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Properties

Label 2736.2.a.i.1.1
Level $2736$
Weight $2$
Character 2736.1
Self dual yes
Analytic conductor $21.847$
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] = [2736,2,Mod(1,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, 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("2736.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 456)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2736.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} +3.00000 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +3.00000 q^{7} -5.00000 q^{11} -2.00000 q^{13} +1.00000 q^{17} -1.00000 q^{19} +4.00000 q^{23} -4.00000 q^{25} +6.00000 q^{29} +10.0000 q^{31} -3.00000 q^{35} +11.0000 q^{43} +9.00000 q^{47} +2.00000 q^{49} -10.0000 q^{53} +5.00000 q^{55} +4.00000 q^{59} -5.00000 q^{61} +2.00000 q^{65} +4.00000 q^{67} +8.00000 q^{71} +13.0000 q^{73} -15.0000 q^{77} -4.00000 q^{79} -4.00000 q^{83} -1.00000 q^{85} +6.00000 q^{89} -6.00000 q^{91} +1.00000 q^{95} +2.00000 q^{97} +O(q^{100})\)

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
\(5\) −1.00000 −0.447214 −0.223607 − 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) 3.00000 1.13389 0.566947 − 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.00000 −1.50756 −0.753778 − 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 − 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 0.242536 0.121268 − 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 − 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 − 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 11.0000 1.67748 0.838742 − 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.00000 1.31278 0.656392 − 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 − 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) −5.00000 −0.640184 −0.320092 − 0.947386i \(-0.603714\pi\)
−0.320092 + 0.947386i \(0.603714\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 − 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 13.0000 1.52153 0.760767 − 0.649025i \(-0.224823\pi\)
0.760767 + 0.649025i \(0.224823\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −15.0000 −1.70941
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 − 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 − 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 − 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 − 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 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
\(109\) −8.00000 −0.766261 −0.383131 − 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 − 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −19.0000 −1.66004 −0.830019 − 0.557735i \(-0.811670\pi\)
−0.830019 + 0.557735i \(0.811670\pi\)
\(132\) 0 0
\(133\) −3.00000 −0.260133
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 0.768922 0.384461 − 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) 0 0
\(139\) 15.0000 1.27228 0.636142 − 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.0000 0.836242
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.00000 0.0819232 0.0409616 − 0.999161i \(-0.486958\pi\)
0.0409616 + 0.999161i \(0.486958\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 − 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −10.0000 −0.803219
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) 24.0000 1.87983 0.939913 − 0.341415i \(-0.110906\pi\)
0.939913 + 0.341415i \(0.110906\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 18.0000 1.39288 0.696441 − 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.0000 1.36851 0.684257 − 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 0 0
\(175\) −12.0000 −0.907115
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.00000 0.448461 0.224231 − 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 − 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5.00000 −0.365636
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 − 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) −16.0000 −1.15171 −0.575853 − 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 11.0000 0.779769 0.389885 − 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 18.0000 1.26335
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 − 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.0000 −0.750194
\(216\) 0 0
\(217\) 30.0000 2.03653
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 − 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.00000 −0.398234 −0.199117 − 0.979976i \(-0.563807\pi\)
−0.199117 + 0.979976i \(0.563807\pi\)
\(228\) 0 0
\(229\) −11.0000 −0.726900 −0.363450 − 0.931614i \(-0.618401\pi\)
−0.363450 + 0.931614i \(0.618401\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 23.0000 1.50678 0.753390 − 0.657574i \(-0.228417\pi\)
0.753390 + 0.657574i \(0.228417\pi\)
\(234\) 0 0
\(235\) −9.00000 −0.587095
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 11.0000 0.711531 0.355765 − 0.934575i \(-0.384220\pi\)
0.355765 + 0.934575i \(0.384220\pi\)
\(240\) 0 0
\(241\) −12.0000 −0.772988 −0.386494 − 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.00000 −0.127775
\(246\) 0 0
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −19.0000 −1.19927 −0.599635 − 0.800274i \(-0.704687\pi\)
−0.599635 + 0.800274i \(0.704687\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 16.0000 0.998053 0.499026 − 0.866587i \(-0.333691\pi\)
0.499026 + 0.866587i \(0.333691\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −23.0000 −1.41824 −0.709120 − 0.705087i \(-0.750908\pi\)
−0.709120 + 0.705087i \(0.750908\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 22.0000 1.34136 0.670682 − 0.741745i \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 − 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 20.0000 1.20605
\(276\) 0 0
\(277\) 25.0000 1.50210 0.751052 − 0.660243i \(-0.229547\pi\)
0.751052 + 0.660243i \(0.229547\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 − 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 0 0
\(283\) 7.00000 0.416107 0.208053 − 0.978117i \(-0.433287\pi\)
0.208053 + 0.978117i \(0.433287\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −12.0000 −0.701047 −0.350524 − 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.00000 −0.462652
\(300\) 0 0
\(301\) 33.0000 1.90209
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5.00000 0.286299
\(306\) 0 0
\(307\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −27.0000 −1.53103 −0.765515 − 0.643418i \(-0.777516\pi\)
−0.765515 + 0.643418i \(0.777516\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 − 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.0000 −1.34797 −0.673987 − 0.738743i \(-0.735420\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(318\) 0 0
\(319\) −30.0000 −1.67968
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.00000 −0.0556415
\(324\) 0 0
\(325\) 8.00000 0.443760
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 27.0000 1.48856
\(330\) 0 0
\(331\) −32.0000 −1.75888 −0.879440 − 0.476011i \(-0.842082\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 − 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −50.0000 −2.70765
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 21.0000 1.12734 0.563670 − 0.826000i \(-0.309389\pi\)
0.563670 + 0.826000i \(0.309389\pi\)
\(348\) 0 0
\(349\) −27.0000 −1.44528 −0.722638 − 0.691226i \(-0.757071\pi\)
−0.722638 + 0.691226i \(0.757071\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.0000 −0.745145 −0.372572 − 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) 0 0
\(355\) −8.00000 −0.424596
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −21.0000 −1.10834 −0.554169 − 0.832404i \(-0.686964\pi\)
−0.554169 + 0.832404i \(0.686964\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −13.0000 −0.680451
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 − 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −30.0000 −1.55752
\(372\) 0 0
\(373\) −16.0000 −0.828449 −0.414224 − 0.910175i \(-0.635947\pi\)
−0.414224 + 0.910175i \(0.635947\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 34.0000 1.74646 0.873231 − 0.487306i \(-0.162020\pi\)
0.873231 + 0.487306i \(0.162020\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 − 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 15.0000 0.764471
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −25.0000 −1.26755 −0.633775 − 0.773517i \(-0.718496\pi\)
−0.633775 + 0.773517i \(0.718496\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) −19.0000 −0.953583 −0.476791 − 0.879017i \(-0.658200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −24.0000 −1.19850 −0.599251 − 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 0 0
\(403\) −20.0000 −0.996271
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 18.0000 0.890043 0.445021 − 0.895520i \(-0.353196\pi\)
0.445021 + 0.895520i \(0.353196\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) 4.00000 0.196352
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 − 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) −15.0000 −0.725901
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.0000 −0.481683 −0.240842 − 0.970564i \(-0.577423\pi\)
−0.240842 + 0.970564i \(0.577423\pi\)
\(432\) 0 0
\(433\) 34.0000 1.63394 0.816968 − 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.00000 −0.191346
\(438\) 0 0
\(439\) 30.0000 1.43182 0.715911 − 0.698192i \(-0.246012\pi\)
0.715911 + 0.698192i \(0.246012\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.00000 −0.332580 −0.166290 − 0.986077i \(-0.553179\pi\)
−0.166290 + 0.986077i \(0.553179\pi\)
\(444\) 0 0
\(445\) −6.00000 −0.284427
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.0000 0.943858 0.471929 − 0.881636i \(-0.343558\pi\)
0.471929 + 0.881636i \(0.343558\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.00000 0.281284
\(456\) 0 0
\(457\) 35.0000 1.63723 0.818615 − 0.574342i \(-0.194742\pi\)
0.818615 + 0.574342i \(0.194742\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.00000 −0.326023 −0.163011 − 0.986624i \(-0.552121\pi\)
−0.163011 + 0.986624i \(0.552121\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 − 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.0000 −0.694117 −0.347059 − 0.937843i \(-0.612820\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −55.0000 −2.52890
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −16.0000 −0.731059 −0.365529 − 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 − 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 − 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 6.00000 0.270226
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.0000 1.07655
\(498\) 0 0
\(499\) −39.0000 −1.74588 −0.872940 − 0.487828i \(-0.837789\pi\)
−0.872940 + 0.487828i \(0.837789\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 − 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) 39.0000 1.72526
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.0000 0.440653
\(516\) 0 0
\(517\) −45.0000 −1.97910
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8.00000 −0.350486 −0.175243 − 0.984525i \(-0.556071\pi\)
−0.175243 + 0.984525i \(0.556071\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 − 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0000 0.435607
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −18.0000 −0.778208
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10.0000 −0.430730
\(540\) 0 0
\(541\) 15.0000 0.644900 0.322450 − 0.946586i \(-0.395494\pi\)
0.322450 + 0.946586i \(0.395494\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 10.0000 0.427569 0.213785 − 0.976881i \(-0.431421\pi\)
0.213785 + 0.976881i \(0.431421\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) −12.0000 −0.510292
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.00000 0.211857 0.105928 − 0.994374i \(-0.466219\pi\)
0.105928 + 0.994374i \(0.466219\pi\)
\(558\) 0 0
\(559\) −22.0000 −0.930501
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −20.0000 −0.842900 −0.421450 − 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 0 0
\(565\) 6.00000 0.252422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −34.0000 −1.42535 −0.712677 − 0.701492i \(-0.752517\pi\)
−0.712677 + 0.701492i \(0.752517\pi\)
\(570\) 0 0
\(571\) −24.0000 −1.00437 −0.502184 − 0.864761i \(-0.667470\pi\)
−0.502184 + 0.864761i \(0.667470\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16.0000 −0.667246
\(576\) 0 0
\(577\) 35.0000 1.45707 0.728535 − 0.685009i \(-0.240202\pi\)
0.728535 + 0.685009i \(0.240202\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 50.0000 2.07079
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −35.0000 −1.44460 −0.722302 − 0.691577i \(-0.756916\pi\)
−0.722302 + 0.691577i \(0.756916\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.0000 0.574911 0.287456 − 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(594\) 0 0
\(595\) −3.00000 −0.122988
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 36.0000 1.47092 0.735460 − 0.677568i \(-0.236966\pi\)
0.735460 + 0.677568i \(0.236966\pi\)
\(600\) 0 0
\(601\) −44.0000 −1.79480 −0.897399 − 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −14.0000 −0.569181
\(606\) 0 0
\(607\) 22.0000 0.892952 0.446476 − 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −18.0000 −0.728202
\(612\) 0 0
\(613\) 5.00000 0.201948 0.100974 − 0.994889i \(-0.467804\pi\)
0.100974 + 0.994889i \(0.467804\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −27.0000 −1.08698 −0.543490 − 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 − 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 18.0000 0.721155
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 47.0000 1.87104 0.935520 − 0.353273i \(-0.114931\pi\)
0.935520 + 0.353273i \(0.114931\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.00000 −0.0793676
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 26.0000 1.02694 0.513469 − 0.858108i \(-0.328360\pi\)
0.513469 + 0.858108i \(0.328360\pi\)
\(642\) 0 0
\(643\) −21.0000 −0.828159 −0.414080 − 0.910241i \(-0.635896\pi\)
−0.414080 + 0.910241i \(0.635896\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25.0000 −0.982851 −0.491426 − 0.870919i \(-0.663524\pi\)
−0.491426 + 0.870919i \(0.663524\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.00000 0.352197 0.176099 − 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(654\) 0 0
\(655\) 19.0000 0.742391
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 − 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) −28.0000 −1.08907 −0.544537 − 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.00000 0.116335
\(666\) 0 0
\(667\) 24.0000 0.929284
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 25.0000 0.965114
\(672\) 0 0
\(673\) −44.0000 −1.69608 −0.848038 − 0.529936i \(-0.822216\pi\)
−0.848038 + 0.529936i \(0.822216\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.00000 0.0768662 0.0384331 − 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 6.00000 0.230259
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34.0000 1.30097 0.650487 − 0.759517i \(-0.274565\pi\)
0.650487 + 0.759517i \(0.274565\pi\)
\(684\) 0 0
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20.0000 0.761939
\(690\) 0 0
\(691\) −35.0000 −1.33146 −0.665731 − 0.746191i \(-0.731880\pi\)
−0.665731 + 0.746191i \(0.731880\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −15.0000 −0.568982
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −42.0000 −1.58632 −0.793159 − 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18.0000 0.676960
\(708\) 0 0
\(709\) −34.0000 −1.27690 −0.638448 − 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 40.0000 1.49801
\(714\) 0 0
\(715\) −10.0000 −0.373979
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17.0000 −0.633993 −0.316997 − 0.948427i \(-0.602674\pi\)
−0.316997 + 0.948427i \(0.602674\pi\)
\(720\) 0 0
\(721\) −30.0000 −1.11726
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −24.0000 −0.891338
\(726\) 0 0
\(727\) −39.0000 −1.44643 −0.723215 − 0.690623i \(-0.757336\pi\)
−0.723215 + 0.690623i \(0.757336\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11.0000 0.406850
\(732\) 0 0
\(733\) −46.0000 −1.69905 −0.849524 − 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −20.0000 −0.736709
\(738\) 0 0
\(739\) 7.00000 0.257499 0.128750 − 0.991677i \(-0.458904\pi\)
0.128750 + 0.991677i \(0.458904\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −44.0000 −1.61420 −0.807102 − 0.590412i \(-0.798965\pi\)
−0.807102 + 0.590412i \(0.798965\pi\)
\(744\) 0 0
\(745\) −1.00000 −0.0366372
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 54.0000 1.97312
\(750\) 0 0
\(751\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 20.0000 0.727875
\(756\) 0 0
\(757\) 35.0000 1.27210 0.636048 − 0.771649i \(-0.280568\pi\)
0.636048 + 0.771649i \(0.280568\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.00000 0.0362500 0.0181250 − 0.999836i \(-0.494230\pi\)
0.0181250 + 0.999836i \(0.494230\pi\)
\(762\) 0 0
\(763\) −24.0000 −0.868858
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.00000 −0.288863
\(768\) 0 0
\(769\) −37.0000 −1.33425 −0.667127 − 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −24.0000 −0.863220 −0.431610 − 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) −40.0000 −1.43684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −40.0000 −1.43131
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.00000 0.0713831
\(786\) 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
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −40.0000 −1.41687 −0.708436 − 0.705775i \(-0.750599\pi\)
−0.708436 + 0.705775i \(0.750599\pi\)
\(798\) 0 0
\(799\) 9.00000 0.318397
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −65.0000 −2.29380
\(804\) 0 0
\(805\) −12.0000 −0.422944
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −17.0000 −0.597688 −0.298844 − 0.954302i \(-0.596601\pi\)
−0.298844 + 0.954302i \(0.596601\pi\)
\(810\) 0 0
\(811\) 14.0000 0.491606 0.245803 − 0.969320i \(-0.420948\pi\)
0.245803 + 0.969320i \(0.420948\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −24.0000 −0.840683
\(816\) 0 0
\(817\) −11.0000 −0.384841
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 9.00000 0.314102 0.157051 − 0.987590i \(-0.449801\pi\)
0.157051 + 0.987590i \(0.449801\pi\)
\(822\) 0 0
\(823\) −5.00000 −0.174289 −0.0871445 − 0.996196i \(-0.527774\pi\)
−0.0871445 + 0.996196i \(0.527774\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 32.0000 1.11275 0.556375 − 0.830932i \(-0.312192\pi\)
0.556375 + 0.830932i \(0.312192\pi\)
\(828\) 0 0
\(829\) 4.00000 0.138926 0.0694629 − 0.997585i \(-0.477871\pi\)
0.0694629 + 0.997585i \(0.477871\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.00000 0.0692959
\(834\) 0 0
\(835\) −18.0000 −0.622916
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 18.0000 0.621429 0.310715 − 0.950503i \(-0.399432\pi\)
0.310715 + 0.950503i \(0.399432\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 9.00000 0.309609
\(846\) 0 0
\(847\) 42.0000 1.44314
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 26.0000 0.890223 0.445112 − 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −12.0000 −0.409912 −0.204956 − 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) 0 0
\(859\) 15.0000 0.511793 0.255897 − 0.966704i \(-0.417629\pi\)
0.255897 + 0.966704i \(0.417629\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 28.0000 0.953131 0.476566 − 0.879139i \(-0.341881\pi\)
0.476566 + 0.879139i \(0.341881\pi\)
\(864\) 0 0
\(865\) −18.0000 −0.612018
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 20.0000 0.678454
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 27.0000 0.912767
\(876\) 0 0
\(877\) 18.0000 0.607817 0.303908 − 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 37.0000 1.24656 0.623281 − 0.781998i \(-0.285799\pi\)
0.623281 + 0.781998i \(0.285799\pi\)
\(882\) 0 0
\(883\) 31.0000 1.04323 0.521617 − 0.853180i \(-0.325329\pi\)
0.521617 + 0.853180i \(0.325329\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 56.0000 1.88030 0.940148 − 0.340766i \(-0.110687\pi\)
0.940148 + 0.340766i \(0.110687\pi\)
\(888\) 0 0
\(889\) 6.00000 0.201234
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −9.00000 −0.301174
\(894\) 0 0
\(895\) −6.00000 −0.200558
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 60.0000 2.00111
\(900\) 0 0
\(901\) −10.0000 −0.333148
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −18.0000 −0.598340
\(906\) 0 0
\(907\) −10.0000 −0.332045 −0.166022 − 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −50.0000 −1.65657 −0.828287 − 0.560304i \(-0.810684\pi\)
−0.828287 + 0.560304i \(0.810684\pi\)
\(912\) 0 0
\(913\) 20.0000 0.661903
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −57.0000 −1.88231
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −16.0000 −0.526646
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 34.0000 1.11550 0.557752 − 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 5.00000 0.163517
\(936\) 0 0
\(937\) −3.00000 −0.0980057 −0.0490029 − 0.998799i \(-0.515604\pi\)
−0.0490029 + 0.998799i \(0.515604\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −42.0000 −1.36916 −0.684580 − 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) −26.0000 −0.843996
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −12.0000 −0.388718 −0.194359 − 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) 0 0
\(955\) −15.0000 −0.485389
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 27.0000 0.871875
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 16.0000 0.515058
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 − 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −12.0000 −0.385098 −0.192549 − 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 0 0
\(973\) 45.0000 1.44263
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −30.0000 −0.959785 −0.479893 − 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) −30.0000 −0.958804
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 12.0000 0.382741 0.191370 − 0.981518i \(-0.438707\pi\)
0.191370 + 0.981518i \(0.438707\pi\)
\(984\) 0 0
\(985\) 6.00000 0.191176
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 44.0000 1.39912
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 − 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −11.0000 −0.348723
\(996\) 0 0
\(997\) −35.0000 −1.10846 −0.554231 − 0.832363i \(-0.686987\pi\)
−0.554231 + 0.832363i \(0.686987\pi\)
\(998\) 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 2736.2.a.i.1.1 1
3.2 odd 2 912.2.a.i.1.1 1
4.3 odd 2 1368.2.a.d.1.1 1
12.11 even 2 456.2.a.a.1.1 ✓ 1
24.5 odd 2 3648.2.a.g.1.1 1
24.11 even 2 3648.2.a.z.1.1 1
228.227 odd 2 8664.2.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.a.a.1.1 ✓ 1 12.11 even 2
912.2.a.i.1.1 1 3.2 odd 2
1368.2.a.d.1.1 1 4.3 odd 2
2736.2.a.i.1.1 1 1.1 even 1 trivial
3648.2.a.g.1.1 1 24.5 odd 2
3648.2.a.z.1.1 1 24.11 even 2
8664.2.a.l.1.1 1 228.227 odd 2