Properties

Label 6048.2.h.i.2591.7
Level 6048
Weight 2
Character 6048.2591
Analytic conductor 48.294
Analytic rank 0
Dimension 24
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.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.7
Character \(\chi\) = 6048.2591
Dual form 6048.2.h.i.2591.8

$q$-expansion

\(f(q)\) \(=\) \(q-2.76574i q^{5} +1.00000i q^{7} +O(q^{10})\) \(q-2.76574i q^{5} +1.00000i q^{7} +2.55543 q^{11} -2.32854 q^{13} -7.36547i q^{17} +1.78261i q^{19} +3.87170 q^{23} -2.64930 q^{25} -7.32622i q^{29} +2.17647i q^{31} +2.76574 q^{35} -1.24968 q^{37} +3.52679i q^{41} -5.28762i q^{43} -5.77479 q^{47} -1.00000 q^{49} +7.29178i q^{53} -7.06766i q^{55} +4.98108 q^{59} +3.15465 q^{61} +6.44014i q^{65} -7.72509i q^{67} -7.98532 q^{71} -10.7548 q^{73} +2.55543i q^{77} -2.10858i q^{79} +12.1458 q^{83} -20.3710 q^{85} -9.71061i q^{89} -2.32854i q^{91} +4.93024 q^{95} +15.6053 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + O(q^{10}) \) \( 24q - 8q^{13} - 24q^{25} + 48q^{37} - 24q^{49} - 48q^{61} - 32q^{73} - 80q^{85} + 64q^{97} + O(q^{100}) \)

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
\(5\) − 2.76574i − 1.23688i −0.785834 0.618438i \(-0.787766\pi\)
0.785834 0.618438i \(-0.212234\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.55543 0.770493 0.385246 0.922814i \(-0.374116\pi\)
0.385246 + 0.922814i \(0.374116\pi\)
\(12\) 0 0
\(13\) −2.32854 −0.645822 −0.322911 0.946429i \(-0.604661\pi\)
−0.322911 + 0.946429i \(0.604661\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 7.36547i − 1.78639i −0.449669 0.893195i \(-0.648458\pi\)
0.449669 0.893195i \(-0.351542\pi\)
\(18\) 0 0
\(19\) 1.78261i 0.408959i 0.978871 + 0.204480i \(0.0655503\pi\)
−0.978871 + 0.204480i \(0.934450\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.87170 0.807305 0.403653 0.914912i \(-0.367740\pi\)
0.403653 + 0.914912i \(0.367740\pi\)
\(24\) 0 0
\(25\) −2.64930 −0.529861
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 7.32622i − 1.36044i −0.733006 0.680222i \(-0.761883\pi\)
0.733006 0.680222i \(-0.238117\pi\)
\(30\) 0 0
\(31\) 2.17647i 0.390905i 0.980713 + 0.195453i \(0.0626176\pi\)
−0.980713 + 0.195453i \(0.937382\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.76574 0.467495
\(36\) 0 0
\(37\) −1.24968 −0.205445 −0.102723 0.994710i \(-0.532755\pi\)
−0.102723 + 0.994710i \(0.532755\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.52679i 0.550792i 0.961331 + 0.275396i \(0.0888090\pi\)
−0.961331 + 0.275396i \(0.911191\pi\)
\(42\) 0 0
\(43\) − 5.28762i − 0.806355i −0.915122 0.403178i \(-0.867906\pi\)
0.915122 0.403178i \(-0.132094\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.77479 −0.842340 −0.421170 0.906982i \(-0.638380\pi\)
−0.421170 + 0.906982i \(0.638380\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.29178i 1.00160i 0.865562 + 0.500801i \(0.166961\pi\)
−0.865562 + 0.500801i \(0.833039\pi\)
\(54\) 0 0
\(55\) − 7.06766i − 0.953003i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.98108 0.648482 0.324241 0.945975i \(-0.394891\pi\)
0.324241 + 0.945975i \(0.394891\pi\)
\(60\) 0 0
\(61\) 3.15465 0.403912 0.201956 0.979395i \(-0.435270\pi\)
0.201956 + 0.979395i \(0.435270\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.44014i 0.798801i
\(66\) 0 0
\(67\) − 7.72509i − 0.943770i −0.881660 0.471885i \(-0.843574\pi\)
0.881660 0.471885i \(-0.156426\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.98532 −0.947683 −0.473842 0.880610i \(-0.657133\pi\)
−0.473842 + 0.880610i \(0.657133\pi\)
\(72\) 0 0
\(73\) −10.7548 −1.25875 −0.629377 0.777100i \(-0.716690\pi\)
−0.629377 + 0.777100i \(0.716690\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.55543i 0.291219i
\(78\) 0 0
\(79\) − 2.10858i − 0.237234i −0.992940 0.118617i \(-0.962154\pi\)
0.992940 0.118617i \(-0.0378461\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.1458 1.33318 0.666590 0.745425i \(-0.267753\pi\)
0.666590 + 0.745425i \(0.267753\pi\)
\(84\) 0 0
\(85\) −20.3710 −2.20954
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 9.71061i − 1.02932i −0.857394 0.514661i \(-0.827918\pi\)
0.857394 0.514661i \(-0.172082\pi\)
\(90\) 0 0
\(91\) − 2.32854i − 0.244098i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.93024 0.505832
\(96\) 0 0
\(97\) 15.6053 1.58448 0.792239 0.610211i \(-0.208915\pi\)
0.792239 + 0.610211i \(0.208915\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 8.43842i − 0.839654i −0.907604 0.419827i \(-0.862091\pi\)
0.907604 0.419827i \(-0.137909\pi\)
\(102\) 0 0
\(103\) − 1.53472i − 0.151221i −0.997137 0.0756105i \(-0.975909\pi\)
0.997137 0.0756105i \(-0.0240905\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.42794 −0.524739 −0.262369 0.964967i \(-0.584504\pi\)
−0.262369 + 0.964967i \(0.584504\pi\)
\(108\) 0 0
\(109\) −7.47199 −0.715687 −0.357843 0.933782i \(-0.616488\pi\)
−0.357843 + 0.933782i \(0.616488\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.64780i 0.249084i 0.992214 + 0.124542i \(0.0397461\pi\)
−0.992214 + 0.124542i \(0.960254\pi\)
\(114\) 0 0
\(115\) − 10.7081i − 0.998536i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.36547 0.675192
\(120\) 0 0
\(121\) −4.46975 −0.406341
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 6.50141i − 0.581504i
\(126\) 0 0
\(127\) 19.2079i 1.70443i 0.523195 + 0.852213i \(0.324740\pi\)
−0.523195 + 0.852213i \(0.675260\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.182412 0.0159374 0.00796869 0.999968i \(-0.497463\pi\)
0.00796869 + 0.999968i \(0.497463\pi\)
\(132\) 0 0
\(133\) −1.78261 −0.154572
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.55207i 0.474345i 0.971467 + 0.237173i \(0.0762207\pi\)
−0.971467 + 0.237173i \(0.923779\pi\)
\(138\) 0 0
\(139\) − 18.7949i − 1.59416i −0.603873 0.797080i \(-0.706377\pi\)
0.603873 0.797080i \(-0.293623\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −5.95044 −0.497601
\(144\) 0 0
\(145\) −20.2624 −1.68270
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.82804i 0.805144i 0.915388 + 0.402572i \(0.131884\pi\)
−0.915388 + 0.402572i \(0.868116\pi\)
\(150\) 0 0
\(151\) − 8.96087i − 0.729225i −0.931159 0.364613i \(-0.881201\pi\)
0.931159 0.364613i \(-0.118799\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.01954 0.483501
\(156\) 0 0
\(157\) 14.4314 1.15175 0.575876 0.817537i \(-0.304661\pi\)
0.575876 + 0.817537i \(0.304661\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.87170i 0.305133i
\(162\) 0 0
\(163\) − 14.4908i − 1.13500i −0.823372 0.567502i \(-0.807910\pi\)
0.823372 0.567502i \(-0.192090\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.88572 −0.610215 −0.305108 0.952318i \(-0.598692\pi\)
−0.305108 + 0.952318i \(0.598692\pi\)
\(168\) 0 0
\(169\) −7.57788 −0.582914
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 15.8802i − 1.20735i −0.797230 0.603676i \(-0.793702\pi\)
0.797230 0.603676i \(-0.206298\pi\)
\(174\) 0 0
\(175\) − 2.64930i − 0.200269i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.2503 1.36409 0.682046 0.731309i \(-0.261090\pi\)
0.682046 + 0.731309i \(0.261090\pi\)
\(180\) 0 0
\(181\) −24.1717 −1.79667 −0.898335 0.439311i \(-0.855223\pi\)
−0.898335 + 0.439311i \(0.855223\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.45628i 0.254110i
\(186\) 0 0
\(187\) − 18.8220i − 1.37640i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18.6845 −1.35197 −0.675983 0.736917i \(-0.736281\pi\)
−0.675983 + 0.736917i \(0.736281\pi\)
\(192\) 0 0
\(193\) 6.89411 0.496249 0.248124 0.968728i \(-0.420186\pi\)
0.248124 + 0.968728i \(0.420186\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.10853i 0.648956i 0.945893 + 0.324478i \(0.105189\pi\)
−0.945893 + 0.324478i \(0.894811\pi\)
\(198\) 0 0
\(199\) 9.53988i 0.676264i 0.941099 + 0.338132i \(0.109795\pi\)
−0.941099 + 0.338132i \(0.890205\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.32622 0.514200
\(204\) 0 0
\(205\) 9.75418 0.681261
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.55535i 0.315100i
\(210\) 0 0
\(211\) − 16.0066i − 1.10194i −0.834525 0.550970i \(-0.814258\pi\)
0.834525 0.550970i \(-0.185742\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −14.6242 −0.997361
\(216\) 0 0
\(217\) −2.17647 −0.147748
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.1508i 1.15369i
\(222\) 0 0
\(223\) 3.28527i 0.219998i 0.993932 + 0.109999i \(0.0350848\pi\)
−0.993932 + 0.109999i \(0.964915\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −13.2772 −0.881238 −0.440619 0.897694i \(-0.645241\pi\)
−0.440619 + 0.897694i \(0.645241\pi\)
\(228\) 0 0
\(229\) 5.23836 0.346160 0.173080 0.984908i \(-0.444628\pi\)
0.173080 + 0.984908i \(0.444628\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 6.32608i − 0.414435i −0.978295 0.207218i \(-0.933559\pi\)
0.978295 0.207218i \(-0.0664408\pi\)
\(234\) 0 0
\(235\) 15.9716i 1.04187i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 17.2297 1.11450 0.557249 0.830346i \(-0.311857\pi\)
0.557249 + 0.830346i \(0.311857\pi\)
\(240\) 0 0
\(241\) −27.6743 −1.78266 −0.891328 0.453358i \(-0.850226\pi\)
−0.891328 + 0.453358i \(0.850226\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.76574i 0.176696i
\(246\) 0 0
\(247\) − 4.15089i − 0.264115i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −16.3083 −1.02937 −0.514685 0.857380i \(-0.672091\pi\)
−0.514685 + 0.857380i \(0.672091\pi\)
\(252\) 0 0
\(253\) 9.89388 0.622023
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 1.98554i − 0.123855i −0.998081 0.0619274i \(-0.980275\pi\)
0.998081 0.0619274i \(-0.0197247\pi\)
\(258\) 0 0
\(259\) − 1.24968i − 0.0776511i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5.93854 −0.366186 −0.183093 0.983096i \(-0.558611\pi\)
−0.183093 + 0.983096i \(0.558611\pi\)
\(264\) 0 0
\(265\) 20.1671 1.23886
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 11.1048i − 0.677073i −0.940953 0.338537i \(-0.890068\pi\)
0.940953 0.338537i \(-0.109932\pi\)
\(270\) 0 0
\(271\) − 23.6992i − 1.43962i −0.694170 0.719811i \(-0.744228\pi\)
0.694170 0.719811i \(-0.255772\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.77012 −0.408254
\(276\) 0 0
\(277\) −23.7917 −1.42951 −0.714753 0.699377i \(-0.753461\pi\)
−0.714753 + 0.699377i \(0.753461\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.1589i 1.32189i 0.750434 + 0.660945i \(0.229844\pi\)
−0.750434 + 0.660945i \(0.770156\pi\)
\(282\) 0 0
\(283\) − 6.58388i − 0.391371i −0.980667 0.195686i \(-0.937307\pi\)
0.980667 0.195686i \(-0.0626932\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.52679 −0.208180
\(288\) 0 0
\(289\) −37.2502 −2.19119
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 23.1727i 1.35376i 0.736091 + 0.676882i \(0.236669\pi\)
−0.736091 + 0.676882i \(0.763331\pi\)
\(294\) 0 0
\(295\) − 13.7764i − 0.802091i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.01543 −0.521376
\(300\) 0 0
\(301\) 5.28762 0.304774
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 8.72494i − 0.499589i
\(306\) 0 0
\(307\) − 12.7944i − 0.730216i −0.930965 0.365108i \(-0.881032\pi\)
0.930965 0.365108i \(-0.118968\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −29.6695 −1.68240 −0.841202 0.540720i \(-0.818152\pi\)
−0.841202 + 0.540720i \(0.818152\pi\)
\(312\) 0 0
\(313\) 4.54381 0.256831 0.128416 0.991720i \(-0.459011\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 9.93868i − 0.558212i −0.960260 0.279106i \(-0.909962\pi\)
0.960260 0.279106i \(-0.0900381\pi\)
\(318\) 0 0
\(319\) − 18.7217i − 1.04821i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 13.1298 0.730561
\(324\) 0 0
\(325\) 6.16902 0.342196
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 5.77479i − 0.318375i
\(330\) 0 0
\(331\) 19.7766i 1.08702i 0.839403 + 0.543509i \(0.182905\pi\)
−0.839403 + 0.543509i \(0.817095\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −21.3656 −1.16733
\(336\) 0 0
\(337\) −30.5056 −1.66175 −0.830873 0.556462i \(-0.812158\pi\)
−0.830873 + 0.556462i \(0.812158\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.56182i 0.301189i
\(342\) 0 0
\(343\) − 1.00000i − 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.0080 1.50355 0.751773 0.659422i \(-0.229199\pi\)
0.751773 + 0.659422i \(0.229199\pi\)
\(348\) 0 0
\(349\) −6.47317 −0.346501 −0.173251 0.984878i \(-0.555427\pi\)
−0.173251 + 0.984878i \(0.555427\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 33.5190i − 1.78404i −0.452000 0.892018i \(-0.649289\pi\)
0.452000 0.892018i \(-0.350711\pi\)
\(354\) 0 0
\(355\) 22.0853i 1.17217i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −33.2112 −1.75282 −0.876410 0.481565i \(-0.840069\pi\)
−0.876410 + 0.481565i \(0.840069\pi\)
\(360\) 0 0
\(361\) 15.8223 0.832752
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 29.7450i 1.55692i
\(366\) 0 0
\(367\) − 15.5534i − 0.811883i −0.913899 0.405941i \(-0.866944\pi\)
0.913899 0.405941i \(-0.133056\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.29178 −0.378570
\(372\) 0 0
\(373\) −7.84450 −0.406173 −0.203086 0.979161i \(-0.565097\pi\)
−0.203086 + 0.979161i \(0.565097\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 17.0594i 0.878605i
\(378\) 0 0
\(379\) 34.6551i 1.78011i 0.455851 + 0.890056i \(0.349335\pi\)
−0.455851 + 0.890056i \(0.650665\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6.57082 0.335753 0.167877 0.985808i \(-0.446309\pi\)
0.167877 + 0.985808i \(0.446309\pi\)
\(384\) 0 0
\(385\) 7.06766 0.360201
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7.56366i 0.383493i 0.981444 + 0.191746i \(0.0614151\pi\)
−0.981444 + 0.191746i \(0.938585\pi\)
\(390\) 0 0
\(391\) − 28.5169i − 1.44216i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.83178 −0.293429
\(396\) 0 0
\(397\) 9.26100 0.464796 0.232398 0.972621i \(-0.425343\pi\)
0.232398 + 0.972621i \(0.425343\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.158397i 0.00790995i 0.999992 + 0.00395497i \(0.00125891\pi\)
−0.999992 + 0.00395497i \(0.998741\pi\)
\(402\) 0 0
\(403\) − 5.06800i − 0.252455i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.19347 −0.158294
\(408\) 0 0
\(409\) −6.79241 −0.335863 −0.167932 0.985799i \(-0.553709\pi\)
−0.167932 + 0.985799i \(0.553709\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.98108i 0.245103i
\(414\) 0 0
\(415\) − 33.5922i − 1.64898i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 35.2185 1.72054 0.860269 0.509841i \(-0.170296\pi\)
0.860269 + 0.509841i \(0.170296\pi\)
\(420\) 0 0
\(421\) −28.1907 −1.37393 −0.686966 0.726689i \(-0.741058\pi\)
−0.686966 + 0.726689i \(0.741058\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 19.5134i 0.946538i
\(426\) 0 0
\(427\) 3.15465i 0.152664i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −18.5840 −0.895160 −0.447580 0.894244i \(-0.647714\pi\)
−0.447580 + 0.894244i \(0.647714\pi\)
\(432\) 0 0
\(433\) −10.1063 −0.485680 −0.242840 0.970066i \(-0.578079\pi\)
−0.242840 + 0.970066i \(0.578079\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.90174i 0.330155i
\(438\) 0 0
\(439\) − 33.9732i − 1.62145i −0.585426 0.810726i \(-0.699073\pi\)
0.585426 0.810726i \(-0.300927\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 18.6709 0.887082 0.443541 0.896254i \(-0.353722\pi\)
0.443541 + 0.896254i \(0.353722\pi\)
\(444\) 0 0
\(445\) −26.8570 −1.27314
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 18.2721i 0.862316i 0.902276 + 0.431158i \(0.141895\pi\)
−0.902276 + 0.431158i \(0.858105\pi\)
\(450\) 0 0
\(451\) 9.01249i 0.424381i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.44014 −0.301918
\(456\) 0 0
\(457\) 23.1665 1.08369 0.541843 0.840480i \(-0.317727\pi\)
0.541843 + 0.840480i \(0.317727\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 27.0478i − 1.25974i −0.776700 0.629870i \(-0.783108\pi\)
0.776700 0.629870i \(-0.216892\pi\)
\(462\) 0 0
\(463\) 28.2067i 1.31088i 0.755249 + 0.655438i \(0.227516\pi\)
−0.755249 + 0.655438i \(0.772484\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.3299 0.987029 0.493514 0.869738i \(-0.335712\pi\)
0.493514 + 0.869738i \(0.335712\pi\)
\(468\) 0 0
\(469\) 7.72509 0.356711
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 13.5122i − 0.621291i
\(474\) 0 0
\(475\) − 4.72268i − 0.216692i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −22.5415 −1.02995 −0.514973 0.857207i \(-0.672198\pi\)
−0.514973 + 0.857207i \(0.672198\pi\)
\(480\) 0 0
\(481\) 2.90993 0.132681
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 43.1602i − 1.95980i
\(486\) 0 0
\(487\) 4.51090i 0.204408i 0.994763 + 0.102204i \(0.0325895\pi\)
−0.994763 + 0.102204i \(0.967410\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 30.4636 1.37480 0.687401 0.726278i \(-0.258752\pi\)
0.687401 + 0.726278i \(0.258752\pi\)
\(492\) 0 0
\(493\) −53.9611 −2.43028
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 7.98532i − 0.358191i
\(498\) 0 0
\(499\) − 11.7384i − 0.525482i −0.964866 0.262741i \(-0.915373\pi\)
0.964866 0.262741i \(-0.0846265\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 18.7589 0.836419 0.418210 0.908351i \(-0.362658\pi\)
0.418210 + 0.908351i \(0.362658\pi\)
\(504\) 0 0
\(505\) −23.3385 −1.03855
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.97172i 0.309016i 0.987992 + 0.154508i \(0.0493792\pi\)
−0.987992 + 0.154508i \(0.950621\pi\)
\(510\) 0 0
\(511\) − 10.7548i − 0.475764i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.24465 −0.187041
\(516\) 0 0
\(517\) −14.7571 −0.649017
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 40.2146i − 1.76183i −0.473270 0.880917i \(-0.656926\pi\)
0.473270 0.880917i \(-0.343074\pi\)
\(522\) 0 0
\(523\) − 29.6607i − 1.29697i −0.761226 0.648486i \(-0.775402\pi\)
0.761226 0.648486i \(-0.224598\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.0307 0.698309
\(528\) 0 0
\(529\) −8.00993 −0.348258
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 8.21229i − 0.355714i
\(534\) 0 0
\(535\) 15.0123i 0.649037i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.55543 −0.110070
\(540\) 0 0
\(541\) 40.6687 1.74849 0.874243 0.485489i \(-0.161359\pi\)
0.874243 + 0.485489i \(0.161359\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 20.6656i 0.885215i
\(546\) 0 0
\(547\) 18.0822i 0.773137i 0.922261 + 0.386569i \(0.126340\pi\)
−0.922261 + 0.386569i \(0.873660\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 13.0598 0.556366
\(552\) 0 0
\(553\) 2.10858 0.0896660
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 21.7467i − 0.921436i −0.887547 0.460718i \(-0.847592\pi\)
0.887547 0.460718i \(-0.152408\pi\)
\(558\) 0 0
\(559\) 12.3125i 0.520762i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19.1061 0.805228 0.402614 0.915370i \(-0.368102\pi\)
0.402614 + 0.915370i \(0.368102\pi\)
\(564\) 0 0
\(565\) 7.32311 0.308086
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 1.98917i − 0.0833903i −0.999130 0.0416952i \(-0.986724\pi\)
0.999130 0.0416952i \(-0.0132758\pi\)
\(570\) 0 0
\(571\) 25.5278i 1.06831i 0.845388 + 0.534153i \(0.179369\pi\)
−0.845388 + 0.534153i \(0.820631\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −10.2573 −0.427759
\(576\) 0 0
\(577\) 16.8837 0.702879 0.351439 0.936211i \(-0.385692\pi\)
0.351439 + 0.936211i \(0.385692\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.1458i 0.503894i
\(582\) 0 0
\(583\) 18.6337i 0.771727i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 41.7731 1.72416 0.862080 0.506773i \(-0.169162\pi\)
0.862080 + 0.506773i \(0.169162\pi\)
\(588\) 0 0
\(589\) −3.87980 −0.159864
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 29.6707i − 1.21843i −0.793006 0.609214i \(-0.791485\pi\)
0.793006 0.609214i \(-0.208515\pi\)
\(594\) 0 0
\(595\) − 20.3710i − 0.835128i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 31.1882 1.27432 0.637158 0.770733i \(-0.280110\pi\)
0.637158 + 0.770733i \(0.280110\pi\)
\(600\) 0 0
\(601\) 34.4671 1.40594 0.702972 0.711218i \(-0.251856\pi\)
0.702972 + 0.711218i \(0.251856\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 12.3622i 0.502593i
\(606\) 0 0
\(607\) 11.7335i 0.476249i 0.971235 + 0.238124i \(0.0765326\pi\)
−0.971235 + 0.238124i \(0.923467\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 13.4469 0.544002
\(612\) 0 0
\(613\) 0.772139 0.0311864 0.0155932 0.999878i \(-0.495036\pi\)
0.0155932 + 0.999878i \(0.495036\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.9376i 0.641625i 0.947143 + 0.320812i \(0.103956\pi\)
−0.947143 + 0.320812i \(0.896044\pi\)
\(618\) 0 0
\(619\) − 8.41774i − 0.338337i −0.985587 0.169169i \(-0.945892\pi\)
0.985587 0.169169i \(-0.0541083\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 9.71061 0.389047
\(624\) 0 0
\(625\) −31.2277 −1.24911
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.20446i 0.367006i
\(630\) 0 0
\(631\) − 35.0824i − 1.39661i −0.715800 0.698305i \(-0.753938\pi\)
0.715800 0.698305i \(-0.246062\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 53.1240 2.10816
\(636\) 0 0
\(637\) 2.32854 0.0922603
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 7.02263i − 0.277377i −0.990336 0.138689i \(-0.955711\pi\)
0.990336 0.138689i \(-0.0442887\pi\)
\(642\) 0 0
\(643\) 19.4292i 0.766214i 0.923704 + 0.383107i \(0.125146\pi\)
−0.923704 + 0.383107i \(0.874854\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −11.3921 −0.447869 −0.223935 0.974604i \(-0.571890\pi\)
−0.223935 + 0.974604i \(0.571890\pi\)
\(648\) 0 0
\(649\) 12.7288 0.499650
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 37.4801i − 1.46671i −0.679845 0.733356i \(-0.737953\pi\)
0.679845 0.733356i \(-0.262047\pi\)
\(654\) 0 0
\(655\) − 0.504503i − 0.0197126i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 31.6058 1.23119 0.615594 0.788063i \(-0.288916\pi\)
0.615594 + 0.788063i \(0.288916\pi\)
\(660\) 0 0
\(661\) −38.7889 −1.50871 −0.754356 0.656466i \(-0.772051\pi\)
−0.754356 + 0.656466i \(0.772051\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.93024i 0.191186i
\(666\) 0 0
\(667\) − 28.3649i − 1.09829i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.06151 0.311211
\(672\) 0 0
\(673\) −12.7203 −0.490331 −0.245166 0.969481i \(-0.578842\pi\)
−0.245166 + 0.969481i \(0.578842\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21.8409i 0.839414i 0.907660 + 0.419707i \(0.137867\pi\)
−0.907660 + 0.419707i \(0.862133\pi\)
\(678\) 0 0
\(679\) 15.6053i 0.598876i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −28.5781 −1.09351 −0.546755 0.837293i \(-0.684137\pi\)
−0.546755 + 0.837293i \(0.684137\pi\)
\(684\) 0 0
\(685\) 15.3556 0.586706
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 16.9792i − 0.646857i
\(690\) 0 0
\(691\) 12.4404i 0.473254i 0.971601 + 0.236627i \(0.0760420\pi\)
−0.971601 + 0.236627i \(0.923958\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −51.9817 −1.97178
\(696\) 0 0
\(697\) 25.9765 0.983930
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 30.1067i − 1.13711i −0.822644 0.568557i \(-0.807502\pi\)
0.822644 0.568557i \(-0.192498\pi\)
\(702\) 0 0
\(703\) − 2.22769i − 0.0840189i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.43842 0.317359
\(708\) 0 0
\(709\) 50.3032 1.88918 0.944589 0.328256i \(-0.106461\pi\)
0.944589 + 0.328256i \(0.106461\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.42663i 0.315580i
\(714\) 0 0
\(715\) 16.4574i 0.615470i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17.3376 −0.646583 −0.323291 0.946299i \(-0.604789\pi\)
−0.323291 + 0.946299i \(0.604789\pi\)
\(720\) 0 0
\(721\) 1.53472 0.0571561
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 19.4094i 0.720846i
\(726\) 0 0
\(727\) 42.4708i 1.57515i 0.616217 + 0.787576i \(0.288664\pi\)
−0.616217 + 0.787576i \(0.711336\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −38.9459 −1.44046
\(732\) 0 0
\(733\) 20.4759 0.756294 0.378147 0.925746i \(-0.376561\pi\)
0.378147 + 0.925746i \(0.376561\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 19.7410i − 0.727168i
\(738\) 0 0
\(739\) − 5.95637i − 0.219109i −0.993981 0.109554i \(-0.965058\pi\)
0.993981 0.109554i \(-0.0349424\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.66621 −0.0611274 −0.0305637 0.999533i \(-0.509730\pi\)
−0.0305637 + 0.999533i \(0.509730\pi\)
\(744\) 0 0
\(745\) 27.1818 0.995863
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 5.42794i − 0.198333i
\(750\) 0 0
\(751\) − 49.1354i − 1.79298i −0.443068 0.896488i \(-0.646110\pi\)
0.443068 0.896488i \(-0.353890\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −24.7834 −0.901961
\(756\) 0 0
\(757\) 36.9665 1.34357 0.671785 0.740747i \(-0.265528\pi\)
0.671785 + 0.740747i \(0.265528\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 36.5213i 1.32390i 0.749550 + 0.661948i \(0.230270\pi\)
−0.749550 + 0.661948i \(0.769730\pi\)
\(762\) 0 0
\(763\) − 7.47199i − 0.270504i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11.5987 −0.418804
\(768\) 0 0
\(769\) 27.9601 1.00827 0.504133 0.863626i \(-0.331812\pi\)
0.504133 + 0.863626i \(0.331812\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 13.1835i − 0.474178i −0.971488 0.237089i \(-0.923807\pi\)
0.971488 0.237089i \(-0.0761933\pi\)
\(774\) 0 0
\(775\) − 5.76612i − 0.207125i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.28690 −0.225252
\(780\) 0 0
\(781\) −20.4060 −0.730183
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 39.9135i − 1.42457i
\(786\) 0 0
\(787\) 36.1472i 1.28851i 0.764812 + 0.644254i \(0.222832\pi\)
−0.764812 + 0.644254i \(0.777168\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.64780 −0.0941448
\(792\) 0 0
\(793\) −7.34575 −0.260855
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.63891i 0.0580531i 0.999579 + 0.0290266i \(0.00924074\pi\)
−0.999579 + 0.0290266i \(0.990759\pi\)
\(798\) 0 0
\(799\) 42.5341i 1.50475i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −27.4832 −0.969861
\(804\) 0 0
\(805\) 10.7081 0.377411
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 32.2010i 1.13213i 0.824362 + 0.566063i \(0.191534\pi\)
−0.824362 + 0.566063i \(0.808466\pi\)
\(810\) 0 0
\(811\) − 18.6552i − 0.655072i −0.944839 0.327536i \(-0.893782\pi\)
0.944839 0.327536i \(-0.106218\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −40.0776 −1.40386
\(816\) 0 0
\(817\) 9.42579 0.329767
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 6.85032i − 0.239078i −0.992830 0.119539i \(-0.961858\pi\)
0.992830 0.119539i \(-0.0381416\pi\)
\(822\) 0 0
\(823\) 20.8948i 0.728348i 0.931331 + 0.364174i \(0.118649\pi\)
−0.931331 + 0.364174i \(0.881351\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −39.4714 −1.37255 −0.686277 0.727341i \(-0.740756\pi\)
−0.686277 + 0.727341i \(0.740756\pi\)
\(828\) 0 0
\(829\) 7.23657 0.251336 0.125668 0.992072i \(-0.459893\pi\)
0.125668 + 0.992072i \(0.459893\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 7.36547i 0.255199i
\(834\) 0 0
\(835\) 21.8098i 0.754760i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 6.32006 0.218193 0.109096 0.994031i \(-0.465204\pi\)
0.109096 + 0.994031i \(0.465204\pi\)
\(840\) 0 0
\(841\) −24.6734 −0.850808
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 20.9584i 0.720992i
\(846\) 0 0
\(847\) − 4.46975i − 0.153583i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.83837 −0.165857
\(852\) 0 0
\(853\) −28.4940 −0.975615 −0.487807 0.872951i \(-0.662203\pi\)
−0.487807 + 0.872951i \(0.662203\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 25.4708i 0.870067i 0.900414 + 0.435034i \(0.143264\pi\)
−0.900414 + 0.435034i \(0.856736\pi\)
\(858\) 0 0
\(859\) − 48.0030i − 1.63784i −0.573907 0.818921i \(-0.694573\pi\)
0.573907 0.818921i \(-0.305427\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 34.5532 1.17621 0.588103 0.808786i \(-0.299875\pi\)
0.588103 + 0.808786i \(0.299875\pi\)
\(864\) 0 0
\(865\) −43.9205 −1.49334
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 5.38834i − 0.182787i
\(870\) 0 0
\(871\) 17.9882i 0.609507i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 6.50141 0.219788
\(876\) 0 0
\(877\) −4.46779 −0.150867 −0.0754333 0.997151i \(-0.524034\pi\)
−0.0754333 + 0.997151i \(0.524034\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 47.9230i − 1.61457i −0.590164 0.807283i \(-0.700937\pi\)
0.590164 0.807283i \(-0.299063\pi\)
\(882\) 0 0
\(883\) 7.50033i 0.252406i 0.992004 + 0.126203i \(0.0402791\pi\)
−0.992004 + 0.126203i \(0.959721\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −11.8246 −0.397030 −0.198515 0.980098i \(-0.563612\pi\)
−0.198515 + 0.980098i \(0.563612\pi\)
\(888\) 0 0
\(889\) −19.2079 −0.644213
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 10.2942i − 0.344483i
\(894\) 0 0
\(895\) − 50.4755i − 1.68721i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 15.9453 0.531804
\(900\) 0 0
\(901\) 53.7074 1.78925
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 66.8527i 2.22226i
\(906\) 0 0
\(907\) 34.2557i 1.13744i 0.822531 + 0.568721i \(0.192562\pi\)
−0.822531 + 0.568721i \(0.807438\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 13.8731 0.459638 0.229819 0.973233i \(-0.426187\pi\)
0.229819 + 0.973233i \(0.426187\pi\)
\(912\) 0 0
\(913\) 31.0379 1.02720
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.182412i 0.00602376i
\(918\) 0 0
\(919\) 19.0500i 0.628402i 0.949356 + 0.314201i \(0.101737\pi\)
−0.949356 + 0.314201i \(0.898263\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 18.5942 0.612035
\(924\) 0 0
\(925\) 3.31077 0.108857
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 6.93319i − 0.227470i −0.993511 0.113735i \(-0.963718\pi\)
0.993511 0.113735i \(-0.0362816\pi\)
\(930\) 0 0
\(931\) − 1.78261i − 0.0584228i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −52.0567 −1.70244
\(936\) 0 0
\(937\) 16.7279 0.546475 0.273238 0.961947i \(-0.411905\pi\)
0.273238 + 0.961947i \(0.411905\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 13.5223i 0.440814i 0.975408 + 0.220407i \(0.0707386\pi\)
−0.975408 + 0.220407i \(0.929261\pi\)
\(942\) 0 0
\(943\) 13.6547i 0.444658i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 15.4695 0.502692 0.251346 0.967897i \(-0.419127\pi\)
0.251346 + 0.967897i \(0.419127\pi\)
\(948\) 0 0
\(949\) 25.0430 0.812931
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 16.4797i − 0.533831i −0.963720 0.266915i \(-0.913996\pi\)
0.963720 0.266915i \(-0.0860044\pi\)
\(954\) 0 0
\(955\) 51.6765i 1.67221i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.55207 −0.179286
\(960\) 0 0
\(961\) 26.2630 0.847193
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 19.0673i − 0.613798i
\(966\) 0 0
\(967\) 43.1895i 1.38888i 0.719550 + 0.694441i \(0.244348\pi\)
−0.719550 + 0.694441i \(0.755652\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 21.5954 0.693029 0.346515 0.938045i \(-0.387365\pi\)
0.346515 + 0.938045i \(0.387365\pi\)
\(972\) 0 0
\(973\) 18.7949 0.602536
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 9.08900i 0.290783i 0.989374 + 0.145391i \(0.0464442\pi\)
−0.989374 + 0.145391i \(0.953556\pi\)
\(978\) 0 0
\(979\) − 24.8148i − 0.793085i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 22.7430 0.725388 0.362694 0.931908i \(-0.381857\pi\)
0.362694 + 0.931908i \(0.381857\pi\)
\(984\) 0 0
\(985\) 25.1918 0.802678
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 20.4721i − 0.650975i
\(990\) 0 0
\(991\) 5.96925i 0.189619i 0.995495 + 0.0948097i \(0.0302243\pi\)
−0.995495 + 0.0948097i \(0.969776\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 26.3848 0.836454
\(996\) 0 0
\(997\) −42.1258 −1.33414 −0.667069 0.744996i \(-0.732451\pi\)
−0.667069 + 0.744996i \(0.732451\pi\)
\(998\) 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.h.i.2591.7 24
3.2 odd 2 inner 6048.2.h.i.2591.18 yes 24
4.3 odd 2 inner 6048.2.h.i.2591.17 yes 24
12.11 even 2 inner 6048.2.h.i.2591.8 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6048.2.h.i.2591.7 24 1.1 even 1 trivial
6048.2.h.i.2591.8 yes 24 12.11 even 2 inner
6048.2.h.i.2591.17 yes 24 4.3 odd 2 inner
6048.2.h.i.2591.18 yes 24 3.2 odd 2 inner