Properties

Label 640.2.f.f.449.1
Level $640$
Weight $2$
Character 640.449
Analytic conductor $5.110$
Analytic rank $0$
Dimension $4$
CM discriminant -20
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.11042572936\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-5})\)
Defining polynomial: \(x^{4} - 4 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 449.1
Root \(1.58114 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 640.449
Dual form 640.2.f.f.449.2

$q$-expansion

\(f(q)\) \(=\) \(q-3.16228 q^{3} -2.23607i q^{5} -4.24264i q^{7} +7.00000 q^{9} +O(q^{10})\) \(q-3.16228 q^{3} -2.23607i q^{5} -4.24264i q^{7} +7.00000 q^{9} +7.07107i q^{15} +13.4164i q^{21} -1.41421i q^{23} -5.00000 q^{25} -12.6491 q^{27} -8.94427i q^{29} -9.48683 q^{35} -12.0000 q^{41} -3.16228 q^{43} -15.6525i q^{45} +9.89949i q^{47} -11.0000 q^{49} +13.4164i q^{61} -29.6985i q^{63} +15.8114 q^{67} +4.47214i q^{69} +15.8114 q^{75} +19.0000 q^{81} -9.48683 q^{83} +28.2843i q^{87} -6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 28 q^{9} + O(q^{10}) \) \( 4 q + 28 q^{9} - 20 q^{25} - 48 q^{41} - 44 q^{49} + 76 q^{81} - 24 q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) −3.16228 −1.82574 −0.912871 0.408248i \(-0.866140\pi\)
−0.912871 + 0.408248i \(0.866140\pi\)
\(4\) 0 0
\(5\) − 2.23607i − 1.00000i
\(6\) 0 0
\(7\) − 4.24264i − 1.60357i −0.597614 0.801784i \(-0.703885\pi\)
0.597614 0.801784i \(-0.296115\pi\)
\(8\) 0 0
\(9\) 7.00000 2.33333
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 7.07107i 1.82574i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 13.4164i 2.92770i
\(22\) 0 0
\(23\) − 1.41421i − 0.294884i −0.989071 0.147442i \(-0.952896\pi\)
0.989071 0.147442i \(-0.0471040\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −12.6491 −2.43432
\(28\) 0 0
\(29\) − 8.94427i − 1.66091i −0.557086 0.830455i \(-0.688081\pi\)
0.557086 0.830455i \(-0.311919\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.48683 −1.60357
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 0 0
\(43\) −3.16228 −0.482243 −0.241121 0.970495i \(-0.577515\pi\)
−0.241121 + 0.970495i \(0.577515\pi\)
\(44\) 0 0
\(45\) − 15.6525i − 2.33333i
\(46\) 0 0
\(47\) 9.89949i 1.44399i 0.691898 + 0.721995i \(0.256775\pi\)
−0.691898 + 0.721995i \(0.743225\pi\)
\(48\) 0 0
\(49\) −11.0000 −1.57143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 13.4164i 1.71780i 0.512148 + 0.858898i \(0.328850\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) − 29.6985i − 3.74166i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 15.8114 1.93167 0.965834 0.259161i \(-0.0834459\pi\)
0.965834 + 0.259161i \(0.0834459\pi\)
\(68\) 0 0
\(69\) 4.47214i 0.538382i
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 15.8114 1.82574
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 19.0000 2.11111
\(82\) 0 0
\(83\) −9.48683 −1.04132 −0.520658 0.853766i \(-0.674313\pi\)
−0.520658 + 0.853766i \(0.674313\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 28.2843i 3.03239i
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.94427i 0.889988i 0.895533 + 0.444994i \(0.146794\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) − 12.7279i − 1.25412i −0.778971 0.627060i \(-0.784258\pi\)
0.778971 0.627060i \(-0.215742\pi\)
\(104\) 0 0
\(105\) 30.0000 2.92770
\(106\) 0 0
\(107\) −9.48683 −0.917127 −0.458563 0.888662i \(-0.651636\pi\)
−0.458563 + 0.888662i \(0.651636\pi\)
\(108\) 0 0
\(109\) − 13.4164i − 1.28506i −0.766261 0.642529i \(-0.777885\pi\)
0.766261 0.642529i \(-0.222115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −3.16228 −0.294884
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) 37.9473 3.42160
\(124\) 0 0
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) − 4.24264i − 0.376473i −0.982124 0.188237i \(-0.939723\pi\)
0.982124 0.188237i \(-0.0602772\pi\)
\(128\) 0 0
\(129\) 10.0000 0.880451
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 28.2843i 2.43432i
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) − 31.3050i − 2.63635i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −20.0000 −1.66091
\(146\) 0 0
\(147\) 34.7851 2.86902
\(148\) 0 0
\(149\) 4.47214i 0.366372i 0.983078 + 0.183186i \(0.0586410\pi\)
−0.983078 + 0.183186i \(0.941359\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 22.1359 1.73382 0.866910 0.498464i \(-0.166102\pi\)
0.866910 + 0.498464i \(0.166102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 24.0416i − 1.86040i −0.367057 0.930199i \(-0.619634\pi\)
0.367057 0.930199i \(-0.380366\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 21.2132i 1.60357i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) − 26.8328i − 1.99447i −0.0743294 0.997234i \(-0.523682\pi\)
0.0743294 0.997234i \(-0.476318\pi\)
\(182\) 0 0
\(183\) − 42.4264i − 3.13625i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 53.6656i 3.90360i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −50.0000 −3.52673
\(202\) 0 0
\(203\) −37.9473 −2.66338
\(204\) 0 0
\(205\) 26.8328i 1.87409i
\(206\) 0 0
\(207\) − 9.89949i − 0.688062i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7.07107i 0.482243i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 29.6985i 1.98876i 0.105881 + 0.994379i \(0.466234\pi\)
−0.105881 + 0.994379i \(0.533766\pi\)
\(224\) 0 0
\(225\) −35.0000 −2.33333
\(226\) 0 0
\(227\) −28.4605 −1.88899 −0.944495 0.328526i \(-0.893448\pi\)
−0.944495 + 0.328526i \(0.893448\pi\)
\(228\) 0 0
\(229\) − 26.8328i − 1.77316i −0.462573 0.886581i \(-0.653074\pi\)
0.462573 0.886581i \(-0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 22.1359 1.44399
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 28.0000 1.80364 0.901819 0.432113i \(-0.142232\pi\)
0.901819 + 0.432113i \(0.142232\pi\)
\(242\) 0 0
\(243\) −22.1359 −1.42002
\(244\) 0 0
\(245\) 24.5967i 1.57143i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 30.0000 1.90117
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) − 62.6099i − 3.87546i
\(262\) 0 0
\(263\) − 15.5563i − 0.959246i −0.877475 0.479623i \(-0.840774\pi\)
0.877475 0.479623i \(-0.159226\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 18.9737 1.16117
\(268\) 0 0
\(269\) − 22.3607i − 1.36335i −0.731653 0.681677i \(-0.761251\pi\)
0.731653 0.681677i \(-0.238749\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 0 0
\(283\) 15.8114 0.939889 0.469945 0.882696i \(-0.344274\pi\)
0.469945 + 0.882696i \(0.344274\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 50.9117i 3.00522i
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 13.4164i 0.773309i
\(302\) 0 0
\(303\) − 28.2843i − 1.62489i
\(304\) 0 0
\(305\) 30.0000 1.71780
\(306\) 0 0
\(307\) −34.7851 −1.98529 −0.992644 0.121070i \(-0.961367\pi\)
−0.992644 + 0.121070i \(0.961367\pi\)
\(308\) 0 0
\(309\) 40.2492i 2.28970i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) −66.4078 −3.74166
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 30.0000 1.67444
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 42.4264i 2.34619i
\(328\) 0 0
\(329\) 42.0000 2.31553
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 35.3553i − 1.93167i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) 0 0
\(345\) 10.0000 0.538382
\(346\) 0 0
\(347\) −28.4605 −1.52784 −0.763920 0.645311i \(-0.776728\pi\)
−0.763920 + 0.645311i \(0.776728\pi\)
\(348\) 0 0
\(349\) 26.8328i 1.43633i 0.695874 + 0.718164i \(0.255017\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) −34.7851 −1.82574
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 38.1838i − 1.99318i −0.0825348 0.996588i \(-0.526302\pi\)
0.0825348 0.996588i \(-0.473698\pi\)
\(368\) 0 0
\(369\) −84.0000 −4.37287
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) − 35.3553i − 1.82574i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 13.4164i 0.687343i
\(382\) 0 0
\(383\) − 26.8701i − 1.37300i −0.727132 0.686498i \(-0.759147\pi\)
0.727132 0.686498i \(-0.240853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −22.1359 −1.12523
\(388\) 0 0
\(389\) − 31.3050i − 1.58722i −0.608424 0.793612i \(-0.708198\pi\)
0.608424 0.793612i \(-0.291802\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) − 42.4853i − 2.11111i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 4.00000 0.197787 0.0988936 0.995098i \(-0.468470\pi\)
0.0988936 + 0.995098i \(0.468470\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 21.2132i 1.04132i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 40.2492i 1.96163i 0.194948 + 0.980814i \(0.437546\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 0 0
\(423\) 69.2965i 3.36931i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 56.9210 2.75460
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 63.2456 3.03239
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −77.0000 −3.66667
\(442\) 0 0
\(443\) −9.48683 −0.450733 −0.225367 0.974274i \(-0.572358\pi\)
−0.225367 + 0.974274i \(0.572358\pi\)
\(444\) 0 0
\(445\) 13.4164i 0.635999i
\(446\) 0 0
\(447\) − 14.1421i − 0.668900i
\(448\) 0 0
\(449\) −36.0000 −1.69895 −0.849473 0.527633i \(-0.823080\pi\)
−0.849473 + 0.527633i \(0.823080\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 8.94427i − 0.416576i −0.978068 0.208288i \(-0.933211\pi\)
0.978068 0.208288i \(-0.0667892\pi\)
\(462\) 0 0
\(463\) − 12.7279i − 0.591517i −0.955263 0.295758i \(-0.904428\pi\)
0.955263 0.295758i \(-0.0955723\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −28.4605 −1.31699 −0.658497 0.752583i \(-0.728808\pi\)
−0.658497 + 0.752583i \(0.728808\pi\)
\(468\) 0 0
\(469\) − 67.0820i − 3.09756i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 18.9737 0.863332
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 38.1838i − 1.73027i −0.501538 0.865136i \(-0.667232\pi\)
0.501538 0.865136i \(-0.332768\pi\)
\(488\) 0 0
\(489\) −70.0000 −3.16551
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 76.0263i 3.39661i
\(502\) 0 0
\(503\) 43.8406i 1.95476i 0.211498 + 0.977378i \(0.432166\pi\)
−0.211498 + 0.977378i \(0.567834\pi\)
\(504\) 0 0
\(505\) 20.0000 0.889988
\(506\) 0 0
\(507\) 41.1096 1.82574
\(508\) 0 0
\(509\) − 44.7214i − 1.98224i −0.132973 0.991120i \(-0.542452\pi\)
0.132973 0.991120i \(-0.457548\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −28.4605 −1.25412
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) −34.7851 −1.52104 −0.760522 0.649312i \(-0.775057\pi\)
−0.760522 + 0.649312i \(0.775057\pi\)
\(524\) 0 0
\(525\) − 67.0820i − 2.92770i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 21.0000 0.913043
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 21.2132i 0.917127i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 26.8328i 1.15363i 0.816874 + 0.576816i \(0.195705\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 0 0
\(543\) 84.8528i 3.64138i
\(544\) 0 0
\(545\) −30.0000 −1.28506
\(546\) 0 0
\(547\) −3.16228 −0.135209 −0.0676046 0.997712i \(-0.521536\pi\)
−0.0676046 + 0.997712i \(0.521536\pi\)
\(548\) 0 0
\(549\) 93.9149i 4.00819i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 47.4342 1.99911 0.999556 0.0298010i \(-0.00948736\pi\)
0.999556 + 0.0298010i \(0.00948736\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 80.6102i − 3.38531i
\(568\) 0 0
\(569\) 36.0000 1.50920 0.754599 0.656186i \(-0.227831\pi\)
0.754599 + 0.656186i \(0.227831\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7.07107i 0.294884i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 40.2492i 1.66982i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 47.4342 1.95782 0.978909 0.204298i \(-0.0654911\pi\)
0.978909 + 0.204298i \(0.0654911\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 0 0
\(603\) 110.680 4.50723
\(604\) 0 0
\(605\) − 24.5967i − 1.00000i
\(606\) 0 0
\(607\) − 46.6690i − 1.89424i −0.320882 0.947119i \(-0.603979\pi\)
0.320882 0.947119i \(-0.396021\pi\)
\(608\) 0 0
\(609\) 120.000 4.86265
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) − 84.8528i − 3.42160i
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 17.8885i 0.717843i
\(622\) 0 0
\(623\) 25.4558i 1.01987i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.48683 −0.376473
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12.0000 0.473972 0.236986 0.971513i \(-0.423841\pi\)
0.236986 + 0.971513i \(0.423841\pi\)
\(642\) 0 0
\(643\) 41.1096 1.62120 0.810602 0.585597i \(-0.199140\pi\)
0.810602 + 0.585597i \(0.199140\pi\)
\(644\) 0 0
\(645\) − 22.3607i − 0.880451i
\(646\) 0 0
\(647\) 18.3848i 0.722780i 0.932415 + 0.361390i \(0.117698\pi\)
−0.932415 + 0.361390i \(0.882302\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) − 40.2492i − 1.56551i −0.622328 0.782757i \(-0.713813\pi\)
0.622328 0.782757i \(-0.286187\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −12.6491 −0.489776
\(668\) 0 0
\(669\) − 93.9149i − 3.63096i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 63.2456 2.43432
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 90.0000 3.44881
\(682\) 0 0
\(683\) −28.4605 −1.08901 −0.544505 0.838757i \(-0.683283\pi\)
−0.544505 + 0.838757i \(0.683283\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 84.8528i 3.23734i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.3607i 0.844551i 0.906467 + 0.422276i \(0.138769\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −70.0000 −2.63635
\(706\) 0 0
\(707\) 37.9473 1.42716
\(708\) 0 0
\(709\) − 26.8328i − 1.00773i −0.863783 0.503864i \(-0.831911\pi\)
0.863783 0.503864i \(-0.168089\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −54.0000 −2.01107
\(722\) 0 0
\(723\) −88.5438 −3.29298
\(724\) 0 0
\(725\) 44.7214i 1.66091i
\(726\) 0 0
\(727\) − 4.24264i − 0.157351i −0.996900 0.0786754i \(-0.974931\pi\)
0.996900 0.0786754i \(-0.0250691\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) − 77.7817i − 2.86902i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 26.8701i − 0.985767i −0.870095 0.492883i \(-0.835943\pi\)
0.870095 0.492883i \(-0.164057\pi\)
\(744\) 0 0
\(745\) 10.0000 0.366372
\(746\) 0 0
\(747\) −66.4078 −2.42974
\(748\) 0 0
\(749\) 40.2492i 1.47067i
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) −56.9210 −2.06068
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 113.137i 4.04319i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 41.1096 1.46540 0.732700 0.680552i \(-0.238260\pi\)
0.732700 + 0.680552i \(0.238260\pi\)
\(788\) 0 0
\(789\) 49.1935i 1.75133i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −42.0000 −1.48400
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 13.4164i 0.472866i
\(806\) 0 0
\(807\) 70.7107i 2.48913i
\(808\) 0 0
\(809\) −54.0000 −1.89854 −0.949269 0.314464i \(-0.898175\pi\)
−0.949269 + 0.314464i \(0.898175\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 49.4975i − 1.73382i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31.3050i 1.09255i 0.837606 + 0.546275i \(0.183955\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) 0 0
\(823\) 55.1543i 1.92256i 0.275575 + 0.961280i \(0.411132\pi\)
−0.275575 + 0.961280i \(0.588868\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 47.4342 1.64945 0.824724 0.565536i \(-0.191331\pi\)
0.824724 + 0.565536i \(0.191331\pi\)
\(828\) 0 0
\(829\) 13.4164i 0.465971i 0.972480 + 0.232986i \(0.0748495\pi\)
−0.972480 + 0.232986i \(0.925151\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −53.7587 −1.86040
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −51.0000 −1.75862
\(842\) 0 0
\(843\) 37.9473 1.30698
\(844\) 0 0
\(845\) 29.0689i 1.00000i
\(846\) 0 0
\(847\) − 46.6690i − 1.60357i
\(848\) 0 0
\(849\) −50.0000 −1.71600
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) − 160.997i − 5.48676i
\(862\) 0 0
\(863\) − 57.9828i − 1.97376i −0.161468 0.986878i \(-0.551623\pi\)
0.161468 0.986878i \(-0.448377\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −53.7587 −1.82574
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 47.4342 1.60357
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 12.0000 0.404290 0.202145 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 0 0
\(883\) 22.1359 0.744934 0.372467 0.928045i \(-0.378512\pi\)
0.372467 + 0.928045i \(0.378512\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 52.3259i 1.75693i 0.477805 + 0.878466i \(0.341433\pi\)
−0.477805 + 0.878466i \(0.658567\pi\)
\(888\) 0 0
\(889\) −18.0000 −0.603701
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) − 42.4264i − 1.41186i
\(904\) 0 0
\(905\) −60.0000 −1.99447
\(906\) 0 0
\(907\) −60.0833 −1.99503 −0.997516 0.0704373i \(-0.977561\pi\)
−0.997516 + 0.0704373i \(0.977561\pi\)
\(908\) 0 0
\(909\) 62.6099i 2.07664i
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −94.8683 −3.13625
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 110.000 3.62462
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 89.0955i − 2.92628i
\(928\) 0 0
\(929\) −36.0000 −1.18112 −0.590561 0.806993i \(-0.701093\pi\)
−0.590561 + 0.806993i \(0.701093\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 44.7214i − 1.45787i −0.684580 0.728937i \(-0.740015\pi\)
0.684580 0.728937i \(-0.259985\pi\)
\(942\) 0 0
\(943\) 16.9706i 0.552638i
\(944\) 0 0
\(945\) 120.000 3.90360
\(946\) 0 0
\(947\) −9.48683 −0.308281 −0.154140 0.988049i \(-0.549261\pi\)
−0.154140 + 0.988049i \(0.549261\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) −66.4078 −2.13996
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 46.6690i − 1.50078i −0.660998 0.750388i \(-0.729867\pi\)
0.660998 0.750388i \(-0.270133\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) − 93.9149i − 2.99847i
\(982\) 0 0
\(983\) 41.0122i 1.30809i 0.756457 + 0.654043i \(0.226928\pi\)
−0.756457 + 0.654043i \(0.773072\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −132.816 −4.22757
\(988\) 0 0
\(989\) 4.47214i 0.142206i
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 640.2.f.f.449.1 4
4.3 odd 2 inner 640.2.f.f.449.3 yes 4
5.2 odd 4 3200.2.d.i.1601.4 4
5.3 odd 4 3200.2.d.i.1601.1 4
5.4 even 2 inner 640.2.f.f.449.3 yes 4
8.3 odd 2 inner 640.2.f.f.449.2 yes 4
8.5 even 2 inner 640.2.f.f.449.4 yes 4
16.3 odd 4 1280.2.c.f.769.3 4
16.5 even 4 1280.2.c.f.769.4 4
16.11 odd 4 1280.2.c.f.769.2 4
16.13 even 4 1280.2.c.f.769.1 4
20.3 even 4 3200.2.d.i.1601.4 4
20.7 even 4 3200.2.d.i.1601.1 4
20.19 odd 2 CM 640.2.f.f.449.1 4
40.3 even 4 3200.2.d.i.1601.2 4
40.13 odd 4 3200.2.d.i.1601.3 4
40.19 odd 2 inner 640.2.f.f.449.4 yes 4
40.27 even 4 3200.2.d.i.1601.3 4
40.29 even 2 inner 640.2.f.f.449.2 yes 4
40.37 odd 4 3200.2.d.i.1601.2 4
80.3 even 4 6400.2.a.cv.1.1 4
80.13 odd 4 6400.2.a.cv.1.4 4
80.19 odd 4 1280.2.c.f.769.1 4
80.27 even 4 6400.2.a.cv.1.2 4
80.29 even 4 1280.2.c.f.769.3 4
80.37 odd 4 6400.2.a.cv.1.3 4
80.43 even 4 6400.2.a.cv.1.3 4
80.53 odd 4 6400.2.a.cv.1.2 4
80.59 odd 4 1280.2.c.f.769.4 4
80.67 even 4 6400.2.a.cv.1.4 4
80.69 even 4 1280.2.c.f.769.2 4
80.77 odd 4 6400.2.a.cv.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.f.f.449.1 4 1.1 even 1 trivial
640.2.f.f.449.1 4 20.19 odd 2 CM
640.2.f.f.449.2 yes 4 8.3 odd 2 inner
640.2.f.f.449.2 yes 4 40.29 even 2 inner
640.2.f.f.449.3 yes 4 4.3 odd 2 inner
640.2.f.f.449.3 yes 4 5.4 even 2 inner
640.2.f.f.449.4 yes 4 8.5 even 2 inner
640.2.f.f.449.4 yes 4 40.19 odd 2 inner
1280.2.c.f.769.1 4 16.13 even 4
1280.2.c.f.769.1 4 80.19 odd 4
1280.2.c.f.769.2 4 16.11 odd 4
1280.2.c.f.769.2 4 80.69 even 4
1280.2.c.f.769.3 4 16.3 odd 4
1280.2.c.f.769.3 4 80.29 even 4
1280.2.c.f.769.4 4 16.5 even 4
1280.2.c.f.769.4 4 80.59 odd 4
3200.2.d.i.1601.1 4 5.3 odd 4
3200.2.d.i.1601.1 4 20.7 even 4
3200.2.d.i.1601.2 4 40.3 even 4
3200.2.d.i.1601.2 4 40.37 odd 4
3200.2.d.i.1601.3 4 40.13 odd 4
3200.2.d.i.1601.3 4 40.27 even 4
3200.2.d.i.1601.4 4 5.2 odd 4
3200.2.d.i.1601.4 4 20.3 even 4
6400.2.a.cv.1.1 4 80.3 even 4
6400.2.a.cv.1.1 4 80.77 odd 4
6400.2.a.cv.1.2 4 80.27 even 4
6400.2.a.cv.1.2 4 80.53 odd 4
6400.2.a.cv.1.3 4 80.37 odd 4
6400.2.a.cv.1.3 4 80.43 even 4
6400.2.a.cv.1.4 4 80.13 odd 4
6400.2.a.cv.1.4 4 80.67 even 4