↑

Properties

Label 2160.4.a.s.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 $1$

Related objects

Downloads

Learn more

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 540)
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)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} +22.0000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +22.0000 q^{7} -9.00000 q^{11} +17.0000 q^{13} +75.0000 q^{17} +4.00000 q^{19} +183.000 q^{23} +25.0000 q^{25} -129.000 q^{29} +187.000 q^{31} +110.000 q^{35} -34.0000 q^{37} -264.000 q^{41} -443.000 q^{43} +609.000 q^{47} +141.000 q^{49} +228.000 q^{53} -45.0000 q^{55} +60.0000 q^{59} -454.000 q^{61} +85.0000 q^{65} +244.000 q^{67} +444.000 q^{71} +398.000 q^{73} -198.000 q^{77} +349.000 q^{79} +1038.00 q^{83} +375.000 q^{85} -852.000 q^{89} +374.000 q^{91} +20.0000 q^{95} +914.000 q^{97} +O(q^{100})\)

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
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 22.0000 1.18789 0.593944 − 0.804506i \(-0.297570\pi\)
0.593944 + 0.804506i \(0.297570\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −9.00000 −0.246691 −0.123346 − 0.992364i \(-0.539362\pi\)
−0.123346 + 0.992364i \(0.539362\pi\)
\(12\) 0 0
\(13\) 17.0000 0.362689 0.181344 − 0.983420i \(-0.441955\pi\)
0.181344 + 0.983420i \(0.441955\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 75.0000 1.07001 0.535005 − 0.844849i \(-0.320310\pi\)
0.535005 + 0.844849i \(0.320310\pi\)
\(18\) 0 0
\(19\) 4.00000 0.0482980 0.0241490 − 0.999708i \(-0.492312\pi\)
0.0241490 + 0.999708i \(0.492312\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 183.000 1.65905 0.829525 − 0.558470i \(-0.188611\pi\)
0.829525 + 0.558470i \(0.188611\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −129.000 −0.826024 −0.413012 − 0.910726i \(-0.635523\pi\)
−0.413012 + 0.910726i \(0.635523\pi\)
\(30\) 0 0
\(31\) 187.000 1.08343 0.541713 − 0.840564i \(-0.317776\pi\)
0.541713 + 0.840564i \(0.317776\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 110.000 0.531240
\(36\) 0 0
\(37\) −34.0000 −0.151069 −0.0755347 − 0.997143i \(-0.524066\pi\)
−0.0755347 + 0.997143i \(0.524066\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −264.000 −1.00561 −0.502803 − 0.864401i \(-0.667698\pi\)
−0.502803 + 0.864401i \(0.667698\pi\)
\(42\) 0 0
\(43\) −443.000 −1.57109 −0.785545 − 0.618805i \(-0.787617\pi\)
−0.785545 + 0.618805i \(0.787617\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 609.000 1.89004 0.945019 − 0.327016i \(-0.106043\pi\)
0.945019 + 0.327016i \(0.106043\pi\)
\(48\) 0 0
\(49\) 141.000 0.411079
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 228.000 0.590910 0.295455 − 0.955357i \(-0.404529\pi\)
0.295455 + 0.955357i \(0.404529\pi\)
\(54\) 0 0
\(55\) −45.0000 −0.110324
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 60.0000 0.132396 0.0661978 − 0.997807i \(-0.478913\pi\)
0.0661978 + 0.997807i \(0.478913\pi\)
\(60\) 0 0
\(61\) −454.000 −0.952930 −0.476465 − 0.879193i \(-0.658082\pi\)
−0.476465 + 0.879193i \(0.658082\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 85.0000 0.162199
\(66\) 0 0
\(67\) 244.000 0.444916 0.222458 − 0.974942i \(-0.428592\pi\)
0.222458 + 0.974942i \(0.428592\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 444.000 0.742156 0.371078 − 0.928602i \(-0.378988\pi\)
0.371078 + 0.928602i \(0.378988\pi\)
\(72\) 0 0
\(73\) 398.000 0.638115 0.319057 − 0.947735i \(-0.396634\pi\)
0.319057 + 0.947735i \(0.396634\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −198.000 −0.293041
\(78\) 0 0
\(79\) 349.000 0.497033 0.248516 − 0.968628i \(-0.420057\pi\)
0.248516 + 0.968628i \(0.420057\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1038.00 1.37271 0.686357 − 0.727265i \(-0.259209\pi\)
0.686357 + 0.727265i \(0.259209\pi\)
\(84\) 0 0
\(85\) 375.000 0.478523
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −852.000 −1.01474 −0.507370 − 0.861728i \(-0.669382\pi\)
−0.507370 + 0.861728i \(0.669382\pi\)
\(90\) 0 0
\(91\) 374.000 0.430834
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 20.0000 0.0215995
\(96\) 0 0
\(97\) 914.000 0.956728 0.478364 − 0.878162i \(-0.341230\pi\)
0.478364 + 0.878162i \(0.341230\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1155.00 −1.13789 −0.568945 − 0.822376i \(-0.692648\pi\)
−0.568945 + 0.822376i \(0.692648\pi\)
\(102\) 0 0
\(103\) 574.000 0.549106 0.274553 − 0.961572i \(-0.411470\pi\)
0.274553 + 0.961572i \(0.411470\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 294.000 0.265627 0.132813 − 0.991141i \(-0.457599\pi\)
0.132813 + 0.991141i \(0.457599\pi\)
\(108\) 0 0
\(109\) −340.000 −0.298772 −0.149386 − 0.988779i \(-0.547730\pi\)
−0.149386 + 0.988779i \(0.547730\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −681.000 −0.566930 −0.283465 − 0.958983i \(-0.591484\pi\)
−0.283465 + 0.958983i \(0.591484\pi\)
\(114\) 0 0
\(115\) 915.000 0.741949
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1650.00 1.27105
\(120\) 0 0
\(121\) −1250.00 −0.939144
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −578.000 −0.403852 −0.201926 − 0.979401i \(-0.564720\pi\)
−0.201926 + 0.979401i \(0.564720\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −783.000 −0.522222 −0.261111 − 0.965309i \(-0.584089\pi\)
−0.261111 + 0.965309i \(0.584089\pi\)
\(132\) 0 0
\(133\) 88.0000 0.0573727
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −234.000 −0.145927 −0.0729634 − 0.997335i \(-0.523246\pi\)
−0.0729634 + 0.997335i \(0.523246\pi\)
\(138\) 0 0
\(139\) −3170.00 −1.93436 −0.967179 − 0.254094i \(-0.918223\pi\)
−0.967179 + 0.254094i \(0.918223\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −153.000 −0.0894720
\(144\) 0 0
\(145\) −645.000 −0.369409
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1263.00 0.694423 0.347211 − 0.937787i \(-0.387129\pi\)
0.347211 + 0.937787i \(0.387129\pi\)
\(150\) 0 0
\(151\) −851.000 −0.458632 −0.229316 − 0.973352i \(-0.573649\pi\)
−0.229316 + 0.973352i \(0.573649\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 935.000 0.484523
\(156\) 0 0
\(157\) 2279.00 1.15850 0.579248 − 0.815151i \(-0.303346\pi\)
0.579248 + 0.815151i \(0.303346\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4026.00 1.97077
\(162\) 0 0
\(163\) 1297.00 0.623245 0.311622 − 0.950206i \(-0.399128\pi\)
0.311622 + 0.950206i \(0.399128\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 324.000 0.150131 0.0750655 − 0.997179i \(-0.476083\pi\)
0.0750655 + 0.997179i \(0.476083\pi\)
\(168\) 0 0
\(169\) −1908.00 −0.868457
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 174.000 0.0764681 0.0382340 − 0.999269i \(-0.487827\pi\)
0.0382340 + 0.999269i \(0.487827\pi\)
\(174\) 0 0
\(175\) 550.000 0.237578
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4596.00 −1.91911 −0.959556 − 0.281517i \(-0.909163\pi\)
−0.959556 + 0.281517i \(0.909163\pi\)
\(180\) 0 0
\(181\) 548.000 0.225042 0.112521 − 0.993649i \(-0.464108\pi\)
0.112521 + 0.993649i \(0.464108\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −170.000 −0.0675603
\(186\) 0 0
\(187\) −675.000 −0.263962
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4638.00 1.75704 0.878518 − 0.477709i \(-0.158533\pi\)
0.878518 + 0.477709i \(0.158533\pi\)
\(192\) 0 0
\(193\) −3442.00 −1.28373 −0.641867 − 0.766816i \(-0.721840\pi\)
−0.641867 + 0.766816i \(0.721840\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3312.00 1.19782 0.598909 − 0.800817i \(-0.295601\pi\)
0.598909 + 0.800817i \(0.295601\pi\)
\(198\) 0 0
\(199\) −1745.00 −0.621607 −0.310803 − 0.950474i \(-0.600598\pi\)
−0.310803 + 0.950474i \(0.600598\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2838.00 −0.981224
\(204\) 0 0
\(205\) −1320.00 −0.449721
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −36.0000 −0.0119147
\(210\) 0 0
\(211\) 3358.00 1.09561 0.547806 − 0.836605i \(-0.315463\pi\)
0.547806 + 0.836605i \(0.315463\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2215.00 −0.702613
\(216\) 0 0
\(217\) 4114.00 1.28699
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1275.00 0.388080
\(222\) 0 0
\(223\) −3512.00 −1.05462 −0.527311 − 0.849672i \(-0.676800\pi\)
−0.527311 + 0.849672i \(0.676800\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2112.00 0.617526 0.308763 − 0.951139i \(-0.400085\pi\)
0.308763 + 0.951139i \(0.400085\pi\)
\(228\) 0 0
\(229\) 2900.00 0.836845 0.418422 − 0.908253i \(-0.362583\pi\)
0.418422 + 0.908253i \(0.362583\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5178.00 1.45589 0.727944 − 0.685636i \(-0.240476\pi\)
0.727944 + 0.685636i \(0.240476\pi\)
\(234\) 0 0
\(235\) 3045.00 0.845251
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5010.00 1.35594 0.677971 − 0.735089i \(-0.262860\pi\)
0.677971 + 0.735089i \(0.262860\pi\)
\(240\) 0 0
\(241\) −5203.00 −1.39068 −0.695342 − 0.718679i \(-0.744747\pi\)
−0.695342 + 0.718679i \(0.744747\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 705.000 0.183840
\(246\) 0 0
\(247\) 68.0000 0.0175172
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −549.000 −0.138058 −0.0690290 − 0.997615i \(-0.521990\pi\)
−0.0690290 + 0.997615i \(0.521990\pi\)
\(252\) 0 0
\(253\) −1647.00 −0.409273
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7095.00 1.72208 0.861039 − 0.508539i \(-0.169814\pi\)
0.861039 + 0.508539i \(0.169814\pi\)
\(258\) 0 0
\(259\) −748.000 −0.179454
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4284.00 1.00442 0.502211 − 0.864745i \(-0.332520\pi\)
0.502211 + 0.864745i \(0.332520\pi\)
\(264\) 0 0
\(265\) 1140.00 0.264263
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6669.00 1.51158 0.755792 − 0.654812i \(-0.227252\pi\)
0.755792 + 0.654812i \(0.227252\pi\)
\(270\) 0 0
\(271\) 5560.00 1.24630 0.623148 − 0.782104i \(-0.285854\pi\)
0.623148 + 0.782104i \(0.285854\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −225.000 −0.0493382
\(276\) 0 0
\(277\) 6734.00 1.46067 0.730337 − 0.683087i \(-0.239363\pi\)
0.730337 + 0.683087i \(0.239363\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7710.00 1.63680 0.818399 − 0.574651i \(-0.194862\pi\)
0.818399 + 0.574651i \(0.194862\pi\)
\(282\) 0 0
\(283\) −4736.00 −0.994791 −0.497396 − 0.867524i \(-0.665710\pi\)
−0.497396 + 0.867524i \(0.665710\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5808.00 −1.19455
\(288\) 0 0
\(289\) 712.000 0.144922
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5550.00 1.10660 0.553301 − 0.832981i \(-0.313368\pi\)
0.553301 + 0.832981i \(0.313368\pi\)
\(294\) 0 0
\(295\) 300.000 0.0592091
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3111.00 0.601718
\(300\) 0 0
\(301\) −9746.00 −1.86628
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2270.00 −0.426163
\(306\) 0 0
\(307\) −5663.00 −1.05278 −0.526392 − 0.850242i \(-0.676455\pi\)
−0.526392 + 0.850242i \(0.676455\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1920.00 −0.350075 −0.175037 − 0.984562i \(-0.556005\pi\)
−0.175037 + 0.984562i \(0.556005\pi\)
\(312\) 0 0
\(313\) 2816.00 0.508529 0.254265 − 0.967135i \(-0.418167\pi\)
0.254265 + 0.967135i \(0.418167\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5784.00 −1.02480 −0.512400 − 0.858747i \(-0.671244\pi\)
−0.512400 + 0.858747i \(0.671244\pi\)
\(318\) 0 0
\(319\) 1161.00 0.203773
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 300.000 0.0516794
\(324\) 0 0
\(325\) 425.000 0.0725377
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 13398.0 2.24515
\(330\) 0 0
\(331\) 4354.00 0.723014 0.361507 − 0.932369i \(-0.382262\pi\)
0.361507 + 0.932369i \(0.382262\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1220.00 0.198972
\(336\) 0 0
\(337\) 3896.00 0.629759 0.314879 − 0.949132i \(-0.398036\pi\)
0.314879 + 0.949132i \(0.398036\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1683.00 −0.267271
\(342\) 0 0
\(343\) −4444.00 −0.699573
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7608.00 1.17700 0.588500 − 0.808497i \(-0.299719\pi\)
0.588500 + 0.808497i \(0.299719\pi\)
\(348\) 0 0
\(349\) 4286.00 0.657376 0.328688 − 0.944439i \(-0.393393\pi\)
0.328688 + 0.944439i \(0.393393\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2907.00 −0.438312 −0.219156 − 0.975690i \(-0.570330\pi\)
−0.219156 + 0.975690i \(0.570330\pi\)
\(354\) 0 0
\(355\) 2220.00 0.331902
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5988.00 0.880319 0.440160 − 0.897920i \(-0.354922\pi\)
0.440160 + 0.897920i \(0.354922\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1990.00 0.285374
\(366\) 0 0
\(367\) 3214.00 0.457137 0.228569 − 0.973528i \(-0.426595\pi\)
0.228569 + 0.973528i \(0.426595\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5016.00 0.701935
\(372\) 0 0
\(373\) 9419.00 1.30750 0.653750 − 0.756711i \(-0.273195\pi\)
0.653750 + 0.756711i \(0.273195\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2193.00 −0.299590
\(378\) 0 0
\(379\) −4544.00 −0.615856 −0.307928 − 0.951410i \(-0.599636\pi\)
−0.307928 + 0.951410i \(0.599636\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11487.0 1.53253 0.766264 − 0.642526i \(-0.222113\pi\)
0.766264 + 0.642526i \(0.222113\pi\)
\(384\) 0 0
\(385\) −990.000 −0.131052
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7845.00 −1.02251 −0.511256 − 0.859428i \(-0.670820\pi\)
−0.511256 + 0.859428i \(0.670820\pi\)
\(390\) 0 0
\(391\) 13725.0 1.77520
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1745.00 0.222280
\(396\) 0 0
\(397\) 4133.00 0.522492 0.261246 − 0.965272i \(-0.415867\pi\)
0.261246 + 0.965272i \(0.415867\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3324.00 −0.413947 −0.206973 − 0.978347i \(-0.566361\pi\)
−0.206973 + 0.978347i \(0.566361\pi\)
\(402\) 0 0
\(403\) 3179.00 0.392946
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 306.000 0.0372675
\(408\) 0 0
\(409\) 1871.00 0.226198 0.113099 − 0.993584i \(-0.463922\pi\)
0.113099 + 0.993584i \(0.463922\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1320.00 0.157271
\(414\) 0 0
\(415\) 5190.00 0.613897
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5409.00 0.630661 0.315330 − 0.948982i \(-0.397885\pi\)
0.315330 + 0.948982i \(0.397885\pi\)
\(420\) 0 0
\(421\) −13084.0 −1.51467 −0.757334 − 0.653028i \(-0.773498\pi\)
−0.757334 + 0.653028i \(0.773498\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1875.00 0.214002
\(426\) 0 0
\(427\) −9988.00 −1.13197
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7848.00 −0.877088 −0.438544 − 0.898710i \(-0.644506\pi\)
−0.438544 + 0.898710i \(0.644506\pi\)
\(432\) 0 0
\(433\) −10222.0 −1.13450 −0.567249 − 0.823546i \(-0.691992\pi\)
−0.567249 + 0.823546i \(0.691992\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 732.000 0.0801289
\(438\) 0 0
\(439\) −5672.00 −0.616651 −0.308326 − 0.951281i \(-0.599769\pi\)
−0.308326 + 0.951281i \(0.599769\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 444.000 0.0476187 0.0238093 − 0.999717i \(-0.492421\pi\)
0.0238093 + 0.999717i \(0.492421\pi\)
\(444\) 0 0
\(445\) −4260.00 −0.453805
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10434.0 −1.09668 −0.548342 − 0.836254i \(-0.684741\pi\)
−0.548342 + 0.836254i \(0.684741\pi\)
\(450\) 0 0
\(451\) 2376.00 0.248074
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1870.00 0.192675
\(456\) 0 0
\(457\) 11180.0 1.14437 0.572186 − 0.820124i \(-0.306095\pi\)
0.572186 + 0.820124i \(0.306095\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −15018.0 −1.51726 −0.758631 − 0.651520i \(-0.774132\pi\)
−0.758631 + 0.651520i \(0.774132\pi\)
\(462\) 0 0
\(463\) −16166.0 −1.62267 −0.811337 − 0.584579i \(-0.801260\pi\)
−0.811337 + 0.584579i \(0.801260\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2964.00 0.293699 0.146850 − 0.989159i \(-0.453087\pi\)
0.146850 + 0.989159i \(0.453087\pi\)
\(468\) 0 0
\(469\) 5368.00 0.528510
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3987.00 0.387574
\(474\) 0 0
\(475\) 100.000 0.00965961
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5412.00 −0.516243 −0.258122 − 0.966112i \(-0.583104\pi\)
−0.258122 + 0.966112i \(0.583104\pi\)
\(480\) 0 0
\(481\) −578.000 −0.0547911
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4570.00 0.427862
\(486\) 0 0
\(487\) −12356.0 −1.14970 −0.574850 − 0.818259i \(-0.694940\pi\)
−0.574850 + 0.818259i \(0.694940\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16740.0 1.53863 0.769313 − 0.638872i \(-0.220599\pi\)
0.769313 + 0.638872i \(0.220599\pi\)
\(492\) 0 0
\(493\) −9675.00 −0.883854
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9768.00 0.881599
\(498\) 0 0
\(499\) 14092.0 1.26422 0.632109 − 0.774880i \(-0.282190\pi\)
0.632109 + 0.774880i \(0.282190\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2313.00 −0.205033 −0.102516 − 0.994731i \(-0.532689\pi\)
−0.102516 + 0.994731i \(0.532689\pi\)
\(504\) 0 0
\(505\) −5775.00 −0.508879
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14925.0 −1.29968 −0.649842 − 0.760069i \(-0.725165\pi\)
−0.649842 + 0.760069i \(0.725165\pi\)
\(510\) 0 0
\(511\) 8756.00 0.758009
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2870.00 0.245568
\(516\) 0 0
\(517\) −5481.00 −0.466256
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5820.00 −0.489403 −0.244701 − 0.969598i \(-0.578690\pi\)
−0.244701 + 0.969598i \(0.578690\pi\)
\(522\) 0 0
\(523\) 20875.0 1.74532 0.872658 − 0.488332i \(-0.162395\pi\)
0.872658 + 0.488332i \(0.162395\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14025.0 1.15928
\(528\) 0 0
\(529\) 21322.0 1.75245
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4488.00 −0.364722
\(534\) 0 0
\(535\) 1470.00 0.118792
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1269.00 −0.101409
\(540\) 0 0
\(541\) 22442.0 1.78347 0.891735 − 0.452559i \(-0.149489\pi\)
0.891735 + 0.452559i \(0.149489\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1700.00 −0.133615
\(546\) 0 0
\(547\) −8615.00 −0.673402 −0.336701 − 0.941612i \(-0.609311\pi\)
−0.336701 + 0.941612i \(0.609311\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −516.000 −0.0398954
\(552\) 0 0
\(553\) 7678.00 0.590419
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19524.0 −1.48520 −0.742602 − 0.669733i \(-0.766408\pi\)
−0.742602 + 0.669733i \(0.766408\pi\)
\(558\) 0 0
\(559\) −7531.00 −0.569816
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 13014.0 0.974200 0.487100 − 0.873346i \(-0.338055\pi\)
0.487100 + 0.873346i \(0.338055\pi\)
\(564\) 0 0
\(565\) −3405.00 −0.253539
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18336.0 1.35094 0.675470 − 0.737387i \(-0.263941\pi\)
0.675470 + 0.737387i \(0.263941\pi\)
\(570\) 0 0
\(571\) −3182.00 −0.233209 −0.116605 − 0.993178i \(-0.537201\pi\)
−0.116605 + 0.993178i \(0.537201\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4575.00 0.331810
\(576\) 0 0
\(577\) 7088.00 0.511399 0.255700 − 0.966756i \(-0.417694\pi\)
0.255700 + 0.966756i \(0.417694\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 22836.0 1.63063
\(582\) 0 0
\(583\) −2052.00 −0.145772
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6342.00 0.445932 0.222966 − 0.974826i \(-0.428426\pi\)
0.222966 + 0.974826i \(0.428426\pi\)
\(588\) 0 0
\(589\) 748.000 0.0523273
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −26253.0 −1.81801 −0.909006 − 0.416782i \(-0.863158\pi\)
−0.909006 + 0.416782i \(0.863158\pi\)
\(594\) 0 0
\(595\) 8250.00 0.568432
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5382.00 −0.367116 −0.183558 − 0.983009i \(-0.558762\pi\)
−0.183558 + 0.983009i \(0.558762\pi\)
\(600\) 0 0
\(601\) −28411.0 −1.92830 −0.964150 − 0.265356i \(-0.914510\pi\)
−0.964150 + 0.265356i \(0.914510\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6250.00 −0.419998
\(606\) 0 0
\(607\) −15374.0 −1.02803 −0.514013 − 0.857783i \(-0.671842\pi\)
−0.514013 + 0.857783i \(0.671842\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10353.0 0.685495
\(612\) 0 0
\(613\) −23983.0 −1.58020 −0.790101 − 0.612976i \(-0.789972\pi\)
−0.790101 + 0.612976i \(0.789972\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13773.0 0.898671 0.449336 − 0.893363i \(-0.351661\pi\)
0.449336 + 0.893363i \(0.351661\pi\)
\(618\) 0 0
\(619\) 11146.0 0.723741 0.361870 − 0.932228i \(-0.382138\pi\)
0.361870 + 0.932228i \(0.382138\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −18744.0 −1.20540
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2550.00 −0.161646
\(630\) 0 0
\(631\) 2080.00 0.131226 0.0656129 − 0.997845i \(-0.479100\pi\)
0.0656129 + 0.997845i \(0.479100\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2890.00 −0.180608
\(636\) 0 0
\(637\) 2397.00 0.149094
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 31050.0 1.91326 0.956631 − 0.291302i \(-0.0940883\pi\)
0.956631 + 0.291302i \(0.0940883\pi\)
\(642\) 0 0
\(643\) −9083.00 −0.557074 −0.278537 − 0.960426i \(-0.589849\pi\)
−0.278537 + 0.960426i \(0.589849\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4740.00 −0.288020 −0.144010 − 0.989576i \(-0.546000\pi\)
−0.144010 + 0.989576i \(0.546000\pi\)
\(648\) 0 0
\(649\) −540.000 −0.0326608
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8196.00 0.491170 0.245585 − 0.969375i \(-0.421020\pi\)
0.245585 + 0.969375i \(0.421020\pi\)
\(654\) 0 0
\(655\) −3915.00 −0.233545
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6912.00 0.408579 0.204289 − 0.978911i \(-0.434512\pi\)
0.204289 + 0.978911i \(0.434512\pi\)
\(660\) 0 0
\(661\) −28438.0 −1.67339 −0.836694 − 0.547670i \(-0.815515\pi\)
−0.836694 + 0.547670i \(0.815515\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 440.000 0.0256578
\(666\) 0 0
\(667\) −23607.0 −1.37041
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4086.00 0.235079
\(672\) 0 0
\(673\) 1946.00 0.111460 0.0557302 − 0.998446i \(-0.482251\pi\)
0.0557302 + 0.998446i \(0.482251\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 25956.0 1.47352 0.736758 − 0.676157i \(-0.236356\pi\)
0.736758 + 0.676157i \(0.236356\pi\)
\(678\) 0 0
\(679\) 20108.0 1.13649
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8184.00 −0.458495 −0.229247 − 0.973368i \(-0.573627\pi\)
−0.229247 + 0.973368i \(0.573627\pi\)
\(684\) 0 0
\(685\) −1170.00 −0.0652604
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3876.00 0.214316
\(690\) 0 0
\(691\) −30422.0 −1.67483 −0.837415 − 0.546568i \(-0.815934\pi\)
−0.837415 + 0.546568i \(0.815934\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −15850.0 −0.865072
\(696\) 0 0
\(697\) −19800.0 −1.07601
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27273.0 −1.46945 −0.734727 − 0.678363i \(-0.762690\pi\)
−0.734727 + 0.678363i \(0.762690\pi\)
\(702\) 0 0
\(703\) −136.000 −0.00729635
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −25410.0 −1.35169
\(708\) 0 0
\(709\) 28940.0 1.53295 0.766477 − 0.642272i \(-0.222008\pi\)
0.766477 + 0.642272i \(0.222008\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 34221.0 1.79746
\(714\) 0 0
\(715\) −765.000 −0.0400131
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −606.000 −0.0314325 −0.0157163 − 0.999876i \(-0.505003\pi\)
−0.0157163 + 0.999876i \(0.505003\pi\)
\(720\) 0 0
\(721\) 12628.0 0.652276
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3225.00 −0.165205
\(726\) 0 0
\(727\) 13084.0 0.667481 0.333741 − 0.942665i \(-0.391689\pi\)
0.333741 + 0.942665i \(0.391689\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −33225.0 −1.68108
\(732\) 0 0
\(733\) 27074.0 1.36426 0.682129 − 0.731232i \(-0.261054\pi\)
0.682129 + 0.731232i \(0.261054\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2196.00 −0.109757
\(738\) 0 0
\(739\) 3580.00 0.178204 0.0891018 − 0.996023i \(-0.471600\pi\)
0.0891018 + 0.996023i \(0.471600\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −13947.0 −0.688648 −0.344324 − 0.938851i \(-0.611892\pi\)
−0.344324 + 0.938851i \(0.611892\pi\)
\(744\) 0 0
\(745\) 6315.00 0.310555
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6468.00 0.315535
\(750\) 0 0
\(751\) 31273.0 1.51953 0.759766 − 0.650197i \(-0.225314\pi\)
0.759766 + 0.650197i \(0.225314\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4255.00 −0.205106
\(756\) 0 0
\(757\) −31729.0 −1.52340 −0.761698 − 0.647933i \(-0.775634\pi\)
−0.761698 + 0.647933i \(0.775634\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3138.00 0.149478 0.0747388 − 0.997203i \(-0.476188\pi\)
0.0747388 + 0.997203i \(0.476188\pi\)
\(762\) 0 0
\(763\) −7480.00 −0.354907
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1020.00 0.0480183
\(768\) 0 0
\(769\) 20807.0 0.975708 0.487854 − 0.872925i \(-0.337780\pi\)
0.487854 + 0.872925i \(0.337780\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −33078.0 −1.53911 −0.769556 − 0.638580i \(-0.779522\pi\)
−0.769556 + 0.638580i \(0.779522\pi\)
\(774\) 0 0
\(775\) 4675.00 0.216685
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1056.00 −0.0485688
\(780\) 0 0
\(781\) −3996.00 −0.183083
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11395.0 0.518096
\(786\) 0 0
\(787\) 12541.0 0.568028 0.284014 − 0.958820i \(-0.408334\pi\)
0.284014 + 0.958820i \(0.408334\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14982.0 −0.673450
\(792\) 0 0
\(793\) −7718.00 −0.345617
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −31980.0 −1.42132 −0.710659 − 0.703537i \(-0.751603\pi\)
−0.710659 + 0.703537i \(0.751603\pi\)
\(798\) 0 0
\(799\) 45675.0 2.02236
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3582.00 −0.157417
\(804\) 0 0
\(805\) 20130.0 0.881353
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 3792.00 0.164796 0.0823978 − 0.996600i \(-0.473742\pi\)
0.0823978 + 0.996600i \(0.473742\pi\)
\(810\) 0 0
\(811\) −24086.0 −1.04288 −0.521439 − 0.853289i \(-0.674605\pi\)
−0.521439 + 0.853289i \(0.674605\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6485.00 0.278723
\(816\) 0 0
\(817\) −1772.00 −0.0758806
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −9774.00 −0.415487 −0.207744 − 0.978183i \(-0.566612\pi\)
−0.207744 + 0.978183i \(0.566612\pi\)
\(822\) 0 0
\(823\) −38636.0 −1.63641 −0.818206 − 0.574926i \(-0.805031\pi\)
−0.818206 + 0.574926i \(0.805031\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −16458.0 −0.692020 −0.346010 − 0.938231i \(-0.612464\pi\)
−0.346010 + 0.938231i \(0.612464\pi\)
\(828\) 0 0
\(829\) 20252.0 0.848469 0.424235 − 0.905552i \(-0.360543\pi\)
0.424235 + 0.905552i \(0.360543\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 10575.0 0.439858
\(834\) 0 0
\(835\) 1620.00 0.0671406
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −40722.0 −1.67566 −0.837830 − 0.545930i \(-0.816176\pi\)
−0.837830 + 0.545930i \(0.816176\pi\)
\(840\) 0 0
\(841\) −7748.00 −0.317684
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9540.00 −0.388386
\(846\) 0 0
\(847\) −27500.0 −1.11560
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −6222.00 −0.250632
\(852\) 0 0
\(853\) 12113.0 0.486215 0.243107 − 0.969999i \(-0.421833\pi\)
0.243107 + 0.969999i \(0.421833\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1926.00 0.0767689 0.0383844 − 0.999263i \(-0.487779\pi\)
0.0383844 + 0.999263i \(0.487779\pi\)
\(858\) 0 0
\(859\) −4394.00 −0.174530 −0.0872650 − 0.996185i \(-0.527813\pi\)
−0.0872650 + 0.996185i \(0.527813\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −37491.0 −1.47880 −0.739402 − 0.673264i \(-0.764892\pi\)
−0.739402 + 0.673264i \(0.764892\pi\)
\(864\) 0 0
\(865\) 870.000 0.0341976
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −3141.00 −0.122613
\(870\) 0 0
\(871\) 4148.00 0.161366
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2750.00 0.106248
\(876\) 0 0
\(877\) −21325.0 −0.821088 −0.410544 − 0.911841i \(-0.634661\pi\)
−0.410544 + 0.911841i \(0.634661\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −17982.0 −0.687661 −0.343830 − 0.939032i \(-0.611724\pi\)
−0.343830 + 0.939032i \(0.611724\pi\)
\(882\) 0 0
\(883\) 25636.0 0.977033 0.488516 − 0.872555i \(-0.337538\pi\)
0.488516 + 0.872555i \(0.337538\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 4221.00 0.159783 0.0798914 − 0.996804i \(-0.474543\pi\)
0.0798914 + 0.996804i \(0.474543\pi\)
\(888\) 0 0
\(889\) −12716.0 −0.479731
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2436.00 0.0912851
\(894\) 0 0
\(895\) −22980.0 −0.858253
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −24123.0 −0.894936
\(900\) 0 0
\(901\) 17100.0 0.632279
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2740.00 0.100642
\(906\) 0 0
\(907\) 28393.0 1.03944 0.519721 − 0.854336i \(-0.326036\pi\)
0.519721 + 0.854336i \(0.326036\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −10056.0 −0.365719 −0.182860 − 0.983139i \(-0.558535\pi\)
−0.182860 + 0.983139i \(0.558535\pi\)
\(912\) 0 0
\(913\) −9342.00 −0.338636
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −17226.0 −0.620341
\(918\) 0 0
\(919\) 37249.0 1.33703 0.668515 − 0.743698i \(-0.266930\pi\)
0.668515 + 0.743698i \(0.266930\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 7548.00 0.269172
\(924\) 0 0
\(925\) −850.000 −0.0302139
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1668.00 0.0589078 0.0294539 − 0.999566i \(-0.490623\pi\)
0.0294539 + 0.999566i \(0.490623\pi\)
\(930\) 0 0
\(931\) 564.000 0.0198543
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3375.00 −0.118047
\(936\) 0 0
\(937\) 2786.00 0.0971341 0.0485671 − 0.998820i \(-0.484535\pi\)
0.0485671 + 0.998820i \(0.484535\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −8613.00 −0.298380 −0.149190 − 0.988809i \(-0.547667\pi\)
−0.149190 + 0.988809i \(0.547667\pi\)
\(942\) 0 0
\(943\) −48312.0 −1.66835
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −55602.0 −1.90794 −0.953972 − 0.299897i \(-0.903048\pi\)
−0.953972 + 0.299897i \(0.903048\pi\)
\(948\) 0 0
\(949\) 6766.00 0.231437
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 10785.0 0.366590 0.183295 − 0.983058i \(-0.441324\pi\)
0.183295 + 0.983058i \(0.441324\pi\)
\(954\) 0 0
\(955\) 23190.0 0.785770
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5148.00 −0.173345
\(960\) 0 0
\(961\) 5178.00 0.173811
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −17210.0 −0.574103
\(966\) 0 0
\(967\) 35062.0 1.16600 0.582998 − 0.812474i \(-0.301880\pi\)
0.582998 + 0.812474i \(0.301880\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −49701.0 −1.64262 −0.821308 − 0.570484i \(-0.806755\pi\)
−0.821308 + 0.570484i \(0.806755\pi\)
\(972\) 0 0
\(973\) −69740.0 −2.29780
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 7911.00 0.259054 0.129527 − 0.991576i \(-0.458654\pi\)
0.129527 + 0.991576i \(0.458654\pi\)
\(978\) 0 0
\(979\) 7668.00 0.250327
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 37719.0 1.22385 0.611927 − 0.790914i \(-0.290394\pi\)
0.611927 + 0.790914i \(0.290394\pi\)
\(984\) 0 0
\(985\) 16560.0 0.535681
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −81069.0 −2.60652
\(990\) 0 0
\(991\) −54725.0 −1.75418 −0.877092 − 0.480322i \(-0.840520\pi\)
−0.877092 + 0.480322i \(0.840520\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8725.00 −0.277991
\(996\) 0 0
\(997\) −6505.00 −0.206635 −0.103318 − 0.994648i \(-0.532946\pi\)
−0.103318 + 0.994648i \(0.532946\pi\)
\(998\) 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.s.1.1 1
3.2 odd 2 2160.4.a.h.1.1 1
4.3 odd 2 540.4.a.c.1.1 yes 1
12.11 even 2 540.4.a.a.1.1 ✓ 1
36.7 odd 6 1620.4.i.e.1081.1 2
36.11 even 6 1620.4.i.k.1081.1 2
36.23 even 6 1620.4.i.k.541.1 2
36.31 odd 6 1620.4.i.e.541.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
540.4.a.a.1.1 ✓ 1 12.11 even 2
540.4.a.c.1.1 yes 1 4.3 odd 2
1620.4.i.e.541.1 2 36.31 odd 6
1620.4.i.e.1081.1 2 36.7 odd 6
1620.4.i.k.541.1 2 36.23 even 6
1620.4.i.k.1081.1 2 36.11 even 6
2160.4.a.h.1.1 1 3.2 odd 2
2160.4.a.s.1.1 1 1.1 even 1 trivial