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Properties

Label 1800.4.a.bf.1.1
Level $1800$
Weight $4$
Character 1800.1
Self dual yes
Analytic conductor $106.203$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1800,4,Mod(1,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1800.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.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: \(106.203438010\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 600)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+19.0000 q^{7} +O(q^{10})\) \(q+19.0000 q^{7} -22.0000 q^{11} -1.00000 q^{13} -58.0000 q^{17} -53.0000 q^{19} +58.0000 q^{23} -22.0000 q^{29} -35.0000 q^{31} +270.000 q^{37} +468.000 q^{41} +431.000 q^{43} -230.000 q^{47} +18.0000 q^{49} -446.000 q^{59} +127.000 q^{61} +811.000 q^{67} -36.0000 q^{71} -522.000 q^{73} -418.000 q^{77} +1368.00 q^{79} -1138.00 q^{83} -144.000 q^{89} -19.0000 q^{91} +1079.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) 0 0
\(6\) 0 0
\(7\) 19.0000 1.02590 0.512952 − 0.858417i \(-0.328552\pi\)
0.512952 + 0.858417i \(0.328552\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −22.0000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.0213346 −0.0106673 − 0.999943i \(-0.503396\pi\)
−0.0106673 + 0.999943i \(0.503396\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −58.0000 −0.827474 −0.413737 − 0.910396i \(-0.635777\pi\)
−0.413737 + 0.910396i \(0.635777\pi\)
\(18\) 0 0
\(19\) −53.0000 −0.639949 −0.319975 − 0.947426i \(-0.603674\pi\)
−0.319975 + 0.947426i \(0.603674\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 58.0000 0.525819 0.262909 − 0.964821i \(-0.415318\pi\)
0.262909 + 0.964821i \(0.415318\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −22.0000 −0.140872 −0.0704362 − 0.997516i \(-0.522439\pi\)
−0.0704362 + 0.997516i \(0.522439\pi\)
\(30\) 0 0
\(31\) −35.0000 −0.202780 −0.101390 − 0.994847i \(-0.532329\pi\)
−0.101390 + 0.994847i \(0.532329\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 270.000 1.19967 0.599834 − 0.800124i \(-0.295233\pi\)
0.599834 + 0.800124i \(0.295233\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 468.000 1.78267 0.891333 − 0.453349i \(-0.149771\pi\)
0.891333 + 0.453349i \(0.149771\pi\)
\(42\) 0 0
\(43\) 431.000 1.52853 0.764266 − 0.644901i \(-0.223101\pi\)
0.764266 + 0.644901i \(0.223101\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −230.000 −0.713807 −0.356904 − 0.934141i \(-0.616168\pi\)
−0.356904 + 0.934141i \(0.616168\pi\)
\(48\) 0 0
\(49\) 18.0000 0.0524781
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −446.000 −0.984140 −0.492070 − 0.870556i \(-0.663760\pi\)
−0.492070 + 0.870556i \(0.663760\pi\)
\(60\) 0 0
\(61\) 127.000 0.266569 0.133284 − 0.991078i \(-0.457448\pi\)
0.133284 + 0.991078i \(0.457448\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 811.000 1.47880 0.739399 − 0.673268i \(-0.235110\pi\)
0.739399 + 0.673268i \(0.235110\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −36.0000 −0.0601748 −0.0300874 − 0.999547i \(-0.509579\pi\)
−0.0300874 + 0.999547i \(0.509579\pi\)
\(72\) 0 0
\(73\) −522.000 −0.836924 −0.418462 − 0.908234i \(-0.637431\pi\)
−0.418462 + 0.908234i \(0.637431\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −418.000 −0.618643
\(78\) 0 0
\(79\) 1368.00 1.94825 0.974127 − 0.226002i \(-0.0725657\pi\)
0.974127 + 0.226002i \(0.0725657\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1138.00 −1.50496 −0.752480 − 0.658615i \(-0.771143\pi\)
−0.752480 + 0.658615i \(0.771143\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −144.000 −0.171505 −0.0857526 − 0.996316i \(-0.527329\pi\)
−0.0857526 + 0.996316i \(0.527329\pi\)
\(90\) 0 0
\(91\) −19.0000 −0.0218873
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1079.00 1.12944 0.564721 − 0.825282i \(-0.308984\pi\)
0.564721 + 0.825282i \(0.308984\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1440.00 1.41867 0.709333 − 0.704873i \(-0.248996\pi\)
0.709333 + 0.704873i \(0.248996\pi\)
\(102\) 0 0
\(103\) −124.000 −0.118622 −0.0593111 − 0.998240i \(-0.518890\pi\)
−0.0593111 + 0.998240i \(0.518890\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −432.000 −0.390309 −0.195154 − 0.980773i \(-0.562521\pi\)
−0.195154 + 0.980773i \(0.562521\pi\)
\(108\) 0 0
\(109\) 701.000 0.615997 0.307998 − 0.951387i \(-0.400341\pi\)
0.307998 + 0.951387i \(0.400341\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1044.00 −0.869126 −0.434563 − 0.900641i \(-0.643097\pi\)
−0.434563 + 0.900641i \(0.643097\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1102.00 −0.848909
\(120\) 0 0
\(121\) −847.000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −504.000 −0.352148 −0.176074 − 0.984377i \(-0.556340\pi\)
−0.176074 + 0.984377i \(0.556340\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −72.0000 −0.0480204 −0.0240102 − 0.999712i \(-0.507643\pi\)
−0.0240102 + 0.999712i \(0.507643\pi\)
\(132\) 0 0
\(133\) −1007.00 −0.656526
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1850.00 −1.15369 −0.576847 − 0.816852i \(-0.695717\pi\)
−0.576847 + 0.816852i \(0.695717\pi\)
\(138\) 0 0
\(139\) 1836.00 1.12034 0.560171 − 0.828377i \(-0.310735\pi\)
0.560171 + 0.828377i \(0.310735\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 22.0000 0.0128653
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2398.00 1.31847 0.659234 − 0.751938i \(-0.270881\pi\)
0.659234 + 0.751938i \(0.270881\pi\)
\(150\) 0 0
\(151\) 1871.00 1.00834 0.504172 − 0.863604i \(-0.331798\pi\)
0.504172 + 0.863604i \(0.331798\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 3293.00 1.67395 0.836975 − 0.547242i \(-0.184322\pi\)
0.836975 + 0.547242i \(0.184322\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1102.00 0.539440
\(162\) 0 0
\(163\) −883.000 −0.424306 −0.212153 − 0.977236i \(-0.568048\pi\)
−0.212153 + 0.977236i \(0.568048\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4104.00 1.90166 0.950830 − 0.309715i \(-0.100234\pi\)
0.950830 + 0.309715i \(0.100234\pi\)
\(168\) 0 0
\(169\) −2196.00 −0.999545
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1706.00 0.749739 0.374869 − 0.927078i \(-0.377688\pi\)
0.374869 + 0.927078i \(0.377688\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −662.000 −0.276426 −0.138213 − 0.990403i \(-0.544136\pi\)
−0.138213 + 0.990403i \(0.544136\pi\)
\(180\) 0 0
\(181\) 4121.00 1.69233 0.846164 − 0.532922i \(-0.178906\pi\)
0.846164 + 0.532922i \(0.178906\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1276.00 0.498986
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 958.000 0.362924 0.181462 − 0.983398i \(-0.441917\pi\)
0.181462 + 0.983398i \(0.441917\pi\)
\(192\) 0 0
\(193\) −3187.00 −1.18863 −0.594314 − 0.804233i \(-0.702576\pi\)
−0.594314 + 0.804233i \(0.702576\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2282.00 −0.825308 −0.412654 − 0.910888i \(-0.635398\pi\)
−0.412654 + 0.910888i \(0.635398\pi\)
\(198\) 0 0
\(199\) 1043.00 0.371539 0.185770 − 0.982593i \(-0.440522\pi\)
0.185770 + 0.982593i \(0.440522\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −418.000 −0.144521
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1166.00 0.385904
\(210\) 0 0
\(211\) 4139.00 1.35043 0.675214 − 0.737621i \(-0.264051\pi\)
0.675214 + 0.737621i \(0.264051\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −665.000 −0.208033
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 58.0000 0.0176539
\(222\) 0 0
\(223\) −413.000 −0.124020 −0.0620101 − 0.998076i \(-0.519751\pi\)
−0.0620101 + 0.998076i \(0.519751\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5652.00 1.65258 0.826292 − 0.563242i \(-0.190446\pi\)
0.826292 + 0.563242i \(0.190446\pi\)
\(228\) 0 0
\(229\) −4391.00 −1.26710 −0.633549 − 0.773703i \(-0.718403\pi\)
−0.633549 + 0.773703i \(0.718403\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2052.00 −0.576957 −0.288479 − 0.957486i \(-0.593149\pi\)
−0.288479 + 0.957486i \(0.593149\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4320.00 1.16919 0.584597 − 0.811324i \(-0.301252\pi\)
0.584597 + 0.811324i \(0.301252\pi\)
\(240\) 0 0
\(241\) 4265.00 1.13997 0.569985 − 0.821655i \(-0.306949\pi\)
0.569985 + 0.821655i \(0.306949\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 53.0000 0.0136531
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2412.00 0.606550 0.303275 − 0.952903i \(-0.401920\pi\)
0.303275 + 0.952903i \(0.401920\pi\)
\(252\) 0 0
\(253\) −1276.00 −0.317081
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6948.00 1.68640 0.843199 − 0.537601i \(-0.180669\pi\)
0.843199 + 0.537601i \(0.180669\pi\)
\(258\) 0 0
\(259\) 5130.00 1.23074
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3564.00 −0.835611 −0.417805 − 0.908537i \(-0.637201\pi\)
−0.417805 + 0.908537i \(0.637201\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1534.00 0.347694 0.173847 − 0.984773i \(-0.444380\pi\)
0.173847 + 0.984773i \(0.444380\pi\)
\(270\) 0 0
\(271\) 7704.00 1.72688 0.863440 − 0.504451i \(-0.168305\pi\)
0.863440 + 0.504451i \(0.168305\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −4877.00 −1.05787 −0.528936 − 0.848662i \(-0.677409\pi\)
−0.528936 + 0.848662i \(0.677409\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3758.00 0.797806 0.398903 − 0.916993i \(-0.369391\pi\)
0.398903 + 0.916993i \(0.369391\pi\)
\(282\) 0 0
\(283\) −935.000 −0.196396 −0.0981978 − 0.995167i \(-0.531308\pi\)
−0.0981978 + 0.995167i \(0.531308\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8892.00 1.82884
\(288\) 0 0
\(289\) −1549.00 −0.315286
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6214.00 1.23900 0.619498 − 0.784998i \(-0.287336\pi\)
0.619498 + 0.784998i \(0.287336\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −58.0000 −0.0112181
\(300\) 0 0
\(301\) 8189.00 1.56813
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3905.00 0.725961 0.362981 − 0.931797i \(-0.381759\pi\)
0.362981 + 0.931797i \(0.381759\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9662.00 −1.76168 −0.880839 − 0.473416i \(-0.843021\pi\)
−0.880839 + 0.473416i \(0.843021\pi\)
\(312\) 0 0
\(313\) −5147.00 −0.929475 −0.464737 − 0.885449i \(-0.653851\pi\)
−0.464737 + 0.885449i \(0.653851\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9216.00 −1.63288 −0.816439 − 0.577432i \(-0.804055\pi\)
−0.816439 + 0.577432i \(0.804055\pi\)
\(318\) 0 0
\(319\) 484.000 0.0849492
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3074.00 0.529542
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4370.00 −0.732298
\(330\) 0 0
\(331\) 2196.00 0.364662 0.182331 − 0.983237i \(-0.441636\pi\)
0.182331 + 0.983237i \(0.441636\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −2521.00 −0.407500 −0.203750 − 0.979023i \(-0.565313\pi\)
−0.203750 + 0.979023i \(0.565313\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 770.000 0.122281
\(342\) 0 0
\(343\) −6175.00 −0.972066
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7034.00 1.08820 0.544099 − 0.839021i \(-0.316871\pi\)
0.544099 + 0.839021i \(0.316871\pi\)
\(348\) 0 0
\(349\) 7362.00 1.12917 0.564583 − 0.825376i \(-0.309037\pi\)
0.564583 + 0.825376i \(0.309037\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9382.00 −1.41460 −0.707300 − 0.706914i \(-0.750087\pi\)
−0.707300 + 0.706914i \(0.750087\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10116.0 1.48719 0.743596 − 0.668629i \(-0.233119\pi\)
0.743596 + 0.668629i \(0.233119\pi\)
\(360\) 0 0
\(361\) −4050.00 −0.590465
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 3277.00 0.466098 0.233049 − 0.972465i \(-0.425130\pi\)
0.233049 + 0.972465i \(0.425130\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10891.0 −1.51184 −0.755918 − 0.654667i \(-0.772809\pi\)
−0.755918 + 0.654667i \(0.772809\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 22.0000 0.00300546
\(378\) 0 0
\(379\) −2591.00 −0.351163 −0.175581 − 0.984465i \(-0.556181\pi\)
−0.175581 + 0.984465i \(0.556181\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −612.000 −0.0816494 −0.0408247 − 0.999166i \(-0.512999\pi\)
−0.0408247 + 0.999166i \(0.512999\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3708.00 −0.483298 −0.241649 − 0.970364i \(-0.577688\pi\)
−0.241649 + 0.970364i \(0.577688\pi\)
\(390\) 0 0
\(391\) −3364.00 −0.435102
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3833.00 0.484566 0.242283 − 0.970206i \(-0.422104\pi\)
0.242283 + 0.970206i \(0.422104\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9288.00 1.15666 0.578330 − 0.815803i \(-0.303705\pi\)
0.578330 + 0.815803i \(0.303705\pi\)
\(402\) 0 0
\(403\) 35.0000 0.00432624
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5940.00 −0.723427
\(408\) 0 0
\(409\) −755.000 −0.0912771 −0.0456386 − 0.998958i \(-0.514532\pi\)
−0.0456386 + 0.998958i \(0.514532\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8474.00 −1.00963
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9576.00 1.11651 0.558256 − 0.829669i \(-0.311471\pi\)
0.558256 + 0.829669i \(0.311471\pi\)
\(420\) 0 0
\(421\) 9414.00 1.08981 0.544905 − 0.838498i \(-0.316566\pi\)
0.544905 + 0.838498i \(0.316566\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2413.00 0.273474
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2254.00 0.251906 0.125953 − 0.992036i \(-0.459801\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(432\) 0 0
\(433\) 6301.00 0.699323 0.349661 − 0.936876i \(-0.386297\pi\)
0.349661 + 0.936876i \(0.386297\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3074.00 −0.336497
\(438\) 0 0
\(439\) −3779.00 −0.410847 −0.205423 − 0.978673i \(-0.565857\pi\)
−0.205423 + 0.978673i \(0.565857\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7632.00 0.818527 0.409263 − 0.912416i \(-0.365786\pi\)
0.409263 + 0.912416i \(0.365786\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2988.00 −0.314059 −0.157029 − 0.987594i \(-0.550192\pi\)
−0.157029 + 0.987594i \(0.550192\pi\)
\(450\) 0 0
\(451\) −10296.0 −1.07499
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1370.00 0.140232 0.0701159 − 0.997539i \(-0.477663\pi\)
0.0701159 + 0.997539i \(0.477663\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7992.00 0.807429 0.403714 − 0.914885i \(-0.367719\pi\)
0.403714 + 0.914885i \(0.367719\pi\)
\(462\) 0 0
\(463\) 3096.00 0.310763 0.155382 − 0.987855i \(-0.450339\pi\)
0.155382 + 0.987855i \(0.450339\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8338.00 −0.826203 −0.413101 − 0.910685i \(-0.635554\pi\)
−0.413101 + 0.910685i \(0.635554\pi\)
\(468\) 0 0
\(469\) 15409.0 1.51710
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9482.00 −0.921740
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4918.00 −0.469121 −0.234561 − 0.972101i \(-0.575365\pi\)
−0.234561 + 0.972101i \(0.575365\pi\)
\(480\) 0 0
\(481\) −270.000 −0.0255945
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 19637.0 1.82718 0.913591 − 0.406635i \(-0.133298\pi\)
0.913591 + 0.406635i \(0.133298\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3096.00 −0.284563 −0.142282 − 0.989826i \(-0.545444\pi\)
−0.142282 + 0.989826i \(0.545444\pi\)
\(492\) 0 0
\(493\) 1276.00 0.116568
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −684.000 −0.0617336
\(498\) 0 0
\(499\) 6875.00 0.616768 0.308384 − 0.951262i \(-0.400212\pi\)
0.308384 + 0.951262i \(0.400212\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 11268.0 0.998838 0.499419 − 0.866361i \(-0.333547\pi\)
0.499419 + 0.866361i \(0.333547\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16078.0 −1.40009 −0.700044 − 0.714100i \(-0.746836\pi\)
−0.700044 + 0.714100i \(0.746836\pi\)
\(510\) 0 0
\(511\) −9918.00 −0.858604
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5060.00 0.430442
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17366.0 1.46030 0.730152 − 0.683285i \(-0.239449\pi\)
0.730152 + 0.683285i \(0.239449\pi\)
\(522\) 0 0
\(523\) 4913.00 0.410766 0.205383 − 0.978682i \(-0.434156\pi\)
0.205383 + 0.978682i \(0.434156\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2030.00 0.167795
\(528\) 0 0
\(529\) −8803.00 −0.723514
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −468.000 −0.0380325
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −396.000 −0.0316455
\(540\) 0 0
\(541\) 17605.0 1.39907 0.699536 − 0.714597i \(-0.253390\pi\)
0.699536 + 0.714597i \(0.253390\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 14560.0 1.13810 0.569050 − 0.822303i \(-0.307311\pi\)
0.569050 + 0.822303i \(0.307311\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1166.00 0.0901511
\(552\) 0 0
\(553\) 25992.0 1.99872
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20614.0 −1.56812 −0.784060 − 0.620685i \(-0.786855\pi\)
−0.784060 + 0.620685i \(0.786855\pi\)
\(558\) 0 0
\(559\) −431.000 −0.0326107
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3442.00 0.257661 0.128830 − 0.991667i \(-0.458878\pi\)
0.128830 + 0.991667i \(0.458878\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22082.0 −1.62693 −0.813467 − 0.581611i \(-0.802423\pi\)
−0.813467 + 0.581611i \(0.802423\pi\)
\(570\) 0 0
\(571\) 451.000 0.0330539 0.0165269 − 0.999863i \(-0.494739\pi\)
0.0165269 + 0.999863i \(0.494739\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −20987.0 −1.51421 −0.757106 − 0.653292i \(-0.773387\pi\)
−0.757106 + 0.653292i \(0.773387\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −21622.0 −1.54394
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3888.00 0.273381 0.136691 − 0.990614i \(-0.456353\pi\)
0.136691 + 0.990614i \(0.456353\pi\)
\(588\) 0 0
\(589\) 1855.00 0.129769
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11268.0 −0.780306 −0.390153 − 0.920750i \(-0.627578\pi\)
−0.390153 + 0.920750i \(0.627578\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3996.00 0.272575 0.136287 − 0.990669i \(-0.456483\pi\)
0.136287 + 0.990669i \(0.456483\pi\)
\(600\) 0 0
\(601\) −24965.0 −1.69442 −0.847208 − 0.531262i \(-0.821718\pi\)
−0.847208 + 0.531262i \(0.821718\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −4176.00 −0.279240 −0.139620 − 0.990205i \(-0.544588\pi\)
−0.139620 + 0.990205i \(0.544588\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 230.000 0.0152288
\(612\) 0 0
\(613\) 9558.00 0.629762 0.314881 − 0.949131i \(-0.398035\pi\)
0.314881 + 0.949131i \(0.398035\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9000.00 −0.587239 −0.293619 − 0.955922i \(-0.594860\pi\)
−0.293619 + 0.955922i \(0.594860\pi\)
\(618\) 0 0
\(619\) −15625.0 −1.01457 −0.507287 − 0.861777i \(-0.669352\pi\)
−0.507287 + 0.861777i \(0.669352\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2736.00 −0.175948
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −15660.0 −0.992695
\(630\) 0 0
\(631\) −31175.0 −1.96681 −0.983405 − 0.181424i \(-0.941929\pi\)
−0.983405 + 0.181424i \(0.941929\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −18.0000 −0.00111960
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6732.00 0.414817 0.207409 − 0.978254i \(-0.433497\pi\)
0.207409 + 0.978254i \(0.433497\pi\)
\(642\) 0 0
\(643\) 6228.00 0.381973 0.190986 − 0.981593i \(-0.438831\pi\)
0.190986 + 0.981593i \(0.438831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −396.000 −0.0240624 −0.0120312 − 0.999928i \(-0.503830\pi\)
−0.0120312 + 0.999928i \(0.503830\pi\)
\(648\) 0 0
\(649\) 9812.00 0.593459
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4702.00 −0.281782 −0.140891 − 0.990025i \(-0.544997\pi\)
−0.140891 + 0.990025i \(0.544997\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22140.0 1.30873 0.654364 − 0.756180i \(-0.272936\pi\)
0.654364 + 0.756180i \(0.272936\pi\)
\(660\) 0 0
\(661\) −13518.0 −0.795445 −0.397723 − 0.917506i \(-0.630199\pi\)
−0.397723 + 0.917506i \(0.630199\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1276.00 −0.0740733
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2794.00 −0.160747
\(672\) 0 0
\(673\) 11250.0 0.644362 0.322181 − 0.946678i \(-0.395584\pi\)
0.322181 + 0.946678i \(0.395584\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15170.0 −0.861197 −0.430599 − 0.902544i \(-0.641698\pi\)
−0.430599 + 0.902544i \(0.641698\pi\)
\(678\) 0 0
\(679\) 20501.0 1.15870
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 22680.0 1.27061 0.635305 − 0.772262i \(-0.280875\pi\)
0.635305 + 0.772262i \(0.280875\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 128.000 0.00704682 0.00352341 − 0.999994i \(-0.498878\pi\)
0.00352341 + 0.999994i \(0.498878\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −27144.0 −1.47511
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −25682.0 −1.38373 −0.691866 − 0.722026i \(-0.743211\pi\)
−0.691866 + 0.722026i \(0.743211\pi\)
\(702\) 0 0
\(703\) −14310.0 −0.767727
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27360.0 1.45542
\(708\) 0 0
\(709\) −4951.00 −0.262255 −0.131127 − 0.991366i \(-0.541860\pi\)
−0.131127 + 0.991366i \(0.541860\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2030.00 −0.106626
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 22190.0 1.15097 0.575485 − 0.817812i \(-0.304813\pi\)
0.575485 + 0.817812i \(0.304813\pi\)
\(720\) 0 0
\(721\) −2356.00 −0.121695
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −7685.00 −0.392051 −0.196025 − 0.980599i \(-0.562803\pi\)
−0.196025 + 0.980599i \(0.562803\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24998.0 −1.26482
\(732\) 0 0
\(733\) −29574.0 −1.49023 −0.745116 − 0.666934i \(-0.767606\pi\)
−0.745116 + 0.666934i \(0.767606\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −17842.0 −0.891748
\(738\) 0 0
\(739\) −32580.0 −1.62175 −0.810876 − 0.585218i \(-0.801009\pi\)
−0.810876 + 0.585218i \(0.801009\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3060.00 −0.151091 −0.0755454 − 0.997142i \(-0.524070\pi\)
−0.0755454 + 0.997142i \(0.524070\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8208.00 −0.400419
\(750\) 0 0
\(751\) −7992.00 −0.388325 −0.194163 − 0.980969i \(-0.562199\pi\)
−0.194163 + 0.980969i \(0.562199\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −22841.0 −1.09666 −0.548329 − 0.836263i \(-0.684736\pi\)
−0.548329 + 0.836263i \(0.684736\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17172.0 0.817982 0.408991 − 0.912538i \(-0.365881\pi\)
0.408991 + 0.912538i \(0.365881\pi\)
\(762\) 0 0
\(763\) 13319.0 0.631953
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 446.000 0.0209963
\(768\) 0 0
\(769\) −30869.0 −1.44755 −0.723774 − 0.690037i \(-0.757594\pi\)
−0.723774 + 0.690037i \(0.757594\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34884.0 1.62314 0.811572 − 0.584252i \(-0.198612\pi\)
0.811572 + 0.584252i \(0.198612\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24804.0 −1.14082
\(780\) 0 0
\(781\) 792.000 0.0362868
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −5039.00 −0.228235 −0.114118 − 0.993467i \(-0.536404\pi\)
−0.114118 + 0.993467i \(0.536404\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −19836.0 −0.891640
\(792\) 0 0
\(793\) −127.000 −0.00568714
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 540.000 0.0239997 0.0119999 − 0.999928i \(-0.496180\pi\)
0.0119999 + 0.999928i \(0.496180\pi\)
\(798\) 0 0
\(799\) 13340.0 0.590657
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11484.0 0.504684
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 41328.0 1.79606 0.898032 − 0.439931i \(-0.144997\pi\)
0.898032 + 0.439931i \(0.144997\pi\)
\(810\) 0 0
\(811\) −12853.0 −0.556510 −0.278255 − 0.960507i \(-0.589756\pi\)
−0.278255 + 0.960507i \(0.589756\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −22843.0 −0.978183
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29470.0 −1.25275 −0.626376 − 0.779521i \(-0.715463\pi\)
−0.626376 + 0.779521i \(0.715463\pi\)
\(822\) 0 0
\(823\) 24407.0 1.03375 0.516874 − 0.856062i \(-0.327096\pi\)
0.516874 + 0.856062i \(0.327096\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 15048.0 0.632733 0.316367 − 0.948637i \(-0.397537\pi\)
0.316367 + 0.948637i \(0.397537\pi\)
\(828\) 0 0
\(829\) −28406.0 −1.19009 −0.595043 − 0.803694i \(-0.702865\pi\)
−0.595043 + 0.803694i \(0.702865\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1044.00 −0.0434243
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26914.0 1.10748 0.553739 − 0.832690i \(-0.313200\pi\)
0.553739 + 0.832690i \(0.313200\pi\)
\(840\) 0 0
\(841\) −23905.0 −0.980155
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −16093.0 −0.652848
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 15660.0 0.630808
\(852\) 0 0
\(853\) −21275.0 −0.853977 −0.426988 − 0.904257i \(-0.640425\pi\)
−0.426988 + 0.904257i \(0.640425\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 39132.0 1.55977 0.779885 − 0.625922i \(-0.215277\pi\)
0.779885 + 0.625922i \(0.215277\pi\)
\(858\) 0 0
\(859\) −448.000 −0.0177946 −0.00889730 − 0.999960i \(-0.502832\pi\)
−0.00889730 + 0.999960i \(0.502832\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −26856.0 −1.05932 −0.529658 − 0.848212i \(-0.677680\pi\)
−0.529658 + 0.848212i \(0.677680\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −30096.0 −1.17484
\(870\) 0 0
\(871\) −811.000 −0.0315496
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 3653.00 0.140653 0.0703267 − 0.997524i \(-0.477596\pi\)
0.0703267 + 0.997524i \(0.477596\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 6552.00 0.250559 0.125280 − 0.992121i \(-0.460017\pi\)
0.125280 + 0.992121i \(0.460017\pi\)
\(882\) 0 0
\(883\) −4481.00 −0.170779 −0.0853894 − 0.996348i \(-0.527213\pi\)
−0.0853894 + 0.996348i \(0.527213\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −14666.0 −0.555170 −0.277585 − 0.960701i \(-0.589534\pi\)
−0.277585 + 0.960701i \(0.589534\pi\)
\(888\) 0 0
\(889\) −9576.00 −0.361270
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 12190.0 0.456800
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 770.000 0.0285661
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −51804.0 −1.89650 −0.948249 − 0.317528i \(-0.897147\pi\)
−0.948249 + 0.317528i \(0.897147\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −31198.0 −1.13462 −0.567308 − 0.823505i \(-0.692015\pi\)
−0.567308 + 0.823505i \(0.692015\pi\)
\(912\) 0 0
\(913\) 25036.0 0.907525
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1368.00 −0.0492643
\(918\) 0 0
\(919\) −27001.0 −0.969185 −0.484592 − 0.874740i \(-0.661032\pi\)
−0.484592 + 0.874740i \(0.661032\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 36.0000 0.00128381
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 22694.0 0.801470 0.400735 − 0.916194i \(-0.368755\pi\)
0.400735 + 0.916194i \(0.368755\pi\)
\(930\) 0 0
\(931\) −954.000 −0.0335833
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −29503.0 −1.02862 −0.514312 − 0.857603i \(-0.671953\pi\)
−0.514312 + 0.857603i \(0.671953\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14566.0 −0.504610 −0.252305 − 0.967648i \(-0.581189\pi\)
−0.252305 + 0.967648i \(0.581189\pi\)
\(942\) 0 0
\(943\) 27144.0 0.937360
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 42322.0 1.45225 0.726125 − 0.687563i \(-0.241319\pi\)
0.726125 + 0.687563i \(0.241319\pi\)
\(948\) 0 0
\(949\) 522.000 0.0178555
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 43416.0 1.47574 0.737871 − 0.674942i \(-0.235831\pi\)
0.737871 + 0.674942i \(0.235831\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −35150.0 −1.18358
\(960\) 0 0
\(961\) −28566.0 −0.958880
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −21528.0 −0.715919 −0.357960 − 0.933737i \(-0.616527\pi\)
−0.357960 + 0.933737i \(0.616527\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −27050.0 −0.894002 −0.447001 − 0.894533i \(-0.647508\pi\)
−0.447001 + 0.894533i \(0.647508\pi\)
\(972\) 0 0
\(973\) 34884.0 1.14936
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −24934.0 −0.816489 −0.408244 − 0.912873i \(-0.633859\pi\)
−0.408244 + 0.912873i \(0.633859\pi\)
\(978\) 0 0
\(979\) 3168.00 0.103422
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 8388.00 0.272162 0.136081 − 0.990698i \(-0.456549\pi\)
0.136081 + 0.990698i \(0.456549\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 24998.0 0.803731
\(990\) 0 0
\(991\) 29033.0 0.930639 0.465320 − 0.885143i \(-0.345939\pi\)
0.465320 + 0.885143i \(0.345939\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 25326.0 0.804496 0.402248 − 0.915531i \(-0.368229\pi\)
0.402248 + 0.915531i \(0.368229\pi\)
\(998\) 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 1800.4.a.bf.1.1 1
3.2 odd 2 600.4.a.g.1.1 ✓ 1
5.2 odd 4 1800.4.f.g.649.2 2
5.3 odd 4 1800.4.f.g.649.1 2
5.4 even 2 1800.4.a.g.1.1 1
12.11 even 2 1200.4.a.x.1.1 1
15.2 even 4 600.4.f.h.49.2 2
15.8 even 4 600.4.f.h.49.1 2
15.14 odd 2 600.4.a.j.1.1 yes 1
60.23 odd 4 1200.4.f.f.49.2 2
60.47 odd 4 1200.4.f.f.49.1 2
60.59 even 2 1200.4.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.4.a.g.1.1 ✓ 1 3.2 odd 2
600.4.a.j.1.1 yes 1 15.14 odd 2
600.4.f.h.49.1 2 15.8 even 4
600.4.f.h.49.2 2 15.2 even 4
1200.4.a.n.1.1 1 60.59 even 2
1200.4.a.x.1.1 1 12.11 even 2
1200.4.f.f.49.1 2 60.47 odd 4
1200.4.f.f.49.2 2 60.23 odd 4
1800.4.a.g.1.1 1 5.4 even 2
1800.4.a.bf.1.1 1 1.1 even 1 trivial
1800.4.f.g.649.1 2 5.3 odd 4
1800.4.f.g.649.2 2 5.2 odd 4