Properties

Label 7800.2.a.be.1.1
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
Defining polynomial: \( x^{2} - x - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.70156\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.70156 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.70156 q^{7} +1.00000 q^{9} +0.701562 q^{11} +1.00000 q^{13} +0.701562 q^{17} -2.00000 q^{19} -2.70156 q^{21} -6.70156 q^{23} +1.00000 q^{27} +9.40312 q^{29} -9.40312 q^{31} +0.701562 q^{33} +6.70156 q^{37} +1.00000 q^{39} +10.7016 q^{41} -4.00000 q^{43} +1.40312 q^{47} +0.298438 q^{49} +0.701562 q^{51} -10.7016 q^{53} -2.00000 q^{57} -14.8062 q^{59} +2.70156 q^{61} -2.70156 q^{63} +4.00000 q^{67} -6.70156 q^{69} +15.5078 q^{71} -13.4031 q^{73} -1.89531 q^{77} +4.70156 q^{79} +1.00000 q^{81} -4.00000 q^{83} +9.40312 q^{87} +8.10469 q^{89} -2.70156 q^{91} -9.40312 q^{93} -18.1047 q^{97} +0.701562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + q^{7} + 2 q^{9} - 5 q^{11} + 2 q^{13} - 5 q^{17} - 4 q^{19} + q^{21} - 7 q^{23} + 2 q^{27} + 6 q^{29} - 6 q^{31} - 5 q^{33} + 7 q^{37} + 2 q^{39} + 15 q^{41} - 8 q^{43} - 10 q^{47} + 7 q^{49} - 5 q^{51} - 15 q^{53} - 4 q^{57} - 4 q^{59} - q^{61} + q^{63} + 8 q^{67} - 7 q^{69} - q^{71} - 14 q^{73} - 23 q^{77} + 3 q^{79} + 2 q^{81} - 8 q^{83} + 6 q^{87} - 3 q^{89} + q^{91} - 6 q^{93} - 17 q^{97} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.70156 −1.02109 −0.510547 0.859850i \(-0.670557\pi\)
−0.510547 + 0.859850i \(0.670557\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.701562 0.211529 0.105764 0.994391i \(-0.466271\pi\)
0.105764 + 0.994391i \(0.466271\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.701562 0.170154 0.0850769 0.996374i \(-0.472886\pi\)
0.0850769 + 0.996374i \(0.472886\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) −2.70156 −0.589529
\(22\) 0 0
\(23\) −6.70156 −1.39737 −0.698686 0.715428i \(-0.746232\pi\)
−0.698686 + 0.715428i \(0.746232\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 9.40312 1.74612 0.873058 0.487616i \(-0.162133\pi\)
0.873058 + 0.487616i \(0.162133\pi\)
\(30\) 0 0
\(31\) −9.40312 −1.68885 −0.844425 0.535673i \(-0.820058\pi\)
−0.844425 + 0.535673i \(0.820058\pi\)
\(32\) 0 0
\(33\) 0.701562 0.122126
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.70156 1.10173 0.550865 0.834594i \(-0.314298\pi\)
0.550865 + 0.834594i \(0.314298\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 10.7016 1.67130 0.835652 0.549260i \(-0.185090\pi\)
0.835652 + 0.549260i \(0.185090\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.40312 0.204667 0.102333 0.994750i \(-0.467369\pi\)
0.102333 + 0.994750i \(0.467369\pi\)
\(48\) 0 0
\(49\) 0.298438 0.0426340
\(50\) 0 0
\(51\) 0.701562 0.0982383
\(52\) 0 0
\(53\) −10.7016 −1.46997 −0.734986 0.678082i \(-0.762811\pi\)
−0.734986 + 0.678082i \(0.762811\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −14.8062 −1.92761 −0.963805 0.266609i \(-0.914097\pi\)
−0.963805 + 0.266609i \(0.914097\pi\)
\(60\) 0 0
\(61\) 2.70156 0.345900 0.172950 0.984931i \(-0.444670\pi\)
0.172950 + 0.984931i \(0.444670\pi\)
\(62\) 0 0
\(63\) −2.70156 −0.340365
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) −6.70156 −0.806773
\(70\) 0 0
\(71\) 15.5078 1.84044 0.920219 0.391403i \(-0.128010\pi\)
0.920219 + 0.391403i \(0.128010\pi\)
\(72\) 0 0
\(73\) −13.4031 −1.56872 −0.784359 0.620308i \(-0.787008\pi\)
−0.784359 + 0.620308i \(0.787008\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.89531 −0.215991
\(78\) 0 0
\(79\) 4.70156 0.528967 0.264484 0.964390i \(-0.414799\pi\)
0.264484 + 0.964390i \(0.414799\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 9.40312 1.00812
\(88\) 0 0
\(89\) 8.10469 0.859095 0.429548 0.903044i \(-0.358673\pi\)
0.429548 + 0.903044i \(0.358673\pi\)
\(90\) 0 0
\(91\) −2.70156 −0.283201
\(92\) 0 0
\(93\) −9.40312 −0.975059
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −18.1047 −1.83825 −0.919126 0.393963i \(-0.871104\pi\)
−0.919126 + 0.393963i \(0.871104\pi\)
\(98\) 0 0
\(99\) 0.701562 0.0705096
\(100\) 0 0
\(101\) −6.80625 −0.677247 −0.338624 0.940922i \(-0.609961\pi\)
−0.338624 + 0.940922i \(0.609961\pi\)
\(102\) 0 0
\(103\) −12.0000 −1.18240 −0.591198 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −18.1047 −1.75025 −0.875123 0.483900i \(-0.839220\pi\)
−0.875123 + 0.483900i \(0.839220\pi\)
\(108\) 0 0
\(109\) 10.8062 1.03505 0.517525 0.855668i \(-0.326853\pi\)
0.517525 + 0.855668i \(0.326853\pi\)
\(110\) 0 0
\(111\) 6.70156 0.636084
\(112\) 0 0
\(113\) −6.59688 −0.620582 −0.310291 0.950642i \(-0.600426\pi\)
−0.310291 + 0.950642i \(0.600426\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −1.89531 −0.173743
\(120\) 0 0
\(121\) −10.5078 −0.955256
\(122\) 0 0
\(123\) 10.7016 0.964927
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 13.4031 1.18933 0.594667 0.803972i \(-0.297284\pi\)
0.594667 + 0.803972i \(0.297284\pi\)
\(128\) 0 0
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) −12.8062 −1.11889 −0.559444 0.828868i \(-0.688985\pi\)
−0.559444 + 0.828868i \(0.688985\pi\)
\(132\) 0 0
\(133\) 5.40312 0.468510
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) −4.70156 −0.398781 −0.199391 0.979920i \(-0.563896\pi\)
−0.199391 + 0.979920i \(0.563896\pi\)
\(140\) 0 0
\(141\) 1.40312 0.118164
\(142\) 0 0
\(143\) 0.701562 0.0586676
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0.298438 0.0246147
\(148\) 0 0
\(149\) 1.29844 0.106372 0.0531861 0.998585i \(-0.483062\pi\)
0.0531861 + 0.998585i \(0.483062\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0.701562 0.0567179
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.80625 −0.702815 −0.351408 0.936223i \(-0.614297\pi\)
−0.351408 + 0.936223i \(0.614297\pi\)
\(158\) 0 0
\(159\) −10.7016 −0.848689
\(160\) 0 0
\(161\) 18.1047 1.42685
\(162\) 0 0
\(163\) −11.2984 −0.884962 −0.442481 0.896778i \(-0.645902\pi\)
−0.442481 + 0.896778i \(0.645902\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 22.8062 1.76480 0.882400 0.470500i \(-0.155926\pi\)
0.882400 + 0.470500i \(0.155926\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 0 0
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −14.8062 −1.11291
\(178\) 0 0
\(179\) −22.0000 −1.64436 −0.822179 0.569230i \(-0.807242\pi\)
−0.822179 + 0.569230i \(0.807242\pi\)
\(180\) 0 0
\(181\) −1.29844 −0.0965121 −0.0482561 0.998835i \(-0.515366\pi\)
−0.0482561 + 0.998835i \(0.515366\pi\)
\(182\) 0 0
\(183\) 2.70156 0.199705
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.492189 0.0359925
\(188\) 0 0
\(189\) −2.70156 −0.196510
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 22.1047 1.59113 0.795565 0.605868i \(-0.207174\pi\)
0.795565 + 0.605868i \(0.207174\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.2094 1.01238 0.506188 0.862423i \(-0.331054\pi\)
0.506188 + 0.862423i \(0.331054\pi\)
\(198\) 0 0
\(199\) 2.80625 0.198930 0.0994648 0.995041i \(-0.468287\pi\)
0.0994648 + 0.995041i \(0.468287\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 0 0
\(203\) −25.4031 −1.78295
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −6.70156 −0.465791
\(208\) 0 0
\(209\) −1.40312 −0.0970561
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) 15.5078 1.06258
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 25.4031 1.72448
\(218\) 0 0
\(219\) −13.4031 −0.905699
\(220\) 0 0
\(221\) 0.701562 0.0471922
\(222\) 0 0
\(223\) −3.40312 −0.227890 −0.113945 0.993487i \(-0.536349\pi\)
−0.113945 + 0.993487i \(0.536349\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.5969 0.703339 0.351670 0.936124i \(-0.385614\pi\)
0.351670 + 0.936124i \(0.385614\pi\)
\(228\) 0 0
\(229\) −25.4031 −1.67869 −0.839343 0.543602i \(-0.817060\pi\)
−0.839343 + 0.543602i \(0.817060\pi\)
\(230\) 0 0
\(231\) −1.89531 −0.124702
\(232\) 0 0
\(233\) 10.1047 0.661980 0.330990 0.943634i \(-0.392617\pi\)
0.330990 + 0.943634i \(0.392617\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 4.70156 0.305399
\(238\) 0 0
\(239\) −6.10469 −0.394879 −0.197440 0.980315i \(-0.563263\pi\)
−0.197440 + 0.980315i \(0.563263\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 0 0
\(251\) −18.2094 −1.14937 −0.574683 0.818376i \(-0.694875\pi\)
−0.574683 + 0.818376i \(0.694875\pi\)
\(252\) 0 0
\(253\) −4.70156 −0.295585
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −20.2094 −1.26063 −0.630313 0.776341i \(-0.717073\pi\)
−0.630313 + 0.776341i \(0.717073\pi\)
\(258\) 0 0
\(259\) −18.1047 −1.12497
\(260\) 0 0
\(261\) 9.40312 0.582039
\(262\) 0 0
\(263\) −4.59688 −0.283456 −0.141728 0.989906i \(-0.545266\pi\)
−0.141728 + 0.989906i \(0.545266\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 8.10469 0.495999
\(268\) 0 0
\(269\) −14.8062 −0.902753 −0.451376 0.892334i \(-0.649067\pi\)
−0.451376 + 0.892334i \(0.649067\pi\)
\(270\) 0 0
\(271\) −6.59688 −0.400732 −0.200366 0.979721i \(-0.564213\pi\)
−0.200366 + 0.979721i \(0.564213\pi\)
\(272\) 0 0
\(273\) −2.70156 −0.163506
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −8.80625 −0.529116 −0.264558 0.964370i \(-0.585226\pi\)
−0.264558 + 0.964370i \(0.585226\pi\)
\(278\) 0 0
\(279\) −9.40312 −0.562950
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −28.9109 −1.70656
\(288\) 0 0
\(289\) −16.5078 −0.971048
\(290\) 0 0
\(291\) −18.1047 −1.06132
\(292\) 0 0
\(293\) −15.4031 −0.899860 −0.449930 0.893064i \(-0.648551\pi\)
−0.449930 + 0.893064i \(0.648551\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0.701562 0.0407088
\(298\) 0 0
\(299\) −6.70156 −0.387561
\(300\) 0 0
\(301\) 10.8062 0.622862
\(302\) 0 0
\(303\) −6.80625 −0.391009
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 13.8953 0.793047 0.396524 0.918024i \(-0.370216\pi\)
0.396524 + 0.918024i \(0.370216\pi\)
\(308\) 0 0
\(309\) −12.0000 −0.682656
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) −16.8062 −0.949945 −0.474973 0.880001i \(-0.657542\pi\)
−0.474973 + 0.880001i \(0.657542\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.2094 −0.798078 −0.399039 0.916934i \(-0.630656\pi\)
−0.399039 + 0.916934i \(0.630656\pi\)
\(318\) 0 0
\(319\) 6.59688 0.369354
\(320\) 0 0
\(321\) −18.1047 −1.01051
\(322\) 0 0
\(323\) −1.40312 −0.0780719
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 10.8062 0.597587
\(328\) 0 0
\(329\) −3.79063 −0.208984
\(330\) 0 0
\(331\) −14.2094 −0.781018 −0.390509 0.920599i \(-0.627701\pi\)
−0.390509 + 0.920599i \(0.627701\pi\)
\(332\) 0 0
\(333\) 6.70156 0.367243
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 6.20937 0.338246 0.169123 0.985595i \(-0.445906\pi\)
0.169123 + 0.985595i \(0.445906\pi\)
\(338\) 0 0
\(339\) −6.59688 −0.358293
\(340\) 0 0
\(341\) −6.59688 −0.357241
\(342\) 0 0
\(343\) 18.1047 0.977561
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.10469 −0.327717 −0.163858 0.986484i \(-0.552394\pi\)
−0.163858 + 0.986484i \(0.552394\pi\)
\(348\) 0 0
\(349\) −34.8062 −1.86314 −0.931568 0.363567i \(-0.881559\pi\)
−0.931568 + 0.363567i \(0.881559\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −12.8062 −0.681608 −0.340804 0.940134i \(-0.610699\pi\)
−0.340804 + 0.940134i \(0.610699\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.89531 −0.100311
\(358\) 0 0
\(359\) −21.6125 −1.14066 −0.570332 0.821414i \(-0.693185\pi\)
−0.570332 + 0.821414i \(0.693185\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) −10.5078 −0.551517
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.19375 −0.0623133 −0.0311567 0.999515i \(-0.509919\pi\)
−0.0311567 + 0.999515i \(0.509919\pi\)
\(368\) 0 0
\(369\) 10.7016 0.557101
\(370\) 0 0
\(371\) 28.9109 1.50098
\(372\) 0 0
\(373\) 8.59688 0.445129 0.222565 0.974918i \(-0.428557\pi\)
0.222565 + 0.974918i \(0.428557\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.40312 0.484286
\(378\) 0 0
\(379\) 15.6125 0.801960 0.400980 0.916087i \(-0.368670\pi\)
0.400980 + 0.916087i \(0.368670\pi\)
\(380\) 0 0
\(381\) 13.4031 0.686663
\(382\) 0 0
\(383\) 5.40312 0.276087 0.138043 0.990426i \(-0.455919\pi\)
0.138043 + 0.990426i \(0.455919\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.00000 −0.203331
\(388\) 0 0
\(389\) 25.6125 1.29861 0.649303 0.760530i \(-0.275061\pi\)
0.649303 + 0.760530i \(0.275061\pi\)
\(390\) 0 0
\(391\) −4.70156 −0.237768
\(392\) 0 0
\(393\) −12.8062 −0.645990
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 22.7016 1.13936 0.569679 0.821867i \(-0.307067\pi\)
0.569679 + 0.821867i \(0.307067\pi\)
\(398\) 0 0
\(399\) 5.40312 0.270495
\(400\) 0 0
\(401\) 0.806248 0.0402621 0.0201311 0.999797i \(-0.493592\pi\)
0.0201311 + 0.999797i \(0.493592\pi\)
\(402\) 0 0
\(403\) −9.40312 −0.468403
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.70156 0.233048
\(408\) 0 0
\(409\) −4.80625 −0.237654 −0.118827 0.992915i \(-0.537913\pi\)
−0.118827 + 0.992915i \(0.537913\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) 0 0
\(413\) 40.0000 1.96827
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.70156 −0.230236
\(418\) 0 0
\(419\) 27.6125 1.34896 0.674479 0.738294i \(-0.264368\pi\)
0.674479 + 0.738294i \(0.264368\pi\)
\(420\) 0 0
\(421\) −25.6125 −1.24828 −0.624138 0.781314i \(-0.714550\pi\)
−0.624138 + 0.781314i \(0.714550\pi\)
\(422\) 0 0
\(423\) 1.40312 0.0682222
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7.29844 −0.353196
\(428\) 0 0
\(429\) 0.701562 0.0338717
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) −12.5969 −0.605367 −0.302684 0.953091i \(-0.597883\pi\)
−0.302684 + 0.953091i \(0.597883\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13.4031 0.641158
\(438\) 0 0
\(439\) −1.89531 −0.0904584 −0.0452292 0.998977i \(-0.514402\pi\)
−0.0452292 + 0.998977i \(0.514402\pi\)
\(440\) 0 0
\(441\) 0.298438 0.0142113
\(442\) 0 0
\(443\) 26.3141 1.25022 0.625109 0.780537i \(-0.285054\pi\)
0.625109 + 0.780537i \(0.285054\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.29844 0.0614140
\(448\) 0 0
\(449\) 3.89531 0.183831 0.0919156 0.995767i \(-0.470701\pi\)
0.0919156 + 0.995767i \(0.470701\pi\)
\(450\) 0 0
\(451\) 7.50781 0.353529
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.29844 −0.341407 −0.170703 0.985322i \(-0.554604\pi\)
−0.170703 + 0.985322i \(0.554604\pi\)
\(458\) 0 0
\(459\) 0.701562 0.0327461
\(460\) 0 0
\(461\) 19.8953 0.926617 0.463309 0.886197i \(-0.346662\pi\)
0.463309 + 0.886197i \(0.346662\pi\)
\(462\) 0 0
\(463\) 4.10469 0.190761 0.0953805 0.995441i \(-0.469593\pi\)
0.0953805 + 0.995441i \(0.469593\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.1047 −0.837785 −0.418892 0.908036i \(-0.637582\pi\)
−0.418892 + 0.908036i \(0.637582\pi\)
\(468\) 0 0
\(469\) −10.8062 −0.498986
\(470\) 0 0
\(471\) −8.80625 −0.405771
\(472\) 0 0
\(473\) −2.80625 −0.129031
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −10.7016 −0.489991
\(478\) 0 0
\(479\) −28.7016 −1.31141 −0.655704 0.755018i \(-0.727628\pi\)
−0.655704 + 0.755018i \(0.727628\pi\)
\(480\) 0 0
\(481\) 6.70156 0.305565
\(482\) 0 0
\(483\) 18.1047 0.823792
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 36.3141 1.64555 0.822774 0.568369i \(-0.192426\pi\)
0.822774 + 0.568369i \(0.192426\pi\)
\(488\) 0 0
\(489\) −11.2984 −0.510933
\(490\) 0 0
\(491\) −6.20937 −0.280225 −0.140113 0.990136i \(-0.544746\pi\)
−0.140113 + 0.990136i \(0.544746\pi\)
\(492\) 0 0
\(493\) 6.59688 0.297108
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −41.8953 −1.87926
\(498\) 0 0
\(499\) 15.1938 0.680166 0.340083 0.940395i \(-0.389545\pi\)
0.340083 + 0.940395i \(0.389545\pi\)
\(500\) 0 0
\(501\) 22.8062 1.01891
\(502\) 0 0
\(503\) −31.4031 −1.40020 −0.700098 0.714047i \(-0.746860\pi\)
−0.700098 + 0.714047i \(0.746860\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) −32.3141 −1.43230 −0.716148 0.697949i \(-0.754096\pi\)
−0.716148 + 0.697949i \(0.754096\pi\)
\(510\) 0 0
\(511\) 36.2094 1.60181
\(512\) 0 0
\(513\) −2.00000 −0.0883022
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.984379 0.0432929
\(518\) 0 0
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.59688 −0.287364
\(528\) 0 0
\(529\) 21.9109 0.952649
\(530\) 0 0
\(531\) −14.8062 −0.642536
\(532\) 0 0
\(533\) 10.7016 0.463536
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −22.0000 −0.949370
\(538\) 0 0
\(539\) 0.209373 0.00901832
\(540\) 0 0
\(541\) 40.2094 1.72874 0.864368 0.502860i \(-0.167719\pi\)
0.864368 + 0.502860i \(0.167719\pi\)
\(542\) 0 0
\(543\) −1.29844 −0.0557213
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 25.6125 1.09511 0.547556 0.836769i \(-0.315558\pi\)
0.547556 + 0.836769i \(0.315558\pi\)
\(548\) 0 0
\(549\) 2.70156 0.115300
\(550\) 0 0
\(551\) −18.8062 −0.801173
\(552\) 0 0
\(553\) −12.7016 −0.540125
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.00000 −0.0847427 −0.0423714 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 0.492189 0.0207803
\(562\) 0 0
\(563\) −22.1047 −0.931601 −0.465801 0.884890i \(-0.654234\pi\)
−0.465801 + 0.884890i \(0.654234\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.70156 −0.113455
\(568\) 0 0
\(569\) −27.4031 −1.14880 −0.574399 0.818575i \(-0.694764\pi\)
−0.574399 + 0.818575i \(0.694764\pi\)
\(570\) 0 0
\(571\) 26.3141 1.10121 0.550605 0.834766i \(-0.314397\pi\)
0.550605 + 0.834766i \(0.314397\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 31.5078 1.31169 0.655844 0.754897i \(-0.272313\pi\)
0.655844 + 0.754897i \(0.272313\pi\)
\(578\) 0 0
\(579\) 22.1047 0.918639
\(580\) 0 0
\(581\) 10.8062 0.448319
\(582\) 0 0
\(583\) −7.50781 −0.310942
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.2094 0.999228 0.499614 0.866248i \(-0.333475\pi\)
0.499614 + 0.866248i \(0.333475\pi\)
\(588\) 0 0
\(589\) 18.8062 0.774898
\(590\) 0 0
\(591\) 14.2094 0.584495
\(592\) 0 0
\(593\) 3.40312 0.139750 0.0698748 0.997556i \(-0.477740\pi\)
0.0698748 + 0.997556i \(0.477740\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.80625 0.114852
\(598\) 0 0
\(599\) −42.8062 −1.74902 −0.874508 0.485011i \(-0.838816\pi\)
−0.874508 + 0.485011i \(0.838816\pi\)
\(600\) 0 0
\(601\) 9.29844 0.379291 0.189646 0.981853i \(-0.439266\pi\)
0.189646 + 0.981853i \(0.439266\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 41.6125 1.68900 0.844500 0.535556i \(-0.179898\pi\)
0.844500 + 0.535556i \(0.179898\pi\)
\(608\) 0 0
\(609\) −25.4031 −1.02939
\(610\) 0 0
\(611\) 1.40312 0.0567643
\(612\) 0 0
\(613\) 45.7172 1.84650 0.923250 0.384200i \(-0.125523\pi\)
0.923250 + 0.384200i \(0.125523\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.00000 −0.0805170 −0.0402585 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 0 0
\(619\) 39.6125 1.59216 0.796080 0.605191i \(-0.206903\pi\)
0.796080 + 0.605191i \(0.206903\pi\)
\(620\) 0 0
\(621\) −6.70156 −0.268924
\(622\) 0 0
\(623\) −21.8953 −0.877217
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.40312 −0.0560354
\(628\) 0 0
\(629\) 4.70156 0.187464
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 0 0
\(633\) 20.0000 0.794929
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.298438 0.0118245
\(638\) 0 0
\(639\) 15.5078 0.613480
\(640\) 0 0
\(641\) −10.2094 −0.403246 −0.201623 0.979463i \(-0.564622\pi\)
−0.201623 + 0.979463i \(0.564622\pi\)
\(642\) 0 0
\(643\) −31.2984 −1.23429 −0.617145 0.786849i \(-0.711711\pi\)
−0.617145 + 0.786849i \(0.711711\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.1047 −0.790397 −0.395198 0.918596i \(-0.629324\pi\)
−0.395198 + 0.918596i \(0.629324\pi\)
\(648\) 0 0
\(649\) −10.3875 −0.407745
\(650\) 0 0
\(651\) 25.4031 0.995627
\(652\) 0 0
\(653\) −15.6125 −0.610964 −0.305482 0.952198i \(-0.598818\pi\)
−0.305482 + 0.952198i \(0.598818\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −13.4031 −0.522906
\(658\) 0 0
\(659\) −27.4031 −1.06747 −0.533737 0.845650i \(-0.679213\pi\)
−0.533737 + 0.845650i \(0.679213\pi\)
\(660\) 0 0
\(661\) −12.0000 −0.466746 −0.233373 0.972387i \(-0.574976\pi\)
−0.233373 + 0.972387i \(0.574976\pi\)
\(662\) 0 0
\(663\) 0.701562 0.0272464
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −63.0156 −2.43997
\(668\) 0 0
\(669\) −3.40312 −0.131572
\(670\) 0 0
\(671\) 1.89531 0.0731678
\(672\) 0 0
\(673\) 3.19375 0.123110 0.0615550 0.998104i \(-0.480394\pi\)
0.0615550 + 0.998104i \(0.480394\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.10469 0.157756 0.0788780 0.996884i \(-0.474866\pi\)
0.0788780 + 0.996884i \(0.474866\pi\)
\(678\) 0 0
\(679\) 48.9109 1.87703
\(680\) 0 0
\(681\) 10.5969 0.406073
\(682\) 0 0
\(683\) −28.0000 −1.07139 −0.535695 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −25.4031 −0.969190
\(688\) 0 0
\(689\) −10.7016 −0.407697
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 0 0
\(693\) −1.89531 −0.0719970
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 7.50781 0.284379
\(698\) 0 0
\(699\) 10.1047 0.382194
\(700\) 0 0
\(701\) −25.6125 −0.967371 −0.483685 0.875242i \(-0.660702\pi\)
−0.483685 + 0.875242i \(0.660702\pi\)
\(702\) 0 0
\(703\) −13.4031 −0.505508
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18.3875 0.691533
\(708\) 0 0
\(709\) 42.8062 1.60762 0.803811 0.594884i \(-0.202802\pi\)
0.803811 + 0.594884i \(0.202802\pi\)
\(710\) 0 0
\(711\) 4.70156 0.176322
\(712\) 0 0
\(713\) 63.0156 2.35995
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.10469 −0.227984
\(718\) 0 0
\(719\) 9.19375 0.342869 0.171435 0.985196i \(-0.445160\pi\)
0.171435 + 0.985196i \(0.445160\pi\)
\(720\) 0 0
\(721\) 32.4187 1.20734
\(722\) 0 0
\(723\) 2.00000 0.0743808
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 9.40312 0.348743 0.174371 0.984680i \(-0.444211\pi\)
0.174371 + 0.984680i \(0.444211\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.80625 −0.103793
\(732\) 0 0
\(733\) −41.7172 −1.54086 −0.770430 0.637525i \(-0.779958\pi\)
−0.770430 + 0.637525i \(0.779958\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.80625 0.103369
\(738\) 0 0
\(739\) −8.80625 −0.323943 −0.161972 0.986795i \(-0.551785\pi\)
−0.161972 + 0.986795i \(0.551785\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 10.5969 0.388762 0.194381 0.980926i \(-0.437730\pi\)
0.194381 + 0.980926i \(0.437730\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 48.9109 1.78717
\(750\) 0 0
\(751\) −42.3141 −1.54406 −0.772031 0.635585i \(-0.780759\pi\)
−0.772031 + 0.635585i \(0.780759\pi\)
\(752\) 0 0
\(753\) −18.2094 −0.663586
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 47.4031 1.72290 0.861448 0.507846i \(-0.169558\pi\)
0.861448 + 0.507846i \(0.169558\pi\)
\(758\) 0 0
\(759\) −4.70156 −0.170656
\(760\) 0 0
\(761\) −10.0000 −0.362500 −0.181250 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) 0 0
\(763\) −29.1938 −1.05688
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14.8062 −0.534623
\(768\) 0 0
\(769\) 51.4031 1.85364 0.926822 0.375501i \(-0.122529\pi\)
0.926822 + 0.375501i \(0.122529\pi\)
\(770\) 0 0
\(771\) −20.2094 −0.727823
\(772\) 0 0
\(773\) 32.5969 1.17243 0.586214 0.810156i \(-0.300618\pi\)
0.586214 + 0.810156i \(0.300618\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −18.1047 −0.649502
\(778\) 0 0
\(779\) −21.4031 −0.766847
\(780\) 0 0
\(781\) 10.8797 0.389306
\(782\) 0 0
\(783\) 9.40312 0.336040
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −5.19375 −0.185137 −0.0925686 0.995706i \(-0.529508\pi\)
−0.0925686 + 0.995706i \(0.529508\pi\)
\(788\) 0 0
\(789\) −4.59688 −0.163653
\(790\) 0 0
\(791\) 17.8219 0.633673
\(792\) 0 0
\(793\) 2.70156 0.0959353
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14.7016 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(798\) 0 0
\(799\) 0.984379 0.0348248
\(800\) 0 0
\(801\) 8.10469 0.286365
\(802\) 0 0
\(803\) −9.40312 −0.331829
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −14.8062 −0.521205
\(808\) 0 0
\(809\) −0.806248 −0.0283462 −0.0141731 0.999900i \(-0.504512\pi\)
−0.0141731 + 0.999900i \(0.504512\pi\)
\(810\) 0 0
\(811\) −14.2094 −0.498959 −0.249479 0.968380i \(-0.580259\pi\)
−0.249479 + 0.968380i \(0.580259\pi\)
\(812\) 0 0
\(813\) −6.59688 −0.231363
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 8.00000 0.279885
\(818\) 0 0
\(819\) −2.70156 −0.0944002
\(820\) 0 0
\(821\) −2.49219 −0.0869780 −0.0434890 0.999054i \(-0.513847\pi\)
−0.0434890 + 0.999054i \(0.513847\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −34.5969 −1.20305 −0.601526 0.798854i \(-0.705440\pi\)
−0.601526 + 0.798854i \(0.705440\pi\)
\(828\) 0 0
\(829\) −47.6125 −1.65365 −0.826825 0.562459i \(-0.809855\pi\)
−0.826825 + 0.562459i \(0.809855\pi\)
\(830\) 0 0
\(831\) −8.80625 −0.305485
\(832\) 0 0
\(833\) 0.209373 0.00725433
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −9.40312 −0.325020
\(838\) 0 0
\(839\) 45.1203 1.55773 0.778863 0.627194i \(-0.215797\pi\)
0.778863 + 0.627194i \(0.215797\pi\)
\(840\) 0 0
\(841\) 59.4187 2.04892
\(842\) 0 0
\(843\) 10.0000 0.344418
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 28.3875 0.975406
\(848\) 0 0
\(849\) −20.0000 −0.686398
\(850\) 0 0
\(851\) −44.9109 −1.53953
\(852\) 0 0
\(853\) 21.7172 0.743582 0.371791 0.928316i \(-0.378744\pi\)
0.371791 + 0.928316i \(0.378744\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −12.7016 −0.433877 −0.216939 0.976185i \(-0.569607\pi\)
−0.216939 + 0.976185i \(0.569607\pi\)
\(858\) 0 0
\(859\) 31.2984 1.06789 0.533944 0.845520i \(-0.320709\pi\)
0.533944 + 0.845520i \(0.320709\pi\)
\(860\) 0 0
\(861\) −28.9109 −0.985282
\(862\) 0 0
\(863\) −13.4031 −0.456248 −0.228124 0.973632i \(-0.573259\pi\)
−0.228124 + 0.973632i \(0.573259\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −16.5078 −0.560635
\(868\) 0 0
\(869\) 3.29844 0.111892
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 0 0
\(873\) −18.1047 −0.612751
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 3.61250 0.121985 0.0609927 0.998138i \(-0.480573\pi\)
0.0609927 + 0.998138i \(0.480573\pi\)
\(878\) 0 0
\(879\) −15.4031 −0.519534
\(880\) 0 0
\(881\) −12.8062 −0.431453 −0.215727 0.976454i \(-0.569212\pi\)
−0.215727 + 0.976454i \(0.569212\pi\)
\(882\) 0 0
\(883\) 17.6125 0.592708 0.296354 0.955078i \(-0.404229\pi\)
0.296354 + 0.955078i \(0.404229\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −18.4922 −0.620907 −0.310453 0.950589i \(-0.600481\pi\)
−0.310453 + 0.950589i \(0.600481\pi\)
\(888\) 0 0
\(889\) −36.2094 −1.21442
\(890\) 0 0
\(891\) 0.701562 0.0235032
\(892\) 0 0
\(893\) −2.80625 −0.0939075
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −6.70156 −0.223759
\(898\) 0 0
\(899\) −88.4187 −2.94893
\(900\) 0 0
\(901\) −7.50781 −0.250121
\(902\) 0 0
\(903\) 10.8062 0.359609
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 16.2094 0.538223 0.269112 0.963109i \(-0.413270\pi\)
0.269112 + 0.963109i \(0.413270\pi\)
\(908\) 0 0
\(909\) −6.80625 −0.225749
\(910\) 0 0
\(911\) 6.80625 0.225501 0.112751 0.993623i \(-0.464034\pi\)
0.112751 + 0.993623i \(0.464034\pi\)
\(912\) 0 0
\(913\) −2.80625 −0.0928733
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 34.5969 1.14249
\(918\) 0 0
\(919\) 7.08907 0.233847 0.116923 0.993141i \(-0.462697\pi\)
0.116923 + 0.993141i \(0.462697\pi\)
\(920\) 0 0
\(921\) 13.8953 0.457866
\(922\) 0 0
\(923\) 15.5078 0.510446
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −12.0000 −0.394132
\(928\) 0 0
\(929\) 8.10469 0.265906 0.132953 0.991122i \(-0.457554\pi\)
0.132953 + 0.991122i \(0.457554\pi\)
\(930\) 0 0
\(931\) −0.596876 −0.0195618
\(932\) 0 0
\(933\) 8.00000 0.261908
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −52.8062 −1.72510 −0.862552 0.505968i \(-0.831136\pi\)
−0.862552 + 0.505968i \(0.831136\pi\)
\(938\) 0 0
\(939\) −16.8062 −0.548451
\(940\) 0 0
\(941\) −54.7016 −1.78322 −0.891610 0.452804i \(-0.850424\pi\)
−0.891610 + 0.452804i \(0.850424\pi\)
\(942\) 0 0
\(943\) −71.7172 −2.33543
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 9.61250 0.312364 0.156182 0.987728i \(-0.450081\pi\)
0.156182 + 0.987728i \(0.450081\pi\)
\(948\) 0 0
\(949\) −13.4031 −0.435084
\(950\) 0 0
\(951\) −14.2094 −0.460770
\(952\) 0 0
\(953\) −4.91093 −0.159081 −0.0795404 0.996832i \(-0.525345\pi\)
−0.0795404 + 0.996832i \(0.525345\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 6.59688 0.213247
\(958\) 0 0
\(959\) 48.6281 1.57028
\(960\) 0 0
\(961\) 57.4187 1.85222
\(962\) 0 0
\(963\) −18.1047 −0.583415
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −39.8219 −1.28058 −0.640292 0.768131i \(-0.721187\pi\)
−0.640292 + 0.768131i \(0.721187\pi\)
\(968\) 0 0
\(969\) −1.40312 −0.0450748
\(970\) 0 0
\(971\) 57.0156 1.82972 0.914859 0.403773i \(-0.132301\pi\)
0.914859 + 0.403773i \(0.132301\pi\)
\(972\) 0 0
\(973\) 12.7016 0.407193
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −26.2094 −0.838512 −0.419256 0.907868i \(-0.637709\pi\)
−0.419256 + 0.907868i \(0.637709\pi\)
\(978\) 0 0
\(979\) 5.68594 0.181723
\(980\) 0 0
\(981\) 10.8062 0.345017
\(982\) 0 0
\(983\) 20.0000 0.637901 0.318950 0.947771i \(-0.396670\pi\)
0.318950 + 0.947771i \(0.396670\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −3.79063 −0.120657
\(988\) 0 0
\(989\) 26.8062 0.852389
\(990\) 0 0
\(991\) 27.7172 0.880465 0.440233 0.897884i \(-0.354896\pi\)
0.440233 + 0.897884i \(0.354896\pi\)
\(992\) 0 0
\(993\) −14.2094 −0.450921
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 51.4031 1.62795 0.813977 0.580898i \(-0.197298\pi\)
0.813977 + 0.580898i \(0.197298\pi\)
\(998\) 0 0
\(999\) 6.70156 0.212028
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 7800.2.a.be.1.1 2
5.4 even 2 1560.2.a.m.1.2 2
15.14 odd 2 4680.2.a.bb.1.2 2
20.19 odd 2 3120.2.a.bf.1.1 2
60.59 even 2 9360.2.a.ct.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.a.m.1.2 2 5.4 even 2
3120.2.a.bf.1.1 2 20.19 odd 2
4680.2.a.bb.1.2 2 15.14 odd 2
7800.2.a.be.1.1 2 1.1 even 1 trivial
9360.2.a.ct.1.1 2 60.59 even 2