Properties

Label 288.3.h.a.17.4
Level $288$
Weight $3$
Character 288.17
Analytic conductor $7.847$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,3,Mod(17,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.h (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.33808912384.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 11x^{6} - 18x^{5} + 47x^{4} - 28x^{3} - 44x^{2} + 48x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 17.4
Root \(-0.651388 + 2.66948i\) of defining polynomial
Character \(\chi\) \(=\) 288.17
Dual form 288.3.h.a.17.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.07498 q^{5} -7.21110 q^{7} +O(q^{10})\) \(q-1.07498 q^{5} -7.21110 q^{7} +16.3517 q^{11} +21.6045i q^{13} +18.9819i q^{17} +17.0438i q^{19} -1.11567i q^{23} -23.8444 q^{25} +29.4784 q^{29} -5.63331 q^{31} +7.75182 q^{35} +17.0438i q^{37} -27.4671i q^{41} +52.3306i q^{43} +64.5352i q^{47} +3.00000 q^{49} +35.9283 q^{53} -17.5778 q^{55} -56.8069 q^{59} -69.3743i q^{61} -23.2245i q^{65} -69.3743i q^{67} -98.4764i q^{71} +37.6888 q^{73} -117.914 q^{77} +127.322 q^{79} -7.75182 q^{83} -20.4052i q^{85} +76.1475i q^{89} -155.792i q^{91} -18.3218i q^{95} +4.84441 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 40 q^{25} + 128 q^{31} + 24 q^{49} - 256 q^{55} - 160 q^{73} + 384 q^{79} - 192 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(5\) −1.07498 −0.214997 −0.107498 0.994205i \(-0.534284\pi\)
−0.107498 + 0.994205i \(0.534284\pi\)
\(6\) 0 0
\(7\) −7.21110 −1.03016 −0.515079 0.857143i \(-0.672237\pi\)
−0.515079 + 0.857143i \(0.672237\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 16.3517 1.48652 0.743258 0.669004i \(-0.233279\pi\)
0.743258 + 0.669004i \(0.233279\pi\)
\(12\) 0 0
\(13\) 21.6045i 1.66189i 0.556357 + 0.830943i \(0.312199\pi\)
−0.556357 + 0.830943i \(0.687801\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 18.9819i 1.11658i 0.829646 + 0.558290i \(0.188542\pi\)
−0.829646 + 0.558290i \(0.811458\pi\)
\(18\) 0 0
\(19\) 17.0438i 0.897040i 0.893773 + 0.448520i \(0.148049\pi\)
−0.893773 + 0.448520i \(0.851951\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 1.11567i − 0.0485074i −0.999706 0.0242537i \(-0.992279\pi\)
0.999706 0.0242537i \(-0.00772094\pi\)
\(24\) 0 0
\(25\) −23.8444 −0.953776
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 29.4784 1.01650 0.508249 0.861210i \(-0.330293\pi\)
0.508249 + 0.861210i \(0.330293\pi\)
\(30\) 0 0
\(31\) −5.63331 −0.181720 −0.0908598 0.995864i \(-0.528962\pi\)
−0.0908598 + 0.995864i \(0.528962\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 7.75182 0.221480
\(36\) 0 0
\(37\) 17.0438i 0.460642i 0.973115 + 0.230321i \(0.0739776\pi\)
−0.973115 + 0.230321i \(0.926022\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 27.4671i − 0.669930i −0.942231 0.334965i \(-0.891275\pi\)
0.942231 0.334965i \(-0.108725\pi\)
\(42\) 0 0
\(43\) 52.3306i 1.21699i 0.793558 + 0.608495i \(0.208226\pi\)
−0.793558 + 0.608495i \(0.791774\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 64.5352i 1.37309i 0.727087 + 0.686545i \(0.240874\pi\)
−0.727087 + 0.686545i \(0.759126\pi\)
\(48\) 0 0
\(49\) 3.00000 0.0612245
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 35.9283 0.677893 0.338946 0.940806i \(-0.389929\pi\)
0.338946 + 0.940806i \(0.389929\pi\)
\(54\) 0 0
\(55\) −17.5778 −0.319596
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −56.8069 −0.962828 −0.481414 0.876493i \(-0.659877\pi\)
−0.481414 + 0.876493i \(0.659877\pi\)
\(60\) 0 0
\(61\) − 69.3743i − 1.13728i −0.822585 0.568642i \(-0.807469\pi\)
0.822585 0.568642i \(-0.192531\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 23.2245i − 0.357300i
\(66\) 0 0
\(67\) − 69.3743i − 1.03544i −0.855551 0.517719i \(-0.826781\pi\)
0.855551 0.517719i \(-0.173219\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 98.4764i − 1.38699i −0.720461 0.693496i \(-0.756070\pi\)
0.720461 0.693496i \(-0.243930\pi\)
\(72\) 0 0
\(73\) 37.6888 0.516285 0.258143 0.966107i \(-0.416890\pi\)
0.258143 + 0.966107i \(0.416890\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −117.914 −1.53135
\(78\) 0 0
\(79\) 127.322 1.61167 0.805836 0.592138i \(-0.201716\pi\)
0.805836 + 0.592138i \(0.201716\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.75182 −0.0933954 −0.0466977 0.998909i \(-0.514870\pi\)
−0.0466977 + 0.998909i \(0.514870\pi\)
\(84\) 0 0
\(85\) − 20.4052i − 0.240061i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 76.1475i 0.855590i 0.903876 + 0.427795i \(0.140709\pi\)
−0.903876 + 0.427795i \(0.859291\pi\)
\(90\) 0 0
\(91\) − 155.792i − 1.71200i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) − 18.3218i − 0.192861i
\(96\) 0 0
\(97\) 4.84441 0.0499424 0.0249712 0.999688i \(-0.492051\pi\)
0.0249712 + 0.999688i \(0.492051\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −105.635 −1.04589 −0.522946 0.852366i \(-0.675167\pi\)
−0.522946 + 0.852366i \(0.675167\pi\)
\(102\) 0 0
\(103\) −104.789 −1.01737 −0.508684 0.860953i \(-0.669868\pi\)
−0.508684 + 0.860953i \(0.669868\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 65.4067 0.611278 0.305639 0.952147i \(-0.401130\pi\)
0.305639 + 0.952147i \(0.401130\pi\)
\(108\) 0 0
\(109\) − 3.36144i − 0.0308389i −0.999881 0.0154195i \(-0.995092\pi\)
0.999881 0.0154195i \(-0.00490836\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 84.1927i − 0.745068i −0.928019 0.372534i \(-0.878489\pi\)
0.928019 0.372534i \(-0.121511\pi\)
\(114\) 0 0
\(115\) 1.19933i 0.0104289i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) − 136.880i − 1.15025i
\(120\) 0 0
\(121\) 146.378 1.20973
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 52.5069 0.420056
\(126\) 0 0
\(127\) 45.5223 0.358443 0.179222 0.983809i \(-0.442642\pi\)
0.179222 + 0.983809i \(0.442642\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −129.117 −0.985629 −0.492814 0.870134i \(-0.664032\pi\)
−0.492814 + 0.870134i \(0.664032\pi\)
\(132\) 0 0
\(133\) − 122.904i − 0.924092i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 10.9367i − 0.0798296i −0.999203 0.0399148i \(-0.987291\pi\)
0.999203 0.0399148i \(-0.0127087\pi\)
\(138\) 0 0
\(139\) − 1.19933i − 0.00862825i −0.999991 0.00431412i \(-0.998627\pi\)
0.999991 0.00431412i \(-0.00137323\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 353.270i 2.47042i
\(144\) 0 0
\(145\) −31.6888 −0.218544
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −29.9323 −0.200888 −0.100444 0.994943i \(-0.532026\pi\)
−0.100444 + 0.994943i \(0.532026\pi\)
\(150\) 0 0
\(151\) −61.5223 −0.407432 −0.203716 0.979030i \(-0.565302\pi\)
−0.203716 + 0.979030i \(0.565302\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.05571 0.0390691
\(156\) 0 0
\(157\) 137.549i 0.876110i 0.898948 + 0.438055i \(0.144333\pi\)
−0.898948 + 0.438055i \(0.855667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 8.04521i 0.0499702i
\(162\) 0 0
\(163\) 191.079i 1.17227i 0.810215 + 0.586133i \(0.199350\pi\)
−0.810215 + 0.586133i \(0.800650\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 233.125i − 1.39596i −0.716118 0.697980i \(-0.754083\pi\)
0.716118 0.697980i \(-0.245917\pi\)
\(168\) 0 0
\(169\) −297.755 −1.76187
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 323.809 1.87173 0.935864 0.352363i \(-0.114622\pi\)
0.935864 + 0.352363i \(0.114622\pi\)
\(174\) 0 0
\(175\) 171.944 0.982540
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 185.924 1.03868 0.519342 0.854567i \(-0.326177\pi\)
0.519342 + 0.854567i \(0.326177\pi\)
\(180\) 0 0
\(181\) 126.266i 0.697600i 0.937197 + 0.348800i \(0.113411\pi\)
−0.937197 + 0.348800i \(0.886589\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 18.3218i − 0.0990365i
\(186\) 0 0
\(187\) 310.385i 1.65982i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 233.125i 1.22055i 0.792189 + 0.610275i \(0.208941\pi\)
−0.792189 + 0.610275i \(0.791059\pi\)
\(192\) 0 0
\(193\) −117.378 −0.608174 −0.304087 0.952644i \(-0.598351\pi\)
−0.304087 + 0.952644i \(0.598351\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 296.313 1.50413 0.752064 0.659091i \(-0.229059\pi\)
0.752064 + 0.659091i \(0.229059\pi\)
\(198\) 0 0
\(199\) −233.011 −1.17091 −0.585455 0.810705i \(-0.699084\pi\)
−0.585455 + 0.810705i \(0.699084\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −212.572 −1.04715
\(204\) 0 0
\(205\) 29.5267i 0.144033i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 278.694i 1.33346i
\(210\) 0 0
\(211\) − 35.2868i − 0.167236i −0.996498 0.0836181i \(-0.973352\pi\)
0.996498 0.0836181i \(-0.0266476\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 56.2545i − 0.261649i
\(216\) 0 0
\(217\) 40.6224 0.187200
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −410.094 −1.85563
\(222\) 0 0
\(223\) 51.8335 0.232437 0.116219 0.993224i \(-0.462923\pi\)
0.116219 + 0.993224i \(0.462923\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 334.786 1.47483 0.737413 0.675442i \(-0.236047\pi\)
0.737413 + 0.675442i \(0.236047\pi\)
\(228\) 0 0
\(229\) 219.407i 0.958108i 0.877786 + 0.479054i \(0.159020\pi\)
−0.877786 + 0.479054i \(0.840980\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 203.867i − 0.874965i −0.899227 0.437482i \(-0.855870\pi\)
0.899227 0.437482i \(-0.144130\pi\)
\(234\) 0 0
\(235\) − 69.3743i − 0.295210i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 54.0232i 0.226038i 0.993593 + 0.113019i \(0.0360522\pi\)
−0.993593 + 0.113019i \(0.963948\pi\)
\(240\) 0 0
\(241\) 327.600 1.35933 0.679667 0.733520i \(-0.262124\pi\)
0.679667 + 0.733520i \(0.262124\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.22495 −0.0131631
\(246\) 0 0
\(247\) −368.222 −1.49078
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 362.281 1.44335 0.721676 0.692231i \(-0.243372\pi\)
0.721676 + 0.692231i \(0.243372\pi\)
\(252\) 0 0
\(253\) − 18.2431i − 0.0721070i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 21.2132i − 0.0825416i −0.999148 0.0412708i \(-0.986859\pi\)
0.999148 0.0412708i \(-0.0131406\pi\)
\(258\) 0 0
\(259\) − 122.904i − 0.474534i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 205.878i − 0.782806i −0.920219 0.391403i \(-0.871990\pi\)
0.920219 0.391403i \(-0.128010\pi\)
\(264\) 0 0
\(265\) −38.6224 −0.145745
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.77109 −0.0103014 −0.00515072 0.999987i \(-0.501640\pi\)
−0.00515072 + 0.999987i \(0.501640\pi\)
\(270\) 0 0
\(271\) 125.744 0.464001 0.232001 0.972716i \(-0.425473\pi\)
0.232001 + 0.972716i \(0.425473\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −389.896 −1.41780
\(276\) 0 0
\(277\) 162.752i 0.587552i 0.955874 + 0.293776i \(0.0949119\pi\)
−0.955874 + 0.293776i \(0.905088\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 301.227i 1.07198i 0.844223 + 0.535992i \(0.180062\pi\)
−0.844223 + 0.535992i \(0.819938\pi\)
\(282\) 0 0
\(283\) − 31.6888i − 0.111975i −0.998431 0.0559874i \(-0.982169\pi\)
0.998431 0.0559874i \(-0.0178307\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 198.068i 0.690134i
\(288\) 0 0
\(289\) −71.3112 −0.246751
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −304.913 −1.04066 −0.520329 0.853966i \(-0.674191\pi\)
−0.520329 + 0.853966i \(0.674191\pi\)
\(294\) 0 0
\(295\) 61.0665 0.207005
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 24.1035 0.0806137
\(300\) 0 0
\(301\) − 377.361i − 1.25369i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 74.5763i 0.244512i
\(306\) 0 0
\(307\) − 105.860i − 0.344822i −0.985025 0.172411i \(-0.944844\pi\)
0.985025 0.172411i \(-0.0551558\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 555.157i − 1.78507i −0.450978 0.892535i \(-0.648925\pi\)
0.450978 0.892535i \(-0.351075\pi\)
\(312\) 0 0
\(313\) 158.000 0.504792 0.252396 0.967624i \(-0.418781\pi\)
0.252396 + 0.967624i \(0.418781\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 97.0351 0.306105 0.153052 0.988218i \(-0.451090\pi\)
0.153052 + 0.988218i \(0.451090\pi\)
\(318\) 0 0
\(319\) 482.022 1.51104
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −323.522 −1.00162
\(324\) 0 0
\(325\) − 515.147i − 1.58507i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 465.370i − 1.41450i
\(330\) 0 0
\(331\) − 619.572i − 1.87182i −0.352242 0.935909i \(-0.614581\pi\)
0.352242 0.935909i \(-0.385419\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 74.5763i 0.222616i
\(336\) 0 0
\(337\) −170.755 −0.506692 −0.253346 0.967376i \(-0.581531\pi\)
−0.253346 + 0.967376i \(0.581531\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −92.1141 −0.270129
\(342\) 0 0
\(343\) 331.711 0.967087
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −300.386 −0.865666 −0.432833 0.901474i \(-0.642486\pi\)
−0.432833 + 0.901474i \(0.642486\pi\)
\(348\) 0 0
\(349\) 53.5299i 0.153381i 0.997055 + 0.0766904i \(0.0244353\pi\)
−0.997055 + 0.0766904i \(0.975565\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 600.475i − 1.70106i −0.525925 0.850531i \(-0.676281\pi\)
0.525925 0.850531i \(-0.323719\pi\)
\(354\) 0 0
\(355\) 105.860i 0.298199i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 148.508i 0.413671i 0.978376 + 0.206836i \(0.0663165\pi\)
−0.978376 + 0.206836i \(0.933683\pi\)
\(360\) 0 0
\(361\) 70.5106 0.195320
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −40.5149 −0.111000
\(366\) 0 0
\(367\) −316.389 −0.862094 −0.431047 0.902329i \(-0.641856\pi\)
−0.431047 + 0.902329i \(0.641856\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −259.083 −0.698336
\(372\) 0 0
\(373\) − 626.768i − 1.68034i −0.542321 0.840171i \(-0.682455\pi\)
0.542321 0.840171i \(-0.317545\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 636.867i 1.68930i
\(378\) 0 0
\(379\) 331.027i 0.873423i 0.899602 + 0.436711i \(0.143857\pi\)
−0.899602 + 0.436711i \(0.856143\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 407.765i 1.06466i 0.846537 + 0.532330i \(0.178683\pi\)
−0.846537 + 0.532330i \(0.821317\pi\)
\(384\) 0 0
\(385\) 126.755 0.329234
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 53.5819 0.137743 0.0688714 0.997626i \(-0.478060\pi\)
0.0688714 + 0.997626i \(0.478060\pi\)
\(390\) 0 0
\(391\) 21.1775 0.0541624
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −136.869 −0.346504
\(396\) 0 0
\(397\) 289.744i 0.729833i 0.931040 + 0.364917i \(0.118902\pi\)
−0.931040 + 0.364917i \(0.881098\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 203.458i − 0.507376i −0.967286 0.253688i \(-0.918356\pi\)
0.967286 0.253688i \(-0.0816436\pi\)
\(402\) 0 0
\(403\) − 121.705i − 0.301997i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 278.694i 0.684752i
\(408\) 0 0
\(409\) 412.844 1.00940 0.504700 0.863295i \(-0.331603\pi\)
0.504700 + 0.863295i \(0.331603\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 409.640 0.991865
\(414\) 0 0
\(415\) 8.33308 0.0200797
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 336.482 0.803059 0.401529 0.915846i \(-0.368479\pi\)
0.401529 + 0.915846i \(0.368479\pi\)
\(420\) 0 0
\(421\) 217.481i 0.516582i 0.966067 + 0.258291i \(0.0831594\pi\)
−0.966067 + 0.258291i \(0.916841\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 452.611i − 1.06497i
\(426\) 0 0
\(427\) 500.265i 1.17158i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 750.994i − 1.74245i −0.490888 0.871223i \(-0.663328\pi\)
0.490888 0.871223i \(-0.336672\pi\)
\(432\) 0 0
\(433\) −176.133 −0.406773 −0.203387 0.979098i \(-0.565195\pi\)
−0.203387 + 0.979098i \(0.565195\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 19.0152 0.0435130
\(438\) 0 0
\(439\) −417.788 −0.951681 −0.475841 0.879531i \(-0.657856\pi\)
−0.475841 + 0.879531i \(0.657856\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −61.0471 −0.137804 −0.0689020 0.997623i \(-0.521950\pi\)
−0.0689020 + 0.997623i \(0.521950\pi\)
\(444\) 0 0
\(445\) − 81.8573i − 0.183949i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 182.905i 0.407360i 0.979038 + 0.203680i \(0.0652902\pi\)
−0.979038 + 0.203680i \(0.934710\pi\)
\(450\) 0 0
\(451\) − 449.134i − 0.995863i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 167.474i 0.368075i
\(456\) 0 0
\(457\) −443.600 −0.970678 −0.485339 0.874326i \(-0.661304\pi\)
−0.485339 + 0.874326i \(0.661304\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −728.241 −1.57970 −0.789850 0.613301i \(-0.789841\pi\)
−0.789850 + 0.613301i \(0.789841\pi\)
\(462\) 0 0
\(463\) 107.722 0.232662 0.116331 0.993211i \(-0.462887\pi\)
0.116331 + 0.993211i \(0.462887\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 820.248 1.75642 0.878210 0.478276i \(-0.158738\pi\)
0.878210 + 0.478276i \(0.158738\pi\)
\(468\) 0 0
\(469\) 500.265i 1.06666i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 855.693i 1.80908i
\(474\) 0 0
\(475\) − 406.398i − 0.855575i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) − 120.790i − 0.252171i −0.992019 0.126085i \(-0.959759\pi\)
0.992019 0.126085i \(-0.0402413\pi\)
\(480\) 0 0
\(481\) −368.222 −0.765534
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5.20766 −0.0107374
\(486\) 0 0
\(487\) 128.234 0.263314 0.131657 0.991295i \(-0.457970\pi\)
0.131657 + 0.991295i \(0.457970\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 382.144 0.778298 0.389149 0.921175i \(-0.372769\pi\)
0.389149 + 0.921175i \(0.372769\pi\)
\(492\) 0 0
\(493\) 559.555i 1.13500i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 710.123i 1.42882i
\(498\) 0 0
\(499\) 554.995i 1.11221i 0.831111 + 0.556107i \(0.187705\pi\)
−0.831111 + 0.556107i \(0.812295\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 78.3943i − 0.155854i −0.996959 0.0779268i \(-0.975170\pi\)
0.996959 0.0779268i \(-0.0248300\pi\)
\(504\) 0 0
\(505\) 113.556 0.224863
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 514.941 1.01167 0.505836 0.862630i \(-0.331184\pi\)
0.505836 + 0.862630i \(0.331184\pi\)
\(510\) 0 0
\(511\) −271.778 −0.531855
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 112.646 0.218731
\(516\) 0 0
\(517\) 1055.26i 2.04112i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 489.695i − 0.939914i −0.882689 0.469957i \(-0.844270\pi\)
0.882689 0.469957i \(-0.155730\pi\)
\(522\) 0 0
\(523\) 774.165i 1.48024i 0.672476 + 0.740119i \(0.265231\pi\)
−0.672476 + 0.740119i \(0.734769\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 106.931i − 0.202905i
\(528\) 0 0
\(529\) 527.755 0.997647
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 593.415 1.11335
\(534\) 0 0
\(535\) −70.3112 −0.131423
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 49.0551 0.0910112
\(540\) 0 0
\(541\) − 590.045i − 1.09066i −0.838223 0.545328i \(-0.816405\pi\)
0.838223 0.545328i \(-0.183595\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.61350i 0.00663027i
\(546\) 0 0
\(547\) 707.189i 1.29285i 0.762977 + 0.646425i \(0.223737\pi\)
−0.762977 + 0.646425i \(0.776263\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 502.423i 0.911838i
\(552\) 0 0
\(553\) −918.133 −1.66028
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −75.0816 −0.134796 −0.0673982 0.997726i \(-0.521470\pi\)
−0.0673982 + 0.997726i \(0.521470\pi\)
\(558\) 0 0
\(559\) −1130.58 −2.02250
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 114.462 0.203307 0.101653 0.994820i \(-0.467587\pi\)
0.101653 + 0.994820i \(0.467587\pi\)
\(564\) 0 0
\(565\) 90.5058i 0.160187i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 45.8199i − 0.0805270i −0.999189 0.0402635i \(-0.987180\pi\)
0.999189 0.0402635i \(-0.0128197\pi\)
\(570\) 0 0
\(571\) − 830.093i − 1.45375i −0.686768 0.726877i \(-0.740971\pi\)
0.686768 0.726877i \(-0.259029\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 26.6025i 0.0462652i
\(576\) 0 0
\(577\) −69.3776 −0.120239 −0.0601193 0.998191i \(-0.519148\pi\)
−0.0601193 + 0.998191i \(0.519148\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 55.8991 0.0962120
\(582\) 0 0
\(583\) 587.489 1.00770
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 428.655 0.730248 0.365124 0.930959i \(-0.381027\pi\)
0.365124 + 0.930959i \(0.381027\pi\)
\(588\) 0 0
\(589\) − 96.0127i − 0.163010i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 77.0276i 0.129895i 0.997889 + 0.0649474i \(0.0206880\pi\)
−0.997889 + 0.0649474i \(0.979312\pi\)
\(594\) 0 0
\(595\) 147.144i 0.247301i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 963.566i 1.60862i 0.594207 + 0.804312i \(0.297466\pi\)
−0.594207 + 0.804312i \(0.702534\pi\)
\(600\) 0 0
\(601\) 840.133 1.39789 0.698946 0.715175i \(-0.253653\pi\)
0.698946 + 0.715175i \(0.253653\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −157.354 −0.260089
\(606\) 0 0
\(607\) −156.611 −0.258008 −0.129004 0.991644i \(-0.541178\pi\)
−0.129004 + 0.991644i \(0.541178\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1394.25 −2.28192
\(612\) 0 0
\(613\) − 426.094i − 0.695096i −0.937662 0.347548i \(-0.887014\pi\)
0.937662 0.347548i \(-0.112986\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 963.520i − 1.56162i −0.624769 0.780810i \(-0.714807\pi\)
0.624769 0.780810i \(-0.285193\pi\)
\(618\) 0 0
\(619\) 175.235i 0.283093i 0.989932 + 0.141547i \(0.0452075\pi\)
−0.989932 + 0.141547i \(0.954792\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 549.107i − 0.881392i
\(624\) 0 0
\(625\) 539.666 0.863466
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −323.522 −0.514344
\(630\) 0 0
\(631\) 1140.72 1.80780 0.903900 0.427744i \(-0.140692\pi\)
0.903900 + 0.427744i \(0.140692\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −48.9357 −0.0770641
\(636\) 0 0
\(637\) 64.8136i 0.101748i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 351.730i − 0.548721i −0.961627 0.274360i \(-0.911534\pi\)
0.961627 0.274360i \(-0.0884661\pi\)
\(642\) 0 0
\(643\) − 86.4181i − 0.134398i −0.997740 0.0671991i \(-0.978594\pi\)
0.997740 0.0671991i \(-0.0214063\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 430.723i 0.665723i 0.942976 + 0.332861i \(0.108014\pi\)
−0.942976 + 0.332861i \(0.891986\pi\)
\(648\) 0 0
\(649\) −928.888 −1.43126
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 886.670 1.35784 0.678920 0.734212i \(-0.262448\pi\)
0.678920 + 0.734212i \(0.262448\pi\)
\(654\) 0 0
\(655\) 138.799 0.211907
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −352.833 −0.535407 −0.267704 0.963501i \(-0.586265\pi\)
−0.267704 + 0.963501i \(0.586265\pi\)
\(660\) 0 0
\(661\) − 1206.26i − 1.82489i −0.409195 0.912447i \(-0.634190\pi\)
0.409195 0.912447i \(-0.365810\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 132.120i 0.198677i
\(666\) 0 0
\(667\) − 32.8882i − 0.0493076i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) − 1134.39i − 1.69059i
\(672\) 0 0
\(673\) −956.133 −1.42070 −0.710351 0.703847i \(-0.751464\pi\)
−0.710351 + 0.703847i \(0.751464\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 420.557 0.621207 0.310604 0.950540i \(-0.399469\pi\)
0.310604 + 0.950540i \(0.399469\pi\)
\(678\) 0 0
\(679\) −34.9335 −0.0514485
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −539.725 −0.790227 −0.395113 0.918632i \(-0.629295\pi\)
−0.395113 + 0.918632i \(0.629295\pi\)
\(684\) 0 0
\(685\) 11.7567i 0.0171631i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 776.214i 1.12658i
\(690\) 0 0
\(691\) − 432.090i − 0.625312i −0.949866 0.312656i \(-0.898781\pi\)
0.949866 0.312656i \(-0.101219\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.28926i 0.00185504i
\(696\) 0 0
\(697\) 521.378 0.748031
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −880.339 −1.25583 −0.627917 0.778280i \(-0.716092\pi\)
−0.627917 + 0.778280i \(0.716092\pi\)
\(702\) 0 0
\(703\) −290.489 −0.413214
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 761.745 1.07743
\(708\) 0 0
\(709\) − 799.367i − 1.12746i −0.825960 0.563729i \(-0.809366\pi\)
0.825960 0.563729i \(-0.190634\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.28491i 0.00881474i
\(714\) 0 0
\(715\) − 379.760i − 0.531133i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 258.786i − 0.359924i −0.983674 0.179962i \(-0.942402\pi\)
0.983674 0.179962i \(-0.0575975\pi\)
\(720\) 0 0
\(721\) 755.643 1.04805
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −702.896 −0.969511
\(726\) 0 0
\(727\) 663.211 0.912257 0.456129 0.889914i \(-0.349236\pi\)
0.456129 + 0.889914i \(0.349236\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −993.332 −1.35887
\(732\) 0 0
\(733\) 908.826i 1.23987i 0.784653 + 0.619936i \(0.212841\pi\)
−0.784653 + 0.619936i \(0.787159\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 1134.39i − 1.53920i
\(738\) 0 0
\(739\) − 1112.39i − 1.50526i −0.658443 0.752631i \(-0.728785\pi\)
0.658443 0.752631i \(-0.271215\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 541.298i 0.728530i 0.931295 + 0.364265i \(0.118680\pi\)
−0.931295 + 0.364265i \(0.881320\pi\)
\(744\) 0 0
\(745\) 32.1767 0.0431902
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −471.655 −0.629713
\(750\) 0 0
\(751\) 763.699 1.01691 0.508455 0.861089i \(-0.330217\pi\)
0.508455 + 0.861089i \(0.330217\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 66.1354 0.0875966
\(756\) 0 0
\(757\) 419.134i 0.553678i 0.960916 + 0.276839i \(0.0892869\pi\)
−0.960916 + 0.276839i \(0.910713\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1330.24i 1.74802i 0.485912 + 0.874008i \(0.338488\pi\)
−0.485912 + 0.874008i \(0.661512\pi\)
\(762\) 0 0
\(763\) 24.2397i 0.0317690i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 1227.29i − 1.60011i
\(768\) 0 0
\(769\) 671.511 0.873226 0.436613 0.899649i \(-0.356178\pi\)
0.436613 + 0.899649i \(0.356178\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1421.13 −1.83846 −0.919229 0.393724i \(-0.871187\pi\)
−0.919229 + 0.393724i \(0.871187\pi\)
\(774\) 0 0
\(775\) 134.323 0.173320
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 468.143 0.600954
\(780\) 0 0
\(781\) − 1610.25i − 2.06179i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 147.863i − 0.188361i
\(786\) 0 0
\(787\) − 649.808i − 0.825677i −0.910804 0.412839i \(-0.864537\pi\)
0.910804 0.412839i \(-0.135463\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 607.122i 0.767538i
\(792\) 0 0
\(793\) 1498.80 1.89004
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 422.946 0.530672 0.265336 0.964156i \(-0.414517\pi\)
0.265336 + 0.964156i \(0.414517\pi\)
\(798\) 0 0
\(799\) −1225.00 −1.53317
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 616.276 0.767467
\(804\) 0 0
\(805\) − 8.64847i − 0.0107434i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 1353.87i − 1.67351i −0.547574 0.836757i \(-0.684448\pi\)
0.547574 0.836757i \(-0.315552\pi\)
\(810\) 0 0
\(811\) − 842.340i − 1.03864i −0.854579 0.519322i \(-0.826185\pi\)
0.854579 0.519322i \(-0.173815\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 205.407i − 0.252033i
\(816\) 0 0
\(817\) −891.909 −1.09169
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −616.897 −0.751397 −0.375698 0.926742i \(-0.622597\pi\)
−0.375698 + 0.926742i \(0.622597\pi\)
\(822\) 0 0
\(823\) −980.500 −1.19137 −0.595686 0.803217i \(-0.703120\pi\)
−0.595686 + 0.803217i \(0.703120\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 70.4951 0.0852419 0.0426210 0.999091i \(-0.486429\pi\)
0.0426210 + 0.999091i \(0.486429\pi\)
\(828\) 0 0
\(829\) 515.147i 0.621408i 0.950507 + 0.310704i \(0.100565\pi\)
−0.950507 + 0.310704i \(0.899435\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 56.9456i 0.0683621i
\(834\) 0 0
\(835\) 250.606i 0.300127i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 47.1556i − 0.0562045i −0.999605 0.0281022i \(-0.991054\pi\)
0.999605 0.0281022i \(-0.00894640\pi\)
\(840\) 0 0
\(841\) 27.9773 0.0332667
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 320.082 0.378795
\(846\) 0 0
\(847\) −1055.54 −1.24622
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 19.0152 0.0223445
\(852\) 0 0
\(853\) 763.118i 0.894628i 0.894377 + 0.447314i \(0.147619\pi\)
−0.894377 + 0.447314i \(0.852381\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1641.05i 1.91488i 0.288631 + 0.957440i \(0.406800\pi\)
−0.288631 + 0.957440i \(0.593200\pi\)
\(858\) 0 0
\(859\) 1366.84i 1.59120i 0.605819 + 0.795602i \(0.292845\pi\)
−0.605819 + 0.795602i \(0.707155\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 836.082i − 0.968809i −0.874844 0.484405i \(-0.839036\pi\)
0.874844 0.484405i \(-0.160964\pi\)
\(864\) 0 0
\(865\) −348.089 −0.402415
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2081.93 2.39578
\(870\) 0 0
\(871\) 1498.80 1.72078
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −378.633 −0.432723
\(876\) 0 0
\(877\) 158.191i 0.180377i 0.995925 + 0.0901887i \(0.0287470\pi\)
−0.995925 + 0.0901887i \(0.971253\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 237.430i − 0.269500i −0.990880 0.134750i \(-0.956977\pi\)
0.990880 0.134750i \(-0.0430232\pi\)
\(882\) 0 0
\(883\) 592.933i 0.671499i 0.941951 + 0.335749i \(0.108989\pi\)
−0.941951 + 0.335749i \(0.891011\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1420.72i 1.60171i 0.598858 + 0.800855i \(0.295621\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(888\) 0 0
\(889\) −328.266 −0.369253
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1099.92 −1.23172
\(894\) 0 0
\(895\) −199.866 −0.223313
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −166.061 −0.184717
\(900\) 0 0
\(901\) 681.987i 0.756922i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 135.734i − 0.149982i
\(906\) 0 0
\(907\) 816.648i 0.900383i 0.892932 + 0.450192i \(0.148644\pi\)
−0.892932 + 0.450192i \(0.851356\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 469.895i 0.515801i 0.966171 + 0.257901i \(0.0830307\pi\)
−0.966171 + 0.257901i \(0.916969\pi\)
\(912\) 0 0
\(913\) −126.755 −0.138834
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 931.079 1.01535
\(918\) 0 0
\(919\) 1648.21 1.79348 0.896741 0.442555i \(-0.145928\pi\)
0.896741 + 0.442555i \(0.145928\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2127.53 2.30502
\(924\) 0 0
\(925\) − 406.398i − 0.439349i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 421.311i − 0.453510i −0.973952 0.226755i \(-0.927188\pi\)
0.973952 0.226755i \(-0.0728116\pi\)
\(930\) 0 0
\(931\) 51.1313i 0.0549208i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 333.659i − 0.356855i
\(936\) 0 0
\(937\) −1434.27 −1.53070 −0.765350 0.643614i \(-0.777434\pi\)
−0.765350 + 0.643614i \(0.777434\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 732.876 0.778827 0.389413 0.921063i \(-0.372678\pi\)
0.389413 + 0.921063i \(0.372678\pi\)
\(942\) 0 0
\(943\) −30.6443 −0.0324966
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1385.53 −1.46308 −0.731538 0.681800i \(-0.761197\pi\)
−0.731538 + 0.681800i \(0.761197\pi\)
\(948\) 0 0
\(949\) 814.249i 0.858007i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 957.328i 1.00454i 0.864711 + 0.502270i \(0.167502\pi\)
−0.864711 + 0.502270i \(0.832498\pi\)
\(954\) 0 0
\(955\) − 250.606i − 0.262414i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 78.8654i 0.0822371i
\(960\) 0 0
\(961\) −929.266 −0.966978
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 126.179 0.130755
\(966\) 0 0
\(967\) −1225.90 −1.26773 −0.633867 0.773442i \(-0.718533\pi\)
−0.633867 + 0.773442i \(0.718533\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −752.906 −0.775393 −0.387696 0.921787i \(-0.626729\pi\)
−0.387696 + 0.921787i \(0.626729\pi\)
\(972\) 0 0
\(973\) 8.64847i 0.00888845i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 642.932i 0.658068i 0.944318 + 0.329034i \(0.106723\pi\)
−0.944318 + 0.329034i \(0.893277\pi\)
\(978\) 0 0
\(979\) 1245.14i 1.27185i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 161.251i 0.164040i 0.996631 + 0.0820200i \(0.0261371\pi\)
−0.996631 + 0.0820200i \(0.973863\pi\)
\(984\) 0 0
\(985\) −318.532 −0.323382
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 58.3836 0.0590330
\(990\) 0 0
\(991\) −811.500 −0.818870 −0.409435 0.912339i \(-0.634274\pi\)
−0.409435 + 0.912339i \(0.634274\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 250.483 0.251742
\(996\) 0 0
\(997\) − 390.554i − 0.391729i −0.980631 0.195864i \(-0.937249\pi\)
0.980631 0.195864i \(-0.0627513\pi\)
\(998\) 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 288.3.h.a.17.4 8
3.2 odd 2 inner 288.3.h.a.17.6 8
4.3 odd 2 72.3.h.a.53.7 yes 8
8.3 odd 2 72.3.h.a.53.1 8
8.5 even 2 inner 288.3.h.a.17.5 8
12.11 even 2 72.3.h.a.53.2 yes 8
16.3 odd 4 2304.3.e.n.1025.5 8
16.5 even 4 2304.3.e.o.1025.4 8
16.11 odd 4 2304.3.e.n.1025.4 8
16.13 even 4 2304.3.e.o.1025.5 8
24.5 odd 2 inner 288.3.h.a.17.3 8
24.11 even 2 72.3.h.a.53.8 yes 8
48.5 odd 4 2304.3.e.o.1025.6 8
48.11 even 4 2304.3.e.n.1025.6 8
48.29 odd 4 2304.3.e.o.1025.3 8
48.35 even 4 2304.3.e.n.1025.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.h.a.53.1 8 8.3 odd 2
72.3.h.a.53.2 yes 8 12.11 even 2
72.3.h.a.53.7 yes 8 4.3 odd 2
72.3.h.a.53.8 yes 8 24.11 even 2
288.3.h.a.17.3 8 24.5 odd 2 inner
288.3.h.a.17.4 8 1.1 even 1 trivial
288.3.h.a.17.5 8 8.5 even 2 inner
288.3.h.a.17.6 8 3.2 odd 2 inner
2304.3.e.n.1025.3 8 48.35 even 4
2304.3.e.n.1025.4 8 16.11 odd 4
2304.3.e.n.1025.5 8 16.3 odd 4
2304.3.e.n.1025.6 8 48.11 even 4
2304.3.e.o.1025.3 8 48.29 odd 4
2304.3.e.o.1025.4 8 16.5 even 4
2304.3.e.o.1025.5 8 16.13 even 4
2304.3.e.o.1025.6 8 48.5 odd 4