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Properties

Label 252.4.a.a.1.1
Level $252$
Weight $4$
Character 252.1
Self dual yes
Analytic conductor $14.868$
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] = [252,4,Mod(1,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.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: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 252.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-14.0000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q-14.0000 q^{5} -7.00000 q^{7} -4.00000 q^{11} +54.0000 q^{13} +14.0000 q^{17} +92.0000 q^{19} +152.000 q^{23} +71.0000 q^{25} +106.000 q^{29} -144.000 q^{31} +98.0000 q^{35} +158.000 q^{37} +390.000 q^{41} -508.000 q^{43} +528.000 q^{47} +49.0000 q^{49} -606.000 q^{53} +56.0000 q^{55} +364.000 q^{59} +678.000 q^{61} -756.000 q^{65} +844.000 q^{67} +8.00000 q^{71} -422.000 q^{73} +28.0000 q^{77} +384.000 q^{79} +548.000 q^{83} -196.000 q^{85} -1194.00 q^{89} -378.000 q^{91} -1288.00 q^{95} -1502.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −14.0000 −1.25220 −0.626099 − 0.779744i \(-0.715349\pi\)
−0.626099 + 0.779744i \(0.715349\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.00000 −0.109640 −0.0548202 − 0.998496i \(-0.517459\pi\)
−0.0548202 + 0.998496i \(0.517459\pi\)
\(12\) 0 0
\(13\) 54.0000 1.15207 0.576035 − 0.817425i \(-0.304599\pi\)
0.576035 + 0.817425i \(0.304599\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 14.0000 0.199735 0.0998676 − 0.995001i \(-0.468158\pi\)
0.0998676 + 0.995001i \(0.468158\pi\)
\(18\) 0 0
\(19\) 92.0000 1.11086 0.555428 − 0.831565i \(-0.312555\pi\)
0.555428 + 0.831565i \(0.312555\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 152.000 1.37801 0.689004 − 0.724757i \(-0.258048\pi\)
0.689004 + 0.724757i \(0.258048\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 106.000 0.678748 0.339374 − 0.940651i \(-0.389785\pi\)
0.339374 + 0.940651i \(0.389785\pi\)
\(30\) 0 0
\(31\) −144.000 −0.834296 −0.417148 − 0.908839i \(-0.636970\pi\)
−0.417148 + 0.908839i \(0.636970\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 98.0000 0.473286
\(36\) 0 0
\(37\) 158.000 0.702028 0.351014 − 0.936370i \(-0.385837\pi\)
0.351014 + 0.936370i \(0.385837\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 390.000 1.48556 0.742778 − 0.669538i \(-0.233508\pi\)
0.742778 + 0.669538i \(0.233508\pi\)
\(42\) 0 0
\(43\) −508.000 −1.80161 −0.900806 − 0.434223i \(-0.857023\pi\)
−0.900806 + 0.434223i \(0.857023\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 528.000 1.63865 0.819327 − 0.573327i \(-0.194347\pi\)
0.819327 + 0.573327i \(0.194347\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −606.000 −1.57058 −0.785288 − 0.619131i \(-0.787485\pi\)
−0.785288 + 0.619131i \(0.787485\pi\)
\(54\) 0 0
\(55\) 56.0000 0.137292
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 364.000 0.803199 0.401600 − 0.915815i \(-0.368454\pi\)
0.401600 + 0.915815i \(0.368454\pi\)
\(60\) 0 0
\(61\) 678.000 1.42310 0.711549 − 0.702636i \(-0.247994\pi\)
0.711549 + 0.702636i \(0.247994\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −756.000 −1.44262
\(66\) 0 0
\(67\) 844.000 1.53897 0.769485 − 0.638665i \(-0.220513\pi\)
0.769485 + 0.638665i \(0.220513\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.0133722 0.00668609 − 0.999978i \(-0.497872\pi\)
0.00668609 + 0.999978i \(0.497872\pi\)
\(72\) 0 0
\(73\) −422.000 −0.676594 −0.338297 − 0.941039i \(-0.609851\pi\)
−0.338297 + 0.941039i \(0.609851\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 28.0000 0.0414402
\(78\) 0 0
\(79\) 384.000 0.546878 0.273439 − 0.961889i \(-0.411839\pi\)
0.273439 + 0.961889i \(0.411839\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 548.000 0.724709 0.362354 − 0.932040i \(-0.381973\pi\)
0.362354 + 0.932040i \(0.381973\pi\)
\(84\) 0 0
\(85\) −196.000 −0.250108
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1194.00 −1.42206 −0.711032 − 0.703159i \(-0.751772\pi\)
−0.711032 + 0.703159i \(0.751772\pi\)
\(90\) 0 0
\(91\) −378.000 −0.435441
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1288.00 −1.39101
\(96\) 0 0
\(97\) −1502.00 −1.57222 −0.786108 − 0.618089i \(-0.787907\pi\)
−0.786108 + 0.618089i \(0.787907\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −398.000 −0.392104 −0.196052 − 0.980594i \(-0.562812\pi\)
−0.196052 + 0.980594i \(0.562812\pi\)
\(102\) 0 0
\(103\) 1160.00 1.10969 0.554846 − 0.831953i \(-0.312777\pi\)
0.554846 + 0.831953i \(0.312777\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −324.000 −0.292731 −0.146366 − 0.989231i \(-0.546758\pi\)
−0.146366 + 0.989231i \(0.546758\pi\)
\(108\) 0 0
\(109\) −938.000 −0.824258 −0.412129 − 0.911126i \(-0.635215\pi\)
−0.412129 + 0.911126i \(0.635215\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 622.000 0.517813 0.258906 − 0.965902i \(-0.416638\pi\)
0.258906 + 0.965902i \(0.416638\pi\)
\(114\) 0 0
\(115\) −2128.00 −1.72554
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −98.0000 −0.0754928
\(120\) 0 0
\(121\) −1315.00 −0.987979
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 756.000 0.540950
\(126\) 0 0
\(127\) 1200.00 0.838447 0.419224 − 0.907883i \(-0.362302\pi\)
0.419224 + 0.907883i \(0.362302\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1396.00 0.931062 0.465531 − 0.885032i \(-0.345863\pi\)
0.465531 + 0.885032i \(0.345863\pi\)
\(132\) 0 0
\(133\) −644.000 −0.419864
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2810.00 −1.75237 −0.876184 − 0.481976i \(-0.839919\pi\)
−0.876184 + 0.481976i \(0.839919\pi\)
\(138\) 0 0
\(139\) 4.00000 0.00244083 0.00122042 − 0.999999i \(-0.499612\pi\)
0.00122042 + 0.999999i \(0.499612\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −216.000 −0.126313
\(144\) 0 0
\(145\) −1484.00 −0.849928
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1374.00 −0.755453 −0.377726 − 0.925917i \(-0.623294\pi\)
−0.377726 + 0.925917i \(0.623294\pi\)
\(150\) 0 0
\(151\) 2104.00 1.13391 0.566957 − 0.823747i \(-0.308120\pi\)
0.566957 + 0.823747i \(0.308120\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2016.00 1.04470
\(156\) 0 0
\(157\) 3206.00 1.62972 0.814862 − 0.579655i \(-0.196813\pi\)
0.814862 + 0.579655i \(0.196813\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1064.00 −0.520838
\(162\) 0 0
\(163\) 332.000 0.159535 0.0797676 − 0.996813i \(-0.474582\pi\)
0.0797676 + 0.996813i \(0.474582\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1496.00 −0.693197 −0.346599 − 0.938014i \(-0.612663\pi\)
−0.346599 + 0.938014i \(0.612663\pi\)
\(168\) 0 0
\(169\) 719.000 0.327264
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3322.00 1.45992 0.729962 − 0.683487i \(-0.239538\pi\)
0.729962 + 0.683487i \(0.239538\pi\)
\(174\) 0 0
\(175\) −497.000 −0.214684
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 900.000 0.375805 0.187903 − 0.982188i \(-0.439831\pi\)
0.187903 + 0.982188i \(0.439831\pi\)
\(180\) 0 0
\(181\) 1902.00 0.781075 0.390537 − 0.920587i \(-0.372289\pi\)
0.390537 + 0.920587i \(0.372289\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2212.00 −0.879078
\(186\) 0 0
\(187\) −56.0000 −0.0218991
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4128.00 −1.56383 −0.781915 − 0.623385i \(-0.785757\pi\)
−0.781915 + 0.623385i \(0.785757\pi\)
\(192\) 0 0
\(193\) −1342.00 −0.500514 −0.250257 − 0.968179i \(-0.580515\pi\)
−0.250257 + 0.968179i \(0.580515\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3506.00 1.26798 0.633990 − 0.773341i \(-0.281416\pi\)
0.633990 + 0.773341i \(0.281416\pi\)
\(198\) 0 0
\(199\) 680.000 0.242231 0.121115 − 0.992638i \(-0.461353\pi\)
0.121115 + 0.992638i \(0.461353\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −742.000 −0.256543
\(204\) 0 0
\(205\) −5460.00 −1.86021
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −368.000 −0.121795
\(210\) 0 0
\(211\) 5372.00 1.75272 0.876360 − 0.481657i \(-0.159965\pi\)
0.876360 + 0.481657i \(0.159965\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7112.00 2.25597
\(216\) 0 0
\(217\) 1008.00 0.315334
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 756.000 0.230109
\(222\) 0 0
\(223\) −1072.00 −0.321912 −0.160956 − 0.986962i \(-0.551458\pi\)
−0.160956 + 0.986962i \(0.551458\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2868.00 0.838572 0.419286 − 0.907854i \(-0.362280\pi\)
0.419286 + 0.907854i \(0.362280\pi\)
\(228\) 0 0
\(229\) 4798.00 1.38454 0.692272 − 0.721636i \(-0.256610\pi\)
0.692272 + 0.721636i \(0.256610\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5126.00 1.44127 0.720634 − 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) 0 0
\(235\) −7392.00 −2.05192
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 528.000 0.142902 0.0714508 − 0.997444i \(-0.477237\pi\)
0.0714508 + 0.997444i \(0.477237\pi\)
\(240\) 0 0
\(241\) −814.000 −0.217570 −0.108785 − 0.994065i \(-0.534696\pi\)
−0.108785 + 0.994065i \(0.534696\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −686.000 −0.178885
\(246\) 0 0
\(247\) 4968.00 1.27978
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1932.00 0.485844 0.242922 − 0.970046i \(-0.421894\pi\)
0.242922 + 0.970046i \(0.421894\pi\)
\(252\) 0 0
\(253\) −608.000 −0.151086
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3294.00 0.799510 0.399755 − 0.916622i \(-0.369095\pi\)
0.399755 + 0.916622i \(0.369095\pi\)
\(258\) 0 0
\(259\) −1106.00 −0.265342
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7080.00 1.65997 0.829984 − 0.557787i \(-0.188350\pi\)
0.829984 + 0.557787i \(0.188350\pi\)
\(264\) 0 0
\(265\) 8484.00 1.96667
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7814.00 −1.77111 −0.885554 − 0.464537i \(-0.846221\pi\)
−0.885554 + 0.464537i \(0.846221\pi\)
\(270\) 0 0
\(271\) 3168.00 0.710119 0.355060 − 0.934844i \(-0.384461\pi\)
0.355060 + 0.934844i \(0.384461\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −284.000 −0.0622758
\(276\) 0 0
\(277\) −7858.00 −1.70448 −0.852241 − 0.523150i \(-0.824757\pi\)
−0.852241 + 0.523150i \(0.824757\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6730.00 −1.42875 −0.714374 − 0.699764i \(-0.753288\pi\)
−0.714374 + 0.699764i \(0.753288\pi\)
\(282\) 0 0
\(283\) −3020.00 −0.634348 −0.317174 − 0.948367i \(-0.602734\pi\)
−0.317174 + 0.948367i \(0.602734\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2730.00 −0.561487
\(288\) 0 0
\(289\) −4717.00 −0.960106
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6834.00 1.36262 0.681308 − 0.731997i \(-0.261411\pi\)
0.681308 + 0.731997i \(0.261411\pi\)
\(294\) 0 0
\(295\) −5096.00 −1.00576
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 8208.00 1.58756
\(300\) 0 0
\(301\) 3556.00 0.680945
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −9492.00 −1.78200
\(306\) 0 0
\(307\) 2332.00 0.433532 0.216766 − 0.976224i \(-0.430449\pi\)
0.216766 + 0.976224i \(0.430449\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8840.00 −1.61180 −0.805901 − 0.592050i \(-0.798319\pi\)
−0.805901 + 0.592050i \(0.798319\pi\)
\(312\) 0 0
\(313\) −1046.00 −0.188893 −0.0944464 − 0.995530i \(-0.530108\pi\)
−0.0944464 + 0.995530i \(0.530108\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7542.00 −1.33628 −0.668140 − 0.744035i \(-0.732909\pi\)
−0.668140 + 0.744035i \(0.732909\pi\)
\(318\) 0 0
\(319\) −424.000 −0.0744183
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1288.00 0.221877
\(324\) 0 0
\(325\) 3834.00 0.654376
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3696.00 −0.619353
\(330\) 0 0
\(331\) 2756.00 0.457654 0.228827 − 0.973467i \(-0.426511\pi\)
0.228827 + 0.973467i \(0.426511\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −11816.0 −1.92710
\(336\) 0 0
\(337\) 3954.00 0.639134 0.319567 − 0.947564i \(-0.396463\pi\)
0.319567 + 0.947564i \(0.396463\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 576.000 0.0914726
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6900.00 −1.06747 −0.533734 − 0.845652i \(-0.679212\pi\)
−0.533734 + 0.845652i \(0.679212\pi\)
\(348\) 0 0
\(349\) −2426.00 −0.372094 −0.186047 − 0.982541i \(-0.559568\pi\)
−0.186047 + 0.982541i \(0.559568\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1470.00 0.221644 0.110822 − 0.993840i \(-0.464652\pi\)
0.110822 + 0.993840i \(0.464652\pi\)
\(354\) 0 0
\(355\) −112.000 −0.0167446
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6872.00 −1.01028 −0.505140 − 0.863038i \(-0.668559\pi\)
−0.505140 + 0.863038i \(0.668559\pi\)
\(360\) 0 0
\(361\) 1605.00 0.233999
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5908.00 0.847230
\(366\) 0 0
\(367\) −7072.00 −1.00587 −0.502937 − 0.864323i \(-0.667747\pi\)
−0.502937 + 0.864323i \(0.667747\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4242.00 0.593622
\(372\) 0 0
\(373\) −818.000 −0.113551 −0.0567754 − 0.998387i \(-0.518082\pi\)
−0.0567754 + 0.998387i \(0.518082\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5724.00 0.781966
\(378\) 0 0
\(379\) −5132.00 −0.695549 −0.347775 − 0.937578i \(-0.613063\pi\)
−0.347775 + 0.937578i \(0.613063\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8576.00 1.14416 0.572080 − 0.820198i \(-0.306137\pi\)
0.572080 + 0.820198i \(0.306137\pi\)
\(384\) 0 0
\(385\) −392.000 −0.0518914
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3730.00 0.486166 0.243083 − 0.970006i \(-0.421841\pi\)
0.243083 + 0.970006i \(0.421841\pi\)
\(390\) 0 0
\(391\) 2128.00 0.275237
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5376.00 −0.684800
\(396\) 0 0
\(397\) 6678.00 0.844230 0.422115 − 0.906542i \(-0.361288\pi\)
0.422115 + 0.906542i \(0.361288\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3054.00 0.380323 0.190161 − 0.981753i \(-0.439099\pi\)
0.190161 + 0.981753i \(0.439099\pi\)
\(402\) 0 0
\(403\) −7776.00 −0.961167
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −632.000 −0.0769707
\(408\) 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
\(413\) −2548.00 −0.303581
\(414\) 0 0
\(415\) −7672.00 −0.907479
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −8844.00 −1.03116 −0.515582 − 0.856840i \(-0.672424\pi\)
−0.515582 + 0.856840i \(0.672424\pi\)
\(420\) 0 0
\(421\) −4482.00 −0.518858 −0.259429 − 0.965762i \(-0.583534\pi\)
−0.259429 + 0.965762i \(0.583534\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 994.000 0.113450
\(426\) 0 0
\(427\) −4746.00 −0.537881
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9936.00 −1.11044 −0.555221 − 0.831703i \(-0.687366\pi\)
−0.555221 + 0.831703i \(0.687366\pi\)
\(432\) 0 0
\(433\) −11758.0 −1.30497 −0.652487 − 0.757800i \(-0.726274\pi\)
−0.652487 + 0.757800i \(0.726274\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13984.0 1.53077
\(438\) 0 0
\(439\) −4104.00 −0.446180 −0.223090 − 0.974798i \(-0.571614\pi\)
−0.223090 + 0.974798i \(0.571614\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9748.00 −1.04547 −0.522733 − 0.852496i \(-0.675088\pi\)
−0.522733 + 0.852496i \(0.675088\pi\)
\(444\) 0 0
\(445\) 16716.0 1.78071
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 478.000 0.0502410 0.0251205 − 0.999684i \(-0.492003\pi\)
0.0251205 + 0.999684i \(0.492003\pi\)
\(450\) 0 0
\(451\) −1560.00 −0.162877
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5292.00 0.545259
\(456\) 0 0
\(457\) −11174.0 −1.14376 −0.571879 − 0.820338i \(-0.693785\pi\)
−0.571879 + 0.820338i \(0.693785\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11674.0 1.17942 0.589710 − 0.807615i \(-0.299242\pi\)
0.589710 + 0.807615i \(0.299242\pi\)
\(462\) 0 0
\(463\) 10528.0 1.05676 0.528378 − 0.849009i \(-0.322801\pi\)
0.528378 + 0.849009i \(0.322801\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16604.0 −1.64527 −0.822635 − 0.568569i \(-0.807497\pi\)
−0.822635 + 0.568569i \(0.807497\pi\)
\(468\) 0 0
\(469\) −5908.00 −0.581676
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2032.00 0.197530
\(474\) 0 0
\(475\) 6532.00 0.630966
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8576.00 0.818053 0.409027 − 0.912522i \(-0.365868\pi\)
0.409027 + 0.912522i \(0.365868\pi\)
\(480\) 0 0
\(481\) 8532.00 0.808785
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 21028.0 1.96873
\(486\) 0 0
\(487\) 9704.00 0.902937 0.451468 − 0.892287i \(-0.350900\pi\)
0.451468 + 0.892287i \(0.350900\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4092.00 0.376109 0.188054 − 0.982159i \(-0.439782\pi\)
0.188054 + 0.982159i \(0.439782\pi\)
\(492\) 0 0
\(493\) 1484.00 0.135570
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −56.0000 −0.00505421
\(498\) 0 0
\(499\) 17884.0 1.60440 0.802202 − 0.597052i \(-0.203662\pi\)
0.802202 + 0.597052i \(0.203662\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7704.00 0.682911 0.341456 − 0.939898i \(-0.389080\pi\)
0.341456 + 0.939898i \(0.389080\pi\)
\(504\) 0 0
\(505\) 5572.00 0.490992
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14358.0 −1.25031 −0.625154 − 0.780501i \(-0.714964\pi\)
−0.625154 + 0.780501i \(0.714964\pi\)
\(510\) 0 0
\(511\) 2954.00 0.255729
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −16240.0 −1.38955
\(516\) 0 0
\(517\) −2112.00 −0.179663
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5082.00 −0.427344 −0.213672 − 0.976905i \(-0.568542\pi\)
−0.213672 + 0.976905i \(0.568542\pi\)
\(522\) 0 0
\(523\) −1756.00 −0.146816 −0.0734078 − 0.997302i \(-0.523387\pi\)
−0.0734078 + 0.997302i \(0.523387\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2016.00 −0.166638
\(528\) 0 0
\(529\) 10937.0 0.898907
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 21060.0 1.71146
\(534\) 0 0
\(535\) 4536.00 0.366558
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −196.000 −0.0156629
\(540\) 0 0
\(541\) 16230.0 1.28980 0.644900 − 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 13132.0 1.03213
\(546\) 0 0
\(547\) 17676.0 1.38167 0.690833 − 0.723014i \(-0.257244\pi\)
0.690833 + 0.723014i \(0.257244\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9752.00 0.753991
\(552\) 0 0
\(553\) −2688.00 −0.206701
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12250.0 0.931866 0.465933 − 0.884820i \(-0.345719\pi\)
0.465933 + 0.884820i \(0.345719\pi\)
\(558\) 0 0
\(559\) −27432.0 −2.07558
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10052.0 0.752471 0.376236 − 0.926524i \(-0.377218\pi\)
0.376236 + 0.926524i \(0.377218\pi\)
\(564\) 0 0
\(565\) −8708.00 −0.648404
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −25674.0 −1.89158 −0.945791 − 0.324776i \(-0.894711\pi\)
−0.945791 + 0.324776i \(0.894711\pi\)
\(570\) 0 0
\(571\) 3732.00 0.273519 0.136759 − 0.990604i \(-0.456331\pi\)
0.136759 + 0.990604i \(0.456331\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10792.0 0.782709
\(576\) 0 0
\(577\) −1214.00 −0.0875901 −0.0437950 − 0.999041i \(-0.513945\pi\)
−0.0437950 + 0.999041i \(0.513945\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3836.00 −0.273914
\(582\) 0 0
\(583\) 2424.00 0.172199
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7108.00 −0.499793 −0.249897 − 0.968273i \(-0.580397\pi\)
−0.249897 + 0.968273i \(0.580397\pi\)
\(588\) 0 0
\(589\) −13248.0 −0.926782
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6162.00 −0.426717 −0.213358 − 0.976974i \(-0.568440\pi\)
−0.213358 + 0.976974i \(0.568440\pi\)
\(594\) 0 0
\(595\) 1372.00 0.0945320
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2472.00 −0.168620 −0.0843098 − 0.996440i \(-0.526869\pi\)
−0.0843098 + 0.996440i \(0.526869\pi\)
\(600\) 0 0
\(601\) −13750.0 −0.933235 −0.466617 − 0.884459i \(-0.654528\pi\)
−0.466617 + 0.884459i \(0.654528\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 18410.0 1.23715
\(606\) 0 0
\(607\) −11376.0 −0.760688 −0.380344 − 0.924845i \(-0.624194\pi\)
−0.380344 + 0.924845i \(0.624194\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 28512.0 1.88784
\(612\) 0 0
\(613\) 20382.0 1.34294 0.671469 − 0.741032i \(-0.265664\pi\)
0.671469 + 0.741032i \(0.265664\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21178.0 −1.38184 −0.690919 − 0.722932i \(-0.742794\pi\)
−0.690919 + 0.722932i \(0.742794\pi\)
\(618\) 0 0
\(619\) −4700.00 −0.305184 −0.152592 − 0.988289i \(-0.548762\pi\)
−0.152592 + 0.988289i \(0.548762\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8358.00 0.537490
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2212.00 0.140220
\(630\) 0 0
\(631\) −21736.0 −1.37131 −0.685655 − 0.727927i \(-0.740484\pi\)
−0.685655 + 0.727927i \(0.740484\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −16800.0 −1.04990
\(636\) 0 0
\(637\) 2646.00 0.164581
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 13022.0 0.802399 0.401200 − 0.915991i \(-0.368593\pi\)
0.401200 + 0.915991i \(0.368593\pi\)
\(642\) 0 0
\(643\) 3308.00 0.202885 0.101442 − 0.994841i \(-0.467654\pi\)
0.101442 + 0.994841i \(0.467654\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13800.0 0.838538 0.419269 − 0.907862i \(-0.362286\pi\)
0.419269 + 0.907862i \(0.362286\pi\)
\(648\) 0 0
\(649\) −1456.00 −0.0880632
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2682.00 0.160727 0.0803635 − 0.996766i \(-0.474392\pi\)
0.0803635 + 0.996766i \(0.474392\pi\)
\(654\) 0 0
\(655\) −19544.0 −1.16587
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −23836.0 −1.40898 −0.704491 − 0.709713i \(-0.748825\pi\)
−0.704491 + 0.709713i \(0.748825\pi\)
\(660\) 0 0
\(661\) −11282.0 −0.663871 −0.331936 − 0.943302i \(-0.607702\pi\)
−0.331936 + 0.943302i \(0.607702\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9016.00 0.525753
\(666\) 0 0
\(667\) 16112.0 0.935321
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2712.00 −0.156029
\(672\) 0 0
\(673\) −13726.0 −0.786179 −0.393089 − 0.919500i \(-0.628594\pi\)
−0.393089 + 0.919500i \(0.628594\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4974.00 −0.282373 −0.141186 − 0.989983i \(-0.545092\pi\)
−0.141186 + 0.989983i \(0.545092\pi\)
\(678\) 0 0
\(679\) 10514.0 0.594242
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8988.00 0.503538 0.251769 − 0.967787i \(-0.418988\pi\)
0.251769 + 0.967787i \(0.418988\pi\)
\(684\) 0 0
\(685\) 39340.0 2.19431
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −32724.0 −1.80941
\(690\) 0 0
\(691\) 10172.0 0.560002 0.280001 − 0.960000i \(-0.409665\pi\)
0.280001 + 0.960000i \(0.409665\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −56.0000 −0.00305640
\(696\) 0 0
\(697\) 5460.00 0.296718
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27446.0 −1.47877 −0.739387 − 0.673280i \(-0.764885\pi\)
−0.739387 + 0.673280i \(0.764885\pi\)
\(702\) 0 0
\(703\) 14536.0 0.779852
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2786.00 0.148201
\(708\) 0 0
\(709\) 3998.00 0.211774 0.105887 − 0.994378i \(-0.466232\pi\)
0.105887 + 0.994378i \(0.466232\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −21888.0 −1.14967
\(714\) 0 0
\(715\) 3024.00 0.158169
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −25872.0 −1.34195 −0.670976 − 0.741480i \(-0.734124\pi\)
−0.670976 + 0.741480i \(0.734124\pi\)
\(720\) 0 0
\(721\) −8120.00 −0.419424
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7526.00 0.385529
\(726\) 0 0
\(727\) 12088.0 0.616670 0.308335 − 0.951278i \(-0.400228\pi\)
0.308335 + 0.951278i \(0.400228\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7112.00 −0.359845
\(732\) 0 0
\(733\) 7974.00 0.401810 0.200905 − 0.979611i \(-0.435612\pi\)
0.200905 + 0.979611i \(0.435612\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3376.00 −0.168733
\(738\) 0 0
\(739\) −31764.0 −1.58113 −0.790567 − 0.612376i \(-0.790214\pi\)
−0.790567 + 0.612376i \(0.790214\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −888.000 −0.0438460 −0.0219230 − 0.999760i \(-0.506979\pi\)
−0.0219230 + 0.999760i \(0.506979\pi\)
\(744\) 0 0
\(745\) 19236.0 0.945977
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2268.00 0.110642
\(750\) 0 0
\(751\) −34656.0 −1.68391 −0.841954 − 0.539549i \(-0.818595\pi\)
−0.841954 + 0.539549i \(0.818595\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −29456.0 −1.41989
\(756\) 0 0
\(757\) −22866.0 −1.09786 −0.548929 − 0.835869i \(-0.684964\pi\)
−0.548929 + 0.835869i \(0.684964\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22570.0 −1.07511 −0.537557 − 0.843227i \(-0.680653\pi\)
−0.537557 + 0.843227i \(0.680653\pi\)
\(762\) 0 0
\(763\) 6566.00 0.311540
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 19656.0 0.925342
\(768\) 0 0
\(769\) −1790.00 −0.0839389 −0.0419695 − 0.999119i \(-0.513363\pi\)
−0.0419695 + 0.999119i \(0.513363\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2990.00 −0.139124 −0.0695620 − 0.997578i \(-0.522160\pi\)
−0.0695620 + 0.997578i \(0.522160\pi\)
\(774\) 0 0
\(775\) −10224.0 −0.473880
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 35880.0 1.65024
\(780\) 0 0
\(781\) −32.0000 −0.00146613
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −44884.0 −2.04074
\(786\) 0 0
\(787\) −30756.0 −1.39305 −0.696527 − 0.717531i \(-0.745272\pi\)
−0.696527 + 0.717531i \(0.745272\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4354.00 −0.195715
\(792\) 0 0
\(793\) 36612.0 1.63951
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −15126.0 −0.672259 −0.336129 − 0.941816i \(-0.609118\pi\)
−0.336129 + 0.941816i \(0.609118\pi\)
\(798\) 0 0
\(799\) 7392.00 0.327297
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1688.00 0.0741821
\(804\) 0 0
\(805\) 14896.0 0.652193
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6502.00 0.282569 0.141284 − 0.989969i \(-0.454877\pi\)
0.141284 + 0.989969i \(0.454877\pi\)
\(810\) 0 0
\(811\) −8252.00 −0.357296 −0.178648 − 0.983913i \(-0.557172\pi\)
−0.178648 + 0.983913i \(0.557172\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −4648.00 −0.199770
\(816\) 0 0
\(817\) −46736.0 −2.00133
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 21986.0 0.934612 0.467306 − 0.884096i \(-0.345225\pi\)
0.467306 + 0.884096i \(0.345225\pi\)
\(822\) 0 0
\(823\) 3736.00 0.158237 0.0791183 − 0.996865i \(-0.474790\pi\)
0.0791183 + 0.996865i \(0.474790\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 23820.0 1.00158 0.500788 − 0.865570i \(-0.333044\pi\)
0.500788 + 0.865570i \(0.333044\pi\)
\(828\) 0 0
\(829\) 7942.00 0.332735 0.166367 − 0.986064i \(-0.446796\pi\)
0.166367 + 0.986064i \(0.446796\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 686.000 0.0285336
\(834\) 0 0
\(835\) 20944.0 0.868020
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −21016.0 −0.864783 −0.432391 − 0.901686i \(-0.642330\pi\)
−0.432391 + 0.901686i \(0.642330\pi\)
\(840\) 0 0
\(841\) −13153.0 −0.539301
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10066.0 −0.409800
\(846\) 0 0
\(847\) 9205.00 0.373421
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 24016.0 0.967401
\(852\) 0 0
\(853\) 24878.0 0.998601 0.499300 − 0.866429i \(-0.333590\pi\)
0.499300 + 0.866429i \(0.333590\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6390.00 0.254700 0.127350 − 0.991858i \(-0.459353\pi\)
0.127350 + 0.991858i \(0.459353\pi\)
\(858\) 0 0
\(859\) −46444.0 −1.84476 −0.922380 − 0.386284i \(-0.873759\pi\)
−0.922380 + 0.386284i \(0.873759\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 25408.0 1.00220 0.501100 − 0.865389i \(-0.332929\pi\)
0.501100 + 0.865389i \(0.332929\pi\)
\(864\) 0 0
\(865\) −46508.0 −1.82811
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1536.00 −0.0599600
\(870\) 0 0
\(871\) 45576.0 1.77300
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −5292.00 −0.204460
\(876\) 0 0
\(877\) 1078.00 0.0415068 0.0207534 − 0.999785i \(-0.493394\pi\)
0.0207534 + 0.999785i \(0.493394\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 45006.0 1.72110 0.860551 − 0.509364i \(-0.170119\pi\)
0.860551 + 0.509364i \(0.170119\pi\)
\(882\) 0 0
\(883\) 4028.00 0.153514 0.0767571 − 0.997050i \(-0.475543\pi\)
0.0767571 + 0.997050i \(0.475543\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 29304.0 1.10928 0.554640 − 0.832090i \(-0.312856\pi\)
0.554640 + 0.832090i \(0.312856\pi\)
\(888\) 0 0
\(889\) −8400.00 −0.316903
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 48576.0 1.82031
\(894\) 0 0
\(895\) −12600.0 −0.470583
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −15264.0 −0.566277
\(900\) 0 0
\(901\) −8484.00 −0.313699
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −26628.0 −0.978060
\(906\) 0 0
\(907\) 50916.0 1.86399 0.931995 − 0.362472i \(-0.118067\pi\)
0.931995 + 0.362472i \(0.118067\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 24432.0 0.888549 0.444275 − 0.895891i \(-0.353461\pi\)
0.444275 + 0.895891i \(0.353461\pi\)
\(912\) 0 0
\(913\) −2192.00 −0.0794574
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −9772.00 −0.351908
\(918\) 0 0
\(919\) −20360.0 −0.730810 −0.365405 − 0.930849i \(-0.619070\pi\)
−0.365405 + 0.930849i \(0.619070\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 432.000 0.0154057
\(924\) 0 0
\(925\) 11218.0 0.398752
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −23202.0 −0.819411 −0.409706 − 0.912218i \(-0.634369\pi\)
−0.409706 + 0.912218i \(0.634369\pi\)
\(930\) 0 0
\(931\) 4508.00 0.158694
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 784.000 0.0274220
\(936\) 0 0
\(937\) −1990.00 −0.0693815 −0.0346908 − 0.999398i \(-0.511045\pi\)
−0.0346908 + 0.999398i \(0.511045\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 51130.0 1.77130 0.885648 − 0.464356i \(-0.153714\pi\)
0.885648 + 0.464356i \(0.153714\pi\)
\(942\) 0 0
\(943\) 59280.0 2.04711
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 47044.0 1.61428 0.807141 − 0.590359i \(-0.201014\pi\)
0.807141 + 0.590359i \(0.201014\pi\)
\(948\) 0 0
\(949\) −22788.0 −0.779483
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −46858.0 −1.59274 −0.796369 − 0.604811i \(-0.793249\pi\)
−0.796369 + 0.604811i \(0.793249\pi\)
\(954\) 0 0
\(955\) 57792.0 1.95823
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 19670.0 0.662333
\(960\) 0 0
\(961\) −9055.00 −0.303951
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 18788.0 0.626743
\(966\) 0 0
\(967\) 30632.0 1.01867 0.509337 − 0.860567i \(-0.329890\pi\)
0.509337 + 0.860567i \(0.329890\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3804.00 0.125722 0.0628611 − 0.998022i \(-0.479978\pi\)
0.0628611 + 0.998022i \(0.479978\pi\)
\(972\) 0 0
\(973\) −28.0000 −0.000922548 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 49326.0 1.61523 0.807614 − 0.589711i \(-0.200758\pi\)
0.807614 + 0.589711i \(0.200758\pi\)
\(978\) 0 0
\(979\) 4776.00 0.155916
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −11112.0 −0.360547 −0.180274 − 0.983617i \(-0.557698\pi\)
−0.180274 + 0.983617i \(0.557698\pi\)
\(984\) 0 0
\(985\) −49084.0 −1.58776
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −77216.0 −2.48263
\(990\) 0 0
\(991\) 13616.0 0.436455 0.218227 − 0.975898i \(-0.429973\pi\)
0.218227 + 0.975898i \(0.429973\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −9520.00 −0.303321
\(996\) 0 0
\(997\) −56674.0 −1.80028 −0.900142 − 0.435596i \(-0.856538\pi\)
−0.900142 + 0.435596i \(0.856538\pi\)
\(998\) 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 252.4.a.a.1.1 1
3.2 odd 2 84.4.a.b.1.1 ✓ 1
4.3 odd 2 1008.4.a.d.1.1 1
7.2 even 3 1764.4.k.n.361.1 2
7.3 odd 6 1764.4.k.c.1549.1 2
7.4 even 3 1764.4.k.n.1549.1 2
7.5 odd 6 1764.4.k.c.361.1 2
7.6 odd 2 1764.4.a.l.1.1 1
12.11 even 2 336.4.a.e.1.1 1
15.2 even 4 2100.4.k.g.1849.1 2
15.8 even 4 2100.4.k.g.1849.2 2
15.14 odd 2 2100.4.a.g.1.1 1
21.2 odd 6 588.4.i.a.361.1 2
21.5 even 6 588.4.i.h.361.1 2
21.11 odd 6 588.4.i.a.373.1 2
21.17 even 6 588.4.i.h.373.1 2
21.20 even 2 588.4.a.a.1.1 1
24.5 odd 2 1344.4.a.b.1.1 1
24.11 even 2 1344.4.a.p.1.1 1
84.83 odd 2 2352.4.a.v.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.4.a.b.1.1 ✓ 1 3.2 odd 2
252.4.a.a.1.1 1 1.1 even 1 trivial
336.4.a.e.1.1 1 12.11 even 2
588.4.a.a.1.1 1 21.20 even 2
588.4.i.a.361.1 2 21.2 odd 6
588.4.i.a.373.1 2 21.11 odd 6
588.4.i.h.361.1 2 21.5 even 6
588.4.i.h.373.1 2 21.17 even 6
1008.4.a.d.1.1 1 4.3 odd 2
1344.4.a.b.1.1 1 24.5 odd 2
1344.4.a.p.1.1 1 24.11 even 2
1764.4.a.l.1.1 1 7.6 odd 2
1764.4.k.c.361.1 2 7.5 odd 6
1764.4.k.c.1549.1 2 7.3 odd 6
1764.4.k.n.361.1 2 7.2 even 3
1764.4.k.n.1549.1 2 7.4 even 3
2100.4.a.g.1.1 1 15.14 odd 2
2100.4.k.g.1849.1 2 15.2 even 4
2100.4.k.g.1849.2 2 15.8 even 4
2352.4.a.v.1.1 1 84.83 odd 2