Properties

Label 2736.2.d.a.2015.11
Level $2736$
Weight $2$
Character 2736.2015
Analytic conductor $21.847$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 12 x^{10} + 47 x^{8} - 44 x^{6} + 81 x^{4} + 848 x^{2} + 1600\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2015.11
Root \(1.49887 + 1.07270i\) of defining polynomial
Character \(\chi\) \(=\) 2736.2015
Dual form 2736.2.d.a.2015.2

$q$-expansion

\(f(q)\) \(=\) \(q+3.55961i q^{5} -3.63675i q^{7} +O(q^{10})\) \(q+3.55961i q^{5} -3.63675i q^{7} +4.12147 q^{11} -1.20541 q^{13} +1.58353i q^{17} -1.00000i q^{19} +3.68078 q^{23} -7.67079 q^{25} +0.561860i q^{29} +5.20541i q^{31} +12.9454 q^{35} +9.27349 q^{37} +3.72892i q^{41} -9.46538i q^{43} +6.33989 q^{47} -6.22593 q^{49} -11.9719i q^{53} +14.6708i q^{55} -10.2863 q^{59} +2.60270 q^{61} -4.29078i q^{65} -2.06808i q^{67} +7.36156 q^{71} -0.363253 q^{73} -14.9887i q^{77} +11.6573i q^{79} +3.68078 q^{83} -5.63675 q^{85} +6.79970i q^{89} +4.38377i q^{91} +3.55961 q^{95} +8.86267 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + O(q^{10}) \) \( 12q + 4q^{25} + 8q^{37} - 52q^{49} + 24q^{61} - 56q^{73} - 16q^{85} + 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 3.55961i 1.59190i 0.605360 + 0.795952i \(0.293029\pi\)
−0.605360 + 0.795952i \(0.706971\pi\)
\(6\) 0 0
\(7\) − 3.63675i − 1.37456i −0.726392 0.687281i \(-0.758804\pi\)
0.726392 0.687281i \(-0.241196\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.12147 1.24267 0.621334 0.783546i \(-0.286591\pi\)
0.621334 + 0.783546i \(0.286591\pi\)
\(12\) 0 0
\(13\) −1.20541 −0.334321 −0.167160 0.985930i \(-0.553460\pi\)
−0.167160 + 0.985930i \(0.553460\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.58353i 0.384063i 0.981389 + 0.192031i \(0.0615075\pi\)
−0.981389 + 0.192031i \(0.938492\pi\)
\(18\) 0 0
\(19\) − 1.00000i − 0.229416i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.68078 0.767496 0.383748 0.923438i \(-0.374633\pi\)
0.383748 + 0.923438i \(0.374633\pi\)
\(24\) 0 0
\(25\) −7.67079 −1.53416
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.561860i 0.104335i 0.998638 + 0.0521674i \(0.0166129\pi\)
−0.998638 + 0.0521674i \(0.983387\pi\)
\(30\) 0 0
\(31\) 5.20541i 0.934919i 0.884014 + 0.467460i \(0.154831\pi\)
−0.884014 + 0.467460i \(0.845169\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 12.9454 2.18817
\(36\) 0 0
\(37\) 9.27349 1.52455 0.762276 0.647252i \(-0.224082\pi\)
0.762276 + 0.647252i \(0.224082\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.72892i 0.582360i 0.956668 + 0.291180i \(0.0940478\pi\)
−0.956668 + 0.291180i \(0.905952\pi\)
\(42\) 0 0
\(43\) − 9.46538i − 1.44346i −0.692176 0.721728i \(-0.743348\pi\)
0.692176 0.721728i \(-0.256652\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.33989 0.924768 0.462384 0.886680i \(-0.346994\pi\)
0.462384 + 0.886680i \(0.346994\pi\)
\(48\) 0 0
\(49\) −6.22593 −0.889418
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 11.9719i − 1.64446i −0.569155 0.822230i \(-0.692730\pi\)
0.569155 0.822230i \(-0.307270\pi\)
\(54\) 0 0
\(55\) 14.6708i 1.97821i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.2863 −1.33916 −0.669579 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(60\) 0 0
\(61\) 2.60270 0.333242 0.166621 0.986021i \(-0.446714\pi\)
0.166621 + 0.986021i \(0.446714\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 4.29078i − 0.532206i
\(66\) 0 0
\(67\) − 2.06808i − 0.252657i −0.991988 0.126328i \(-0.959681\pi\)
0.991988 0.126328i \(-0.0403193\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.36156 0.873657 0.436828 0.899545i \(-0.356102\pi\)
0.436828 + 0.899545i \(0.356102\pi\)
\(72\) 0 0
\(73\) −0.363253 −0.0425156 −0.0212578 0.999774i \(-0.506767\pi\)
−0.0212578 + 0.999774i \(0.506767\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 14.9887i − 1.70812i
\(78\) 0 0
\(79\) 11.6573i 1.31154i 0.754959 + 0.655772i \(0.227657\pi\)
−0.754959 + 0.655772i \(0.772343\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.68078 0.404018 0.202009 0.979384i \(-0.435253\pi\)
0.202009 + 0.979384i \(0.435253\pi\)
\(84\) 0 0
\(85\) −5.63675 −0.611391
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.79970i 0.720767i 0.932804 + 0.360383i \(0.117354\pi\)
−0.932804 + 0.360383i \(0.882646\pi\)
\(90\) 0 0
\(91\) 4.38377i 0.459544i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.55961 0.365208
\(96\) 0 0
\(97\) 8.86267 0.899868 0.449934 0.893062i \(-0.351447\pi\)
0.449934 + 0.893062i \(0.351447\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.6526i 1.55750i 0.627337 + 0.778748i \(0.284145\pi\)
−0.627337 + 0.778748i \(0.715855\pi\)
\(102\) 0 0
\(103\) 17.6843i 1.74249i 0.490851 + 0.871244i \(0.336686\pi\)
−0.490851 + 0.871244i \(0.663314\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.24293 0.796874 0.398437 0.917196i \(-0.369553\pi\)
0.398437 + 0.917196i \(0.369553\pi\)
\(108\) 0 0
\(109\) 14.5470 1.39335 0.696674 0.717388i \(-0.254662\pi\)
0.696674 + 0.717388i \(0.254662\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 3.97127i − 0.373586i −0.982399 0.186793i \(-0.940191\pi\)
0.982399 0.186793i \(-0.0598094\pi\)
\(114\) 0 0
\(115\) 13.1021i 1.22178i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.75890 0.527918
\(120\) 0 0
\(121\) 5.98648 0.544225
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 9.50695i − 0.850328i
\(126\) 0 0
\(127\) 16.8627i 1.49632i 0.663518 + 0.748160i \(0.269063\pi\)
−0.663518 + 0.748160i \(0.730937\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.38323 0.732446 0.366223 0.930527i \(-0.380651\pi\)
0.366223 + 0.930527i \(0.380651\pi\)
\(132\) 0 0
\(133\) −3.63675 −0.315346
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.61255i 0.137769i 0.997625 + 0.0688846i \(0.0219440\pi\)
−0.997625 + 0.0688846i \(0.978056\pi\)
\(138\) 0 0
\(139\) 3.63675i 0.308465i 0.988035 + 0.154232i \(0.0492905\pi\)
−0.988035 + 0.154232i \(0.950710\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.96805 −0.415450
\(144\) 0 0
\(145\) −2.00000 −0.166091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.702162i 0.0575234i 0.999586 + 0.0287617i \(0.00915639\pi\)
−0.999586 + 0.0287617i \(0.990844\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −18.5292 −1.48830
\(156\) 0 0
\(157\) 14.8627 1.18617 0.593085 0.805140i \(-0.297910\pi\)
0.593085 + 0.805140i \(0.297910\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 13.3861i − 1.05497i
\(162\) 0 0
\(163\) − 13.7253i − 1.07505i −0.843247 0.537526i \(-0.819359\pi\)
0.843247 0.537526i \(-0.180641\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −21.4539 −1.66015 −0.830077 0.557649i \(-0.811704\pi\)
−0.830077 + 0.557649i \(0.811704\pi\)
\(168\) 0 0
\(169\) −11.5470 −0.888230
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 21.0381i 1.59950i 0.600334 + 0.799749i \(0.295034\pi\)
−0.600334 + 0.799749i \(0.704966\pi\)
\(174\) 0 0
\(175\) 27.8967i 2.10879i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.5292 1.38494 0.692469 0.721448i \(-0.256523\pi\)
0.692469 + 0.721448i \(0.256523\pi\)
\(180\) 0 0
\(181\) −18.9308 −1.40711 −0.703556 0.710640i \(-0.748406\pi\)
−0.703556 + 0.710640i \(0.748406\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 33.0100i 2.42694i
\(186\) 0 0
\(187\) 6.52647i 0.477263i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 26.9124 1.94732 0.973658 0.228014i \(-0.0732233\pi\)
0.973658 + 0.228014i \(0.0732233\pi\)
\(192\) 0 0
\(193\) −12.4519 −0.896304 −0.448152 0.893957i \(-0.647918\pi\)
−0.448152 + 0.893957i \(0.647918\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.99578i 0.712170i 0.934454 + 0.356085i \(0.115889\pi\)
−0.934454 + 0.356085i \(0.884111\pi\)
\(198\) 0 0
\(199\) − 24.0124i − 1.70219i −0.525011 0.851096i \(-0.675939\pi\)
0.525011 0.851096i \(-0.324061\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.04334 0.143415
\(204\) 0 0
\(205\) −13.2735 −0.927061
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 4.12147i − 0.285088i
\(210\) 0 0
\(211\) − 16.6151i − 1.14383i −0.820313 0.571914i \(-0.806201\pi\)
0.820313 0.571914i \(-0.193799\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 33.6930 2.29784
\(216\) 0 0
\(217\) 18.9308 1.28510
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 1.90880i − 0.128400i
\(222\) 0 0
\(223\) 11.6573i 0.780628i 0.920682 + 0.390314i \(0.127634\pi\)
−0.920682 + 0.390314i \(0.872366\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 25.8908 1.71843 0.859215 0.511614i \(-0.170952\pi\)
0.859215 + 0.511614i \(0.170952\pi\)
\(228\) 0 0
\(229\) −24.3961 −1.61214 −0.806071 0.591819i \(-0.798410\pi\)
−0.806071 + 0.591819i \(0.798410\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 4.07332i − 0.266852i −0.991059 0.133426i \(-0.957402\pi\)
0.991059 0.133426i \(-0.0425979\pi\)
\(234\) 0 0
\(235\) 22.5675i 1.47214i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.3079 −0.731450 −0.365725 0.930723i \(-0.619179\pi\)
−0.365725 + 0.930723i \(0.619179\pi\)
\(240\) 0 0
\(241\) −20.4789 −1.31916 −0.659581 0.751633i \(-0.729266\pi\)
−0.659581 + 0.751633i \(0.729266\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 22.1618i − 1.41587i
\(246\) 0 0
\(247\) 1.20541i 0.0766984i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.43968 −0.595828 −0.297914 0.954593i \(-0.596291\pi\)
−0.297914 + 0.954593i \(0.596291\pi\)
\(252\) 0 0
\(253\) 15.1702 0.953743
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 8.35834i − 0.521379i −0.965423 0.260690i \(-0.916050\pi\)
0.965423 0.260690i \(-0.0839499\pi\)
\(258\) 0 0
\(259\) − 33.7253i − 2.09559i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.6940 1.52270 0.761349 0.648342i \(-0.224537\pi\)
0.761349 + 0.648342i \(0.224537\pi\)
\(264\) 0 0
\(265\) 42.6151 2.61782
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 18.2097i − 1.11026i −0.831762 0.555132i \(-0.812668\pi\)
0.831762 0.555132i \(-0.187332\pi\)
\(270\) 0 0
\(271\) − 8.51994i − 0.517549i −0.965938 0.258775i \(-0.916681\pi\)
0.965938 0.258775i \(-0.0833187\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −31.6149 −1.90645
\(276\) 0 0
\(277\) −25.6015 −1.53825 −0.769124 0.639100i \(-0.779307\pi\)
−0.769124 + 0.639100i \(0.779307\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.01971i 0.478416i 0.970968 + 0.239208i \(0.0768877\pi\)
−0.970968 + 0.239208i \(0.923112\pi\)
\(282\) 0 0
\(283\) − 0.945441i − 0.0562006i −0.999605 0.0281003i \(-0.991054\pi\)
0.999605 0.0281003i \(-0.00894579\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 13.5611 0.800489
\(288\) 0 0
\(289\) 14.4924 0.852496
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 15.1389i 0.884425i 0.896910 + 0.442212i \(0.145806\pi\)
−0.896910 + 0.442212i \(0.854194\pi\)
\(294\) 0 0
\(295\) − 36.6151i − 2.13181i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.43685 −0.256590
\(300\) 0 0
\(301\) −34.4232 −1.98412
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.26460i 0.530490i
\(306\) 0 0
\(307\) − 14.5470i − 0.830240i −0.909767 0.415120i \(-0.863740\pi\)
0.909767 0.415120i \(-0.136260\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −11.3079 −0.641215 −0.320607 0.947212i \(-0.603887\pi\)
−0.320607 + 0.947212i \(0.603887\pi\)
\(312\) 0 0
\(313\) −10.8627 −0.613995 −0.306997 0.951710i \(-0.599324\pi\)
−0.306997 + 0.951710i \(0.599324\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.83165i 0.102876i 0.998676 + 0.0514378i \(0.0163804\pi\)
−0.998676 + 0.0514378i \(0.983620\pi\)
\(318\) 0 0
\(319\) 2.31569i 0.129654i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.58353 0.0881100
\(324\) 0 0
\(325\) 9.24644 0.512900
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 23.0566i − 1.27115i
\(330\) 0 0
\(331\) − 32.4789i − 1.78520i −0.450848 0.892601i \(-0.648878\pi\)
0.450848 0.892601i \(-0.351122\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.36156 0.402205
\(336\) 0 0
\(337\) 18.5880 1.01255 0.506277 0.862371i \(-0.331021\pi\)
0.506277 + 0.862371i \(0.331021\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 21.4539i 1.16179i
\(342\) 0 0
\(343\) − 2.81511i − 0.152002i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.38323 −0.450036 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(348\) 0 0
\(349\) 35.4572 1.89798 0.948991 0.315303i \(-0.102106\pi\)
0.948991 + 0.315303i \(0.102106\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 31.6920i − 1.68680i −0.537288 0.843399i \(-0.680551\pi\)
0.537288 0.843399i \(-0.319449\pi\)
\(354\) 0 0
\(355\) 26.2043i 1.39078i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.1140 0.797688 0.398844 0.917019i \(-0.369412\pi\)
0.398844 + 0.917019i \(0.369412\pi\)
\(360\) 0 0
\(361\) −1.00000 −0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 1.29304i − 0.0676807i
\(366\) 0 0
\(367\) − 4.38377i − 0.228831i −0.993433 0.114415i \(-0.963500\pi\)
0.993433 0.114415i \(-0.0364995\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −43.5386 −2.26041
\(372\) 0 0
\(373\) −0.794590 −0.0411423 −0.0205712 0.999788i \(-0.506548\pi\)
−0.0205712 + 0.999788i \(0.506548\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 0.677272i − 0.0348813i
\(378\) 0 0
\(379\) 21.8205i 1.12084i 0.828208 + 0.560421i \(0.189361\pi\)
−0.828208 + 0.560421i \(0.810639\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16.7665 0.856726 0.428363 0.903607i \(-0.359090\pi\)
0.428363 + 0.903607i \(0.359090\pi\)
\(384\) 0 0
\(385\) 53.3539 2.71917
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 23.9686i − 1.21526i −0.794222 0.607628i \(-0.792121\pi\)
0.794222 0.607628i \(-0.207879\pi\)
\(390\) 0 0
\(391\) 5.82863i 0.294767i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −41.4953 −2.08785
\(396\) 0 0
\(397\) 36.1837 1.81601 0.908005 0.418960i \(-0.137605\pi\)
0.908005 + 0.418960i \(0.137605\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 20.7958i 1.03849i 0.854625 + 0.519246i \(0.173787\pi\)
−0.854625 + 0.519246i \(0.826213\pi\)
\(402\) 0 0
\(403\) − 6.27465i − 0.312563i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 38.2204 1.89451
\(408\) 0 0
\(409\) −15.6162 −0.772173 −0.386086 0.922463i \(-0.626173\pi\)
−0.386086 + 0.922463i \(0.626173\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 37.4086i 1.84076i
\(414\) 0 0
\(415\) 13.1021i 0.643158i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −17.2419 −0.842323 −0.421162 0.906986i \(-0.638378\pi\)
−0.421162 + 0.906986i \(0.638378\pi\)
\(420\) 0 0
\(421\) 26.9308 1.31252 0.656262 0.754533i \(-0.272136\pi\)
0.656262 + 0.754533i \(0.272136\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 12.1469i − 0.589213i
\(426\) 0 0
\(427\) − 9.46538i − 0.458062i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11.1676 −0.537926 −0.268963 0.963150i \(-0.586681\pi\)
−0.268963 + 0.963150i \(0.586681\pi\)
\(432\) 0 0
\(433\) −34.7512 −1.67004 −0.835019 0.550221i \(-0.814543\pi\)
−0.835019 + 0.550221i \(0.814543\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 3.68078i − 0.176076i
\(438\) 0 0
\(439\) − 29.3416i − 1.40040i −0.713948 0.700199i \(-0.753095\pi\)
0.713948 0.700199i \(-0.246905\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −37.5489 −1.78400 −0.892000 0.452035i \(-0.850698\pi\)
−0.892000 + 0.452035i \(0.850698\pi\)
\(444\) 0 0
\(445\) −24.2043 −1.14739
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 18.5483i − 0.875350i −0.899133 0.437675i \(-0.855802\pi\)
0.899133 0.437675i \(-0.144198\pi\)
\(450\) 0 0
\(451\) 15.3686i 0.723680i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −15.6045 −0.731550
\(456\) 0 0
\(457\) −28.4994 −1.33315 −0.666573 0.745439i \(-0.732240\pi\)
−0.666573 + 0.745439i \(0.732240\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16.7033i 0.777951i 0.921248 + 0.388976i \(0.127171\pi\)
−0.921248 + 0.388976i \(0.872829\pi\)
\(462\) 0 0
\(463\) − 13.6015i − 0.632117i −0.948740 0.316059i \(-0.897640\pi\)
0.948740 0.316059i \(-0.102360\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.5264 0.625926 0.312963 0.949765i \(-0.398678\pi\)
0.312963 + 0.949765i \(0.398678\pi\)
\(468\) 0 0
\(469\) −7.52110 −0.347292
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 39.0112i − 1.79374i
\(474\) 0 0
\(475\) 7.67079i 0.351960i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −13.9671 −0.638171 −0.319085 0.947726i \(-0.603376\pi\)
−0.319085 + 0.947726i \(0.603376\pi\)
\(480\) 0 0
\(481\) −11.1784 −0.509689
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 31.5476i 1.43250i
\(486\) 0 0
\(487\) 35.7934i 1.62196i 0.585077 + 0.810978i \(0.301064\pi\)
−0.585077 + 0.810978i \(0.698936\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.4549 0.562083 0.281041 0.959696i \(-0.409320\pi\)
0.281041 + 0.959696i \(0.409320\pi\)
\(492\) 0 0
\(493\) −0.889723 −0.0400711
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 26.7721i − 1.20089i
\(498\) 0 0
\(499\) − 24.4584i − 1.09491i −0.836836 0.547454i \(-0.815597\pi\)
0.836836 0.547454i \(-0.184403\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21.3286 −0.950996 −0.475498 0.879717i \(-0.657732\pi\)
−0.475498 + 0.879717i \(0.657732\pi\)
\(504\) 0 0
\(505\) −55.7172 −2.47938
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 41.4761i − 1.83840i −0.393794 0.919199i \(-0.628838\pi\)
0.393794 0.919199i \(-0.371162\pi\)
\(510\) 0 0
\(511\) 1.32106i 0.0584403i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −62.9492 −2.77387
\(516\) 0 0
\(517\) 26.1296 1.14918
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16.8436i 0.737933i 0.929443 + 0.368966i \(0.120288\pi\)
−0.929443 + 0.368966i \(0.879712\pi\)
\(522\) 0 0
\(523\) − 8.09513i − 0.353975i −0.984213 0.176988i \(-0.943365\pi\)
0.984213 0.176988i \(-0.0566353\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.24293 −0.359068
\(528\) 0 0
\(529\) −9.45185 −0.410950
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 4.49488i − 0.194695i
\(534\) 0 0
\(535\) 29.3416i 1.26855i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −25.6599 −1.10525
\(540\) 0 0
\(541\) −45.6344 −1.96198 −0.980989 0.194065i \(-0.937833\pi\)
−0.980989 + 0.194065i \(0.937833\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 51.7815i 2.21808i
\(546\) 0 0
\(547\) − 14.7946i − 0.632571i −0.948664 0.316285i \(-0.897564\pi\)
0.948664 0.316285i \(-0.102436\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.561860 0.0239360
\(552\) 0 0
\(553\) 42.3945 1.80280
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 34.4682i 1.46046i 0.683199 + 0.730232i \(0.260588\pi\)
−0.683199 + 0.730232i \(0.739412\pi\)
\(558\) 0 0
\(559\) 11.4097i 0.482577i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.43685 −0.186991 −0.0934955 0.995620i \(-0.529804\pi\)
−0.0934955 + 0.995620i \(0.529804\pi\)
\(564\) 0 0
\(565\) 14.1362 0.594713
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.6407i 1.36837i 0.729309 + 0.684184i \(0.239842\pi\)
−0.729309 + 0.684184i \(0.760158\pi\)
\(570\) 0 0
\(571\) 8.51994i 0.356548i 0.983981 + 0.178274i \(0.0570514\pi\)
−0.983981 + 0.178274i \(0.942949\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −28.2345 −1.17746
\(576\) 0 0
\(577\) 14.6027 0.607919 0.303959 0.952685i \(-0.401691\pi\)
0.303959 + 0.952685i \(0.401691\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 13.3861i − 0.555348i
\(582\) 0 0
\(583\) − 49.3416i − 2.04352i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −38.2552 −1.57896 −0.789480 0.613777i \(-0.789650\pi\)
−0.789480 + 0.613777i \(0.789650\pi\)
\(588\) 0 0
\(589\) 5.20541 0.214485
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 30.9185i − 1.26967i −0.772648 0.634835i \(-0.781068\pi\)
0.772648 0.634835i \(-0.218932\pi\)
\(594\) 0 0
\(595\) 20.4994i 0.840394i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.36156 −0.300785 −0.150393 0.988626i \(-0.548054\pi\)
−0.150393 + 0.988626i \(0.548054\pi\)
\(600\) 0 0
\(601\) −13.8886 −0.566526 −0.283263 0.959042i \(-0.591417\pi\)
−0.283263 + 0.959042i \(0.591417\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 21.3095i 0.866354i
\(606\) 0 0
\(607\) 1.06924i 0.0433992i 0.999765 + 0.0216996i \(0.00690774\pi\)
−0.999765 + 0.0216996i \(0.993092\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.64217 −0.309169
\(612\) 0 0
\(613\) −6.35510 −0.256680 −0.128340 0.991730i \(-0.540965\pi\)
−0.128340 + 0.991730i \(0.540965\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.8025i 0.475152i 0.971369 + 0.237576i \(0.0763529\pi\)
−0.971369 + 0.237576i \(0.923647\pi\)
\(618\) 0 0
\(619\) − 15.8638i − 0.637621i −0.947818 0.318811i \(-0.896717\pi\)
0.947818 0.318811i \(-0.103283\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 24.7288 0.990738
\(624\) 0 0
\(625\) −4.51295 −0.180518
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 14.6849i 0.585524i
\(630\) 0 0
\(631\) − 37.3621i − 1.48736i −0.668535 0.743681i \(-0.733078\pi\)
0.668535 0.743681i \(-0.266922\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −60.0245 −2.38200
\(636\) 0 0
\(637\) 7.50479 0.297351
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 24.3513i 0.961817i 0.876771 + 0.480908i \(0.159693\pi\)
−0.876771 + 0.480908i \(0.840307\pi\)
\(642\) 0 0
\(643\) 15.4924i 0.610962i 0.952198 + 0.305481i \(0.0988172\pi\)
−0.952198 + 0.305481i \(0.901183\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.5320 0.925140 0.462570 0.886583i \(-0.346927\pi\)
0.462570 + 0.886583i \(0.346927\pi\)
\(648\) 0 0
\(649\) −42.3945 −1.66413
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 22.4772i − 0.879602i −0.898095 0.439801i \(-0.855049\pi\)
0.898095 0.439801i \(-0.144951\pi\)
\(654\) 0 0
\(655\) 29.8410i 1.16598i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24.3786 0.949656 0.474828 0.880078i \(-0.342510\pi\)
0.474828 + 0.880078i \(0.342510\pi\)
\(660\) 0 0
\(661\) −8.93076 −0.347366 −0.173683 0.984802i \(-0.555567\pi\)
−0.173683 + 0.984802i \(0.555567\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 12.9454i − 0.502000i
\(666\) 0 0
\(667\) 2.06808i 0.0800765i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.7270 0.414110
\(672\) 0 0
\(673\) 23.3416 0.899752 0.449876 0.893091i \(-0.351468\pi\)
0.449876 + 0.893091i \(0.351468\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 17.6670i − 0.678996i −0.940607 0.339498i \(-0.889743\pi\)
0.940607 0.339498i \(-0.110257\pi\)
\(678\) 0 0
\(679\) − 32.2313i − 1.23692i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −36.5272 −1.39767 −0.698837 0.715281i \(-0.746299\pi\)
−0.698837 + 0.715281i \(0.746299\pi\)
\(684\) 0 0
\(685\) −5.74003 −0.219315
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 14.4310i 0.549777i
\(690\) 0 0
\(691\) − 34.6708i − 1.31894i −0.751731 0.659469i \(-0.770781\pi\)
0.751731 0.659469i \(-0.229219\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.9454 −0.491046
\(696\) 0 0
\(697\) −5.90487 −0.223663
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 26.7738i − 1.01123i −0.862759 0.505616i \(-0.831265\pi\)
0.862759 0.505616i \(-0.168735\pi\)
\(702\) 0 0
\(703\) − 9.27349i − 0.349756i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 56.9247 2.14087
\(708\) 0 0
\(709\) −17.5481 −0.659034 −0.329517 0.944150i \(-0.606886\pi\)
−0.329517 + 0.944150i \(0.606886\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 19.1600i 0.717547i
\(714\) 0 0
\(715\) − 17.6843i − 0.661356i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −23.5320 −0.877597 −0.438798 0.898586i \(-0.644596\pi\)
−0.438798 + 0.898586i \(0.644596\pi\)
\(720\) 0 0
\(721\) 64.3134 2.39516
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 4.30991i − 0.160066i
\(726\) 0 0
\(727\) − 15.4924i − 0.574582i −0.957843 0.287291i \(-0.907245\pi\)
0.957843 0.287291i \(-0.0927547\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 14.9887 0.554378
\(732\) 0 0
\(733\) −3.27349 −0.120909 −0.0604546 0.998171i \(-0.519255\pi\)
−0.0604546 + 0.998171i \(0.519255\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 8.52353i − 0.313968i
\(738\) 0 0
\(739\) − 0.499421i − 0.0183715i −0.999958 0.00918574i \(-0.997076\pi\)
0.999958 0.00918574i \(-0.00292395\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.6364 −0.390213 −0.195107 0.980782i \(-0.562505\pi\)
−0.195107 + 0.980782i \(0.562505\pi\)
\(744\) 0 0
\(745\) −2.49942 −0.0915717
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 29.9775i − 1.09535i
\(750\) 0 0
\(751\) 20.8216i 0.759792i 0.925029 + 0.379896i \(0.124040\pi\)
−0.925029 + 0.379896i \(0.875960\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −8.12380 −0.295265 −0.147632 0.989042i \(-0.547165\pi\)
−0.147632 + 0.989042i \(0.547165\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.9151i 0.649421i 0.945813 + 0.324710i \(0.105267\pi\)
−0.945813 + 0.324710i \(0.894733\pi\)
\(762\) 0 0
\(763\) − 52.9037i − 1.91524i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.3992 0.447708
\(768\) 0 0
\(769\) 10.3010 0.371464 0.185732 0.982600i \(-0.440534\pi\)
0.185732 + 0.982600i \(0.440534\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.7844i 0.495789i 0.968787 + 0.247895i \(0.0797387\pi\)
−0.968787 + 0.247895i \(0.920261\pi\)
\(774\) 0 0
\(775\) − 39.9296i − 1.43431i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.72892 0.133603
\(780\) 0 0
\(781\) 30.3404 1.08567
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 52.9052i 1.88827i
\(786\) 0 0
\(787\) 42.0681i 1.49957i 0.661684 + 0.749783i \(0.269842\pi\)
−0.661684 + 0.749783i \(0.730158\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14.4425 −0.513517
\(792\) 0 0
\(793\) −3.13733 −0.111410
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 48.1106i − 1.70417i −0.523407 0.852083i \(-0.675339\pi\)
0.523407 0.852083i \(-0.324661\pi\)
\(798\) 0 0
\(799\) 10.0394i 0.355169i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.49714 −0.0528328
\(804\) 0 0
\(805\) 47.6491 1.67941
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8.64471i 0.303932i 0.988386 + 0.151966i \(0.0485604\pi\)
−0.988386 + 0.151966i \(0.951440\pi\)
\(810\) 0 0
\(811\) − 30.5880i − 1.07409i −0.843553 0.537045i \(-0.819540\pi\)
0.843553 0.537045i \(-0.180460\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 48.8568 1.71138
\(816\) 0 0
\(817\) −9.46538 −0.331152
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 10.3784i 0.362210i 0.983464 + 0.181105i \(0.0579674\pi\)
−0.983464 + 0.181105i \(0.942033\pi\)
\(822\) 0 0
\(823\) − 3.63675i − 0.126769i −0.997989 0.0633845i \(-0.979811\pi\)
0.997989 0.0633845i \(-0.0201895\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 8.52353 0.296392 0.148196 0.988958i \(-0.452653\pi\)
0.148196 + 0.988958i \(0.452653\pi\)
\(828\) 0 0
\(829\) 22.0681 0.766456 0.383228 0.923654i \(-0.374812\pi\)
0.383228 + 0.923654i \(0.374812\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 9.85895i − 0.341592i
\(834\) 0 0
\(835\) − 76.3675i − 2.64281i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −54.1750 −1.87033 −0.935165 0.354212i \(-0.884749\pi\)
−0.935165 + 0.354212i \(0.884749\pi\)
\(840\) 0 0
\(841\) 28.6843 0.989114
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 41.1027i − 1.41398i
\(846\) 0 0
\(847\) − 21.7713i − 0.748071i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 34.1337 1.17009
\(852\) 0 0
\(853\) 25.2325 0.863943 0.431971 0.901887i \(-0.357818\pi\)
0.431971 + 0.901887i \(0.357818\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 22.9852i − 0.785159i −0.919718 0.392579i \(-0.871583\pi\)
0.919718 0.392579i \(-0.128417\pi\)
\(858\) 0 0
\(859\) − 6.12964i − 0.209140i −0.994518 0.104570i \(-0.966653\pi\)
0.994518 0.104570i \(-0.0333467\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 16.4859 0.561185 0.280593 0.959827i \(-0.409469\pi\)
0.280593 + 0.959827i \(0.409469\pi\)
\(864\) 0 0
\(865\) −74.8874 −2.54625
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 48.0450i 1.62982i
\(870\) 0 0
\(871\) 2.49289i 0.0844683i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −34.5744 −1.16883
\(876\) 0 0
\(877\) −12.9718 −0.438026 −0.219013 0.975722i \(-0.570284\pi\)
−0.219013 + 0.975722i \(0.570284\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 1.11960i − 0.0377201i −0.999822 0.0188601i \(-0.993996\pi\)
0.999822 0.0188601i \(-0.00600370\pi\)
\(882\) 0 0
\(883\) − 25.4572i − 0.856704i −0.903612 0.428352i \(-0.859094\pi\)
0.903612 0.428352i \(-0.140906\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 30.0470 1.00888 0.504440 0.863447i \(-0.331699\pi\)
0.504440 + 0.863447i \(0.331699\pi\)
\(888\) 0 0
\(889\) 61.3253 2.05678
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 6.33989i − 0.212156i
\(894\) 0 0
\(895\) 65.9566i 2.20469i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.92471 −0.0975446
\(900\) 0 0
\(901\) 18.9578 0.631576
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 67.3860i − 2.23999i
\(906\) 0 0
\(907\) − 54.7242i − 1.81709i −0.417790 0.908543i \(-0.637195\pi\)
0.417790 0.908543i \(-0.362805\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 39.4519 1.30710 0.653550 0.756883i \(-0.273279\pi\)
0.653550 + 0.756883i \(0.273279\pi\)
\(912\) 0 0
\(913\) 15.1702 0.502061
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 30.4877i − 1.00679i
\(918\) 0 0
\(919\) − 9.58918i − 0.316318i −0.987414 0.158159i \(-0.949444\pi\)
0.987414 0.158159i \(-0.0505558\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −8.87370 −0.292081
\(924\) 0 0
\(925\) −71.1350 −2.33890
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 21.1169i − 0.692824i −0.938083 0.346412i \(-0.887400\pi\)
0.938083 0.346412i \(-0.112600\pi\)
\(930\) 0 0
\(931\) 6.22593i 0.204047i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −23.2317 −0.759756
\(936\) 0 0
\(937\) −40.1837 −1.31275 −0.656373 0.754437i \(-0.727910\pi\)
−0.656373 + 0.754437i \(0.727910\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 9.78244i − 0.318899i −0.987206 0.159449i \(-0.949028\pi\)
0.987206 0.159449i \(-0.0509718\pi\)
\(942\) 0 0
\(943\) 13.7253i 0.446959i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −16.8918 −0.548909 −0.274454 0.961600i \(-0.588497\pi\)
−0.274454 + 0.961600i \(0.588497\pi\)
\(948\) 0 0
\(949\) 0.437869 0.0142138
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 16.3009i 0.528038i 0.964518 + 0.264019i \(0.0850481\pi\)
−0.964518 + 0.264019i \(0.914952\pi\)
\(954\) 0 0
\(955\) 95.7976i 3.09994i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 5.86443 0.189372
\(960\) 0 0
\(961\) 3.90371 0.125926
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 44.3237i − 1.42683i
\(966\) 0 0
\(967\) 11.2325i 0.361212i 0.983556 + 0.180606i \(0.0578058\pi\)
−0.983556 + 0.180606i \(0.942194\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 25.6102 0.821869 0.410935 0.911665i \(-0.365202\pi\)
0.410935 + 0.911665i \(0.365202\pi\)
\(972\) 0 0
\(973\) 13.2259 0.424004
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 24.6401i 0.788307i 0.919045 + 0.394153i \(0.128962\pi\)
−0.919045 + 0.394153i \(0.871038\pi\)
\(978\) 0 0
\(979\) 28.0247i 0.895674i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.92471 −0.0932838 −0.0466419 0.998912i \(-0.514852\pi\)
−0.0466419 + 0.998912i \(0.514852\pi\)
\(984\) 0 0
\(985\) −35.5810 −1.13371
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 34.8400i − 1.10785i
\(990\) 0 0
\(991\) 2.06808i 0.0656948i 0.999460 + 0.0328474i \(0.0104575\pi\)
−0.999460 + 0.0328474i \(0.989542\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 85.4745 2.70973
\(996\) 0 0
\(997\) 19.8081 0.627329 0.313665 0.949534i \(-0.398443\pi\)
0.313665 + 0.949534i \(0.398443\pi\)
\(998\) 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 2736.2.d.a.2015.11 yes 12
3.2 odd 2 inner 2736.2.d.a.2015.1 12
4.3 odd 2 inner 2736.2.d.a.2015.12 yes 12
12.11 even 2 inner 2736.2.d.a.2015.2 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.d.a.2015.1 12 3.2 odd 2 inner
2736.2.d.a.2015.2 yes 12 12.11 even 2 inner
2736.2.d.a.2015.11 yes 12 1.1 even 1 trivial
2736.2.d.a.2015.12 yes 12 4.3 odd 2 inner