Properties

Label 7056.2.a.ci.1.2
Level 7056
Weight 2
Character 7056.1
Self dual yes
Analytic conductor 56.342
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.3424436662\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 882)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.41421\) of defining polynomial
Character \(\chi\) \(=\) 7056.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{5} +O(q^{10})\) \(q+1.41421 q^{5} -4.00000 q^{11} +4.24264 q^{13} -7.07107 q^{17} +5.65685 q^{19} -8.00000 q^{23} -3.00000 q^{25} +2.00000 q^{29} +4.00000 q^{37} +9.89949 q^{41} +4.00000 q^{43} -5.65685 q^{47} +4.00000 q^{53} -5.65685 q^{55} +11.3137 q^{59} +1.41421 q^{61} +6.00000 q^{65} +12.0000 q^{67} -15.5563 q^{73} +16.0000 q^{79} +5.65685 q^{83} -10.0000 q^{85} +7.07107 q^{89} +8.00000 q^{95} +7.07107 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + O(q^{10}) \) \( 2q - 8q^{11} - 16q^{23} - 6q^{25} + 4q^{29} + 8q^{37} + 8q^{43} + 8q^{53} + 12q^{65} + 24q^{67} + 32q^{79} - 20q^{85} + 16q^{95} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.41421 0.632456 0.316228 0.948683i \(-0.397584\pi\)
0.316228 + 0.948683i \(0.397584\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 4.24264 1.17670 0.588348 0.808608i \(-0.299778\pi\)
0.588348 + 0.808608i \(0.299778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.07107 −1.71499 −0.857493 0.514496i \(-0.827979\pi\)
−0.857493 + 0.514496i \(0.827979\pi\)
\(18\) 0 0
\(19\) 5.65685 1.29777 0.648886 0.760886i \(-0.275235\pi\)
0.648886 + 0.760886i \(0.275235\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 0 0
\(25\) −3.00000 −0.600000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.89949 1.54604 0.773021 0.634381i \(-0.218745\pi\)
0.773021 + 0.634381i \(0.218745\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.65685 −0.825137 −0.412568 0.910927i \(-0.635368\pi\)
−0.412568 + 0.910927i \(0.635368\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 0 0
\(55\) −5.65685 −0.762770
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.3137 1.47292 0.736460 0.676481i \(-0.236496\pi\)
0.736460 + 0.676481i \(0.236496\pi\)
\(60\) 0 0
\(61\) 1.41421 0.181071 0.0905357 0.995893i \(-0.471142\pi\)
0.0905357 + 0.995893i \(0.471142\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −15.5563 −1.82073 −0.910366 0.413803i \(-0.864200\pi\)
−0.910366 + 0.413803i \(0.864200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.65685 0.620920 0.310460 0.950586i \(-0.399517\pi\)
0.310460 + 0.950586i \(0.399517\pi\)
\(84\) 0 0
\(85\) −10.0000 −1.08465
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.07107 0.749532 0.374766 0.927119i \(-0.377723\pi\)
0.374766 + 0.927119i \(0.377723\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) 0 0
\(97\) 7.07107 0.717958 0.358979 0.933346i \(-0.383125\pi\)
0.358979 + 0.933346i \(0.383125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.7279 1.26648 0.633238 0.773957i \(-0.281726\pi\)
0.633238 + 0.773957i \(0.281726\pi\)
\(102\) 0 0
\(103\) −5.65685 −0.557386 −0.278693 0.960380i \(-0.589901\pi\)
−0.278693 + 0.960380i \(0.589901\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −11.3137 −1.05501
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.3137 −1.01193
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 16.9706 1.48272 0.741362 0.671105i \(-0.234180\pi\)
0.741362 + 0.671105i \(0.234180\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 5.65685 0.479808 0.239904 0.970797i \(-0.422884\pi\)
0.239904 + 0.970797i \(0.422884\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −16.9706 −1.41915
\(144\) 0 0
\(145\) 2.82843 0.234888
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −20.0000 −1.63846 −0.819232 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −18.3848 −1.46726 −0.733632 0.679546i \(-0.762177\pi\)
−0.733632 + 0.679546i \(0.762177\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.3137 −0.875481 −0.437741 0.899101i \(-0.644221\pi\)
−0.437741 + 0.899101i \(0.644221\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.7279 −0.967686 −0.483843 0.875155i \(-0.660759\pi\)
−0.483843 + 0.875155i \(0.660759\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 12.7279 0.946059 0.473029 0.881047i \(-0.343160\pi\)
0.473029 + 0.881047i \(0.343160\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.65685 0.415900
\(186\) 0 0
\(187\) 28.2843 2.06835
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.00000 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(198\) 0 0
\(199\) −16.9706 −1.20301 −0.601506 0.798869i \(-0.705432\pi\)
−0.601506 + 0.798869i \(0.705432\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 14.0000 0.977802
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −22.6274 −1.56517
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.65685 0.385794
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −30.0000 −2.01802
\(222\) 0 0
\(223\) 16.9706 1.13643 0.568216 0.822879i \(-0.307634\pi\)
0.568216 + 0.822879i \(0.307634\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.9706 −1.12638 −0.563188 0.826329i \(-0.690425\pi\)
−0.563188 + 0.826329i \(0.690425\pi\)
\(228\) 0 0
\(229\) 12.7279 0.841085 0.420542 0.907273i \(-0.361840\pi\)
0.420542 + 0.907273i \(0.361840\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 4.24264 0.273293 0.136646 0.990620i \(-0.456368\pi\)
0.136646 + 0.990620i \(0.456368\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 24.0000 1.52708
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.65685 0.357057 0.178529 0.983935i \(-0.442866\pi\)
0.178529 + 0.983935i \(0.442866\pi\)
\(252\) 0 0
\(253\) 32.0000 2.01182
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.7279 −0.793946 −0.396973 0.917830i \(-0.629939\pi\)
−0.396973 + 0.917830i \(0.629939\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 5.65685 0.347498
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.41421 −0.0862261 −0.0431131 0.999070i \(-0.513728\pi\)
−0.0431131 + 0.999070i \(0.513728\pi\)
\(270\) 0 0
\(271\) 5.65685 0.343629 0.171815 0.985129i \(-0.445037\pi\)
0.171815 + 0.985129i \(0.445037\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.0000 0.723627
\(276\) 0 0
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −22.6274 −1.34506 −0.672530 0.740070i \(-0.734792\pi\)
−0.672530 + 0.740070i \(0.734792\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 33.0000 1.94118
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.0416 1.40453 0.702264 0.711917i \(-0.252173\pi\)
0.702264 + 0.711917i \(0.252173\pi\)
\(294\) 0 0
\(295\) 16.0000 0.931556
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −33.9411 −1.96287
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) −5.65685 −0.322854 −0.161427 0.986885i \(-0.551610\pi\)
−0.161427 + 0.986885i \(0.551610\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.65685 0.320771 0.160385 0.987054i \(-0.448726\pi\)
0.160385 + 0.987054i \(0.448726\pi\)
\(312\) 0 0
\(313\) 21.2132 1.19904 0.599521 0.800359i \(-0.295358\pi\)
0.599521 + 0.800359i \(0.295358\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 28.0000 1.57264 0.786318 0.617822i \(-0.211985\pi\)
0.786318 + 0.617822i \(0.211985\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −40.0000 −2.22566
\(324\) 0 0
\(325\) −12.7279 −0.706018
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 16.9706 0.927201
\(336\) 0 0
\(337\) −16.0000 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −29.6985 −1.58972 −0.794862 0.606791i \(-0.792457\pi\)
−0.794862 + 0.606791i \(0.792457\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.41421 0.0752710 0.0376355 0.999292i \(-0.488017\pi\)
0.0376355 + 0.999292i \(0.488017\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) 13.0000 0.684211
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −22.0000 −1.15153
\(366\) 0 0
\(367\) −5.65685 −0.295285 −0.147643 0.989041i \(-0.547169\pi\)
−0.147643 + 0.989041i \(0.547169\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.0000 0.517780 0.258890 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.48528 0.437014
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5.65685 0.289052 0.144526 0.989501i \(-0.453834\pi\)
0.144526 + 0.989501i \(0.453834\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 0 0
\(391\) 56.5685 2.86079
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 22.6274 1.13851
\(396\) 0 0
\(397\) 7.07107 0.354887 0.177443 0.984131i \(-0.443217\pi\)
0.177443 + 0.984131i \(0.443217\pi\)
\(398\) 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
\(405\) 0 0
\(406\) 0 0
\(407\) −16.0000 −0.793091
\(408\) 0 0
\(409\) −21.2132 −1.04893 −0.524463 0.851433i \(-0.675734\pi\)
−0.524463 + 0.851433i \(0.675734\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −22.6274 −1.10542 −0.552711 0.833373i \(-0.686407\pi\)
−0.552711 + 0.833373i \(0.686407\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 21.2132 1.02899
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −4.24264 −0.203888 −0.101944 0.994790i \(-0.532506\pi\)
−0.101944 + 0.994790i \(0.532506\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −45.2548 −2.16483
\(438\) 0 0
\(439\) −33.9411 −1.61992 −0.809961 0.586484i \(-0.800512\pi\)
−0.809961 + 0.586484i \(0.800512\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 0 0
\(445\) 10.0000 0.474045
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 0 0
\(451\) −39.5980 −1.86460
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6.00000 −0.280668 −0.140334 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.41421 −0.0658665 −0.0329332 0.999458i \(-0.510485\pi\)
−0.0329332 + 0.999458i \(0.510485\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.65685 −0.261768 −0.130884 0.991398i \(-0.541782\pi\)
−0.130884 + 0.991398i \(0.541782\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16.0000 −0.735681
\(474\) 0 0
\(475\) −16.9706 −0.778663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 28.2843 1.29234 0.646171 0.763193i \(-0.276369\pi\)
0.646171 + 0.763193i \(0.276369\pi\)
\(480\) 0 0
\(481\) 16.9706 0.773791
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10.0000 0.454077
\(486\) 0 0
\(487\) 24.0000 1.08754 0.543772 0.839233i \(-0.316996\pi\)
0.543772 + 0.839233i \(0.316996\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −14.1421 −0.636930
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −28.2843 −1.26113 −0.630567 0.776135i \(-0.717177\pi\)
−0.630567 + 0.776135i \(0.717177\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 32.5269 1.44173 0.720865 0.693075i \(-0.243745\pi\)
0.720865 + 0.693075i \(0.243745\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 22.6274 0.995153
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.41421 0.0619578 0.0309789 0.999520i \(-0.490138\pi\)
0.0309789 + 0.999520i \(0.490138\pi\)
\(522\) 0 0
\(523\) 33.9411 1.48414 0.742071 0.670321i \(-0.233844\pi\)
0.742071 + 0.670321i \(0.233844\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 42.0000 1.81922
\(534\) 0 0
\(535\) 5.65685 0.244567
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.65685 0.242313
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 11.3137 0.481980
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 36.0000 1.52537 0.762684 0.646771i \(-0.223881\pi\)
0.762684 + 0.646771i \(0.223881\pi\)
\(558\) 0 0
\(559\) 16.9706 0.717778
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 11.3137 0.476816 0.238408 0.971165i \(-0.423374\pi\)
0.238408 + 0.971165i \(0.423374\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −26.0000 −1.08998 −0.544988 0.838444i \(-0.683466\pi\)
−0.544988 + 0.838444i \(0.683466\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) 12.7279 0.529870 0.264935 0.964266i \(-0.414649\pi\)
0.264935 + 0.964266i \(0.414649\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −16.0000 −0.662652
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.9706 0.700450 0.350225 0.936666i \(-0.386105\pi\)
0.350225 + 0.936666i \(0.386105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −35.3553 −1.45187 −0.725935 0.687763i \(-0.758593\pi\)
−0.725935 + 0.687763i \(0.758593\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) 4.24264 0.173061 0.0865305 0.996249i \(-0.472422\pi\)
0.0865305 + 0.996249i \(0.472422\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.07107 0.287480
\(606\) 0 0
\(607\) −16.9706 −0.688814 −0.344407 0.938820i \(-0.611920\pi\)
−0.344407 + 0.938820i \(0.611920\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) 12.0000 0.484675 0.242338 0.970192i \(-0.422086\pi\)
0.242338 + 0.970192i \(0.422086\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) −11.3137 −0.454736 −0.227368 0.973809i \(-0.573012\pi\)
−0.227368 + 0.973809i \(0.573012\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −28.2843 −1.12777
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 11.3137 0.448971
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 0 0
\(643\) −11.3137 −0.446169 −0.223085 0.974799i \(-0.571613\pi\)
−0.223085 + 0.974799i \(0.571613\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −33.9411 −1.33436 −0.667182 0.744895i \(-0.732500\pi\)
−0.667182 + 0.744895i \(0.732500\pi\)
\(648\) 0 0
\(649\) −45.2548 −1.77641
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 0 0
\(655\) 24.0000 0.937758
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 4.24264 0.165020 0.0825098 0.996590i \(-0.473706\pi\)
0.0825098 + 0.996590i \(0.473706\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −16.0000 −0.619522
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.65685 −0.218380
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.24264 0.163058 0.0815290 0.996671i \(-0.474020\pi\)
0.0815290 + 0.996671i \(0.474020\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 8.48528 0.324206
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 16.9706 0.646527
\(690\) 0 0
\(691\) 50.9117 1.93677 0.968386 0.249457i \(-0.0802520\pi\)
0.968386 + 0.249457i \(0.0802520\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.00000 0.303457
\(696\) 0 0
\(697\) −70.0000 −2.65144
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 22.6274 0.853409
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 28.0000 1.05156 0.525781 0.850620i \(-0.323773\pi\)
0.525781 + 0.850620i \(0.323773\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −39.5980 −1.47676 −0.738378 0.674387i \(-0.764408\pi\)
−0.738378 + 0.674387i \(0.764408\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) −28.2843 −1.04901 −0.524503 0.851409i \(-0.675749\pi\)
−0.524503 + 0.851409i \(0.675749\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −28.2843 −1.04613
\(732\) 0 0
\(733\) 12.7279 0.470117 0.235058 0.971981i \(-0.424472\pi\)
0.235058 + 0.971981i \(0.424472\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −48.0000 −1.76810
\(738\) 0 0
\(739\) −12.0000 −0.441427 −0.220714 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) −28.2843 −1.03626
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 40.0000 1.45962 0.729810 0.683650i \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 22.6274 0.823496
\(756\) 0 0
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.89949 −0.358856 −0.179428 0.983771i \(-0.557425\pi\)
−0.179428 + 0.983771i \(0.557425\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 48.0000 1.73318
\(768\) 0 0
\(769\) −4.24264 −0.152994 −0.0764968 0.997070i \(-0.524373\pi\)
−0.0764968 + 0.997070i \(0.524373\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 32.5269 1.16991 0.584956 0.811065i \(-0.301112\pi\)
0.584956 + 0.811065i \(0.301112\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 56.0000 2.00641
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −26.0000 −0.927980
\(786\) 0 0
\(787\) −5.65685 −0.201645 −0.100823 0.994904i \(-0.532147\pi\)
−0.100823 + 0.994904i \(0.532147\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.7279 0.450846 0.225423 0.974261i \(-0.427624\pi\)
0.225423 + 0.974261i \(0.427624\pi\)
\(798\) 0 0
\(799\) 40.0000 1.41510
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 62.2254 2.19589
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −40.0000 −1.40633 −0.703163 0.711029i \(-0.748229\pi\)
−0.703163 + 0.711029i \(0.748229\pi\)
\(810\) 0 0
\(811\) −33.9411 −1.19183 −0.595917 0.803046i \(-0.703211\pi\)
−0.595917 + 0.803046i \(0.703211\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.65685 −0.198151
\(816\) 0 0
\(817\) 22.6274 0.791633
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −36.0000 −1.25641 −0.628204 0.778048i \(-0.716210\pi\)
−0.628204 + 0.778048i \(0.716210\pi\)
\(822\) 0 0
\(823\) −40.0000 −1.39431 −0.697156 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) 43.8406 1.52265 0.761324 0.648372i \(-0.224550\pi\)
0.761324 + 0.648372i \(0.224550\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −16.0000 −0.553703
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 45.2548 1.56237 0.781185 0.624299i \(-0.214615\pi\)
0.781185 + 0.624299i \(0.214615\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.07107 0.243252
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −32.0000 −1.09695
\(852\) 0 0
\(853\) 21.2132 0.726326 0.363163 0.931726i \(-0.381697\pi\)
0.363163 + 0.931726i \(0.381697\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 24.0416 0.821246 0.410623 0.911805i \(-0.365311\pi\)
0.410623 + 0.911805i \(0.365311\pi\)
\(858\) 0 0
\(859\) −5.65685 −0.193009 −0.0965047 0.995333i \(-0.530766\pi\)
−0.0965047 + 0.995333i \(0.530766\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −8.00000 −0.272323 −0.136162 0.990687i \(-0.543477\pi\)
−0.136162 + 0.990687i \(0.543477\pi\)
\(864\) 0 0
\(865\) −18.0000 −0.612018
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −64.0000 −2.17105
\(870\) 0 0
\(871\) 50.9117 1.72508
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −28.0000 −0.945493 −0.472746 0.881199i \(-0.656737\pi\)
−0.472746 + 0.881199i \(0.656737\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 21.2132 0.714691 0.357345 0.933972i \(-0.383682\pi\)
0.357345 + 0.933972i \(0.383682\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.673054 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 22.6274 0.759754 0.379877 0.925037i \(-0.375966\pi\)
0.379877 + 0.925037i \(0.375966\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −32.0000 −1.07084
\(894\) 0 0
\(895\) 16.9706 0.567263
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −28.2843 −0.942286
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 18.0000 0.598340
\(906\) 0 0
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −56.0000 −1.85536 −0.927681 0.373373i \(-0.878201\pi\)
−0.927681 + 0.373373i \(0.878201\pi\)
\(912\) 0 0
\(913\) −22.6274 −0.748858
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 56.0000 1.84727 0.923635 0.383274i \(-0.125203\pi\)
0.923635 + 0.383274i \(0.125203\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −12.0000 −0.394558
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 18.3848 0.603185 0.301592 0.953437i \(-0.402482\pi\)
0.301592 + 0.953437i \(0.402482\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 40.0000 1.30814
\(936\) 0 0
\(937\) 15.5563 0.508204 0.254102 0.967177i \(-0.418220\pi\)
0.254102 + 0.967177i \(0.418220\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 26.8701 0.875939 0.437969 0.898990i \(-0.355698\pi\)
0.437969 + 0.898990i \(0.355698\pi\)
\(942\) 0 0
\(943\) −79.1960 −2.57898
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 0 0
\(949\) −66.0000 −2.14245
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −8.00000 −0.259145 −0.129573 0.991570i \(-0.541361\pi\)
−0.129573 + 0.991570i \(0.541361\pi\)
\(954\) 0 0
\(955\) 22.6274 0.732206
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 19.7990 0.637352
\(966\) 0 0
\(967\) 48.0000 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 11.3137 0.363074 0.181537 0.983384i \(-0.441893\pi\)
0.181537 + 0.983384i \(0.441893\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.0000 0.959785 0.479893 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) 0 0
\(979\) −28.2843 −0.903969
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −11.3137 −0.360851 −0.180426 0.983589i \(-0.557748\pi\)
−0.180426 + 0.983589i \(0.557748\pi\)
\(984\) 0 0
\(985\) −5.65685 −0.180242
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −32.0000 −1.01754
\(990\) 0 0
\(991\) 40.0000 1.27064 0.635321 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −24.0000 −0.760851
\(996\) 0 0
\(997\) −7.07107 −0.223943 −0.111971 0.993711i \(-0.535717\pi\)
−0.111971 + 0.993711i \(0.535717\pi\)
\(998\) 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 7056.2.a.ci.1.2 2
3.2 odd 2 7056.2.a.cs.1.1 2
4.3 odd 2 882.2.a.o.1.2 yes 2
7.6 odd 2 inner 7056.2.a.ci.1.1 2
12.11 even 2 882.2.a.m.1.1 2
21.20 even 2 7056.2.a.cs.1.2 2
28.3 even 6 882.2.g.k.667.2 4
28.11 odd 6 882.2.g.k.667.1 4
28.19 even 6 882.2.g.k.361.2 4
28.23 odd 6 882.2.g.k.361.1 4
28.27 even 2 882.2.a.o.1.1 yes 2
84.11 even 6 882.2.g.m.667.2 4
84.23 even 6 882.2.g.m.361.2 4
84.47 odd 6 882.2.g.m.361.1 4
84.59 odd 6 882.2.g.m.667.1 4
84.83 odd 2 882.2.a.m.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.a.m.1.1 2 12.11 even 2
882.2.a.m.1.2 yes 2 84.83 odd 2
882.2.a.o.1.1 yes 2 28.27 even 2
882.2.a.o.1.2 yes 2 4.3 odd 2
882.2.g.k.361.1 4 28.23 odd 6
882.2.g.k.361.2 4 28.19 even 6
882.2.g.k.667.1 4 28.11 odd 6
882.2.g.k.667.2 4 28.3 even 6
882.2.g.m.361.1 4 84.47 odd 6
882.2.g.m.361.2 4 84.23 even 6
882.2.g.m.667.1 4 84.59 odd 6
882.2.g.m.667.2 4 84.11 even 6
7056.2.a.ci.1.1 2 7.6 odd 2 inner
7056.2.a.ci.1.2 2 1.1 even 1 trivial
7056.2.a.cs.1.1 2 3.2 odd 2
7056.2.a.cs.1.2 2 21.20 even 2