Properties

Label 5472.2.a.bt.1.4
Level $5472$
Weight $2$
Character 5472.1
Self dual yes
Analytic conductor $43.694$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.6941399860\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.15317.1
Defining polynomial: \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 608)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.69353\) of defining polynomial
Character \(\chi\) \(=\) 5472.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.20608 q^{5} -1.74252 q^{7} +O(q^{10})\) \(q+4.20608 q^{5} -1.74252 q^{7} +6.20608 q^{11} +4.82550 q^{13} +5.12957 q^{17} -1.00000 q^{19} +0.463560 q^{23} +12.6911 q^{25} -4.82550 q^{29} +1.63806 q^{31} -7.32919 q^{35} +3.63806 q^{37} +5.28906 q^{41} -1.08298 q^{43} -0.555087 q^{47} -3.96362 q^{49} -2.65955 q^{53} +26.1033 q^{55} -1.85061 q^{59} -9.32919 q^{61} +20.2964 q^{65} -4.72751 q^{67} -11.4850 q^{71} -0.00646614 q^{73} -10.8142 q^{77} -6.76117 q^{79} -11.8972 q^{83} +21.5754 q^{85} +7.31909 q^{89} -8.40853 q^{91} -4.20608 q^{95} -10.4122 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{5} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{5} + q^{7} + 7 q^{11} + 10 q^{13} - 5 q^{17} - 4 q^{19} - 8 q^{23} + 17 q^{25} - 10 q^{29} + 6 q^{31} + 5 q^{35} + 14 q^{37} + 2 q^{41} - 3 q^{43} - 3 q^{47} + 7 q^{49} - 4 q^{53} + 35 q^{55} + 20 q^{59} - 3 q^{61} + 12 q^{65} - 8 q^{67} - 30 q^{71} + 9 q^{73} + 7 q^{77} - 10 q^{79} + 4 q^{83} + 19 q^{85} + 16 q^{89} - 10 q^{91} + q^{95} - 6 q^{97}+O(q^{100}) \) 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
\(5\) 4.20608 1.88102 0.940508 0.339770i \(-0.110349\pi\)
0.940508 + 0.339770i \(0.110349\pi\)
\(6\) 0 0
\(7\) −1.74252 −0.658611 −0.329306 0.944223i \(-0.606815\pi\)
−0.329306 + 0.944223i \(0.606815\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.20608 1.87120 0.935602 0.353056i \(-0.114858\pi\)
0.935602 + 0.353056i \(0.114858\pi\)
\(12\) 0 0
\(13\) 4.82550 1.33835 0.669176 0.743104i \(-0.266647\pi\)
0.669176 + 0.743104i \(0.266647\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.12957 1.24410 0.622052 0.782976i \(-0.286299\pi\)
0.622052 + 0.782976i \(0.286299\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.463560 0.0966590 0.0483295 0.998831i \(-0.484610\pi\)
0.0483295 + 0.998831i \(0.484610\pi\)
\(24\) 0 0
\(25\) 12.6911 2.53822
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.82550 −0.896072 −0.448036 0.894015i \(-0.647876\pi\)
−0.448036 + 0.894015i \(0.647876\pi\)
\(30\) 0 0
\(31\) 1.63806 0.294205 0.147102 0.989121i \(-0.453005\pi\)
0.147102 + 0.989121i \(0.453005\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −7.32919 −1.23886
\(36\) 0 0
\(37\) 3.63806 0.598094 0.299047 0.954238i \(-0.403331\pi\)
0.299047 + 0.954238i \(0.403331\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.28906 0.826012 0.413006 0.910728i \(-0.364479\pi\)
0.413006 + 0.910728i \(0.364479\pi\)
\(42\) 0 0
\(43\) −1.08298 −0.165152 −0.0825762 0.996585i \(-0.526315\pi\)
−0.0825762 + 0.996585i \(0.526315\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.555087 −0.0809677 −0.0404839 0.999180i \(-0.512890\pi\)
−0.0404839 + 0.999180i \(0.512890\pi\)
\(48\) 0 0
\(49\) −3.96362 −0.566231
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.65955 −0.365317 −0.182658 0.983176i \(-0.558470\pi\)
−0.182658 + 0.983176i \(0.558470\pi\)
\(54\) 0 0
\(55\) 26.1033 3.51977
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.85061 −0.240929 −0.120465 0.992718i \(-0.538438\pi\)
−0.120465 + 0.992718i \(0.538438\pi\)
\(60\) 0 0
\(61\) −9.32919 −1.19448 −0.597240 0.802063i \(-0.703736\pi\)
−0.597240 + 0.802063i \(0.703736\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 20.2964 2.51746
\(66\) 0 0
\(67\) −4.72751 −0.577557 −0.288778 0.957396i \(-0.593249\pi\)
−0.288778 + 0.957396i \(0.593249\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −11.4850 −1.36302 −0.681512 0.731807i \(-0.738677\pi\)
−0.681512 + 0.731807i \(0.738677\pi\)
\(72\) 0 0
\(73\) −0.00646614 −0.000756804 0 −0.000378402 1.00000i \(-0.500120\pi\)
−0.000378402 1.00000i \(0.500120\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10.8142 −1.23240
\(78\) 0 0
\(79\) −6.76117 −0.760691 −0.380345 0.924844i \(-0.624195\pi\)
−0.380345 + 0.924844i \(0.624195\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −11.8972 −1.30589 −0.652944 0.757406i \(-0.726466\pi\)
−0.652944 + 0.757406i \(0.726466\pi\)
\(84\) 0 0
\(85\) 21.5754 2.34018
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.31909 0.775822 0.387911 0.921697i \(-0.373197\pi\)
0.387911 + 0.921697i \(0.373197\pi\)
\(90\) 0 0
\(91\) −8.40853 −0.881454
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.20608 −0.431535
\(96\) 0 0
\(97\) −10.4122 −1.05720 −0.528598 0.848873i \(-0.677282\pi\)
−0.528598 + 0.848873i \(0.677282\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.246211 −0.0244989 −0.0122495 0.999925i \(-0.503899\pi\)
−0.0122495 + 0.999925i \(0.503899\pi\)
\(102\) 0 0
\(103\) −0.710942 −0.0700512 −0.0350256 0.999386i \(-0.511151\pi\)
−0.0350256 + 0.999386i \(0.511151\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.6976 −1.13085 −0.565424 0.824800i \(-0.691288\pi\)
−0.565424 + 0.824800i \(0.691288\pi\)
\(108\) 0 0
\(109\) −2.99145 −0.286529 −0.143264 0.989684i \(-0.545760\pi\)
−0.143264 + 0.989684i \(0.545760\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.41216 −0.603206 −0.301603 0.953434i \(-0.597522\pi\)
−0.301603 + 0.953434i \(0.597522\pi\)
\(114\) 0 0
\(115\) 1.94977 0.181817
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −8.93839 −0.819381
\(120\) 0 0
\(121\) 27.5155 2.50140
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 32.3495 2.89343
\(126\) 0 0
\(127\) 18.1434 1.60997 0.804984 0.593297i \(-0.202174\pi\)
0.804984 + 0.593297i \(0.202174\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12.4652 1.08909 0.544546 0.838731i \(-0.316702\pi\)
0.544546 + 0.838731i \(0.316702\pi\)
\(132\) 0 0
\(133\) 1.74252 0.151096
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.41863 −0.719252 −0.359626 0.933097i \(-0.617096\pi\)
−0.359626 + 0.933097i \(0.617096\pi\)
\(138\) 0 0
\(139\) −11.3292 −0.960929 −0.480465 0.877014i \(-0.659532\pi\)
−0.480465 + 0.877014i \(0.659532\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 29.9474 2.50433
\(144\) 0 0
\(145\) −20.2964 −1.68553
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.321808 0.0263635 0.0131818 0.999913i \(-0.495804\pi\)
0.0131818 + 0.999913i \(0.495804\pi\)
\(150\) 0 0
\(151\) 2.95715 0.240650 0.120325 0.992735i \(-0.461606\pi\)
0.120325 + 0.992735i \(0.461606\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.88983 0.553404
\(156\) 0 0
\(157\) 6.52789 0.520982 0.260491 0.965476i \(-0.416116\pi\)
0.260491 + 0.965476i \(0.416116\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.807764 −0.0636607
\(162\) 0 0
\(163\) −2.05023 −0.160586 −0.0802931 0.996771i \(-0.525586\pi\)
−0.0802931 + 0.996771i \(0.525586\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.2462 −0.792876 −0.396438 0.918062i \(-0.629754\pi\)
−0.396438 + 0.918062i \(0.629754\pi\)
\(168\) 0 0
\(169\) 10.2854 0.791187
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.05023 −0.612047 −0.306024 0.952024i \(-0.598999\pi\)
−0.306024 + 0.952024i \(0.598999\pi\)
\(174\) 0 0
\(175\) −22.1146 −1.67170
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.75379 0.131084 0.0655422 0.997850i \(-0.479122\pi\)
0.0655422 + 0.997850i \(0.479122\pi\)
\(180\) 0 0
\(181\) −11.0203 −0.819133 −0.409567 0.912280i \(-0.634320\pi\)
−0.409567 + 0.912280i \(0.634320\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 15.3020 1.12502
\(186\) 0 0
\(187\) 31.8345 2.32797
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.2276 −0.957113 −0.478556 0.878057i \(-0.658840\pi\)
−0.478556 + 0.878057i \(0.658840\pi\)
\(192\) 0 0
\(193\) 1.47211 0.105965 0.0529824 0.998595i \(-0.483127\pi\)
0.0529824 + 0.998595i \(0.483127\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.84698 −0.559074 −0.279537 0.960135i \(-0.590181\pi\)
−0.279537 + 0.960135i \(0.590181\pi\)
\(198\) 0 0
\(199\) 11.8057 0.836882 0.418441 0.908244i \(-0.362577\pi\)
0.418441 + 0.908244i \(0.362577\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.40853 0.590163
\(204\) 0 0
\(205\) 22.2462 1.55374
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −6.20608 −0.429284
\(210\) 0 0
\(211\) 14.5745 1.00335 0.501674 0.865056i \(-0.332718\pi\)
0.501674 + 0.865056i \(0.332718\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.55509 −0.310654
\(216\) 0 0
\(217\) −2.85436 −0.193767
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 24.7527 1.66505
\(222\) 0 0
\(223\) −26.6713 −1.78604 −0.893021 0.450014i \(-0.851419\pi\)
−0.893021 + 0.450014i \(0.851419\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.01656 −0.266589 −0.133294 0.991076i \(-0.542556\pi\)
−0.133294 + 0.991076i \(0.542556\pi\)
\(228\) 0 0
\(229\) 23.1834 1.53200 0.766002 0.642838i \(-0.222243\pi\)
0.766002 + 0.642838i \(0.222243\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −22.2692 −1.45891 −0.729453 0.684031i \(-0.760225\pi\)
−0.729453 + 0.684031i \(0.760225\pi\)
\(234\) 0 0
\(235\) −2.33474 −0.152302
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −23.0818 −1.49304 −0.746519 0.665364i \(-0.768276\pi\)
−0.746519 + 0.665364i \(0.768276\pi\)
\(240\) 0 0
\(241\) −0.565184 −0.0364067 −0.0182033 0.999834i \(-0.505795\pi\)
−0.0182033 + 0.999834i \(0.505795\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −16.6713 −1.06509
\(246\) 0 0
\(247\) −4.82550 −0.307039
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.8441 1.00007 0.500037 0.866004i \(-0.333320\pi\)
0.500037 + 0.866004i \(0.333320\pi\)
\(252\) 0 0
\(253\) 2.87689 0.180869
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.0632 −0.752479 −0.376240 0.926522i \(-0.622783\pi\)
−0.376240 + 0.926522i \(0.622783\pi\)
\(258\) 0 0
\(259\) −6.33940 −0.393911
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 23.2135 1.43140 0.715702 0.698406i \(-0.246107\pi\)
0.715702 + 0.698406i \(0.246107\pi\)
\(264\) 0 0
\(265\) −11.1863 −0.687167
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −26.2964 −1.60332 −0.801661 0.597779i \(-0.796050\pi\)
−0.801661 + 0.597779i \(0.796050\pi\)
\(270\) 0 0
\(271\) −12.9560 −0.787020 −0.393510 0.919320i \(-0.628739\pi\)
−0.393510 + 0.919320i \(0.628739\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 78.7622 4.74954
\(276\) 0 0
\(277\) −10.8645 −0.652782 −0.326391 0.945235i \(-0.605833\pi\)
−0.326391 + 0.945235i \(0.605833\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 15.8470 0.945352 0.472676 0.881236i \(-0.343288\pi\)
0.472676 + 0.881236i \(0.343288\pi\)
\(282\) 0 0
\(283\) 27.6740 1.64505 0.822525 0.568729i \(-0.192565\pi\)
0.822525 + 0.568729i \(0.192565\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.21630 −0.544021
\(288\) 0 0
\(289\) 9.31251 0.547795
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.3179 1.24541 0.622703 0.782458i \(-0.286034\pi\)
0.622703 + 0.782458i \(0.286034\pi\)
\(294\) 0 0
\(295\) −7.78382 −0.453192
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.23691 0.129364
\(300\) 0 0
\(301\) 1.88711 0.108771
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −39.2393 −2.24684
\(306\) 0 0
\(307\) 26.6584 1.52147 0.760737 0.649060i \(-0.224838\pi\)
0.760737 + 0.649060i \(0.224838\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 20.0690 1.13801 0.569004 0.822335i \(-0.307329\pi\)
0.569004 + 0.822335i \(0.307329\pi\)
\(312\) 0 0
\(313\) −11.1397 −0.629651 −0.314826 0.949150i \(-0.601946\pi\)
−0.314826 + 0.949150i \(0.601946\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −33.1349 −1.86104 −0.930520 0.366242i \(-0.880644\pi\)
−0.930520 + 0.366242i \(0.880644\pi\)
\(318\) 0 0
\(319\) −29.9474 −1.67673
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.12957 −0.285417
\(324\) 0 0
\(325\) 61.2410 3.39704
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.967250 0.0533262
\(330\) 0 0
\(331\) −4.30241 −0.236482 −0.118241 0.992985i \(-0.537726\pi\)
−0.118241 + 0.992985i \(0.537726\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −19.8843 −1.08639
\(336\) 0 0
\(337\) 31.3393 1.70716 0.853580 0.520962i \(-0.174427\pi\)
0.853580 + 0.520962i \(0.174427\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10.1660 0.550517
\(342\) 0 0
\(343\) 19.1043 1.03154
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −21.6782 −1.16375 −0.581873 0.813280i \(-0.697680\pi\)
−0.581873 + 0.813280i \(0.697680\pi\)
\(348\) 0 0
\(349\) 4.50486 0.241140 0.120570 0.992705i \(-0.461528\pi\)
0.120570 + 0.992705i \(0.461528\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 22.4158 1.19307 0.596536 0.802586i \(-0.296543\pi\)
0.596536 + 0.802586i \(0.296543\pi\)
\(354\) 0 0
\(355\) −48.3070 −2.56387
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.4940 0.606629 0.303314 0.952891i \(-0.401907\pi\)
0.303314 + 0.952891i \(0.401907\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.0271971 −0.00142356
\(366\) 0 0
\(367\) 19.7944 1.03326 0.516630 0.856209i \(-0.327186\pi\)
0.516630 + 0.856209i \(0.327186\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.63431 0.240602
\(372\) 0 0
\(373\) −16.6199 −0.860546 −0.430273 0.902699i \(-0.641583\pi\)
−0.430273 + 0.902699i \(0.641583\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −23.2854 −1.19926
\(378\) 0 0
\(379\) −16.3956 −0.842185 −0.421093 0.907018i \(-0.638353\pi\)
−0.421093 + 0.907018i \(0.638353\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −30.6915 −1.56826 −0.784131 0.620595i \(-0.786891\pi\)
−0.784131 + 0.620595i \(0.786891\pi\)
\(384\) 0 0
\(385\) −45.4855 −2.31816
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.24905 0.114031 0.0570156 0.998373i \(-0.481842\pi\)
0.0570156 + 0.998373i \(0.481842\pi\)
\(390\) 0 0
\(391\) 2.37787 0.120254
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −28.4380 −1.43087
\(396\) 0 0
\(397\) −4.12582 −0.207069 −0.103535 0.994626i \(-0.533015\pi\)
−0.103535 + 0.994626i \(0.533015\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.3992 1.11856 0.559282 0.828977i \(-0.311077\pi\)
0.559282 + 0.828977i \(0.311077\pi\)
\(402\) 0 0
\(403\) 7.90447 0.393750
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 22.5781 1.11916
\(408\) 0 0
\(409\) 13.1992 0.652658 0.326329 0.945256i \(-0.394188\pi\)
0.326329 + 0.945256i \(0.394188\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.22473 0.158679
\(414\) 0 0
\(415\) −50.0406 −2.45640
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −31.5984 −1.54368 −0.771842 0.635814i \(-0.780664\pi\)
−0.771842 + 0.635814i \(0.780664\pi\)
\(420\) 0 0
\(421\) −25.8587 −1.26028 −0.630139 0.776482i \(-0.717002\pi\)
−0.630139 + 0.776482i \(0.717002\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 65.1000 3.15782
\(426\) 0 0
\(427\) 16.2563 0.786698
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −31.8972 −1.53643 −0.768217 0.640189i \(-0.778856\pi\)
−0.768217 + 0.640189i \(0.778856\pi\)
\(432\) 0 0
\(433\) 23.1006 1.11014 0.555071 0.831803i \(-0.312691\pi\)
0.555071 + 0.831803i \(0.312691\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.463560 −0.0221751
\(438\) 0 0
\(439\) −15.7944 −0.753826 −0.376913 0.926249i \(-0.623014\pi\)
−0.376913 + 0.926249i \(0.623014\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 40.5584 1.92699 0.963494 0.267729i \(-0.0862732\pi\)
0.963494 + 0.267729i \(0.0862732\pi\)
\(444\) 0 0
\(445\) 30.7847 1.45933
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 30.4026 1.43479 0.717393 0.696669i \(-0.245335\pi\)
0.717393 + 0.696669i \(0.245335\pi\)
\(450\) 0 0
\(451\) 32.8243 1.54564
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −35.3670 −1.65803
\(456\) 0 0
\(457\) 1.33516 0.0624561 0.0312280 0.999512i \(-0.490058\pi\)
0.0312280 + 0.999512i \(0.490058\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 23.0604 1.07403 0.537016 0.843572i \(-0.319552\pi\)
0.537016 + 0.843572i \(0.319552\pi\)
\(462\) 0 0
\(463\) −9.29916 −0.432168 −0.216084 0.976375i \(-0.569329\pi\)
−0.216084 + 0.976375i \(0.569329\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.8344 −0.871553 −0.435777 0.900055i \(-0.643526\pi\)
−0.435777 + 0.900055i \(0.643526\pi\)
\(468\) 0 0
\(469\) 8.23778 0.380385
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.72104 −0.309034
\(474\) 0 0
\(475\) −12.6911 −0.582309
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10.9701 0.501236 0.250618 0.968086i \(-0.419366\pi\)
0.250618 + 0.968086i \(0.419366\pi\)
\(480\) 0 0
\(481\) 17.5555 0.800460
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −43.7944 −1.98860
\(486\) 0 0
\(487\) −19.3895 −0.878623 −0.439311 0.898335i \(-0.644777\pi\)
−0.439311 + 0.898335i \(0.644777\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 33.1562 1.49632 0.748160 0.663518i \(-0.230938\pi\)
0.748160 + 0.663518i \(0.230938\pi\)
\(492\) 0 0
\(493\) −24.7527 −1.11481
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.0129 0.897703
\(498\) 0 0
\(499\) 25.8814 1.15861 0.579306 0.815110i \(-0.303324\pi\)
0.579306 + 0.815110i \(0.303324\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10.3178 0.460048 0.230024 0.973185i \(-0.426120\pi\)
0.230024 + 0.973185i \(0.426120\pi\)
\(504\) 0 0
\(505\) −1.03558 −0.0460829
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.21618 0.275527 0.137764 0.990465i \(-0.456009\pi\)
0.137764 + 0.990465i \(0.456009\pi\)
\(510\) 0 0
\(511\) 0.0112674 0.000498440 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.99028 −0.131767
\(516\) 0 0
\(517\) −3.44491 −0.151507
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −22.8917 −1.00290 −0.501451 0.865186i \(-0.667200\pi\)
−0.501451 + 0.865186i \(0.667200\pi\)
\(522\) 0 0
\(523\) −9.02628 −0.394692 −0.197346 0.980334i \(-0.563232\pi\)
−0.197346 + 0.980334i \(0.563232\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.40256 0.366021
\(528\) 0 0
\(529\) −22.7851 −0.990657
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 25.5223 1.10550
\(534\) 0 0
\(535\) −49.2010 −2.12715
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −24.5985 −1.05953
\(540\) 0 0
\(541\) −21.2937 −0.915489 −0.457744 0.889084i \(-0.651342\pi\)
−0.457744 + 0.889084i \(0.651342\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.5823 −0.538966
\(546\) 0 0
\(547\) −3.60803 −0.154268 −0.0771341 0.997021i \(-0.524577\pi\)
−0.0771341 + 0.997021i \(0.524577\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.82550 0.205573
\(552\) 0 0
\(553\) 11.7815 0.501000
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 34.8645 1.47725 0.738627 0.674114i \(-0.235474\pi\)
0.738627 + 0.674114i \(0.235474\pi\)
\(558\) 0 0
\(559\) −5.22590 −0.221032
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 41.3167 1.74129 0.870647 0.491909i \(-0.163701\pi\)
0.870647 + 0.491909i \(0.163701\pi\)
\(564\) 0 0
\(565\) −26.9701 −1.13464
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −41.0835 −1.72231 −0.861154 0.508344i \(-0.830258\pi\)
−0.861154 + 0.508344i \(0.830258\pi\)
\(570\) 0 0
\(571\) 36.8243 1.54105 0.770525 0.637410i \(-0.219994\pi\)
0.770525 + 0.637410i \(0.219994\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.88310 0.245342
\(576\) 0 0
\(577\) 15.7004 0.653617 0.326809 0.945091i \(-0.394027\pi\)
0.326809 + 0.945091i \(0.394027\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 20.7311 0.860072
\(582\) 0 0
\(583\) −16.5054 −0.683582
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 34.3099 1.41612 0.708060 0.706152i \(-0.249571\pi\)
0.708060 + 0.706152i \(0.249571\pi\)
\(588\) 0 0
\(589\) −1.63806 −0.0674952
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −7.11584 −0.292213 −0.146106 0.989269i \(-0.546674\pi\)
−0.146106 + 0.989269i \(0.546674\pi\)
\(594\) 0 0
\(595\) −37.5956 −1.54127
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13.8340 −0.565244 −0.282622 0.959231i \(-0.591204\pi\)
−0.282622 + 0.959231i \(0.591204\pi\)
\(600\) 0 0
\(601\) 39.2140 1.59957 0.799785 0.600286i \(-0.204947\pi\)
0.799785 + 0.600286i \(0.204947\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 115.732 4.70518
\(606\) 0 0
\(607\) −35.1733 −1.42764 −0.713821 0.700328i \(-0.753037\pi\)
−0.713821 + 0.700328i \(0.753037\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.67857 −0.108363
\(612\) 0 0
\(613\) 6.24905 0.252397 0.126198 0.992005i \(-0.459722\pi\)
0.126198 + 0.992005i \(0.459722\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 42.0378 1.69238 0.846189 0.532883i \(-0.178891\pi\)
0.846189 + 0.532883i \(0.178891\pi\)
\(618\) 0 0
\(619\) −31.0633 −1.24854 −0.624269 0.781209i \(-0.714603\pi\)
−0.624269 + 0.781209i \(0.714603\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.7537 −0.510965
\(624\) 0 0
\(625\) 72.6090 2.90436
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 18.6617 0.744091
\(630\) 0 0
\(631\) 40.0378 1.59388 0.796940 0.604059i \(-0.206451\pi\)
0.796940 + 0.604059i \(0.206451\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 76.3127 3.02838
\(636\) 0 0
\(637\) −19.1264 −0.757817
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.3619 0.804248 0.402124 0.915585i \(-0.368272\pi\)
0.402124 + 0.915585i \(0.368272\pi\)
\(642\) 0 0
\(643\) −13.7041 −0.540435 −0.270218 0.962799i \(-0.587096\pi\)
−0.270218 + 0.962799i \(0.587096\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.9588 1.05986 0.529930 0.848041i \(-0.322218\pi\)
0.529930 + 0.848041i \(0.322218\pi\)
\(648\) 0 0
\(649\) −11.4850 −0.450827
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −30.7842 −1.20468 −0.602339 0.798240i \(-0.705765\pi\)
−0.602339 + 0.798240i \(0.705765\pi\)
\(654\) 0 0
\(655\) 52.4298 2.04860
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.57854 0.295218 0.147609 0.989046i \(-0.452842\pi\)
0.147609 + 0.989046i \(0.452842\pi\)
\(660\) 0 0
\(661\) 47.8191 1.85995 0.929974 0.367626i \(-0.119829\pi\)
0.929974 + 0.367626i \(0.119829\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.32919 0.284214
\(666\) 0 0
\(667\) −2.23691 −0.0866135
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −57.8977 −2.23512
\(672\) 0 0
\(673\) 12.2389 0.471777 0.235888 0.971780i \(-0.424200\pi\)
0.235888 + 0.971780i \(0.424200\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23.3609 −0.897832 −0.448916 0.893574i \(-0.648190\pi\)
−0.448916 + 0.893574i \(0.648190\pi\)
\(678\) 0 0
\(679\) 18.1434 0.696280
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.7239 0.946033 0.473016 0.881054i \(-0.343165\pi\)
0.473016 + 0.881054i \(0.343165\pi\)
\(684\) 0 0
\(685\) −35.4094 −1.35293
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −12.8336 −0.488922
\(690\) 0 0
\(691\) −6.78837 −0.258242 −0.129121 0.991629i \(-0.541215\pi\)
−0.129121 + 0.991629i \(0.541215\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −47.6515 −1.80752
\(696\) 0 0
\(697\) 27.1306 1.02764
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −26.9175 −1.01666 −0.508330 0.861162i \(-0.669737\pi\)
−0.508330 + 0.861162i \(0.669737\pi\)
\(702\) 0 0
\(703\) −3.63806 −0.137212
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.429028 0.0161353
\(708\) 0 0
\(709\) −21.5984 −0.811146 −0.405573 0.914063i \(-0.632928\pi\)
−0.405573 + 0.914063i \(0.632928\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.759341 0.0284376
\(714\) 0 0
\(715\) 125.961 4.71069
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22.2575 −0.830064 −0.415032 0.909807i \(-0.636230\pi\)
−0.415032 + 0.909807i \(0.636230\pi\)
\(720\) 0 0
\(721\) 1.23883 0.0461365
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −61.2410 −2.27443
\(726\) 0 0
\(727\) 51.9118 1.92530 0.962651 0.270745i \(-0.0872700\pi\)
0.962651 + 0.270745i \(0.0872700\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5.55520 −0.205467
\(732\) 0 0
\(733\) 20.0575 0.740840 0.370420 0.928864i \(-0.379214\pi\)
0.370420 + 0.928864i \(0.379214\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −29.3393 −1.08073
\(738\) 0 0
\(739\) −7.36465 −0.270913 −0.135457 0.990783i \(-0.543250\pi\)
−0.135457 + 0.990783i \(0.543250\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.85436 −0.104716 −0.0523581 0.998628i \(-0.516674\pi\)
−0.0523581 + 0.998628i \(0.516674\pi\)
\(744\) 0 0
\(745\) 1.35355 0.0495902
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 20.3833 0.744790
\(750\) 0 0
\(751\) 22.3725 0.816385 0.408193 0.912896i \(-0.366159\pi\)
0.408193 + 0.912896i \(0.366159\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12.4380 0.452666
\(756\) 0 0
\(757\) 6.07326 0.220736 0.110368 0.993891i \(-0.464797\pi\)
0.110368 + 0.993891i \(0.464797\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13.1166 −0.475478 −0.237739 0.971329i \(-0.576406\pi\)
−0.237739 + 0.971329i \(0.576406\pi\)
\(762\) 0 0
\(763\) 5.21267 0.188711
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.93012 −0.322448
\(768\) 0 0
\(769\) −44.5791 −1.60757 −0.803783 0.594923i \(-0.797182\pi\)
−0.803783 + 0.594923i \(0.797182\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.43920 0.159667 0.0798334 0.996808i \(-0.474561\pi\)
0.0798334 + 0.996808i \(0.474561\pi\)
\(774\) 0 0
\(775\) 20.7889 0.746758
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.28906 −0.189500
\(780\) 0 0
\(781\) −71.2771 −2.55050
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 27.4568 0.979977
\(786\) 0 0
\(787\) −0.315342 −0.0112407 −0.00562036 0.999984i \(-0.501789\pi\)
−0.00562036 + 0.999984i \(0.501789\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 11.1733 0.397278
\(792\) 0 0
\(793\) −45.0180 −1.59864
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.16712 −0.218451 −0.109225 0.994017i \(-0.534837\pi\)
−0.109225 + 0.994017i \(0.534837\pi\)
\(798\) 0 0
\(799\) −2.84736 −0.100732
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −0.0401294 −0.00141614
\(804\) 0 0
\(805\) −3.39752 −0.119747
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −20.4057 −0.717426 −0.358713 0.933448i \(-0.616784\pi\)
−0.358713 + 0.933448i \(0.616784\pi\)
\(810\) 0 0
\(811\) 36.5763 1.28437 0.642184 0.766551i \(-0.278029\pi\)
0.642184 + 0.766551i \(0.278029\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.62342 −0.302065
\(816\) 0 0
\(817\) 1.08298 0.0378885
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −19.6686 −0.686439 −0.343219 0.939255i \(-0.611517\pi\)
−0.343219 + 0.939255i \(0.611517\pi\)
\(822\) 0 0
\(823\) 36.7328 1.28042 0.640212 0.768198i \(-0.278846\pi\)
0.640212 + 0.768198i \(0.278846\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 27.4920 0.955991 0.477995 0.878362i \(-0.341364\pi\)
0.477995 + 0.878362i \(0.341364\pi\)
\(828\) 0 0
\(829\) −12.1016 −0.420307 −0.210153 0.977668i \(-0.567396\pi\)
−0.210153 + 0.977668i \(0.567396\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −20.3317 −0.704451
\(834\) 0 0
\(835\) −43.0964 −1.49141
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −51.4731 −1.77705 −0.888524 0.458829i \(-0.848269\pi\)
−0.888524 + 0.458829i \(0.848269\pi\)
\(840\) 0 0
\(841\) −5.71457 −0.197054
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 43.2613 1.48824
\(846\) 0 0
\(847\) −47.9463 −1.64745
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.68646 0.0578112
\(852\) 0 0
\(853\) −42.6187 −1.45924 −0.729619 0.683854i \(-0.760303\pi\)
−0.729619 + 0.683854i \(0.760303\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.45501 −0.118021 −0.0590105 0.998257i \(-0.518795\pi\)
−0.0590105 + 0.998257i \(0.518795\pi\)
\(858\) 0 0
\(859\) −17.1161 −0.583994 −0.291997 0.956419i \(-0.594320\pi\)
−0.291997 + 0.956419i \(0.594320\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −13.0130 −0.442969 −0.221485 0.975164i \(-0.571090\pi\)
−0.221485 + 0.975164i \(0.571090\pi\)
\(864\) 0 0
\(865\) −33.8599 −1.15127
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −41.9604 −1.42341
\(870\) 0 0
\(871\) −22.8126 −0.772974
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −56.3697 −1.90564
\(876\) 0 0
\(877\) 0.908097 0.0306642 0.0153321 0.999882i \(-0.495119\pi\)
0.0153321 + 0.999882i \(0.495119\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −29.1332 −0.981523 −0.490761 0.871294i \(-0.663281\pi\)
−0.490761 + 0.871294i \(0.663281\pi\)
\(882\) 0 0
\(883\) 31.4780 1.05932 0.529660 0.848210i \(-0.322319\pi\)
0.529660 + 0.848210i \(0.322319\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 37.0933 1.24547 0.622736 0.782432i \(-0.286021\pi\)
0.622736 + 0.782432i \(0.286021\pi\)
\(888\) 0 0
\(889\) −31.6153 −1.06034
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0.555087 0.0185753
\(894\) 0 0
\(895\) 7.37658 0.246572
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7.90447 −0.263629
\(900\) 0 0
\(901\) −13.6423 −0.454492
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −46.3523 −1.54080
\(906\) 0 0
\(907\) 24.0295 0.797886 0.398943 0.916976i \(-0.369377\pi\)
0.398943 + 0.916976i \(0.369377\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −45.7644 −1.51624 −0.758121 0.652114i \(-0.773882\pi\)
−0.758121 + 0.652114i \(0.773882\pi\)
\(912\) 0 0
\(913\) −73.8350 −2.44358
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −21.7209 −0.717288
\(918\) 0 0
\(919\) 2.91536 0.0961688 0.0480844 0.998843i \(-0.484688\pi\)
0.0480844 + 0.998843i \(0.484688\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −55.4210 −1.82421
\(924\) 0 0
\(925\) 46.1711 1.51810
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 14.4417 0.473815 0.236908 0.971532i \(-0.423866\pi\)
0.236908 + 0.971532i \(0.423866\pi\)
\(930\) 0 0
\(931\) 3.96362 0.129902
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 133.899 4.37896
\(936\) 0 0
\(937\) 39.3960 1.28701 0.643505 0.765442i \(-0.277479\pi\)
0.643505 + 0.765442i \(0.277479\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −37.5954 −1.22558 −0.612788 0.790247i \(-0.709952\pi\)
−0.612788 + 0.790247i \(0.709952\pi\)
\(942\) 0 0
\(943\) 2.45180 0.0798415
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −21.3522 −0.693854 −0.346927 0.937892i \(-0.612775\pi\)
−0.346927 + 0.937892i \(0.612775\pi\)
\(948\) 0 0
\(949\) −0.0312023 −0.00101287
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −37.5726 −1.21709 −0.608547 0.793518i \(-0.708247\pi\)
−0.608547 + 0.793518i \(0.708247\pi\)
\(954\) 0 0
\(955\) −55.6362 −1.80035
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 14.6696 0.473707
\(960\) 0 0
\(961\) −28.3167 −0.913444
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 6.19182 0.199322
\(966\) 0 0
\(967\) −11.5676 −0.371990 −0.185995 0.982551i \(-0.559551\pi\)
−0.185995 + 0.982551i \(0.559551\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −60.2009 −1.93194 −0.965970 0.258656i \(-0.916720\pi\)
−0.965970 + 0.258656i \(0.916720\pi\)
\(972\) 0 0
\(973\) 19.7414 0.632879
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −41.2738 −1.32047 −0.660233 0.751061i \(-0.729542\pi\)
−0.660233 + 0.751061i \(0.729542\pi\)
\(978\) 0 0
\(979\) 45.4229 1.45172
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 16.5610 0.528214 0.264107 0.964493i \(-0.414923\pi\)
0.264107 + 0.964493i \(0.414923\pi\)
\(984\) 0 0
\(985\) −33.0050 −1.05163
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.502025 −0.0159635
\(990\) 0 0
\(991\) −35.6243 −1.13164 −0.565821 0.824528i \(-0.691441\pi\)
−0.565821 + 0.824528i \(0.691441\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 49.6557 1.57419
\(996\) 0 0
\(997\) 41.0563 1.30027 0.650133 0.759821i \(-0.274713\pi\)
0.650133 + 0.759821i \(0.274713\pi\)
\(998\) 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 5472.2.a.bt.1.4 4
3.2 odd 2 608.2.a.i.1.1 4
4.3 odd 2 5472.2.a.bs.1.4 4
12.11 even 2 608.2.a.j.1.3 yes 4
24.5 odd 2 1216.2.a.x.1.4 4
24.11 even 2 1216.2.a.w.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
608.2.a.i.1.1 4 3.2 odd 2
608.2.a.j.1.3 yes 4 12.11 even 2
1216.2.a.w.1.2 4 24.11 even 2
1216.2.a.x.1.4 4 24.5 odd 2
5472.2.a.bs.1.4 4 4.3 odd 2
5472.2.a.bt.1.4 4 1.1 even 1 trivial