Properties

Label 6026.2.a.i.1.19
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.50502 q^{3}\) \(+1.00000 q^{4}\) \(-2.72563 q^{5}\) \(-1.50502 q^{6}\) \(-2.36491 q^{7}\) \(-1.00000 q^{8}\) \(-0.734912 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.50502 q^{3}\) \(+1.00000 q^{4}\) \(-2.72563 q^{5}\) \(-1.50502 q^{6}\) \(-2.36491 q^{7}\) \(-1.00000 q^{8}\) \(-0.734912 q^{9}\) \(+2.72563 q^{10}\) \(+3.29273 q^{11}\) \(+1.50502 q^{12}\) \(-0.0258940 q^{13}\) \(+2.36491 q^{14}\) \(-4.10213 q^{15}\) \(+1.00000 q^{16}\) \(+1.25710 q^{17}\) \(+0.734912 q^{18}\) \(-1.42633 q^{19}\) \(-2.72563 q^{20}\) \(-3.55924 q^{21}\) \(-3.29273 q^{22}\) \(+1.00000 q^{23}\) \(-1.50502 q^{24}\) \(+2.42906 q^{25}\) \(+0.0258940 q^{26}\) \(-5.62112 q^{27}\) \(-2.36491 q^{28}\) \(+1.18615 q^{29}\) \(+4.10213 q^{30}\) \(+5.97814 q^{31}\) \(-1.00000 q^{32}\) \(+4.95562 q^{33}\) \(-1.25710 q^{34}\) \(+6.44587 q^{35}\) \(-0.734912 q^{36}\) \(+6.53848 q^{37}\) \(+1.42633 q^{38}\) \(-0.0389711 q^{39}\) \(+2.72563 q^{40}\) \(+1.11334 q^{41}\) \(+3.55924 q^{42}\) \(+3.03969 q^{43}\) \(+3.29273 q^{44}\) \(+2.00310 q^{45}\) \(-1.00000 q^{46}\) \(+11.9054 q^{47}\) \(+1.50502 q^{48}\) \(-1.40721 q^{49}\) \(-2.42906 q^{50}\) \(+1.89196 q^{51}\) \(-0.0258940 q^{52}\) \(-8.79403 q^{53}\) \(+5.62112 q^{54}\) \(-8.97475 q^{55}\) \(+2.36491 q^{56}\) \(-2.14666 q^{57}\) \(-1.18615 q^{58}\) \(-0.637130 q^{59}\) \(-4.10213 q^{60}\) \(-10.4294 q^{61}\) \(-5.97814 q^{62}\) \(+1.73800 q^{63}\) \(+1.00000 q^{64}\) \(+0.0705775 q^{65}\) \(-4.95562 q^{66}\) \(+4.76854 q^{67}\) \(+1.25710 q^{68}\) \(+1.50502 q^{69}\) \(-6.44587 q^{70}\) \(-7.69944 q^{71}\) \(+0.734912 q^{72}\) \(-6.63515 q^{73}\) \(-6.53848 q^{74}\) \(+3.65578 q^{75}\) \(-1.42633 q^{76}\) \(-7.78700 q^{77}\) \(+0.0389711 q^{78}\) \(+7.08175 q^{79}\) \(-2.72563 q^{80}\) \(-6.25517 q^{81}\) \(-1.11334 q^{82}\) \(-13.3908 q^{83}\) \(-3.55924 q^{84}\) \(-3.42638 q^{85}\) \(-3.03969 q^{86}\) \(+1.78519 q^{87}\) \(-3.29273 q^{88}\) \(+11.0810 q^{89}\) \(-2.00310 q^{90}\) \(+0.0612370 q^{91}\) \(+1.00000 q^{92}\) \(+8.99723 q^{93}\) \(-11.9054 q^{94}\) \(+3.88765 q^{95}\) \(-1.50502 q^{96}\) \(+2.00602 q^{97}\) \(+1.40721 q^{98}\) \(-2.41986 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.50502 0.868924 0.434462 0.900690i \(-0.356938\pi\)
0.434462 + 0.900690i \(0.356938\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.72563 −1.21894 −0.609469 0.792810i \(-0.708617\pi\)
−0.609469 + 0.792810i \(0.708617\pi\)
\(6\) −1.50502 −0.614422
\(7\) −2.36491 −0.893851 −0.446926 0.894571i \(-0.647481\pi\)
−0.446926 + 0.894571i \(0.647481\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.734912 −0.244971
\(10\) 2.72563 0.861920
\(11\) 3.29273 0.992794 0.496397 0.868095i \(-0.334656\pi\)
0.496397 + 0.868095i \(0.334656\pi\)
\(12\) 1.50502 0.434462
\(13\) −0.0258940 −0.00718171 −0.00359086 0.999994i \(-0.501143\pi\)
−0.00359086 + 0.999994i \(0.501143\pi\)
\(14\) 2.36491 0.632048
\(15\) −4.10213 −1.05917
\(16\) 1.00000 0.250000
\(17\) 1.25710 0.304891 0.152445 0.988312i \(-0.451285\pi\)
0.152445 + 0.988312i \(0.451285\pi\)
\(18\) 0.734912 0.173220
\(19\) −1.42633 −0.327223 −0.163612 0.986525i \(-0.552314\pi\)
−0.163612 + 0.986525i \(0.552314\pi\)
\(20\) −2.72563 −0.609469
\(21\) −3.55924 −0.776689
\(22\) −3.29273 −0.702012
\(23\) 1.00000 0.208514
\(24\) −1.50502 −0.307211
\(25\) 2.42906 0.485812
\(26\) 0.0258940 0.00507824
\(27\) −5.62112 −1.08179
\(28\) −2.36491 −0.446926
\(29\) 1.18615 0.220263 0.110132 0.993917i \(-0.464873\pi\)
0.110132 + 0.993917i \(0.464873\pi\)
\(30\) 4.10213 0.748943
\(31\) 5.97814 1.07371 0.536853 0.843676i \(-0.319613\pi\)
0.536853 + 0.843676i \(0.319613\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.95562 0.862663
\(34\) −1.25710 −0.215590
\(35\) 6.44587 1.08955
\(36\) −0.734912 −0.122485
\(37\) 6.53848 1.07492 0.537460 0.843289i \(-0.319384\pi\)
0.537460 + 0.843289i \(0.319384\pi\)
\(38\) 1.42633 0.231382
\(39\) −0.0389711 −0.00624036
\(40\) 2.72563 0.430960
\(41\) 1.11334 0.173874 0.0869370 0.996214i \(-0.472292\pi\)
0.0869370 + 0.996214i \(0.472292\pi\)
\(42\) 3.55924 0.549202
\(43\) 3.03969 0.463549 0.231774 0.972770i \(-0.425547\pi\)
0.231774 + 0.972770i \(0.425547\pi\)
\(44\) 3.29273 0.496397
\(45\) 2.00310 0.298604
\(46\) −1.00000 −0.147442
\(47\) 11.9054 1.73658 0.868288 0.496061i \(-0.165221\pi\)
0.868288 + 0.496061i \(0.165221\pi\)
\(48\) 1.50502 0.217231
\(49\) −1.40721 −0.201030
\(50\) −2.42906 −0.343521
\(51\) 1.89196 0.264927
\(52\) −0.0258940 −0.00359086
\(53\) −8.79403 −1.20795 −0.603977 0.797002i \(-0.706418\pi\)
−0.603977 + 0.797002i \(0.706418\pi\)
\(54\) 5.62112 0.764938
\(55\) −8.97475 −1.21016
\(56\) 2.36491 0.316024
\(57\) −2.14666 −0.284332
\(58\) −1.18615 −0.155750
\(59\) −0.637130 −0.0829473 −0.0414737 0.999140i \(-0.513205\pi\)
−0.0414737 + 0.999140i \(0.513205\pi\)
\(60\) −4.10213 −0.529583
\(61\) −10.4294 −1.33534 −0.667672 0.744456i \(-0.732709\pi\)
−0.667672 + 0.744456i \(0.732709\pi\)
\(62\) −5.97814 −0.759225
\(63\) 1.73800 0.218967
\(64\) 1.00000 0.125000
\(65\) 0.0705775 0.00875407
\(66\) −4.95562 −0.609995
\(67\) 4.76854 0.582570 0.291285 0.956636i \(-0.405917\pi\)
0.291285 + 0.956636i \(0.405917\pi\)
\(68\) 1.25710 0.152445
\(69\) 1.50502 0.181183
\(70\) −6.44587 −0.770428
\(71\) −7.69944 −0.913756 −0.456878 0.889529i \(-0.651032\pi\)
−0.456878 + 0.889529i \(0.651032\pi\)
\(72\) 0.734912 0.0866102
\(73\) −6.63515 −0.776586 −0.388293 0.921536i \(-0.626935\pi\)
−0.388293 + 0.921536i \(0.626935\pi\)
\(74\) −6.53848 −0.760083
\(75\) 3.65578 0.422134
\(76\) −1.42633 −0.163612
\(77\) −7.78700 −0.887411
\(78\) 0.0389711 0.00441260
\(79\) 7.08175 0.796760 0.398380 0.917221i \(-0.369573\pi\)
0.398380 + 0.917221i \(0.369573\pi\)
\(80\) −2.72563 −0.304735
\(81\) −6.25517 −0.695019
\(82\) −1.11334 −0.122947
\(83\) −13.3908 −1.46983 −0.734913 0.678162i \(-0.762777\pi\)
−0.734913 + 0.678162i \(0.762777\pi\)
\(84\) −3.55924 −0.388345
\(85\) −3.42638 −0.371643
\(86\) −3.03969 −0.327778
\(87\) 1.78519 0.191392
\(88\) −3.29273 −0.351006
\(89\) 11.0810 1.17458 0.587292 0.809375i \(-0.300194\pi\)
0.587292 + 0.809375i \(0.300194\pi\)
\(90\) −2.00310 −0.211145
\(91\) 0.0612370 0.00641938
\(92\) 1.00000 0.104257
\(93\) 8.99723 0.932969
\(94\) −11.9054 −1.22794
\(95\) 3.88765 0.398865
\(96\) −1.50502 −0.153606
\(97\) 2.00602 0.203680 0.101840 0.994801i \(-0.467527\pi\)
0.101840 + 0.994801i \(0.467527\pi\)
\(98\) 1.40721 0.142150
\(99\) −2.41986 −0.243206
\(100\) 2.42906 0.242906
\(101\) −12.6988 −1.26358 −0.631790 0.775140i \(-0.717679\pi\)
−0.631790 + 0.775140i \(0.717679\pi\)
\(102\) −1.89196 −0.187332
\(103\) 2.47387 0.243758 0.121879 0.992545i \(-0.461108\pi\)
0.121879 + 0.992545i \(0.461108\pi\)
\(104\) 0.0258940 0.00253912
\(105\) 9.70116 0.946736
\(106\) 8.79403 0.854152
\(107\) −19.8351 −1.91753 −0.958763 0.284205i \(-0.908270\pi\)
−0.958763 + 0.284205i \(0.908270\pi\)
\(108\) −5.62112 −0.540893
\(109\) 1.14841 0.109997 0.0549987 0.998486i \(-0.482485\pi\)
0.0549987 + 0.998486i \(0.482485\pi\)
\(110\) 8.97475 0.855709
\(111\) 9.84056 0.934024
\(112\) −2.36491 −0.223463
\(113\) 20.1469 1.89526 0.947630 0.319369i \(-0.103471\pi\)
0.947630 + 0.319369i \(0.103471\pi\)
\(114\) 2.14666 0.201053
\(115\) −2.72563 −0.254166
\(116\) 1.18615 0.110132
\(117\) 0.0190298 0.00175931
\(118\) 0.637130 0.0586526
\(119\) −2.97292 −0.272527
\(120\) 4.10213 0.374472
\(121\) −0.157950 −0.0143591
\(122\) 10.4294 0.944230
\(123\) 1.67559 0.151083
\(124\) 5.97814 0.536853
\(125\) 7.00744 0.626764
\(126\) −1.73800 −0.154833
\(127\) 7.11064 0.630967 0.315484 0.948931i \(-0.397833\pi\)
0.315484 + 0.948931i \(0.397833\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.57480 0.402789
\(130\) −0.0705775 −0.00619006
\(131\) 1.00000 0.0873704
\(132\) 4.95562 0.431332
\(133\) 3.37315 0.292489
\(134\) −4.76854 −0.411939
\(135\) 15.3211 1.31863
\(136\) −1.25710 −0.107795
\(137\) −18.3591 −1.56853 −0.784264 0.620427i \(-0.786959\pi\)
−0.784264 + 0.620427i \(0.786959\pi\)
\(138\) −1.50502 −0.128116
\(139\) −16.4313 −1.39368 −0.696841 0.717226i \(-0.745412\pi\)
−0.696841 + 0.717226i \(0.745412\pi\)
\(140\) 6.44587 0.544775
\(141\) 17.9178 1.50895
\(142\) 7.69944 0.646123
\(143\) −0.0852620 −0.00712996
\(144\) −0.734912 −0.0612427
\(145\) −3.23302 −0.268488
\(146\) 6.63515 0.549129
\(147\) −2.11788 −0.174680
\(148\) 6.53848 0.537460
\(149\) −8.63910 −0.707743 −0.353871 0.935294i \(-0.615135\pi\)
−0.353871 + 0.935294i \(0.615135\pi\)
\(150\) −3.65578 −0.298493
\(151\) 0.717568 0.0583948 0.0291974 0.999574i \(-0.490705\pi\)
0.0291974 + 0.999574i \(0.490705\pi\)
\(152\) 1.42633 0.115691
\(153\) −0.923856 −0.0746893
\(154\) 7.78700 0.627494
\(155\) −16.2942 −1.30878
\(156\) −0.0389711 −0.00312018
\(157\) −6.64964 −0.530699 −0.265349 0.964152i \(-0.585487\pi\)
−0.265349 + 0.964152i \(0.585487\pi\)
\(158\) −7.08175 −0.563394
\(159\) −13.2352 −1.04962
\(160\) 2.72563 0.215480
\(161\) −2.36491 −0.186381
\(162\) 6.25517 0.491452
\(163\) −10.6956 −0.837741 −0.418871 0.908046i \(-0.637574\pi\)
−0.418871 + 0.908046i \(0.637574\pi\)
\(164\) 1.11334 0.0869370
\(165\) −13.5072 −1.05153
\(166\) 13.3908 1.03932
\(167\) 0.226009 0.0174891 0.00874453 0.999962i \(-0.497216\pi\)
0.00874453 + 0.999962i \(0.497216\pi\)
\(168\) 3.55924 0.274601
\(169\) −12.9993 −0.999948
\(170\) 3.42638 0.262791
\(171\) 1.04823 0.0801601
\(172\) 3.03969 0.231774
\(173\) 8.60643 0.654335 0.327167 0.944966i \(-0.393906\pi\)
0.327167 + 0.944966i \(0.393906\pi\)
\(174\) −1.78519 −0.135335
\(175\) −5.74450 −0.434243
\(176\) 3.29273 0.248199
\(177\) −0.958895 −0.0720749
\(178\) −11.0810 −0.830556
\(179\) 16.1662 1.20832 0.604159 0.796864i \(-0.293509\pi\)
0.604159 + 0.796864i \(0.293509\pi\)
\(180\) 2.00310 0.149302
\(181\) −13.0720 −0.971636 −0.485818 0.874060i \(-0.661478\pi\)
−0.485818 + 0.874060i \(0.661478\pi\)
\(182\) −0.0612370 −0.00453919
\(183\) −15.6964 −1.16031
\(184\) −1.00000 −0.0737210
\(185\) −17.8215 −1.31026
\(186\) −8.99723 −0.659709
\(187\) 4.13928 0.302694
\(188\) 11.9054 0.868288
\(189\) 13.2934 0.966955
\(190\) −3.88765 −0.282040
\(191\) 26.9462 1.94976 0.974878 0.222737i \(-0.0714993\pi\)
0.974878 + 0.222737i \(0.0714993\pi\)
\(192\) 1.50502 0.108616
\(193\) −14.5321 −1.04604 −0.523021 0.852320i \(-0.675195\pi\)
−0.523021 + 0.852320i \(0.675195\pi\)
\(194\) −2.00602 −0.144024
\(195\) 0.106221 0.00760662
\(196\) −1.40721 −0.100515
\(197\) −22.9483 −1.63500 −0.817499 0.575930i \(-0.804640\pi\)
−0.817499 + 0.575930i \(0.804640\pi\)
\(198\) 2.41986 0.171972
\(199\) 12.6803 0.898880 0.449440 0.893311i \(-0.351624\pi\)
0.449440 + 0.893311i \(0.351624\pi\)
\(200\) −2.42906 −0.171760
\(201\) 7.17676 0.506209
\(202\) 12.6988 0.893485
\(203\) −2.80515 −0.196883
\(204\) 1.89196 0.132464
\(205\) −3.03454 −0.211942
\(206\) −2.47387 −0.172363
\(207\) −0.734912 −0.0510799
\(208\) −0.0258940 −0.00179543
\(209\) −4.69652 −0.324865
\(210\) −9.70116 −0.669444
\(211\) −28.6231 −1.97050 −0.985249 0.171126i \(-0.945259\pi\)
−0.985249 + 0.171126i \(0.945259\pi\)
\(212\) −8.79403 −0.603977
\(213\) −11.5878 −0.793984
\(214\) 19.8351 1.35590
\(215\) −8.28508 −0.565038
\(216\) 5.62112 0.382469
\(217\) −14.1378 −0.959733
\(218\) −1.14841 −0.0777799
\(219\) −9.98604 −0.674794
\(220\) −8.97475 −0.605078
\(221\) −0.0325513 −0.00218964
\(222\) −9.84056 −0.660455
\(223\) −21.6945 −1.45277 −0.726385 0.687288i \(-0.758801\pi\)
−0.726385 + 0.687288i \(0.758801\pi\)
\(224\) 2.36491 0.158012
\(225\) −1.78514 −0.119010
\(226\) −20.1469 −1.34015
\(227\) −10.9881 −0.729303 −0.364652 0.931144i \(-0.618812\pi\)
−0.364652 + 0.931144i \(0.618812\pi\)
\(228\) −2.14666 −0.142166
\(229\) 11.6536 0.770089 0.385045 0.922898i \(-0.374186\pi\)
0.385045 + 0.922898i \(0.374186\pi\)
\(230\) 2.72563 0.179723
\(231\) −11.7196 −0.771093
\(232\) −1.18615 −0.0778749
\(233\) 14.5619 0.953980 0.476990 0.878909i \(-0.341728\pi\)
0.476990 + 0.878909i \(0.341728\pi\)
\(234\) −0.0190298 −0.00124402
\(235\) −32.4496 −2.11678
\(236\) −0.637130 −0.0414737
\(237\) 10.6582 0.692324
\(238\) 2.97292 0.192706
\(239\) −23.8632 −1.54358 −0.771791 0.635877i \(-0.780639\pi\)
−0.771791 + 0.635877i \(0.780639\pi\)
\(240\) −4.10213 −0.264791
\(241\) −22.7518 −1.46557 −0.732786 0.680459i \(-0.761780\pi\)
−0.732786 + 0.680459i \(0.761780\pi\)
\(242\) 0.157950 0.0101534
\(243\) 7.44920 0.477867
\(244\) −10.4294 −0.667672
\(245\) 3.83553 0.245043
\(246\) −1.67559 −0.106832
\(247\) 0.0369335 0.00235002
\(248\) −5.97814 −0.379612
\(249\) −20.1534 −1.27717
\(250\) −7.00744 −0.443189
\(251\) −21.0619 −1.32942 −0.664708 0.747103i \(-0.731444\pi\)
−0.664708 + 0.747103i \(0.731444\pi\)
\(252\) 1.73800 0.109484
\(253\) 3.29273 0.207012
\(254\) −7.11064 −0.446161
\(255\) −5.15678 −0.322930
\(256\) 1.00000 0.0625000
\(257\) 0.995340 0.0620876 0.0310438 0.999518i \(-0.490117\pi\)
0.0310438 + 0.999518i \(0.490117\pi\)
\(258\) −4.57480 −0.284815
\(259\) −15.4629 −0.960819
\(260\) 0.0705775 0.00437703
\(261\) −0.871719 −0.0539581
\(262\) −1.00000 −0.0617802
\(263\) 19.0437 1.17429 0.587143 0.809483i \(-0.300253\pi\)
0.587143 + 0.809483i \(0.300253\pi\)
\(264\) −4.95562 −0.304997
\(265\) 23.9693 1.47242
\(266\) −3.37315 −0.206821
\(267\) 16.6771 1.02062
\(268\) 4.76854 0.291285
\(269\) 23.1840 1.41355 0.706777 0.707437i \(-0.250149\pi\)
0.706777 + 0.707437i \(0.250149\pi\)
\(270\) −15.3211 −0.932412
\(271\) −0.0952327 −0.00578497 −0.00289249 0.999996i \(-0.500921\pi\)
−0.00289249 + 0.999996i \(0.500921\pi\)
\(272\) 1.25710 0.0762227
\(273\) 0.0921630 0.00557796
\(274\) 18.3591 1.10912
\(275\) 7.99823 0.482311
\(276\) 1.50502 0.0905916
\(277\) −10.8520 −0.652033 −0.326016 0.945364i \(-0.605706\pi\)
−0.326016 + 0.945364i \(0.605706\pi\)
\(278\) 16.4313 0.985482
\(279\) −4.39341 −0.263026
\(280\) −6.44587 −0.385214
\(281\) −8.69946 −0.518966 −0.259483 0.965748i \(-0.583552\pi\)
−0.259483 + 0.965748i \(0.583552\pi\)
\(282\) −17.9178 −1.06699
\(283\) −13.0236 −0.774174 −0.387087 0.922043i \(-0.626519\pi\)
−0.387087 + 0.922043i \(0.626519\pi\)
\(284\) −7.69944 −0.456878
\(285\) 5.85100 0.346583
\(286\) 0.0852620 0.00504165
\(287\) −2.63294 −0.155417
\(288\) 0.734912 0.0433051
\(289\) −15.4197 −0.907042
\(290\) 3.23302 0.189849
\(291\) 3.01910 0.176983
\(292\) −6.63515 −0.388293
\(293\) 13.7640 0.804100 0.402050 0.915618i \(-0.368298\pi\)
0.402050 + 0.915618i \(0.368298\pi\)
\(294\) 2.11788 0.123517
\(295\) 1.73658 0.101108
\(296\) −6.53848 −0.380042
\(297\) −18.5088 −1.07399
\(298\) 8.63910 0.500450
\(299\) −0.0258940 −0.00149749
\(300\) 3.65578 0.211067
\(301\) −7.18859 −0.414344
\(302\) −0.717568 −0.0412914
\(303\) −19.1120 −1.09795
\(304\) −1.42633 −0.0818058
\(305\) 28.4266 1.62770
\(306\) 0.923856 0.0528133
\(307\) 32.3442 1.84598 0.922990 0.384825i \(-0.125738\pi\)
0.922990 + 0.384825i \(0.125738\pi\)
\(308\) −7.78700 −0.443705
\(309\) 3.72323 0.211807
\(310\) 16.2942 0.925448
\(311\) −4.72919 −0.268168 −0.134084 0.990970i \(-0.542809\pi\)
−0.134084 + 0.990970i \(0.542809\pi\)
\(312\) 0.0389711 0.00220630
\(313\) −21.3739 −1.20812 −0.604061 0.796938i \(-0.706452\pi\)
−0.604061 + 0.796938i \(0.706452\pi\)
\(314\) 6.64964 0.375261
\(315\) −4.73714 −0.266908
\(316\) 7.08175 0.398380
\(317\) −16.9856 −0.954006 −0.477003 0.878902i \(-0.658277\pi\)
−0.477003 + 0.878902i \(0.658277\pi\)
\(318\) 13.2352 0.742193
\(319\) 3.90568 0.218676
\(320\) −2.72563 −0.152367
\(321\) −29.8522 −1.66619
\(322\) 2.36491 0.131791
\(323\) −1.79304 −0.0997673
\(324\) −6.25517 −0.347509
\(325\) −0.0628981 −0.00348896
\(326\) 10.6956 0.592373
\(327\) 1.72838 0.0955794
\(328\) −1.11334 −0.0614737
\(329\) −28.1551 −1.55224
\(330\) 13.5072 0.743547
\(331\) −29.0657 −1.59760 −0.798799 0.601598i \(-0.794531\pi\)
−0.798799 + 0.601598i \(0.794531\pi\)
\(332\) −13.3908 −0.734913
\(333\) −4.80521 −0.263324
\(334\) −0.226009 −0.0123666
\(335\) −12.9973 −0.710117
\(336\) −3.55924 −0.194172
\(337\) 19.9216 1.08520 0.542599 0.839992i \(-0.317440\pi\)
0.542599 + 0.839992i \(0.317440\pi\)
\(338\) 12.9993 0.707070
\(339\) 30.3215 1.64684
\(340\) −3.42638 −0.185822
\(341\) 19.6844 1.06597
\(342\) −1.04823 −0.0566817
\(343\) 19.8823 1.07354
\(344\) −3.03969 −0.163889
\(345\) −4.10213 −0.220851
\(346\) −8.60643 −0.462685
\(347\) 31.5949 1.69610 0.848051 0.529914i \(-0.177776\pi\)
0.848051 + 0.529914i \(0.177776\pi\)
\(348\) 1.78519 0.0956961
\(349\) 2.88986 0.154691 0.0773454 0.997004i \(-0.475356\pi\)
0.0773454 + 0.997004i \(0.475356\pi\)
\(350\) 5.74450 0.307056
\(351\) 0.145553 0.00776907
\(352\) −3.29273 −0.175503
\(353\) −12.6049 −0.670890 −0.335445 0.942060i \(-0.608887\pi\)
−0.335445 + 0.942060i \(0.608887\pi\)
\(354\) 0.958895 0.0509647
\(355\) 20.9858 1.11381
\(356\) 11.0810 0.587292
\(357\) −4.47431 −0.236805
\(358\) −16.1662 −0.854410
\(359\) 11.3247 0.597697 0.298848 0.954301i \(-0.403397\pi\)
0.298848 + 0.954301i \(0.403397\pi\)
\(360\) −2.00310 −0.105573
\(361\) −16.9656 −0.892925
\(362\) 13.0720 0.687051
\(363\) −0.237719 −0.0124770
\(364\) 0.0612370 0.00320969
\(365\) 18.0850 0.946611
\(366\) 15.6964 0.820464
\(367\) −12.3212 −0.643162 −0.321581 0.946882i \(-0.604214\pi\)
−0.321581 + 0.946882i \(0.604214\pi\)
\(368\) 1.00000 0.0521286
\(369\) −0.818204 −0.0425940
\(370\) 17.8215 0.926495
\(371\) 20.7971 1.07973
\(372\) 8.99723 0.466484
\(373\) −31.4290 −1.62733 −0.813667 0.581331i \(-0.802532\pi\)
−0.813667 + 0.581331i \(0.802532\pi\)
\(374\) −4.13928 −0.214037
\(375\) 10.5463 0.544610
\(376\) −11.9054 −0.613972
\(377\) −0.0307143 −0.00158187
\(378\) −13.2934 −0.683741
\(379\) 4.54449 0.233435 0.116717 0.993165i \(-0.462763\pi\)
0.116717 + 0.993165i \(0.462763\pi\)
\(380\) 3.88765 0.199432
\(381\) 10.7017 0.548263
\(382\) −26.9462 −1.37869
\(383\) 2.24326 0.114625 0.0573127 0.998356i \(-0.481747\pi\)
0.0573127 + 0.998356i \(0.481747\pi\)
\(384\) −1.50502 −0.0768028
\(385\) 21.2245 1.08170
\(386\) 14.5321 0.739663
\(387\) −2.23391 −0.113556
\(388\) 2.00602 0.101840
\(389\) −18.5644 −0.941251 −0.470626 0.882333i \(-0.655972\pi\)
−0.470626 + 0.882333i \(0.655972\pi\)
\(390\) −0.106221 −0.00537869
\(391\) 1.25710 0.0635741
\(392\) 1.40721 0.0710748
\(393\) 1.50502 0.0759183
\(394\) 22.9483 1.15612
\(395\) −19.3022 −0.971201
\(396\) −2.41986 −0.121603
\(397\) 0.594174 0.0298207 0.0149104 0.999889i \(-0.495254\pi\)
0.0149104 + 0.999889i \(0.495254\pi\)
\(398\) −12.6803 −0.635604
\(399\) 5.07666 0.254151
\(400\) 2.42906 0.121453
\(401\) 0.754936 0.0376997 0.0188499 0.999822i \(-0.494000\pi\)
0.0188499 + 0.999822i \(0.494000\pi\)
\(402\) −7.17676 −0.357944
\(403\) −0.154798 −0.00771104
\(404\) −12.6988 −0.631790
\(405\) 17.0493 0.847185
\(406\) 2.80515 0.139217
\(407\) 21.5294 1.06717
\(408\) −1.89196 −0.0936658
\(409\) −25.8626 −1.27882 −0.639411 0.768865i \(-0.720822\pi\)
−0.639411 + 0.768865i \(0.720822\pi\)
\(410\) 3.03454 0.149865
\(411\) −27.6309 −1.36293
\(412\) 2.47387 0.121879
\(413\) 1.50676 0.0741426
\(414\) 0.734912 0.0361190
\(415\) 36.4982 1.79163
\(416\) 0.0258940 0.00126956
\(417\) −24.7294 −1.21100
\(418\) 4.69652 0.229714
\(419\) 17.2461 0.842525 0.421263 0.906939i \(-0.361587\pi\)
0.421263 + 0.906939i \(0.361587\pi\)
\(420\) 9.70116 0.473368
\(421\) 36.3621 1.77218 0.886091 0.463511i \(-0.153410\pi\)
0.886091 + 0.463511i \(0.153410\pi\)
\(422\) 28.6231 1.39335
\(423\) −8.74939 −0.425410
\(424\) 8.79403 0.427076
\(425\) 3.05356 0.148120
\(426\) 11.5878 0.561432
\(427\) 24.6645 1.19360
\(428\) −19.8351 −0.958763
\(429\) −0.128321 −0.00619540
\(430\) 8.28508 0.399542
\(431\) −21.9180 −1.05575 −0.527875 0.849322i \(-0.677011\pi\)
−0.527875 + 0.849322i \(0.677011\pi\)
\(432\) −5.62112 −0.270446
\(433\) −32.9831 −1.58507 −0.792533 0.609829i \(-0.791238\pi\)
−0.792533 + 0.609829i \(0.791238\pi\)
\(434\) 14.1378 0.678634
\(435\) −4.86576 −0.233295
\(436\) 1.14841 0.0549987
\(437\) −1.42633 −0.0682307
\(438\) 9.98604 0.477152
\(439\) 35.6717 1.70252 0.851260 0.524744i \(-0.175839\pi\)
0.851260 + 0.524744i \(0.175839\pi\)
\(440\) 8.97475 0.427855
\(441\) 1.03417 0.0492464
\(442\) 0.0325513 0.00154831
\(443\) 19.4406 0.923653 0.461826 0.886970i \(-0.347194\pi\)
0.461826 + 0.886970i \(0.347194\pi\)
\(444\) 9.84056 0.467012
\(445\) −30.2027 −1.43175
\(446\) 21.6945 1.02726
\(447\) −13.0020 −0.614975
\(448\) −2.36491 −0.111731
\(449\) −30.5372 −1.44114 −0.720571 0.693382i \(-0.756120\pi\)
−0.720571 + 0.693382i \(0.756120\pi\)
\(450\) 1.78514 0.0841525
\(451\) 3.66591 0.172621
\(452\) 20.1469 0.947630
\(453\) 1.07995 0.0507407
\(454\) 10.9881 0.515695
\(455\) −0.166909 −0.00782483
\(456\) 2.14666 0.100527
\(457\) −19.9037 −0.931055 −0.465527 0.885033i \(-0.654135\pi\)
−0.465527 + 0.885033i \(0.654135\pi\)
\(458\) −11.6536 −0.544535
\(459\) −7.06629 −0.329826
\(460\) −2.72563 −0.127083
\(461\) −4.60202 −0.214337 −0.107169 0.994241i \(-0.534178\pi\)
−0.107169 + 0.994241i \(0.534178\pi\)
\(462\) 11.7196 0.545245
\(463\) −9.67270 −0.449528 −0.224764 0.974413i \(-0.572161\pi\)
−0.224764 + 0.974413i \(0.572161\pi\)
\(464\) 1.18615 0.0550659
\(465\) −24.5231 −1.13723
\(466\) −14.5619 −0.674566
\(467\) 38.8060 1.79573 0.897864 0.440273i \(-0.145118\pi\)
0.897864 + 0.440273i \(0.145118\pi\)
\(468\) 0.0190298 0.000879654 0
\(469\) −11.2772 −0.520731
\(470\) 32.4496 1.49679
\(471\) −10.0078 −0.461137
\(472\) 0.637130 0.0293263
\(473\) 10.0089 0.460209
\(474\) −10.6582 −0.489547
\(475\) −3.46465 −0.158969
\(476\) −2.97292 −0.136264
\(477\) 6.46284 0.295913
\(478\) 23.8632 1.09148
\(479\) 21.0216 0.960501 0.480250 0.877131i \(-0.340546\pi\)
0.480250 + 0.877131i \(0.340546\pi\)
\(480\) 4.10213 0.187236
\(481\) −0.169308 −0.00771977
\(482\) 22.7518 1.03632
\(483\) −3.55924 −0.161951
\(484\) −0.157950 −0.00717956
\(485\) −5.46767 −0.248274
\(486\) −7.44920 −0.337903
\(487\) −15.4903 −0.701934 −0.350967 0.936388i \(-0.614147\pi\)
−0.350967 + 0.936388i \(0.614147\pi\)
\(488\) 10.4294 0.472115
\(489\) −16.0970 −0.727934
\(490\) −3.83553 −0.173272
\(491\) −6.46100 −0.291581 −0.145791 0.989315i \(-0.546573\pi\)
−0.145791 + 0.989315i \(0.546573\pi\)
\(492\) 1.67559 0.0755416
\(493\) 1.49111 0.0671563
\(494\) −0.0369335 −0.00166172
\(495\) 6.59566 0.296453
\(496\) 5.97814 0.268426
\(497\) 18.2085 0.816762
\(498\) 20.1534 0.903094
\(499\) −35.8164 −1.60336 −0.801681 0.597752i \(-0.796061\pi\)
−0.801681 + 0.597752i \(0.796061\pi\)
\(500\) 7.00744 0.313382
\(501\) 0.340148 0.0151967
\(502\) 21.0619 0.940039
\(503\) 7.48407 0.333698 0.166849 0.985982i \(-0.446641\pi\)
0.166849 + 0.985982i \(0.446641\pi\)
\(504\) −1.73800 −0.0774167
\(505\) 34.6123 1.54023
\(506\) −3.29273 −0.146380
\(507\) −19.5643 −0.868879
\(508\) 7.11064 0.315484
\(509\) −43.0640 −1.90878 −0.954390 0.298563i \(-0.903493\pi\)
−0.954390 + 0.298563i \(0.903493\pi\)
\(510\) 5.15678 0.228346
\(511\) 15.6915 0.694152
\(512\) −1.00000 −0.0441942
\(513\) 8.01759 0.353985
\(514\) −0.995340 −0.0439026
\(515\) −6.74286 −0.297126
\(516\) 4.57480 0.201394
\(517\) 39.2011 1.72406
\(518\) 15.4629 0.679402
\(519\) 12.9529 0.568567
\(520\) −0.0705775 −0.00309503
\(521\) −7.08185 −0.310261 −0.155131 0.987894i \(-0.549580\pi\)
−0.155131 + 0.987894i \(0.549580\pi\)
\(522\) 0.871719 0.0381541
\(523\) 12.8597 0.562315 0.281158 0.959662i \(-0.409282\pi\)
0.281158 + 0.959662i \(0.409282\pi\)
\(524\) 1.00000 0.0436852
\(525\) −8.64559 −0.377325
\(526\) −19.0437 −0.830345
\(527\) 7.51510 0.327363
\(528\) 4.95562 0.215666
\(529\) 1.00000 0.0434783
\(530\) −23.9693 −1.04116
\(531\) 0.468235 0.0203197
\(532\) 3.37315 0.146244
\(533\) −0.0288288 −0.00124871
\(534\) −16.6771 −0.721690
\(535\) 54.0630 2.33735
\(536\) −4.76854 −0.205970
\(537\) 24.3305 1.04994
\(538\) −23.1840 −0.999533
\(539\) −4.63355 −0.199581
\(540\) 15.3211 0.659315
\(541\) −8.15798 −0.350739 −0.175369 0.984503i \(-0.556112\pi\)
−0.175369 + 0.984503i \(0.556112\pi\)
\(542\) 0.0952327 0.00409059
\(543\) −19.6737 −0.844278
\(544\) −1.25710 −0.0538976
\(545\) −3.13013 −0.134080
\(546\) −0.0921630 −0.00394421
\(547\) −3.69883 −0.158150 −0.0790752 0.996869i \(-0.525197\pi\)
−0.0790752 + 0.996869i \(0.525197\pi\)
\(548\) −18.3591 −0.784264
\(549\) 7.66467 0.327120
\(550\) −7.99823 −0.341045
\(551\) −1.69185 −0.0720753
\(552\) −1.50502 −0.0640579
\(553\) −16.7477 −0.712185
\(554\) 10.8520 0.461057
\(555\) −26.8217 −1.13852
\(556\) −16.4313 −0.696841
\(557\) 20.0270 0.848569 0.424285 0.905529i \(-0.360526\pi\)
0.424285 + 0.905529i \(0.360526\pi\)
\(558\) 4.39341 0.185988
\(559\) −0.0787099 −0.00332907
\(560\) 6.44587 0.272388
\(561\) 6.22970 0.263018
\(562\) 8.69946 0.366965
\(563\) −13.1630 −0.554755 −0.277378 0.960761i \(-0.589465\pi\)
−0.277378 + 0.960761i \(0.589465\pi\)
\(564\) 17.9178 0.754476
\(565\) −54.9130 −2.31021
\(566\) 13.0236 0.547424
\(567\) 14.7929 0.621243
\(568\) 7.69944 0.323061
\(569\) 20.6842 0.867129 0.433564 0.901123i \(-0.357256\pi\)
0.433564 + 0.901123i \(0.357256\pi\)
\(570\) −5.85100 −0.245071
\(571\) −19.4022 −0.811958 −0.405979 0.913882i \(-0.633069\pi\)
−0.405979 + 0.913882i \(0.633069\pi\)
\(572\) −0.0852620 −0.00356498
\(573\) 40.5546 1.69419
\(574\) 2.63294 0.109897
\(575\) 2.42906 0.101299
\(576\) −0.734912 −0.0306213
\(577\) 17.4130 0.724912 0.362456 0.932001i \(-0.381938\pi\)
0.362456 + 0.932001i \(0.381938\pi\)
\(578\) 15.4197 0.641375
\(579\) −21.8711 −0.908930
\(580\) −3.23302 −0.134244
\(581\) 31.6679 1.31381
\(582\) −3.01910 −0.125146
\(583\) −28.9563 −1.19925
\(584\) 6.63515 0.274565
\(585\) −0.0518683 −0.00214449
\(586\) −13.7640 −0.568585
\(587\) 43.8593 1.81027 0.905133 0.425129i \(-0.139771\pi\)
0.905133 + 0.425129i \(0.139771\pi\)
\(588\) −2.11788 −0.0873398
\(589\) −8.52682 −0.351341
\(590\) −1.73658 −0.0714939
\(591\) −34.5376 −1.42069
\(592\) 6.53848 0.268730
\(593\) 42.1191 1.72962 0.864812 0.502097i \(-0.167438\pi\)
0.864812 + 0.502097i \(0.167438\pi\)
\(594\) 18.5088 0.759426
\(595\) 8.10308 0.332194
\(596\) −8.63910 −0.353871
\(597\) 19.0841 0.781059
\(598\) 0.0258940 0.00105889
\(599\) −2.44539 −0.0999160 −0.0499580 0.998751i \(-0.515909\pi\)
−0.0499580 + 0.998751i \(0.515909\pi\)
\(600\) −3.65578 −0.149247
\(601\) 8.82383 0.359932 0.179966 0.983673i \(-0.442401\pi\)
0.179966 + 0.983673i \(0.442401\pi\)
\(602\) 7.18859 0.292985
\(603\) −3.50446 −0.142713
\(604\) 0.717568 0.0291974
\(605\) 0.430514 0.0175029
\(606\) 19.1120 0.776371
\(607\) −15.1174 −0.613596 −0.306798 0.951775i \(-0.599258\pi\)
−0.306798 + 0.951775i \(0.599258\pi\)
\(608\) 1.42633 0.0578454
\(609\) −4.22181 −0.171076
\(610\) −28.4266 −1.15096
\(611\) −0.308278 −0.0124716
\(612\) −0.923856 −0.0373447
\(613\) −37.7298 −1.52389 −0.761946 0.647640i \(-0.775756\pi\)
−0.761946 + 0.647640i \(0.775756\pi\)
\(614\) −32.3442 −1.30530
\(615\) −4.56705 −0.184161
\(616\) 7.78700 0.313747
\(617\) 8.20391 0.330277 0.165138 0.986270i \(-0.447193\pi\)
0.165138 + 0.986270i \(0.447193\pi\)
\(618\) −3.72323 −0.149770
\(619\) 23.4058 0.940760 0.470380 0.882464i \(-0.344117\pi\)
0.470380 + 0.882464i \(0.344117\pi\)
\(620\) −16.2942 −0.654391
\(621\) −5.62112 −0.225568
\(622\) 4.72919 0.189623
\(623\) −26.2055 −1.04990
\(624\) −0.0389711 −0.00156009
\(625\) −31.2450 −1.24980
\(626\) 21.3739 0.854271
\(627\) −7.06837 −0.282283
\(628\) −6.64964 −0.265349
\(629\) 8.21951 0.327733
\(630\) 4.73714 0.188732
\(631\) 7.69701 0.306413 0.153206 0.988194i \(-0.451040\pi\)
0.153206 + 0.988194i \(0.451040\pi\)
\(632\) −7.08175 −0.281697
\(633\) −43.0784 −1.71221
\(634\) 16.9856 0.674584
\(635\) −19.3810 −0.769110
\(636\) −13.2352 −0.524810
\(637\) 0.0364383 0.00144374
\(638\) −3.90568 −0.154627
\(639\) 5.65841 0.223843
\(640\) 2.72563 0.107740
\(641\) 5.82604 0.230115 0.115057 0.993359i \(-0.463295\pi\)
0.115057 + 0.993359i \(0.463295\pi\)
\(642\) 29.8522 1.17817
\(643\) 14.2332 0.561304 0.280652 0.959810i \(-0.409449\pi\)
0.280652 + 0.959810i \(0.409449\pi\)
\(644\) −2.36491 −0.0931904
\(645\) −12.4692 −0.490975
\(646\) 1.79304 0.0705462
\(647\) −26.2737 −1.03292 −0.516462 0.856310i \(-0.672751\pi\)
−0.516462 + 0.856310i \(0.672751\pi\)
\(648\) 6.25517 0.245726
\(649\) −2.09790 −0.0823496
\(650\) 0.0628981 0.00246707
\(651\) −21.2776 −0.833936
\(652\) −10.6956 −0.418871
\(653\) 42.9247 1.67977 0.839887 0.542762i \(-0.182621\pi\)
0.839887 + 0.542762i \(0.182621\pi\)
\(654\) −1.72838 −0.0675849
\(655\) −2.72563 −0.106499
\(656\) 1.11334 0.0434685
\(657\) 4.87625 0.190241
\(658\) 28.1551 1.09760
\(659\) −19.0280 −0.741224 −0.370612 0.928788i \(-0.620852\pi\)
−0.370612 + 0.928788i \(0.620852\pi\)
\(660\) −13.5072 −0.525767
\(661\) 2.91174 0.113253 0.0566267 0.998395i \(-0.481966\pi\)
0.0566267 + 0.998395i \(0.481966\pi\)
\(662\) 29.0657 1.12967
\(663\) −0.0489904 −0.00190263
\(664\) 13.3908 0.519662
\(665\) −9.19395 −0.356526
\(666\) 4.80521 0.186198
\(667\) 1.18615 0.0459281
\(668\) 0.226009 0.00874453
\(669\) −32.6506 −1.26235
\(670\) 12.9973 0.502129
\(671\) −34.3410 −1.32572
\(672\) 3.55924 0.137301
\(673\) 37.1715 1.43285 0.716427 0.697662i \(-0.245776\pi\)
0.716427 + 0.697662i \(0.245776\pi\)
\(674\) −19.9216 −0.767350
\(675\) −13.6540 −0.525544
\(676\) −12.9993 −0.499974
\(677\) −30.5435 −1.17388 −0.586941 0.809630i \(-0.699668\pi\)
−0.586941 + 0.809630i \(0.699668\pi\)
\(678\) −30.3215 −1.16449
\(679\) −4.74405 −0.182060
\(680\) 3.42638 0.131396
\(681\) −16.5373 −0.633709
\(682\) −19.6844 −0.753754
\(683\) −2.73959 −0.104827 −0.0524137 0.998625i \(-0.516691\pi\)
−0.0524137 + 0.998625i \(0.516691\pi\)
\(684\) 1.04823 0.0400800
\(685\) 50.0402 1.91194
\(686\) −19.8823 −0.759109
\(687\) 17.5389 0.669149
\(688\) 3.03969 0.115887
\(689\) 0.227713 0.00867517
\(690\) 4.10213 0.156165
\(691\) −28.5369 −1.08560 −0.542798 0.839863i \(-0.682635\pi\)
−0.542798 + 0.839863i \(0.682635\pi\)
\(692\) 8.60643 0.327167
\(693\) 5.72276 0.217390
\(694\) −31.5949 −1.19933
\(695\) 44.7856 1.69881
\(696\) −1.78519 −0.0676674
\(697\) 1.39957 0.0530126
\(698\) −2.88986 −0.109383
\(699\) 21.9159 0.828937
\(700\) −5.74450 −0.217122
\(701\) 2.55875 0.0966426 0.0483213 0.998832i \(-0.484613\pi\)
0.0483213 + 0.998832i \(0.484613\pi\)
\(702\) −0.145553 −0.00549356
\(703\) −9.32605 −0.351739
\(704\) 3.29273 0.124099
\(705\) −48.8373 −1.83932
\(706\) 12.6049 0.474391
\(707\) 30.0315 1.12945
\(708\) −0.958895 −0.0360375
\(709\) 27.6084 1.03686 0.518428 0.855121i \(-0.326517\pi\)
0.518428 + 0.855121i \(0.326517\pi\)
\(710\) −20.9858 −0.787584
\(711\) −5.20447 −0.195183
\(712\) −11.0810 −0.415278
\(713\) 5.97814 0.223883
\(714\) 4.47431 0.167447
\(715\) 0.232393 0.00869099
\(716\) 16.1662 0.604159
\(717\) −35.9146 −1.34126
\(718\) −11.3247 −0.422636
\(719\) −27.6135 −1.02981 −0.514905 0.857247i \(-0.672173\pi\)
−0.514905 + 0.857247i \(0.672173\pi\)
\(720\) 2.00310 0.0746511
\(721\) −5.85048 −0.217883
\(722\) 16.9656 0.631393
\(723\) −34.2419 −1.27347
\(724\) −13.0720 −0.485818
\(725\) 2.88124 0.107007
\(726\) 0.237719 0.00882256
\(727\) −1.00716 −0.0373534 −0.0186767 0.999826i \(-0.505945\pi\)
−0.0186767 + 0.999826i \(0.505945\pi\)
\(728\) −0.0612370 −0.00226959
\(729\) 29.9767 1.11025
\(730\) −18.0850 −0.669355
\(731\) 3.82119 0.141332
\(732\) −15.6964 −0.580156
\(733\) −52.7200 −1.94726 −0.973630 0.228135i \(-0.926737\pi\)
−0.973630 + 0.228135i \(0.926737\pi\)
\(734\) 12.3212 0.454784
\(735\) 5.77255 0.212924
\(736\) −1.00000 −0.0368605
\(737\) 15.7015 0.578372
\(738\) 0.818204 0.0301185
\(739\) 36.1844 1.33106 0.665532 0.746369i \(-0.268205\pi\)
0.665532 + 0.746369i \(0.268205\pi\)
\(740\) −17.8215 −0.655131
\(741\) 0.0555857 0.00204199
\(742\) −20.7971 −0.763485
\(743\) 23.9930 0.880219 0.440109 0.897944i \(-0.354940\pi\)
0.440109 + 0.897944i \(0.354940\pi\)
\(744\) −8.99723 −0.329854
\(745\) 23.5470 0.862695
\(746\) 31.4290 1.15070
\(747\) 9.84102 0.360064
\(748\) 4.13928 0.151347
\(749\) 46.9081 1.71398
\(750\) −10.5463 −0.385098
\(751\) 20.9951 0.766121 0.383061 0.923723i \(-0.374870\pi\)
0.383061 + 0.923723i \(0.374870\pi\)
\(752\) 11.9054 0.434144
\(753\) −31.6986 −1.15516
\(754\) 0.0307143 0.00111855
\(755\) −1.95582 −0.0711797
\(756\) 13.2934 0.483478
\(757\) −53.9004 −1.95904 −0.979521 0.201341i \(-0.935470\pi\)
−0.979521 + 0.201341i \(0.935470\pi\)
\(758\) −4.54449 −0.165063
\(759\) 4.95562 0.179878
\(760\) −3.88765 −0.141020
\(761\) −52.8201 −1.91473 −0.957364 0.288886i \(-0.906715\pi\)
−0.957364 + 0.288886i \(0.906715\pi\)
\(762\) −10.7017 −0.387680
\(763\) −2.71588 −0.0983214
\(764\) 26.9462 0.974878
\(765\) 2.51809 0.0910417
\(766\) −2.24326 −0.0810524
\(767\) 0.0164979 0.000595704 0
\(768\) 1.50502 0.0543078
\(769\) 11.1251 0.401180 0.200590 0.979675i \(-0.435714\pi\)
0.200590 + 0.979675i \(0.435714\pi\)
\(770\) −21.2245 −0.764877
\(771\) 1.49801 0.0539494
\(772\) −14.5321 −0.523021
\(773\) −15.4461 −0.555557 −0.277779 0.960645i \(-0.589598\pi\)
−0.277779 + 0.960645i \(0.589598\pi\)
\(774\) 2.23391 0.0802961
\(775\) 14.5213 0.521619
\(776\) −2.00602 −0.0720119
\(777\) −23.2720 −0.834879
\(778\) 18.5644 0.665565
\(779\) −1.58799 −0.0568956
\(780\) 0.106221 0.00380331
\(781\) −25.3522 −0.907172
\(782\) −1.25710 −0.0449537
\(783\) −6.66752 −0.238278
\(784\) −1.40721 −0.0502574
\(785\) 18.1244 0.646889
\(786\) −1.50502 −0.0536823
\(787\) −29.2598 −1.04300 −0.521500 0.853251i \(-0.674627\pi\)
−0.521500 + 0.853251i \(0.674627\pi\)
\(788\) −22.9483 −0.817499
\(789\) 28.6612 1.02036
\(790\) 19.3022 0.686743
\(791\) −47.6456 −1.69408
\(792\) 2.41986 0.0859862
\(793\) 0.270058 0.00959005
\(794\) −0.594174 −0.0210864
\(795\) 36.0743 1.27942
\(796\) 12.6803 0.449440
\(797\) 36.7528 1.30185 0.650926 0.759141i \(-0.274381\pi\)
0.650926 + 0.759141i \(0.274381\pi\)
\(798\) −5.07666 −0.179712
\(799\) 14.9662 0.529466
\(800\) −2.42906 −0.0858802
\(801\) −8.14356 −0.287739
\(802\) −0.754936 −0.0266577
\(803\) −21.8477 −0.770990
\(804\) 7.17676 0.253105
\(805\) 6.44587 0.227187
\(806\) 0.154798 0.00545253
\(807\) 34.8924 1.22827
\(808\) 12.6988 0.446743
\(809\) 22.0877 0.776561 0.388280 0.921541i \(-0.373069\pi\)
0.388280 + 0.921541i \(0.373069\pi\)
\(810\) −17.0493 −0.599050
\(811\) −32.2394 −1.13208 −0.566039 0.824378i \(-0.691525\pi\)
−0.566039 + 0.824378i \(0.691525\pi\)
\(812\) −2.80515 −0.0984414
\(813\) −0.143327 −0.00502670
\(814\) −21.5294 −0.754607
\(815\) 29.1522 1.02116
\(816\) 1.89196 0.0662318
\(817\) −4.33561 −0.151684
\(818\) 25.8626 0.904263
\(819\) −0.0450038 −0.00157256
\(820\) −3.03454 −0.105971
\(821\) 42.6236 1.48757 0.743786 0.668418i \(-0.233028\pi\)
0.743786 + 0.668418i \(0.233028\pi\)
\(822\) 27.6309 0.963738
\(823\) 22.7196 0.791955 0.395978 0.918260i \(-0.370406\pi\)
0.395978 + 0.918260i \(0.370406\pi\)
\(824\) −2.47387 −0.0861815
\(825\) 12.0375 0.419092
\(826\) −1.50676 −0.0524267
\(827\) 26.8990 0.935368 0.467684 0.883896i \(-0.345088\pi\)
0.467684 + 0.883896i \(0.345088\pi\)
\(828\) −0.734912 −0.0255400
\(829\) −22.5320 −0.782569 −0.391285 0.920270i \(-0.627969\pi\)
−0.391285 + 0.920270i \(0.627969\pi\)
\(830\) −36.4982 −1.26687
\(831\) −16.3325 −0.566567
\(832\) −0.0258940 −0.000897714 0
\(833\) −1.76900 −0.0612921
\(834\) 24.7294 0.856309
\(835\) −0.616016 −0.0213181
\(836\) −4.69652 −0.162433
\(837\) −33.6039 −1.16152
\(838\) −17.2461 −0.595755
\(839\) −6.74190 −0.232756 −0.116378 0.993205i \(-0.537128\pi\)
−0.116378 + 0.993205i \(0.537128\pi\)
\(840\) −9.70116 −0.334722
\(841\) −27.5930 −0.951484
\(842\) −36.3621 −1.25312
\(843\) −13.0929 −0.450942
\(844\) −28.6231 −0.985249
\(845\) 35.4314 1.21888
\(846\) 8.74939 0.300810
\(847\) 0.373538 0.0128349
\(848\) −8.79403 −0.301988
\(849\) −19.6008 −0.672698
\(850\) −3.05356 −0.104736
\(851\) 6.53848 0.224136
\(852\) −11.5878 −0.396992
\(853\) 56.3687 1.93003 0.965013 0.262200i \(-0.0844482\pi\)
0.965013 + 0.262200i \(0.0844482\pi\)
\(854\) −24.6645 −0.844001
\(855\) −2.85708 −0.0977102
\(856\) 19.8351 0.677948
\(857\) −16.5555 −0.565524 −0.282762 0.959190i \(-0.591251\pi\)
−0.282762 + 0.959190i \(0.591251\pi\)
\(858\) 0.128321 0.00438081
\(859\) −7.21115 −0.246041 −0.123021 0.992404i \(-0.539258\pi\)
−0.123021 + 0.992404i \(0.539258\pi\)
\(860\) −8.28508 −0.282519
\(861\) −3.96263 −0.135046
\(862\) 21.9180 0.746528
\(863\) −40.5122 −1.37905 −0.689526 0.724261i \(-0.742181\pi\)
−0.689526 + 0.724261i \(0.742181\pi\)
\(864\) 5.62112 0.191234
\(865\) −23.4579 −0.797594
\(866\) 32.9831 1.12081
\(867\) −23.2070 −0.788150
\(868\) −14.1378 −0.479867
\(869\) 23.3183 0.791018
\(870\) 4.86576 0.164965
\(871\) −0.123477 −0.00418385
\(872\) −1.14841 −0.0388900
\(873\) −1.47425 −0.0498957
\(874\) 1.42633 0.0482464
\(875\) −16.5719 −0.560234
\(876\) −9.98604 −0.337397
\(877\) −35.4033 −1.19549 −0.597743 0.801688i \(-0.703936\pi\)
−0.597743 + 0.801688i \(0.703936\pi\)
\(878\) −35.6717 −1.20386
\(879\) 20.7151 0.698702
\(880\) −8.97475 −0.302539
\(881\) −38.3142 −1.29084 −0.645418 0.763829i \(-0.723317\pi\)
−0.645418 + 0.763829i \(0.723317\pi\)
\(882\) −1.03417 −0.0348225
\(883\) −5.41348 −0.182178 −0.0910891 0.995843i \(-0.529035\pi\)
−0.0910891 + 0.995843i \(0.529035\pi\)
\(884\) −0.0325513 −0.00109482
\(885\) 2.61359 0.0878549
\(886\) −19.4406 −0.653121
\(887\) 24.3464 0.817471 0.408736 0.912653i \(-0.365970\pi\)
0.408736 + 0.912653i \(0.365970\pi\)
\(888\) −9.84056 −0.330227
\(889\) −16.8160 −0.563991
\(890\) 30.2027 1.01240
\(891\) −20.5966 −0.690011
\(892\) −21.6945 −0.726385
\(893\) −16.9810 −0.568248
\(894\) 13.0020 0.434853
\(895\) −44.0631 −1.47287
\(896\) 2.36491 0.0790060
\(897\) −0.0389711 −0.00130121
\(898\) 30.5372 1.01904
\(899\) 7.09100 0.236498
\(900\) −1.78514 −0.0595048
\(901\) −11.0550 −0.368294
\(902\) −3.66591 −0.122062
\(903\) −10.8190 −0.360033
\(904\) −20.1469 −0.670076
\(905\) 35.6295 1.18437
\(906\) −1.07995 −0.0358791
\(907\) −36.5304 −1.21297 −0.606486 0.795094i \(-0.707422\pi\)
−0.606486 + 0.795094i \(0.707422\pi\)
\(908\) −10.9881 −0.364652
\(909\) 9.33251 0.309540
\(910\) 0.166909 0.00553299
\(911\) −42.7219 −1.41544 −0.707720 0.706493i \(-0.750276\pi\)
−0.707720 + 0.706493i \(0.750276\pi\)
\(912\) −2.14666 −0.0710830
\(913\) −44.0921 −1.45923
\(914\) 19.9037 0.658355
\(915\) 42.7826 1.41435
\(916\) 11.6536 0.385045
\(917\) −2.36491 −0.0780962
\(918\) 7.06629 0.233222
\(919\) 41.5850 1.37176 0.685881 0.727714i \(-0.259417\pi\)
0.685881 + 0.727714i \(0.259417\pi\)
\(920\) 2.72563 0.0898614
\(921\) 48.6787 1.60402
\(922\) 4.60202 0.151559
\(923\) 0.199370 0.00656233
\(924\) −11.7196 −0.385546
\(925\) 15.8824 0.522209
\(926\) 9.67270 0.317865
\(927\) −1.81808 −0.0597136
\(928\) −1.18615 −0.0389374
\(929\) −1.27879 −0.0419559 −0.0209780 0.999780i \(-0.506678\pi\)
−0.0209780 + 0.999780i \(0.506678\pi\)
\(930\) 24.5231 0.804144
\(931\) 2.00715 0.0657816
\(932\) 14.5619 0.476990
\(933\) −7.11753 −0.233018
\(934\) −38.8060 −1.26977
\(935\) −11.2821 −0.368965
\(936\) −0.0190298 −0.000622010 0
\(937\) −23.5815 −0.770375 −0.385188 0.922838i \(-0.625863\pi\)
−0.385188 + 0.922838i \(0.625863\pi\)
\(938\) 11.2772 0.368213
\(939\) −32.1681 −1.04977
\(940\) −32.4496 −1.05839
\(941\) 8.58786 0.279956 0.139978 0.990155i \(-0.455297\pi\)
0.139978 + 0.990155i \(0.455297\pi\)
\(942\) 10.0078 0.326073
\(943\) 1.11334 0.0362552
\(944\) −0.637130 −0.0207368
\(945\) −36.2330 −1.17866
\(946\) −10.0089 −0.325417
\(947\) −19.1246 −0.621465 −0.310733 0.950497i \(-0.600574\pi\)
−0.310733 + 0.950497i \(0.600574\pi\)
\(948\) 10.6582 0.346162
\(949\) 0.171811 0.00557722
\(950\) 3.46465 0.112408
\(951\) −25.5637 −0.828959
\(952\) 2.97292 0.0963529
\(953\) 37.7713 1.22353 0.611766 0.791038i \(-0.290459\pi\)
0.611766 + 0.791038i \(0.290459\pi\)
\(954\) −6.46284 −0.209242
\(955\) −73.4453 −2.37663
\(956\) −23.8632 −0.771791
\(957\) 5.87814 0.190013
\(958\) −21.0216 −0.679177
\(959\) 43.4177 1.40203
\(960\) −4.10213 −0.132396
\(961\) 4.73817 0.152844
\(962\) 0.169308 0.00545870
\(963\) 14.5770 0.469738
\(964\) −22.7518 −0.732786
\(965\) 39.6090 1.27506
\(966\) 3.55924 0.114517
\(967\) −17.0636 −0.548728 −0.274364 0.961626i \(-0.588467\pi\)
−0.274364 + 0.961626i \(0.588467\pi\)
\(968\) 0.157950 0.00507672
\(969\) −2.69856 −0.0866903
\(970\) 5.46767 0.175556
\(971\) −36.6032 −1.17465 −0.587326 0.809350i \(-0.699819\pi\)
−0.587326 + 0.809350i \(0.699819\pi\)
\(972\) 7.44920 0.238933
\(973\) 38.8584 1.24574
\(974\) 15.4903 0.496342
\(975\) −0.0946630 −0.00303164
\(976\) −10.4294 −0.333836
\(977\) −12.6657 −0.405212 −0.202606 0.979260i \(-0.564941\pi\)
−0.202606 + 0.979260i \(0.564941\pi\)
\(978\) 16.0970 0.514727
\(979\) 36.4867 1.16612
\(980\) 3.83553 0.122521
\(981\) −0.843978 −0.0269462
\(982\) 6.46100 0.206179
\(983\) 16.9931 0.541995 0.270997 0.962580i \(-0.412647\pi\)
0.270997 + 0.962580i \(0.412647\pi\)
\(984\) −1.67559 −0.0534160
\(985\) 62.5485 1.99296
\(986\) −1.49111 −0.0474867
\(987\) −42.3740 −1.34878
\(988\) 0.0369335 0.00117501
\(989\) 3.03969 0.0966566
\(990\) −6.59566 −0.209624
\(991\) −8.90226 −0.282790 −0.141395 0.989953i \(-0.545159\pi\)
−0.141395 + 0.989953i \(0.545159\pi\)
\(992\) −5.97814 −0.189806
\(993\) −43.7446 −1.38819
\(994\) −18.2085 −0.577538
\(995\) −34.5617 −1.09568
\(996\) −20.1534 −0.638584
\(997\) 0.603734 0.0191204 0.00956022 0.999954i \(-0.496957\pi\)
0.00956022 + 0.999954i \(0.496957\pi\)
\(998\) 35.8164 1.13375
\(999\) −36.7536 −1.16283
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 \(a_p\))