Properties

Label 8280.2.a.bu.1.4
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8280,2,Mod(1,8280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8280.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-3.32949\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} +1.49704 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +1.49704 q^{7} +4.73349 q^{11} -1.92548 q^{13} +6.33757 q^{17} +6.73349 q^{19} +1.00000 q^{23} +1.00000 q^{25} -1.74063 q^{29} +6.26306 q^{31} +1.49704 q^{35} +9.53082 q^{37} +2.07573 q^{41} +8.65897 q^{43} -6.29437 q^{47} -4.75888 q^{49} -8.00247 q^{53} +4.73349 q^{55} +0.428447 q^{59} -4.42966 q^{61} -1.92548 q^{65} -12.5249 q^{67} -7.08742 q^{71} -3.43748 q^{73} +7.08621 q^{77} -13.1631 q^{79} +11.1802 q^{83} +6.33757 q^{85} -8.52369 q^{89} -2.88252 q^{91} +6.73349 q^{95} -1.71568 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{5} - 2 q^{7} - 4 q^{11} + 4 q^{17} + 8 q^{19} + 6 q^{23} + 6 q^{25} + 18 q^{29} - 8 q^{31} - 2 q^{35} + 6 q^{37} + 6 q^{41} + 8 q^{43} - 8 q^{47} + 10 q^{49} + 8 q^{53} - 4 q^{55} + 2 q^{59} - 8 q^{61} - 2 q^{67} + 2 q^{71} + 8 q^{73} + 16 q^{77} - 28 q^{79} + 24 q^{83} + 4 q^{85} + 4 q^{89} - 8 q^{91} + 8 q^{95} + 24 q^{97}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.49704 0.565827 0.282913 0.959145i \(-0.408699\pi\)
0.282913 + 0.959145i \(0.408699\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.73349 1.42720 0.713600 0.700553i \(-0.247063\pi\)
0.713600 + 0.700553i \(0.247063\pi\)
\(12\) 0 0
\(13\) −1.92548 −0.534033 −0.267017 0.963692i \(-0.586038\pi\)
−0.267017 + 0.963692i \(0.586038\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.33757 1.53709 0.768543 0.639798i \(-0.220982\pi\)
0.768543 + 0.639798i \(0.220982\pi\)
\(18\) 0 0
\(19\) 6.73349 1.54477 0.772384 0.635156i \(-0.219064\pi\)
0.772384 + 0.635156i \(0.219064\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.74063 −0.323226 −0.161613 0.986854i \(-0.551670\pi\)
−0.161613 + 0.986854i \(0.551670\pi\)
\(30\) 0 0
\(31\) 6.26306 1.12488 0.562439 0.826839i \(-0.309863\pi\)
0.562439 + 0.826839i \(0.309863\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.49704 0.253045
\(36\) 0 0
\(37\) 9.53082 1.56686 0.783429 0.621481i \(-0.213469\pi\)
0.783429 + 0.621481i \(0.213469\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.07573 0.324174 0.162087 0.986776i \(-0.448177\pi\)
0.162087 + 0.986776i \(0.448177\pi\)
\(42\) 0 0
\(43\) 8.65897 1.32048 0.660241 0.751054i \(-0.270454\pi\)
0.660241 + 0.751054i \(0.270454\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.29437 −0.918128 −0.459064 0.888403i \(-0.651815\pi\)
−0.459064 + 0.888403i \(0.651815\pi\)
\(48\) 0 0
\(49\) −4.75888 −0.679840
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.00247 −1.09922 −0.549612 0.835420i \(-0.685224\pi\)
−0.549612 + 0.835420i \(0.685224\pi\)
\(54\) 0 0
\(55\) 4.73349 0.638264
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.428447 0.0557791 0.0278895 0.999611i \(-0.491121\pi\)
0.0278895 + 0.999611i \(0.491121\pi\)
\(60\) 0 0
\(61\) −4.42966 −0.567160 −0.283580 0.958949i \(-0.591522\pi\)
−0.283580 + 0.958949i \(0.591522\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.92548 −0.238827
\(66\) 0 0
\(67\) −12.5249 −1.53016 −0.765080 0.643935i \(-0.777301\pi\)
−0.765080 + 0.643935i \(0.777301\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.08742 −0.841122 −0.420561 0.907264i \(-0.638167\pi\)
−0.420561 + 0.907264i \(0.638167\pi\)
\(72\) 0 0
\(73\) −3.43748 −0.402326 −0.201163 0.979558i \(-0.564472\pi\)
−0.201163 + 0.979558i \(0.564472\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.08621 0.807548
\(78\) 0 0
\(79\) −13.1631 −1.48097 −0.740485 0.672073i \(-0.765404\pi\)
−0.740485 + 0.672073i \(0.765404\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.1802 1.22719 0.613593 0.789623i \(-0.289724\pi\)
0.613593 + 0.789623i \(0.289724\pi\)
\(84\) 0 0
\(85\) 6.33757 0.687406
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.52369 −0.903509 −0.451754 0.892142i \(-0.649202\pi\)
−0.451754 + 0.892142i \(0.649202\pi\)
\(90\) 0 0
\(91\) −2.88252 −0.302170
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.73349 0.690841
\(96\) 0 0
\(97\) −1.71568 −0.174201 −0.0871005 0.996200i \(-0.527760\pi\)
−0.0871005 + 0.996200i \(0.527760\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 16.1466 1.60664 0.803321 0.595546i \(-0.203064\pi\)
0.803321 + 0.595546i \(0.203064\pi\)
\(102\) 0 0
\(103\) 13.7181 1.35169 0.675843 0.737046i \(-0.263780\pi\)
0.675843 + 0.737046i \(0.263780\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.839322 −0.0811403 −0.0405702 0.999177i \(-0.512917\pi\)
−0.0405702 + 0.999177i \(0.512917\pi\)
\(108\) 0 0
\(109\) −15.9474 −1.52749 −0.763743 0.645521i \(-0.776640\pi\)
−0.763743 + 0.645521i \(0.776640\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.89845 0.931168 0.465584 0.885004i \(-0.345844\pi\)
0.465584 + 0.885004i \(0.345844\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 9.48758 0.869725
\(120\) 0 0
\(121\) 11.4059 1.03690
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −19.0735 −1.69250 −0.846251 0.532784i \(-0.821146\pi\)
−0.846251 + 0.532784i \(0.821146\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 21.1480 1.84771 0.923857 0.382738i \(-0.125019\pi\)
0.923857 + 0.382738i \(0.125019\pi\)
\(132\) 0 0
\(133\) 10.0803 0.874071
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 20.9828 1.79269 0.896343 0.443362i \(-0.146214\pi\)
0.896343 + 0.443362i \(0.146214\pi\)
\(138\) 0 0
\(139\) 1.90791 0.161827 0.0809135 0.996721i \(-0.474216\pi\)
0.0809135 + 0.996721i \(0.474216\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.11426 −0.762173
\(144\) 0 0
\(145\) −1.74063 −0.144551
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −13.2596 −1.08627 −0.543134 0.839646i \(-0.682763\pi\)
−0.543134 + 0.839646i \(0.682763\pi\)
\(150\) 0 0
\(151\) −14.0338 −1.14205 −0.571027 0.820931i \(-0.693455\pi\)
−0.571027 + 0.820931i \(0.693455\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.26306 0.503061
\(156\) 0 0
\(157\) 1.57395 0.125615 0.0628073 0.998026i \(-0.479995\pi\)
0.0628073 + 0.998026i \(0.479995\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.49704 0.117983
\(162\) 0 0
\(163\) −20.3771 −1.59606 −0.798028 0.602620i \(-0.794123\pi\)
−0.798028 + 0.602620i \(0.794123\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.22931 0.482039 0.241019 0.970520i \(-0.422518\pi\)
0.241019 + 0.970520i \(0.422518\pi\)
\(168\) 0 0
\(169\) −9.29251 −0.714808
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −16.9126 −1.28584 −0.642921 0.765932i \(-0.722278\pi\)
−0.642921 + 0.765932i \(0.722278\pi\)
\(174\) 0 0
\(175\) 1.49704 0.113165
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −22.8162 −1.70536 −0.852681 0.522431i \(-0.825025\pi\)
−0.852681 + 0.522431i \(0.825025\pi\)
\(180\) 0 0
\(181\) −4.84179 −0.359888 −0.179944 0.983677i \(-0.557592\pi\)
−0.179944 + 0.983677i \(0.557592\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 9.53082 0.700720
\(186\) 0 0
\(187\) 29.9988 2.19373
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.11748 0.659718 0.329859 0.944030i \(-0.392999\pi\)
0.329859 + 0.944030i \(0.392999\pi\)
\(192\) 0 0
\(193\) 20.8476 1.50064 0.750320 0.661075i \(-0.229899\pi\)
0.750320 + 0.661075i \(0.229899\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.05320 −0.288779 −0.144389 0.989521i \(-0.546122\pi\)
−0.144389 + 0.989521i \(0.546122\pi\)
\(198\) 0 0
\(199\) 4.37131 0.309874 0.154937 0.987924i \(-0.450483\pi\)
0.154937 + 0.987924i \(0.450483\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.60578 −0.182890
\(204\) 0 0
\(205\) 2.07573 0.144975
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 31.8729 2.20469
\(210\) 0 0
\(211\) −20.9396 −1.44154 −0.720772 0.693172i \(-0.756213\pi\)
−0.720772 + 0.693172i \(0.756213\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.65897 0.590537
\(216\) 0 0
\(217\) 9.37603 0.636486
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.2029 −0.820855
\(222\) 0 0
\(223\) −17.6336 −1.18084 −0.590418 0.807098i \(-0.701037\pi\)
−0.590418 + 0.807098i \(0.701037\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.7708 0.914001 0.457000 0.889467i \(-0.348924\pi\)
0.457000 + 0.889467i \(0.348924\pi\)
\(228\) 0 0
\(229\) −25.6726 −1.69649 −0.848245 0.529604i \(-0.822341\pi\)
−0.848245 + 0.529604i \(0.822341\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.0049 1.17954 0.589771 0.807570i \(-0.299218\pi\)
0.589771 + 0.807570i \(0.299218\pi\)
\(234\) 0 0
\(235\) −6.29437 −0.410600
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.391410 0.0253182 0.0126591 0.999920i \(-0.495970\pi\)
0.0126591 + 0.999920i \(0.495970\pi\)
\(240\) 0 0
\(241\) 12.6709 0.816202 0.408101 0.912937i \(-0.366191\pi\)
0.408101 + 0.912937i \(0.366191\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.75888 −0.304034
\(246\) 0 0
\(247\) −12.9652 −0.824958
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.14903 0.388123 0.194062 0.980989i \(-0.437834\pi\)
0.194062 + 0.980989i \(0.437834\pi\)
\(252\) 0 0
\(253\) 4.73349 0.297592
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.6064 −0.786365 −0.393183 0.919460i \(-0.628626\pi\)
−0.393183 + 0.919460i \(0.628626\pi\)
\(258\) 0 0
\(259\) 14.2680 0.886570
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −20.4492 −1.26095 −0.630477 0.776208i \(-0.717141\pi\)
−0.630477 + 0.776208i \(0.717141\pi\)
\(264\) 0 0
\(265\) −8.00247 −0.491588
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 27.2100 1.65902 0.829512 0.558488i \(-0.188618\pi\)
0.829512 + 0.558488i \(0.188618\pi\)
\(270\) 0 0
\(271\) 19.0142 1.15503 0.577515 0.816380i \(-0.304022\pi\)
0.577515 + 0.816380i \(0.304022\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.73349 0.285440
\(276\) 0 0
\(277\) 15.7200 0.944525 0.472262 0.881458i \(-0.343437\pi\)
0.472262 + 0.881458i \(0.343437\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −23.3247 −1.39143 −0.695716 0.718317i \(-0.744913\pi\)
−0.695716 + 0.718317i \(0.744913\pi\)
\(282\) 0 0
\(283\) −1.96500 −0.116807 −0.0584036 0.998293i \(-0.518601\pi\)
−0.0584036 + 0.998293i \(0.518601\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.10744 0.183426
\(288\) 0 0
\(289\) 23.1648 1.36264
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 30.6463 1.79038 0.895189 0.445686i \(-0.147040\pi\)
0.895189 + 0.445686i \(0.147040\pi\)
\(294\) 0 0
\(295\) 0.428447 0.0249452
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.92548 −0.111354
\(300\) 0 0
\(301\) 12.9628 0.747164
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.42966 −0.253642
\(306\) 0 0
\(307\) −19.9845 −1.14057 −0.570287 0.821446i \(-0.693168\pi\)
−0.570287 + 0.821446i \(0.693168\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 17.8985 1.01493 0.507465 0.861672i \(-0.330583\pi\)
0.507465 + 0.861672i \(0.330583\pi\)
\(312\) 0 0
\(313\) 12.4765 0.705216 0.352608 0.935771i \(-0.385295\pi\)
0.352608 + 0.935771i \(0.385295\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.9455 1.00792 0.503961 0.863727i \(-0.331876\pi\)
0.503961 + 0.863727i \(0.331876\pi\)
\(318\) 0 0
\(319\) −8.23924 −0.461309
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 42.6740 2.37444
\(324\) 0 0
\(325\) −1.92548 −0.106807
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9.42291 −0.519502
\(330\) 0 0
\(331\) 1.47122 0.0808654 0.0404327 0.999182i \(-0.487126\pi\)
0.0404327 + 0.999182i \(0.487126\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.5249 −0.684308
\(336\) 0 0
\(337\) 25.2139 1.37349 0.686745 0.726898i \(-0.259039\pi\)
0.686745 + 0.726898i \(0.259039\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 29.6461 1.60543
\(342\) 0 0
\(343\) −17.6035 −0.950499
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9.31795 −0.500214 −0.250107 0.968218i \(-0.580466\pi\)
−0.250107 + 0.968218i \(0.580466\pi\)
\(348\) 0 0
\(349\) −2.52733 −0.135285 −0.0676425 0.997710i \(-0.521548\pi\)
−0.0676425 + 0.997710i \(0.521548\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −34.2875 −1.82494 −0.912469 0.409146i \(-0.865827\pi\)
−0.912469 + 0.409146i \(0.865827\pi\)
\(354\) 0 0
\(355\) −7.08742 −0.376161
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −28.5751 −1.50814 −0.754069 0.656796i \(-0.771911\pi\)
−0.754069 + 0.656796i \(0.771911\pi\)
\(360\) 0 0
\(361\) 26.3399 1.38631
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.43748 −0.179926
\(366\) 0 0
\(367\) −9.85218 −0.514280 −0.257140 0.966374i \(-0.582780\pi\)
−0.257140 + 0.966374i \(0.582780\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −11.9800 −0.621970
\(372\) 0 0
\(373\) 9.06102 0.469162 0.234581 0.972097i \(-0.424628\pi\)
0.234581 + 0.972097i \(0.424628\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.35155 0.172614
\(378\) 0 0
\(379\) −12.3721 −0.635514 −0.317757 0.948172i \(-0.602930\pi\)
−0.317757 + 0.948172i \(0.602930\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11.2724 −0.575990 −0.287995 0.957632i \(-0.592989\pi\)
−0.287995 + 0.957632i \(0.592989\pi\)
\(384\) 0 0
\(385\) 7.08621 0.361147
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.8750 0.855594 0.427797 0.903875i \(-0.359290\pi\)
0.427797 + 0.903875i \(0.359290\pi\)
\(390\) 0 0
\(391\) 6.33757 0.320505
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −13.1631 −0.662310
\(396\) 0 0
\(397\) 0.759942 0.0381404 0.0190702 0.999818i \(-0.493929\pi\)
0.0190702 + 0.999818i \(0.493929\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.37806 0.0688172 0.0344086 0.999408i \(-0.489045\pi\)
0.0344086 + 0.999408i \(0.489045\pi\)
\(402\) 0 0
\(403\) −12.0594 −0.600722
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 45.1141 2.23622
\(408\) 0 0
\(409\) −12.0619 −0.596422 −0.298211 0.954500i \(-0.596390\pi\)
−0.298211 + 0.954500i \(0.596390\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.641401 0.0315613
\(414\) 0 0
\(415\) 11.1802 0.548814
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.75748 −0.183565 −0.0917823 0.995779i \(-0.529256\pi\)
−0.0917823 + 0.995779i \(0.529256\pi\)
\(420\) 0 0
\(421\) −37.1073 −1.80850 −0.904250 0.427003i \(-0.859569\pi\)
−0.904250 + 0.427003i \(0.859569\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.33757 0.307417
\(426\) 0 0
\(427\) −6.63136 −0.320914
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −27.7368 −1.33603 −0.668017 0.744146i \(-0.732857\pi\)
−0.668017 + 0.744146i \(0.732857\pi\)
\(432\) 0 0
\(433\) −18.8473 −0.905744 −0.452872 0.891575i \(-0.649601\pi\)
−0.452872 + 0.891575i \(0.649601\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.73349 0.322106
\(438\) 0 0
\(439\) 29.8271 1.42357 0.711784 0.702398i \(-0.247887\pi\)
0.711784 + 0.702398i \(0.247887\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 41.4514 1.96942 0.984709 0.174210i \(-0.0557371\pi\)
0.984709 + 0.174210i \(0.0557371\pi\)
\(444\) 0 0
\(445\) −8.52369 −0.404061
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 29.6805 1.40071 0.700354 0.713795i \(-0.253025\pi\)
0.700354 + 0.713795i \(0.253025\pi\)
\(450\) 0 0
\(451\) 9.82544 0.462662
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.88252 −0.135135
\(456\) 0 0
\(457\) 19.6148 0.917542 0.458771 0.888555i \(-0.348290\pi\)
0.458771 + 0.888555i \(0.348290\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.76237 0.128656 0.0643281 0.997929i \(-0.479510\pi\)
0.0643281 + 0.997929i \(0.479510\pi\)
\(462\) 0 0
\(463\) −20.4516 −0.950466 −0.475233 0.879860i \(-0.657636\pi\)
−0.475233 + 0.879860i \(0.657636\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −23.6917 −1.09632 −0.548161 0.836373i \(-0.684672\pi\)
−0.548161 + 0.836373i \(0.684672\pi\)
\(468\) 0 0
\(469\) −18.7502 −0.865805
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 40.9872 1.88459
\(474\) 0 0
\(475\) 6.73349 0.308954
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0.781847 0.0357235 0.0178617 0.999840i \(-0.494314\pi\)
0.0178617 + 0.999840i \(0.494314\pi\)
\(480\) 0 0
\(481\) −18.3515 −0.836754
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.71568 −0.0779051
\(486\) 0 0
\(487\) 39.2992 1.78081 0.890407 0.455165i \(-0.150420\pi\)
0.890407 + 0.455165i \(0.150420\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.27204 −0.237924 −0.118962 0.992899i \(-0.537957\pi\)
−0.118962 + 0.992899i \(0.537957\pi\)
\(492\) 0 0
\(493\) −11.0314 −0.496827
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.6101 −0.475929
\(498\) 0 0
\(499\) −22.1074 −0.989664 −0.494832 0.868989i \(-0.664770\pi\)
−0.494832 + 0.868989i \(0.664770\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −8.62248 −0.384458 −0.192229 0.981350i \(-0.561572\pi\)
−0.192229 + 0.981350i \(0.561572\pi\)
\(504\) 0 0
\(505\) 16.1466 0.718512
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11.1176 −0.492779 −0.246390 0.969171i \(-0.579244\pi\)
−0.246390 + 0.969171i \(0.579244\pi\)
\(510\) 0 0
\(511\) −5.14603 −0.227647
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 13.7181 0.604492
\(516\) 0 0
\(517\) −29.7943 −1.31035
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −29.7301 −1.30250 −0.651249 0.758864i \(-0.725755\pi\)
−0.651249 + 0.758864i \(0.725755\pi\)
\(522\) 0 0
\(523\) −39.3418 −1.72030 −0.860148 0.510045i \(-0.829629\pi\)
−0.860148 + 0.510045i \(0.829629\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 39.6926 1.72903
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.99678 −0.173120
\(534\) 0 0
\(535\) −0.839322 −0.0362871
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −22.5261 −0.970268
\(540\) 0 0
\(541\) 43.4938 1.86994 0.934971 0.354723i \(-0.115425\pi\)
0.934971 + 0.354723i \(0.115425\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −15.9474 −0.683112
\(546\) 0 0
\(547\) 24.6776 1.05514 0.527568 0.849513i \(-0.323104\pi\)
0.527568 + 0.849513i \(0.323104\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.7205 −0.499310
\(552\) 0 0
\(553\) −19.7057 −0.837972
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.2698 0.943600 0.471800 0.881706i \(-0.343604\pi\)
0.471800 + 0.881706i \(0.343604\pi\)
\(558\) 0 0
\(559\) −16.6727 −0.705181
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 24.8156 1.04585 0.522927 0.852378i \(-0.324840\pi\)
0.522927 + 0.852378i \(0.324840\pi\)
\(564\) 0 0
\(565\) 9.89845 0.416431
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25.7790 1.08071 0.540356 0.841437i \(-0.318290\pi\)
0.540356 + 0.841437i \(0.318290\pi\)
\(570\) 0 0
\(571\) −11.4651 −0.479800 −0.239900 0.970798i \(-0.577115\pi\)
−0.239900 + 0.970798i \(0.577115\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 18.3005 0.761859 0.380930 0.924604i \(-0.375604\pi\)
0.380930 + 0.924604i \(0.375604\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16.7372 0.694374
\(582\) 0 0
\(583\) −37.8796 −1.56881
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 27.8559 1.14974 0.574868 0.818246i \(-0.305053\pi\)
0.574868 + 0.818246i \(0.305053\pi\)
\(588\) 0 0
\(589\) 42.1722 1.73768
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.97885 −0.122327 −0.0611633 0.998128i \(-0.519481\pi\)
−0.0611633 + 0.998128i \(0.519481\pi\)
\(594\) 0 0
\(595\) 9.48758 0.388953
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 28.5143 1.16506 0.582531 0.812808i \(-0.302062\pi\)
0.582531 + 0.812808i \(0.302062\pi\)
\(600\) 0 0
\(601\) 45.0058 1.83582 0.917912 0.396784i \(-0.129874\pi\)
0.917912 + 0.396784i \(0.129874\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11.4059 0.463717
\(606\) 0 0
\(607\) −15.2267 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.1197 0.490311
\(612\) 0 0
\(613\) −25.0817 −1.01304 −0.506520 0.862228i \(-0.669068\pi\)
−0.506520 + 0.862228i \(0.669068\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.26659 −0.0509909 −0.0254955 0.999675i \(-0.508116\pi\)
−0.0254955 + 0.999675i \(0.508116\pi\)
\(618\) 0 0
\(619\) −37.3545 −1.50140 −0.750701 0.660642i \(-0.770284\pi\)
−0.750701 + 0.660642i \(0.770284\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.7603 −0.511230
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 60.4023 2.40840
\(630\) 0 0
\(631\) −9.82336 −0.391062 −0.195531 0.980698i \(-0.562643\pi\)
−0.195531 + 0.980698i \(0.562643\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −19.0735 −0.756910
\(636\) 0 0
\(637\) 9.16315 0.363057
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 14.8077 0.584867 0.292434 0.956286i \(-0.405535\pi\)
0.292434 + 0.956286i \(0.405535\pi\)
\(642\) 0 0
\(643\) −4.05527 −0.159924 −0.0799622 0.996798i \(-0.525480\pi\)
−0.0799622 + 0.996798i \(0.525480\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24.7763 0.974057 0.487028 0.873386i \(-0.338081\pi\)
0.487028 + 0.873386i \(0.338081\pi\)
\(648\) 0 0
\(649\) 2.02805 0.0796079
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −15.5591 −0.608875 −0.304438 0.952532i \(-0.598469\pi\)
−0.304438 + 0.952532i \(0.598469\pi\)
\(654\) 0 0
\(655\) 21.1480 0.826323
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 35.2777 1.37422 0.687111 0.726552i \(-0.258878\pi\)
0.687111 + 0.726552i \(0.258878\pi\)
\(660\) 0 0
\(661\) 46.1647 1.79560 0.897799 0.440405i \(-0.145165\pi\)
0.897799 + 0.440405i \(0.145165\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10.0803 0.390897
\(666\) 0 0
\(667\) −1.74063 −0.0673974
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −20.9677 −0.809451
\(672\) 0 0
\(673\) −20.1114 −0.775236 −0.387618 0.921820i \(-0.626702\pi\)
−0.387618 + 0.921820i \(0.626702\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12.9433 −0.497453 −0.248726 0.968574i \(-0.580012\pi\)
−0.248726 + 0.968574i \(0.580012\pi\)
\(678\) 0 0
\(679\) −2.56844 −0.0985676
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.80047 0.260213 0.130106 0.991500i \(-0.458468\pi\)
0.130106 + 0.991500i \(0.458468\pi\)
\(684\) 0 0
\(685\) 20.9828 0.801713
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 15.4086 0.587022
\(690\) 0 0
\(691\) −21.7072 −0.825780 −0.412890 0.910781i \(-0.635481\pi\)
−0.412890 + 0.910781i \(0.635481\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.90791 0.0723712
\(696\) 0 0
\(697\) 13.1551 0.498284
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −20.3077 −0.767013 −0.383506 0.923538i \(-0.625284\pi\)
−0.383506 + 0.923538i \(0.625284\pi\)
\(702\) 0 0
\(703\) 64.1757 2.42043
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 24.1720 0.909081
\(708\) 0 0
\(709\) −26.9415 −1.01181 −0.505905 0.862589i \(-0.668841\pi\)
−0.505905 + 0.862589i \(0.668841\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.26306 0.234553
\(714\) 0 0
\(715\) −9.11426 −0.340854
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.58226 0.208183 0.104092 0.994568i \(-0.466806\pi\)
0.104092 + 0.994568i \(0.466806\pi\)
\(720\) 0 0
\(721\) 20.5365 0.764820
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.74063 −0.0646453
\(726\) 0 0
\(727\) −24.5285 −0.909711 −0.454856 0.890565i \(-0.650309\pi\)
−0.454856 + 0.890565i \(0.650309\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 54.8769 2.02969
\(732\) 0 0
\(733\) 22.6383 0.836165 0.418083 0.908409i \(-0.362702\pi\)
0.418083 + 0.908409i \(0.362702\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −59.2865 −2.18385
\(738\) 0 0
\(739\) −18.6000 −0.684214 −0.342107 0.939661i \(-0.611140\pi\)
−0.342107 + 0.939661i \(0.611140\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12.3333 0.452465 0.226232 0.974073i \(-0.427359\pi\)
0.226232 + 0.974073i \(0.427359\pi\)
\(744\) 0 0
\(745\) −13.2596 −0.485794
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.25650 −0.0459114
\(750\) 0 0
\(751\) −23.9642 −0.874467 −0.437233 0.899348i \(-0.644042\pi\)
−0.437233 + 0.899348i \(0.644042\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −14.0338 −0.510742
\(756\) 0 0
\(757\) 22.4936 0.817545 0.408772 0.912636i \(-0.365957\pi\)
0.408772 + 0.912636i \(0.365957\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33.0079 1.19653 0.598267 0.801297i \(-0.295856\pi\)
0.598267 + 0.801297i \(0.295856\pi\)
\(762\) 0 0
\(763\) −23.8739 −0.864292
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.824968 −0.0297879
\(768\) 0 0
\(769\) −3.42291 −0.123433 −0.0617166 0.998094i \(-0.519657\pi\)
−0.0617166 + 0.998094i \(0.519657\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.866323 −0.0311595 −0.0155797 0.999879i \(-0.504959\pi\)
−0.0155797 + 0.999879i \(0.504959\pi\)
\(774\) 0 0
\(775\) 6.26306 0.224976
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 13.9769 0.500774
\(780\) 0 0
\(781\) −33.5482 −1.20045
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.57395 0.0561765
\(786\) 0 0
\(787\) 42.8550 1.52762 0.763808 0.645444i \(-0.223328\pi\)
0.763808 + 0.645444i \(0.223328\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14.8184 0.526880
\(792\) 0 0
\(793\) 8.52924 0.302882
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −37.0736 −1.31321 −0.656607 0.754233i \(-0.728009\pi\)
−0.656607 + 0.754233i \(0.728009\pi\)
\(798\) 0 0
\(799\) −39.8910 −1.41124
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −16.2713 −0.574200
\(804\) 0 0
\(805\) 1.49704 0.0527636
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 5.89436 0.207235 0.103617 0.994617i \(-0.466958\pi\)
0.103617 + 0.994617i \(0.466958\pi\)
\(810\) 0 0
\(811\) −16.8029 −0.590031 −0.295016 0.955492i \(-0.595325\pi\)
−0.295016 + 0.955492i \(0.595325\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −20.3771 −0.713778
\(816\) 0 0
\(817\) 58.3051 2.03984
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 38.7218 1.35140 0.675699 0.737177i \(-0.263842\pi\)
0.675699 + 0.737177i \(0.263842\pi\)
\(822\) 0 0
\(823\) −14.1457 −0.493088 −0.246544 0.969132i \(-0.579295\pi\)
−0.246544 + 0.969132i \(0.579295\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −40.9508 −1.42400 −0.711999 0.702181i \(-0.752210\pi\)
−0.711999 + 0.702181i \(0.752210\pi\)
\(828\) 0 0
\(829\) −24.4522 −0.849259 −0.424630 0.905367i \(-0.639596\pi\)
−0.424630 + 0.905367i \(0.639596\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −30.1597 −1.04497
\(834\) 0 0
\(835\) 6.22931 0.215574
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 17.7425 0.612539 0.306269 0.951945i \(-0.400919\pi\)
0.306269 + 0.951945i \(0.400919\pi\)
\(840\) 0 0
\(841\) −25.9702 −0.895525
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9.29251 −0.319672
\(846\) 0 0
\(847\) 17.0751 0.586707
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 9.53082 0.326712
\(852\) 0 0
\(853\) 33.9338 1.16187 0.580936 0.813950i \(-0.302687\pi\)
0.580936 + 0.813950i \(0.302687\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −44.9241 −1.53458 −0.767288 0.641302i \(-0.778394\pi\)
−0.767288 + 0.641302i \(0.778394\pi\)
\(858\) 0 0
\(859\) 22.0733 0.753132 0.376566 0.926390i \(-0.377105\pi\)
0.376566 + 0.926390i \(0.377105\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 44.1613 1.50327 0.751635 0.659580i \(-0.229266\pi\)
0.751635 + 0.659580i \(0.229266\pi\)
\(864\) 0 0
\(865\) −16.9126 −0.575046
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −62.3076 −2.11364
\(870\) 0 0
\(871\) 24.1165 0.817156
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.49704 0.0506091
\(876\) 0 0
\(877\) −3.09723 −0.104586 −0.0522931 0.998632i \(-0.516653\pi\)
−0.0522931 + 0.998632i \(0.516653\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −50.5068 −1.70162 −0.850808 0.525476i \(-0.823887\pi\)
−0.850808 + 0.525476i \(0.823887\pi\)
\(882\) 0 0
\(883\) −22.9737 −0.773126 −0.386563 0.922263i \(-0.626338\pi\)
−0.386563 + 0.922263i \(0.626338\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −23.4277 −0.786626 −0.393313 0.919405i \(-0.628671\pi\)
−0.393313 + 0.919405i \(0.628671\pi\)
\(888\) 0 0
\(889\) −28.5538 −0.957663
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −42.3831 −1.41830
\(894\) 0 0
\(895\) −22.8162 −0.762661
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −10.9016 −0.363590
\(900\) 0 0
\(901\) −50.7162 −1.68960
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.84179 −0.160947
\(906\) 0 0
\(907\) 13.9870 0.464432 0.232216 0.972664i \(-0.425402\pi\)
0.232216 + 0.972664i \(0.425402\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −8.25544 −0.273515 −0.136757 0.990605i \(-0.543668\pi\)
−0.136757 + 0.990605i \(0.543668\pi\)
\(912\) 0 0
\(913\) 52.9213 1.75144
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 31.6594 1.04549
\(918\) 0 0
\(919\) 1.68684 0.0556436 0.0278218 0.999613i \(-0.491143\pi\)
0.0278218 + 0.999613i \(0.491143\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 13.6467 0.449187
\(924\) 0 0
\(925\) 9.53082 0.313372
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.41408 0.144821 0.0724106 0.997375i \(-0.476931\pi\)
0.0724106 + 0.997375i \(0.476931\pi\)
\(930\) 0 0
\(931\) −32.0439 −1.05020
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 29.9988 0.981067
\(936\) 0 0
\(937\) 31.0221 1.01345 0.506724 0.862108i \(-0.330856\pi\)
0.506724 + 0.862108i \(0.330856\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −42.5490 −1.38706 −0.693529 0.720429i \(-0.743945\pi\)
−0.693529 + 0.720429i \(0.743945\pi\)
\(942\) 0 0
\(943\) 2.07573 0.0675950
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −40.1679 −1.30528 −0.652641 0.757667i \(-0.726339\pi\)
−0.652641 + 0.757667i \(0.726339\pi\)
\(948\) 0 0
\(949\) 6.61881 0.214856
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −34.8233 −1.12804 −0.564019 0.825762i \(-0.690746\pi\)
−0.564019 + 0.825762i \(0.690746\pi\)
\(954\) 0 0
\(955\) 9.11748 0.295035
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 31.4121 1.01435
\(960\) 0 0
\(961\) 8.22586 0.265350
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 20.8476 0.671107
\(966\) 0 0
\(967\) 23.3241 0.750053 0.375027 0.927014i \(-0.377634\pi\)
0.375027 + 0.927014i \(0.377634\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −7.52104 −0.241362 −0.120681 0.992691i \(-0.538508\pi\)
−0.120681 + 0.992691i \(0.538508\pi\)
\(972\) 0 0
\(973\) 2.85621 0.0915660
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −30.0158 −0.960291 −0.480145 0.877189i \(-0.659416\pi\)
−0.480145 + 0.877189i \(0.659416\pi\)
\(978\) 0 0
\(979\) −40.3468 −1.28949
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 29.6034 0.944203 0.472102 0.881544i \(-0.343496\pi\)
0.472102 + 0.881544i \(0.343496\pi\)
\(984\) 0 0
\(985\) −4.05320 −0.129146
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 8.65897 0.275339
\(990\) 0 0
\(991\) −19.8686 −0.631146 −0.315573 0.948901i \(-0.602197\pi\)
−0.315573 + 0.948901i \(0.602197\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4.37131 0.138580
\(996\) 0 0
\(997\) −5.60419 −0.177487 −0.0887433 0.996055i \(-0.528285\pi\)
−0.0887433 + 0.996055i \(0.528285\pi\)
\(998\) 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 8280.2.a.bu.1.4 yes 6
3.2 odd 2 8280.2.a.bt.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bt.1.4 6 3.2 odd 2
8280.2.a.bu.1.4 yes 6 1.1 even 1 trivial