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Properties

Label 2160.4.a.l.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
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] = [2160,4,Mod(1,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, 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("2160.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.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: \(127.444125612\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -14.0000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -14.0000 q^{7} -3.00000 q^{11} +47.0000 q^{13} -39.0000 q^{17} -32.0000 q^{19} +99.0000 q^{23} +25.0000 q^{25} +51.0000 q^{29} -83.0000 q^{31} -70.0000 q^{35} +314.000 q^{37} -108.000 q^{41} -299.000 q^{43} -531.000 q^{47} -147.000 q^{49} +564.000 q^{53} -15.0000 q^{55} -12.0000 q^{59} +230.000 q^{61} +235.000 q^{65} +268.000 q^{67} -120.000 q^{71} +1106.00 q^{73} +42.0000 q^{77} +739.000 q^{79} -1086.00 q^{83} -195.000 q^{85} -120.000 q^{89} -658.000 q^{91} -160.000 q^{95} -1642.00 q^{97} +O(q^{100})\)

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
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −14.0000 −0.755929 −0.377964 − 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.00000 −0.0822304 −0.0411152 − 0.999154i \(-0.513091\pi\)
−0.0411152 + 0.999154i \(0.513091\pi\)
\(12\) 0 0
\(13\) 47.0000 1.00273 0.501364 − 0.865237i \(-0.332832\pi\)
0.501364 + 0.865237i \(0.332832\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −39.0000 −0.556405 −0.278203 − 0.960522i \(-0.589739\pi\)
−0.278203 + 0.960522i \(0.589739\pi\)
\(18\) 0 0
\(19\) −32.0000 −0.386384 −0.193192 − 0.981161i \(-0.561884\pi\)
−0.193192 + 0.981161i \(0.561884\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 99.0000 0.897519 0.448759 − 0.893653i \(-0.351866\pi\)
0.448759 + 0.893653i \(0.351866\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 51.0000 0.326568 0.163284 − 0.986579i \(-0.447791\pi\)
0.163284 + 0.986579i \(0.447791\pi\)
\(30\) 0 0
\(31\) −83.0000 −0.480879 −0.240439 − 0.970664i \(-0.577292\pi\)
−0.240439 + 0.970664i \(0.577292\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −70.0000 −0.338062
\(36\) 0 0
\(37\) 314.000 1.39517 0.697585 − 0.716502i \(-0.254258\pi\)
0.697585 + 0.716502i \(0.254258\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −108.000 −0.411385 −0.205692 − 0.978617i \(-0.565945\pi\)
−0.205692 + 0.978617i \(0.565945\pi\)
\(42\) 0 0
\(43\) −299.000 −1.06040 −0.530199 − 0.847874i \(-0.677883\pi\)
−0.530199 + 0.847874i \(0.677883\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −531.000 −1.64796 −0.823982 − 0.566616i \(-0.808252\pi\)
−0.823982 + 0.566616i \(0.808252\pi\)
\(48\) 0 0
\(49\) −147.000 −0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 564.000 1.46172 0.730862 − 0.682525i \(-0.239118\pi\)
0.730862 + 0.682525i \(0.239118\pi\)
\(54\) 0 0
\(55\) −15.0000 −0.0367745
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −12.0000 −0.0264791 −0.0132396 − 0.999912i \(-0.504214\pi\)
−0.0132396 + 0.999912i \(0.504214\pi\)
\(60\) 0 0
\(61\) 230.000 0.482762 0.241381 − 0.970430i \(-0.422400\pi\)
0.241381 + 0.970430i \(0.422400\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 235.000 0.448433
\(66\) 0 0
\(67\) 268.000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −120.000 −0.200583 −0.100291 − 0.994958i \(-0.531978\pi\)
−0.100291 + 0.994958i \(0.531978\pi\)
\(72\) 0 0
\(73\) 1106.00 1.77325 0.886627 − 0.462486i \(-0.153042\pi\)
0.886627 + 0.462486i \(0.153042\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 42.0000 0.0621603
\(78\) 0 0
\(79\) 739.000 1.05246 0.526228 − 0.850344i \(-0.323606\pi\)
0.526228 + 0.850344i \(0.323606\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1086.00 −1.43619 −0.718096 − 0.695944i \(-0.754986\pi\)
−0.718096 + 0.695944i \(0.754986\pi\)
\(84\) 0 0
\(85\) −195.000 −0.248832
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −120.000 −0.142921 −0.0714605 − 0.997443i \(-0.522766\pi\)
−0.0714605 + 0.997443i \(0.522766\pi\)
\(90\) 0 0
\(91\) −658.000 −0.757991
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −160.000 −0.172796
\(96\) 0 0
\(97\) −1642.00 −1.71876 −0.859381 − 0.511336i \(-0.829151\pi\)
−0.859381 + 0.511336i \(0.829151\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 33.0000 0.0325111 0.0162556 − 0.999868i \(-0.494825\pi\)
0.0162556 + 0.999868i \(0.494825\pi\)
\(102\) 0 0
\(103\) 1198.00 1.14604 0.573022 − 0.819540i \(-0.305771\pi\)
0.573022 + 0.819540i \(0.305771\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1542.00 1.39318 0.696592 − 0.717467i \(-0.254699\pi\)
0.696592 + 0.717467i \(0.254699\pi\)
\(108\) 0 0
\(109\) −556.000 −0.488579 −0.244290 − 0.969702i \(-0.578555\pi\)
−0.244290 + 0.969702i \(0.578555\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1605.00 1.33616 0.668078 − 0.744091i \(-0.267117\pi\)
0.668078 + 0.744091i \(0.267117\pi\)
\(114\) 0 0
\(115\) 495.000 0.401383
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 546.000 0.420603
\(120\) 0 0
\(121\) −1322.00 −0.993238
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1334.00 −0.932074 −0.466037 − 0.884765i \(-0.654319\pi\)
−0.466037 + 0.884765i \(0.654319\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2883.00 1.92282 0.961408 − 0.275127i \(-0.0887199\pi\)
0.961408 + 0.275127i \(0.0887199\pi\)
\(132\) 0 0
\(133\) 448.000 0.292079
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 282.000 0.175860 0.0879302 − 0.996127i \(-0.471975\pi\)
0.0879302 + 0.996127i \(0.471975\pi\)
\(138\) 0 0
\(139\) 2494.00 1.52186 0.760929 − 0.648835i \(-0.224743\pi\)
0.760929 + 0.648835i \(0.224743\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −141.000 −0.0824546
\(144\) 0 0
\(145\) 255.000 0.146045
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2595.00 1.42678 0.713392 − 0.700766i \(-0.247158\pi\)
0.713392 + 0.700766i \(0.247158\pi\)
\(150\) 0 0
\(151\) −1229.00 −0.662348 −0.331174 − 0.943570i \(-0.607445\pi\)
−0.331174 + 0.943570i \(0.607445\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −415.000 −0.215055
\(156\) 0 0
\(157\) −1591.00 −0.808762 −0.404381 − 0.914591i \(-0.632513\pi\)
−0.404381 + 0.914591i \(0.632513\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1386.00 −0.678460
\(162\) 0 0
\(163\) 457.000 0.219601 0.109801 − 0.993954i \(-0.464979\pi\)
0.109801 + 0.993954i \(0.464979\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1164.00 0.539359 0.269680 − 0.962950i \(-0.413082\pi\)
0.269680 + 0.962950i \(0.413082\pi\)
\(168\) 0 0
\(169\) 12.0000 0.00546199
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3942.00 1.73240 0.866199 − 0.499700i \(-0.166556\pi\)
0.866199 + 0.499700i \(0.166556\pi\)
\(174\) 0 0
\(175\) −350.000 −0.151186
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1212.00 0.506085 0.253042 − 0.967455i \(-0.418569\pi\)
0.253042 + 0.967455i \(0.418569\pi\)
\(180\) 0 0
\(181\) 2288.00 0.939590 0.469795 − 0.882776i \(-0.344328\pi\)
0.469795 + 0.882776i \(0.344328\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1570.00 0.623939
\(186\) 0 0
\(187\) 117.000 0.0457534
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1938.00 0.734182 0.367091 − 0.930185i \(-0.380354\pi\)
0.367091 + 0.930185i \(0.380354\pi\)
\(192\) 0 0
\(193\) −1498.00 −0.558696 −0.279348 − 0.960190i \(-0.590118\pi\)
−0.279348 + 0.960190i \(0.590118\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2124.00 −0.768166 −0.384083 − 0.923299i \(-0.625482\pi\)
−0.384083 + 0.923299i \(0.625482\pi\)
\(198\) 0 0
\(199\) 385.000 0.137145 0.0685727 − 0.997646i \(-0.478155\pi\)
0.0685727 + 0.997646i \(0.478155\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −714.000 −0.246862
\(204\) 0 0
\(205\) −540.000 −0.183977
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 96.0000 0.0317725
\(210\) 0 0
\(211\) −3170.00 −1.03427 −0.517137 − 0.855903i \(-0.673002\pi\)
−0.517137 + 0.855903i \(0.673002\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1495.00 −0.474224
\(216\) 0 0
\(217\) 1162.00 0.363510
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1833.00 −0.557923
\(222\) 0 0
\(223\) −1388.00 −0.416804 −0.208402 − 0.978043i \(-0.566826\pi\)
−0.208402 + 0.978043i \(0.566826\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4644.00 1.35786 0.678928 − 0.734205i \(-0.262445\pi\)
0.678928 + 0.734205i \(0.262445\pi\)
\(228\) 0 0
\(229\) 4736.00 1.36665 0.683327 − 0.730113i \(-0.260532\pi\)
0.683327 + 0.730113i \(0.260532\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2814.00 0.791207 0.395604 − 0.918421i \(-0.370535\pi\)
0.395604 + 0.918421i \(0.370535\pi\)
\(234\) 0 0
\(235\) −2655.00 −0.736992
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2202.00 0.595965 0.297982 − 0.954571i \(-0.403686\pi\)
0.297982 + 0.954571i \(0.403686\pi\)
\(240\) 0 0
\(241\) 3485.00 0.931488 0.465744 − 0.884920i \(-0.345787\pi\)
0.465744 + 0.884920i \(0.345787\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −735.000 −0.191663
\(246\) 0 0
\(247\) −1504.00 −0.387438
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6345.00 1.59559 0.797795 − 0.602929i \(-0.206000\pi\)
0.797795 + 0.602929i \(0.206000\pi\)
\(252\) 0 0
\(253\) −297.000 −0.0738033
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 525.000 0.127426 0.0637132 − 0.997968i \(-0.479706\pi\)
0.0637132 + 0.997968i \(0.479706\pi\)
\(258\) 0 0
\(259\) −4396.00 −1.05465
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5196.00 −1.21825 −0.609124 − 0.793075i \(-0.708479\pi\)
−0.609124 + 0.793075i \(0.708479\pi\)
\(264\) 0 0
\(265\) 2820.00 0.653703
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7479.00 −1.69518 −0.847589 − 0.530654i \(-0.821946\pi\)
−0.847589 + 0.530654i \(0.821946\pi\)
\(270\) 0 0
\(271\) 856.000 0.191876 0.0959378 − 0.995387i \(-0.469415\pi\)
0.0959378 + 0.995387i \(0.469415\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −75.0000 −0.0164461
\(276\) 0 0
\(277\) −7054.00 −1.53009 −0.765043 − 0.643979i \(-0.777282\pi\)
−0.765043 + 0.643979i \(0.777282\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1014.00 0.215268 0.107634 − 0.994191i \(-0.465673\pi\)
0.107634 + 0.994191i \(0.465673\pi\)
\(282\) 0 0
\(283\) −992.000 −0.208368 −0.104184 − 0.994558i \(-0.533223\pi\)
−0.104184 + 0.994558i \(0.533223\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1512.00 0.310977
\(288\) 0 0
\(289\) −3392.00 −0.690413
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4950.00 −0.986970 −0.493485 − 0.869754i \(-0.664277\pi\)
−0.493485 + 0.869754i \(0.664277\pi\)
\(294\) 0 0
\(295\) −60.0000 −0.0118418
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4653.00 0.899966
\(300\) 0 0
\(301\) 4186.00 0.801585
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1150.00 0.215898
\(306\) 0 0
\(307\) 4777.00 0.888071 0.444035 − 0.896009i \(-0.353546\pi\)
0.444035 + 0.896009i \(0.353546\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7692.00 1.40249 0.701243 − 0.712922i \(-0.252629\pi\)
0.701243 + 0.712922i \(0.252629\pi\)
\(312\) 0 0
\(313\) −2932.00 −0.529477 −0.264739 − 0.964320i \(-0.585286\pi\)
−0.264739 + 0.964320i \(0.585286\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8352.00 1.47980 0.739898 − 0.672720i \(-0.234874\pi\)
0.739898 + 0.672720i \(0.234874\pi\)
\(318\) 0 0
\(319\) −153.000 −0.0268538
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1248.00 0.214986
\(324\) 0 0
\(325\) 1175.00 0.200545
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7434.00 1.24574
\(330\) 0 0
\(331\) 3070.00 0.509796 0.254898 − 0.966968i \(-0.417958\pi\)
0.254898 + 0.966968i \(0.417958\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1340.00 0.218543
\(336\) 0 0
\(337\) −1672.00 −0.270266 −0.135133 − 0.990827i \(-0.543146\pi\)
−0.135133 + 0.990827i \(0.543146\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 249.000 0.0395428
\(342\) 0 0
\(343\) 6860.00 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5076.00 0.785285 0.392643 − 0.919691i \(-0.371561\pi\)
0.392643 + 0.919691i \(0.371561\pi\)
\(348\) 0 0
\(349\) 8594.00 1.31813 0.659063 − 0.752087i \(-0.270953\pi\)
0.659063 + 0.752087i \(0.270953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12711.0 1.91654 0.958269 − 0.285866i \(-0.0922813\pi\)
0.958269 + 0.285866i \(0.0922813\pi\)
\(354\) 0 0
\(355\) −600.000 −0.0897034
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1464.00 0.215228 0.107614 − 0.994193i \(-0.465679\pi\)
0.107614 + 0.994193i \(0.465679\pi\)
\(360\) 0 0
\(361\) −5835.00 −0.850707
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5530.00 0.793023
\(366\) 0 0
\(367\) 7630.00 1.08524 0.542620 − 0.839979i \(-0.317433\pi\)
0.542620 + 0.839979i \(0.317433\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7896.00 −1.10496
\(372\) 0 0
\(373\) −3883.00 −0.539019 −0.269510 − 0.962998i \(-0.586862\pi\)
−0.269510 + 0.962998i \(0.586862\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2397.00 0.327458
\(378\) 0 0
\(379\) 13768.0 1.86600 0.933001 − 0.359874i \(-0.117180\pi\)
0.933001 + 0.359874i \(0.117180\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 14139.0 1.88634 0.943171 − 0.332307i \(-0.107827\pi\)
0.943171 + 0.332307i \(0.107827\pi\)
\(384\) 0 0
\(385\) 210.000 0.0277989
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 567.000 0.0739024 0.0369512 − 0.999317i \(-0.488235\pi\)
0.0369512 + 0.999317i \(0.488235\pi\)
\(390\) 0 0
\(391\) −3861.00 −0.499384
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3695.00 0.470672
\(396\) 0 0
\(397\) −6685.00 −0.845115 −0.422557 − 0.906336i \(-0.638867\pi\)
−0.422557 + 0.906336i \(0.638867\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4572.00 0.569364 0.284682 − 0.958622i \(-0.408112\pi\)
0.284682 + 0.958622i \(0.408112\pi\)
\(402\) 0 0
\(403\) −3901.00 −0.482190
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −942.000 −0.114725
\(408\) 0 0
\(409\) −25.0000 −0.00302242 −0.00151121 − 0.999999i \(-0.500481\pi\)
−0.00151121 + 0.999999i \(0.500481\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 168.000 0.0200163
\(414\) 0 0
\(415\) −5430.00 −0.642285
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −12453.0 −1.45195 −0.725977 − 0.687719i \(-0.758612\pi\)
−0.725977 + 0.687719i \(0.758612\pi\)
\(420\) 0 0
\(421\) 5048.00 0.584381 0.292191 − 0.956360i \(-0.405616\pi\)
0.292191 + 0.956360i \(0.405616\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −975.000 −0.111281
\(426\) 0 0
\(427\) −3220.00 −0.364934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5400.00 −0.603501 −0.301750 − 0.953387i \(-0.597571\pi\)
−0.301750 + 0.953387i \(0.597571\pi\)
\(432\) 0 0
\(433\) −6298.00 −0.698990 −0.349495 − 0.936938i \(-0.613647\pi\)
−0.349495 + 0.936938i \(0.613647\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3168.00 −0.346787
\(438\) 0 0
\(439\) 6208.00 0.674924 0.337462 − 0.941339i \(-0.390432\pi\)
0.337462 + 0.941339i \(0.390432\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3360.00 0.360358 0.180179 − 0.983634i \(-0.442332\pi\)
0.180179 + 0.983634i \(0.442332\pi\)
\(444\) 0 0
\(445\) −600.000 −0.0639162
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14394.0 1.51291 0.756453 − 0.654048i \(-0.226931\pi\)
0.756453 + 0.654048i \(0.226931\pi\)
\(450\) 0 0
\(451\) 324.000 0.0338283
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3290.00 −0.338984
\(456\) 0 0
\(457\) −916.000 −0.0937608 −0.0468804 − 0.998901i \(-0.514928\pi\)
−0.0468804 + 0.998901i \(0.514928\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8550.00 0.863803 0.431902 − 0.901921i \(-0.357843\pi\)
0.431902 + 0.901921i \(0.357843\pi\)
\(462\) 0 0
\(463\) −3734.00 −0.374803 −0.187401 − 0.982283i \(-0.560007\pi\)
−0.187401 + 0.982283i \(0.560007\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9840.00 −0.975034 −0.487517 − 0.873113i \(-0.662097\pi\)
−0.487517 + 0.873113i \(0.662097\pi\)
\(468\) 0 0
\(469\) −3752.00 −0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 897.000 0.0871968
\(474\) 0 0
\(475\) −800.000 −0.0772769
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17280.0 1.64832 0.824158 − 0.566360i \(-0.191649\pi\)
0.824158 + 0.566360i \(0.191649\pi\)
\(480\) 0 0
\(481\) 14758.0 1.39897
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8210.00 −0.768653
\(486\) 0 0
\(487\) 4588.00 0.426904 0.213452 − 0.976954i \(-0.431529\pi\)
0.213452 + 0.976954i \(0.431529\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −636.000 −0.0584568 −0.0292284 − 0.999573i \(-0.509305\pi\)
−0.0292284 + 0.999573i \(0.509305\pi\)
\(492\) 0 0
\(493\) −1989.00 −0.181704
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1680.00 0.151626
\(498\) 0 0
\(499\) 11716.0 1.05106 0.525531 − 0.850774i \(-0.323867\pi\)
0.525531 + 0.850774i \(0.323867\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4653.00 −0.412459 −0.206230 − 0.978504i \(-0.566119\pi\)
−0.206230 + 0.978504i \(0.566119\pi\)
\(504\) 0 0
\(505\) 165.000 0.0145394
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16479.0 1.43501 0.717504 − 0.696555i \(-0.245285\pi\)
0.717504 + 0.696555i \(0.245285\pi\)
\(510\) 0 0
\(511\) −15484.0 −1.34045
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5990.00 0.512526
\(516\) 0 0
\(517\) 1593.00 0.135513
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3120.00 0.262360 0.131180 − 0.991359i \(-0.458123\pi\)
0.131180 + 0.991359i \(0.458123\pi\)
\(522\) 0 0
\(523\) −17645.0 −1.47526 −0.737631 − 0.675204i \(-0.764056\pi\)
−0.737631 + 0.675204i \(0.764056\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3237.00 0.267563
\(528\) 0 0
\(529\) −2366.00 −0.194460
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5076.00 −0.412507
\(534\) 0 0
\(535\) 7710.00 0.623051
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 441.000 0.0352416
\(540\) 0 0
\(541\) −2182.00 −0.173404 −0.0867019 − 0.996234i \(-0.527633\pi\)
−0.0867019 + 0.996234i \(0.527633\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2780.00 −0.218499
\(546\) 0 0
\(547\) 4033.00 0.315244 0.157622 − 0.987499i \(-0.449617\pi\)
0.157622 + 0.987499i \(0.449617\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1632.00 −0.126181
\(552\) 0 0
\(553\) −10346.0 −0.795582
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −960.000 −0.0730278 −0.0365139 − 0.999333i \(-0.511625\pi\)
−0.0365139 + 0.999333i \(0.511625\pi\)
\(558\) 0 0
\(559\) −14053.0 −1.06329
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23754.0 1.77817 0.889087 − 0.457739i \(-0.151340\pi\)
0.889087 + 0.457739i \(0.151340\pi\)
\(564\) 0 0
\(565\) 8025.00 0.597547
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22536.0 −1.66038 −0.830192 − 0.557478i \(-0.811769\pi\)
−0.830192 + 0.557478i \(0.811769\pi\)
\(570\) 0 0
\(571\) −17726.0 −1.29914 −0.649571 − 0.760301i \(-0.725051\pi\)
−0.649571 + 0.760301i \(0.725051\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2475.00 0.179504
\(576\) 0 0
\(577\) 17168.0 1.23867 0.619336 − 0.785126i \(-0.287402\pi\)
0.619336 + 0.785126i \(0.287402\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 15204.0 1.08566
\(582\) 0 0
\(583\) −1692.00 −0.120198
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7542.00 −0.530309 −0.265155 − 0.964206i \(-0.585423\pi\)
−0.265155 + 0.964206i \(0.585423\pi\)
\(588\) 0 0
\(589\) 2656.00 0.185804
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15543.0 −1.07635 −0.538174 − 0.842834i \(-0.680886\pi\)
−0.538174 + 0.842834i \(0.680886\pi\)
\(594\) 0 0
\(595\) 2730.00 0.188099
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16026.0 −1.09316 −0.546581 − 0.837406i \(-0.684071\pi\)
−0.546581 + 0.837406i \(0.684071\pi\)
\(600\) 0 0
\(601\) 10469.0 0.710548 0.355274 − 0.934762i \(-0.384388\pi\)
0.355274 + 0.934762i \(0.384388\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6610.00 −0.444190
\(606\) 0 0
\(607\) 8074.00 0.539891 0.269945 − 0.962876i \(-0.412994\pi\)
0.269945 + 0.962876i \(0.412994\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −24957.0 −1.65246
\(612\) 0 0
\(613\) 26855.0 1.76943 0.884717 − 0.466128i \(-0.154351\pi\)
0.884717 + 0.466128i \(0.154351\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24447.0 1.59514 0.797568 − 0.603229i \(-0.206119\pi\)
0.797568 + 0.603229i \(0.206119\pi\)
\(618\) 0 0
\(619\) −1850.00 −0.120126 −0.0600628 − 0.998195i \(-0.519130\pi\)
−0.0600628 + 0.998195i \(0.519130\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1680.00 0.108038
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12246.0 −0.776280
\(630\) 0 0
\(631\) −21728.0 −1.37081 −0.685403 − 0.728164i \(-0.740374\pi\)
−0.685403 + 0.728164i \(0.740374\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6670.00 −0.416836
\(636\) 0 0
\(637\) −6909.00 −0.429740
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23862.0 1.47035 0.735173 − 0.677879i \(-0.237101\pi\)
0.735173 + 0.677879i \(0.237101\pi\)
\(642\) 0 0
\(643\) −10523.0 −0.645391 −0.322696 − 0.946503i \(-0.604589\pi\)
−0.322696 + 0.946503i \(0.604589\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5484.00 −0.333228 −0.166614 − 0.986022i \(-0.553283\pi\)
−0.166614 + 0.986022i \(0.553283\pi\)
\(648\) 0 0
\(649\) 36.0000 0.00217739
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −26784.0 −1.60511 −0.802557 − 0.596576i \(-0.796527\pi\)
−0.802557 + 0.596576i \(0.796527\pi\)
\(654\) 0 0
\(655\) 14415.0 0.859909
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12120.0 0.716431 0.358216 − 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(660\) 0 0
\(661\) −18226.0 −1.07248 −0.536240 − 0.844066i \(-0.680156\pi\)
−0.536240 + 0.844066i \(0.680156\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2240.00 0.130622
\(666\) 0 0
\(667\) 5049.00 0.293101
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −690.000 −0.0396977
\(672\) 0 0
\(673\) −11062.0 −0.633594 −0.316797 − 0.948493i \(-0.602607\pi\)
−0.316797 + 0.948493i \(0.602607\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9348.00 −0.530684 −0.265342 − 0.964154i \(-0.585485\pi\)
−0.265342 + 0.964154i \(0.585485\pi\)
\(678\) 0 0
\(679\) 22988.0 1.29926
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −19248.0 −1.07834 −0.539169 − 0.842198i \(-0.681261\pi\)
−0.539169 + 0.842198i \(0.681261\pi\)
\(684\) 0 0
\(685\) 1410.00 0.0786472
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 26508.0 1.46571
\(690\) 0 0
\(691\) 17710.0 0.974993 0.487496 − 0.873125i \(-0.337910\pi\)
0.487496 + 0.873125i \(0.337910\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12470.0 0.680596
\(696\) 0 0
\(697\) 4212.00 0.228897
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19437.0 −1.04725 −0.523627 − 0.851947i \(-0.675422\pi\)
−0.523627 + 0.851947i \(0.675422\pi\)
\(702\) 0 0
\(703\) −10048.0 −0.539072
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −462.000 −0.0245761
\(708\) 0 0
\(709\) −19516.0 −1.03376 −0.516882 − 0.856057i \(-0.672907\pi\)
−0.516882 + 0.856057i \(0.672907\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8217.00 −0.431598
\(714\) 0 0
\(715\) −705.000 −0.0368748
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17358.0 −0.900340 −0.450170 − 0.892943i \(-0.648637\pi\)
−0.450170 + 0.892943i \(0.648637\pi\)
\(720\) 0 0
\(721\) −16772.0 −0.866327
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1275.00 0.0653135
\(726\) 0 0
\(727\) −24428.0 −1.24620 −0.623098 − 0.782144i \(-0.714126\pi\)
−0.623098 + 0.782144i \(0.714126\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11661.0 0.590010
\(732\) 0 0
\(733\) −21418.0 −1.07925 −0.539626 − 0.841905i \(-0.681434\pi\)
−0.539626 + 0.841905i \(0.681434\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −804.000 −0.0401842
\(738\) 0 0
\(739\) 664.000 0.0330523 0.0165261 − 0.999863i \(-0.494739\pi\)
0.0165261 + 0.999863i \(0.494739\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 34209.0 1.68911 0.844553 − 0.535471i \(-0.179866\pi\)
0.844553 + 0.535471i \(0.179866\pi\)
\(744\) 0 0
\(745\) 12975.0 0.638077
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −21588.0 −1.05315
\(750\) 0 0
\(751\) −6857.00 −0.333176 −0.166588 − 0.986027i \(-0.553275\pi\)
−0.166588 + 0.986027i \(0.553275\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −6145.00 −0.296211
\(756\) 0 0
\(757\) −23719.0 −1.13881 −0.569407 − 0.822056i \(-0.692827\pi\)
−0.569407 + 0.822056i \(0.692827\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −14418.0 −0.686796 −0.343398 − 0.939190i \(-0.611578\pi\)
−0.343398 + 0.939190i \(0.611578\pi\)
\(762\) 0 0
\(763\) 7784.00 0.369331
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −564.000 −0.0265513
\(768\) 0 0
\(769\) −4849.00 −0.227385 −0.113693 − 0.993516i \(-0.536268\pi\)
−0.113693 + 0.993516i \(0.536268\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −36258.0 −1.68708 −0.843538 − 0.537070i \(-0.819531\pi\)
−0.843538 + 0.537070i \(0.819531\pi\)
\(774\) 0 0
\(775\) −2075.00 −0.0961757
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3456.00 0.158953
\(780\) 0 0
\(781\) 360.000 0.0164940
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7955.00 −0.361689
\(786\) 0 0
\(787\) 18877.0 0.855009 0.427505 − 0.904013i \(-0.359393\pi\)
0.427505 + 0.904013i \(0.359393\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −22470.0 −1.01004
\(792\) 0 0
\(793\) 10810.0 0.484079
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −16200.0 −0.719992 −0.359996 − 0.932954i \(-0.617222\pi\)
−0.359996 + 0.932954i \(0.617222\pi\)
\(798\) 0 0
\(799\) 20709.0 0.916936
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3318.00 −0.145815
\(804\) 0 0
\(805\) −6930.00 −0.303417
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26760.0 −1.16296 −0.581478 − 0.813562i \(-0.697525\pi\)
−0.581478 + 0.813562i \(0.697525\pi\)
\(810\) 0 0
\(811\) 10510.0 0.455063 0.227531 − 0.973771i \(-0.426935\pi\)
0.227531 + 0.973771i \(0.426935\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2285.00 0.0982087
\(816\) 0 0
\(817\) 9568.00 0.409721
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −28230.0 −1.20004 −0.600021 − 0.799985i \(-0.704841\pi\)
−0.600021 + 0.799985i \(0.704841\pi\)
\(822\) 0 0
\(823\) 39868.0 1.68859 0.844296 − 0.535877i \(-0.180019\pi\)
0.844296 + 0.535877i \(0.180019\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32394.0 −1.36209 −0.681046 − 0.732241i \(-0.738475\pi\)
−0.681046 + 0.732241i \(0.738475\pi\)
\(828\) 0 0
\(829\) 34820.0 1.45880 0.729402 − 0.684085i \(-0.239798\pi\)
0.729402 + 0.684085i \(0.239798\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5733.00 0.238459
\(834\) 0 0
\(835\) 5820.00 0.241209
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1146.00 0.0471565 0.0235783 − 0.999722i \(-0.492494\pi\)
0.0235783 + 0.999722i \(0.492494\pi\)
\(840\) 0 0
\(841\) −21788.0 −0.893354
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 60.0000 0.00244268
\(846\) 0 0
\(847\) 18508.0 0.750817
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 31086.0 1.25219
\(852\) 0 0
\(853\) −19393.0 −0.778433 −0.389217 − 0.921146i \(-0.627254\pi\)
−0.389217 + 0.921146i \(0.627254\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8430.00 −0.336013 −0.168007 − 0.985786i \(-0.553733\pi\)
−0.168007 + 0.985786i \(0.553733\pi\)
\(858\) 0 0
\(859\) −15470.0 −0.614470 −0.307235 − 0.951634i \(-0.599404\pi\)
−0.307235 + 0.951634i \(0.599404\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −5871.00 −0.231577 −0.115789 − 0.993274i \(-0.536940\pi\)
−0.115789 + 0.993274i \(0.536940\pi\)
\(864\) 0 0
\(865\) 19710.0 0.774752
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2217.00 −0.0865438
\(870\) 0 0
\(871\) 12596.0 0.490011
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1750.00 −0.0676123
\(876\) 0 0
\(877\) −11299.0 −0.435051 −0.217526 − 0.976055i \(-0.569799\pi\)
−0.217526 + 0.976055i \(0.569799\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 29682.0 1.13509 0.567544 − 0.823343i \(-0.307894\pi\)
0.567544 + 0.823343i \(0.307894\pi\)
\(882\) 0 0
\(883\) −40316.0 −1.53651 −0.768257 − 0.640142i \(-0.778876\pi\)
−0.768257 + 0.640142i \(0.778876\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 21945.0 0.830711 0.415356 − 0.909659i \(-0.363657\pi\)
0.415356 + 0.909659i \(0.363657\pi\)
\(888\) 0 0
\(889\) 18676.0 0.704581
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 16992.0 0.636748
\(894\) 0 0
\(895\) 6060.00 0.226328
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4233.00 −0.157039
\(900\) 0 0
\(901\) −21996.0 −0.813311
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 11440.0 0.420197
\(906\) 0 0
\(907\) −24911.0 −0.911969 −0.455985 − 0.889988i \(-0.650713\pi\)
−0.455985 + 0.889988i \(0.650713\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −33264.0 −1.20975 −0.604877 − 0.796319i \(-0.706778\pi\)
−0.604877 + 0.796319i \(0.706778\pi\)
\(912\) 0 0
\(913\) 3258.00 0.118099
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −40362.0 −1.45351
\(918\) 0 0
\(919\) 23191.0 0.832427 0.416214 − 0.909267i \(-0.363357\pi\)
0.416214 + 0.909267i \(0.363357\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5640.00 −0.201130
\(924\) 0 0
\(925\) 7850.00 0.279034
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2160.00 0.0762834 0.0381417 − 0.999272i \(-0.487856\pi\)
0.0381417 + 0.999272i \(0.487856\pi\)
\(930\) 0 0
\(931\) 4704.00 0.165593
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 585.000 0.0204615
\(936\) 0 0
\(937\) 2066.00 0.0720312 0.0360156 − 0.999351i \(-0.488533\pi\)
0.0360156 + 0.999351i \(0.488533\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −22233.0 −0.770218 −0.385109 − 0.922871i \(-0.625836\pi\)
−0.385109 + 0.922871i \(0.625836\pi\)
\(942\) 0 0
\(943\) −10692.0 −0.369225
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 17754.0 0.609216 0.304608 − 0.952478i \(-0.401475\pi\)
0.304608 + 0.952478i \(0.401475\pi\)
\(948\) 0 0
\(949\) 51982.0 1.77809
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 33891.0 1.15198 0.575990 − 0.817457i \(-0.304617\pi\)
0.575990 + 0.817457i \(0.304617\pi\)
\(954\) 0 0
\(955\) 9690.00 0.328336
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −3948.00 −0.132938
\(960\) 0 0
\(961\) −22902.0 −0.768756
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −7490.00 −0.249857
\(966\) 0 0
\(967\) −51074.0 −1.69848 −0.849239 − 0.528008i \(-0.822939\pi\)
−0.849239 + 0.528008i \(0.822939\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −20967.0 −0.692959 −0.346479 − 0.938058i \(-0.612623\pi\)
−0.346479 + 0.938058i \(0.612623\pi\)
\(972\) 0 0
\(973\) −34916.0 −1.15042
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 31749.0 1.03965 0.519826 − 0.854272i \(-0.325997\pi\)
0.519826 + 0.854272i \(0.325997\pi\)
\(978\) 0 0
\(979\) 360.000 0.0117525
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −47325.0 −1.53554 −0.767769 − 0.640727i \(-0.778633\pi\)
−0.767769 + 0.640727i \(0.778633\pi\)
\(984\) 0 0
\(985\) −10620.0 −0.343534
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −29601.0 −0.951726
\(990\) 0 0
\(991\) −2363.00 −0.0757449 −0.0378724 − 0.999283i \(-0.512058\pi\)
−0.0378724 + 0.999283i \(0.512058\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1925.00 0.0613333
\(996\) 0 0
\(997\) 45569.0 1.44753 0.723764 − 0.690048i \(-0.242411\pi\)
0.723764 + 0.690048i \(0.242411\pi\)
\(998\) 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 2160.4.a.l.1.1 1
3.2 odd 2 2160.4.a.b.1.1 1
4.3 odd 2 270.4.a.f.1.1 ✓ 1
12.11 even 2 270.4.a.j.1.1 yes 1
20.3 even 4 1350.4.c.k.649.2 2
20.7 even 4 1350.4.c.k.649.1 2
20.19 odd 2 1350.4.a.r.1.1 1
36.7 odd 6 810.4.e.n.271.1 2
36.11 even 6 810.4.e.f.271.1 2
36.23 even 6 810.4.e.f.541.1 2
36.31 odd 6 810.4.e.n.541.1 2
60.23 odd 4 1350.4.c.j.649.1 2
60.47 odd 4 1350.4.c.j.649.2 2
60.59 even 2 1350.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.f.1.1 ✓ 1 4.3 odd 2
270.4.a.j.1.1 yes 1 12.11 even 2
810.4.e.f.271.1 2 36.11 even 6
810.4.e.f.541.1 2 36.23 even 6
810.4.e.n.271.1 2 36.7 odd 6
810.4.e.n.541.1 2 36.31 odd 6
1350.4.a.e.1.1 1 60.59 even 2
1350.4.a.r.1.1 1 20.19 odd 2
1350.4.c.j.649.1 2 60.23 odd 4
1350.4.c.j.649.2 2 60.47 odd 4
1350.4.c.k.649.1 2 20.7 even 4
1350.4.c.k.649.2 2 20.3 even 4
2160.4.a.b.1.1 1 3.2 odd 2
2160.4.a.l.1.1 1 1.1 even 1 trivial