Properties

Label 2736.2.d.b.2015.4
Level $2736$
Weight $2$
Character 2736.2015
Analytic conductor $21.847$
Analytic rank $0$
Dimension $24$
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: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2015.4
Character \(\chi\) \(=\) 2736.2015
Dual form 2736.2.d.b.2015.21

$q$-expansion

\(f(q)\) \(=\) \(q-2.62670i q^{5} +0.815178i q^{7} +O(q^{10})\) \(q-2.62670i q^{5} +0.815178i q^{7} +2.98902 q^{11} -1.44280 q^{13} +8.05095i q^{17} -1.00000i q^{19} +2.16106 q^{23} -1.89953 q^{25} +9.88713i q^{29} +10.1936i q^{31} +2.14122 q^{35} -7.24187 q^{37} -3.87898i q^{41} -11.2492i q^{43} +12.5575 q^{47} +6.33549 q^{49} +8.04858i q^{53} -7.85124i q^{55} -9.48367 q^{59} +4.22088 q^{61} +3.78981i q^{65} -11.4294i q^{67} -4.11099 q^{71} +12.1166 q^{73} +2.43658i q^{77} +15.4488i q^{79} -0.745515 q^{83} +21.1474 q^{85} +6.82012i q^{89} -1.17614i q^{91} -2.62670 q^{95} -0.975205 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + O(q^{10}) \) \( 24q + 8q^{25} - 32q^{37} - 32q^{49} + 8q^{73} + 40q^{85} + 16q^{97} + O(q^{100}) \)

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
\(5\) − 2.62670i − 1.17469i −0.809335 0.587347i \(-0.800172\pi\)
0.809335 0.587347i \(-0.199828\pi\)
\(6\) 0 0
\(7\) 0.815178i 0.308108i 0.988062 + 0.154054i \(0.0492330\pi\)
−0.988062 + 0.154054i \(0.950767\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.98902 0.901222 0.450611 0.892720i \(-0.351206\pi\)
0.450611 + 0.892720i \(0.351206\pi\)
\(12\) 0 0
\(13\) −1.44280 −0.400162 −0.200081 0.979779i \(-0.564121\pi\)
−0.200081 + 0.979779i \(0.564121\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 8.05095i 1.95264i 0.216324 + 0.976322i \(0.430593\pi\)
−0.216324 + 0.976322i \(0.569407\pi\)
\(18\) 0 0
\(19\) − 1.00000i − 0.229416i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.16106 0.450613 0.225307 0.974288i \(-0.427662\pi\)
0.225307 + 0.974288i \(0.427662\pi\)
\(24\) 0 0
\(25\) −1.89953 −0.379906
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.88713i 1.83599i 0.396586 + 0.917997i \(0.370195\pi\)
−0.396586 + 0.917997i \(0.629805\pi\)
\(30\) 0 0
\(31\) 10.1936i 1.83082i 0.402523 + 0.915410i \(0.368133\pi\)
−0.402523 + 0.915410i \(0.631867\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.14122 0.361933
\(36\) 0 0
\(37\) −7.24187 −1.19056 −0.595278 0.803520i \(-0.702958\pi\)
−0.595278 + 0.803520i \(0.702958\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 3.87898i − 0.605796i −0.953023 0.302898i \(-0.902046\pi\)
0.953023 0.302898i \(-0.0979541\pi\)
\(42\) 0 0
\(43\) − 11.2492i − 1.71549i −0.514073 0.857747i \(-0.671864\pi\)
0.514073 0.857747i \(-0.328136\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.5575 1.83170 0.915849 0.401522i \(-0.131519\pi\)
0.915849 + 0.401522i \(0.131519\pi\)
\(48\) 0 0
\(49\) 6.33549 0.905069
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.04858i 1.10556i 0.833328 + 0.552779i \(0.186433\pi\)
−0.833328 + 0.552779i \(0.813567\pi\)
\(54\) 0 0
\(55\) − 7.85124i − 1.05866i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.48367 −1.23467 −0.617334 0.786701i \(-0.711787\pi\)
−0.617334 + 0.786701i \(0.711787\pi\)
\(60\) 0 0
\(61\) 4.22088 0.540428 0.270214 0.962800i \(-0.412905\pi\)
0.270214 + 0.962800i \(0.412905\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.78981i 0.470068i
\(66\) 0 0
\(67\) − 11.4294i − 1.39633i −0.715939 0.698163i \(-0.754001\pi\)
0.715939 0.698163i \(-0.245999\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.11099 −0.487884 −0.243942 0.969790i \(-0.578441\pi\)
−0.243942 + 0.969790i \(0.578441\pi\)
\(72\) 0 0
\(73\) 12.1166 1.41814 0.709070 0.705138i \(-0.249115\pi\)
0.709070 + 0.705138i \(0.249115\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.43658i 0.277674i
\(78\) 0 0
\(79\) 15.4488i 1.73813i 0.494699 + 0.869064i \(0.335278\pi\)
−0.494699 + 0.869064i \(0.664722\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.745515 −0.0818309 −0.0409154 0.999163i \(-0.513027\pi\)
−0.0409154 + 0.999163i \(0.513027\pi\)
\(84\) 0 0
\(85\) 21.1474 2.29376
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.82012i 0.722931i 0.932385 + 0.361466i \(0.117724\pi\)
−0.932385 + 0.361466i \(0.882276\pi\)
\(90\) 0 0
\(91\) − 1.17614i − 0.123293i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.62670 −0.269493
\(96\) 0 0
\(97\) −0.975205 −0.0990170 −0.0495085 0.998774i \(-0.515765\pi\)
−0.0495085 + 0.998774i \(0.515765\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.91044i 0.389103i 0.980892 + 0.194552i \(0.0623252\pi\)
−0.980892 + 0.194552i \(0.937675\pi\)
\(102\) 0 0
\(103\) − 9.64976i − 0.950819i −0.879765 0.475410i \(-0.842300\pi\)
0.879765 0.475410i \(-0.157700\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.6478 1.70607 0.853037 0.521850i \(-0.174758\pi\)
0.853037 + 0.521850i \(0.174758\pi\)
\(108\) 0 0
\(109\) 5.17205 0.495392 0.247696 0.968838i \(-0.420327\pi\)
0.247696 + 0.968838i \(0.420327\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 7.02859i − 0.661194i −0.943772 0.330597i \(-0.892750\pi\)
0.943772 0.330597i \(-0.107250\pi\)
\(114\) 0 0
\(115\) − 5.67646i − 0.529332i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.56296 −0.601625
\(120\) 0 0
\(121\) −2.06578 −0.187799
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 8.14399i − 0.728420i
\(126\) 0 0
\(127\) 9.16207i 0.813002i 0.913650 + 0.406501i \(0.133251\pi\)
−0.913650 + 0.406501i \(0.866749\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.31020 0.376584 0.188292 0.982113i \(-0.439705\pi\)
0.188292 + 0.982113i \(0.439705\pi\)
\(132\) 0 0
\(133\) 0.815178 0.0706849
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.1028i 1.20488i 0.798164 + 0.602440i \(0.205805\pi\)
−0.798164 + 0.602440i \(0.794195\pi\)
\(138\) 0 0
\(139\) − 16.9257i − 1.43562i −0.696239 0.717810i \(-0.745145\pi\)
0.696239 0.717810i \(-0.254855\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.31257 −0.360635
\(144\) 0 0
\(145\) 25.9705 2.15673
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 4.94464i − 0.405081i −0.979274 0.202540i \(-0.935080\pi\)
0.979274 0.202540i \(-0.0649198\pi\)
\(150\) 0 0
\(151\) − 18.8312i − 1.53246i −0.642564 0.766232i \(-0.722129\pi\)
0.642564 0.766232i \(-0.277871\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 26.7754 2.15065
\(156\) 0 0
\(157\) 0.840497 0.0670790 0.0335395 0.999437i \(-0.489322\pi\)
0.0335395 + 0.999437i \(0.489322\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.76165i 0.138838i
\(162\) 0 0
\(163\) 16.9323i 1.32624i 0.748512 + 0.663121i \(0.230769\pi\)
−0.748512 + 0.663121i \(0.769231\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.59532 0.665126 0.332563 0.943081i \(-0.392087\pi\)
0.332563 + 0.943081i \(0.392087\pi\)
\(168\) 0 0
\(169\) −10.9183 −0.839870
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 14.1459i 1.07549i 0.843106 + 0.537747i \(0.180724\pi\)
−0.843106 + 0.537747i \(0.819276\pi\)
\(174\) 0 0
\(175\) − 1.54846i − 0.117052i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.62685 −0.196340 −0.0981699 0.995170i \(-0.531299\pi\)
−0.0981699 + 0.995170i \(0.531299\pi\)
\(180\) 0 0
\(181\) 8.58001 0.637747 0.318874 0.947797i \(-0.396695\pi\)
0.318874 + 0.947797i \(0.396695\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 19.0222i 1.39854i
\(186\) 0 0
\(187\) 24.0644i 1.75977i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.11622 0.153124 0.0765620 0.997065i \(-0.475606\pi\)
0.0765620 + 0.997065i \(0.475606\pi\)
\(192\) 0 0
\(193\) 5.89795 0.424544 0.212272 0.977211i \(-0.431914\pi\)
0.212272 + 0.977211i \(0.431914\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.6364i 1.11405i 0.830496 + 0.557025i \(0.188057\pi\)
−0.830496 + 0.557025i \(0.811943\pi\)
\(198\) 0 0
\(199\) 12.5687i 0.890972i 0.895289 + 0.445486i \(0.146969\pi\)
−0.895289 + 0.445486i \(0.853031\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.05977 −0.565685
\(204\) 0 0
\(205\) −10.1889 −0.711625
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 2.98902i − 0.206755i
\(210\) 0 0
\(211\) − 23.7537i − 1.63527i −0.575734 0.817637i \(-0.695283\pi\)
0.575734 0.817637i \(-0.304717\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −29.5483 −2.01518
\(216\) 0 0
\(217\) −8.30957 −0.564090
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 11.6160i − 0.781374i
\(222\) 0 0
\(223\) − 3.35923i − 0.224951i −0.993655 0.112475i \(-0.964122\pi\)
0.993655 0.112475i \(-0.0358779\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.95039 0.195824 0.0979122 0.995195i \(-0.468784\pi\)
0.0979122 + 0.995195i \(0.468784\pi\)
\(228\) 0 0
\(229\) −12.8160 −0.846902 −0.423451 0.905919i \(-0.639181\pi\)
−0.423451 + 0.905919i \(0.639181\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 19.5210i 1.27886i 0.768849 + 0.639431i \(0.220830\pi\)
−0.768849 + 0.639431i \(0.779170\pi\)
\(234\) 0 0
\(235\) − 32.9847i − 2.15169i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 19.7166 1.27536 0.637679 0.770302i \(-0.279895\pi\)
0.637679 + 0.770302i \(0.279895\pi\)
\(240\) 0 0
\(241\) −4.12716 −0.265854 −0.132927 0.991126i \(-0.542438\pi\)
−0.132927 + 0.991126i \(0.542438\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 16.6414i − 1.06318i
\(246\) 0 0
\(247\) 1.44280i 0.0918035i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 21.9478 1.38534 0.692668 0.721257i \(-0.256435\pi\)
0.692668 + 0.721257i \(0.256435\pi\)
\(252\) 0 0
\(253\) 6.45945 0.406102
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 11.6748i − 0.728253i −0.931349 0.364127i \(-0.881368\pi\)
0.931349 0.364127i \(-0.118632\pi\)
\(258\) 0 0
\(259\) − 5.90341i − 0.366820i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.65873 −0.102281 −0.0511407 0.998691i \(-0.516286\pi\)
−0.0511407 + 0.998691i \(0.516286\pi\)
\(264\) 0 0
\(265\) 21.1412 1.29869
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 13.7028i 0.835472i 0.908568 + 0.417736i \(0.137176\pi\)
−0.908568 + 0.417736i \(0.862824\pi\)
\(270\) 0 0
\(271\) − 17.9008i − 1.08740i −0.839280 0.543699i \(-0.817023\pi\)
0.839280 0.543699i \(-0.182977\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.67773 −0.342380
\(276\) 0 0
\(277\) 23.0519 1.38505 0.692526 0.721393i \(-0.256498\pi\)
0.692526 + 0.721393i \(0.256498\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 8.20853i − 0.489680i −0.969564 0.244840i \(-0.921265\pi\)
0.969564 0.244840i \(-0.0787354\pi\)
\(282\) 0 0
\(283\) 13.1878i 0.783932i 0.919980 + 0.391966i \(0.128205\pi\)
−0.919980 + 0.391966i \(0.871795\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.16206 0.186651
\(288\) 0 0
\(289\) −47.8179 −2.81282
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 0.489522i − 0.0285982i −0.999898 0.0142991i \(-0.995448\pi\)
0.999898 0.0142991i \(-0.00455169\pi\)
\(294\) 0 0
\(295\) 24.9107i 1.45036i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.11799 −0.180318
\(300\) 0 0
\(301\) 9.17013 0.528558
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 11.0870i − 0.634838i
\(306\) 0 0
\(307\) 8.90843i 0.508431i 0.967148 + 0.254215i \(0.0818172\pi\)
−0.967148 + 0.254215i \(0.918183\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6.96237 −0.394800 −0.197400 0.980323i \(-0.563250\pi\)
−0.197400 + 0.980323i \(0.563250\pi\)
\(312\) 0 0
\(313\) −22.8625 −1.29227 −0.646133 0.763225i \(-0.723615\pi\)
−0.646133 + 0.763225i \(0.723615\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.9416i 1.40086i 0.713721 + 0.700430i \(0.247008\pi\)
−0.713721 + 0.700430i \(0.752992\pi\)
\(318\) 0 0
\(319\) 29.5528i 1.65464i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.05095 0.447967
\(324\) 0 0
\(325\) 2.74065 0.152024
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.2366i 0.564361i
\(330\) 0 0
\(331\) 1.69211i 0.0930066i 0.998918 + 0.0465033i \(0.0148078\pi\)
−0.998918 + 0.0465033i \(0.985192\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −30.0216 −1.64026
\(336\) 0 0
\(337\) −20.1584 −1.09810 −0.549048 0.835791i \(-0.685010\pi\)
−0.549048 + 0.835791i \(0.685010\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 30.4687i 1.64998i
\(342\) 0 0
\(343\) 10.8708i 0.586967i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.673741 0.0361683 0.0180842 0.999836i \(-0.494243\pi\)
0.0180842 + 0.999836i \(0.494243\pi\)
\(348\) 0 0
\(349\) −27.4224 −1.46788 −0.733942 0.679212i \(-0.762322\pi\)
−0.733942 + 0.679212i \(0.762322\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 9.57862i − 0.509819i −0.966965 0.254909i \(-0.917954\pi\)
0.966965 0.254909i \(-0.0820456\pi\)
\(354\) 0 0
\(355\) 10.7983i 0.573115i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.7692 0.990598 0.495299 0.868723i \(-0.335059\pi\)
0.495299 + 0.868723i \(0.335059\pi\)
\(360\) 0 0
\(361\) −1.00000 −0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 31.8266i − 1.66588i
\(366\) 0 0
\(367\) 31.3903i 1.63856i 0.573392 + 0.819281i \(0.305627\pi\)
−0.573392 + 0.819281i \(0.694373\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.56103 −0.340631
\(372\) 0 0
\(373\) −26.7527 −1.38520 −0.692601 0.721321i \(-0.743535\pi\)
−0.692601 + 0.721321i \(0.743535\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 14.2652i − 0.734695i
\(378\) 0 0
\(379\) − 17.6222i − 0.905190i −0.891716 0.452595i \(-0.850498\pi\)
0.891716 0.452595i \(-0.149502\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.04666 −0.411165 −0.205582 0.978640i \(-0.565909\pi\)
−0.205582 + 0.978640i \(0.565909\pi\)
\(384\) 0 0
\(385\) 6.40015 0.326182
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 28.7529i − 1.45783i −0.684605 0.728914i \(-0.740025\pi\)
0.684605 0.728914i \(-0.259975\pi\)
\(390\) 0 0
\(391\) 17.3986i 0.879886i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 40.5794 2.04177
\(396\) 0 0
\(397\) 5.56594 0.279347 0.139673 0.990198i \(-0.455395\pi\)
0.139673 + 0.990198i \(0.455395\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 28.1170i 1.40410i 0.712129 + 0.702049i \(0.247731\pi\)
−0.712129 + 0.702049i \(0.752269\pi\)
\(402\) 0 0
\(403\) − 14.7073i − 0.732624i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −21.6461 −1.07296
\(408\) 0 0
\(409\) 18.8681 0.932969 0.466484 0.884529i \(-0.345520\pi\)
0.466484 + 0.884529i \(0.345520\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 7.73088i − 0.380412i
\(414\) 0 0
\(415\) 1.95824i 0.0961262i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.59047 −0.224259 −0.112129 0.993694i \(-0.535767\pi\)
−0.112129 + 0.993694i \(0.535767\pi\)
\(420\) 0 0
\(421\) −4.44038 −0.216411 −0.108205 0.994129i \(-0.534510\pi\)
−0.108205 + 0.994129i \(0.534510\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 15.2930i − 0.741821i
\(426\) 0 0
\(427\) 3.44077i 0.166510i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −28.0492 −1.35108 −0.675542 0.737321i \(-0.736090\pi\)
−0.675542 + 0.737321i \(0.736090\pi\)
\(432\) 0 0
\(433\) 34.3499 1.65075 0.825375 0.564585i \(-0.190964\pi\)
0.825375 + 0.564585i \(0.190964\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 2.16106i − 0.103378i
\(438\) 0 0
\(439\) − 15.6394i − 0.746429i −0.927745 0.373214i \(-0.878256\pi\)
0.927745 0.373214i \(-0.121744\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.9846 0.806961 0.403481 0.914988i \(-0.367800\pi\)
0.403481 + 0.914988i \(0.367800\pi\)
\(444\) 0 0
\(445\) 17.9144 0.849223
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 18.0721i − 0.852875i −0.904517 0.426438i \(-0.859768\pi\)
0.904517 0.426438i \(-0.140232\pi\)
\(450\) 0 0
\(451\) − 11.5943i − 0.545956i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.08937 −0.144832
\(456\) 0 0
\(457\) 21.7270 1.01635 0.508174 0.861254i \(-0.330321\pi\)
0.508174 + 0.861254i \(0.330321\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 30.8407i − 1.43640i −0.695839 0.718198i \(-0.744967\pi\)
0.695839 0.718198i \(-0.255033\pi\)
\(462\) 0 0
\(463\) − 13.7137i − 0.637328i −0.947868 0.318664i \(-0.896766\pi\)
0.947868 0.318664i \(-0.103234\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.7056 0.819319 0.409660 0.912239i \(-0.365648\pi\)
0.409660 + 0.912239i \(0.365648\pi\)
\(468\) 0 0
\(469\) 9.31701 0.430219
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 33.6242i − 1.54604i
\(474\) 0 0
\(475\) 1.89953i 0.0871565i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −41.3976 −1.89151 −0.945753 0.324886i \(-0.894674\pi\)
−0.945753 + 0.324886i \(0.894674\pi\)
\(480\) 0 0
\(481\) 10.4486 0.476415
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.56157i 0.116315i
\(486\) 0 0
\(487\) − 29.8467i − 1.35249i −0.736679 0.676243i \(-0.763607\pi\)
0.736679 0.676243i \(-0.236393\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −21.7538 −0.981736 −0.490868 0.871234i \(-0.663320\pi\)
−0.490868 + 0.871234i \(0.663320\pi\)
\(492\) 0 0
\(493\) −79.6009 −3.58504
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 3.35118i − 0.150321i
\(498\) 0 0
\(499\) − 27.1040i − 1.21334i −0.794954 0.606670i \(-0.792505\pi\)
0.794954 0.606670i \(-0.207495\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −15.6118 −0.696096 −0.348048 0.937477i \(-0.613155\pi\)
−0.348048 + 0.937477i \(0.613155\pi\)
\(504\) 0 0
\(505\) 10.2715 0.457077
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.87470i 0.127419i 0.997968 + 0.0637093i \(0.0202930\pi\)
−0.997968 + 0.0637093i \(0.979707\pi\)
\(510\) 0 0
\(511\) 9.87717i 0.436940i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −25.3470 −1.11692
\(516\) 0 0
\(517\) 37.5346 1.65077
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 36.1305i − 1.58291i −0.611229 0.791454i \(-0.709325\pi\)
0.611229 0.791454i \(-0.290675\pi\)
\(522\) 0 0
\(523\) 25.1009i 1.09759i 0.835959 + 0.548793i \(0.184912\pi\)
−0.835959 + 0.548793i \(0.815088\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −82.0680 −3.57494
\(528\) 0 0
\(529\) −18.3298 −0.796948
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.59662i 0.242416i
\(534\) 0 0
\(535\) − 46.3553i − 2.00412i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 18.9369 0.815669
\(540\) 0 0
\(541\) 2.51424 0.108096 0.0540478 0.998538i \(-0.482788\pi\)
0.0540478 + 0.998538i \(0.482788\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 13.5854i − 0.581935i
\(546\) 0 0
\(547\) 21.0986i 0.902110i 0.892496 + 0.451055i \(0.148952\pi\)
−0.892496 + 0.451055i \(0.851048\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.88713 0.421206
\(552\) 0 0
\(553\) −12.5935 −0.535532
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 9.86835i − 0.418136i −0.977901 0.209068i \(-0.932957\pi\)
0.977901 0.209068i \(-0.0670429\pi\)
\(558\) 0 0
\(559\) 16.2305i 0.686475i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 30.1845 1.27212 0.636062 0.771638i \(-0.280562\pi\)
0.636062 + 0.771638i \(0.280562\pi\)
\(564\) 0 0
\(565\) −18.4620 −0.776701
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 35.9090i − 1.50538i −0.658374 0.752691i \(-0.728755\pi\)
0.658374 0.752691i \(-0.271245\pi\)
\(570\) 0 0
\(571\) 30.2305i 1.26511i 0.774517 + 0.632553i \(0.217993\pi\)
−0.774517 + 0.632553i \(0.782007\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.10501 −0.171191
\(576\) 0 0
\(577\) −4.96144 −0.206547 −0.103274 0.994653i \(-0.532932\pi\)
−0.103274 + 0.994653i \(0.532932\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 0.607727i − 0.0252128i
\(582\) 0 0
\(583\) 24.0573i 0.996353i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 30.9544 1.27762 0.638812 0.769363i \(-0.279426\pi\)
0.638812 + 0.769363i \(0.279426\pi\)
\(588\) 0 0
\(589\) 10.1936 0.420019
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10.1038i 0.414911i 0.978244 + 0.207456i \(0.0665183\pi\)
−0.978244 + 0.207456i \(0.933482\pi\)
\(594\) 0 0
\(595\) 17.2389i 0.706726i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13.0183 0.531911 0.265956 0.963985i \(-0.414313\pi\)
0.265956 + 0.963985i \(0.414313\pi\)
\(600\) 0 0
\(601\) −29.1678 −1.18978 −0.594889 0.803808i \(-0.702804\pi\)
−0.594889 + 0.803808i \(0.702804\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.42619i 0.220606i
\(606\) 0 0
\(607\) − 24.6729i − 1.00144i −0.865609 0.500721i \(-0.833068\pi\)
0.865609 0.500721i \(-0.166932\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −18.1180 −0.732976
\(612\) 0 0
\(613\) −23.1751 −0.936032 −0.468016 0.883720i \(-0.655031\pi\)
−0.468016 + 0.883720i \(0.655031\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13.3422i 0.537138i 0.963260 + 0.268569i \(0.0865507\pi\)
−0.963260 + 0.268569i \(0.913449\pi\)
\(618\) 0 0
\(619\) 5.93322i 0.238476i 0.992866 + 0.119238i \(0.0380452\pi\)
−0.992866 + 0.119238i \(0.961955\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5.55961 −0.222741
\(624\) 0 0
\(625\) −30.8894 −1.23558
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 58.3039i − 2.32473i
\(630\) 0 0
\(631\) − 5.73792i − 0.228423i −0.993456 0.114212i \(-0.963566\pi\)
0.993456 0.114212i \(-0.0364342\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 24.0660 0.955029
\(636\) 0 0
\(637\) −9.14087 −0.362174
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21.7901i 0.860656i 0.902673 + 0.430328i \(0.141602\pi\)
−0.902673 + 0.430328i \(0.858398\pi\)
\(642\) 0 0
\(643\) − 6.09045i − 0.240184i −0.992763 0.120092i \(-0.961681\pi\)
0.992763 0.120092i \(-0.0383189\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 19.0718 0.749791 0.374896 0.927067i \(-0.377679\pi\)
0.374896 + 0.927067i \(0.377679\pi\)
\(648\) 0 0
\(649\) −28.3468 −1.11271
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 20.9126i − 0.818374i −0.912451 0.409187i \(-0.865812\pi\)
0.912451 0.409187i \(-0.134188\pi\)
\(654\) 0 0
\(655\) − 11.3216i − 0.442370i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −24.5980 −0.958201 −0.479100 0.877760i \(-0.659037\pi\)
−0.479100 + 0.877760i \(0.659037\pi\)
\(660\) 0 0
\(661\) −8.18377 −0.318312 −0.159156 0.987253i \(-0.550877\pi\)
−0.159156 + 0.987253i \(0.550877\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 2.14122i − 0.0830331i
\(666\) 0 0
\(667\) 21.3667i 0.827323i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.6163 0.487046
\(672\) 0 0
\(673\) −8.98555 −0.346367 −0.173184 0.984890i \(-0.555405\pi\)
−0.173184 + 0.984890i \(0.555405\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 41.0215i 1.57658i 0.615302 + 0.788291i \(0.289034\pi\)
−0.615302 + 0.788291i \(0.710966\pi\)
\(678\) 0 0
\(679\) − 0.794965i − 0.0305080i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −23.6744 −0.905878 −0.452939 0.891542i \(-0.649624\pi\)
−0.452939 + 0.891542i \(0.649624\pi\)
\(684\) 0 0
\(685\) 37.0437 1.41537
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 11.6125i − 0.442402i
\(690\) 0 0
\(691\) 25.5371i 0.971476i 0.874105 + 0.485738i \(0.161449\pi\)
−0.874105 + 0.485738i \(0.838551\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −44.4587 −1.68641
\(696\) 0 0
\(697\) 31.2295 1.18290
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 16.8830i − 0.637663i −0.947811 0.318832i \(-0.896710\pi\)
0.947811 0.318832i \(-0.103290\pi\)
\(702\) 0 0
\(703\) 7.24187i 0.273132i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.18770 −0.119886
\(708\) 0 0
\(709\) −20.2233 −0.759503 −0.379751 0.925089i \(-0.623990\pi\)
−0.379751 + 0.925089i \(0.623990\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 22.0290i 0.824991i
\(714\) 0 0
\(715\) 11.3278i 0.423636i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −32.5986 −1.21572 −0.607862 0.794043i \(-0.707972\pi\)
−0.607862 + 0.794043i \(0.707972\pi\)
\(720\) 0 0
\(721\) 7.86627 0.292955
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 18.7809i − 0.697506i
\(726\) 0 0
\(727\) 4.01163i 0.148783i 0.997229 + 0.0743915i \(0.0237014\pi\)
−0.997229 + 0.0743915i \(0.976299\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 90.5671 3.34975
\(732\) 0 0
\(733\) 0.936390 0.0345863 0.0172932 0.999850i \(-0.494495\pi\)
0.0172932 + 0.999850i \(0.494495\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 34.1627i − 1.25840i
\(738\) 0 0
\(739\) − 43.4973i − 1.60008i −0.599949 0.800038i \(-0.704813\pi\)
0.599949 0.800038i \(-0.295187\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −33.3942 −1.22512 −0.612558 0.790426i \(-0.709859\pi\)
−0.612558 + 0.790426i \(0.709859\pi\)
\(744\) 0 0
\(745\) −12.9881 −0.475846
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 14.3861i 0.525656i
\(750\) 0 0
\(751\) 44.3664i 1.61895i 0.587153 + 0.809476i \(0.300249\pi\)
−0.587153 + 0.809476i \(0.699751\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −49.4639 −1.80018
\(756\) 0 0
\(757\) −25.6121 −0.930888 −0.465444 0.885077i \(-0.654105\pi\)
−0.465444 + 0.885077i \(0.654105\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 14.4372i − 0.523348i −0.965156 0.261674i \(-0.915726\pi\)
0.965156 0.261674i \(-0.0842745\pi\)
\(762\) 0 0
\(763\) 4.21614i 0.152634i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 13.6831 0.494068
\(768\) 0 0
\(769\) 29.6580 1.06949 0.534747 0.845012i \(-0.320407\pi\)
0.534747 + 0.845012i \(0.320407\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 16.4950i − 0.593282i −0.954989 0.296641i \(-0.904133\pi\)
0.954989 0.296641i \(-0.0958665\pi\)
\(774\) 0 0
\(775\) − 19.3630i − 0.695540i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.87898 −0.138979
\(780\) 0 0
\(781\) −12.2878 −0.439692
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 2.20773i − 0.0787973i
\(786\) 0 0
\(787\) − 33.6571i − 1.19975i −0.800095 0.599874i \(-0.795217\pi\)
0.800095 0.599874i \(-0.204783\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.72955 0.203719
\(792\) 0 0
\(793\) −6.08991 −0.216259
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 17.4632i − 0.618578i −0.950968 0.309289i \(-0.899909\pi\)
0.950968 0.309289i \(-0.100091\pi\)
\(798\) 0 0
\(799\) 101.100i 3.57665i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 36.2167 1.27806
\(804\) 0 0
\(805\) 4.62732 0.163092
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 0.726707i − 0.0255496i −0.999918 0.0127748i \(-0.995934\pi\)
0.999918 0.0127748i \(-0.00406646\pi\)
\(810\) 0 0
\(811\) 6.24583i 0.219321i 0.993969 + 0.109660i \(0.0349763\pi\)
−0.993969 + 0.109660i \(0.965024\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 44.4761 1.55793
\(816\) 0 0
\(817\) −11.2492 −0.393561
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 24.0958i − 0.840948i −0.907305 0.420474i \(-0.861864\pi\)
0.907305 0.420474i \(-0.138136\pi\)
\(822\) 0 0
\(823\) 29.8946i 1.04206i 0.853538 + 0.521030i \(0.174452\pi\)
−0.853538 + 0.521030i \(0.825548\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32.0577 −1.11476 −0.557378 0.830259i \(-0.688193\pi\)
−0.557378 + 0.830259i \(0.688193\pi\)
\(828\) 0 0
\(829\) 14.2197 0.493870 0.246935 0.969032i \(-0.420577\pi\)
0.246935 + 0.969032i \(0.420577\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 51.0067i 1.76728i
\(834\) 0 0
\(835\) − 22.5773i − 0.781319i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 6.93757 0.239511 0.119756 0.992803i \(-0.461789\pi\)
0.119756 + 0.992803i \(0.461789\pi\)
\(840\) 0 0
\(841\) −68.7554 −2.37088
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 28.6791i 0.986591i
\(846\) 0 0
\(847\) − 1.68398i − 0.0578623i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −15.6501 −0.536480
\(852\) 0 0
\(853\) 15.3000 0.523861 0.261931 0.965087i \(-0.415641\pi\)
0.261931 + 0.965087i \(0.415641\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 40.5820i 1.38626i 0.720815 + 0.693128i \(0.243768\pi\)
−0.720815 + 0.693128i \(0.756232\pi\)
\(858\) 0 0
\(859\) − 23.3837i − 0.797842i −0.916985 0.398921i \(-0.869385\pi\)
0.916985 0.398921i \(-0.130615\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 15.5016 0.527681 0.263840 0.964566i \(-0.415011\pi\)
0.263840 + 0.964566i \(0.415011\pi\)
\(864\) 0 0
\(865\) 37.1570 1.26338
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 46.1768i 1.56644i
\(870\) 0 0
\(871\) 16.4904i 0.558756i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 6.63880 0.224432
\(876\) 0 0
\(877\) 17.0316 0.575117 0.287558 0.957763i \(-0.407156\pi\)
0.287558 + 0.957763i \(0.407156\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 6.42144i − 0.216344i −0.994132 0.108172i \(-0.965500\pi\)
0.994132 0.108172i \(-0.0344997\pi\)
\(882\) 0 0
\(883\) 10.2267i 0.344157i 0.985083 + 0.172078i \(0.0550482\pi\)
−0.985083 + 0.172078i \(0.944952\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.61770 0.289354 0.144677 0.989479i \(-0.453786\pi\)
0.144677 + 0.989479i \(0.453786\pi\)
\(888\) 0 0
\(889\) −7.46872 −0.250493
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 12.5575i − 0.420221i
\(894\) 0 0
\(895\) 6.89993i 0.230639i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −100.785 −3.36138
\(900\) 0 0
\(901\) −64.7988 −2.15876
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 22.5371i − 0.749158i
\(906\) 0 0
\(907\) − 30.3232i − 1.00687i −0.864034 0.503433i \(-0.832070\pi\)
0.864034 0.503433i \(-0.167930\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5.84477 −0.193646 −0.0968229 0.995302i \(-0.530868\pi\)
−0.0968229 + 0.995302i \(0.530868\pi\)
\(912\) 0 0
\(913\) −2.22835 −0.0737478
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.51357i 0.116028i
\(918\) 0 0
\(919\) 4.02134i 0.132652i 0.997798 + 0.0663259i \(0.0211277\pi\)
−0.997798 + 0.0663259i \(0.978872\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5.93135 0.195233
\(924\) 0 0
\(925\) 13.7562 0.452300
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 10.4138i 0.341664i 0.985300 + 0.170832i \(0.0546456\pi\)
−0.985300 + 0.170832i \(0.945354\pi\)
\(930\) 0 0
\(931\) − 6.33549i − 0.207637i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 63.2099 2.06719
\(936\) 0 0
\(937\) 14.6965 0.480113 0.240056 0.970759i \(-0.422834\pi\)
0.240056 + 0.970759i \(0.422834\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 25.9949i 0.847411i 0.905800 + 0.423705i \(0.139271\pi\)
−0.905800 + 0.423705i \(0.860729\pi\)
\(942\) 0 0
\(943\) − 8.38274i − 0.272979i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 26.0210 0.845568 0.422784 0.906230i \(-0.361053\pi\)
0.422784 + 0.906230i \(0.361053\pi\)
\(948\) 0 0
\(949\) −17.4819 −0.567486
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 25.9572i − 0.840835i −0.907331 0.420417i \(-0.861884\pi\)
0.907331 0.420417i \(-0.138116\pi\)
\(954\) 0 0
\(955\) − 5.55865i − 0.179874i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −11.4963 −0.371234
\(960\) 0 0
\(961\) −72.9089 −2.35190
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 15.4921i − 0.498709i
\(966\) 0 0
\(967\) − 36.8551i − 1.18518i −0.805504 0.592590i \(-0.798105\pi\)
0.805504 0.592590i \(-0.201895\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 25.3533 0.813625 0.406813 0.913512i \(-0.366640\pi\)
0.406813 + 0.913512i \(0.366640\pi\)
\(972\) 0 0
\(973\) 13.7975 0.442326
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.3795i 0.971925i 0.873980 + 0.485962i \(0.161531\pi\)
−0.873980 + 0.485962i \(0.838469\pi\)
\(978\) 0 0
\(979\) 20.3854i 0.651522i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −5.94251 −0.189536 −0.0947682 0.995499i \(-0.530211\pi\)
−0.0947682 + 0.995499i \(0.530211\pi\)
\(984\) 0 0
\(985\) 41.0721 1.30867
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 24.3103i − 0.773024i
\(990\) 0 0
\(991\) − 4.74708i − 0.150796i −0.997154 0.0753981i \(-0.975977\pi\)
0.997154 0.0753981i \(-0.0240227\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 33.0142 1.04662
\(996\) 0 0
\(997\) −15.8258 −0.501209 −0.250604 0.968090i \(-0.580629\pi\)
−0.250604 + 0.968090i \(0.580629\pi\)
\(998\) 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.b.2015.4 yes 24
3.2 odd 2 inner 2736.2.d.b.2015.22 yes 24
4.3 odd 2 inner 2736.2.d.b.2015.3 24
12.11 even 2 inner 2736.2.d.b.2015.21 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.d.b.2015.3 24 4.3 odd 2 inner
2736.2.d.b.2015.4 yes 24 1.1 even 1 trivial
2736.2.d.b.2015.21 yes 24 12.11 even 2 inner
2736.2.d.b.2015.22 yes 24 3.2 odd 2 inner