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Properties

Label 5733.2.a.d.1.1
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [5733,2,Mod(1,5733)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5733.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5733, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,-1,0,0,0,3,0,0,3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(45.7782354788\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5733.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{4} +3.00000 q^{8} +3.00000 q^{11} +1.00000 q^{13} -1.00000 q^{16} +7.00000 q^{17} +7.00000 q^{19} -3.00000 q^{22} +6.00000 q^{23} -5.00000 q^{25} -1.00000 q^{26} +5.00000 q^{29} -5.00000 q^{32} -7.00000 q^{34} +8.00000 q^{37} -7.00000 q^{38} +2.00000 q^{43} -3.00000 q^{44} -6.00000 q^{46} +7.00000 q^{47} +5.00000 q^{50} -1.00000 q^{52} +3.00000 q^{53} -5.00000 q^{58} -7.00000 q^{59} +7.00000 q^{61} +7.00000 q^{64} -3.00000 q^{67} -7.00000 q^{68} +5.00000 q^{71} -14.0000 q^{73} -8.00000 q^{74} -7.00000 q^{76} -6.00000 q^{79} -2.00000 q^{86} +9.00000 q^{88} -6.00000 q^{92} -7.00000 q^{94} +14.0000 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 − 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 − 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 7.00000 1.69775 0.848875 − 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) 7.00000 1.60591 0.802955 − 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 − 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) 0 0
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 − 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −7.00000 −1.13555
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 − 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 7.00000 1.02105 0.510527 − 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) 3.00000 0.412082 0.206041 − 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −5.00000 −0.656532
\(59\) −7.00000 −0.911322 −0.455661 − 0.890153i \(-0.650597\pi\)
−0.455661 + 0.890153i \(0.650597\pi\)
\(60\) 0 0
\(61\) 7.00000 0.896258 0.448129 − 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) −3.00000 −0.366508 −0.183254 − 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) −7.00000 −0.848875
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 0.593391 0.296695 − 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 − 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) −7.00000 −0.802955
\(77\) 0 0
\(78\) 0 0
\(79\) −6.00000 −0.675053 −0.337526 − 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) 9.00000 0.959403
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) −7.00000 −0.721995
\(95\) 0 0
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 − 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.00000 0.500000
\(101\) −14.0000 −1.39305 −0.696526 − 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 − 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 3.00000 0.294174
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) −8.00000 −0.773389 −0.386695 − 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 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
\(113\) −9.00000 −0.846649 −0.423324 − 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −5.00000 −0.464238
\(117\) 0 0
\(118\) 7.00000 0.644402
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −7.00000 −0.633750
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 − 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) 0 0
\(131\) 14.0000 1.22319 0.611593 − 0.791173i \(-0.290529\pi\)
0.611593 + 0.791173i \(0.290529\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) 21.0000 1.80074
\(137\) −4.00000 −0.341743 −0.170872 − 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(138\) 0 0
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.00000 −0.419591
\(143\) 3.00000 0.250873
\(144\) 0 0
\(145\) 0 0
\(146\) 14.0000 1.15865
\(147\) 0 0
\(148\) −8.00000 −0.657596
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −3.00000 −0.244137 −0.122068 − 0.992522i \(-0.538953\pi\)
−0.122068 + 0.992522i \(0.538953\pi\)
\(152\) 21.0000 1.70332
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 − 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 6.00000 0.477334
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −13.0000 −1.01824 −0.509119 − 0.860696i \(-0.670029\pi\)
−0.509119 + 0.860696i \(0.670029\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.00000 −0.541676 −0.270838 − 0.962625i \(-0.587301\pi\)
−0.270838 + 0.962625i \(0.587301\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) −2.00000 −0.152499
\(173\) 7.00000 0.532200 0.266100 − 0.963945i \(-0.414265\pi\)
0.266100 + 0.963945i \(0.414265\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 0 0
\(179\) 10.0000 0.747435 0.373718 − 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 − 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 18.0000 1.32698
\(185\) 0 0
\(186\) 0 0
\(187\) 21.0000 1.53567
\(188\) −7.00000 −0.510527
\(189\) 0 0
\(190\) 0 0
\(191\) 20.0000 1.44715 0.723575 − 0.690246i \(-0.242498\pi\)
0.723575 + 0.690246i \(0.242498\pi\)
\(192\) 0 0
\(193\) 4.00000 0.287926 0.143963 − 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 − 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 14.0000 0.992434 0.496217 − 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(200\) −15.0000 −1.06066
\(201\) 0 0
\(202\) 14.0000 0.985037
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 14.0000 0.975426
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 21.0000 1.45260
\(210\) 0 0
\(211\) −26.0000 −1.78991 −0.894957 − 0.446153i \(-0.852794\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(212\) −3.00000 −0.206041
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −4.00000 −0.270914
\(219\) 0 0
\(220\) 0 0
\(221\) 7.00000 0.470871
\(222\) 0 0
\(223\) −21.0000 −1.40626 −0.703132 − 0.711059i \(-0.748216\pi\)
−0.703132 + 0.711059i \(0.748216\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) −28.0000 −1.85843 −0.929213 − 0.369546i \(-0.879513\pi\)
−0.929213 + 0.369546i \(0.879513\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 − 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 15.0000 0.984798
\(233\) 27.0000 1.76883 0.884414 − 0.466702i \(-0.154558\pi\)
0.884414 + 0.466702i \(0.154558\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.00000 0.455661
\(237\) 0 0
\(238\) 0 0
\(239\) 19.0000 1.22901 0.614504 − 0.788914i \(-0.289356\pi\)
0.614504 + 0.788914i \(0.289356\pi\)
\(240\) 0 0
\(241\) −28.0000 −1.80364 −0.901819 − 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(242\) 2.00000 0.128565
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) 7.00000 0.445399
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −14.0000 −0.883672 −0.441836 − 0.897096i \(-0.645673\pi\)
−0.441836 + 0.897096i \(0.645673\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) −14.0000 −0.873296 −0.436648 − 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −14.0000 −0.864923
\(263\) 24.0000 1.47990 0.739952 − 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 3.00000 0.183254
\(269\) −21.0000 −1.28039 −0.640196 − 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 0 0
\(271\) 7.00000 0.425220 0.212610 − 0.977137i \(-0.431804\pi\)
0.212610 + 0.977137i \(0.431804\pi\)
\(272\) −7.00000 −0.424437
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) −15.0000 −0.904534
\(276\) 0 0
\(277\) −17.0000 −1.02143 −0.510716 − 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 − 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) 14.0000 0.832214 0.416107 − 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −5.00000 −0.296695
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) 0 0
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 0 0
\(292\) 14.0000 0.819288
\(293\) 14.0000 0.817889 0.408944 − 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 24.0000 1.39497
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) 0 0
\(302\) 3.00000 0.172631
\(303\) 0 0
\(304\) −7.00000 −0.401478
\(305\) 0 0
\(306\) 0 0
\(307\) −21.0000 −1.19853 −0.599267 − 0.800549i \(-0.704541\pi\)
−0.599267 + 0.800549i \(0.704541\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 − 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 7.00000 0.395033
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 6.00000 0.336994 0.168497 − 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 15.0000 0.839839
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 49.0000 2.72643
\(324\) 0 0
\(325\) −5.00000 −0.277350
\(326\) 13.0000 0.720003
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 − 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 7.00000 0.383023
\(335\) 0 0
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 − 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) −7.00000 −0.376322
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 − 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −15.0000 −0.799503
\(353\) 14.0000 0.745145 0.372572 − 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −10.0000 −0.528516
\(359\) −8.00000 −0.422224 −0.211112 − 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) −7.00000 −0.367912
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −14.0000 −0.730794 −0.365397 − 0.930852i \(-0.619067\pi\)
−0.365397 + 0.930852i \(0.619067\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 15.0000 0.776671 0.388335 − 0.921518i \(-0.373050\pi\)
0.388335 + 0.921518i \(0.373050\pi\)
\(374\) −21.0000 −1.08588
\(375\) 0 0
\(376\) 21.0000 1.08299
\(377\) 5.00000 0.257513
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 − 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −20.0000 −1.02329
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4.00000 −0.203595
\(387\) 0 0
\(388\) −14.0000 −0.710742
\(389\) 3.00000 0.152106 0.0760530 − 0.997104i \(-0.475768\pi\)
0.0760530 + 0.997104i \(0.475768\pi\)
\(390\) 0 0
\(391\) 42.0000 2.12403
\(392\) 0 0
\(393\) 0 0
\(394\) 2.00000 0.100759
\(395\) 0 0
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 − 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) −14.0000 −0.701757
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) −22.0000 −1.09863 −0.549314 − 0.835616i \(-0.685111\pi\)
−0.549314 + 0.835616i \(0.685111\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 14.0000 0.696526
\(405\) 0 0
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) 28.0000 1.38451 0.692255 − 0.721653i \(-0.256617\pi\)
0.692255 + 0.721653i \(0.256617\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 14.0000 0.689730
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −5.00000 −0.245145
\(417\) 0 0
\(418\) −21.0000 −1.02714
\(419\) 14.0000 0.683945 0.341972 − 0.939710i \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 − 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 26.0000 1.26566
\(423\) 0 0
\(424\) 9.00000 0.437079
\(425\) −35.0000 −1.69775
\(426\) 0 0
\(427\) 0 0
\(428\) 8.00000 0.386695
\(429\) 0 0
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 − 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) −21.0000 −1.00920 −0.504598 − 0.863355i \(-0.668359\pi\)
−0.504598 + 0.863355i \(0.668359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.00000 −0.191565
\(437\) 42.0000 2.00913
\(438\) 0 0
\(439\) −14.0000 −0.668184 −0.334092 − 0.942541i \(-0.608430\pi\)
−0.334092 + 0.942541i \(0.608430\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −7.00000 −0.332956
\(443\) 20.0000 0.950229 0.475114 − 0.879924i \(-0.342407\pi\)
0.475114 + 0.879924i \(0.342407\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 21.0000 0.994379
\(447\) 0 0
\(448\) 0 0
\(449\) 12.0000 0.566315 0.283158 − 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 9.00000 0.423324
\(453\) 0 0
\(454\) 28.0000 1.31411
\(455\) 0 0
\(456\) 0 0
\(457\) −6.00000 −0.280668 −0.140334 − 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 − 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 − 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −5.00000 −0.232119
\(465\) 0 0
\(466\) −27.0000 −1.25075
\(467\) 14.0000 0.647843 0.323921 − 0.946084i \(-0.394999\pi\)
0.323921 + 0.946084i \(0.394999\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −21.0000 −0.966603
\(473\) 6.00000 0.275880
\(474\) 0 0
\(475\) −35.0000 −1.60591
\(476\) 0 0
\(477\) 0 0
\(478\) −19.0000 −0.869040
\(479\) 7.00000 0.319838 0.159919 − 0.987130i \(-0.448877\pi\)
0.159919 + 0.987130i \(0.448877\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 0 0
\(487\) 25.0000 1.13286 0.566429 − 0.824110i \(-0.308325\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) 21.0000 0.950625
\(489\) 0 0
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 − 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 0 0
\(493\) 35.0000 1.57632
\(494\) −7.00000 −0.314945
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 8.00000 0.358129 0.179065 − 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 14.0000 0.624851
\(503\) −28.0000 −1.24846 −0.624229 − 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −18.0000 −0.800198
\(507\) 0 0
\(508\) −2.00000 −0.0887357
\(509\) −28.0000 −1.24108 −0.620539 − 0.784176i \(-0.713086\pi\)
−0.620539 + 0.784176i \(0.713086\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) 14.0000 0.617514
\(515\) 0 0
\(516\) 0 0
\(517\) 21.0000 0.923579
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −14.0000 −0.613351 −0.306676 − 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 0 0
\(523\) 14.0000 0.612177 0.306089 − 0.952003i \(-0.400980\pi\)
0.306089 + 0.952003i \(0.400980\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −9.00000 −0.388741
\(537\) 0 0
\(538\) 21.0000 0.905374
\(539\) 0 0
\(540\) 0 0
\(541\) 8.00000 0.343947 0.171973 − 0.985102i \(-0.444986\pi\)
0.171973 + 0.985102i \(0.444986\pi\)
\(542\) −7.00000 −0.300676
\(543\) 0 0
\(544\) −35.0000 −1.50061
\(545\) 0 0
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 − 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 4.00000 0.170872
\(549\) 0 0
\(550\) 15.0000 0.639602
\(551\) 35.0000 1.49105
\(552\) 0 0
\(553\) 0 0
\(554\) 17.0000 0.722261
\(555\) 0 0
\(556\) 0 0
\(557\) −18.0000 −0.762684 −0.381342 − 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) −12.0000 −0.506189
\(563\) 28.0000 1.18006 0.590030 − 0.807382i \(-0.299116\pi\)
0.590030 + 0.807382i \(0.299116\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 15.0000 0.629386
\(569\) −1.00000 −0.0419222 −0.0209611 − 0.999780i \(-0.506673\pi\)
−0.0209611 + 0.999780i \(0.506673\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 − 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) −3.00000 −0.125436
\(573\) 0 0
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) 0 0
\(577\) −14.0000 −0.582828 −0.291414 − 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) −32.0000 −1.33102
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 9.00000 0.372742
\(584\) −42.0000 −1.73797
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) 21.0000 0.866763 0.433381 − 0.901211i \(-0.357320\pi\)
0.433381 + 0.901211i \(0.357320\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) −6.00000 −0.245358
\(599\) −32.0000 −1.30748 −0.653742 − 0.756717i \(-0.726802\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 − 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3.00000 0.122068
\(605\) 0 0
\(606\) 0 0
\(607\) −14.0000 −0.568242 −0.284121 − 0.958788i \(-0.591702\pi\)
−0.284121 + 0.958788i \(0.591702\pi\)
\(608\) −35.0000 −1.41944
\(609\) 0 0
\(610\) 0 0
\(611\) 7.00000 0.283190
\(612\) 0 0
\(613\) 32.0000 1.29247 0.646234 − 0.763139i \(-0.276343\pi\)
0.646234 + 0.763139i \(0.276343\pi\)
\(614\) 21.0000 0.847491
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 − 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 − 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) 7.00000 0.279330
\(629\) 56.0000 2.23287
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 − 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) −18.0000 −0.716002
\(633\) 0 0
\(634\) −6.00000 −0.238290
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −15.0000 −0.593856
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 − 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) 7.00000 0.276053 0.138027 − 0.990429i \(-0.455924\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −49.0000 −1.92788
\(647\) −42.0000 −1.65119 −0.825595 − 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 0 0
\(649\) −21.0000 −0.824322
\(650\) 5.00000 0.196116
\(651\) 0 0
\(652\) 13.0000 0.509119
\(653\) 6.00000 0.234798 0.117399 − 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 40.0000 1.55818 0.779089 − 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 30.0000 1.16160
\(668\) 7.00000 0.270838
\(669\) 0 0
\(670\) 0 0
\(671\) 21.0000 0.810696
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 − 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) −23.0000 −0.885927
\(675\) 0 0
\(676\) −1.00000 −0.0384615
\(677\) −35.0000 −1.34516 −0.672580 − 0.740025i \(-0.734814\pi\)
−0.672580 + 0.740025i \(0.734814\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 − 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −2.00000 −0.0762493
\(689\) 3.00000 0.114291
\(690\) 0 0
\(691\) −35.0000 −1.33146 −0.665731 − 0.746191i \(-0.731880\pi\)
−0.665731 + 0.746191i \(0.731880\pi\)
\(692\) −7.00000 −0.266100
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 14.0000 0.529908
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 − 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 56.0000 2.11208
\(704\) 21.0000 0.791467
\(705\) 0 0
\(706\) −14.0000 −0.526897
\(707\) 0 0
\(708\) 0 0
\(709\) 50.0000 1.87779 0.938895 − 0.344204i \(-0.111851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −10.0000 −0.373718
\(717\) 0 0
\(718\) 8.00000 0.298557
\(719\) −42.0000 −1.56634 −0.783168 − 0.621810i \(-0.786397\pi\)
−0.783168 + 0.621810i \(0.786397\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −30.0000 −1.11648
\(723\) 0 0
\(724\) −7.00000 −0.260153
\(725\) −25.0000 −0.928477
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 − 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 14.0000 0.517809
\(732\) 0 0
\(733\) −42.0000 −1.55131 −0.775653 − 0.631160i \(-0.782579\pi\)
−0.775653 + 0.631160i \(0.782579\pi\)
\(734\) 14.0000 0.516749
\(735\) 0 0
\(736\) −30.0000 −1.10581
\(737\) −9.00000 −0.331519
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 − 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.00000 −0.330178 −0.165089 − 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −15.0000 −0.549189
\(747\) 0 0
\(748\) −21.0000 −0.767836
\(749\) 0 0
\(750\) 0 0
\(751\) −20.0000 −0.729810 −0.364905 − 0.931045i \(-0.618899\pi\)
−0.364905 + 0.931045i \(0.618899\pi\)
\(752\) −7.00000 −0.255264
\(753\) 0 0
\(754\) −5.00000 −0.182089
\(755\) 0 0
\(756\) 0 0
\(757\) 9.00000 0.327111 0.163555 − 0.986534i \(-0.447704\pi\)
0.163555 + 0.986534i \(0.447704\pi\)
\(758\) 12.0000 0.435860
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 0 0
\(767\) −7.00000 −0.252755
\(768\) 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
\(772\) −4.00000 −0.143963
\(773\) 42.0000 1.51064 0.755318 − 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 42.0000 1.50771
\(777\) 0 0
\(778\) −3.00000 −0.107555
\(779\) 0 0
\(780\) 0 0
\(781\) 15.0000 0.536742
\(782\) −42.0000 −1.50192
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −7.00000 −0.249523 −0.124762 − 0.992187i \(-0.539817\pi\)
−0.124762 + 0.992187i \(0.539817\pi\)
\(788\) 2.00000 0.0712470
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 7.00000 0.248577
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) −14.0000 −0.496217
\(797\) −42.0000 −1.48772 −0.743858 − 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 49.0000 1.73350
\(800\) 25.0000 0.883883
\(801\) 0 0
\(802\) 22.0000 0.776847
\(803\) −42.0000 −1.48215
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −42.0000 −1.47755
\(809\) 31.0000 1.08990 0.544951 − 0.838468i \(-0.316548\pi\)
0.544951 + 0.838468i \(0.316548\pi\)
\(810\) 0 0
\(811\) 28.0000 0.983213 0.491606 − 0.870817i \(-0.336410\pi\)
0.491606 + 0.870817i \(0.336410\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −24.0000 −0.841200
\(815\) 0 0
\(816\) 0 0
\(817\) 14.0000 0.489798
\(818\) −28.0000 −0.978997
\(819\) 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
\(823\) 4.00000 0.139431 0.0697156 − 0.997567i \(-0.477791\pi\)
0.0697156 + 0.997567i \(0.477791\pi\)
\(824\) −42.0000 −1.46314
\(825\) 0 0
\(826\) 0 0
\(827\) 5.00000 0.173867 0.0869335 − 0.996214i \(-0.472293\pi\)
0.0869335 + 0.996214i \(0.472293\pi\)
\(828\) 0 0
\(829\) −35.0000 −1.21560 −0.607800 − 0.794090i \(-0.707948\pi\)
−0.607800 + 0.794090i \(0.707948\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 7.00000 0.242681
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) −21.0000 −0.726300
\(837\) 0 0
\(838\) −14.0000 −0.483622
\(839\) 7.00000 0.241667 0.120833 − 0.992673i \(-0.461443\pi\)
0.120833 + 0.992673i \(0.461443\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) −30.0000 −1.03387
\(843\) 0 0
\(844\) 26.0000 0.894957
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −3.00000 −0.103020
\(849\) 0 0
\(850\) 35.0000 1.20049
\(851\) 48.0000 1.64542
\(852\) 0 0
\(853\) 42.0000 1.43805 0.719026 − 0.694983i \(-0.244588\pi\)
0.719026 + 0.694983i \(0.244588\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −24.0000 −0.820303
\(857\) 21.0000 0.717346 0.358673 − 0.933463i \(-0.383229\pi\)
0.358673 + 0.933463i \(0.383229\pi\)
\(858\) 0 0
\(859\) 56.0000 1.91070 0.955348 − 0.295484i \(-0.0954809\pi\)
0.955348 + 0.295484i \(0.0954809\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) 20.0000 0.680808 0.340404 − 0.940279i \(-0.389436\pi\)
0.340404 + 0.940279i \(0.389436\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 21.0000 0.713609
\(867\) 0 0
\(868\) 0 0
\(869\) −18.0000 −0.610608
\(870\) 0 0
\(871\) −3.00000 −0.101651
\(872\) 12.0000 0.406371
\(873\) 0 0
\(874\) −42.0000 −1.42067
\(875\) 0 0
\(876\) 0 0
\(877\) −48.0000 −1.62084 −0.810422 − 0.585846i \(-0.800762\pi\)
−0.810422 + 0.585846i \(0.800762\pi\)
\(878\) 14.0000 0.472477
\(879\) 0 0
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 − 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) 0 0
\(883\) −40.0000 −1.34611 −0.673054 − 0.739594i \(-0.735018\pi\)
−0.673054 + 0.739594i \(0.735018\pi\)
\(884\) −7.00000 −0.235435
\(885\) 0 0
\(886\) −20.0000 −0.671913
\(887\) 42.0000 1.41022 0.705111 − 0.709097i \(-0.250897\pi\)
0.705111 + 0.709097i \(0.250897\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 21.0000 0.703132
\(893\) 49.0000 1.63972
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −12.0000 −0.400445
\(899\) 0 0
\(900\) 0 0
\(901\) 21.0000 0.699611
\(902\) 0 0
\(903\) 0 0
\(904\) −27.0000 −0.898007
\(905\) 0 0
\(906\) 0 0
\(907\) −38.0000 −1.26177 −0.630885 − 0.775877i \(-0.717308\pi\)
−0.630885 + 0.775877i \(0.717308\pi\)
\(908\) 28.0000 0.929213
\(909\) 0 0
\(910\) 0 0
\(911\) 54.0000 1.78910 0.894550 − 0.446968i \(-0.147496\pi\)
0.894550 + 0.446968i \(0.147496\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 6.00000 0.198462
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) 0 0
\(918\) 0 0
\(919\) 50.0000 1.64935 0.824674 − 0.565608i \(-0.191359\pi\)
0.824674 + 0.565608i \(0.191359\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 28.0000 0.922131
\(923\) 5.00000 0.164577
\(924\) 0 0
\(925\) −40.0000 −1.31519
\(926\) −16.0000 −0.525793
\(927\) 0 0
\(928\) −25.0000 −0.820665
\(929\) 14.0000 0.459325 0.229663 − 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −27.0000 −0.884414
\(933\) 0 0
\(934\) −14.0000 −0.458094
\(935\) 0 0
\(936\) 0 0
\(937\) −7.00000 −0.228680 −0.114340 − 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 28.0000 0.912774 0.456387 − 0.889781i \(-0.349143\pi\)
0.456387 + 0.889781i \(0.349143\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 7.00000 0.227831
\(945\) 0 0
\(946\) −6.00000 −0.195077
\(947\) 27.0000 0.877382 0.438691 − 0.898638i \(-0.355442\pi\)
0.438691 + 0.898638i \(0.355442\pi\)
\(948\) 0 0
\(949\) −14.0000 −0.454459
\(950\) 35.0000 1.13555
\(951\) 0 0
\(952\) 0 0
\(953\) −9.00000 −0.291539 −0.145769 − 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −19.0000 −0.614504
\(957\) 0 0
\(958\) −7.00000 −0.226160
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) −8.00000 −0.257930
\(963\) 0 0
\(964\) 28.0000 0.901819
\(965\) 0 0
\(966\) 0 0
\(967\) −5.00000 −0.160789 −0.0803946 − 0.996763i \(-0.525618\pi\)
−0.0803946 + 0.996763i \(0.525618\pi\)
\(968\) −6.00000 −0.192847
\(969\) 0 0
\(970\) 0 0
\(971\) −28.0000 −0.898563 −0.449281 − 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −25.0000 −0.801052
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) 38.0000 1.21573 0.607864 − 0.794041i \(-0.292027\pi\)
0.607864 + 0.794041i \(0.292027\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 30.0000 0.957338
\(983\) −7.00000 −0.223265 −0.111633 − 0.993750i \(-0.535608\pi\)
−0.111633 + 0.993750i \(0.535608\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −35.0000 −1.11463
\(987\) 0 0
\(988\) −7.00000 −0.222700
\(989\) 12.0000 0.381578
\(990\) 0 0
\(991\) 4.00000 0.127064 0.0635321 − 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 7.00000 0.221692 0.110846 − 0.993838i \(-0.464644\pi\)
0.110846 + 0.993838i \(0.464644\pi\)
\(998\) −8.00000 −0.253236
\(999\) 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 5733.2.a.d.1.1 1
3.2 odd 2 637.2.a.d.1.1 1
7.3 odd 6 819.2.j.b.352.1 2
7.5 odd 6 819.2.j.b.235.1 2
7.6 odd 2 5733.2.a.c.1.1 1
21.2 odd 6 637.2.e.a.508.1 2
21.5 even 6 91.2.e.a.53.1 ✓ 2
21.11 odd 6 637.2.e.a.79.1 2
21.17 even 6 91.2.e.a.79.1 yes 2
21.20 even 2 637.2.a.c.1.1 1
39.38 odd 2 8281.2.a.e.1.1 1
84.47 odd 6 1456.2.r.g.417.1 2
84.59 odd 6 1456.2.r.g.625.1 2
273.38 even 6 1183.2.e.b.170.1 2
273.194 even 6 1183.2.e.b.508.1 2
273.272 even 2 8281.2.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.a.53.1 ✓ 2 21.5 even 6
91.2.e.a.79.1 yes 2 21.17 even 6
637.2.a.c.1.1 1 21.20 even 2
637.2.a.d.1.1 1 3.2 odd 2
637.2.e.a.79.1 2 21.11 odd 6
637.2.e.a.508.1 2 21.2 odd 6
819.2.j.b.235.1 2 7.5 odd 6
819.2.j.b.352.1 2 7.3 odd 6
1183.2.e.b.170.1 2 273.38 even 6
1183.2.e.b.508.1 2 273.194 even 6
1456.2.r.g.417.1 2 84.47 odd 6
1456.2.r.g.625.1 2 84.59 odd 6
5733.2.a.c.1.1 1 7.6 odd 2
5733.2.a.d.1.1 1 1.1 even 1 trivial
8281.2.a.e.1.1 1 39.38 odd 2
8281.2.a.f.1.1 1 273.272 even 2