Properties

Label 2736.2.d.b.2015.24
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 2015.24
Character \(\chi\) \(=\) 2736.2015
Dual form 2736.2.d.b.2015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.95877i q^{5} +0.569970i q^{7} +O(q^{10})\) \(q+2.95877i q^{5} +0.569970i q^{7} +1.70925 q^{11} +3.55382 q^{13} +4.91049i q^{17} +1.00000i q^{19} +8.27966 q^{23} -3.75430 q^{25} +2.39518i q^{29} -4.25776i q^{31} -1.68641 q^{35} -5.95478 q^{37} -3.11214i q^{41} -3.81744i q^{43} -5.85841 q^{47} +6.67513 q^{49} +4.30890i q^{53} +5.05728i q^{55} +2.13451 q^{59} +4.19721 q^{61} +10.5149i q^{65} +12.3687i q^{67} +12.7533 q^{71} -10.8387 q^{73} +0.974222i q^{77} -2.29006i q^{79} +1.73885 q^{83} -14.5290 q^{85} +14.6261i q^{89} +2.02557i q^{91} -2.95877 q^{95} -5.53416 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + O(q^{10}) \) \( 24q + 8q^{25} - 32q^{37} - 32q^{49} + 8q^{73} + 40q^{85} + 16q^{97} + O(q^{100}) \)

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
\(5\) 2.95877i 1.32320i 0.749857 + 0.661600i \(0.230122\pi\)
−0.749857 + 0.661600i \(0.769878\pi\)
\(6\) 0 0
\(7\) 0.569970i 0.215428i 0.994182 + 0.107714i \(0.0343531\pi\)
−0.994182 + 0.107714i \(0.965647\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.70925 0.515359 0.257679 0.966230i \(-0.417042\pi\)
0.257679 + 0.966230i \(0.417042\pi\)
\(12\) 0 0
\(13\) 3.55382 0.985651 0.492826 0.870128i \(-0.335964\pi\)
0.492826 + 0.870128i \(0.335964\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.91049i 1.19097i 0.803366 + 0.595485i \(0.203040\pi\)
−0.803366 + 0.595485i \(0.796960\pi\)
\(18\) 0 0
\(19\) 1.00000i 0.229416i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.27966 1.72643 0.863214 0.504838i \(-0.168448\pi\)
0.863214 + 0.504838i \(0.168448\pi\)
\(24\) 0 0
\(25\) −3.75430 −0.750859
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.39518i 0.444775i 0.974958 + 0.222387i \(0.0713849\pi\)
−0.974958 + 0.222387i \(0.928615\pi\)
\(30\) 0 0
\(31\) − 4.25776i − 0.764716i −0.924014 0.382358i \(-0.875112\pi\)
0.924014 0.382358i \(-0.124888\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.68641 −0.285055
\(36\) 0 0
\(37\) −5.95478 −0.978959 −0.489480 0.872015i \(-0.662813\pi\)
−0.489480 + 0.872015i \(0.662813\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 3.11214i − 0.486034i −0.970022 0.243017i \(-0.921863\pi\)
0.970022 0.243017i \(-0.0781371\pi\)
\(42\) 0 0
\(43\) − 3.81744i − 0.582154i −0.956700 0.291077i \(-0.905986\pi\)
0.956700 0.291077i \(-0.0940135\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.85841 −0.854537 −0.427268 0.904125i \(-0.640524\pi\)
−0.427268 + 0.904125i \(0.640524\pi\)
\(48\) 0 0
\(49\) 6.67513 0.953591
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.30890i 0.591873i 0.955208 + 0.295937i \(0.0956317\pi\)
−0.955208 + 0.295937i \(0.904368\pi\)
\(54\) 0 0
\(55\) 5.05728i 0.681923i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.13451 0.277889 0.138945 0.990300i \(-0.455629\pi\)
0.138945 + 0.990300i \(0.455629\pi\)
\(60\) 0 0
\(61\) 4.19721 0.537398 0.268699 0.963224i \(-0.413406\pi\)
0.268699 + 0.963224i \(0.413406\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.5149i 1.30421i
\(66\) 0 0
\(67\) 12.3687i 1.51107i 0.655107 + 0.755536i \(0.272623\pi\)
−0.655107 + 0.755536i \(0.727377\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.7533 1.51353 0.756767 0.653685i \(-0.226778\pi\)
0.756767 + 0.653685i \(0.226778\pi\)
\(72\) 0 0
\(73\) −10.8387 −1.26858 −0.634288 0.773097i \(-0.718707\pi\)
−0.634288 + 0.773097i \(0.718707\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.974222i 0.111023i
\(78\) 0 0
\(79\) − 2.29006i − 0.257652i −0.991667 0.128826i \(-0.958879\pi\)
0.991667 0.128826i \(-0.0411209\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.73885 0.190863 0.0954316 0.995436i \(-0.469577\pi\)
0.0954316 + 0.995436i \(0.469577\pi\)
\(84\) 0 0
\(85\) −14.5290 −1.57589
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.6261i 1.55036i 0.631741 + 0.775179i \(0.282341\pi\)
−0.631741 + 0.775179i \(0.717659\pi\)
\(90\) 0 0
\(91\) 2.02557i 0.212337i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.95877 −0.303563
\(96\) 0 0
\(97\) −5.53416 −0.561909 −0.280954 0.959721i \(-0.590651\pi\)
−0.280954 + 0.959721i \(0.590651\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 2.79060i − 0.277675i −0.990315 0.138838i \(-0.955663\pi\)
0.990315 0.138838i \(-0.0443366\pi\)
\(102\) 0 0
\(103\) − 7.21853i − 0.711263i −0.934626 0.355631i \(-0.884266\pi\)
0.934626 0.355631i \(-0.115734\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.58913 0.830342 0.415171 0.909743i \(-0.363722\pi\)
0.415171 + 0.909743i \(0.363722\pi\)
\(108\) 0 0
\(109\) −17.2842 −1.65553 −0.827763 0.561077i \(-0.810387\pi\)
−0.827763 + 0.561077i \(0.810387\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 2.52206i − 0.237255i −0.992939 0.118628i \(-0.962150\pi\)
0.992939 0.118628i \(-0.0378495\pi\)
\(114\) 0 0
\(115\) 24.4976i 2.28441i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.79883 −0.256569
\(120\) 0 0
\(121\) −8.07846 −0.734405
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.68574i 0.329663i
\(126\) 0 0
\(127\) − 9.49347i − 0.842410i −0.906966 0.421205i \(-0.861607\pi\)
0.906966 0.421205i \(-0.138393\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.47277 −0.478159 −0.239079 0.971000i \(-0.576846\pi\)
−0.239079 + 0.971000i \(0.576846\pi\)
\(132\) 0 0
\(133\) −0.569970 −0.0494226
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.6155i 0.906946i 0.891270 + 0.453473i \(0.149815\pi\)
−0.891270 + 0.453473i \(0.850185\pi\)
\(138\) 0 0
\(139\) 20.6801i 1.75407i 0.480430 + 0.877033i \(0.340481\pi\)
−0.480430 + 0.877033i \(0.659519\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.07437 0.507964
\(144\) 0 0
\(145\) −7.08679 −0.588526
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.11655i 0.173395i 0.996235 + 0.0866973i \(0.0276313\pi\)
−0.996235 + 0.0866973i \(0.972369\pi\)
\(150\) 0 0
\(151\) − 11.8036i − 0.960567i −0.877113 0.480284i \(-0.840534\pi\)
0.877113 0.480284i \(-0.159466\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 12.5977 1.01187
\(156\) 0 0
\(157\) −15.4017 −1.22919 −0.614594 0.788843i \(-0.710680\pi\)
−0.614594 + 0.788843i \(0.710680\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.71915i 0.371921i
\(162\) 0 0
\(163\) 17.2526i 1.35133i 0.737209 + 0.675665i \(0.236143\pi\)
−0.737209 + 0.675665i \(0.763857\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −23.0656 −1.78487 −0.892437 0.451173i \(-0.851006\pi\)
−0.892437 + 0.451173i \(0.851006\pi\)
\(168\) 0 0
\(169\) −0.370392 −0.0284917
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 3.81082i − 0.289731i −0.989451 0.144866i \(-0.953725\pi\)
0.989451 0.144866i \(-0.0462750\pi\)
\(174\) 0 0
\(175\) − 2.13984i − 0.161756i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.85047 0.287798 0.143899 0.989592i \(-0.454036\pi\)
0.143899 + 0.989592i \(0.454036\pi\)
\(180\) 0 0
\(181\) 16.3304 1.21383 0.606916 0.794766i \(-0.292406\pi\)
0.606916 + 0.794766i \(0.292406\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 17.6188i − 1.29536i
\(186\) 0 0
\(187\) 8.39327i 0.613777i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.711877 −0.0515096 −0.0257548 0.999668i \(-0.508199\pi\)
−0.0257548 + 0.999668i \(0.508199\pi\)
\(192\) 0 0
\(193\) −5.08186 −0.365800 −0.182900 0.983132i \(-0.558548\pi\)
−0.182900 + 0.983132i \(0.558548\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.3093i 0.805757i 0.915254 + 0.402878i \(0.131990\pi\)
−0.915254 + 0.402878i \(0.868010\pi\)
\(198\) 0 0
\(199\) 16.5428i 1.17269i 0.810062 + 0.586345i \(0.199434\pi\)
−0.810062 + 0.586345i \(0.800566\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.36518 −0.0958170
\(204\) 0 0
\(205\) 9.20808 0.643120
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.70925i 0.118231i
\(210\) 0 0
\(211\) − 13.6026i − 0.936439i −0.883612 0.468220i \(-0.844896\pi\)
0.883612 0.468220i \(-0.155104\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11.2949 0.770306
\(216\) 0 0
\(217\) 2.42679 0.164741
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.4510i 1.17388i
\(222\) 0 0
\(223\) − 24.3517i − 1.63071i −0.578960 0.815356i \(-0.696541\pi\)
0.578960 0.815356i \(-0.303459\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 24.7382 1.64193 0.820967 0.570976i \(-0.193435\pi\)
0.820967 + 0.570976i \(0.193435\pi\)
\(228\) 0 0
\(229\) 8.04362 0.531537 0.265769 0.964037i \(-0.414374\pi\)
0.265769 + 0.964037i \(0.414374\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 13.8280i − 0.905901i −0.891536 0.452951i \(-0.850371\pi\)
0.891536 0.452951i \(-0.149629\pi\)
\(234\) 0 0
\(235\) − 17.3337i − 1.13072i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.99484 0.129036 0.0645178 0.997917i \(-0.479449\pi\)
0.0645178 + 0.997917i \(0.479449\pi\)
\(240\) 0 0
\(241\) 6.12602 0.394611 0.197306 0.980342i \(-0.436781\pi\)
0.197306 + 0.980342i \(0.436781\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 19.7502i 1.26179i
\(246\) 0 0
\(247\) 3.55382i 0.226124i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.97473 0.566480 0.283240 0.959049i \(-0.408591\pi\)
0.283240 + 0.959049i \(0.408591\pi\)
\(252\) 0 0
\(253\) 14.1520 0.889730
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 9.65103i − 0.602015i −0.953622 0.301007i \(-0.902677\pi\)
0.953622 0.301007i \(-0.0973229\pi\)
\(258\) 0 0
\(259\) − 3.39404i − 0.210896i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2.74147 0.169046 0.0845231 0.996422i \(-0.473063\pi\)
0.0845231 + 0.996422i \(0.473063\pi\)
\(264\) 0 0
\(265\) −12.7490 −0.783167
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.8606i 0.967040i 0.875333 + 0.483520i \(0.160642\pi\)
−0.875333 + 0.483520i \(0.839358\pi\)
\(270\) 0 0
\(271\) − 10.0169i − 0.608484i −0.952595 0.304242i \(-0.901597\pi\)
0.952595 0.304242i \(-0.0984031\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.41704 −0.386962
\(276\) 0 0
\(277\) 1.21067 0.0727419 0.0363709 0.999338i \(-0.488420\pi\)
0.0363709 + 0.999338i \(0.488420\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 29.4526i 1.75699i 0.477748 + 0.878497i \(0.341453\pi\)
−0.477748 + 0.878497i \(0.658547\pi\)
\(282\) 0 0
\(283\) − 17.8603i − 1.06168i −0.847471 0.530841i \(-0.821876\pi\)
0.847471 0.530841i \(-0.178124\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.77382 0.104705
\(288\) 0 0
\(289\) −7.11296 −0.418409
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 8.61432i − 0.503254i −0.967824 0.251627i \(-0.919034\pi\)
0.967824 0.251627i \(-0.0809656\pi\)
\(294\) 0 0
\(295\) 6.31551i 0.367703i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 29.4244 1.70166
\(300\) 0 0
\(301\) 2.17582 0.125412
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12.4186i 0.711086i
\(306\) 0 0
\(307\) − 1.66899i − 0.0952541i −0.998865 0.0476271i \(-0.984834\pi\)
0.998865 0.0476271i \(-0.0151659\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.7976 −0.895802 −0.447901 0.894083i \(-0.647828\pi\)
−0.447901 + 0.894083i \(0.647828\pi\)
\(312\) 0 0
\(313\) 32.4916 1.83653 0.918267 0.395961i \(-0.129589\pi\)
0.918267 + 0.395961i \(0.129589\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 9.48080i − 0.532495i −0.963905 0.266247i \(-0.914216\pi\)
0.963905 0.266247i \(-0.0857838\pi\)
\(318\) 0 0
\(319\) 4.09397i 0.229218i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.91049 −0.273227
\(324\) 0 0
\(325\) −13.3421 −0.740085
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 3.33911i − 0.184091i
\(330\) 0 0
\(331\) 10.2220i 0.561852i 0.959729 + 0.280926i \(0.0906416\pi\)
−0.959729 + 0.280926i \(0.909358\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −36.5960 −1.99945
\(336\) 0 0
\(337\) 11.6998 0.637326 0.318663 0.947868i \(-0.396766\pi\)
0.318663 + 0.947868i \(0.396766\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 7.27758i − 0.394103i
\(342\) 0 0
\(343\) 7.79441i 0.420859i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 19.7600 1.06078 0.530388 0.847755i \(-0.322046\pi\)
0.530388 + 0.847755i \(0.322046\pi\)
\(348\) 0 0
\(349\) 2.61480 0.139967 0.0699836 0.997548i \(-0.477705\pi\)
0.0699836 + 0.997548i \(0.477705\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 1.48062i − 0.0788056i −0.999223 0.0394028i \(-0.987454\pi\)
0.999223 0.0394028i \(-0.0125456\pi\)
\(354\) 0 0
\(355\) 37.7339i 2.00271i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −29.0406 −1.53271 −0.766353 0.642420i \(-0.777931\pi\)
−0.766353 + 0.642420i \(0.777931\pi\)
\(360\) 0 0
\(361\) −1.00000 −0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 32.0693i − 1.67858i
\(366\) 0 0
\(367\) − 17.9185i − 0.935337i −0.883904 0.467668i \(-0.845094\pi\)
0.883904 0.467668i \(-0.154906\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.45594 −0.127506
\(372\) 0 0
\(373\) 5.65432 0.292770 0.146385 0.989228i \(-0.453236\pi\)
0.146385 + 0.989228i \(0.453236\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.51204i 0.438393i
\(378\) 0 0
\(379\) − 31.7595i − 1.63138i −0.578493 0.815688i \(-0.696359\pi\)
0.578493 0.815688i \(-0.303641\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −26.2692 −1.34229 −0.671146 0.741325i \(-0.734198\pi\)
−0.671146 + 0.741325i \(0.734198\pi\)
\(384\) 0 0
\(385\) −2.88249 −0.146905
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 8.02764i − 0.407017i −0.979073 0.203509i \(-0.934765\pi\)
0.979073 0.203509i \(-0.0652345\pi\)
\(390\) 0 0
\(391\) 40.6572i 2.05612i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.77576 0.340926
\(396\) 0 0
\(397\) 3.24160 0.162691 0.0813457 0.996686i \(-0.474078\pi\)
0.0813457 + 0.996686i \(0.474078\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 7.12034i − 0.355573i −0.984069 0.177786i \(-0.943106\pi\)
0.984069 0.177786i \(-0.0568936\pi\)
\(402\) 0 0
\(403\) − 15.1313i − 0.753743i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.1782 −0.504515
\(408\) 0 0
\(409\) −8.49493 −0.420047 −0.210024 0.977696i \(-0.567354\pi\)
−0.210024 + 0.977696i \(0.567354\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.21660i 0.0598652i
\(414\) 0 0
\(415\) 5.14484i 0.252550i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.98442 0.194652 0.0973258 0.995253i \(-0.468971\pi\)
0.0973258 + 0.995253i \(0.468971\pi\)
\(420\) 0 0
\(421\) 30.1475 1.46930 0.734650 0.678446i \(-0.237346\pi\)
0.734650 + 0.678446i \(0.237346\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 18.4355i − 0.894251i
\(426\) 0 0
\(427\) 2.39229i 0.115771i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 28.6558 1.38030 0.690152 0.723665i \(-0.257544\pi\)
0.690152 + 0.723665i \(0.257544\pi\)
\(432\) 0 0
\(433\) 11.7254 0.563487 0.281743 0.959490i \(-0.409087\pi\)
0.281743 + 0.959490i \(0.409087\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.27966i 0.396070i
\(438\) 0 0
\(439\) − 39.5668i − 1.88842i −0.329343 0.944211i \(-0.606827\pi\)
0.329343 0.944211i \(-0.393173\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 20.5909 0.978303 0.489151 0.872199i \(-0.337307\pi\)
0.489151 + 0.872199i \(0.337307\pi\)
\(444\) 0 0
\(445\) −43.2751 −2.05144
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 30.6253i − 1.44530i −0.691217 0.722648i \(-0.742925\pi\)
0.691217 0.722648i \(-0.257075\pi\)
\(450\) 0 0
\(451\) − 5.31942i − 0.250482i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.99318 −0.280965
\(456\) 0 0
\(457\) 32.4736 1.51905 0.759525 0.650478i \(-0.225431\pi\)
0.759525 + 0.650478i \(0.225431\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 7.17109i − 0.333991i −0.985958 0.166995i \(-0.946594\pi\)
0.985958 0.166995i \(-0.0534065\pi\)
\(462\) 0 0
\(463\) − 24.9553i − 1.15977i −0.814699 0.579884i \(-0.803098\pi\)
0.814699 0.579884i \(-0.196902\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −36.4340 −1.68596 −0.842981 0.537943i \(-0.819202\pi\)
−0.842981 + 0.537943i \(0.819202\pi\)
\(468\) 0 0
\(469\) −7.04976 −0.325528
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 6.52496i − 0.300018i
\(474\) 0 0
\(475\) − 3.75430i − 0.172259i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −36.0402 −1.64672 −0.823360 0.567520i \(-0.807903\pi\)
−0.823360 + 0.567520i \(0.807903\pi\)
\(480\) 0 0
\(481\) −21.1622 −0.964913
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 16.3743i − 0.743518i
\(486\) 0 0
\(487\) 23.8944i 1.08276i 0.840778 + 0.541380i \(0.182098\pi\)
−0.840778 + 0.541380i \(0.817902\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.453416 0.0204624 0.0102312 0.999948i \(-0.496743\pi\)
0.0102312 + 0.999948i \(0.496743\pi\)
\(492\) 0 0
\(493\) −11.7615 −0.529713
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.26897i 0.326058i
\(498\) 0 0
\(499\) − 37.4719i − 1.67747i −0.544539 0.838735i \(-0.683295\pi\)
0.544539 0.838735i \(-0.316705\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −37.9757 −1.69325 −0.846626 0.532188i \(-0.821370\pi\)
−0.846626 + 0.532188i \(0.821370\pi\)
\(504\) 0 0
\(505\) 8.25674 0.367420
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 41.8041i − 1.85294i −0.376374 0.926468i \(-0.622829\pi\)
0.376374 0.926468i \(-0.377171\pi\)
\(510\) 0 0
\(511\) − 6.17774i − 0.273287i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 21.3579 0.941143
\(516\) 0 0
\(517\) −10.0135 −0.440393
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 30.4902i − 1.33580i −0.744252 0.667899i \(-0.767194\pi\)
0.744252 0.667899i \(-0.232806\pi\)
\(522\) 0 0
\(523\) 28.9130i 1.26428i 0.774856 + 0.632138i \(0.217822\pi\)
−0.774856 + 0.632138i \(0.782178\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.9077 0.910753
\(528\) 0 0
\(529\) 45.5528 1.98055
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 11.0600i − 0.479060i
\(534\) 0 0
\(535\) 25.4132i 1.09871i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 11.4095 0.491441
\(540\) 0 0
\(541\) 32.3339 1.39014 0.695072 0.718940i \(-0.255372\pi\)
0.695072 + 0.718940i \(0.255372\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 51.1399i − 2.19059i
\(546\) 0 0
\(547\) 8.92847i 0.381754i 0.981614 + 0.190877i \(0.0611331\pi\)
−0.981614 + 0.190877i \(0.938867\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.39518 −0.102038
\(552\) 0 0
\(553\) 1.30527 0.0555056
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 0.828782i − 0.0351166i −0.999846 0.0175583i \(-0.994411\pi\)
0.999846 0.0175583i \(-0.00558927\pi\)
\(558\) 0 0
\(559\) − 13.5665i − 0.573800i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −16.3635 −0.689638 −0.344819 0.938669i \(-0.612060\pi\)
−0.344819 + 0.938669i \(0.612060\pi\)
\(564\) 0 0
\(565\) 7.46218 0.313936
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 0.104329i − 0.00437368i −0.999998 0.00218684i \(-0.999304\pi\)
0.999998 0.00218684i \(-0.000696093\pi\)
\(570\) 0 0
\(571\) 4.44526i 0.186028i 0.995665 + 0.0930142i \(0.0296502\pi\)
−0.995665 + 0.0930142i \(0.970350\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −31.0843 −1.29630
\(576\) 0 0
\(577\) −23.9811 −0.998346 −0.499173 0.866502i \(-0.666363\pi\)
−0.499173 + 0.866502i \(0.666363\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.991089i 0.0411173i
\(582\) 0 0
\(583\) 7.36500i 0.305027i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.8155 −0.446401 −0.223201 0.974773i \(-0.571651\pi\)
−0.223201 + 0.974773i \(0.571651\pi\)
\(588\) 0 0
\(589\) 4.25776 0.175438
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 29.0703i 1.19377i 0.802325 + 0.596887i \(0.203596\pi\)
−0.802325 + 0.596887i \(0.796404\pi\)
\(594\) 0 0
\(595\) − 8.28109i − 0.339492i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.11836 0.209131 0.104565 0.994518i \(-0.466655\pi\)
0.104565 + 0.994518i \(0.466655\pi\)
\(600\) 0 0
\(601\) −22.3642 −0.912254 −0.456127 0.889915i \(-0.650764\pi\)
−0.456127 + 0.889915i \(0.650764\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 23.9023i − 0.971765i
\(606\) 0 0
\(607\) − 6.11562i − 0.248226i −0.992268 0.124113i \(-0.960392\pi\)
0.992268 0.124113i \(-0.0396085\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20.8197 −0.842275
\(612\) 0 0
\(613\) −37.7179 −1.52341 −0.761707 0.647922i \(-0.775638\pi\)
−0.761707 + 0.647922i \(0.775638\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 38.3799i 1.54512i 0.634943 + 0.772559i \(0.281024\pi\)
−0.634943 + 0.772559i \(0.718976\pi\)
\(618\) 0 0
\(619\) 5.86517i 0.235741i 0.993029 + 0.117871i \(0.0376068\pi\)
−0.993029 + 0.117871i \(0.962393\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8.33641 −0.333991
\(624\) 0 0
\(625\) −29.6767 −1.18707
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 29.2409i − 1.16591i
\(630\) 0 0
\(631\) − 11.1860i − 0.445307i −0.974898 0.222654i \(-0.928528\pi\)
0.974898 0.222654i \(-0.0714719\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 28.0890 1.11468
\(636\) 0 0
\(637\) 23.7222 0.939908
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 39.4688i − 1.55892i −0.626450 0.779462i \(-0.715493\pi\)
0.626450 0.779462i \(-0.284507\pi\)
\(642\) 0 0
\(643\) 37.3994i 1.47489i 0.675409 + 0.737443i \(0.263967\pi\)
−0.675409 + 0.737443i \(0.736033\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.71980 −0.0676122 −0.0338061 0.999428i \(-0.510763\pi\)
−0.0338061 + 0.999428i \(0.510763\pi\)
\(648\) 0 0
\(649\) 3.64841 0.143213
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.8547i 0.737840i 0.929461 + 0.368920i \(0.120272\pi\)
−0.929461 + 0.368920i \(0.879728\pi\)
\(654\) 0 0
\(655\) − 16.1927i − 0.632700i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10.6461 0.414714 0.207357 0.978265i \(-0.433514\pi\)
0.207357 + 0.978265i \(0.433514\pi\)
\(660\) 0 0
\(661\) 13.9227 0.541532 0.270766 0.962645i \(-0.412723\pi\)
0.270766 + 0.962645i \(0.412723\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 1.68641i − 0.0653961i
\(666\) 0 0
\(667\) 19.8313i 0.767871i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7.17410 0.276953
\(672\) 0 0
\(673\) 36.2932 1.39900 0.699500 0.714633i \(-0.253406\pi\)
0.699500 + 0.714633i \(0.253406\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.72096i 0.296741i 0.988932 + 0.148370i \(0.0474028\pi\)
−0.988932 + 0.148370i \(0.952597\pi\)
\(678\) 0 0
\(679\) − 3.15430i − 0.121051i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18.9531 −0.725220 −0.362610 0.931941i \(-0.618114\pi\)
−0.362610 + 0.931941i \(0.618114\pi\)
\(684\) 0 0
\(685\) −31.4089 −1.20007
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 15.3131i 0.583381i
\(690\) 0 0
\(691\) − 32.5480i − 1.23818i −0.785319 0.619091i \(-0.787501\pi\)
0.785319 0.619091i \(-0.212499\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −61.1877 −2.32098
\(696\) 0 0
\(697\) 15.2821 0.578852
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4.55361i 0.171987i 0.996296 + 0.0859937i \(0.0274065\pi\)
−0.996296 + 0.0859937i \(0.972593\pi\)
\(702\) 0 0
\(703\) − 5.95478i − 0.224589i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.59056 0.0598191
\(708\) 0 0
\(709\) 49.6482 1.86458 0.932289 0.361715i \(-0.117809\pi\)
0.932289 + 0.361715i \(0.117809\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 35.2528i − 1.32023i
\(714\) 0 0
\(715\) 17.9726i 0.672138i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.55893 0.0581381 0.0290691 0.999577i \(-0.490746\pi\)
0.0290691 + 0.999577i \(0.490746\pi\)
\(720\) 0 0
\(721\) 4.11434 0.153226
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 8.99223i − 0.333963i
\(726\) 0 0
\(727\) − 39.8464i − 1.47782i −0.673803 0.738911i \(-0.735340\pi\)
0.673803 0.738911i \(-0.264660\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 18.7455 0.693328
\(732\) 0 0
\(733\) 33.6913 1.24442 0.622209 0.782851i \(-0.286235\pi\)
0.622209 + 0.782851i \(0.286235\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21.1411i 0.778744i
\(738\) 0 0
\(739\) − 6.29537i − 0.231579i −0.993274 0.115789i \(-0.963060\pi\)
0.993274 0.115789i \(-0.0369398\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 46.2166 1.69552 0.847760 0.530379i \(-0.177950\pi\)
0.847760 + 0.530379i \(0.177950\pi\)
\(744\) 0 0
\(745\) −6.26238 −0.229436
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.89554i 0.178879i
\(750\) 0 0
\(751\) − 33.6850i − 1.22918i −0.788846 0.614591i \(-0.789321\pi\)
0.788846 0.614591i \(-0.210679\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 34.9242 1.27102
\(756\) 0 0
\(757\) 35.5063 1.29050 0.645249 0.763973i \(-0.276754\pi\)
0.645249 + 0.763973i \(0.276754\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 2.95585i − 0.107150i −0.998564 0.0535748i \(-0.982938\pi\)
0.998564 0.0535748i \(-0.0170616\pi\)
\(762\) 0 0
\(763\) − 9.85147i − 0.356647i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.58564 0.273902
\(768\) 0 0
\(769\) −0.239047 −0.00862026 −0.00431013 0.999991i \(-0.501372\pi\)
−0.00431013 + 0.999991i \(0.501372\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 13.2405i − 0.476229i −0.971237 0.238114i \(-0.923471\pi\)
0.971237 0.238114i \(-0.0765293\pi\)
\(774\) 0 0
\(775\) 15.9849i 0.574194i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.11214 0.111504
\(780\) 0 0
\(781\) 21.7985 0.780013
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 45.5700i − 1.62646i
\(786\) 0 0
\(787\) − 12.9966i − 0.463279i −0.972802 0.231640i \(-0.925591\pi\)
0.972802 0.231640i \(-0.0744090\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.43750 0.0511115
\(792\) 0 0
\(793\) 14.9161 0.529687
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 24.1127i 0.854114i 0.904225 + 0.427057i \(0.140450\pi\)
−0.904225 + 0.427057i \(0.859550\pi\)
\(798\) 0 0
\(799\) − 28.7677i − 1.01773i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −18.5261 −0.653772
\(804\) 0 0
\(805\) −13.9629 −0.492127
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 10.5178i 0.369788i 0.982758 + 0.184894i \(0.0591942\pi\)
−0.982758 + 0.184894i \(0.940806\pi\)
\(810\) 0 0
\(811\) 25.3137i 0.888883i 0.895808 + 0.444441i \(0.146598\pi\)
−0.895808 + 0.444441i \(0.853402\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −51.0465 −1.78808
\(816\) 0 0
\(817\) 3.81744 0.133555
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 18.8811i 0.658956i 0.944163 + 0.329478i \(0.106873\pi\)
−0.944163 + 0.329478i \(0.893127\pi\)
\(822\) 0 0
\(823\) − 3.76306i − 0.131172i −0.997847 0.0655860i \(-0.979108\pi\)
0.997847 0.0655860i \(-0.0208917\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 30.5208 1.06131 0.530656 0.847587i \(-0.321946\pi\)
0.530656 + 0.847587i \(0.321946\pi\)
\(828\) 0 0
\(829\) 46.1222 1.60189 0.800945 0.598738i \(-0.204331\pi\)
0.800945 + 0.598738i \(0.204331\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 32.7782i 1.13570i
\(834\) 0 0
\(835\) − 68.2459i − 2.36175i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −30.1716 −1.04164 −0.520819 0.853667i \(-0.674374\pi\)
−0.520819 + 0.853667i \(0.674374\pi\)
\(840\) 0 0
\(841\) 23.2631 0.802176
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 1.09590i − 0.0377002i
\(846\) 0 0
\(847\) − 4.60448i − 0.158212i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −49.3035 −1.69010
\(852\) 0 0
\(853\) 18.4674 0.632313 0.316156 0.948707i \(-0.397608\pi\)
0.316156 + 0.948707i \(0.397608\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 23.9843i − 0.819290i −0.912245 0.409645i \(-0.865653\pi\)
0.912245 0.409645i \(-0.134347\pi\)
\(858\) 0 0
\(859\) − 17.4158i − 0.594219i −0.954843 0.297110i \(-0.903977\pi\)
0.954843 0.297110i \(-0.0960227\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −17.4424 −0.593746 −0.296873 0.954917i \(-0.595944\pi\)
−0.296873 + 0.954917i \(0.595944\pi\)
\(864\) 0 0
\(865\) 11.2753 0.383373
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 3.91429i − 0.132783i
\(870\) 0 0
\(871\) 43.9559i 1.48939i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.10076 −0.0710187
\(876\) 0 0
\(877\) −7.46831 −0.252187 −0.126093 0.992018i \(-0.540244\pi\)
−0.126093 + 0.992018i \(0.540244\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 23.2123i − 0.782042i −0.920382 0.391021i \(-0.872122\pi\)
0.920382 0.391021i \(-0.127878\pi\)
\(882\) 0 0
\(883\) 36.7029i 1.23515i 0.786512 + 0.617575i \(0.211885\pi\)
−0.786512 + 0.617575i \(0.788115\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 50.1244 1.68301 0.841507 0.540246i \(-0.181669\pi\)
0.841507 + 0.540246i \(0.181669\pi\)
\(888\) 0 0
\(889\) 5.41099 0.181479
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 5.85841i − 0.196044i
\(894\) 0 0
\(895\) 11.3926i 0.380814i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 10.1981 0.340126
\(900\) 0 0
\(901\) −21.1588 −0.704903
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 48.3179i 1.60614i
\(906\) 0 0
\(907\) 35.8688i 1.19101i 0.803353 + 0.595503i \(0.203047\pi\)
−0.803353 + 0.595503i \(0.796953\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −43.0961 −1.42784 −0.713919 0.700229i \(-0.753081\pi\)
−0.713919 + 0.700229i \(0.753081\pi\)
\(912\) 0 0
\(913\) 2.97212 0.0983630
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 3.11932i − 0.103009i
\(918\) 0 0
\(919\) − 21.5024i − 0.709300i −0.934999 0.354650i \(-0.884600\pi\)
0.934999 0.354650i \(-0.115400\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 45.3227 1.49182
\(924\) 0 0
\(925\) 22.3560 0.735061
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 19.3969i 0.636391i 0.948025 + 0.318196i \(0.103077\pi\)
−0.948025 + 0.318196i \(0.896923\pi\)
\(930\) 0 0
\(931\) 6.67513i 0.218769i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −24.8337 −0.812150
\(936\) 0 0
\(937\) −38.4396 −1.25577 −0.627884 0.778307i \(-0.716079\pi\)
−0.627884 + 0.778307i \(0.716079\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 46.5127i 1.51627i 0.652098 + 0.758135i \(0.273889\pi\)
−0.652098 + 0.758135i \(0.726111\pi\)
\(942\) 0 0
\(943\) − 25.7674i − 0.839103i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 43.8937 1.42635 0.713177 0.700984i \(-0.247256\pi\)
0.713177 + 0.700984i \(0.247256\pi\)
\(948\) 0 0
\(949\) −38.5188 −1.25037
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 4.72133i − 0.152939i −0.997072 0.0764694i \(-0.975635\pi\)
0.997072 0.0764694i \(-0.0243648\pi\)
\(954\) 0 0
\(955\) − 2.10628i − 0.0681576i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.05053 −0.195382
\(960\) 0 0
\(961\) 12.8715 0.415210
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 15.0360i − 0.484027i
\(966\) 0 0
\(967\) − 33.2550i − 1.06941i −0.845039 0.534704i \(-0.820423\pi\)
0.845039 0.534704i \(-0.179577\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 11.3041 0.362766 0.181383 0.983413i \(-0.441943\pi\)
0.181383 + 0.983413i \(0.441943\pi\)
\(972\) 0 0
\(973\) −11.7871 −0.377875
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 28.7282i 0.919095i 0.888153 + 0.459548i \(0.151988\pi\)
−0.888153 + 0.459548i \(0.848012\pi\)
\(978\) 0 0
\(979\) 24.9996i 0.798991i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 28.4309 0.906806 0.453403 0.891306i \(-0.350210\pi\)
0.453403 + 0.891306i \(0.350210\pi\)
\(984\) 0 0
\(985\) −33.4617 −1.06618
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 31.6071i − 1.00505i
\(990\) 0 0
\(991\) − 6.74590i − 0.214290i −0.994243 0.107145i \(-0.965829\pi\)
0.994243 0.107145i \(-0.0341710\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −48.9463 −1.55170
\(996\) 0 0
\(997\) −56.9248 −1.80283 −0.901414 0.432959i \(-0.857469\pi\)
−0.901414 + 0.432959i \(0.857469\pi\)
\(998\) 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.2015.24 yes 24
3.2 odd 2 inner 2736.2.d.b.2015.2 yes 24
4.3 odd 2 inner 2736.2.d.b.2015.23 yes 24
12.11 even 2 inner 2736.2.d.b.2015.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.d.b.2015.1 24 12.11 even 2 inner
2736.2.d.b.2015.2 yes 24 3.2 odd 2 inner
2736.2.d.b.2015.23 yes 24 4.3 odd 2 inner
2736.2.d.b.2015.24 yes 24 1.1 even 1 trivial