Properties

Label 8016.2.a.bb.1.2
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 1.2
Root \(2.69402\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -1.69402 q^{5} +4.12928 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -1.69402 q^{5} +4.12928 q^{7} +1.00000 q^{9} -2.48865 q^{11} +1.35347 q^{13} +1.69402 q^{15} -7.89205 q^{17} -5.08686 q^{19} -4.12928 q^{21} -6.55829 q^{23} -2.13028 q^{25} -1.00000 q^{27} +7.41203 q^{29} -4.69564 q^{31} +2.48865 q^{33} -6.99510 q^{35} -0.0133728 q^{37} -1.35347 q^{39} -1.02270 q^{41} +8.67968 q^{43} -1.69402 q^{45} -5.31896 q^{47} +10.0509 q^{49} +7.89205 q^{51} +12.1374 q^{53} +4.21584 q^{55} +5.08686 q^{57} +0.0660655 q^{59} +10.3680 q^{61} +4.12928 q^{63} -2.29282 q^{65} -6.10634 q^{67} +6.55829 q^{69} +9.95916 q^{71} -3.76173 q^{73} +2.13028 q^{75} -10.2764 q^{77} -11.4241 q^{79} +1.00000 q^{81} -10.4077 q^{83} +13.3693 q^{85} -7.41203 q^{87} +6.46475 q^{89} +5.58886 q^{91} +4.69564 q^{93} +8.61727 q^{95} +18.7791 q^{97} -2.48865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} - 7q^{11} + 6q^{13} - 9q^{15} + 7q^{17} - 2q^{19} + 2q^{21} - 19q^{23} + 22q^{25} - 9q^{27} + 13q^{29} - 12q^{31} + 7q^{33} - 4q^{35} + 15q^{37} - 6q^{39} + 18q^{41} + 6q^{43} + 9q^{45} - 25q^{47} + 19q^{49} - 7q^{51} + 17q^{53} + 3q^{55} + 2q^{57} - 3q^{59} + 14q^{61} - 2q^{63} + 14q^{65} + 4q^{67} + 19q^{69} - 17q^{71} - 20q^{73} - 22q^{75} + 14q^{77} + 8q^{79} + 9q^{81} + q^{83} + 5q^{85} - 13q^{87} + 36q^{89} + 41q^{91} + 12q^{93} - 5q^{95} + 31q^{97} - 7q^{99} + O(q^{100}) \)

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
\(5\) −1.69402 −0.757591 −0.378795 0.925480i \(-0.623662\pi\)
−0.378795 + 0.925480i \(0.623662\pi\)
\(6\) 0 0
\(7\) 4.12928 1.56072 0.780360 0.625330i \(-0.215036\pi\)
0.780360 + 0.625330i \(0.215036\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.48865 −0.750358 −0.375179 0.926952i \(-0.622419\pi\)
−0.375179 + 0.926952i \(0.622419\pi\)
\(12\) 0 0
\(13\) 1.35347 0.375386 0.187693 0.982228i \(-0.439899\pi\)
0.187693 + 0.982228i \(0.439899\pi\)
\(14\) 0 0
\(15\) 1.69402 0.437395
\(16\) 0 0
\(17\) −7.89205 −1.91410 −0.957052 0.289918i \(-0.906372\pi\)
−0.957052 + 0.289918i \(0.906372\pi\)
\(18\) 0 0
\(19\) −5.08686 −1.16701 −0.583503 0.812111i \(-0.698318\pi\)
−0.583503 + 0.812111i \(0.698318\pi\)
\(20\) 0 0
\(21\) −4.12928 −0.901083
\(22\) 0 0
\(23\) −6.55829 −1.36750 −0.683749 0.729717i \(-0.739652\pi\)
−0.683749 + 0.729717i \(0.739652\pi\)
\(24\) 0 0
\(25\) −2.13028 −0.426056
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 7.41203 1.37638 0.688189 0.725531i \(-0.258406\pi\)
0.688189 + 0.725531i \(0.258406\pi\)
\(30\) 0 0
\(31\) −4.69564 −0.843361 −0.421681 0.906744i \(-0.638560\pi\)
−0.421681 + 0.906744i \(0.638560\pi\)
\(32\) 0 0
\(33\) 2.48865 0.433219
\(34\) 0 0
\(35\) −6.99510 −1.18239
\(36\) 0 0
\(37\) −0.0133728 −0.00219847 −0.00109924 0.999999i \(-0.500350\pi\)
−0.00109924 + 0.999999i \(0.500350\pi\)
\(38\) 0 0
\(39\) −1.35347 −0.216729
\(40\) 0 0
\(41\) −1.02270 −0.159719 −0.0798593 0.996806i \(-0.525447\pi\)
−0.0798593 + 0.996806i \(0.525447\pi\)
\(42\) 0 0
\(43\) 8.67968 1.32364 0.661819 0.749663i \(-0.269785\pi\)
0.661819 + 0.749663i \(0.269785\pi\)
\(44\) 0 0
\(45\) −1.69402 −0.252530
\(46\) 0 0
\(47\) −5.31896 −0.775850 −0.387925 0.921691i \(-0.626808\pi\)
−0.387925 + 0.921691i \(0.626808\pi\)
\(48\) 0 0
\(49\) 10.0509 1.43585
\(50\) 0 0
\(51\) 7.89205 1.10511
\(52\) 0 0
\(53\) 12.1374 1.66720 0.833601 0.552367i \(-0.186275\pi\)
0.833601 + 0.552367i \(0.186275\pi\)
\(54\) 0 0
\(55\) 4.21584 0.568464
\(56\) 0 0
\(57\) 5.08686 0.673772
\(58\) 0 0
\(59\) 0.0660655 0.00860099 0.00430050 0.999991i \(-0.498631\pi\)
0.00430050 + 0.999991i \(0.498631\pi\)
\(60\) 0 0
\(61\) 10.3680 1.32749 0.663746 0.747958i \(-0.268966\pi\)
0.663746 + 0.747958i \(0.268966\pi\)
\(62\) 0 0
\(63\) 4.12928 0.520240
\(64\) 0 0
\(65\) −2.29282 −0.284389
\(66\) 0 0
\(67\) −6.10634 −0.746008 −0.373004 0.927830i \(-0.621672\pi\)
−0.373004 + 0.927830i \(0.621672\pi\)
\(68\) 0 0
\(69\) 6.55829 0.789526
\(70\) 0 0
\(71\) 9.95916 1.18193 0.590967 0.806696i \(-0.298746\pi\)
0.590967 + 0.806696i \(0.298746\pi\)
\(72\) 0 0
\(73\) −3.76173 −0.440277 −0.220139 0.975469i \(-0.570651\pi\)
−0.220139 + 0.975469i \(0.570651\pi\)
\(74\) 0 0
\(75\) 2.13028 0.245984
\(76\) 0 0
\(77\) −10.2764 −1.17110
\(78\) 0 0
\(79\) −11.4241 −1.28531 −0.642655 0.766155i \(-0.722167\pi\)
−0.642655 + 0.766155i \(0.722167\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −10.4077 −1.14240 −0.571199 0.820811i \(-0.693522\pi\)
−0.571199 + 0.820811i \(0.693522\pi\)
\(84\) 0 0
\(85\) 13.3693 1.45011
\(86\) 0 0
\(87\) −7.41203 −0.794653
\(88\) 0 0
\(89\) 6.46475 0.685262 0.342631 0.939470i \(-0.388682\pi\)
0.342631 + 0.939470i \(0.388682\pi\)
\(90\) 0 0
\(91\) 5.58886 0.585872
\(92\) 0 0
\(93\) 4.69564 0.486915
\(94\) 0 0
\(95\) 8.61727 0.884114
\(96\) 0 0
\(97\) 18.7791 1.90673 0.953364 0.301822i \(-0.0975947\pi\)
0.953364 + 0.301822i \(0.0975947\pi\)
\(98\) 0 0
\(99\) −2.48865 −0.250119
\(100\) 0 0
\(101\) 14.0599 1.39901 0.699507 0.714625i \(-0.253403\pi\)
0.699507 + 0.714625i \(0.253403\pi\)
\(102\) 0 0
\(103\) 17.8777 1.76154 0.880770 0.473545i \(-0.157026\pi\)
0.880770 + 0.473545i \(0.157026\pi\)
\(104\) 0 0
\(105\) 6.99510 0.682652
\(106\) 0 0
\(107\) −13.1294 −1.26926 −0.634632 0.772815i \(-0.718848\pi\)
−0.634632 + 0.772815i \(0.718848\pi\)
\(108\) 0 0
\(109\) 8.71046 0.834311 0.417155 0.908835i \(-0.363027\pi\)
0.417155 + 0.908835i \(0.363027\pi\)
\(110\) 0 0
\(111\) 0.0133728 0.00126929
\(112\) 0 0
\(113\) −3.25013 −0.305747 −0.152873 0.988246i \(-0.548853\pi\)
−0.152873 + 0.988246i \(0.548853\pi\)
\(114\) 0 0
\(115\) 11.1099 1.03600
\(116\) 0 0
\(117\) 1.35347 0.125129
\(118\) 0 0
\(119\) −32.5885 −2.98738
\(120\) 0 0
\(121\) −4.80660 −0.436963
\(122\) 0 0
\(123\) 1.02270 0.0922136
\(124\) 0 0
\(125\) 12.0789 1.08037
\(126\) 0 0
\(127\) 16.6967 1.48159 0.740797 0.671729i \(-0.234448\pi\)
0.740797 + 0.671729i \(0.234448\pi\)
\(128\) 0 0
\(129\) −8.67968 −0.764203
\(130\) 0 0
\(131\) 9.32465 0.814699 0.407349 0.913272i \(-0.366453\pi\)
0.407349 + 0.913272i \(0.366453\pi\)
\(132\) 0 0
\(133\) −21.0051 −1.82137
\(134\) 0 0
\(135\) 1.69402 0.145798
\(136\) 0 0
\(137\) −22.0786 −1.88630 −0.943150 0.332367i \(-0.892153\pi\)
−0.943150 + 0.332367i \(0.892153\pi\)
\(138\) 0 0
\(139\) −1.95579 −0.165888 −0.0829441 0.996554i \(-0.526432\pi\)
−0.0829441 + 0.996554i \(0.526432\pi\)
\(140\) 0 0
\(141\) 5.31896 0.447937
\(142\) 0 0
\(143\) −3.36832 −0.281673
\(144\) 0 0
\(145\) −12.5562 −1.04273
\(146\) 0 0
\(147\) −10.0509 −0.828988
\(148\) 0 0
\(149\) −1.90601 −0.156146 −0.0780730 0.996948i \(-0.524877\pi\)
−0.0780730 + 0.996948i \(0.524877\pi\)
\(150\) 0 0
\(151\) 6.47280 0.526749 0.263374 0.964694i \(-0.415165\pi\)
0.263374 + 0.964694i \(0.415165\pi\)
\(152\) 0 0
\(153\) −7.89205 −0.638034
\(154\) 0 0
\(155\) 7.95452 0.638923
\(156\) 0 0
\(157\) 0.438526 0.0349982 0.0174991 0.999847i \(-0.494430\pi\)
0.0174991 + 0.999847i \(0.494430\pi\)
\(158\) 0 0
\(159\) −12.1374 −0.962560
\(160\) 0 0
\(161\) −27.0810 −2.13428
\(162\) 0 0
\(163\) 12.2469 0.959252 0.479626 0.877473i \(-0.340772\pi\)
0.479626 + 0.877473i \(0.340772\pi\)
\(164\) 0 0
\(165\) −4.21584 −0.328203
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −11.1681 −0.859086
\(170\) 0 0
\(171\) −5.08686 −0.389002
\(172\) 0 0
\(173\) 8.71361 0.662483 0.331242 0.943546i \(-0.392532\pi\)
0.331242 + 0.943546i \(0.392532\pi\)
\(174\) 0 0
\(175\) −8.79652 −0.664955
\(176\) 0 0
\(177\) −0.0660655 −0.00496579
\(178\) 0 0
\(179\) −21.3884 −1.59864 −0.799322 0.600903i \(-0.794808\pi\)
−0.799322 + 0.600903i \(0.794808\pi\)
\(180\) 0 0
\(181\) −1.85644 −0.137988 −0.0689942 0.997617i \(-0.521979\pi\)
−0.0689942 + 0.997617i \(0.521979\pi\)
\(182\) 0 0
\(183\) −10.3680 −0.766428
\(184\) 0 0
\(185\) 0.0226538 0.00166554
\(186\) 0 0
\(187\) 19.6406 1.43626
\(188\) 0 0
\(189\) −4.12928 −0.300361
\(190\) 0 0
\(191\) −11.4811 −0.830746 −0.415373 0.909651i \(-0.636349\pi\)
−0.415373 + 0.909651i \(0.636349\pi\)
\(192\) 0 0
\(193\) −25.0096 −1.80023 −0.900115 0.435653i \(-0.856518\pi\)
−0.900115 + 0.435653i \(0.856518\pi\)
\(194\) 0 0
\(195\) 2.29282 0.164192
\(196\) 0 0
\(197\) 25.2259 1.79727 0.898634 0.438699i \(-0.144561\pi\)
0.898634 + 0.438699i \(0.144561\pi\)
\(198\) 0 0
\(199\) 25.2035 1.78663 0.893315 0.449431i \(-0.148373\pi\)
0.893315 + 0.449431i \(0.148373\pi\)
\(200\) 0 0
\(201\) 6.10634 0.430708
\(202\) 0 0
\(203\) 30.6063 2.14814
\(204\) 0 0
\(205\) 1.73248 0.121001
\(206\) 0 0
\(207\) −6.55829 −0.455833
\(208\) 0 0
\(209\) 12.6594 0.875672
\(210\) 0 0
\(211\) 5.16157 0.355337 0.177669 0.984090i \(-0.443145\pi\)
0.177669 + 0.984090i \(0.443145\pi\)
\(212\) 0 0
\(213\) −9.95916 −0.682390
\(214\) 0 0
\(215\) −14.7036 −1.00278
\(216\) 0 0
\(217\) −19.3896 −1.31625
\(218\) 0 0
\(219\) 3.76173 0.254194
\(220\) 0 0
\(221\) −10.6817 −0.718527
\(222\) 0 0
\(223\) −2.36856 −0.158610 −0.0793052 0.996850i \(-0.525270\pi\)
−0.0793052 + 0.996850i \(0.525270\pi\)
\(224\) 0 0
\(225\) −2.13028 −0.142019
\(226\) 0 0
\(227\) 0.662698 0.0439848 0.0219924 0.999758i \(-0.492999\pi\)
0.0219924 + 0.999758i \(0.492999\pi\)
\(228\) 0 0
\(229\) 28.4020 1.87686 0.938428 0.345475i \(-0.112282\pi\)
0.938428 + 0.345475i \(0.112282\pi\)
\(230\) 0 0
\(231\) 10.2764 0.676134
\(232\) 0 0
\(233\) 1.11158 0.0728218 0.0364109 0.999337i \(-0.488407\pi\)
0.0364109 + 0.999337i \(0.488407\pi\)
\(234\) 0 0
\(235\) 9.01045 0.587777
\(236\) 0 0
\(237\) 11.4241 0.742074
\(238\) 0 0
\(239\) 5.03519 0.325700 0.162850 0.986651i \(-0.447931\pi\)
0.162850 + 0.986651i \(0.447931\pi\)
\(240\) 0 0
\(241\) 15.9384 1.02668 0.513341 0.858185i \(-0.328408\pi\)
0.513341 + 0.858185i \(0.328408\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −17.0266 −1.08779
\(246\) 0 0
\(247\) −6.88493 −0.438078
\(248\) 0 0
\(249\) 10.4077 0.659564
\(250\) 0 0
\(251\) −12.4875 −0.788205 −0.394102 0.919067i \(-0.628944\pi\)
−0.394102 + 0.919067i \(0.628944\pi\)
\(252\) 0 0
\(253\) 16.3213 1.02611
\(254\) 0 0
\(255\) −13.3693 −0.837220
\(256\) 0 0
\(257\) 13.4024 0.836016 0.418008 0.908443i \(-0.362728\pi\)
0.418008 + 0.908443i \(0.362728\pi\)
\(258\) 0 0
\(259\) −0.0552200 −0.00343120
\(260\) 0 0
\(261\) 7.41203 0.458793
\(262\) 0 0
\(263\) −10.2710 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(264\) 0 0
\(265\) −20.5611 −1.26306
\(266\) 0 0
\(267\) −6.46475 −0.395636
\(268\) 0 0
\(269\) 21.0795 1.28524 0.642619 0.766186i \(-0.277848\pi\)
0.642619 + 0.766186i \(0.277848\pi\)
\(270\) 0 0
\(271\) 22.7180 1.38002 0.690011 0.723799i \(-0.257606\pi\)
0.690011 + 0.723799i \(0.257606\pi\)
\(272\) 0 0
\(273\) −5.58886 −0.338253
\(274\) 0 0
\(275\) 5.30153 0.319694
\(276\) 0 0
\(277\) −25.7334 −1.54617 −0.773084 0.634303i \(-0.781287\pi\)
−0.773084 + 0.634303i \(0.781287\pi\)
\(278\) 0 0
\(279\) −4.69564 −0.281120
\(280\) 0 0
\(281\) −20.0242 −1.19454 −0.597271 0.802039i \(-0.703748\pi\)
−0.597271 + 0.802039i \(0.703748\pi\)
\(282\) 0 0
\(283\) 7.01267 0.416860 0.208430 0.978037i \(-0.433165\pi\)
0.208430 + 0.978037i \(0.433165\pi\)
\(284\) 0 0
\(285\) −8.61727 −0.510443
\(286\) 0 0
\(287\) −4.22301 −0.249276
\(288\) 0 0
\(289\) 45.2844 2.66379
\(290\) 0 0
\(291\) −18.7791 −1.10085
\(292\) 0 0
\(293\) 2.63359 0.153856 0.0769279 0.997037i \(-0.475489\pi\)
0.0769279 + 0.997037i \(0.475489\pi\)
\(294\) 0 0
\(295\) −0.111917 −0.00651603
\(296\) 0 0
\(297\) 2.48865 0.144406
\(298\) 0 0
\(299\) −8.87647 −0.513339
\(300\) 0 0
\(301\) 35.8408 2.06583
\(302\) 0 0
\(303\) −14.0599 −0.807722
\(304\) 0 0
\(305\) −17.5637 −1.00570
\(306\) 0 0
\(307\) −12.3105 −0.702597 −0.351299 0.936263i \(-0.614260\pi\)
−0.351299 + 0.936263i \(0.614260\pi\)
\(308\) 0 0
\(309\) −17.8777 −1.01703
\(310\) 0 0
\(311\) −23.9999 −1.36091 −0.680453 0.732791i \(-0.738217\pi\)
−0.680453 + 0.732791i \(0.738217\pi\)
\(312\) 0 0
\(313\) 3.38113 0.191113 0.0955564 0.995424i \(-0.469537\pi\)
0.0955564 + 0.995424i \(0.469537\pi\)
\(314\) 0 0
\(315\) −6.99510 −0.394129
\(316\) 0 0
\(317\) −7.85532 −0.441199 −0.220599 0.975365i \(-0.570801\pi\)
−0.220599 + 0.975365i \(0.570801\pi\)
\(318\) 0 0
\(319\) −18.4460 −1.03278
\(320\) 0 0
\(321\) 13.1294 0.732810
\(322\) 0 0
\(323\) 40.1458 2.23377
\(324\) 0 0
\(325\) −2.88327 −0.159935
\(326\) 0 0
\(327\) −8.71046 −0.481689
\(328\) 0 0
\(329\) −21.9635 −1.21089
\(330\) 0 0
\(331\) 24.1080 1.32510 0.662548 0.749019i \(-0.269475\pi\)
0.662548 + 0.749019i \(0.269475\pi\)
\(332\) 0 0
\(333\) −0.0133728 −0.000732825 0
\(334\) 0 0
\(335\) 10.3443 0.565169
\(336\) 0 0
\(337\) 12.7093 0.692321 0.346161 0.938175i \(-0.387485\pi\)
0.346161 + 0.938175i \(0.387485\pi\)
\(338\) 0 0
\(339\) 3.25013 0.176523
\(340\) 0 0
\(341\) 11.6858 0.632822
\(342\) 0 0
\(343\) 12.5982 0.680240
\(344\) 0 0
\(345\) −11.1099 −0.598138
\(346\) 0 0
\(347\) 21.7727 1.16882 0.584410 0.811459i \(-0.301326\pi\)
0.584410 + 0.811459i \(0.301326\pi\)
\(348\) 0 0
\(349\) −35.7390 −1.91307 −0.956533 0.291625i \(-0.905804\pi\)
−0.956533 + 0.291625i \(0.905804\pi\)
\(350\) 0 0
\(351\) −1.35347 −0.0722430
\(352\) 0 0
\(353\) −3.84039 −0.204403 −0.102202 0.994764i \(-0.532589\pi\)
−0.102202 + 0.994764i \(0.532589\pi\)
\(354\) 0 0
\(355\) −16.8711 −0.895423
\(356\) 0 0
\(357\) 32.5885 1.72477
\(358\) 0 0
\(359\) 19.9436 1.05258 0.526292 0.850304i \(-0.323582\pi\)
0.526292 + 0.850304i \(0.323582\pi\)
\(360\) 0 0
\(361\) 6.87619 0.361905
\(362\) 0 0
\(363\) 4.80660 0.252281
\(364\) 0 0
\(365\) 6.37246 0.333550
\(366\) 0 0
\(367\) 11.6497 0.608108 0.304054 0.952655i \(-0.401660\pi\)
0.304054 + 0.952655i \(0.401660\pi\)
\(368\) 0 0
\(369\) −1.02270 −0.0532395
\(370\) 0 0
\(371\) 50.1188 2.60204
\(372\) 0 0
\(373\) −14.0130 −0.725568 −0.362784 0.931873i \(-0.618174\pi\)
−0.362784 + 0.931873i \(0.618174\pi\)
\(374\) 0 0
\(375\) −12.0789 −0.623750
\(376\) 0 0
\(377\) 10.0320 0.516673
\(378\) 0 0
\(379\) −3.20637 −0.164700 −0.0823502 0.996603i \(-0.526243\pi\)
−0.0823502 + 0.996603i \(0.526243\pi\)
\(380\) 0 0
\(381\) −16.6967 −0.855398
\(382\) 0 0
\(383\) 1.38840 0.0709437 0.0354719 0.999371i \(-0.488707\pi\)
0.0354719 + 0.999371i \(0.488707\pi\)
\(384\) 0 0
\(385\) 17.4084 0.887214
\(386\) 0 0
\(387\) 8.67968 0.441213
\(388\) 0 0
\(389\) −18.6756 −0.946891 −0.473446 0.880823i \(-0.656990\pi\)
−0.473446 + 0.880823i \(0.656990\pi\)
\(390\) 0 0
\(391\) 51.7584 2.61753
\(392\) 0 0
\(393\) −9.32465 −0.470367
\(394\) 0 0
\(395\) 19.3527 0.973740
\(396\) 0 0
\(397\) 37.4874 1.88144 0.940719 0.339187i \(-0.110152\pi\)
0.940719 + 0.339187i \(0.110152\pi\)
\(398\) 0 0
\(399\) 21.0051 1.05157
\(400\) 0 0
\(401\) 17.6036 0.879084 0.439542 0.898222i \(-0.355141\pi\)
0.439542 + 0.898222i \(0.355141\pi\)
\(402\) 0 0
\(403\) −6.35541 −0.316586
\(404\) 0 0
\(405\) −1.69402 −0.0841768
\(406\) 0 0
\(407\) 0.0332803 0.00164964
\(408\) 0 0
\(409\) 6.15357 0.304275 0.152137 0.988359i \(-0.451384\pi\)
0.152137 + 0.988359i \(0.451384\pi\)
\(410\) 0 0
\(411\) 22.0786 1.08906
\(412\) 0 0
\(413\) 0.272803 0.0134237
\(414\) 0 0
\(415\) 17.6310 0.865471
\(416\) 0 0
\(417\) 1.95579 0.0957756
\(418\) 0 0
\(419\) 20.1239 0.983118 0.491559 0.870844i \(-0.336427\pi\)
0.491559 + 0.870844i \(0.336427\pi\)
\(420\) 0 0
\(421\) 18.2139 0.887691 0.443846 0.896103i \(-0.353614\pi\)
0.443846 + 0.896103i \(0.353614\pi\)
\(422\) 0 0
\(423\) −5.31896 −0.258617
\(424\) 0 0
\(425\) 16.8123 0.815515
\(426\) 0 0
\(427\) 42.8125 2.07184
\(428\) 0 0
\(429\) 3.36832 0.162624
\(430\) 0 0
\(431\) −20.4864 −0.986795 −0.493398 0.869804i \(-0.664245\pi\)
−0.493398 + 0.869804i \(0.664245\pi\)
\(432\) 0 0
\(433\) 20.7693 0.998111 0.499055 0.866570i \(-0.333680\pi\)
0.499055 + 0.866570i \(0.333680\pi\)
\(434\) 0 0
\(435\) 12.5562 0.602022
\(436\) 0 0
\(437\) 33.3612 1.59588
\(438\) 0 0
\(439\) −12.5543 −0.599186 −0.299593 0.954067i \(-0.596851\pi\)
−0.299593 + 0.954067i \(0.596851\pi\)
\(440\) 0 0
\(441\) 10.0509 0.478617
\(442\) 0 0
\(443\) −0.828246 −0.0393511 −0.0196756 0.999806i \(-0.506263\pi\)
−0.0196756 + 0.999806i \(0.506263\pi\)
\(444\) 0 0
\(445\) −10.9514 −0.519148
\(446\) 0 0
\(447\) 1.90601 0.0901510
\(448\) 0 0
\(449\) 18.6090 0.878213 0.439107 0.898435i \(-0.355295\pi\)
0.439107 + 0.898435i \(0.355295\pi\)
\(450\) 0 0
\(451\) 2.54514 0.119846
\(452\) 0 0
\(453\) −6.47280 −0.304119
\(454\) 0 0
\(455\) −9.46768 −0.443851
\(456\) 0 0
\(457\) −25.2882 −1.18293 −0.591466 0.806330i \(-0.701451\pi\)
−0.591466 + 0.806330i \(0.701451\pi\)
\(458\) 0 0
\(459\) 7.89205 0.368369
\(460\) 0 0
\(461\) 31.4877 1.46653 0.733263 0.679945i \(-0.237996\pi\)
0.733263 + 0.679945i \(0.237996\pi\)
\(462\) 0 0
\(463\) −17.3225 −0.805044 −0.402522 0.915410i \(-0.631866\pi\)
−0.402522 + 0.915410i \(0.631866\pi\)
\(464\) 0 0
\(465\) −7.95452 −0.368882
\(466\) 0 0
\(467\) 25.6138 1.18527 0.592633 0.805473i \(-0.298089\pi\)
0.592633 + 0.805473i \(0.298089\pi\)
\(468\) 0 0
\(469\) −25.2148 −1.16431
\(470\) 0 0
\(471\) −0.438526 −0.0202062
\(472\) 0 0
\(473\) −21.6007 −0.993202
\(474\) 0 0
\(475\) 10.8364 0.497210
\(476\) 0 0
\(477\) 12.1374 0.555734
\(478\) 0 0
\(479\) −19.1003 −0.872717 −0.436359 0.899773i \(-0.643732\pi\)
−0.436359 + 0.899773i \(0.643732\pi\)
\(480\) 0 0
\(481\) −0.0180997 −0.000825276 0
\(482\) 0 0
\(483\) 27.0810 1.23223
\(484\) 0 0
\(485\) −31.8123 −1.44452
\(486\) 0 0
\(487\) −15.8243 −0.717068 −0.358534 0.933517i \(-0.616723\pi\)
−0.358534 + 0.933517i \(0.616723\pi\)
\(488\) 0 0
\(489\) −12.2469 −0.553825
\(490\) 0 0
\(491\) 14.8932 0.672121 0.336061 0.941840i \(-0.390905\pi\)
0.336061 + 0.941840i \(0.390905\pi\)
\(492\) 0 0
\(493\) −58.4961 −2.63453
\(494\) 0 0
\(495\) 4.21584 0.189488
\(496\) 0 0
\(497\) 41.1241 1.84467
\(498\) 0 0
\(499\) 5.95799 0.266716 0.133358 0.991068i \(-0.457424\pi\)
0.133358 + 0.991068i \(0.457424\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 31.4302 1.40140 0.700701 0.713455i \(-0.252871\pi\)
0.700701 + 0.713455i \(0.252871\pi\)
\(504\) 0 0
\(505\) −23.8179 −1.05988
\(506\) 0 0
\(507\) 11.1681 0.495993
\(508\) 0 0
\(509\) −4.98258 −0.220849 −0.110424 0.993885i \(-0.535221\pi\)
−0.110424 + 0.993885i \(0.535221\pi\)
\(510\) 0 0
\(511\) −15.5332 −0.687150
\(512\) 0 0
\(513\) 5.08686 0.224591
\(514\) 0 0
\(515\) −30.2852 −1.33453
\(516\) 0 0
\(517\) 13.2371 0.582165
\(518\) 0 0
\(519\) −8.71361 −0.382485
\(520\) 0 0
\(521\) 33.7533 1.47876 0.739379 0.673289i \(-0.235119\pi\)
0.739379 + 0.673289i \(0.235119\pi\)
\(522\) 0 0
\(523\) −43.7117 −1.91138 −0.955690 0.294376i \(-0.904888\pi\)
−0.955690 + 0.294376i \(0.904888\pi\)
\(524\) 0 0
\(525\) 8.79652 0.383912
\(526\) 0 0
\(527\) 37.0582 1.61428
\(528\) 0 0
\(529\) 20.0112 0.870053
\(530\) 0 0
\(531\) 0.0660655 0.00286700
\(532\) 0 0
\(533\) −1.38419 −0.0599561
\(534\) 0 0
\(535\) 22.2415 0.961583
\(536\) 0 0
\(537\) 21.3884 0.922977
\(538\) 0 0
\(539\) −25.0133 −1.07740
\(540\) 0 0
\(541\) −24.6423 −1.05946 −0.529728 0.848168i \(-0.677706\pi\)
−0.529728 + 0.848168i \(0.677706\pi\)
\(542\) 0 0
\(543\) 1.85644 0.0796676
\(544\) 0 0
\(545\) −14.7557 −0.632066
\(546\) 0 0
\(547\) 17.1292 0.732390 0.366195 0.930538i \(-0.380660\pi\)
0.366195 + 0.930538i \(0.380660\pi\)
\(548\) 0 0
\(549\) 10.3680 0.442497
\(550\) 0 0
\(551\) −37.7040 −1.60624
\(552\) 0 0
\(553\) −47.1733 −2.00601
\(554\) 0 0
\(555\) −0.0226538 −0.000961602 0
\(556\) 0 0
\(557\) 4.33857 0.183831 0.0919155 0.995767i \(-0.470701\pi\)
0.0919155 + 0.995767i \(0.470701\pi\)
\(558\) 0 0
\(559\) 11.7477 0.496875
\(560\) 0 0
\(561\) −19.6406 −0.829226
\(562\) 0 0
\(563\) 0.824504 0.0347487 0.0173744 0.999849i \(-0.494469\pi\)
0.0173744 + 0.999849i \(0.494469\pi\)
\(564\) 0 0
\(565\) 5.50580 0.231631
\(566\) 0 0
\(567\) 4.12928 0.173413
\(568\) 0 0
\(569\) 9.12359 0.382481 0.191240 0.981543i \(-0.438749\pi\)
0.191240 + 0.981543i \(0.438749\pi\)
\(570\) 0 0
\(571\) 6.28710 0.263107 0.131553 0.991309i \(-0.458003\pi\)
0.131553 + 0.991309i \(0.458003\pi\)
\(572\) 0 0
\(573\) 11.4811 0.479632
\(574\) 0 0
\(575\) 13.9710 0.582631
\(576\) 0 0
\(577\) 16.0704 0.669020 0.334510 0.942392i \(-0.391429\pi\)
0.334510 + 0.942392i \(0.391429\pi\)
\(578\) 0 0
\(579\) 25.0096 1.03936
\(580\) 0 0
\(581\) −42.9765 −1.78296
\(582\) 0 0
\(583\) −30.2058 −1.25100
\(584\) 0 0
\(585\) −2.29282 −0.0947962
\(586\) 0 0
\(587\) 8.45147 0.348829 0.174415 0.984672i \(-0.444197\pi\)
0.174415 + 0.984672i \(0.444197\pi\)
\(588\) 0 0
\(589\) 23.8861 0.984208
\(590\) 0 0
\(591\) −25.2259 −1.03765
\(592\) 0 0
\(593\) 31.4745 1.29250 0.646250 0.763125i \(-0.276336\pi\)
0.646250 + 0.763125i \(0.276336\pi\)
\(594\) 0 0
\(595\) 55.2057 2.26321
\(596\) 0 0
\(597\) −25.2035 −1.03151
\(598\) 0 0
\(599\) 4.26080 0.174091 0.0870457 0.996204i \(-0.472257\pi\)
0.0870457 + 0.996204i \(0.472257\pi\)
\(600\) 0 0
\(601\) −33.6592 −1.37299 −0.686493 0.727136i \(-0.740851\pi\)
−0.686493 + 0.727136i \(0.740851\pi\)
\(602\) 0 0
\(603\) −6.10634 −0.248669
\(604\) 0 0
\(605\) 8.14250 0.331040
\(606\) 0 0
\(607\) 42.0428 1.70647 0.853233 0.521530i \(-0.174639\pi\)
0.853233 + 0.521530i \(0.174639\pi\)
\(608\) 0 0
\(609\) −30.6063 −1.24023
\(610\) 0 0
\(611\) −7.19907 −0.291243
\(612\) 0 0
\(613\) 40.1736 1.62260 0.811298 0.584632i \(-0.198761\pi\)
0.811298 + 0.584632i \(0.198761\pi\)
\(614\) 0 0
\(615\) −1.73248 −0.0698602
\(616\) 0 0
\(617\) −2.71175 −0.109171 −0.0545855 0.998509i \(-0.517384\pi\)
−0.0545855 + 0.998509i \(0.517384\pi\)
\(618\) 0 0
\(619\) 19.3649 0.778340 0.389170 0.921166i \(-0.372762\pi\)
0.389170 + 0.921166i \(0.372762\pi\)
\(620\) 0 0
\(621\) 6.55829 0.263175
\(622\) 0 0
\(623\) 26.6948 1.06950
\(624\) 0 0
\(625\) −9.81051 −0.392420
\(626\) 0 0
\(627\) −12.6594 −0.505570
\(628\) 0 0
\(629\) 0.105539 0.00420811
\(630\) 0 0
\(631\) −31.9758 −1.27294 −0.636469 0.771302i \(-0.719606\pi\)
−0.636469 + 0.771302i \(0.719606\pi\)
\(632\) 0 0
\(633\) −5.16157 −0.205154
\(634\) 0 0
\(635\) −28.2846 −1.12244
\(636\) 0 0
\(637\) 13.6037 0.538997
\(638\) 0 0
\(639\) 9.95916 0.393978
\(640\) 0 0
\(641\) −33.4659 −1.32182 −0.660912 0.750464i \(-0.729830\pi\)
−0.660912 + 0.750464i \(0.729830\pi\)
\(642\) 0 0
\(643\) 17.3135 0.682777 0.341388 0.939922i \(-0.389103\pi\)
0.341388 + 0.939922i \(0.389103\pi\)
\(644\) 0 0
\(645\) 14.7036 0.578953
\(646\) 0 0
\(647\) −25.6129 −1.00695 −0.503473 0.864011i \(-0.667945\pi\)
−0.503473 + 0.864011i \(0.667945\pi\)
\(648\) 0 0
\(649\) −0.164414 −0.00645382
\(650\) 0 0
\(651\) 19.3896 0.759938
\(652\) 0 0
\(653\) 9.35684 0.366161 0.183081 0.983098i \(-0.441393\pi\)
0.183081 + 0.983098i \(0.441393\pi\)
\(654\) 0 0
\(655\) −15.7962 −0.617208
\(656\) 0 0
\(657\) −3.76173 −0.146759
\(658\) 0 0
\(659\) −1.42266 −0.0554188 −0.0277094 0.999616i \(-0.508821\pi\)
−0.0277094 + 0.999616i \(0.508821\pi\)
\(660\) 0 0
\(661\) 4.25492 0.165497 0.0827485 0.996570i \(-0.473630\pi\)
0.0827485 + 0.996570i \(0.473630\pi\)
\(662\) 0 0
\(663\) 10.6817 0.414842
\(664\) 0 0
\(665\) 35.5831 1.37985
\(666\) 0 0
\(667\) −48.6103 −1.88220
\(668\) 0 0
\(669\) 2.36856 0.0915738
\(670\) 0 0
\(671\) −25.8025 −0.996093
\(672\) 0 0
\(673\) −38.0475 −1.46663 −0.733313 0.679892i \(-0.762027\pi\)
−0.733313 + 0.679892i \(0.762027\pi\)
\(674\) 0 0
\(675\) 2.13028 0.0819945
\(676\) 0 0
\(677\) −38.7193 −1.48810 −0.744052 0.668122i \(-0.767098\pi\)
−0.744052 + 0.668122i \(0.767098\pi\)
\(678\) 0 0
\(679\) 77.5442 2.97587
\(680\) 0 0
\(681\) −0.662698 −0.0253946
\(682\) 0 0
\(683\) 8.56755 0.327828 0.163914 0.986475i \(-0.447588\pi\)
0.163914 + 0.986475i \(0.447588\pi\)
\(684\) 0 0
\(685\) 37.4017 1.42904
\(686\) 0 0
\(687\) −28.4020 −1.08360
\(688\) 0 0
\(689\) 16.4277 0.625844
\(690\) 0 0
\(691\) −31.7047 −1.20610 −0.603051 0.797702i \(-0.706049\pi\)
−0.603051 + 0.797702i \(0.706049\pi\)
\(692\) 0 0
\(693\) −10.2764 −0.390366
\(694\) 0 0
\(695\) 3.31316 0.125675
\(696\) 0 0
\(697\) 8.07118 0.305718
\(698\) 0 0
\(699\) −1.11158 −0.0420437
\(700\) 0 0
\(701\) −43.0946 −1.62766 −0.813830 0.581103i \(-0.802621\pi\)
−0.813830 + 0.581103i \(0.802621\pi\)
\(702\) 0 0
\(703\) 0.0680256 0.00256563
\(704\) 0 0
\(705\) −9.01045 −0.339353
\(706\) 0 0
\(707\) 58.0574 2.18347
\(708\) 0 0
\(709\) −23.8750 −0.896643 −0.448321 0.893872i \(-0.647978\pi\)
−0.448321 + 0.893872i \(0.647978\pi\)
\(710\) 0 0
\(711\) −11.4241 −0.428437
\(712\) 0 0
\(713\) 30.7954 1.15330
\(714\) 0 0
\(715\) 5.70603 0.213393
\(716\) 0 0
\(717\) −5.03519 −0.188043
\(718\) 0 0
\(719\) 10.9206 0.407269 0.203635 0.979047i \(-0.434725\pi\)
0.203635 + 0.979047i \(0.434725\pi\)
\(720\) 0 0
\(721\) 73.8219 2.74927
\(722\) 0 0
\(723\) −15.9384 −0.592755
\(724\) 0 0
\(725\) −15.7897 −0.586415
\(726\) 0 0
\(727\) 15.2704 0.566348 0.283174 0.959069i \(-0.408613\pi\)
0.283174 + 0.959069i \(0.408613\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −68.5005 −2.53358
\(732\) 0 0
\(733\) 21.4949 0.793931 0.396966 0.917834i \(-0.370063\pi\)
0.396966 + 0.917834i \(0.370063\pi\)
\(734\) 0 0
\(735\) 17.0266 0.628034
\(736\) 0 0
\(737\) 15.1966 0.559773
\(738\) 0 0
\(739\) −24.6120 −0.905368 −0.452684 0.891671i \(-0.649533\pi\)
−0.452684 + 0.891671i \(0.649533\pi\)
\(740\) 0 0
\(741\) 6.88493 0.252924
\(742\) 0 0
\(743\) 29.9574 1.09903 0.549514 0.835484i \(-0.314813\pi\)
0.549514 + 0.835484i \(0.314813\pi\)
\(744\) 0 0
\(745\) 3.22882 0.118295
\(746\) 0 0
\(747\) −10.4077 −0.380799
\(748\) 0 0
\(749\) −54.2148 −1.98097
\(750\) 0 0
\(751\) −33.9459 −1.23870 −0.619351 0.785114i \(-0.712604\pi\)
−0.619351 + 0.785114i \(0.712604\pi\)
\(752\) 0 0
\(753\) 12.4875 0.455070
\(754\) 0 0
\(755\) −10.9651 −0.399060
\(756\) 0 0
\(757\) 13.7652 0.500303 0.250152 0.968207i \(-0.419520\pi\)
0.250152 + 0.968207i \(0.419520\pi\)
\(758\) 0 0
\(759\) −16.3213 −0.592427
\(760\) 0 0
\(761\) 9.19742 0.333406 0.166703 0.986007i \(-0.446688\pi\)
0.166703 + 0.986007i \(0.446688\pi\)
\(762\) 0 0
\(763\) 35.9679 1.30213
\(764\) 0 0
\(765\) 13.3693 0.483369
\(766\) 0 0
\(767\) 0.0894178 0.00322869
\(768\) 0 0
\(769\) 23.3873 0.843368 0.421684 0.906743i \(-0.361439\pi\)
0.421684 + 0.906743i \(0.361439\pi\)
\(770\) 0 0
\(771\) −13.4024 −0.482674
\(772\) 0 0
\(773\) 2.59137 0.0932050 0.0466025 0.998914i \(-0.485161\pi\)
0.0466025 + 0.998914i \(0.485161\pi\)
\(774\) 0 0
\(775\) 10.0030 0.359319
\(776\) 0 0
\(777\) 0.0552200 0.00198101
\(778\) 0 0
\(779\) 5.20233 0.186393
\(780\) 0 0
\(781\) −24.7849 −0.886873
\(782\) 0 0
\(783\) −7.41203 −0.264884
\(784\) 0 0
\(785\) −0.742874 −0.0265143
\(786\) 0 0
\(787\) −7.99368 −0.284944 −0.142472 0.989799i \(-0.545505\pi\)
−0.142472 + 0.989799i \(0.545505\pi\)
\(788\) 0 0
\(789\) 10.2710 0.365657
\(790\) 0 0
\(791\) −13.4207 −0.477185
\(792\) 0 0
\(793\) 14.0329 0.498321
\(794\) 0 0
\(795\) 20.5611 0.729227
\(796\) 0 0
\(797\) 15.4523 0.547348 0.273674 0.961823i \(-0.411761\pi\)
0.273674 + 0.961823i \(0.411761\pi\)
\(798\) 0 0
\(799\) 41.9775 1.48506
\(800\) 0 0
\(801\) 6.46475 0.228421
\(802\) 0 0
\(803\) 9.36165 0.330365
\(804\) 0 0
\(805\) 45.8759 1.61691
\(806\) 0 0
\(807\) −21.0795 −0.742032
\(808\) 0 0
\(809\) −8.25639 −0.290279 −0.145140 0.989411i \(-0.546363\pi\)
−0.145140 + 0.989411i \(0.546363\pi\)
\(810\) 0 0
\(811\) 26.6623 0.936240 0.468120 0.883665i \(-0.344932\pi\)
0.468120 + 0.883665i \(0.344932\pi\)
\(812\) 0 0
\(813\) −22.7180 −0.796756
\(814\) 0 0
\(815\) −20.7466 −0.726721
\(816\) 0 0
\(817\) −44.1523 −1.54470
\(818\) 0 0
\(819\) 5.58886 0.195291
\(820\) 0 0
\(821\) −7.60659 −0.265472 −0.132736 0.991151i \(-0.542376\pi\)
−0.132736 + 0.991151i \(0.542376\pi\)
\(822\) 0 0
\(823\) −33.8995 −1.18166 −0.590832 0.806795i \(-0.701200\pi\)
−0.590832 + 0.806795i \(0.701200\pi\)
\(824\) 0 0
\(825\) −5.30153 −0.184576
\(826\) 0 0
\(827\) −22.3492 −0.777157 −0.388578 0.921416i \(-0.627034\pi\)
−0.388578 + 0.921416i \(0.627034\pi\)
\(828\) 0 0
\(829\) 15.8694 0.551166 0.275583 0.961277i \(-0.411129\pi\)
0.275583 + 0.961277i \(0.411129\pi\)
\(830\) 0 0
\(831\) 25.7334 0.892681
\(832\) 0 0
\(833\) −79.3226 −2.74836
\(834\) 0 0
\(835\) 1.69402 0.0586241
\(836\) 0 0
\(837\) 4.69564 0.162305
\(838\) 0 0
\(839\) −7.54100 −0.260344 −0.130172 0.991491i \(-0.541553\pi\)
−0.130172 + 0.991491i \(0.541553\pi\)
\(840\) 0 0
\(841\) 25.9382 0.894419
\(842\) 0 0
\(843\) 20.0242 0.689669
\(844\) 0 0
\(845\) 18.9191 0.650835
\(846\) 0 0
\(847\) −19.8478 −0.681978
\(848\) 0 0
\(849\) −7.01267 −0.240674
\(850\) 0 0
\(851\) 0.0877027 0.00300641
\(852\) 0 0
\(853\) 39.5679 1.35478 0.677389 0.735625i \(-0.263111\pi\)
0.677389 + 0.735625i \(0.263111\pi\)
\(854\) 0 0
\(855\) 8.61727 0.294705
\(856\) 0 0
\(857\) 23.3571 0.797864 0.398932 0.916981i \(-0.369381\pi\)
0.398932 + 0.916981i \(0.369381\pi\)
\(858\) 0 0
\(859\) 43.6810 1.49038 0.745189 0.666854i \(-0.232359\pi\)
0.745189 + 0.666854i \(0.232359\pi\)
\(860\) 0 0
\(861\) 4.22301 0.143920
\(862\) 0 0
\(863\) 41.6590 1.41809 0.709044 0.705165i \(-0.249127\pi\)
0.709044 + 0.705165i \(0.249127\pi\)
\(864\) 0 0
\(865\) −14.7611 −0.501891
\(866\) 0 0
\(867\) −45.2844 −1.53794
\(868\) 0 0
\(869\) 28.4306 0.964443
\(870\) 0 0
\(871\) −8.26476 −0.280041
\(872\) 0 0
\(873\) 18.7791 0.635576
\(874\) 0 0
\(875\) 49.8770 1.68615
\(876\) 0 0
\(877\) −44.4805 −1.50200 −0.751000 0.660302i \(-0.770428\pi\)
−0.751000 + 0.660302i \(0.770428\pi\)
\(878\) 0 0
\(879\) −2.63359 −0.0888287
\(880\) 0 0
\(881\) −4.85366 −0.163524 −0.0817619 0.996652i \(-0.526055\pi\)
−0.0817619 + 0.996652i \(0.526055\pi\)
\(882\) 0 0
\(883\) −31.3649 −1.05551 −0.527757 0.849395i \(-0.676967\pi\)
−0.527757 + 0.849395i \(0.676967\pi\)
\(884\) 0 0
\(885\) 0.111917 0.00376203
\(886\) 0 0
\(887\) 14.4960 0.486727 0.243364 0.969935i \(-0.421749\pi\)
0.243364 + 0.969935i \(0.421749\pi\)
\(888\) 0 0
\(889\) 68.9454 2.31235
\(890\) 0 0
\(891\) −2.48865 −0.0833731
\(892\) 0 0
\(893\) 27.0568 0.905423
\(894\) 0 0
\(895\) 36.2325 1.21112
\(896\) 0 0
\(897\) 8.87647 0.296377
\(898\) 0 0
\(899\) −34.8042 −1.16078
\(900\) 0 0
\(901\) −95.7891 −3.19120
\(902\) 0 0
\(903\) −35.8408 −1.19271
\(904\) 0 0
\(905\) 3.14486 0.104539
\(906\) 0 0
\(907\) −3.11429 −0.103408 −0.0517042 0.998662i \(-0.516465\pi\)
−0.0517042 + 0.998662i \(0.516465\pi\)
\(908\) 0 0
\(909\) 14.0599 0.466338
\(910\) 0 0
\(911\) 56.8426 1.88328 0.941640 0.336620i \(-0.109284\pi\)
0.941640 + 0.336620i \(0.109284\pi\)
\(912\) 0 0
\(913\) 25.9013 0.857207
\(914\) 0 0
\(915\) 17.5637 0.580639
\(916\) 0 0
\(917\) 38.5041 1.27152
\(918\) 0 0
\(919\) −35.0944 −1.15766 −0.578829 0.815449i \(-0.696490\pi\)
−0.578829 + 0.815449i \(0.696490\pi\)
\(920\) 0 0
\(921\) 12.3105 0.405645
\(922\) 0 0
\(923\) 13.4794 0.443681
\(924\) 0 0
\(925\) 0.0284878 0.000936673 0
\(926\) 0 0
\(927\) 17.8777 0.587180
\(928\) 0 0
\(929\) −11.1328 −0.365255 −0.182627 0.983182i \(-0.558460\pi\)
−0.182627 + 0.983182i \(0.558460\pi\)
\(930\) 0 0
\(931\) −51.1278 −1.67565
\(932\) 0 0
\(933\) 23.9999 0.785720
\(934\) 0 0
\(935\) −33.2716 −1.08810
\(936\) 0 0
\(937\) 1.43915 0.0470149 0.0235075 0.999724i \(-0.492517\pi\)
0.0235075 + 0.999724i \(0.492517\pi\)
\(938\) 0 0
\(939\) −3.38113 −0.110339
\(940\) 0 0
\(941\) −27.6688 −0.901976 −0.450988 0.892530i \(-0.648928\pi\)
−0.450988 + 0.892530i \(0.648928\pi\)
\(942\) 0 0
\(943\) 6.70715 0.218415
\(944\) 0 0
\(945\) 6.99510 0.227551
\(946\) 0 0
\(947\) −22.1562 −0.719979 −0.359989 0.932956i \(-0.617220\pi\)
−0.359989 + 0.932956i \(0.617220\pi\)
\(948\) 0 0
\(949\) −5.09140 −0.165274
\(950\) 0 0
\(951\) 7.85532 0.254726
\(952\) 0 0
\(953\) 18.1214 0.587010 0.293505 0.955957i \(-0.405178\pi\)
0.293505 + 0.955957i \(0.405178\pi\)
\(954\) 0 0
\(955\) 19.4493 0.629366
\(956\) 0 0
\(957\) 18.4460 0.596274
\(958\) 0 0
\(959\) −91.1686 −2.94399
\(960\) 0 0
\(961\) −8.95101 −0.288742
\(962\) 0 0
\(963\) −13.1294 −0.423088
\(964\) 0 0
\(965\) 42.3669 1.36384
\(966\) 0 0
\(967\) −40.2636 −1.29479 −0.647395 0.762155i \(-0.724142\pi\)
−0.647395 + 0.762155i \(0.724142\pi\)
\(968\) 0 0
\(969\) −40.1458 −1.28967
\(970\) 0 0
\(971\) −16.8192 −0.539752 −0.269876 0.962895i \(-0.586983\pi\)
−0.269876 + 0.962895i \(0.586983\pi\)
\(972\) 0 0
\(973\) −8.07601 −0.258905
\(974\) 0 0
\(975\) 2.88327 0.0923387
\(976\) 0 0
\(977\) 18.1817 0.581685 0.290842 0.956771i \(-0.406064\pi\)
0.290842 + 0.956771i \(0.406064\pi\)
\(978\) 0 0
\(979\) −16.0885 −0.514192
\(980\) 0 0
\(981\) 8.71046 0.278104
\(982\) 0 0
\(983\) −38.6117 −1.23152 −0.615761 0.787933i \(-0.711151\pi\)
−0.615761 + 0.787933i \(0.711151\pi\)
\(984\) 0 0
\(985\) −42.7332 −1.36159
\(986\) 0 0
\(987\) 21.9635 0.699105
\(988\) 0 0
\(989\) −56.9239 −1.81007
\(990\) 0 0
\(991\) −6.98885 −0.222008 −0.111004 0.993820i \(-0.535407\pi\)
−0.111004 + 0.993820i \(0.535407\pi\)
\(992\) 0 0
\(993\) −24.1080 −0.765045
\(994\) 0 0
\(995\) −42.6954 −1.35353
\(996\) 0 0
\(997\) −5.03760 −0.159542 −0.0797712 0.996813i \(-0.525419\pi\)
−0.0797712 + 0.996813i \(0.525419\pi\)
\(998\) 0 0
\(999\) 0.0133728 0.000423097 0
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.1.2 9
4.3 odd 2 2004.2.a.d.1.2 9
12.11 even 2 6012.2.a.h.1.8 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.d.1.2 9 4.3 odd 2
6012.2.a.h.1.8 9 12.11 even 2
8016.2.a.bb.1.2 9 1.1 even 1 trivial