Properties

Label 6400.2.a.y.1.1
Level $6400$
Weight $2$
Character 6400.1
Self dual yes
Analytic conductor $51.104$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6400 = 2^{8} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.1042572936\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
Defining polynomial: \(x^{2} - 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 320)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 6400.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73205 q^{3} -4.73205 q^{7} +4.46410 q^{9} +O(q^{10})\) \(q-2.73205 q^{3} -4.73205 q^{7} +4.46410 q^{9} -3.46410 q^{11} -3.46410 q^{13} +3.46410 q^{17} -2.00000 q^{19} +12.9282 q^{21} +2.19615 q^{23} -4.00000 q^{27} +2.53590 q^{31} +9.46410 q^{33} +6.00000 q^{37} +9.46410 q^{39} -9.46410 q^{41} -0.196152 q^{43} +2.19615 q^{47} +15.3923 q^{49} -9.46410 q^{51} +10.3923 q^{53} +5.46410 q^{57} -6.00000 q^{59} -0.928203 q^{61} -21.1244 q^{63} +0.196152 q^{67} -6.00000 q^{69} +16.3923 q^{71} +6.39230 q^{73} +16.3923 q^{77} +12.0000 q^{79} -2.46410 q^{81} -1.26795 q^{83} +12.9282 q^{89} +16.3923 q^{91} -6.92820 q^{93} -14.3923 q^{97} -15.4641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} - 6q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - 6q^{7} + 2q^{9} - 4q^{19} + 12q^{21} - 6q^{23} - 8q^{27} + 12q^{31} + 12q^{33} + 12q^{37} + 12q^{39} - 12q^{41} + 10q^{43} - 6q^{47} + 10q^{49} - 12q^{51} + 4q^{57} - 12q^{59} + 12q^{61} - 18q^{63} - 10q^{67} - 12q^{69} + 12q^{71} - 8q^{73} + 12q^{77} + 24q^{79} + 2q^{81} - 6q^{83} + 12q^{89} + 12q^{91} - 8q^{97} - 24q^{99} + O(q^{100}) \)

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
\(3\) −2.73205 −1.57735 −0.788675 0.614810i \(-0.789233\pi\)
−0.788675 + 0.614810i \(0.789233\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.73205 −1.78855 −0.894274 0.447521i \(-0.852307\pi\)
−0.894274 + 0.447521i \(0.852307\pi\)
\(8\) 0 0
\(9\) 4.46410 1.48803
\(10\) 0 0
\(11\) −3.46410 −1.04447 −0.522233 0.852803i \(-0.674901\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 0 0
\(13\) −3.46410 −0.960769 −0.480384 0.877058i \(-0.659503\pi\)
−0.480384 + 0.877058i \(0.659503\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.46410 0.840168 0.420084 0.907485i \(-0.362001\pi\)
0.420084 + 0.907485i \(0.362001\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 12.9282 2.82117
\(22\) 0 0
\(23\) 2.19615 0.457929 0.228965 0.973435i \(-0.426466\pi\)
0.228965 + 0.973435i \(0.426466\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 2.53590 0.455461 0.227730 0.973724i \(-0.426870\pi\)
0.227730 + 0.973724i \(0.426870\pi\)
\(32\) 0 0
\(33\) 9.46410 1.64749
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) 9.46410 1.51547
\(40\) 0 0
\(41\) −9.46410 −1.47804 −0.739022 0.673681i \(-0.764712\pi\)
−0.739022 + 0.673681i \(0.764712\pi\)
\(42\) 0 0
\(43\) −0.196152 −0.0299130 −0.0149565 0.999888i \(-0.504761\pi\)
−0.0149565 + 0.999888i \(0.504761\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.19615 0.320342 0.160171 0.987089i \(-0.448795\pi\)
0.160171 + 0.987089i \(0.448795\pi\)
\(48\) 0 0
\(49\) 15.3923 2.19890
\(50\) 0 0
\(51\) −9.46410 −1.32524
\(52\) 0 0
\(53\) 10.3923 1.42749 0.713746 0.700404i \(-0.246997\pi\)
0.713746 + 0.700404i \(0.246997\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.46410 0.723738
\(58\) 0 0
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −0.928203 −0.118844 −0.0594221 0.998233i \(-0.518926\pi\)
−0.0594221 + 0.998233i \(0.518926\pi\)
\(62\) 0 0
\(63\) −21.1244 −2.66142
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0.196152 0.0239638 0.0119819 0.999928i \(-0.496186\pi\)
0.0119819 + 0.999928i \(0.496186\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 16.3923 1.94541 0.972704 0.232048i \(-0.0745426\pi\)
0.972704 + 0.232048i \(0.0745426\pi\)
\(72\) 0 0
\(73\) 6.39230 0.748163 0.374081 0.927396i \(-0.377958\pi\)
0.374081 + 0.927396i \(0.377958\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 16.3923 1.86808
\(78\) 0 0
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 0 0
\(81\) −2.46410 −0.273789
\(82\) 0 0
\(83\) −1.26795 −0.139176 −0.0695878 0.997576i \(-0.522168\pi\)
−0.0695878 + 0.997576i \(0.522168\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.9282 1.37039 0.685193 0.728361i \(-0.259718\pi\)
0.685193 + 0.728361i \(0.259718\pi\)
\(90\) 0 0
\(91\) 16.3923 1.71838
\(92\) 0 0
\(93\) −6.92820 −0.718421
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.3923 −1.46132 −0.730659 0.682743i \(-0.760787\pi\)
−0.730659 + 0.682743i \(0.760787\pi\)
\(98\) 0 0
\(99\) −15.4641 −1.55420
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) 2.19615 0.216393 0.108197 0.994130i \(-0.465492\pi\)
0.108197 + 0.994130i \(0.465492\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.2679 −1.28266 −0.641331 0.767265i \(-0.721617\pi\)
−0.641331 + 0.767265i \(0.721617\pi\)
\(108\) 0 0
\(109\) −12.9282 −1.23830 −0.619149 0.785274i \(-0.712522\pi\)
−0.619149 + 0.785274i \(0.712522\pi\)
\(110\) 0 0
\(111\) −16.3923 −1.55589
\(112\) 0 0
\(113\) 12.9282 1.21618 0.608092 0.793867i \(-0.291935\pi\)
0.608092 + 0.793867i \(0.291935\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −15.4641 −1.42966
\(118\) 0 0
\(119\) −16.3923 −1.50268
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 25.8564 2.33139
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −14.1962 −1.25970 −0.629852 0.776715i \(-0.716885\pi\)
−0.629852 + 0.776715i \(0.716885\pi\)
\(128\) 0 0
\(129\) 0.535898 0.0471832
\(130\) 0 0
\(131\) 10.3923 0.907980 0.453990 0.891007i \(-0.350000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(132\) 0 0
\(133\) 9.46410 0.820642
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.928203 −0.0793018 −0.0396509 0.999214i \(-0.512625\pi\)
−0.0396509 + 0.999214i \(0.512625\pi\)
\(138\) 0 0
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −42.0526 −3.46844
\(148\) 0 0
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) 9.46410 0.770178 0.385089 0.922880i \(-0.374171\pi\)
0.385089 + 0.922880i \(0.374171\pi\)
\(152\) 0 0
\(153\) 15.4641 1.25020
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.9282 −1.03178 −0.515891 0.856654i \(-0.672539\pi\)
−0.515891 + 0.856654i \(0.672539\pi\)
\(158\) 0 0
\(159\) −28.3923 −2.25166
\(160\) 0 0
\(161\) −10.3923 −0.819028
\(162\) 0 0
\(163\) 16.1962 1.26858 0.634290 0.773095i \(-0.281292\pi\)
0.634290 + 0.773095i \(0.281292\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.19615 −0.169943 −0.0849717 0.996383i \(-0.527080\pi\)
−0.0849717 + 0.996383i \(0.527080\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) −8.92820 −0.682757
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 16.3923 1.23212
\(178\) 0 0
\(179\) 7.85641 0.587215 0.293608 0.955926i \(-0.405144\pi\)
0.293608 + 0.955926i \(0.405144\pi\)
\(180\) 0 0
\(181\) −6.92820 −0.514969 −0.257485 0.966282i \(-0.582894\pi\)
−0.257485 + 0.966282i \(0.582894\pi\)
\(182\) 0 0
\(183\) 2.53590 0.187459
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.0000 −0.877527
\(188\) 0 0
\(189\) 18.9282 1.37682
\(190\) 0 0
\(191\) 4.39230 0.317816 0.158908 0.987293i \(-0.449203\pi\)
0.158908 + 0.987293i \(0.449203\pi\)
\(192\) 0 0
\(193\) 14.3923 1.03598 0.517990 0.855386i \(-0.326680\pi\)
0.517990 + 0.855386i \(0.326680\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.3923 −0.740421 −0.370211 0.928948i \(-0.620714\pi\)
−0.370211 + 0.928948i \(0.620714\pi\)
\(198\) 0 0
\(199\) 6.92820 0.491127 0.245564 0.969380i \(-0.421027\pi\)
0.245564 + 0.969380i \(0.421027\pi\)
\(200\) 0 0
\(201\) −0.535898 −0.0377994
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 9.80385 0.681415
\(208\) 0 0
\(209\) 6.92820 0.479234
\(210\) 0 0
\(211\) −14.3923 −0.990807 −0.495404 0.868663i \(-0.664980\pi\)
−0.495404 + 0.868663i \(0.664980\pi\)
\(212\) 0 0
\(213\) −44.7846 −3.06859
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −12.0000 −0.814613
\(218\) 0 0
\(219\) −17.4641 −1.18011
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 9.12436 0.611012 0.305506 0.952190i \(-0.401174\pi\)
0.305506 + 0.952190i \(0.401174\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.5885 0.835525 0.417763 0.908556i \(-0.362814\pi\)
0.417763 + 0.908556i \(0.362814\pi\)
\(228\) 0 0
\(229\) −5.07180 −0.335154 −0.167577 0.985859i \(-0.553594\pi\)
−0.167577 + 0.985859i \(0.553594\pi\)
\(230\) 0 0
\(231\) −44.7846 −2.94661
\(232\) 0 0
\(233\) −22.3923 −1.46697 −0.733484 0.679706i \(-0.762107\pi\)
−0.733484 + 0.679706i \(0.762107\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −32.7846 −2.12959
\(238\) 0 0
\(239\) 20.7846 1.34444 0.672222 0.740349i \(-0.265340\pi\)
0.672222 + 0.740349i \(0.265340\pi\)
\(240\) 0 0
\(241\) 0.392305 0.0252706 0.0126353 0.999920i \(-0.495978\pi\)
0.0126353 + 0.999920i \(0.495978\pi\)
\(242\) 0 0
\(243\) 18.7321 1.20166
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.92820 0.440831
\(248\) 0 0
\(249\) 3.46410 0.219529
\(250\) 0 0
\(251\) −8.53590 −0.538781 −0.269391 0.963031i \(-0.586822\pi\)
−0.269391 + 0.963031i \(0.586822\pi\)
\(252\) 0 0
\(253\) −7.60770 −0.478292
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 0 0
\(259\) −28.3923 −1.76421
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.80385 0.604531 0.302266 0.953224i \(-0.402257\pi\)
0.302266 + 0.953224i \(0.402257\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −35.3205 −2.16158
\(268\) 0 0
\(269\) 26.7846 1.63309 0.816543 0.577284i \(-0.195888\pi\)
0.816543 + 0.577284i \(0.195888\pi\)
\(270\) 0 0
\(271\) 16.3923 0.995762 0.497881 0.867245i \(-0.334112\pi\)
0.497881 + 0.867245i \(0.334112\pi\)
\(272\) 0 0
\(273\) −44.7846 −2.71049
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.85641 0.472046 0.236023 0.971748i \(-0.424156\pi\)
0.236023 + 0.971748i \(0.424156\pi\)
\(278\) 0 0
\(279\) 11.3205 0.677741
\(280\) 0 0
\(281\) 7.60770 0.453837 0.226919 0.973914i \(-0.427135\pi\)
0.226919 + 0.973914i \(0.427135\pi\)
\(282\) 0 0
\(283\) −20.5885 −1.22386 −0.611928 0.790913i \(-0.709606\pi\)
−0.611928 + 0.790913i \(0.709606\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 44.7846 2.64355
\(288\) 0 0
\(289\) −5.00000 −0.294118
\(290\) 0 0
\(291\) 39.3205 2.30501
\(292\) 0 0
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 13.8564 0.804030
\(298\) 0 0
\(299\) −7.60770 −0.439964
\(300\) 0 0
\(301\) 0.928203 0.0535007
\(302\) 0 0
\(303\) 32.7846 1.88343
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −23.8038 −1.35856 −0.679279 0.733880i \(-0.737707\pi\)
−0.679279 + 0.733880i \(0.737707\pi\)
\(308\) 0 0
\(309\) −6.00000 −0.341328
\(310\) 0 0
\(311\) −28.3923 −1.60998 −0.804990 0.593288i \(-0.797829\pi\)
−0.804990 + 0.593288i \(0.797829\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.60770 −0.0902972 −0.0451486 0.998980i \(-0.514376\pi\)
−0.0451486 + 0.998980i \(0.514376\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 36.2487 2.02321
\(322\) 0 0
\(323\) −6.92820 −0.385496
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 35.3205 1.95323
\(328\) 0 0
\(329\) −10.3923 −0.572946
\(330\) 0 0
\(331\) −26.3923 −1.45065 −0.725326 0.688405i \(-0.758311\pi\)
−0.725326 + 0.688405i \(0.758311\pi\)
\(332\) 0 0
\(333\) 26.7846 1.46779
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) −35.3205 −1.91835
\(340\) 0 0
\(341\) −8.78461 −0.475713
\(342\) 0 0
\(343\) −39.7128 −2.14429
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.0526 0.539650 0.269825 0.962909i \(-0.413034\pi\)
0.269825 + 0.962909i \(0.413034\pi\)
\(348\) 0 0
\(349\) −32.7846 −1.75492 −0.877460 0.479650i \(-0.840764\pi\)
−0.877460 + 0.479650i \(0.840764\pi\)
\(350\) 0 0
\(351\) 13.8564 0.739600
\(352\) 0 0
\(353\) −26.7846 −1.42560 −0.712800 0.701367i \(-0.752573\pi\)
−0.712800 + 0.701367i \(0.752573\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 44.7846 2.37025
\(358\) 0 0
\(359\) −32.7846 −1.73031 −0.865153 0.501508i \(-0.832779\pi\)
−0.865153 + 0.501508i \(0.832779\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) −2.73205 −0.143395
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −28.0526 −1.46433 −0.732166 0.681126i \(-0.761490\pi\)
−0.732166 + 0.681126i \(0.761490\pi\)
\(368\) 0 0
\(369\) −42.2487 −2.19938
\(370\) 0 0
\(371\) −49.1769 −2.55314
\(372\) 0 0
\(373\) −19.8564 −1.02813 −0.514063 0.857753i \(-0.671860\pi\)
−0.514063 + 0.857753i \(0.671860\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −2.00000 −0.102733 −0.0513665 0.998680i \(-0.516358\pi\)
−0.0513665 + 0.998680i \(0.516358\pi\)
\(380\) 0 0
\(381\) 38.7846 1.98700
\(382\) 0 0
\(383\) 14.1962 0.725390 0.362695 0.931908i \(-0.381857\pi\)
0.362695 + 0.931908i \(0.381857\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.875644 −0.0445115
\(388\) 0 0
\(389\) −14.7846 −0.749609 −0.374805 0.927104i \(-0.622290\pi\)
−0.374805 + 0.927104i \(0.622290\pi\)
\(390\) 0 0
\(391\) 7.60770 0.384738
\(392\) 0 0
\(393\) −28.3923 −1.43220
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 20.5359 1.03067 0.515334 0.856990i \(-0.327668\pi\)
0.515334 + 0.856990i \(0.327668\pi\)
\(398\) 0 0
\(399\) −25.8564 −1.29444
\(400\) 0 0
\(401\) −31.8564 −1.59083 −0.795417 0.606063i \(-0.792748\pi\)
−0.795417 + 0.606063i \(0.792748\pi\)
\(402\) 0 0
\(403\) −8.78461 −0.437593
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −20.7846 −1.03025
\(408\) 0 0
\(409\) −24.3923 −1.20612 −0.603061 0.797695i \(-0.706052\pi\)
−0.603061 + 0.797695i \(0.706052\pi\)
\(410\) 0 0
\(411\) 2.53590 0.125087
\(412\) 0 0
\(413\) 28.3923 1.39709
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 27.3205 1.33789
\(418\) 0 0
\(419\) 12.9282 0.631584 0.315792 0.948828i \(-0.397730\pi\)
0.315792 + 0.948828i \(0.397730\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 0 0
\(423\) 9.80385 0.476679
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.39230 0.212559
\(428\) 0 0
\(429\) −32.7846 −1.58286
\(430\) 0 0
\(431\) −7.60770 −0.366450 −0.183225 0.983071i \(-0.558654\pi\)
−0.183225 + 0.983071i \(0.558654\pi\)
\(432\) 0 0
\(433\) −5.60770 −0.269489 −0.134744 0.990880i \(-0.543021\pi\)
−0.134744 + 0.990880i \(0.543021\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.39230 −0.210112
\(438\) 0 0
\(439\) 5.07180 0.242064 0.121032 0.992649i \(-0.461380\pi\)
0.121032 + 0.992649i \(0.461380\pi\)
\(440\) 0 0
\(441\) 68.7128 3.27204
\(442\) 0 0
\(443\) −17.6603 −0.839064 −0.419532 0.907741i \(-0.637806\pi\)
−0.419532 + 0.907741i \(0.637806\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −49.1769 −2.32599
\(448\) 0 0
\(449\) −9.46410 −0.446639 −0.223319 0.974745i \(-0.571689\pi\)
−0.223319 + 0.974745i \(0.571689\pi\)
\(450\) 0 0
\(451\) 32.7846 1.54377
\(452\) 0 0
\(453\) −25.8564 −1.21484
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.7846 −0.878707 −0.439353 0.898314i \(-0.644792\pi\)
−0.439353 + 0.898314i \(0.644792\pi\)
\(458\) 0 0
\(459\) −13.8564 −0.646762
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) −26.1962 −1.21744 −0.608719 0.793386i \(-0.708316\pi\)
−0.608719 + 0.793386i \(0.708316\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −28.9808 −1.34107 −0.670535 0.741878i \(-0.733935\pi\)
−0.670535 + 0.741878i \(0.733935\pi\)
\(468\) 0 0
\(469\) −0.928203 −0.0428604
\(470\) 0 0
\(471\) 35.3205 1.62748
\(472\) 0 0
\(473\) 0.679492 0.0312431
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 46.3923 2.12416
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −20.7846 −0.947697
\(482\) 0 0
\(483\) 28.3923 1.29189
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −14.8756 −0.674080 −0.337040 0.941490i \(-0.609426\pi\)
−0.337040 + 0.941490i \(0.609426\pi\)
\(488\) 0 0
\(489\) −44.2487 −2.00100
\(490\) 0 0
\(491\) −1.60770 −0.0725543 −0.0362771 0.999342i \(-0.511550\pi\)
−0.0362771 + 0.999342i \(0.511550\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −77.5692 −3.47946
\(498\) 0 0
\(499\) 43.5692 1.95043 0.975213 0.221268i \(-0.0710195\pi\)
0.975213 + 0.221268i \(0.0710195\pi\)
\(500\) 0 0
\(501\) 6.00000 0.268060
\(502\) 0 0
\(503\) 2.19615 0.0979216 0.0489608 0.998801i \(-0.484409\pi\)
0.0489608 + 0.998801i \(0.484409\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.73205 0.121335
\(508\) 0 0
\(509\) 32.7846 1.45315 0.726576 0.687086i \(-0.241110\pi\)
0.726576 + 0.687086i \(0.241110\pi\)
\(510\) 0 0
\(511\) −30.2487 −1.33812
\(512\) 0 0
\(513\) 8.00000 0.353209
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −7.60770 −0.334586
\(518\) 0 0
\(519\) −16.3923 −0.719542
\(520\) 0 0
\(521\) −4.14359 −0.181534 −0.0907671 0.995872i \(-0.528932\pi\)
−0.0907671 + 0.995872i \(0.528932\pi\)
\(522\) 0 0
\(523\) 36.9808 1.61706 0.808528 0.588458i \(-0.200265\pi\)
0.808528 + 0.588458i \(0.200265\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.78461 0.382664
\(528\) 0 0
\(529\) −18.1769 −0.790301
\(530\) 0 0
\(531\) −26.7846 −1.16235
\(532\) 0 0
\(533\) 32.7846 1.42006
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −21.4641 −0.926244
\(538\) 0 0
\(539\) −53.3205 −2.29668
\(540\) 0 0
\(541\) 39.7128 1.70739 0.853694 0.520776i \(-0.174357\pi\)
0.853694 + 0.520776i \(0.174357\pi\)
\(542\) 0 0
\(543\) 18.9282 0.812287
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −12.1962 −0.521470 −0.260735 0.965410i \(-0.583965\pi\)
−0.260735 + 0.965410i \(0.583965\pi\)
\(548\) 0 0
\(549\) −4.14359 −0.176844
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −56.7846 −2.41473
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 26.7846 1.13490 0.567450 0.823408i \(-0.307930\pi\)
0.567450 + 0.823408i \(0.307930\pi\)
\(558\) 0 0
\(559\) 0.679492 0.0287394
\(560\) 0 0
\(561\) 32.7846 1.38417
\(562\) 0 0
\(563\) −15.8038 −0.666053 −0.333026 0.942918i \(-0.608070\pi\)
−0.333026 + 0.942918i \(0.608070\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 11.6603 0.489685
\(568\) 0 0
\(569\) −6.24871 −0.261960 −0.130980 0.991385i \(-0.541812\pi\)
−0.130980 + 0.991385i \(0.541812\pi\)
\(570\) 0 0
\(571\) 9.60770 0.402070 0.201035 0.979584i \(-0.435570\pi\)
0.201035 + 0.979584i \(0.435570\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) −39.3205 −1.63410
\(580\) 0 0
\(581\) 6.00000 0.248922
\(582\) 0 0
\(583\) −36.0000 −1.49097
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −31.5167 −1.30083 −0.650416 0.759578i \(-0.725405\pi\)
−0.650416 + 0.759578i \(0.725405\pi\)
\(588\) 0 0
\(589\) −5.07180 −0.208980
\(590\) 0 0
\(591\) 28.3923 1.16790
\(592\) 0 0
\(593\) −12.9282 −0.530898 −0.265449 0.964125i \(-0.585520\pi\)
−0.265449 + 0.964125i \(0.585520\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −18.9282 −0.774680
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) −0.392305 −0.0160024 −0.00800122 0.999968i \(-0.502547\pi\)
−0.00800122 + 0.999968i \(0.502547\pi\)
\(602\) 0 0
\(603\) 0.875644 0.0356590
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 2.19615 0.0891391 0.0445695 0.999006i \(-0.485808\pi\)
0.0445695 + 0.999006i \(0.485808\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.60770 −0.307774
\(612\) 0 0
\(613\) −34.3923 −1.38909 −0.694546 0.719448i \(-0.744395\pi\)
−0.694546 + 0.719448i \(0.744395\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.3923 1.38458 0.692291 0.721618i \(-0.256601\pi\)
0.692291 + 0.721618i \(0.256601\pi\)
\(618\) 0 0
\(619\) 34.7846 1.39811 0.699056 0.715067i \(-0.253604\pi\)
0.699056 + 0.715067i \(0.253604\pi\)
\(620\) 0 0
\(621\) −8.78461 −0.352514
\(622\) 0 0
\(623\) −61.1769 −2.45100
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −18.9282 −0.755920
\(628\) 0 0
\(629\) 20.7846 0.828737
\(630\) 0 0
\(631\) 14.5359 0.578665 0.289332 0.957229i \(-0.406567\pi\)
0.289332 + 0.957229i \(0.406567\pi\)
\(632\) 0 0
\(633\) 39.3205 1.56285
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −53.3205 −2.11264
\(638\) 0 0
\(639\) 73.1769 2.89483
\(640\) 0 0
\(641\) 16.3923 0.647457 0.323729 0.946150i \(-0.395064\pi\)
0.323729 + 0.946150i \(0.395064\pi\)
\(642\) 0 0
\(643\) 20.5885 0.811929 0.405965 0.913889i \(-0.366936\pi\)
0.405965 + 0.913889i \(0.366936\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.41154 0.212750 0.106375 0.994326i \(-0.466076\pi\)
0.106375 + 0.994326i \(0.466076\pi\)
\(648\) 0 0
\(649\) 20.7846 0.815867
\(650\) 0 0
\(651\) 32.7846 1.28493
\(652\) 0 0
\(653\) −43.1769 −1.68964 −0.844822 0.535048i \(-0.820293\pi\)
−0.844822 + 0.535048i \(0.820293\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 28.5359 1.11329
\(658\) 0 0
\(659\) −28.6410 −1.11570 −0.557848 0.829943i \(-0.688373\pi\)
−0.557848 + 0.829943i \(0.688373\pi\)
\(660\) 0 0
\(661\) 47.5692 1.85023 0.925114 0.379689i \(-0.123969\pi\)
0.925114 + 0.379689i \(0.123969\pi\)
\(662\) 0 0
\(663\) 32.7846 1.27325
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −24.9282 −0.963780
\(670\) 0 0
\(671\) 3.21539 0.124129
\(672\) 0 0
\(673\) −23.1769 −0.893404 −0.446702 0.894683i \(-0.647402\pi\)
−0.446702 + 0.894683i \(0.647402\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −19.1769 −0.737029 −0.368514 0.929622i \(-0.620133\pi\)
−0.368514 + 0.929622i \(0.620133\pi\)
\(678\) 0 0
\(679\) 68.1051 2.61363
\(680\) 0 0
\(681\) −34.3923 −1.31792
\(682\) 0 0
\(683\) 5.66025 0.216584 0.108292 0.994119i \(-0.465462\pi\)
0.108292 + 0.994119i \(0.465462\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 13.8564 0.528655
\(688\) 0 0
\(689\) −36.0000 −1.37149
\(690\) 0 0
\(691\) 26.3923 1.00401 0.502005 0.864865i \(-0.332596\pi\)
0.502005 + 0.864865i \(0.332596\pi\)
\(692\) 0 0
\(693\) 73.1769 2.77976
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −32.7846 −1.24181
\(698\) 0 0
\(699\) 61.1769 2.31392
\(700\) 0 0
\(701\) −26.7846 −1.01164 −0.505820 0.862639i \(-0.668810\pi\)
−0.505820 + 0.862639i \(0.668810\pi\)
\(702\) 0 0
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 56.7846 2.13561
\(708\) 0 0
\(709\) 37.8564 1.42173 0.710864 0.703330i \(-0.248304\pi\)
0.710864 + 0.703330i \(0.248304\pi\)
\(710\) 0 0
\(711\) 53.5692 2.00900
\(712\) 0 0
\(713\) 5.56922 0.208569
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −56.7846 −2.12066
\(718\) 0 0
\(719\) −3.21539 −0.119914 −0.0599569 0.998201i \(-0.519096\pi\)
−0.0599569 + 0.998201i \(0.519096\pi\)
\(720\) 0 0
\(721\) −10.3923 −0.387030
\(722\) 0 0
\(723\) −1.07180 −0.0398606
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4.05256 0.150301 0.0751505 0.997172i \(-0.476056\pi\)
0.0751505 + 0.997172i \(0.476056\pi\)
\(728\) 0 0
\(729\) −43.7846 −1.62165
\(730\) 0 0
\(731\) −0.679492 −0.0251319
\(732\) 0 0
\(733\) −2.78461 −0.102852 −0.0514260 0.998677i \(-0.516377\pi\)
−0.0514260 + 0.998677i \(0.516377\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.679492 −0.0250294
\(738\) 0 0
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) 0 0
\(741\) −18.9282 −0.695345
\(742\) 0 0
\(743\) −5.41154 −0.198530 −0.0992651 0.995061i \(-0.531649\pi\)
−0.0992651 + 0.995061i \(0.531649\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.66025 −0.207098
\(748\) 0 0
\(749\) 62.7846 2.29410
\(750\) 0 0
\(751\) 19.6077 0.715495 0.357747 0.933818i \(-0.383545\pi\)
0.357747 + 0.933818i \(0.383545\pi\)
\(752\) 0 0
\(753\) 23.3205 0.849847
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 36.9282 1.34218 0.671089 0.741377i \(-0.265827\pi\)
0.671089 + 0.741377i \(0.265827\pi\)
\(758\) 0 0
\(759\) 20.7846 0.754434
\(760\) 0 0
\(761\) −33.7128 −1.22209 −0.611044 0.791596i \(-0.709250\pi\)
−0.611044 + 0.791596i \(0.709250\pi\)
\(762\) 0 0
\(763\) 61.1769 2.21475
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 20.7846 0.750489
\(768\) 0 0
\(769\) 34.7846 1.25437 0.627183 0.778872i \(-0.284208\pi\)
0.627183 + 0.778872i \(0.284208\pi\)
\(770\) 0 0
\(771\) 16.3923 0.590354
\(772\) 0 0
\(773\) −25.6077 −0.921045 −0.460522 0.887648i \(-0.652338\pi\)
−0.460522 + 0.887648i \(0.652338\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 77.5692 2.78278
\(778\) 0 0
\(779\) 18.9282 0.678173
\(780\) 0 0
\(781\) −56.7846 −2.03191
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 16.1962 0.577330 0.288665 0.957430i \(-0.406789\pi\)
0.288665 + 0.957430i \(0.406789\pi\)
\(788\) 0 0
\(789\) −26.7846 −0.953557
\(790\) 0 0
\(791\) −61.1769 −2.17520
\(792\) 0 0
\(793\) 3.21539 0.114182
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 22.3923 0.793176 0.396588 0.917997i \(-0.370194\pi\)
0.396588 + 0.917997i \(0.370194\pi\)
\(798\) 0 0
\(799\) 7.60770 0.269141
\(800\) 0 0
\(801\) 57.7128 2.03918
\(802\) 0 0
\(803\) −22.1436 −0.781430
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −73.1769 −2.57595
\(808\) 0 0
\(809\) 47.5692 1.67244 0.836222 0.548391i \(-0.184759\pi\)
0.836222 + 0.548391i \(0.184759\pi\)
\(810\) 0 0
\(811\) 17.6077 0.618290 0.309145 0.951015i \(-0.399957\pi\)
0.309145 + 0.951015i \(0.399957\pi\)
\(812\) 0 0
\(813\) −44.7846 −1.57066
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.392305 0.0137250
\(818\) 0 0
\(819\) 73.1769 2.55701
\(820\) 0 0
\(821\) −9.21539 −0.321619 −0.160810 0.986985i \(-0.551411\pi\)
−0.160810 + 0.986985i \(0.551411\pi\)
\(822\) 0 0
\(823\) 48.8372 1.70236 0.851178 0.524877i \(-0.175889\pi\)
0.851178 + 0.524877i \(0.175889\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.26795 0.0440909 0.0220455 0.999757i \(-0.492982\pi\)
0.0220455 + 0.999757i \(0.492982\pi\)
\(828\) 0 0
\(829\) 9.21539 0.320064 0.160032 0.987112i \(-0.448840\pi\)
0.160032 + 0.987112i \(0.448840\pi\)
\(830\) 0 0
\(831\) −21.4641 −0.744581
\(832\) 0 0
\(833\) 53.3205 1.84745
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −10.1436 −0.350614
\(838\) 0 0
\(839\) −32.7846 −1.13185 −0.565925 0.824457i \(-0.691481\pi\)
−0.565925 + 0.824457i \(0.691481\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −20.7846 −0.715860
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −4.73205 −0.162595
\(848\) 0 0
\(849\) 56.2487 1.93045
\(850\) 0 0
\(851\) 13.1769 0.451699
\(852\) 0 0
\(853\) 3.46410 0.118609 0.0593043 0.998240i \(-0.481112\pi\)
0.0593043 + 0.998240i \(0.481112\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −43.8564 −1.49811 −0.749053 0.662510i \(-0.769491\pi\)
−0.749053 + 0.662510i \(0.769491\pi\)
\(858\) 0 0
\(859\) −31.5692 −1.07713 −0.538564 0.842585i \(-0.681033\pi\)
−0.538564 + 0.842585i \(0.681033\pi\)
\(860\) 0 0
\(861\) −122.354 −4.16981
\(862\) 0 0
\(863\) −10.9808 −0.373789 −0.186895 0.982380i \(-0.559842\pi\)
−0.186895 + 0.982380i \(0.559842\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 13.6603 0.463927
\(868\) 0 0
\(869\) −41.5692 −1.41014
\(870\) 0 0
\(871\) −0.679492 −0.0230237
\(872\) 0 0
\(873\) −64.2487 −2.17449
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 19.8564 0.670503 0.335252 0.942129i \(-0.391179\pi\)
0.335252 + 0.942129i \(0.391179\pi\)
\(878\) 0 0
\(879\) −81.9615 −2.76449
\(880\) 0 0
\(881\) −28.3923 −0.956561 −0.478281 0.878207i \(-0.658740\pi\)
−0.478281 + 0.878207i \(0.658740\pi\)
\(882\) 0 0
\(883\) 16.1962 0.545044 0.272522 0.962150i \(-0.412142\pi\)
0.272522 + 0.962150i \(0.412142\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −51.3731 −1.72494 −0.862469 0.506109i \(-0.831083\pi\)
−0.862469 + 0.506109i \(0.831083\pi\)
\(888\) 0 0
\(889\) 67.1769 2.25304
\(890\) 0 0
\(891\) 8.53590 0.285963
\(892\) 0 0
\(893\) −4.39230 −0.146983
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 20.7846 0.693978
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) −2.53590 −0.0843894
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 32.5885 1.08208 0.541041 0.840996i \(-0.318030\pi\)
0.541041 + 0.840996i \(0.318030\pi\)
\(908\) 0 0
\(909\) −53.5692 −1.77678
\(910\) 0 0
\(911\) −25.1769 −0.834148 −0.417074 0.908872i \(-0.636944\pi\)
−0.417074 + 0.908872i \(0.636944\pi\)
\(912\) 0 0
\(913\) 4.39230 0.145364
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −49.1769 −1.62396
\(918\) 0 0
\(919\) −15.7128 −0.518318 −0.259159 0.965835i \(-0.583445\pi\)
−0.259159 + 0.965835i \(0.583445\pi\)
\(920\) 0 0
\(921\) 65.0333 2.14292
\(922\) 0 0
\(923\) −56.7846 −1.86909
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 9.80385 0.322001
\(928\) 0 0
\(929\) 28.3923 0.931521 0.465761 0.884911i \(-0.345781\pi\)
0.465761 + 0.884911i \(0.345781\pi\)
\(930\) 0 0
\(931\) −30.7846 −1.00892
\(932\) 0 0
\(933\) 77.5692 2.53950
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −30.3923 −0.992873 −0.496437 0.868073i \(-0.665359\pi\)
−0.496437 + 0.868073i \(0.665359\pi\)
\(938\) 0 0
\(939\) −60.1051 −1.96146
\(940\) 0 0
\(941\) 20.7846 0.677559 0.338779 0.940866i \(-0.389986\pi\)
0.338779 + 0.940866i \(0.389986\pi\)
\(942\) 0 0
\(943\) −20.7846 −0.676840
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 56.1962 1.82613 0.913065 0.407815i \(-0.133709\pi\)
0.913065 + 0.407815i \(0.133709\pi\)
\(948\) 0 0
\(949\) −22.1436 −0.718811
\(950\) 0 0
\(951\) 4.39230 0.142430
\(952\) 0 0
\(953\) 11.0718 0.358651 0.179325 0.983790i \(-0.442609\pi\)
0.179325 + 0.983790i \(0.442609\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 4.39230 0.141835
\(960\) 0 0
\(961\) −24.5692 −0.792555
\(962\) 0 0
\(963\) −59.2295 −1.90864
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −2.19615 −0.0706235 −0.0353118 0.999376i \(-0.511242\pi\)
−0.0353118 + 0.999376i \(0.511242\pi\)
\(968\) 0 0
\(969\) 18.9282 0.608061
\(970\) 0 0
\(971\) −57.0333 −1.83029 −0.915143 0.403129i \(-0.867923\pi\)
−0.915143 + 0.403129i \(0.867923\pi\)
\(972\) 0 0
\(973\) 47.3205 1.51703
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 29.3205 0.938046 0.469023 0.883186i \(-0.344606\pi\)
0.469023 + 0.883186i \(0.344606\pi\)
\(978\) 0 0
\(979\) −44.7846 −1.43132
\(980\) 0 0
\(981\) −57.7128 −1.84263
\(982\) 0 0
\(983\) 42.5885 1.35836 0.679180 0.733971i \(-0.262335\pi\)
0.679180 + 0.733971i \(0.262335\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 28.3923 0.903737
\(988\) 0 0
\(989\) −0.430781 −0.0136980
\(990\) 0 0
\(991\) 32.1051 1.01985 0.509926 0.860218i \(-0.329673\pi\)
0.509926 + 0.860218i \(0.329673\pi\)
\(992\) 0 0
\(993\) 72.1051 2.28819
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −46.3923 −1.46926 −0.734630 0.678468i \(-0.762644\pi\)
−0.734630 + 0.678468i \(0.762644\pi\)
\(998\) 0 0
\(999\) −24.0000 −0.759326
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 6400.2.a.y.1.1 2
4.3 odd 2 6400.2.a.ck.1.2 2
5.4 even 2 1280.2.a.p.1.2 2
8.3 odd 2 6400.2.a.bf.1.1 2
8.5 even 2 6400.2.a.cd.1.2 2
16.3 odd 4 1600.2.d.b.801.4 4
16.5 even 4 1600.2.d.h.801.4 4
16.11 odd 4 1600.2.d.b.801.1 4
16.13 even 4 1600.2.d.h.801.1 4
20.19 odd 2 1280.2.a.c.1.1 2
40.19 odd 2 1280.2.a.m.1.2 2
40.29 even 2 1280.2.a.b.1.1 2
80.3 even 4 1600.2.f.d.1249.2 4
80.13 odd 4 1600.2.f.i.1249.3 4
80.19 odd 4 320.2.d.b.161.1 yes 4
80.27 even 4 1600.2.f.d.1249.1 4
80.29 even 4 320.2.d.a.161.4 yes 4
80.37 odd 4 1600.2.f.i.1249.4 4
80.43 even 4 1600.2.f.h.1249.4 4
80.53 odd 4 1600.2.f.e.1249.1 4
80.59 odd 4 320.2.d.b.161.4 yes 4
80.67 even 4 1600.2.f.h.1249.3 4
80.69 even 4 320.2.d.a.161.1 4
80.77 odd 4 1600.2.f.e.1249.2 4
240.29 odd 4 2880.2.k.e.1441.3 4
240.59 even 4 2880.2.k.l.1441.2 4
240.149 odd 4 2880.2.k.e.1441.1 4
240.179 even 4 2880.2.k.l.1441.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
320.2.d.a.161.1 4 80.69 even 4
320.2.d.a.161.4 yes 4 80.29 even 4
320.2.d.b.161.1 yes 4 80.19 odd 4
320.2.d.b.161.4 yes 4 80.59 odd 4
1280.2.a.b.1.1 2 40.29 even 2
1280.2.a.c.1.1 2 20.19 odd 2
1280.2.a.m.1.2 2 40.19 odd 2
1280.2.a.p.1.2 2 5.4 even 2
1600.2.d.b.801.1 4 16.11 odd 4
1600.2.d.b.801.4 4 16.3 odd 4
1600.2.d.h.801.1 4 16.13 even 4
1600.2.d.h.801.4 4 16.5 even 4
1600.2.f.d.1249.1 4 80.27 even 4
1600.2.f.d.1249.2 4 80.3 even 4
1600.2.f.e.1249.1 4 80.53 odd 4
1600.2.f.e.1249.2 4 80.77 odd 4
1600.2.f.h.1249.3 4 80.67 even 4
1600.2.f.h.1249.4 4 80.43 even 4
1600.2.f.i.1249.3 4 80.13 odd 4
1600.2.f.i.1249.4 4 80.37 odd 4
2880.2.k.e.1441.1 4 240.149 odd 4
2880.2.k.e.1441.3 4 240.29 odd 4
2880.2.k.l.1441.2 4 240.59 even 4
2880.2.k.l.1441.4 4 240.179 even 4
6400.2.a.y.1.1 2 1.1 even 1 trivial
6400.2.a.bf.1.1 2 8.3 odd 2
6400.2.a.cd.1.2 2 8.5 even 2
6400.2.a.ck.1.2 2 4.3 odd 2