467 0.939894i \(-0.610924\pi\)
−0.341467 + 0.939894i \(0.610924\pi\)
\(158\) 17.2366 1.37127
\(159\) −11.4472 −0.907820
\(160\) 1.33631 0.105645
\(161\) −12.0350 −0.948492
\(162\) −11.1556 −0.876468
\(163\) 2.50839 0.196473 0.0982363 0.995163i \(-0.468680\pi\)
0.0982363 + 0.995163i \(0.468680\pi\)
\(164\) −8.72443 −0.681264
\(165\) −9.47878 −0.737922
\(166\) −7.67587 −0.595763
\(167\) 19.2405 1.48887 0.744436 0.667694i \(-0.232718\pi\)
0.744436 + 0.667694i \(0.232718\pi\)
\(168\) 10.9430 0.844267
\(169\) 2.46636 0.189720
\(170\) 3.07668 0.235970
\(171\) −1.80723 −0.138202
\(172\) 9.15875 0.698348
\(173\) −6.74408 −0.512743 −0.256371 0.966578i \(-0.582527\pi\)
−0.256371 + 0.966578i \(0.582527\pi\)
\(174\) −16.8572 −1.27794
\(175\) 16.0424 1.21269
\(176\) 3.23517 0.243860
\(177\) 19.8970 1.49555
\(178\) 16.3005 1.22178
\(179\) 10.3164 0.771086 0.385543 0.922690i \(-0.374014\pi\)
0.385543 + 0.922690i \(0.374014\pi\)
\(180\) 2.41502 0.180005
\(181\) −12.0472 −0.895460 −0.447730 0.894169i \(-0.647767\pi\)
−0.447730 + 0.894169i \(0.647767\pi\)
\(182\) −19.6282 −1.45494
\(183\) 2.22851 0.164736
\(184\) 2.41135 0.177767
\(185\) 4.91496 0.361355
\(186\) 22.3258 1.63701
\(187\) 7.44852 0.544690
\(188\) −9.14506 −0.666972
\(189\) −13.0524 −0.949426
\(190\) −1.33631 −0.0969464
\(191\) 20.9811 1.51814 0.759070 0.651009i \(-0.225654\pi\)
0.759070 + 0.651009i \(0.225654\pi\)
\(192\) −2.19254 −0.158233
\(193\) −14.1088 −1.01557 −0.507787 0.861482i \(-0.669536\pi\)
−0.507787 + 0.861482i \(0.669536\pi\)
\(194\) −11.3545 −0.815205
\(195\) −11.5226 −0.825149
\(196\) 17.9101 1.27929
\(197\) 16.6726 1.18788 0.593938 0.804511i \(-0.297572\pi\)
0.593938 + 0.804511i \(0.297572\pi\)
\(198\) 5.84668 0.415506
\(199\) 21.2816 1.50862 0.754308 0.656521i \(-0.227973\pi\)
0.754308 + 0.656521i \(0.227973\pi\)
\(200\) −3.21427 −0.227283
\(201\) 31.3149 2.20878
\(202\) 7.04416 0.495625
\(203\) −38.3730 −2.69326
\(204\) −5.04802 −0.353432
\(205\) −11.6586 −0.814271
\(206\) 0.709413 0.0494272
\(207\) 4.35785 0.302892
\(208\) 3.93273 0.272686
\(209\) −3.23517 −0.223781
\(210\) 14.6232 1.00910
\(211\) −1.00000 −0.0688428
\(212\) 5.22097 0.358577
\(213\) 11.0473 0.756946
\(214\) −5.94411 −0.406331
\(215\) 12.2390 0.834690
\(216\) 2.61520 0.177942
\(217\) 50.8215 3.44999
\(218\) 17.7690 1.20347
\(219\) −0.147579 −0.00997246
\(220\) 4.32320 0.291470
\(221\) 9.05457 0.609076
\(222\) −8.06416 −0.541231
\(223\) −2.15682 −0.144431 −0.0722157 0.997389i \(-0.523007\pi\)
−0.0722157 + 0.997389i \(0.523007\pi\)
\(224\) −4.99100 −0.333475
\(225\) −5.80891 −0.387261
\(226\) 3.00814 0.200099
\(227\) 29.2424 1.94089 0.970444 0.241325i \(-0.0775820\pi\)
0.970444 + 0.241325i \(0.0775820\pi\)
\(228\) 2.19254 0.145204
\(229\) −12.3363 −0.815209 −0.407604 0.913159i \(-0.633636\pi\)
−0.407604 + 0.913159i \(0.633636\pi\)
\(230\) 3.22231 0.212473
\(231\) 35.4023 2.32930
\(232\) 7.68845 0.504771
\(233\) 28.8405 1.88940 0.944701 0.327934i \(-0.106352\pi\)
0.944701 + 0.327934i \(0.106352\pi\)
\(234\) 7.10734 0.464621
\(235\) −12.2207 −0.797188
\(236\) −9.07487 −0.590724
\(237\) −37.7919 −2.45485
\(238\) −11.4911 −0.744856
\(239\) 6.55775 0.424186 0.212093 0.977250i \(-0.431972\pi\)
0.212093 + 0.977250i \(0.431972\pi\)
\(240\) −2.92992 −0.189126
\(241\) 5.31595 0.342431 0.171215 0.985234i \(-0.445231\pi\)
0.171215 + 0.985234i \(0.445231\pi\)
\(242\) −0.533707 −0.0343080
\(243\) 16.6135 1.06576
\(244\) −1.01640 −0.0650686
\(245\) 23.9334 1.52905
\(246\) 19.1287 1.21960
\(247\) −3.93273 −0.250234
\(248\) −10.1826 −0.646597
\(249\) 16.8297 1.06654
\(250\) −10.9768 −0.694236
\(251\) −9.63221 −0.607980 −0.303990 0.952675i \(-0.598319\pi\)
−0.303990 + 0.952675i \(0.598319\pi\)
\(252\) −9.01987 −0.568199
\(253\) 7.80110 0.490451
\(254\) 19.8593 1.24608
\(255\) −6.74574 −0.422434
\(256\) 1.00000 0.0625000
\(257\) 15.4729 0.965173 0.482586 0.875848i \(-0.339697\pi\)
0.482586 + 0.875848i \(0.339697\pi\)
\(258\) −20.0809 −1.25018
\(259\) −18.3569 −1.14064
\(260\) 5.25536 0.325924
\(261\) 13.8948 0.860065
\(262\) 18.9722 1.17211
\(263\) 24.2296 1.49406 0.747032 0.664788i \(-0.231478\pi\)
0.747032 + 0.664788i \(0.231478\pi\)
\(264\) −7.09323 −0.436558
\(265\) 6.97685 0.428585
\(266\) 4.99100 0.306018
\(267\) −35.7395 −2.18722
\(268\) −14.2825 −0.872440
\(269\) 9.02170 0.550063 0.275032 0.961435i \(-0.411312\pi\)
0.275032 + 0.961435i \(0.411312\pi\)
\(270\) 3.49472 0.212682
\(271\) −8.19166 −0.497608 −0.248804 0.968554i \(-0.580038\pi\)
−0.248804 + 0.968554i \(0.580038\pi\)
\(272\) 2.30236 0.139601
\(273\) 43.0357 2.60464
\(274\) 17.6422 1.06580
\(275\) −10.3987 −0.627064
\(276\) −5.28697 −0.318238
\(277\) −3.13487 −0.188356 −0.0941779 0.995555i \(-0.530022\pi\)
−0.0941779 + 0.995555i \(0.530022\pi\)
\(278\) −15.5679 −0.933702
\(279\) −18.4023 −1.10172
\(280\) −6.66954 −0.398581
\(281\) −9.92812 −0.592262 −0.296131 0.955147i \(-0.595696\pi\)
−0.296131 + 0.955147i \(0.595696\pi\)
\(282\) 20.0509 1.19401
\(283\) 13.7063 0.814752 0.407376 0.913260i \(-0.366444\pi\)
0.407376 + 0.913260i \(0.366444\pi\)
\(284\) −5.03857 −0.298984
\(285\) 2.92992 0.173554
\(286\) 12.7230 0.752328
\(287\) 43.5436 2.57030
\(288\) 1.80723 0.106492
\(289\) −11.6991 −0.688184
\(290\) 10.2742 0.603320
\(291\) 24.8952 1.45938
\(292\) 0.0673096 0.00393900
\(293\) 19.6345 1.14706 0.573529 0.819185i \(-0.305574\pi\)
0.573529 + 0.819185i \(0.305574\pi\)
\(294\) −39.2685 −2.29018
\(295\) −12.1269 −0.706054
\(296\) 3.67800 0.213779
\(297\) 8.46060 0.490934
\(298\) −4.97748 −0.288338
\(299\) 9.48317 0.548426
\(300\) 7.04740 0.406882
\(301\) −45.7113 −2.63476
\(302\) −3.25853 −0.187507
\(303\) −15.4446 −0.887268
\(304\) −1.00000 −0.0573539
\(305\) −1.35824 −0.0777724
\(306\) 4.16090 0.237863
\(307\) 6.29086 0.359039 0.179519 0.983754i \(-0.442546\pi\)
0.179519 + 0.983754i \(0.442546\pi\)
\(308\) −16.1467 −0.920044
\(309\) −1.55542 −0.0884845
\(310\) −13.6072 −0.772836
\(311\) 28.9522 1.64173 0.820865 0.571122i \(-0.193492\pi\)
0.820865 + 0.571122i \(0.193492\pi\)
\(312\) −8.62266 −0.488162
\(313\) 28.9569 1.63674 0.818370 0.574692i \(-0.194878\pi\)
0.818370 + 0.574692i \(0.194878\pi\)
\(314\) −8.55713 −0.482907
\(315\) −12.0534 −0.679131
\(316\) 17.2366 0.969634
\(317\) −0.740200 −0.0415737 −0.0207869 0.999784i \(-0.506617\pi\)
−0.0207869 + 0.999784i \(0.506617\pi\)
\(318\) −11.4472 −0.641926
\(319\) 24.8734 1.39264
\(320\) 1.33631 0.0747022
\(321\) 13.0327 0.727414
\(322\) −12.0350 −0.670685
\(323\) −2.30236 −0.128107
\(324\) −11.1556 −0.619756
\(325\) −12.6408 −0.701187
\(326\) 2.50839 0.138927
\(327\) −38.9593 −2.15445
\(328\) −8.72443 −0.481726
\(329\) 45.6429 2.51638
\(330\) −9.47878 −0.521789
\(331\) −17.8704 −0.982247 −0.491123 0.871090i \(-0.663414\pi\)
−0.491123 + 0.871090i \(0.663414\pi\)
\(332\) −7.67587 −0.421268
\(333\) 6.64699 0.364253
\(334\) 19.2405 1.05279
\(335\) −19.0858 −1.04277
\(336\) 10.9430 0.596987
\(337\) −28.7954 −1.56858 −0.784292 0.620392i \(-0.786974\pi\)
−0.784292 + 0.620392i \(0.786974\pi\)
\(338\) 2.46636 0.134152
\(339\) −6.59547 −0.358217
\(340\) 3.07668 0.166856
\(341\) −32.9425 −1.78394
\(342\) −1.80723 −0.0977237
\(343\) −54.4520 −2.94013
\(344\) 9.15875 0.493807
\(345\) −7.06505 −0.380369
\(346\) −6.74408 −0.362564
\(347\) −14.9958 −0.805017 −0.402508 0.915416i \(-0.631862\pi\)
−0.402508 + 0.915416i \(0.631862\pi\)
\(348\) −16.8572 −0.903642
\(349\) −17.8998 −0.958155 −0.479077 0.877773i \(-0.659029\pi\)
−0.479077 + 0.877773i \(0.659029\pi\)
\(350\) 16.0424 0.857502
\(351\) 10.2849 0.548965
\(352\) 3.23517 0.172435
\(353\) −2.11526 −0.112584 −0.0562920 0.998414i \(-0.517928\pi\)
−0.0562920 + 0.998414i \(0.517928\pi\)
\(354\) 19.8970 1.05751
\(355\) −6.73311 −0.357356
\(356\) 16.3005 0.863926
\(357\) 25.1946 1.33344
\(358\) 10.3164 0.545240
\(359\) 1.71122 0.0903146 0.0451573 0.998980i \(-0.485621\pi\)
0.0451573 + 0.998980i \(0.485621\pi\)
\(360\) 2.41502 0.127283
\(361\) 1.00000 0.0526316
\(362\) −12.0472 −0.633186
\(363\) 1.17017 0.0614182
\(364\) −19.6282 −1.02880
\(365\) 0.0899468 0.00470803
\(366\) 2.22851 0.116486
\(367\) −11.7588 −0.613802 −0.306901 0.951741i \(-0.599292\pi\)
−0.306901 + 0.951741i \(0.599292\pi\)
\(368\) 2.41135 0.125700
\(369\) −15.7670 −0.820800
\(370\) 4.91496 0.255517
\(371\) −26.0578 −1.35286
\(372\) 22.3258 1.15754
\(373\) 16.5240 0.855582 0.427791 0.903878i \(-0.359292\pi\)
0.427791 + 0.903878i \(0.359292\pi\)
\(374\) 7.44852 0.385154
\(375\) 24.0671 1.24282
\(376\) −9.14506 −0.471620
\(377\) 30.2366 1.55726
\(378\) −13.0524 −0.671345
\(379\) 1.84920 0.0949869 0.0474934 0.998872i \(-0.484877\pi\)
0.0474934 + 0.998872i \(0.484877\pi\)
\(380\) −1.33631 −0.0685515
\(381\) −43.5423 −2.23074
\(382\) 20.9811 1.07349
\(383\) 33.4345 1.70842 0.854211 0.519926i \(-0.174041\pi\)
0.854211 + 0.519926i \(0.174041\pi\)
\(384\) −2.19254 −0.111888
\(385\) −21.5771 −1.09967
\(386\) −14.1088 −0.718120
\(387\) 16.5520 0.841383
\(388\) −11.3545 −0.576437
\(389\) 16.6873 0.846081 0.423041 0.906111i \(-0.360963\pi\)
0.423041 + 0.906111i \(0.360963\pi\)
\(390\) −11.5226 −0.583469
\(391\) 5.55179 0.280766
\(392\) 17.9101 0.904594
\(393\) −41.5974 −2.09831
\(394\) 16.6726 0.839955
\(395\) 23.0335 1.15894
\(396\) 5.84668 0.293807
\(397\) −3.09856 −0.155512 −0.0777562 0.996972i \(-0.524776\pi\)
−0.0777562 + 0.996972i \(0.524776\pi\)
\(398\) 21.2816 1.06675
\(399\) −10.9430 −0.547833
\(400\) −3.21427 −0.160713
\(401\) −18.0100 −0.899377 −0.449688 0.893186i \(-0.648465\pi\)
−0.449688 + 0.893186i \(0.648465\pi\)
\(402\) 31.3149 1.56184
\(403\) −40.0455 −1.99481
\(404\) 7.04416 0.350460
\(405\) −14.9074 −0.740754
\(406\) −38.3730 −1.90442
\(407\) 11.8989 0.589808
\(408\) −5.04802 −0.249914
\(409\) 17.0555 0.843341 0.421671 0.906749i \(-0.361444\pi\)
0.421671 + 0.906749i \(0.361444\pi\)
\(410\) −11.6586 −0.575776
\(411\) −38.6812 −1.90800
\(412\) 0.709413 0.0349503
\(413\) 45.2927 2.22871
\(414\) 4.35785 0.214177
\(415\) −10.2574 −0.503515
\(416\) 3.93273 0.192818
\(417\) 34.1333 1.67151
\(418\) −3.23517 −0.158237
\(419\) −3.00770 −0.146936 −0.0734678 0.997298i \(-0.523407\pi\)
−0.0734678 + 0.997298i \(0.523407\pi\)
\(420\) 14.6232 0.713540
\(421\) −4.14400 −0.201966 −0.100983 0.994888i \(-0.532199\pi\)
−0.100983 + 0.994888i \(0.532199\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −16.5272 −0.803580
\(424\) 5.22097 0.253553
\(425\) −7.40040 −0.358972
\(426\) 11.0473 0.535242
\(427\) 5.07287 0.245494
\(428\) −5.94411 −0.287319
\(429\) −27.8957 −1.34682
\(430\) 12.2390 0.590215
\(431\) 2.40162 0.115682 0.0578411 0.998326i \(-0.481578\pi\)
0.0578411 + 0.998326i \(0.481578\pi\)
\(432\) 2.61520 0.125824
\(433\) 7.86916 0.378167 0.189084 0.981961i \(-0.439448\pi\)
0.189084 + 0.981961i \(0.439448\pi\)
\(434\) 50.8215 2.43951
\(435\) −22.5265 −1.08006
\(436\) 17.7690 0.850982
\(437\) −2.41135 −0.115350
\(438\) −0.147579 −0.00705160
\(439\) −11.3294 −0.540723 −0.270361 0.962759i \(-0.587143\pi\)
−0.270361 + 0.962759i \(0.587143\pi\)
\(440\) 4.32320 0.206100
\(441\) 32.3676 1.54131
\(442\) 9.05457 0.430682
\(443\) −26.2483 −1.24709 −0.623547 0.781786i \(-0.714309\pi\)
−0.623547 + 0.781786i \(0.714309\pi\)
\(444\) −8.06416 −0.382708
\(445\) 21.7826 1.03260
\(446\) −2.15682 −0.102128
\(447\) 10.9133 0.516183
\(448\) −4.99100 −0.235802
\(449\) −29.4362 −1.38918 −0.694589 0.719407i \(-0.744414\pi\)
−0.694589 + 0.719407i \(0.744414\pi\)
\(450\) −5.80891 −0.273835
\(451\) −28.2250 −1.32906
\(452\) 3.00814 0.141491
\(453\) 7.14445 0.335676
\(454\) 29.2424 1.37242
\(455\) −26.2295 −1.22966
\(456\) 2.19254 0.102675
\(457\) 23.6629 1.10690 0.553451 0.832882i \(-0.313310\pi\)
0.553451 + 0.832882i \(0.313310\pi\)
\(458\) −12.3363 −0.576440
\(459\) 6.02113 0.281042
\(460\) 3.22231 0.150241
\(461\) −5.91987 −0.275716 −0.137858 0.990452i \(-0.544022\pi\)
−0.137858 + 0.990452i \(0.544022\pi\)
\(462\) 35.4023 1.64706
\(463\) −37.3810 −1.73724 −0.868620 0.495479i \(-0.834993\pi\)
−0.868620 + 0.495479i \(0.834993\pi\)
\(464\) 7.68845 0.356927
\(465\) 29.8343 1.38353
\(466\) 28.8405 1.33601
\(467\) 11.9819 0.554458 0.277229 0.960804i \(-0.410584\pi\)
0.277229 + 0.960804i \(0.410584\pi\)
\(468\) 7.10734 0.328537
\(469\) 71.2837 3.29158
\(470\) −12.2207 −0.563697
\(471\) 18.7618 0.864500
\(472\) −9.07487 −0.417705
\(473\) 29.6301 1.36239
\(474\) −37.7919 −1.73584
\(475\) 3.21427 0.147481
\(476\) −11.4911 −0.526693
\(477\) 9.43548 0.432021
\(478\) 6.55775 0.299945
\(479\) 6.69002 0.305675 0.152837 0.988251i \(-0.451159\pi\)
0.152837 + 0.988251i \(0.451159\pi\)
\(480\) −2.92992 −0.133732
\(481\) 14.4646 0.659528
\(482\) 5.31595 0.242135
\(483\) 26.3872 1.20066
\(484\) −0.533707 −0.0242594
\(485\) −15.1732 −0.688978
\(486\) 16.6135 0.753605
\(487\) 4.59844 0.208375 0.104188 0.994558i \(-0.466776\pi\)
0.104188 + 0.994558i \(0.466776\pi\)
\(488\) −1.01640 −0.0460105
\(489\) −5.49975 −0.248707
\(490\) 23.9334 1.08120
\(491\) 28.7851 1.29905 0.649526 0.760339i \(-0.274967\pi\)
0.649526 + 0.760339i \(0.274967\pi\)
\(492\) 19.1287 0.862387
\(493\) 17.7016 0.797239
\(494\) −3.93273 −0.176942
\(495\) 7.81300 0.351168
\(496\) −10.1826 −0.457213
\(497\) 25.1475 1.12802
\(498\) 16.8297 0.754155
\(499\) 1.70779 0.0764511 0.0382256 0.999269i \(-0.487829\pi\)
0.0382256 + 0.999269i \(0.487829\pi\)
\(500\) −10.9768 −0.490899
\(501\) −42.1855 −1.88471
\(502\) −9.63221 −0.429906
\(503\) −29.1985 −1.30190 −0.650949 0.759121i \(-0.725629\pi\)
−0.650949 + 0.759121i \(0.725629\pi\)
\(504\) −9.01987 −0.401777
\(505\) 9.41320 0.418882
\(506\) 7.80110 0.346801
\(507\) −5.40759 −0.240160
\(508\) 19.8593 0.881114
\(509\) 8.51309 0.377336 0.188668 0.982041i \(-0.439583\pi\)
0.188668 + 0.982041i \(0.439583\pi\)
\(510\) −6.74574 −0.298706
\(511\) −0.335942 −0.0148612
\(512\) 1.00000 0.0441942
\(513\) −2.61520 −0.115464
\(514\) 15.4729 0.682480
\(515\) 0.947999 0.0417738
\(516\) −20.0809 −0.884013
\(517\) −29.5858 −1.30118
\(518\) −18.3569 −0.806555
\(519\) 14.7867 0.649062
\(520\) 5.25536 0.230463
\(521\) 8.87578 0.388855 0.194428 0.980917i \(-0.437715\pi\)
0.194428 + 0.980917i \(0.437715\pi\)
\(522\) 13.8948 0.608158
\(523\) 35.5373 1.55394 0.776969 0.629539i \(-0.216756\pi\)
0.776969 + 0.629539i \(0.216756\pi\)
\(524\) 18.9722 0.828806
\(525\) −35.1736 −1.53510
\(526\) 24.2296 1.05646
\(527\) −23.4441 −1.02124
\(528\) −7.09323 −0.308693
\(529\) −17.1854 −0.747192
\(530\) 6.97685 0.303055
\(531\) −16.4004 −0.711716
\(532\) 4.99100 0.216387
\(533\) −34.3108 −1.48617
\(534\) −35.7395 −1.54660
\(535\) −7.94320 −0.343414
\(536\) −14.2825 −0.616908
\(537\) −22.6192 −0.976090
\(538\) 9.02170 0.388953
\(539\) 57.9420 2.49574
\(540\) 3.49472 0.150389
\(541\) 44.3652 1.90741 0.953704 0.300747i \(-0.0972360\pi\)
0.953704 + 0.300747i \(0.0972360\pi\)
\(542\) −8.19166 −0.351862
\(543\) 26.4139 1.13353
\(544\) 2.30236 0.0987130
\(545\) 23.7450 1.01712
\(546\) 43.0357 1.84176
\(547\) 31.6895 1.35494 0.677472 0.735549i \(-0.263076\pi\)
0.677472 + 0.735549i \(0.263076\pi\)
\(548\) 17.6422 0.753638
\(549\) −1.83688 −0.0783960
\(550\) −10.3987 −0.443401
\(551\) −7.68845 −0.327539
\(552\) −5.28697 −0.225028
\(553\) −86.0278 −3.65827
\(554\) −3.13487 −0.133188
\(555\) −10.7762 −0.457426
\(556\) −15.5679 −0.660227
\(557\) 24.5966 1.04219 0.521095 0.853498i \(-0.325524\pi\)
0.521095 + 0.853498i \(0.325524\pi\)
\(558\) −18.4023 −0.779033
\(559\) 36.0189 1.52344
\(560\) −6.66954 −0.281839
\(561\) −16.3312 −0.689503
\(562\) −9.92812 −0.418792
\(563\) −9.55585 −0.402731 −0.201365 0.979516i \(-0.564538\pi\)
−0.201365 + 0.979516i \(0.564538\pi\)
\(564\) 20.0509 0.844295
\(565\) 4.01982 0.169115
\(566\) 13.7063 0.576117
\(567\) 55.6776 2.33824
\(568\) −5.03857 −0.211414
\(569\) −35.6967 −1.49648 −0.748241 0.663427i \(-0.769102\pi\)
−0.748241 + 0.663427i \(0.769102\pi\)
\(570\) 2.92992 0.122721
\(571\) −24.3701 −1.01986 −0.509928 0.860217i \(-0.670328\pi\)
−0.509928 + 0.860217i \(0.670328\pi\)
\(572\) 12.7230 0.531977
\(573\) −46.0019 −1.92176
\(574\) 43.5436 1.81748
\(575\) −7.75070 −0.323227
\(576\) 1.80723 0.0753012
\(577\) −15.0012 −0.624510 −0.312255 0.949998i \(-0.601084\pi\)
−0.312255 + 0.949998i \(0.601084\pi\)
\(578\) −11.6991 −0.486620
\(579\) 30.9341 1.28558
\(580\) 10.2742 0.426612
\(581\) 38.3103 1.58938
\(582\) 24.8952 1.03194
\(583\) 16.8907 0.699541
\(584\) 0.0673096 0.00278529
\(585\) 9.49764 0.392679
\(586\) 19.6345 0.811092
\(587\) 19.8294 0.818445 0.409223 0.912435i \(-0.365800\pi\)
0.409223 + 0.912435i \(0.365800\pi\)
\(588\) −39.2685 −1.61941
\(589\) 10.1826 0.419568
\(590\) −12.1269 −0.499256
\(591\) −36.5554 −1.50369
\(592\) 3.67800 0.151165
\(593\) −4.18410 −0.171820 −0.0859101 0.996303i \(-0.527380\pi\)
−0.0859101 + 0.996303i \(0.527380\pi\)
\(594\) 8.46060 0.347142
\(595\) −15.3557 −0.629522
\(596\) −4.97748 −0.203886
\(597\) −46.6608 −1.90970
\(598\) 9.48317 0.387796
\(599\) −2.87767 −0.117578 −0.0587891 0.998270i \(-0.518724\pi\)
−0.0587891 + 0.998270i \(0.518724\pi\)
\(600\) 7.04740 0.287709
\(601\) −1.95912 −0.0799140 −0.0399570 0.999201i \(-0.512722\pi\)
−0.0399570 + 0.999201i \(0.512722\pi\)
\(602\) −45.7113 −1.86305
\(603\) −25.8117 −1.05113
\(604\) −3.25853 −0.132588
\(605\) −0.713200 −0.0289957
\(606\) −15.4446 −0.627393
\(607\) −31.9372 −1.29629 −0.648146 0.761516i \(-0.724456\pi\)
−0.648146 + 0.761516i \(0.724456\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 84.1343 3.40930
\(610\) −1.35824 −0.0549934
\(611\) −35.9650 −1.45499
\(612\) 4.16090 0.168194
\(613\) 19.6450 0.793454 0.396727 0.917937i \(-0.370146\pi\)
0.396727 + 0.917937i \(0.370146\pi\)
\(614\) 6.29086 0.253879
\(615\) 25.5619 1.03076
\(616\) −16.1467 −0.650569
\(617\) 3.49695 0.140782 0.0703909 0.997519i \(-0.477575\pi\)
0.0703909 + 0.997519i \(0.477575\pi\)
\(618\) −1.55542 −0.0625680
\(619\) 42.6753 1.71527 0.857633 0.514263i \(-0.171934\pi\)
0.857633 + 0.514263i \(0.171934\pi\)
\(620\) −13.6072 −0.546478
\(621\) 6.30614 0.253057
\(622\) 28.9522 1.16088
\(623\) −81.3559 −3.25945
\(624\) −8.62266 −0.345183
\(625\) 1.40283 0.0561132
\(626\) 28.9569 1.15735
\(627\) 7.09323 0.283276
\(628\) −8.55713 −0.341467
\(629\) 8.46809 0.337645
\(630\) −12.0534 −0.480218
\(631\) −38.2894 −1.52428 −0.762139 0.647413i \(-0.775851\pi\)
−0.762139 + 0.647413i \(0.775851\pi\)
\(632\) 17.2366 0.685635
\(633\) 2.19254 0.0871456
\(634\) −0.740200 −0.0293971
\(635\) 26.5382 1.05314
\(636\) −11.4472 −0.453910
\(637\) 70.4354 2.79075
\(638\) 24.8734 0.984747
\(639\) −9.10585 −0.360222
\(640\) 1.33631 0.0528224
\(641\) 38.0316 1.50216 0.751079 0.660212i \(-0.229534\pi\)
0.751079 + 0.660212i \(0.229534\pi\)
\(642\) 13.0327 0.514360
\(643\) 6.93025 0.273302 0.136651 0.990619i \(-0.456366\pi\)
0.136651 + 0.990619i \(0.456366\pi\)
\(644\) −12.0350 −0.474246
\(645\) −26.8344 −1.05660
\(646\) −2.30236 −0.0905852
\(647\) 11.7510 0.461981 0.230990 0.972956i \(-0.425803\pi\)
0.230990 + 0.972956i \(0.425803\pi\)
\(648\) −11.1556 −0.438234
\(649\) −29.3587 −1.15243
\(650\) −12.6408 −0.495814
\(651\) −111.428 −4.36721
\(652\) 2.50839 0.0982363
\(653\) 4.23626 0.165778 0.0828888 0.996559i \(-0.473585\pi\)
0.0828888 + 0.996559i \(0.473585\pi\)
\(654\) −38.9593 −1.52343
\(655\) 25.3529 0.990618
\(656\) −8.72443 −0.340632
\(657\) 0.121644 0.00474578
\(658\) 45.6429 1.77935
\(659\) 13.5463 0.527690 0.263845 0.964565i \(-0.415009\pi\)
0.263845 + 0.964565i \(0.415009\pi\)
\(660\) −9.47878 −0.368961
\(661\) −24.5334 −0.954240 −0.477120 0.878838i \(-0.658319\pi\)
−0.477120 + 0.878838i \(0.658319\pi\)
\(662\) −17.8704 −0.694553
\(663\) −19.8525 −0.771007
\(664\) −7.67587 −0.297882
\(665\) 6.66954 0.258634
\(666\) 6.64699 0.257565
\(667\) 18.5395 0.717852
\(668\) 19.2405 0.744436
\(669\) 4.72892 0.182830
\(670\) −19.0858 −0.737351
\(671\) −3.28824 −0.126941
\(672\) 10.9430 0.422134
\(673\) 35.0924 1.35271 0.676356 0.736575i \(-0.263558\pi\)
0.676356 + 0.736575i \(0.263558\pi\)
\(674\) −28.7954 −1.10916
\(675\) −8.40594 −0.323545
\(676\) 2.46636 0.0948601
\(677\) 8.87742 0.341187 0.170593 0.985341i \(-0.445432\pi\)
0.170593 + 0.985341i \(0.445432\pi\)
\(678\) −6.59547 −0.253297
\(679\) 56.6702 2.17480
\(680\) 3.07668 0.117985
\(681\) −64.1152 −2.45690
\(682\) −32.9425 −1.26143
\(683\) −27.3260 −1.04560 −0.522800 0.852455i \(-0.675113\pi\)
−0.522800 + 0.852455i \(0.675113\pi\)
\(684\) −1.80723 −0.0691011
\(685\) 23.5755 0.900774
\(686\) −54.4520 −2.07899
\(687\) 27.0479 1.03194
\(688\) 9.15875 0.349174
\(689\) 20.5327 0.782232
\(690\) −7.06505 −0.268962
\(691\) −30.1592 −1.14731 −0.573655 0.819097i \(-0.694475\pi\)
−0.573655 + 0.819097i \(0.694475\pi\)
\(692\) −6.74408 −0.256371
\(693\) −29.1808 −1.10849
\(694\) −14.9958 −0.569233
\(695\) −20.8036 −0.789127
\(696\) −16.8572 −0.638971
\(697\) −20.0868 −0.760842
\(698\) −17.8998 −0.677518
\(699\) −63.2338 −2.39172
\(700\) 16.0424 0.606345
\(701\) −15.8188 −0.597469 −0.298734 0.954336i \(-0.596564\pi\)
−0.298734 + 0.954336i \(0.596564\pi\)
\(702\) 10.2849 0.388177
\(703\) −3.67800 −0.138718
\(704\) 3.23517 0.121930
\(705\) 26.7943 1.00913
\(706\) −2.11526 −0.0796089
\(707\) −35.1574 −1.32223
\(708\) 19.8970 0.747776
\(709\) 36.1780 1.35870 0.679348 0.733817i \(-0.262263\pi\)
0.679348 + 0.733817i \(0.262263\pi\)
\(710\) −6.73311 −0.252689
\(711\) 31.1505 1.16823
\(712\) 16.3005 0.610888
\(713\) −24.5538 −0.919548
\(714\) 25.1946 0.942886
\(715\) 17.0020 0.635837
\(716\) 10.3164 0.385543
\(717\) −14.3781 −0.536961
\(718\) 1.71122 0.0638621
\(719\) −30.7886 −1.14822 −0.574111 0.818777i \(-0.694652\pi\)
−0.574111 + 0.818777i \(0.694652\pi\)
\(720\) 2.41502 0.0900027
\(721\) −3.54068 −0.131862
\(722\) 1.00000 0.0372161
\(723\) −11.6554 −0.433470
\(724\) −12.0472 −0.447730
\(725\) −24.7127 −0.917807
\(726\) 1.17017 0.0434292
\(727\) −3.16482 −0.117377 −0.0586883 0.998276i \(-0.518692\pi\)
−0.0586883 + 0.998276i \(0.518692\pi\)
\(728\) −19.6282 −0.727471
\(729\) −2.95897 −0.109591
\(730\) 0.0899468 0.00332908
\(731\) 21.0868 0.779922
\(732\) 2.22851 0.0823680
\(733\) −25.2690 −0.933333 −0.466666 0.884433i \(-0.654545\pi\)
−0.466666 + 0.884433i \(0.654545\pi\)
\(734\) −11.7588 −0.434024
\(735\) −52.4750 −1.93557
\(736\) 2.41135 0.0888834
\(737\) −46.2061 −1.70202
\(738\) −15.7670 −0.580393
\(739\) 19.2091 0.706619 0.353310 0.935506i \(-0.385056\pi\)
0.353310 + 0.935506i \(0.385056\pi\)
\(740\) 4.91496 0.180678
\(741\) 8.62266 0.316761
\(742\) −26.0578 −0.956613
\(743\) −19.1594 −0.702892 −0.351446 0.936208i \(-0.614310\pi\)
−0.351446 + 0.936208i \(0.614310\pi\)
\(744\) 22.3258 0.818504
\(745\) −6.65148 −0.243691
\(746\) 16.5240 0.604988
\(747\) −13.8721 −0.507552
\(748\) 7.44852 0.272345
\(749\) 29.6670 1.08401
\(750\) 24.0671 0.878808
\(751\) 28.2882 1.03225 0.516126 0.856513i \(-0.327374\pi\)
0.516126 + 0.856513i \(0.327374\pi\)
\(752\) −9.14506 −0.333486
\(753\) 21.1190 0.769619
\(754\) 30.2366 1.10115
\(755\) −4.35442 −0.158473
\(756\) −13.0524 −0.474713
\(757\) −8.86453 −0.322187 −0.161093 0.986939i \(-0.551502\pi\)
−0.161093 + 0.986939i \(0.551502\pi\)
\(758\) 1.84920 0.0671659
\(759\) −17.1042 −0.620844
\(760\) −1.33631 −0.0484732
\(761\) 37.9858 1.37698 0.688491 0.725245i \(-0.258273\pi\)
0.688491 + 0.725245i \(0.258273\pi\)
\(762\) −43.5423 −1.57737
\(763\) −88.6852 −3.21062
\(764\) 20.9811 0.759070
\(765\) 5.56026 0.201032
\(766\) 33.4345 1.20804
\(767\) −35.6890 −1.28866
\(768\) −2.19254 −0.0791164
\(769\) 52.1302 1.87986 0.939932 0.341363i \(-0.110888\pi\)
0.939932 + 0.341363i \(0.110888\pi\)
\(770\) −21.5771 −0.777583
\(771\) −33.9249 −1.22178
\(772\) −14.1088 −0.507787
\(773\) 37.1755 1.33711 0.668555 0.743663i \(-0.266913\pi\)
0.668555 + 0.743663i \(0.266913\pi\)
\(774\) 16.5520 0.594948
\(775\) 32.7297 1.17568
\(776\) −11.3545 −0.407602
\(777\) 40.2482 1.44390
\(778\) 16.6873 0.598270
\(779\) 8.72443 0.312585
\(780\) −11.5226 −0.412575
\(781\) −16.3006 −0.583281
\(782\) 5.55179 0.198532
\(783\) 20.1068 0.718559
\(784\) 17.9101 0.639645
\(785\) −11.4350 −0.408133
\(786\) −41.5974 −1.48373
\(787\) 33.7975 1.20475 0.602376 0.798213i \(-0.294221\pi\)
0.602376 + 0.798213i \(0.294221\pi\)
\(788\) 16.6726 0.593938
\(789\) −53.1244 −1.89128
\(790\) 23.0335 0.819495
\(791\) −15.0136 −0.533823
\(792\) 5.84668 0.207753
\(793\) −3.99725 −0.141946
\(794\) −3.09856 −0.109964
\(795\) −15.2970 −0.542529
\(796\) 21.2816 0.754308
\(797\) 0.371231 0.0131497 0.00657484 0.999978i \(-0.497907\pi\)
0.00657484 + 0.999978i \(0.497907\pi\)
\(798\) −10.9430 −0.387376
\(799\) −21.0552 −0.744880
\(800\) −3.21427 −0.113641
\(801\) 29.4588 1.04087
\(802\) −18.0100 −0.635955
\(803\) 0.217758 0.00768450
\(804\) 31.3149 1.10439
\(805\) −16.0826 −0.566836
\(806\) −40.0455 −1.41054
\(807\) −19.7804 −0.696305
\(808\) 7.04416 0.247813
\(809\) −13.5546 −0.476554 −0.238277 0.971197i \(-0.576583\pi\)
−0.238277 + 0.971197i \(0.576583\pi\)
\(810\) −14.9074 −0.523793
\(811\) 8.47837 0.297716 0.148858 0.988859i \(-0.452440\pi\)
0.148858 + 0.988859i \(0.452440\pi\)
\(812\) −38.3730 −1.34663
\(813\) 17.9605 0.629904
\(814\) 11.8989 0.417057
\(815\) 3.35200 0.117415
\(816\) −5.04802 −0.176716
\(817\) −9.15875 −0.320424
\(818\) 17.0555 0.596332
\(819\) −35.4727 −1.23952
\(820\) −11.6586 −0.407135
\(821\) 47.8117 1.66864 0.834321 0.551279i \(-0.185860\pi\)
0.834321 + 0.551279i \(0.185860\pi\)
\(822\) −38.6812 −1.34916
\(823\) 50.9241 1.77510 0.887551 0.460710i \(-0.152405\pi\)
0.887551 + 0.460710i \(0.152405\pi\)
\(824\) 0.709413 0.0247136
\(825\) 22.7995 0.793777
\(826\) 45.2927 1.57593
\(827\) 9.99451 0.347543 0.173771 0.984786i \(-0.444405\pi\)
0.173771 + 0.984786i \(0.444405\pi\)
\(828\) 4.35785 0.151446
\(829\) −8.74134 −0.303599 −0.151800 0.988411i \(-0.548507\pi\)
−0.151800 + 0.988411i \(0.548507\pi\)
\(830\) −10.2574 −0.356039
\(831\) 6.87332 0.238433
\(832\) 3.93273 0.136343
\(833\) 41.2354 1.42872
\(834\) 34.1333 1.18194
\(835\) 25.7113 0.889776
\(836\) −3.23517 −0.111891
\(837\) −26.6296 −0.920453
\(838\) −3.00770 −0.103899
\(839\) −3.74913 −0.129434 −0.0647171 0.997904i \(-0.520615\pi\)
−0.0647171 + 0.997904i \(0.520615\pi\)
\(840\) 14.6232 0.504549
\(841\) 30.1122 1.03835
\(842\) −4.14400 −0.142812
\(843\) 21.7678 0.749723
\(844\) −1.00000 −0.0344214
\(845\) 3.29583 0.113380
\(846\) −16.5272 −0.568217
\(847\) 2.66373 0.0915269
\(848\) 5.22097 0.179289
\(849\) −30.0515 −1.03137
\(850\) −7.40040 −0.253832
\(851\) 8.86893 0.304023
\(852\) 11.0473 0.378473
\(853\) −22.9842 −0.786964 −0.393482 0.919332i \(-0.628730\pi\)
−0.393482 + 0.919332i \(0.628730\pi\)
\(854\) 5.07287 0.173590
\(855\) −2.41502 −0.0825921
\(856\) −5.94411 −0.203166
\(857\) −10.9938 −0.375541 −0.187771 0.982213i \(-0.560126\pi\)
−0.187771 + 0.982213i \(0.560126\pi\)
\(858\) −27.8957 −0.952345
\(859\) −38.9355 −1.32846 −0.664231 0.747528i \(-0.731241\pi\)
−0.664231 + 0.747528i \(0.731241\pi\)
\(860\) 12.2390 0.417345
\(861\) −95.4711 −3.25365
\(862\) 2.40162 0.0817997
\(863\) −14.4753 −0.492745 −0.246372 0.969175i \(-0.579239\pi\)
−0.246372 + 0.969175i \(0.579239\pi\)
\(864\) 2.61520 0.0889708
\(865\) −9.01220 −0.306424
\(866\) 7.86916 0.267405
\(867\) 25.6508 0.871147
\(868\) 50.8215 1.72499
\(869\) 55.7632 1.89164
\(870\) −22.5265 −0.763721
\(871\) −56.1690 −1.90322
\(872\) 17.7690 0.601735
\(873\) −20.5202 −0.694502
\(874\) −2.41135 −0.0815650
\(875\) 54.7854 1.85208
\(876\) −0.147579 −0.00498623
\(877\) 0.776551 0.0262223 0.0131111 0.999914i \(-0.495826\pi\)
0.0131111 + 0.999914i \(0.495826\pi\)
\(878\) −11.3294 −0.382349
\(879\) −43.0493 −1.45202
\(880\) 4.32320 0.145735
\(881\) −1.16197 −0.0391479 −0.0195740 0.999808i \(-0.506231\pi\)
−0.0195740 + 0.999808i \(0.506231\pi\)
\(882\) 32.3676 1.08987
\(883\) −2.42935 −0.0817542 −0.0408771 0.999164i \(-0.513015\pi\)
−0.0408771 + 0.999164i \(0.513015\pi\)
\(884\) 9.05457 0.304538
\(885\) 26.5887 0.893768
\(886\) −26.2483 −0.881829
\(887\) 49.7491 1.67041 0.835206 0.549937i \(-0.185348\pi\)
0.835206 + 0.549937i \(0.185348\pi\)
\(888\) −8.06416 −0.270615
\(889\) −99.1177 −3.32430
\(890\) 21.7826 0.730155
\(891\) −36.0902 −1.20907
\(892\) −2.15682 −0.0722157
\(893\) 9.14506 0.306028
\(894\) 10.9133 0.364996
\(895\) 13.7860 0.460815
\(896\) −4.99100 −0.166738
\(897\) −20.7922 −0.694232
\(898\) −29.4362 −0.982297
\(899\) −78.2886 −2.61107
\(900\) −5.80891 −0.193630
\(901\) 12.0206 0.400463
\(902\) −28.2250 −0.939789
\(903\) 100.224 3.33524
\(904\) 3.00814 0.100049
\(905\) −16.0988 −0.535143
\(906\) 7.14445 0.237359
\(907\) −27.6025 −0.916524 −0.458262 0.888817i \(-0.651528\pi\)
−0.458262 + 0.888817i \(0.651528\pi\)
\(908\) 29.2424 0.970444
\(909\) 12.7304 0.422241
\(910\) −26.2295 −0.869499
\(911\) −36.9587 −1.22450 −0.612249 0.790665i \(-0.709735\pi\)
−0.612249 + 0.790665i \(0.709735\pi\)
\(912\) 2.19254 0.0726022
\(913\) −24.8327 −0.821843
\(914\) 23.6629 0.782698
\(915\) 2.97799 0.0984492
\(916\) −12.3363 −0.407604
\(917\) −94.6903 −3.12695
\(918\) 6.02113 0.198727
\(919\) −3.24644 −0.107090 −0.0535451 0.998565i \(-0.517052\pi\)
−0.0535451 + 0.998565i \(0.517052\pi\)
\(920\) 3.22231 0.106237
\(921\) −13.7930 −0.454494
\(922\) −5.91987 −0.194961
\(923\) −19.8153 −0.652230
\(924\) 35.4023 1.16465
\(925\) −11.8221 −0.388707
\(926\) −37.3810 −1.22841
\(927\) 1.28207 0.0421088
\(928\) 7.68845 0.252386
\(929\) −22.2003 −0.728367 −0.364184 0.931327i \(-0.618652\pi\)
−0.364184 + 0.931327i \(0.618652\pi\)
\(930\) 29.8343 0.978305
\(931\) −17.9101 −0.586978
\(932\) 28.8405 0.944701
\(933\) −63.4789 −2.07821
\(934\) 11.9819 0.392061
\(935\) 9.95356 0.325516
\(936\) 7.10734 0.232311
\(937\) −51.1455 −1.67085 −0.835426 0.549603i \(-0.814779\pi\)
−0.835426 + 0.549603i \(0.814779\pi\)
\(938\) 71.2837 2.32750
\(939\) −63.4891 −2.07189
\(940\) −12.2207 −0.398594
\(941\) 48.9670 1.59628 0.798139 0.602473i \(-0.205818\pi\)
0.798139 + 0.602473i \(0.205818\pi\)
\(942\) 18.7618 0.611294
\(943\) −21.0376 −0.685079
\(944\) −9.07487 −0.295362
\(945\) −17.4422 −0.567394
\(946\) 29.6301 0.963357
\(947\) 23.8941 0.776455 0.388228 0.921564i \(-0.373087\pi\)
0.388228 + 0.921564i \(0.373087\pi\)
\(948\) −37.7919 −1.22742
\(949\) 0.264711 0.00859287
\(950\) 3.21427 0.104285
\(951\) 1.62292 0.0526267
\(952\) −11.4911 −0.372428
\(953\) 45.1211 1.46162 0.730808 0.682583i \(-0.239143\pi\)
0.730808 + 0.682583i \(0.239143\pi\)
\(954\) 9.43548 0.305485
\(955\) 28.0374 0.907268
\(956\) 6.55775 0.212093
\(957\) −54.5359 −1.76289
\(958\) 6.69002 0.216145
\(959\) −88.0522 −2.84335
\(960\) −2.92992 −0.0945628
\(961\) 72.6859 2.34471
\(962\) 14.4646 0.466357
\(963\) −10.7424 −0.346168
\(964\) 5.31595 0.171215
\(965\) −18.8538 −0.606926
\(966\) 26.3872 0.848996
\(967\) 16.5881 0.533436 0.266718 0.963775i \(-0.414061\pi\)
0.266718 + 0.963775i \(0.414061\pi\)
\(968\) −0.533707 −0.0171540
\(969\) 5.04802 0.162166
\(970\) −15.1732 −0.487181
\(971\) −33.9360 −1.08906 −0.544530 0.838742i \(-0.683292\pi\)
−0.544530 + 0.838742i \(0.683292\pi\)
\(972\) 16.6135 0.532879
\(973\) 77.6995 2.49093
\(974\) 4.59844 0.147343
\(975\) 27.7155 0.887607
\(976\) −1.01640 −0.0325343
\(977\) 23.7267 0.759083 0.379541 0.925175i \(-0.376082\pi\)
0.379541 + 0.925175i \(0.376082\pi\)
\(978\) −5.49975 −0.175863
\(979\) 52.7349 1.68541
\(980\) 23.9334 0.764526
\(981\) 32.1127 1.02528
\(982\) 28.7851 0.918569
\(983\) 47.7146 1.52186 0.760929 0.648835i \(-0.224743\pi\)
0.760929 + 0.648835i \(0.224743\pi\)
\(984\) 19.1287 0.609800
\(985\) 22.2799 0.709896
\(986\) 17.7016 0.563733
\(987\) −100.074 −3.18539
\(988\) −3.93273 −0.125117
\(989\) 22.0849 0.702259
\(990\) 7.81300 0.248314
\(991\) −58.4226 −1.85585 −0.927927 0.372762i \(-0.878411\pi\)
−0.927927 + 0.372762i \(0.878411\pi\)
\(992\) −10.1826 −0.323299
\(993\) 39.1816 1.24339
\(994\) 25.1475 0.797630
\(995\) 28.4390 0.901575
\(996\) 16.8297 0.533268
\(997\) 33.1597 1.05018 0.525089 0.851048i \(-0.324032\pi\)
0.525089 + 0.851048i \(0.324032\pi\)
\(998\) 1.70779 0.0540591
\(999\) 9.61870 0.304322
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 \(a_p\))