Properties

Label 6048.2.c.d.3025.10
Level 6048
Weight 2
Character 6048.3025
Analytic conductor 48.294
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\Q(\zeta_{40})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3025.10
Root \(-0.987688 - 0.156434i\)
Character \(\chi\) = 6048.3025
Dual form 6048.2.c.d.3025.7

$q$-expansion

\(f(q)\) \(=\) \(q+0.0549306i q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+0.0549306i q^{5} +1.00000 q^{7} +2.63506i q^{11} +3.67853i q^{13} -3.16228 q^{17} +3.07768i q^{19} +2.86834 q^{23} +4.99698 q^{25} +10.1898i q^{29} -9.32437 q^{31} +0.0549306i q^{35} -0.774554i q^{37} -6.36183 q^{41} -9.98927i q^{43} -12.3126 q^{47} +1.00000 q^{49} -3.39291i q^{53} -0.144746 q^{55} -6.93263i q^{59} +8.35114i q^{61} -0.202064 q^{65} -8.93584i q^{67} +4.28255 q^{71} +8.38081 q^{73} +2.63506i q^{77} +3.03186 q^{79} -10.3255i q^{83} -0.173706i q^{85} -12.8155 q^{89} +3.67853i q^{91} -0.169059 q^{95} -10.1803 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{7} + O(q^{10}) \) \( 16q + 16q^{7} - 32q^{25} - 40q^{31} + 16q^{49} + 72q^{55} + 24q^{73} - 24q^{79} + 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).

\(n\) \(2593\) \(3781\) \(3809\) \(4159\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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
\(5\) 0.0549306i 0.0245657i 0.999925 + 0.0122828i \(0.00390985\pi\)
−0.999925 + 0.0122828i \(0.996090\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.63506i 0.794502i 0.917710 + 0.397251i \(0.130036\pi\)
−0.917710 + 0.397251i \(0.869964\pi\)
\(12\) 0 0
\(13\) 3.67853i 1.02024i 0.860103 + 0.510121i \(0.170399\pi\)
−0.860103 + 0.510121i \(0.829601\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.16228 −0.766965 −0.383482 0.923548i \(-0.625275\pi\)
−0.383482 + 0.923548i \(0.625275\pi\)
\(18\) 0 0
\(19\) 3.07768i 0.706069i 0.935610 + 0.353035i \(0.114850\pi\)
−0.935610 + 0.353035i \(0.885150\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.86834 0.598090 0.299045 0.954239i \(-0.403332\pi\)
0.299045 + 0.954239i \(0.403332\pi\)
\(24\) 0 0
\(25\) 4.99698 0.999397
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 10.1898i 1.89219i 0.323890 + 0.946095i \(0.395009\pi\)
−0.323890 + 0.946095i \(0.604991\pi\)
\(30\) 0 0
\(31\) −9.32437 −1.67471 −0.837353 0.546662i \(-0.815898\pi\)
−0.837353 + 0.546662i \(0.815898\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.0549306i 0.00928496i
\(36\) 0 0
\(37\) − 0.774554i − 0.127336i −0.997971 0.0636679i \(-0.979720\pi\)
0.997971 0.0636679i \(-0.0202798\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.36183 −0.993551 −0.496775 0.867879i \(-0.665483\pi\)
−0.496775 + 0.867879i \(0.665483\pi\)
\(42\) 0 0
\(43\) − 9.98927i − 1.52335i −0.647960 0.761674i \(-0.724378\pi\)
0.647960 0.761674i \(-0.275622\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.3126 −1.79598 −0.897990 0.440015i \(-0.854973\pi\)
−0.897990 + 0.440015i \(0.854973\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 3.39291i − 0.466052i −0.972470 0.233026i \(-0.925137\pi\)
0.972470 0.233026i \(-0.0748628\pi\)
\(54\) 0 0
\(55\) −0.144746 −0.0195175
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 6.93263i − 0.902552i −0.892384 0.451276i \(-0.850969\pi\)
0.892384 0.451276i \(-0.149031\pi\)
\(60\) 0 0
\(61\) 8.35114i 1.06925i 0.845088 + 0.534627i \(0.179548\pi\)
−0.845088 + 0.534627i \(0.820452\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.202064 −0.0250629
\(66\) 0 0
\(67\) − 8.93584i − 1.09169i −0.837887 0.545843i \(-0.816209\pi\)
0.837887 0.545843i \(-0.183791\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.28255 0.508245 0.254123 0.967172i \(-0.418213\pi\)
0.254123 + 0.967172i \(0.418213\pi\)
\(72\) 0 0
\(73\) 8.38081 0.980900 0.490450 0.871469i \(-0.336832\pi\)
0.490450 + 0.871469i \(0.336832\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.63506i 0.300293i
\(78\) 0 0
\(79\) 3.03186 0.341111 0.170556 0.985348i \(-0.445444\pi\)
0.170556 + 0.985348i \(0.445444\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 10.3255i − 1.13338i −0.823932 0.566688i \(-0.808224\pi\)
0.823932 0.566688i \(-0.191776\pi\)
\(84\) 0 0
\(85\) − 0.173706i − 0.0188410i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −12.8155 −1.35844 −0.679222 0.733933i \(-0.737683\pi\)
−0.679222 + 0.733933i \(0.737683\pi\)
\(90\) 0 0
\(91\) 3.67853i 0.385615i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.169059 −0.0173451
\(96\) 0 0
\(97\) −10.1803 −1.03366 −0.516828 0.856089i \(-0.672887\pi\)
−0.516828 + 0.856089i \(0.672887\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.02749i 0.102239i 0.998693 + 0.0511194i \(0.0162789\pi\)
−0.998693 + 0.0511194i \(0.983721\pi\)
\(102\) 0 0
\(103\) −1.72905 −0.170368 −0.0851842 0.996365i \(-0.527148\pi\)
−0.0851842 + 0.996365i \(0.527148\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 6.11985i − 0.591629i −0.955245 0.295814i \(-0.904409\pi\)
0.955245 0.295814i \(-0.0955910\pi\)
\(108\) 0 0
\(109\) 8.85597i 0.848248i 0.905604 + 0.424124i \(0.139418\pi\)
−0.905604 + 0.424124i \(0.860582\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.02383 −0.848891 −0.424445 0.905454i \(-0.639531\pi\)
−0.424445 + 0.905454i \(0.639531\pi\)
\(114\) 0 0
\(115\) 0.157559i 0.0146925i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.16228 −0.289886
\(120\) 0 0
\(121\) 4.05644 0.368767
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.549140i 0.0491166i
\(126\) 0 0
\(127\) −18.2656 −1.62081 −0.810406 0.585868i \(-0.800754\pi\)
−0.810406 + 0.585868i \(0.800754\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 17.4470i 1.52435i 0.647373 + 0.762174i \(0.275868\pi\)
−0.647373 + 0.762174i \(0.724132\pi\)
\(132\) 0 0
\(133\) 3.07768i 0.266869i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.73613 −0.660942 −0.330471 0.943816i \(-0.607208\pi\)
−0.330471 + 0.943816i \(0.607208\pi\)
\(138\) 0 0
\(139\) 0.802034i 0.0680276i 0.999421 + 0.0340138i \(0.0108290\pi\)
−0.999421 + 0.0340138i \(0.989171\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.69316 −0.810583
\(144\) 0 0
\(145\) −0.559729 −0.0464829
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.7165i 1.28755i 0.765215 + 0.643775i \(0.222633\pi\)
−0.765215 + 0.643775i \(0.777367\pi\)
\(150\) 0 0
\(151\) −2.58129 −0.210062 −0.105031 0.994469i \(-0.533494\pi\)
−0.105031 + 0.994469i \(0.533494\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 0.512193i − 0.0411403i
\(156\) 0 0
\(157\) 0.680724i 0.0543277i 0.999631 + 0.0271638i \(0.00864758\pi\)
−0.999631 + 0.0271638i \(0.991352\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.86834 0.226057
\(162\) 0 0
\(163\) − 21.8339i − 1.71016i −0.518494 0.855081i \(-0.673507\pi\)
0.518494 0.855081i \(-0.326493\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −17.2203 −1.33255 −0.666274 0.745707i \(-0.732112\pi\)
−0.666274 + 0.745707i \(0.732112\pi\)
\(168\) 0 0
\(169\) −0.531594 −0.0408918
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.57218i 0.195559i 0.995208 + 0.0977797i \(0.0311741\pi\)
−0.995208 + 0.0977797i \(0.968826\pi\)
\(174\) 0 0
\(175\) 4.99698 0.377736
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.26703i 0.393676i 0.980436 + 0.196838i \(0.0630673\pi\)
−0.980436 + 0.196838i \(0.936933\pi\)
\(180\) 0 0
\(181\) − 16.0189i − 1.19068i −0.803475 0.595339i \(-0.797018\pi\)
0.803475 0.595339i \(-0.202982\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.0425467 0.00312809
\(186\) 0 0
\(187\) − 8.33280i − 0.609355i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.83730 −0.132943 −0.0664713 0.997788i \(-0.521174\pi\)
−0.0664713 + 0.997788i \(0.521174\pi\)
\(192\) 0 0
\(193\) 15.3429 1.10441 0.552204 0.833709i \(-0.313787\pi\)
0.552204 + 0.833709i \(0.313787\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 5.02447i − 0.357979i −0.983851 0.178989i \(-0.942717\pi\)
0.983851 0.178989i \(-0.0572828\pi\)
\(198\) 0 0
\(199\) 22.0333 1.56190 0.780949 0.624595i \(-0.214736\pi\)
0.780949 + 0.624595i \(0.214736\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10.1898i 0.715180i
\(204\) 0 0
\(205\) − 0.349459i − 0.0244073i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.10989 −0.560973
\(210\) 0 0
\(211\) 8.50651i 0.585612i 0.956172 + 0.292806i \(0.0945890\pi\)
−0.956172 + 0.292806i \(0.905411\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.548716 0.0374221
\(216\) 0 0
\(217\) −9.32437 −0.632980
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 11.6325i − 0.782489i
\(222\) 0 0
\(223\) 13.5574 0.907872 0.453936 0.891034i \(-0.350019\pi\)
0.453936 + 0.891034i \(0.350019\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 16.0721i 1.06674i 0.845882 + 0.533370i \(0.179075\pi\)
−0.845882 + 0.533370i \(0.820925\pi\)
\(228\) 0 0
\(229\) 5.50870i 0.364025i 0.983296 + 0.182013i \(0.0582612\pi\)
−0.983296 + 0.182013i \(0.941739\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −28.6599 −1.87757 −0.938787 0.344498i \(-0.888049\pi\)
−0.938787 + 0.344498i \(0.888049\pi\)
\(234\) 0 0
\(235\) − 0.676339i − 0.0441195i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3.82998 0.247741 0.123870 0.992298i \(-0.460469\pi\)
0.123870 + 0.992298i \(0.460469\pi\)
\(240\) 0 0
\(241\) −1.72834 −0.111332 −0.0556660 0.998449i \(-0.517728\pi\)
−0.0556660 + 0.998449i \(0.517728\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.0549306i 0.00350938i
\(246\) 0 0
\(247\) −11.3214 −0.720361
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 0.245657i − 0.0155057i −0.999970 0.00775286i \(-0.997532\pi\)
0.999970 0.00775286i \(-0.00246784\pi\)
\(252\) 0 0
\(253\) 7.55825i 0.475183i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 16.2120 1.01128 0.505638 0.862746i \(-0.331257\pi\)
0.505638 + 0.862746i \(0.331257\pi\)
\(258\) 0 0
\(259\) − 0.774554i − 0.0481284i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −23.3265 −1.43837 −0.719187 0.694817i \(-0.755485\pi\)
−0.719187 + 0.694817i \(0.755485\pi\)
\(264\) 0 0
\(265\) 0.186375 0.0114489
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 23.6947i − 1.44469i −0.691534 0.722344i \(-0.743065\pi\)
0.691534 0.722344i \(-0.256935\pi\)
\(270\) 0 0
\(271\) −3.52786 −0.214302 −0.107151 0.994243i \(-0.534173\pi\)
−0.107151 + 0.994243i \(0.534173\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 13.1674i 0.794022i
\(276\) 0 0
\(277\) 28.6014i 1.71849i 0.511561 + 0.859247i \(0.329068\pi\)
−0.511561 + 0.859247i \(0.670932\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 25.6546 1.53043 0.765214 0.643776i \(-0.222633\pi\)
0.765214 + 0.643776i \(0.222633\pi\)
\(282\) 0 0
\(283\) 14.8539i 0.882974i 0.897268 + 0.441487i \(0.145549\pi\)
−0.897268 + 0.441487i \(0.854451\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.36183 −0.375527
\(288\) 0 0
\(289\) −7.00000 −0.411765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.6946i 1.26741i 0.773574 + 0.633706i \(0.218467\pi\)
−0.773574 + 0.633706i \(0.781533\pi\)
\(294\) 0 0
\(295\) 0.380813 0.0221718
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10.5513i 0.610195i
\(300\) 0 0
\(301\) − 9.98927i − 0.575772i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.458733 −0.0262670
\(306\) 0 0
\(307\) − 0.422903i − 0.0241363i −0.999927 0.0120682i \(-0.996158\pi\)
0.999927 0.0120682i \(-0.00384151\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −13.6732 −0.775338 −0.387669 0.921799i \(-0.626720\pi\)
−0.387669 + 0.921799i \(0.626720\pi\)
\(312\) 0 0
\(313\) −7.68665 −0.434475 −0.217237 0.976119i \(-0.569705\pi\)
−0.217237 + 0.976119i \(0.569705\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.2068i 1.35959i 0.733401 + 0.679796i \(0.237932\pi\)
−0.733401 + 0.679796i \(0.762068\pi\)
\(318\) 0 0
\(319\) −26.8506 −1.50335
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 9.73249i − 0.541530i
\(324\) 0 0
\(325\) 18.3816i 1.01963i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −12.3126 −0.678817
\(330\) 0 0
\(331\) 9.15756i 0.503345i 0.967812 + 0.251672i \(0.0809806\pi\)
−0.967812 + 0.251672i \(0.919019\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.490851 0.0268180
\(336\) 0 0
\(337\) 33.2441 1.81092 0.905460 0.424432i \(-0.139526\pi\)
0.905460 + 0.424432i \(0.139526\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 24.5703i − 1.33056i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.03418i 0.431297i 0.976471 + 0.215649i \(0.0691866\pi\)
−0.976471 + 0.215649i \(0.930813\pi\)
\(348\) 0 0
\(349\) − 5.46493i − 0.292531i −0.989245 0.146265i \(-0.953275\pi\)
0.989245 0.146265i \(-0.0467254\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.85159 0.417898 0.208949 0.977927i \(-0.432996\pi\)
0.208949 + 0.977927i \(0.432996\pi\)
\(354\) 0 0
\(355\) 0.235243i 0.0124854i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −30.4616 −1.60770 −0.803851 0.594831i \(-0.797219\pi\)
−0.803851 + 0.594831i \(0.797219\pi\)
\(360\) 0 0
\(361\) 9.52786 0.501467
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.460363i 0.0240965i
\(366\) 0 0
\(367\) −8.97241 −0.468356 −0.234178 0.972194i \(-0.575240\pi\)
−0.234178 + 0.972194i \(0.575240\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 3.39291i − 0.176151i
\(372\) 0 0
\(373\) − 19.6614i − 1.01803i −0.860759 0.509013i \(-0.830010\pi\)
0.860759 0.509013i \(-0.169990\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −37.4833 −1.93049
\(378\) 0 0
\(379\) 24.9871i 1.28350i 0.766914 + 0.641750i \(0.221791\pi\)
−0.766914 + 0.641750i \(0.778209\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −20.3323 −1.03893 −0.519465 0.854492i \(-0.673869\pi\)
−0.519465 + 0.854492i \(0.673869\pi\)
\(384\) 0 0
\(385\) −0.144746 −0.00737691
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.92753i 0.148432i 0.997242 + 0.0742159i \(0.0236454\pi\)
−0.997242 + 0.0742159i \(0.976355\pi\)
\(390\) 0 0
\(391\) −9.07048 −0.458714
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.166542i 0.00837964i
\(396\) 0 0
\(397\) − 8.20287i − 0.411690i −0.978585 0.205845i \(-0.934006\pi\)
0.978585 0.205845i \(-0.0659943\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −36.5590 −1.82567 −0.912834 0.408332i \(-0.866111\pi\)
−0.912834 + 0.408332i \(0.866111\pi\)
\(402\) 0 0
\(403\) − 34.3000i − 1.70860i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.04100 0.101169
\(408\) 0 0
\(409\) −6.01783 −0.297562 −0.148781 0.988870i \(-0.547535\pi\)
−0.148781 + 0.988870i \(0.547535\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 6.93263i − 0.341133i
\(414\) 0 0
\(415\) 0.567188 0.0278422
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 2.25247i − 0.110040i −0.998485 0.0550201i \(-0.982478\pi\)
0.998485 0.0550201i \(-0.0175223\pi\)
\(420\) 0 0
\(421\) 2.87431i 0.140085i 0.997544 + 0.0700425i \(0.0223135\pi\)
−0.997544 + 0.0700425i \(0.977686\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −15.8018 −0.766502
\(426\) 0 0
\(427\) 8.35114i 0.404140i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.7211 −0.757261 −0.378630 0.925548i \(-0.623605\pi\)
−0.378630 + 0.925548i \(0.623605\pi\)
\(432\) 0 0
\(433\) −3.44027 −0.165329 −0.0826644 0.996577i \(-0.526343\pi\)
−0.0826644 + 0.996577i \(0.526343\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.82783i 0.422292i
\(438\) 0 0
\(439\) 12.2955 0.586833 0.293417 0.955985i \(-0.405208\pi\)
0.293417 + 0.955985i \(0.405208\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 15.8932i − 0.755107i −0.925988 0.377553i \(-0.876765\pi\)
0.925988 0.377553i \(-0.123235\pi\)
\(444\) 0 0
\(445\) − 0.703964i − 0.0333711i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −8.97450 −0.423533 −0.211766 0.977320i \(-0.567922\pi\)
−0.211766 + 0.977320i \(0.567922\pi\)
\(450\) 0 0
\(451\) − 16.7638i − 0.789377i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.202064 −0.00947290
\(456\) 0 0
\(457\) −15.0037 −0.701845 −0.350922 0.936405i \(-0.614132\pi\)
−0.350922 + 0.936405i \(0.614132\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 8.69884i − 0.405145i −0.979267 0.202573i \(-0.935070\pi\)
0.979267 0.202573i \(-0.0649303\pi\)
\(462\) 0 0
\(463\) 9.34522 0.434309 0.217155 0.976137i \(-0.430322\pi\)
0.217155 + 0.976137i \(0.430322\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 9.23326i − 0.427265i −0.976914 0.213632i \(-0.931471\pi\)
0.976914 0.213632i \(-0.0685294\pi\)
\(468\) 0 0
\(469\) − 8.93584i − 0.412619i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 26.3223 1.21030
\(474\) 0 0
\(475\) 15.3791i 0.705643i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.66050 0.395708 0.197854 0.980231i \(-0.436603\pi\)
0.197854 + 0.980231i \(0.436603\pi\)
\(480\) 0 0
\(481\) 2.84922 0.129913
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 0.559212i − 0.0253925i
\(486\) 0 0
\(487\) −11.1424 −0.504912 −0.252456 0.967608i \(-0.581238\pi\)
−0.252456 + 0.967608i \(0.581238\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 25.4479i 1.14845i 0.818698 + 0.574224i \(0.194696\pi\)
−0.818698 + 0.574224i \(0.805304\pi\)
\(492\) 0 0
\(493\) − 32.2228i − 1.45124i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.28255 0.192099
\(498\) 0 0
\(499\) − 4.17422i − 0.186864i −0.995626 0.0934318i \(-0.970216\pi\)
0.995626 0.0934318i \(-0.0297837\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10.6106 −0.473105 −0.236552 0.971619i \(-0.576017\pi\)
−0.236552 + 0.971619i \(0.576017\pi\)
\(504\) 0 0
\(505\) −0.0564404 −0.00251156
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 24.1111i 1.06871i 0.845262 + 0.534353i \(0.179445\pi\)
−0.845262 + 0.534353i \(0.820555\pi\)
\(510\) 0 0
\(511\) 8.38081 0.370745
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 0.0949777i − 0.00418522i
\(516\) 0 0
\(517\) − 32.4445i − 1.42691i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 32.5642 1.42666 0.713331 0.700827i \(-0.247185\pi\)
0.713331 + 0.700827i \(0.247185\pi\)
\(522\) 0 0
\(523\) − 18.6166i − 0.814046i −0.913418 0.407023i \(-0.866567\pi\)
0.913418 0.407023i \(-0.133433\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 29.4863 1.28444
\(528\) 0 0
\(529\) −14.7726 −0.642289
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 23.4022i − 1.01366i
\(534\) 0 0
\(535\) 0.336167 0.0145338
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.63506i 0.113500i
\(540\) 0 0
\(541\) 41.3556i 1.77802i 0.457891 + 0.889008i \(0.348605\pi\)
−0.457891 + 0.889008i \(0.651395\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.486463 −0.0208378
\(546\) 0 0
\(547\) − 18.8135i − 0.804408i −0.915550 0.402204i \(-0.868244\pi\)
0.915550 0.402204i \(-0.131756\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −31.3608 −1.33602
\(552\) 0 0
\(553\) 3.03186 0.128928
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 4.05808i − 0.171946i −0.996297 0.0859731i \(-0.972600\pi\)
0.996297 0.0859731i \(-0.0273999\pi\)
\(558\) 0 0
\(559\) 36.7458 1.55418
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 45.2454i 1.90687i 0.301605 + 0.953433i \(0.402478\pi\)
−0.301605 + 0.953433i \(0.597522\pi\)
\(564\) 0 0
\(565\) − 0.495684i − 0.0208536i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13.6255 −0.571212 −0.285606 0.958347i \(-0.592195\pi\)
−0.285606 + 0.958347i \(0.592195\pi\)
\(570\) 0 0
\(571\) 30.9574i 1.29553i 0.761842 + 0.647763i \(0.224295\pi\)
−0.761842 + 0.647763i \(0.775705\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 14.3330 0.597729
\(576\) 0 0
\(577\) −38.4675 −1.60142 −0.800712 0.599049i \(-0.795545\pi\)
−0.800712 + 0.599049i \(0.795545\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 10.3255i − 0.428376i
\(582\) 0 0
\(583\) 8.94054 0.370279
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 28.6131i 1.18099i 0.807041 + 0.590495i \(0.201068\pi\)
−0.807041 + 0.590495i \(0.798932\pi\)
\(588\) 0 0
\(589\) − 28.6975i − 1.18246i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −22.5554 −0.926239 −0.463119 0.886296i \(-0.653270\pi\)
−0.463119 + 0.886296i \(0.653270\pi\)
\(594\) 0 0
\(595\) − 0.173706i − 0.00712124i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 42.1743 1.72319 0.861597 0.507593i \(-0.169465\pi\)
0.861597 + 0.507593i \(0.169465\pi\)
\(600\) 0 0
\(601\) −14.0155 −0.571705 −0.285853 0.958274i \(-0.592277\pi\)
−0.285853 + 0.958274i \(0.592277\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.222823i 0.00905902i
\(606\) 0 0
\(607\) 21.5893 0.876282 0.438141 0.898906i \(-0.355637\pi\)
0.438141 + 0.898906i \(0.355637\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 45.2924i − 1.83233i
\(612\) 0 0
\(613\) 0.788508i 0.0318475i 0.999873 + 0.0159238i \(0.00506891\pi\)
−0.999873 + 0.0159238i \(0.994931\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.4936 1.38866 0.694331 0.719656i \(-0.255701\pi\)
0.694331 + 0.719656i \(0.255701\pi\)
\(618\) 0 0
\(619\) 47.8005i 1.92127i 0.277822 + 0.960633i \(0.410388\pi\)
−0.277822 + 0.960633i \(0.589612\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.8155 −0.513443
\(624\) 0 0
\(625\) 24.9547 0.998190
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.44935i 0.0976621i
\(630\) 0 0
\(631\) 21.7200 0.864659 0.432330 0.901716i \(-0.357692\pi\)
0.432330 + 0.901716i \(0.357692\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 1.00334i − 0.0398164i
\(636\) 0 0
\(637\) 3.67853i 0.145749i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17.0166 −0.672117 −0.336058 0.941841i \(-0.609094\pi\)
−0.336058 + 0.941841i \(0.609094\pi\)
\(642\) 0 0
\(643\) 38.4170i 1.51502i 0.652824 + 0.757509i \(0.273584\pi\)
−0.652824 + 0.757509i \(0.726416\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 22.7497 0.894382 0.447191 0.894439i \(-0.352425\pi\)
0.447191 + 0.894439i \(0.352425\pi\)
\(648\) 0 0
\(649\) 18.2679 0.717079
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12.9198i 0.505591i 0.967520 + 0.252795i \(0.0813499\pi\)
−0.967520 + 0.252795i \(0.918650\pi\)
\(654\) 0 0
\(655\) −0.958371 −0.0374466
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 47.1905i − 1.83828i −0.393932 0.919140i \(-0.628885\pi\)
0.393932 0.919140i \(-0.371115\pi\)
\(660\) 0 0
\(661\) − 31.5648i − 1.22773i −0.789412 0.613864i \(-0.789614\pi\)
0.789412 0.613864i \(-0.210386\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.169059 −0.00655582
\(666\) 0 0
\(667\) 29.2276i 1.13170i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −22.0058 −0.849524
\(672\) 0 0
\(673\) −37.1186 −1.43082 −0.715408 0.698707i \(-0.753759\pi\)
−0.715408 + 0.698707i \(0.753759\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.8912i 0.610750i 0.952232 + 0.305375i \(0.0987818\pi\)
−0.952232 + 0.305375i \(0.901218\pi\)
\(678\) 0 0
\(679\) −10.1803 −0.390686
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 27.4319i − 1.04965i −0.851210 0.524826i \(-0.824131\pi\)
0.851210 0.524826i \(-0.175869\pi\)
\(684\) 0 0
\(685\) − 0.424950i − 0.0162365i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12.4809 0.475486
\(690\) 0 0
\(691\) 6.57770i 0.250227i 0.992142 + 0.125114i \(0.0399296\pi\)
−0.992142 + 0.125114i \(0.960070\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.0440562 −0.00167115
\(696\) 0 0
\(697\) 20.1179 0.762018
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 9.07153i − 0.342627i −0.985217 0.171314i \(-0.945199\pi\)
0.985217 0.171314i \(-0.0548011\pi\)
\(702\) 0 0
\(703\) 2.38383 0.0899079
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.02749i 0.0386426i
\(708\) 0 0
\(709\) − 6.16889i − 0.231678i −0.993268 0.115839i \(-0.963044\pi\)
0.993268 0.115839i \(-0.0369556\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −26.7454 −1.00162
\(714\) 0 0
\(715\) − 0.532451i − 0.0199125i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −30.5440 −1.13910 −0.569550 0.821956i \(-0.692883\pi\)
−0.569550 + 0.821956i \(0.692883\pi\)
\(720\) 0 0
\(721\) −1.72905 −0.0643932
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 50.9180i 1.89105i
\(726\) 0 0
\(727\) 21.3429 0.791565 0.395782 0.918344i \(-0.370473\pi\)
0.395782 + 0.918344i \(0.370473\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 31.5888i 1.16836i
\(732\) 0 0
\(733\) 15.1235i 0.558599i 0.960204 + 0.279300i \(0.0901023\pi\)
−0.960204 + 0.279300i \(0.909898\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 23.5465 0.867347
\(738\) 0 0
\(739\) − 38.7212i − 1.42438i −0.701985 0.712192i \(-0.747703\pi\)
0.701985 0.712192i \(-0.252297\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 39.7258 1.45740 0.728698 0.684835i \(-0.240126\pi\)
0.728698 + 0.684835i \(0.240126\pi\)
\(744\) 0 0
\(745\) −0.863319 −0.0316296
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 6.11985i − 0.223615i
\(750\) 0 0
\(751\) 2.96814 0.108309 0.0541544 0.998533i \(-0.482754\pi\)
0.0541544 + 0.998533i \(0.482754\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 0.141792i − 0.00516032i
\(756\) 0 0
\(757\) − 47.1588i − 1.71401i −0.515305 0.857007i \(-0.672321\pi\)
0.515305 0.857007i \(-0.327679\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −40.8000 −1.47900 −0.739499 0.673158i \(-0.764937\pi\)
−0.739499 + 0.673158i \(0.764937\pi\)
\(762\) 0 0
\(763\) 8.85597i 0.320608i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 25.5019 0.920821
\(768\) 0 0
\(769\) −52.9121 −1.90806 −0.954029 0.299714i \(-0.903109\pi\)
−0.954029 + 0.299714i \(0.903109\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 39.0168i − 1.40334i −0.712503 0.701669i \(-0.752439\pi\)
0.712503 0.701669i \(-0.247561\pi\)
\(774\) 0 0
\(775\) −46.5937 −1.67370
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 19.5797i − 0.701515i
\(780\) 0 0
\(781\) 11.2848i 0.403802i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.0373925 −0.00133460
\(786\) 0 0
\(787\) 1.01675i 0.0362431i 0.999836 + 0.0181215i \(0.00576858\pi\)
−0.999836 + 0.0181215i \(0.994231\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.02383 −0.320851
\(792\) 0 0
\(793\) −30.7199 −1.09090
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 50.9667i 1.80533i 0.430339 + 0.902667i \(0.358394\pi\)
−0.430339 + 0.902667i \(0.641606\pi\)
\(798\) 0 0
\(799\) 38.9359 1.37745
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 22.0840i 0.779327i
\(804\) 0 0
\(805\) 0.157559i 0.00555324i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 20.3800 0.716522 0.358261 0.933622i \(-0.383370\pi\)
0.358261 + 0.933622i \(0.383370\pi\)
\(810\) 0 0
\(811\) 40.7638i 1.43141i 0.698402 + 0.715706i \(0.253895\pi\)
−0.698402 + 0.715706i \(0.746105\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.19935 0.0420113
\(816\) 0 0
\(817\) 30.7438 1.07559
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 35.8394i 1.25080i 0.780303 + 0.625402i \(0.215065\pi\)
−0.780303 + 0.625402i \(0.784935\pi\)
\(822\) 0 0
\(823\) −34.8745 −1.21565 −0.607824 0.794071i \(-0.707958\pi\)
−0.607824 + 0.794071i \(0.707958\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 42.4727i − 1.47692i −0.674296 0.738461i \(-0.735553\pi\)
0.674296 0.738461i \(-0.264447\pi\)
\(828\) 0 0
\(829\) − 33.1210i − 1.15034i −0.818034 0.575169i \(-0.804936\pi\)
0.818034 0.575169i \(-0.195064\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.16228 −0.109566
\(834\) 0 0
\(835\) − 0.945922i − 0.0327350i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 43.5817 1.50461 0.752304 0.658817i \(-0.228943\pi\)
0.752304 + 0.658817i \(0.228943\pi\)
\(840\) 0 0
\(841\) −74.8311 −2.58038
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 0.0292007i − 0.00100454i
\(846\) 0 0
\(847\) 4.05644 0.139381
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 2.22168i − 0.0761582i
\(852\) 0 0
\(853\) 36.8928i 1.26319i 0.775300 + 0.631593i \(0.217599\pi\)
−0.775300 + 0.631593i \(0.782401\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 19.2607 0.657933 0.328967 0.944342i \(-0.393300\pi\)
0.328967 + 0.944342i \(0.393300\pi\)
\(858\) 0 0
\(859\) − 19.4667i − 0.664195i −0.943245 0.332098i \(-0.892244\pi\)
0.943245 0.332098i \(-0.107756\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 21.4715 0.730898 0.365449 0.930831i \(-0.380915\pi\)
0.365449 + 0.930831i \(0.380915\pi\)
\(864\) 0 0
\(865\) −0.141291 −0.00480405
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 7.98916i 0.271014i
\(870\) 0 0
\(871\) 32.8708 1.11378
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0.549140i 0.0185643i
\(876\) 0 0
\(877\) 23.8421i 0.805091i 0.915400 + 0.402545i \(0.131874\pi\)
−0.915400 + 0.402545i \(0.868126\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 8.81134 0.296862 0.148431 0.988923i \(-0.452578\pi\)
0.148431 + 0.988923i \(0.452578\pi\)
\(882\) 0 0
\(883\) 30.0935i 1.01273i 0.862320 + 0.506363i \(0.169011\pi\)
−0.862320 + 0.506363i \(0.830989\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 13.0549 0.438340 0.219170 0.975687i \(-0.429665\pi\)
0.219170 + 0.975687i \(0.429665\pi\)
\(888\) 0 0
\(889\) −18.2656 −0.612609
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 37.8944i − 1.26809i
\(894\) 0 0
\(895\) −0.289321 −0.00967092
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 95.0131i − 3.16886i
\(900\) 0 0
\(901\) 10.7293i 0.357446i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.879929 0.0292498
\(906\) 0 0
\(907\) − 35.8987i − 1.19200i −0.802985 0.595999i \(-0.796756\pi\)
0.802985 0.595999i \(-0.203244\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 46.3926 1.53705 0.768527 0.639817i \(-0.220990\pi\)
0.768527 + 0.639817i \(0.220990\pi\)
\(912\) 0 0
\(913\) 27.2085 0.900469
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 17.4470i 0.576149i
\(918\) 0 0
\(919\) 9.87878 0.325871 0.162935 0.986637i \(-0.447904\pi\)
0.162935 + 0.986637i \(0.447904\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 15.7535i 0.518533i
\(924\) 0 0
\(925\) − 3.87043i − 0.127259i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3.21688 0.105543 0.0527713 0.998607i \(-0.483195\pi\)
0.0527713 + 0.998607i \(0.483195\pi\)
\(930\) 0 0
\(931\) 3.07768i 0.100867i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.457725 0.0149692
\(936\) 0 0
\(937\) 54.7874 1.78983 0.894913 0.446241i \(-0.147237\pi\)
0.894913 + 0.446241i \(0.147237\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 8.31449i 0.271045i 0.990774 + 0.135522i \(0.0432713\pi\)
−0.990774 + 0.135522i \(0.956729\pi\)
\(942\) 0 0
\(943\) −18.2479 −0.594232
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.2157i 0.396958i 0.980105 + 0.198479i \(0.0636001\pi\)
−0.980105 + 0.198479i \(0.936400\pi\)
\(948\) 0 0
\(949\) 30.8291i 1.00075i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 50.2955 1.62923 0.814615 0.580002i \(-0.196948\pi\)
0.814615 + 0.580002i \(0.196948\pi\)
\(954\) 0 0
\(955\) − 0.100924i − 0.00326583i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.73613 −0.249813
\(960\) 0 0
\(961\) 55.9439 1.80464
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0.842795i 0.0271305i
\(966\) 0 0
\(967\) −6.17661 −0.198626 −0.0993132 0.995056i \(-0.531665\pi\)
−0.0993132 + 0.995056i \(0.531665\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 3.74342i − 0.120132i −0.998194 0.0600660i \(-0.980869\pi\)
0.998194 0.0600660i \(-0.0191311\pi\)
\(972\) 0 0
\(973\) 0.802034i 0.0257120i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 43.1012 1.37893 0.689464 0.724320i \(-0.257846\pi\)
0.689464 + 0.724320i \(0.257846\pi\)
\(978\) 0 0
\(979\) − 33.7697i − 1.07929i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 46.8079 1.49294 0.746470 0.665419i \(-0.231747\pi\)
0.746470 + 0.665419i \(0.231747\pi\)
\(984\) 0 0
\(985\) 0.275997 0.00879399
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 28.6526i − 0.911099i
\(990\) 0 0
\(991\) 44.6923 1.41970 0.709850 0.704353i \(-0.248763\pi\)
0.709850 + 0.704353i \(0.248763\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.21030i 0.0383691i
\(996\) 0 0
\(997\) − 41.1361i − 1.30279i −0.758737 0.651397i \(-0.774183\pi\)
0.758737 0.651397i \(-0.225817\pi\)
\(998\) 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 6048.2.c.d.3025.10 16
3.2 odd 2 inner 6048.2.c.d.3025.8 16
4.3 odd 2 1512.2.c.d.757.7 yes 16
8.3 odd 2 1512.2.c.d.757.6 16
8.5 even 2 inner 6048.2.c.d.3025.7 16
12.11 even 2 1512.2.c.d.757.10 yes 16
24.5 odd 2 inner 6048.2.c.d.3025.9 16
24.11 even 2 1512.2.c.d.757.11 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.c.d.757.6 16 8.3 odd 2
1512.2.c.d.757.7 yes 16 4.3 odd 2
1512.2.c.d.757.10 yes 16 12.11 even 2
1512.2.c.d.757.11 yes 16 24.11 even 2
6048.2.c.d.3025.7 16 8.5 even 2 inner
6048.2.c.d.3025.8 16 3.2 odd 2 inner
6048.2.c.d.3025.9 16 24.5 odd 2 inner
6048.2.c.d.3025.10 16 1.1 even 1 trivial