Properties

Label 8016.2.a.bb.1.1
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 1.1
Root \(4.16840\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -3.16840 q^{5} +0.230890 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -3.16840 q^{5} +0.230890 q^{7} +1.00000 q^{9} -0.534912 q^{11} +2.40467 q^{13} +3.16840 q^{15} +3.83643 q^{17} +7.74980 q^{19} -0.230890 q^{21} -5.14190 q^{23} +5.03875 q^{25} -1.00000 q^{27} +0.602944 q^{29} +4.43840 q^{31} +0.534912 q^{33} -0.731551 q^{35} +8.52496 q^{37} -2.40467 q^{39} +1.40231 q^{41} +3.66794 q^{43} -3.16840 q^{45} -12.4809 q^{47} -6.94669 q^{49} -3.83643 q^{51} +4.85598 q^{53} +1.69482 q^{55} -7.74980 q^{57} -9.66413 q^{59} -1.49131 q^{61} +0.230890 q^{63} -7.61896 q^{65} -12.0615 q^{67} +5.14190 q^{69} -11.4038 q^{71} +4.16407 q^{73} -5.03875 q^{75} -0.123506 q^{77} +7.52893 q^{79} +1.00000 q^{81} -7.44885 q^{83} -12.1553 q^{85} -0.602944 q^{87} +9.40223 q^{89} +0.555214 q^{91} -4.43840 q^{93} -24.5544 q^{95} +12.2203 q^{97} -0.534912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} - 7q^{11} + 6q^{13} - 9q^{15} + 7q^{17} - 2q^{19} + 2q^{21} - 19q^{23} + 22q^{25} - 9q^{27} + 13q^{29} - 12q^{31} + 7q^{33} - 4q^{35} + 15q^{37} - 6q^{39} + 18q^{41} + 6q^{43} + 9q^{45} - 25q^{47} + 19q^{49} - 7q^{51} + 17q^{53} + 3q^{55} + 2q^{57} - 3q^{59} + 14q^{61} - 2q^{63} + 14q^{65} + 4q^{67} + 19q^{69} - 17q^{71} - 20q^{73} - 22q^{75} + 14q^{77} + 8q^{79} + 9q^{81} + q^{83} + 5q^{85} - 13q^{87} + 36q^{89} + 41q^{91} + 12q^{93} - 5q^{95} + 31q^{97} - 7q^{99} + O(q^{100}) \)

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
\(5\) −3.16840 −1.41695 −0.708476 0.705735i \(-0.750617\pi\)
−0.708476 + 0.705735i \(0.750617\pi\)
\(6\) 0 0
\(7\) 0.230890 0.0872681 0.0436341 0.999048i \(-0.486106\pi\)
0.0436341 + 0.999048i \(0.486106\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.534912 −0.161282 −0.0806411 0.996743i \(-0.525697\pi\)
−0.0806411 + 0.996743i \(0.525697\pi\)
\(12\) 0 0
\(13\) 2.40467 0.666936 0.333468 0.942761i \(-0.391781\pi\)
0.333468 + 0.942761i \(0.391781\pi\)
\(14\) 0 0
\(15\) 3.16840 0.818077
\(16\) 0 0
\(17\) 3.83643 0.930471 0.465235 0.885187i \(-0.345970\pi\)
0.465235 + 0.885187i \(0.345970\pi\)
\(18\) 0 0
\(19\) 7.74980 1.77793 0.888963 0.457980i \(-0.151427\pi\)
0.888963 + 0.457980i \(0.151427\pi\)
\(20\) 0 0
\(21\) −0.230890 −0.0503843
\(22\) 0 0
\(23\) −5.14190 −1.07216 −0.536080 0.844167i \(-0.680095\pi\)
−0.536080 + 0.844167i \(0.680095\pi\)
\(24\) 0 0
\(25\) 5.03875 1.00775
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.602944 0.111964 0.0559820 0.998432i \(-0.482171\pi\)
0.0559820 + 0.998432i \(0.482171\pi\)
\(30\) 0 0
\(31\) 4.43840 0.797161 0.398580 0.917133i \(-0.369503\pi\)
0.398580 + 0.917133i \(0.369503\pi\)
\(32\) 0 0
\(33\) 0.534912 0.0931163
\(34\) 0 0
\(35\) −0.731551 −0.123655
\(36\) 0 0
\(37\) 8.52496 1.40149 0.700747 0.713410i \(-0.252850\pi\)
0.700747 + 0.713410i \(0.252850\pi\)
\(38\) 0 0
\(39\) −2.40467 −0.385056
\(40\) 0 0
\(41\) 1.40231 0.219004 0.109502 0.993987i \(-0.465074\pi\)
0.109502 + 0.993987i \(0.465074\pi\)
\(42\) 0 0
\(43\) 3.66794 0.559356 0.279678 0.960094i \(-0.409772\pi\)
0.279678 + 0.960094i \(0.409772\pi\)
\(44\) 0 0
\(45\) −3.16840 −0.472317
\(46\) 0 0
\(47\) −12.4809 −1.82052 −0.910262 0.414032i \(-0.864120\pi\)
−0.910262 + 0.414032i \(0.864120\pi\)
\(48\) 0 0
\(49\) −6.94669 −0.992384
\(50\) 0 0
\(51\) −3.83643 −0.537208
\(52\) 0 0
\(53\) 4.85598 0.667020 0.333510 0.942747i \(-0.391767\pi\)
0.333510 + 0.942747i \(0.391767\pi\)
\(54\) 0 0
\(55\) 1.69482 0.228529
\(56\) 0 0
\(57\) −7.74980 −1.02649
\(58\) 0 0
\(59\) −9.66413 −1.25816 −0.629081 0.777339i \(-0.716569\pi\)
−0.629081 + 0.777339i \(0.716569\pi\)
\(60\) 0 0
\(61\) −1.49131 −0.190942 −0.0954712 0.995432i \(-0.530436\pi\)
−0.0954712 + 0.995432i \(0.530436\pi\)
\(62\) 0 0
\(63\) 0.230890 0.0290894
\(64\) 0 0
\(65\) −7.61896 −0.945015
\(66\) 0 0
\(67\) −12.0615 −1.47355 −0.736773 0.676140i \(-0.763652\pi\)
−0.736773 + 0.676140i \(0.763652\pi\)
\(68\) 0 0
\(69\) 5.14190 0.619012
\(70\) 0 0
\(71\) −11.4038 −1.35338 −0.676691 0.736267i \(-0.736587\pi\)
−0.676691 + 0.736267i \(0.736587\pi\)
\(72\) 0 0
\(73\) 4.16407 0.487368 0.243684 0.969855i \(-0.421644\pi\)
0.243684 + 0.969855i \(0.421644\pi\)
\(74\) 0 0
\(75\) −5.03875 −0.581825
\(76\) 0 0
\(77\) −0.123506 −0.0140748
\(78\) 0 0
\(79\) 7.52893 0.847071 0.423536 0.905879i \(-0.360789\pi\)
0.423536 + 0.905879i \(0.360789\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.44885 −0.817617 −0.408809 0.912620i \(-0.634056\pi\)
−0.408809 + 0.912620i \(0.634056\pi\)
\(84\) 0 0
\(85\) −12.1553 −1.31843
\(86\) 0 0
\(87\) −0.602944 −0.0646424
\(88\) 0 0
\(89\) 9.40223 0.996635 0.498317 0.866995i \(-0.333951\pi\)
0.498317 + 0.866995i \(0.333951\pi\)
\(90\) 0 0
\(91\) 0.555214 0.0582022
\(92\) 0 0
\(93\) −4.43840 −0.460241
\(94\) 0 0
\(95\) −24.5544 −2.51923
\(96\) 0 0
\(97\) 12.2203 1.24078 0.620391 0.784293i \(-0.286974\pi\)
0.620391 + 0.784293i \(0.286974\pi\)
\(98\) 0 0
\(99\) −0.534912 −0.0537607
\(100\) 0 0
\(101\) 3.01977 0.300478 0.150239 0.988650i \(-0.451996\pi\)
0.150239 + 0.988650i \(0.451996\pi\)
\(102\) 0 0
\(103\) −11.2753 −1.11099 −0.555496 0.831519i \(-0.687472\pi\)
−0.555496 + 0.831519i \(0.687472\pi\)
\(104\) 0 0
\(105\) 0.731551 0.0713920
\(106\) 0 0
\(107\) 20.1981 1.95263 0.976314 0.216360i \(-0.0694185\pi\)
0.976314 + 0.216360i \(0.0694185\pi\)
\(108\) 0 0
\(109\) 0.443113 0.0424425 0.0212212 0.999775i \(-0.493245\pi\)
0.0212212 + 0.999775i \(0.493245\pi\)
\(110\) 0 0
\(111\) −8.52496 −0.809153
\(112\) 0 0
\(113\) 12.4535 1.17152 0.585762 0.810483i \(-0.300795\pi\)
0.585762 + 0.810483i \(0.300795\pi\)
\(114\) 0 0
\(115\) 16.2916 1.51920
\(116\) 0 0
\(117\) 2.40467 0.222312
\(118\) 0 0
\(119\) 0.885792 0.0812004
\(120\) 0 0
\(121\) −10.7139 −0.973988
\(122\) 0 0
\(123\) −1.40231 −0.126442
\(124\) 0 0
\(125\) −0.122782 −0.0109819
\(126\) 0 0
\(127\) −20.7466 −1.84096 −0.920480 0.390790i \(-0.872202\pi\)
−0.920480 + 0.390790i \(0.872202\pi\)
\(128\) 0 0
\(129\) −3.66794 −0.322944
\(130\) 0 0
\(131\) 2.73611 0.239055 0.119527 0.992831i \(-0.461862\pi\)
0.119527 + 0.992831i \(0.461862\pi\)
\(132\) 0 0
\(133\) 1.78935 0.155156
\(134\) 0 0
\(135\) 3.16840 0.272692
\(136\) 0 0
\(137\) 5.01418 0.428391 0.214195 0.976791i \(-0.431287\pi\)
0.214195 + 0.976791i \(0.431287\pi\)
\(138\) 0 0
\(139\) 0.0795501 0.00674735 0.00337367 0.999994i \(-0.498926\pi\)
0.00337367 + 0.999994i \(0.498926\pi\)
\(140\) 0 0
\(141\) 12.4809 1.05108
\(142\) 0 0
\(143\) −1.28629 −0.107565
\(144\) 0 0
\(145\) −1.91037 −0.158647
\(146\) 0 0
\(147\) 6.94669 0.572953
\(148\) 0 0
\(149\) −14.9835 −1.22749 −0.613746 0.789503i \(-0.710338\pi\)
−0.613746 + 0.789503i \(0.710338\pi\)
\(150\) 0 0
\(151\) 16.8126 1.36819 0.684097 0.729391i \(-0.260197\pi\)
0.684097 + 0.729391i \(0.260197\pi\)
\(152\) 0 0
\(153\) 3.83643 0.310157
\(154\) 0 0
\(155\) −14.0626 −1.12954
\(156\) 0 0
\(157\) 8.50629 0.678876 0.339438 0.940628i \(-0.389763\pi\)
0.339438 + 0.940628i \(0.389763\pi\)
\(158\) 0 0
\(159\) −4.85598 −0.385104
\(160\) 0 0
\(161\) −1.18721 −0.0935653
\(162\) 0 0
\(163\) 15.6607 1.22664 0.613320 0.789835i \(-0.289834\pi\)
0.613320 + 0.789835i \(0.289834\pi\)
\(164\) 0 0
\(165\) −1.69482 −0.131941
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −7.21756 −0.555197
\(170\) 0 0
\(171\) 7.74980 0.592642
\(172\) 0 0
\(173\) −17.1435 −1.30340 −0.651700 0.758477i \(-0.725944\pi\)
−0.651700 + 0.758477i \(0.725944\pi\)
\(174\) 0 0
\(175\) 1.16340 0.0879445
\(176\) 0 0
\(177\) 9.66413 0.726401
\(178\) 0 0
\(179\) 26.4251 1.97510 0.987551 0.157297i \(-0.0502779\pi\)
0.987551 + 0.157297i \(0.0502779\pi\)
\(180\) 0 0
\(181\) 3.49842 0.260036 0.130018 0.991512i \(-0.458497\pi\)
0.130018 + 0.991512i \(0.458497\pi\)
\(182\) 0 0
\(183\) 1.49131 0.110241
\(184\) 0 0
\(185\) −27.0105 −1.98585
\(186\) 0 0
\(187\) −2.05215 −0.150068
\(188\) 0 0
\(189\) −0.230890 −0.0167948
\(190\) 0 0
\(191\) 21.6136 1.56390 0.781952 0.623339i \(-0.214224\pi\)
0.781952 + 0.623339i \(0.214224\pi\)
\(192\) 0 0
\(193\) −8.20183 −0.590381 −0.295190 0.955438i \(-0.595383\pi\)
−0.295190 + 0.955438i \(0.595383\pi\)
\(194\) 0 0
\(195\) 7.61896 0.545605
\(196\) 0 0
\(197\) 2.73231 0.194669 0.0973345 0.995252i \(-0.468968\pi\)
0.0973345 + 0.995252i \(0.468968\pi\)
\(198\) 0 0
\(199\) −24.5661 −1.74144 −0.870721 0.491778i \(-0.836347\pi\)
−0.870721 + 0.491778i \(0.836347\pi\)
\(200\) 0 0
\(201\) 12.0615 0.850753
\(202\) 0 0
\(203\) 0.139214 0.00977088
\(204\) 0 0
\(205\) −4.44308 −0.310318
\(206\) 0 0
\(207\) −5.14190 −0.357387
\(208\) 0 0
\(209\) −4.14546 −0.286748
\(210\) 0 0
\(211\) 13.0986 0.901748 0.450874 0.892588i \(-0.351112\pi\)
0.450874 + 0.892588i \(0.351112\pi\)
\(212\) 0 0
\(213\) 11.4038 0.781376
\(214\) 0 0
\(215\) −11.6215 −0.792580
\(216\) 0 0
\(217\) 1.02478 0.0695667
\(218\) 0 0
\(219\) −4.16407 −0.281382
\(220\) 0 0
\(221\) 9.22535 0.620564
\(222\) 0 0
\(223\) 3.90957 0.261804 0.130902 0.991395i \(-0.458213\pi\)
0.130902 + 0.991395i \(0.458213\pi\)
\(224\) 0 0
\(225\) 5.03875 0.335917
\(226\) 0 0
\(227\) −6.24862 −0.414736 −0.207368 0.978263i \(-0.566490\pi\)
−0.207368 + 0.978263i \(0.566490\pi\)
\(228\) 0 0
\(229\) 25.5918 1.69116 0.845578 0.533851i \(-0.179256\pi\)
0.845578 + 0.533851i \(0.179256\pi\)
\(230\) 0 0
\(231\) 0.123506 0.00812608
\(232\) 0 0
\(233\) −13.0269 −0.853421 −0.426711 0.904388i \(-0.640328\pi\)
−0.426711 + 0.904388i \(0.640328\pi\)
\(234\) 0 0
\(235\) 39.5444 2.57959
\(236\) 0 0
\(237\) −7.52893 −0.489057
\(238\) 0 0
\(239\) −8.54827 −0.552942 −0.276471 0.961022i \(-0.589165\pi\)
−0.276471 + 0.961022i \(0.589165\pi\)
\(240\) 0 0
\(241\) −16.8836 −1.08757 −0.543783 0.839226i \(-0.683008\pi\)
−0.543783 + 0.839226i \(0.683008\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 22.0099 1.40616
\(246\) 0 0
\(247\) 18.6357 1.18576
\(248\) 0 0
\(249\) 7.44885 0.472051
\(250\) 0 0
\(251\) 1.92874 0.121741 0.0608704 0.998146i \(-0.480612\pi\)
0.0608704 + 0.998146i \(0.480612\pi\)
\(252\) 0 0
\(253\) 2.75046 0.172920
\(254\) 0 0
\(255\) 12.1553 0.761197
\(256\) 0 0
\(257\) 18.9215 1.18029 0.590145 0.807297i \(-0.299071\pi\)
0.590145 + 0.807297i \(0.299071\pi\)
\(258\) 0 0
\(259\) 1.96833 0.122306
\(260\) 0 0
\(261\) 0.602944 0.0373213
\(262\) 0 0
\(263\) 8.99207 0.554475 0.277237 0.960801i \(-0.410581\pi\)
0.277237 + 0.960801i \(0.410581\pi\)
\(264\) 0 0
\(265\) −15.3857 −0.945135
\(266\) 0 0
\(267\) −9.40223 −0.575407
\(268\) 0 0
\(269\) 11.8434 0.722102 0.361051 0.932546i \(-0.382418\pi\)
0.361051 + 0.932546i \(0.382418\pi\)
\(270\) 0 0
\(271\) −3.28934 −0.199813 −0.0999065 0.994997i \(-0.531854\pi\)
−0.0999065 + 0.994997i \(0.531854\pi\)
\(272\) 0 0
\(273\) −0.555214 −0.0336031
\(274\) 0 0
\(275\) −2.69529 −0.162532
\(276\) 0 0
\(277\) 8.25296 0.495872 0.247936 0.968776i \(-0.420248\pi\)
0.247936 + 0.968776i \(0.420248\pi\)
\(278\) 0 0
\(279\) 4.43840 0.265720
\(280\) 0 0
\(281\) 15.3602 0.916313 0.458156 0.888872i \(-0.348510\pi\)
0.458156 + 0.888872i \(0.348510\pi\)
\(282\) 0 0
\(283\) −11.8821 −0.706320 −0.353160 0.935563i \(-0.614893\pi\)
−0.353160 + 0.935563i \(0.614893\pi\)
\(284\) 0 0
\(285\) 24.5544 1.45448
\(286\) 0 0
\(287\) 0.323779 0.0191121
\(288\) 0 0
\(289\) −2.28181 −0.134224
\(290\) 0 0
\(291\) −12.2203 −0.716366
\(292\) 0 0
\(293\) −22.7646 −1.32992 −0.664960 0.746879i \(-0.731551\pi\)
−0.664960 + 0.746879i \(0.731551\pi\)
\(294\) 0 0
\(295\) 30.6198 1.78276
\(296\) 0 0
\(297\) 0.534912 0.0310388
\(298\) 0 0
\(299\) −12.3646 −0.715062
\(300\) 0 0
\(301\) 0.846890 0.0488140
\(302\) 0 0
\(303\) −3.01977 −0.173481
\(304\) 0 0
\(305\) 4.72506 0.270556
\(306\) 0 0
\(307\) 33.2061 1.89517 0.947585 0.319503i \(-0.103516\pi\)
0.947585 + 0.319503i \(0.103516\pi\)
\(308\) 0 0
\(309\) 11.2753 0.641432
\(310\) 0 0
\(311\) 11.8693 0.673047 0.336523 0.941675i \(-0.390749\pi\)
0.336523 + 0.941675i \(0.390749\pi\)
\(312\) 0 0
\(313\) −8.72134 −0.492959 −0.246480 0.969148i \(-0.579274\pi\)
−0.246480 + 0.969148i \(0.579274\pi\)
\(314\) 0 0
\(315\) −0.731551 −0.0412182
\(316\) 0 0
\(317\) 21.0893 1.18449 0.592246 0.805757i \(-0.298241\pi\)
0.592246 + 0.805757i \(0.298241\pi\)
\(318\) 0 0
\(319\) −0.322522 −0.0180578
\(320\) 0 0
\(321\) −20.1981 −1.12735
\(322\) 0 0
\(323\) 29.7315 1.65431
\(324\) 0 0
\(325\) 12.1165 0.672105
\(326\) 0 0
\(327\) −0.443113 −0.0245042
\(328\) 0 0
\(329\) −2.88171 −0.158874
\(330\) 0 0
\(331\) 10.9529 0.602026 0.301013 0.953620i \(-0.402675\pi\)
0.301013 + 0.953620i \(0.402675\pi\)
\(332\) 0 0
\(333\) 8.52496 0.467165
\(334\) 0 0
\(335\) 38.2156 2.08794
\(336\) 0 0
\(337\) −16.1884 −0.881839 −0.440920 0.897547i \(-0.645348\pi\)
−0.440920 + 0.897547i \(0.645348\pi\)
\(338\) 0 0
\(339\) −12.4535 −0.676379
\(340\) 0 0
\(341\) −2.37416 −0.128568
\(342\) 0 0
\(343\) −3.22015 −0.173872
\(344\) 0 0
\(345\) −16.2916 −0.877109
\(346\) 0 0
\(347\) −5.29375 −0.284183 −0.142092 0.989854i \(-0.545383\pi\)
−0.142092 + 0.989854i \(0.545383\pi\)
\(348\) 0 0
\(349\) 33.7932 1.80891 0.904453 0.426573i \(-0.140279\pi\)
0.904453 + 0.426573i \(0.140279\pi\)
\(350\) 0 0
\(351\) −2.40467 −0.128352
\(352\) 0 0
\(353\) 14.1450 0.752864 0.376432 0.926444i \(-0.377151\pi\)
0.376432 + 0.926444i \(0.377151\pi\)
\(354\) 0 0
\(355\) 36.1318 1.91768
\(356\) 0 0
\(357\) −0.885792 −0.0468811
\(358\) 0 0
\(359\) 9.66904 0.510312 0.255156 0.966900i \(-0.417873\pi\)
0.255156 + 0.966900i \(0.417873\pi\)
\(360\) 0 0
\(361\) 41.0593 2.16102
\(362\) 0 0
\(363\) 10.7139 0.562332
\(364\) 0 0
\(365\) −13.1934 −0.690577
\(366\) 0 0
\(367\) −13.1304 −0.685399 −0.342700 0.939445i \(-0.611341\pi\)
−0.342700 + 0.939445i \(0.611341\pi\)
\(368\) 0 0
\(369\) 1.40231 0.0730014
\(370\) 0 0
\(371\) 1.12120 0.0582096
\(372\) 0 0
\(373\) −3.67027 −0.190039 −0.0950197 0.995475i \(-0.530291\pi\)
−0.0950197 + 0.995475i \(0.530291\pi\)
\(374\) 0 0
\(375\) 0.122782 0.00634042
\(376\) 0 0
\(377\) 1.44988 0.0746727
\(378\) 0 0
\(379\) −21.9612 −1.12807 −0.564036 0.825750i \(-0.690752\pi\)
−0.564036 + 0.825750i \(0.690752\pi\)
\(380\) 0 0
\(381\) 20.7466 1.06288
\(382\) 0 0
\(383\) −13.5332 −0.691515 −0.345757 0.938324i \(-0.612378\pi\)
−0.345757 + 0.938324i \(0.612378\pi\)
\(384\) 0 0
\(385\) 0.391315 0.0199433
\(386\) 0 0
\(387\) 3.66794 0.186452
\(388\) 0 0
\(389\) −5.09521 −0.258337 −0.129169 0.991623i \(-0.541231\pi\)
−0.129169 + 0.991623i \(0.541231\pi\)
\(390\) 0 0
\(391\) −19.7265 −0.997613
\(392\) 0 0
\(393\) −2.73611 −0.138018
\(394\) 0 0
\(395\) −23.8547 −1.20026
\(396\) 0 0
\(397\) 10.9338 0.548751 0.274376 0.961623i \(-0.411529\pi\)
0.274376 + 0.961623i \(0.411529\pi\)
\(398\) 0 0
\(399\) −1.78935 −0.0895795
\(400\) 0 0
\(401\) 11.6204 0.580296 0.290148 0.956982i \(-0.406295\pi\)
0.290148 + 0.956982i \(0.406295\pi\)
\(402\) 0 0
\(403\) 10.6729 0.531655
\(404\) 0 0
\(405\) −3.16840 −0.157439
\(406\) 0 0
\(407\) −4.56011 −0.226036
\(408\) 0 0
\(409\) 24.7043 1.22155 0.610774 0.791805i \(-0.290858\pi\)
0.610774 + 0.791805i \(0.290858\pi\)
\(410\) 0 0
\(411\) −5.01418 −0.247331
\(412\) 0 0
\(413\) −2.23135 −0.109797
\(414\) 0 0
\(415\) 23.6009 1.15852
\(416\) 0 0
\(417\) −0.0795501 −0.00389558
\(418\) 0 0
\(419\) 17.9832 0.878535 0.439267 0.898356i \(-0.355238\pi\)
0.439267 + 0.898356i \(0.355238\pi\)
\(420\) 0 0
\(421\) −20.8040 −1.01393 −0.506963 0.861968i \(-0.669232\pi\)
−0.506963 + 0.861968i \(0.669232\pi\)
\(422\) 0 0
\(423\) −12.4809 −0.606841
\(424\) 0 0
\(425\) 19.3308 0.937682
\(426\) 0 0
\(427\) −0.344328 −0.0166632
\(428\) 0 0
\(429\) 1.28629 0.0621026
\(430\) 0 0
\(431\) −33.8156 −1.62884 −0.814419 0.580277i \(-0.802944\pi\)
−0.814419 + 0.580277i \(0.802944\pi\)
\(432\) 0 0
\(433\) 19.3923 0.931936 0.465968 0.884802i \(-0.345706\pi\)
0.465968 + 0.884802i \(0.345706\pi\)
\(434\) 0 0
\(435\) 1.91037 0.0915951
\(436\) 0 0
\(437\) −39.8486 −1.90622
\(438\) 0 0
\(439\) 24.3827 1.16372 0.581861 0.813288i \(-0.302325\pi\)
0.581861 + 0.813288i \(0.302325\pi\)
\(440\) 0 0
\(441\) −6.94669 −0.330795
\(442\) 0 0
\(443\) −3.26405 −0.155080 −0.0775399 0.996989i \(-0.524707\pi\)
−0.0775399 + 0.996989i \(0.524707\pi\)
\(444\) 0 0
\(445\) −29.7900 −1.41218
\(446\) 0 0
\(447\) 14.9835 0.708693
\(448\) 0 0
\(449\) 7.62351 0.359775 0.179888 0.983687i \(-0.442427\pi\)
0.179888 + 0.983687i \(0.442427\pi\)
\(450\) 0 0
\(451\) −0.750113 −0.0353215
\(452\) 0 0
\(453\) −16.8126 −0.789927
\(454\) 0 0
\(455\) −1.75914 −0.0824697
\(456\) 0 0
\(457\) −20.3938 −0.953980 −0.476990 0.878909i \(-0.658272\pi\)
−0.476990 + 0.878909i \(0.658272\pi\)
\(458\) 0 0
\(459\) −3.83643 −0.179069
\(460\) 0 0
\(461\) −4.34942 −0.202573 −0.101286 0.994857i \(-0.532296\pi\)
−0.101286 + 0.994857i \(0.532296\pi\)
\(462\) 0 0
\(463\) 34.5171 1.60415 0.802074 0.597225i \(-0.203730\pi\)
0.802074 + 0.597225i \(0.203730\pi\)
\(464\) 0 0
\(465\) 14.0626 0.652139
\(466\) 0 0
\(467\) −23.4037 −1.08300 −0.541498 0.840702i \(-0.682142\pi\)
−0.541498 + 0.840702i \(0.682142\pi\)
\(468\) 0 0
\(469\) −2.78488 −0.128594
\(470\) 0 0
\(471\) −8.50629 −0.391949
\(472\) 0 0
\(473\) −1.96203 −0.0902141
\(474\) 0 0
\(475\) 39.0493 1.79170
\(476\) 0 0
\(477\) 4.85598 0.222340
\(478\) 0 0
\(479\) −4.86695 −0.222377 −0.111188 0.993799i \(-0.535466\pi\)
−0.111188 + 0.993799i \(0.535466\pi\)
\(480\) 0 0
\(481\) 20.4997 0.934707
\(482\) 0 0
\(483\) 1.18721 0.0540200
\(484\) 0 0
\(485\) −38.7187 −1.75813
\(486\) 0 0
\(487\) −21.2862 −0.964570 −0.482285 0.876014i \(-0.660193\pi\)
−0.482285 + 0.876014i \(0.660193\pi\)
\(488\) 0 0
\(489\) −15.6607 −0.708201
\(490\) 0 0
\(491\) 27.1615 1.22578 0.612891 0.790168i \(-0.290007\pi\)
0.612891 + 0.790168i \(0.290007\pi\)
\(492\) 0 0
\(493\) 2.31315 0.104179
\(494\) 0 0
\(495\) 1.69482 0.0761763
\(496\) 0 0
\(497\) −2.63302 −0.118107
\(498\) 0 0
\(499\) 29.7335 1.33105 0.665526 0.746375i \(-0.268207\pi\)
0.665526 + 0.746375i \(0.268207\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −25.1206 −1.12007 −0.560037 0.828467i \(-0.689213\pi\)
−0.560037 + 0.828467i \(0.689213\pi\)
\(504\) 0 0
\(505\) −9.56783 −0.425763
\(506\) 0 0
\(507\) 7.21756 0.320543
\(508\) 0 0
\(509\) −9.98009 −0.442360 −0.221180 0.975233i \(-0.570991\pi\)
−0.221180 + 0.975233i \(0.570991\pi\)
\(510\) 0 0
\(511\) 0.961442 0.0425317
\(512\) 0 0
\(513\) −7.74980 −0.342162
\(514\) 0 0
\(515\) 35.7248 1.57422
\(516\) 0 0
\(517\) 6.67618 0.293618
\(518\) 0 0
\(519\) 17.1435 0.752518
\(520\) 0 0
\(521\) −36.5986 −1.60341 −0.801707 0.597717i \(-0.796075\pi\)
−0.801707 + 0.597717i \(0.796075\pi\)
\(522\) 0 0
\(523\) 19.5958 0.856865 0.428433 0.903574i \(-0.359066\pi\)
0.428433 + 0.903574i \(0.359066\pi\)
\(524\) 0 0
\(525\) −1.16340 −0.0507748
\(526\) 0 0
\(527\) 17.0276 0.741735
\(528\) 0 0
\(529\) 3.43910 0.149526
\(530\) 0 0
\(531\) −9.66413 −0.419388
\(532\) 0 0
\(533\) 3.37210 0.146062
\(534\) 0 0
\(535\) −63.9957 −2.76678
\(536\) 0 0
\(537\) −26.4251 −1.14033
\(538\) 0 0
\(539\) 3.71587 0.160054
\(540\) 0 0
\(541\) 40.4214 1.73785 0.868927 0.494941i \(-0.164810\pi\)
0.868927 + 0.494941i \(0.164810\pi\)
\(542\) 0 0
\(543\) −3.49842 −0.150132
\(544\) 0 0
\(545\) −1.40396 −0.0601389
\(546\) 0 0
\(547\) 29.7069 1.27018 0.635088 0.772440i \(-0.280964\pi\)
0.635088 + 0.772440i \(0.280964\pi\)
\(548\) 0 0
\(549\) −1.49131 −0.0636475
\(550\) 0 0
\(551\) 4.67269 0.199063
\(552\) 0 0
\(553\) 1.73835 0.0739223
\(554\) 0 0
\(555\) 27.0105 1.14653
\(556\) 0 0
\(557\) 41.9127 1.77590 0.887950 0.459940i \(-0.152129\pi\)
0.887950 + 0.459940i \(0.152129\pi\)
\(558\) 0 0
\(559\) 8.82020 0.373055
\(560\) 0 0
\(561\) 2.05215 0.0866420
\(562\) 0 0
\(563\) 25.6677 1.08176 0.540882 0.841099i \(-0.318091\pi\)
0.540882 + 0.841099i \(0.318091\pi\)
\(564\) 0 0
\(565\) −39.4575 −1.65999
\(566\) 0 0
\(567\) 0.230890 0.00969646
\(568\) 0 0
\(569\) 20.1215 0.843538 0.421769 0.906703i \(-0.361409\pi\)
0.421769 + 0.906703i \(0.361409\pi\)
\(570\) 0 0
\(571\) 2.50467 0.104817 0.0524085 0.998626i \(-0.483310\pi\)
0.0524085 + 0.998626i \(0.483310\pi\)
\(572\) 0 0
\(573\) −21.6136 −0.902920
\(574\) 0 0
\(575\) −25.9087 −1.08047
\(576\) 0 0
\(577\) 8.39885 0.349649 0.174824 0.984600i \(-0.444064\pi\)
0.174824 + 0.984600i \(0.444064\pi\)
\(578\) 0 0
\(579\) 8.20183 0.340857
\(580\) 0 0
\(581\) −1.71986 −0.0713519
\(582\) 0 0
\(583\) −2.59752 −0.107578
\(584\) 0 0
\(585\) −7.61896 −0.315005
\(586\) 0 0
\(587\) 5.75584 0.237569 0.118784 0.992920i \(-0.462100\pi\)
0.118784 + 0.992920i \(0.462100\pi\)
\(588\) 0 0
\(589\) 34.3967 1.41729
\(590\) 0 0
\(591\) −2.73231 −0.112392
\(592\) 0 0
\(593\) −1.97459 −0.0810867 −0.0405434 0.999178i \(-0.512909\pi\)
−0.0405434 + 0.999178i \(0.512909\pi\)
\(594\) 0 0
\(595\) −2.80654 −0.115057
\(596\) 0 0
\(597\) 24.5661 1.00542
\(598\) 0 0
\(599\) −15.4063 −0.629486 −0.314743 0.949177i \(-0.601918\pi\)
−0.314743 + 0.949177i \(0.601918\pi\)
\(600\) 0 0
\(601\) −36.5939 −1.49269 −0.746347 0.665557i \(-0.768194\pi\)
−0.746347 + 0.665557i \(0.768194\pi\)
\(602\) 0 0
\(603\) −12.0615 −0.491182
\(604\) 0 0
\(605\) 33.9458 1.38009
\(606\) 0 0
\(607\) 17.4777 0.709398 0.354699 0.934981i \(-0.384583\pi\)
0.354699 + 0.934981i \(0.384583\pi\)
\(608\) 0 0
\(609\) −0.139214 −0.00564122
\(610\) 0 0
\(611\) −30.0124 −1.21417
\(612\) 0 0
\(613\) −27.2259 −1.09964 −0.549821 0.835282i \(-0.685304\pi\)
−0.549821 + 0.835282i \(0.685304\pi\)
\(614\) 0 0
\(615\) 4.44308 0.179162
\(616\) 0 0
\(617\) −22.0487 −0.887648 −0.443824 0.896114i \(-0.646378\pi\)
−0.443824 + 0.896114i \(0.646378\pi\)
\(618\) 0 0
\(619\) 20.9615 0.842513 0.421257 0.906942i \(-0.361589\pi\)
0.421257 + 0.906942i \(0.361589\pi\)
\(620\) 0 0
\(621\) 5.14190 0.206337
\(622\) 0 0
\(623\) 2.17088 0.0869744
\(624\) 0 0
\(625\) −24.8047 −0.992190
\(626\) 0 0
\(627\) 4.14546 0.165554
\(628\) 0 0
\(629\) 32.7054 1.30405
\(630\) 0 0
\(631\) 23.8805 0.950668 0.475334 0.879805i \(-0.342327\pi\)
0.475334 + 0.879805i \(0.342327\pi\)
\(632\) 0 0
\(633\) −13.0986 −0.520624
\(634\) 0 0
\(635\) 65.7334 2.60855
\(636\) 0 0
\(637\) −16.7045 −0.661857
\(638\) 0 0
\(639\) −11.4038 −0.451128
\(640\) 0 0
\(641\) 5.17791 0.204515 0.102258 0.994758i \(-0.467393\pi\)
0.102258 + 0.994758i \(0.467393\pi\)
\(642\) 0 0
\(643\) −22.0105 −0.868010 −0.434005 0.900911i \(-0.642900\pi\)
−0.434005 + 0.900911i \(0.642900\pi\)
\(644\) 0 0
\(645\) 11.6215 0.457596
\(646\) 0 0
\(647\) 7.73591 0.304130 0.152065 0.988370i \(-0.451408\pi\)
0.152065 + 0.988370i \(0.451408\pi\)
\(648\) 0 0
\(649\) 5.16946 0.202919
\(650\) 0 0
\(651\) −1.02478 −0.0401644
\(652\) 0 0
\(653\) 14.5886 0.570896 0.285448 0.958394i \(-0.407858\pi\)
0.285448 + 0.958394i \(0.407858\pi\)
\(654\) 0 0
\(655\) −8.66908 −0.338729
\(656\) 0 0
\(657\) 4.16407 0.162456
\(658\) 0 0
\(659\) 20.8462 0.812053 0.406027 0.913861i \(-0.366914\pi\)
0.406027 + 0.913861i \(0.366914\pi\)
\(660\) 0 0
\(661\) −21.8177 −0.848609 −0.424305 0.905519i \(-0.639481\pi\)
−0.424305 + 0.905519i \(0.639481\pi\)
\(662\) 0 0
\(663\) −9.22535 −0.358283
\(664\) 0 0
\(665\) −5.66937 −0.219849
\(666\) 0 0
\(667\) −3.10028 −0.120043
\(668\) 0 0
\(669\) −3.90957 −0.151153
\(670\) 0 0
\(671\) 0.797719 0.0307956
\(672\) 0 0
\(673\) 21.9795 0.847247 0.423623 0.905838i \(-0.360758\pi\)
0.423623 + 0.905838i \(0.360758\pi\)
\(674\) 0 0
\(675\) −5.03875 −0.193942
\(676\) 0 0
\(677\) −31.8610 −1.22452 −0.612260 0.790657i \(-0.709739\pi\)
−0.612260 + 0.790657i \(0.709739\pi\)
\(678\) 0 0
\(679\) 2.82154 0.108281
\(680\) 0 0
\(681\) 6.24862 0.239448
\(682\) 0 0
\(683\) −29.1729 −1.11627 −0.558134 0.829751i \(-0.688483\pi\)
−0.558134 + 0.829751i \(0.688483\pi\)
\(684\) 0 0
\(685\) −15.8869 −0.607009
\(686\) 0 0
\(687\) −25.5918 −0.976390
\(688\) 0 0
\(689\) 11.6770 0.444859
\(690\) 0 0
\(691\) 3.35450 0.127611 0.0638056 0.997962i \(-0.479676\pi\)
0.0638056 + 0.997962i \(0.479676\pi\)
\(692\) 0 0
\(693\) −0.123506 −0.00469160
\(694\) 0 0
\(695\) −0.252046 −0.00956066
\(696\) 0 0
\(697\) 5.37987 0.203777
\(698\) 0 0
\(699\) 13.0269 0.492723
\(700\) 0 0
\(701\) 36.7230 1.38701 0.693504 0.720453i \(-0.256066\pi\)
0.693504 + 0.720453i \(0.256066\pi\)
\(702\) 0 0
\(703\) 66.0667 2.49175
\(704\) 0 0
\(705\) −39.5444 −1.48933
\(706\) 0 0
\(707\) 0.697234 0.0262222
\(708\) 0 0
\(709\) −10.3615 −0.389136 −0.194568 0.980889i \(-0.562330\pi\)
−0.194568 + 0.980889i \(0.562330\pi\)
\(710\) 0 0
\(711\) 7.52893 0.282357
\(712\) 0 0
\(713\) −22.8218 −0.854684
\(714\) 0 0
\(715\) 4.07547 0.152414
\(716\) 0 0
\(717\) 8.54827 0.319241
\(718\) 0 0
\(719\) −19.4718 −0.726175 −0.363088 0.931755i \(-0.618277\pi\)
−0.363088 + 0.931755i \(0.618277\pi\)
\(720\) 0 0
\(721\) −2.60336 −0.0969542
\(722\) 0 0
\(723\) 16.8836 0.627906
\(724\) 0 0
\(725\) 3.03809 0.112832
\(726\) 0 0
\(727\) 39.9158 1.48040 0.740198 0.672389i \(-0.234732\pi\)
0.740198 + 0.672389i \(0.234732\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 14.0718 0.520464
\(732\) 0 0
\(733\) 51.3551 1.89684 0.948422 0.317009i \(-0.102679\pi\)
0.948422 + 0.317009i \(0.102679\pi\)
\(734\) 0 0
\(735\) −22.0099 −0.811847
\(736\) 0 0
\(737\) 6.45184 0.237657
\(738\) 0 0
\(739\) −7.93272 −0.291810 −0.145905 0.989299i \(-0.546609\pi\)
−0.145905 + 0.989299i \(0.546609\pi\)
\(740\) 0 0
\(741\) −18.6357 −0.684600
\(742\) 0 0
\(743\) 31.2211 1.14539 0.572695 0.819769i \(-0.305898\pi\)
0.572695 + 0.819769i \(0.305898\pi\)
\(744\) 0 0
\(745\) 47.4736 1.73930
\(746\) 0 0
\(747\) −7.44885 −0.272539
\(748\) 0 0
\(749\) 4.66354 0.170402
\(750\) 0 0
\(751\) 15.5552 0.567619 0.283810 0.958881i \(-0.408402\pi\)
0.283810 + 0.958881i \(0.408402\pi\)
\(752\) 0 0
\(753\) −1.92874 −0.0702871
\(754\) 0 0
\(755\) −53.2692 −1.93866
\(756\) 0 0
\(757\) 12.1429 0.441340 0.220670 0.975348i \(-0.429176\pi\)
0.220670 + 0.975348i \(0.429176\pi\)
\(758\) 0 0
\(759\) −2.75046 −0.0998355
\(760\) 0 0
\(761\) 50.6261 1.83519 0.917597 0.397513i \(-0.130127\pi\)
0.917597 + 0.397513i \(0.130127\pi\)
\(762\) 0 0
\(763\) 0.102310 0.00370388
\(764\) 0 0
\(765\) −12.1553 −0.439477
\(766\) 0 0
\(767\) −23.2391 −0.839114
\(768\) 0 0
\(769\) 2.38129 0.0858716 0.0429358 0.999078i \(-0.486329\pi\)
0.0429358 + 0.999078i \(0.486329\pi\)
\(770\) 0 0
\(771\) −18.9215 −0.681441
\(772\) 0 0
\(773\) 43.0022 1.54668 0.773340 0.633991i \(-0.218584\pi\)
0.773340 + 0.633991i \(0.218584\pi\)
\(774\) 0 0
\(775\) 22.3640 0.803339
\(776\) 0 0
\(777\) −1.96833 −0.0706133
\(778\) 0 0
\(779\) 10.8676 0.389373
\(780\) 0 0
\(781\) 6.10003 0.218276
\(782\) 0 0
\(783\) −0.602944 −0.0215475
\(784\) 0 0
\(785\) −26.9513 −0.961934
\(786\) 0 0
\(787\) −4.51599 −0.160978 −0.0804889 0.996756i \(-0.525648\pi\)
−0.0804889 + 0.996756i \(0.525648\pi\)
\(788\) 0 0
\(789\) −8.99207 −0.320126
\(790\) 0 0
\(791\) 2.87538 0.102237
\(792\) 0 0
\(793\) −3.58611 −0.127346
\(794\) 0 0
\(795\) 15.3857 0.545674
\(796\) 0 0
\(797\) −37.2925 −1.32097 −0.660484 0.750840i \(-0.729649\pi\)
−0.660484 + 0.750840i \(0.729649\pi\)
\(798\) 0 0
\(799\) −47.8820 −1.69394
\(800\) 0 0
\(801\) 9.40223 0.332212
\(802\) 0 0
\(803\) −2.22741 −0.0786038
\(804\) 0 0
\(805\) 3.76156 0.132578
\(806\) 0 0
\(807\) −11.8434 −0.416906
\(808\) 0 0
\(809\) 11.4322 0.401935 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(810\) 0 0
\(811\) 29.1204 1.02256 0.511278 0.859415i \(-0.329172\pi\)
0.511278 + 0.859415i \(0.329172\pi\)
\(812\) 0 0
\(813\) 3.28934 0.115362
\(814\) 0 0
\(815\) −49.6193 −1.73809
\(816\) 0 0
\(817\) 28.4258 0.994493
\(818\) 0 0
\(819\) 0.555214 0.0194007
\(820\) 0 0
\(821\) −24.3833 −0.850982 −0.425491 0.904963i \(-0.639899\pi\)
−0.425491 + 0.904963i \(0.639899\pi\)
\(822\) 0 0
\(823\) −33.2495 −1.15901 −0.579503 0.814970i \(-0.696753\pi\)
−0.579503 + 0.814970i \(0.696753\pi\)
\(824\) 0 0
\(825\) 2.69529 0.0938380
\(826\) 0 0
\(827\) −24.7980 −0.862312 −0.431156 0.902277i \(-0.641894\pi\)
−0.431156 + 0.902277i \(0.641894\pi\)
\(828\) 0 0
\(829\) 0.0759189 0.00263677 0.00131839 0.999999i \(-0.499580\pi\)
0.00131839 + 0.999999i \(0.499580\pi\)
\(830\) 0 0
\(831\) −8.25296 −0.286292
\(832\) 0 0
\(833\) −26.6505 −0.923384
\(834\) 0 0
\(835\) 3.16840 0.109647
\(836\) 0 0
\(837\) −4.43840 −0.153414
\(838\) 0 0
\(839\) 36.3774 1.25589 0.627944 0.778259i \(-0.283897\pi\)
0.627944 + 0.778259i \(0.283897\pi\)
\(840\) 0 0
\(841\) −28.6365 −0.987464
\(842\) 0 0
\(843\) −15.3602 −0.529033
\(844\) 0 0
\(845\) 22.8681 0.786687
\(846\) 0 0
\(847\) −2.47372 −0.0849981
\(848\) 0 0
\(849\) 11.8821 0.407794
\(850\) 0 0
\(851\) −43.8345 −1.50263
\(852\) 0 0
\(853\) −29.0407 −0.994334 −0.497167 0.867655i \(-0.665626\pi\)
−0.497167 + 0.867655i \(0.665626\pi\)
\(854\) 0 0
\(855\) −24.5544 −0.839744
\(856\) 0 0
\(857\) 41.1252 1.40481 0.702406 0.711777i \(-0.252109\pi\)
0.702406 + 0.711777i \(0.252109\pi\)
\(858\) 0 0
\(859\) −8.21249 −0.280206 −0.140103 0.990137i \(-0.544743\pi\)
−0.140103 + 0.990137i \(0.544743\pi\)
\(860\) 0 0
\(861\) −0.323779 −0.0110344
\(862\) 0 0
\(863\) −9.51360 −0.323847 −0.161923 0.986803i \(-0.551770\pi\)
−0.161923 + 0.986803i \(0.551770\pi\)
\(864\) 0 0
\(865\) 54.3176 1.84685
\(866\) 0 0
\(867\) 2.28181 0.0774944
\(868\) 0 0
\(869\) −4.02732 −0.136617
\(870\) 0 0
\(871\) −29.0039 −0.982761
\(872\) 0 0
\(873\) 12.2203 0.413594
\(874\) 0 0
\(875\) −0.0283490 −0.000958372 0
\(876\) 0 0
\(877\) −15.4443 −0.521517 −0.260758 0.965404i \(-0.583973\pi\)
−0.260758 + 0.965404i \(0.583973\pi\)
\(878\) 0 0
\(879\) 22.7646 0.767830
\(880\) 0 0
\(881\) 8.94074 0.301221 0.150611 0.988593i \(-0.451876\pi\)
0.150611 + 0.988593i \(0.451876\pi\)
\(882\) 0 0
\(883\) −32.6275 −1.09800 −0.549001 0.835822i \(-0.684992\pi\)
−0.549001 + 0.835822i \(0.684992\pi\)
\(884\) 0 0
\(885\) −30.6198 −1.02927
\(886\) 0 0
\(887\) 45.4740 1.52687 0.763434 0.645886i \(-0.223512\pi\)
0.763434 + 0.645886i \(0.223512\pi\)
\(888\) 0 0
\(889\) −4.79017 −0.160657
\(890\) 0 0
\(891\) −0.534912 −0.0179202
\(892\) 0 0
\(893\) −96.7243 −3.23676
\(894\) 0 0
\(895\) −83.7252 −2.79862
\(896\) 0 0
\(897\) 12.3646 0.412841
\(898\) 0 0
\(899\) 2.67611 0.0892533
\(900\) 0 0
\(901\) 18.6296 0.620642
\(902\) 0 0
\(903\) −0.846890 −0.0281827
\(904\) 0 0
\(905\) −11.0844 −0.368458
\(906\) 0 0
\(907\) −21.4979 −0.713826 −0.356913 0.934138i \(-0.616171\pi\)
−0.356913 + 0.934138i \(0.616171\pi\)
\(908\) 0 0
\(909\) 3.01977 0.100159
\(910\) 0 0
\(911\) −44.8385 −1.48556 −0.742782 0.669533i \(-0.766494\pi\)
−0.742782 + 0.669533i \(0.766494\pi\)
\(912\) 0 0
\(913\) 3.98448 0.131867
\(914\) 0 0
\(915\) −4.72506 −0.156206
\(916\) 0 0
\(917\) 0.631739 0.0208619
\(918\) 0 0
\(919\) −46.0171 −1.51796 −0.758982 0.651112i \(-0.774303\pi\)
−0.758982 + 0.651112i \(0.774303\pi\)
\(920\) 0 0
\(921\) −33.2061 −1.09418
\(922\) 0 0
\(923\) −27.4224 −0.902619
\(924\) 0 0
\(925\) 42.9552 1.41236
\(926\) 0 0
\(927\) −11.2753 −0.370331
\(928\) 0 0
\(929\) 11.8004 0.387159 0.193580 0.981085i \(-0.437990\pi\)
0.193580 + 0.981085i \(0.437990\pi\)
\(930\) 0 0
\(931\) −53.8354 −1.76438
\(932\) 0 0
\(933\) −11.8693 −0.388584
\(934\) 0 0
\(935\) 6.50204 0.212639
\(936\) 0 0
\(937\) 42.2945 1.38170 0.690850 0.722998i \(-0.257237\pi\)
0.690850 + 0.722998i \(0.257237\pi\)
\(938\) 0 0
\(939\) 8.72134 0.284610
\(940\) 0 0
\(941\) 6.50734 0.212133 0.106067 0.994359i \(-0.466174\pi\)
0.106067 + 0.994359i \(0.466174\pi\)
\(942\) 0 0
\(943\) −7.21054 −0.234807
\(944\) 0 0
\(945\) 0.731551 0.0237973
\(946\) 0 0
\(947\) 2.52120 0.0819278 0.0409639 0.999161i \(-0.486957\pi\)
0.0409639 + 0.999161i \(0.486957\pi\)
\(948\) 0 0
\(949\) 10.0132 0.325043
\(950\) 0 0
\(951\) −21.0893 −0.683867
\(952\) 0 0
\(953\) 23.7358 0.768879 0.384439 0.923150i \(-0.374395\pi\)
0.384439 + 0.923150i \(0.374395\pi\)
\(954\) 0 0
\(955\) −68.4804 −2.21597
\(956\) 0 0
\(957\) 0.322522 0.0104257
\(958\) 0 0
\(959\) 1.15772 0.0373848
\(960\) 0 0
\(961\) −11.3006 −0.364534
\(962\) 0 0
\(963\) 20.1981 0.650876
\(964\) 0 0
\(965\) 25.9867 0.836541
\(966\) 0 0
\(967\) −12.9742 −0.417223 −0.208612 0.977999i \(-0.566894\pi\)
−0.208612 + 0.977999i \(0.566894\pi\)
\(968\) 0 0
\(969\) −29.7315 −0.955115
\(970\) 0 0
\(971\) 38.0031 1.21958 0.609789 0.792564i \(-0.291254\pi\)
0.609789 + 0.792564i \(0.291254\pi\)
\(972\) 0 0
\(973\) 0.0183673 0.000588828 0
\(974\) 0 0
\(975\) −12.1165 −0.388040
\(976\) 0 0
\(977\) 32.3943 1.03639 0.518193 0.855264i \(-0.326605\pi\)
0.518193 + 0.855264i \(0.326605\pi\)
\(978\) 0 0
\(979\) −5.02937 −0.160739
\(980\) 0 0
\(981\) 0.443113 0.0141475
\(982\) 0 0
\(983\) 13.9912 0.446249 0.223124 0.974790i \(-0.428374\pi\)
0.223124 + 0.974790i \(0.428374\pi\)
\(984\) 0 0
\(985\) −8.65705 −0.275836
\(986\) 0 0
\(987\) 2.88171 0.0917258
\(988\) 0 0
\(989\) −18.8602 −0.599719
\(990\) 0 0
\(991\) 6.34209 0.201463 0.100732 0.994914i \(-0.467882\pi\)
0.100732 + 0.994914i \(0.467882\pi\)
\(992\) 0 0
\(993\) −10.9529 −0.347580
\(994\) 0 0
\(995\) 77.8351 2.46754
\(996\) 0 0
\(997\) 39.1554 1.24006 0.620032 0.784576i \(-0.287119\pi\)
0.620032 + 0.784576i \(0.287119\pi\)
\(998\) 0 0
\(999\) −8.52496 −0.269718
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.1.1 9
4.3 odd 2 2004.2.a.d.1.1 9
12.11 even 2 6012.2.a.h.1.9 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.d.1.1 9 4.3 odd 2
6012.2.a.h.1.9 9 12.11 even 2
8016.2.a.bb.1.1 9 1.1 even 1 trivial