Properties

Label 8002.2.a.d.1.2
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.40667 q^{3}\) \(+1.00000 q^{4}\) \(+2.18421 q^{5}\) \(-3.40667 q^{6}\) \(-1.24057 q^{7}\) \(+1.00000 q^{8}\) \(+8.60538 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.40667 q^{3}\) \(+1.00000 q^{4}\) \(+2.18421 q^{5}\) \(-3.40667 q^{6}\) \(-1.24057 q^{7}\) \(+1.00000 q^{8}\) \(+8.60538 q^{9}\) \(+2.18421 q^{10}\) \(+3.12896 q^{11}\) \(-3.40667 q^{12}\) \(-1.99513 q^{13}\) \(-1.24057 q^{14}\) \(-7.44089 q^{15}\) \(+1.00000 q^{16}\) \(-2.59036 q^{17}\) \(+8.60538 q^{18}\) \(+6.38500 q^{19}\) \(+2.18421 q^{20}\) \(+4.22621 q^{21}\) \(+3.12896 q^{22}\) \(-2.47389 q^{23}\) \(-3.40667 q^{24}\) \(-0.229210 q^{25}\) \(-1.99513 q^{26}\) \(-19.0957 q^{27}\) \(-1.24057 q^{28}\) \(-7.09981 q^{29}\) \(-7.44089 q^{30}\) \(+1.66000 q^{31}\) \(+1.00000 q^{32}\) \(-10.6593 q^{33}\) \(-2.59036 q^{34}\) \(-2.70967 q^{35}\) \(+8.60538 q^{36}\) \(-7.59708 q^{37}\) \(+6.38500 q^{38}\) \(+6.79676 q^{39}\) \(+2.18421 q^{40}\) \(+10.4866 q^{41}\) \(+4.22621 q^{42}\) \(-7.73770 q^{43}\) \(+3.12896 q^{44}\) \(+18.7960 q^{45}\) \(-2.47389 q^{46}\) \(+2.02672 q^{47}\) \(-3.40667 q^{48}\) \(-5.46098 q^{49}\) \(-0.229210 q^{50}\) \(+8.82448 q^{51}\) \(-1.99513 q^{52}\) \(-12.3391 q^{53}\) \(-19.0957 q^{54}\) \(+6.83431 q^{55}\) \(-1.24057 q^{56}\) \(-21.7516 q^{57}\) \(-7.09981 q^{58}\) \(-5.00543 q^{59}\) \(-7.44089 q^{60}\) \(-10.1642 q^{61}\) \(+1.66000 q^{62}\) \(-10.6756 q^{63}\) \(+1.00000 q^{64}\) \(-4.35780 q^{65}\) \(-10.6593 q^{66}\) \(+5.74299 q^{67}\) \(-2.59036 q^{68}\) \(+8.42774 q^{69}\) \(-2.70967 q^{70}\) \(+3.73012 q^{71}\) \(+8.60538 q^{72}\) \(+0.446822 q^{73}\) \(-7.59708 q^{74}\) \(+0.780844 q^{75}\) \(+6.38500 q^{76}\) \(-3.88169 q^{77}\) \(+6.79676 q^{78}\) \(+5.38480 q^{79}\) \(+2.18421 q^{80}\) \(+39.2365 q^{81}\) \(+10.4866 q^{82}\) \(-4.50553 q^{83}\) \(+4.22621 q^{84}\) \(-5.65789 q^{85}\) \(-7.73770 q^{86}\) \(+24.1867 q^{87}\) \(+3.12896 q^{88}\) \(-12.6524 q^{89}\) \(+18.7960 q^{90}\) \(+2.47510 q^{91}\) \(-2.47389 q^{92}\) \(-5.65508 q^{93}\) \(+2.02672 q^{94}\) \(+13.9462 q^{95}\) \(-3.40667 q^{96}\) \(-14.8116 q^{97}\) \(-5.46098 q^{98}\) \(+26.9259 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.40667 −1.96684 −0.983420 0.181342i \(-0.941956\pi\)
−0.983420 + 0.181342i \(0.941956\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.18421 0.976810 0.488405 0.872617i \(-0.337579\pi\)
0.488405 + 0.872617i \(0.337579\pi\)
\(6\) −3.40667 −1.39077
\(7\) −1.24057 −0.468892 −0.234446 0.972129i \(-0.575328\pi\)
−0.234446 + 0.972129i \(0.575328\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.60538 2.86846
\(10\) 2.18421 0.690709
\(11\) 3.12896 0.943416 0.471708 0.881755i \(-0.343638\pi\)
0.471708 + 0.881755i \(0.343638\pi\)
\(12\) −3.40667 −0.983420
\(13\) −1.99513 −0.553351 −0.276675 0.960963i \(-0.589233\pi\)
−0.276675 + 0.960963i \(0.589233\pi\)
\(14\) −1.24057 −0.331556
\(15\) −7.44089 −1.92123
\(16\) 1.00000 0.250000
\(17\) −2.59036 −0.628254 −0.314127 0.949381i \(-0.601712\pi\)
−0.314127 + 0.949381i \(0.601712\pi\)
\(18\) 8.60538 2.02831
\(19\) 6.38500 1.46482 0.732410 0.680864i \(-0.238396\pi\)
0.732410 + 0.680864i \(0.238396\pi\)
\(20\) 2.18421 0.488405
\(21\) 4.22621 0.922235
\(22\) 3.12896 0.667096
\(23\) −2.47389 −0.515843 −0.257921 0.966166i \(-0.583038\pi\)
−0.257921 + 0.966166i \(0.583038\pi\)
\(24\) −3.40667 −0.695383
\(25\) −0.229210 −0.0458421
\(26\) −1.99513 −0.391278
\(27\) −19.0957 −3.67496
\(28\) −1.24057 −0.234446
\(29\) −7.09981 −1.31840 −0.659201 0.751967i \(-0.729105\pi\)
−0.659201 + 0.751967i \(0.729105\pi\)
\(30\) −7.44089 −1.35851
\(31\) 1.66000 0.298145 0.149073 0.988826i \(-0.452371\pi\)
0.149073 + 0.988826i \(0.452371\pi\)
\(32\) 1.00000 0.176777
\(33\) −10.6593 −1.85555
\(34\) −2.59036 −0.444242
\(35\) −2.70967 −0.458018
\(36\) 8.60538 1.43423
\(37\) −7.59708 −1.24895 −0.624476 0.781044i \(-0.714688\pi\)
−0.624476 + 0.781044i \(0.714688\pi\)
\(38\) 6.38500 1.03578
\(39\) 6.79676 1.08835
\(40\) 2.18421 0.345355
\(41\) 10.4866 1.63773 0.818864 0.573988i \(-0.194604\pi\)
0.818864 + 0.573988i \(0.194604\pi\)
\(42\) 4.22621 0.652119
\(43\) −7.73770 −1.17999 −0.589994 0.807408i \(-0.700870\pi\)
−0.589994 + 0.807408i \(0.700870\pi\)
\(44\) 3.12896 0.471708
\(45\) 18.7960 2.80194
\(46\) −2.47389 −0.364756
\(47\) 2.02672 0.295628 0.147814 0.989015i \(-0.452776\pi\)
0.147814 + 0.989015i \(0.452776\pi\)
\(48\) −3.40667 −0.491710
\(49\) −5.46098 −0.780141
\(50\) −0.229210 −0.0324152
\(51\) 8.82448 1.23567
\(52\) −1.99513 −0.276675
\(53\) −12.3391 −1.69491 −0.847455 0.530867i \(-0.821866\pi\)
−0.847455 + 0.530867i \(0.821866\pi\)
\(54\) −19.0957 −2.59859
\(55\) 6.83431 0.921538
\(56\) −1.24057 −0.165778
\(57\) −21.7516 −2.88107
\(58\) −7.09981 −0.932251
\(59\) −5.00543 −0.651652 −0.325826 0.945430i \(-0.605642\pi\)
−0.325826 + 0.945430i \(0.605642\pi\)
\(60\) −7.44089 −0.960615
\(61\) −10.1642 −1.30140 −0.650699 0.759336i \(-0.725524\pi\)
−0.650699 + 0.759336i \(0.725524\pi\)
\(62\) 1.66000 0.210821
\(63\) −10.6756 −1.34500
\(64\) 1.00000 0.125000
\(65\) −4.35780 −0.540518
\(66\) −10.6593 −1.31207
\(67\) 5.74299 0.701618 0.350809 0.936447i \(-0.385907\pi\)
0.350809 + 0.936447i \(0.385907\pi\)
\(68\) −2.59036 −0.314127
\(69\) 8.42774 1.01458
\(70\) −2.70967 −0.323868
\(71\) 3.73012 0.442684 0.221342 0.975196i \(-0.428956\pi\)
0.221342 + 0.975196i \(0.428956\pi\)
\(72\) 8.60538 1.01415
\(73\) 0.446822 0.0522965 0.0261483 0.999658i \(-0.491676\pi\)
0.0261483 + 0.999658i \(0.491676\pi\)
\(74\) −7.59708 −0.883143
\(75\) 0.780844 0.0901640
\(76\) 6.38500 0.732410
\(77\) −3.88169 −0.442360
\(78\) 6.79676 0.769581
\(79\) 5.38480 0.605837 0.302919 0.953016i \(-0.402039\pi\)
0.302919 + 0.953016i \(0.402039\pi\)
\(80\) 2.18421 0.244203
\(81\) 39.2365 4.35961
\(82\) 10.4866 1.15805
\(83\) −4.50553 −0.494546 −0.247273 0.968946i \(-0.579534\pi\)
−0.247273 + 0.968946i \(0.579534\pi\)
\(84\) 4.22621 0.461117
\(85\) −5.65789 −0.613684
\(86\) −7.73770 −0.834378
\(87\) 24.1867 2.59309
\(88\) 3.12896 0.333548
\(89\) −12.6524 −1.34115 −0.670574 0.741843i \(-0.733952\pi\)
−0.670574 + 0.741843i \(0.733952\pi\)
\(90\) 18.7960 1.98127
\(91\) 2.47510 0.259461
\(92\) −2.47389 −0.257921
\(93\) −5.65508 −0.586404
\(94\) 2.02672 0.209040
\(95\) 13.9462 1.43085
\(96\) −3.40667 −0.347692
\(97\) −14.8116 −1.50389 −0.751943 0.659228i \(-0.770883\pi\)
−0.751943 + 0.659228i \(0.770883\pi\)
\(98\) −5.46098 −0.551643
\(99\) 26.9259 2.70615
\(100\) −0.229210 −0.0229210
\(101\) 1.04857 0.104336 0.0521682 0.998638i \(-0.483387\pi\)
0.0521682 + 0.998638i \(0.483387\pi\)
\(102\) 8.82448 0.873754
\(103\) 0.178606 0.0175985 0.00879927 0.999961i \(-0.497199\pi\)
0.00879927 + 0.999961i \(0.497199\pi\)
\(104\) −1.99513 −0.195639
\(105\) 9.23095 0.900848
\(106\) −12.3391 −1.19848
\(107\) −0.325185 −0.0314368 −0.0157184 0.999876i \(-0.505004\pi\)
−0.0157184 + 0.999876i \(0.505004\pi\)
\(108\) −19.0957 −1.83748
\(109\) 14.0632 1.34701 0.673504 0.739183i \(-0.264788\pi\)
0.673504 + 0.739183i \(0.264788\pi\)
\(110\) 6.83431 0.651626
\(111\) 25.8807 2.45649
\(112\) −1.24057 −0.117223
\(113\) 11.2841 1.06152 0.530760 0.847522i \(-0.321907\pi\)
0.530760 + 0.847522i \(0.321907\pi\)
\(114\) −21.7516 −2.03722
\(115\) −5.40351 −0.503880
\(116\) −7.09981 −0.659201
\(117\) −17.1689 −1.58726
\(118\) −5.00543 −0.460787
\(119\) 3.21352 0.294583
\(120\) −7.44089 −0.679257
\(121\) −1.20962 −0.109966
\(122\) −10.1642 −0.920227
\(123\) −35.7243 −3.22115
\(124\) 1.66000 0.149073
\(125\) −11.4217 −1.02159
\(126\) −10.6756 −0.951057
\(127\) 13.3360 1.18338 0.591690 0.806166i \(-0.298461\pi\)
0.591690 + 0.806166i \(0.298461\pi\)
\(128\) 1.00000 0.0883883
\(129\) 26.3598 2.32085
\(130\) −4.35780 −0.382204
\(131\) −4.62266 −0.403883 −0.201942 0.979398i \(-0.564725\pi\)
−0.201942 + 0.979398i \(0.564725\pi\)
\(132\) −10.6593 −0.927775
\(133\) −7.92104 −0.686841
\(134\) 5.74299 0.496119
\(135\) −41.7090 −3.58974
\(136\) −2.59036 −0.222121
\(137\) 2.86310 0.244611 0.122306 0.992492i \(-0.460971\pi\)
0.122306 + 0.992492i \(0.460971\pi\)
\(138\) 8.42774 0.717417
\(139\) 5.34512 0.453367 0.226684 0.973968i \(-0.427212\pi\)
0.226684 + 0.973968i \(0.427212\pi\)
\(140\) −2.70967 −0.229009
\(141\) −6.90436 −0.581452
\(142\) 3.73012 0.313025
\(143\) −6.24269 −0.522040
\(144\) 8.60538 0.717115
\(145\) −15.5075 −1.28783
\(146\) 0.446822 0.0369792
\(147\) 18.6038 1.53441
\(148\) −7.59708 −0.624476
\(149\) −19.8374 −1.62515 −0.812573 0.582860i \(-0.801934\pi\)
−0.812573 + 0.582860i \(0.801934\pi\)
\(150\) 0.780844 0.0637556
\(151\) −19.1586 −1.55911 −0.779553 0.626336i \(-0.784554\pi\)
−0.779553 + 0.626336i \(0.784554\pi\)
\(152\) 6.38500 0.517892
\(153\) −22.2910 −1.80212
\(154\) −3.88169 −0.312796
\(155\) 3.62580 0.291231
\(156\) 6.79676 0.544176
\(157\) −1.99863 −0.159508 −0.0797540 0.996815i \(-0.525413\pi\)
−0.0797540 + 0.996815i \(0.525413\pi\)
\(158\) 5.38480 0.428392
\(159\) 42.0353 3.33362
\(160\) 2.18421 0.172677
\(161\) 3.06904 0.241874
\(162\) 39.2365 3.08271
\(163\) 20.0518 1.57058 0.785290 0.619128i \(-0.212514\pi\)
0.785290 + 0.619128i \(0.212514\pi\)
\(164\) 10.4866 0.818864
\(165\) −23.2822 −1.81252
\(166\) −4.50553 −0.349697
\(167\) 5.91510 0.457724 0.228862 0.973459i \(-0.426500\pi\)
0.228862 + 0.973459i \(0.426500\pi\)
\(168\) 4.22621 0.326059
\(169\) −9.01944 −0.693803
\(170\) −5.65789 −0.433940
\(171\) 54.9454 4.20178
\(172\) −7.73770 −0.589994
\(173\) 6.42835 0.488738 0.244369 0.969682i \(-0.421419\pi\)
0.244369 + 0.969682i \(0.421419\pi\)
\(174\) 24.1867 1.83359
\(175\) 0.284352 0.0214950
\(176\) 3.12896 0.235854
\(177\) 17.0518 1.28170
\(178\) −12.6524 −0.948335
\(179\) 6.81874 0.509656 0.254828 0.966986i \(-0.417981\pi\)
0.254828 + 0.966986i \(0.417981\pi\)
\(180\) 18.7960 1.40097
\(181\) 3.76552 0.279889 0.139944 0.990159i \(-0.455308\pi\)
0.139944 + 0.990159i \(0.455308\pi\)
\(182\) 2.47510 0.183467
\(183\) 34.6262 2.55964
\(184\) −2.47389 −0.182378
\(185\) −16.5936 −1.21999
\(186\) −5.65508 −0.414650
\(187\) −8.10511 −0.592705
\(188\) 2.02672 0.147814
\(189\) 23.6895 1.72316
\(190\) 13.9462 1.01176
\(191\) 7.37336 0.533517 0.266759 0.963763i \(-0.414047\pi\)
0.266759 + 0.963763i \(0.414047\pi\)
\(192\) −3.40667 −0.245855
\(193\) 15.6558 1.12693 0.563466 0.826140i \(-0.309468\pi\)
0.563466 + 0.826140i \(0.309468\pi\)
\(194\) −14.8116 −1.06341
\(195\) 14.8456 1.06311
\(196\) −5.46098 −0.390070
\(197\) 1.29758 0.0924485 0.0462242 0.998931i \(-0.485281\pi\)
0.0462242 + 0.998931i \(0.485281\pi\)
\(198\) 26.9259 1.91354
\(199\) −23.4585 −1.66293 −0.831463 0.555580i \(-0.812496\pi\)
−0.831463 + 0.555580i \(0.812496\pi\)
\(200\) −0.229210 −0.0162076
\(201\) −19.5645 −1.37997
\(202\) 1.04857 0.0737769
\(203\) 8.80782 0.618187
\(204\) 8.82448 0.617837
\(205\) 22.9049 1.59975
\(206\) 0.178606 0.0124440
\(207\) −21.2888 −1.47967
\(208\) −1.99513 −0.138338
\(209\) 19.9784 1.38193
\(210\) 9.23095 0.636996
\(211\) −1.71669 −0.118182 −0.0590909 0.998253i \(-0.518820\pi\)
−0.0590909 + 0.998253i \(0.518820\pi\)
\(212\) −12.3391 −0.847455
\(213\) −12.7073 −0.870688
\(214\) −0.325185 −0.0222292
\(215\) −16.9008 −1.15262
\(216\) −19.0957 −1.29930
\(217\) −2.05935 −0.139798
\(218\) 14.0632 0.952479
\(219\) −1.52217 −0.102859
\(220\) 6.83431 0.460769
\(221\) 5.16811 0.347644
\(222\) 25.8807 1.73700
\(223\) −12.2684 −0.821554 −0.410777 0.911736i \(-0.634742\pi\)
−0.410777 + 0.911736i \(0.634742\pi\)
\(224\) −1.24057 −0.0828891
\(225\) −1.97244 −0.131496
\(226\) 11.2841 0.750608
\(227\) −11.2272 −0.745173 −0.372586 0.927998i \(-0.621529\pi\)
−0.372586 + 0.927998i \(0.621529\pi\)
\(228\) −21.7516 −1.44053
\(229\) 21.3645 1.41180 0.705902 0.708309i \(-0.250542\pi\)
0.705902 + 0.708309i \(0.250542\pi\)
\(230\) −5.40351 −0.356297
\(231\) 13.2236 0.870051
\(232\) −7.09981 −0.466125
\(233\) −16.5906 −1.08689 −0.543443 0.839446i \(-0.682880\pi\)
−0.543443 + 0.839446i \(0.682880\pi\)
\(234\) −17.1689 −1.12237
\(235\) 4.42679 0.288772
\(236\) −5.00543 −0.325826
\(237\) −18.3442 −1.19159
\(238\) 3.21352 0.208301
\(239\) 17.3345 1.12127 0.560636 0.828062i \(-0.310557\pi\)
0.560636 + 0.828062i \(0.310557\pi\)
\(240\) −7.44089 −0.480307
\(241\) −19.4544 −1.25317 −0.626584 0.779354i \(-0.715547\pi\)
−0.626584 + 0.779354i \(0.715547\pi\)
\(242\) −1.20962 −0.0777576
\(243\) −76.3786 −4.89969
\(244\) −10.1642 −0.650699
\(245\) −11.9280 −0.762049
\(246\) −35.7243 −2.27770
\(247\) −12.7389 −0.810558
\(248\) 1.66000 0.105410
\(249\) 15.3488 0.972692
\(250\) −11.4217 −0.722373
\(251\) −3.45087 −0.217817 −0.108908 0.994052i \(-0.534736\pi\)
−0.108908 + 0.994052i \(0.534736\pi\)
\(252\) −10.6756 −0.672499
\(253\) −7.74071 −0.486654
\(254\) 13.3360 0.836776
\(255\) 19.2746 1.20702
\(256\) 1.00000 0.0625000
\(257\) −20.1091 −1.25437 −0.627185 0.778871i \(-0.715793\pi\)
−0.627185 + 0.778871i \(0.715793\pi\)
\(258\) 26.3598 1.64109
\(259\) 9.42471 0.585623
\(260\) −4.35780 −0.270259
\(261\) −61.0966 −3.78178
\(262\) −4.62266 −0.285589
\(263\) 15.8997 0.980415 0.490208 0.871606i \(-0.336921\pi\)
0.490208 + 0.871606i \(0.336921\pi\)
\(264\) −10.6593 −0.656036
\(265\) −26.9513 −1.65561
\(266\) −7.92104 −0.485670
\(267\) 43.1024 2.63782
\(268\) 5.74299 0.350809
\(269\) 21.0403 1.28285 0.641425 0.767186i \(-0.278344\pi\)
0.641425 + 0.767186i \(0.278344\pi\)
\(270\) −41.7090 −2.53833
\(271\) 9.09976 0.552771 0.276386 0.961047i \(-0.410863\pi\)
0.276386 + 0.961047i \(0.410863\pi\)
\(272\) −2.59036 −0.157063
\(273\) −8.43186 −0.510319
\(274\) 2.86310 0.172966
\(275\) −0.717190 −0.0432482
\(276\) 8.42774 0.507290
\(277\) −17.5912 −1.05695 −0.528477 0.848948i \(-0.677237\pi\)
−0.528477 + 0.848948i \(0.677237\pi\)
\(278\) 5.34512 0.320579
\(279\) 14.2850 0.855218
\(280\) −2.70967 −0.161934
\(281\) −4.98580 −0.297428 −0.148714 0.988880i \(-0.547513\pi\)
−0.148714 + 0.988880i \(0.547513\pi\)
\(282\) −6.90436 −0.411149
\(283\) −3.98301 −0.236765 −0.118383 0.992968i \(-0.537771\pi\)
−0.118383 + 0.992968i \(0.537771\pi\)
\(284\) 3.73012 0.221342
\(285\) −47.5101 −2.81425
\(286\) −6.24269 −0.369138
\(287\) −13.0093 −0.767916
\(288\) 8.60538 0.507077
\(289\) −10.2901 −0.605298
\(290\) −15.5075 −0.910632
\(291\) 50.4581 2.95790
\(292\) 0.446822 0.0261483
\(293\) −12.2987 −0.718497 −0.359249 0.933242i \(-0.616967\pi\)
−0.359249 + 0.933242i \(0.616967\pi\)
\(294\) 18.6038 1.08499
\(295\) −10.9329 −0.636540
\(296\) −7.59708 −0.441571
\(297\) −59.7496 −3.46702
\(298\) −19.8374 −1.14915
\(299\) 4.93575 0.285442
\(300\) 0.780844 0.0450820
\(301\) 9.59916 0.553286
\(302\) −19.1586 −1.10245
\(303\) −3.57212 −0.205213
\(304\) 6.38500 0.366205
\(305\) −22.2009 −1.27122
\(306\) −22.2910 −1.27429
\(307\) −4.59629 −0.262324 −0.131162 0.991361i \(-0.541871\pi\)
−0.131162 + 0.991361i \(0.541871\pi\)
\(308\) −3.88169 −0.221180
\(309\) −0.608450 −0.0346135
\(310\) 3.62580 0.205932
\(311\) −11.0806 −0.628323 −0.314162 0.949370i \(-0.601723\pi\)
−0.314162 + 0.949370i \(0.601723\pi\)
\(312\) 6.79676 0.384791
\(313\) 1.73003 0.0977869 0.0488935 0.998804i \(-0.484431\pi\)
0.0488935 + 0.998804i \(0.484431\pi\)
\(314\) −1.99863 −0.112789
\(315\) −23.3178 −1.31381
\(316\) 5.38480 0.302919
\(317\) −14.5987 −0.819946 −0.409973 0.912098i \(-0.634462\pi\)
−0.409973 + 0.912098i \(0.634462\pi\)
\(318\) 42.0353 2.35722
\(319\) −22.2150 −1.24380
\(320\) 2.18421 0.122101
\(321\) 1.10780 0.0618312
\(322\) 3.06904 0.171031
\(323\) −16.5394 −0.920278
\(324\) 39.2365 2.17980
\(325\) 0.457305 0.0253667
\(326\) 20.0518 1.11057
\(327\) −47.9086 −2.64935
\(328\) 10.4866 0.579024
\(329\) −2.51429 −0.138617
\(330\) −23.2822 −1.28164
\(331\) −0.810115 −0.0445280 −0.0222640 0.999752i \(-0.507087\pi\)
−0.0222640 + 0.999752i \(0.507087\pi\)
\(332\) −4.50553 −0.247273
\(333\) −65.3758 −3.58257
\(334\) 5.91510 0.323660
\(335\) 12.5439 0.685347
\(336\) 4.22621 0.230559
\(337\) 35.1262 1.91345 0.956724 0.290998i \(-0.0939874\pi\)
0.956724 + 0.290998i \(0.0939874\pi\)
\(338\) −9.01944 −0.490593
\(339\) −38.4412 −2.08784
\(340\) −5.65789 −0.306842
\(341\) 5.19408 0.281275
\(342\) 54.9454 2.97110
\(343\) 15.4587 0.834693
\(344\) −7.73770 −0.417189
\(345\) 18.4080 0.991052
\(346\) 6.42835 0.345590
\(347\) −10.8891 −0.584559 −0.292279 0.956333i \(-0.594414\pi\)
−0.292279 + 0.956333i \(0.594414\pi\)
\(348\) 24.1867 1.29654
\(349\) −23.8404 −1.27615 −0.638074 0.769975i \(-0.720269\pi\)
−0.638074 + 0.769975i \(0.720269\pi\)
\(350\) 0.284352 0.0151992
\(351\) 38.0984 2.03354
\(352\) 3.12896 0.166774
\(353\) 0.117951 0.00627791 0.00313896 0.999995i \(-0.499001\pi\)
0.00313896 + 0.999995i \(0.499001\pi\)
\(354\) 17.0518 0.906295
\(355\) 8.14738 0.432418
\(356\) −12.6524 −0.670574
\(357\) −10.9474 −0.579397
\(358\) 6.81874 0.360381
\(359\) −18.7826 −0.991310 −0.495655 0.868520i \(-0.665072\pi\)
−0.495655 + 0.868520i \(0.665072\pi\)
\(360\) 18.7960 0.990636
\(361\) 21.7682 1.14570
\(362\) 3.76552 0.197911
\(363\) 4.12079 0.216285
\(364\) 2.47510 0.129731
\(365\) 0.975954 0.0510838
\(366\) 34.6262 1.80994
\(367\) −27.4418 −1.43245 −0.716224 0.697870i \(-0.754131\pi\)
−0.716224 + 0.697870i \(0.754131\pi\)
\(368\) −2.47389 −0.128961
\(369\) 90.2410 4.69776
\(370\) −16.5936 −0.862663
\(371\) 15.3076 0.794729
\(372\) −5.65508 −0.293202
\(373\) −14.4700 −0.749228 −0.374614 0.927181i \(-0.622225\pi\)
−0.374614 + 0.927181i \(0.622225\pi\)
\(374\) −8.10511 −0.419105
\(375\) 38.9100 2.00930
\(376\) 2.02672 0.104520
\(377\) 14.1651 0.729538
\(378\) 23.6895 1.21846
\(379\) 4.00097 0.205516 0.102758 0.994706i \(-0.467233\pi\)
0.102758 + 0.994706i \(0.467233\pi\)
\(380\) 13.9462 0.715425
\(381\) −45.4313 −2.32752
\(382\) 7.37336 0.377254
\(383\) 5.83486 0.298147 0.149074 0.988826i \(-0.452371\pi\)
0.149074 + 0.988826i \(0.452371\pi\)
\(384\) −3.40667 −0.173846
\(385\) −8.47845 −0.432102
\(386\) 15.6558 0.796861
\(387\) −66.5859 −3.38475
\(388\) −14.8116 −0.751943
\(389\) 1.54890 0.0785326 0.0392663 0.999229i \(-0.487498\pi\)
0.0392663 + 0.999229i \(0.487498\pi\)
\(390\) 14.8456 0.751735
\(391\) 6.40827 0.324080
\(392\) −5.46098 −0.275821
\(393\) 15.7479 0.794374
\(394\) 1.29758 0.0653709
\(395\) 11.7616 0.591788
\(396\) 26.9259 1.35308
\(397\) 8.79677 0.441497 0.220749 0.975331i \(-0.429150\pi\)
0.220749 + 0.975331i \(0.429150\pi\)
\(398\) −23.4585 −1.17587
\(399\) 26.9844 1.35091
\(400\) −0.229210 −0.0114605
\(401\) −21.7856 −1.08792 −0.543961 0.839110i \(-0.683076\pi\)
−0.543961 + 0.839110i \(0.683076\pi\)
\(402\) −19.5645 −0.975786
\(403\) −3.31193 −0.164979
\(404\) 1.04857 0.0521682
\(405\) 85.7008 4.25851
\(406\) 8.80782 0.437125
\(407\) −23.7709 −1.17828
\(408\) 8.82448 0.436877
\(409\) −1.33713 −0.0661167 −0.0330584 0.999453i \(-0.510525\pi\)
−0.0330584 + 0.999453i \(0.510525\pi\)
\(410\) 22.9049 1.13119
\(411\) −9.75363 −0.481111
\(412\) 0.178606 0.00879927
\(413\) 6.20959 0.305554
\(414\) −21.2888 −1.04629
\(415\) −9.84103 −0.483077
\(416\) −1.99513 −0.0978195
\(417\) −18.2090 −0.891701
\(418\) 19.9784 0.977175
\(419\) −37.1393 −1.81438 −0.907188 0.420726i \(-0.861775\pi\)
−0.907188 + 0.420726i \(0.861775\pi\)
\(420\) 9.23095 0.450424
\(421\) 22.0995 1.07706 0.538531 0.842605i \(-0.318979\pi\)
0.538531 + 0.842605i \(0.318979\pi\)
\(422\) −1.71669 −0.0835671
\(423\) 17.4407 0.847996
\(424\) −12.3391 −0.599241
\(425\) 0.593736 0.0288004
\(426\) −12.7073 −0.615670
\(427\) 12.6095 0.610214
\(428\) −0.325185 −0.0157184
\(429\) 21.2668 1.02677
\(430\) −16.9008 −0.815028
\(431\) 16.6790 0.803398 0.401699 0.915772i \(-0.368420\pi\)
0.401699 + 0.915772i \(0.368420\pi\)
\(432\) −19.0957 −0.918741
\(433\) 15.0939 0.725368 0.362684 0.931912i \(-0.381861\pi\)
0.362684 + 0.931912i \(0.381861\pi\)
\(434\) −2.05935 −0.0988520
\(435\) 52.8289 2.53295
\(436\) 14.0632 0.673504
\(437\) −15.7958 −0.755616
\(438\) −1.52217 −0.0727322
\(439\) 10.2442 0.488931 0.244465 0.969658i \(-0.421388\pi\)
0.244465 + 0.969658i \(0.421388\pi\)
\(440\) 6.83431 0.325813
\(441\) −46.9939 −2.23780
\(442\) 5.16811 0.245822
\(443\) 0.727793 0.0345785 0.0172892 0.999851i \(-0.494496\pi\)
0.0172892 + 0.999851i \(0.494496\pi\)
\(444\) 25.8807 1.22825
\(445\) −27.6355 −1.31005
\(446\) −12.2684 −0.580926
\(447\) 67.5795 3.19640
\(448\) −1.24057 −0.0586114
\(449\) 32.5788 1.53749 0.768743 0.639557i \(-0.220882\pi\)
0.768743 + 0.639557i \(0.220882\pi\)
\(450\) −1.97244 −0.0929819
\(451\) 32.8120 1.54506
\(452\) 11.2841 0.530760
\(453\) 65.2670 3.06651
\(454\) −11.2272 −0.526917
\(455\) 5.40616 0.253445
\(456\) −21.7516 −1.01861
\(457\) −22.4254 −1.04902 −0.524509 0.851405i \(-0.675751\pi\)
−0.524509 + 0.851405i \(0.675751\pi\)
\(458\) 21.3645 0.998297
\(459\) 49.4646 2.30881
\(460\) −5.40351 −0.251940
\(461\) 1.07914 0.0502608 0.0251304 0.999684i \(-0.492000\pi\)
0.0251304 + 0.999684i \(0.492000\pi\)
\(462\) 13.2236 0.615219
\(463\) −27.2368 −1.26580 −0.632900 0.774234i \(-0.718135\pi\)
−0.632900 + 0.774234i \(0.718135\pi\)
\(464\) −7.09981 −0.329600
\(465\) −12.3519 −0.572806
\(466\) −16.5906 −0.768545
\(467\) 13.6387 0.631123 0.315561 0.948905i \(-0.397807\pi\)
0.315561 + 0.948905i \(0.397807\pi\)
\(468\) −17.1689 −0.793632
\(469\) −7.12458 −0.328983
\(470\) 4.42679 0.204193
\(471\) 6.80866 0.313727
\(472\) −5.00543 −0.230394
\(473\) −24.2109 −1.11322
\(474\) −18.3442 −0.842578
\(475\) −1.46351 −0.0671504
\(476\) 3.21352 0.147291
\(477\) −106.183 −4.86178
\(478\) 17.3345 0.792859
\(479\) −38.8629 −1.77569 −0.887845 0.460142i \(-0.847799\pi\)
−0.887845 + 0.460142i \(0.847799\pi\)
\(480\) −7.44089 −0.339629
\(481\) 15.1572 0.691109
\(482\) −19.4544 −0.886124
\(483\) −10.4552 −0.475728
\(484\) −1.20962 −0.0549829
\(485\) −32.3516 −1.46901
\(486\) −76.3786 −3.46460
\(487\) −34.2190 −1.55061 −0.775305 0.631587i \(-0.782404\pi\)
−0.775305 + 0.631587i \(0.782404\pi\)
\(488\) −10.1642 −0.460114
\(489\) −68.3099 −3.08908
\(490\) −11.9280 −0.538850
\(491\) 28.9422 1.30614 0.653072 0.757296i \(-0.273480\pi\)
0.653072 + 0.757296i \(0.273480\pi\)
\(492\) −35.7243 −1.61057
\(493\) 18.3910 0.828290
\(494\) −12.7389 −0.573151
\(495\) 58.8119 2.64340
\(496\) 1.66000 0.0745363
\(497\) −4.62748 −0.207571
\(498\) 15.3488 0.687797
\(499\) −32.0218 −1.43349 −0.716746 0.697334i \(-0.754369\pi\)
−0.716746 + 0.697334i \(0.754369\pi\)
\(500\) −11.4217 −0.510795
\(501\) −20.1508 −0.900270
\(502\) −3.45087 −0.154020
\(503\) 22.1446 0.987380 0.493690 0.869638i \(-0.335648\pi\)
0.493690 + 0.869638i \(0.335648\pi\)
\(504\) −10.6756 −0.475528
\(505\) 2.29029 0.101917
\(506\) −7.74071 −0.344117
\(507\) 30.7262 1.36460
\(508\) 13.3360 0.591690
\(509\) −3.27128 −0.144997 −0.0724984 0.997369i \(-0.523097\pi\)
−0.0724984 + 0.997369i \(0.523097\pi\)
\(510\) 19.2746 0.853491
\(511\) −0.554314 −0.0245214
\(512\) 1.00000 0.0441942
\(513\) −121.926 −5.38316
\(514\) −20.1091 −0.886973
\(515\) 0.390113 0.0171904
\(516\) 26.3598 1.16042
\(517\) 6.34152 0.278900
\(518\) 9.42471 0.414098
\(519\) −21.8993 −0.961271
\(520\) −4.35780 −0.191102
\(521\) −34.2898 −1.50226 −0.751132 0.660152i \(-0.770492\pi\)
−0.751132 + 0.660152i \(0.770492\pi\)
\(522\) −61.0966 −2.67412
\(523\) −35.5228 −1.55331 −0.776653 0.629929i \(-0.783084\pi\)
−0.776653 + 0.629929i \(0.783084\pi\)
\(524\) −4.62266 −0.201942
\(525\) −0.968691 −0.0422772
\(526\) 15.8997 0.693258
\(527\) −4.30000 −0.187311
\(528\) −10.6593 −0.463887
\(529\) −16.8798 −0.733906
\(530\) −26.9513 −1.17069
\(531\) −43.0737 −1.86924
\(532\) −7.92104 −0.343421
\(533\) −20.9221 −0.906237
\(534\) 43.1024 1.86522
\(535\) −0.710273 −0.0307078
\(536\) 5.74299 0.248059
\(537\) −23.2292 −1.00241
\(538\) 21.0403 0.907111
\(539\) −17.0872 −0.735997
\(540\) −41.7090 −1.79487
\(541\) 10.3266 0.443976 0.221988 0.975049i \(-0.428745\pi\)
0.221988 + 0.975049i \(0.428745\pi\)
\(542\) 9.09976 0.390868
\(543\) −12.8279 −0.550497
\(544\) −2.59036 −0.111061
\(545\) 30.7170 1.31577
\(546\) −8.43186 −0.360850
\(547\) 6.79187 0.290399 0.145200 0.989402i \(-0.453618\pi\)
0.145200 + 0.989402i \(0.453618\pi\)
\(548\) 2.86310 0.122306
\(549\) −87.4672 −3.73301
\(550\) −0.717190 −0.0305811
\(551\) −45.3323 −1.93122
\(552\) 8.42774 0.358708
\(553\) −6.68022 −0.284072
\(554\) −17.5912 −0.747379
\(555\) 56.5290 2.39952
\(556\) 5.34512 0.226684
\(557\) 22.2839 0.944199 0.472099 0.881545i \(-0.343496\pi\)
0.472099 + 0.881545i \(0.343496\pi\)
\(558\) 14.2850 0.604731
\(559\) 15.4377 0.652947
\(560\) −2.70967 −0.114505
\(561\) 27.6114 1.16576
\(562\) −4.98580 −0.210313
\(563\) −9.61350 −0.405161 −0.202580 0.979266i \(-0.564933\pi\)
−0.202580 + 0.979266i \(0.564933\pi\)
\(564\) −6.90436 −0.290726
\(565\) 24.6469 1.03690
\(566\) −3.98301 −0.167418
\(567\) −48.6756 −2.04418
\(568\) 3.73012 0.156512
\(569\) 23.3837 0.980298 0.490149 0.871639i \(-0.336942\pi\)
0.490149 + 0.871639i \(0.336942\pi\)
\(570\) −47.5101 −1.98998
\(571\) −17.3851 −0.727546 −0.363773 0.931488i \(-0.618512\pi\)
−0.363773 + 0.931488i \(0.618512\pi\)
\(572\) −6.24269 −0.261020
\(573\) −25.1186 −1.04934
\(574\) −13.0093 −0.542999
\(575\) 0.567042 0.0236473
\(576\) 8.60538 0.358558
\(577\) −33.3301 −1.38755 −0.693774 0.720192i \(-0.744054\pi\)
−0.693774 + 0.720192i \(0.744054\pi\)
\(578\) −10.2901 −0.428010
\(579\) −53.3342 −2.21649
\(580\) −15.5075 −0.643914
\(581\) 5.58942 0.231888
\(582\) 50.4581 2.09155
\(583\) −38.6086 −1.59901
\(584\) 0.446822 0.0184896
\(585\) −37.5005 −1.55046
\(586\) −12.2987 −0.508054
\(587\) −17.6014 −0.726486 −0.363243 0.931694i \(-0.618331\pi\)
−0.363243 + 0.931694i \(0.618331\pi\)
\(588\) 18.6038 0.767206
\(589\) 10.5991 0.436729
\(590\) −10.9329 −0.450102
\(591\) −4.42041 −0.181831
\(592\) −7.59708 −0.312238
\(593\) 7.78790 0.319811 0.159905 0.987132i \(-0.448881\pi\)
0.159905 + 0.987132i \(0.448881\pi\)
\(594\) −59.7496 −2.45155
\(595\) 7.01901 0.287751
\(596\) −19.8374 −0.812573
\(597\) 79.9151 3.27071
\(598\) 4.93575 0.201838
\(599\) 35.4160 1.44706 0.723529 0.690294i \(-0.242519\pi\)
0.723529 + 0.690294i \(0.242519\pi\)
\(600\) 0.780844 0.0318778
\(601\) 2.75677 0.112451 0.0562254 0.998418i \(-0.482093\pi\)
0.0562254 + 0.998418i \(0.482093\pi\)
\(602\) 9.59916 0.391233
\(603\) 49.4206 2.01256
\(604\) −19.1586 −0.779553
\(605\) −2.64208 −0.107416
\(606\) −3.57212 −0.145107
\(607\) −33.1773 −1.34662 −0.673312 0.739358i \(-0.735129\pi\)
−0.673312 + 0.739358i \(0.735129\pi\)
\(608\) 6.38500 0.258946
\(609\) −30.0053 −1.21588
\(610\) −22.2009 −0.898887
\(611\) −4.04358 −0.163586
\(612\) −22.2910 −0.901060
\(613\) 16.3866 0.661848 0.330924 0.943657i \(-0.392640\pi\)
0.330924 + 0.943657i \(0.392640\pi\)
\(614\) −4.59629 −0.185491
\(615\) −78.0294 −3.14645
\(616\) −3.88169 −0.156398
\(617\) 29.2740 1.17853 0.589264 0.807940i \(-0.299418\pi\)
0.589264 + 0.807940i \(0.299418\pi\)
\(618\) −0.608450 −0.0244754
\(619\) −31.7136 −1.27468 −0.637338 0.770584i \(-0.719965\pi\)
−0.637338 + 0.770584i \(0.719965\pi\)
\(620\) 3.62580 0.145616
\(621\) 47.2407 1.89570
\(622\) −11.0806 −0.444292
\(623\) 15.6962 0.628853
\(624\) 6.79676 0.272088
\(625\) −23.8014 −0.952056
\(626\) 1.73003 0.0691458
\(627\) −68.0597 −2.71804
\(628\) −1.99863 −0.0797540
\(629\) 19.6791 0.784659
\(630\) −23.3178 −0.929002
\(631\) 27.3071 1.08708 0.543539 0.839384i \(-0.317084\pi\)
0.543539 + 0.839384i \(0.317084\pi\)
\(632\) 5.38480 0.214196
\(633\) 5.84819 0.232445
\(634\) −14.5987 −0.579790
\(635\) 29.1287 1.15594
\(636\) 42.0353 1.66681
\(637\) 10.8954 0.431691
\(638\) −22.2150 −0.879500
\(639\) 32.0991 1.26982
\(640\) 2.18421 0.0863386
\(641\) −43.2563 −1.70852 −0.854261 0.519845i \(-0.825990\pi\)
−0.854261 + 0.519845i \(0.825990\pi\)
\(642\) 1.10780 0.0437212
\(643\) 16.2752 0.641833 0.320916 0.947108i \(-0.396009\pi\)
0.320916 + 0.947108i \(0.396009\pi\)
\(644\) 3.06904 0.120937
\(645\) 57.5754 2.26703
\(646\) −16.5394 −0.650735
\(647\) 18.5191 0.728062 0.364031 0.931387i \(-0.381400\pi\)
0.364031 + 0.931387i \(0.381400\pi\)
\(648\) 39.2365 1.54135
\(649\) −15.6618 −0.614779
\(650\) 0.457305 0.0179370
\(651\) 7.01552 0.274960
\(652\) 20.0518 0.785290
\(653\) −29.4032 −1.15064 −0.575319 0.817929i \(-0.695122\pi\)
−0.575319 + 0.817929i \(0.695122\pi\)
\(654\) −47.9086 −1.87337
\(655\) −10.0969 −0.394517
\(656\) 10.4866 0.409432
\(657\) 3.84507 0.150011
\(658\) −2.51429 −0.0980172
\(659\) −27.4789 −1.07042 −0.535212 0.844718i \(-0.679768\pi\)
−0.535212 + 0.844718i \(0.679768\pi\)
\(660\) −23.2822 −0.906260
\(661\) 31.7819 1.23617 0.618086 0.786111i \(-0.287908\pi\)
0.618086 + 0.786111i \(0.287908\pi\)
\(662\) −0.810115 −0.0314860
\(663\) −17.6060 −0.683761
\(664\) −4.50553 −0.174848
\(665\) −17.3012 −0.670914
\(666\) −65.3758 −2.53326
\(667\) 17.5642 0.680088
\(668\) 5.91510 0.228862
\(669\) 41.7944 1.61586
\(670\) 12.5439 0.484614
\(671\) −31.8035 −1.22776
\(672\) 4.22621 0.163030
\(673\) 37.5834 1.44873 0.724366 0.689416i \(-0.242133\pi\)
0.724366 + 0.689416i \(0.242133\pi\)
\(674\) 35.1262 1.35301
\(675\) 4.37693 0.168468
\(676\) −9.01944 −0.346902
\(677\) −25.2287 −0.969617 −0.484808 0.874620i \(-0.661111\pi\)
−0.484808 + 0.874620i \(0.661111\pi\)
\(678\) −38.4412 −1.47633
\(679\) 18.3748 0.705159
\(680\) −5.65789 −0.216970
\(681\) 38.2472 1.46564
\(682\) 5.19408 0.198892
\(683\) 45.8812 1.75560 0.877798 0.479031i \(-0.159012\pi\)
0.877798 + 0.479031i \(0.159012\pi\)
\(684\) 54.9454 2.10089
\(685\) 6.25362 0.238939
\(686\) 15.4587 0.590217
\(687\) −72.7817 −2.77679
\(688\) −7.73770 −0.294997
\(689\) 24.6182 0.937880
\(690\) 18.4080 0.700780
\(691\) −8.25520 −0.314043 −0.157021 0.987595i \(-0.550189\pi\)
−0.157021 + 0.987595i \(0.550189\pi\)
\(692\) 6.42835 0.244369
\(693\) −33.4034 −1.26889
\(694\) −10.8891 −0.413345
\(695\) 11.6749 0.442854
\(696\) 24.1867 0.916794
\(697\) −27.1639 −1.02891
\(698\) −23.8404 −0.902373
\(699\) 56.5187 2.13773
\(700\) 0.284352 0.0107475
\(701\) 38.7440 1.46334 0.731671 0.681658i \(-0.238741\pi\)
0.731671 + 0.681658i \(0.238741\pi\)
\(702\) 38.0984 1.43793
\(703\) −48.5074 −1.82949
\(704\) 3.12896 0.117927
\(705\) −15.0806 −0.567968
\(706\) 0.117951 0.00443916
\(707\) −1.30082 −0.0489224
\(708\) 17.0518 0.640848
\(709\) −32.0807 −1.20481 −0.602407 0.798189i \(-0.705792\pi\)
−0.602407 + 0.798189i \(0.705792\pi\)
\(710\) 8.14738 0.305766
\(711\) 46.3383 1.73782
\(712\) −12.6524 −0.474168
\(713\) −4.10667 −0.153796
\(714\) −10.9474 −0.409696
\(715\) −13.6354 −0.509934
\(716\) 6.81874 0.254828
\(717\) −59.0527 −2.20536
\(718\) −18.7826 −0.700962
\(719\) 31.4735 1.17377 0.586883 0.809672i \(-0.300355\pi\)
0.586883 + 0.809672i \(0.300355\pi\)
\(720\) 18.7960 0.700485
\(721\) −0.221573 −0.00825181
\(722\) 21.7682 0.810129
\(723\) 66.2747 2.46478
\(724\) 3.76552 0.139944
\(725\) 1.62735 0.0604383
\(726\) 4.12079 0.152937
\(727\) 33.8918 1.25698 0.628489 0.777818i \(-0.283674\pi\)
0.628489 + 0.777818i \(0.283674\pi\)
\(728\) 2.47510 0.0917335
\(729\) 142.487 5.27730
\(730\) 0.975954 0.0361217
\(731\) 20.0434 0.741332
\(732\) 34.6262 1.27982
\(733\) 0.336785 0.0124395 0.00621973 0.999981i \(-0.498020\pi\)
0.00621973 + 0.999981i \(0.498020\pi\)
\(734\) −27.4418 −1.01289
\(735\) 40.6346 1.49883
\(736\) −2.47389 −0.0911890
\(737\) 17.9696 0.661918
\(738\) 90.2410 3.32182
\(739\) −14.5796 −0.536320 −0.268160 0.963374i \(-0.586416\pi\)
−0.268160 + 0.963374i \(0.586416\pi\)
\(740\) −16.5936 −0.609995
\(741\) 43.3973 1.59424
\(742\) 15.3076 0.561958
\(743\) −43.0797 −1.58044 −0.790220 0.612824i \(-0.790034\pi\)
−0.790220 + 0.612824i \(0.790034\pi\)
\(744\) −5.65508 −0.207325
\(745\) −43.3292 −1.58746
\(746\) −14.4700 −0.529784
\(747\) −38.7718 −1.41859
\(748\) −8.10511 −0.296352
\(749\) 0.403415 0.0147405
\(750\) 38.9100 1.42079
\(751\) 13.5188 0.493309 0.246655 0.969103i \(-0.420669\pi\)
0.246655 + 0.969103i \(0.420669\pi\)
\(752\) 2.02672 0.0739069
\(753\) 11.7560 0.428411
\(754\) 14.1651 0.515861
\(755\) −41.8465 −1.52295
\(756\) 23.6895 0.861580
\(757\) 28.2087 1.02526 0.512632 0.858609i \(-0.328671\pi\)
0.512632 + 0.858609i \(0.328671\pi\)
\(758\) 4.00097 0.145322
\(759\) 26.3700 0.957171
\(760\) 13.9462 0.505882
\(761\) 33.2311 1.20462 0.602312 0.798260i \(-0.294246\pi\)
0.602312 + 0.798260i \(0.294246\pi\)
\(762\) −45.4313 −1.64580
\(763\) −17.4464 −0.631601
\(764\) 7.37336 0.266759
\(765\) −48.6883 −1.76033
\(766\) 5.83486 0.210822
\(767\) 9.98651 0.360592
\(768\) −3.40667 −0.122928
\(769\) −37.0884 −1.33744 −0.668721 0.743514i \(-0.733158\pi\)
−0.668721 + 0.743514i \(0.733158\pi\)
\(770\) −8.47845 −0.305542
\(771\) 68.5049 2.46714
\(772\) 15.6558 0.563466
\(773\) 3.38354 0.121698 0.0608488 0.998147i \(-0.480619\pi\)
0.0608488 + 0.998147i \(0.480619\pi\)
\(774\) −66.5859 −2.39338
\(775\) −0.380490 −0.0136676
\(776\) −14.8116 −0.531704
\(777\) −32.1069 −1.15183
\(778\) 1.54890 0.0555309
\(779\) 66.9567 2.39897
\(780\) 14.8456 0.531557
\(781\) 11.6714 0.417635
\(782\) 6.40827 0.229159
\(783\) 135.576 4.84508
\(784\) −5.46098 −0.195035
\(785\) −4.36543 −0.155809
\(786\) 15.7479 0.561707
\(787\) 23.9531 0.853835 0.426917 0.904291i \(-0.359600\pi\)
0.426917 + 0.904291i \(0.359600\pi\)
\(788\) 1.29758 0.0462242
\(789\) −54.1649 −1.92832
\(790\) 11.7616 0.418457
\(791\) −13.9987 −0.497738
\(792\) 26.9259 0.956769
\(793\) 20.2790 0.720129
\(794\) 8.79677 0.312186
\(795\) 91.8141 3.25631
\(796\) −23.4585 −0.831463
\(797\) 29.2232 1.03514 0.517570 0.855641i \(-0.326837\pi\)
0.517570 + 0.855641i \(0.326837\pi\)
\(798\) 26.9844 0.955236
\(799\) −5.24993 −0.185729
\(800\) −0.229210 −0.00810381
\(801\) −108.878 −3.84703
\(802\) −21.7856 −0.769277
\(803\) 1.39809 0.0493374
\(804\) −19.5645 −0.689985
\(805\) 6.70344 0.236265
\(806\) −3.31193 −0.116658
\(807\) −71.6773 −2.52316
\(808\) 1.04857 0.0368885
\(809\) 18.1604 0.638487 0.319244 0.947673i \(-0.396571\pi\)
0.319244 + 0.947673i \(0.396571\pi\)
\(810\) 85.7008 3.01122
\(811\) −48.8565 −1.71558 −0.857792 0.513997i \(-0.828164\pi\)
−0.857792 + 0.513997i \(0.828164\pi\)
\(812\) 8.80782 0.309094
\(813\) −30.9999 −1.08721
\(814\) −23.7709 −0.833171
\(815\) 43.7975 1.53416
\(816\) 8.82448 0.308919
\(817\) −49.4052 −1.72847
\(818\) −1.33713 −0.0467516
\(819\) 21.2992 0.744255
\(820\) 22.9049 0.799874
\(821\) 11.2135 0.391352 0.195676 0.980669i \(-0.437310\pi\)
0.195676 + 0.980669i \(0.437310\pi\)
\(822\) −9.75363 −0.340197
\(823\) −5.85760 −0.204183 −0.102092 0.994775i \(-0.532553\pi\)
−0.102092 + 0.994775i \(0.532553\pi\)
\(824\) 0.178606 0.00622202
\(825\) 2.44323 0.0850622
\(826\) 6.20959 0.216059
\(827\) −20.4737 −0.711940 −0.355970 0.934497i \(-0.615849\pi\)
−0.355970 + 0.934497i \(0.615849\pi\)
\(828\) −21.2888 −0.739837
\(829\) −32.3365 −1.12309 −0.561547 0.827445i \(-0.689794\pi\)
−0.561547 + 0.827445i \(0.689794\pi\)
\(830\) −9.84103 −0.341587
\(831\) 59.9274 2.07886
\(832\) −1.99513 −0.0691688
\(833\) 14.1459 0.490126
\(834\) −18.2090 −0.630528
\(835\) 12.9198 0.447109
\(836\) 19.9784 0.690967
\(837\) −31.6989 −1.09567
\(838\) −37.1393 −1.28296
\(839\) −8.11697 −0.280229 −0.140114 0.990135i \(-0.544747\pi\)
−0.140114 + 0.990135i \(0.544747\pi\)
\(840\) 9.23095 0.318498
\(841\) 21.4073 0.738183
\(842\) 22.0995 0.761599
\(843\) 16.9850 0.584994
\(844\) −1.71669 −0.0590909
\(845\) −19.7004 −0.677714
\(846\) 17.4407 0.599624
\(847\) 1.50062 0.0515621
\(848\) −12.3391 −0.423728
\(849\) 13.5688 0.465680
\(850\) 0.593736 0.0203650
\(851\) 18.7944 0.644263
\(852\) −12.7073 −0.435344
\(853\) −29.4219 −1.00739 −0.503693 0.863883i \(-0.668026\pi\)
−0.503693 + 0.863883i \(0.668026\pi\)
\(854\) 12.6095 0.431487
\(855\) 120.012 4.10434
\(856\) −0.325185 −0.0111146
\(857\) 39.6284 1.35368 0.676840 0.736130i \(-0.263349\pi\)
0.676840 + 0.736130i \(0.263349\pi\)
\(858\) 21.2668 0.726035
\(859\) −36.7906 −1.25528 −0.627640 0.778504i \(-0.715979\pi\)
−0.627640 + 0.778504i \(0.715979\pi\)
\(860\) −16.9008 −0.576312
\(861\) 44.3185 1.51037
\(862\) 16.6790 0.568088
\(863\) 37.6883 1.28293 0.641463 0.767154i \(-0.278328\pi\)
0.641463 + 0.767154i \(0.278328\pi\)
\(864\) −19.0957 −0.649648
\(865\) 14.0409 0.477405
\(866\) 15.0939 0.512912
\(867\) 35.0548 1.19052
\(868\) −2.05935 −0.0698989
\(869\) 16.8488 0.571557
\(870\) 52.8289 1.79107
\(871\) −11.4580 −0.388241
\(872\) 14.0632 0.476240
\(873\) −127.459 −4.31384
\(874\) −15.7958 −0.534301
\(875\) 14.1694 0.479015
\(876\) −1.52217 −0.0514295
\(877\) −7.17712 −0.242354 −0.121177 0.992631i \(-0.538667\pi\)
−0.121177 + 0.992631i \(0.538667\pi\)
\(878\) 10.2442 0.345726
\(879\) 41.8976 1.41317
\(880\) 6.83431 0.230385
\(881\) −48.3501 −1.62896 −0.814479 0.580193i \(-0.802977\pi\)
−0.814479 + 0.580193i \(0.802977\pi\)
\(882\) −46.9939 −1.58237
\(883\) 12.5406 0.422024 0.211012 0.977483i \(-0.432324\pi\)
0.211012 + 0.977483i \(0.432324\pi\)
\(884\) 5.16811 0.173822
\(885\) 37.2449 1.25197
\(886\) 0.727793 0.0244507
\(887\) 11.8974 0.399475 0.199738 0.979849i \(-0.435991\pi\)
0.199738 + 0.979849i \(0.435991\pi\)
\(888\) 25.8807 0.868500
\(889\) −16.5443 −0.554877
\(890\) −27.6355 −0.926343
\(891\) 122.769 4.11292
\(892\) −12.2684 −0.410777
\(893\) 12.9406 0.433041
\(894\) 67.5795 2.26020
\(895\) 14.8936 0.497837
\(896\) −1.24057 −0.0414446
\(897\) −16.8145 −0.561419
\(898\) 32.5788 1.08717
\(899\) −11.7857 −0.393075
\(900\) −1.97244 −0.0657481
\(901\) 31.9627 1.06483
\(902\) 32.8120 1.09252
\(903\) −32.7011 −1.08823
\(904\) 11.2841 0.375304
\(905\) 8.22470 0.273398
\(906\) 65.2670 2.16835
\(907\) −32.3048 −1.07266 −0.536331 0.844007i \(-0.680190\pi\)
−0.536331 + 0.844007i \(0.680190\pi\)
\(908\) −11.2272 −0.372586
\(909\) 9.02332 0.299285
\(910\) 5.40616 0.179212
\(911\) 55.5945 1.84193 0.920964 0.389647i \(-0.127403\pi\)
0.920964 + 0.389647i \(0.127403\pi\)
\(912\) −21.7516 −0.720266
\(913\) −14.0976 −0.466562
\(914\) −22.4254 −0.741768
\(915\) 75.6310 2.50028
\(916\) 21.3645 0.705902
\(917\) 5.73473 0.189378
\(918\) 49.4646 1.63257
\(919\) −14.5392 −0.479605 −0.239803 0.970822i \(-0.577083\pi\)
−0.239803 + 0.970822i \(0.577083\pi\)
\(920\) −5.40351 −0.178149
\(921\) 15.6580 0.515950
\(922\) 1.07914 0.0355397
\(923\) −7.44209 −0.244959
\(924\) 13.2236 0.435026
\(925\) 1.74133 0.0572546
\(926\) −27.2368 −0.895055
\(927\) 1.53697 0.0504807
\(928\) −7.09981 −0.233063
\(929\) −35.8937 −1.17763 −0.588817 0.808266i \(-0.700406\pi\)
−0.588817 + 0.808266i \(0.700406\pi\)
\(930\) −12.3519 −0.405035
\(931\) −34.8684 −1.14277
\(932\) −16.5906 −0.543443
\(933\) 37.7479 1.23581
\(934\) 13.6387 0.446271
\(935\) −17.7033 −0.578960
\(936\) −17.1689 −0.561183
\(937\) −8.98337 −0.293474 −0.146737 0.989176i \(-0.546877\pi\)
−0.146737 + 0.989176i \(0.546877\pi\)
\(938\) −7.12458 −0.232626
\(939\) −5.89363 −0.192331
\(940\) 4.42679 0.144386
\(941\) −25.5842 −0.834020 −0.417010 0.908902i \(-0.636922\pi\)
−0.417010 + 0.908902i \(0.636922\pi\)
\(942\) 6.80866 0.221838
\(943\) −25.9427 −0.844810
\(944\) −5.00543 −0.162913
\(945\) 51.7430 1.68320
\(946\) −24.2109 −0.787165
\(947\) 27.9479 0.908186 0.454093 0.890954i \(-0.349963\pi\)
0.454093 + 0.890954i \(0.349963\pi\)
\(948\) −18.3442 −0.595793
\(949\) −0.891469 −0.0289383
\(950\) −1.46351 −0.0474825
\(951\) 49.7330 1.61270
\(952\) 3.21352 0.104151
\(953\) 18.7833 0.608452 0.304226 0.952600i \(-0.401602\pi\)
0.304226 + 0.952600i \(0.401602\pi\)
\(954\) −106.183 −3.43780
\(955\) 16.1050 0.521145
\(956\) 17.3345 0.560636
\(957\) 75.6791 2.44636
\(958\) −38.8629 −1.25560
\(959\) −3.55188 −0.114696
\(960\) −7.44089 −0.240154
\(961\) −28.2444 −0.911109
\(962\) 15.1572 0.488688
\(963\) −2.79834 −0.0901752
\(964\) −19.4544 −0.626584
\(965\) 34.1957 1.10080
\(966\) −10.4552 −0.336391
\(967\) 56.6176 1.82070 0.910350 0.413839i \(-0.135812\pi\)
0.910350 + 0.413839i \(0.135812\pi\)
\(968\) −1.20962 −0.0388788
\(969\) 56.3443 1.81004
\(970\) −32.3516 −1.03875
\(971\) 40.3249 1.29409 0.647044 0.762452i \(-0.276005\pi\)
0.647044 + 0.762452i \(0.276005\pi\)
\(972\) −76.3786 −2.44984
\(973\) −6.63100 −0.212580
\(974\) −34.2190 −1.09645
\(975\) −1.55789 −0.0498923
\(976\) −10.1642 −0.325349
\(977\) −33.1556 −1.06074 −0.530371 0.847766i \(-0.677947\pi\)
−0.530371 + 0.847766i \(0.677947\pi\)
\(978\) −68.3099 −2.18431
\(979\) −39.5887 −1.26526
\(980\) −11.9280 −0.381025
\(981\) 121.019 3.86384
\(982\) 28.9422 0.923583
\(983\) 6.88230 0.219511 0.109756 0.993959i \(-0.464993\pi\)
0.109756 + 0.993959i \(0.464993\pi\)
\(984\) −35.7243 −1.13885
\(985\) 2.83418 0.0903046
\(986\) 18.3910 0.585690
\(987\) 8.56535 0.272638
\(988\) −12.7389 −0.405279
\(989\) 19.1423 0.608688
\(990\) 58.8119 1.86916
\(991\) 46.2279 1.46848 0.734239 0.678891i \(-0.237539\pi\)
0.734239 + 0.678891i \(0.237539\pi\)
\(992\) 1.66000 0.0527052
\(993\) 2.75979 0.0875794
\(994\) −4.62748 −0.146775
\(995\) −51.2383 −1.62436
\(996\) 15.3488 0.486346
\(997\) −42.9040 −1.35878 −0.679392 0.733775i \(-0.737756\pi\)
−0.679392 + 0.733775i \(0.737756\pi\)
\(998\) −32.0218 −1.01363
\(999\) 145.071 4.58986
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 \(a_p\))