Properties

Label 8016.2.a.bb.1.8
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 1.8
Root \(-3.19525\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +4.19525 q^{5} -1.43344 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +4.19525 q^{5} -1.43344 q^{7} +1.00000 q^{9} -5.55413 q^{11} -2.46575 q^{13} -4.19525 q^{15} -0.151828 q^{17} -0.370208 q^{19} +1.43344 q^{21} +5.22489 q^{23} +12.6001 q^{25} -1.00000 q^{27} -9.43548 q^{29} -6.03892 q^{31} +5.55413 q^{33} -6.01363 q^{35} +9.91270 q^{37} +2.46575 q^{39} -8.03882 q^{41} +12.3613 q^{43} +4.19525 q^{45} +5.19319 q^{47} -4.94525 q^{49} +0.151828 q^{51} +6.02724 q^{53} -23.3010 q^{55} +0.370208 q^{57} +6.13698 q^{59} -4.70024 q^{61} -1.43344 q^{63} -10.3445 q^{65} +6.05931 q^{67} -5.22489 q^{69} -3.38205 q^{71} -13.2561 q^{73} -12.6001 q^{75} +7.96151 q^{77} +5.34461 q^{79} +1.00000 q^{81} -1.83389 q^{83} -0.636958 q^{85} +9.43548 q^{87} +7.69442 q^{89} +3.53451 q^{91} +6.03892 q^{93} -1.55312 q^{95} +18.7449 q^{97} -5.55413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} - 7q^{11} + 6q^{13} - 9q^{15} + 7q^{17} - 2q^{19} + 2q^{21} - 19q^{23} + 22q^{25} - 9q^{27} + 13q^{29} - 12q^{31} + 7q^{33} - 4q^{35} + 15q^{37} - 6q^{39} + 18q^{41} + 6q^{43} + 9q^{45} - 25q^{47} + 19q^{49} - 7q^{51} + 17q^{53} + 3q^{55} + 2q^{57} - 3q^{59} + 14q^{61} - 2q^{63} + 14q^{65} + 4q^{67} + 19q^{69} - 17q^{71} - 20q^{73} - 22q^{75} + 14q^{77} + 8q^{79} + 9q^{81} + q^{83} + 5q^{85} - 13q^{87} + 36q^{89} + 41q^{91} + 12q^{93} - 5q^{95} + 31q^{97} - 7q^{99} + O(q^{100}) \)

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
\(5\) 4.19525 1.87617 0.938087 0.346400i \(-0.112596\pi\)
0.938087 + 0.346400i \(0.112596\pi\)
\(6\) 0 0
\(7\) −1.43344 −0.541789 −0.270894 0.962609i \(-0.587319\pi\)
−0.270894 + 0.962609i \(0.587319\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.55413 −1.67463 −0.837317 0.546718i \(-0.815877\pi\)
−0.837317 + 0.546718i \(0.815877\pi\)
\(12\) 0 0
\(13\) −2.46575 −0.683877 −0.341938 0.939722i \(-0.611083\pi\)
−0.341938 + 0.939722i \(0.611083\pi\)
\(14\) 0 0
\(15\) −4.19525 −1.08321
\(16\) 0 0
\(17\) −0.151828 −0.0368237 −0.0184119 0.999830i \(-0.505861\pi\)
−0.0184119 + 0.999830i \(0.505861\pi\)
\(18\) 0 0
\(19\) −0.370208 −0.0849316 −0.0424658 0.999098i \(-0.513521\pi\)
−0.0424658 + 0.999098i \(0.513521\pi\)
\(20\) 0 0
\(21\) 1.43344 0.312802
\(22\) 0 0
\(23\) 5.22489 1.08946 0.544732 0.838610i \(-0.316631\pi\)
0.544732 + 0.838610i \(0.316631\pi\)
\(24\) 0 0
\(25\) 12.6001 2.52003
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −9.43548 −1.75212 −0.876062 0.482198i \(-0.839839\pi\)
−0.876062 + 0.482198i \(0.839839\pi\)
\(30\) 0 0
\(31\) −6.03892 −1.08462 −0.542311 0.840178i \(-0.682451\pi\)
−0.542311 + 0.840178i \(0.682451\pi\)
\(32\) 0 0
\(33\) 5.55413 0.966850
\(34\) 0 0
\(35\) −6.01363 −1.01649
\(36\) 0 0
\(37\) 9.91270 1.62964 0.814819 0.579715i \(-0.196836\pi\)
0.814819 + 0.579715i \(0.196836\pi\)
\(38\) 0 0
\(39\) 2.46575 0.394837
\(40\) 0 0
\(41\) −8.03882 −1.25545 −0.627727 0.778434i \(-0.716014\pi\)
−0.627727 + 0.778434i \(0.716014\pi\)
\(42\) 0 0
\(43\) 12.3613 1.88508 0.942539 0.334097i \(-0.108431\pi\)
0.942539 + 0.334097i \(0.108431\pi\)
\(44\) 0 0
\(45\) 4.19525 0.625391
\(46\) 0 0
\(47\) 5.19319 0.757505 0.378752 0.925498i \(-0.376353\pi\)
0.378752 + 0.925498i \(0.376353\pi\)
\(48\) 0 0
\(49\) −4.94525 −0.706465
\(50\) 0 0
\(51\) 0.151828 0.0212602
\(52\) 0 0
\(53\) 6.02724 0.827906 0.413953 0.910298i \(-0.364148\pi\)
0.413953 + 0.910298i \(0.364148\pi\)
\(54\) 0 0
\(55\) −23.3010 −3.14190
\(56\) 0 0
\(57\) 0.370208 0.0490353
\(58\) 0 0
\(59\) 6.13698 0.798966 0.399483 0.916741i \(-0.369190\pi\)
0.399483 + 0.916741i \(0.369190\pi\)
\(60\) 0 0
\(61\) −4.70024 −0.601805 −0.300902 0.953655i \(-0.597288\pi\)
−0.300902 + 0.953655i \(0.597288\pi\)
\(62\) 0 0
\(63\) −1.43344 −0.180596
\(64\) 0 0
\(65\) −10.3445 −1.28307
\(66\) 0 0
\(67\) 6.05931 0.740263 0.370132 0.928979i \(-0.379313\pi\)
0.370132 + 0.928979i \(0.379313\pi\)
\(68\) 0 0
\(69\) −5.22489 −0.629003
\(70\) 0 0
\(71\) −3.38205 −0.401376 −0.200688 0.979655i \(-0.564318\pi\)
−0.200688 + 0.979655i \(0.564318\pi\)
\(72\) 0 0
\(73\) −13.2561 −1.55151 −0.775756 0.631033i \(-0.782631\pi\)
−0.775756 + 0.631033i \(0.782631\pi\)
\(74\) 0 0
\(75\) −12.6001 −1.45494
\(76\) 0 0
\(77\) 7.96151 0.907298
\(78\) 0 0
\(79\) 5.34461 0.601315 0.300658 0.953732i \(-0.402794\pi\)
0.300658 + 0.953732i \(0.402794\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.83389 −0.201296 −0.100648 0.994922i \(-0.532092\pi\)
−0.100648 + 0.994922i \(0.532092\pi\)
\(84\) 0 0
\(85\) −0.636958 −0.0690877
\(86\) 0 0
\(87\) 9.43548 1.01159
\(88\) 0 0
\(89\) 7.69442 0.815607 0.407804 0.913070i \(-0.366295\pi\)
0.407804 + 0.913070i \(0.366295\pi\)
\(90\) 0 0
\(91\) 3.53451 0.370517
\(92\) 0 0
\(93\) 6.03892 0.626207
\(94\) 0 0
\(95\) −1.55312 −0.159346
\(96\) 0 0
\(97\) 18.7449 1.90325 0.951626 0.307260i \(-0.0994121\pi\)
0.951626 + 0.307260i \(0.0994121\pi\)
\(98\) 0 0
\(99\) −5.55413 −0.558211
\(100\) 0 0
\(101\) 8.67739 0.863433 0.431717 0.902009i \(-0.357908\pi\)
0.431717 + 0.902009i \(0.357908\pi\)
\(102\) 0 0
\(103\) 17.6281 1.73695 0.868476 0.495731i \(-0.165100\pi\)
0.868476 + 0.495731i \(0.165100\pi\)
\(104\) 0 0
\(105\) 6.01363 0.586871
\(106\) 0 0
\(107\) 5.19885 0.502591 0.251296 0.967910i \(-0.419143\pi\)
0.251296 + 0.967910i \(0.419143\pi\)
\(108\) 0 0
\(109\) −6.27648 −0.601178 −0.300589 0.953754i \(-0.597183\pi\)
−0.300589 + 0.953754i \(0.597183\pi\)
\(110\) 0 0
\(111\) −9.91270 −0.940872
\(112\) 0 0
\(113\) 17.8990 1.68379 0.841897 0.539638i \(-0.181439\pi\)
0.841897 + 0.539638i \(0.181439\pi\)
\(114\) 0 0
\(115\) 21.9197 2.04403
\(116\) 0 0
\(117\) −2.46575 −0.227959
\(118\) 0 0
\(119\) 0.217636 0.0199507
\(120\) 0 0
\(121\) 19.8484 1.80440
\(122\) 0 0
\(123\) 8.03882 0.724836
\(124\) 0 0
\(125\) 31.8845 2.85183
\(126\) 0 0
\(127\) 14.1924 1.25937 0.629686 0.776850i \(-0.283184\pi\)
0.629686 + 0.776850i \(0.283184\pi\)
\(128\) 0 0
\(129\) −12.3613 −1.08835
\(130\) 0 0
\(131\) 6.35032 0.554830 0.277415 0.960750i \(-0.410522\pi\)
0.277415 + 0.960750i \(0.410522\pi\)
\(132\) 0 0
\(133\) 0.530671 0.0460150
\(134\) 0 0
\(135\) −4.19525 −0.361070
\(136\) 0 0
\(137\) −5.75224 −0.491447 −0.245724 0.969340i \(-0.579026\pi\)
−0.245724 + 0.969340i \(0.579026\pi\)
\(138\) 0 0
\(139\) 7.26012 0.615795 0.307898 0.951420i \(-0.400375\pi\)
0.307898 + 0.951420i \(0.400375\pi\)
\(140\) 0 0
\(141\) −5.19319 −0.437346
\(142\) 0 0
\(143\) 13.6951 1.14524
\(144\) 0 0
\(145\) −39.5842 −3.28729
\(146\) 0 0
\(147\) 4.94525 0.407878
\(148\) 0 0
\(149\) 9.28898 0.760983 0.380491 0.924784i \(-0.375755\pi\)
0.380491 + 0.924784i \(0.375755\pi\)
\(150\) 0 0
\(151\) −13.5816 −1.10526 −0.552629 0.833428i \(-0.686375\pi\)
−0.552629 + 0.833428i \(0.686375\pi\)
\(152\) 0 0
\(153\) −0.151828 −0.0122746
\(154\) 0 0
\(155\) −25.3348 −2.03494
\(156\) 0 0
\(157\) 6.50310 0.519004 0.259502 0.965743i \(-0.416442\pi\)
0.259502 + 0.965743i \(0.416442\pi\)
\(158\) 0 0
\(159\) −6.02724 −0.477992
\(160\) 0 0
\(161\) −7.48956 −0.590260
\(162\) 0 0
\(163\) −2.73367 −0.214118 −0.107059 0.994253i \(-0.534143\pi\)
−0.107059 + 0.994253i \(0.534143\pi\)
\(164\) 0 0
\(165\) 23.3010 1.81398
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −6.92006 −0.532312
\(170\) 0 0
\(171\) −0.370208 −0.0283105
\(172\) 0 0
\(173\) −2.63491 −0.200329 −0.100164 0.994971i \(-0.531937\pi\)
−0.100164 + 0.994971i \(0.531937\pi\)
\(174\) 0 0
\(175\) −18.0615 −1.36532
\(176\) 0 0
\(177\) −6.13698 −0.461283
\(178\) 0 0
\(179\) −4.99385 −0.373258 −0.186629 0.982430i \(-0.559756\pi\)
−0.186629 + 0.982430i \(0.559756\pi\)
\(180\) 0 0
\(181\) 10.5484 0.784055 0.392027 0.919954i \(-0.371774\pi\)
0.392027 + 0.919954i \(0.371774\pi\)
\(182\) 0 0
\(183\) 4.70024 0.347452
\(184\) 0 0
\(185\) 41.5863 3.05748
\(186\) 0 0
\(187\) 0.843274 0.0616663
\(188\) 0 0
\(189\) 1.43344 0.104267
\(190\) 0 0
\(191\) 11.9556 0.865074 0.432537 0.901616i \(-0.357619\pi\)
0.432537 + 0.901616i \(0.357619\pi\)
\(192\) 0 0
\(193\) −5.12509 −0.368912 −0.184456 0.982841i \(-0.559052\pi\)
−0.184456 + 0.982841i \(0.559052\pi\)
\(194\) 0 0
\(195\) 10.3445 0.740782
\(196\) 0 0
\(197\) 26.0322 1.85471 0.927357 0.374177i \(-0.122075\pi\)
0.927357 + 0.374177i \(0.122075\pi\)
\(198\) 0 0
\(199\) −21.5874 −1.53029 −0.765143 0.643860i \(-0.777332\pi\)
−0.765143 + 0.643860i \(0.777332\pi\)
\(200\) 0 0
\(201\) −6.05931 −0.427391
\(202\) 0 0
\(203\) 13.5252 0.949282
\(204\) 0 0
\(205\) −33.7249 −2.35545
\(206\) 0 0
\(207\) 5.22489 0.363155
\(208\) 0 0
\(209\) 2.05619 0.142229
\(210\) 0 0
\(211\) −17.3410 −1.19381 −0.596903 0.802313i \(-0.703602\pi\)
−0.596903 + 0.802313i \(0.703602\pi\)
\(212\) 0 0
\(213\) 3.38205 0.231734
\(214\) 0 0
\(215\) 51.8587 3.53673
\(216\) 0 0
\(217\) 8.65642 0.587636
\(218\) 0 0
\(219\) 13.2561 0.895766
\(220\) 0 0
\(221\) 0.374371 0.0251829
\(222\) 0 0
\(223\) −11.0841 −0.742247 −0.371124 0.928584i \(-0.621027\pi\)
−0.371124 + 0.928584i \(0.621027\pi\)
\(224\) 0 0
\(225\) 12.6001 0.840009
\(226\) 0 0
\(227\) −5.62010 −0.373019 −0.186510 0.982453i \(-0.559718\pi\)
−0.186510 + 0.982453i \(0.559718\pi\)
\(228\) 0 0
\(229\) 6.45735 0.426714 0.213357 0.976974i \(-0.431560\pi\)
0.213357 + 0.976974i \(0.431560\pi\)
\(230\) 0 0
\(231\) −7.96151 −0.523829
\(232\) 0 0
\(233\) −19.4269 −1.27270 −0.636349 0.771401i \(-0.719556\pi\)
−0.636349 + 0.771401i \(0.719556\pi\)
\(234\) 0 0
\(235\) 21.7867 1.42121
\(236\) 0 0
\(237\) −5.34461 −0.347169
\(238\) 0 0
\(239\) −16.2016 −1.04799 −0.523997 0.851720i \(-0.675560\pi\)
−0.523997 + 0.851720i \(0.675560\pi\)
\(240\) 0 0
\(241\) 22.1313 1.42560 0.712800 0.701367i \(-0.247427\pi\)
0.712800 + 0.701367i \(0.247427\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −20.7466 −1.32545
\(246\) 0 0
\(247\) 0.912842 0.0580828
\(248\) 0 0
\(249\) 1.83389 0.116218
\(250\) 0 0
\(251\) −8.70622 −0.549532 −0.274766 0.961511i \(-0.588600\pi\)
−0.274766 + 0.961511i \(0.588600\pi\)
\(252\) 0 0
\(253\) −29.0197 −1.82446
\(254\) 0 0
\(255\) 0.636958 0.0398878
\(256\) 0 0
\(257\) −8.73325 −0.544765 −0.272383 0.962189i \(-0.587812\pi\)
−0.272383 + 0.962189i \(0.587812\pi\)
\(258\) 0 0
\(259\) −14.2093 −0.882920
\(260\) 0 0
\(261\) −9.43548 −0.584042
\(262\) 0 0
\(263\) 17.1621 1.05826 0.529131 0.848540i \(-0.322518\pi\)
0.529131 + 0.848540i \(0.322518\pi\)
\(264\) 0 0
\(265\) 25.2858 1.55329
\(266\) 0 0
\(267\) −7.69442 −0.470891
\(268\) 0 0
\(269\) 23.1618 1.41220 0.706101 0.708112i \(-0.250453\pi\)
0.706101 + 0.708112i \(0.250453\pi\)
\(270\) 0 0
\(271\) 27.3302 1.66019 0.830097 0.557619i \(-0.188285\pi\)
0.830097 + 0.557619i \(0.188285\pi\)
\(272\) 0 0
\(273\) −3.53451 −0.213918
\(274\) 0 0
\(275\) −69.9828 −4.22012
\(276\) 0 0
\(277\) 26.8048 1.61055 0.805274 0.592904i \(-0.202018\pi\)
0.805274 + 0.592904i \(0.202018\pi\)
\(278\) 0 0
\(279\) −6.03892 −0.361541
\(280\) 0 0
\(281\) 19.5511 1.16632 0.583161 0.812357i \(-0.301816\pi\)
0.583161 + 0.812357i \(0.301816\pi\)
\(282\) 0 0
\(283\) −9.70821 −0.577093 −0.288546 0.957466i \(-0.593172\pi\)
−0.288546 + 0.957466i \(0.593172\pi\)
\(284\) 0 0
\(285\) 1.55312 0.0919987
\(286\) 0 0
\(287\) 11.5232 0.680191
\(288\) 0 0
\(289\) −16.9769 −0.998644
\(290\) 0 0
\(291\) −18.7449 −1.09884
\(292\) 0 0
\(293\) 19.0093 1.11053 0.555267 0.831672i \(-0.312616\pi\)
0.555267 + 0.831672i \(0.312616\pi\)
\(294\) 0 0
\(295\) 25.7462 1.49900
\(296\) 0 0
\(297\) 5.55413 0.322283
\(298\) 0 0
\(299\) −12.8833 −0.745060
\(300\) 0 0
\(301\) −17.7191 −1.02131
\(302\) 0 0
\(303\) −8.67739 −0.498503
\(304\) 0 0
\(305\) −19.7187 −1.12909
\(306\) 0 0
\(307\) 15.8337 0.903677 0.451838 0.892100i \(-0.350768\pi\)
0.451838 + 0.892100i \(0.350768\pi\)
\(308\) 0 0
\(309\) −17.6281 −1.00283
\(310\) 0 0
\(311\) 7.16509 0.406295 0.203148 0.979148i \(-0.434883\pi\)
0.203148 + 0.979148i \(0.434883\pi\)
\(312\) 0 0
\(313\) −11.2093 −0.633586 −0.316793 0.948495i \(-0.602606\pi\)
−0.316793 + 0.948495i \(0.602606\pi\)
\(314\) 0 0
\(315\) −6.01363 −0.338830
\(316\) 0 0
\(317\) −33.7170 −1.89374 −0.946868 0.321621i \(-0.895772\pi\)
−0.946868 + 0.321621i \(0.895772\pi\)
\(318\) 0 0
\(319\) 52.4059 2.93417
\(320\) 0 0
\(321\) −5.19885 −0.290171
\(322\) 0 0
\(323\) 0.0562080 0.00312750
\(324\) 0 0
\(325\) −31.0688 −1.72339
\(326\) 0 0
\(327\) 6.27648 0.347090
\(328\) 0 0
\(329\) −7.44412 −0.410408
\(330\) 0 0
\(331\) −0.859249 −0.0472286 −0.0236143 0.999721i \(-0.507517\pi\)
−0.0236143 + 0.999721i \(0.507517\pi\)
\(332\) 0 0
\(333\) 9.91270 0.543213
\(334\) 0 0
\(335\) 25.4203 1.38886
\(336\) 0 0
\(337\) −23.0099 −1.25343 −0.626714 0.779250i \(-0.715600\pi\)
−0.626714 + 0.779250i \(0.715600\pi\)
\(338\) 0 0
\(339\) −17.8990 −0.972139
\(340\) 0 0
\(341\) 33.5410 1.81635
\(342\) 0 0
\(343\) 17.1228 0.924544
\(344\) 0 0
\(345\) −21.9197 −1.18012
\(346\) 0 0
\(347\) 1.36127 0.0730768 0.0365384 0.999332i \(-0.488367\pi\)
0.0365384 + 0.999332i \(0.488367\pi\)
\(348\) 0 0
\(349\) −12.4163 −0.664629 −0.332315 0.943169i \(-0.607830\pi\)
−0.332315 + 0.943169i \(0.607830\pi\)
\(350\) 0 0
\(351\) 2.46575 0.131612
\(352\) 0 0
\(353\) 9.14770 0.486883 0.243442 0.969916i \(-0.421724\pi\)
0.243442 + 0.969916i \(0.421724\pi\)
\(354\) 0 0
\(355\) −14.1886 −0.753050
\(356\) 0 0
\(357\) −0.217636 −0.0115185
\(358\) 0 0
\(359\) −35.7239 −1.88544 −0.942718 0.333592i \(-0.891739\pi\)
−0.942718 + 0.333592i \(0.891739\pi\)
\(360\) 0 0
\(361\) −18.8629 −0.992787
\(362\) 0 0
\(363\) −19.8484 −1.04177
\(364\) 0 0
\(365\) −55.6128 −2.91091
\(366\) 0 0
\(367\) 15.4781 0.807949 0.403975 0.914770i \(-0.367628\pi\)
0.403975 + 0.914770i \(0.367628\pi\)
\(368\) 0 0
\(369\) −8.03882 −0.418485
\(370\) 0 0
\(371\) −8.63968 −0.448550
\(372\) 0 0
\(373\) 5.05019 0.261489 0.130744 0.991416i \(-0.458263\pi\)
0.130744 + 0.991416i \(0.458263\pi\)
\(374\) 0 0
\(375\) −31.8845 −1.64651
\(376\) 0 0
\(377\) 23.2656 1.19824
\(378\) 0 0
\(379\) −4.06656 −0.208885 −0.104443 0.994531i \(-0.533306\pi\)
−0.104443 + 0.994531i \(0.533306\pi\)
\(380\) 0 0
\(381\) −14.1924 −0.727099
\(382\) 0 0
\(383\) 3.04908 0.155801 0.0779005 0.996961i \(-0.475178\pi\)
0.0779005 + 0.996961i \(0.475178\pi\)
\(384\) 0 0
\(385\) 33.4005 1.70225
\(386\) 0 0
\(387\) 12.3613 0.628359
\(388\) 0 0
\(389\) −15.1210 −0.766665 −0.383333 0.923610i \(-0.625224\pi\)
−0.383333 + 0.923610i \(0.625224\pi\)
\(390\) 0 0
\(391\) −0.793286 −0.0401182
\(392\) 0 0
\(393\) −6.35032 −0.320331
\(394\) 0 0
\(395\) 22.4220 1.12817
\(396\) 0 0
\(397\) −28.9642 −1.45367 −0.726836 0.686811i \(-0.759010\pi\)
−0.726836 + 0.686811i \(0.759010\pi\)
\(398\) 0 0
\(399\) −0.530671 −0.0265668
\(400\) 0 0
\(401\) −22.2008 −1.10865 −0.554327 0.832299i \(-0.687024\pi\)
−0.554327 + 0.832299i \(0.687024\pi\)
\(402\) 0 0
\(403\) 14.8905 0.741748
\(404\) 0 0
\(405\) 4.19525 0.208464
\(406\) 0 0
\(407\) −55.0565 −2.72905
\(408\) 0 0
\(409\) 35.7127 1.76588 0.882939 0.469489i \(-0.155562\pi\)
0.882939 + 0.469489i \(0.155562\pi\)
\(410\) 0 0
\(411\) 5.75224 0.283737
\(412\) 0 0
\(413\) −8.79698 −0.432871
\(414\) 0 0
\(415\) −7.69364 −0.377666
\(416\) 0 0
\(417\) −7.26012 −0.355529
\(418\) 0 0
\(419\) 9.16518 0.447748 0.223874 0.974618i \(-0.428130\pi\)
0.223874 + 0.974618i \(0.428130\pi\)
\(420\) 0 0
\(421\) −10.2729 −0.500671 −0.250336 0.968159i \(-0.580541\pi\)
−0.250336 + 0.968159i \(0.580541\pi\)
\(422\) 0 0
\(423\) 5.19319 0.252502
\(424\) 0 0
\(425\) −1.91306 −0.0927968
\(426\) 0 0
\(427\) 6.73751 0.326051
\(428\) 0 0
\(429\) −13.6951 −0.661207
\(430\) 0 0
\(431\) 3.83372 0.184664 0.0923319 0.995728i \(-0.470568\pi\)
0.0923319 + 0.995728i \(0.470568\pi\)
\(432\) 0 0
\(433\) 5.96106 0.286470 0.143235 0.989689i \(-0.454249\pi\)
0.143235 + 0.989689i \(0.454249\pi\)
\(434\) 0 0
\(435\) 39.5842 1.89792
\(436\) 0 0
\(437\) −1.93430 −0.0925300
\(438\) 0 0
\(439\) −2.00545 −0.0957149 −0.0478574 0.998854i \(-0.515239\pi\)
−0.0478574 + 0.998854i \(0.515239\pi\)
\(440\) 0 0
\(441\) −4.94525 −0.235488
\(442\) 0 0
\(443\) −4.02748 −0.191351 −0.0956757 0.995413i \(-0.530501\pi\)
−0.0956757 + 0.995413i \(0.530501\pi\)
\(444\) 0 0
\(445\) 32.2800 1.53022
\(446\) 0 0
\(447\) −9.28898 −0.439354
\(448\) 0 0
\(449\) −7.75720 −0.366085 −0.183042 0.983105i \(-0.558595\pi\)
−0.183042 + 0.983105i \(0.558595\pi\)
\(450\) 0 0
\(451\) 44.6487 2.10243
\(452\) 0 0
\(453\) 13.5816 0.638121
\(454\) 0 0
\(455\) 14.8281 0.695154
\(456\) 0 0
\(457\) −0.952815 −0.0445708 −0.0222854 0.999752i \(-0.507094\pi\)
−0.0222854 + 0.999752i \(0.507094\pi\)
\(458\) 0 0
\(459\) 0.151828 0.00708673
\(460\) 0 0
\(461\) 0.288626 0.0134427 0.00672133 0.999977i \(-0.497861\pi\)
0.00672133 + 0.999977i \(0.497861\pi\)
\(462\) 0 0
\(463\) 37.0632 1.72248 0.861238 0.508202i \(-0.169690\pi\)
0.861238 + 0.508202i \(0.169690\pi\)
\(464\) 0 0
\(465\) 25.3348 1.17487
\(466\) 0 0
\(467\) −18.5601 −0.858860 −0.429430 0.903100i \(-0.641286\pi\)
−0.429430 + 0.903100i \(0.641286\pi\)
\(468\) 0 0
\(469\) −8.68565 −0.401066
\(470\) 0 0
\(471\) −6.50310 −0.299647
\(472\) 0 0
\(473\) −68.6562 −3.15682
\(474\) 0 0
\(475\) −4.66467 −0.214030
\(476\) 0 0
\(477\) 6.02724 0.275969
\(478\) 0 0
\(479\) 20.1854 0.922295 0.461147 0.887324i \(-0.347438\pi\)
0.461147 + 0.887324i \(0.347438\pi\)
\(480\) 0 0
\(481\) −24.4423 −1.11447
\(482\) 0 0
\(483\) 7.48956 0.340787
\(484\) 0 0
\(485\) 78.6394 3.57083
\(486\) 0 0
\(487\) 35.2838 1.59886 0.799430 0.600760i \(-0.205135\pi\)
0.799430 + 0.600760i \(0.205135\pi\)
\(488\) 0 0
\(489\) 2.73367 0.123621
\(490\) 0 0
\(491\) 25.3811 1.14543 0.572715 0.819754i \(-0.305890\pi\)
0.572715 + 0.819754i \(0.305890\pi\)
\(492\) 0 0
\(493\) 1.43257 0.0645198
\(494\) 0 0
\(495\) −23.3010 −1.04730
\(496\) 0 0
\(497\) 4.84796 0.217461
\(498\) 0 0
\(499\) 26.0391 1.16567 0.582836 0.812590i \(-0.301943\pi\)
0.582836 + 0.812590i \(0.301943\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −36.5383 −1.62916 −0.814580 0.580051i \(-0.803033\pi\)
−0.814580 + 0.580051i \(0.803033\pi\)
\(504\) 0 0
\(505\) 36.4039 1.61995
\(506\) 0 0
\(507\) 6.92006 0.307331
\(508\) 0 0
\(509\) 13.7212 0.608181 0.304091 0.952643i \(-0.401647\pi\)
0.304091 + 0.952643i \(0.401647\pi\)
\(510\) 0 0
\(511\) 19.0018 0.840592
\(512\) 0 0
\(513\) 0.370208 0.0163451
\(514\) 0 0
\(515\) 73.9545 3.25882
\(516\) 0 0
\(517\) −28.8437 −1.26854
\(518\) 0 0
\(519\) 2.63491 0.115660
\(520\) 0 0
\(521\) −4.28133 −0.187568 −0.0937842 0.995593i \(-0.529896\pi\)
−0.0937842 + 0.995593i \(0.529896\pi\)
\(522\) 0 0
\(523\) −13.7039 −0.599228 −0.299614 0.954061i \(-0.596858\pi\)
−0.299614 + 0.954061i \(0.596858\pi\)
\(524\) 0 0
\(525\) 18.0615 0.788269
\(526\) 0 0
\(527\) 0.916879 0.0399399
\(528\) 0 0
\(529\) 4.29948 0.186934
\(530\) 0 0
\(531\) 6.13698 0.266322
\(532\) 0 0
\(533\) 19.8218 0.858576
\(534\) 0 0
\(535\) 21.8105 0.942949
\(536\) 0 0
\(537\) 4.99385 0.215501
\(538\) 0 0
\(539\) 27.4666 1.18307
\(540\) 0 0
\(541\) −10.9801 −0.472073 −0.236037 0.971744i \(-0.575849\pi\)
−0.236037 + 0.971744i \(0.575849\pi\)
\(542\) 0 0
\(543\) −10.5484 −0.452674
\(544\) 0 0
\(545\) −26.3314 −1.12791
\(546\) 0 0
\(547\) −16.5207 −0.706375 −0.353188 0.935553i \(-0.614902\pi\)
−0.353188 + 0.935553i \(0.614902\pi\)
\(548\) 0 0
\(549\) −4.70024 −0.200602
\(550\) 0 0
\(551\) 3.49309 0.148811
\(552\) 0 0
\(553\) −7.66116 −0.325786
\(554\) 0 0
\(555\) −41.5863 −1.76524
\(556\) 0 0
\(557\) 42.4409 1.79828 0.899140 0.437661i \(-0.144193\pi\)
0.899140 + 0.437661i \(0.144193\pi\)
\(558\) 0 0
\(559\) −30.4799 −1.28916
\(560\) 0 0
\(561\) −0.843274 −0.0356031
\(562\) 0 0
\(563\) 9.07135 0.382312 0.191156 0.981560i \(-0.438776\pi\)
0.191156 + 0.981560i \(0.438776\pi\)
\(564\) 0 0
\(565\) 75.0907 3.15909
\(566\) 0 0
\(567\) −1.43344 −0.0601988
\(568\) 0 0
\(569\) 22.1508 0.928611 0.464305 0.885675i \(-0.346304\pi\)
0.464305 + 0.885675i \(0.346304\pi\)
\(570\) 0 0
\(571\) −20.7569 −0.868649 −0.434325 0.900756i \(-0.643013\pi\)
−0.434325 + 0.900756i \(0.643013\pi\)
\(572\) 0 0
\(573\) −11.9556 −0.499451
\(574\) 0 0
\(575\) 65.8343 2.74548
\(576\) 0 0
\(577\) 19.8491 0.826328 0.413164 0.910657i \(-0.364424\pi\)
0.413164 + 0.910657i \(0.364424\pi\)
\(578\) 0 0
\(579\) 5.12509 0.212991
\(580\) 0 0
\(581\) 2.62877 0.109060
\(582\) 0 0
\(583\) −33.4761 −1.38644
\(584\) 0 0
\(585\) −10.3445 −0.427691
\(586\) 0 0
\(587\) 15.1902 0.626968 0.313484 0.949593i \(-0.398504\pi\)
0.313484 + 0.949593i \(0.398504\pi\)
\(588\) 0 0
\(589\) 2.23566 0.0921187
\(590\) 0 0
\(591\) −26.0322 −1.07082
\(592\) 0 0
\(593\) −29.5658 −1.21412 −0.607061 0.794655i \(-0.707652\pi\)
−0.607061 + 0.794655i \(0.707652\pi\)
\(594\) 0 0
\(595\) 0.913039 0.0374310
\(596\) 0 0
\(597\) 21.5874 0.883512
\(598\) 0 0
\(599\) −46.2469 −1.88960 −0.944798 0.327653i \(-0.893742\pi\)
−0.944798 + 0.327653i \(0.893742\pi\)
\(600\) 0 0
\(601\) 8.66483 0.353446 0.176723 0.984261i \(-0.443450\pi\)
0.176723 + 0.984261i \(0.443450\pi\)
\(602\) 0 0
\(603\) 6.05931 0.246754
\(604\) 0 0
\(605\) 83.2690 3.38537
\(606\) 0 0
\(607\) −4.70252 −0.190869 −0.0954347 0.995436i \(-0.530424\pi\)
−0.0954347 + 0.995436i \(0.530424\pi\)
\(608\) 0 0
\(609\) −13.5252 −0.548068
\(610\) 0 0
\(611\) −12.8051 −0.518040
\(612\) 0 0
\(613\) −25.5121 −1.03042 −0.515212 0.857063i \(-0.672287\pi\)
−0.515212 + 0.857063i \(0.672287\pi\)
\(614\) 0 0
\(615\) 33.7249 1.35992
\(616\) 0 0
\(617\) −10.1033 −0.406745 −0.203372 0.979101i \(-0.565190\pi\)
−0.203372 + 0.979101i \(0.565190\pi\)
\(618\) 0 0
\(619\) 32.4406 1.30390 0.651948 0.758264i \(-0.273952\pi\)
0.651948 + 0.758264i \(0.273952\pi\)
\(620\) 0 0
\(621\) −5.22489 −0.209668
\(622\) 0 0
\(623\) −11.0295 −0.441887
\(624\) 0 0
\(625\) 70.7627 2.83051
\(626\) 0 0
\(627\) −2.05619 −0.0821161
\(628\) 0 0
\(629\) −1.50503 −0.0600094
\(630\) 0 0
\(631\) −8.97751 −0.357389 −0.178695 0.983905i \(-0.557187\pi\)
−0.178695 + 0.983905i \(0.557187\pi\)
\(632\) 0 0
\(633\) 17.3410 0.689245
\(634\) 0 0
\(635\) 59.5407 2.36280
\(636\) 0 0
\(637\) 12.1938 0.483135
\(638\) 0 0
\(639\) −3.38205 −0.133792
\(640\) 0 0
\(641\) 34.1975 1.35072 0.675361 0.737488i \(-0.263988\pi\)
0.675361 + 0.737488i \(0.263988\pi\)
\(642\) 0 0
\(643\) 29.3516 1.15751 0.578757 0.815500i \(-0.303538\pi\)
0.578757 + 0.815500i \(0.303538\pi\)
\(644\) 0 0
\(645\) −51.8587 −2.04193
\(646\) 0 0
\(647\) 19.4963 0.766480 0.383240 0.923649i \(-0.374808\pi\)
0.383240 + 0.923649i \(0.374808\pi\)
\(648\) 0 0
\(649\) −34.0856 −1.33798
\(650\) 0 0
\(651\) −8.65642 −0.339272
\(652\) 0 0
\(653\) 23.8805 0.934516 0.467258 0.884121i \(-0.345242\pi\)
0.467258 + 0.884121i \(0.345242\pi\)
\(654\) 0 0
\(655\) 26.6412 1.04096
\(656\) 0 0
\(657\) −13.2561 −0.517171
\(658\) 0 0
\(659\) −4.22675 −0.164651 −0.0823255 0.996605i \(-0.526235\pi\)
−0.0823255 + 0.996605i \(0.526235\pi\)
\(660\) 0 0
\(661\) 28.7013 1.11635 0.558176 0.829723i \(-0.311501\pi\)
0.558176 + 0.829723i \(0.311501\pi\)
\(662\) 0 0
\(663\) −0.374371 −0.0145394
\(664\) 0 0
\(665\) 2.22630 0.0863321
\(666\) 0 0
\(667\) −49.2994 −1.90888
\(668\) 0 0
\(669\) 11.0841 0.428537
\(670\) 0 0
\(671\) 26.1058 1.00780
\(672\) 0 0
\(673\) 38.2119 1.47296 0.736479 0.676460i \(-0.236487\pi\)
0.736479 + 0.676460i \(0.236487\pi\)
\(674\) 0 0
\(675\) −12.6001 −0.484979
\(676\) 0 0
\(677\) −27.3849 −1.05249 −0.526243 0.850334i \(-0.676400\pi\)
−0.526243 + 0.850334i \(0.676400\pi\)
\(678\) 0 0
\(679\) −26.8696 −1.03116
\(680\) 0 0
\(681\) 5.62010 0.215363
\(682\) 0 0
\(683\) 13.5496 0.518459 0.259230 0.965816i \(-0.416531\pi\)
0.259230 + 0.965816i \(0.416531\pi\)
\(684\) 0 0
\(685\) −24.1321 −0.922040
\(686\) 0 0
\(687\) −6.45735 −0.246363
\(688\) 0 0
\(689\) −14.8617 −0.566186
\(690\) 0 0
\(691\) 45.6661 1.73722 0.868610 0.495496i \(-0.165014\pi\)
0.868610 + 0.495496i \(0.165014\pi\)
\(692\) 0 0
\(693\) 7.96151 0.302433
\(694\) 0 0
\(695\) 30.4580 1.15534
\(696\) 0 0
\(697\) 1.22052 0.0462305
\(698\) 0 0
\(699\) 19.4269 0.734793
\(700\) 0 0
\(701\) −2.52975 −0.0955472 −0.0477736 0.998858i \(-0.515213\pi\)
−0.0477736 + 0.998858i \(0.515213\pi\)
\(702\) 0 0
\(703\) −3.66976 −0.138408
\(704\) 0 0
\(705\) −21.7867 −0.820536
\(706\) 0 0
\(707\) −12.4385 −0.467798
\(708\) 0 0
\(709\) 3.67220 0.137912 0.0689562 0.997620i \(-0.478033\pi\)
0.0689562 + 0.997620i \(0.478033\pi\)
\(710\) 0 0
\(711\) 5.34461 0.200438
\(712\) 0 0
\(713\) −31.5527 −1.18166
\(714\) 0 0
\(715\) 57.4545 2.14868
\(716\) 0 0
\(717\) 16.2016 0.605060
\(718\) 0 0
\(719\) −39.6398 −1.47831 −0.739157 0.673533i \(-0.764776\pi\)
−0.739157 + 0.673533i \(0.764776\pi\)
\(720\) 0 0
\(721\) −25.2688 −0.941061
\(722\) 0 0
\(723\) −22.1313 −0.823071
\(724\) 0 0
\(725\) −118.888 −4.41540
\(726\) 0 0
\(727\) −40.4405 −1.49986 −0.749928 0.661520i \(-0.769912\pi\)
−0.749928 + 0.661520i \(0.769912\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −1.87679 −0.0694156
\(732\) 0 0
\(733\) −22.7634 −0.840784 −0.420392 0.907343i \(-0.638107\pi\)
−0.420392 + 0.907343i \(0.638107\pi\)
\(734\) 0 0
\(735\) 20.7466 0.765249
\(736\) 0 0
\(737\) −33.6542 −1.23967
\(738\) 0 0
\(739\) 2.74636 0.101026 0.0505132 0.998723i \(-0.483914\pi\)
0.0505132 + 0.998723i \(0.483914\pi\)
\(740\) 0 0
\(741\) −0.912842 −0.0335341
\(742\) 0 0
\(743\) −13.5644 −0.497631 −0.248815 0.968551i \(-0.580041\pi\)
−0.248815 + 0.968551i \(0.580041\pi\)
\(744\) 0 0
\(745\) 38.9696 1.42774
\(746\) 0 0
\(747\) −1.83389 −0.0670986
\(748\) 0 0
\(749\) −7.45223 −0.272298
\(750\) 0 0
\(751\) 48.4821 1.76914 0.884568 0.466411i \(-0.154453\pi\)
0.884568 + 0.466411i \(0.154453\pi\)
\(752\) 0 0
\(753\) 8.70622 0.317272
\(754\) 0 0
\(755\) −56.9784 −2.07365
\(756\) 0 0
\(757\) 25.7718 0.936692 0.468346 0.883545i \(-0.344850\pi\)
0.468346 + 0.883545i \(0.344850\pi\)
\(758\) 0 0
\(759\) 29.0197 1.05335
\(760\) 0 0
\(761\) −15.9928 −0.579739 −0.289869 0.957066i \(-0.593612\pi\)
−0.289869 + 0.957066i \(0.593612\pi\)
\(762\) 0 0
\(763\) 8.99695 0.325711
\(764\) 0 0
\(765\) −0.636958 −0.0230292
\(766\) 0 0
\(767\) −15.1323 −0.546395
\(768\) 0 0
\(769\) −35.3541 −1.27490 −0.637451 0.770491i \(-0.720011\pi\)
−0.637451 + 0.770491i \(0.720011\pi\)
\(770\) 0 0
\(771\) 8.73325 0.314520
\(772\) 0 0
\(773\) 22.7866 0.819578 0.409789 0.912180i \(-0.365602\pi\)
0.409789 + 0.912180i \(0.365602\pi\)
\(774\) 0 0
\(775\) −76.0912 −2.73328
\(776\) 0 0
\(777\) 14.2093 0.509754
\(778\) 0 0
\(779\) 2.97604 0.106628
\(780\) 0 0
\(781\) 18.7844 0.672157
\(782\) 0 0
\(783\) 9.43548 0.337197
\(784\) 0 0
\(785\) 27.2821 0.973741
\(786\) 0 0
\(787\) −12.5300 −0.446645 −0.223322 0.974745i \(-0.571690\pi\)
−0.223322 + 0.974745i \(0.571690\pi\)
\(788\) 0 0
\(789\) −17.1621 −0.610988
\(790\) 0 0
\(791\) −25.6571 −0.912261
\(792\) 0 0
\(793\) 11.5896 0.411560
\(794\) 0 0
\(795\) −25.2858 −0.896795
\(796\) 0 0
\(797\) −2.33137 −0.0825815 −0.0412907 0.999147i \(-0.513147\pi\)
−0.0412907 + 0.999147i \(0.513147\pi\)
\(798\) 0 0
\(799\) −0.788473 −0.0278942
\(800\) 0 0
\(801\) 7.69442 0.271869
\(802\) 0 0
\(803\) 73.6263 2.59821
\(804\) 0 0
\(805\) −31.4206 −1.10743
\(806\) 0 0
\(807\) −23.1618 −0.815335
\(808\) 0 0
\(809\) 19.6327 0.690250 0.345125 0.938557i \(-0.387836\pi\)
0.345125 + 0.938557i \(0.387836\pi\)
\(810\) 0 0
\(811\) −1.25282 −0.0439926 −0.0219963 0.999758i \(-0.507002\pi\)
−0.0219963 + 0.999758i \(0.507002\pi\)
\(812\) 0 0
\(813\) −27.3302 −0.958514
\(814\) 0 0
\(815\) −11.4684 −0.401722
\(816\) 0 0
\(817\) −4.57625 −0.160103
\(818\) 0 0
\(819\) 3.53451 0.123506
\(820\) 0 0
\(821\) −4.53393 −0.158235 −0.0791176 0.996865i \(-0.525210\pi\)
−0.0791176 + 0.996865i \(0.525210\pi\)
\(822\) 0 0
\(823\) −2.81623 −0.0981677 −0.0490838 0.998795i \(-0.515630\pi\)
−0.0490838 + 0.998795i \(0.515630\pi\)
\(824\) 0 0
\(825\) 69.9828 2.43649
\(826\) 0 0
\(827\) 10.2247 0.355546 0.177773 0.984071i \(-0.443111\pi\)
0.177773 + 0.984071i \(0.443111\pi\)
\(828\) 0 0
\(829\) 3.66108 0.127155 0.0635773 0.997977i \(-0.479749\pi\)
0.0635773 + 0.997977i \(0.479749\pi\)
\(830\) 0 0
\(831\) −26.8048 −0.929850
\(832\) 0 0
\(833\) 0.750829 0.0260147
\(834\) 0 0
\(835\) −4.19525 −0.145183
\(836\) 0 0
\(837\) 6.03892 0.208736
\(838\) 0 0
\(839\) −19.7190 −0.680774 −0.340387 0.940285i \(-0.610558\pi\)
−0.340387 + 0.940285i \(0.610558\pi\)
\(840\) 0 0
\(841\) 60.0283 2.06994
\(842\) 0 0
\(843\) −19.5511 −0.673376
\(844\) 0 0
\(845\) −29.0314 −0.998710
\(846\) 0 0
\(847\) −28.4514 −0.977603
\(848\) 0 0
\(849\) 9.70821 0.333185
\(850\) 0 0
\(851\) 51.7928 1.77543
\(852\) 0 0
\(853\) 57.5393 1.97011 0.985055 0.172241i \(-0.0551008\pi\)
0.985055 + 0.172241i \(0.0551008\pi\)
\(854\) 0 0
\(855\) −1.55312 −0.0531155
\(856\) 0 0
\(857\) −43.1197 −1.47294 −0.736471 0.676469i \(-0.763509\pi\)
−0.736471 + 0.676469i \(0.763509\pi\)
\(858\) 0 0
\(859\) 27.5816 0.941071 0.470535 0.882381i \(-0.344061\pi\)
0.470535 + 0.882381i \(0.344061\pi\)
\(860\) 0 0
\(861\) −11.5232 −0.392708
\(862\) 0 0
\(863\) −46.9199 −1.59717 −0.798586 0.601881i \(-0.794418\pi\)
−0.798586 + 0.601881i \(0.794418\pi\)
\(864\) 0 0
\(865\) −11.0541 −0.375852
\(866\) 0 0
\(867\) 16.9769 0.576567
\(868\) 0 0
\(869\) −29.6846 −1.00698
\(870\) 0 0
\(871\) −14.9408 −0.506249
\(872\) 0 0
\(873\) 18.7449 0.634417
\(874\) 0 0
\(875\) −45.7044 −1.54509
\(876\) 0 0
\(877\) −16.2003 −0.547046 −0.273523 0.961866i \(-0.588189\pi\)
−0.273523 + 0.961866i \(0.588189\pi\)
\(878\) 0 0
\(879\) −19.0093 −0.641167
\(880\) 0 0
\(881\) −30.8652 −1.03988 −0.519938 0.854204i \(-0.674045\pi\)
−0.519938 + 0.854204i \(0.674045\pi\)
\(882\) 0 0
\(883\) 22.8934 0.770423 0.385211 0.922828i \(-0.374129\pi\)
0.385211 + 0.922828i \(0.374129\pi\)
\(884\) 0 0
\(885\) −25.7462 −0.865448
\(886\) 0 0
\(887\) 12.1260 0.407152 0.203576 0.979059i \(-0.434744\pi\)
0.203576 + 0.979059i \(0.434744\pi\)
\(888\) 0 0
\(889\) −20.3439 −0.682313
\(890\) 0 0
\(891\) −5.55413 −0.186070
\(892\) 0 0
\(893\) −1.92256 −0.0643361
\(894\) 0 0
\(895\) −20.9505 −0.700297
\(896\) 0 0
\(897\) 12.8833 0.430161
\(898\) 0 0
\(899\) 56.9801 1.90039
\(900\) 0 0
\(901\) −0.915106 −0.0304866
\(902\) 0 0
\(903\) 17.7191 0.589656
\(904\) 0 0
\(905\) 44.2531 1.47102
\(906\) 0 0
\(907\) 27.7756 0.922274 0.461137 0.887329i \(-0.347442\pi\)
0.461137 + 0.887329i \(0.347442\pi\)
\(908\) 0 0
\(909\) 8.67739 0.287811
\(910\) 0 0
\(911\) 15.6800 0.519502 0.259751 0.965676i \(-0.416359\pi\)
0.259751 + 0.965676i \(0.416359\pi\)
\(912\) 0 0
\(913\) 10.1857 0.337097
\(914\) 0 0
\(915\) 19.7187 0.651880
\(916\) 0 0
\(917\) −9.10280 −0.300601
\(918\) 0 0
\(919\) 40.1610 1.32479 0.662395 0.749154i \(-0.269540\pi\)
0.662395 + 0.749154i \(0.269540\pi\)
\(920\) 0 0
\(921\) −15.8337 −0.521738
\(922\) 0 0
\(923\) 8.33930 0.274491
\(924\) 0 0
\(925\) 124.901 4.10673
\(926\) 0 0
\(927\) 17.6281 0.578984
\(928\) 0 0
\(929\) 7.74113 0.253978 0.126989 0.991904i \(-0.459469\pi\)
0.126989 + 0.991904i \(0.459469\pi\)
\(930\) 0 0
\(931\) 1.83077 0.0600012
\(932\) 0 0
\(933\) −7.16509 −0.234575
\(934\) 0 0
\(935\) 3.53775 0.115697
\(936\) 0 0
\(937\) 9.97774 0.325959 0.162979 0.986629i \(-0.447890\pi\)
0.162979 + 0.986629i \(0.447890\pi\)
\(938\) 0 0
\(939\) 11.2093 0.365801
\(940\) 0 0
\(941\) 42.7867 1.39481 0.697404 0.716679i \(-0.254339\pi\)
0.697404 + 0.716679i \(0.254339\pi\)
\(942\) 0 0
\(943\) −42.0020 −1.36777
\(944\) 0 0
\(945\) 6.01363 0.195624
\(946\) 0 0
\(947\) −53.9412 −1.75285 −0.876427 0.481534i \(-0.840080\pi\)
−0.876427 + 0.481534i \(0.840080\pi\)
\(948\) 0 0
\(949\) 32.6863 1.06104
\(950\) 0 0
\(951\) 33.7170 1.09335
\(952\) 0 0
\(953\) −28.9693 −0.938408 −0.469204 0.883090i \(-0.655459\pi\)
−0.469204 + 0.883090i \(0.655459\pi\)
\(954\) 0 0
\(955\) 50.1566 1.62303
\(956\) 0 0
\(957\) −52.4059 −1.69404
\(958\) 0 0
\(959\) 8.24548 0.266261
\(960\) 0 0
\(961\) 5.46858 0.176406
\(962\) 0 0
\(963\) 5.19885 0.167530
\(964\) 0 0
\(965\) −21.5010 −0.692143
\(966\) 0 0
\(967\) 9.27228 0.298176 0.149088 0.988824i \(-0.452366\pi\)
0.149088 + 0.988824i \(0.452366\pi\)
\(968\) 0 0
\(969\) −0.0562080 −0.00180566
\(970\) 0 0
\(971\) −32.9233 −1.05656 −0.528279 0.849071i \(-0.677162\pi\)
−0.528279 + 0.849071i \(0.677162\pi\)
\(972\) 0 0
\(973\) −10.4069 −0.333631
\(974\) 0 0
\(975\) 31.0688 0.994999
\(976\) 0 0
\(977\) 39.9873 1.27931 0.639654 0.768663i \(-0.279078\pi\)
0.639654 + 0.768663i \(0.279078\pi\)
\(978\) 0 0
\(979\) −42.7358 −1.36584
\(980\) 0 0
\(981\) −6.27648 −0.200393
\(982\) 0 0
\(983\) 6.71964 0.214323 0.107162 0.994242i \(-0.465824\pi\)
0.107162 + 0.994242i \(0.465824\pi\)
\(984\) 0 0
\(985\) 109.211 3.47977
\(986\) 0 0
\(987\) 7.44412 0.236949
\(988\) 0 0
\(989\) 64.5863 2.05373
\(990\) 0 0
\(991\) −39.0547 −1.24061 −0.620306 0.784360i \(-0.712992\pi\)
−0.620306 + 0.784360i \(0.712992\pi\)
\(992\) 0 0
\(993\) 0.859249 0.0272674
\(994\) 0 0
\(995\) −90.5644 −2.87108
\(996\) 0 0
\(997\) 23.1084 0.731849 0.365924 0.930645i \(-0.380753\pi\)
0.365924 + 0.930645i \(0.380753\pi\)
\(998\) 0 0
\(999\) −9.91270 −0.313624
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.1.8 9
4.3 odd 2 2004.2.a.d.1.8 9
12.11 even 2 6012.2.a.h.1.2 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.d.1.8 9 4.3 odd 2
6012.2.a.h.1.2 9 12.11 even 2
8016.2.a.bb.1.8 9 1.1 even 1 trivial