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Properties

Label 2448.4.a.f.1.1
Level $2448$
Weight $4$
Character 2448.1
Self dual yes
Analytic conductor $144.437$
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] = [2448,4,Mod(1,2448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2448, 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("2448.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2448.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: \(144.436675694\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2448.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-6.00000 q^{5} +28.0000 q^{7} +O(q^{10})\) \(q-6.00000 q^{5} +28.0000 q^{7} -24.0000 q^{11} -58.0000 q^{13} -17.0000 q^{17} -116.000 q^{19} -60.0000 q^{23} -89.0000 q^{25} -30.0000 q^{29} +172.000 q^{31} -168.000 q^{35} -58.0000 q^{37} +342.000 q^{41} +148.000 q^{43} +288.000 q^{47} +441.000 q^{49} -318.000 q^{53} +144.000 q^{55} +252.000 q^{59} +110.000 q^{61} +348.000 q^{65} +484.000 q^{67} -708.000 q^{71} +362.000 q^{73} -672.000 q^{77} +484.000 q^{79} +756.000 q^{83} +102.000 q^{85} +774.000 q^{89} -1624.00 q^{91} +696.000 q^{95} -382.000 q^{97} +O(q^{100})\)

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
\(5\) −6.00000 −0.536656 −0.268328 − 0.963328i \(-0.586471\pi\)
−0.268328 + 0.963328i \(0.586471\pi\)
\(6\) 0 0
\(7\) 28.0000 1.51186 0.755929 − 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −24.0000 −0.657843 −0.328921 − 0.944357i \(-0.606685\pi\)
−0.328921 + 0.944357i \(0.606685\pi\)
\(12\) 0 0
\(13\) −58.0000 −1.23741 −0.618704 − 0.785624i \(-0.712342\pi\)
−0.618704 + 0.785624i \(0.712342\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −17.0000 −0.242536
\(18\) 0 0
\(19\) −116.000 −1.40064 −0.700322 − 0.713827i \(-0.746960\pi\)
−0.700322 + 0.713827i \(0.746960\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −60.0000 −0.543951 −0.271975 − 0.962304i \(-0.587677\pi\)
−0.271975 + 0.962304i \(0.587677\pi\)
\(24\) 0 0
\(25\) −89.0000 −0.712000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −30.0000 −0.192099 −0.0960493 − 0.995377i \(-0.530621\pi\)
−0.0960493 + 0.995377i \(0.530621\pi\)
\(30\) 0 0
\(31\) 172.000 0.996520 0.498260 − 0.867028i \(-0.333973\pi\)
0.498260 + 0.867028i \(0.333973\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −168.000 −0.811348
\(36\) 0 0
\(37\) −58.0000 −0.257707 −0.128853 − 0.991664i \(-0.541130\pi\)
−0.128853 + 0.991664i \(0.541130\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 342.000 1.30272 0.651359 − 0.758770i \(-0.274199\pi\)
0.651359 + 0.758770i \(0.274199\pi\)
\(42\) 0 0
\(43\) 148.000 0.524879 0.262439 − 0.964948i \(-0.415473\pi\)
0.262439 + 0.964948i \(0.415473\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 288.000 0.893811 0.446906 − 0.894581i \(-0.352526\pi\)
0.446906 + 0.894581i \(0.352526\pi\)
\(48\) 0 0
\(49\) 441.000 1.28571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −318.000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 144.000 0.353036
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 252.000 0.556061 0.278031 − 0.960572i \(-0.410318\pi\)
0.278031 + 0.960572i \(0.410318\pi\)
\(60\) 0 0
\(61\) 110.000 0.230886 0.115443 − 0.993314i \(-0.463171\pi\)
0.115443 + 0.993314i \(0.463171\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 348.000 0.664063
\(66\) 0 0
\(67\) 484.000 0.882537 0.441269 − 0.897375i \(-0.354529\pi\)
0.441269 + 0.897375i \(0.354529\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −708.000 −1.18344 −0.591719 − 0.806144i \(-0.701551\pi\)
−0.591719 + 0.806144i \(0.701551\pi\)
\(72\) 0 0
\(73\) 362.000 0.580396 0.290198 − 0.956967i \(-0.406279\pi\)
0.290198 + 0.956967i \(0.406279\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −672.000 −0.994565
\(78\) 0 0
\(79\) 484.000 0.689294 0.344647 − 0.938732i \(-0.387999\pi\)
0.344647 + 0.938732i \(0.387999\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 756.000 0.999780 0.499890 − 0.866089i \(-0.333374\pi\)
0.499890 + 0.866089i \(0.333374\pi\)
\(84\) 0 0
\(85\) 102.000 0.130158
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 774.000 0.921841 0.460920 − 0.887441i \(-0.347519\pi\)
0.460920 + 0.887441i \(0.347519\pi\)
\(90\) 0 0
\(91\) −1624.00 −1.87079
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 696.000 0.751664
\(96\) 0 0
\(97\) −382.000 −0.399858 −0.199929 − 0.979810i \(-0.564071\pi\)
−0.199929 + 0.979810i \(0.564071\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 210.000 0.206889 0.103444 − 0.994635i \(-0.467014\pi\)
0.103444 + 0.994635i \(0.467014\pi\)
\(102\) 0 0
\(103\) 232.000 0.221938 0.110969 − 0.993824i \(-0.464605\pi\)
0.110969 + 0.993824i \(0.464605\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 432.000 0.390309 0.195154 − 0.980773i \(-0.437479\pi\)
0.195154 + 0.980773i \(0.437479\pi\)
\(108\) 0 0
\(109\) −1186.00 −1.04219 −0.521093 − 0.853500i \(-0.674475\pi\)
−0.521093 + 0.853500i \(0.674475\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 366.000 0.304694 0.152347 − 0.988327i \(-0.451317\pi\)
0.152347 + 0.988327i \(0.451317\pi\)
\(114\) 0 0
\(115\) 360.000 0.291915
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −476.000 −0.366679
\(120\) 0 0
\(121\) −755.000 −0.567243
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1284.00 0.918756
\(126\) 0 0
\(127\) 472.000 0.329789 0.164895 − 0.986311i \(-0.447272\pi\)
0.164895 + 0.986311i \(0.447272\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2760.00 1.84078 0.920391 − 0.391000i \(-0.127871\pi\)
0.920391 + 0.391000i \(0.127871\pi\)
\(132\) 0 0
\(133\) −3248.00 −2.11757
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1098.00 −0.684733 −0.342367 − 0.939566i \(-0.611229\pi\)
−0.342367 + 0.939566i \(0.611229\pi\)
\(138\) 0 0
\(139\) −2528.00 −1.54261 −0.771303 − 0.636468i \(-0.780395\pi\)
−0.771303 + 0.636468i \(0.780395\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1392.00 0.814020
\(144\) 0 0
\(145\) 180.000 0.103091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1614.00 −0.887410 −0.443705 − 0.896173i \(-0.646336\pi\)
−0.443705 + 0.896173i \(0.646336\pi\)
\(150\) 0 0
\(151\) 3328.00 1.79357 0.896784 − 0.442468i \(-0.145897\pi\)
0.896784 + 0.442468i \(0.145897\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1032.00 −0.534789
\(156\) 0 0
\(157\) −2458.00 −1.24949 −0.624744 − 0.780829i \(-0.714797\pi\)
−0.624744 + 0.780829i \(0.714797\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1680.00 −0.822376
\(162\) 0 0
\(163\) −272.000 −0.130704 −0.0653518 − 0.997862i \(-0.520817\pi\)
−0.0653518 + 0.997862i \(0.520817\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3516.00 1.62920 0.814600 − 0.580024i \(-0.196957\pi\)
0.814600 + 0.580024i \(0.196957\pi\)
\(168\) 0 0
\(169\) 1167.00 0.531179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1842.00 0.809507 0.404753 − 0.914426i \(-0.367357\pi\)
0.404753 + 0.914426i \(0.367357\pi\)
\(174\) 0 0
\(175\) −2492.00 −1.07644
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3516.00 −1.46815 −0.734073 − 0.679070i \(-0.762383\pi\)
−0.734073 + 0.679070i \(0.762383\pi\)
\(180\) 0 0
\(181\) 3398.00 1.39542 0.697711 − 0.716379i \(-0.254202\pi\)
0.697711 + 0.716379i \(0.254202\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 348.000 0.138300
\(186\) 0 0
\(187\) 408.000 0.159550
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2640.00 −1.00012 −0.500062 − 0.865990i \(-0.666689\pi\)
−0.500062 + 0.865990i \(0.666689\pi\)
\(192\) 0 0
\(193\) 2882.00 1.07488 0.537438 − 0.843304i \(-0.319392\pi\)
0.537438 + 0.843304i \(0.319392\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 42.0000 0.0151897 0.00759486 − 0.999971i \(-0.497582\pi\)
0.00759486 + 0.999971i \(0.497582\pi\)
\(198\) 0 0
\(199\) 3220.00 1.14703 0.573517 − 0.819194i \(-0.305579\pi\)
0.573517 + 0.819194i \(0.305579\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −840.000 −0.290426
\(204\) 0 0
\(205\) −2052.00 −0.699112
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2784.00 0.921403
\(210\) 0 0
\(211\) 2080.00 0.678640 0.339320 − 0.940671i \(-0.389803\pi\)
0.339320 + 0.940671i \(0.389803\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −888.000 −0.281680
\(216\) 0 0
\(217\) 4816.00 1.50660
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 986.000 0.300116
\(222\) 0 0
\(223\) −4664.00 −1.40056 −0.700279 − 0.713869i \(-0.746941\pi\)
−0.700279 + 0.713869i \(0.746941\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1440.00 −0.421040 −0.210520 − 0.977590i \(-0.567516\pi\)
−0.210520 + 0.977590i \(0.567516\pi\)
\(228\) 0 0
\(229\) −1186.00 −0.342241 −0.171120 − 0.985250i \(-0.554739\pi\)
−0.171120 + 0.985250i \(0.554739\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5334.00 1.49975 0.749875 − 0.661579i \(-0.230113\pi\)
0.749875 + 0.661579i \(0.230113\pi\)
\(234\) 0 0
\(235\) −1728.00 −0.479669
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5328.00 1.44201 0.721003 − 0.692931i \(-0.243681\pi\)
0.721003 + 0.692931i \(0.243681\pi\)
\(240\) 0 0
\(241\) 5618.00 1.50161 0.750803 − 0.660526i \(-0.229667\pi\)
0.750803 + 0.660526i \(0.229667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2646.00 −0.689987
\(246\) 0 0
\(247\) 6728.00 1.73317
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2028.00 −0.509985 −0.254992 − 0.966943i \(-0.582073\pi\)
−0.254992 + 0.966943i \(0.582073\pi\)
\(252\) 0 0
\(253\) 1440.00 0.357834
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1902.00 0.461648 0.230824 − 0.972996i \(-0.425858\pi\)
0.230824 + 0.972996i \(0.425858\pi\)
\(258\) 0 0
\(259\) −1624.00 −0.389616
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5472.00 −1.28296 −0.641479 − 0.767141i \(-0.721679\pi\)
−0.641479 + 0.767141i \(0.721679\pi\)
\(264\) 0 0
\(265\) 1908.00 0.442292
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3570.00 0.809170 0.404585 − 0.914500i \(-0.367416\pi\)
0.404585 + 0.914500i \(0.367416\pi\)
\(270\) 0 0
\(271\) −272.000 −0.0609698 −0.0304849 − 0.999535i \(-0.509705\pi\)
−0.0304849 + 0.999535i \(0.509705\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2136.00 0.468384
\(276\) 0 0
\(277\) 3830.00 0.830767 0.415383 − 0.909646i \(-0.363647\pi\)
0.415383 + 0.909646i \(0.363647\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8874.00 −1.88391 −0.941955 − 0.335740i \(-0.891014\pi\)
−0.941955 + 0.335740i \(0.891014\pi\)
\(282\) 0 0
\(283\) 2632.00 0.552849 0.276424 − 0.961036i \(-0.410850\pi\)
0.276424 + 0.961036i \(0.410850\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9576.00 1.96952
\(288\) 0 0
\(289\) 289.000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6402.00 1.27648 0.638240 − 0.769837i \(-0.279663\pi\)
0.638240 + 0.769837i \(0.279663\pi\)
\(294\) 0 0
\(295\) −1512.00 −0.298414
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3480.00 0.673089
\(300\) 0 0
\(301\) 4144.00 0.793542
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −660.000 −0.123907
\(306\) 0 0
\(307\) 8980.00 1.66943 0.834716 − 0.550681i \(-0.185632\pi\)
0.834716 + 0.550681i \(0.185632\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3972.00 −0.724217 −0.362108 − 0.932136i \(-0.617943\pi\)
−0.362108 + 0.932136i \(0.617943\pi\)
\(312\) 0 0
\(313\) 4730.00 0.854171 0.427085 − 0.904211i \(-0.359540\pi\)
0.427085 + 0.904211i \(0.359540\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2898.00 0.513463 0.256732 − 0.966483i \(-0.417354\pi\)
0.256732 + 0.966483i \(0.417354\pi\)
\(318\) 0 0
\(319\) 720.000 0.126371
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1972.00 0.339706
\(324\) 0 0
\(325\) 5162.00 0.881035
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8064.00 1.35132
\(330\) 0 0
\(331\) 4564.00 0.757886 0.378943 − 0.925420i \(-0.376288\pi\)
0.378943 + 0.925420i \(0.376288\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2904.00 −0.473619
\(336\) 0 0
\(337\) 722.000 0.116706 0.0583529 − 0.998296i \(-0.481415\pi\)
0.0583529 + 0.998296i \(0.481415\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4128.00 −0.655553
\(342\) 0 0
\(343\) 2744.00 0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5544.00 0.857687 0.428844 − 0.903379i \(-0.358921\pi\)
0.428844 + 0.903379i \(0.358921\pi\)
\(348\) 0 0
\(349\) 11126.0 1.70648 0.853239 − 0.521519i \(-0.174635\pi\)
0.853239 + 0.521519i \(0.174635\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7842.00 −1.18240 −0.591200 − 0.806525i \(-0.701346\pi\)
−0.591200 + 0.806525i \(0.701346\pi\)
\(354\) 0 0
\(355\) 4248.00 0.635100
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5040.00 0.740950 0.370475 − 0.928842i \(-0.379195\pi\)
0.370475 + 0.928842i \(0.379195\pi\)
\(360\) 0 0
\(361\) 6597.00 0.961802
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2172.00 −0.311473
\(366\) 0 0
\(367\) 8404.00 1.19533 0.597664 − 0.801747i \(-0.296096\pi\)
0.597664 + 0.801747i \(0.296096\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8904.00 −1.24602
\(372\) 0 0
\(373\) −8098.00 −1.12412 −0.562062 − 0.827095i \(-0.689992\pi\)
−0.562062 + 0.827095i \(0.689992\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1740.00 0.237704
\(378\) 0 0
\(379\) −320.000 −0.0433702 −0.0216851 − 0.999765i \(-0.506903\pi\)
−0.0216851 + 0.999765i \(0.506903\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −10872.0 −1.45048 −0.725239 − 0.688497i \(-0.758271\pi\)
−0.725239 + 0.688497i \(0.758271\pi\)
\(384\) 0 0
\(385\) 4032.00 0.533740
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1374.00 −0.179086 −0.0895431 − 0.995983i \(-0.528541\pi\)
−0.0895431 + 0.995983i \(0.528541\pi\)
\(390\) 0 0
\(391\) 1020.00 0.131927
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2904.00 −0.369914
\(396\) 0 0
\(397\) −7522.00 −0.950928 −0.475464 − 0.879735i \(-0.657720\pi\)
−0.475464 + 0.879735i \(0.657720\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2706.00 −0.336986 −0.168493 − 0.985703i \(-0.553890\pi\)
−0.168493 + 0.985703i \(0.553890\pi\)
\(402\) 0 0
\(403\) −9976.00 −1.23310
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1392.00 0.169530
\(408\) 0 0
\(409\) 266.000 0.0321586 0.0160793 − 0.999871i \(-0.494882\pi\)
0.0160793 + 0.999871i \(0.494882\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7056.00 0.840685
\(414\) 0 0
\(415\) −4536.00 −0.536539
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2688.00 0.313407 0.156703 − 0.987646i \(-0.449913\pi\)
0.156703 + 0.987646i \(0.449913\pi\)
\(420\) 0 0
\(421\) −13810.0 −1.59871 −0.799357 − 0.600857i \(-0.794826\pi\)
−0.799357 + 0.600857i \(0.794826\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1513.00 0.172685
\(426\) 0 0
\(427\) 3080.00 0.349067
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3036.00 0.339302 0.169651 − 0.985504i \(-0.445736\pi\)
0.169651 + 0.985504i \(0.445736\pi\)
\(432\) 0 0
\(433\) −11422.0 −1.26768 −0.633841 − 0.773463i \(-0.718523\pi\)
−0.633841 + 0.773463i \(0.718523\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6960.00 0.761881
\(438\) 0 0
\(439\) 52.0000 0.00565336 0.00282668 − 0.999996i \(-0.499100\pi\)
0.00282668 + 0.999996i \(0.499100\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3108.00 0.333331 0.166665 − 0.986014i \(-0.446700\pi\)
0.166665 + 0.986014i \(0.446700\pi\)
\(444\) 0 0
\(445\) −4644.00 −0.494712
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6114.00 −0.642622 −0.321311 − 0.946974i \(-0.604124\pi\)
−0.321311 + 0.946974i \(0.604124\pi\)
\(450\) 0 0
\(451\) −8208.00 −0.856984
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9744.00 1.00397
\(456\) 0 0
\(457\) 4106.00 0.420286 0.210143 − 0.977671i \(-0.432607\pi\)
0.210143 + 0.977671i \(0.432607\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3366.00 −0.340066 −0.170033 − 0.985438i \(-0.554387\pi\)
−0.170033 + 0.985438i \(0.554387\pi\)
\(462\) 0 0
\(463\) −896.000 −0.0899366 −0.0449683 − 0.998988i \(-0.514319\pi\)
−0.0449683 + 0.998988i \(0.514319\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10236.0 −1.01427 −0.507137 − 0.861866i \(-0.669296\pi\)
−0.507137 + 0.861866i \(0.669296\pi\)
\(468\) 0 0
\(469\) 13552.0 1.33427
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3552.00 −0.345288
\(474\) 0 0
\(475\) 10324.0 0.997258
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5172.00 0.493350 0.246675 − 0.969098i \(-0.420662\pi\)
0.246675 + 0.969098i \(0.420662\pi\)
\(480\) 0 0
\(481\) 3364.00 0.318888
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2292.00 0.214586
\(486\) 0 0
\(487\) 15052.0 1.40056 0.700278 − 0.713870i \(-0.253059\pi\)
0.700278 + 0.713870i \(0.253059\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8700.00 0.799645 0.399822 − 0.916593i \(-0.369072\pi\)
0.399822 + 0.916593i \(0.369072\pi\)
\(492\) 0 0
\(493\) 510.000 0.0465908
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −19824.0 −1.78919
\(498\) 0 0
\(499\) 1168.00 0.104783 0.0523916 − 0.998627i \(-0.483316\pi\)
0.0523916 + 0.998627i \(0.483316\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1740.00 −0.154240 −0.0771200 − 0.997022i \(-0.524572\pi\)
−0.0771200 + 0.997022i \(0.524572\pi\)
\(504\) 0 0
\(505\) −1260.00 −0.111028
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12570.0 1.09461 0.547304 − 0.836934i \(-0.315654\pi\)
0.547304 + 0.836934i \(0.315654\pi\)
\(510\) 0 0
\(511\) 10136.0 0.877476
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1392.00 −0.119105
\(516\) 0 0
\(517\) −6912.00 −0.587987
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −11658.0 −0.980319 −0.490160 − 0.871633i \(-0.663061\pi\)
−0.490160 + 0.871633i \(0.663061\pi\)
\(522\) 0 0
\(523\) −13700.0 −1.14543 −0.572714 − 0.819755i \(-0.694110\pi\)
−0.572714 + 0.819755i \(0.694110\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2924.00 −0.241692
\(528\) 0 0
\(529\) −8567.00 −0.704118
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −19836.0 −1.61199
\(534\) 0 0
\(535\) −2592.00 −0.209462
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10584.0 −0.845798
\(540\) 0 0
\(541\) 17822.0 1.41632 0.708159 − 0.706053i \(-0.249526\pi\)
0.708159 + 0.706053i \(0.249526\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7116.00 0.559295
\(546\) 0 0
\(547\) −3800.00 −0.297032 −0.148516 − 0.988910i \(-0.547450\pi\)
−0.148516 + 0.988910i \(0.547450\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3480.00 0.269062
\(552\) 0 0
\(553\) 13552.0 1.04212
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10074.0 0.766336 0.383168 − 0.923679i \(-0.374833\pi\)
0.383168 + 0.923679i \(0.374833\pi\)
\(558\) 0 0
\(559\) −8584.00 −0.649489
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −15948.0 −1.19383 −0.596917 − 0.802303i \(-0.703608\pi\)
−0.596917 + 0.802303i \(0.703608\pi\)
\(564\) 0 0
\(565\) −2196.00 −0.163516
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −21834.0 −1.60866 −0.804331 − 0.594181i \(-0.797476\pi\)
−0.804331 + 0.594181i \(0.797476\pi\)
\(570\) 0 0
\(571\) 21208.0 1.55434 0.777169 − 0.629292i \(-0.216655\pi\)
0.777169 + 0.629292i \(0.216655\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5340.00 0.387293
\(576\) 0 0
\(577\) 12530.0 0.904039 0.452020 − 0.892008i \(-0.350704\pi\)
0.452020 + 0.892008i \(0.350704\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 21168.0 1.51153
\(582\) 0 0
\(583\) 7632.00 0.542170
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2220.00 0.156097 0.0780487 − 0.996950i \(-0.475131\pi\)
0.0780487 + 0.996950i \(0.475131\pi\)
\(588\) 0 0
\(589\) −19952.0 −1.39577
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25038.0 1.73387 0.866937 − 0.498418i \(-0.166085\pi\)
0.866937 + 0.498418i \(0.166085\pi\)
\(594\) 0 0
\(595\) 2856.00 0.196781
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5784.00 0.394537 0.197269 − 0.980349i \(-0.436793\pi\)
0.197269 + 0.980349i \(0.436793\pi\)
\(600\) 0 0
\(601\) −4198.00 −0.284925 −0.142463 − 0.989800i \(-0.545502\pi\)
−0.142463 + 0.989800i \(0.545502\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4530.00 0.304414
\(606\) 0 0
\(607\) 12124.0 0.810705 0.405353 − 0.914160i \(-0.367149\pi\)
0.405353 + 0.914160i \(0.367149\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16704.0 −1.10601
\(612\) 0 0
\(613\) 7454.00 0.491133 0.245566 − 0.969380i \(-0.421026\pi\)
0.245566 + 0.969380i \(0.421026\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28842.0 −1.88190 −0.940952 − 0.338539i \(-0.890067\pi\)
−0.940952 + 0.338539i \(0.890067\pi\)
\(618\) 0 0
\(619\) 17224.0 1.11840 0.559201 − 0.829032i \(-0.311108\pi\)
0.559201 + 0.829032i \(0.311108\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 21672.0 1.39369
\(624\) 0 0
\(625\) 3421.00 0.218944
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 986.000 0.0625030
\(630\) 0 0
\(631\) 12448.0 0.785336 0.392668 − 0.919680i \(-0.371552\pi\)
0.392668 + 0.919680i \(0.371552\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2832.00 −0.176983
\(636\) 0 0
\(637\) −25578.0 −1.59095
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 25182.0 1.55168 0.775842 − 0.630927i \(-0.217325\pi\)
0.775842 + 0.630927i \(0.217325\pi\)
\(642\) 0 0
\(643\) −17048.0 −1.04558 −0.522790 − 0.852462i \(-0.675109\pi\)
−0.522790 + 0.852462i \(0.675109\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7128.00 0.433123 0.216562 − 0.976269i \(-0.430516\pi\)
0.216562 + 0.976269i \(0.430516\pi\)
\(648\) 0 0
\(649\) −6048.00 −0.365801
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −18462.0 −1.10639 −0.553196 − 0.833051i \(-0.686592\pi\)
−0.553196 + 0.833051i \(0.686592\pi\)
\(654\) 0 0
\(655\) −16560.0 −0.987867
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 28092.0 1.66056 0.830280 − 0.557347i \(-0.188181\pi\)
0.830280 + 0.557347i \(0.188181\pi\)
\(660\) 0 0
\(661\) 10910.0 0.641982 0.320991 − 0.947082i \(-0.395984\pi\)
0.320991 + 0.947082i \(0.395984\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 19488.0 1.13641
\(666\) 0 0
\(667\) 1800.00 0.104492
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2640.00 −0.151887
\(672\) 0 0
\(673\) −28414.0 −1.62746 −0.813729 − 0.581244i \(-0.802566\pi\)
−0.813729 + 0.581244i \(0.802566\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6042.00 0.343003 0.171501 − 0.985184i \(-0.445138\pi\)
0.171501 + 0.985184i \(0.445138\pi\)
\(678\) 0 0
\(679\) −10696.0 −0.604528
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34752.0 1.94692 0.973461 − 0.228851i \(-0.0734969\pi\)
0.973461 + 0.228851i \(0.0734969\pi\)
\(684\) 0 0
\(685\) 6588.00 0.367466
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 18444.0 1.01983
\(690\) 0 0
\(691\) −18320.0 −1.00858 −0.504288 − 0.863536i \(-0.668245\pi\)
−0.504288 + 0.863536i \(0.668245\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 15168.0 0.827849
\(696\) 0 0
\(697\) −5814.00 −0.315955
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22890.0 1.23330 0.616650 − 0.787237i \(-0.288489\pi\)
0.616650 + 0.787237i \(0.288489\pi\)
\(702\) 0 0
\(703\) 6728.00 0.360955
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5880.00 0.312787
\(708\) 0 0
\(709\) 22886.0 1.21227 0.606137 − 0.795361i \(-0.292718\pi\)
0.606137 + 0.795361i \(0.292718\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10320.0 −0.542058
\(714\) 0 0
\(715\) −8352.00 −0.436849
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13452.0 −0.697740 −0.348870 − 0.937171i \(-0.613435\pi\)
−0.348870 + 0.937171i \(0.613435\pi\)
\(720\) 0 0
\(721\) 6496.00 0.335539
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2670.00 0.136774
\(726\) 0 0
\(727\) 27304.0 1.39292 0.696458 − 0.717598i \(-0.254758\pi\)
0.696458 + 0.717598i \(0.254758\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2516.00 −0.127302
\(732\) 0 0
\(733\) 24470.0 1.23304 0.616521 − 0.787338i \(-0.288541\pi\)
0.616521 + 0.787338i \(0.288541\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11616.0 −0.580571
\(738\) 0 0
\(739\) −35252.0 −1.75476 −0.877379 − 0.479798i \(-0.840710\pi\)
−0.877379 + 0.479798i \(0.840710\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1548.00 0.0764342 0.0382171 − 0.999269i \(-0.487832\pi\)
0.0382171 + 0.999269i \(0.487832\pi\)
\(744\) 0 0
\(745\) 9684.00 0.476234
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12096.0 0.590091
\(750\) 0 0
\(751\) −2948.00 −0.143241 −0.0716205 − 0.997432i \(-0.522817\pi\)
−0.0716205 + 0.997432i \(0.522817\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −19968.0 −0.962530
\(756\) 0 0
\(757\) −754.000 −0.0362016 −0.0181008 − 0.999836i \(-0.505762\pi\)
−0.0181008 + 0.999836i \(0.505762\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 41574.0 1.98036 0.990182 − 0.139787i \(-0.0446419\pi\)
0.990182 + 0.139787i \(0.0446419\pi\)
\(762\) 0 0
\(763\) −33208.0 −1.57564
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14616.0 −0.688075
\(768\) 0 0
\(769\) −15118.0 −0.708932 −0.354466 − 0.935069i \(-0.615337\pi\)
−0.354466 + 0.935069i \(0.615337\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −23550.0 −1.09578 −0.547888 − 0.836552i \(-0.684568\pi\)
−0.547888 + 0.836552i \(0.684568\pi\)
\(774\) 0 0
\(775\) −15308.0 −0.709522
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −39672.0 −1.82464
\(780\) 0 0
\(781\) 16992.0 0.778517
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14748.0 0.670546
\(786\) 0 0
\(787\) −5240.00 −0.237339 −0.118670 − 0.992934i \(-0.537863\pi\)
−0.118670 + 0.992934i \(0.537863\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10248.0 0.460654
\(792\) 0 0
\(793\) −6380.00 −0.285700
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5526.00 −0.245597 −0.122799 − 0.992432i \(-0.539187\pi\)
−0.122799 + 0.992432i \(0.539187\pi\)
\(798\) 0 0
\(799\) −4896.00 −0.216781
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8688.00 −0.381809
\(804\) 0 0
\(805\) 10080.0 0.441333
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 438.000 0.0190349 0.00951747 − 0.999955i \(-0.496970\pi\)
0.00951747 + 0.999955i \(0.496970\pi\)
\(810\) 0 0
\(811\) 30448.0 1.31834 0.659170 − 0.751994i \(-0.270908\pi\)
0.659170 + 0.751994i \(0.270908\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1632.00 0.0701429
\(816\) 0 0
\(817\) −17168.0 −0.735168
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 21930.0 0.932232 0.466116 − 0.884724i \(-0.345653\pi\)
0.466116 + 0.884724i \(0.345653\pi\)
\(822\) 0 0
\(823\) 27436.0 1.16204 0.581020 − 0.813889i \(-0.302654\pi\)
0.581020 + 0.813889i \(0.302654\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −17832.0 −0.749794 −0.374897 − 0.927067i \(-0.622322\pi\)
−0.374897 + 0.927067i \(0.622322\pi\)
\(828\) 0 0
\(829\) −4090.00 −0.171353 −0.0856765 − 0.996323i \(-0.527305\pi\)
−0.0856765 + 0.996323i \(0.527305\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −7497.00 −0.311832
\(834\) 0 0
\(835\) −21096.0 −0.874320
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2508.00 −0.103201 −0.0516006 − 0.998668i \(-0.516432\pi\)
−0.0516006 + 0.998668i \(0.516432\pi\)
\(840\) 0 0
\(841\) −23489.0 −0.963098
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7002.00 −0.285061
\(846\) 0 0
\(847\) −21140.0 −0.857590
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3480.00 0.140180
\(852\) 0 0
\(853\) −42442.0 −1.70362 −0.851809 − 0.523852i \(-0.824494\pi\)
−0.851809 + 0.523852i \(0.824494\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −32730.0 −1.30459 −0.652296 − 0.757964i \(-0.726194\pi\)
−0.652296 + 0.757964i \(0.726194\pi\)
\(858\) 0 0
\(859\) 6148.00 0.244199 0.122100 − 0.992518i \(-0.461037\pi\)
0.122100 + 0.992518i \(0.461037\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −22512.0 −0.887969 −0.443985 − 0.896034i \(-0.646436\pi\)
−0.443985 + 0.896034i \(0.646436\pi\)
\(864\) 0 0
\(865\) −11052.0 −0.434427
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −11616.0 −0.453447
\(870\) 0 0
\(871\) −28072.0 −1.09206
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 35952.0 1.38903
\(876\) 0 0
\(877\) 9182.00 0.353539 0.176770 − 0.984252i \(-0.443435\pi\)
0.176770 + 0.984252i \(0.443435\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −28530.0 −1.09103 −0.545517 − 0.838100i \(-0.683666\pi\)
−0.545517 + 0.838100i \(0.683666\pi\)
\(882\) 0 0
\(883\) 12436.0 0.473958 0.236979 − 0.971515i \(-0.423843\pi\)
0.236979 + 0.971515i \(0.423843\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 7404.00 0.280273 0.140136 − 0.990132i \(-0.455246\pi\)
0.140136 + 0.990132i \(0.455246\pi\)
\(888\) 0 0
\(889\) 13216.0 0.498594
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −33408.0 −1.25191
\(894\) 0 0
\(895\) 21096.0 0.787890
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5160.00 −0.191430
\(900\) 0 0
\(901\) 5406.00 0.199889
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −20388.0 −0.748862
\(906\) 0 0
\(907\) −15368.0 −0.562609 −0.281304 − 0.959619i \(-0.590767\pi\)
−0.281304 + 0.959619i \(0.590767\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 27276.0 0.991980 0.495990 − 0.868328i \(-0.334805\pi\)
0.495990 + 0.868328i \(0.334805\pi\)
\(912\) 0 0
\(913\) −18144.0 −0.657699
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 77280.0 2.78300
\(918\) 0 0
\(919\) 46456.0 1.66751 0.833755 − 0.552134i \(-0.186186\pi\)
0.833755 + 0.552134i \(0.186186\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 41064.0 1.46440
\(924\) 0 0
\(925\) 5162.00 0.183487
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −13026.0 −0.460031 −0.230016 − 0.973187i \(-0.573878\pi\)
−0.230016 + 0.973187i \(0.573878\pi\)
\(930\) 0 0
\(931\) −51156.0 −1.80083
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2448.00 −0.0856237
\(936\) 0 0
\(937\) 26330.0 0.917997 0.458999 − 0.888437i \(-0.348208\pi\)
0.458999 + 0.888437i \(0.348208\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −28254.0 −0.978803 −0.489402 − 0.872058i \(-0.662785\pi\)
−0.489402 + 0.872058i \(0.662785\pi\)
\(942\) 0 0
\(943\) −20520.0 −0.708614
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 49272.0 1.69073 0.845367 − 0.534186i \(-0.179382\pi\)
0.845367 + 0.534186i \(0.179382\pi\)
\(948\) 0 0
\(949\) −20996.0 −0.718187
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −32922.0 −1.11904 −0.559522 − 0.828816i \(-0.689015\pi\)
−0.559522 + 0.828816i \(0.689015\pi\)
\(954\) 0 0
\(955\) 15840.0 0.536723
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −30744.0 −1.03522
\(960\) 0 0
\(961\) −207.000 −0.00694841
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −17292.0 −0.576839
\(966\) 0 0
\(967\) 1168.00 0.0388421 0.0194211 − 0.999811i \(-0.493818\pi\)
0.0194211 + 0.999811i \(0.493818\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −19812.0 −0.654786 −0.327393 − 0.944888i \(-0.606170\pi\)
−0.327393 + 0.944888i \(0.606170\pi\)
\(972\) 0 0
\(973\) −70784.0 −2.33220
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 28494.0 0.933064 0.466532 − 0.884504i \(-0.345503\pi\)
0.466532 + 0.884504i \(0.345503\pi\)
\(978\) 0 0
\(979\) −18576.0 −0.606426
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −42708.0 −1.38573 −0.692866 − 0.721067i \(-0.743652\pi\)
−0.692866 + 0.721067i \(0.743652\pi\)
\(984\) 0 0
\(985\) −252.000 −0.00815166
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8880.00 −0.285508
\(990\) 0 0
\(991\) 29500.0 0.945609 0.472804 − 0.881167i \(-0.343242\pi\)
0.472804 + 0.881167i \(0.343242\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −19320.0 −0.615563
\(996\) 0 0
\(997\) −9322.00 −0.296119 −0.148060 − 0.988978i \(-0.547303\pi\)
−0.148060 + 0.988978i \(0.547303\pi\)
\(998\) 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 2448.4.a.f.1.1 1
3.2 odd 2 272.4.a.d.1.1 1
4.3 odd 2 153.4.a.d.1.1 1
12.11 even 2 17.4.a.a.1.1 ✓ 1
24.5 odd 2 1088.4.a.a.1.1 1
24.11 even 2 1088.4.a.l.1.1 1
60.23 odd 4 425.4.b.c.324.2 2
60.47 odd 4 425.4.b.c.324.1 2
60.59 even 2 425.4.a.d.1.1 1
84.83 odd 2 833.4.a.a.1.1 1
132.131 odd 2 2057.4.a.d.1.1 1
204.47 even 4 289.4.b.a.288.1 2
204.191 even 4 289.4.b.a.288.2 2
204.203 even 2 289.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.a.a.1.1 ✓ 1 12.11 even 2
153.4.a.d.1.1 1 4.3 odd 2
272.4.a.d.1.1 1 3.2 odd 2
289.4.a.a.1.1 1 204.203 even 2
289.4.b.a.288.1 2 204.47 even 4
289.4.b.a.288.2 2 204.191 even 4
425.4.a.d.1.1 1 60.59 even 2
425.4.b.c.324.1 2 60.47 odd 4
425.4.b.c.324.2 2 60.23 odd 4
833.4.a.a.1.1 1 84.83 odd 2
1088.4.a.a.1.1 1 24.5 odd 2
1088.4.a.l.1.1 1 24.11 even 2
2057.4.a.d.1.1 1 132.131 odd 2
2448.4.a.f.1.1 1 1.1 even 1 trivial