Properties

Label 2592.2.a.o.1.2
Level $2592$
Weight $2$
Character 2592.1
Self dual yes
Analytic conductor $20.697$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.6972242039\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
Defining polynomial: \( x^{2} - 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 288)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.44949\) of defining polynomial
Character \(\chi\) \(=\) 2592.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +1.44949 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +1.44949 q^{7} -3.44949 q^{11} -3.89898 q^{13} +4.89898 q^{17} -4.00000 q^{19} -0.550510 q^{23} -4.00000 q^{25} -9.89898 q^{29} -7.44949 q^{31} +1.44949 q^{35} +8.89898 q^{37} +2.10102 q^{41} -12.3485 q^{43} +8.34847 q^{47} -4.89898 q^{49} +0.898979 q^{53} -3.44949 q^{55} -0.348469 q^{59} +1.89898 q^{61} -3.89898 q^{65} +2.34847 q^{67} -11.7980 q^{71} +4.89898 q^{73} -5.00000 q^{77} -8.55051 q^{79} -5.44949 q^{83} +4.89898 q^{85} +3.10102 q^{89} -5.65153 q^{91} -4.00000 q^{95} +5.89898 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} - 2 q^{7} - 2 q^{11} + 2 q^{13} - 8 q^{19} - 6 q^{23} - 8 q^{25} - 10 q^{29} - 10 q^{31} - 2 q^{35} + 8 q^{37} + 14 q^{41} - 10 q^{43} + 2 q^{47} - 8 q^{53} - 2 q^{55} + 14 q^{59} - 6 q^{61} + 2 q^{65} - 10 q^{67} - 4 q^{71} - 10 q^{77} - 22 q^{79} - 6 q^{83} + 16 q^{89} - 26 q^{91} - 8 q^{95} + 2 q^{97}+O(q^{100}) \) 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 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) 1.44949 0.547856 0.273928 0.961750i \(-0.411677\pi\)
0.273928 + 0.961750i \(0.411677\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.44949 −1.04006 −0.520030 0.854148i \(-0.674079\pi\)
−0.520030 + 0.854148i \(0.674079\pi\)
\(12\) 0 0
\(13\) −3.89898 −1.08138 −0.540691 0.841221i \(-0.681837\pi\)
−0.540691 + 0.841221i \(0.681837\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.89898 1.18818 0.594089 0.804400i \(-0.297513\pi\)
0.594089 + 0.804400i \(0.297513\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.550510 −0.114789 −0.0573947 0.998352i \(-0.518279\pi\)
−0.0573947 + 0.998352i \(0.518279\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −9.89898 −1.83819 −0.919097 0.394031i \(-0.871080\pi\)
−0.919097 + 0.394031i \(0.871080\pi\)
\(30\) 0 0
\(31\) −7.44949 −1.33797 −0.668984 0.743277i \(-0.733271\pi\)
−0.668984 + 0.743277i \(0.733271\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.44949 0.245008
\(36\) 0 0
\(37\) 8.89898 1.46298 0.731492 0.681850i \(-0.238825\pi\)
0.731492 + 0.681850i \(0.238825\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.10102 0.328124 0.164062 0.986450i \(-0.447540\pi\)
0.164062 + 0.986450i \(0.447540\pi\)
\(42\) 0 0
\(43\) −12.3485 −1.88312 −0.941562 0.336840i \(-0.890642\pi\)
−0.941562 + 0.336840i \(0.890642\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.34847 1.21775 0.608875 0.793266i \(-0.291621\pi\)
0.608875 + 0.793266i \(0.291621\pi\)
\(48\) 0 0
\(49\) −4.89898 −0.699854
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.898979 0.123484 0.0617422 0.998092i \(-0.480334\pi\)
0.0617422 + 0.998092i \(0.480334\pi\)
\(54\) 0 0
\(55\) −3.44949 −0.465129
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.348469 −0.0453668 −0.0226834 0.999743i \(-0.507221\pi\)
−0.0226834 + 0.999743i \(0.507221\pi\)
\(60\) 0 0
\(61\) 1.89898 0.243139 0.121570 0.992583i \(-0.461207\pi\)
0.121570 + 0.992583i \(0.461207\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.89898 −0.483609
\(66\) 0 0
\(67\) 2.34847 0.286911 0.143456 0.989657i \(-0.454179\pi\)
0.143456 + 0.989657i \(0.454179\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −11.7980 −1.40016 −0.700080 0.714064i \(-0.746852\pi\)
−0.700080 + 0.714064i \(0.746852\pi\)
\(72\) 0 0
\(73\) 4.89898 0.573382 0.286691 0.958023i \(-0.407445\pi\)
0.286691 + 0.958023i \(0.407445\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.00000 −0.569803
\(78\) 0 0
\(79\) −8.55051 −0.962008 −0.481004 0.876719i \(-0.659728\pi\)
−0.481004 + 0.876719i \(0.659728\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.44949 −0.598159 −0.299080 0.954228i \(-0.596680\pi\)
−0.299080 + 0.954228i \(0.596680\pi\)
\(84\) 0 0
\(85\) 4.89898 0.531369
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.10102 0.328708 0.164354 0.986401i \(-0.447446\pi\)
0.164354 + 0.986401i \(0.447446\pi\)
\(90\) 0 0
\(91\) −5.65153 −0.592441
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) 5.89898 0.598951 0.299475 0.954104i \(-0.403188\pi\)
0.299475 + 0.954104i \(0.403188\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.79796 0.676422 0.338211 0.941070i \(-0.390178\pi\)
0.338211 + 0.941070i \(0.390178\pi\)
\(102\) 0 0
\(103\) −17.4495 −1.71935 −0.859675 0.510842i \(-0.829334\pi\)
−0.859675 + 0.510842i \(0.829334\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.7980 1.33390 0.666950 0.745103i \(-0.267600\pi\)
0.666950 + 0.745103i \(0.267600\pi\)
\(108\) 0 0
\(109\) −8.89898 −0.852368 −0.426184 0.904637i \(-0.640142\pi\)
−0.426184 + 0.904637i \(0.640142\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.7980 1.01579 0.507893 0.861420i \(-0.330424\pi\)
0.507893 + 0.861420i \(0.330424\pi\)
\(114\) 0 0
\(115\) −0.550510 −0.0513353
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.10102 0.650949
\(120\) 0 0
\(121\) 0.898979 0.0817254
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 11.2474 0.982694 0.491347 0.870964i \(-0.336505\pi\)
0.491347 + 0.870964i \(0.336505\pi\)
\(132\) 0 0
\(133\) −5.79796 −0.502747
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19.8990 1.70008 0.850042 0.526714i \(-0.176576\pi\)
0.850042 + 0.526714i \(0.176576\pi\)
\(138\) 0 0
\(139\) −1.44949 −0.122944 −0.0614721 0.998109i \(-0.519580\pi\)
−0.0614721 + 0.998109i \(0.519580\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 13.4495 1.12470
\(144\) 0 0
\(145\) −9.89898 −0.822066
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −13.8990 −1.13865 −0.569324 0.822113i \(-0.692795\pi\)
−0.569324 + 0.822113i \(0.692795\pi\)
\(150\) 0 0
\(151\) 9.24745 0.752547 0.376273 0.926509i \(-0.377205\pi\)
0.376273 + 0.926509i \(0.377205\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.44949 −0.598357
\(156\) 0 0
\(157\) 8.79796 0.702154 0.351077 0.936347i \(-0.385816\pi\)
0.351077 + 0.936347i \(0.385816\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.797959 −0.0628880
\(162\) 0 0
\(163\) −13.7980 −1.08074 −0.540370 0.841428i \(-0.681716\pi\)
−0.540370 + 0.841428i \(0.681716\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.44949 0.731223 0.365612 0.930767i \(-0.380860\pi\)
0.365612 + 0.930767i \(0.380860\pi\)
\(168\) 0 0
\(169\) 2.20204 0.169388
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.00000 −0.228086 −0.114043 0.993476i \(-0.536380\pi\)
−0.114043 + 0.993476i \(0.536380\pi\)
\(174\) 0 0
\(175\) −5.79796 −0.438285
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −18.6969 −1.38973 −0.694866 0.719139i \(-0.744536\pi\)
−0.694866 + 0.719139i \(0.744536\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.89898 0.654266
\(186\) 0 0
\(187\) −16.8990 −1.23578
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.4495 −1.26260 −0.631300 0.775538i \(-0.717478\pi\)
−0.631300 + 0.775538i \(0.717478\pi\)
\(192\) 0 0
\(193\) 13.8990 1.00047 0.500235 0.865890i \(-0.333247\pi\)
0.500235 + 0.865890i \(0.333247\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −21.5959 −1.53865 −0.769323 0.638860i \(-0.779406\pi\)
−0.769323 + 0.638860i \(0.779406\pi\)
\(198\) 0 0
\(199\) −11.7980 −0.836335 −0.418168 0.908370i \(-0.637328\pi\)
−0.418168 + 0.908370i \(0.637328\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −14.3485 −1.00707
\(204\) 0 0
\(205\) 2.10102 0.146742
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 13.7980 0.954425
\(210\) 0 0
\(211\) −15.4495 −1.06359 −0.531793 0.846874i \(-0.678482\pi\)
−0.531793 + 0.846874i \(0.678482\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −12.3485 −0.842159
\(216\) 0 0
\(217\) −10.7980 −0.733013
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −19.1010 −1.28487
\(222\) 0 0
\(223\) −18.1464 −1.21517 −0.607587 0.794253i \(-0.707863\pi\)
−0.607587 + 0.794253i \(0.707863\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 22.3485 1.48332 0.741660 0.670776i \(-0.234039\pi\)
0.741660 + 0.670776i \(0.234039\pi\)
\(228\) 0 0
\(229\) −1.00000 −0.0660819 −0.0330409 0.999454i \(-0.510519\pi\)
−0.0330409 + 0.999454i \(0.510519\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 8.34847 0.544594
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −20.1464 −1.30316 −0.651582 0.758578i \(-0.725894\pi\)
−0.651582 + 0.758578i \(0.725894\pi\)
\(240\) 0 0
\(241\) 7.00000 0.450910 0.225455 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.89898 −0.312984
\(246\) 0 0
\(247\) 15.5959 0.992344
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.20204 0.138992 0.0694958 0.997582i \(-0.477861\pi\)
0.0694958 + 0.997582i \(0.477861\pi\)
\(252\) 0 0
\(253\) 1.89898 0.119388
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.79796 −0.548802 −0.274401 0.961615i \(-0.588479\pi\)
−0.274401 + 0.961615i \(0.588479\pi\)
\(258\) 0 0
\(259\) 12.8990 0.801504
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.550510 0.0339459 0.0169730 0.999856i \(-0.494597\pi\)
0.0169730 + 0.999856i \(0.494597\pi\)
\(264\) 0 0
\(265\) 0.898979 0.0552239
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −16.8990 −1.03035 −0.515174 0.857085i \(-0.672273\pi\)
−0.515174 + 0.857085i \(0.672273\pi\)
\(270\) 0 0
\(271\) 29.3939 1.78555 0.892775 0.450502i \(-0.148755\pi\)
0.892775 + 0.450502i \(0.148755\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 13.7980 0.832048
\(276\) 0 0
\(277\) 4.79796 0.288281 0.144141 0.989557i \(-0.453958\pi\)
0.144141 + 0.989557i \(0.453958\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 19.8990 1.18707 0.593537 0.804807i \(-0.297731\pi\)
0.593537 + 0.804807i \(0.297731\pi\)
\(282\) 0 0
\(283\) −1.44949 −0.0861632 −0.0430816 0.999072i \(-0.513718\pi\)
−0.0430816 + 0.999072i \(0.513718\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.04541 0.179765
\(288\) 0 0
\(289\) 7.00000 0.411765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 18.7980 1.09819 0.549094 0.835760i \(-0.314973\pi\)
0.549094 + 0.835760i \(0.314973\pi\)
\(294\) 0 0
\(295\) −0.348469 −0.0202887
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.14643 0.124131
\(300\) 0 0
\(301\) −17.8990 −1.03168
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.89898 0.108735
\(306\) 0 0
\(307\) 2.20204 0.125677 0.0628386 0.998024i \(-0.479985\pi\)
0.0628386 + 0.998024i \(0.479985\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.24745 0.524375 0.262187 0.965017i \(-0.415556\pi\)
0.262187 + 0.965017i \(0.415556\pi\)
\(312\) 0 0
\(313\) −17.0000 −0.960897 −0.480448 0.877023i \(-0.659526\pi\)
−0.480448 + 0.877023i \(0.659526\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.1010 −0.904323 −0.452162 0.891936i \(-0.649347\pi\)
−0.452162 + 0.891936i \(0.649347\pi\)
\(318\) 0 0
\(319\) 34.1464 1.91183
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −19.5959 −1.09035
\(324\) 0 0
\(325\) 15.5959 0.865106
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 12.1010 0.667151
\(330\) 0 0
\(331\) 13.2474 0.728146 0.364073 0.931370i \(-0.381386\pi\)
0.364073 + 0.931370i \(0.381386\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.34847 0.128311
\(336\) 0 0
\(337\) 8.79796 0.479255 0.239628 0.970865i \(-0.422975\pi\)
0.239628 + 0.970865i \(0.422975\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 25.6969 1.39157
\(342\) 0 0
\(343\) −17.2474 −0.931275
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −28.1464 −1.51098 −0.755490 0.655161i \(-0.772601\pi\)
−0.755490 + 0.655161i \(0.772601\pi\)
\(348\) 0 0
\(349\) 4.79796 0.256829 0.128414 0.991721i \(-0.459011\pi\)
0.128414 + 0.991721i \(0.459011\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −15.6969 −0.835464 −0.417732 0.908570i \(-0.637175\pi\)
−0.417732 + 0.908570i \(0.637175\pi\)
\(354\) 0 0
\(355\) −11.7980 −0.626171
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.7980 0.939340 0.469670 0.882842i \(-0.344373\pi\)
0.469670 + 0.882842i \(0.344373\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.89898 0.256424
\(366\) 0 0
\(367\) −10.3485 −0.540186 −0.270093 0.962834i \(-0.587054\pi\)
−0.270093 + 0.962834i \(0.587054\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.30306 0.0676516
\(372\) 0 0
\(373\) 2.30306 0.119248 0.0596240 0.998221i \(-0.481010\pi\)
0.0596240 + 0.998221i \(0.481010\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 38.5959 1.98779
\(378\) 0 0
\(379\) 26.0000 1.33553 0.667765 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 33.4495 1.70919 0.854595 0.519296i \(-0.173806\pi\)
0.854595 + 0.519296i \(0.173806\pi\)
\(384\) 0 0
\(385\) −5.00000 −0.254824
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −12.7980 −0.648882 −0.324441 0.945906i \(-0.605176\pi\)
−0.324441 + 0.945906i \(0.605176\pi\)
\(390\) 0 0
\(391\) −2.69694 −0.136390
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.55051 −0.430223
\(396\) 0 0
\(397\) 18.6969 0.938372 0.469186 0.883099i \(-0.344547\pi\)
0.469186 + 0.883099i \(0.344547\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.6969 −0.783868 −0.391934 0.919993i \(-0.628194\pi\)
−0.391934 + 0.919993i \(0.628194\pi\)
\(402\) 0 0
\(403\) 29.0454 1.44685
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −30.6969 −1.52159
\(408\) 0 0
\(409\) −12.5959 −0.622828 −0.311414 0.950274i \(-0.600803\pi\)
−0.311414 + 0.950274i \(0.600803\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.505103 −0.0248545
\(414\) 0 0
\(415\) −5.44949 −0.267505
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.75255 −0.329884 −0.164942 0.986303i \(-0.552744\pi\)
−0.164942 + 0.986303i \(0.552744\pi\)
\(420\) 0 0
\(421\) 9.89898 0.482447 0.241223 0.970470i \(-0.422451\pi\)
0.241223 + 0.970470i \(0.422451\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −19.5959 −0.950542
\(426\) 0 0
\(427\) 2.75255 0.133205
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 33.7980 1.62799 0.813995 0.580872i \(-0.197288\pi\)
0.813995 + 0.580872i \(0.197288\pi\)
\(432\) 0 0
\(433\) 40.4949 1.94606 0.973030 0.230677i \(-0.0740942\pi\)
0.973030 + 0.230677i \(0.0740942\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.20204 0.105338
\(438\) 0 0
\(439\) 21.6515 1.03337 0.516686 0.856175i \(-0.327166\pi\)
0.516686 + 0.856175i \(0.327166\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 18.5505 0.881361 0.440681 0.897664i \(-0.354737\pi\)
0.440681 + 0.897664i \(0.354737\pi\)
\(444\) 0 0
\(445\) 3.10102 0.147002
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.8990 −0.986284 −0.493142 0.869949i \(-0.664152\pi\)
−0.493142 + 0.869949i \(0.664152\pi\)
\(450\) 0 0
\(451\) −7.24745 −0.341269
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.65153 −0.264948
\(456\) 0 0
\(457\) 17.4949 0.818377 0.409188 0.912450i \(-0.365812\pi\)
0.409188 + 0.912450i \(0.365812\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.30306 −0.293563 −0.146781 0.989169i \(-0.546891\pi\)
−0.146781 + 0.989169i \(0.546891\pi\)
\(462\) 0 0
\(463\) 6.75255 0.313818 0.156909 0.987613i \(-0.449847\pi\)
0.156909 + 0.987613i \(0.449847\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.404082 0.0186987 0.00934934 0.999956i \(-0.497024\pi\)
0.00934934 + 0.999956i \(0.497024\pi\)
\(468\) 0 0
\(469\) 3.40408 0.157186
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 42.5959 1.95856
\(474\) 0 0
\(475\) 16.0000 0.734130
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −19.0454 −0.870207 −0.435103 0.900380i \(-0.643288\pi\)
−0.435103 + 0.900380i \(0.643288\pi\)
\(480\) 0 0
\(481\) −34.6969 −1.58204
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.89898 0.267859
\(486\) 0 0
\(487\) −1.79796 −0.0814733 −0.0407366 0.999170i \(-0.512970\pi\)
−0.0407366 + 0.999170i \(0.512970\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 35.2474 1.59070 0.795348 0.606154i \(-0.207288\pi\)
0.795348 + 0.606154i \(0.207288\pi\)
\(492\) 0 0
\(493\) −48.4949 −2.18410
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −17.1010 −0.767086
\(498\) 0 0
\(499\) 16.3485 0.731858 0.365929 0.930643i \(-0.380751\pi\)
0.365929 + 0.930643i \(0.380751\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −20.2020 −0.900764 −0.450382 0.892836i \(-0.648712\pi\)
−0.450382 + 0.892836i \(0.648712\pi\)
\(504\) 0 0
\(505\) 6.79796 0.302505
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −33.4949 −1.48464 −0.742318 0.670048i \(-0.766273\pi\)
−0.742318 + 0.670048i \(0.766273\pi\)
\(510\) 0 0
\(511\) 7.10102 0.314131
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −17.4495 −0.768916
\(516\) 0 0
\(517\) −28.7980 −1.26653
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 25.5959 1.11923 0.559616 0.828752i \(-0.310949\pi\)
0.559616 + 0.828752i \(0.310949\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −36.4949 −1.58974
\(528\) 0 0
\(529\) −22.6969 −0.986823
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −8.19184 −0.354828
\(534\) 0 0
\(535\) 13.7980 0.596538
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 16.8990 0.727891
\(540\) 0 0
\(541\) −9.59592 −0.412561 −0.206280 0.978493i \(-0.566136\pi\)
−0.206280 + 0.978493i \(0.566136\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.89898 −0.381190
\(546\) 0 0
\(547\) 11.4495 0.489545 0.244772 0.969581i \(-0.421287\pi\)
0.244772 + 0.969581i \(0.421287\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 39.5959 1.68684
\(552\) 0 0
\(553\) −12.3939 −0.527041
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.6969 −0.453244 −0.226622 0.973983i \(-0.572768\pi\)
−0.226622 + 0.973983i \(0.572768\pi\)
\(558\) 0 0
\(559\) 48.1464 2.03638
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −10.3485 −0.436136 −0.218068 0.975934i \(-0.569975\pi\)
−0.218068 + 0.975934i \(0.569975\pi\)
\(564\) 0 0
\(565\) 10.7980 0.454274
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.00000 0.0419222 0.0209611 0.999780i \(-0.493327\pi\)
0.0209611 + 0.999780i \(0.493327\pi\)
\(570\) 0 0
\(571\) 18.3485 0.767860 0.383930 0.923362i \(-0.374570\pi\)
0.383930 + 0.923362i \(0.374570\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.20204 0.0918315
\(576\) 0 0
\(577\) −28.8990 −1.20308 −0.601540 0.798843i \(-0.705446\pi\)
−0.601540 + 0.798843i \(0.705446\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7.89898 −0.327705
\(582\) 0 0
\(583\) −3.10102 −0.128431
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23.9444 0.988291 0.494145 0.869379i \(-0.335481\pi\)
0.494145 + 0.869379i \(0.335481\pi\)
\(588\) 0 0
\(589\) 29.7980 1.22780
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −19.1010 −0.784385 −0.392192 0.919883i \(-0.628283\pi\)
−0.392192 + 0.919883i \(0.628283\pi\)
\(594\) 0 0
\(595\) 7.10102 0.291113
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 33.4495 1.36671 0.683355 0.730087i \(-0.260520\pi\)
0.683355 + 0.730087i \(0.260520\pi\)
\(600\) 0 0
\(601\) 39.6969 1.61927 0.809636 0.586932i \(-0.199665\pi\)
0.809636 + 0.586932i \(0.199665\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.898979 0.0365487
\(606\) 0 0
\(607\) 27.9444 1.13423 0.567114 0.823639i \(-0.308060\pi\)
0.567114 + 0.823639i \(0.308060\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −32.5505 −1.31685
\(612\) 0 0
\(613\) 2.69694 0.108928 0.0544642 0.998516i \(-0.482655\pi\)
0.0544642 + 0.998516i \(0.482655\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.69694 0.229350 0.114675 0.993403i \(-0.463417\pi\)
0.114675 + 0.993403i \(0.463417\pi\)
\(618\) 0 0
\(619\) −8.14643 −0.327433 −0.163716 0.986507i \(-0.552348\pi\)
−0.163716 + 0.986507i \(0.552348\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.49490 0.180084
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 43.5959 1.73828
\(630\) 0 0
\(631\) 25.7980 1.02700 0.513500 0.858089i \(-0.328349\pi\)
0.513500 + 0.858089i \(0.328349\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.00000 −0.317470
\(636\) 0 0
\(637\) 19.1010 0.756810
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12.5959 0.497509 0.248754 0.968567i \(-0.419979\pi\)
0.248754 + 0.968567i \(0.419979\pi\)
\(642\) 0 0
\(643\) 10.3485 0.408104 0.204052 0.978960i \(-0.434589\pi\)
0.204052 + 0.978960i \(0.434589\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.79796 −0.385198 −0.192599 0.981278i \(-0.561692\pi\)
−0.192599 + 0.981278i \(0.561692\pi\)
\(648\) 0 0
\(649\) 1.20204 0.0471842
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.0000 0.665261 0.332631 0.943057i \(-0.392064\pi\)
0.332631 + 0.943057i \(0.392064\pi\)
\(654\) 0 0
\(655\) 11.2474 0.439474
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22.3485 0.870573 0.435286 0.900292i \(-0.356647\pi\)
0.435286 + 0.900292i \(0.356647\pi\)
\(660\) 0 0
\(661\) 28.3939 1.10439 0.552197 0.833714i \(-0.313790\pi\)
0.552197 + 0.833714i \(0.313790\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.79796 −0.224835
\(666\) 0 0
\(667\) 5.44949 0.211005
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.55051 −0.252880
\(672\) 0 0
\(673\) −41.2929 −1.59172 −0.795861 0.605479i \(-0.792982\pi\)
−0.795861 + 0.605479i \(0.792982\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.3939 1.32186 0.660932 0.750446i \(-0.270161\pi\)
0.660932 + 0.750446i \(0.270161\pi\)
\(678\) 0 0
\(679\) 8.55051 0.328138
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 41.3939 1.58389 0.791946 0.610591i \(-0.209068\pi\)
0.791946 + 0.610591i \(0.209068\pi\)
\(684\) 0 0
\(685\) 19.8990 0.760301
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.50510 −0.133534
\(690\) 0 0
\(691\) −15.9444 −0.606553 −0.303277 0.952903i \(-0.598081\pi\)
−0.303277 + 0.952903i \(0.598081\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.44949 −0.0549823
\(696\) 0 0
\(697\) 10.2929 0.389870
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −36.4949 −1.37839 −0.689197 0.724574i \(-0.742036\pi\)
−0.689197 + 0.724574i \(0.742036\pi\)
\(702\) 0 0
\(703\) −35.5959 −1.34253
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.85357 0.370582
\(708\) 0 0
\(709\) −5.00000 −0.187779 −0.0938895 0.995583i \(-0.529930\pi\)
−0.0938895 + 0.995583i \(0.529930\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.10102 0.153584
\(714\) 0 0
\(715\) 13.4495 0.502982
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −47.1918 −1.75996 −0.879979 0.475012i \(-0.842444\pi\)
−0.879979 + 0.475012i \(0.842444\pi\)
\(720\) 0 0
\(721\) −25.2929 −0.941955
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 39.5959 1.47056
\(726\) 0 0
\(727\) 23.4495 0.869693 0.434847 0.900504i \(-0.356803\pi\)
0.434847 + 0.900504i \(0.356803\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −60.4949 −2.23748
\(732\) 0 0
\(733\) −2.10102 −0.0776030 −0.0388015 0.999247i \(-0.512354\pi\)
−0.0388015 + 0.999247i \(0.512354\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.10102 −0.298405
\(738\) 0 0
\(739\) 14.0000 0.514998 0.257499 0.966279i \(-0.417102\pi\)
0.257499 + 0.966279i \(0.417102\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30.5505 −1.12079 −0.560395 0.828226i \(-0.689351\pi\)
−0.560395 + 0.828226i \(0.689351\pi\)
\(744\) 0 0
\(745\) −13.8990 −0.509219
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) −40.6413 −1.48302 −0.741512 0.670940i \(-0.765891\pi\)
−0.741512 + 0.670940i \(0.765891\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.24745 0.336549
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −43.2929 −1.56936 −0.784682 0.619898i \(-0.787174\pi\)
−0.784682 + 0.619898i \(0.787174\pi\)
\(762\) 0 0
\(763\) −12.8990 −0.466974
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.35867 0.0490589
\(768\) 0 0
\(769\) 2.59592 0.0936112 0.0468056 0.998904i \(-0.485096\pi\)
0.0468056 + 0.998904i \(0.485096\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.4949 −0.449410 −0.224705 0.974427i \(-0.572142\pi\)
−0.224705 + 0.974427i \(0.572142\pi\)
\(774\) 0 0
\(775\) 29.7980 1.07037
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.40408 −0.301107
\(780\) 0 0
\(781\) 40.6969 1.45625
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8.79796 0.314013
\(786\) 0 0
\(787\) −3.24745 −0.115759 −0.0578795 0.998324i \(-0.518434\pi\)
−0.0578795 + 0.998324i \(0.518434\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 15.6515 0.556504
\(792\) 0 0
\(793\) −7.40408 −0.262927
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.3031 −0.648328 −0.324164 0.946001i \(-0.605083\pi\)
−0.324164 + 0.946001i \(0.605083\pi\)
\(798\) 0 0
\(799\) 40.8990 1.44690
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −16.8990 −0.596352
\(804\) 0 0
\(805\) −0.797959 −0.0281244
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −16.4949 −0.579930 −0.289965 0.957037i \(-0.593644\pi\)
−0.289965 + 0.957037i \(0.593644\pi\)
\(810\) 0 0
\(811\) −47.5959 −1.67132 −0.835659 0.549248i \(-0.814914\pi\)
−0.835659 + 0.549248i \(0.814914\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −13.7980 −0.483321
\(816\) 0 0
\(817\) 49.3939 1.72807
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 53.2929 1.85993 0.929967 0.367644i \(-0.119835\pi\)
0.929967 + 0.367644i \(0.119835\pi\)
\(822\) 0 0
\(823\) −15.4495 −0.538535 −0.269268 0.963065i \(-0.586782\pi\)
−0.269268 + 0.963065i \(0.586782\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −28.0000 −0.973655 −0.486828 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) 0 0
\(829\) −32.8990 −1.14263 −0.571314 0.820731i \(-0.693566\pi\)
−0.571314 + 0.820731i \(0.693566\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −24.0000 −0.831551
\(834\) 0 0
\(835\) 9.44949 0.327013
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −15.6515 −0.540351 −0.270175 0.962811i \(-0.587082\pi\)
−0.270175 + 0.962811i \(0.587082\pi\)
\(840\) 0 0
\(841\) 68.9898 2.37896
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.20204 0.0757525
\(846\) 0 0
\(847\) 1.30306 0.0447737
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.89898 −0.167935
\(852\) 0 0
\(853\) 1.89898 0.0650198 0.0325099 0.999471i \(-0.489650\pi\)
0.0325099 + 0.999471i \(0.489650\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.1010 0.618319 0.309160 0.951010i \(-0.399952\pi\)
0.309160 + 0.951010i \(0.399952\pi\)
\(858\) 0 0
\(859\) 16.5505 0.564696 0.282348 0.959312i \(-0.408887\pi\)
0.282348 + 0.959312i \(0.408887\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.79796 0.0612032 0.0306016 0.999532i \(-0.490258\pi\)
0.0306016 + 0.999532i \(0.490258\pi\)
\(864\) 0 0
\(865\) −3.00000 −0.102003
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 29.4949 1.00055
\(870\) 0 0
\(871\) −9.15663 −0.310261
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −13.0454 −0.441015
\(876\) 0 0
\(877\) −18.1010 −0.611228 −0.305614 0.952155i \(-0.598862\pi\)
−0.305614 + 0.952155i \(0.598862\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −24.4949 −0.825254 −0.412627 0.910900i \(-0.635389\pi\)
−0.412627 + 0.910900i \(0.635389\pi\)
\(882\) 0 0
\(883\) −0.404082 −0.0135984 −0.00679922 0.999977i \(-0.502164\pi\)
−0.00679922 + 0.999977i \(0.502164\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 28.8434 0.968465 0.484233 0.874939i \(-0.339099\pi\)
0.484233 + 0.874939i \(0.339099\pi\)
\(888\) 0 0
\(889\) −11.5959 −0.388915
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −33.3939 −1.11748
\(894\) 0 0
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 73.7423 2.45944
\(900\) 0 0
\(901\) 4.40408 0.146721
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −18.6969 −0.621507
\(906\) 0 0
\(907\) −0.752551 −0.0249881 −0.0124940 0.999922i \(-0.503977\pi\)
−0.0124940 + 0.999922i \(0.503977\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 49.5403 1.64134 0.820672 0.571400i \(-0.193599\pi\)
0.820672 + 0.571400i \(0.193599\pi\)
\(912\) 0 0
\(913\) 18.7980 0.622122
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 16.3031 0.538375
\(918\) 0 0
\(919\) −9.79796 −0.323205 −0.161602 0.986856i \(-0.551666\pi\)
−0.161602 + 0.986856i \(0.551666\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 46.0000 1.51411
\(924\) 0 0
\(925\) −35.5959 −1.17039
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −18.3031 −0.600504 −0.300252 0.953860i \(-0.597071\pi\)
−0.300252 + 0.953860i \(0.597071\pi\)
\(930\) 0 0
\(931\) 19.5959 0.642230
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −16.8990 −0.552656
\(936\) 0 0
\(937\) 7.50510 0.245181 0.122591 0.992457i \(-0.460880\pi\)
0.122591 + 0.992457i \(0.460880\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −7.00000 −0.228193 −0.114097 0.993470i \(-0.536397\pi\)
−0.114097 + 0.993470i \(0.536397\pi\)
\(942\) 0 0
\(943\) −1.15663 −0.0376652
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −45.2474 −1.47034 −0.735172 0.677880i \(-0.762899\pi\)
−0.735172 + 0.677880i \(0.762899\pi\)
\(948\) 0 0
\(949\) −19.1010 −0.620045
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −52.8990 −1.71357 −0.856783 0.515677i \(-0.827540\pi\)
−0.856783 + 0.515677i \(0.827540\pi\)
\(954\) 0 0
\(955\) −17.4495 −0.564652
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 28.8434 0.931401
\(960\) 0 0
\(961\) 24.4949 0.790158
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 13.8990 0.447424
\(966\) 0 0
\(967\) −9.24745 −0.297378 −0.148689 0.988884i \(-0.547505\pi\)
−0.148689 + 0.988884i \(0.547505\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −10.0000 −0.320915 −0.160458 0.987043i \(-0.551297\pi\)
−0.160458 + 0.987043i \(0.551297\pi\)
\(972\) 0 0
\(973\) −2.10102 −0.0673556
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −32.7980 −1.04930 −0.524650 0.851318i \(-0.675804\pi\)
−0.524650 + 0.851318i \(0.675804\pi\)
\(978\) 0 0
\(979\) −10.6969 −0.341876
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 34.3485 1.09555 0.547773 0.836627i \(-0.315476\pi\)
0.547773 + 0.836627i \(0.315476\pi\)
\(984\) 0 0
\(985\) −21.5959 −0.688103
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.79796 0.216163
\(990\) 0 0
\(991\) −37.3939 −1.18786 −0.593928 0.804518i \(-0.702424\pi\)
−0.593928 + 0.804518i \(0.702424\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −11.7980 −0.374020
\(996\) 0 0
\(997\) −26.3939 −0.835902 −0.417951 0.908469i \(-0.637252\pi\)
−0.417951 + 0.908469i \(0.637252\pi\)
\(998\) 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 2592.2.a.o.1.2 2
3.2 odd 2 2592.2.a.j.1.2 2
4.3 odd 2 2592.2.a.s.1.1 2
8.3 odd 2 5184.2.a.bn.1.1 2
8.5 even 2 5184.2.a.bj.1.2 2
9.2 odd 6 288.2.i.c.193.1 yes 4
9.4 even 3 864.2.i.e.289.1 4
9.5 odd 6 288.2.i.c.97.2 4
9.7 even 3 864.2.i.e.577.1 4
12.11 even 2 2592.2.a.n.1.1 2
24.5 odd 2 5184.2.a.bu.1.2 2
24.11 even 2 5184.2.a.by.1.1 2
36.7 odd 6 864.2.i.c.577.2 4
36.11 even 6 288.2.i.e.193.2 yes 4
36.23 even 6 288.2.i.e.97.1 yes 4
36.31 odd 6 864.2.i.c.289.2 4
72.5 odd 6 576.2.i.m.385.1 4
72.11 even 6 576.2.i.i.193.1 4
72.13 even 6 1728.2.i.m.1153.1 4
72.29 odd 6 576.2.i.m.193.2 4
72.43 odd 6 1728.2.i.k.577.2 4
72.59 even 6 576.2.i.i.385.2 4
72.61 even 6 1728.2.i.m.577.1 4
72.67 odd 6 1728.2.i.k.1153.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.i.c.97.2 4 9.5 odd 6
288.2.i.c.193.1 yes 4 9.2 odd 6
288.2.i.e.97.1 yes 4 36.23 even 6
288.2.i.e.193.2 yes 4 36.11 even 6
576.2.i.i.193.1 4 72.11 even 6
576.2.i.i.385.2 4 72.59 even 6
576.2.i.m.193.2 4 72.29 odd 6
576.2.i.m.385.1 4 72.5 odd 6
864.2.i.c.289.2 4 36.31 odd 6
864.2.i.c.577.2 4 36.7 odd 6
864.2.i.e.289.1 4 9.4 even 3
864.2.i.e.577.1 4 9.7 even 3
1728.2.i.k.577.2 4 72.43 odd 6
1728.2.i.k.1153.2 4 72.67 odd 6
1728.2.i.m.577.1 4 72.61 even 6
1728.2.i.m.1153.1 4 72.13 even 6
2592.2.a.j.1.2 2 3.2 odd 2
2592.2.a.n.1.1 2 12.11 even 2
2592.2.a.o.1.2 2 1.1 even 1 trivial
2592.2.a.s.1.1 2 4.3 odd 2
5184.2.a.bj.1.2 2 8.5 even 2
5184.2.a.bn.1.1 2 8.3 odd 2
5184.2.a.bu.1.2 2 24.5 odd 2
5184.2.a.by.1.1 2 24.11 even 2