Properties

Label 8002.2.a.d.1.9
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 1.9
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.76808 q^{3}\) \(+1.00000 q^{4}\) \(+4.07666 q^{5}\) \(-2.76808 q^{6}\) \(+2.61903 q^{7}\) \(+1.00000 q^{8}\) \(+4.66227 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.76808 q^{3}\) \(+1.00000 q^{4}\) \(+4.07666 q^{5}\) \(-2.76808 q^{6}\) \(+2.61903 q^{7}\) \(+1.00000 q^{8}\) \(+4.66227 q^{9}\) \(+4.07666 q^{10}\) \(-4.42706 q^{11}\) \(-2.76808 q^{12}\) \(-6.42164 q^{13}\) \(+2.61903 q^{14}\) \(-11.2845 q^{15}\) \(+1.00000 q^{16}\) \(-4.31227 q^{17}\) \(+4.66227 q^{18}\) \(-3.26346 q^{19}\) \(+4.07666 q^{20}\) \(-7.24969 q^{21}\) \(-4.42706 q^{22}\) \(+3.62139 q^{23}\) \(-2.76808 q^{24}\) \(+11.6192 q^{25}\) \(-6.42164 q^{26}\) \(-4.60130 q^{27}\) \(+2.61903 q^{28}\) \(-1.10363 q^{29}\) \(-11.2845 q^{30}\) \(+10.0846 q^{31}\) \(+1.00000 q^{32}\) \(+12.2544 q^{33}\) \(-4.31227 q^{34}\) \(+10.6769 q^{35}\) \(+4.66227 q^{36}\) \(-1.48795 q^{37}\) \(-3.26346 q^{38}\) \(+17.7756 q^{39}\) \(+4.07666 q^{40}\) \(-2.84887 q^{41}\) \(-7.24969 q^{42}\) \(-9.08959 q^{43}\) \(-4.42706 q^{44}\) \(+19.0065 q^{45}\) \(+3.62139 q^{46}\) \(-5.38514 q^{47}\) \(-2.76808 q^{48}\) \(-0.140671 q^{49}\) \(+11.6192 q^{50}\) \(+11.9367 q^{51}\) \(-6.42164 q^{52}\) \(-8.55357 q^{53}\) \(-4.60130 q^{54}\) \(-18.0476 q^{55}\) \(+2.61903 q^{56}\) \(+9.03353 q^{57}\) \(-1.10363 q^{58}\) \(+12.1824 q^{59}\) \(-11.2845 q^{60}\) \(-6.07490 q^{61}\) \(+10.0846 q^{62}\) \(+12.2106 q^{63}\) \(+1.00000 q^{64}\) \(-26.1788 q^{65}\) \(+12.2544 q^{66}\) \(-7.23324 q^{67}\) \(-4.31227 q^{68}\) \(-10.0243 q^{69}\) \(+10.6769 q^{70}\) \(+3.42135 q^{71}\) \(+4.66227 q^{72}\) \(-16.3826 q^{73}\) \(-1.48795 q^{74}\) \(-32.1627 q^{75}\) \(-3.26346 q^{76}\) \(-11.5946 q^{77}\) \(+17.7756 q^{78}\) \(+0.250564 q^{79}\) \(+4.07666 q^{80}\) \(-1.25004 q^{81}\) \(-2.84887 q^{82}\) \(+12.3640 q^{83}\) \(-7.24969 q^{84}\) \(-17.5796 q^{85}\) \(-9.08959 q^{86}\) \(+3.05494 q^{87}\) \(-4.42706 q^{88}\) \(-6.26669 q^{89}\) \(+19.0065 q^{90}\) \(-16.8185 q^{91}\) \(+3.62139 q^{92}\) \(-27.9149 q^{93}\) \(-5.38514 q^{94}\) \(-13.3040 q^{95}\) \(-2.76808 q^{96}\) \(+11.0161 q^{97}\) \(-0.140671 q^{98}\) \(-20.6401 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.76808 −1.59815 −0.799076 0.601230i \(-0.794678\pi\)
−0.799076 + 0.601230i \(0.794678\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.07666 1.82314 0.911569 0.411148i \(-0.134872\pi\)
0.911569 + 0.411148i \(0.134872\pi\)
\(6\) −2.76808 −1.13006
\(7\) 2.61903 0.989901 0.494951 0.868921i \(-0.335186\pi\)
0.494951 + 0.868921i \(0.335186\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.66227 1.55409
\(10\) 4.07666 1.28915
\(11\) −4.42706 −1.33481 −0.667404 0.744696i \(-0.732594\pi\)
−0.667404 + 0.744696i \(0.732594\pi\)
\(12\) −2.76808 −0.799076
\(13\) −6.42164 −1.78104 −0.890522 0.454941i \(-0.849660\pi\)
−0.890522 + 0.454941i \(0.849660\pi\)
\(14\) 2.61903 0.699966
\(15\) −11.2845 −2.91365
\(16\) 1.00000 0.250000
\(17\) −4.31227 −1.04588 −0.522939 0.852370i \(-0.675165\pi\)
−0.522939 + 0.852370i \(0.675165\pi\)
\(18\) 4.66227 1.09891
\(19\) −3.26346 −0.748690 −0.374345 0.927289i \(-0.622132\pi\)
−0.374345 + 0.927289i \(0.622132\pi\)
\(20\) 4.07666 0.911569
\(21\) −7.24969 −1.58201
\(22\) −4.42706 −0.943851
\(23\) 3.62139 0.755113 0.377557 0.925987i \(-0.376764\pi\)
0.377557 + 0.925987i \(0.376764\pi\)
\(24\) −2.76808 −0.565032
\(25\) 11.6192 2.32383
\(26\) −6.42164 −1.25939
\(27\) −4.60130 −0.885521
\(28\) 2.61903 0.494951
\(29\) −1.10363 −0.204939 −0.102470 0.994736i \(-0.532674\pi\)
−0.102470 + 0.994736i \(0.532674\pi\)
\(30\) −11.2845 −2.06026
\(31\) 10.0846 1.81124 0.905620 0.424091i \(-0.139406\pi\)
0.905620 + 0.424091i \(0.139406\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.2544 2.13323
\(34\) −4.31227 −0.739548
\(35\) 10.6769 1.80473
\(36\) 4.66227 0.777045
\(37\) −1.48795 −0.244617 −0.122309 0.992492i \(-0.539030\pi\)
−0.122309 + 0.992492i \(0.539030\pi\)
\(38\) −3.26346 −0.529404
\(39\) 17.7756 2.84638
\(40\) 4.07666 0.644576
\(41\) −2.84887 −0.444919 −0.222459 0.974942i \(-0.571409\pi\)
−0.222459 + 0.974942i \(0.571409\pi\)
\(42\) −7.24969 −1.11865
\(43\) −9.08959 −1.38615 −0.693075 0.720866i \(-0.743744\pi\)
−0.693075 + 0.720866i \(0.743744\pi\)
\(44\) −4.42706 −0.667404
\(45\) 19.0065 2.83332
\(46\) 3.62139 0.533946
\(47\) −5.38514 −0.785504 −0.392752 0.919644i \(-0.628477\pi\)
−0.392752 + 0.919644i \(0.628477\pi\)
\(48\) −2.76808 −0.399538
\(49\) −0.140671 −0.0200958
\(50\) 11.6192 1.64320
\(51\) 11.9367 1.67147
\(52\) −6.42164 −0.890522
\(53\) −8.55357 −1.17492 −0.587461 0.809252i \(-0.699873\pi\)
−0.587461 + 0.809252i \(0.699873\pi\)
\(54\) −4.60130 −0.626158
\(55\) −18.0476 −2.43354
\(56\) 2.61903 0.349983
\(57\) 9.03353 1.19652
\(58\) −1.10363 −0.144914
\(59\) 12.1824 1.58601 0.793006 0.609214i \(-0.208515\pi\)
0.793006 + 0.609214i \(0.208515\pi\)
\(60\) −11.2845 −1.45683
\(61\) −6.07490 −0.777811 −0.388906 0.921278i \(-0.627147\pi\)
−0.388906 + 0.921278i \(0.627147\pi\)
\(62\) 10.0846 1.28074
\(63\) 12.2106 1.53840
\(64\) 1.00000 0.125000
\(65\) −26.1788 −3.24709
\(66\) 12.2544 1.50842
\(67\) −7.23324 −0.883681 −0.441841 0.897094i \(-0.645674\pi\)
−0.441841 + 0.897094i \(0.645674\pi\)
\(68\) −4.31227 −0.522939
\(69\) −10.0243 −1.20679
\(70\) 10.6769 1.27613
\(71\) 3.42135 0.406040 0.203020 0.979175i \(-0.434924\pi\)
0.203020 + 0.979175i \(0.434924\pi\)
\(72\) 4.66227 0.549454
\(73\) −16.3826 −1.91743 −0.958717 0.284362i \(-0.908218\pi\)
−0.958717 + 0.284362i \(0.908218\pi\)
\(74\) −1.48795 −0.172970
\(75\) −32.1627 −3.71383
\(76\) −3.26346 −0.374345
\(77\) −11.5946 −1.32133
\(78\) 17.7756 2.01269
\(79\) 0.250564 0.0281906 0.0140953 0.999901i \(-0.495513\pi\)
0.0140953 + 0.999901i \(0.495513\pi\)
\(80\) 4.07666 0.455784
\(81\) −1.25004 −0.138894
\(82\) −2.84887 −0.314605
\(83\) 12.3640 1.35713 0.678565 0.734541i \(-0.262602\pi\)
0.678565 + 0.734541i \(0.262602\pi\)
\(84\) −7.24969 −0.791006
\(85\) −17.5796 −1.90678
\(86\) −9.08959 −0.980155
\(87\) 3.05494 0.327524
\(88\) −4.42706 −0.471926
\(89\) −6.26669 −0.664268 −0.332134 0.943232i \(-0.607769\pi\)
−0.332134 + 0.943232i \(0.607769\pi\)
\(90\) 19.0065 2.00346
\(91\) −16.8185 −1.76306
\(92\) 3.62139 0.377557
\(93\) −27.9149 −2.89464
\(94\) −5.38514 −0.555435
\(95\) −13.3040 −1.36497
\(96\) −2.76808 −0.282516
\(97\) 11.0161 1.11852 0.559259 0.828993i \(-0.311086\pi\)
0.559259 + 0.828993i \(0.311086\pi\)
\(98\) −0.140671 −0.0142099
\(99\) −20.6401 −2.07441
\(100\) 11.6192 1.16192
\(101\) 12.9098 1.28457 0.642285 0.766466i \(-0.277987\pi\)
0.642285 + 0.766466i \(0.277987\pi\)
\(102\) 11.9367 1.18191
\(103\) 1.88415 0.185651 0.0928253 0.995682i \(-0.470410\pi\)
0.0928253 + 0.995682i \(0.470410\pi\)
\(104\) −6.42164 −0.629694
\(105\) −29.5545 −2.88423
\(106\) −8.55357 −0.830796
\(107\) −16.7897 −1.62312 −0.811559 0.584271i \(-0.801381\pi\)
−0.811559 + 0.584271i \(0.801381\pi\)
\(108\) −4.60130 −0.442760
\(109\) 8.89079 0.851583 0.425792 0.904821i \(-0.359996\pi\)
0.425792 + 0.904821i \(0.359996\pi\)
\(110\) −18.0476 −1.72077
\(111\) 4.11876 0.390935
\(112\) 2.61903 0.247475
\(113\) −3.81909 −0.359270 −0.179635 0.983733i \(-0.557492\pi\)
−0.179635 + 0.983733i \(0.557492\pi\)
\(114\) 9.03353 0.846068
\(115\) 14.7632 1.37667
\(116\) −1.10363 −0.102470
\(117\) −29.9394 −2.76790
\(118\) 12.1824 1.12148
\(119\) −11.2940 −1.03532
\(120\) −11.2845 −1.03013
\(121\) 8.59882 0.781711
\(122\) −6.07490 −0.549996
\(123\) 7.88591 0.711048
\(124\) 10.0846 0.905620
\(125\) 26.9840 2.41352
\(126\) 12.2106 1.08781
\(127\) −14.8373 −1.31660 −0.658299 0.752756i \(-0.728724\pi\)
−0.658299 + 0.752756i \(0.728724\pi\)
\(128\) 1.00000 0.0883883
\(129\) 25.1607 2.21528
\(130\) −26.1788 −2.29604
\(131\) −12.5690 −1.09816 −0.549081 0.835769i \(-0.685022\pi\)
−0.549081 + 0.835769i \(0.685022\pi\)
\(132\) 12.2544 1.06661
\(133\) −8.54712 −0.741129
\(134\) −7.23324 −0.624857
\(135\) −18.7579 −1.61443
\(136\) −4.31227 −0.369774
\(137\) −10.5628 −0.902442 −0.451221 0.892412i \(-0.649011\pi\)
−0.451221 + 0.892412i \(0.649011\pi\)
\(138\) −10.0243 −0.853326
\(139\) −1.94959 −0.165362 −0.0826812 0.996576i \(-0.526348\pi\)
−0.0826812 + 0.996576i \(0.526348\pi\)
\(140\) 10.6769 0.902363
\(141\) 14.9065 1.25535
\(142\) 3.42135 0.287114
\(143\) 28.4290 2.37735
\(144\) 4.66227 0.388523
\(145\) −4.49913 −0.373632
\(146\) −16.3826 −1.35583
\(147\) 0.389388 0.0321162
\(148\) −1.48795 −0.122309
\(149\) −4.53225 −0.371296 −0.185648 0.982616i \(-0.559438\pi\)
−0.185648 + 0.982616i \(0.559438\pi\)
\(150\) −32.1627 −2.62608
\(151\) 8.66262 0.704954 0.352477 0.935820i \(-0.385339\pi\)
0.352477 + 0.935820i \(0.385339\pi\)
\(152\) −3.26346 −0.264702
\(153\) −20.1050 −1.62539
\(154\) −11.5946 −0.934319
\(155\) 41.1113 3.30214
\(156\) 17.7756 1.42319
\(157\) −23.2800 −1.85794 −0.928972 0.370150i \(-0.879306\pi\)
−0.928972 + 0.370150i \(0.879306\pi\)
\(158\) 0.250564 0.0199338
\(159\) 23.6770 1.87771
\(160\) 4.07666 0.322288
\(161\) 9.48455 0.747487
\(162\) −1.25004 −0.0982126
\(163\) −2.91089 −0.227999 −0.113999 0.993481i \(-0.536366\pi\)
−0.113999 + 0.993481i \(0.536366\pi\)
\(164\) −2.84887 −0.222459
\(165\) 49.9572 3.88916
\(166\) 12.3640 0.959635
\(167\) −18.5603 −1.43624 −0.718118 0.695921i \(-0.754996\pi\)
−0.718118 + 0.695921i \(0.754996\pi\)
\(168\) −7.24969 −0.559326
\(169\) 28.2375 2.17211
\(170\) −17.5796 −1.34830
\(171\) −15.2152 −1.16353
\(172\) −9.08959 −0.693075
\(173\) −9.08924 −0.691042 −0.345521 0.938411i \(-0.612298\pi\)
−0.345521 + 0.938411i \(0.612298\pi\)
\(174\) 3.05494 0.231594
\(175\) 30.4309 2.30036
\(176\) −4.42706 −0.333702
\(177\) −33.7218 −2.53469
\(178\) −6.26669 −0.469708
\(179\) 12.1436 0.907659 0.453829 0.891089i \(-0.350058\pi\)
0.453829 + 0.891089i \(0.350058\pi\)
\(180\) 19.0065 1.41666
\(181\) −6.12127 −0.454990 −0.227495 0.973779i \(-0.573054\pi\)
−0.227495 + 0.973779i \(0.573054\pi\)
\(182\) −16.8185 −1.24667
\(183\) 16.8158 1.24306
\(184\) 3.62139 0.266973
\(185\) −6.06586 −0.445971
\(186\) −27.9149 −2.04682
\(187\) 19.0906 1.39605
\(188\) −5.38514 −0.392752
\(189\) −12.0510 −0.876578
\(190\) −13.3040 −0.965176
\(191\) −13.8874 −1.00486 −0.502428 0.864619i \(-0.667560\pi\)
−0.502428 + 0.864619i \(0.667560\pi\)
\(192\) −2.76808 −0.199769
\(193\) −8.86002 −0.637758 −0.318879 0.947795i \(-0.603306\pi\)
−0.318879 + 0.947795i \(0.603306\pi\)
\(194\) 11.0161 0.790912
\(195\) 72.4652 5.18934
\(196\) −0.140671 −0.0100479
\(197\) −0.0391097 −0.00278645 −0.00139323 0.999999i \(-0.500443\pi\)
−0.00139323 + 0.999999i \(0.500443\pi\)
\(198\) −20.6401 −1.46683
\(199\) 14.8184 1.05045 0.525224 0.850964i \(-0.323981\pi\)
0.525224 + 0.850964i \(0.323981\pi\)
\(200\) 11.6192 0.821598
\(201\) 20.0222 1.41226
\(202\) 12.9098 0.908328
\(203\) −2.89044 −0.202869
\(204\) 11.9367 0.835736
\(205\) −11.6139 −0.811148
\(206\) 1.88415 0.131275
\(207\) 16.8839 1.17351
\(208\) −6.42164 −0.445261
\(209\) 14.4475 0.999357
\(210\) −29.5545 −2.03946
\(211\) −13.3946 −0.922125 −0.461062 0.887368i \(-0.652532\pi\)
−0.461062 + 0.887368i \(0.652532\pi\)
\(212\) −8.55357 −0.587461
\(213\) −9.47058 −0.648914
\(214\) −16.7897 −1.14772
\(215\) −37.0552 −2.52714
\(216\) −4.60130 −0.313079
\(217\) 26.4118 1.79295
\(218\) 8.89079 0.602160
\(219\) 45.3483 3.06435
\(220\) −18.0476 −1.21677
\(221\) 27.6918 1.86275
\(222\) 4.11876 0.276433
\(223\) 20.0938 1.34558 0.672789 0.739834i \(-0.265096\pi\)
0.672789 + 0.739834i \(0.265096\pi\)
\(224\) 2.61903 0.174991
\(225\) 54.1716 3.61144
\(226\) −3.81909 −0.254042
\(227\) −13.8976 −0.922416 −0.461208 0.887292i \(-0.652584\pi\)
−0.461208 + 0.887292i \(0.652584\pi\)
\(228\) 9.03353 0.598260
\(229\) −18.1092 −1.19669 −0.598345 0.801239i \(-0.704175\pi\)
−0.598345 + 0.801239i \(0.704175\pi\)
\(230\) 14.7632 0.973456
\(231\) 32.0948 2.11168
\(232\) −1.10363 −0.0724569
\(233\) −0.852296 −0.0558358 −0.0279179 0.999610i \(-0.508888\pi\)
−0.0279179 + 0.999610i \(0.508888\pi\)
\(234\) −29.9394 −1.95720
\(235\) −21.9534 −1.43208
\(236\) 12.1824 0.793006
\(237\) −0.693581 −0.0450529
\(238\) −11.2940 −0.732079
\(239\) 12.4646 0.806271 0.403135 0.915140i \(-0.367920\pi\)
0.403135 + 0.915140i \(0.367920\pi\)
\(240\) −11.2845 −0.728413
\(241\) 1.75884 0.113297 0.0566484 0.998394i \(-0.481959\pi\)
0.0566484 + 0.998394i \(0.481959\pi\)
\(242\) 8.59882 0.552753
\(243\) 17.2641 1.10749
\(244\) −6.07490 −0.388906
\(245\) −0.573466 −0.0366374
\(246\) 7.88591 0.502787
\(247\) 20.9568 1.33345
\(248\) 10.0846 0.640370
\(249\) −34.2246 −2.16890
\(250\) 26.9840 1.70662
\(251\) −17.6318 −1.11291 −0.556454 0.830879i \(-0.687838\pi\)
−0.556454 + 0.830879i \(0.687838\pi\)
\(252\) 12.2106 0.769198
\(253\) −16.0321 −1.00793
\(254\) −14.8373 −0.930976
\(255\) 48.6619 3.04732
\(256\) 1.00000 0.0625000
\(257\) −11.5580 −0.720970 −0.360485 0.932765i \(-0.617389\pi\)
−0.360485 + 0.932765i \(0.617389\pi\)
\(258\) 25.1607 1.56644
\(259\) −3.89698 −0.242147
\(260\) −26.1788 −1.62354
\(261\) −5.14543 −0.318494
\(262\) −12.5690 −0.776518
\(263\) 24.5521 1.51395 0.756975 0.653444i \(-0.226677\pi\)
0.756975 + 0.653444i \(0.226677\pi\)
\(264\) 12.2544 0.754209
\(265\) −34.8700 −2.14205
\(266\) −8.54712 −0.524057
\(267\) 17.3467 1.06160
\(268\) −7.23324 −0.441841
\(269\) −16.4425 −1.00252 −0.501258 0.865298i \(-0.667129\pi\)
−0.501258 + 0.865298i \(0.667129\pi\)
\(270\) −18.7579 −1.14157
\(271\) −27.0026 −1.64029 −0.820146 0.572155i \(-0.806108\pi\)
−0.820146 + 0.572155i \(0.806108\pi\)
\(272\) −4.31227 −0.261470
\(273\) 46.5549 2.81763
\(274\) −10.5628 −0.638123
\(275\) −51.4386 −3.10187
\(276\) −10.0243 −0.603393
\(277\) 20.4994 1.23169 0.615843 0.787869i \(-0.288815\pi\)
0.615843 + 0.787869i \(0.288815\pi\)
\(278\) −1.94959 −0.116929
\(279\) 47.0169 2.81483
\(280\) 10.6769 0.638067
\(281\) −11.4124 −0.680807 −0.340404 0.940279i \(-0.610564\pi\)
−0.340404 + 0.940279i \(0.610564\pi\)
\(282\) 14.9065 0.887670
\(283\) 27.2109 1.61752 0.808760 0.588139i \(-0.200139\pi\)
0.808760 + 0.588139i \(0.200139\pi\)
\(284\) 3.42135 0.203020
\(285\) 36.8266 2.18142
\(286\) 28.4290 1.68104
\(287\) −7.46129 −0.440426
\(288\) 4.66227 0.274727
\(289\) 1.59565 0.0938618
\(290\) −4.49913 −0.264198
\(291\) −30.4935 −1.78756
\(292\) −16.3826 −0.958717
\(293\) −17.6980 −1.03393 −0.516964 0.856007i \(-0.672938\pi\)
−0.516964 + 0.856007i \(0.672938\pi\)
\(294\) 0.389388 0.0227096
\(295\) 49.6634 2.89152
\(296\) −1.48795 −0.0864852
\(297\) 20.3702 1.18200
\(298\) −4.53225 −0.262546
\(299\) −23.2553 −1.34489
\(300\) −32.1627 −1.85692
\(301\) −23.8059 −1.37215
\(302\) 8.66262 0.498478
\(303\) −35.7353 −2.05294
\(304\) −3.26346 −0.187173
\(305\) −24.7653 −1.41806
\(306\) −20.1050 −1.14932
\(307\) 1.99344 0.113772 0.0568858 0.998381i \(-0.481883\pi\)
0.0568858 + 0.998381i \(0.481883\pi\)
\(308\) −11.5946 −0.660664
\(309\) −5.21547 −0.296698
\(310\) 41.1113 2.33496
\(311\) 8.59382 0.487311 0.243655 0.969862i \(-0.421653\pi\)
0.243655 + 0.969862i \(0.421653\pi\)
\(312\) 17.7756 1.00635
\(313\) −6.30633 −0.356455 −0.178228 0.983989i \(-0.557036\pi\)
−0.178228 + 0.983989i \(0.557036\pi\)
\(314\) −23.2800 −1.31376
\(315\) 49.7786 2.80471
\(316\) 0.250564 0.0140953
\(317\) 21.9281 1.23160 0.615802 0.787901i \(-0.288832\pi\)
0.615802 + 0.787901i \(0.288832\pi\)
\(318\) 23.6770 1.32774
\(319\) 4.88583 0.273554
\(320\) 4.07666 0.227892
\(321\) 46.4751 2.59399
\(322\) 9.48455 0.528553
\(323\) 14.0729 0.783039
\(324\) −1.25004 −0.0694468
\(325\) −74.6140 −4.13884
\(326\) −2.91089 −0.161219
\(327\) −24.6104 −1.36096
\(328\) −2.84887 −0.157303
\(329\) −14.1039 −0.777571
\(330\) 49.9572 2.75005
\(331\) 16.8527 0.926308 0.463154 0.886278i \(-0.346718\pi\)
0.463154 + 0.886278i \(0.346718\pi\)
\(332\) 12.3640 0.678565
\(333\) −6.93721 −0.380157
\(334\) −18.5603 −1.01557
\(335\) −29.4875 −1.61107
\(336\) −7.24969 −0.395503
\(337\) 0.979731 0.0533693 0.0266847 0.999644i \(-0.491505\pi\)
0.0266847 + 0.999644i \(0.491505\pi\)
\(338\) 28.2375 1.53592
\(339\) 10.5716 0.574168
\(340\) −17.5796 −0.953390
\(341\) −44.6449 −2.41766
\(342\) −15.2152 −0.822741
\(343\) −18.7016 −1.00979
\(344\) −9.08959 −0.490078
\(345\) −40.8657 −2.20014
\(346\) −9.08924 −0.488640
\(347\) 31.1263 1.67095 0.835474 0.549530i \(-0.185193\pi\)
0.835474 + 0.549530i \(0.185193\pi\)
\(348\) 3.05494 0.163762
\(349\) −15.6169 −0.835953 −0.417977 0.908458i \(-0.637261\pi\)
−0.417977 + 0.908458i \(0.637261\pi\)
\(350\) 30.4309 1.62660
\(351\) 29.5479 1.57715
\(352\) −4.42706 −0.235963
\(353\) 0.904647 0.0481495 0.0240748 0.999710i \(-0.492336\pi\)
0.0240748 + 0.999710i \(0.492336\pi\)
\(354\) −33.7218 −1.79230
\(355\) 13.9477 0.740267
\(356\) −6.26669 −0.332134
\(357\) 31.2626 1.65459
\(358\) 12.1436 0.641812
\(359\) 14.0762 0.742914 0.371457 0.928450i \(-0.378858\pi\)
0.371457 + 0.928450i \(0.378858\pi\)
\(360\) 19.0065 1.00173
\(361\) −8.34980 −0.439463
\(362\) −6.12127 −0.321727
\(363\) −23.8022 −1.24929
\(364\) −16.8185 −0.881528
\(365\) −66.7861 −3.49575
\(366\) 16.8158 0.878977
\(367\) 24.3904 1.27317 0.636584 0.771208i \(-0.280347\pi\)
0.636584 + 0.771208i \(0.280347\pi\)
\(368\) 3.62139 0.188778
\(369\) −13.2822 −0.691444
\(370\) −6.06586 −0.315349
\(371\) −22.4021 −1.16306
\(372\) −27.9149 −1.44732
\(373\) 17.3071 0.896130 0.448065 0.894001i \(-0.352113\pi\)
0.448065 + 0.894001i \(0.352113\pi\)
\(374\) 19.0906 0.987154
\(375\) −74.6939 −3.85718
\(376\) −5.38514 −0.277717
\(377\) 7.08712 0.365005
\(378\) −12.0510 −0.619834
\(379\) −1.53442 −0.0788181 −0.0394090 0.999223i \(-0.512548\pi\)
−0.0394090 + 0.999223i \(0.512548\pi\)
\(380\) −13.3040 −0.682483
\(381\) 41.0709 2.10412
\(382\) −13.8874 −0.710540
\(383\) 15.2502 0.779250 0.389625 0.920974i \(-0.372605\pi\)
0.389625 + 0.920974i \(0.372605\pi\)
\(384\) −2.76808 −0.141258
\(385\) −47.2672 −2.40896
\(386\) −8.86002 −0.450963
\(387\) −42.3781 −2.15420
\(388\) 11.0161 0.559259
\(389\) 9.01331 0.456993 0.228497 0.973545i \(-0.426619\pi\)
0.228497 + 0.973545i \(0.426619\pi\)
\(390\) 72.4652 3.66942
\(391\) −15.6164 −0.789756
\(392\) −0.140671 −0.00710494
\(393\) 34.7921 1.75503
\(394\) −0.0391097 −0.00197032
\(395\) 1.02146 0.0513954
\(396\) −20.6401 −1.03721
\(397\) 13.3055 0.667786 0.333893 0.942611i \(-0.391638\pi\)
0.333893 + 0.942611i \(0.391638\pi\)
\(398\) 14.8184 0.742779
\(399\) 23.6591 1.18444
\(400\) 11.6192 0.580958
\(401\) 21.7260 1.08495 0.542473 0.840073i \(-0.317488\pi\)
0.542473 + 0.840073i \(0.317488\pi\)
\(402\) 20.0222 0.998616
\(403\) −64.7594 −3.22589
\(404\) 12.9098 0.642285
\(405\) −5.09600 −0.253222
\(406\) −2.89044 −0.143450
\(407\) 6.58723 0.326517
\(408\) 11.9367 0.590955
\(409\) −18.7793 −0.928576 −0.464288 0.885684i \(-0.653690\pi\)
−0.464288 + 0.885684i \(0.653690\pi\)
\(410\) −11.6139 −0.573569
\(411\) 29.2387 1.44224
\(412\) 1.88415 0.0928253
\(413\) 31.9061 1.56999
\(414\) 16.8839 0.829800
\(415\) 50.4040 2.47423
\(416\) −6.42164 −0.314847
\(417\) 5.39663 0.264274
\(418\) 14.4475 0.706652
\(419\) −31.9674 −1.56171 −0.780855 0.624712i \(-0.785216\pi\)
−0.780855 + 0.624712i \(0.785216\pi\)
\(420\) −29.5545 −1.44211
\(421\) −0.152108 −0.00741329 −0.00370664 0.999993i \(-0.501180\pi\)
−0.00370664 + 0.999993i \(0.501180\pi\)
\(422\) −13.3946 −0.652040
\(423\) −25.1070 −1.22074
\(424\) −8.55357 −0.415398
\(425\) −50.1049 −2.43044
\(426\) −9.47058 −0.458851
\(427\) −15.9104 −0.769956
\(428\) −16.7897 −0.811559
\(429\) −78.6937 −3.79937
\(430\) −37.0552 −1.78696
\(431\) 20.7945 1.00164 0.500819 0.865552i \(-0.333032\pi\)
0.500819 + 0.865552i \(0.333032\pi\)
\(432\) −4.60130 −0.221380
\(433\) 16.8286 0.808731 0.404365 0.914598i \(-0.367492\pi\)
0.404365 + 0.914598i \(0.367492\pi\)
\(434\) 26.4118 1.26781
\(435\) 12.4539 0.597121
\(436\) 8.89079 0.425792
\(437\) −11.8183 −0.565346
\(438\) 45.3483 2.16682
\(439\) 9.79890 0.467676 0.233838 0.972276i \(-0.424871\pi\)
0.233838 + 0.972276i \(0.424871\pi\)
\(440\) −18.0476 −0.860385
\(441\) −0.655845 −0.0312307
\(442\) 27.6918 1.31717
\(443\) −14.8303 −0.704610 −0.352305 0.935885i \(-0.614602\pi\)
−0.352305 + 0.935885i \(0.614602\pi\)
\(444\) 4.11876 0.195468
\(445\) −25.5472 −1.21105
\(446\) 20.0938 0.951467
\(447\) 12.5456 0.593388
\(448\) 2.61903 0.123738
\(449\) 16.6571 0.786098 0.393049 0.919518i \(-0.371420\pi\)
0.393049 + 0.919518i \(0.371420\pi\)
\(450\) 54.1716 2.55368
\(451\) 12.6121 0.593881
\(452\) −3.81909 −0.179635
\(453\) −23.9788 −1.12662
\(454\) −13.8976 −0.652247
\(455\) −68.5632 −3.21429
\(456\) 9.03353 0.423034
\(457\) −4.84273 −0.226533 −0.113267 0.993565i \(-0.536131\pi\)
−0.113267 + 0.993565i \(0.536131\pi\)
\(458\) −18.1092 −0.846187
\(459\) 19.8420 0.926147
\(460\) 14.7632 0.688337
\(461\) −12.0470 −0.561083 −0.280541 0.959842i \(-0.590514\pi\)
−0.280541 + 0.959842i \(0.590514\pi\)
\(462\) 32.0948 1.49318
\(463\) 29.5573 1.37364 0.686821 0.726827i \(-0.259006\pi\)
0.686821 + 0.726827i \(0.259006\pi\)
\(464\) −1.10363 −0.0512348
\(465\) −113.799 −5.27732
\(466\) −0.852296 −0.0394819
\(467\) −26.9216 −1.24578 −0.622891 0.782309i \(-0.714042\pi\)
−0.622891 + 0.782309i \(0.714042\pi\)
\(468\) −29.9394 −1.38395
\(469\) −18.9441 −0.874757
\(470\) −21.9534 −1.01263
\(471\) 64.4408 2.96928
\(472\) 12.1824 0.560740
\(473\) 40.2401 1.85024
\(474\) −0.693581 −0.0318572
\(475\) −37.9187 −1.73983
\(476\) −11.2940 −0.517658
\(477\) −39.8790 −1.82594
\(478\) 12.4646 0.570120
\(479\) −4.54626 −0.207724 −0.103862 0.994592i \(-0.533120\pi\)
−0.103862 + 0.994592i \(0.533120\pi\)
\(480\) −11.2845 −0.515066
\(481\) 9.55507 0.435674
\(482\) 1.75884 0.0801129
\(483\) −26.2540 −1.19460
\(484\) 8.59882 0.390855
\(485\) 44.9090 2.03921
\(486\) 17.2641 0.783116
\(487\) −18.4525 −0.836165 −0.418082 0.908409i \(-0.637298\pi\)
−0.418082 + 0.908409i \(0.637298\pi\)
\(488\) −6.07490 −0.274998
\(489\) 8.05759 0.364377
\(490\) −0.573466 −0.0259066
\(491\) 24.6500 1.11244 0.556220 0.831035i \(-0.312251\pi\)
0.556220 + 0.831035i \(0.312251\pi\)
\(492\) 7.88591 0.355524
\(493\) 4.75915 0.214341
\(494\) 20.9568 0.942891
\(495\) −84.1428 −3.78194
\(496\) 10.0846 0.452810
\(497\) 8.96063 0.401939
\(498\) −34.2246 −1.53364
\(499\) −40.5470 −1.81513 −0.907566 0.419910i \(-0.862062\pi\)
−0.907566 + 0.419910i \(0.862062\pi\)
\(500\) 26.9840 1.20676
\(501\) 51.3763 2.29532
\(502\) −17.6318 −0.786945
\(503\) 5.55903 0.247865 0.123932 0.992291i \(-0.460449\pi\)
0.123932 + 0.992291i \(0.460449\pi\)
\(504\) 12.2106 0.543905
\(505\) 52.6287 2.34195
\(506\) −16.0321 −0.712714
\(507\) −78.1636 −3.47137
\(508\) −14.8373 −0.658299
\(509\) −42.5344 −1.88530 −0.942651 0.333779i \(-0.891676\pi\)
−0.942651 + 0.333779i \(0.891676\pi\)
\(510\) 48.6619 2.15478
\(511\) −42.9065 −1.89807
\(512\) 1.00000 0.0441942
\(513\) 15.0162 0.662981
\(514\) −11.5580 −0.509803
\(515\) 7.68103 0.338467
\(516\) 25.1607 1.10764
\(517\) 23.8403 1.04850
\(518\) −3.89698 −0.171224
\(519\) 25.1597 1.10439
\(520\) −26.1788 −1.14802
\(521\) 6.56873 0.287781 0.143891 0.989594i \(-0.454039\pi\)
0.143891 + 0.989594i \(0.454039\pi\)
\(522\) −5.14543 −0.225209
\(523\) 5.40387 0.236295 0.118147 0.992996i \(-0.462304\pi\)
0.118147 + 0.992996i \(0.462304\pi\)
\(524\) −12.5690 −0.549081
\(525\) −84.2353 −3.67633
\(526\) 24.5521 1.07052
\(527\) −43.4873 −1.89434
\(528\) 12.2544 0.533306
\(529\) −9.88550 −0.429804
\(530\) −34.8700 −1.51465
\(531\) 56.7976 2.46481
\(532\) −8.54712 −0.370565
\(533\) 18.2944 0.792420
\(534\) 17.3467 0.750665
\(535\) −68.4457 −2.95917
\(536\) −7.23324 −0.312428
\(537\) −33.6146 −1.45058
\(538\) −16.4425 −0.708886
\(539\) 0.622757 0.0268240
\(540\) −18.7579 −0.807213
\(541\) −2.60376 −0.111944 −0.0559721 0.998432i \(-0.517826\pi\)
−0.0559721 + 0.998432i \(0.517826\pi\)
\(542\) −27.0026 −1.15986
\(543\) 16.9442 0.727144
\(544\) −4.31227 −0.184887
\(545\) 36.2447 1.55255
\(546\) 46.5549 1.99237
\(547\) −19.5946 −0.837807 −0.418903 0.908031i \(-0.637585\pi\)
−0.418903 + 0.908031i \(0.637585\pi\)
\(548\) −10.5628 −0.451221
\(549\) −28.3228 −1.20879
\(550\) −51.4386 −2.19335
\(551\) 3.60166 0.153436
\(552\) −10.0243 −0.426663
\(553\) 0.656235 0.0279059
\(554\) 20.4994 0.870934
\(555\) 16.7908 0.712729
\(556\) −1.94959 −0.0826812
\(557\) −13.7897 −0.584289 −0.292144 0.956374i \(-0.594369\pi\)
−0.292144 + 0.956374i \(0.594369\pi\)
\(558\) 47.0169 1.99038
\(559\) 58.3701 2.46879
\(560\) 10.6769 0.451181
\(561\) −52.8444 −2.23109
\(562\) −11.4124 −0.481404
\(563\) −28.1674 −1.18712 −0.593558 0.804791i \(-0.702277\pi\)
−0.593558 + 0.804791i \(0.702277\pi\)
\(564\) 14.9065 0.627677
\(565\) −15.5691 −0.654998
\(566\) 27.2109 1.14376
\(567\) −3.27390 −0.137491
\(568\) 3.42135 0.143557
\(569\) 26.6749 1.11827 0.559135 0.829077i \(-0.311133\pi\)
0.559135 + 0.829077i \(0.311133\pi\)
\(570\) 36.8266 1.54250
\(571\) −21.2917 −0.891031 −0.445516 0.895274i \(-0.646980\pi\)
−0.445516 + 0.895274i \(0.646980\pi\)
\(572\) 28.4290 1.18867
\(573\) 38.4414 1.60591
\(574\) −7.46129 −0.311428
\(575\) 42.0775 1.75475
\(576\) 4.66227 0.194261
\(577\) −28.7089 −1.19517 −0.597584 0.801806i \(-0.703873\pi\)
−0.597584 + 0.801806i \(0.703873\pi\)
\(578\) 1.59565 0.0663703
\(579\) 24.5252 1.01923
\(580\) −4.49913 −0.186816
\(581\) 32.3818 1.34342
\(582\) −30.4935 −1.26400
\(583\) 37.8671 1.56830
\(584\) −16.3826 −0.677915
\(585\) −122.053 −5.04627
\(586\) −17.6980 −0.731098
\(587\) −4.92944 −0.203460 −0.101730 0.994812i \(-0.532438\pi\)
−0.101730 + 0.994812i \(0.532438\pi\)
\(588\) 0.389388 0.0160581
\(589\) −32.9106 −1.35606
\(590\) 49.6634 2.04461
\(591\) 0.108259 0.00445317
\(592\) −1.48795 −0.0611543
\(593\) −8.14147 −0.334330 −0.167165 0.985929i \(-0.553461\pi\)
−0.167165 + 0.985929i \(0.553461\pi\)
\(594\) 20.3702 0.835800
\(595\) −46.0417 −1.88752
\(596\) −4.53225 −0.185648
\(597\) −41.0185 −1.67878
\(598\) −23.2553 −0.950980
\(599\) −5.47770 −0.223813 −0.111906 0.993719i \(-0.535696\pi\)
−0.111906 + 0.993719i \(0.535696\pi\)
\(600\) −32.1627 −1.31304
\(601\) −11.2020 −0.456938 −0.228469 0.973551i \(-0.573372\pi\)
−0.228469 + 0.973551i \(0.573372\pi\)
\(602\) −23.8059 −0.970257
\(603\) −33.7233 −1.37332
\(604\) 8.66262 0.352477
\(605\) 35.0544 1.42517
\(606\) −35.7353 −1.45165
\(607\) 44.3486 1.80005 0.900027 0.435834i \(-0.143547\pi\)
0.900027 + 0.435834i \(0.143547\pi\)
\(608\) −3.26346 −0.132351
\(609\) 8.00098 0.324216
\(610\) −24.7653 −1.00272
\(611\) 34.5815 1.39902
\(612\) −20.1050 −0.812695
\(613\) 5.82769 0.235378 0.117689 0.993050i \(-0.462451\pi\)
0.117689 + 0.993050i \(0.462451\pi\)
\(614\) 1.99344 0.0804487
\(615\) 32.1481 1.29634
\(616\) −11.5946 −0.467160
\(617\) −9.86089 −0.396985 −0.198492 0.980102i \(-0.563604\pi\)
−0.198492 + 0.980102i \(0.563604\pi\)
\(618\) −5.21547 −0.209797
\(619\) −11.7007 −0.470289 −0.235144 0.971960i \(-0.575556\pi\)
−0.235144 + 0.971960i \(0.575556\pi\)
\(620\) 41.1113 1.65107
\(621\) −16.6631 −0.668668
\(622\) 8.59382 0.344581
\(623\) −16.4127 −0.657560
\(624\) 17.7756 0.711594
\(625\) 51.9089 2.07636
\(626\) −6.30633 −0.252052
\(627\) −39.9920 −1.59712
\(628\) −23.2800 −0.928972
\(629\) 6.41643 0.255840
\(630\) 49.7786 1.98323
\(631\) 28.9703 1.15329 0.576644 0.816996i \(-0.304362\pi\)
0.576644 + 0.816996i \(0.304362\pi\)
\(632\) 0.250564 0.00996689
\(633\) 37.0774 1.47370
\(634\) 21.9281 0.870875
\(635\) −60.4866 −2.40034
\(636\) 23.6770 0.938853
\(637\) 0.903337 0.0357915
\(638\) 4.88583 0.193432
\(639\) 15.9513 0.631023
\(640\) 4.07666 0.161144
\(641\) 0.106120 0.00419148 0.00209574 0.999998i \(-0.499333\pi\)
0.00209574 + 0.999998i \(0.499333\pi\)
\(642\) 46.4751 1.83423
\(643\) −1.78669 −0.0704604 −0.0352302 0.999379i \(-0.511216\pi\)
−0.0352302 + 0.999379i \(0.511216\pi\)
\(644\) 9.48455 0.373744
\(645\) 102.572 4.03875
\(646\) 14.0729 0.553692
\(647\) −19.6340 −0.771892 −0.385946 0.922521i \(-0.626125\pi\)
−0.385946 + 0.922521i \(0.626125\pi\)
\(648\) −1.25004 −0.0491063
\(649\) −53.9321 −2.11702
\(650\) −74.6140 −2.92660
\(651\) −73.1099 −2.86540
\(652\) −2.91089 −0.113999
\(653\) −6.77993 −0.265319 −0.132660 0.991162i \(-0.542352\pi\)
−0.132660 + 0.991162i \(0.542352\pi\)
\(654\) −24.6104 −0.962344
\(655\) −51.2397 −2.00210
\(656\) −2.84887 −0.111230
\(657\) −76.3799 −2.97987
\(658\) −14.1039 −0.549826
\(659\) −21.2496 −0.827767 −0.413884 0.910330i \(-0.635828\pi\)
−0.413884 + 0.910330i \(0.635828\pi\)
\(660\) 49.9572 1.94458
\(661\) −21.5810 −0.839402 −0.419701 0.907662i \(-0.637865\pi\)
−0.419701 + 0.907662i \(0.637865\pi\)
\(662\) 16.8527 0.654999
\(663\) −76.6532 −2.97697
\(664\) 12.3640 0.479818
\(665\) −34.8437 −1.35118
\(666\) −6.93721 −0.268812
\(667\) −3.99668 −0.154752
\(668\) −18.5603 −0.718118
\(669\) −55.6212 −2.15044
\(670\) −29.4875 −1.13920
\(671\) 26.8939 1.03823
\(672\) −7.24969 −0.279663
\(673\) −41.7443 −1.60912 −0.804562 0.593869i \(-0.797600\pi\)
−0.804562 + 0.593869i \(0.797600\pi\)
\(674\) 0.979731 0.0377378
\(675\) −53.4632 −2.05780
\(676\) 28.2375 1.08606
\(677\) 1.35759 0.0521765 0.0260882 0.999660i \(-0.491695\pi\)
0.0260882 + 0.999660i \(0.491695\pi\)
\(678\) 10.5716 0.405998
\(679\) 28.8516 1.10722
\(680\) −17.5796 −0.674149
\(681\) 38.4697 1.47416
\(682\) −44.6449 −1.70954
\(683\) 12.0638 0.461607 0.230803 0.973000i \(-0.425865\pi\)
0.230803 + 0.973000i \(0.425865\pi\)
\(684\) −15.2152 −0.581766
\(685\) −43.0610 −1.64528
\(686\) −18.7016 −0.714032
\(687\) 50.1277 1.91249
\(688\) −9.08959 −0.346537
\(689\) 54.9279 2.09259
\(690\) −40.8657 −1.55573
\(691\) 47.8693 1.82103 0.910517 0.413472i \(-0.135684\pi\)
0.910517 + 0.413472i \(0.135684\pi\)
\(692\) −9.08924 −0.345521
\(693\) −54.0572 −2.05346
\(694\) 31.1263 1.18154
\(695\) −7.94783 −0.301478
\(696\) 3.05494 0.115797
\(697\) 12.2851 0.465331
\(698\) −15.6169 −0.591108
\(699\) 2.35923 0.0892341
\(700\) 30.4309 1.15018
\(701\) 14.1512 0.534485 0.267242 0.963629i \(-0.413888\pi\)
0.267242 + 0.963629i \(0.413888\pi\)
\(702\) 29.5479 1.11521
\(703\) 4.85586 0.183142
\(704\) −4.42706 −0.166851
\(705\) 60.7688 2.28868
\(706\) 0.904647 0.0340469
\(707\) 33.8111 1.27160
\(708\) −33.7218 −1.26734
\(709\) −17.5721 −0.659934 −0.329967 0.943992i \(-0.607038\pi\)
−0.329967 + 0.943992i \(0.607038\pi\)
\(710\) 13.9477 0.523447
\(711\) 1.16820 0.0438108
\(712\) −6.26669 −0.234854
\(713\) 36.5201 1.36769
\(714\) 31.2626 1.16997
\(715\) 115.895 4.33423
\(716\) 12.1436 0.453829
\(717\) −34.5031 −1.28854
\(718\) 14.0762 0.525320
\(719\) 48.9097 1.82402 0.912012 0.410164i \(-0.134529\pi\)
0.912012 + 0.410164i \(0.134529\pi\)
\(720\) 19.0065 0.708330
\(721\) 4.93464 0.183776
\(722\) −8.34980 −0.310747
\(723\) −4.86861 −0.181065
\(724\) −6.12127 −0.227495
\(725\) −12.8233 −0.476244
\(726\) −23.8022 −0.883383
\(727\) −48.5496 −1.80060 −0.900302 0.435266i \(-0.856654\pi\)
−0.900302 + 0.435266i \(0.856654\pi\)
\(728\) −16.8185 −0.623335
\(729\) −44.0383 −1.63105
\(730\) −66.7861 −2.47187
\(731\) 39.1967 1.44974
\(732\) 16.8158 0.621530
\(733\) 35.8106 1.32270 0.661348 0.750079i \(-0.269985\pi\)
0.661348 + 0.750079i \(0.269985\pi\)
\(734\) 24.3904 0.900265
\(735\) 1.58740 0.0585522
\(736\) 3.62139 0.133486
\(737\) 32.0220 1.17954
\(738\) −13.2822 −0.488925
\(739\) −17.7784 −0.653989 −0.326995 0.945026i \(-0.606036\pi\)
−0.326995 + 0.945026i \(0.606036\pi\)
\(740\) −6.06586 −0.222985
\(741\) −58.0101 −2.13105
\(742\) −22.4021 −0.822406
\(743\) −43.6704 −1.60211 −0.801056 0.598589i \(-0.795728\pi\)
−0.801056 + 0.598589i \(0.795728\pi\)
\(744\) −27.9149 −1.02341
\(745\) −18.4764 −0.676924
\(746\) 17.3071 0.633659
\(747\) 57.6445 2.10910
\(748\) 19.0906 0.698023
\(749\) −43.9727 −1.60673
\(750\) −74.6939 −2.72744
\(751\) 25.9057 0.945312 0.472656 0.881247i \(-0.343295\pi\)
0.472656 + 0.881247i \(0.343295\pi\)
\(752\) −5.38514 −0.196376
\(753\) 48.8062 1.77860
\(754\) 7.08712 0.258098
\(755\) 35.3145 1.28523
\(756\) −12.0510 −0.438289
\(757\) 23.7023 0.861476 0.430738 0.902477i \(-0.358253\pi\)
0.430738 + 0.902477i \(0.358253\pi\)
\(758\) −1.53442 −0.0557328
\(759\) 44.3782 1.61083
\(760\) −13.3040 −0.482588
\(761\) −11.5547 −0.418858 −0.209429 0.977824i \(-0.567160\pi\)
−0.209429 + 0.977824i \(0.567160\pi\)
\(762\) 41.0709 1.48784
\(763\) 23.2853 0.842983
\(764\) −13.8874 −0.502428
\(765\) −81.9611 −2.96331
\(766\) 15.2502 0.551013
\(767\) −78.2309 −2.82476
\(768\) −2.76808 −0.0998845
\(769\) −32.2203 −1.16189 −0.580946 0.813942i \(-0.697317\pi\)
−0.580946 + 0.813942i \(0.697317\pi\)
\(770\) −47.2672 −1.70339
\(771\) 31.9936 1.15222
\(772\) −8.86002 −0.318879
\(773\) 43.7149 1.57231 0.786157 0.618026i \(-0.212068\pi\)
0.786157 + 0.618026i \(0.212068\pi\)
\(774\) −42.3781 −1.52325
\(775\) 117.174 4.20901
\(776\) 11.0161 0.395456
\(777\) 10.7872 0.386987
\(778\) 9.01331 0.323143
\(779\) 9.29719 0.333106
\(780\) 72.4652 2.59467
\(781\) −15.1465 −0.541985
\(782\) −15.6164 −0.558442
\(783\) 5.07814 0.181478
\(784\) −0.140671 −0.00502395
\(785\) −94.9045 −3.38729
\(786\) 34.7921 1.24099
\(787\) 20.3664 0.725984 0.362992 0.931792i \(-0.381755\pi\)
0.362992 + 0.931792i \(0.381755\pi\)
\(788\) −0.0391097 −0.00139323
\(789\) −67.9623 −2.41952
\(790\) 1.02146 0.0363420
\(791\) −10.0023 −0.355642
\(792\) −20.6401 −0.733415
\(793\) 39.0108 1.38532
\(794\) 13.3055 0.472196
\(795\) 96.5229 3.42331
\(796\) 14.8184 0.525224
\(797\) 21.6137 0.765597 0.382798 0.923832i \(-0.374960\pi\)
0.382798 + 0.923832i \(0.374960\pi\)
\(798\) 23.6591 0.837524
\(799\) 23.2222 0.821541
\(800\) 11.6192 0.410799
\(801\) −29.2170 −1.03233
\(802\) 21.7260 0.767173
\(803\) 72.5265 2.55940
\(804\) 20.0222 0.706128
\(805\) 38.6653 1.36277
\(806\) −64.7594 −2.28105
\(807\) 45.5141 1.60217
\(808\) 12.9098 0.454164
\(809\) 3.17882 0.111761 0.0558806 0.998437i \(-0.482203\pi\)
0.0558806 + 0.998437i \(0.482203\pi\)
\(810\) −5.09600 −0.179055
\(811\) 15.0015 0.526775 0.263388 0.964690i \(-0.415160\pi\)
0.263388 + 0.964690i \(0.415160\pi\)
\(812\) −2.89044 −0.101435
\(813\) 74.7454 2.62144
\(814\) 6.58723 0.230882
\(815\) −11.8667 −0.415673
\(816\) 11.9367 0.417868
\(817\) 29.6635 1.03780
\(818\) −18.7793 −0.656602
\(819\) −78.4123 −2.73995
\(820\) −11.6139 −0.405574
\(821\) 42.0632 1.46802 0.734008 0.679141i \(-0.237648\pi\)
0.734008 + 0.679141i \(0.237648\pi\)
\(822\) 29.2387 1.01982
\(823\) 25.1776 0.877636 0.438818 0.898576i \(-0.355397\pi\)
0.438818 + 0.898576i \(0.355397\pi\)
\(824\) 1.88415 0.0656374
\(825\) 142.386 4.95725
\(826\) 31.9061 1.11015
\(827\) 25.7884 0.896751 0.448375 0.893845i \(-0.352003\pi\)
0.448375 + 0.893845i \(0.352003\pi\)
\(828\) 16.8839 0.586757
\(829\) −46.5701 −1.61745 −0.808723 0.588190i \(-0.799841\pi\)
−0.808723 + 0.588190i \(0.799841\pi\)
\(830\) 50.4040 1.74955
\(831\) −56.7439 −1.96842
\(832\) −6.42164 −0.222630
\(833\) 0.606609 0.0210178
\(834\) 5.39663 0.186870
\(835\) −75.6638 −2.61846
\(836\) 14.4475 0.499679
\(837\) −46.4021 −1.60389
\(838\) −31.9674 −1.10430
\(839\) 27.1817 0.938417 0.469208 0.883088i \(-0.344539\pi\)
0.469208 + 0.883088i \(0.344539\pi\)
\(840\) −29.5545 −1.01973
\(841\) −27.7820 −0.958000
\(842\) −0.152108 −0.00524199
\(843\) 31.5905 1.08803
\(844\) −13.3946 −0.461062
\(845\) 115.115 3.96006
\(846\) −25.1070 −0.863196
\(847\) 22.5206 0.773816
\(848\) −8.55357 −0.293731
\(849\) −75.3220 −2.58504
\(850\) −50.1049 −1.71858
\(851\) −5.38845 −0.184714
\(852\) −9.47058 −0.324457
\(853\) 43.4306 1.48704 0.743518 0.668716i \(-0.233156\pi\)
0.743518 + 0.668716i \(0.233156\pi\)
\(854\) −15.9104 −0.544441
\(855\) −62.0270 −2.12128
\(856\) −16.7897 −0.573859
\(857\) 13.6322 0.465667 0.232833 0.972517i \(-0.425200\pi\)
0.232833 + 0.972517i \(0.425200\pi\)
\(858\) −78.6937 −2.68656
\(859\) 2.83685 0.0967921 0.0483960 0.998828i \(-0.484589\pi\)
0.0483960 + 0.998828i \(0.484589\pi\)
\(860\) −37.0552 −1.26357
\(861\) 20.6534 0.703867
\(862\) 20.7945 0.708264
\(863\) 2.18430 0.0743546 0.0371773 0.999309i \(-0.488163\pi\)
0.0371773 + 0.999309i \(0.488163\pi\)
\(864\) −4.60130 −0.156539
\(865\) −37.0537 −1.25986
\(866\) 16.8286 0.571859
\(867\) −4.41689 −0.150005
\(868\) 26.4118 0.896474
\(869\) −1.10926 −0.0376291
\(870\) 12.4539 0.422228
\(871\) 46.4493 1.57387
\(872\) 8.89079 0.301080
\(873\) 51.3602 1.73828
\(874\) −11.8183 −0.399760
\(875\) 70.6720 2.38915
\(876\) 45.3483 1.53218
\(877\) 56.1083 1.89464 0.947321 0.320285i \(-0.103779\pi\)
0.947321 + 0.320285i \(0.103779\pi\)
\(878\) 9.79890 0.330697
\(879\) 48.9895 1.65237
\(880\) −18.0476 −0.608384
\(881\) 23.8877 0.804798 0.402399 0.915464i \(-0.368177\pi\)
0.402399 + 0.915464i \(0.368177\pi\)
\(882\) −0.655845 −0.0220834
\(883\) −58.3397 −1.96329 −0.981644 0.190721i \(-0.938917\pi\)
−0.981644 + 0.190721i \(0.938917\pi\)
\(884\) 27.6918 0.931377
\(885\) −137.472 −4.62108
\(886\) −14.8303 −0.498234
\(887\) −40.1668 −1.34867 −0.674334 0.738426i \(-0.735569\pi\)
−0.674334 + 0.738426i \(0.735569\pi\)
\(888\) 4.11876 0.138217
\(889\) −38.8594 −1.30330
\(890\) −25.5472 −0.856343
\(891\) 5.53401 0.185396
\(892\) 20.0938 0.672789
\(893\) 17.5742 0.588099
\(894\) 12.5456 0.419589
\(895\) 49.5055 1.65479
\(896\) 2.61903 0.0874957
\(897\) 64.3725 2.14934
\(898\) 16.6571 0.555855
\(899\) −11.1296 −0.371194
\(900\) 54.1716 1.80572
\(901\) 36.8853 1.22883
\(902\) 12.6121 0.419937
\(903\) 65.8967 2.19291
\(904\) −3.81909 −0.127021
\(905\) −24.9543 −0.829510
\(906\) −23.9788 −0.796643
\(907\) 43.4544 1.44288 0.721439 0.692478i \(-0.243481\pi\)
0.721439 + 0.692478i \(0.243481\pi\)
\(908\) −13.8976 −0.461208
\(909\) 60.1888 1.99634
\(910\) −68.5632 −2.27285
\(911\) −7.91301 −0.262170 −0.131085 0.991371i \(-0.541846\pi\)
−0.131085 + 0.991371i \(0.541846\pi\)
\(912\) 9.03353 0.299130
\(913\) −54.7363 −1.81151
\(914\) −4.84273 −0.160183
\(915\) 68.5524 2.26627
\(916\) −18.1092 −0.598345
\(917\) −32.9187 −1.08707
\(918\) 19.8420 0.654885
\(919\) −17.1197 −0.564727 −0.282363 0.959308i \(-0.591118\pi\)
−0.282363 + 0.959308i \(0.591118\pi\)
\(920\) 14.7632 0.486728
\(921\) −5.51800 −0.181824
\(922\) −12.0470 −0.396745
\(923\) −21.9707 −0.723175
\(924\) 32.0948 1.05584
\(925\) −17.2887 −0.568449
\(926\) 29.5573 0.971312
\(927\) 8.78441 0.288518
\(928\) −1.10363 −0.0362285
\(929\) 15.9814 0.524334 0.262167 0.965023i \(-0.415563\pi\)
0.262167 + 0.965023i \(0.415563\pi\)
\(930\) −113.799 −3.73163
\(931\) 0.459074 0.0150455
\(932\) −0.852296 −0.0279179
\(933\) −23.7884 −0.778797
\(934\) −26.9216 −0.880901
\(935\) 77.8261 2.54518
\(936\) −29.9394 −0.978601
\(937\) 1.31248 0.0428770 0.0214385 0.999770i \(-0.493175\pi\)
0.0214385 + 0.999770i \(0.493175\pi\)
\(938\) −18.9441 −0.618546
\(939\) 17.4564 0.569669
\(940\) −21.9534 −0.716041
\(941\) −13.7344 −0.447728 −0.223864 0.974620i \(-0.571867\pi\)
−0.223864 + 0.974620i \(0.571867\pi\)
\(942\) 64.4408 2.09960
\(943\) −10.3169 −0.335964
\(944\) 12.1824 0.396503
\(945\) −49.1276 −1.59812
\(946\) 40.2401 1.30832
\(947\) −50.6953 −1.64738 −0.823689 0.567042i \(-0.808088\pi\)
−0.823689 + 0.567042i \(0.808088\pi\)
\(948\) −0.693581 −0.0225265
\(949\) 105.203 3.41503
\(950\) −37.9187 −1.23024
\(951\) −60.6987 −1.96829
\(952\) −11.2940 −0.366040
\(953\) 29.9770 0.971051 0.485525 0.874223i \(-0.338628\pi\)
0.485525 + 0.874223i \(0.338628\pi\)
\(954\) −39.8790 −1.29113
\(955\) −56.6141 −1.83199
\(956\) 12.4646 0.403135
\(957\) −13.5244 −0.437181
\(958\) −4.54626 −0.146883
\(959\) −27.6643 −0.893328
\(960\) −11.2845 −0.364206
\(961\) 70.6982 2.28059
\(962\) 9.55507 0.308068
\(963\) −78.2779 −2.52247
\(964\) 1.75884 0.0566484
\(965\) −36.1193 −1.16272
\(966\) −26.2540 −0.844709
\(967\) −47.2758 −1.52029 −0.760143 0.649756i \(-0.774871\pi\)
−0.760143 + 0.649756i \(0.774871\pi\)
\(968\) 8.59882 0.276376
\(969\) −38.9550 −1.25142
\(970\) 44.9090 1.44194
\(971\) 57.2167 1.83617 0.918086 0.396382i \(-0.129734\pi\)
0.918086 + 0.396382i \(0.129734\pi\)
\(972\) 17.2641 0.553747
\(973\) −5.10605 −0.163692
\(974\) −18.4525 −0.591258
\(975\) 206.538 6.61450
\(976\) −6.07490 −0.194453
\(977\) −17.2206 −0.550935 −0.275468 0.961310i \(-0.588833\pi\)
−0.275468 + 0.961310i \(0.588833\pi\)
\(978\) 8.05759 0.257653
\(979\) 27.7430 0.886670
\(980\) −0.573466 −0.0183187
\(981\) 41.4513 1.32344
\(982\) 24.6500 0.786614
\(983\) −15.4510 −0.492810 −0.246405 0.969167i \(-0.579249\pi\)
−0.246405 + 0.969167i \(0.579249\pi\)
\(984\) 7.88591 0.251393
\(985\) −0.159437 −0.00508008
\(986\) 4.75915 0.151562
\(987\) 39.0406 1.24268
\(988\) 20.9568 0.666725
\(989\) −32.9170 −1.04670
\(990\) −84.1428 −2.67423
\(991\) 59.2672 1.88269 0.941343 0.337452i \(-0.109565\pi\)
0.941343 + 0.337452i \(0.109565\pi\)
\(992\) 10.0846 0.320185
\(993\) −46.6496 −1.48038
\(994\) 8.96063 0.284214
\(995\) 60.4096 1.91511
\(996\) −34.2246 −1.08445
\(997\) −32.8228 −1.03951 −0.519754 0.854316i \(-0.673976\pi\)
−0.519754 + 0.854316i \(0.673976\pi\)
\(998\) −40.5470 −1.28349
\(999\) 6.84649 0.216613
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 \(a_p\))