Properties

Label 1584.4.a.x.1.2
Level $1584$
Weight $4$
Character 1584.1
Self dual yes
Analytic conductor $93.459$
Analytic rank $1$
Dimension $2$
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] = [1584,4,Mod(1,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, 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("1584.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1584.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: \(93.4590254491\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{33}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 33)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.37228\) of defining polynomial
Character \(\chi\) \(=\) 1584.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.48913 q^{5} +4.74456 q^{7} +O(q^{10})\) \(q+3.48913 q^{5} +4.74456 q^{7} +11.0000 q^{11} -15.0217 q^{13} -73.1684 q^{17} +78.7011 q^{19} +112.000 q^{23} -112.826 q^{25} -243.125 q^{29} -278.717 q^{31} +16.5544 q^{35} +102.380 q^{37} +241.255 q^{41} +280.016 q^{43} -169.870 q^{47} -320.489 q^{49} +409.652 q^{53} +38.3804 q^{55} +196.000 q^{59} -701.359 q^{61} -52.4128 q^{65} -900.587 q^{67} +756.500 q^{71} -1019.81 q^{73} +52.1902 q^{77} +327.549 q^{79} -756.619 q^{83} -255.294 q^{85} -508.978 q^{89} -71.2716 q^{91} +274.598 q^{95} +614.358 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 16 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 16 q^{5} - 2 q^{7} + 22 q^{11} - 76 q^{13} + 26 q^{17} + 54 q^{19} + 224 q^{23} + 142 q^{25} - 222 q^{29} + 40 q^{31} + 148 q^{35} - 48 q^{37} + 494 q^{41} + 66 q^{43} - 64 q^{47} - 618 q^{49} + 84 q^{53} - 176 q^{55} + 392 q^{59} - 1104 q^{61} + 1136 q^{65} - 928 q^{67} + 456 q^{71} - 592 q^{73} - 22 q^{77} + 230 q^{79} + 348 q^{83} - 2188 q^{85} - 972 q^{89} + 340 q^{91} + 756 q^{95} - 1184 q^{97}+O(q^{100}) \) 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
\(5\) 3.48913 0.312077 0.156038 0.987751i \(-0.450128\pi\)
0.156038 + 0.987751i \(0.450128\pi\)
\(6\) 0 0
\(7\) 4.74456 0.256182 0.128091 0.991762i \(-0.459115\pi\)
0.128091 + 0.991762i \(0.459115\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −15.0217 −0.320483 −0.160242 0.987078i \(-0.551227\pi\)
−0.160242 + 0.987078i \(0.551227\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −73.1684 −1.04388 −0.521940 0.852982i \(-0.674791\pi\)
−0.521940 + 0.852982i \(0.674791\pi\)
\(18\) 0 0
\(19\) 78.7011 0.950277 0.475138 0.879911i \(-0.342398\pi\)
0.475138 + 0.879911i \(0.342398\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 112.000 1.01537 0.507687 0.861541i \(-0.330501\pi\)
0.507687 + 0.861541i \(0.330501\pi\)
\(24\) 0 0
\(25\) −112.826 −0.902608
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −243.125 −1.55680 −0.778399 0.627769i \(-0.783968\pi\)
−0.778399 + 0.627769i \(0.783968\pi\)
\(30\) 0 0
\(31\) −278.717 −1.61481 −0.807405 0.589998i \(-0.799129\pi\)
−0.807405 + 0.589998i \(0.799129\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 16.5544 0.0799486
\(36\) 0 0
\(37\) 102.380 0.454898 0.227449 0.973790i \(-0.426961\pi\)
0.227449 + 0.973790i \(0.426961\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 241.255 0.918970 0.459485 0.888186i \(-0.348034\pi\)
0.459485 + 0.888186i \(0.348034\pi\)
\(42\) 0 0
\(43\) 280.016 0.993071 0.496536 0.868016i \(-0.334605\pi\)
0.496536 + 0.868016i \(0.334605\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −169.870 −0.527192 −0.263596 0.964633i \(-0.584909\pi\)
−0.263596 + 0.964633i \(0.584909\pi\)
\(48\) 0 0
\(49\) −320.489 −0.934371
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 409.652 1.06170 0.530849 0.847466i \(-0.321873\pi\)
0.530849 + 0.847466i \(0.321873\pi\)
\(54\) 0 0
\(55\) 38.3804 0.0940947
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 196.000 0.432492 0.216246 0.976339i \(-0.430619\pi\)
0.216246 + 0.976339i \(0.430619\pi\)
\(60\) 0 0
\(61\) −701.359 −1.47213 −0.736064 0.676912i \(-0.763318\pi\)
−0.736064 + 0.676912i \(0.763318\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −52.4128 −0.100015
\(66\) 0 0
\(67\) −900.587 −1.64215 −0.821076 0.570819i \(-0.806626\pi\)
−0.821076 + 0.570819i \(0.806626\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 756.500 1.26451 0.632254 0.774762i \(-0.282130\pi\)
0.632254 + 0.774762i \(0.282130\pi\)
\(72\) 0 0
\(73\) −1019.81 −1.63507 −0.817536 0.575877i \(-0.804661\pi\)
−0.817536 + 0.575877i \(0.804661\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 52.1902 0.0772419
\(78\) 0 0
\(79\) 327.549 0.466483 0.233241 0.972419i \(-0.425067\pi\)
0.233241 + 0.972419i \(0.425067\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −756.619 −1.00060 −0.500300 0.865852i \(-0.666777\pi\)
−0.500300 + 0.865852i \(0.666777\pi\)
\(84\) 0 0
\(85\) −255.294 −0.325771
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −508.978 −0.606198 −0.303099 0.952959i \(-0.598021\pi\)
−0.303099 + 0.952959i \(0.598021\pi\)
\(90\) 0 0
\(91\) −71.2716 −0.0821022
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 274.598 0.296559
\(96\) 0 0
\(97\) 614.358 0.643079 0.321539 0.946896i \(-0.395800\pi\)
0.321539 + 0.946896i \(0.395800\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1015.92 1.00087 0.500434 0.865775i \(-0.333174\pi\)
0.500434 + 0.865775i \(0.333174\pi\)
\(102\) 0 0
\(103\) −1102.16 −1.05436 −0.527181 0.849753i \(-0.676751\pi\)
−0.527181 + 0.849753i \(0.676751\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1377.58 1.24463 0.622315 0.782767i \(-0.286192\pi\)
0.622315 + 0.782767i \(0.286192\pi\)
\(108\) 0 0
\(109\) 320.217 0.281388 0.140694 0.990053i \(-0.455067\pi\)
0.140694 + 0.990053i \(0.455067\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1629.45 1.35651 0.678254 0.734828i \(-0.262737\pi\)
0.678254 + 0.734828i \(0.262737\pi\)
\(114\) 0 0
\(115\) 390.782 0.316875
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −347.152 −0.267423
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −829.805 −0.593760
\(126\) 0 0
\(127\) −2291.26 −1.60091 −0.800457 0.599390i \(-0.795410\pi\)
−0.800457 + 0.599390i \(0.795410\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1147.41 −0.765267 −0.382633 0.923900i \(-0.624983\pi\)
−0.382633 + 0.923900i \(0.624983\pi\)
\(132\) 0 0
\(133\) 373.402 0.243444
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1268.60 −0.791121 −0.395561 0.918440i \(-0.629450\pi\)
−0.395561 + 0.918440i \(0.629450\pi\)
\(138\) 0 0
\(139\) 486.288 0.296737 0.148368 0.988932i \(-0.452598\pi\)
0.148368 + 0.988932i \(0.452598\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −165.239 −0.0966294
\(144\) 0 0
\(145\) −848.293 −0.485841
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2354.11 −1.29434 −0.647169 0.762346i \(-0.724047\pi\)
−0.647169 + 0.762346i \(0.724047\pi\)
\(150\) 0 0
\(151\) 570.070 0.307229 0.153615 0.988131i \(-0.450909\pi\)
0.153615 + 0.988131i \(0.450909\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −972.479 −0.503945
\(156\) 0 0
\(157\) −2072.67 −1.05361 −0.526807 0.849985i \(-0.676611\pi\)
−0.526807 + 0.849985i \(0.676611\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 531.391 0.260121
\(162\) 0 0
\(163\) −2676.51 −1.28614 −0.643069 0.765808i \(-0.722339\pi\)
−0.643069 + 0.765808i \(0.722339\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1188.12 −0.550536 −0.275268 0.961368i \(-0.588767\pi\)
−0.275268 + 0.961368i \(0.588767\pi\)
\(168\) 0 0
\(169\) −1971.35 −0.897290
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −807.147 −0.354718 −0.177359 0.984146i \(-0.556755\pi\)
−0.177359 + 0.984146i \(0.556755\pi\)
\(174\) 0 0
\(175\) −535.310 −0.231232
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1950.39 −0.814408 −0.407204 0.913337i \(-0.633496\pi\)
−0.407204 + 0.913337i \(0.633496\pi\)
\(180\) 0 0
\(181\) 1061.61 0.435959 0.217980 0.975953i \(-0.430053\pi\)
0.217980 + 0.975953i \(0.430053\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 357.218 0.141963
\(186\) 0 0
\(187\) −804.853 −0.314742
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2136.41 0.809348 0.404674 0.914461i \(-0.367385\pi\)
0.404674 + 0.914461i \(0.367385\pi\)
\(192\) 0 0
\(193\) 3947.76 1.47236 0.736181 0.676784i \(-0.236627\pi\)
0.736181 + 0.676784i \(0.236627\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −923.886 −0.334133 −0.167066 0.985946i \(-0.553429\pi\)
−0.167066 + 0.985946i \(0.553429\pi\)
\(198\) 0 0
\(199\) 476.152 0.169616 0.0848078 0.996397i \(-0.472972\pi\)
0.0848078 + 0.996397i \(0.472972\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1153.52 −0.398824
\(204\) 0 0
\(205\) 841.770 0.286789
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 865.712 0.286519
\(210\) 0 0
\(211\) 4918.24 1.60467 0.802336 0.596872i \(-0.203590\pi\)
0.802336 + 0.596872i \(0.203590\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 977.012 0.309915
\(216\) 0 0
\(217\) −1322.39 −0.413686
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1099.12 0.334546
\(222\) 0 0
\(223\) −2100.29 −0.630700 −0.315350 0.948975i \(-0.602122\pi\)
−0.315350 + 0.948975i \(0.602122\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2257.16 −0.659970 −0.329985 0.943986i \(-0.607044\pi\)
−0.329985 + 0.943986i \(0.607044\pi\)
\(228\) 0 0
\(229\) −5311.07 −1.53260 −0.766301 0.642482i \(-0.777905\pi\)
−0.766301 + 0.642482i \(0.777905\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2466.27 −0.693435 −0.346718 0.937970i \(-0.612704\pi\)
−0.346718 + 0.937970i \(0.612704\pi\)
\(234\) 0 0
\(235\) −592.696 −0.164524
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1429.40 0.386863 0.193432 0.981114i \(-0.438038\pi\)
0.193432 + 0.981114i \(0.438038\pi\)
\(240\) 0 0
\(241\) −978.989 −0.261669 −0.130835 0.991404i \(-0.541766\pi\)
−0.130835 + 0.991404i \(0.541766\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1118.23 −0.291595
\(246\) 0 0
\(247\) −1182.23 −0.304548
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6530.63 −1.64227 −0.821135 0.570734i \(-0.806659\pi\)
−0.821135 + 0.570734i \(0.806659\pi\)
\(252\) 0 0
\(253\) 1232.00 0.306147
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8130.26 −1.97335 −0.986676 0.162696i \(-0.947981\pi\)
−0.986676 + 0.162696i \(0.947981\pi\)
\(258\) 0 0
\(259\) 485.750 0.116537
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4549.42 −1.06665 −0.533326 0.845910i \(-0.679058\pi\)
−0.533326 + 0.845910i \(0.679058\pi\)
\(264\) 0 0
\(265\) 1429.33 0.331332
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.1522 0.00660760 0.00330380 0.999995i \(-0.498948\pi\)
0.00330380 + 0.999995i \(0.498948\pi\)
\(270\) 0 0
\(271\) −7711.22 −1.72850 −0.864250 0.503063i \(-0.832206\pi\)
−0.864250 + 0.503063i \(0.832206\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1241.09 −0.272147
\(276\) 0 0
\(277\) 1127.52 0.244571 0.122286 0.992495i \(-0.460978\pi\)
0.122286 + 0.992495i \(0.460978\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1872.47 0.397517 0.198758 0.980049i \(-0.436309\pi\)
0.198758 + 0.980049i \(0.436309\pi\)
\(282\) 0 0
\(283\) −2124.48 −0.446245 −0.223123 0.974790i \(-0.571625\pi\)
−0.223123 + 0.974790i \(0.571625\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1144.65 0.235424
\(288\) 0 0
\(289\) 440.621 0.0896846
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3324.19 0.662802 0.331401 0.943490i \(-0.392479\pi\)
0.331401 + 0.943490i \(0.392479\pi\)
\(294\) 0 0
\(295\) 683.869 0.134971
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1682.44 −0.325411
\(300\) 0 0
\(301\) 1328.55 0.254407
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2447.13 −0.459417
\(306\) 0 0
\(307\) 1698.94 0.315843 0.157921 0.987452i \(-0.449521\pi\)
0.157921 + 0.987452i \(0.449521\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 6928.83 1.26334 0.631668 0.775239i \(-0.282370\pi\)
0.631668 + 0.775239i \(0.282370\pi\)
\(312\) 0 0
\(313\) −3560.75 −0.643020 −0.321510 0.946906i \(-0.604190\pi\)
−0.321510 + 0.946906i \(0.604190\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −332.750 −0.0589561 −0.0294780 0.999565i \(-0.509385\pi\)
−0.0294780 + 0.999565i \(0.509385\pi\)
\(318\) 0 0
\(319\) −2674.37 −0.469393
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5758.43 −0.991975
\(324\) 0 0
\(325\) 1694.84 0.289271
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −805.957 −0.135057
\(330\) 0 0
\(331\) 541.445 0.0899108 0.0449554 0.998989i \(-0.485685\pi\)
0.0449554 + 0.998989i \(0.485685\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3142.26 −0.512478
\(336\) 0 0
\(337\) 816.531 0.131986 0.0659930 0.997820i \(-0.478978\pi\)
0.0659930 + 0.997820i \(0.478978\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3065.89 −0.486883
\(342\) 0 0
\(343\) −3147.97 −0.495552
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6260.53 0.968539 0.484269 0.874919i \(-0.339086\pi\)
0.484269 + 0.874919i \(0.339086\pi\)
\(348\) 0 0
\(349\) −12768.5 −1.95840 −0.979198 0.202906i \(-0.934961\pi\)
−0.979198 + 0.202906i \(0.934961\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2649.28 0.399453 0.199727 0.979852i \(-0.435995\pi\)
0.199727 + 0.979852i \(0.435995\pi\)
\(354\) 0 0
\(355\) 2639.52 0.394623
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3203.91 −0.471020 −0.235510 0.971872i \(-0.575676\pi\)
−0.235510 + 0.971872i \(0.575676\pi\)
\(360\) 0 0
\(361\) −665.143 −0.0969737
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3558.26 −0.510268
\(366\) 0 0
\(367\) 8429.40 1.19894 0.599470 0.800397i \(-0.295378\pi\)
0.599470 + 0.800397i \(0.295378\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1943.62 0.271988
\(372\) 0 0
\(373\) −9388.53 −1.30327 −0.651635 0.758533i \(-0.725917\pi\)
−0.651635 + 0.758533i \(0.725917\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3652.16 0.498928
\(378\) 0 0
\(379\) 14264.5 1.93329 0.966647 0.256112i \(-0.0824415\pi\)
0.966647 + 0.256112i \(0.0824415\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 13462.2 1.79605 0.898026 0.439942i \(-0.145001\pi\)
0.898026 + 0.439942i \(0.145001\pi\)
\(384\) 0 0
\(385\) 182.098 0.0241054
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 941.881 0.122764 0.0613821 0.998114i \(-0.480449\pi\)
0.0613821 + 0.998114i \(0.480449\pi\)
\(390\) 0 0
\(391\) −8194.87 −1.05993
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1142.86 0.145578
\(396\) 0 0
\(397\) −847.839 −0.107183 −0.0535917 0.998563i \(-0.517067\pi\)
−0.0535917 + 0.998563i \(0.517067\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12203.6 −1.51975 −0.759875 0.650069i \(-0.774740\pi\)
−0.759875 + 0.650069i \(0.774740\pi\)
\(402\) 0 0
\(403\) 4186.82 0.517520
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1126.18 0.137157
\(408\) 0 0
\(409\) 8759.53 1.05900 0.529500 0.848310i \(-0.322380\pi\)
0.529500 + 0.848310i \(0.322380\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 929.934 0.110797
\(414\) 0 0
\(415\) −2639.94 −0.312264
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −11188.4 −1.30451 −0.652256 0.757999i \(-0.726177\pi\)
−0.652256 + 0.757999i \(0.726177\pi\)
\(420\) 0 0
\(421\) −14082.3 −1.63023 −0.815116 0.579298i \(-0.803327\pi\)
−0.815116 + 0.579298i \(0.803327\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8255.30 0.942214
\(426\) 0 0
\(427\) −3327.64 −0.377133
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5616.05 −0.627647 −0.313823 0.949481i \(-0.601610\pi\)
−0.313823 + 0.949481i \(0.601610\pi\)
\(432\) 0 0
\(433\) 7195.75 0.798627 0.399314 0.916814i \(-0.369248\pi\)
0.399314 + 0.916814i \(0.369248\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8814.52 0.964887
\(438\) 0 0
\(439\) −101.959 −0.0110848 −0.00554240 0.999985i \(-0.501764\pi\)
−0.00554240 + 0.999985i \(0.501764\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4953.74 0.531285 0.265642 0.964072i \(-0.414416\pi\)
0.265642 + 0.964072i \(0.414416\pi\)
\(444\) 0 0
\(445\) −1775.89 −0.189180
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11602.0 1.21945 0.609723 0.792615i \(-0.291281\pi\)
0.609723 + 0.792615i \(0.291281\pi\)
\(450\) 0 0
\(451\) 2653.81 0.277080
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −248.676 −0.0256222
\(456\) 0 0
\(457\) −3530.68 −0.361397 −0.180698 0.983539i \(-0.557836\pi\)
−0.180698 + 0.983539i \(0.557836\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −11566.3 −1.16854 −0.584271 0.811559i \(-0.698619\pi\)
−0.584271 + 0.811559i \(0.698619\pi\)
\(462\) 0 0
\(463\) −10888.5 −1.09294 −0.546470 0.837479i \(-0.684029\pi\)
−0.546470 + 0.837479i \(0.684029\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10688.0 1.05906 0.529529 0.848292i \(-0.322369\pi\)
0.529529 + 0.848292i \(0.322369\pi\)
\(468\) 0 0
\(469\) −4272.89 −0.420690
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3080.18 0.299422
\(474\) 0 0
\(475\) −8879.53 −0.857728
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2341.90 0.223391 0.111696 0.993742i \(-0.464372\pi\)
0.111696 + 0.993742i \(0.464372\pi\)
\(480\) 0 0
\(481\) −1537.93 −0.145787
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2143.57 0.200690
\(486\) 0 0
\(487\) −6748.91 −0.627972 −0.313986 0.949428i \(-0.601665\pi\)
−0.313986 + 0.949428i \(0.601665\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7361.40 0.676609 0.338305 0.941037i \(-0.390147\pi\)
0.338305 + 0.941037i \(0.390147\pi\)
\(492\) 0 0
\(493\) 17789.1 1.62511
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3589.26 0.323944
\(498\) 0 0
\(499\) −10381.7 −0.931359 −0.465680 0.884953i \(-0.654190\pi\)
−0.465680 + 0.884953i \(0.654190\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 19149.0 1.69744 0.848721 0.528840i \(-0.177373\pi\)
0.848721 + 0.528840i \(0.177373\pi\)
\(504\) 0 0
\(505\) 3544.67 0.312348
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16073.2 −1.39967 −0.699836 0.714303i \(-0.746744\pi\)
−0.699836 + 0.714303i \(0.746744\pi\)
\(510\) 0 0
\(511\) −4838.58 −0.418877
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3845.58 −0.329042
\(516\) 0 0
\(517\) −1868.56 −0.158954
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18955.3 1.59395 0.796975 0.604012i \(-0.206432\pi\)
0.796975 + 0.604012i \(0.206432\pi\)
\(522\) 0 0
\(523\) 4442.19 0.371402 0.185701 0.982606i \(-0.440544\pi\)
0.185701 + 0.982606i \(0.440544\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20393.3 1.68567
\(528\) 0 0
\(529\) 377.000 0.0309855
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3624.08 −0.294515
\(534\) 0 0
\(535\) 4806.54 0.388420
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3525.38 −0.281723
\(540\) 0 0
\(541\) 2180.90 0.173316 0.0866580 0.996238i \(-0.472381\pi\)
0.0866580 + 0.996238i \(0.472381\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1117.28 0.0878146
\(546\) 0 0
\(547\) −8225.04 −0.642920 −0.321460 0.946923i \(-0.604174\pi\)
−0.321460 + 0.946923i \(0.604174\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −19134.2 −1.47939
\(552\) 0 0
\(553\) 1554.08 0.119505
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 25181.9 1.91561 0.957804 0.287423i \(-0.0927986\pi\)
0.957804 + 0.287423i \(0.0927986\pi\)
\(558\) 0 0
\(559\) −4206.33 −0.318263
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4504.50 −0.337197 −0.168599 0.985685i \(-0.553924\pi\)
−0.168599 + 0.985685i \(0.553924\pi\)
\(564\) 0 0
\(565\) 5685.34 0.423335
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13447.0 0.990732 0.495366 0.868684i \(-0.335034\pi\)
0.495366 + 0.868684i \(0.335034\pi\)
\(570\) 0 0
\(571\) 2605.52 0.190959 0.0954795 0.995431i \(-0.469562\pi\)
0.0954795 + 0.995431i \(0.469562\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12636.5 −0.916485
\(576\) 0 0
\(577\) 6339.65 0.457406 0.228703 0.973496i \(-0.426552\pi\)
0.228703 + 0.973496i \(0.426552\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3589.83 −0.256336
\(582\) 0 0
\(583\) 4506.17 0.320114
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13370.6 −0.940140 −0.470070 0.882629i \(-0.655771\pi\)
−0.470070 + 0.882629i \(0.655771\pi\)
\(588\) 0 0
\(589\) −21935.3 −1.53452
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14319.3 −0.991608 −0.495804 0.868434i \(-0.665127\pi\)
−0.495804 + 0.868434i \(0.665127\pi\)
\(594\) 0 0
\(595\) −1211.26 −0.0834567
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5788.63 −0.394853 −0.197427 0.980318i \(-0.563258\pi\)
−0.197427 + 0.980318i \(0.563258\pi\)
\(600\) 0 0
\(601\) 23968.1 1.62675 0.813375 0.581739i \(-0.197628\pi\)
0.813375 + 0.581739i \(0.197628\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 422.184 0.0283706
\(606\) 0 0
\(607\) 23526.6 1.57317 0.786585 0.617482i \(-0.211847\pi\)
0.786585 + 0.617482i \(0.211847\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2551.74 0.168956
\(612\) 0 0
\(613\) 1228.07 0.0809159 0.0404579 0.999181i \(-0.487118\pi\)
0.0404579 + 0.999181i \(0.487118\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9844.90 0.642368 0.321184 0.947017i \(-0.395919\pi\)
0.321184 + 0.947017i \(0.395919\pi\)
\(618\) 0 0
\(619\) 6551.68 0.425419 0.212709 0.977115i \(-0.431771\pi\)
0.212709 + 0.977115i \(0.431771\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2414.88 −0.155297
\(624\) 0 0
\(625\) 11208.0 0.717309
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7491.01 −0.474859
\(630\) 0 0
\(631\) 26440.5 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7994.48 −0.499608
\(636\) 0 0
\(637\) 4814.31 0.299450
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 27927.2 1.72084 0.860421 0.509584i \(-0.170201\pi\)
0.860421 + 0.509584i \(0.170201\pi\)
\(642\) 0 0
\(643\) 16737.7 1.02655 0.513274 0.858225i \(-0.328432\pi\)
0.513274 + 0.858225i \(0.328432\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7818.70 0.475092 0.237546 0.971376i \(-0.423657\pi\)
0.237546 + 0.971376i \(0.423657\pi\)
\(648\) 0 0
\(649\) 2156.00 0.130401
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19747.6 −1.18344 −0.591719 0.806144i \(-0.701550\pi\)
−0.591719 + 0.806144i \(0.701550\pi\)
\(654\) 0 0
\(655\) −4003.47 −0.238822
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7867.72 0.465072 0.232536 0.972588i \(-0.425298\pi\)
0.232536 + 0.972588i \(0.425298\pi\)
\(660\) 0 0
\(661\) 4227.41 0.248755 0.124378 0.992235i \(-0.460307\pi\)
0.124378 + 0.992235i \(0.460307\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1302.85 0.0759733
\(666\) 0 0
\(667\) −27230.0 −1.58073
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7714.94 −0.443863
\(672\) 0 0
\(673\) 29397.6 1.68379 0.841897 0.539638i \(-0.181439\pi\)
0.841897 + 0.539638i \(0.181439\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5737.14 −0.325696 −0.162848 0.986651i \(-0.552068\pi\)
−0.162848 + 0.986651i \(0.552068\pi\)
\(678\) 0 0
\(679\) 2914.86 0.164745
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 32097.6 1.79821 0.899107 0.437729i \(-0.144217\pi\)
0.899107 + 0.437729i \(0.144217\pi\)
\(684\) 0 0
\(685\) −4426.30 −0.246891
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6153.69 −0.340257
\(690\) 0 0
\(691\) 16456.2 0.905965 0.452983 0.891519i \(-0.350360\pi\)
0.452983 + 0.891519i \(0.350360\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1696.72 0.0926047
\(696\) 0 0
\(697\) −17652.3 −0.959294
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27238.1 −1.46758 −0.733788 0.679379i \(-0.762249\pi\)
−0.733788 + 0.679379i \(0.762249\pi\)
\(702\) 0 0
\(703\) 8057.44 0.432279
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4820.09 0.256405
\(708\) 0 0
\(709\) 28761.4 1.52349 0.761747 0.647875i \(-0.224342\pi\)
0.761747 + 0.647875i \(0.224342\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −31216.3 −1.63964
\(714\) 0 0
\(715\) −576.540 −0.0301558
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −27272.0 −1.41456 −0.707282 0.706931i \(-0.750079\pi\)
−0.707282 + 0.706931i \(0.750079\pi\)
\(720\) 0 0
\(721\) −5229.28 −0.270109
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 27430.8 1.40518
\(726\) 0 0
\(727\) −3979.75 −0.203027 −0.101514 0.994834i \(-0.532369\pi\)
−0.101514 + 0.994834i \(0.532369\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −20488.3 −1.03665
\(732\) 0 0
\(733\) 9342.48 0.470767 0.235384 0.971903i \(-0.424365\pi\)
0.235384 + 0.971903i \(0.424365\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9906.45 −0.495127
\(738\) 0 0
\(739\) 28928.0 1.43997 0.719983 0.693992i \(-0.244150\pi\)
0.719983 + 0.693992i \(0.244150\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4857.04 0.239822 0.119911 0.992785i \(-0.461739\pi\)
0.119911 + 0.992785i \(0.461739\pi\)
\(744\) 0 0
\(745\) −8213.80 −0.403933
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6536.00 0.318852
\(750\) 0 0
\(751\) −14355.4 −0.697517 −0.348759 0.937213i \(-0.613397\pi\)
−0.348759 + 0.937213i \(0.613397\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1989.05 0.0958792
\(756\) 0 0
\(757\) −17714.9 −0.850538 −0.425269 0.905067i \(-0.639821\pi\)
−0.425269 + 0.905067i \(0.639821\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7945.82 0.378497 0.189248 0.981929i \(-0.439395\pi\)
0.189248 + 0.981929i \(0.439395\pi\)
\(762\) 0 0
\(763\) 1519.29 0.0720866
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2944.26 −0.138606
\(768\) 0 0
\(769\) 27308.1 1.28057 0.640284 0.768139i \(-0.278817\pi\)
0.640284 + 0.768139i \(0.278817\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 18872.6 0.878136 0.439068 0.898454i \(-0.355309\pi\)
0.439068 + 0.898454i \(0.355309\pi\)
\(774\) 0 0
\(775\) 31446.6 1.45754
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18987.1 0.873276
\(780\) 0 0
\(781\) 8321.50 0.381263
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7231.82 −0.328808
\(786\) 0 0
\(787\) 14512.1 0.657307 0.328654 0.944450i \(-0.393405\pi\)
0.328654 + 0.944450i \(0.393405\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7731.01 0.347513
\(792\) 0 0
\(793\) 10535.6 0.471792
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −29108.9 −1.29371 −0.646856 0.762612i \(-0.723917\pi\)
−0.646856 + 0.762612i \(0.723917\pi\)
\(798\) 0 0
\(799\) 12429.1 0.550325
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −11218.0 −0.492993
\(804\) 0 0
\(805\) 1854.09 0.0811777
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 3000.83 0.130413 0.0652063 0.997872i \(-0.479229\pi\)
0.0652063 + 0.997872i \(0.479229\pi\)
\(810\) 0 0
\(811\) −6239.39 −0.270154 −0.135077 0.990835i \(-0.543128\pi\)
−0.135077 + 0.990835i \(0.543128\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −9338.68 −0.401374
\(816\) 0 0
\(817\) 22037.6 0.943693
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −14922.4 −0.634342 −0.317171 0.948368i \(-0.602733\pi\)
−0.317171 + 0.948368i \(0.602733\pi\)
\(822\) 0 0
\(823\) 25737.8 1.09011 0.545057 0.838399i \(-0.316508\pi\)
0.545057 + 0.838399i \(0.316508\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 27043.4 1.13711 0.568555 0.822645i \(-0.307503\pi\)
0.568555 + 0.822645i \(0.307503\pi\)
\(828\) 0 0
\(829\) −9795.41 −0.410384 −0.205192 0.978722i \(-0.565782\pi\)
−0.205192 + 0.978722i \(0.565782\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 23449.7 0.975370
\(834\) 0 0
\(835\) −4145.50 −0.171809
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 28875.5 1.18819 0.594095 0.804395i \(-0.297510\pi\)
0.594095 + 0.804395i \(0.297510\pi\)
\(840\) 0 0
\(841\) 34720.7 1.42362
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −6878.28 −0.280024
\(846\) 0 0
\(847\) 574.092 0.0232893
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 11466.6 0.461892
\(852\) 0 0
\(853\) −47157.1 −1.89288 −0.946441 0.322878i \(-0.895350\pi\)
−0.946441 + 0.322878i \(0.895350\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −5021.31 −0.200145 −0.100073 0.994980i \(-0.531908\pi\)
−0.100073 + 0.994980i \(0.531908\pi\)
\(858\) 0 0
\(859\) 22921.1 0.910428 0.455214 0.890382i \(-0.349563\pi\)
0.455214 + 0.890382i \(0.349563\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −19488.1 −0.768693 −0.384347 0.923189i \(-0.625573\pi\)
−0.384347 + 0.923189i \(0.625573\pi\)
\(864\) 0 0
\(865\) −2816.24 −0.110699
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3603.04 0.140650
\(870\) 0 0
\(871\) 13528.4 0.526282
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3937.06 −0.152111
\(876\) 0 0
\(877\) −8455.67 −0.325573 −0.162787 0.986661i \(-0.552048\pi\)
−0.162787 + 0.986661i \(0.552048\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 11291.2 0.431794 0.215897 0.976416i \(-0.430732\pi\)
0.215897 + 0.976416i \(0.430732\pi\)
\(882\) 0 0
\(883\) −31818.1 −1.21264 −0.606322 0.795219i \(-0.707356\pi\)
−0.606322 + 0.795219i \(0.707356\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 17481.1 0.661732 0.330866 0.943678i \(-0.392659\pi\)
0.330866 + 0.943678i \(0.392659\pi\)
\(888\) 0 0
\(889\) −10871.0 −0.410126
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −13368.9 −0.500978
\(894\) 0 0
\(895\) −6805.16 −0.254158
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 67763.1 2.51393
\(900\) 0 0
\(901\) −29973.6 −1.10829
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3704.08 0.136053
\(906\) 0 0
\(907\) −10607.4 −0.388326 −0.194163 0.980969i \(-0.562199\pi\)
−0.194163 + 0.980969i \(0.562199\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −41249.2 −1.50016 −0.750080 0.661347i \(-0.769985\pi\)
−0.750080 + 0.661347i \(0.769985\pi\)
\(912\) 0 0
\(913\) −8322.81 −0.301692
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −5443.97 −0.196048
\(918\) 0 0
\(919\) 13858.1 0.497429 0.248714 0.968577i \(-0.419992\pi\)
0.248714 + 0.968577i \(0.419992\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −11363.9 −0.405253
\(924\) 0 0
\(925\) −11551.2 −0.410595
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −20893.7 −0.737890 −0.368945 0.929451i \(-0.620281\pi\)
−0.368945 + 0.929451i \(0.620281\pi\)
\(930\) 0 0
\(931\) −25222.8 −0.887911
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2808.23 −0.0982236
\(936\) 0 0
\(937\) 3203.52 0.111691 0.0558454 0.998439i \(-0.482215\pi\)
0.0558454 + 0.998439i \(0.482215\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −19951.6 −0.691182 −0.345591 0.938385i \(-0.612322\pi\)
−0.345591 + 0.938385i \(0.612322\pi\)
\(942\) 0 0
\(943\) 27020.6 0.933099
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −38216.7 −1.31138 −0.655689 0.755031i \(-0.727622\pi\)
−0.655689 + 0.755031i \(0.727622\pi\)
\(948\) 0 0
\(949\) 15319.4 0.524014
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 47661.4 1.62004 0.810022 0.586399i \(-0.199455\pi\)
0.810022 + 0.586399i \(0.199455\pi\)
\(954\) 0 0
\(955\) 7454.21 0.252579
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6018.94 −0.202671
\(960\) 0 0
\(961\) 47892.3 1.60761
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 13774.2 0.459490
\(966\) 0 0
\(967\) −18933.2 −0.629628 −0.314814 0.949153i \(-0.601942\pi\)
−0.314814 + 0.949153i \(0.601942\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −40660.3 −1.34382 −0.671911 0.740632i \(-0.734526\pi\)
−0.671911 + 0.740632i \(0.734526\pi\)
\(972\) 0 0
\(973\) 2307.23 0.0760188
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 22502.8 0.736876 0.368438 0.929652i \(-0.379893\pi\)
0.368438 + 0.929652i \(0.379893\pi\)
\(978\) 0 0
\(979\) −5598.76 −0.182775
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4435.20 −0.143907 −0.0719536 0.997408i \(-0.522923\pi\)
−0.0719536 + 0.997408i \(0.522923\pi\)
\(984\) 0 0
\(985\) −3223.55 −0.104275
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 31361.8 1.00834
\(990\) 0 0
\(991\) −7362.76 −0.236010 −0.118005 0.993013i \(-0.537650\pi\)
−0.118005 + 0.993013i \(0.537650\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1661.35 0.0529331
\(996\) 0 0
\(997\) −53480.1 −1.69883 −0.849413 0.527728i \(-0.823044\pi\)
−0.849413 + 0.527728i \(0.823044\pi\)
\(998\) 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 1584.4.a.x.1.2 2
3.2 odd 2 528.4.a.o.1.1 2
4.3 odd 2 99.4.a.e.1.1 2
12.11 even 2 33.4.a.d.1.2 2
20.19 odd 2 2475.4.a.o.1.2 2
24.5 odd 2 2112.4.a.bh.1.2 2
24.11 even 2 2112.4.a.ba.1.2 2
44.43 even 2 1089.4.a.t.1.2 2
60.23 odd 4 825.4.c.i.199.1 4
60.47 odd 4 825.4.c.i.199.4 4
60.59 even 2 825.4.a.k.1.1 2
84.83 odd 2 1617.4.a.j.1.2 2
132.131 odd 2 363.4.a.j.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.a.d.1.2 2 12.11 even 2
99.4.a.e.1.1 2 4.3 odd 2
363.4.a.j.1.1 2 132.131 odd 2
528.4.a.o.1.1 2 3.2 odd 2
825.4.a.k.1.1 2 60.59 even 2
825.4.c.i.199.1 4 60.23 odd 4
825.4.c.i.199.4 4 60.47 odd 4
1089.4.a.t.1.2 2 44.43 even 2
1584.4.a.x.1.2 2 1.1 even 1 trivial
1617.4.a.j.1.2 2 84.83 odd 2
2112.4.a.ba.1.2 2 24.11 even 2
2112.4.a.bh.1.2 2 24.5 odd 2
2475.4.a.o.1.2 2 20.19 odd 2