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Properties

Label 1008.2.a.i.1.1
Level $1008$
Weight $2$
Character 1008.1
Self dual yes
Analytic conductor $8.049$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(8.04892052375\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+2.00000 q^{5} -1.00000 q^{7} -6.00000 q^{11} -6.00000 q^{13} -2.00000 q^{17} -4.00000 q^{19} -2.00000 q^{23} -1.00000 q^{25} +8.00000 q^{29} -4.00000 q^{31} -2.00000 q^{35} -6.00000 q^{37} +10.0000 q^{41} +4.00000 q^{43} +4.00000 q^{47} +1.00000 q^{49} -4.00000 q^{53} -12.0000 q^{55} +12.0000 q^{59} -2.00000 q^{61} -12.0000 q^{65} -12.0000 q^{67} -6.00000 q^{71} -2.00000 q^{73} +6.00000 q^{77} +8.00000 q^{79} -4.00000 q^{85} -14.0000 q^{89} +6.00000 q^{91} -8.00000 q^{95} -2.00000 q^{97} +O(q^{100})\)

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
\(5\) 2.00000 0.894427 0.447214 − 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −6.00000 −1.80907 −0.904534 − 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 − 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 − 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 −0.417029 −0.208514 − 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 − 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 − 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.00000 0.583460 0.291730 − 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 − 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 − 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.0000 −1.48842
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 − 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 − 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 − 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −14.0000 −1.48400 −0.741999 − 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 − 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.0000 −1.79107 −0.895533 − 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) 12.0000 1.18240 0.591198 − 0.806527i \(-0.298655\pi\)
0.591198 + 0.806527i \(0.298655\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18.0000 1.74013 0.870063 − 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 − 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 − 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 20.0000 1.70872 0.854358 − 0.519685i \(-0.173951\pi\)
0.854358 + 0.519685i \(0.173951\pi\)
\(138\) 0 0
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 36.0000 3.01047
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.00000 0.327693 0.163846 − 0.986486i \(-0.447610\pi\)
0.163846 + 0.986486i \(0.447610\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 − 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 − 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.00000 0.157622
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 − 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.0000 −0.760286 −0.380143 − 0.924928i \(-0.624125\pi\)
−0.380143 + 0.924928i \(0.624125\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.00000 −0.149487 −0.0747435 − 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 − 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −12.0000 −0.882258
\(186\) 0 0
\(187\) 12.0000 0.877527
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.00000 0.144715 0.0723575 − 0.997379i \(-0.476948\pi\)
0.0723575 + 0.997379i \(0.476948\pi\)
\(192\) 0 0
\(193\) 6.00000 0.431889 0.215945 − 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 − 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 − 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.00000 −0.561490
\(204\) 0 0
\(205\) 20.0000 1.39686
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 28.0000 1.92760 0.963800 − 0.266627i \(-0.0859092\pi\)
0.963800 + 0.266627i \(0.0859092\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.00000 0.545595
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 − 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.0000 −1.32745 −0.663723 − 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 − 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.00000 −0.262049 −0.131024 − 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −26.0000 −1.68180 −0.840900 − 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 − 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.00000 0.127775
\(246\) 0 0
\(247\) 24.0000 1.52708
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 − 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.0000 1.12281 0.561405 − 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 0.369976 0.184988 − 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 0 0
\(265\) −8.00000 −0.491436
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 − 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 4.00000 0.242983 0.121491 − 0.992592i \(-0.461232\pi\)
0.121491 + 0.992592i \(0.461232\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.00000 0.361814
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 − 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) −20.0000 −1.18888 −0.594438 − 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −10.0000 −0.590281
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 − 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 12.0000 0.693978
\(300\) 0 0
\(301\) −4.00000 −0.230556
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.00000 −0.229039
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 − 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 − 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 − 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0000 −0.673987 −0.336994 − 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) −48.0000 −2.68748
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) 6.00000 0.332820
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 − 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.0000 −0.966291 −0.483145 − 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 − 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −18.0000 −0.958043 −0.479022 − 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) −12.0000 −0.636894
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −30.0000 −1.58334 −0.791670 − 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) 16.0000 0.835193 0.417597 − 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 − 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −48.0000 −2.47213
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 − 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 24.0000 1.22634 0.613171 − 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) 12.0000 0.611577
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.0000 0.811232 0.405616 − 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 16.0000 0.805047
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 − 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.0000 0.599251 0.299626 − 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 0 0
\(403\) 24.0000 1.19553
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 36.0000 1.78445
\(408\) 0 0
\(409\) −18.0000 −0.890043 −0.445021 − 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 28.0000 1.36789 0.683945 − 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 − 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) 2.00000 0.0967868
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 18.0000 0.867029 0.433515 − 0.901146i \(-0.357273\pi\)
0.433515 + 0.901146i \(0.357273\pi\)
\(432\) 0 0
\(433\) −38.0000 −1.82616 −0.913082 − 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.00000 0.382692
\(438\) 0 0
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 22.0000 1.04525 0.522626 − 0.852562i \(-0.324953\pi\)
0.522626 + 0.852562i \(0.324953\pi\)
\(444\) 0 0
\(445\) −28.0000 −1.32733
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −8.00000 −0.377543 −0.188772 − 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) 0 0
\(451\) −60.0000 −2.82529
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 − 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 − 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 − 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 − 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −24.0000 −1.10352
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.00000 −0.182765 −0.0913823 − 0.995816i \(-0.529129\pi\)
−0.0913823 + 0.995816i \(0.529129\pi\)
\(480\) 0 0
\(481\) 36.0000 1.64146
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.00000 −0.181631
\(486\) 0 0
\(487\) −40.0000 −1.81257 −0.906287 − 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 − 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 0 0
\(493\) −16.0000 −0.720604
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.00000 0.269137
\(498\) 0 0
\(499\) −28.0000 −1.25345 −0.626726 − 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 32.0000 1.42681 0.713405 − 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −30.0000 −1.32973 −0.664863 − 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 24.0000 1.05757
\(516\) 0 0
\(517\) −24.0000 −1.05552
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 − 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) 16.0000 0.699631 0.349816 − 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −60.0000 −2.59889
\(534\) 0 0
\(535\) 36.0000 1.55642
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 − 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −28.0000 −1.19939
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 − 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −32.0000 −1.36325
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20.0000 −0.847427 −0.423714 − 0.905796i \(-0.639274\pi\)
−0.423714 + 0.905796i \(0.639274\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −28.0000 −1.18006 −0.590030 − 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.0000 0.503066 0.251533 − 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 − 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.00000 0.0834058
\(576\) 0 0
\(577\) −30.0000 −1.24892 −0.624458 − 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 24.0000 0.993978
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −28.0000 −1.15568 −0.577842 − 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18.0000 −0.739171 −0.369586 − 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 26.0000 1.06233 0.531166 − 0.847268i \(-0.321754\pi\)
0.531166 + 0.847268i \(0.321754\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 − 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 50.0000 2.03279
\(606\) 0 0
\(607\) 8.00000 0.324710 0.162355 − 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) 22.0000 0.888572 0.444286 − 0.895885i \(-0.353457\pi\)
0.444286 + 0.895885i \(0.353457\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 − 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 0 0
\(619\) −24.0000 −0.964641 −0.482321 − 0.875995i \(-0.660206\pi\)
−0.482321 + 0.875995i \(0.660206\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 14.0000 0.560898
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 − 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −16.0000 −0.634941
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20.0000 −0.789953 −0.394976 − 0.918691i \(-0.629247\pi\)
−0.394976 + 0.918691i \(0.629247\pi\)
\(642\) 0 0
\(643\) −28.0000 −1.10421 −0.552106 − 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −36.0000 −1.41531 −0.707653 − 0.706560i \(-0.750246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(648\) 0 0
\(649\) −72.0000 −2.82625
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.00000 0.313064 0.156532 − 0.987673i \(-0.449969\pi\)
0.156532 + 0.987673i \(0.449969\pi\)
\(654\) 0 0
\(655\) −16.0000 −0.625172
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 34.0000 1.32445 0.662226 − 0.749304i \(-0.269612\pi\)
0.662226 + 0.749304i \(0.269612\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 8.00000 0.310227
\(666\) 0 0
\(667\) −16.0000 −0.619522
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 − 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.0000 −0.691796 −0.345898 − 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) 2.00000 0.0767530
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.00000 0.229584 0.114792 − 0.993390i \(-0.463380\pi\)
0.114792 + 0.993390i \(0.463380\pi\)
\(684\) 0 0
\(685\) 40.0000 1.52832
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 − 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −20.0000 −0.757554
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 40.0000 1.51078 0.755390 − 0.655276i \(-0.227448\pi\)
0.755390 + 0.655276i \(0.227448\pi\)
\(702\) 0 0
\(703\) 24.0000 0.905177
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18.0000 0.676960
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 − 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 0 0
\(715\) 72.0000 2.69265
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −48.0000 −1.79010 −0.895049 − 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) −12.0000 −0.446903
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.00000 −0.297113
\(726\) 0 0
\(727\) −20.0000 −0.741759 −0.370879 − 0.928681i \(-0.620944\pi\)
−0.370879 + 0.928681i \(0.620944\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) 34.0000 1.25582 0.627909 − 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 72.0000 2.65215
\(738\) 0 0
\(739\) −4.00000 −0.147142 −0.0735712 − 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.0000 0.366864 0.183432 − 0.983032i \(-0.441279\pi\)
0.183432 + 0.983032i \(0.441279\pi\)
\(744\) 0 0
\(745\) 8.00000 0.293097
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.0000 −0.657706
\(750\) 0 0
\(751\) −8.00000 −0.291924 −0.145962 − 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 − 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 − 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 0 0
\(763\) 14.0000 0.506834
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −72.0000 −2.59977
\(768\) 0 0
\(769\) 10.0000 0.360609 0.180305 − 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.0000 0.791285 0.395643 − 0.918405i \(-0.370522\pi\)
0.395643 + 0.918405i \(0.370522\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −40.0000 −1.43315
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −36.0000 −1.28490
\(786\) 0 0
\(787\) −16.0000 −0.570338 −0.285169 − 0.958477i \(-0.592050\pi\)
−0.285169 + 0.958477i \(0.592050\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.0000 −0.637593 −0.318796 − 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) −8.00000 −0.283020
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 12.0000 0.423471
\(804\) 0 0
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 48.0000 1.68551 0.842754 − 0.538299i \(-0.180933\pi\)
0.842754 + 0.538299i \(0.180933\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.00000 −0.280228
\(816\) 0 0
\(817\) −16.0000 −0.559769
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −12.0000 −0.418803 −0.209401 − 0.977830i \(-0.567152\pi\)
−0.209401 + 0.977830i \(0.567152\pi\)
\(822\) 0 0
\(823\) 16.0000 0.557725 0.278862 − 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 18.0000 0.625921 0.312961 − 0.949766i \(-0.398679\pi\)
0.312961 + 0.949766i \(0.398679\pi\)
\(828\) 0 0
\(829\) 26.0000 0.903017 0.451509 − 0.892267i \(-0.350886\pi\)
0.451509 + 0.892267i \(0.350886\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.00000 −0.0692959
\(834\) 0 0
\(835\) −24.0000 −0.830554
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 12.0000 0.414286 0.207143 − 0.978311i \(-0.433583\pi\)
0.207143 + 0.978311i \(0.433583\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 46.0000 1.58245
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) 0 0
\(853\) −2.00000 −0.0684787 −0.0342393 − 0.999414i \(-0.510901\pi\)
−0.0342393 + 0.999414i \(0.510901\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42.0000 1.43469 0.717346 − 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 − 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −26.0000 −0.885050 −0.442525 − 0.896756i \(-0.645917\pi\)
−0.442525 + 0.896756i \(0.645917\pi\)
\(864\) 0 0
\(865\) −20.0000 −0.680020
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −48.0000 −1.62829
\(870\) 0 0
\(871\) 72.0000 2.43963
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 12.0000 0.405674
\(876\) 0 0
\(877\) −34.0000 −1.14810 −0.574049 − 0.818821i \(-0.694628\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.00000 −0.0673817 −0.0336909 − 0.999432i \(-0.510726\pi\)
−0.0336909 + 0.999432i \(0.510726\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 36.0000 1.20876 0.604381 − 0.796696i \(-0.293421\pi\)
0.604381 + 0.796696i \(0.293421\pi\)
\(888\) 0 0
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −16.0000 −0.535420
\(894\) 0 0
\(895\) −4.00000 −0.133705
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −32.0000 −1.06726
\(900\) 0 0
\(901\) 8.00000 0.266519
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −44.0000 −1.46261
\(906\) 0 0
\(907\) 28.0000 0.929725 0.464862 − 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.00000 0.0662630 0.0331315 − 0.999451i \(-0.489452\pi\)
0.0331315 + 0.999451i \(0.489452\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.00000 0.264183
\(918\) 0 0
\(919\) 32.0000 1.05558 0.527791 − 0.849374i \(-0.323020\pi\)
0.527791 + 0.849374i \(0.323020\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 36.0000 1.18495
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 10.0000 0.328089 0.164045 − 0.986453i \(-0.447546\pi\)
0.164045 + 0.986453i \(0.447546\pi\)
\(930\) 0 0
\(931\) −4.00000 −0.131095
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 24.0000 0.784884
\(936\) 0 0
\(937\) −30.0000 −0.980057 −0.490029 − 0.871706i \(-0.663014\pi\)
−0.490029 + 0.871706i \(0.663014\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6.00000 −0.195594 −0.0977972 − 0.995206i \(-0.531180\pi\)
−0.0977972 + 0.995206i \(0.531180\pi\)
\(942\) 0 0
\(943\) −20.0000 −0.651290
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −22.0000 −0.714904 −0.357452 − 0.933932i \(-0.616354\pi\)
−0.357452 + 0.933932i \(0.616354\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 40.0000 1.29573 0.647864 − 0.761756i \(-0.275663\pi\)
0.647864 + 0.761756i \(0.275663\pi\)
\(954\) 0 0
\(955\) 4.00000 0.129437
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −20.0000 −0.645834
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 12.0000 0.386294
\(966\) 0 0
\(967\) −48.0000 −1.54358 −0.771788 − 0.635880i \(-0.780637\pi\)
−0.771788 + 0.635880i \(0.780637\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −16.0000 −0.513464 −0.256732 − 0.966483i \(-0.582646\pi\)
−0.256732 + 0.966483i \(0.582646\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −36.0000 −1.15174 −0.575871 − 0.817541i \(-0.695337\pi\)
−0.575871 + 0.817541i \(0.695337\pi\)
\(978\) 0 0
\(979\) 84.0000 2.68465
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −24.0000 −0.765481 −0.382741 − 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 0 0
\(985\) 24.0000 0.764704
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.00000 −0.254385
\(990\) 0 0
\(991\) 24.0000 0.762385 0.381193 − 0.924496i \(-0.375513\pi\)
0.381193 + 0.924496i \(0.375513\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 32.0000 1.01447
\(996\) 0 0
\(997\) 46.0000 1.45683 0.728417 − 0.685134i \(-0.240256\pi\)
0.728417 + 0.685134i \(0.240256\pi\)
\(998\) 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 1008.2.a.i.1.1 1
3.2 odd 2 1008.2.a.c.1.1 1
4.3 odd 2 504.2.a.g.1.1 yes 1
7.6 odd 2 7056.2.a.j.1.1 1
8.3 odd 2 4032.2.a.j.1.1 1
8.5 even 2 4032.2.a.i.1.1 1
12.11 even 2 504.2.a.d.1.1 ✓ 1
21.20 even 2 7056.2.a.bv.1.1 1
24.5 odd 2 4032.2.a.ba.1.1 1
24.11 even 2 4032.2.a.bl.1.1 1
28.3 even 6 3528.2.s.s.3313.1 2
28.11 odd 6 3528.2.s.c.3313.1 2
28.19 even 6 3528.2.s.s.361.1 2
28.23 odd 6 3528.2.s.c.361.1 2
28.27 even 2 3528.2.a.g.1.1 1
84.11 even 6 3528.2.s.z.3313.1 2
84.23 even 6 3528.2.s.z.361.1 2
84.47 odd 6 3528.2.s.k.361.1 2
84.59 odd 6 3528.2.s.k.3313.1 2
84.83 odd 2 3528.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.a.d.1.1 ✓ 1 12.11 even 2
504.2.a.g.1.1 yes 1 4.3 odd 2
1008.2.a.c.1.1 1 3.2 odd 2
1008.2.a.i.1.1 1 1.1 even 1 trivial
3528.2.a.g.1.1 1 28.27 even 2
3528.2.a.t.1.1 1 84.83 odd 2
3528.2.s.c.361.1 2 28.23 odd 6
3528.2.s.c.3313.1 2 28.11 odd 6
3528.2.s.k.361.1 2 84.47 odd 6
3528.2.s.k.3313.1 2 84.59 odd 6
3528.2.s.s.361.1 2 28.19 even 6
3528.2.s.s.3313.1 2 28.3 even 6
3528.2.s.z.361.1 2 84.23 even 6
3528.2.s.z.3313.1 2 84.11 even 6
4032.2.a.i.1.1 1 8.5 even 2
4032.2.a.j.1.1 1 8.3 odd 2
4032.2.a.ba.1.1 1 24.5 odd 2
4032.2.a.bl.1.1 1 24.11 even 2
7056.2.a.j.1.1 1 7.6 odd 2
7056.2.a.bv.1.1 1 21.20 even 2