Properties

Label 3240.2.a.i.1.2
Level $3240$
Weight $2$
Character 3240.1
Self dual yes
Analytic conductor $25.872$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.8715302549\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{33}) \)
Defining polynomial: \(x^{2} - x - 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.37228\) of defining polynomial
Character \(\chi\) \(=\) 3240.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +3.37228 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +3.37228 q^{7} -2.37228 q^{11} -3.37228 q^{13} +6.74456 q^{17} +1.00000 q^{19} -5.37228 q^{23} +1.00000 q^{25} -2.37228 q^{29} +11.1168 q^{31} -3.37228 q^{35} +6.00000 q^{37} -0.255437 q^{41} -4.74456 q^{43} +9.37228 q^{47} +4.37228 q^{49} -10.1168 q^{53} +2.37228 q^{55} -5.00000 q^{59} +12.7446 q^{61} +3.37228 q^{65} -0.744563 q^{67} +4.37228 q^{71} +14.7446 q^{73} -8.00000 q^{77} -2.74456 q^{79} +10.0000 q^{83} -6.74456 q^{85} +4.37228 q^{89} -11.3723 q^{91} -1.00000 q^{95} -4.74456 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + q^{7} + O(q^{10}) \) \( 2 q - 2 q^{5} + q^{7} + q^{11} - q^{13} + 2 q^{17} + 2 q^{19} - 5 q^{23} + 2 q^{25} + q^{29} + 5 q^{31} - q^{35} + 12 q^{37} - 12 q^{41} + 2 q^{43} + 13 q^{47} + 3 q^{49} - 3 q^{53} - q^{55} - 10 q^{59} + 14 q^{61} + q^{65} + 10 q^{67} + 3 q^{71} + 18 q^{73} - 16 q^{77} + 6 q^{79} + 20 q^{83} - 2 q^{85} + 3 q^{89} - 17 q^{91} - 2 q^{95} + 2 q^{97} + O(q^{100}) \)

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
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.37228 1.27460 0.637301 0.770615i \(-0.280051\pi\)
0.637301 + 0.770615i \(0.280051\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.37228 −0.715270 −0.357635 0.933862i \(-0.616417\pi\)
−0.357635 + 0.933862i \(0.616417\pi\)
\(12\) 0 0
\(13\) −3.37228 −0.935303 −0.467651 0.883913i \(-0.654900\pi\)
−0.467651 + 0.883913i \(0.654900\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.74456 1.63580 0.817898 0.575363i \(-0.195139\pi\)
0.817898 + 0.575363i \(0.195139\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.37228 −1.12020 −0.560099 0.828426i \(-0.689237\pi\)
−0.560099 + 0.828426i \(0.689237\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.37228 −0.440522 −0.220261 0.975441i \(-0.570691\pi\)
−0.220261 + 0.975441i \(0.570691\pi\)
\(30\) 0 0
\(31\) 11.1168 1.99664 0.998322 0.0579057i \(-0.0184423\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.37228 −0.570020
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.255437 −0.0398926 −0.0199463 0.999801i \(-0.506350\pi\)
−0.0199463 + 0.999801i \(0.506350\pi\)
\(42\) 0 0
\(43\) −4.74456 −0.723539 −0.361770 0.932268i \(-0.617827\pi\)
−0.361770 + 0.932268i \(0.617827\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.37228 1.36709 0.683544 0.729909i \(-0.260438\pi\)
0.683544 + 0.729909i \(0.260438\pi\)
\(48\) 0 0
\(49\) 4.37228 0.624612
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10.1168 −1.38966 −0.694828 0.719176i \(-0.744519\pi\)
−0.694828 + 0.719176i \(0.744519\pi\)
\(54\) 0 0
\(55\) 2.37228 0.319878
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.00000 −0.650945 −0.325472 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(60\) 0 0
\(61\) 12.7446 1.63177 0.815887 0.578211i \(-0.196249\pi\)
0.815887 + 0.578211i \(0.196249\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.37228 0.418280
\(66\) 0 0
\(67\) −0.744563 −0.0909628 −0.0454814 0.998965i \(-0.514482\pi\)
−0.0454814 + 0.998965i \(0.514482\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.37228 0.518894 0.259447 0.965757i \(-0.416460\pi\)
0.259447 + 0.965757i \(0.416460\pi\)
\(72\) 0 0
\(73\) 14.7446 1.72572 0.862860 0.505443i \(-0.168671\pi\)
0.862860 + 0.505443i \(0.168671\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.00000 −0.911685
\(78\) 0 0
\(79\) −2.74456 −0.308787 −0.154394 0.988009i \(-0.549342\pi\)
−0.154394 + 0.988009i \(0.549342\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) 0 0
\(85\) −6.74456 −0.731551
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.37228 0.463461 0.231730 0.972780i \(-0.425561\pi\)
0.231730 + 0.972780i \(0.425561\pi\)
\(90\) 0 0
\(91\) −11.3723 −1.19214
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) −4.74456 −0.481737 −0.240869 0.970558i \(-0.577432\pi\)
−0.240869 + 0.970558i \(0.577432\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.8614 1.57827 0.789134 0.614220i \(-0.210529\pi\)
0.789134 + 0.614220i \(0.210529\pi\)
\(102\) 0 0
\(103\) −0.116844 −0.0115130 −0.00575649 0.999983i \(-0.501832\pi\)
−0.00575649 + 0.999983i \(0.501832\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 0 0
\(109\) 0.883156 0.0845910 0.0422955 0.999105i \(-0.486533\pi\)
0.0422955 + 0.999105i \(0.486533\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −14.7446 −1.38705 −0.693526 0.720432i \(-0.743944\pi\)
−0.693526 + 0.720432i \(0.743944\pi\)
\(114\) 0 0
\(115\) 5.37228 0.500968
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 22.7446 2.08499
\(120\) 0 0
\(121\) −5.37228 −0.488389
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −12.8614 −1.14127 −0.570633 0.821205i \(-0.693302\pi\)
−0.570633 + 0.821205i \(0.693302\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.25544 −0.546540 −0.273270 0.961937i \(-0.588105\pi\)
−0.273270 + 0.961937i \(0.588105\pi\)
\(132\) 0 0
\(133\) 3.37228 0.292414
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.25544 0.449002 0.224501 0.974474i \(-0.427925\pi\)
0.224501 + 0.974474i \(0.427925\pi\)
\(138\) 0 0
\(139\) 15.0000 1.27228 0.636142 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) 2.37228 0.197007
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −19.4891 −1.59661 −0.798306 0.602252i \(-0.794270\pi\)
−0.798306 + 0.602252i \(0.794270\pi\)
\(150\) 0 0
\(151\) 24.3723 1.98339 0.991694 0.128619i \(-0.0410545\pi\)
0.991694 + 0.128619i \(0.0410545\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11.1168 −0.892926
\(156\) 0 0
\(157\) 22.8614 1.82454 0.912269 0.409591i \(-0.134328\pi\)
0.912269 + 0.409591i \(0.134328\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −18.1168 −1.42781
\(162\) 0 0
\(163\) 9.48913 0.743246 0.371623 0.928384i \(-0.378801\pi\)
0.371623 + 0.928384i \(0.378801\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −1.62772 −0.125209
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −14.8614 −1.12989 −0.564946 0.825128i \(-0.691103\pi\)
−0.564946 + 0.825128i \(0.691103\pi\)
\(174\) 0 0
\(175\) 3.37228 0.254921
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.25544 0.318066 0.159033 0.987273i \(-0.449162\pi\)
0.159033 + 0.987273i \(0.449162\pi\)
\(180\) 0 0
\(181\) −13.8614 −1.03031 −0.515155 0.857097i \(-0.672266\pi\)
−0.515155 + 0.857097i \(0.672266\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) −16.0000 −1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.62772 0.407207 0.203604 0.979053i \(-0.434735\pi\)
0.203604 + 0.979053i \(0.434735\pi\)
\(192\) 0 0
\(193\) 0.744563 0.0535948 0.0267974 0.999641i \(-0.491469\pi\)
0.0267974 + 0.999641i \(0.491469\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.627719 0.0447231 0.0223616 0.999750i \(-0.492882\pi\)
0.0223616 + 0.999750i \(0.492882\pi\)
\(198\) 0 0
\(199\) 13.4891 0.956219 0.478109 0.878300i \(-0.341322\pi\)
0.478109 + 0.878300i \(0.341322\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.00000 −0.561490
\(204\) 0 0
\(205\) 0.255437 0.0178405
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.37228 −0.164094
\(210\) 0 0
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.74456 0.323576
\(216\) 0 0
\(217\) 37.4891 2.54493
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −22.7446 −1.52996
\(222\) 0 0
\(223\) 25.4891 1.70688 0.853439 0.521193i \(-0.174513\pi\)
0.853439 + 0.521193i \(0.174513\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 17.4891 1.16079 0.580397 0.814334i \(-0.302897\pi\)
0.580397 + 0.814334i \(0.302897\pi\)
\(228\) 0 0
\(229\) −16.7446 −1.10651 −0.553256 0.833011i \(-0.686615\pi\)
−0.553256 + 0.833011i \(0.686615\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.2337 0.932480 0.466240 0.884658i \(-0.345608\pi\)
0.466240 + 0.884658i \(0.345608\pi\)
\(234\) 0 0
\(235\) −9.37228 −0.611380
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 20.2337 1.30881 0.654404 0.756145i \(-0.272919\pi\)
0.654404 + 0.756145i \(0.272919\pi\)
\(240\) 0 0
\(241\) −10.6060 −0.683191 −0.341595 0.939847i \(-0.610967\pi\)
−0.341595 + 0.939847i \(0.610967\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.37228 −0.279335
\(246\) 0 0
\(247\) −3.37228 −0.214573
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.8614 0.811805 0.405902 0.913916i \(-0.366957\pi\)
0.405902 + 0.913916i \(0.366957\pi\)
\(252\) 0 0
\(253\) 12.7446 0.801244
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −0.510875 −0.0318675 −0.0159337 0.999873i \(-0.505072\pi\)
−0.0159337 + 0.999873i \(0.505072\pi\)
\(258\) 0 0
\(259\) 20.2337 1.25726
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.11684 −0.253855 −0.126928 0.991912i \(-0.540512\pi\)
−0.126928 + 0.991912i \(0.540512\pi\)
\(264\) 0 0
\(265\) 10.1168 0.621473
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.11684 0.311979 0.155990 0.987759i \(-0.450143\pi\)
0.155990 + 0.987759i \(0.450143\pi\)
\(270\) 0 0
\(271\) −9.25544 −0.562228 −0.281114 0.959674i \(-0.590704\pi\)
−0.281114 + 0.959674i \(0.590704\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.37228 −0.143054
\(276\) 0 0
\(277\) 0.116844 0.00702047 0.00351024 0.999994i \(-0.498883\pi\)
0.00351024 + 0.999994i \(0.498883\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −17.3723 −1.03634 −0.518172 0.855277i \(-0.673387\pi\)
−0.518172 + 0.855277i \(0.673387\pi\)
\(282\) 0 0
\(283\) 16.7446 0.995361 0.497680 0.867360i \(-0.334185\pi\)
0.497680 + 0.867360i \(0.334185\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.861407 −0.0508472
\(288\) 0 0
\(289\) 28.4891 1.67583
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.8614 0.868213 0.434106 0.900862i \(-0.357064\pi\)
0.434106 + 0.900862i \(0.357064\pi\)
\(294\) 0 0
\(295\) 5.00000 0.291111
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 18.1168 1.04772
\(300\) 0 0
\(301\) −16.0000 −0.922225
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −12.7446 −0.729752
\(306\) 0 0
\(307\) 0.744563 0.0424944 0.0212472 0.999774i \(-0.493236\pi\)
0.0212472 + 0.999774i \(0.493236\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −17.8614 −1.01283 −0.506414 0.862291i \(-0.669029\pi\)
−0.506414 + 0.862291i \(0.669029\pi\)
\(312\) 0 0
\(313\) −4.00000 −0.226093 −0.113047 0.993590i \(-0.536061\pi\)
−0.113047 + 0.993590i \(0.536061\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.6277 0.596912 0.298456 0.954423i \(-0.403528\pi\)
0.298456 + 0.954423i \(0.403528\pi\)
\(318\) 0 0
\(319\) 5.62772 0.315092
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.74456 0.375278
\(324\) 0 0
\(325\) −3.37228 −0.187061
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 31.6060 1.74249
\(330\) 0 0
\(331\) 13.6277 0.749047 0.374524 0.927217i \(-0.377806\pi\)
0.374524 + 0.927217i \(0.377806\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.744563 0.0406798
\(336\) 0 0
\(337\) −10.7446 −0.585294 −0.292647 0.956221i \(-0.594536\pi\)
−0.292647 + 0.956221i \(0.594536\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −26.3723 −1.42814
\(342\) 0 0
\(343\) −8.86141 −0.478471
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.23369 −0.227276 −0.113638 0.993522i \(-0.536250\pi\)
−0.113638 + 0.993522i \(0.536250\pi\)
\(348\) 0 0
\(349\) −19.6277 −1.05065 −0.525324 0.850902i \(-0.676056\pi\)
−0.525324 + 0.850902i \(0.676056\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 20.9783 1.11656 0.558280 0.829653i \(-0.311462\pi\)
0.558280 + 0.829653i \(0.311462\pi\)
\(354\) 0 0
\(355\) −4.37228 −0.232057
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 16.3723 0.864096 0.432048 0.901851i \(-0.357791\pi\)
0.432048 + 0.901851i \(0.357791\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −14.7446 −0.771766
\(366\) 0 0
\(367\) −30.2337 −1.57819 −0.789093 0.614274i \(-0.789449\pi\)
−0.789093 + 0.614274i \(0.789449\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −34.1168 −1.77126
\(372\) 0 0
\(373\) −10.7446 −0.556332 −0.278166 0.960533i \(-0.589727\pi\)
−0.278166 + 0.960533i \(0.589727\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −26.3505 −1.35354 −0.676768 0.736196i \(-0.736620\pi\)
−0.676768 + 0.736196i \(0.736620\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 19.3723 0.989877 0.494939 0.868928i \(-0.335191\pi\)
0.494939 + 0.868928i \(0.335191\pi\)
\(384\) 0 0
\(385\) 8.00000 0.407718
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −20.7446 −1.05179 −0.525896 0.850549i \(-0.676270\pi\)
−0.525896 + 0.850549i \(0.676270\pi\)
\(390\) 0 0
\(391\) −36.2337 −1.83242
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.74456 0.138094
\(396\) 0 0
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −36.3505 −1.81526 −0.907629 0.419772i \(-0.862110\pi\)
−0.907629 + 0.419772i \(0.862110\pi\)
\(402\) 0 0
\(403\) −37.4891 −1.86747
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −14.2337 −0.705538
\(408\) 0 0
\(409\) −21.3723 −1.05679 −0.528396 0.848998i \(-0.677206\pi\)
−0.528396 + 0.848998i \(0.677206\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −16.8614 −0.829696
\(414\) 0 0
\(415\) −10.0000 −0.490881
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −34.9783 −1.70880 −0.854400 0.519616i \(-0.826075\pi\)
−0.854400 + 0.519616i \(0.826075\pi\)
\(420\) 0 0
\(421\) 28.3723 1.38278 0.691390 0.722482i \(-0.256999\pi\)
0.691390 + 0.722482i \(0.256999\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.74456 0.327159
\(426\) 0 0
\(427\) 42.9783 2.07986
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.62772 −0.463751 −0.231875 0.972745i \(-0.574486\pi\)
−0.231875 + 0.972745i \(0.574486\pi\)
\(432\) 0 0
\(433\) −41.2119 −1.98052 −0.990260 0.139233i \(-0.955536\pi\)
−0.990260 + 0.139233i \(0.955536\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.37228 −0.256991
\(438\) 0 0
\(439\) −32.0951 −1.53182 −0.765908 0.642951i \(-0.777710\pi\)
−0.765908 + 0.642951i \(0.777710\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 28.9783 1.37680 0.688399 0.725332i \(-0.258314\pi\)
0.688399 + 0.725332i \(0.258314\pi\)
\(444\) 0 0
\(445\) −4.37228 −0.207266
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −34.7228 −1.63867 −0.819335 0.573314i \(-0.805657\pi\)
−0.819335 + 0.573314i \(0.805657\pi\)
\(450\) 0 0
\(451\) 0.605969 0.0285340
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 11.3723 0.533141
\(456\) 0 0
\(457\) −5.76631 −0.269737 −0.134868 0.990864i \(-0.543061\pi\)
−0.134868 + 0.990864i \(0.543061\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −31.1168 −1.44926 −0.724628 0.689140i \(-0.757988\pi\)
−0.724628 + 0.689140i \(0.757988\pi\)
\(462\) 0 0
\(463\) 6.86141 0.318877 0.159438 0.987208i \(-0.449032\pi\)
0.159438 + 0.987208i \(0.449032\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.2337 −0.751205 −0.375603 0.926781i \(-0.622564\pi\)
−0.375603 + 0.926781i \(0.622564\pi\)
\(468\) 0 0
\(469\) −2.51087 −0.115941
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11.2554 0.517526
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.88316 0.314499 0.157250 0.987559i \(-0.449737\pi\)
0.157250 + 0.987559i \(0.449737\pi\)
\(480\) 0 0
\(481\) −20.2337 −0.922577
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.74456 0.215439
\(486\) 0 0
\(487\) 19.6060 0.888431 0.444216 0.895920i \(-0.353482\pi\)
0.444216 + 0.895920i \(0.353482\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 25.9783 1.17238 0.586191 0.810173i \(-0.300627\pi\)
0.586191 + 0.810173i \(0.300627\pi\)
\(492\) 0 0
\(493\) −16.0000 −0.720604
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14.7446 0.661384
\(498\) 0 0
\(499\) 19.7446 0.883888 0.441944 0.897043i \(-0.354289\pi\)
0.441944 + 0.897043i \(0.354289\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10.9783 −0.489496 −0.244748 0.969587i \(-0.578705\pi\)
−0.244748 + 0.969587i \(0.578705\pi\)
\(504\) 0 0
\(505\) −15.8614 −0.705823
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 38.0000 1.68432 0.842160 0.539227i \(-0.181284\pi\)
0.842160 + 0.539227i \(0.181284\pi\)
\(510\) 0 0
\(511\) 49.7228 2.19961
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.116844 0.00514876
\(516\) 0 0
\(517\) −22.2337 −0.977836
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.116844 0.00511903 0.00255951 0.999997i \(-0.499185\pi\)
0.00255951 + 0.999997i \(0.499185\pi\)
\(522\) 0 0
\(523\) −40.2337 −1.75930 −0.879648 0.475625i \(-0.842222\pi\)
−0.879648 + 0.475625i \(0.842222\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 74.9783 3.26610
\(528\) 0 0
\(529\) 5.86141 0.254844
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.861407 0.0373117
\(534\) 0 0
\(535\) −6.00000 −0.259403
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10.3723 −0.446766
\(540\) 0 0
\(541\) 13.3505 0.573984 0.286992 0.957933i \(-0.407345\pi\)
0.286992 + 0.957933i \(0.407345\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.883156 −0.0378302
\(546\) 0 0
\(547\) −40.0000 −1.71028 −0.855138 0.518400i \(-0.826528\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.37228 −0.101063
\(552\) 0 0
\(553\) −9.25544 −0.393581
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 31.6060 1.33919 0.669594 0.742727i \(-0.266468\pi\)
0.669594 + 0.742727i \(0.266468\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.2337 0.431299 0.215649 0.976471i \(-0.430813\pi\)
0.215649 + 0.976471i \(0.430813\pi\)
\(564\) 0 0
\(565\) 14.7446 0.620308
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.76631 −0.367503 −0.183751 0.982973i \(-0.558824\pi\)
−0.183751 + 0.982973i \(0.558824\pi\)
\(570\) 0 0
\(571\) −3.11684 −0.130436 −0.0652179 0.997871i \(-0.520774\pi\)
−0.0652179 + 0.997871i \(0.520774\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.37228 −0.224040
\(576\) 0 0
\(577\) −9.48913 −0.395037 −0.197519 0.980299i \(-0.563288\pi\)
−0.197519 + 0.980299i \(0.563288\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 33.7228 1.39906
\(582\) 0 0
\(583\) 24.0000 0.993978
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 0 0
\(589\) 11.1168 0.458062
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 28.9783 1.18999 0.594997 0.803728i \(-0.297153\pi\)
0.594997 + 0.803728i \(0.297153\pi\)
\(594\) 0 0
\(595\) −22.7446 −0.932436
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −15.3505 −0.627206 −0.313603 0.949554i \(-0.601536\pi\)
−0.313603 + 0.949554i \(0.601536\pi\)
\(600\) 0 0
\(601\) 13.0000 0.530281 0.265141 0.964210i \(-0.414582\pi\)
0.265141 + 0.964210i \(0.414582\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.37228 0.218414
\(606\) 0 0
\(607\) −44.7446 −1.81613 −0.908063 0.418834i \(-0.862439\pi\)
−0.908063 + 0.418834i \(0.862439\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −31.6060 −1.27864
\(612\) 0 0
\(613\) 18.3505 0.741171 0.370586 0.928798i \(-0.379157\pi\)
0.370586 + 0.928798i \(0.379157\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.7228 −0.552460 −0.276230 0.961092i \(-0.589085\pi\)
−0.276230 + 0.961092i \(0.589085\pi\)
\(618\) 0 0
\(619\) −32.6277 −1.31142 −0.655709 0.755013i \(-0.727630\pi\)
−0.655709 + 0.755013i \(0.727630\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 14.7446 0.590728
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 40.4674 1.61354
\(630\) 0 0
\(631\) −42.3723 −1.68681 −0.843407 0.537275i \(-0.819454\pi\)
−0.843407 + 0.537275i \(0.819454\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 12.8614 0.510389
\(636\) 0 0
\(637\) −14.7446 −0.584201
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −42.6060 −1.68283 −0.841417 0.540386i \(-0.818278\pi\)
−0.841417 + 0.540386i \(0.818278\pi\)
\(642\) 0 0
\(643\) 32.7446 1.29132 0.645660 0.763625i \(-0.276582\pi\)
0.645660 + 0.763625i \(0.276582\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 31.7228 1.24715 0.623576 0.781763i \(-0.285679\pi\)
0.623576 + 0.781763i \(0.285679\pi\)
\(648\) 0 0
\(649\) 11.8614 0.465601
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.2554 0.518725 0.259363 0.965780i \(-0.416488\pi\)
0.259363 + 0.965780i \(0.416488\pi\)
\(654\) 0 0
\(655\) 6.25544 0.244420
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −38.5842 −1.50303 −0.751514 0.659717i \(-0.770676\pi\)
−0.751514 + 0.659717i \(0.770676\pi\)
\(660\) 0 0
\(661\) 18.0951 0.703818 0.351909 0.936034i \(-0.385533\pi\)
0.351909 + 0.936034i \(0.385533\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.37228 −0.130771
\(666\) 0 0
\(667\) 12.7446 0.493471
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −30.2337 −1.16716
\(672\) 0 0
\(673\) −23.4891 −0.905439 −0.452720 0.891653i \(-0.649546\pi\)
−0.452720 + 0.891653i \(0.649546\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.88316 0.149242 0.0746209 0.997212i \(-0.476225\pi\)
0.0746209 + 0.997212i \(0.476225\pi\)
\(678\) 0 0
\(679\) −16.0000 −0.614024
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3.76631 −0.144114 −0.0720570 0.997401i \(-0.522956\pi\)
−0.0720570 + 0.997401i \(0.522956\pi\)
\(684\) 0 0
\(685\) −5.25544 −0.200800
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 34.1168 1.29975
\(690\) 0 0
\(691\) −10.3505 −0.393753 −0.196876 0.980428i \(-0.563080\pi\)
−0.196876 + 0.980428i \(0.563080\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −15.0000 −0.568982
\(696\) 0 0
\(697\) −1.72281 −0.0652562
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −9.11684 −0.344338 −0.172169 0.985067i \(-0.555078\pi\)
−0.172169 + 0.985067i \(0.555078\pi\)
\(702\) 0 0
\(703\) 6.00000 0.226294
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 53.4891 2.01167
\(708\) 0 0
\(709\) −50.4674 −1.89534 −0.947671 0.319248i \(-0.896570\pi\)
−0.947671 + 0.319248i \(0.896570\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −59.7228 −2.23664
\(714\) 0 0
\(715\) −8.00000 −0.299183
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 50.6060 1.88728 0.943642 0.330968i \(-0.107375\pi\)
0.943642 + 0.330968i \(0.107375\pi\)
\(720\) 0 0
\(721\) −0.394031 −0.0146745
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.37228 −0.0881043
\(726\) 0 0
\(727\) −29.8832 −1.10830 −0.554152 0.832415i \(-0.686958\pi\)
−0.554152 + 0.832415i \(0.686958\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −32.0000 −1.18356
\(732\) 0 0
\(733\) 16.9783 0.627106 0.313553 0.949571i \(-0.398481\pi\)
0.313553 + 0.949571i \(0.398481\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.76631 0.0650629
\(738\) 0 0
\(739\) 15.8614 0.583471 0.291736 0.956499i \(-0.405767\pi\)
0.291736 + 0.956499i \(0.405767\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6.51087 0.238861 0.119430 0.992843i \(-0.461893\pi\)
0.119430 + 0.992843i \(0.461893\pi\)
\(744\) 0 0
\(745\) 19.4891 0.714026
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 20.2337 0.739323
\(750\) 0 0
\(751\) −3.76631 −0.137435 −0.0687173 0.997636i \(-0.521891\pi\)
−0.0687173 + 0.997636i \(0.521891\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −24.3723 −0.886998
\(756\) 0 0
\(757\) 9.88316 0.359209 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17.2337 −0.624721 −0.312360 0.949964i \(-0.601120\pi\)
−0.312360 + 0.949964i \(0.601120\pi\)
\(762\) 0 0
\(763\) 2.97825 0.107820
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16.8614 0.608830
\(768\) 0 0
\(769\) 19.3505 0.697798 0.348899 0.937160i \(-0.386556\pi\)
0.348899 + 0.937160i \(0.386556\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) 11.1168 0.399329
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.255437 −0.00915199
\(780\) 0 0
\(781\) −10.3723 −0.371149
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −22.8614 −0.815959
\(786\) 0 0
\(787\) −41.7228 −1.48726 −0.743629 0.668593i \(-0.766897\pi\)
−0.743629 + 0.668593i \(0.766897\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −49.7228 −1.76794
\(792\) 0 0
\(793\) −42.9783 −1.52620
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20.2337 0.716714 0.358357 0.933585i \(-0.383337\pi\)
0.358357 + 0.933585i \(0.383337\pi\)
\(798\) 0 0
\(799\) 63.2119 2.23628
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −34.9783 −1.23436
\(804\) 0 0
\(805\) 18.1168 0.638535
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −46.2119 −1.62473 −0.812363 0.583153i \(-0.801819\pi\)
−0.812363 + 0.583153i \(0.801819\pi\)
\(810\) 0 0
\(811\) −37.3505 −1.31155 −0.655777 0.754954i \(-0.727659\pi\)
−0.655777 + 0.754954i \(0.727659\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −9.48913 −0.332390
\(816\) 0 0
\(817\) −4.74456 −0.165991
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −35.6277 −1.24342 −0.621708 0.783249i \(-0.713561\pi\)
−0.621708 + 0.783249i \(0.713561\pi\)
\(822\) 0 0
\(823\) −23.2554 −0.810634 −0.405317 0.914176i \(-0.632839\pi\)
−0.405317 + 0.914176i \(0.632839\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 45.9565 1.59806 0.799032 0.601288i \(-0.205346\pi\)
0.799032 + 0.601288i \(0.205346\pi\)
\(828\) 0 0
\(829\) −43.5842 −1.51374 −0.756871 0.653564i \(-0.773273\pi\)
−0.756871 + 0.653564i \(0.773273\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 29.4891 1.02174
\(834\) 0 0
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 28.6060 0.987588 0.493794 0.869579i \(-0.335610\pi\)
0.493794 + 0.869579i \(0.335610\pi\)
\(840\) 0 0
\(841\) −23.3723 −0.805941
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.62772 0.0559952
\(846\) 0 0
\(847\) −18.1168 −0.622502
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −32.2337 −1.10496
\(852\) 0 0
\(853\) 10.7446 0.367887 0.183943 0.982937i \(-0.441114\pi\)
0.183943 + 0.982937i \(0.441114\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 33.2554 1.13598 0.567992 0.823034i \(-0.307720\pi\)
0.567992 + 0.823034i \(0.307720\pi\)
\(858\) 0 0
\(859\) −1.35053 −0.0460796 −0.0230398 0.999735i \(-0.507334\pi\)
−0.0230398 + 0.999735i \(0.507334\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 51.6060 1.75669 0.878344 0.478029i \(-0.158649\pi\)
0.878344 + 0.478029i \(0.158649\pi\)
\(864\) 0 0
\(865\) 14.8614 0.505303
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6.51087 0.220866
\(870\) 0 0
\(871\) 2.51087 0.0850777
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3.37228 −0.114004
\(876\) 0 0
\(877\) 26.1168 0.881903 0.440952 0.897531i \(-0.354641\pi\)
0.440952 + 0.897531i \(0.354641\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −19.6277 −0.661275 −0.330637 0.943758i \(-0.607264\pi\)
−0.330637 + 0.943758i \(0.607264\pi\)
\(882\) 0 0
\(883\) 40.2337 1.35397 0.676986 0.735996i \(-0.263286\pi\)
0.676986 + 0.735996i \(0.263286\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 13.1386 0.441151 0.220575 0.975370i \(-0.429206\pi\)
0.220575 + 0.975370i \(0.429206\pi\)
\(888\) 0 0
\(889\) −43.3723 −1.45466
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 9.37228 0.313631
\(894\) 0 0
\(895\) −4.25544 −0.142244
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −26.3723 −0.879565
\(900\) 0 0
\(901\) −68.2337 −2.27319
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 13.8614 0.460769
\(906\) 0 0
\(907\) −12.5109 −0.415417 −0.207708 0.978191i \(-0.566601\pi\)
−0.207708 + 0.978191i \(0.566601\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 55.0733 1.82466 0.912331 0.409454i \(-0.134281\pi\)
0.912331 + 0.409454i \(0.134281\pi\)
\(912\) 0 0
\(913\) −23.7228 −0.785111
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −21.0951 −0.696621
\(918\) 0 0
\(919\) 24.8832 0.820820 0.410410 0.911901i \(-0.365386\pi\)
0.410410 + 0.911901i \(0.365386\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −14.7446 −0.485323
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −25.8614 −0.848485 −0.424243 0.905549i \(-0.639460\pi\)
−0.424243 + 0.905549i \(0.639460\pi\)
\(930\) 0 0
\(931\) 4.37228 0.143296
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 16.0000 0.523256
\(936\) 0 0
\(937\) 31.2554 1.02107 0.510535 0.859857i \(-0.329447\pi\)
0.510535 + 0.859857i \(0.329447\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 42.4674 1.38440 0.692198 0.721707i \(-0.256642\pi\)
0.692198 + 0.721707i \(0.256642\pi\)
\(942\) 0 0
\(943\) 1.37228 0.0446876
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −48.7446 −1.58399 −0.791993 0.610531i \(-0.790956\pi\)
−0.791993 + 0.610531i \(0.790956\pi\)
\(948\) 0 0
\(949\) −49.7228 −1.61407
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 12.0000 0.388718 0.194359 0.980930i \(-0.437737\pi\)
0.194359 + 0.980930i \(0.437737\pi\)
\(954\) 0 0
\(955\) −5.62772 −0.182109
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 17.7228 0.572299
\(960\) 0 0
\(961\) 92.5842 2.98659
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.744563 −0.0239683
\(966\) 0 0
\(967\) −41.4891 −1.33420 −0.667100 0.744968i \(-0.732465\pi\)
−0.667100 + 0.744968i \(0.732465\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −48.7228 −1.56359 −0.781795 0.623536i \(-0.785696\pi\)
−0.781795 + 0.623536i \(0.785696\pi\)
\(972\) 0 0
\(973\) 50.5842 1.62166
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −52.2337 −1.67110 −0.835552 0.549412i \(-0.814852\pi\)
−0.835552 + 0.549412i \(0.814852\pi\)
\(978\) 0 0
\(979\) −10.3723 −0.331500
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −17.4891 −0.557816 −0.278908 0.960318i \(-0.589973\pi\)
−0.278908 + 0.960318i \(0.589973\pi\)
\(984\) 0 0
\(985\) −0.627719 −0.0200008
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 25.4891 0.810507
\(990\) 0 0
\(991\) −2.37228 −0.0753580 −0.0376790 0.999290i \(-0.511996\pi\)
−0.0376790 + 0.999290i \(0.511996\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −13.4891 −0.427634
\(996\) 0 0
\(997\) −42.3505 −1.34125 −0.670627 0.741794i \(-0.733975\pi\)
−0.670627 + 0.741794i \(0.733975\pi\)
\(998\) 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 3240.2.a.i.1.2 2
3.2 odd 2 3240.2.a.m.1.2 yes 2
4.3 odd 2 6480.2.a.bd.1.1 2
9.2 odd 6 3240.2.q.ba.1081.1 4
9.4 even 3 3240.2.q.bd.2161.1 4
9.5 odd 6 3240.2.q.ba.2161.1 4
9.7 even 3 3240.2.q.bd.1081.1 4
12.11 even 2 6480.2.a.bo.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3240.2.a.i.1.2 2 1.1 even 1 trivial
3240.2.a.m.1.2 yes 2 3.2 odd 2
3240.2.q.ba.1081.1 4 9.2 odd 6
3240.2.q.ba.2161.1 4 9.5 odd 6
3240.2.q.bd.1081.1 4 9.7 even 3
3240.2.q.bd.2161.1 4 9.4 even 3
6480.2.a.bd.1.1 2 4.3 odd 2
6480.2.a.bo.1.1 2 12.11 even 2