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Properties

Label 576.4.a.e.1.1
Level $576$
Weight $4$
Character 576.1
Self dual yes
Analytic conductor $33.985$
Analytic rank $0$
Dimension $1$
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] = [576,4,Mod(1,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("576.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.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: \(33.9851001633\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 96)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-14.0000 q^{5} -36.0000 q^{7} +O(q^{10})\) \(q-14.0000 q^{5} -36.0000 q^{7} -36.0000 q^{11} -54.0000 q^{13} +22.0000 q^{17} -36.0000 q^{19} +144.000 q^{23} +71.0000 q^{25} +50.0000 q^{29} -108.000 q^{31} +504.000 q^{35} -214.000 q^{37} +446.000 q^{41} -252.000 q^{43} -72.0000 q^{47} +953.000 q^{49} -22.0000 q^{53} +504.000 q^{55} -684.000 q^{59} +466.000 q^{61} +756.000 q^{65} +180.000 q^{67} -576.000 q^{71} -54.0000 q^{73} +1296.00 q^{77} -972.000 q^{79} -684.000 q^{83} -308.000 q^{85} -346.000 q^{89} +1944.00 q^{91} +504.000 q^{95} -1134.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −14.0000 −1.25220 −0.626099 − 0.779744i \(-0.715349\pi\)
−0.626099 + 0.779744i \(0.715349\pi\)
\(6\) 0 0
\(7\) −36.0000 −1.94382 −0.971909 − 0.235358i \(-0.924374\pi\)
−0.971909 + 0.235358i \(0.924374\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −36.0000 −0.986764 −0.493382 − 0.869813i \(-0.664240\pi\)
−0.493382 + 0.869813i \(0.664240\pi\)
\(12\) 0 0
\(13\) −54.0000 −1.15207 −0.576035 − 0.817425i \(-0.695401\pi\)
−0.576035 + 0.817425i \(0.695401\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 22.0000 0.313870 0.156935 − 0.987609i \(-0.449839\pi\)
0.156935 + 0.987609i \(0.449839\pi\)
\(18\) 0 0
\(19\) −36.0000 −0.434682 −0.217341 − 0.976096i \(-0.569738\pi\)
−0.217341 + 0.976096i \(0.569738\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 144.000 1.30548 0.652741 − 0.757581i \(-0.273619\pi\)
0.652741 + 0.757581i \(0.273619\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 50.0000 0.320164 0.160082 − 0.987104i \(-0.448824\pi\)
0.160082 + 0.987104i \(0.448824\pi\)
\(30\) 0 0
\(31\) −108.000 −0.625722 −0.312861 − 0.949799i \(-0.601287\pi\)
−0.312861 + 0.949799i \(0.601287\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 504.000 2.43404
\(36\) 0 0
\(37\) −214.000 −0.950848 −0.475424 − 0.879757i \(-0.657705\pi\)
−0.475424 + 0.879757i \(0.657705\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 446.000 1.69887 0.849433 − 0.527697i \(-0.176944\pi\)
0.849433 + 0.527697i \(0.176944\pi\)
\(42\) 0 0
\(43\) −252.000 −0.893713 −0.446856 − 0.894606i \(-0.647456\pi\)
−0.446856 + 0.894606i \(0.647456\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −72.0000 −0.223453 −0.111726 − 0.993739i \(-0.535638\pi\)
−0.111726 + 0.993739i \(0.535638\pi\)
\(48\) 0 0
\(49\) 953.000 2.77843
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −22.0000 −0.0570176 −0.0285088 − 0.999594i \(-0.509076\pi\)
−0.0285088 + 0.999594i \(0.509076\pi\)
\(54\) 0 0
\(55\) 504.000 1.23562
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −684.000 −1.50931 −0.754654 − 0.656123i \(-0.772195\pi\)
−0.754654 + 0.656123i \(0.772195\pi\)
\(60\) 0 0
\(61\) 466.000 0.978118 0.489059 − 0.872251i \(-0.337340\pi\)
0.489059 + 0.872251i \(0.337340\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 756.000 1.44262
\(66\) 0 0
\(67\) 180.000 0.328216 0.164108 − 0.986442i \(-0.447525\pi\)
0.164108 + 0.986442i \(0.447525\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −576.000 −0.962798 −0.481399 − 0.876502i \(-0.659871\pi\)
−0.481399 + 0.876502i \(0.659871\pi\)
\(72\) 0 0
\(73\) −54.0000 −0.0865784 −0.0432892 − 0.999063i \(-0.513784\pi\)
−0.0432892 + 0.999063i \(0.513784\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1296.00 1.91809
\(78\) 0 0
\(79\) −972.000 −1.38429 −0.692143 − 0.721761i \(-0.743333\pi\)
−0.692143 + 0.721761i \(0.743333\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −684.000 −0.904563 −0.452282 − 0.891875i \(-0.649390\pi\)
−0.452282 + 0.891875i \(0.649390\pi\)
\(84\) 0 0
\(85\) −308.000 −0.393027
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −346.000 −0.412089 −0.206045 − 0.978543i \(-0.566059\pi\)
−0.206045 + 0.978543i \(0.566059\pi\)
\(90\) 0 0
\(91\) 1944.00 2.23941
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 504.000 0.544309
\(96\) 0 0
\(97\) −1134.00 −1.18701 −0.593506 − 0.804829i \(-0.702257\pi\)
−0.593506 + 0.804829i \(0.702257\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 58.0000 0.0571407 0.0285704 − 0.999592i \(-0.490905\pi\)
0.0285704 + 0.999592i \(0.490905\pi\)
\(102\) 0 0
\(103\) 1332.00 1.27423 0.637116 − 0.770768i \(-0.280127\pi\)
0.637116 + 0.770768i \(0.280127\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −396.000 −0.357783 −0.178891 − 0.983869i \(-0.557251\pi\)
−0.178891 + 0.983869i \(0.557251\pi\)
\(108\) 0 0
\(109\) 1242.00 1.09139 0.545697 − 0.837982i \(-0.316265\pi\)
0.545697 + 0.837982i \(0.316265\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 446.000 0.371293 0.185647 − 0.982617i \(-0.440562\pi\)
0.185647 + 0.982617i \(0.440562\pi\)
\(114\) 0 0
\(115\) −2016.00 −1.63472
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −792.000 −0.610105
\(120\) 0 0
\(121\) −35.0000 −0.0262960
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 756.000 0.540950
\(126\) 0 0
\(127\) 1116.00 0.779756 0.389878 − 0.920867i \(-0.372517\pi\)
0.389878 + 0.920867i \(0.372517\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2700.00 1.80076 0.900382 − 0.435100i \(-0.143287\pi\)
0.900382 + 0.435100i \(0.143287\pi\)
\(132\) 0 0
\(133\) 1296.00 0.844943
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1678.00 1.04643 0.523216 − 0.852200i \(-0.324732\pi\)
0.523216 + 0.852200i \(0.324732\pi\)
\(138\) 0 0
\(139\) −36.0000 −0.0219675 −0.0109837 − 0.999940i \(-0.503496\pi\)
−0.0109837 + 0.999940i \(0.503496\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1944.00 1.13682
\(144\) 0 0
\(145\) −700.000 −0.400909
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1634.00 0.898406 0.449203 − 0.893430i \(-0.351708\pi\)
0.449203 + 0.893430i \(0.351708\pi\)
\(150\) 0 0
\(151\) −1908.00 −1.02828 −0.514142 − 0.857705i \(-0.671890\pi\)
−0.514142 + 0.857705i \(0.671890\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1512.00 0.783528
\(156\) 0 0
\(157\) 2306.00 1.17222 0.586111 − 0.810231i \(-0.300658\pi\)
0.586111 + 0.810231i \(0.300658\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5184.00 −2.53762
\(162\) 0 0
\(163\) −1476.00 −0.709259 −0.354630 − 0.935007i \(-0.615393\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2808.00 −1.30114 −0.650568 − 0.759448i \(-0.725469\pi\)
−0.650568 + 0.759448i \(0.725469\pi\)
\(168\) 0 0
\(169\) 719.000 0.327264
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 58.0000 0.0254894 0.0127447 − 0.999919i \(-0.495943\pi\)
0.0127447 + 0.999919i \(0.495943\pi\)
\(174\) 0 0
\(175\) −2556.00 −1.10409
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3492.00 −1.45812 −0.729062 − 0.684447i \(-0.760044\pi\)
−0.729062 + 0.684447i \(0.760044\pi\)
\(180\) 0 0
\(181\) 162.000 0.0665269 0.0332634 − 0.999447i \(-0.489410\pi\)
0.0332634 + 0.999447i \(0.489410\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2996.00 1.19065
\(186\) 0 0
\(187\) −792.000 −0.309715
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2880.00 1.09104 0.545522 − 0.838096i \(-0.316331\pi\)
0.545522 + 0.838096i \(0.316331\pi\)
\(192\) 0 0
\(193\) −2414.00 −0.900329 −0.450165 − 0.892946i \(-0.648635\pi\)
−0.450165 + 0.892946i \(0.648635\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2678.00 −0.968526 −0.484263 − 0.874923i \(-0.660912\pi\)
−0.484263 + 0.874923i \(0.660912\pi\)
\(198\) 0 0
\(199\) −828.000 −0.294952 −0.147476 − 0.989066i \(-0.547115\pi\)
−0.147476 + 0.989066i \(0.547115\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1800.00 −0.622341
\(204\) 0 0
\(205\) −6244.00 −2.12732
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1296.00 0.428929
\(210\) 0 0
\(211\) 1476.00 0.481574 0.240787 − 0.970578i \(-0.422595\pi\)
0.240787 + 0.970578i \(0.422595\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3528.00 1.11911
\(216\) 0 0
\(217\) 3888.00 1.21629
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1188.00 −0.361600
\(222\) 0 0
\(223\) 1260.00 0.378367 0.189183 − 0.981942i \(-0.439416\pi\)
0.189183 + 0.981942i \(0.439416\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3060.00 0.894711 0.447355 − 0.894356i \(-0.352366\pi\)
0.447355 + 0.894356i \(0.352366\pi\)
\(228\) 0 0
\(229\) −1566.00 −0.451896 −0.225948 − 0.974139i \(-0.572548\pi\)
−0.225948 + 0.974139i \(0.572548\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3434.00 −0.965531 −0.482766 − 0.875750i \(-0.660368\pi\)
−0.482766 + 0.875750i \(0.660368\pi\)
\(234\) 0 0
\(235\) 1008.00 0.279807
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1440.00 −0.389732 −0.194866 − 0.980830i \(-0.562427\pi\)
−0.194866 + 0.980830i \(0.562427\pi\)
\(240\) 0 0
\(241\) −270.000 −0.0721669 −0.0360835 − 0.999349i \(-0.511488\pi\)
−0.0360835 + 0.999349i \(0.511488\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −13342.0 −3.47914
\(246\) 0 0
\(247\) 1944.00 0.500784
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3564.00 0.896246 0.448123 − 0.893972i \(-0.352093\pi\)
0.448123 + 0.893972i \(0.352093\pi\)
\(252\) 0 0
\(253\) −5184.00 −1.28820
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7682.00 −1.86455 −0.932276 − 0.361747i \(-0.882180\pi\)
−0.932276 + 0.361747i \(0.882180\pi\)
\(258\) 0 0
\(259\) 7704.00 1.84828
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1368.00 −0.320740 −0.160370 − 0.987057i \(-0.551269\pi\)
−0.160370 + 0.987057i \(0.551269\pi\)
\(264\) 0 0
\(265\) 308.000 0.0713973
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4450.00 1.00863 0.504315 − 0.863520i \(-0.331745\pi\)
0.504315 + 0.863520i \(0.331745\pi\)
\(270\) 0 0
\(271\) 3420.00 0.766606 0.383303 − 0.923623i \(-0.374787\pi\)
0.383303 + 0.923623i \(0.374787\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2556.00 −0.560482
\(276\) 0 0
\(277\) −7614.00 −1.65156 −0.825778 − 0.563996i \(-0.809264\pi\)
−0.825778 + 0.563996i \(0.809264\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6422.00 1.36336 0.681680 − 0.731650i \(-0.261249\pi\)
0.681680 + 0.731650i \(0.261249\pi\)
\(282\) 0 0
\(283\) −5364.00 −1.12670 −0.563351 − 0.826218i \(-0.690488\pi\)
−0.563351 + 0.826218i \(0.690488\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −16056.0 −3.30228
\(288\) 0 0
\(289\) −4429.00 −0.901486
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 122.000 0.0243253 0.0121627 − 0.999926i \(-0.496128\pi\)
0.0121627 + 0.999926i \(0.496128\pi\)
\(294\) 0 0
\(295\) 9576.00 1.88995
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7776.00 −1.50401
\(300\) 0 0
\(301\) 9072.00 1.73721
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6524.00 −1.22480
\(306\) 0 0
\(307\) −6876.00 −1.27829 −0.639143 − 0.769088i \(-0.720711\pi\)
−0.639143 + 0.769088i \(0.720711\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9288.00 1.69349 0.846743 − 0.532002i \(-0.178560\pi\)
0.846743 + 0.532002i \(0.178560\pi\)
\(312\) 0 0
\(313\) 2234.00 0.403429 0.201714 − 0.979444i \(-0.435349\pi\)
0.201714 + 0.979444i \(0.435349\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3614.00 −0.640323 −0.320162 − 0.947363i \(-0.603737\pi\)
−0.320162 + 0.947363i \(0.603737\pi\)
\(318\) 0 0
\(319\) −1800.00 −0.315927
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −792.000 −0.136434
\(324\) 0 0
\(325\) −3834.00 −0.654376
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2592.00 0.434351
\(330\) 0 0
\(331\) 684.000 0.113583 0.0567916 − 0.998386i \(-0.481913\pi\)
0.0567916 + 0.998386i \(0.481913\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2520.00 −0.410992
\(336\) 0 0
\(337\) 10530.0 1.70209 0.851047 − 0.525090i \(-0.175968\pi\)
0.851047 + 0.525090i \(0.175968\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3888.00 0.617440
\(342\) 0 0
\(343\) −21960.0 −3.45693
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1548.00 0.239484 0.119742 − 0.992805i \(-0.461793\pi\)
0.119742 + 0.992805i \(0.461793\pi\)
\(348\) 0 0
\(349\) 4786.00 0.734065 0.367033 − 0.930208i \(-0.380374\pi\)
0.367033 + 0.930208i \(0.380374\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6638.00 1.00086 0.500432 − 0.865776i \(-0.333174\pi\)
0.500432 + 0.865776i \(0.333174\pi\)
\(354\) 0 0
\(355\) 8064.00 1.20561
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4320.00 0.635100 0.317550 − 0.948242i \(-0.397140\pi\)
0.317550 + 0.948242i \(0.397140\pi\)
\(360\) 0 0
\(361\) −5563.00 −0.811051
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 756.000 0.108413
\(366\) 0 0
\(367\) 2340.00 0.332826 0.166413 − 0.986056i \(-0.446782\pi\)
0.166413 + 0.986056i \(0.446782\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 792.000 0.110832
\(372\) 0 0
\(373\) 3850.00 0.534438 0.267219 − 0.963636i \(-0.413895\pi\)
0.267219 + 0.963636i \(0.413895\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2700.00 −0.368852
\(378\) 0 0
\(379\) 2052.00 0.278111 0.139056 − 0.990285i \(-0.455593\pi\)
0.139056 + 0.990285i \(0.455593\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9504.00 1.26797 0.633984 − 0.773346i \(-0.281419\pi\)
0.633984 + 0.773346i \(0.281419\pi\)
\(384\) 0 0
\(385\) −18144.0 −2.40183
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7726.00 −1.00700 −0.503501 − 0.863995i \(-0.667955\pi\)
−0.503501 + 0.863995i \(0.667955\pi\)
\(390\) 0 0
\(391\) 3168.00 0.409751
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 13608.0 1.73340
\(396\) 0 0
\(397\) 9826.00 1.24220 0.621099 − 0.783732i \(-0.286686\pi\)
0.621099 + 0.783732i \(0.286686\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13082.0 −1.62914 −0.814568 − 0.580067i \(-0.803026\pi\)
−0.814568 + 0.580067i \(0.803026\pi\)
\(402\) 0 0
\(403\) 5832.00 0.720875
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7704.00 0.938263
\(408\) 0 0
\(409\) 6426.00 0.776883 0.388442 − 0.921473i \(-0.373014\pi\)
0.388442 + 0.921473i \(0.373014\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24624.0 2.93382
\(414\) 0 0
\(415\) 9576.00 1.13269
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6444.00 −0.751337 −0.375668 − 0.926754i \(-0.622587\pi\)
−0.375668 + 0.926754i \(0.622587\pi\)
\(420\) 0 0
\(421\) 2322.00 0.268806 0.134403 − 0.990927i \(-0.457088\pi\)
0.134403 + 0.990927i \(0.457088\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1562.00 0.178278
\(426\) 0 0
\(427\) −16776.0 −1.90128
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16488.0 1.84269 0.921345 − 0.388747i \(-0.127092\pi\)
0.921345 + 0.388747i \(0.127092\pi\)
\(432\) 0 0
\(433\) −3566.00 −0.395776 −0.197888 − 0.980225i \(-0.563408\pi\)
−0.197888 + 0.980225i \(0.563408\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5184.00 −0.567470
\(438\) 0 0
\(439\) −6588.00 −0.716237 −0.358119 − 0.933676i \(-0.616582\pi\)
−0.358119 + 0.933676i \(0.616582\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9900.00 1.06177 0.530884 − 0.847445i \(-0.321860\pi\)
0.530884 + 0.847445i \(0.321860\pi\)
\(444\) 0 0
\(445\) 4844.00 0.516017
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1382.00 0.145257 0.0726287 − 0.997359i \(-0.476861\pi\)
0.0726287 + 0.997359i \(0.476861\pi\)
\(450\) 0 0
\(451\) −16056.0 −1.67638
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −27216.0 −2.80419
\(456\) 0 0
\(457\) −13878.0 −1.42054 −0.710269 − 0.703931i \(-0.751426\pi\)
−0.710269 + 0.703931i \(0.751426\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7610.00 0.768835 0.384418 − 0.923159i \(-0.374402\pi\)
0.384418 + 0.923159i \(0.374402\pi\)
\(462\) 0 0
\(463\) −8388.00 −0.841951 −0.420976 − 0.907072i \(-0.638312\pi\)
−0.420976 + 0.907072i \(0.638312\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1116.00 −0.110583 −0.0552916 − 0.998470i \(-0.517609\pi\)
−0.0552916 + 0.998470i \(0.517609\pi\)
\(468\) 0 0
\(469\) −6480.00 −0.637993
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9072.00 0.881884
\(474\) 0 0
\(475\) −2556.00 −0.246900
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15048.0 −1.43541 −0.717704 − 0.696348i \(-0.754807\pi\)
−0.717704 + 0.696348i \(0.754807\pi\)
\(480\) 0 0
\(481\) 11556.0 1.09544
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 15876.0 1.48638
\(486\) 0 0
\(487\) 6300.00 0.586202 0.293101 − 0.956082i \(-0.405313\pi\)
0.293101 + 0.956082i \(0.405313\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9684.00 0.890087 0.445044 − 0.895509i \(-0.353188\pi\)
0.445044 + 0.895509i \(0.353188\pi\)
\(492\) 0 0
\(493\) 1100.00 0.100490
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20736.0 1.87150
\(498\) 0 0
\(499\) 14436.0 1.29508 0.647539 − 0.762032i \(-0.275798\pi\)
0.647539 + 0.762032i \(0.275798\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1008.00 −0.0893529 −0.0446764 − 0.999002i \(-0.514226\pi\)
−0.0446764 + 0.999002i \(0.514226\pi\)
\(504\) 0 0
\(505\) −812.000 −0.0715515
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3550.00 −0.309137 −0.154569 − 0.987982i \(-0.549399\pi\)
−0.154569 + 0.987982i \(0.549399\pi\)
\(510\) 0 0
\(511\) 1944.00 0.168293
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −18648.0 −1.59559
\(516\) 0 0
\(517\) 2592.00 0.220495
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12766.0 1.07349 0.536745 − 0.843744i \(-0.319654\pi\)
0.536745 + 0.843744i \(0.319654\pi\)
\(522\) 0 0
\(523\) 20628.0 1.72466 0.862332 − 0.506343i \(-0.169003\pi\)
0.862332 + 0.506343i \(0.169003\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2376.00 −0.196395
\(528\) 0 0
\(529\) 8569.00 0.704282
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −24084.0 −1.95721
\(534\) 0 0
\(535\) 5544.00 0.448015
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −34308.0 −2.74165
\(540\) 0 0
\(541\) 6858.00 0.545006 0.272503 − 0.962155i \(-0.412148\pi\)
0.272503 + 0.962155i \(0.412148\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −17388.0 −1.36664
\(546\) 0 0
\(547\) −15444.0 −1.20720 −0.603599 − 0.797288i \(-0.706267\pi\)
−0.603599 + 0.797288i \(0.706267\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1800.00 −0.139170
\(552\) 0 0
\(553\) 34992.0 2.69080
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12938.0 0.984202 0.492101 − 0.870538i \(-0.336229\pi\)
0.492101 + 0.870538i \(0.336229\pi\)
\(558\) 0 0
\(559\) 13608.0 1.02962
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 17748.0 1.32858 0.664289 − 0.747476i \(-0.268735\pi\)
0.664289 + 0.747476i \(0.268735\pi\)
\(564\) 0 0
\(565\) −6244.00 −0.464933
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10318.0 0.760199 0.380099 − 0.924946i \(-0.375890\pi\)
0.380099 + 0.924946i \(0.375890\pi\)
\(570\) 0 0
\(571\) 14652.0 1.07385 0.536924 − 0.843631i \(-0.319586\pi\)
0.536924 + 0.843631i \(0.319586\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10224.0 0.741514
\(576\) 0 0
\(577\) 18578.0 1.34040 0.670201 − 0.742179i \(-0.266208\pi\)
0.670201 + 0.742179i \(0.266208\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 24624.0 1.75831
\(582\) 0 0
\(583\) 792.000 0.0562629
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1620.00 0.113909 0.0569545 − 0.998377i \(-0.481861\pi\)
0.0569545 + 0.998377i \(0.481861\pi\)
\(588\) 0 0
\(589\) 3888.00 0.271990
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4126.00 0.285724 0.142862 − 0.989743i \(-0.454369\pi\)
0.142862 + 0.989743i \(0.454369\pi\)
\(594\) 0 0
\(595\) 11088.0 0.763973
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16992.0 1.15906 0.579528 − 0.814952i \(-0.303237\pi\)
0.579528 + 0.814952i \(0.303237\pi\)
\(600\) 0 0
\(601\) −11846.0 −0.804007 −0.402004 − 0.915638i \(-0.631686\pi\)
−0.402004 + 0.915638i \(0.631686\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 490.000 0.0329278
\(606\) 0 0
\(607\) −8676.00 −0.580145 −0.290072 − 0.957005i \(-0.593679\pi\)
−0.290072 + 0.957005i \(0.593679\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3888.00 0.257433
\(612\) 0 0
\(613\) 9178.00 0.604724 0.302362 − 0.953193i \(-0.402225\pi\)
0.302362 + 0.953193i \(0.402225\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16646.0 1.08613 0.543065 − 0.839690i \(-0.317264\pi\)
0.543065 + 0.839690i \(0.317264\pi\)
\(618\) 0 0
\(619\) 10044.0 0.652185 0.326092 − 0.945338i \(-0.394268\pi\)
0.326092 + 0.945338i \(0.394268\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12456.0 0.801026
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4708.00 −0.298442
\(630\) 0 0
\(631\) −1620.00 −0.102205 −0.0511024 − 0.998693i \(-0.516273\pi\)
−0.0511024 + 0.998693i \(0.516273\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −15624.0 −0.976409
\(636\) 0 0
\(637\) −51462.0 −3.20094
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7078.00 0.436138 0.218069 − 0.975933i \(-0.430024\pi\)
0.218069 + 0.975933i \(0.430024\pi\)
\(642\) 0 0
\(643\) −13716.0 −0.841223 −0.420611 − 0.907241i \(-0.638184\pi\)
−0.420611 + 0.907241i \(0.638184\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16704.0 −1.01500 −0.507498 − 0.861653i \(-0.669429\pi\)
−0.507498 + 0.861653i \(0.669429\pi\)
\(648\) 0 0
\(649\) 24624.0 1.48933
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19670.0 −1.17878 −0.589392 − 0.807847i \(-0.700633\pi\)
−0.589392 + 0.807847i \(0.700633\pi\)
\(654\) 0 0
\(655\) −37800.0 −2.25491
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 31500.0 1.86201 0.931006 − 0.365004i \(-0.118932\pi\)
0.931006 + 0.365004i \(0.118932\pi\)
\(660\) 0 0
\(661\) 20666.0 1.21606 0.608029 − 0.793915i \(-0.291960\pi\)
0.608029 + 0.793915i \(0.291960\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −18144.0 −1.05804
\(666\) 0 0
\(667\) 7200.00 0.417969
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −16776.0 −0.965172
\(672\) 0 0
\(673\) −574.000 −0.0328768 −0.0164384 − 0.999865i \(-0.505233\pi\)
−0.0164384 + 0.999865i \(0.505233\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7934.00 −0.450411 −0.225206 − 0.974311i \(-0.572305\pi\)
−0.225206 + 0.974311i \(0.572305\pi\)
\(678\) 0 0
\(679\) 40824.0 2.30734
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1548.00 0.0867241 0.0433621 − 0.999059i \(-0.486193\pi\)
0.0433621 + 0.999059i \(0.486193\pi\)
\(684\) 0 0
\(685\) −23492.0 −1.31034
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1188.00 0.0656882
\(690\) 0 0
\(691\) −26100.0 −1.43689 −0.718445 − 0.695584i \(-0.755146\pi\)
−0.718445 + 0.695584i \(0.755146\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 504.000 0.0275076
\(696\) 0 0
\(697\) 9812.00 0.533222
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −35230.0 −1.89817 −0.949086 − 0.315017i \(-0.897990\pi\)
−0.949086 + 0.315017i \(0.897990\pi\)
\(702\) 0 0
\(703\) 7704.00 0.413317
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2088.00 −0.111071
\(708\) 0 0
\(709\) −19710.0 −1.04404 −0.522020 − 0.852933i \(-0.674821\pi\)
−0.522020 + 0.852933i \(0.674821\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −15552.0 −0.816868
\(714\) 0 0
\(715\) −27216.0 −1.42353
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −23112.0 −1.19879 −0.599396 − 0.800452i \(-0.704593\pi\)
−0.599396 + 0.800452i \(0.704593\pi\)
\(720\) 0 0
\(721\) −47952.0 −2.47687
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3550.00 0.181853
\(726\) 0 0
\(727\) 1548.00 0.0789713 0.0394857 − 0.999220i \(-0.487428\pi\)
0.0394857 + 0.999220i \(0.487428\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5544.00 −0.280509
\(732\) 0 0
\(733\) 25434.0 1.28162 0.640809 − 0.767700i \(-0.278599\pi\)
0.640809 + 0.767700i \(0.278599\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6480.00 −0.323872
\(738\) 0 0
\(739\) 2340.00 0.116479 0.0582397 − 0.998303i \(-0.481451\pi\)
0.0582397 + 0.998303i \(0.481451\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 20664.0 1.02031 0.510154 − 0.860083i \(-0.329588\pi\)
0.510154 + 0.860083i \(0.329588\pi\)
\(744\) 0 0
\(745\) −22876.0 −1.12498
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 14256.0 0.695464
\(750\) 0 0
\(751\) −26892.0 −1.30666 −0.653331 − 0.757072i \(-0.726629\pi\)
−0.653331 + 0.757072i \(0.726629\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 26712.0 1.28761
\(756\) 0 0
\(757\) −29646.0 −1.42338 −0.711692 − 0.702491i \(-0.752071\pi\)
−0.711692 + 0.702491i \(0.752071\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −14242.0 −0.678413 −0.339206 − 0.940712i \(-0.610158\pi\)
−0.339206 + 0.940712i \(0.610158\pi\)
\(762\) 0 0
\(763\) −44712.0 −2.12147
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 36936.0 1.73883
\(768\) 0 0
\(769\) 20018.0 0.938709 0.469355 − 0.883010i \(-0.344487\pi\)
0.469355 + 0.883010i \(0.344487\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12938.0 0.602002 0.301001 − 0.953624i \(-0.402679\pi\)
0.301001 + 0.953624i \(0.402679\pi\)
\(774\) 0 0
\(775\) −7668.00 −0.355410
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16056.0 −0.738467
\(780\) 0 0
\(781\) 20736.0 0.950054
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −32284.0 −1.46785
\(786\) 0 0
\(787\) 21708.0 0.983236 0.491618 − 0.870811i \(-0.336406\pi\)
0.491618 + 0.870811i \(0.336406\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −16056.0 −0.721726
\(792\) 0 0
\(793\) −25164.0 −1.12686
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30470.0 −1.35421 −0.677103 − 0.735888i \(-0.736765\pi\)
−0.677103 + 0.735888i \(0.736765\pi\)
\(798\) 0 0
\(799\) −1584.00 −0.0701350
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1944.00 0.0854325
\(804\) 0 0
\(805\) 72576.0 3.17760
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −18706.0 −0.812939 −0.406470 − 0.913664i \(-0.633240\pi\)
−0.406470 + 0.913664i \(0.633240\pi\)
\(810\) 0 0
\(811\) 20196.0 0.874448 0.437224 − 0.899353i \(-0.355962\pi\)
0.437224 + 0.899353i \(0.355962\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 20664.0 0.888133
\(816\) 0 0
\(817\) 9072.00 0.388481
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 14746.0 0.626844 0.313422 − 0.949614i \(-0.398525\pi\)
0.313422 + 0.949614i \(0.398525\pi\)
\(822\) 0 0
\(823\) −26244.0 −1.11155 −0.555777 − 0.831332i \(-0.687579\pi\)
−0.555777 + 0.831332i \(0.687579\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 29124.0 1.22460 0.612298 − 0.790627i \(-0.290245\pi\)
0.612298 + 0.790627i \(0.290245\pi\)
\(828\) 0 0
\(829\) 16362.0 0.685495 0.342748 − 0.939427i \(-0.388642\pi\)
0.342748 + 0.939427i \(0.388642\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 20966.0 0.872063
\(834\) 0 0
\(835\) 39312.0 1.62928
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −21168.0 −0.871038 −0.435519 − 0.900180i \(-0.643435\pi\)
−0.435519 + 0.900180i \(0.643435\pi\)
\(840\) 0 0
\(841\) −21889.0 −0.897495
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10066.0 −0.409800
\(846\) 0 0
\(847\) 1260.00 0.0511147
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −30816.0 −1.24131
\(852\) 0 0
\(853\) −31462.0 −1.26288 −0.631441 − 0.775424i \(-0.717536\pi\)
−0.631441 + 0.775424i \(0.717536\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −41746.0 −1.66396 −0.831981 − 0.554803i \(-0.812793\pi\)
−0.831981 + 0.554803i \(0.812793\pi\)
\(858\) 0 0
\(859\) 44388.0 1.76310 0.881548 − 0.472095i \(-0.156502\pi\)
0.881548 + 0.472095i \(0.156502\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22752.0 0.897436 0.448718 − 0.893673i \(-0.351881\pi\)
0.448718 + 0.893673i \(0.351881\pi\)
\(864\) 0 0
\(865\) −812.000 −0.0319177
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 34992.0 1.36596
\(870\) 0 0
\(871\) −9720.00 −0.378128
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −27216.0 −1.05151
\(876\) 0 0
\(877\) −8030.00 −0.309183 −0.154592 − 0.987978i \(-0.549406\pi\)
−0.154592 + 0.987978i \(0.549406\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2354.00 −0.0900207 −0.0450104 − 0.998987i \(-0.514332\pi\)
−0.0450104 + 0.998987i \(0.514332\pi\)
\(882\) 0 0
\(883\) −41364.0 −1.57645 −0.788227 − 0.615384i \(-0.789001\pi\)
−0.788227 + 0.615384i \(0.789001\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 17496.0 0.662298 0.331149 − 0.943579i \(-0.392564\pi\)
0.331149 + 0.943579i \(0.392564\pi\)
\(888\) 0 0
\(889\) −40176.0 −1.51570
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2592.00 0.0971310
\(894\) 0 0
\(895\) 48888.0 1.82586
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5400.00 −0.200334
\(900\) 0 0
\(901\) −484.000 −0.0178961
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2268.00 −0.0833048
\(906\) 0 0
\(907\) 45108.0 1.65136 0.825682 − 0.564136i \(-0.190791\pi\)
0.825682 + 0.564136i \(0.190791\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −20448.0 −0.743658 −0.371829 − 0.928301i \(-0.621269\pi\)
−0.371829 + 0.928301i \(0.621269\pi\)
\(912\) 0 0
\(913\) 24624.0 0.892591
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −97200.0 −3.50036
\(918\) 0 0
\(919\) 33948.0 1.21854 0.609272 − 0.792962i \(-0.291462\pi\)
0.609272 + 0.792962i \(0.291462\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 31104.0 1.10921
\(924\) 0 0
\(925\) −15194.0 −0.540082
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 54166.0 1.91295 0.956474 − 0.291817i \(-0.0942599\pi\)
0.956474 + 0.291817i \(0.0942599\pi\)
\(930\) 0 0
\(931\) −34308.0 −1.20773
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 11088.0 0.387825
\(936\) 0 0
\(937\) −8966.00 −0.312600 −0.156300 − 0.987710i \(-0.549957\pi\)
−0.156300 + 0.987710i \(0.549957\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 27770.0 0.962036 0.481018 − 0.876711i \(-0.340267\pi\)
0.481018 + 0.876711i \(0.340267\pi\)
\(942\) 0 0
\(943\) 64224.0 2.21784
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −42660.0 −1.46385 −0.731924 − 0.681386i \(-0.761377\pi\)
−0.731924 + 0.681386i \(0.761377\pi\)
\(948\) 0 0
\(949\) 2916.00 0.0997443
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −16178.0 −0.549902 −0.274951 − 0.961458i \(-0.588662\pi\)
−0.274951 + 0.961458i \(0.588662\pi\)
\(954\) 0 0
\(955\) −40320.0 −1.36620
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −60408.0 −2.03407
\(960\) 0 0
\(961\) −18127.0 −0.608472
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 33796.0 1.12739
\(966\) 0 0
\(967\) −52236.0 −1.73712 −0.868561 − 0.495583i \(-0.834955\pi\)
−0.868561 + 0.495583i \(0.834955\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −12276.0 −0.405722 −0.202861 − 0.979208i \(-0.565024\pi\)
−0.202861 + 0.979208i \(0.565024\pi\)
\(972\) 0 0
\(973\) 1296.00 0.0427008
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −12730.0 −0.416856 −0.208428 − 0.978038i \(-0.566835\pi\)
−0.208428 + 0.978038i \(0.566835\pi\)
\(978\) 0 0
\(979\) 12456.0 0.406635
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −48744.0 −1.58158 −0.790789 − 0.612088i \(-0.790330\pi\)
−0.790789 + 0.612088i \(0.790330\pi\)
\(984\) 0 0
\(985\) 37492.0 1.21279
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −36288.0 −1.16673
\(990\) 0 0
\(991\) −57852.0 −1.85442 −0.927210 − 0.374543i \(-0.877800\pi\)
−0.927210 + 0.374543i \(0.877800\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 11592.0 0.369338
\(996\) 0 0
\(997\) 13210.0 0.419624 0.209812 − 0.977742i \(-0.432715\pi\)
0.209812 + 0.977742i \(0.432715\pi\)
\(998\) 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 576.4.a.e.1.1 1
3.2 odd 2 192.4.a.e.1.1 1
4.3 odd 2 576.4.a.f.1.1 1
8.3 odd 2 288.4.a.k.1.1 1
8.5 even 2 288.4.a.j.1.1 1
12.11 even 2 192.4.a.k.1.1 1
24.5 odd 2 96.4.a.d.1.1 yes 1
24.11 even 2 96.4.a.a.1.1 ✓ 1
48.5 odd 4 768.4.d.p.385.2 2
48.11 even 4 768.4.d.a.385.1 2
48.29 odd 4 768.4.d.p.385.1 2
48.35 even 4 768.4.d.a.385.2 2
120.29 odd 2 2400.4.a.k.1.1 1
120.59 even 2 2400.4.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.4.a.a.1.1 ✓ 1 24.11 even 2
96.4.a.d.1.1 yes 1 24.5 odd 2
192.4.a.e.1.1 1 3.2 odd 2
192.4.a.k.1.1 1 12.11 even 2
288.4.a.j.1.1 1 8.5 even 2
288.4.a.k.1.1 1 8.3 odd 2
576.4.a.e.1.1 1 1.1 even 1 trivial
576.4.a.f.1.1 1 4.3 odd 2
768.4.d.a.385.1 2 48.11 even 4
768.4.d.a.385.2 2 48.35 even 4
768.4.d.p.385.1 2 48.29 odd 4
768.4.d.p.385.2 2 48.5 odd 4
2400.4.a.k.1.1 1 120.29 odd 2
2400.4.a.l.1.1 1 120.59 even 2