Properties

Label 8008.2.a.k.1.3
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.244558277.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.287253\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.287253 q^{3}\) \(-0.115270 q^{5}\) \(+1.00000 q^{7}\) \(-2.91749 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.287253 q^{3}\) \(-0.115270 q^{5}\) \(+1.00000 q^{7}\) \(-2.91749 q^{9}\) \(-1.00000 q^{11}\) \(-1.00000 q^{13}\) \(+0.0331118 q^{15}\) \(-5.96127 q^{17}\) \(+2.56157 q^{19}\) \(-0.287253 q^{21}\) \(+1.63059 q^{23}\) \(-4.98671 q^{25}\) \(+1.69982 q^{27}\) \(-4.27397 q^{29}\) \(+9.90455 q^{31}\) \(+0.287253 q^{33}\) \(-0.115270 q^{35}\) \(+3.82766 q^{37}\) \(+0.287253 q^{39}\) \(-6.84847 q^{41}\) \(+2.08216 q^{43}\) \(+0.336300 q^{45}\) \(-10.6507 q^{47}\) \(+1.00000 q^{49}\) \(+1.71239 q^{51}\) \(+13.3842 q^{53}\) \(+0.115270 q^{55}\) \(-0.735820 q^{57}\) \(+12.8664 q^{59}\) \(-14.3889 q^{61}\) \(-2.91749 q^{63}\) \(+0.115270 q^{65}\) \(-6.75900 q^{67}\) \(-0.468391 q^{69}\) \(-6.49199 q^{71}\) \(-12.6248 q^{73}\) \(+1.43245 q^{75}\) \(-1.00000 q^{77}\) \(-3.16884 q^{79}\) \(+8.26418 q^{81}\) \(+2.81798 q^{83}\) \(+0.687158 q^{85}\) \(+1.22771 q^{87}\) \(+13.7455 q^{89}\) \(-1.00000 q^{91}\) \(-2.84511 q^{93}\) \(-0.295274 q^{95}\) \(+16.6252 q^{97}\) \(+2.91749 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut -\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut -\mathstrut q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut +\mathstrut 29q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 42q^{81} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 46q^{85} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 55q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 41q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.287253 −0.165846 −0.0829228 0.996556i \(-0.526425\pi\)
−0.0829228 + 0.996556i \(0.526425\pi\)
\(4\) 0 0
\(5\) −0.115270 −0.0515505 −0.0257753 0.999668i \(-0.508205\pi\)
−0.0257753 + 0.999668i \(0.508205\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.91749 −0.972495
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.0331118 0.00854942
\(16\) 0 0
\(17\) −5.96127 −1.44582 −0.722910 0.690943i \(-0.757196\pi\)
−0.722910 + 0.690943i \(0.757196\pi\)
\(18\) 0 0
\(19\) 2.56157 0.587665 0.293833 0.955857i \(-0.405069\pi\)
0.293833 + 0.955857i \(0.405069\pi\)
\(20\) 0 0
\(21\) −0.287253 −0.0626837
\(22\) 0 0
\(23\) 1.63059 0.340001 0.170001 0.985444i \(-0.445623\pi\)
0.170001 + 0.985444i \(0.445623\pi\)
\(24\) 0 0
\(25\) −4.98671 −0.997343
\(26\) 0 0
\(27\) 1.69982 0.327130
\(28\) 0 0
\(29\) −4.27397 −0.793656 −0.396828 0.917893i \(-0.629889\pi\)
−0.396828 + 0.917893i \(0.629889\pi\)
\(30\) 0 0
\(31\) 9.90455 1.77891 0.889455 0.457022i \(-0.151084\pi\)
0.889455 + 0.457022i \(0.151084\pi\)
\(32\) 0 0
\(33\) 0.287253 0.0500043
\(34\) 0 0
\(35\) −0.115270 −0.0194843
\(36\) 0 0
\(37\) 3.82766 0.629264 0.314632 0.949214i \(-0.398119\pi\)
0.314632 + 0.949214i \(0.398119\pi\)
\(38\) 0 0
\(39\) 0.287253 0.0459973
\(40\) 0 0
\(41\) −6.84847 −1.06955 −0.534776 0.844994i \(-0.679604\pi\)
−0.534776 + 0.844994i \(0.679604\pi\)
\(42\) 0 0
\(43\) 2.08216 0.317526 0.158763 0.987317i \(-0.449249\pi\)
0.158763 + 0.987317i \(0.449249\pi\)
\(44\) 0 0
\(45\) 0.336300 0.0501326
\(46\) 0 0
\(47\) −10.6507 −1.55356 −0.776781 0.629771i \(-0.783149\pi\)
−0.776781 + 0.629771i \(0.783149\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 1.71239 0.239783
\(52\) 0 0
\(53\) 13.3842 1.83847 0.919234 0.393712i \(-0.128809\pi\)
0.919234 + 0.393712i \(0.128809\pi\)
\(54\) 0 0
\(55\) 0.115270 0.0155431
\(56\) 0 0
\(57\) −0.735820 −0.0974617
\(58\) 0 0
\(59\) 12.8664 1.67507 0.837535 0.546384i \(-0.183996\pi\)
0.837535 + 0.546384i \(0.183996\pi\)
\(60\) 0 0
\(61\) −14.3889 −1.84231 −0.921154 0.389199i \(-0.872752\pi\)
−0.921154 + 0.389199i \(0.872752\pi\)
\(62\) 0 0
\(63\) −2.91749 −0.367569
\(64\) 0 0
\(65\) 0.115270 0.0142975
\(66\) 0 0
\(67\) −6.75900 −0.825744 −0.412872 0.910789i \(-0.635474\pi\)
−0.412872 + 0.910789i \(0.635474\pi\)
\(68\) 0 0
\(69\) −0.468391 −0.0563877
\(70\) 0 0
\(71\) −6.49199 −0.770458 −0.385229 0.922821i \(-0.625877\pi\)
−0.385229 + 0.922821i \(0.625877\pi\)
\(72\) 0 0
\(73\) −12.6248 −1.47762 −0.738812 0.673912i \(-0.764613\pi\)
−0.738812 + 0.673912i \(0.764613\pi\)
\(74\) 0 0
\(75\) 1.43245 0.165405
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −3.16884 −0.356522 −0.178261 0.983983i \(-0.557047\pi\)
−0.178261 + 0.983983i \(0.557047\pi\)
\(80\) 0 0
\(81\) 8.26418 0.918242
\(82\) 0 0
\(83\) 2.81798 0.309313 0.154657 0.987968i \(-0.450573\pi\)
0.154657 + 0.987968i \(0.450573\pi\)
\(84\) 0 0
\(85\) 0.687158 0.0745327
\(86\) 0 0
\(87\) 1.22771 0.131624
\(88\) 0 0
\(89\) 13.7455 1.45702 0.728510 0.685035i \(-0.240213\pi\)
0.728510 + 0.685035i \(0.240213\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −2.84511 −0.295024
\(94\) 0 0
\(95\) −0.295274 −0.0302945
\(96\) 0 0
\(97\) 16.6252 1.68804 0.844019 0.536314i \(-0.180184\pi\)
0.844019 + 0.536314i \(0.180184\pi\)
\(98\) 0 0
\(99\) 2.91749 0.293218
\(100\) 0 0
\(101\) 13.3659 1.32996 0.664979 0.746862i \(-0.268441\pi\)
0.664979 + 0.746862i \(0.268441\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0.0331118 0.00323138
\(106\) 0 0
\(107\) 13.8913 1.34292 0.671460 0.741041i \(-0.265668\pi\)
0.671460 + 0.741041i \(0.265668\pi\)
\(108\) 0 0
\(109\) −7.71239 −0.738713 −0.369357 0.929288i \(-0.620422\pi\)
−0.369357 + 0.929288i \(0.620422\pi\)
\(110\) 0 0
\(111\) −1.09951 −0.104361
\(112\) 0 0
\(113\) 10.5796 0.995241 0.497620 0.867395i \(-0.334207\pi\)
0.497620 + 0.867395i \(0.334207\pi\)
\(114\) 0 0
\(115\) −0.187959 −0.0175272
\(116\) 0 0
\(117\) 2.91749 0.269722
\(118\) 0 0
\(119\) −5.96127 −0.546468
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 1.96724 0.177380
\(124\) 0 0
\(125\) 1.15117 0.102964
\(126\) 0 0
\(127\) −6.25037 −0.554630 −0.277315 0.960779i \(-0.589445\pi\)
−0.277315 + 0.960779i \(0.589445\pi\)
\(128\) 0 0
\(129\) −0.598106 −0.0526603
\(130\) 0 0
\(131\) 17.8784 1.56204 0.781021 0.624504i \(-0.214699\pi\)
0.781021 + 0.624504i \(0.214699\pi\)
\(132\) 0 0
\(133\) 2.56157 0.222117
\(134\) 0 0
\(135\) −0.195938 −0.0168637
\(136\) 0 0
\(137\) 15.9046 1.35882 0.679409 0.733760i \(-0.262236\pi\)
0.679409 + 0.733760i \(0.262236\pi\)
\(138\) 0 0
\(139\) 1.65603 0.140463 0.0702315 0.997531i \(-0.477626\pi\)
0.0702315 + 0.997531i \(0.477626\pi\)
\(140\) 0 0
\(141\) 3.05944 0.257651
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 0.492662 0.0409133
\(146\) 0 0
\(147\) −0.287253 −0.0236922
\(148\) 0 0
\(149\) 10.5634 0.865386 0.432693 0.901541i \(-0.357563\pi\)
0.432693 + 0.901541i \(0.357563\pi\)
\(150\) 0 0
\(151\) −21.9294 −1.78459 −0.892296 0.451452i \(-0.850906\pi\)
−0.892296 + 0.451452i \(0.850906\pi\)
\(152\) 0 0
\(153\) 17.3919 1.40605
\(154\) 0 0
\(155\) −1.14170 −0.0917037
\(156\) 0 0
\(157\) −18.0117 −1.43749 −0.718745 0.695274i \(-0.755283\pi\)
−0.718745 + 0.695274i \(0.755283\pi\)
\(158\) 0 0
\(159\) −3.84466 −0.304902
\(160\) 0 0
\(161\) 1.63059 0.128508
\(162\) 0 0
\(163\) −15.5890 −1.22102 −0.610512 0.792007i \(-0.709036\pi\)
−0.610512 + 0.792007i \(0.709036\pi\)
\(164\) 0 0
\(165\) −0.0331118 −0.00257775
\(166\) 0 0
\(167\) −6.76560 −0.523538 −0.261769 0.965131i \(-0.584306\pi\)
−0.261769 + 0.965131i \(0.584306\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −7.47336 −0.571502
\(172\) 0 0
\(173\) 1.71059 0.130053 0.0650267 0.997884i \(-0.479287\pi\)
0.0650267 + 0.997884i \(0.479287\pi\)
\(174\) 0 0
\(175\) −4.98671 −0.376960
\(176\) 0 0
\(177\) −3.69593 −0.277803
\(178\) 0 0
\(179\) 8.82483 0.659599 0.329799 0.944051i \(-0.393019\pi\)
0.329799 + 0.944051i \(0.393019\pi\)
\(180\) 0 0
\(181\) 5.88642 0.437534 0.218767 0.975777i \(-0.429797\pi\)
0.218767 + 0.975777i \(0.429797\pi\)
\(182\) 0 0
\(183\) 4.13325 0.305539
\(184\) 0 0
\(185\) −0.441216 −0.0324389
\(186\) 0 0
\(187\) 5.96127 0.435931
\(188\) 0 0
\(189\) 1.69982 0.123643
\(190\) 0 0
\(191\) 15.6022 1.12894 0.564468 0.825455i \(-0.309081\pi\)
0.564468 + 0.825455i \(0.309081\pi\)
\(192\) 0 0
\(193\) 13.9499 1.00413 0.502067 0.864828i \(-0.332573\pi\)
0.502067 + 0.864828i \(0.332573\pi\)
\(194\) 0 0
\(195\) −0.0331118 −0.00237118
\(196\) 0 0
\(197\) 4.63080 0.329931 0.164965 0.986299i \(-0.447249\pi\)
0.164965 + 0.986299i \(0.447249\pi\)
\(198\) 0 0
\(199\) −12.5869 −0.892259 −0.446129 0.894968i \(-0.647198\pi\)
−0.446129 + 0.894968i \(0.647198\pi\)
\(200\) 0 0
\(201\) 1.94154 0.136946
\(202\) 0 0
\(203\) −4.27397 −0.299974
\(204\) 0 0
\(205\) 0.789426 0.0551359
\(206\) 0 0
\(207\) −4.75722 −0.330650
\(208\) 0 0
\(209\) −2.56157 −0.177188
\(210\) 0 0
\(211\) 11.7016 0.805574 0.402787 0.915294i \(-0.368042\pi\)
0.402787 + 0.915294i \(0.368042\pi\)
\(212\) 0 0
\(213\) 1.86484 0.127777
\(214\) 0 0
\(215\) −0.240011 −0.0163686
\(216\) 0 0
\(217\) 9.90455 0.672365
\(218\) 0 0
\(219\) 3.62652 0.245057
\(220\) 0 0
\(221\) 5.96127 0.400998
\(222\) 0 0
\(223\) 17.6129 1.17945 0.589723 0.807606i \(-0.299237\pi\)
0.589723 + 0.807606i \(0.299237\pi\)
\(224\) 0 0
\(225\) 14.5487 0.969911
\(226\) 0 0
\(227\) −20.4255 −1.35569 −0.677846 0.735204i \(-0.737086\pi\)
−0.677846 + 0.735204i \(0.737086\pi\)
\(228\) 0 0
\(229\) −3.90607 −0.258120 −0.129060 0.991637i \(-0.541196\pi\)
−0.129060 + 0.991637i \(0.541196\pi\)
\(230\) 0 0
\(231\) 0.287253 0.0188999
\(232\) 0 0
\(233\) 0.102756 0.00673174 0.00336587 0.999994i \(-0.498929\pi\)
0.00336587 + 0.999994i \(0.498929\pi\)
\(234\) 0 0
\(235\) 1.22771 0.0800869
\(236\) 0 0
\(237\) 0.910258 0.0591276
\(238\) 0 0
\(239\) 10.3614 0.670223 0.335111 0.942179i \(-0.391226\pi\)
0.335111 + 0.942179i \(0.391226\pi\)
\(240\) 0 0
\(241\) −28.1851 −1.81556 −0.907782 0.419443i \(-0.862225\pi\)
−0.907782 + 0.419443i \(0.862225\pi\)
\(242\) 0 0
\(243\) −7.47336 −0.479416
\(244\) 0 0
\(245\) −0.115270 −0.00736436
\(246\) 0 0
\(247\) −2.56157 −0.162989
\(248\) 0 0
\(249\) −0.809473 −0.0512982
\(250\) 0 0
\(251\) −5.37645 −0.339358 −0.169679 0.985499i \(-0.554273\pi\)
−0.169679 + 0.985499i \(0.554273\pi\)
\(252\) 0 0
\(253\) −1.63059 −0.102514
\(254\) 0 0
\(255\) −0.197388 −0.0123609
\(256\) 0 0
\(257\) 15.1917 0.947634 0.473817 0.880623i \(-0.342876\pi\)
0.473817 + 0.880623i \(0.342876\pi\)
\(258\) 0 0
\(259\) 3.82766 0.237839
\(260\) 0 0
\(261\) 12.4692 0.771826
\(262\) 0 0
\(263\) 17.8548 1.10097 0.550487 0.834844i \(-0.314442\pi\)
0.550487 + 0.834844i \(0.314442\pi\)
\(264\) 0 0
\(265\) −1.54281 −0.0947739
\(266\) 0 0
\(267\) −3.94844 −0.241640
\(268\) 0 0
\(269\) 10.6834 0.651381 0.325691 0.945476i \(-0.394403\pi\)
0.325691 + 0.945476i \(0.394403\pi\)
\(270\) 0 0
\(271\) 26.6735 1.62030 0.810150 0.586222i \(-0.199385\pi\)
0.810150 + 0.586222i \(0.199385\pi\)
\(272\) 0 0
\(273\) 0.287253 0.0173853
\(274\) 0 0
\(275\) 4.98671 0.300710
\(276\) 0 0
\(277\) −5.25866 −0.315962 −0.157981 0.987442i \(-0.550499\pi\)
−0.157981 + 0.987442i \(0.550499\pi\)
\(278\) 0 0
\(279\) −28.8964 −1.72998
\(280\) 0 0
\(281\) −5.06808 −0.302336 −0.151168 0.988508i \(-0.548304\pi\)
−0.151168 + 0.988508i \(0.548304\pi\)
\(282\) 0 0
\(283\) −25.6354 −1.52387 −0.761933 0.647656i \(-0.775749\pi\)
−0.761933 + 0.647656i \(0.775749\pi\)
\(284\) 0 0
\(285\) 0.0848183 0.00502420
\(286\) 0 0
\(287\) −6.84847 −0.404252
\(288\) 0 0
\(289\) 18.5367 1.09039
\(290\) 0 0
\(291\) −4.77565 −0.279954
\(292\) 0 0
\(293\) 29.4704 1.72168 0.860838 0.508879i \(-0.169940\pi\)
0.860838 + 0.508879i \(0.169940\pi\)
\(294\) 0 0
\(295\) −1.48312 −0.0863507
\(296\) 0 0
\(297\) −1.69982 −0.0986333
\(298\) 0 0
\(299\) −1.63059 −0.0942994
\(300\) 0 0
\(301\) 2.08216 0.120014
\(302\) 0 0
\(303\) −3.83940 −0.220568
\(304\) 0 0
\(305\) 1.65861 0.0949719
\(306\) 0 0
\(307\) 23.1581 1.32170 0.660851 0.750517i \(-0.270196\pi\)
0.660851 + 0.750517i \(0.270196\pi\)
\(308\) 0 0
\(309\) −2.29802 −0.130730
\(310\) 0 0
\(311\) 3.49999 0.198466 0.0992330 0.995064i \(-0.468361\pi\)
0.0992330 + 0.995064i \(0.468361\pi\)
\(312\) 0 0
\(313\) 12.1931 0.689197 0.344598 0.938750i \(-0.388015\pi\)
0.344598 + 0.938750i \(0.388015\pi\)
\(314\) 0 0
\(315\) 0.336300 0.0189484
\(316\) 0 0
\(317\) −30.6592 −1.72199 −0.860997 0.508610i \(-0.830159\pi\)
−0.860997 + 0.508610i \(0.830159\pi\)
\(318\) 0 0
\(319\) 4.27397 0.239296
\(320\) 0 0
\(321\) −3.99031 −0.222717
\(322\) 0 0
\(323\) −15.2702 −0.849658
\(324\) 0 0
\(325\) 4.98671 0.276613
\(326\) 0 0
\(327\) 2.21541 0.122512
\(328\) 0 0
\(329\) −10.6507 −0.587191
\(330\) 0 0
\(331\) −13.4671 −0.740217 −0.370109 0.928988i \(-0.620680\pi\)
−0.370109 + 0.928988i \(0.620680\pi\)
\(332\) 0 0
\(333\) −11.1671 −0.611956
\(334\) 0 0
\(335\) 0.779113 0.0425675
\(336\) 0 0
\(337\) 14.7100 0.801306 0.400653 0.916230i \(-0.368783\pi\)
0.400653 + 0.916230i \(0.368783\pi\)
\(338\) 0 0
\(339\) −3.03901 −0.165056
\(340\) 0 0
\(341\) −9.90455 −0.536362
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0.0539917 0.00290681
\(346\) 0 0
\(347\) 16.0242 0.860224 0.430112 0.902775i \(-0.358474\pi\)
0.430112 + 0.902775i \(0.358474\pi\)
\(348\) 0 0
\(349\) −32.2852 −1.72819 −0.864095 0.503330i \(-0.832108\pi\)
−0.864095 + 0.503330i \(0.832108\pi\)
\(350\) 0 0
\(351\) −1.69982 −0.0907294
\(352\) 0 0
\(353\) −33.2173 −1.76798 −0.883990 0.467505i \(-0.845153\pi\)
−0.883990 + 0.467505i \(0.845153\pi\)
\(354\) 0 0
\(355\) 0.748335 0.0397175
\(356\) 0 0
\(357\) 1.71239 0.0906294
\(358\) 0 0
\(359\) 5.32488 0.281037 0.140518 0.990078i \(-0.455123\pi\)
0.140518 + 0.990078i \(0.455123\pi\)
\(360\) 0 0
\(361\) −12.4383 −0.654649
\(362\) 0 0
\(363\) −0.287253 −0.0150769
\(364\) 0 0
\(365\) 1.45527 0.0761723
\(366\) 0 0
\(367\) 10.4334 0.544621 0.272310 0.962209i \(-0.412212\pi\)
0.272310 + 0.962209i \(0.412212\pi\)
\(368\) 0 0
\(369\) 19.9803 1.04013
\(370\) 0 0
\(371\) 13.3842 0.694875
\(372\) 0 0
\(373\) 11.5332 0.597167 0.298583 0.954384i \(-0.403486\pi\)
0.298583 + 0.954384i \(0.403486\pi\)
\(374\) 0 0
\(375\) −0.330678 −0.0170761
\(376\) 0 0
\(377\) 4.27397 0.220120
\(378\) 0 0
\(379\) 14.4503 0.742261 0.371131 0.928581i \(-0.378970\pi\)
0.371131 + 0.928581i \(0.378970\pi\)
\(380\) 0 0
\(381\) 1.79544 0.0919830
\(382\) 0 0
\(383\) 8.20043 0.419023 0.209511 0.977806i \(-0.432813\pi\)
0.209511 + 0.977806i \(0.432813\pi\)
\(384\) 0 0
\(385\) 0.115270 0.00587473
\(386\) 0 0
\(387\) −6.07467 −0.308793
\(388\) 0 0
\(389\) 24.8649 1.26070 0.630351 0.776310i \(-0.282911\pi\)
0.630351 + 0.776310i \(0.282911\pi\)
\(390\) 0 0
\(391\) −9.72037 −0.491580
\(392\) 0 0
\(393\) −5.13562 −0.259058
\(394\) 0 0
\(395\) 0.365273 0.0183789
\(396\) 0 0
\(397\) 24.0136 1.20521 0.602604 0.798040i \(-0.294130\pi\)
0.602604 + 0.798040i \(0.294130\pi\)
\(398\) 0 0
\(399\) −0.735820 −0.0368371
\(400\) 0 0
\(401\) 1.76568 0.0881740 0.0440870 0.999028i \(-0.485962\pi\)
0.0440870 + 0.999028i \(0.485962\pi\)
\(402\) 0 0
\(403\) −9.90455 −0.493381
\(404\) 0 0
\(405\) −0.952616 −0.0473359
\(406\) 0 0
\(407\) −3.82766 −0.189730
\(408\) 0 0
\(409\) 27.9268 1.38089 0.690445 0.723385i \(-0.257415\pi\)
0.690445 + 0.723385i \(0.257415\pi\)
\(410\) 0 0
\(411\) −4.56863 −0.225354
\(412\) 0 0
\(413\) 12.8664 0.633117
\(414\) 0 0
\(415\) −0.324830 −0.0159453
\(416\) 0 0
\(417\) −0.475701 −0.0232952
\(418\) 0 0
\(419\) 11.8510 0.578961 0.289481 0.957184i \(-0.406517\pi\)
0.289481 + 0.957184i \(0.406517\pi\)
\(420\) 0 0
\(421\) −11.9756 −0.583654 −0.291827 0.956471i \(-0.594263\pi\)
−0.291827 + 0.956471i \(0.594263\pi\)
\(422\) 0 0
\(423\) 31.0732 1.51083
\(424\) 0 0
\(425\) 29.7271 1.44198
\(426\) 0 0
\(427\) −14.3889 −0.696327
\(428\) 0 0
\(429\) −0.287253 −0.0138687
\(430\) 0 0
\(431\) 1.65137 0.0795438 0.0397719 0.999209i \(-0.487337\pi\)
0.0397719 + 0.999209i \(0.487337\pi\)
\(432\) 0 0
\(433\) 29.2014 1.40333 0.701665 0.712507i \(-0.252440\pi\)
0.701665 + 0.712507i \(0.252440\pi\)
\(434\) 0 0
\(435\) −0.141519 −0.00678530
\(436\) 0 0
\(437\) 4.17687 0.199807
\(438\) 0 0
\(439\) 24.1437 1.15231 0.576157 0.817339i \(-0.304552\pi\)
0.576157 + 0.817339i \(0.304552\pi\)
\(440\) 0 0
\(441\) −2.91749 −0.138928
\(442\) 0 0
\(443\) 21.6224 1.02731 0.513656 0.857996i \(-0.328291\pi\)
0.513656 + 0.857996i \(0.328291\pi\)
\(444\) 0 0
\(445\) −1.58445 −0.0751101
\(446\) 0 0
\(447\) −3.03436 −0.143520
\(448\) 0 0
\(449\) −8.90848 −0.420417 −0.210209 0.977657i \(-0.567414\pi\)
−0.210209 + 0.977657i \(0.567414\pi\)
\(450\) 0 0
\(451\) 6.84847 0.322482
\(452\) 0 0
\(453\) 6.29929 0.295967
\(454\) 0 0
\(455\) 0.115270 0.00540396
\(456\) 0 0
\(457\) 40.0334 1.87269 0.936343 0.351087i \(-0.114188\pi\)
0.936343 + 0.351087i \(0.114188\pi\)
\(458\) 0 0
\(459\) −10.1331 −0.472970
\(460\) 0 0
\(461\) 1.99114 0.0927365 0.0463682 0.998924i \(-0.485235\pi\)
0.0463682 + 0.998924i \(0.485235\pi\)
\(462\) 0 0
\(463\) −26.1779 −1.21659 −0.608296 0.793710i \(-0.708147\pi\)
−0.608296 + 0.793710i \(0.708147\pi\)
\(464\) 0 0
\(465\) 0.327957 0.0152087
\(466\) 0 0
\(467\) 3.13824 0.145220 0.0726102 0.997360i \(-0.476867\pi\)
0.0726102 + 0.997360i \(0.476867\pi\)
\(468\) 0 0
\(469\) −6.75900 −0.312102
\(470\) 0 0
\(471\) 5.17391 0.238401
\(472\) 0 0
\(473\) −2.08216 −0.0957378
\(474\) 0 0
\(475\) −12.7738 −0.586104
\(476\) 0 0
\(477\) −39.0483 −1.78790
\(478\) 0 0
\(479\) 4.74038 0.216593 0.108297 0.994119i \(-0.465460\pi\)
0.108297 + 0.994119i \(0.465460\pi\)
\(480\) 0 0
\(481\) −3.82766 −0.174526
\(482\) 0 0
\(483\) −0.468391 −0.0213125
\(484\) 0 0
\(485\) −1.91640 −0.0870192
\(486\) 0 0
\(487\) 35.1732 1.59385 0.796924 0.604079i \(-0.206459\pi\)
0.796924 + 0.604079i \(0.206459\pi\)
\(488\) 0 0
\(489\) 4.47798 0.202501
\(490\) 0 0
\(491\) −24.1591 −1.09028 −0.545142 0.838344i \(-0.683524\pi\)
−0.545142 + 0.838344i \(0.683524\pi\)
\(492\) 0 0
\(493\) 25.4782 1.14748
\(494\) 0 0
\(495\) −0.336300 −0.0151156
\(496\) 0 0
\(497\) −6.49199 −0.291206
\(498\) 0 0
\(499\) −27.5404 −1.23288 −0.616438 0.787404i \(-0.711425\pi\)
−0.616438 + 0.787404i \(0.711425\pi\)
\(500\) 0 0
\(501\) 1.94344 0.0868265
\(502\) 0 0
\(503\) −19.5891 −0.873435 −0.436717 0.899599i \(-0.643859\pi\)
−0.436717 + 0.899599i \(0.643859\pi\)
\(504\) 0 0
\(505\) −1.54069 −0.0685600
\(506\) 0 0
\(507\) −0.287253 −0.0127574
\(508\) 0 0
\(509\) 30.2158 1.33929 0.669645 0.742681i \(-0.266446\pi\)
0.669645 + 0.742681i \(0.266446\pi\)
\(510\) 0 0
\(511\) −12.6248 −0.558489
\(512\) 0 0
\(513\) 4.35420 0.192243
\(514\) 0 0
\(515\) −0.922164 −0.0406354
\(516\) 0 0
\(517\) 10.6507 0.468417
\(518\) 0 0
\(519\) −0.491371 −0.0215688
\(520\) 0 0
\(521\) −26.3725 −1.15540 −0.577700 0.816249i \(-0.696050\pi\)
−0.577700 + 0.816249i \(0.696050\pi\)
\(522\) 0 0
\(523\) 1.77017 0.0774041 0.0387021 0.999251i \(-0.487678\pi\)
0.0387021 + 0.999251i \(0.487678\pi\)
\(524\) 0 0
\(525\) 1.43245 0.0625172
\(526\) 0 0
\(527\) −59.0437 −2.57198
\(528\) 0 0
\(529\) −20.3412 −0.884399
\(530\) 0 0
\(531\) −37.5377 −1.62900
\(532\) 0 0
\(533\) 6.84847 0.296640
\(534\) 0 0
\(535\) −1.60125 −0.0692282
\(536\) 0 0
\(537\) −2.53496 −0.109392
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 27.6239 1.18764 0.593822 0.804597i \(-0.297618\pi\)
0.593822 + 0.804597i \(0.297618\pi\)
\(542\) 0 0
\(543\) −1.69089 −0.0725631
\(544\) 0 0
\(545\) 0.889011 0.0380810
\(546\) 0 0
\(547\) −22.9165 −0.979839 −0.489919 0.871768i \(-0.662974\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(548\) 0 0
\(549\) 41.9794 1.79164
\(550\) 0 0
\(551\) −10.9481 −0.466404
\(552\) 0 0
\(553\) −3.16884 −0.134753
\(554\) 0 0
\(555\) 0.126741 0.00537984
\(556\) 0 0
\(557\) 14.8411 0.628838 0.314419 0.949284i \(-0.398190\pi\)
0.314419 + 0.949284i \(0.398190\pi\)
\(558\) 0 0
\(559\) −2.08216 −0.0880659
\(560\) 0 0
\(561\) −1.71239 −0.0722972
\(562\) 0 0
\(563\) −10.9507 −0.461516 −0.230758 0.973011i \(-0.574121\pi\)
−0.230758 + 0.973011i \(0.574121\pi\)
\(564\) 0 0
\(565\) −1.21951 −0.0513052
\(566\) 0 0
\(567\) 8.26418 0.347063
\(568\) 0 0
\(569\) −2.51093 −0.105264 −0.0526319 0.998614i \(-0.516761\pi\)
−0.0526319 + 0.998614i \(0.516761\pi\)
\(570\) 0 0
\(571\) 12.8918 0.539504 0.269752 0.962930i \(-0.413058\pi\)
0.269752 + 0.962930i \(0.413058\pi\)
\(572\) 0 0
\(573\) −4.48178 −0.187229
\(574\) 0 0
\(575\) −8.13128 −0.339098
\(576\) 0 0
\(577\) 23.1617 0.964235 0.482118 0.876107i \(-0.339868\pi\)
0.482118 + 0.876107i \(0.339868\pi\)
\(578\) 0 0
\(579\) −4.00715 −0.166531
\(580\) 0 0
\(581\) 2.81798 0.116909
\(582\) 0 0
\(583\) −13.3842 −0.554319
\(584\) 0 0
\(585\) −0.336300 −0.0139043
\(586\) 0 0
\(587\) 2.21369 0.0913688 0.0456844 0.998956i \(-0.485453\pi\)
0.0456844 + 0.998956i \(0.485453\pi\)
\(588\) 0 0
\(589\) 25.3713 1.04540
\(590\) 0 0
\(591\) −1.33021 −0.0547176
\(592\) 0 0
\(593\) 4.49384 0.184540 0.0922699 0.995734i \(-0.470588\pi\)
0.0922699 + 0.995734i \(0.470588\pi\)
\(594\) 0 0
\(595\) 0.687158 0.0281707
\(596\) 0 0
\(597\) 3.61561 0.147977
\(598\) 0 0
\(599\) 35.3870 1.44587 0.722936 0.690915i \(-0.242792\pi\)
0.722936 + 0.690915i \(0.242792\pi\)
\(600\) 0 0
\(601\) 16.6321 0.678437 0.339219 0.940708i \(-0.389837\pi\)
0.339219 + 0.940708i \(0.389837\pi\)
\(602\) 0 0
\(603\) 19.7193 0.803032
\(604\) 0 0
\(605\) −0.115270 −0.00468641
\(606\) 0 0
\(607\) −37.8146 −1.53485 −0.767423 0.641141i \(-0.778461\pi\)
−0.767423 + 0.641141i \(0.778461\pi\)
\(608\) 0 0
\(609\) 1.22771 0.0497493
\(610\) 0 0
\(611\) 10.6507 0.430881
\(612\) 0 0
\(613\) −31.1614 −1.25860 −0.629298 0.777164i \(-0.716658\pi\)
−0.629298 + 0.777164i \(0.716658\pi\)
\(614\) 0 0
\(615\) −0.226765 −0.00914405
\(616\) 0 0
\(617\) −4.88500 −0.196663 −0.0983314 0.995154i \(-0.531351\pi\)
−0.0983314 + 0.995154i \(0.531351\pi\)
\(618\) 0 0
\(619\) 16.2956 0.654976 0.327488 0.944855i \(-0.393798\pi\)
0.327488 + 0.944855i \(0.393798\pi\)
\(620\) 0 0
\(621\) 2.77170 0.111224
\(622\) 0 0
\(623\) 13.7455 0.550702
\(624\) 0 0
\(625\) 24.8009 0.992035
\(626\) 0 0
\(627\) 0.735820 0.0293858
\(628\) 0 0
\(629\) −22.8177 −0.909802
\(630\) 0 0
\(631\) −21.0675 −0.838685 −0.419343 0.907828i \(-0.637739\pi\)
−0.419343 + 0.907828i \(0.637739\pi\)
\(632\) 0 0
\(633\) −3.36133 −0.133601
\(634\) 0 0
\(635\) 0.720482 0.0285915
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 18.9403 0.749266
\(640\) 0 0
\(641\) −40.4302 −1.59690 −0.798448 0.602064i \(-0.794345\pi\)
−0.798448 + 0.602064i \(0.794345\pi\)
\(642\) 0 0
\(643\) 23.7462 0.936460 0.468230 0.883607i \(-0.344892\pi\)
0.468230 + 0.883607i \(0.344892\pi\)
\(644\) 0 0
\(645\) 0.0689440 0.00271467
\(646\) 0 0
\(647\) 39.1410 1.53879 0.769396 0.638772i \(-0.220557\pi\)
0.769396 + 0.638772i \(0.220557\pi\)
\(648\) 0 0
\(649\) −12.8664 −0.505052
\(650\) 0 0
\(651\) −2.84511 −0.111509
\(652\) 0 0
\(653\) 24.3591 0.953246 0.476623 0.879108i \(-0.341861\pi\)
0.476623 + 0.879108i \(0.341861\pi\)
\(654\) 0 0
\(655\) −2.06085 −0.0805241
\(656\) 0 0
\(657\) 36.8327 1.43698
\(658\) 0 0
\(659\) 6.56981 0.255924 0.127962 0.991779i \(-0.459157\pi\)
0.127962 + 0.991779i \(0.459157\pi\)
\(660\) 0 0
\(661\) 36.2255 1.40901 0.704504 0.709700i \(-0.251169\pi\)
0.704504 + 0.709700i \(0.251169\pi\)
\(662\) 0 0
\(663\) −1.71239 −0.0665038
\(664\) 0 0
\(665\) −0.295274 −0.0114502
\(666\) 0 0
\(667\) −6.96908 −0.269844
\(668\) 0 0
\(669\) −5.05935 −0.195606
\(670\) 0 0
\(671\) 14.3889 0.555477
\(672\) 0 0
\(673\) −36.2004 −1.39542 −0.697712 0.716378i \(-0.745799\pi\)
−0.697712 + 0.716378i \(0.745799\pi\)
\(674\) 0 0
\(675\) −8.47649 −0.326260
\(676\) 0 0
\(677\) −19.8264 −0.761992 −0.380996 0.924577i \(-0.624419\pi\)
−0.380996 + 0.924577i \(0.624419\pi\)
\(678\) 0 0
\(679\) 16.6252 0.638018
\(680\) 0 0
\(681\) 5.86730 0.224835
\(682\) 0 0
\(683\) −17.5945 −0.673235 −0.336617 0.941641i \(-0.609283\pi\)
−0.336617 + 0.941641i \(0.609283\pi\)
\(684\) 0 0
\(685\) −1.83332 −0.0700477
\(686\) 0 0
\(687\) 1.12203 0.0428081
\(688\) 0 0
\(689\) −13.3842 −0.509899
\(690\) 0 0
\(691\) −5.38560 −0.204878 −0.102439 0.994739i \(-0.532665\pi\)
−0.102439 + 0.994739i \(0.532665\pi\)
\(692\) 0 0
\(693\) 2.91749 0.110826
\(694\) 0 0
\(695\) −0.190892 −0.00724094
\(696\) 0 0
\(697\) 40.8256 1.54638
\(698\) 0 0
\(699\) −0.0295168 −0.00111643
\(700\) 0 0
\(701\) −0.982549 −0.0371104 −0.0185552 0.999828i \(-0.505907\pi\)
−0.0185552 + 0.999828i \(0.505907\pi\)
\(702\) 0 0
\(703\) 9.80484 0.369797
\(704\) 0 0
\(705\) −0.352663 −0.0132821
\(706\) 0 0
\(707\) 13.3659 0.502677
\(708\) 0 0
\(709\) −22.1721 −0.832689 −0.416344 0.909207i \(-0.636689\pi\)
−0.416344 + 0.909207i \(0.636689\pi\)
\(710\) 0 0
\(711\) 9.24503 0.346716
\(712\) 0 0
\(713\) 16.1503 0.604832
\(714\) 0 0
\(715\) −0.115270 −0.00431087
\(716\) 0 0
\(717\) −2.97634 −0.111153
\(718\) 0 0
\(719\) 28.5900 1.06623 0.533114 0.846043i \(-0.321022\pi\)
0.533114 + 0.846043i \(0.321022\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) 8.09626 0.301103
\(724\) 0 0
\(725\) 21.3130 0.791546
\(726\) 0 0
\(727\) 42.1549 1.56344 0.781719 0.623631i \(-0.214343\pi\)
0.781719 + 0.623631i \(0.214343\pi\)
\(728\) 0 0
\(729\) −22.6458 −0.838733
\(730\) 0 0
\(731\) −12.4123 −0.459086
\(732\) 0 0
\(733\) 42.0529 1.55326 0.776629 0.629958i \(-0.216928\pi\)
0.776629 + 0.629958i \(0.216928\pi\)
\(734\) 0 0
\(735\) 0.0331118 0.00122135
\(736\) 0 0
\(737\) 6.75900 0.248971
\(738\) 0 0
\(739\) 6.65950 0.244974 0.122487 0.992470i \(-0.460913\pi\)
0.122487 + 0.992470i \(0.460913\pi\)
\(740\) 0 0
\(741\) 0.735820 0.0270310
\(742\) 0 0
\(743\) −49.3683 −1.81115 −0.905573 0.424190i \(-0.860559\pi\)
−0.905573 + 0.424190i \(0.860559\pi\)
\(744\) 0 0
\(745\) −1.21765 −0.0446111
\(746\) 0 0
\(747\) −8.22141 −0.300806
\(748\) 0 0
\(749\) 13.8913 0.507576
\(750\) 0 0
\(751\) 31.5732 1.15212 0.576061 0.817406i \(-0.304589\pi\)
0.576061 + 0.817406i \(0.304589\pi\)
\(752\) 0 0
\(753\) 1.54440 0.0562811
\(754\) 0 0
\(755\) 2.52781 0.0919966
\(756\) 0 0
\(757\) −49.8434 −1.81159 −0.905795 0.423717i \(-0.860725\pi\)
−0.905795 + 0.423717i \(0.860725\pi\)
\(758\) 0 0
\(759\) 0.468391 0.0170015
\(760\) 0 0
\(761\) 31.7809 1.15205 0.576027 0.817430i \(-0.304602\pi\)
0.576027 + 0.817430i \(0.304602\pi\)
\(762\) 0 0
\(763\) −7.71239 −0.279207
\(764\) 0 0
\(765\) −2.00477 −0.0724827
\(766\) 0 0
\(767\) −12.8664 −0.464581
\(768\) 0 0
\(769\) 12.0128 0.433193 0.216597 0.976261i \(-0.430504\pi\)
0.216597 + 0.976261i \(0.430504\pi\)
\(770\) 0 0
\(771\) −4.36387 −0.157161
\(772\) 0 0
\(773\) −2.32357 −0.0835731 −0.0417865 0.999127i \(-0.513305\pi\)
−0.0417865 + 0.999127i \(0.513305\pi\)
\(774\) 0 0
\(775\) −49.3912 −1.77418
\(776\) 0 0
\(777\) −1.09951 −0.0394446
\(778\) 0 0
\(779\) −17.5429 −0.628539
\(780\) 0 0
\(781\) 6.49199 0.232302
\(782\) 0 0
\(783\) −7.26495 −0.259628
\(784\) 0 0
\(785\) 2.07621 0.0741033
\(786\) 0 0
\(787\) 26.6235 0.949024 0.474512 0.880249i \(-0.342625\pi\)
0.474512 + 0.880249i \(0.342625\pi\)
\(788\) 0 0
\(789\) −5.12884 −0.182592
\(790\) 0 0
\(791\) 10.5796 0.376166
\(792\) 0 0
\(793\) 14.3889 0.510964
\(794\) 0 0
\(795\) 0.443176 0.0157178
\(796\) 0 0
\(797\) 20.3246 0.719933 0.359967 0.932965i \(-0.382788\pi\)
0.359967 + 0.932965i \(0.382788\pi\)
\(798\) 0 0
\(799\) 63.4916 2.24617
\(800\) 0 0
\(801\) −40.1023 −1.41695
\(802\) 0 0
\(803\) 12.6248 0.445520
\(804\) 0 0
\(805\) −0.187959 −0.00662467
\(806\) 0 0
\(807\) −3.06885 −0.108029
\(808\) 0 0
\(809\) 17.0947 0.601019 0.300509 0.953779i \(-0.402843\pi\)
0.300509 + 0.953779i \(0.402843\pi\)
\(810\) 0 0
\(811\) −17.5207 −0.615237 −0.307618 0.951510i \(-0.599532\pi\)
−0.307618 + 0.951510i \(0.599532\pi\)
\(812\) 0 0
\(813\) −7.66205 −0.268720
\(814\) 0 0
\(815\) 1.79695 0.0629444
\(816\) 0 0
\(817\) 5.33360 0.186599
\(818\) 0 0
\(819\) 2.91749 0.101945
\(820\) 0 0
\(821\) 24.1724 0.843622 0.421811 0.906684i \(-0.361395\pi\)
0.421811 + 0.906684i \(0.361395\pi\)
\(822\) 0 0
\(823\) −26.6302 −0.928270 −0.464135 0.885764i \(-0.653635\pi\)
−0.464135 + 0.885764i \(0.653635\pi\)
\(824\) 0 0
\(825\) −1.43245 −0.0498714
\(826\) 0 0
\(827\) 33.1017 1.15106 0.575529 0.817782i \(-0.304796\pi\)
0.575529 + 0.817782i \(0.304796\pi\)
\(828\) 0 0
\(829\) 10.8905 0.378243 0.189121 0.981954i \(-0.439436\pi\)
0.189121 + 0.981954i \(0.439436\pi\)
\(830\) 0 0
\(831\) 1.51057 0.0524009
\(832\) 0 0
\(833\) −5.96127 −0.206546
\(834\) 0 0
\(835\) 0.779874 0.0269886
\(836\) 0 0
\(837\) 16.8359 0.581934
\(838\) 0 0
\(839\) −6.72858 −0.232297 −0.116148 0.993232i \(-0.537055\pi\)
−0.116148 + 0.993232i \(0.537055\pi\)
\(840\) 0 0
\(841\) −10.7332 −0.370111
\(842\) 0 0
\(843\) 1.45582 0.0501412
\(844\) 0 0
\(845\) −0.115270 −0.00396542
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 7.36384 0.252726
\(850\) 0 0
\(851\) 6.24134 0.213950
\(852\) 0 0
\(853\) −22.3888 −0.766579 −0.383289 0.923628i \(-0.625209\pi\)
−0.383289 + 0.923628i \(0.625209\pi\)
\(854\) 0 0
\(855\) 0.861457 0.0294612
\(856\) 0 0
\(857\) −20.3039 −0.693567 −0.346784 0.937945i \(-0.612726\pi\)
−0.346784 + 0.937945i \(0.612726\pi\)
\(858\) 0 0
\(859\) −11.6094 −0.396107 −0.198054 0.980191i \(-0.563462\pi\)
−0.198054 + 0.980191i \(0.563462\pi\)
\(860\) 0 0
\(861\) 1.96724 0.0670435
\(862\) 0 0
\(863\) −50.6846 −1.72533 −0.862663 0.505780i \(-0.831205\pi\)
−0.862663 + 0.505780i \(0.831205\pi\)
\(864\) 0 0
\(865\) −0.197180 −0.00670432
\(866\) 0 0
\(867\) −5.32472 −0.180837
\(868\) 0 0
\(869\) 3.16884 0.107495
\(870\) 0 0
\(871\) 6.75900 0.229020
\(872\) 0 0
\(873\) −48.5039 −1.64161
\(874\) 0 0
\(875\) 1.15117 0.0389167
\(876\) 0 0
\(877\) 19.9973 0.675260 0.337630 0.941279i \(-0.390375\pi\)
0.337630 + 0.941279i \(0.390375\pi\)
\(878\) 0 0
\(879\) −8.46545 −0.285532
\(880\) 0 0
\(881\) 5.42390 0.182736 0.0913679 0.995817i \(-0.470876\pi\)
0.0913679 + 0.995817i \(0.470876\pi\)
\(882\) 0 0
\(883\) −28.0604 −0.944306 −0.472153 0.881517i \(-0.656523\pi\)
−0.472153 + 0.881517i \(0.656523\pi\)
\(884\) 0 0
\(885\) 0.426031 0.0143209
\(886\) 0 0
\(887\) 5.44069 0.182680 0.0913402 0.995820i \(-0.470885\pi\)
0.0913402 + 0.995820i \(0.470885\pi\)
\(888\) 0 0
\(889\) −6.25037 −0.209631
\(890\) 0 0
\(891\) −8.26418 −0.276860
\(892\) 0 0
\(893\) −27.2825 −0.912975
\(894\) 0 0
\(895\) −1.01724 −0.0340027
\(896\) 0 0
\(897\) 0.468391 0.0156391
\(898\) 0 0
\(899\) −42.3317 −1.41184
\(900\) 0 0
\(901\) −79.7870 −2.65809
\(902\) 0 0
\(903\) −0.598106 −0.0199037
\(904\) 0 0
\(905\) −0.678530 −0.0225551
\(906\) 0 0
\(907\) −36.3503 −1.20699 −0.603496 0.797366i \(-0.706226\pi\)
−0.603496 + 0.797366i \(0.706226\pi\)
\(908\) 0 0
\(909\) −38.9949 −1.29338
\(910\) 0 0
\(911\) −44.9078 −1.48786 −0.743931 0.668256i \(-0.767041\pi\)
−0.743931 + 0.668256i \(0.767041\pi\)
\(912\) 0 0
\(913\) −2.81798 −0.0932615
\(914\) 0 0
\(915\) −0.476441 −0.0157507
\(916\) 0 0
\(917\) 17.8784 0.590397
\(918\) 0 0
\(919\) 18.5831 0.613000 0.306500 0.951871i \(-0.400842\pi\)
0.306500 + 0.951871i \(0.400842\pi\)
\(920\) 0 0
\(921\) −6.65223 −0.219198
\(922\) 0 0
\(923\) 6.49199 0.213687
\(924\) 0 0
\(925\) −19.0875 −0.627591
\(926\) 0 0
\(927\) −23.3399 −0.766582
\(928\) 0 0
\(929\) 27.1285 0.890057 0.445029 0.895516i \(-0.353193\pi\)
0.445029 + 0.895516i \(0.353193\pi\)
\(930\) 0 0
\(931\) 2.56157 0.0839522
\(932\) 0 0
\(933\) −1.00538 −0.0329147
\(934\) 0 0
\(935\) −0.687158 −0.0224725
\(936\) 0 0
\(937\) −5.47991 −0.179021 −0.0895104 0.995986i \(-0.528530\pi\)
−0.0895104 + 0.995986i \(0.528530\pi\)
\(938\) 0 0
\(939\) −3.50252 −0.114300
\(940\) 0 0
\(941\) −43.5989 −1.42129 −0.710643 0.703553i \(-0.751596\pi\)
−0.710643 + 0.703553i \(0.751596\pi\)
\(942\) 0 0
\(943\) −11.1670 −0.363649
\(944\) 0 0
\(945\) −0.195938 −0.00637388
\(946\) 0 0
\(947\) 18.4906 0.600865 0.300433 0.953803i \(-0.402869\pi\)
0.300433 + 0.953803i \(0.402869\pi\)
\(948\) 0 0
\(949\) 12.6248 0.409819
\(950\) 0 0
\(951\) 8.80695 0.285585
\(952\) 0 0
\(953\) 47.6508 1.54356 0.771781 0.635889i \(-0.219366\pi\)
0.771781 + 0.635889i \(0.219366\pi\)
\(954\) 0 0
\(955\) −1.79847 −0.0581972
\(956\) 0 0
\(957\) −1.22771 −0.0396862
\(958\) 0 0
\(959\) 15.9046 0.513585
\(960\) 0 0
\(961\) 67.1002 2.16452
\(962\) 0 0
\(963\) −40.5276 −1.30598
\(964\) 0 0
\(965\) −1.60801 −0.0517637
\(966\) 0 0
\(967\) 45.7793 1.47216 0.736081 0.676893i \(-0.236674\pi\)
0.736081 + 0.676893i \(0.236674\pi\)
\(968\) 0 0
\(969\) 4.38642 0.140912
\(970\) 0 0
\(971\) −19.9612 −0.640585 −0.320293 0.947319i \(-0.603781\pi\)
−0.320293 + 0.947319i \(0.603781\pi\)
\(972\) 0 0
\(973\) 1.65603 0.0530900
\(974\) 0 0
\(975\) −1.43245 −0.0458751
\(976\) 0 0
\(977\) 32.3841 1.03606 0.518029 0.855363i \(-0.326666\pi\)
0.518029 + 0.855363i \(0.326666\pi\)
\(978\) 0 0
\(979\) −13.7455 −0.439308
\(980\) 0 0
\(981\) 22.5008 0.718395
\(982\) 0 0
\(983\) 42.4144 1.35281 0.676404 0.736531i \(-0.263537\pi\)
0.676404 + 0.736531i \(0.263537\pi\)
\(984\) 0 0
\(985\) −0.533794 −0.0170081
\(986\) 0 0
\(987\) 3.05944 0.0973831
\(988\) 0 0
\(989\) 3.39514 0.107959
\(990\) 0 0
\(991\) −8.32557 −0.264470 −0.132235 0.991218i \(-0.542215\pi\)
−0.132235 + 0.991218i \(0.542215\pi\)
\(992\) 0 0
\(993\) 3.86846 0.122762
\(994\) 0 0
\(995\) 1.45089 0.0459964
\(996\) 0 0
\(997\) −40.2962 −1.27619 −0.638097 0.769956i \(-0.720278\pi\)
−0.638097 + 0.769956i \(0.720278\pi\)
\(998\) 0 0
\(999\) 6.50632 0.205851
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 \(a_p\))