Properties

Label 8016.2.a.bg.1.6
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.284022\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+0.284022 q^{5}\) \(+3.90646 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+0.284022 q^{5}\) \(+3.90646 q^{7}\) \(+1.00000 q^{9}\) \(-5.93953 q^{11}\) \(+5.62131 q^{13}\) \(-0.284022 q^{15}\) \(-0.211600 q^{17}\) \(+1.66151 q^{19}\) \(-3.90646 q^{21}\) \(+2.16524 q^{23}\) \(-4.91933 q^{25}\) \(-1.00000 q^{27}\) \(+4.18652 q^{29}\) \(+2.41173 q^{31}\) \(+5.93953 q^{33}\) \(+1.10952 q^{35}\) \(+0.0651212 q^{37}\) \(-5.62131 q^{39}\) \(+6.23450 q^{41}\) \(-2.49039 q^{43}\) \(+0.284022 q^{45}\) \(-5.97532 q^{47}\) \(+8.26040 q^{49}\) \(+0.211600 q^{51}\) \(+4.43542 q^{53}\) \(-1.68695 q^{55}\) \(-1.66151 q^{57}\) \(+3.03679 q^{59}\) \(-5.18295 q^{61}\) \(+3.90646 q^{63}\) \(+1.59657 q^{65}\) \(+5.08568 q^{67}\) \(-2.16524 q^{69}\) \(-6.06371 q^{71}\) \(+8.31501 q^{73}\) \(+4.91933 q^{75}\) \(-23.2025 q^{77}\) \(+2.87558 q^{79}\) \(+1.00000 q^{81}\) \(+5.50738 q^{83}\) \(-0.0600991 q^{85}\) \(-4.18652 q^{87}\) \(+0.660702 q^{89}\) \(+21.9594 q^{91}\) \(-2.41173 q^{93}\) \(+0.471905 q^{95}\) \(+17.4002 q^{97}\) \(-5.93953 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0.284022 0.127018 0.0635092 0.997981i \(-0.479771\pi\)
0.0635092 + 0.997981i \(0.479771\pi\)
\(6\) 0 0
\(7\) 3.90646 1.47650 0.738251 0.674526i \(-0.235652\pi\)
0.738251 + 0.674526i \(0.235652\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.93953 −1.79083 −0.895417 0.445228i \(-0.853123\pi\)
−0.895417 + 0.445228i \(0.853123\pi\)
\(12\) 0 0
\(13\) 5.62131 1.55907 0.779535 0.626358i \(-0.215455\pi\)
0.779535 + 0.626358i \(0.215455\pi\)
\(14\) 0 0
\(15\) −0.284022 −0.0733341
\(16\) 0 0
\(17\) −0.211600 −0.0513206 −0.0256603 0.999671i \(-0.508169\pi\)
−0.0256603 + 0.999671i \(0.508169\pi\)
\(18\) 0 0
\(19\) 1.66151 0.381177 0.190588 0.981670i \(-0.438960\pi\)
0.190588 + 0.981670i \(0.438960\pi\)
\(20\) 0 0
\(21\) −3.90646 −0.852459
\(22\) 0 0
\(23\) 2.16524 0.451484 0.225742 0.974187i \(-0.427519\pi\)
0.225742 + 0.974187i \(0.427519\pi\)
\(24\) 0 0
\(25\) −4.91933 −0.983866
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.18652 0.777416 0.388708 0.921361i \(-0.372921\pi\)
0.388708 + 0.921361i \(0.372921\pi\)
\(30\) 0 0
\(31\) 2.41173 0.433159 0.216580 0.976265i \(-0.430510\pi\)
0.216580 + 0.976265i \(0.430510\pi\)
\(32\) 0 0
\(33\) 5.93953 1.03394
\(34\) 0 0
\(35\) 1.10952 0.187543
\(36\) 0 0
\(37\) 0.0651212 0.0107059 0.00535293 0.999986i \(-0.498296\pi\)
0.00535293 + 0.999986i \(0.498296\pi\)
\(38\) 0 0
\(39\) −5.62131 −0.900130
\(40\) 0 0
\(41\) 6.23450 0.973666 0.486833 0.873495i \(-0.338152\pi\)
0.486833 + 0.873495i \(0.338152\pi\)
\(42\) 0 0
\(43\) −2.49039 −0.379781 −0.189891 0.981805i \(-0.560813\pi\)
−0.189891 + 0.981805i \(0.560813\pi\)
\(44\) 0 0
\(45\) 0.284022 0.0423395
\(46\) 0 0
\(47\) −5.97532 −0.871591 −0.435795 0.900046i \(-0.643533\pi\)
−0.435795 + 0.900046i \(0.643533\pi\)
\(48\) 0 0
\(49\) 8.26040 1.18006
\(50\) 0 0
\(51\) 0.211600 0.0296300
\(52\) 0 0
\(53\) 4.43542 0.609252 0.304626 0.952472i \(-0.401468\pi\)
0.304626 + 0.952472i \(0.401468\pi\)
\(54\) 0 0
\(55\) −1.68695 −0.227469
\(56\) 0 0
\(57\) −1.66151 −0.220072
\(58\) 0 0
\(59\) 3.03679 0.395357 0.197679 0.980267i \(-0.436660\pi\)
0.197679 + 0.980267i \(0.436660\pi\)
\(60\) 0 0
\(61\) −5.18295 −0.663609 −0.331804 0.943348i \(-0.607657\pi\)
−0.331804 + 0.943348i \(0.607657\pi\)
\(62\) 0 0
\(63\) 3.90646 0.492167
\(64\) 0 0
\(65\) 1.59657 0.198031
\(66\) 0 0
\(67\) 5.08568 0.621315 0.310658 0.950522i \(-0.399451\pi\)
0.310658 + 0.950522i \(0.399451\pi\)
\(68\) 0 0
\(69\) −2.16524 −0.260664
\(70\) 0 0
\(71\) −6.06371 −0.719630 −0.359815 0.933024i \(-0.617160\pi\)
−0.359815 + 0.933024i \(0.617160\pi\)
\(72\) 0 0
\(73\) 8.31501 0.973199 0.486599 0.873625i \(-0.338237\pi\)
0.486599 + 0.873625i \(0.338237\pi\)
\(74\) 0 0
\(75\) 4.91933 0.568035
\(76\) 0 0
\(77\) −23.2025 −2.64417
\(78\) 0 0
\(79\) 2.87558 0.323528 0.161764 0.986830i \(-0.448282\pi\)
0.161764 + 0.986830i \(0.448282\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 5.50738 0.604514 0.302257 0.953227i \(-0.402260\pi\)
0.302257 + 0.953227i \(0.402260\pi\)
\(84\) 0 0
\(85\) −0.0600991 −0.00651866
\(86\) 0 0
\(87\) −4.18652 −0.448842
\(88\) 0 0
\(89\) 0.660702 0.0700343 0.0350171 0.999387i \(-0.488851\pi\)
0.0350171 + 0.999387i \(0.488851\pi\)
\(90\) 0 0
\(91\) 21.9594 2.30197
\(92\) 0 0
\(93\) −2.41173 −0.250085
\(94\) 0 0
\(95\) 0.471905 0.0484164
\(96\) 0 0
\(97\) 17.4002 1.76672 0.883360 0.468694i \(-0.155275\pi\)
0.883360 + 0.468694i \(0.155275\pi\)
\(98\) 0 0
\(99\) −5.93953 −0.596945
\(100\) 0 0
\(101\) 0.510196 0.0507664 0.0253832 0.999678i \(-0.491919\pi\)
0.0253832 + 0.999678i \(0.491919\pi\)
\(102\) 0 0
\(103\) −6.73893 −0.664007 −0.332003 0.943278i \(-0.607725\pi\)
−0.332003 + 0.943278i \(0.607725\pi\)
\(104\) 0 0
\(105\) −1.10952 −0.108278
\(106\) 0 0
\(107\) −6.94201 −0.671109 −0.335555 0.942021i \(-0.608924\pi\)
−0.335555 + 0.942021i \(0.608924\pi\)
\(108\) 0 0
\(109\) −2.47553 −0.237112 −0.118556 0.992947i \(-0.537827\pi\)
−0.118556 + 0.992947i \(0.537827\pi\)
\(110\) 0 0
\(111\) −0.0651212 −0.00618104
\(112\) 0 0
\(113\) 5.81283 0.546825 0.273413 0.961897i \(-0.411848\pi\)
0.273413 + 0.961897i \(0.411848\pi\)
\(114\) 0 0
\(115\) 0.614976 0.0573468
\(116\) 0 0
\(117\) 5.62131 0.519690
\(118\) 0 0
\(119\) −0.826607 −0.0757750
\(120\) 0 0
\(121\) 24.2780 2.20709
\(122\) 0 0
\(123\) −6.23450 −0.562146
\(124\) 0 0
\(125\) −2.81731 −0.251987
\(126\) 0 0
\(127\) 9.44159 0.837806 0.418903 0.908031i \(-0.362415\pi\)
0.418903 + 0.908031i \(0.362415\pi\)
\(128\) 0 0
\(129\) 2.49039 0.219267
\(130\) 0 0
\(131\) −10.0575 −0.878731 −0.439365 0.898308i \(-0.644797\pi\)
−0.439365 + 0.898308i \(0.644797\pi\)
\(132\) 0 0
\(133\) 6.49062 0.562808
\(134\) 0 0
\(135\) −0.284022 −0.0244447
\(136\) 0 0
\(137\) 7.06922 0.603964 0.301982 0.953314i \(-0.402352\pi\)
0.301982 + 0.953314i \(0.402352\pi\)
\(138\) 0 0
\(139\) 2.77510 0.235380 0.117690 0.993050i \(-0.462451\pi\)
0.117690 + 0.993050i \(0.462451\pi\)
\(140\) 0 0
\(141\) 5.97532 0.503213
\(142\) 0 0
\(143\) −33.3879 −2.79204
\(144\) 0 0
\(145\) 1.18906 0.0987462
\(146\) 0 0
\(147\) −8.26040 −0.681306
\(148\) 0 0
\(149\) −4.33933 −0.355492 −0.177746 0.984076i \(-0.556881\pi\)
−0.177746 + 0.984076i \(0.556881\pi\)
\(150\) 0 0
\(151\) 10.7758 0.876921 0.438460 0.898751i \(-0.355524\pi\)
0.438460 + 0.898751i \(0.355524\pi\)
\(152\) 0 0
\(153\) −0.211600 −0.0171069
\(154\) 0 0
\(155\) 0.684984 0.0550192
\(156\) 0 0
\(157\) 2.05881 0.164311 0.0821554 0.996620i \(-0.473820\pi\)
0.0821554 + 0.996620i \(0.473820\pi\)
\(158\) 0 0
\(159\) −4.43542 −0.351752
\(160\) 0 0
\(161\) 8.45842 0.666617
\(162\) 0 0
\(163\) −16.7791 −1.31424 −0.657120 0.753786i \(-0.728225\pi\)
−0.657120 + 0.753786i \(0.728225\pi\)
\(164\) 0 0
\(165\) 1.68695 0.131329
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 18.5991 1.43070
\(170\) 0 0
\(171\) 1.66151 0.127059
\(172\) 0 0
\(173\) −5.76336 −0.438180 −0.219090 0.975705i \(-0.570309\pi\)
−0.219090 + 0.975705i \(0.570309\pi\)
\(174\) 0 0
\(175\) −19.2172 −1.45268
\(176\) 0 0
\(177\) −3.03679 −0.228259
\(178\) 0 0
\(179\) −24.6981 −1.84602 −0.923011 0.384774i \(-0.874279\pi\)
−0.923011 + 0.384774i \(0.874279\pi\)
\(180\) 0 0
\(181\) 3.85640 0.286644 0.143322 0.989676i \(-0.454222\pi\)
0.143322 + 0.989676i \(0.454222\pi\)
\(182\) 0 0
\(183\) 5.18295 0.383135
\(184\) 0 0
\(185\) 0.0184959 0.00135984
\(186\) 0 0
\(187\) 1.25681 0.0919067
\(188\) 0 0
\(189\) −3.90646 −0.284153
\(190\) 0 0
\(191\) 10.3499 0.748891 0.374445 0.927249i \(-0.377833\pi\)
0.374445 + 0.927249i \(0.377833\pi\)
\(192\) 0 0
\(193\) 25.4995 1.83549 0.917746 0.397169i \(-0.130007\pi\)
0.917746 + 0.397169i \(0.130007\pi\)
\(194\) 0 0
\(195\) −1.59657 −0.114333
\(196\) 0 0
\(197\) 4.63585 0.330291 0.165145 0.986269i \(-0.447191\pi\)
0.165145 + 0.986269i \(0.447191\pi\)
\(198\) 0 0
\(199\) −3.77710 −0.267752 −0.133876 0.990998i \(-0.542742\pi\)
−0.133876 + 0.990998i \(0.542742\pi\)
\(200\) 0 0
\(201\) −5.08568 −0.358716
\(202\) 0 0
\(203\) 16.3544 1.14786
\(204\) 0 0
\(205\) 1.77073 0.123673
\(206\) 0 0
\(207\) 2.16524 0.150495
\(208\) 0 0
\(209\) −9.86858 −0.682624
\(210\) 0 0
\(211\) 1.10023 0.0757431 0.0378716 0.999283i \(-0.487942\pi\)
0.0378716 + 0.999283i \(0.487942\pi\)
\(212\) 0 0
\(213\) 6.06371 0.415479
\(214\) 0 0
\(215\) −0.707326 −0.0482392
\(216\) 0 0
\(217\) 9.42132 0.639561
\(218\) 0 0
\(219\) −8.31501 −0.561876
\(220\) 0 0
\(221\) −1.18947 −0.0800125
\(222\) 0 0
\(223\) −2.73735 −0.183306 −0.0916531 0.995791i \(-0.529215\pi\)
−0.0916531 + 0.995791i \(0.529215\pi\)
\(224\) 0 0
\(225\) −4.91933 −0.327955
\(226\) 0 0
\(227\) 2.50676 0.166380 0.0831898 0.996534i \(-0.473489\pi\)
0.0831898 + 0.996534i \(0.473489\pi\)
\(228\) 0 0
\(229\) −8.95306 −0.591635 −0.295818 0.955244i \(-0.595592\pi\)
−0.295818 + 0.955244i \(0.595592\pi\)
\(230\) 0 0
\(231\) 23.2025 1.52661
\(232\) 0 0
\(233\) −5.73726 −0.375860 −0.187930 0.982182i \(-0.560178\pi\)
−0.187930 + 0.982182i \(0.560178\pi\)
\(234\) 0 0
\(235\) −1.69712 −0.110708
\(236\) 0 0
\(237\) −2.87558 −0.186789
\(238\) 0 0
\(239\) −27.2677 −1.76380 −0.881901 0.471434i \(-0.843736\pi\)
−0.881901 + 0.471434i \(0.843736\pi\)
\(240\) 0 0
\(241\) −6.56847 −0.423112 −0.211556 0.977366i \(-0.567853\pi\)
−0.211556 + 0.977366i \(0.567853\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 2.34613 0.149889
\(246\) 0 0
\(247\) 9.33986 0.594281
\(248\) 0 0
\(249\) −5.50738 −0.349016
\(250\) 0 0
\(251\) −9.28770 −0.586235 −0.293117 0.956076i \(-0.594693\pi\)
−0.293117 + 0.956076i \(0.594693\pi\)
\(252\) 0 0
\(253\) −12.8605 −0.808533
\(254\) 0 0
\(255\) 0.0600991 0.00376355
\(256\) 0 0
\(257\) 5.88100 0.366847 0.183423 0.983034i \(-0.441282\pi\)
0.183423 + 0.983034i \(0.441282\pi\)
\(258\) 0 0
\(259\) 0.254393 0.0158072
\(260\) 0 0
\(261\) 4.18652 0.259139
\(262\) 0 0
\(263\) 25.2830 1.55902 0.779509 0.626391i \(-0.215469\pi\)
0.779509 + 0.626391i \(0.215469\pi\)
\(264\) 0 0
\(265\) 1.25976 0.0773862
\(266\) 0 0
\(267\) −0.660702 −0.0404343
\(268\) 0 0
\(269\) −28.0769 −1.71188 −0.855940 0.517076i \(-0.827021\pi\)
−0.855940 + 0.517076i \(0.827021\pi\)
\(270\) 0 0
\(271\) 13.1988 0.801767 0.400884 0.916129i \(-0.368703\pi\)
0.400884 + 0.916129i \(0.368703\pi\)
\(272\) 0 0
\(273\) −21.9594 −1.32904
\(274\) 0 0
\(275\) 29.2185 1.76194
\(276\) 0 0
\(277\) 24.7372 1.48631 0.743156 0.669119i \(-0.233328\pi\)
0.743156 + 0.669119i \(0.233328\pi\)
\(278\) 0 0
\(279\) 2.41173 0.144386
\(280\) 0 0
\(281\) 10.9315 0.652119 0.326059 0.945349i \(-0.394279\pi\)
0.326059 + 0.945349i \(0.394279\pi\)
\(282\) 0 0
\(283\) −28.3015 −1.68235 −0.841174 0.540765i \(-0.818135\pi\)
−0.841174 + 0.540765i \(0.818135\pi\)
\(284\) 0 0
\(285\) −0.471905 −0.0279532
\(286\) 0 0
\(287\) 24.3548 1.43762
\(288\) 0 0
\(289\) −16.9552 −0.997366
\(290\) 0 0
\(291\) −17.4002 −1.02002
\(292\) 0 0
\(293\) 8.06024 0.470884 0.235442 0.971888i \(-0.424346\pi\)
0.235442 + 0.971888i \(0.424346\pi\)
\(294\) 0 0
\(295\) 0.862516 0.0502176
\(296\) 0 0
\(297\) 5.93953 0.344646
\(298\) 0 0
\(299\) 12.1715 0.703895
\(300\) 0 0
\(301\) −9.72861 −0.560748
\(302\) 0 0
\(303\) −0.510196 −0.0293100
\(304\) 0 0
\(305\) −1.47207 −0.0842905
\(306\) 0 0
\(307\) 28.5806 1.63118 0.815592 0.578628i \(-0.196412\pi\)
0.815592 + 0.578628i \(0.196412\pi\)
\(308\) 0 0
\(309\) 6.73893 0.383365
\(310\) 0 0
\(311\) 28.5057 1.61641 0.808205 0.588901i \(-0.200439\pi\)
0.808205 + 0.588901i \(0.200439\pi\)
\(312\) 0 0
\(313\) 30.2771 1.71136 0.855682 0.517501i \(-0.173138\pi\)
0.855682 + 0.517501i \(0.173138\pi\)
\(314\) 0 0
\(315\) 1.10952 0.0625143
\(316\) 0 0
\(317\) −27.6851 −1.55495 −0.777475 0.628914i \(-0.783500\pi\)
−0.777475 + 0.628914i \(0.783500\pi\)
\(318\) 0 0
\(319\) −24.8659 −1.39222
\(320\) 0 0
\(321\) 6.94201 0.387465
\(322\) 0 0
\(323\) −0.351576 −0.0195622
\(324\) 0 0
\(325\) −27.6531 −1.53392
\(326\) 0 0
\(327\) 2.47553 0.136897
\(328\) 0 0
\(329\) −23.3423 −1.28690
\(330\) 0 0
\(331\) 19.4216 1.06751 0.533754 0.845640i \(-0.320781\pi\)
0.533754 + 0.845640i \(0.320781\pi\)
\(332\) 0 0
\(333\) 0.0651212 0.00356862
\(334\) 0 0
\(335\) 1.44444 0.0789184
\(336\) 0 0
\(337\) 14.5405 0.792071 0.396036 0.918235i \(-0.370386\pi\)
0.396036 + 0.918235i \(0.370386\pi\)
\(338\) 0 0
\(339\) −5.81283 −0.315710
\(340\) 0 0
\(341\) −14.3245 −0.775717
\(342\) 0 0
\(343\) 4.92369 0.265854
\(344\) 0 0
\(345\) −0.614976 −0.0331092
\(346\) 0 0
\(347\) 16.7308 0.898157 0.449079 0.893492i \(-0.351752\pi\)
0.449079 + 0.893492i \(0.351752\pi\)
\(348\) 0 0
\(349\) 3.21327 0.172002 0.0860011 0.996295i \(-0.472591\pi\)
0.0860011 + 0.996295i \(0.472591\pi\)
\(350\) 0 0
\(351\) −5.62131 −0.300043
\(352\) 0 0
\(353\) −3.58189 −0.190645 −0.0953224 0.995446i \(-0.530388\pi\)
−0.0953224 + 0.995446i \(0.530388\pi\)
\(354\) 0 0
\(355\) −1.72223 −0.0914063
\(356\) 0 0
\(357\) 0.826607 0.0437487
\(358\) 0 0
\(359\) 36.0308 1.90163 0.950815 0.309758i \(-0.100248\pi\)
0.950815 + 0.309758i \(0.100248\pi\)
\(360\) 0 0
\(361\) −16.2394 −0.854704
\(362\) 0 0
\(363\) −24.2780 −1.27426
\(364\) 0 0
\(365\) 2.36164 0.123614
\(366\) 0 0
\(367\) 9.14426 0.477326 0.238663 0.971102i \(-0.423291\pi\)
0.238663 + 0.971102i \(0.423291\pi\)
\(368\) 0 0
\(369\) 6.23450 0.324555
\(370\) 0 0
\(371\) 17.3268 0.899562
\(372\) 0 0
\(373\) 9.07464 0.469867 0.234934 0.972011i \(-0.424513\pi\)
0.234934 + 0.972011i \(0.424513\pi\)
\(374\) 0 0
\(375\) 2.81731 0.145485
\(376\) 0 0
\(377\) 23.5337 1.21205
\(378\) 0 0
\(379\) −24.4853 −1.25773 −0.628863 0.777516i \(-0.716480\pi\)
−0.628863 + 0.777516i \(0.716480\pi\)
\(380\) 0 0
\(381\) −9.44159 −0.483707
\(382\) 0 0
\(383\) −2.13348 −0.109016 −0.0545078 0.998513i \(-0.517359\pi\)
−0.0545078 + 0.998513i \(0.517359\pi\)
\(384\) 0 0
\(385\) −6.59001 −0.335858
\(386\) 0 0
\(387\) −2.49039 −0.126594
\(388\) 0 0
\(389\) 27.5348 1.39607 0.698034 0.716064i \(-0.254058\pi\)
0.698034 + 0.716064i \(0.254058\pi\)
\(390\) 0 0
\(391\) −0.458166 −0.0231704
\(392\) 0 0
\(393\) 10.0575 0.507336
\(394\) 0 0
\(395\) 0.816726 0.0410939
\(396\) 0 0
\(397\) 1.61900 0.0812553 0.0406277 0.999174i \(-0.487064\pi\)
0.0406277 + 0.999174i \(0.487064\pi\)
\(398\) 0 0
\(399\) −6.49062 −0.324937
\(400\) 0 0
\(401\) −15.0026 −0.749193 −0.374597 0.927188i \(-0.622219\pi\)
−0.374597 + 0.927188i \(0.622219\pi\)
\(402\) 0 0
\(403\) 13.5571 0.675326
\(404\) 0 0
\(405\) 0.284022 0.0141132
\(406\) 0 0
\(407\) −0.386789 −0.0191724
\(408\) 0 0
\(409\) 38.1509 1.88644 0.943220 0.332168i \(-0.107780\pi\)
0.943220 + 0.332168i \(0.107780\pi\)
\(410\) 0 0
\(411\) −7.06922 −0.348699
\(412\) 0 0
\(413\) 11.8631 0.583745
\(414\) 0 0
\(415\) 1.56422 0.0767844
\(416\) 0 0
\(417\) −2.77510 −0.135897
\(418\) 0 0
\(419\) 18.3176 0.894871 0.447436 0.894316i \(-0.352337\pi\)
0.447436 + 0.894316i \(0.352337\pi\)
\(420\) 0 0
\(421\) 6.47766 0.315702 0.157851 0.987463i \(-0.449543\pi\)
0.157851 + 0.987463i \(0.449543\pi\)
\(422\) 0 0
\(423\) −5.97532 −0.290530
\(424\) 0 0
\(425\) 1.04093 0.0504926
\(426\) 0 0
\(427\) −20.2470 −0.979820
\(428\) 0 0
\(429\) 33.3879 1.61198
\(430\) 0 0
\(431\) −2.77403 −0.133620 −0.0668102 0.997766i \(-0.521282\pi\)
−0.0668102 + 0.997766i \(0.521282\pi\)
\(432\) 0 0
\(433\) 11.2036 0.538411 0.269205 0.963083i \(-0.413239\pi\)
0.269205 + 0.963083i \(0.413239\pi\)
\(434\) 0 0
\(435\) −1.18906 −0.0570111
\(436\) 0 0
\(437\) 3.59757 0.172095
\(438\) 0 0
\(439\) −18.7525 −0.895007 −0.447503 0.894282i \(-0.647687\pi\)
−0.447503 + 0.894282i \(0.647687\pi\)
\(440\) 0 0
\(441\) 8.26040 0.393352
\(442\) 0 0
\(443\) 27.0953 1.28734 0.643668 0.765305i \(-0.277412\pi\)
0.643668 + 0.765305i \(0.277412\pi\)
\(444\) 0 0
\(445\) 0.187654 0.00889564
\(446\) 0 0
\(447\) 4.33933 0.205243
\(448\) 0 0
\(449\) 6.21568 0.293336 0.146668 0.989186i \(-0.453145\pi\)
0.146668 + 0.989186i \(0.453145\pi\)
\(450\) 0 0
\(451\) −37.0300 −1.74367
\(452\) 0 0
\(453\) −10.7758 −0.506290
\(454\) 0 0
\(455\) 6.23694 0.292392
\(456\) 0 0
\(457\) −6.77365 −0.316858 −0.158429 0.987370i \(-0.550643\pi\)
−0.158429 + 0.987370i \(0.550643\pi\)
\(458\) 0 0
\(459\) 0.211600 0.00987666
\(460\) 0 0
\(461\) −24.4579 −1.13912 −0.569559 0.821950i \(-0.692886\pi\)
−0.569559 + 0.821950i \(0.692886\pi\)
\(462\) 0 0
\(463\) 27.1130 1.26005 0.630023 0.776576i \(-0.283045\pi\)
0.630023 + 0.776576i \(0.283045\pi\)
\(464\) 0 0
\(465\) −0.684984 −0.0317654
\(466\) 0 0
\(467\) 11.3996 0.527509 0.263755 0.964590i \(-0.415039\pi\)
0.263755 + 0.964590i \(0.415039\pi\)
\(468\) 0 0
\(469\) 19.8670 0.917373
\(470\) 0 0
\(471\) −2.05881 −0.0948649
\(472\) 0 0
\(473\) 14.7918 0.680126
\(474\) 0 0
\(475\) −8.17352 −0.375027
\(476\) 0 0
\(477\) 4.43542 0.203084
\(478\) 0 0
\(479\) −14.3408 −0.655249 −0.327624 0.944808i \(-0.606248\pi\)
−0.327624 + 0.944808i \(0.606248\pi\)
\(480\) 0 0
\(481\) 0.366067 0.0166912
\(482\) 0 0
\(483\) −8.45842 −0.384871
\(484\) 0 0
\(485\) 4.94203 0.224406
\(486\) 0 0
\(487\) 18.0212 0.816618 0.408309 0.912844i \(-0.366119\pi\)
0.408309 + 0.912844i \(0.366119\pi\)
\(488\) 0 0
\(489\) 16.7791 0.758776
\(490\) 0 0
\(491\) 6.85437 0.309333 0.154667 0.987967i \(-0.450570\pi\)
0.154667 + 0.987967i \(0.450570\pi\)
\(492\) 0 0
\(493\) −0.885868 −0.0398975
\(494\) 0 0
\(495\) −1.68695 −0.0758230
\(496\) 0 0
\(497\) −23.6876 −1.06254
\(498\) 0 0
\(499\) −22.7551 −1.01866 −0.509329 0.860572i \(-0.670106\pi\)
−0.509329 + 0.860572i \(0.670106\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 25.9313 1.15622 0.578109 0.815960i \(-0.303791\pi\)
0.578109 + 0.815960i \(0.303791\pi\)
\(504\) 0 0
\(505\) 0.144907 0.00644827
\(506\) 0 0
\(507\) −18.5991 −0.826015
\(508\) 0 0
\(509\) −16.4159 −0.727622 −0.363811 0.931473i \(-0.618525\pi\)
−0.363811 + 0.931473i \(0.618525\pi\)
\(510\) 0 0
\(511\) 32.4822 1.43693
\(512\) 0 0
\(513\) −1.66151 −0.0733575
\(514\) 0 0
\(515\) −1.91400 −0.0843411
\(516\) 0 0
\(517\) 35.4906 1.56087
\(518\) 0 0
\(519\) 5.76336 0.252983
\(520\) 0 0
\(521\) −25.2661 −1.10693 −0.553464 0.832873i \(-0.686695\pi\)
−0.553464 + 0.832873i \(0.686695\pi\)
\(522\) 0 0
\(523\) −37.9788 −1.66070 −0.830349 0.557244i \(-0.811859\pi\)
−0.830349 + 0.557244i \(0.811859\pi\)
\(524\) 0 0
\(525\) 19.2172 0.838705
\(526\) 0 0
\(527\) −0.510323 −0.0222300
\(528\) 0 0
\(529\) −18.3117 −0.796162
\(530\) 0 0
\(531\) 3.03679 0.131786
\(532\) 0 0
\(533\) 35.0461 1.51801
\(534\) 0 0
\(535\) −1.97168 −0.0852432
\(536\) 0 0
\(537\) 24.6981 1.06580
\(538\) 0 0
\(539\) −49.0628 −2.11329
\(540\) 0 0
\(541\) −30.2348 −1.29989 −0.649947 0.759979i \(-0.725209\pi\)
−0.649947 + 0.759979i \(0.725209\pi\)
\(542\) 0 0
\(543\) −3.85640 −0.165494
\(544\) 0 0
\(545\) −0.703103 −0.0301176
\(546\) 0 0
\(547\) 31.9660 1.36677 0.683384 0.730059i \(-0.260508\pi\)
0.683384 + 0.730059i \(0.260508\pi\)
\(548\) 0 0
\(549\) −5.18295 −0.221203
\(550\) 0 0
\(551\) 6.95594 0.296333
\(552\) 0 0
\(553\) 11.2333 0.477689
\(554\) 0 0
\(555\) −0.0184959 −0.000785105 0
\(556\) 0 0
\(557\) 9.42023 0.399148 0.199574 0.979883i \(-0.436044\pi\)
0.199574 + 0.979883i \(0.436044\pi\)
\(558\) 0 0
\(559\) −13.9993 −0.592106
\(560\) 0 0
\(561\) −1.25681 −0.0530624
\(562\) 0 0
\(563\) 20.7864 0.876041 0.438020 0.898965i \(-0.355680\pi\)
0.438020 + 0.898965i \(0.355680\pi\)
\(564\) 0 0
\(565\) 1.65097 0.0694569
\(566\) 0 0
\(567\) 3.90646 0.164056
\(568\) 0 0
\(569\) −12.6387 −0.529844 −0.264922 0.964270i \(-0.585346\pi\)
−0.264922 + 0.964270i \(0.585346\pi\)
\(570\) 0 0
\(571\) 25.9073 1.08419 0.542094 0.840318i \(-0.317632\pi\)
0.542094 + 0.840318i \(0.317632\pi\)
\(572\) 0 0
\(573\) −10.3499 −0.432372
\(574\) 0 0
\(575\) −10.6515 −0.444200
\(576\) 0 0
\(577\) −4.33510 −0.180472 −0.0902362 0.995920i \(-0.528762\pi\)
−0.0902362 + 0.995920i \(0.528762\pi\)
\(578\) 0 0
\(579\) −25.4995 −1.05972
\(580\) 0 0
\(581\) 21.5143 0.892565
\(582\) 0 0
\(583\) −26.3443 −1.09107
\(584\) 0 0
\(585\) 1.59657 0.0660102
\(586\) 0 0
\(587\) 11.7232 0.483869 0.241934 0.970293i \(-0.422218\pi\)
0.241934 + 0.970293i \(0.422218\pi\)
\(588\) 0 0
\(589\) 4.00711 0.165110
\(590\) 0 0
\(591\) −4.63585 −0.190693
\(592\) 0 0
\(593\) 6.54590 0.268808 0.134404 0.990927i \(-0.457088\pi\)
0.134404 + 0.990927i \(0.457088\pi\)
\(594\) 0 0
\(595\) −0.234774 −0.00962481
\(596\) 0 0
\(597\) 3.77710 0.154587
\(598\) 0 0
\(599\) 39.9982 1.63428 0.817141 0.576438i \(-0.195558\pi\)
0.817141 + 0.576438i \(0.195558\pi\)
\(600\) 0 0
\(601\) −24.2386 −0.988714 −0.494357 0.869259i \(-0.664596\pi\)
−0.494357 + 0.869259i \(0.664596\pi\)
\(602\) 0 0
\(603\) 5.08568 0.207105
\(604\) 0 0
\(605\) 6.89547 0.280341
\(606\) 0 0
\(607\) −14.4936 −0.588279 −0.294139 0.955762i \(-0.595033\pi\)
−0.294139 + 0.955762i \(0.595033\pi\)
\(608\) 0 0
\(609\) −16.3544 −0.662715
\(610\) 0 0
\(611\) −33.5891 −1.35887
\(612\) 0 0
\(613\) 2.55905 0.103359 0.0516795 0.998664i \(-0.483543\pi\)
0.0516795 + 0.998664i \(0.483543\pi\)
\(614\) 0 0
\(615\) −1.77073 −0.0714029
\(616\) 0 0
\(617\) 27.2707 1.09788 0.548938 0.835863i \(-0.315032\pi\)
0.548938 + 0.835863i \(0.315032\pi\)
\(618\) 0 0
\(619\) 16.4994 0.663166 0.331583 0.943426i \(-0.392417\pi\)
0.331583 + 0.943426i \(0.392417\pi\)
\(620\) 0 0
\(621\) −2.16524 −0.0868881
\(622\) 0 0
\(623\) 2.58100 0.103406
\(624\) 0 0
\(625\) 23.7965 0.951859
\(626\) 0 0
\(627\) 9.86858 0.394113
\(628\) 0 0
\(629\) −0.0137797 −0.000549432 0
\(630\) 0 0
\(631\) 28.3397 1.12818 0.564092 0.825712i \(-0.309226\pi\)
0.564092 + 0.825712i \(0.309226\pi\)
\(632\) 0 0
\(633\) −1.10023 −0.0437303
\(634\) 0 0
\(635\) 2.68162 0.106417
\(636\) 0 0
\(637\) 46.4342 1.83979
\(638\) 0 0
\(639\) −6.06371 −0.239877
\(640\) 0 0
\(641\) 33.4715 1.32204 0.661022 0.750366i \(-0.270123\pi\)
0.661022 + 0.750366i \(0.270123\pi\)
\(642\) 0 0
\(643\) −1.51010 −0.0595524 −0.0297762 0.999557i \(-0.509479\pi\)
−0.0297762 + 0.999557i \(0.509479\pi\)
\(644\) 0 0
\(645\) 0.707326 0.0278509
\(646\) 0 0
\(647\) 21.6453 0.850964 0.425482 0.904967i \(-0.360105\pi\)
0.425482 + 0.904967i \(0.360105\pi\)
\(648\) 0 0
\(649\) −18.0371 −0.708019
\(650\) 0 0
\(651\) −9.42132 −0.369251
\(652\) 0 0
\(653\) 20.2062 0.790731 0.395365 0.918524i \(-0.370618\pi\)
0.395365 + 0.918524i \(0.370618\pi\)
\(654\) 0 0
\(655\) −2.85656 −0.111615
\(656\) 0 0
\(657\) 8.31501 0.324400
\(658\) 0 0
\(659\) 11.5989 0.451828 0.225914 0.974147i \(-0.427463\pi\)
0.225914 + 0.974147i \(0.427463\pi\)
\(660\) 0 0
\(661\) −44.1475 −1.71714 −0.858570 0.512697i \(-0.828646\pi\)
−0.858570 + 0.512697i \(0.828646\pi\)
\(662\) 0 0
\(663\) 1.18947 0.0461952
\(664\) 0 0
\(665\) 1.84348 0.0714869
\(666\) 0 0
\(667\) 9.06482 0.350991
\(668\) 0 0
\(669\) 2.73735 0.105832
\(670\) 0 0
\(671\) 30.7843 1.18841
\(672\) 0 0
\(673\) −21.8201 −0.841104 −0.420552 0.907269i \(-0.638164\pi\)
−0.420552 + 0.907269i \(0.638164\pi\)
\(674\) 0 0
\(675\) 4.91933 0.189345
\(676\) 0 0
\(677\) −31.8137 −1.22270 −0.611351 0.791360i \(-0.709373\pi\)
−0.611351 + 0.791360i \(0.709373\pi\)
\(678\) 0 0
\(679\) 67.9730 2.60857
\(680\) 0 0
\(681\) −2.50676 −0.0960593
\(682\) 0 0
\(683\) 27.4526 1.05045 0.525223 0.850965i \(-0.323982\pi\)
0.525223 + 0.850965i \(0.323982\pi\)
\(684\) 0 0
\(685\) 2.00781 0.0767145
\(686\) 0 0
\(687\) 8.95306 0.341581
\(688\) 0 0
\(689\) 24.9329 0.949867
\(690\) 0 0
\(691\) 23.1220 0.879603 0.439802 0.898095i \(-0.355049\pi\)
0.439802 + 0.898095i \(0.355049\pi\)
\(692\) 0 0
\(693\) −23.2025 −0.881390
\(694\) 0 0
\(695\) 0.788187 0.0298976
\(696\) 0 0
\(697\) −1.31922 −0.0499691
\(698\) 0 0
\(699\) 5.73726 0.217003
\(700\) 0 0
\(701\) 48.6779 1.83854 0.919270 0.393628i \(-0.128780\pi\)
0.919270 + 0.393628i \(0.128780\pi\)
\(702\) 0 0
\(703\) 0.108200 0.00408083
\(704\) 0 0
\(705\) 1.69712 0.0639173
\(706\) 0 0
\(707\) 1.99306 0.0749567
\(708\) 0 0
\(709\) 51.3682 1.92917 0.964587 0.263766i \(-0.0849647\pi\)
0.964587 + 0.263766i \(0.0849647\pi\)
\(710\) 0 0
\(711\) 2.87558 0.107843
\(712\) 0 0
\(713\) 5.22198 0.195565
\(714\) 0 0
\(715\) −9.48289 −0.354640
\(716\) 0 0
\(717\) 27.2677 1.01833
\(718\) 0 0
\(719\) 17.1498 0.639580 0.319790 0.947489i \(-0.396388\pi\)
0.319790 + 0.947489i \(0.396388\pi\)
\(720\) 0 0
\(721\) −26.3253 −0.980407
\(722\) 0 0
\(723\) 6.56847 0.244284
\(724\) 0 0
\(725\) −20.5949 −0.764874
\(726\) 0 0
\(727\) −12.0019 −0.445126 −0.222563 0.974918i \(-0.571442\pi\)
−0.222563 + 0.974918i \(0.571442\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.526968 0.0194906
\(732\) 0 0
\(733\) 4.00307 0.147857 0.0739285 0.997264i \(-0.476446\pi\)
0.0739285 + 0.997264i \(0.476446\pi\)
\(734\) 0 0
\(735\) −2.34613 −0.0865384
\(736\) 0 0
\(737\) −30.2066 −1.11267
\(738\) 0 0
\(739\) 34.4777 1.26828 0.634140 0.773218i \(-0.281354\pi\)
0.634140 + 0.773218i \(0.281354\pi\)
\(740\) 0 0
\(741\) −9.33986 −0.343108
\(742\) 0 0
\(743\) −26.9128 −0.987334 −0.493667 0.869651i \(-0.664344\pi\)
−0.493667 + 0.869651i \(0.664344\pi\)
\(744\) 0 0
\(745\) −1.23246 −0.0451540
\(746\) 0 0
\(747\) 5.50738 0.201505
\(748\) 0 0
\(749\) −27.1186 −0.990894
\(750\) 0 0
\(751\) 41.9616 1.53120 0.765600 0.643317i \(-0.222442\pi\)
0.765600 + 0.643317i \(0.222442\pi\)
\(752\) 0 0
\(753\) 9.28770 0.338463
\(754\) 0 0
\(755\) 3.06056 0.111385
\(756\) 0 0
\(757\) 10.7842 0.391957 0.195979 0.980608i \(-0.437212\pi\)
0.195979 + 0.980608i \(0.437212\pi\)
\(758\) 0 0
\(759\) 12.8605 0.466807
\(760\) 0 0
\(761\) −53.5138 −1.93987 −0.969936 0.243359i \(-0.921751\pi\)
−0.969936 + 0.243359i \(0.921751\pi\)
\(762\) 0 0
\(763\) −9.67053 −0.350097
\(764\) 0 0
\(765\) −0.0600991 −0.00217289
\(766\) 0 0
\(767\) 17.0708 0.616389
\(768\) 0 0
\(769\) 36.2997 1.30900 0.654501 0.756061i \(-0.272879\pi\)
0.654501 + 0.756061i \(0.272879\pi\)
\(770\) 0 0
\(771\) −5.88100 −0.211799
\(772\) 0 0
\(773\) −7.72086 −0.277700 −0.138850 0.990313i \(-0.544341\pi\)
−0.138850 + 0.990313i \(0.544341\pi\)
\(774\) 0 0
\(775\) −11.8641 −0.426171
\(776\) 0 0
\(777\) −0.254393 −0.00912631
\(778\) 0 0
\(779\) 10.3587 0.371139
\(780\) 0 0
\(781\) 36.0156 1.28874
\(782\) 0 0
\(783\) −4.18652 −0.149614
\(784\) 0 0
\(785\) 0.584747 0.0208705
\(786\) 0 0
\(787\) −37.9982 −1.35449 −0.677244 0.735758i \(-0.736826\pi\)
−0.677244 + 0.735758i \(0.736826\pi\)
\(788\) 0 0
\(789\) −25.2830 −0.900099
\(790\) 0 0
\(791\) 22.7076 0.807388
\(792\) 0 0
\(793\) −29.1350 −1.03461
\(794\) 0 0
\(795\) −1.25976 −0.0446790
\(796\) 0 0
\(797\) −3.80242 −0.134689 −0.0673443 0.997730i \(-0.521453\pi\)
−0.0673443 + 0.997730i \(0.521453\pi\)
\(798\) 0 0
\(799\) 1.26438 0.0447306
\(800\) 0 0
\(801\) 0.660702 0.0233448
\(802\) 0 0
\(803\) −49.3872 −1.74284
\(804\) 0 0
\(805\) 2.40238 0.0846726
\(806\) 0 0
\(807\) 28.0769 0.988354
\(808\) 0 0
\(809\) −33.4039 −1.17442 −0.587208 0.809436i \(-0.699773\pi\)
−0.587208 + 0.809436i \(0.699773\pi\)
\(810\) 0 0
\(811\) 36.5294 1.28272 0.641360 0.767240i \(-0.278370\pi\)
0.641360 + 0.767240i \(0.278370\pi\)
\(812\) 0 0
\(813\) −13.1988 −0.462901
\(814\) 0 0
\(815\) −4.76562 −0.166933
\(816\) 0 0
\(817\) −4.13781 −0.144764
\(818\) 0 0
\(819\) 21.9594 0.767323
\(820\) 0 0
\(821\) −13.8920 −0.484833 −0.242416 0.970172i \(-0.577940\pi\)
−0.242416 + 0.970172i \(0.577940\pi\)
\(822\) 0 0
\(823\) −22.8120 −0.795178 −0.397589 0.917564i \(-0.630153\pi\)
−0.397589 + 0.917564i \(0.630153\pi\)
\(824\) 0 0
\(825\) −29.2185 −1.01726
\(826\) 0 0
\(827\) 31.7370 1.10361 0.551803 0.833975i \(-0.313940\pi\)
0.551803 + 0.833975i \(0.313940\pi\)
\(828\) 0 0
\(829\) −16.3832 −0.569012 −0.284506 0.958674i \(-0.591830\pi\)
−0.284506 + 0.958674i \(0.591830\pi\)
\(830\) 0 0
\(831\) −24.7372 −0.858122
\(832\) 0 0
\(833\) −1.74790 −0.0605612
\(834\) 0 0
\(835\) 0.284022 0.00982898
\(836\) 0 0
\(837\) −2.41173 −0.0833616
\(838\) 0 0
\(839\) −36.5169 −1.26070 −0.630352 0.776310i \(-0.717089\pi\)
−0.630352 + 0.776310i \(0.717089\pi\)
\(840\) 0 0
\(841\) −11.4731 −0.395624
\(842\) 0 0
\(843\) −10.9315 −0.376501
\(844\) 0 0
\(845\) 5.28255 0.181725
\(846\) 0 0
\(847\) 94.8408 3.25877
\(848\) 0 0
\(849\) 28.3015 0.971304
\(850\) 0 0
\(851\) 0.141003 0.00483353
\(852\) 0 0
\(853\) 31.9108 1.09261 0.546303 0.837588i \(-0.316035\pi\)
0.546303 + 0.837588i \(0.316035\pi\)
\(854\) 0 0
\(855\) 0.471905 0.0161388
\(856\) 0 0
\(857\) 28.9696 0.989583 0.494791 0.869012i \(-0.335244\pi\)
0.494791 + 0.869012i \(0.335244\pi\)
\(858\) 0 0
\(859\) 45.7885 1.56228 0.781142 0.624354i \(-0.214638\pi\)
0.781142 + 0.624354i \(0.214638\pi\)
\(860\) 0 0
\(861\) −24.3548 −0.830010
\(862\) 0 0
\(863\) −32.1532 −1.09451 −0.547254 0.836966i \(-0.684327\pi\)
−0.547254 + 0.836966i \(0.684327\pi\)
\(864\) 0 0
\(865\) −1.63692 −0.0556569
\(866\) 0 0
\(867\) 16.9552 0.575830
\(868\) 0 0
\(869\) −17.0796 −0.579384
\(870\) 0 0
\(871\) 28.5882 0.968674
\(872\) 0 0
\(873\) 17.4002 0.588907
\(874\) 0 0
\(875\) −11.0057 −0.372060
\(876\) 0 0
\(877\) −28.5974 −0.965664 −0.482832 0.875713i \(-0.660392\pi\)
−0.482832 + 0.875713i \(0.660392\pi\)
\(878\) 0 0
\(879\) −8.06024 −0.271865
\(880\) 0 0
\(881\) 9.33502 0.314505 0.157252 0.987558i \(-0.449736\pi\)
0.157252 + 0.987558i \(0.449736\pi\)
\(882\) 0 0
\(883\) 50.0530 1.68442 0.842209 0.539151i \(-0.181255\pi\)
0.842209 + 0.539151i \(0.181255\pi\)
\(884\) 0 0
\(885\) −0.862516 −0.0289931
\(886\) 0 0
\(887\) 35.2474 1.18349 0.591746 0.806124i \(-0.298439\pi\)
0.591746 + 0.806124i \(0.298439\pi\)
\(888\) 0 0
\(889\) 36.8832 1.23702
\(890\) 0 0
\(891\) −5.93953 −0.198982
\(892\) 0 0
\(893\) −9.92806 −0.332230
\(894\) 0 0
\(895\) −7.01479 −0.234479
\(896\) 0 0
\(897\) −12.1715 −0.406394
\(898\) 0 0
\(899\) 10.0967 0.336745
\(900\) 0 0
\(901\) −0.938537 −0.0312672
\(902\) 0 0
\(903\) 9.72861 0.323748
\(904\) 0 0
\(905\) 1.09530 0.0364090
\(906\) 0 0
\(907\) −3.29975 −0.109566 −0.0547832 0.998498i \(-0.517447\pi\)
−0.0547832 + 0.998498i \(0.517447\pi\)
\(908\) 0 0
\(909\) 0.510196 0.0169221
\(910\) 0 0
\(911\) −9.05582 −0.300033 −0.150016 0.988684i \(-0.547933\pi\)
−0.150016 + 0.988684i \(0.547933\pi\)
\(912\) 0 0
\(913\) −32.7112 −1.08258
\(914\) 0 0
\(915\) 1.47207 0.0486652
\(916\) 0 0
\(917\) −39.2893 −1.29745
\(918\) 0 0
\(919\) −33.3598 −1.10044 −0.550220 0.835020i \(-0.685456\pi\)
−0.550220 + 0.835020i \(0.685456\pi\)
\(920\) 0 0
\(921\) −28.5806 −0.941764
\(922\) 0 0
\(923\) −34.0860 −1.12195
\(924\) 0 0
\(925\) −0.320353 −0.0105331
\(926\) 0 0
\(927\) −6.73893 −0.221336
\(928\) 0 0
\(929\) 15.4418 0.506628 0.253314 0.967384i \(-0.418479\pi\)
0.253314 + 0.967384i \(0.418479\pi\)
\(930\) 0 0
\(931\) 13.7247 0.449810
\(932\) 0 0
\(933\) −28.5057 −0.933235
\(934\) 0 0
\(935\) 0.356960 0.0116738
\(936\) 0 0
\(937\) −6.31490 −0.206299 −0.103149 0.994666i \(-0.532892\pi\)
−0.103149 + 0.994666i \(0.532892\pi\)
\(938\) 0 0
\(939\) −30.2771 −0.988057
\(940\) 0 0
\(941\) −29.4186 −0.959020 −0.479510 0.877536i \(-0.659186\pi\)
−0.479510 + 0.877536i \(0.659186\pi\)
\(942\) 0 0
\(943\) 13.4992 0.439595
\(944\) 0 0
\(945\) −1.10952 −0.0360926
\(946\) 0 0
\(947\) −38.6029 −1.25443 −0.627213 0.778848i \(-0.715804\pi\)
−0.627213 + 0.778848i \(0.715804\pi\)
\(948\) 0 0
\(949\) 46.7412 1.51729
\(950\) 0 0
\(951\) 27.6851 0.897751
\(952\) 0 0
\(953\) 33.7981 1.09483 0.547414 0.836862i \(-0.315612\pi\)
0.547414 + 0.836862i \(0.315612\pi\)
\(954\) 0 0
\(955\) 2.93959 0.0951229
\(956\) 0 0
\(957\) 24.8659 0.803801
\(958\) 0 0
\(959\) 27.6156 0.891754
\(960\) 0 0
\(961\) −25.1836 −0.812373
\(962\) 0 0
\(963\) −6.94201 −0.223703
\(964\) 0 0
\(965\) 7.24240 0.233141
\(966\) 0 0
\(967\) −27.6619 −0.889546 −0.444773 0.895643i \(-0.646716\pi\)
−0.444773 + 0.895643i \(0.646716\pi\)
\(968\) 0 0
\(969\) 0.351576 0.0112943
\(970\) 0 0
\(971\) −39.0471 −1.25308 −0.626540 0.779389i \(-0.715530\pi\)
−0.626540 + 0.779389i \(0.715530\pi\)
\(972\) 0 0
\(973\) 10.8408 0.347540
\(974\) 0 0
\(975\) 27.6531 0.885607
\(976\) 0 0
\(977\) −47.4175 −1.51702 −0.758509 0.651662i \(-0.774072\pi\)
−0.758509 + 0.651662i \(0.774072\pi\)
\(978\) 0 0
\(979\) −3.92426 −0.125420
\(980\) 0 0
\(981\) −2.47553 −0.0790375
\(982\) 0 0
\(983\) −27.5610 −0.879058 −0.439529 0.898228i \(-0.644855\pi\)
−0.439529 + 0.898228i \(0.644855\pi\)
\(984\) 0 0
\(985\) 1.31668 0.0419530
\(986\) 0 0
\(987\) 23.3423 0.742995
\(988\) 0 0
\(989\) −5.39230 −0.171465
\(990\) 0 0
\(991\) −32.5362 −1.03355 −0.516773 0.856122i \(-0.672867\pi\)
−0.516773 + 0.856122i \(0.672867\pi\)
\(992\) 0 0
\(993\) −19.4216 −0.616326
\(994\) 0 0
\(995\) −1.07278 −0.0340094
\(996\) 0 0
\(997\) 8.74378 0.276918 0.138459 0.990368i \(-0.455785\pi\)
0.138459 + 0.990368i \(0.455785\pi\)
\(998\) 0 0
\(999\) −0.0651212 −0.00206035
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 \(a_p\))