Properties

Label 8280.2.a.bp.1.3
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \( x^{3} - x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.12489\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +4.12489 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +4.12489 q^{7} +4.64002 q^{11} +2.64002 q^{13} +4.12489 q^{17} -1.60975 q^{19} -1.00000 q^{23} +1.00000 q^{25} -1.48486 q^{29} -0.515138 q^{31} +4.12489 q^{35} -2.12489 q^{37} +4.51514 q^{41} +5.28005 q^{43} +2.39025 q^{47} +10.0147 q^{49} +4.12489 q^{53} +4.64002 q^{55} -3.79518 q^{59} +2.32970 q^{61} +2.64002 q^{65} -0.185438 q^{67} +14.9541 q^{71} -10.1698 q^{73} +19.1396 q^{77} -1.93945 q^{79} +0.844838 q^{83} +4.12489 q^{85} -0.780505 q^{89} +10.8898 q^{91} -1.60975 q^{95} -9.21949 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{5} + 4 q^{7} + 6 q^{11} + 4 q^{17} + 4 q^{19} - 3 q^{23} + 3 q^{25} - 4 q^{29} - 2 q^{31} + 4 q^{35} + 2 q^{37} + 14 q^{41} + 16 q^{47} - 3 q^{49} + 4 q^{53} + 6 q^{55} + 4 q^{59} + 14 q^{61} + 6 q^{67} + 10 q^{71} + 10 q^{73} + 16 q^{77} - 4 q^{79} + 10 q^{83} + 4 q^{85} - 20 q^{89} + 8 q^{91} + 4 q^{95} - 10 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 4.12489 1.55906 0.779530 0.626365i \(-0.215458\pi\)
0.779530 + 0.626365i \(0.215458\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.64002 1.39902 0.699510 0.714623i \(-0.253402\pi\)
0.699510 + 0.714623i \(0.253402\pi\)
\(12\) 0 0
\(13\) 2.64002 0.732211 0.366105 0.930573i \(-0.380691\pi\)
0.366105 + 0.930573i \(0.380691\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.12489 1.00043 0.500216 0.865901i \(-0.333254\pi\)
0.500216 + 0.865901i \(0.333254\pi\)
\(18\) 0 0
\(19\) −1.60975 −0.369301 −0.184651 0.982804i \(-0.559115\pi\)
−0.184651 + 0.982804i \(0.559115\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.48486 −0.275732 −0.137866 0.990451i \(-0.544024\pi\)
−0.137866 + 0.990451i \(0.544024\pi\)
\(30\) 0 0
\(31\) −0.515138 −0.0925215 −0.0462608 0.998929i \(-0.514731\pi\)
−0.0462608 + 0.998929i \(0.514731\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.12489 0.697233
\(36\) 0 0
\(37\) −2.12489 −0.349329 −0.174665 0.984628i \(-0.555884\pi\)
−0.174665 + 0.984628i \(0.555884\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.51514 0.705146 0.352573 0.935784i \(-0.385307\pi\)
0.352573 + 0.935784i \(0.385307\pi\)
\(42\) 0 0
\(43\) 5.28005 0.805200 0.402600 0.915376i \(-0.368107\pi\)
0.402600 + 0.915376i \(0.368107\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.39025 0.348654 0.174327 0.984688i \(-0.444225\pi\)
0.174327 + 0.984688i \(0.444225\pi\)
\(48\) 0 0
\(49\) 10.0147 1.43067
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.12489 0.566597 0.283298 0.959032i \(-0.408571\pi\)
0.283298 + 0.959032i \(0.408571\pi\)
\(54\) 0 0
\(55\) 4.64002 0.625661
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.79518 −0.494091 −0.247045 0.969004i \(-0.579460\pi\)
−0.247045 + 0.969004i \(0.579460\pi\)
\(60\) 0 0
\(61\) 2.32970 0.298288 0.149144 0.988816i \(-0.452348\pi\)
0.149144 + 0.988816i \(0.452348\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.64002 0.327455
\(66\) 0 0
\(67\) −0.185438 −0.0226548 −0.0113274 0.999936i \(-0.503606\pi\)
−0.0113274 + 0.999936i \(0.503606\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.9541 1.77473 0.887364 0.461069i \(-0.152534\pi\)
0.887364 + 0.461069i \(0.152534\pi\)
\(72\) 0 0
\(73\) −10.1698 −1.19029 −0.595145 0.803618i \(-0.702905\pi\)
−0.595145 + 0.803618i \(0.702905\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 19.1396 2.18116
\(78\) 0 0
\(79\) −1.93945 −0.218205 −0.109102 0.994031i \(-0.534798\pi\)
−0.109102 + 0.994031i \(0.534798\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.844838 0.0927331 0.0463665 0.998924i \(-0.485236\pi\)
0.0463665 + 0.998924i \(0.485236\pi\)
\(84\) 0 0
\(85\) 4.12489 0.447407
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.780505 −0.0827334 −0.0413667 0.999144i \(-0.513171\pi\)
−0.0413667 + 0.999144i \(0.513171\pi\)
\(90\) 0 0
\(91\) 10.8898 1.14156
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.60975 −0.165157
\(96\) 0 0
\(97\) −9.21949 −0.936098 −0.468049 0.883703i \(-0.655043\pi\)
−0.468049 + 0.883703i \(0.655043\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.23509 0.122896 0.0614481 0.998110i \(-0.480428\pi\)
0.0614481 + 0.998110i \(0.480428\pi\)
\(102\) 0 0
\(103\) −16.0294 −1.57942 −0.789710 0.613481i \(-0.789769\pi\)
−0.789710 + 0.613481i \(0.789769\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.185438 0.0179269 0.00896347 0.999960i \(-0.497147\pi\)
0.00896347 + 0.999960i \(0.497147\pi\)
\(108\) 0 0
\(109\) 5.92007 0.567040 0.283520 0.958966i \(-0.408498\pi\)
0.283520 + 0.958966i \(0.408498\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.31410 −0.593981 −0.296990 0.954880i \(-0.595983\pi\)
−0.296990 + 0.954880i \(0.595983\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 17.0147 1.55973
\(120\) 0 0
\(121\) 10.5298 0.957256
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −19.0790 −1.69299 −0.846494 0.532398i \(-0.821291\pi\)
−0.846494 + 0.532398i \(0.821291\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −11.2800 −0.985542 −0.492771 0.870159i \(-0.664016\pi\)
−0.492771 + 0.870159i \(0.664016\pi\)
\(132\) 0 0
\(133\) −6.64002 −0.575763
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.310323 −0.0265127 −0.0132563 0.999912i \(-0.504220\pi\)
−0.0132563 + 0.999912i \(0.504220\pi\)
\(138\) 0 0
\(139\) −7.85574 −0.666315 −0.333157 0.942871i \(-0.608114\pi\)
−0.333157 + 0.942871i \(0.608114\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 12.2498 1.02438
\(144\) 0 0
\(145\) −1.48486 −0.123311
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −10.1698 −0.833146 −0.416573 0.909102i \(-0.636769\pi\)
−0.416573 + 0.909102i \(0.636769\pi\)
\(150\) 0 0
\(151\) 1.03028 0.0838427 0.0419213 0.999121i \(-0.486652\pi\)
0.0419213 + 0.999121i \(0.486652\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.515138 −0.0413769
\(156\) 0 0
\(157\) 4.06433 0.324369 0.162185 0.986760i \(-0.448146\pi\)
0.162185 + 0.986760i \(0.448146\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.12489 −0.325087
\(162\) 0 0
\(163\) 6.18922 0.484777 0.242389 0.970179i \(-0.422069\pi\)
0.242389 + 0.970179i \(0.422069\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.3893 −0.881333 −0.440667 0.897671i \(-0.645258\pi\)
−0.440667 + 0.897671i \(0.645258\pi\)
\(168\) 0 0
\(169\) −6.03028 −0.463867
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.90917 0.525295 0.262647 0.964892i \(-0.415404\pi\)
0.262647 + 0.964892i \(0.415404\pi\)
\(174\) 0 0
\(175\) 4.12489 0.311812
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0294 −0.899117 −0.449558 0.893251i \(-0.648419\pi\)
−0.449558 + 0.893251i \(0.648419\pi\)
\(180\) 0 0
\(181\) −3.81078 −0.283253 −0.141627 0.989920i \(-0.545233\pi\)
−0.141627 + 0.989920i \(0.545233\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.12489 −0.156225
\(186\) 0 0
\(187\) 19.1396 1.39962
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.0799296 0.00578350 0.00289175 0.999996i \(-0.499080\pi\)
0.00289175 + 0.999996i \(0.499080\pi\)
\(192\) 0 0
\(193\) −16.9697 −1.22151 −0.610754 0.791821i \(-0.709133\pi\)
−0.610754 + 0.791821i \(0.709133\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.6206 0.756690 0.378345 0.925665i \(-0.376493\pi\)
0.378345 + 0.925665i \(0.376493\pi\)
\(198\) 0 0
\(199\) −17.5298 −1.24266 −0.621328 0.783551i \(-0.713407\pi\)
−0.621328 + 0.783551i \(0.713407\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.12489 −0.429883
\(204\) 0 0
\(205\) 4.51514 0.315351
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.46927 −0.516660
\(210\) 0 0
\(211\) −2.70436 −0.186176 −0.0930878 0.995658i \(-0.529674\pi\)
−0.0930878 + 0.995658i \(0.529674\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.28005 0.360096
\(216\) 0 0
\(217\) −2.12489 −0.144247
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 10.8898 0.732527
\(222\) 0 0
\(223\) −1.21949 −0.0816634 −0.0408317 0.999166i \(-0.513001\pi\)
−0.0408317 + 0.999166i \(0.513001\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.56009 −0.169919 −0.0849597 0.996384i \(-0.527076\pi\)
−0.0849597 + 0.996384i \(0.527076\pi\)
\(228\) 0 0
\(229\) −17.9688 −1.18741 −0.593706 0.804682i \(-0.702336\pi\)
−0.593706 + 0.804682i \(0.702336\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.18922 0.274445 0.137222 0.990540i \(-0.456182\pi\)
0.137222 + 0.990540i \(0.456182\pi\)
\(234\) 0 0
\(235\) 2.39025 0.155923
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 16.3553 1.05794 0.528968 0.848642i \(-0.322579\pi\)
0.528968 + 0.848642i \(0.322579\pi\)
\(240\) 0 0
\(241\) 11.0790 0.713662 0.356831 0.934169i \(-0.383857\pi\)
0.356831 + 0.934169i \(0.383857\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 10.0147 0.639814
\(246\) 0 0
\(247\) −4.24977 −0.270406
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.2800 0.964468 0.482234 0.876042i \(-0.339825\pi\)
0.482234 + 0.876042i \(0.339825\pi\)
\(252\) 0 0
\(253\) −4.64002 −0.291716
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.14048 0.258276 0.129138 0.991627i \(-0.458779\pi\)
0.129138 + 0.991627i \(0.458779\pi\)
\(258\) 0 0
\(259\) −8.76491 −0.544625
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.5260 0.710726 0.355363 0.934728i \(-0.384357\pi\)
0.355363 + 0.934728i \(0.384357\pi\)
\(264\) 0 0
\(265\) 4.12489 0.253390
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −28.5445 −1.74039 −0.870194 0.492709i \(-0.836007\pi\)
−0.870194 + 0.492709i \(0.836007\pi\)
\(270\) 0 0
\(271\) 22.1736 1.34695 0.673476 0.739209i \(-0.264801\pi\)
0.673476 + 0.739209i \(0.264801\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.64002 0.279804
\(276\) 0 0
\(277\) −4.24977 −0.255344 −0.127672 0.991816i \(-0.540750\pi\)
−0.127672 + 0.991816i \(0.540750\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 11.0109 0.656855 0.328428 0.944529i \(-0.393481\pi\)
0.328428 + 0.944529i \(0.393481\pi\)
\(282\) 0 0
\(283\) 1.21571 0.0722667 0.0361333 0.999347i \(-0.488496\pi\)
0.0361333 + 0.999347i \(0.488496\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 18.6244 1.09937
\(288\) 0 0
\(289\) 0.0146797 0.000863513 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.8439 −0.925612 −0.462806 0.886460i \(-0.653157\pi\)
−0.462806 + 0.886460i \(0.653157\pi\)
\(294\) 0 0
\(295\) −3.79518 −0.220964
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.64002 −0.152676
\(300\) 0 0
\(301\) 21.7796 1.25535
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.32970 0.133398
\(306\) 0 0
\(307\) 8.86043 0.505692 0.252846 0.967507i \(-0.418633\pi\)
0.252846 + 0.967507i \(0.418633\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −22.6888 −1.28656 −0.643281 0.765630i \(-0.722427\pi\)
−0.643281 + 0.765630i \(0.722427\pi\)
\(312\) 0 0
\(313\) 27.6841 1.56480 0.782398 0.622779i \(-0.213996\pi\)
0.782398 + 0.622779i \(0.213996\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 26.9192 1.51193 0.755965 0.654612i \(-0.227168\pi\)
0.755965 + 0.654612i \(0.227168\pi\)
\(318\) 0 0
\(319\) −6.88979 −0.385754
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.64002 −0.369461
\(324\) 0 0
\(325\) 2.64002 0.146442
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9.85952 0.543573
\(330\) 0 0
\(331\) 30.9541 1.70139 0.850696 0.525657i \(-0.176181\pi\)
0.850696 + 0.525657i \(0.176181\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.185438 −0.0101315
\(336\) 0 0
\(337\) −20.1892 −1.09978 −0.549888 0.835238i \(-0.685330\pi\)
−0.549888 + 0.835238i \(0.685330\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.39025 −0.129439
\(342\) 0 0
\(343\) 12.4352 0.671438
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0.0449558 0.00240643 0.00120321 0.999999i \(-0.499617\pi\)
0.00120321 + 0.999999i \(0.499617\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −20.9797 −1.11664 −0.558319 0.829627i \(-0.688553\pi\)
−0.558319 + 0.829627i \(0.688553\pi\)
\(354\) 0 0
\(355\) 14.9541 0.793683
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.1405 0.746306 0.373153 0.927770i \(-0.378277\pi\)
0.373153 + 0.927770i \(0.378277\pi\)
\(360\) 0 0
\(361\) −16.4087 −0.863616
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −10.1698 −0.532314
\(366\) 0 0
\(367\) 9.93567 0.518638 0.259319 0.965792i \(-0.416502\pi\)
0.259319 + 0.965792i \(0.416502\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 17.0147 0.883358
\(372\) 0 0
\(373\) −28.2110 −1.46071 −0.730356 0.683067i \(-0.760646\pi\)
−0.730356 + 0.683067i \(0.760646\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.92007 −0.201894
\(378\) 0 0
\(379\) 23.5592 1.21015 0.605077 0.796167i \(-0.293142\pi\)
0.605077 + 0.796167i \(0.293142\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 29.3444 1.49943 0.749714 0.661762i \(-0.230191\pi\)
0.749714 + 0.661762i \(0.230191\pi\)
\(384\) 0 0
\(385\) 19.1396 0.975443
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.09839 0.258499 0.129249 0.991612i \(-0.458743\pi\)
0.129249 + 0.991612i \(0.458743\pi\)
\(390\) 0 0
\(391\) −4.12489 −0.208604
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.93945 −0.0975842
\(396\) 0 0
\(397\) −22.9385 −1.15125 −0.575626 0.817713i \(-0.695242\pi\)
−0.575626 + 0.817713i \(0.695242\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.1892 1.10808 0.554038 0.832491i \(-0.313086\pi\)
0.554038 + 0.832491i \(0.313086\pi\)
\(402\) 0 0
\(403\) −1.35998 −0.0677453
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.85952 −0.488718
\(408\) 0 0
\(409\) −19.6741 −0.972821 −0.486410 0.873730i \(-0.661694\pi\)
−0.486410 + 0.873730i \(0.661694\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −15.6547 −0.770318
\(414\) 0 0
\(415\) 0.844838 0.0414715
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 30.4196 1.48610 0.743048 0.669239i \(-0.233380\pi\)
0.743048 + 0.669239i \(0.233380\pi\)
\(420\) 0 0
\(421\) −36.8586 −1.79638 −0.898189 0.439609i \(-0.855117\pi\)
−0.898189 + 0.439609i \(0.855117\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.12489 0.200086
\(426\) 0 0
\(427\) 9.60975 0.465048
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −19.0596 −0.918070 −0.459035 0.888418i \(-0.651805\pi\)
−0.459035 + 0.888418i \(0.651805\pi\)
\(432\) 0 0
\(433\) −28.6244 −1.37560 −0.687801 0.725899i \(-0.741424\pi\)
−0.687801 + 0.725899i \(0.741424\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.60975 0.0770047
\(438\) 0 0
\(439\) −20.2498 −0.966469 −0.483234 0.875491i \(-0.660538\pi\)
−0.483234 + 0.875491i \(0.660538\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.76869 0.321590 0.160795 0.986988i \(-0.448594\pi\)
0.160795 + 0.986988i \(0.448594\pi\)
\(444\) 0 0
\(445\) −0.780505 −0.0369995
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 16.3553 0.771853 0.385927 0.922529i \(-0.373882\pi\)
0.385927 + 0.922529i \(0.373882\pi\)
\(450\) 0 0
\(451\) 20.9503 0.986513
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 10.8898 0.510521
\(456\) 0 0
\(457\) −15.4655 −0.723445 −0.361722 0.932286i \(-0.617811\pi\)
−0.361722 + 0.932286i \(0.617811\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.31032 0.200752 0.100376 0.994950i \(-0.467995\pi\)
0.100376 + 0.994950i \(0.467995\pi\)
\(462\) 0 0
\(463\) 18.5483 0.862012 0.431006 0.902349i \(-0.358159\pi\)
0.431006 + 0.902349i \(0.358159\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.2148 0.842880 0.421440 0.906856i \(-0.361525\pi\)
0.421440 + 0.906856i \(0.361525\pi\)
\(468\) 0 0
\(469\) −0.764909 −0.0353202
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 24.4995 1.12649
\(474\) 0 0
\(475\) −1.60975 −0.0738603
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 33.5786 1.53424 0.767122 0.641502i \(-0.221688\pi\)
0.767122 + 0.641502i \(0.221688\pi\)
\(480\) 0 0
\(481\) −5.60975 −0.255782
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9.21949 −0.418636
\(486\) 0 0
\(487\) 40.3591 1.82884 0.914422 0.404763i \(-0.132646\pi\)
0.914422 + 0.404763i \(0.132646\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8.16606 −0.368529 −0.184265 0.982877i \(-0.558990\pi\)
−0.184265 + 0.982877i \(0.558990\pi\)
\(492\) 0 0
\(493\) −6.12489 −0.275851
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 61.6841 2.76691
\(498\) 0 0
\(499\) −25.0147 −1.11981 −0.559905 0.828557i \(-0.689163\pi\)
−0.559905 + 0.828557i \(0.689163\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 35.9944 1.60491 0.802455 0.596712i \(-0.203527\pi\)
0.802455 + 0.596712i \(0.203527\pi\)
\(504\) 0 0
\(505\) 1.23509 0.0549608
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.3179 −0.723278 −0.361639 0.932318i \(-0.617783\pi\)
−0.361639 + 0.932318i \(0.617783\pi\)
\(510\) 0 0
\(511\) −41.9494 −1.85573
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −16.0294 −0.706338
\(516\) 0 0
\(517\) 11.0908 0.487774
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −29.8283 −1.30680 −0.653401 0.757012i \(-0.726659\pi\)
−0.653401 + 0.757012i \(0.726659\pi\)
\(522\) 0 0
\(523\) 35.9688 1.57281 0.786403 0.617714i \(-0.211941\pi\)
0.786403 + 0.617714i \(0.211941\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.12489 −0.0925615
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 11.9201 0.516316
\(534\) 0 0
\(535\) 0.185438 0.00801717
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 46.4683 2.00153
\(540\) 0 0
\(541\) −22.1287 −0.951386 −0.475693 0.879611i \(-0.657803\pi\)
−0.475693 + 0.879611i \(0.657803\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.92007 0.253588
\(546\) 0 0
\(547\) 20.6206 0.881675 0.440838 0.897587i \(-0.354681\pi\)
0.440838 + 0.897587i \(0.354681\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.39025 0.101828
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.5251 −0.784935 −0.392467 0.919766i \(-0.628378\pi\)
−0.392467 + 0.919766i \(0.628378\pi\)
\(558\) 0 0
\(559\) 13.9394 0.589576
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.87511 0.247607 0.123803 0.992307i \(-0.460491\pi\)
0.123803 + 0.992307i \(0.460491\pi\)
\(564\) 0 0
\(565\) −6.31410 −0.265636
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.03028 0.210880 0.105440 0.994426i \(-0.466375\pi\)
0.105440 + 0.994426i \(0.466375\pi\)
\(570\) 0 0
\(571\) 41.8208 1.75014 0.875072 0.483992i \(-0.160814\pi\)
0.875072 + 0.483992i \(0.160814\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −16.4314 −0.684049 −0.342025 0.939691i \(-0.611113\pi\)
−0.342025 + 0.939691i \(0.611113\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.48486 0.144576
\(582\) 0 0
\(583\) 19.1396 0.792680
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.0294 −0.579054 −0.289527 0.957170i \(-0.593498\pi\)
−0.289527 + 0.957170i \(0.593498\pi\)
\(588\) 0 0
\(589\) 0.829242 0.0341683
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 29.1396 1.19662 0.598309 0.801265i \(-0.295839\pi\)
0.598309 + 0.801265i \(0.295839\pi\)
\(594\) 0 0
\(595\) 17.0147 0.697534
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −32.7106 −1.33652 −0.668259 0.743929i \(-0.732960\pi\)
−0.668259 + 0.743929i \(0.732960\pi\)
\(600\) 0 0
\(601\) −16.7044 −0.681385 −0.340692 0.940175i \(-0.610661\pi\)
−0.340692 + 0.940175i \(0.610661\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 10.5298 0.428098
\(606\) 0 0
\(607\) −0.480164 −0.0194893 −0.00974463 0.999953i \(-0.503102\pi\)
−0.00974463 + 0.999953i \(0.503102\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.31032 0.255288
\(612\) 0 0
\(613\) −8.65940 −0.349750 −0.174875 0.984591i \(-0.555952\pi\)
−0.174875 + 0.984591i \(0.555952\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11.0559 −0.445092 −0.222546 0.974922i \(-0.571437\pi\)
−0.222546 + 0.974922i \(0.571437\pi\)
\(618\) 0 0
\(619\) −33.6197 −1.35129 −0.675646 0.737227i \(-0.736135\pi\)
−0.675646 + 0.737227i \(0.736135\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.21949 −0.128986
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8.76491 −0.349480
\(630\) 0 0
\(631\) 3.95883 0.157598 0.0787992 0.996891i \(-0.474891\pi\)
0.0787992 + 0.996891i \(0.474891\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −19.0790 −0.757128
\(636\) 0 0
\(637\) 26.4390 1.04755
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6.26915 0.247616 0.123808 0.992306i \(-0.460489\pi\)
0.123808 + 0.992306i \(0.460489\pi\)
\(642\) 0 0
\(643\) −12.9348 −0.510097 −0.255048 0.966928i \(-0.582091\pi\)
−0.255048 + 0.966928i \(0.582091\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −36.9192 −1.45144 −0.725721 0.687989i \(-0.758494\pi\)
−0.725721 + 0.687989i \(0.758494\pi\)
\(648\) 0 0
\(649\) −17.6097 −0.691243
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16.8898 0.660949 0.330474 0.943815i \(-0.392791\pi\)
0.330474 + 0.943815i \(0.392791\pi\)
\(654\) 0 0
\(655\) −11.2800 −0.440748
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21.4205 0.834425 0.417213 0.908809i \(-0.363007\pi\)
0.417213 + 0.908809i \(0.363007\pi\)
\(660\) 0 0
\(661\) 3.81834 0.148516 0.0742582 0.997239i \(-0.476341\pi\)
0.0742582 + 0.997239i \(0.476341\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.64002 −0.257489
\(666\) 0 0
\(667\) 1.48486 0.0574941
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.8099 0.417310
\(672\) 0 0
\(673\) −40.4802 −1.56040 −0.780198 0.625533i \(-0.784882\pi\)
−0.780198 + 0.625533i \(0.784882\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 27.8751 1.07133 0.535664 0.844431i \(-0.320061\pi\)
0.535664 + 0.844431i \(0.320061\pi\)
\(678\) 0 0
\(679\) −38.0294 −1.45943
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12.3297 −0.471783 −0.235891 0.971779i \(-0.575801\pi\)
−0.235891 + 0.971779i \(0.575801\pi\)
\(684\) 0 0
\(685\) −0.310323 −0.0118568
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 10.8898 0.414868
\(690\) 0 0
\(691\) 49.0890 1.86743 0.933717 0.358013i \(-0.116546\pi\)
0.933717 + 0.358013i \(0.116546\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.85574 −0.297985
\(696\) 0 0
\(697\) 18.6244 0.705450
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 36.7299 1.38727 0.693635 0.720326i \(-0.256008\pi\)
0.693635 + 0.720326i \(0.256008\pi\)
\(702\) 0 0
\(703\) 3.42053 0.129008
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5.09461 0.191603
\(708\) 0 0
\(709\) −1.33062 −0.0499724 −0.0249862 0.999688i \(-0.507954\pi\)
−0.0249862 + 0.999688i \(0.507954\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.515138 0.0192921
\(714\) 0 0
\(715\) 12.2498 0.458115
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 31.7034 1.18234 0.591169 0.806547i \(-0.298666\pi\)
0.591169 + 0.806547i \(0.298666\pi\)
\(720\) 0 0
\(721\) −66.1193 −2.46241
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.48486 −0.0551464
\(726\) 0 0
\(727\) 20.7455 0.769409 0.384705 0.923040i \(-0.374303\pi\)
0.384705 + 0.923040i \(0.374303\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 21.7796 0.805547
\(732\) 0 0
\(733\) −3.81456 −0.140894 −0.0704470 0.997516i \(-0.522443\pi\)
−0.0704470 + 0.997516i \(0.522443\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.860435 −0.0316945
\(738\) 0 0
\(739\) 12.2654 0.451189 0.225594 0.974221i \(-0.427568\pi\)
0.225594 + 0.974221i \(0.427568\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24.9991 −0.917127 −0.458564 0.888662i \(-0.651636\pi\)
−0.458564 + 0.888662i \(0.651636\pi\)
\(744\) 0 0
\(745\) −10.1698 −0.372594
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.764909 0.0279492
\(750\) 0 0
\(751\) −10.7687 −0.392955 −0.196478 0.980508i \(-0.562950\pi\)
−0.196478 + 0.980508i \(0.562950\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.03028 0.0374956
\(756\) 0 0
\(757\) 24.4352 0.888113 0.444056 0.895999i \(-0.353539\pi\)
0.444056 + 0.895999i \(0.353539\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.98532 0.253218 0.126609 0.991953i \(-0.459591\pi\)
0.126609 + 0.991953i \(0.459591\pi\)
\(762\) 0 0
\(763\) 24.4196 0.884049
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.0194 −0.361779
\(768\) 0 0
\(769\) −28.0705 −1.01225 −0.506125 0.862460i \(-0.668922\pi\)
−0.506125 + 0.862460i \(0.668922\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.2791 0.729390 0.364695 0.931127i \(-0.381173\pi\)
0.364695 + 0.931127i \(0.381173\pi\)
\(774\) 0 0
\(775\) −0.515138 −0.0185043
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.26823 −0.260411
\(780\) 0 0
\(781\) 69.3875 2.48288
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.06433 0.145062
\(786\) 0 0
\(787\) 1.50424 0.0536203 0.0268102 0.999641i \(-0.491465\pi\)
0.0268102 + 0.999641i \(0.491465\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −26.0450 −0.926052
\(792\) 0 0
\(793\) 6.15046 0.218409
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 55.0247 1.94907 0.974537 0.224228i \(-0.0719860\pi\)
0.974537 + 0.224228i \(0.0719860\pi\)
\(798\) 0 0
\(799\) 9.85952 0.348805
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −47.1883 −1.66524
\(804\) 0 0
\(805\) −4.12489 −0.145383
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 4.35528 0.153123 0.0765617 0.997065i \(-0.475606\pi\)
0.0765617 + 0.997065i \(0.475606\pi\)
\(810\) 0 0
\(811\) −1.51422 −0.0531715 −0.0265858 0.999647i \(-0.508464\pi\)
−0.0265858 + 0.999647i \(0.508464\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6.18922 0.216799
\(816\) 0 0
\(817\) −8.49954 −0.297361
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −21.1807 −0.739213 −0.369606 0.929188i \(-0.620507\pi\)
−0.369606 + 0.929188i \(0.620507\pi\)
\(822\) 0 0
\(823\) −2.12867 −0.0742006 −0.0371003 0.999312i \(-0.511812\pi\)
−0.0371003 + 0.999312i \(0.511812\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −29.0559 −1.01037 −0.505186 0.863011i \(-0.668576\pi\)
−0.505186 + 0.863011i \(0.668576\pi\)
\(828\) 0 0
\(829\) 3.55298 0.123400 0.0617000 0.998095i \(-0.480348\pi\)
0.0617000 + 0.998095i \(0.480348\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 41.3094 1.43129
\(834\) 0 0
\(835\) −11.3893 −0.394144
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9.03028 0.311760 0.155880 0.987776i \(-0.450179\pi\)
0.155880 + 0.987776i \(0.450179\pi\)
\(840\) 0 0
\(841\) −26.7952 −0.923972
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −6.03028 −0.207448
\(846\) 0 0
\(847\) 43.4343 1.49242
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.12489 0.0728401
\(852\) 0 0
\(853\) 0.530734 0.0181720 0.00908600 0.999959i \(-0.497108\pi\)
0.00908600 + 0.999959i \(0.497108\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −27.2800 −0.931869 −0.465934 0.884819i \(-0.654282\pi\)
−0.465934 + 0.884819i \(0.654282\pi\)
\(858\) 0 0
\(859\) 11.6060 0.395990 0.197995 0.980203i \(-0.436557\pi\)
0.197995 + 0.980203i \(0.436557\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −36.5895 −1.24552 −0.622760 0.782413i \(-0.713989\pi\)
−0.622760 + 0.782413i \(0.713989\pi\)
\(864\) 0 0
\(865\) 6.90917 0.234919
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −8.99908 −0.305273
\(870\) 0 0
\(871\) −0.489560 −0.0165881
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 4.12489 0.139447
\(876\) 0 0
\(877\) 51.9688 1.75486 0.877431 0.479703i \(-0.159256\pi\)
0.877431 + 0.479703i \(0.159256\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 25.7384 0.867149 0.433575 0.901118i \(-0.357252\pi\)
0.433575 + 0.901118i \(0.357252\pi\)
\(882\) 0 0
\(883\) −39.8889 −1.34237 −0.671184 0.741291i \(-0.734214\pi\)
−0.671184 + 0.741291i \(0.734214\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −35.0908 −1.17823 −0.589117 0.808047i \(-0.700524\pi\)
−0.589117 + 0.808047i \(0.700524\pi\)
\(888\) 0 0
\(889\) −78.6987 −2.63947
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.84770 −0.128758
\(894\) 0 0
\(895\) −12.0294 −0.402097
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0.764909 0.0255111
\(900\) 0 0
\(901\) 17.0147 0.566841
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.81078 −0.126675
\(906\) 0 0
\(907\) −18.5932 −0.617378 −0.308689 0.951163i \(-0.599890\pi\)
−0.308689 + 0.951163i \(0.599890\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 24.8392 0.822960 0.411480 0.911419i \(-0.365012\pi\)
0.411480 + 0.911419i \(0.365012\pi\)
\(912\) 0 0
\(913\) 3.92007 0.129735
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −46.5289 −1.53652
\(918\) 0 0
\(919\) 55.8989 1.84393 0.921967 0.387269i \(-0.126582\pi\)
0.921967 + 0.387269i \(0.126582\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 39.4792 1.29948
\(924\) 0 0
\(925\) −2.12489 −0.0698658
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 17.8851 0.586791 0.293395 0.955991i \(-0.405215\pi\)
0.293395 + 0.955991i \(0.405215\pi\)
\(930\) 0 0
\(931\) −16.1211 −0.528348
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 19.1396 0.625931
\(936\) 0 0
\(937\) 46.4608 1.51781 0.758904 0.651203i \(-0.225735\pi\)
0.758904 + 0.651203i \(0.225735\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −17.6703 −0.576035 −0.288018 0.957625i \(-0.592996\pi\)
−0.288018 + 0.957625i \(0.592996\pi\)
\(942\) 0 0
\(943\) −4.51514 −0.147033
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 21.5374 0.699871 0.349935 0.936774i \(-0.386204\pi\)
0.349935 + 0.936774i \(0.386204\pi\)
\(948\) 0 0
\(949\) −26.8486 −0.871543
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 9.62156 0.311673 0.155836 0.987783i \(-0.450193\pi\)
0.155836 + 0.987783i \(0.450193\pi\)
\(954\) 0 0
\(955\) 0.0799296 0.00258646
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.28005 −0.0413349
\(960\) 0 0
\(961\) −30.7346 −0.991440
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −16.9697 −0.546275
\(966\) 0 0
\(967\) 44.8586 1.44256 0.721278 0.692646i \(-0.243555\pi\)
0.721278 + 0.692646i \(0.243555\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −7.19014 −0.230742 −0.115371 0.993322i \(-0.536806\pi\)
−0.115371 + 0.993322i \(0.536806\pi\)
\(972\) 0 0
\(973\) −32.4040 −1.03883
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −18.4428 −0.590037 −0.295018 0.955492i \(-0.595326\pi\)
−0.295018 + 0.955492i \(0.595326\pi\)
\(978\) 0 0
\(979\) −3.62156 −0.115746
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 19.2526 0.614064 0.307032 0.951699i \(-0.400664\pi\)
0.307032 + 0.951699i \(0.400664\pi\)
\(984\) 0 0
\(985\) 10.6206 0.338402
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.28005 −0.167896
\(990\) 0 0
\(991\) −14.3846 −0.456943 −0.228472 0.973551i \(-0.573373\pi\)
−0.228472 + 0.973551i \(0.573373\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −17.5298 −0.555733
\(996\) 0 0
\(997\) 22.0606 0.698665 0.349332 0.936999i \(-0.386408\pi\)
0.349332 + 0.936999i \(0.386408\pi\)
\(998\) 0 0
\(999\) 0 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 8280.2.a.bp.1.3 yes 3
3.2 odd 2 8280.2.a.bk.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bk.1.3 3 3.2 odd 2
8280.2.a.bp.1.3 yes 3 1.1 even 1 trivial