Properties

Label 8016.2.a.bb.1.5
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $9$
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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - 29 x^{7} - 7 x^{6} + 266 x^{5} + 69 x^{4} - 901 x^{3} - 199 x^{2} + 875 x + 391\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.529979\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.52998 q^{5} +1.05249 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.52998 q^{5} +1.05249 q^{7} +1.00000 q^{9} -0.162063 q^{11} +3.63900 q^{13} -1.52998 q^{15} +4.89726 q^{17} -1.02632 q^{19} -1.05249 q^{21} +7.59021 q^{23} -2.65917 q^{25} -1.00000 q^{27} +9.59787 q^{29} -2.68185 q^{31} +0.162063 q^{33} +1.61029 q^{35} +4.12252 q^{37} -3.63900 q^{39} -1.08012 q^{41} -2.77829 q^{43} +1.52998 q^{45} +9.50274 q^{47} -5.89226 q^{49} -4.89726 q^{51} +4.80545 q^{53} -0.247952 q^{55} +1.02632 q^{57} -8.22708 q^{59} +0.510754 q^{61} +1.05249 q^{63} +5.56759 q^{65} +0.317219 q^{67} -7.59021 q^{69} -5.83623 q^{71} +11.2379 q^{73} +2.65917 q^{75} -0.170570 q^{77} -5.59029 q^{79} +1.00000 q^{81} -4.98299 q^{83} +7.49271 q^{85} -9.59787 q^{87} -0.199333 q^{89} +3.83003 q^{91} +2.68185 q^{93} -1.57025 q^{95} -10.9371 q^{97} -0.162063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} - 7q^{11} + 6q^{13} - 9q^{15} + 7q^{17} - 2q^{19} + 2q^{21} - 19q^{23} + 22q^{25} - 9q^{27} + 13q^{29} - 12q^{31} + 7q^{33} - 4q^{35} + 15q^{37} - 6q^{39} + 18q^{41} + 6q^{43} + 9q^{45} - 25q^{47} + 19q^{49} - 7q^{51} + 17q^{53} + 3q^{55} + 2q^{57} - 3q^{59} + 14q^{61} - 2q^{63} + 14q^{65} + 4q^{67} + 19q^{69} - 17q^{71} - 20q^{73} - 22q^{75} + 14q^{77} + 8q^{79} + 9q^{81} + q^{83} + 5q^{85} - 13q^{87} + 36q^{89} + 41q^{91} + 12q^{93} - 5q^{95} + 31q^{97} - 7q^{99} + O(q^{100}) \)

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
\(5\) 1.52998 0.684227 0.342114 0.939659i \(-0.388857\pi\)
0.342114 + 0.939659i \(0.388857\pi\)
\(6\) 0 0
\(7\) 1.05249 0.397806 0.198903 0.980019i \(-0.436262\pi\)
0.198903 + 0.980019i \(0.436262\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.162063 −0.0488637 −0.0244318 0.999701i \(-0.507778\pi\)
−0.0244318 + 0.999701i \(0.507778\pi\)
\(12\) 0 0
\(13\) 3.63900 1.00928 0.504638 0.863331i \(-0.331626\pi\)
0.504638 + 0.863331i \(0.331626\pi\)
\(14\) 0 0
\(15\) −1.52998 −0.395039
\(16\) 0 0
\(17\) 4.89726 1.18776 0.593880 0.804553i \(-0.297595\pi\)
0.593880 + 0.804553i \(0.297595\pi\)
\(18\) 0 0
\(19\) −1.02632 −0.235455 −0.117727 0.993046i \(-0.537561\pi\)
−0.117727 + 0.993046i \(0.537561\pi\)
\(20\) 0 0
\(21\) −1.05249 −0.229673
\(22\) 0 0
\(23\) 7.59021 1.58267 0.791334 0.611384i \(-0.209387\pi\)
0.791334 + 0.611384i \(0.209387\pi\)
\(24\) 0 0
\(25\) −2.65917 −0.531833
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 9.59787 1.78228 0.891140 0.453729i \(-0.149906\pi\)
0.891140 + 0.453729i \(0.149906\pi\)
\(30\) 0 0
\(31\) −2.68185 −0.481675 −0.240837 0.970565i \(-0.577422\pi\)
−0.240837 + 0.970565i \(0.577422\pi\)
\(32\) 0 0
\(33\) 0.162063 0.0282115
\(34\) 0 0
\(35\) 1.61029 0.272189
\(36\) 0 0
\(37\) 4.12252 0.677738 0.338869 0.940834i \(-0.389956\pi\)
0.338869 + 0.940834i \(0.389956\pi\)
\(38\) 0 0
\(39\) −3.63900 −0.582706
\(40\) 0 0
\(41\) −1.08012 −0.168687 −0.0843433 0.996437i \(-0.526879\pi\)
−0.0843433 + 0.996437i \(0.526879\pi\)
\(42\) 0 0
\(43\) −2.77829 −0.423686 −0.211843 0.977304i \(-0.567946\pi\)
−0.211843 + 0.977304i \(0.567946\pi\)
\(44\) 0 0
\(45\) 1.52998 0.228076
\(46\) 0 0
\(47\) 9.50274 1.38612 0.693059 0.720881i \(-0.256263\pi\)
0.693059 + 0.720881i \(0.256263\pi\)
\(48\) 0 0
\(49\) −5.89226 −0.841751
\(50\) 0 0
\(51\) −4.89726 −0.685754
\(52\) 0 0
\(53\) 4.80545 0.660080 0.330040 0.943967i \(-0.392938\pi\)
0.330040 + 0.943967i \(0.392938\pi\)
\(54\) 0 0
\(55\) −0.247952 −0.0334339
\(56\) 0 0
\(57\) 1.02632 0.135940
\(58\) 0 0
\(59\) −8.22708 −1.07107 −0.535537 0.844512i \(-0.679891\pi\)
−0.535537 + 0.844512i \(0.679891\pi\)
\(60\) 0 0
\(61\) 0.510754 0.0653953 0.0326976 0.999465i \(-0.489590\pi\)
0.0326976 + 0.999465i \(0.489590\pi\)
\(62\) 0 0
\(63\) 1.05249 0.132602
\(64\) 0 0
\(65\) 5.56759 0.690575
\(66\) 0 0
\(67\) 0.317219 0.0387544 0.0193772 0.999812i \(-0.493832\pi\)
0.0193772 + 0.999812i \(0.493832\pi\)
\(68\) 0 0
\(69\) −7.59021 −0.913754
\(70\) 0 0
\(71\) −5.83623 −0.692633 −0.346316 0.938118i \(-0.612568\pi\)
−0.346316 + 0.938118i \(0.612568\pi\)
\(72\) 0 0
\(73\) 11.2379 1.31529 0.657647 0.753326i \(-0.271552\pi\)
0.657647 + 0.753326i \(0.271552\pi\)
\(74\) 0 0
\(75\) 2.65917 0.307054
\(76\) 0 0
\(77\) −0.170570 −0.0194382
\(78\) 0 0
\(79\) −5.59029 −0.628957 −0.314478 0.949265i \(-0.601830\pi\)
−0.314478 + 0.949265i \(0.601830\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.98299 −0.546954 −0.273477 0.961879i \(-0.588174\pi\)
−0.273477 + 0.961879i \(0.588174\pi\)
\(84\) 0 0
\(85\) 7.49271 0.812698
\(86\) 0 0
\(87\) −9.59787 −1.02900
\(88\) 0 0
\(89\) −0.199333 −0.0211292 −0.0105646 0.999944i \(-0.503363\pi\)
−0.0105646 + 0.999944i \(0.503363\pi\)
\(90\) 0 0
\(91\) 3.83003 0.401496
\(92\) 0 0
\(93\) 2.68185 0.278095
\(94\) 0 0
\(95\) −1.57025 −0.161104
\(96\) 0 0
\(97\) −10.9371 −1.11049 −0.555247 0.831686i \(-0.687376\pi\)
−0.555247 + 0.831686i \(0.687376\pi\)
\(98\) 0 0
\(99\) −0.162063 −0.0162879
\(100\) 0 0
\(101\) 11.8811 1.18221 0.591107 0.806593i \(-0.298691\pi\)
0.591107 + 0.806593i \(0.298691\pi\)
\(102\) 0 0
\(103\) 1.54707 0.152437 0.0762187 0.997091i \(-0.475715\pi\)
0.0762187 + 0.997091i \(0.475715\pi\)
\(104\) 0 0
\(105\) −1.61029 −0.157149
\(106\) 0 0
\(107\) 2.89728 0.280091 0.140045 0.990145i \(-0.455275\pi\)
0.140045 + 0.990145i \(0.455275\pi\)
\(108\) 0 0
\(109\) 8.16825 0.782377 0.391188 0.920311i \(-0.372064\pi\)
0.391188 + 0.920311i \(0.372064\pi\)
\(110\) 0 0
\(111\) −4.12252 −0.391292
\(112\) 0 0
\(113\) −6.73714 −0.633777 −0.316889 0.948463i \(-0.602638\pi\)
−0.316889 + 0.948463i \(0.602638\pi\)
\(114\) 0 0
\(115\) 11.6129 1.08290
\(116\) 0 0
\(117\) 3.63900 0.336426
\(118\) 0 0
\(119\) 5.15434 0.472498
\(120\) 0 0
\(121\) −10.9737 −0.997612
\(122\) 0 0
\(123\) 1.08012 0.0973912
\(124\) 0 0
\(125\) −11.7184 −1.04812
\(126\) 0 0
\(127\) 15.8812 1.40923 0.704616 0.709588i \(-0.251119\pi\)
0.704616 + 0.709588i \(0.251119\pi\)
\(128\) 0 0
\(129\) 2.77829 0.244615
\(130\) 0 0
\(131\) −9.81474 −0.857517 −0.428759 0.903419i \(-0.641049\pi\)
−0.428759 + 0.903419i \(0.641049\pi\)
\(132\) 0 0
\(133\) −1.08020 −0.0936651
\(134\) 0 0
\(135\) −1.52998 −0.131680
\(136\) 0 0
\(137\) −2.22904 −0.190440 −0.0952199 0.995456i \(-0.530355\pi\)
−0.0952199 + 0.995456i \(0.530355\pi\)
\(138\) 0 0
\(139\) 7.71321 0.654226 0.327113 0.944985i \(-0.393924\pi\)
0.327113 + 0.944985i \(0.393924\pi\)
\(140\) 0 0
\(141\) −9.50274 −0.800275
\(142\) 0 0
\(143\) −0.589745 −0.0493170
\(144\) 0 0
\(145\) 14.6845 1.21948
\(146\) 0 0
\(147\) 5.89226 0.485985
\(148\) 0 0
\(149\) −19.1731 −1.57072 −0.785360 0.619039i \(-0.787522\pi\)
−0.785360 + 0.619039i \(0.787522\pi\)
\(150\) 0 0
\(151\) 8.05210 0.655271 0.327635 0.944804i \(-0.393748\pi\)
0.327635 + 0.944804i \(0.393748\pi\)
\(152\) 0 0
\(153\) 4.89726 0.395920
\(154\) 0 0
\(155\) −4.10318 −0.329575
\(156\) 0 0
\(157\) 10.1858 0.812914 0.406457 0.913670i \(-0.366764\pi\)
0.406457 + 0.913670i \(0.366764\pi\)
\(158\) 0 0
\(159\) −4.80545 −0.381097
\(160\) 0 0
\(161\) 7.98866 0.629594
\(162\) 0 0
\(163\) −0.432916 −0.0339086 −0.0169543 0.999856i \(-0.505397\pi\)
−0.0169543 + 0.999856i \(0.505397\pi\)
\(164\) 0 0
\(165\) 0.247952 0.0193031
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 0.242320 0.0186400
\(170\) 0 0
\(171\) −1.02632 −0.0784848
\(172\) 0 0
\(173\) 17.2653 1.31266 0.656329 0.754475i \(-0.272108\pi\)
0.656329 + 0.754475i \(0.272108\pi\)
\(174\) 0 0
\(175\) −2.79876 −0.211566
\(176\) 0 0
\(177\) 8.22708 0.618385
\(178\) 0 0
\(179\) −7.05820 −0.527554 −0.263777 0.964584i \(-0.584968\pi\)
−0.263777 + 0.964584i \(0.584968\pi\)
\(180\) 0 0
\(181\) −14.7420 −1.09577 −0.547883 0.836555i \(-0.684566\pi\)
−0.547883 + 0.836555i \(0.684566\pi\)
\(182\) 0 0
\(183\) −0.510754 −0.0377560
\(184\) 0 0
\(185\) 6.30737 0.463727
\(186\) 0 0
\(187\) −0.793663 −0.0580384
\(188\) 0 0
\(189\) −1.05249 −0.0765577
\(190\) 0 0
\(191\) −22.5477 −1.63149 −0.815747 0.578409i \(-0.803674\pi\)
−0.815747 + 0.578409i \(0.803674\pi\)
\(192\) 0 0
\(193\) 3.60996 0.259850 0.129925 0.991524i \(-0.458526\pi\)
0.129925 + 0.991524i \(0.458526\pi\)
\(194\) 0 0
\(195\) −5.56759 −0.398704
\(196\) 0 0
\(197\) 12.4286 0.885502 0.442751 0.896645i \(-0.354003\pi\)
0.442751 + 0.896645i \(0.354003\pi\)
\(198\) 0 0
\(199\) −6.92918 −0.491197 −0.245598 0.969372i \(-0.578984\pi\)
−0.245598 + 0.969372i \(0.578984\pi\)
\(200\) 0 0
\(201\) −0.317219 −0.0223749
\(202\) 0 0
\(203\) 10.1017 0.709001
\(204\) 0 0
\(205\) −1.65256 −0.115420
\(206\) 0 0
\(207\) 7.59021 0.527556
\(208\) 0 0
\(209\) 0.166328 0.0115052
\(210\) 0 0
\(211\) 20.3772 1.40283 0.701414 0.712754i \(-0.252553\pi\)
0.701414 + 0.712754i \(0.252553\pi\)
\(212\) 0 0
\(213\) 5.83623 0.399892
\(214\) 0 0
\(215\) −4.25073 −0.289897
\(216\) 0 0
\(217\) −2.82264 −0.191613
\(218\) 0 0
\(219\) −11.2379 −0.759385
\(220\) 0 0
\(221\) 17.8211 1.19878
\(222\) 0 0
\(223\) 20.2826 1.35823 0.679113 0.734033i \(-0.262364\pi\)
0.679113 + 0.734033i \(0.262364\pi\)
\(224\) 0 0
\(225\) −2.65917 −0.177278
\(226\) 0 0
\(227\) −7.39895 −0.491085 −0.245543 0.969386i \(-0.578966\pi\)
−0.245543 + 0.969386i \(0.578966\pi\)
\(228\) 0 0
\(229\) −10.7782 −0.712247 −0.356123 0.934439i \(-0.615902\pi\)
−0.356123 + 0.934439i \(0.615902\pi\)
\(230\) 0 0
\(231\) 0.170570 0.0112227
\(232\) 0 0
\(233\) −7.03570 −0.460924 −0.230462 0.973081i \(-0.574024\pi\)
−0.230462 + 0.973081i \(0.574024\pi\)
\(234\) 0 0
\(235\) 14.5390 0.948420
\(236\) 0 0
\(237\) 5.59029 0.363128
\(238\) 0 0
\(239\) −7.21369 −0.466615 −0.233307 0.972403i \(-0.574955\pi\)
−0.233307 + 0.972403i \(0.574955\pi\)
\(240\) 0 0
\(241\) −6.07039 −0.391028 −0.195514 0.980701i \(-0.562638\pi\)
−0.195514 + 0.980701i \(0.562638\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −9.01502 −0.575949
\(246\) 0 0
\(247\) −3.73479 −0.237639
\(248\) 0 0
\(249\) 4.98299 0.315784
\(250\) 0 0
\(251\) 1.20193 0.0758652 0.0379326 0.999280i \(-0.487923\pi\)
0.0379326 + 0.999280i \(0.487923\pi\)
\(252\) 0 0
\(253\) −1.23009 −0.0773350
\(254\) 0 0
\(255\) −7.49271 −0.469212
\(256\) 0 0
\(257\) −14.5799 −0.909471 −0.454735 0.890627i \(-0.650266\pi\)
−0.454735 + 0.890627i \(0.650266\pi\)
\(258\) 0 0
\(259\) 4.33893 0.269608
\(260\) 0 0
\(261\) 9.59787 0.594093
\(262\) 0 0
\(263\) −16.6235 −1.02505 −0.512524 0.858673i \(-0.671289\pi\)
−0.512524 + 0.858673i \(0.671289\pi\)
\(264\) 0 0
\(265\) 7.35224 0.451644
\(266\) 0 0
\(267\) 0.199333 0.0121990
\(268\) 0 0
\(269\) −8.32925 −0.507843 −0.253922 0.967225i \(-0.581721\pi\)
−0.253922 + 0.967225i \(0.581721\pi\)
\(270\) 0 0
\(271\) 26.8577 1.63149 0.815744 0.578414i \(-0.196328\pi\)
0.815744 + 0.578414i \(0.196328\pi\)
\(272\) 0 0
\(273\) −3.83003 −0.231804
\(274\) 0 0
\(275\) 0.430951 0.0259873
\(276\) 0 0
\(277\) 7.42647 0.446213 0.223107 0.974794i \(-0.428380\pi\)
0.223107 + 0.974794i \(0.428380\pi\)
\(278\) 0 0
\(279\) −2.68185 −0.160558
\(280\) 0 0
\(281\) 2.07711 0.123910 0.0619551 0.998079i \(-0.480266\pi\)
0.0619551 + 0.998079i \(0.480266\pi\)
\(282\) 0 0
\(283\) 22.8081 1.35580 0.677900 0.735154i \(-0.262890\pi\)
0.677900 + 0.735154i \(0.262890\pi\)
\(284\) 0 0
\(285\) 1.57025 0.0930137
\(286\) 0 0
\(287\) −1.13682 −0.0671044
\(288\) 0 0
\(289\) 6.98318 0.410775
\(290\) 0 0
\(291\) 10.9371 0.641144
\(292\) 0 0
\(293\) −19.3193 −1.12864 −0.564322 0.825555i \(-0.690862\pi\)
−0.564322 + 0.825555i \(0.690862\pi\)
\(294\) 0 0
\(295\) −12.5873 −0.732858
\(296\) 0 0
\(297\) 0.162063 0.00940382
\(298\) 0 0
\(299\) 27.6208 1.59735
\(300\) 0 0
\(301\) −2.92414 −0.168544
\(302\) 0 0
\(303\) −11.8811 −0.682552
\(304\) 0 0
\(305\) 0.781442 0.0447452
\(306\) 0 0
\(307\) 9.57084 0.546237 0.273118 0.961980i \(-0.411945\pi\)
0.273118 + 0.961980i \(0.411945\pi\)
\(308\) 0 0
\(309\) −1.54707 −0.0880097
\(310\) 0 0
\(311\) 8.69478 0.493036 0.246518 0.969138i \(-0.420714\pi\)
0.246518 + 0.969138i \(0.420714\pi\)
\(312\) 0 0
\(313\) −24.7334 −1.39802 −0.699009 0.715113i \(-0.746375\pi\)
−0.699009 + 0.715113i \(0.746375\pi\)
\(314\) 0 0
\(315\) 1.61029 0.0907298
\(316\) 0 0
\(317\) 30.3559 1.70496 0.852479 0.522762i \(-0.175098\pi\)
0.852479 + 0.522762i \(0.175098\pi\)
\(318\) 0 0
\(319\) −1.55546 −0.0870888
\(320\) 0 0
\(321\) −2.89728 −0.161710
\(322\) 0 0
\(323\) −5.02617 −0.279664
\(324\) 0 0
\(325\) −9.67670 −0.536767
\(326\) 0 0
\(327\) −8.16825 −0.451705
\(328\) 0 0
\(329\) 10.0016 0.551405
\(330\) 0 0
\(331\) −30.2944 −1.66513 −0.832566 0.553926i \(-0.813129\pi\)
−0.832566 + 0.553926i \(0.813129\pi\)
\(332\) 0 0
\(333\) 4.12252 0.225913
\(334\) 0 0
\(335\) 0.485338 0.0265168
\(336\) 0 0
\(337\) −0.467044 −0.0254415 −0.0127208 0.999919i \(-0.504049\pi\)
−0.0127208 + 0.999919i \(0.504049\pi\)
\(338\) 0 0
\(339\) 6.73714 0.365911
\(340\) 0 0
\(341\) 0.434628 0.0235364
\(342\) 0 0
\(343\) −13.5690 −0.732659
\(344\) 0 0
\(345\) −11.6129 −0.625215
\(346\) 0 0
\(347\) 2.81839 0.151299 0.0756496 0.997134i \(-0.475897\pi\)
0.0756496 + 0.997134i \(0.475897\pi\)
\(348\) 0 0
\(349\) 37.0275 1.98204 0.991018 0.133726i \(-0.0426943\pi\)
0.991018 + 0.133726i \(0.0426943\pi\)
\(350\) 0 0
\(351\) −3.63900 −0.194235
\(352\) 0 0
\(353\) −4.85955 −0.258648 −0.129324 0.991602i \(-0.541281\pi\)
−0.129324 + 0.991602i \(0.541281\pi\)
\(354\) 0 0
\(355\) −8.92930 −0.473918
\(356\) 0 0
\(357\) −5.15434 −0.272797
\(358\) 0 0
\(359\) 0.0868793 0.00458531 0.00229266 0.999997i \(-0.499270\pi\)
0.00229266 + 0.999997i \(0.499270\pi\)
\(360\) 0 0
\(361\) −17.9467 −0.944561
\(362\) 0 0
\(363\) 10.9737 0.575972
\(364\) 0 0
\(365\) 17.1937 0.899960
\(366\) 0 0
\(367\) 15.3217 0.799787 0.399894 0.916562i \(-0.369047\pi\)
0.399894 + 0.916562i \(0.369047\pi\)
\(368\) 0 0
\(369\) −1.08012 −0.0562288
\(370\) 0 0
\(371\) 5.05771 0.262583
\(372\) 0 0
\(373\) 0.349987 0.0181216 0.00906081 0.999959i \(-0.497116\pi\)
0.00906081 + 0.999959i \(0.497116\pi\)
\(374\) 0 0
\(375\) 11.7184 0.605133
\(376\) 0 0
\(377\) 34.9267 1.79881
\(378\) 0 0
\(379\) 29.6312 1.52206 0.761028 0.648720i \(-0.224695\pi\)
0.761028 + 0.648720i \(0.224695\pi\)
\(380\) 0 0
\(381\) −15.8812 −0.813621
\(382\) 0 0
\(383\) 28.4092 1.45164 0.725821 0.687884i \(-0.241460\pi\)
0.725821 + 0.687884i \(0.241460\pi\)
\(384\) 0 0
\(385\) −0.260968 −0.0133002
\(386\) 0 0
\(387\) −2.77829 −0.141229
\(388\) 0 0
\(389\) 18.4318 0.934530 0.467265 0.884117i \(-0.345239\pi\)
0.467265 + 0.884117i \(0.345239\pi\)
\(390\) 0 0
\(391\) 37.1713 1.87983
\(392\) 0 0
\(393\) 9.81474 0.495088
\(394\) 0 0
\(395\) −8.55302 −0.430349
\(396\) 0 0
\(397\) 0.947842 0.0475708 0.0237854 0.999717i \(-0.492428\pi\)
0.0237854 + 0.999717i \(0.492428\pi\)
\(398\) 0 0
\(399\) 1.08020 0.0540776
\(400\) 0 0
\(401\) 1.29454 0.0646464 0.0323232 0.999477i \(-0.489709\pi\)
0.0323232 + 0.999477i \(0.489709\pi\)
\(402\) 0 0
\(403\) −9.75926 −0.486143
\(404\) 0 0
\(405\) 1.52998 0.0760253
\(406\) 0 0
\(407\) −0.668106 −0.0331168
\(408\) 0 0
\(409\) −29.1328 −1.44053 −0.720263 0.693701i \(-0.755979\pi\)
−0.720263 + 0.693701i \(0.755979\pi\)
\(410\) 0 0
\(411\) 2.22904 0.109951
\(412\) 0 0
\(413\) −8.65896 −0.426079
\(414\) 0 0
\(415\) −7.62386 −0.374241
\(416\) 0 0
\(417\) −7.71321 −0.377717
\(418\) 0 0
\(419\) −15.3595 −0.750362 −0.375181 0.926952i \(-0.622419\pi\)
−0.375181 + 0.926952i \(0.622419\pi\)
\(420\) 0 0
\(421\) −22.9588 −1.11894 −0.559472 0.828849i \(-0.688996\pi\)
−0.559472 + 0.828849i \(0.688996\pi\)
\(422\) 0 0
\(423\) 9.50274 0.462039
\(424\) 0 0
\(425\) −13.0226 −0.631690
\(426\) 0 0
\(427\) 0.537565 0.0260146
\(428\) 0 0
\(429\) 0.589745 0.0284732
\(430\) 0 0
\(431\) 23.4208 1.12814 0.564070 0.825727i \(-0.309235\pi\)
0.564070 + 0.825727i \(0.309235\pi\)
\(432\) 0 0
\(433\) −30.2786 −1.45510 −0.727549 0.686056i \(-0.759340\pi\)
−0.727549 + 0.686056i \(0.759340\pi\)
\(434\) 0 0
\(435\) −14.6845 −0.704070
\(436\) 0 0
\(437\) −7.79000 −0.372646
\(438\) 0 0
\(439\) 20.4125 0.974236 0.487118 0.873336i \(-0.338048\pi\)
0.487118 + 0.873336i \(0.338048\pi\)
\(440\) 0 0
\(441\) −5.89226 −0.280584
\(442\) 0 0
\(443\) 30.1725 1.43354 0.716770 0.697310i \(-0.245620\pi\)
0.716770 + 0.697310i \(0.245620\pi\)
\(444\) 0 0
\(445\) −0.304975 −0.0144572
\(446\) 0 0
\(447\) 19.1731 0.906856
\(448\) 0 0
\(449\) −14.7721 −0.697137 −0.348568 0.937283i \(-0.613332\pi\)
−0.348568 + 0.937283i \(0.613332\pi\)
\(450\) 0 0
\(451\) 0.175047 0.00824265
\(452\) 0 0
\(453\) −8.05210 −0.378321
\(454\) 0 0
\(455\) 5.85986 0.274715
\(456\) 0 0
\(457\) 33.0643 1.54668 0.773342 0.633989i \(-0.218583\pi\)
0.773342 + 0.633989i \(0.218583\pi\)
\(458\) 0 0
\(459\) −4.89726 −0.228585
\(460\) 0 0
\(461\) −20.9924 −0.977714 −0.488857 0.872364i \(-0.662586\pi\)
−0.488857 + 0.872364i \(0.662586\pi\)
\(462\) 0 0
\(463\) 38.8607 1.80601 0.903005 0.429631i \(-0.141356\pi\)
0.903005 + 0.429631i \(0.141356\pi\)
\(464\) 0 0
\(465\) 4.10318 0.190280
\(466\) 0 0
\(467\) −30.7010 −1.42067 −0.710335 0.703863i \(-0.751457\pi\)
−0.710335 + 0.703863i \(0.751457\pi\)
\(468\) 0 0
\(469\) 0.333871 0.0154167
\(470\) 0 0
\(471\) −10.1858 −0.469336
\(472\) 0 0
\(473\) 0.450257 0.0207028
\(474\) 0 0
\(475\) 2.72916 0.125222
\(476\) 0 0
\(477\) 4.80545 0.220027
\(478\) 0 0
\(479\) 4.10481 0.187554 0.0937768 0.995593i \(-0.470106\pi\)
0.0937768 + 0.995593i \(0.470106\pi\)
\(480\) 0 0
\(481\) 15.0019 0.684026
\(482\) 0 0
\(483\) −7.98866 −0.363496
\(484\) 0 0
\(485\) −16.7335 −0.759830
\(486\) 0 0
\(487\) −10.0473 −0.455289 −0.227644 0.973744i \(-0.573102\pi\)
−0.227644 + 0.973744i \(0.573102\pi\)
\(488\) 0 0
\(489\) 0.432916 0.0195771
\(490\) 0 0
\(491\) 16.4195 0.741001 0.370500 0.928832i \(-0.379186\pi\)
0.370500 + 0.928832i \(0.379186\pi\)
\(492\) 0 0
\(493\) 47.0033 2.11692
\(494\) 0 0
\(495\) −0.247952 −0.0111446
\(496\) 0 0
\(497\) −6.14260 −0.275533
\(498\) 0 0
\(499\) −11.1636 −0.499753 −0.249877 0.968278i \(-0.580390\pi\)
−0.249877 + 0.968278i \(0.580390\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 22.6818 1.01133 0.505666 0.862729i \(-0.331247\pi\)
0.505666 + 0.862729i \(0.331247\pi\)
\(504\) 0 0
\(505\) 18.1778 0.808903
\(506\) 0 0
\(507\) −0.242320 −0.0107618
\(508\) 0 0
\(509\) −2.92089 −0.129466 −0.0647331 0.997903i \(-0.520620\pi\)
−0.0647331 + 0.997903i \(0.520620\pi\)
\(510\) 0 0
\(511\) 11.8278 0.523231
\(512\) 0 0
\(513\) 1.02632 0.0453132
\(514\) 0 0
\(515\) 2.36698 0.104302
\(516\) 0 0
\(517\) −1.54004 −0.0677308
\(518\) 0 0
\(519\) −17.2653 −0.757864
\(520\) 0 0
\(521\) 28.6454 1.25498 0.627490 0.778625i \(-0.284082\pi\)
0.627490 + 0.778625i \(0.284082\pi\)
\(522\) 0 0
\(523\) 5.60009 0.244875 0.122437 0.992476i \(-0.460929\pi\)
0.122437 + 0.992476i \(0.460929\pi\)
\(524\) 0 0
\(525\) 2.79876 0.122148
\(526\) 0 0
\(527\) −13.1337 −0.572114
\(528\) 0 0
\(529\) 34.6113 1.50484
\(530\) 0 0
\(531\) −8.22708 −0.357025
\(532\) 0 0
\(533\) −3.93056 −0.170251
\(534\) 0 0
\(535\) 4.43278 0.191646
\(536\) 0 0
\(537\) 7.05820 0.304584
\(538\) 0 0
\(539\) 0.954914 0.0411310
\(540\) 0 0
\(541\) −37.7504 −1.62302 −0.811509 0.584341i \(-0.801353\pi\)
−0.811509 + 0.584341i \(0.801353\pi\)
\(542\) 0 0
\(543\) 14.7420 0.632641
\(544\) 0 0
\(545\) 12.4973 0.535323
\(546\) 0 0
\(547\) 8.04129 0.343821 0.171910 0.985113i \(-0.445006\pi\)
0.171910 + 0.985113i \(0.445006\pi\)
\(548\) 0 0
\(549\) 0.510754 0.0217984
\(550\) 0 0
\(551\) −9.85051 −0.419646
\(552\) 0 0
\(553\) −5.88375 −0.250202
\(554\) 0 0
\(555\) −6.30737 −0.267733
\(556\) 0 0
\(557\) 17.6075 0.746052 0.373026 0.927821i \(-0.378320\pi\)
0.373026 + 0.927821i \(0.378320\pi\)
\(558\) 0 0
\(559\) −10.1102 −0.427616
\(560\) 0 0
\(561\) 0.793663 0.0335085
\(562\) 0 0
\(563\) 40.8654 1.72227 0.861135 0.508376i \(-0.169754\pi\)
0.861135 + 0.508376i \(0.169754\pi\)
\(564\) 0 0
\(565\) −10.3077 −0.433648
\(566\) 0 0
\(567\) 1.05249 0.0442006
\(568\) 0 0
\(569\) −28.5716 −1.19779 −0.598893 0.800829i \(-0.704392\pi\)
−0.598893 + 0.800829i \(0.704392\pi\)
\(570\) 0 0
\(571\) 15.5883 0.652352 0.326176 0.945309i \(-0.394240\pi\)
0.326176 + 0.945309i \(0.394240\pi\)
\(572\) 0 0
\(573\) 22.5477 0.941943
\(574\) 0 0
\(575\) −20.1836 −0.841715
\(576\) 0 0
\(577\) −24.1993 −1.00743 −0.503715 0.863870i \(-0.668034\pi\)
−0.503715 + 0.863870i \(0.668034\pi\)
\(578\) 0 0
\(579\) −3.60996 −0.150025
\(580\) 0 0
\(581\) −5.24457 −0.217581
\(582\) 0 0
\(583\) −0.778784 −0.0322539
\(584\) 0 0
\(585\) 5.56759 0.230192
\(586\) 0 0
\(587\) 29.3193 1.21014 0.605069 0.796173i \(-0.293145\pi\)
0.605069 + 0.796173i \(0.293145\pi\)
\(588\) 0 0
\(589\) 2.75245 0.113413
\(590\) 0 0
\(591\) −12.4286 −0.511245
\(592\) 0 0
\(593\) −21.3422 −0.876418 −0.438209 0.898873i \(-0.644387\pi\)
−0.438209 + 0.898873i \(0.644387\pi\)
\(594\) 0 0
\(595\) 7.88603 0.323296
\(596\) 0 0
\(597\) 6.92918 0.283593
\(598\) 0 0
\(599\) 22.3543 0.913373 0.456686 0.889628i \(-0.349036\pi\)
0.456686 + 0.889628i \(0.349036\pi\)
\(600\) 0 0
\(601\) 41.2799 1.68384 0.841921 0.539602i \(-0.181425\pi\)
0.841921 + 0.539602i \(0.181425\pi\)
\(602\) 0 0
\(603\) 0.317219 0.0129181
\(604\) 0 0
\(605\) −16.7896 −0.682594
\(606\) 0 0
\(607\) −6.06522 −0.246180 −0.123090 0.992396i \(-0.539280\pi\)
−0.123090 + 0.992396i \(0.539280\pi\)
\(608\) 0 0
\(609\) −10.1017 −0.409342
\(610\) 0 0
\(611\) 34.5805 1.39898
\(612\) 0 0
\(613\) −11.1383 −0.449871 −0.224935 0.974374i \(-0.572217\pi\)
−0.224935 + 0.974374i \(0.572217\pi\)
\(614\) 0 0
\(615\) 1.65256 0.0666377
\(616\) 0 0
\(617\) 19.1170 0.769621 0.384810 0.922996i \(-0.374267\pi\)
0.384810 + 0.922996i \(0.374267\pi\)
\(618\) 0 0
\(619\) −30.9654 −1.24460 −0.622302 0.782777i \(-0.713803\pi\)
−0.622302 + 0.782777i \(0.713803\pi\)
\(620\) 0 0
\(621\) −7.59021 −0.304585
\(622\) 0 0
\(623\) −0.209797 −0.00840533
\(624\) 0 0
\(625\) −4.63301 −0.185321
\(626\) 0 0
\(627\) −0.166328 −0.00664252
\(628\) 0 0
\(629\) 20.1891 0.804991
\(630\) 0 0
\(631\) −24.1070 −0.959686 −0.479843 0.877354i \(-0.659306\pi\)
−0.479843 + 0.877354i \(0.659306\pi\)
\(632\) 0 0
\(633\) −20.3772 −0.809923
\(634\) 0 0
\(635\) 24.2980 0.964235
\(636\) 0 0
\(637\) −21.4419 −0.849560
\(638\) 0 0
\(639\) −5.83623 −0.230878
\(640\) 0 0
\(641\) −32.5154 −1.28428 −0.642141 0.766586i \(-0.721954\pi\)
−0.642141 + 0.766586i \(0.721954\pi\)
\(642\) 0 0
\(643\) 15.8759 0.626085 0.313042 0.949739i \(-0.398652\pi\)
0.313042 + 0.949739i \(0.398652\pi\)
\(644\) 0 0
\(645\) 4.25073 0.167372
\(646\) 0 0
\(647\) −25.0625 −0.985310 −0.492655 0.870225i \(-0.663974\pi\)
−0.492655 + 0.870225i \(0.663974\pi\)
\(648\) 0 0
\(649\) 1.33330 0.0523366
\(650\) 0 0
\(651\) 2.82264 0.110628
\(652\) 0 0
\(653\) −5.74801 −0.224937 −0.112469 0.993655i \(-0.535876\pi\)
−0.112469 + 0.993655i \(0.535876\pi\)
\(654\) 0 0
\(655\) −15.0163 −0.586737
\(656\) 0 0
\(657\) 11.2379 0.438431
\(658\) 0 0
\(659\) −11.0446 −0.430238 −0.215119 0.976588i \(-0.569014\pi\)
−0.215119 + 0.976588i \(0.569014\pi\)
\(660\) 0 0
\(661\) 27.4709 1.06849 0.534247 0.845329i \(-0.320595\pi\)
0.534247 + 0.845329i \(0.320595\pi\)
\(662\) 0 0
\(663\) −17.8211 −0.692116
\(664\) 0 0
\(665\) −1.65268 −0.0640882
\(666\) 0 0
\(667\) 72.8499 2.82076
\(668\) 0 0
\(669\) −20.2826 −0.784172
\(670\) 0 0
\(671\) −0.0827740 −0.00319545
\(672\) 0 0
\(673\) 13.7360 0.529485 0.264743 0.964319i \(-0.414713\pi\)
0.264743 + 0.964319i \(0.414713\pi\)
\(674\) 0 0
\(675\) 2.65917 0.102351
\(676\) 0 0
\(677\) 35.5759 1.36729 0.683646 0.729814i \(-0.260393\pi\)
0.683646 + 0.729814i \(0.260393\pi\)
\(678\) 0 0
\(679\) −11.5112 −0.441760
\(680\) 0 0
\(681\) 7.39895 0.283528
\(682\) 0 0
\(683\) −4.58516 −0.175446 −0.0877231 0.996145i \(-0.527959\pi\)
−0.0877231 + 0.996145i \(0.527959\pi\)
\(684\) 0 0
\(685\) −3.41039 −0.130304
\(686\) 0 0
\(687\) 10.7782 0.411216
\(688\) 0 0
\(689\) 17.4870 0.666203
\(690\) 0 0
\(691\) −8.54129 −0.324926 −0.162463 0.986715i \(-0.551944\pi\)
−0.162463 + 0.986715i \(0.551944\pi\)
\(692\) 0 0
\(693\) −0.170570 −0.00647942
\(694\) 0 0
\(695\) 11.8010 0.447639
\(696\) 0 0
\(697\) −5.28964 −0.200359
\(698\) 0 0
\(699\) 7.03570 0.266115
\(700\) 0 0
\(701\) 46.3748 1.75155 0.875776 0.482718i \(-0.160350\pi\)
0.875776 + 0.482718i \(0.160350\pi\)
\(702\) 0 0
\(703\) −4.23104 −0.159577
\(704\) 0 0
\(705\) −14.5390 −0.547570
\(706\) 0 0
\(707\) 12.5048 0.470292
\(708\) 0 0
\(709\) 46.4820 1.74567 0.872835 0.488016i \(-0.162279\pi\)
0.872835 + 0.488016i \(0.162279\pi\)
\(710\) 0 0
\(711\) −5.59029 −0.209652
\(712\) 0 0
\(713\) −20.3558 −0.762332
\(714\) 0 0
\(715\) −0.902298 −0.0337440
\(716\) 0 0
\(717\) 7.21369 0.269400
\(718\) 0 0
\(719\) −27.2461 −1.01611 −0.508053 0.861326i \(-0.669635\pi\)
−0.508053 + 0.861326i \(0.669635\pi\)
\(720\) 0 0
\(721\) 1.62828 0.0606404
\(722\) 0 0
\(723\) 6.07039 0.225760
\(724\) 0 0
\(725\) −25.5223 −0.947875
\(726\) 0 0
\(727\) 21.9595 0.814432 0.407216 0.913332i \(-0.366500\pi\)
0.407216 + 0.913332i \(0.366500\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −13.6060 −0.503237
\(732\) 0 0
\(733\) −17.3357 −0.640309 −0.320154 0.947365i \(-0.603735\pi\)
−0.320154 + 0.947365i \(0.603735\pi\)
\(734\) 0 0
\(735\) 9.01502 0.332524
\(736\) 0 0
\(737\) −0.0514092 −0.00189368
\(738\) 0 0
\(739\) −14.7105 −0.541135 −0.270568 0.962701i \(-0.587211\pi\)
−0.270568 + 0.962701i \(0.587211\pi\)
\(740\) 0 0
\(741\) 3.73479 0.137201
\(742\) 0 0
\(743\) −16.0012 −0.587029 −0.293514 0.955955i \(-0.594825\pi\)
−0.293514 + 0.955955i \(0.594825\pi\)
\(744\) 0 0
\(745\) −29.3344 −1.07473
\(746\) 0 0
\(747\) −4.98299 −0.182318
\(748\) 0 0
\(749\) 3.04937 0.111422
\(750\) 0 0
\(751\) −43.2600 −1.57858 −0.789289 0.614022i \(-0.789551\pi\)
−0.789289 + 0.614022i \(0.789551\pi\)
\(752\) 0 0
\(753\) −1.20193 −0.0438008
\(754\) 0 0
\(755\) 12.3195 0.448354
\(756\) 0 0
\(757\) −9.81138 −0.356601 −0.178300 0.983976i \(-0.557060\pi\)
−0.178300 + 0.983976i \(0.557060\pi\)
\(758\) 0 0
\(759\) 1.23009 0.0446494
\(760\) 0 0
\(761\) 15.1070 0.547627 0.273814 0.961783i \(-0.411715\pi\)
0.273814 + 0.961783i \(0.411715\pi\)
\(762\) 0 0
\(763\) 8.59704 0.311234
\(764\) 0 0
\(765\) 7.49271 0.270899
\(766\) 0 0
\(767\) −29.9383 −1.08101
\(768\) 0 0
\(769\) 20.1675 0.727258 0.363629 0.931544i \(-0.381538\pi\)
0.363629 + 0.931544i \(0.381538\pi\)
\(770\) 0 0
\(771\) 14.5799 0.525083
\(772\) 0 0
\(773\) 26.4289 0.950582 0.475291 0.879829i \(-0.342343\pi\)
0.475291 + 0.879829i \(0.342343\pi\)
\(774\) 0 0
\(775\) 7.13149 0.256171
\(776\) 0 0
\(777\) −4.33893 −0.155658
\(778\) 0 0
\(779\) 1.10855 0.0397180
\(780\) 0 0
\(781\) 0.945833 0.0338446
\(782\) 0 0
\(783\) −9.59787 −0.343000
\(784\) 0 0
\(785\) 15.5840 0.556218
\(786\) 0 0
\(787\) 23.9094 0.852280 0.426140 0.904657i \(-0.359873\pi\)
0.426140 + 0.904657i \(0.359873\pi\)
\(788\) 0 0
\(789\) 16.6235 0.591811
\(790\) 0 0
\(791\) −7.09081 −0.252120
\(792\) 0 0
\(793\) 1.85863 0.0660020
\(794\) 0 0
\(795\) −7.35224 −0.260757
\(796\) 0 0
\(797\) 26.2713 0.930578 0.465289 0.885159i \(-0.345950\pi\)
0.465289 + 0.885159i \(0.345950\pi\)
\(798\) 0 0
\(799\) 46.5374 1.64638
\(800\) 0 0
\(801\) −0.199333 −0.00704308
\(802\) 0 0
\(803\) −1.82124 −0.0642701
\(804\) 0 0
\(805\) 12.2225 0.430786
\(806\) 0 0
\(807\) 8.32925 0.293203
\(808\) 0 0
\(809\) −8.70973 −0.306218 −0.153109 0.988209i \(-0.548929\pi\)
−0.153109 + 0.988209i \(0.548929\pi\)
\(810\) 0 0
\(811\) 26.7512 0.939363 0.469682 0.882836i \(-0.344369\pi\)
0.469682 + 0.882836i \(0.344369\pi\)
\(812\) 0 0
\(813\) −26.8577 −0.941940
\(814\) 0 0
\(815\) −0.662352 −0.0232012
\(816\) 0 0
\(817\) 2.85142 0.0997587
\(818\) 0 0
\(819\) 3.83003 0.133832
\(820\) 0 0
\(821\) 4.36277 0.152262 0.0761309 0.997098i \(-0.475743\pi\)
0.0761309 + 0.997098i \(0.475743\pi\)
\(822\) 0 0
\(823\) 8.76960 0.305689 0.152844 0.988250i \(-0.451157\pi\)
0.152844 + 0.988250i \(0.451157\pi\)
\(824\) 0 0
\(825\) −0.430951 −0.0150038
\(826\) 0 0
\(827\) 2.60546 0.0906009 0.0453004 0.998973i \(-0.485575\pi\)
0.0453004 + 0.998973i \(0.485575\pi\)
\(828\) 0 0
\(829\) −21.2663 −0.738608 −0.369304 0.929309i \(-0.620404\pi\)
−0.369304 + 0.929309i \(0.620404\pi\)
\(830\) 0 0
\(831\) −7.42647 −0.257621
\(832\) 0 0
\(833\) −28.8559 −0.999798
\(834\) 0 0
\(835\) −1.52998 −0.0529471
\(836\) 0 0
\(837\) 2.68185 0.0926984
\(838\) 0 0
\(839\) 29.8458 1.03039 0.515195 0.857073i \(-0.327719\pi\)
0.515195 + 0.857073i \(0.327719\pi\)
\(840\) 0 0
\(841\) 63.1191 2.17652
\(842\) 0 0
\(843\) −2.07711 −0.0715396
\(844\) 0 0
\(845\) 0.370744 0.0127540
\(846\) 0 0
\(847\) −11.5498 −0.396856
\(848\) 0 0
\(849\) −22.8081 −0.782771
\(850\) 0 0
\(851\) 31.2908 1.07263
\(852\) 0 0
\(853\) 7.85903 0.269088 0.134544 0.990908i \(-0.457043\pi\)
0.134544 + 0.990908i \(0.457043\pi\)
\(854\) 0 0
\(855\) −1.57025 −0.0537015
\(856\) 0 0
\(857\) −27.2600 −0.931183 −0.465591 0.885000i \(-0.654158\pi\)
−0.465591 + 0.885000i \(0.654158\pi\)
\(858\) 0 0
\(859\) −1.16871 −0.0398758 −0.0199379 0.999801i \(-0.506347\pi\)
−0.0199379 + 0.999801i \(0.506347\pi\)
\(860\) 0 0
\(861\) 1.13682 0.0387428
\(862\) 0 0
\(863\) −57.0280 −1.94126 −0.970628 0.240587i \(-0.922660\pi\)
−0.970628 + 0.240587i \(0.922660\pi\)
\(864\) 0 0
\(865\) 26.4156 0.898157
\(866\) 0 0
\(867\) −6.98318 −0.237161
\(868\) 0 0
\(869\) 0.905976 0.0307331
\(870\) 0 0
\(871\) 1.15436 0.0391139
\(872\) 0 0
\(873\) −10.9371 −0.370164
\(874\) 0 0
\(875\) −12.3335 −0.416949
\(876\) 0 0
\(877\) 25.3813 0.857065 0.428533 0.903526i \(-0.359031\pi\)
0.428533 + 0.903526i \(0.359031\pi\)
\(878\) 0 0
\(879\) 19.3193 0.651623
\(880\) 0 0
\(881\) −22.2777 −0.750554 −0.375277 0.926913i \(-0.622452\pi\)
−0.375277 + 0.926913i \(0.622452\pi\)
\(882\) 0 0
\(883\) −21.8081 −0.733900 −0.366950 0.930241i \(-0.619598\pi\)
−0.366950 + 0.930241i \(0.619598\pi\)
\(884\) 0 0
\(885\) 12.5873 0.423116
\(886\) 0 0
\(887\) −31.0024 −1.04096 −0.520480 0.853874i \(-0.674247\pi\)
−0.520480 + 0.853874i \(0.674247\pi\)
\(888\) 0 0
\(889\) 16.7149 0.560601
\(890\) 0 0
\(891\) −0.162063 −0.00542930
\(892\) 0 0
\(893\) −9.75288 −0.326368
\(894\) 0 0
\(895\) −10.7989 −0.360967
\(896\) 0 0
\(897\) −27.6208 −0.922231
\(898\) 0 0
\(899\) −25.7401 −0.858479
\(900\) 0 0
\(901\) 23.5336 0.784017
\(902\) 0 0
\(903\) 2.92414 0.0973092
\(904\) 0 0
\(905\) −22.5550 −0.749753
\(906\) 0 0
\(907\) 49.9506 1.65858 0.829291 0.558817i \(-0.188745\pi\)
0.829291 + 0.558817i \(0.188745\pi\)
\(908\) 0 0
\(909\) 11.8811 0.394072
\(910\) 0 0
\(911\) −31.1409 −1.03174 −0.515872 0.856666i \(-0.672532\pi\)
−0.515872 + 0.856666i \(0.672532\pi\)
\(912\) 0 0
\(913\) 0.807555 0.0267262
\(914\) 0 0
\(915\) −0.781442 −0.0258337
\(916\) 0 0
\(917\) −10.3300 −0.341125
\(918\) 0 0
\(919\) 50.0648 1.65149 0.825743 0.564046i \(-0.190756\pi\)
0.825743 + 0.564046i \(0.190756\pi\)
\(920\) 0 0
\(921\) −9.57084 −0.315370
\(922\) 0 0
\(923\) −21.2380 −0.699058
\(924\) 0 0
\(925\) −10.9625 −0.360444
\(926\) 0 0
\(927\) 1.54707 0.0508124
\(928\) 0 0
\(929\) 28.2739 0.927638 0.463819 0.885930i \(-0.346479\pi\)
0.463819 + 0.885930i \(0.346479\pi\)
\(930\) 0 0
\(931\) 6.04735 0.198194
\(932\) 0 0
\(933\) −8.69478 −0.284654
\(934\) 0 0
\(935\) −1.21429 −0.0397114
\(936\) 0 0
\(937\) 38.8173 1.26811 0.634053 0.773290i \(-0.281390\pi\)
0.634053 + 0.773290i \(0.281390\pi\)
\(938\) 0 0
\(939\) 24.7334 0.807146
\(940\) 0 0
\(941\) −28.4498 −0.927437 −0.463719 0.885983i \(-0.653485\pi\)
−0.463719 + 0.885983i \(0.653485\pi\)
\(942\) 0 0
\(943\) −8.19834 −0.266975
\(944\) 0 0
\(945\) −1.61029 −0.0523829
\(946\) 0 0
\(947\) −8.80156 −0.286012 −0.143006 0.989722i \(-0.545677\pi\)
−0.143006 + 0.989722i \(0.545677\pi\)
\(948\) 0 0
\(949\) 40.8946 1.32750
\(950\) 0 0
\(951\) −30.3559 −0.984358
\(952\) 0 0
\(953\) −11.0564 −0.358151 −0.179075 0.983835i \(-0.557311\pi\)
−0.179075 + 0.983835i \(0.557311\pi\)
\(954\) 0 0
\(955\) −34.4975 −1.11631
\(956\) 0 0
\(957\) 1.55546 0.0502807
\(958\) 0 0
\(959\) −2.34605 −0.0757581
\(960\) 0 0
\(961\) −23.8077 −0.767989
\(962\) 0 0
\(963\) 2.89728 0.0933636
\(964\) 0 0
\(965\) 5.52316 0.177797
\(966\) 0 0
\(967\) −24.2114 −0.778586 −0.389293 0.921114i \(-0.627281\pi\)
−0.389293 + 0.921114i \(0.627281\pi\)
\(968\) 0 0
\(969\) 5.02617 0.161464
\(970\) 0 0
\(971\) −7.68129 −0.246504 −0.123252 0.992375i \(-0.539332\pi\)
−0.123252 + 0.992375i \(0.539332\pi\)
\(972\) 0 0
\(973\) 8.11811 0.260255
\(974\) 0 0
\(975\) 9.67670 0.309902
\(976\) 0 0
\(977\) −36.4901 −1.16742 −0.583711 0.811961i \(-0.698400\pi\)
−0.583711 + 0.811961i \(0.698400\pi\)
\(978\) 0 0
\(979\) 0.0323044 0.00103245
\(980\) 0 0
\(981\) 8.16825 0.260792
\(982\) 0 0
\(983\) 27.9487 0.891424 0.445712 0.895176i \(-0.352951\pi\)
0.445712 + 0.895176i \(0.352951\pi\)
\(984\) 0 0
\(985\) 19.0155 0.605885
\(986\) 0 0
\(987\) −10.0016 −0.318354
\(988\) 0 0
\(989\) −21.0878 −0.670554
\(990\) 0 0
\(991\) −1.69672 −0.0538980 −0.0269490 0.999637i \(-0.508579\pi\)
−0.0269490 + 0.999637i \(0.508579\pi\)
\(992\) 0 0
\(993\) 30.2944 0.961365
\(994\) 0 0
\(995\) −10.6015 −0.336090
\(996\) 0 0
\(997\) 20.9519 0.663553 0.331777 0.943358i \(-0.392352\pi\)
0.331777 + 0.943358i \(0.392352\pi\)
\(998\) 0 0
\(999\) −4.12252 −0.130431
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8016.2.a.bb.1.5 9
4.3 odd 2 2004.2.a.d.1.5 9
12.11 even 2 6012.2.a.h.1.5 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.d.1.5 9 4.3 odd 2
6012.2.a.h.1.5 9 12.11 even 2
8016.2.a.bb.1.5 9 1.1 even 1 trivial