Properties

Label 1080.4.a.e.1.3
Level $1080$
Weight $4$
Character 1080.1
Self dual yes
Analytic conductor $63.722$
Analytic rank $1$
Dimension $3$
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] = [1080,4,Mod(1,1080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1080, 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("1080.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1080.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: \(63.7220628062\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.4281.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 12x + 15 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.29027\) of defining polynomial
Character \(\chi\) \(=\) 1080.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} +16.4120 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +16.4120 q^{7} -57.6104 q^{11} +38.7864 q^{13} -31.4120 q^{17} +70.6104 q^{19} +7.37433 q^{23} +25.0000 q^{25} +17.1607 q^{29} -50.9847 q^{31} -82.0601 q^{35} -159.693 q^{37} +63.2056 q^{41} -84.6580 q^{43} -434.434 q^{47} -73.6454 q^{49} -138.490 q^{53} +288.052 q^{55} +631.011 q^{59} +82.8743 q^{61} -193.932 q^{65} -431.813 q^{67} -450.284 q^{71} -33.5655 q^{73} -945.504 q^{77} +509.312 q^{79} +811.292 q^{83} +157.060 q^{85} -499.820 q^{89} +636.563 q^{91} -353.052 q^{95} +625.481 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 15 q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 15 q^{5} - 8 q^{7} + 10 q^{11} + 48 q^{13} - 37 q^{17} + 29 q^{19} + 11 q^{23} + 75 q^{25} - 28 q^{29} + 41 q^{31} + 40 q^{35} + 230 q^{37} - 370 q^{41} - 130 q^{43} + 56 q^{47} + 547 q^{49} - 805 q^{53} - 50 q^{55} - 576 q^{59} - 257 q^{61} - 240 q^{65} - 14 q^{67} - 1238 q^{71} - 398 q^{73} - 1296 q^{77} - 321 q^{79} - 687 q^{83} + 185 q^{85} - 2358 q^{89} - 1968 q^{91} - 145 q^{95} + 576 q^{97}+O(q^{100}) \) 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
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 16.4120 0.886166 0.443083 0.896481i \(-0.353885\pi\)
0.443083 + 0.896481i \(0.353885\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −57.6104 −1.57911 −0.789554 0.613681i \(-0.789688\pi\)
−0.789554 + 0.613681i \(0.789688\pi\)
\(12\) 0 0
\(13\) 38.7864 0.827492 0.413746 0.910392i \(-0.364220\pi\)
0.413746 + 0.910392i \(0.364220\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −31.4120 −0.448149 −0.224075 0.974572i \(-0.571936\pi\)
−0.224075 + 0.974572i \(0.571936\pi\)
\(18\) 0 0
\(19\) 70.6104 0.852586 0.426293 0.904585i \(-0.359819\pi\)
0.426293 + 0.904585i \(0.359819\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.37433 0.0668545 0.0334273 0.999441i \(-0.489358\pi\)
0.0334273 + 0.999441i \(0.489358\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 17.1607 0.109885 0.0549424 0.998490i \(-0.482502\pi\)
0.0549424 + 0.998490i \(0.482502\pi\)
\(30\) 0 0
\(31\) −50.9847 −0.295391 −0.147696 0.989033i \(-0.547186\pi\)
−0.147696 + 0.989033i \(0.547186\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −82.0601 −0.396306
\(36\) 0 0
\(37\) −159.693 −0.709550 −0.354775 0.934952i \(-0.615443\pi\)
−0.354775 + 0.934952i \(0.615443\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 63.2056 0.240757 0.120379 0.992728i \(-0.461589\pi\)
0.120379 + 0.992728i \(0.461589\pi\)
\(42\) 0 0
\(43\) −84.6580 −0.300238 −0.150119 0.988668i \(-0.547966\pi\)
−0.150119 + 0.988668i \(0.547966\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −434.434 −1.34827 −0.674135 0.738609i \(-0.735483\pi\)
−0.674135 + 0.738609i \(0.735483\pi\)
\(48\) 0 0
\(49\) −73.6454 −0.214710
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −138.490 −0.358926 −0.179463 0.983765i \(-0.557436\pi\)
−0.179463 + 0.983765i \(0.557436\pi\)
\(54\) 0 0
\(55\) 288.052 0.706199
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 631.011 1.39238 0.696192 0.717856i \(-0.254876\pi\)
0.696192 + 0.717856i \(0.254876\pi\)
\(60\) 0 0
\(61\) 82.8743 0.173950 0.0869751 0.996210i \(-0.472280\pi\)
0.0869751 + 0.996210i \(0.472280\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −193.932 −0.370066
\(66\) 0 0
\(67\) −431.813 −0.787379 −0.393689 0.919244i \(-0.628801\pi\)
−0.393689 + 0.919244i \(0.628801\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −450.284 −0.752660 −0.376330 0.926486i \(-0.622814\pi\)
−0.376330 + 0.926486i \(0.622814\pi\)
\(72\) 0 0
\(73\) −33.5655 −0.0538157 −0.0269079 0.999638i \(-0.508566\pi\)
−0.0269079 + 0.999638i \(0.508566\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −945.504 −1.39935
\(78\) 0 0
\(79\) 509.312 0.725343 0.362672 0.931917i \(-0.381865\pi\)
0.362672 + 0.931917i \(0.381865\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 811.292 1.07290 0.536451 0.843932i \(-0.319765\pi\)
0.536451 + 0.843932i \(0.319765\pi\)
\(84\) 0 0
\(85\) 157.060 0.200418
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −499.820 −0.595290 −0.297645 0.954677i \(-0.596201\pi\)
−0.297645 + 0.954677i \(0.596201\pi\)
\(90\) 0 0
\(91\) 636.563 0.733296
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −353.052 −0.381288
\(96\) 0 0
\(97\) 625.481 0.654722 0.327361 0.944899i \(-0.393841\pi\)
0.327361 + 0.944899i \(0.393841\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −241.156 −0.237583 −0.118792 0.992919i \(-0.537902\pi\)
−0.118792 + 0.992919i \(0.537902\pi\)
\(102\) 0 0
\(103\) −1436.46 −1.37417 −0.687083 0.726579i \(-0.741109\pi\)
−0.687083 + 0.726579i \(0.741109\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −801.329 −0.723995 −0.361997 0.932179i \(-0.617905\pi\)
−0.361997 + 0.932179i \(0.617905\pi\)
\(108\) 0 0
\(109\) −1573.48 −1.38268 −0.691338 0.722531i \(-0.742979\pi\)
−0.691338 + 0.722531i \(0.742979\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1777.62 −1.47986 −0.739930 0.672683i \(-0.765142\pi\)
−0.739930 + 0.672683i \(0.765142\pi\)
\(114\) 0 0
\(115\) −36.8717 −0.0298983
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −515.535 −0.397135
\(120\) 0 0
\(121\) 1987.96 1.49358
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −2006.78 −1.40215 −0.701075 0.713088i \(-0.747296\pi\)
−0.701075 + 0.713088i \(0.747296\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1262.69 −0.842149 −0.421075 0.907026i \(-0.638347\pi\)
−0.421075 + 0.907026i \(0.638347\pi\)
\(132\) 0 0
\(133\) 1158.86 0.755533
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −678.275 −0.422985 −0.211492 0.977380i \(-0.567832\pi\)
−0.211492 + 0.977380i \(0.567832\pi\)
\(138\) 0 0
\(139\) −136.614 −0.0833630 −0.0416815 0.999131i \(-0.513271\pi\)
−0.0416815 + 0.999131i \(0.513271\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2234.50 −1.30670
\(144\) 0 0
\(145\) −85.8034 −0.0491420
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1445.14 −0.794569 −0.397285 0.917695i \(-0.630047\pi\)
−0.397285 + 0.917695i \(0.630047\pi\)
\(150\) 0 0
\(151\) −2635.74 −1.42048 −0.710242 0.703958i \(-0.751414\pi\)
−0.710242 + 0.703958i \(0.751414\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 254.924 0.132103
\(156\) 0 0
\(157\) 1523.92 0.774662 0.387331 0.921941i \(-0.373397\pi\)
0.387331 + 0.921941i \(0.373397\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 121.028 0.0592442
\(162\) 0 0
\(163\) −2382.91 −1.14506 −0.572528 0.819885i \(-0.694037\pi\)
−0.572528 + 0.819885i \(0.694037\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3380.54 −1.56643 −0.783215 0.621751i \(-0.786422\pi\)
−0.783215 + 0.621751i \(0.786422\pi\)
\(168\) 0 0
\(169\) −692.618 −0.315256
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −99.6851 −0.0438088 −0.0219044 0.999760i \(-0.506973\pi\)
−0.0219044 + 0.999760i \(0.506973\pi\)
\(174\) 0 0
\(175\) 410.301 0.177233
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3412.90 −1.42510 −0.712549 0.701622i \(-0.752459\pi\)
−0.712549 + 0.701622i \(0.752459\pi\)
\(180\) 0 0
\(181\) 4063.94 1.66890 0.834448 0.551087i \(-0.185787\pi\)
0.834448 + 0.551087i \(0.185787\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 798.465 0.317321
\(186\) 0 0
\(187\) 1809.66 0.707676
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2163.72 −0.819693 −0.409847 0.912154i \(-0.634418\pi\)
−0.409847 + 0.912154i \(0.634418\pi\)
\(192\) 0 0
\(193\) 4432.06 1.65299 0.826493 0.562946i \(-0.190332\pi\)
0.826493 + 0.562946i \(0.190332\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4233.88 1.53122 0.765612 0.643302i \(-0.222436\pi\)
0.765612 + 0.643302i \(0.222436\pi\)
\(198\) 0 0
\(199\) −2833.94 −1.00951 −0.504755 0.863263i \(-0.668417\pi\)
−0.504755 + 0.863263i \(0.668417\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 281.642 0.0973762
\(204\) 0 0
\(205\) −316.028 −0.107670
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4067.89 −1.34633
\(210\) 0 0
\(211\) 2775.59 0.905589 0.452794 0.891615i \(-0.350427\pi\)
0.452794 + 0.891615i \(0.350427\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 423.290 0.134270
\(216\) 0 0
\(217\) −836.763 −0.261766
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1218.36 −0.370840
\(222\) 0 0
\(223\) 317.706 0.0954043 0.0477021 0.998862i \(-0.484810\pi\)
0.0477021 + 0.998862i \(0.484810\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 855.603 0.250169 0.125085 0.992146i \(-0.460080\pi\)
0.125085 + 0.992146i \(0.460080\pi\)
\(228\) 0 0
\(229\) 687.782 0.198471 0.0992356 0.995064i \(-0.468360\pi\)
0.0992356 + 0.995064i \(0.468360\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4228.01 −1.18878 −0.594390 0.804177i \(-0.702607\pi\)
−0.594390 + 0.804177i \(0.702607\pi\)
\(234\) 0 0
\(235\) 2172.17 0.602964
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3113.46 0.842648 0.421324 0.906910i \(-0.361565\pi\)
0.421324 + 0.906910i \(0.361565\pi\)
\(240\) 0 0
\(241\) −4185.57 −1.11874 −0.559370 0.828918i \(-0.688957\pi\)
−0.559370 + 0.828918i \(0.688957\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 368.227 0.0960210
\(246\) 0 0
\(247\) 2738.72 0.705509
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1137.16 0.285963 0.142981 0.989725i \(-0.454331\pi\)
0.142981 + 0.989725i \(0.454331\pi\)
\(252\) 0 0
\(253\) −424.838 −0.105571
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6957.03 1.68859 0.844295 0.535878i \(-0.180019\pi\)
0.844295 + 0.535878i \(0.180019\pi\)
\(258\) 0 0
\(259\) −2620.89 −0.628780
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1187.16 −0.278339 −0.139169 0.990269i \(-0.544443\pi\)
−0.139169 + 0.990269i \(0.544443\pi\)
\(264\) 0 0
\(265\) 692.451 0.160517
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1879.17 −0.425929 −0.212965 0.977060i \(-0.568312\pi\)
−0.212965 + 0.977060i \(0.568312\pi\)
\(270\) 0 0
\(271\) −8561.28 −1.91904 −0.959522 0.281635i \(-0.909123\pi\)
−0.959522 + 0.281635i \(0.909123\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1440.26 −0.315822
\(276\) 0 0
\(277\) 7204.78 1.56279 0.781396 0.624036i \(-0.214508\pi\)
0.781396 + 0.624036i \(0.214508\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7115.84 −1.51066 −0.755329 0.655345i \(-0.772523\pi\)
−0.755329 + 0.655345i \(0.772523\pi\)
\(282\) 0 0
\(283\) −1361.24 −0.285926 −0.142963 0.989728i \(-0.545663\pi\)
−0.142963 + 0.989728i \(0.545663\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1037.33 0.213351
\(288\) 0 0
\(289\) −3926.28 −0.799162
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1323.60 0.263910 0.131955 0.991256i \(-0.457875\pi\)
0.131955 + 0.991256i \(0.457875\pi\)
\(294\) 0 0
\(295\) −3155.05 −0.622693
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 286.023 0.0553216
\(300\) 0 0
\(301\) −1389.41 −0.266061
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −414.371 −0.0777929
\(306\) 0 0
\(307\) −5864.61 −1.09026 −0.545132 0.838350i \(-0.683521\pi\)
−0.545132 + 0.838350i \(0.683521\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5084.53 0.927065 0.463533 0.886080i \(-0.346582\pi\)
0.463533 + 0.886080i \(0.346582\pi\)
\(312\) 0 0
\(313\) −2964.66 −0.535375 −0.267687 0.963506i \(-0.586259\pi\)
−0.267687 + 0.963506i \(0.586259\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7443.17 −1.31877 −0.659385 0.751806i \(-0.729183\pi\)
−0.659385 + 0.751806i \(0.729183\pi\)
\(318\) 0 0
\(319\) −988.634 −0.173520
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2218.02 −0.382086
\(324\) 0 0
\(325\) 969.659 0.165498
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7129.94 −1.19479
\(330\) 0 0
\(331\) −3965.35 −0.658475 −0.329238 0.944247i \(-0.606792\pi\)
−0.329238 + 0.944247i \(0.606792\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2159.07 0.352127
\(336\) 0 0
\(337\) 10319.1 1.66800 0.834000 0.551765i \(-0.186045\pi\)
0.834000 + 0.551765i \(0.186045\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2937.25 0.466455
\(342\) 0 0
\(343\) −6838.00 −1.07643
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7755.95 −1.19989 −0.599944 0.800042i \(-0.704811\pi\)
−0.599944 + 0.800042i \(0.704811\pi\)
\(348\) 0 0
\(349\) 11579.1 1.77597 0.887987 0.459869i \(-0.152104\pi\)
0.887987 + 0.459869i \(0.152104\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8495.91 1.28100 0.640498 0.767960i \(-0.278728\pi\)
0.640498 + 0.767960i \(0.278728\pi\)
\(354\) 0 0
\(355\) 2251.42 0.336600
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8260.19 1.21436 0.607181 0.794563i \(-0.292300\pi\)
0.607181 + 0.794563i \(0.292300\pi\)
\(360\) 0 0
\(361\) −1873.17 −0.273097
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 167.828 0.0240671
\(366\) 0 0
\(367\) 13765.5 1.95791 0.978953 0.204085i \(-0.0654219\pi\)
0.978953 + 0.204085i \(0.0654219\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2272.90 −0.318068
\(372\) 0 0
\(373\) 1048.30 0.145520 0.0727602 0.997349i \(-0.476819\pi\)
0.0727602 + 0.997349i \(0.476819\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 665.601 0.0909289
\(378\) 0 0
\(379\) −10636.6 −1.44160 −0.720799 0.693144i \(-0.756225\pi\)
−0.720799 + 0.693144i \(0.756225\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1505.81 −0.200896 −0.100448 0.994942i \(-0.532028\pi\)
−0.100448 + 0.994942i \(0.532028\pi\)
\(384\) 0 0
\(385\) 4727.52 0.625809
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12411.4 1.61769 0.808846 0.588020i \(-0.200092\pi\)
0.808846 + 0.588020i \(0.200092\pi\)
\(390\) 0 0
\(391\) −231.643 −0.0299608
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2546.56 −0.324383
\(396\) 0 0
\(397\) 4807.65 0.607781 0.303891 0.952707i \(-0.401714\pi\)
0.303891 + 0.952707i \(0.401714\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8688.87 1.08205 0.541024 0.841007i \(-0.318037\pi\)
0.541024 + 0.841007i \(0.318037\pi\)
\(402\) 0 0
\(403\) −1977.51 −0.244434
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9199.98 1.12046
\(408\) 0 0
\(409\) 10056.9 1.21584 0.607921 0.793997i \(-0.292004\pi\)
0.607921 + 0.793997i \(0.292004\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10356.2 1.23388
\(414\) 0 0
\(415\) −4056.46 −0.479816
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6643.15 0.774556 0.387278 0.921963i \(-0.373415\pi\)
0.387278 + 0.921963i \(0.373415\pi\)
\(420\) 0 0
\(421\) 9771.06 1.13115 0.565573 0.824698i \(-0.308655\pi\)
0.565573 + 0.824698i \(0.308655\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −785.301 −0.0896298
\(426\) 0 0
\(427\) 1360.13 0.154149
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7498.22 0.837997 0.418998 0.907987i \(-0.362381\pi\)
0.418998 + 0.907987i \(0.362381\pi\)
\(432\) 0 0
\(433\) −12325.1 −1.36792 −0.683959 0.729521i \(-0.739743\pi\)
−0.683959 + 0.729521i \(0.739743\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 520.705 0.0569993
\(438\) 0 0
\(439\) −11635.6 −1.26500 −0.632500 0.774560i \(-0.717971\pi\)
−0.632500 + 0.774560i \(0.717971\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12038.6 1.29113 0.645567 0.763703i \(-0.276621\pi\)
0.645567 + 0.763703i \(0.276621\pi\)
\(444\) 0 0
\(445\) 2499.10 0.266222
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10905.2 1.14621 0.573103 0.819483i \(-0.305739\pi\)
0.573103 + 0.819483i \(0.305739\pi\)
\(450\) 0 0
\(451\) −3641.30 −0.380182
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3182.81 −0.327940
\(456\) 0 0
\(457\) 831.136 0.0850742 0.0425371 0.999095i \(-0.486456\pi\)
0.0425371 + 0.999095i \(0.486456\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3846.15 0.388575 0.194288 0.980945i \(-0.437760\pi\)
0.194288 + 0.980945i \(0.437760\pi\)
\(462\) 0 0
\(463\) 2127.77 0.213576 0.106788 0.994282i \(-0.465943\pi\)
0.106788 + 0.994282i \(0.465943\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1169.95 −0.115929 −0.0579647 0.998319i \(-0.518461\pi\)
−0.0579647 + 0.998319i \(0.518461\pi\)
\(468\) 0 0
\(469\) −7086.93 −0.697749
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4877.18 0.474108
\(474\) 0 0
\(475\) 1765.26 0.170517
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 11243.2 1.07247 0.536236 0.844068i \(-0.319846\pi\)
0.536236 + 0.844068i \(0.319846\pi\)
\(480\) 0 0
\(481\) −6193.91 −0.587148
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3127.41 −0.292800
\(486\) 0 0
\(487\) 12169.5 1.13234 0.566172 0.824287i \(-0.308424\pi\)
0.566172 + 0.824287i \(0.308424\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1702.75 0.156505 0.0782524 0.996934i \(-0.475066\pi\)
0.0782524 + 0.996934i \(0.475066\pi\)
\(492\) 0 0
\(493\) −539.052 −0.0492448
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7390.07 −0.666982
\(498\) 0 0
\(499\) −16867.1 −1.51318 −0.756590 0.653890i \(-0.773136\pi\)
−0.756590 + 0.653890i \(0.773136\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10396.8 −0.921608 −0.460804 0.887502i \(-0.652439\pi\)
−0.460804 + 0.887502i \(0.652439\pi\)
\(504\) 0 0
\(505\) 1205.78 0.106251
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5656.96 −0.492614 −0.246307 0.969192i \(-0.579217\pi\)
−0.246307 + 0.969192i \(0.579217\pi\)
\(510\) 0 0
\(511\) −550.878 −0.0476897
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7182.32 0.614546
\(516\) 0 0
\(517\) 25027.9 2.12906
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8808.99 0.740747 0.370373 0.928883i \(-0.379230\pi\)
0.370373 + 0.928883i \(0.379230\pi\)
\(522\) 0 0
\(523\) −6509.27 −0.544227 −0.272113 0.962265i \(-0.587723\pi\)
−0.272113 + 0.962265i \(0.587723\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1601.53 0.132379
\(528\) 0 0
\(529\) −12112.6 −0.995530
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2451.51 0.199225
\(534\) 0 0
\(535\) 4006.65 0.323780
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4242.74 0.339050
\(540\) 0 0
\(541\) −14119.6 −1.12208 −0.561042 0.827787i \(-0.689600\pi\)
−0.561042 + 0.827787i \(0.689600\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7867.38 0.618352
\(546\) 0 0
\(547\) −7536.09 −0.589068 −0.294534 0.955641i \(-0.595164\pi\)
−0.294534 + 0.955641i \(0.595164\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1211.72 0.0936863
\(552\) 0 0
\(553\) 8358.85 0.642775
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7113.19 −0.541105 −0.270553 0.962705i \(-0.587206\pi\)
−0.270553 + 0.962705i \(0.587206\pi\)
\(558\) 0 0
\(559\) −3283.58 −0.248444
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8995.70 0.673399 0.336700 0.941612i \(-0.390689\pi\)
0.336700 + 0.941612i \(0.390689\pi\)
\(564\) 0 0
\(565\) 8888.09 0.661814
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12326.8 −0.908202 −0.454101 0.890950i \(-0.650040\pi\)
−0.454101 + 0.890950i \(0.650040\pi\)
\(570\) 0 0
\(571\) 20671.0 1.51498 0.757492 0.652844i \(-0.226424\pi\)
0.757492 + 0.652844i \(0.226424\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 184.358 0.0133709
\(576\) 0 0
\(577\) 4732.48 0.341448 0.170724 0.985319i \(-0.445389\pi\)
0.170724 + 0.985319i \(0.445389\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 13314.9 0.950769
\(582\) 0 0
\(583\) 7978.47 0.566783
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22571.9 1.58713 0.793564 0.608487i \(-0.208223\pi\)
0.793564 + 0.608487i \(0.208223\pi\)
\(588\) 0 0
\(589\) −3600.05 −0.251847
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8442.07 0.584611 0.292306 0.956325i \(-0.405578\pi\)
0.292306 + 0.956325i \(0.405578\pi\)
\(594\) 0 0
\(595\) 2577.68 0.177604
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1168.01 0.0796722 0.0398361 0.999206i \(-0.487316\pi\)
0.0398361 + 0.999206i \(0.487316\pi\)
\(600\) 0 0
\(601\) 14952.9 1.01488 0.507439 0.861687i \(-0.330592\pi\)
0.507439 + 0.861687i \(0.330592\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9939.80 −0.667951
\(606\) 0 0
\(607\) 15021.3 1.00444 0.502221 0.864739i \(-0.332516\pi\)
0.502221 + 0.864739i \(0.332516\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16850.1 −1.11568
\(612\) 0 0
\(613\) −3705.74 −0.244165 −0.122083 0.992520i \(-0.538957\pi\)
−0.122083 + 0.992520i \(0.538957\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19883.5 1.29737 0.648685 0.761057i \(-0.275319\pi\)
0.648685 + 0.761057i \(0.275319\pi\)
\(618\) 0 0
\(619\) −18451.8 −1.19813 −0.599064 0.800701i \(-0.704461\pi\)
−0.599064 + 0.800701i \(0.704461\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8203.05 −0.527525
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5016.28 0.317984
\(630\) 0 0
\(631\) −24501.2 −1.54576 −0.772882 0.634549i \(-0.781186\pi\)
−0.772882 + 0.634549i \(0.781186\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10033.9 0.627060
\(636\) 0 0
\(637\) −2856.44 −0.177671
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12596.9 −0.776205 −0.388102 0.921616i \(-0.626869\pi\)
−0.388102 + 0.921616i \(0.626869\pi\)
\(642\) 0 0
\(643\) 11302.8 0.693220 0.346610 0.938009i \(-0.387333\pi\)
0.346610 + 0.938009i \(0.387333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1011.85 0.0614839 0.0307419 0.999527i \(-0.490213\pi\)
0.0307419 + 0.999527i \(0.490213\pi\)
\(648\) 0 0
\(649\) −36352.8 −2.19872
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4763.76 −0.285483 −0.142741 0.989760i \(-0.545592\pi\)
−0.142741 + 0.989760i \(0.545592\pi\)
\(654\) 0 0
\(655\) 6313.44 0.376621
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3887.39 −0.229789 −0.114895 0.993378i \(-0.536653\pi\)
−0.114895 + 0.993378i \(0.536653\pi\)
\(660\) 0 0
\(661\) 13798.4 0.811943 0.405972 0.913886i \(-0.366933\pi\)
0.405972 + 0.913886i \(0.366933\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5794.30 −0.337885
\(666\) 0 0
\(667\) 126.549 0.00734630
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4774.42 −0.274686
\(672\) 0 0
\(673\) −22080.3 −1.26469 −0.632343 0.774688i \(-0.717907\pi\)
−0.632343 + 0.774688i \(0.717907\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8197.20 0.465353 0.232677 0.972554i \(-0.425252\pi\)
0.232677 + 0.972554i \(0.425252\pi\)
\(678\) 0 0
\(679\) 10265.4 0.580192
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6789.28 −0.380358 −0.190179 0.981749i \(-0.560907\pi\)
−0.190179 + 0.981749i \(0.560907\pi\)
\(684\) 0 0
\(685\) 3391.37 0.189165
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5371.53 −0.297009
\(690\) 0 0
\(691\) 19512.4 1.07422 0.537109 0.843513i \(-0.319516\pi\)
0.537109 + 0.843513i \(0.319516\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 683.070 0.0372810
\(696\) 0 0
\(697\) −1985.41 −0.107895
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 10670.1 0.574898 0.287449 0.957796i \(-0.407193\pi\)
0.287449 + 0.957796i \(0.407193\pi\)
\(702\) 0 0
\(703\) −11276.0 −0.604953
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3957.86 −0.210538
\(708\) 0 0
\(709\) −27297.4 −1.44595 −0.722973 0.690876i \(-0.757225\pi\)
−0.722973 + 0.690876i \(0.757225\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −375.978 −0.0197482
\(714\) 0 0
\(715\) 11172.5 0.584374
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −23257.1 −1.20632 −0.603159 0.797621i \(-0.706092\pi\)
−0.603159 + 0.797621i \(0.706092\pi\)
\(720\) 0 0
\(721\) −23575.3 −1.21774
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 429.017 0.0219770
\(726\) 0 0
\(727\) 18331.1 0.935163 0.467582 0.883950i \(-0.345125\pi\)
0.467582 + 0.883950i \(0.345125\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2659.28 0.134551
\(732\) 0 0
\(733\) −13078.2 −0.659011 −0.329505 0.944154i \(-0.606882\pi\)
−0.329505 + 0.944154i \(0.606882\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24876.9 1.24336
\(738\) 0 0
\(739\) −12129.6 −0.603782 −0.301891 0.953342i \(-0.597618\pi\)
−0.301891 + 0.953342i \(0.597618\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −33145.5 −1.63660 −0.818298 0.574794i \(-0.805082\pi\)
−0.818298 + 0.574794i \(0.805082\pi\)
\(744\) 0 0
\(745\) 7225.72 0.355342
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13151.4 −0.641580
\(750\) 0 0
\(751\) 2612.04 0.126917 0.0634585 0.997984i \(-0.479787\pi\)
0.0634585 + 0.997984i \(0.479787\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 13178.7 0.635260
\(756\) 0 0
\(757\) 15839.7 0.760506 0.380253 0.924883i \(-0.375837\pi\)
0.380253 + 0.924883i \(0.375837\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 742.568 0.0353720 0.0176860 0.999844i \(-0.494370\pi\)
0.0176860 + 0.999844i \(0.494370\pi\)
\(762\) 0 0
\(763\) −25823.9 −1.22528
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 24474.6 1.15219
\(768\) 0 0
\(769\) −22719.0 −1.06537 −0.532683 0.846315i \(-0.678816\pi\)
−0.532683 + 0.846315i \(0.678816\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 23215.6 1.08022 0.540108 0.841596i \(-0.318383\pi\)
0.540108 + 0.841596i \(0.318383\pi\)
\(774\) 0 0
\(775\) −1274.62 −0.0590783
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4462.97 0.205266
\(780\) 0 0
\(781\) 25941.0 1.18853
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7619.60 −0.346440
\(786\) 0 0
\(787\) 25481.4 1.15415 0.577073 0.816692i \(-0.304195\pi\)
0.577073 + 0.816692i \(0.304195\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −29174.3 −1.31140
\(792\) 0 0
\(793\) 3214.39 0.143942
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22375.2 −0.994440 −0.497220 0.867624i \(-0.665646\pi\)
−0.497220 + 0.867624i \(0.665646\pi\)
\(798\) 0 0
\(799\) 13646.4 0.604226
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1933.72 0.0849809
\(804\) 0 0
\(805\) −605.139 −0.0264948
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −9293.69 −0.403892 −0.201946 0.979397i \(-0.564727\pi\)
−0.201946 + 0.979397i \(0.564727\pi\)
\(810\) 0 0
\(811\) 26415.5 1.14374 0.571871 0.820344i \(-0.306218\pi\)
0.571871 + 0.820344i \(0.306218\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 11914.6 0.512084
\(816\) 0 0
\(817\) −5977.74 −0.255979
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −18148.6 −0.771486 −0.385743 0.922606i \(-0.626055\pi\)
−0.385743 + 0.922606i \(0.626055\pi\)
\(822\) 0 0
\(823\) −10438.4 −0.442115 −0.221058 0.975261i \(-0.570951\pi\)
−0.221058 + 0.975261i \(0.570951\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18909.8 −0.795112 −0.397556 0.917578i \(-0.630142\pi\)
−0.397556 + 0.917578i \(0.630142\pi\)
\(828\) 0 0
\(829\) 10162.8 0.425777 0.212888 0.977077i \(-0.431713\pi\)
0.212888 + 0.977077i \(0.431713\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2313.35 0.0962219
\(834\) 0 0
\(835\) 16902.7 0.700529
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 16310.9 0.671174 0.335587 0.942009i \(-0.391065\pi\)
0.335587 + 0.942009i \(0.391065\pi\)
\(840\) 0 0
\(841\) −24094.5 −0.987925
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3463.09 0.140987
\(846\) 0 0
\(847\) 32626.4 1.32356
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1177.63 −0.0474367
\(852\) 0 0
\(853\) 26423.7 1.06064 0.530322 0.847796i \(-0.322071\pi\)
0.530322 + 0.847796i \(0.322071\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −19242.4 −0.766985 −0.383493 0.923544i \(-0.625279\pi\)
−0.383493 + 0.923544i \(0.625279\pi\)
\(858\) 0 0
\(859\) 3598.56 0.142935 0.0714677 0.997443i \(-0.477232\pi\)
0.0714677 + 0.997443i \(0.477232\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −13195.7 −0.520496 −0.260248 0.965542i \(-0.583804\pi\)
−0.260248 + 0.965542i \(0.583804\pi\)
\(864\) 0 0
\(865\) 498.425 0.0195919
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −29341.7 −1.14540
\(870\) 0 0
\(871\) −16748.5 −0.651550
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2051.50 −0.0792611
\(876\) 0 0
\(877\) 40460.0 1.55785 0.778926 0.627116i \(-0.215765\pi\)
0.778926 + 0.627116i \(0.215765\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 23036.5 0.880955 0.440477 0.897764i \(-0.354809\pi\)
0.440477 + 0.897764i \(0.354809\pi\)
\(882\) 0 0
\(883\) −24591.6 −0.937228 −0.468614 0.883403i \(-0.655246\pi\)
−0.468614 + 0.883403i \(0.655246\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −31117.5 −1.17793 −0.588966 0.808158i \(-0.700465\pi\)
−0.588966 + 0.808158i \(0.700465\pi\)
\(888\) 0 0
\(889\) −32935.3 −1.24254
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −30675.5 −1.14952
\(894\) 0 0
\(895\) 17064.5 0.637323
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −874.933 −0.0324590
\(900\) 0 0
\(901\) 4350.26 0.160852
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −20319.7 −0.746353
\(906\) 0 0
\(907\) 25694.5 0.940651 0.470326 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 19061.3 0.693225 0.346612 0.938008i \(-0.387332\pi\)
0.346612 + 0.938008i \(0.387332\pi\)
\(912\) 0 0
\(913\) −46738.8 −1.69423
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −20723.3 −0.746284
\(918\) 0 0
\(919\) 2322.58 0.0833675 0.0416838 0.999131i \(-0.486728\pi\)
0.0416838 + 0.999131i \(0.486728\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −17464.9 −0.622820
\(924\) 0 0
\(925\) −3992.32 −0.141910
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −25814.2 −0.911664 −0.455832 0.890066i \(-0.650658\pi\)
−0.455832 + 0.890066i \(0.650658\pi\)
\(930\) 0 0
\(931\) −5200.13 −0.183058
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9048.30 −0.316482
\(936\) 0 0
\(937\) 17757.8 0.619128 0.309564 0.950879i \(-0.399817\pi\)
0.309564 + 0.950879i \(0.399817\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1857.32 −0.0643431 −0.0321715 0.999482i \(-0.510242\pi\)
−0.0321715 + 0.999482i \(0.510242\pi\)
\(942\) 0 0
\(943\) 466.099 0.0160957
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −10837.6 −0.371885 −0.185943 0.982561i \(-0.559534\pi\)
−0.185943 + 0.982561i \(0.559534\pi\)
\(948\) 0 0
\(949\) −1301.88 −0.0445321
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2386.31 0.0811125 0.0405562 0.999177i \(-0.487087\pi\)
0.0405562 + 0.999177i \(0.487087\pi\)
\(954\) 0 0
\(955\) 10818.6 0.366578
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −11131.9 −0.374835
\(960\) 0 0
\(961\) −27191.6 −0.912744
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −22160.3 −0.739238
\(966\) 0 0
\(967\) 12418.4 0.412977 0.206489 0.978449i \(-0.433796\pi\)
0.206489 + 0.978449i \(0.433796\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −50399.5 −1.66570 −0.832851 0.553498i \(-0.813293\pi\)
−0.832851 + 0.553498i \(0.813293\pi\)
\(972\) 0 0
\(973\) −2242.11 −0.0738734
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −56849.3 −1.86159 −0.930793 0.365547i \(-0.880882\pi\)
−0.930793 + 0.365547i \(0.880882\pi\)
\(978\) 0 0
\(979\) 28794.8 0.940027
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −13309.5 −0.431850 −0.215925 0.976410i \(-0.569277\pi\)
−0.215925 + 0.976410i \(0.569277\pi\)
\(984\) 0 0
\(985\) −21169.4 −0.684785
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −624.296 −0.0200723
\(990\) 0 0
\(991\) −19322.3 −0.619369 −0.309684 0.950839i \(-0.600223\pi\)
−0.309684 + 0.950839i \(0.600223\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 14169.7 0.451466
\(996\) 0 0
\(997\) 8263.31 0.262489 0.131245 0.991350i \(-0.458103\pi\)
0.131245 + 0.991350i \(0.458103\pi\)
\(998\) 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 1080.4.a.e.1.3 3
3.2 odd 2 1080.4.a.k.1.3 yes 3
4.3 odd 2 2160.4.a.bj.1.1 3
12.11 even 2 2160.4.a.br.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.4.a.e.1.3 3 1.1 even 1 trivial
1080.4.a.k.1.3 yes 3 3.2 odd 2
2160.4.a.bj.1.1 3 4.3 odd 2
2160.4.a.br.1.1 3 12.11 even 2