Properties

Label 6480.2.a.bm.1.1
Level $6480$
Weight $2$
Character 6480.1
Self dual yes
Analytic conductor $51.743$
Analytic rank $0$
Dimension $2$
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] = [6480,2,Mod(1,6480)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6480, 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("6480.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6480.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: \(51.7430605098\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{57}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 14 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3240)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.27492\) of defining polynomial
Character \(\chi\) \(=\) 6480.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} -4.27492 q^{7} +1.27492 q^{11} +6.27492 q^{13} +2.00000 q^{17} -1.00000 q^{19} -0.274917 q^{23} +1.00000 q^{25} -1.27492 q^{29} +1.27492 q^{31} -4.27492 q^{35} +4.54983 q^{37} -7.54983 q^{41} -4.00000 q^{43} -6.27492 q^{47} +11.2749 q^{49} +8.27492 q^{53} +1.27492 q^{55} +13.0000 q^{59} -6.54983 q^{61} +6.27492 q^{65} +14.5498 q^{67} +0.725083 q^{71} -15.0997 q^{73} -5.45017 q^{77} +4.54983 q^{79} -12.5498 q^{83} +2.00000 q^{85} -9.82475 q^{89} -26.8248 q^{91} -1.00000 q^{95} +16.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} - q^{7} - 5 q^{11} + 5 q^{13} + 4 q^{17} - 2 q^{19} + 7 q^{23} + 2 q^{25} + 5 q^{29} - 5 q^{31} - q^{35} - 6 q^{37} - 8 q^{43} - 5 q^{47} + 15 q^{49} + 9 q^{53} - 5 q^{55} + 26 q^{59} + 2 q^{61}+ \cdots + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(6\) 0 0
\(7\) −4.27492 −1.61577 −0.807883 0.589342i \(-0.799387\pi\)
−0.807883 + 0.589342i \(0.799387\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.27492 0.384402 0.192201 0.981356i \(-0.438437\pi\)
0.192201 + 0.981356i \(0.438437\pi\)
\(12\) 0 0
\(13\) 6.27492 1.74035 0.870174 0.492744i \(-0.164006\pi\)
0.870174 + 0.492744i \(0.164006\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.274917 −0.0573242 −0.0286621 0.999589i \(-0.509125\pi\)
−0.0286621 + 0.999589i \(0.509125\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.27492 −0.236746 −0.118373 0.992969i \(-0.537768\pi\)
−0.118373 + 0.992969i \(0.537768\pi\)
\(30\) 0 0
\(31\) 1.27492 0.228982 0.114491 0.993424i \(-0.463476\pi\)
0.114491 + 0.993424i \(0.463476\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.27492 −0.722593
\(36\) 0 0
\(37\) 4.54983 0.747988 0.373994 0.927431i \(-0.377988\pi\)
0.373994 + 0.927431i \(0.377988\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.54983 −1.17909 −0.589543 0.807737i \(-0.700692\pi\)
−0.589543 + 0.807737i \(0.700692\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.27492 −0.915291 −0.457645 0.889135i \(-0.651307\pi\)
−0.457645 + 0.889135i \(0.651307\pi\)
\(48\) 0 0
\(49\) 11.2749 1.61070
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.27492 1.13665 0.568324 0.822805i \(-0.307592\pi\)
0.568324 + 0.822805i \(0.307592\pi\)
\(54\) 0 0
\(55\) 1.27492 0.171910
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13.0000 1.69246 0.846228 0.532821i \(-0.178868\pi\)
0.846228 + 0.532821i \(0.178868\pi\)
\(60\) 0 0
\(61\) −6.54983 −0.838620 −0.419310 0.907843i \(-0.637728\pi\)
−0.419310 + 0.907843i \(0.637728\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.27492 0.778308
\(66\) 0 0
\(67\) 14.5498 1.77755 0.888773 0.458348i \(-0.151559\pi\)
0.888773 + 0.458348i \(0.151559\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.725083 0.0860515 0.0430257 0.999074i \(-0.486300\pi\)
0.0430257 + 0.999074i \(0.486300\pi\)
\(72\) 0 0
\(73\) −15.0997 −1.76728 −0.883641 0.468165i \(-0.844915\pi\)
−0.883641 + 0.468165i \(0.844915\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.45017 −0.621104
\(78\) 0 0
\(79\) 4.54983 0.511896 0.255948 0.966691i \(-0.417612\pi\)
0.255948 + 0.966691i \(0.417612\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −12.5498 −1.37752 −0.688762 0.724988i \(-0.741845\pi\)
−0.688762 + 0.724988i \(0.741845\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −9.82475 −1.04142 −0.520711 0.853733i \(-0.674333\pi\)
−0.520711 + 0.853733i \(0.674333\pi\)
\(90\) 0 0
\(91\) −26.8248 −2.81200
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) 16.0000 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 17.2749 1.71892 0.859459 0.511204i \(-0.170800\pi\)
0.859459 + 0.511204i \(0.170800\pi\)
\(102\) 0 0
\(103\) −16.8248 −1.65779 −0.828896 0.559403i \(-0.811031\pi\)
−0.828896 + 0.559403i \(0.811031\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.0997 1.45974 0.729870 0.683586i \(-0.239581\pi\)
0.729870 + 0.683586i \(0.239581\pi\)
\(108\) 0 0
\(109\) 1.27492 0.122115 0.0610575 0.998134i \(-0.480553\pi\)
0.0610575 + 0.998134i \(0.480553\pi\)
\(110\) 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
\(115\) −0.274917 −0.0256362
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −8.54983 −0.783762
\(120\) 0 0
\(121\) −9.37459 −0.852235
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −3.72508 −0.330548 −0.165274 0.986248i \(-0.552851\pi\)
−0.165274 + 0.986248i \(0.552851\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13.5498 1.18385 0.591927 0.805991i \(-0.298367\pi\)
0.591927 + 0.805991i \(0.298367\pi\)
\(132\) 0 0
\(133\) 4.27492 0.370682
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.549834 −0.0469755 −0.0234878 0.999724i \(-0.507477\pi\)
−0.0234878 + 0.999724i \(0.507477\pi\)
\(138\) 0 0
\(139\) 9.00000 0.763370 0.381685 0.924292i \(-0.375344\pi\)
0.381685 + 0.924292i \(0.375344\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −1.27492 −0.105876
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 0 0
\(151\) 4.72508 0.384522 0.192261 0.981344i \(-0.438418\pi\)
0.192261 + 0.981344i \(0.438418\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.27492 0.102404
\(156\) 0 0
\(157\) 18.2749 1.45850 0.729249 0.684249i \(-0.239870\pi\)
0.729249 + 0.684249i \(0.239870\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.17525 0.0926225
\(162\) 0 0
\(163\) −5.45017 −0.426890 −0.213445 0.976955i \(-0.568468\pi\)
−0.213445 + 0.976955i \(0.568468\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 22.5498 1.74496 0.872479 0.488651i \(-0.162511\pi\)
0.872479 + 0.488651i \(0.162511\pi\)
\(168\) 0 0
\(169\) 26.3746 2.02881
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.2749 1.23736 0.618680 0.785643i \(-0.287668\pi\)
0.618680 + 0.785643i \(0.287668\pi\)
\(174\) 0 0
\(175\) −4.27492 −0.323153
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.54983 −0.265327 −0.132664 0.991161i \(-0.542353\pi\)
−0.132664 + 0.991161i \(0.542353\pi\)
\(180\) 0 0
\(181\) 8.72508 0.648530 0.324265 0.945966i \(-0.394883\pi\)
0.324265 + 0.945966i \(0.394883\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.54983 0.334510
\(186\) 0 0
\(187\) 2.54983 0.186462
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.3746 1.32954 0.664769 0.747049i \(-0.268530\pi\)
0.664769 + 0.747049i \(0.268530\pi\)
\(192\) 0 0
\(193\) 4.00000 0.287926 0.143963 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.3746 1.09539 0.547697 0.836677i \(-0.315505\pi\)
0.547697 + 0.836677i \(0.315505\pi\)
\(198\) 0 0
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.45017 0.382527
\(204\) 0 0
\(205\) −7.54983 −0.527303
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.27492 −0.0881879
\(210\) 0 0
\(211\) −14.0997 −0.970661 −0.485331 0.874331i \(-0.661301\pi\)
−0.485331 + 0.874331i \(0.661301\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) −5.45017 −0.369981
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.5498 0.844193
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 22.5498 1.49669 0.748343 0.663312i \(-0.230850\pi\)
0.748343 + 0.663312i \(0.230850\pi\)
\(228\) 0 0
\(229\) −6.54983 −0.432825 −0.216413 0.976302i \(-0.569436\pi\)
−0.216413 + 0.976302i \(0.569436\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 21.0997 1.38229 0.691143 0.722718i \(-0.257108\pi\)
0.691143 + 0.722718i \(0.257108\pi\)
\(234\) 0 0
\(235\) −6.27492 −0.409330
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 28.5498 1.84674 0.923368 0.383917i \(-0.125425\pi\)
0.923368 + 0.383917i \(0.125425\pi\)
\(240\) 0 0
\(241\) −16.7251 −1.07736 −0.538679 0.842511i \(-0.681076\pi\)
−0.538679 + 0.842511i \(0.681076\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 11.2749 0.720328
\(246\) 0 0
\(247\) −6.27492 −0.399263
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −26.2749 −1.65846 −0.829229 0.558909i \(-0.811220\pi\)
−0.829229 + 0.558909i \(0.811220\pi\)
\(252\) 0 0
\(253\) −0.350497 −0.0220355
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −27.0997 −1.69043 −0.845215 0.534426i \(-0.820528\pi\)
−0.845215 + 0.534426i \(0.820528\pi\)
\(258\) 0 0
\(259\) −19.4502 −1.20857
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.27492 0.510253 0.255127 0.966908i \(-0.417883\pi\)
0.255127 + 0.966908i \(0.417883\pi\)
\(264\) 0 0
\(265\) 8.27492 0.508324
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 26.9244 1.64161 0.820805 0.571208i \(-0.193525\pi\)
0.820805 + 0.571208i \(0.193525\pi\)
\(270\) 0 0
\(271\) −28.5498 −1.73428 −0.867139 0.498065i \(-0.834044\pi\)
−0.867139 + 0.498065i \(0.834044\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.27492 0.0768804
\(276\) 0 0
\(277\) 17.7251 1.06500 0.532499 0.846431i \(-0.321253\pi\)
0.532499 + 0.846431i \(0.321253\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 28.8248 1.71954 0.859770 0.510681i \(-0.170607\pi\)
0.859770 + 0.510681i \(0.170607\pi\)
\(282\) 0 0
\(283\) 26.5498 1.57822 0.789112 0.614249i \(-0.210541\pi\)
0.789112 + 0.614249i \(0.210541\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 32.2749 1.90513
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 18.2749 1.06763 0.533816 0.845601i \(-0.320757\pi\)
0.533816 + 0.845601i \(0.320757\pi\)
\(294\) 0 0
\(295\) 13.0000 0.756889
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.72508 −0.0997641
\(300\) 0 0
\(301\) 17.0997 0.985609
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6.54983 −0.375042
\(306\) 0 0
\(307\) 29.0997 1.66081 0.830403 0.557163i \(-0.188110\pi\)
0.830403 + 0.557163i \(0.188110\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −26.9244 −1.52674 −0.763372 0.645959i \(-0.776458\pi\)
−0.763372 + 0.645959i \(0.776458\pi\)
\(312\) 0 0
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.27492 −0.127772 −0.0638860 0.997957i \(-0.520349\pi\)
−0.0638860 + 0.997957i \(0.520349\pi\)
\(318\) 0 0
\(319\) −1.62541 −0.0910057
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) 0 0
\(325\) 6.27492 0.348070
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 26.8248 1.47890
\(330\) 0 0
\(331\) −3.82475 −0.210227 −0.105114 0.994460i \(-0.533521\pi\)
−0.105114 + 0.994460i \(0.533521\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 14.5498 0.794942
\(336\) 0 0
\(337\) 20.5498 1.11942 0.559710 0.828688i \(-0.310912\pi\)
0.559710 + 0.828688i \(0.310912\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.62541 0.0880211
\(342\) 0 0
\(343\) −18.2749 −0.986753
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.0000 −0.751559 −0.375780 0.926709i \(-0.622625\pi\)
−0.375780 + 0.926709i \(0.622625\pi\)
\(348\) 0 0
\(349\) −9.82475 −0.525907 −0.262953 0.964809i \(-0.584697\pi\)
−0.262953 + 0.964809i \(0.584697\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.54983 −0.455062 −0.227531 0.973771i \(-0.573065\pi\)
−0.227531 + 0.973771i \(0.573065\pi\)
\(354\) 0 0
\(355\) 0.725083 0.0384834
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 21.8248 1.15187 0.575933 0.817497i \(-0.304639\pi\)
0.575933 + 0.817497i \(0.304639\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −15.0997 −0.790353
\(366\) 0 0
\(367\) 2.54983 0.133100 0.0665501 0.997783i \(-0.478801\pi\)
0.0665501 + 0.997783i \(0.478801\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −35.3746 −1.83656
\(372\) 0 0
\(373\) 0.900331 0.0466174 0.0233087 0.999728i \(-0.492580\pi\)
0.0233087 + 0.999728i \(0.492580\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.00000 −0.412021
\(378\) 0 0
\(379\) −1.72508 −0.0886116 −0.0443058 0.999018i \(-0.514108\pi\)
−0.0443058 + 0.999018i \(0.514108\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 35.3746 1.80756 0.903778 0.428001i \(-0.140782\pi\)
0.903778 + 0.428001i \(0.140782\pi\)
\(384\) 0 0
\(385\) −5.45017 −0.277766
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.45017 −0.0735263 −0.0367632 0.999324i \(-0.511705\pi\)
−0.0367632 + 0.999324i \(0.511705\pi\)
\(390\) 0 0
\(391\) −0.549834 −0.0278063
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.54983 0.228927
\(396\) 0 0
\(397\) −23.0997 −1.15934 −0.579670 0.814852i \(-0.696818\pi\)
−0.579670 + 0.814852i \(0.696818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.7251 0.785273 0.392637 0.919694i \(-0.371563\pi\)
0.392637 + 0.919694i \(0.371563\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.80066 0.287528
\(408\) 0 0
\(409\) −7.17525 −0.354793 −0.177397 0.984139i \(-0.556768\pi\)
−0.177397 + 0.984139i \(0.556768\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −55.5739 −2.73461
\(414\) 0 0
\(415\) −12.5498 −0.616047
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −21.0997 −1.03079 −0.515393 0.856954i \(-0.672354\pi\)
−0.515393 + 0.856954i \(0.672354\pi\)
\(420\) 0 0
\(421\) −24.7251 −1.20503 −0.602513 0.798109i \(-0.705834\pi\)
−0.602513 + 0.798109i \(0.705834\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) 28.0000 1.35501
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.27492 −0.0614106 −0.0307053 0.999528i \(-0.509775\pi\)
−0.0307053 + 0.999528i \(0.509775\pi\)
\(432\) 0 0
\(433\) −2.54983 −0.122537 −0.0612686 0.998121i \(-0.519515\pi\)
−0.0612686 + 0.998121i \(0.519515\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.274917 0.0131511
\(438\) 0 0
\(439\) −12.3746 −0.590607 −0.295303 0.955404i \(-0.595421\pi\)
−0.295303 + 0.955404i \(0.595421\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.54983 0.216169 0.108085 0.994142i \(-0.465528\pi\)
0.108085 + 0.994142i \(0.465528\pi\)
\(444\) 0 0
\(445\) −9.82475 −0.465738
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −13.5498 −0.639456 −0.319728 0.947509i \(-0.603592\pi\)
−0.319728 + 0.947509i \(0.603592\pi\)
\(450\) 0 0
\(451\) −9.62541 −0.453243
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −26.8248 −1.25756
\(456\) 0 0
\(457\) 16.0000 0.748448 0.374224 0.927338i \(-0.377909\pi\)
0.374224 + 0.927338i \(0.377909\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.3746 0.669491 0.334746 0.942309i \(-0.391350\pi\)
0.334746 + 0.942309i \(0.391350\pi\)
\(462\) 0 0
\(463\) 26.4743 1.23036 0.615181 0.788386i \(-0.289083\pi\)
0.615181 + 0.788386i \(0.289083\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.1993 −0.934714 −0.467357 0.884069i \(-0.654794\pi\)
−0.467357 + 0.884069i \(0.654794\pi\)
\(468\) 0 0
\(469\) −62.1993 −2.87210
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.09967 −0.234483
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.27492 −0.149635 −0.0748174 0.997197i \(-0.523837\pi\)
−0.0748174 + 0.997197i \(0.523837\pi\)
\(480\) 0 0
\(481\) 28.5498 1.30176
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16.0000 0.726523
\(486\) 0 0
\(487\) 29.7251 1.34697 0.673486 0.739200i \(-0.264796\pi\)
0.673486 + 0.739200i \(0.264796\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −15.0000 −0.676941 −0.338470 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 0 0
\(493\) −2.54983 −0.114839
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.09967 −0.139039
\(498\) 0 0
\(499\) 14.4502 0.646878 0.323439 0.946249i \(-0.395161\pi\)
0.323439 + 0.946249i \(0.395161\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 17.2749 0.768724
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −32.1993 −1.42721 −0.713605 0.700548i \(-0.752939\pi\)
−0.713605 + 0.700548i \(0.752939\pi\)
\(510\) 0 0
\(511\) 64.5498 2.85552
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −16.8248 −0.741387
\(516\) 0 0
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 25.9244 1.13577 0.567885 0.823108i \(-0.307762\pi\)
0.567885 + 0.823108i \(0.307762\pi\)
\(522\) 0 0
\(523\) −5.64950 −0.247036 −0.123518 0.992342i \(-0.539418\pi\)
−0.123518 + 0.992342i \(0.539418\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.54983 0.111073
\(528\) 0 0
\(529\) −22.9244 −0.996714
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −47.3746 −2.05202
\(534\) 0 0
\(535\) 15.0997 0.652816
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.3746 0.619157
\(540\) 0 0
\(541\) −8.92442 −0.383691 −0.191845 0.981425i \(-0.561447\pi\)
−0.191845 + 0.981425i \(0.561447\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.27492 0.0546115
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.27492 0.0543133
\(552\) 0 0
\(553\) −19.4502 −0.827105
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.9244 −0.844225 −0.422112 0.906544i \(-0.638711\pi\)
−0.422112 + 0.906544i \(0.638711\pi\)
\(558\) 0 0
\(559\) −25.0997 −1.06160
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.90033 −0.290814 −0.145407 0.989372i \(-0.546449\pi\)
−0.145407 + 0.989372i \(0.546449\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −41.5498 −1.74186 −0.870930 0.491407i \(-0.836483\pi\)
−0.870930 + 0.491407i \(0.836483\pi\)
\(570\) 0 0
\(571\) 23.8248 0.997035 0.498517 0.866880i \(-0.333878\pi\)
0.498517 + 0.866880i \(0.333878\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.274917 −0.0114648
\(576\) 0 0
\(577\) −26.5498 −1.10528 −0.552642 0.833419i \(-0.686380\pi\)
−0.552642 + 0.833419i \(0.686380\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 53.6495 2.22576
\(582\) 0 0
\(583\) 10.5498 0.436929
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19.4502 0.802794 0.401397 0.915904i \(-0.368525\pi\)
0.401397 + 0.915904i \(0.368525\pi\)
\(588\) 0 0
\(589\) −1.27492 −0.0525320
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 12.1993 0.500967 0.250483 0.968121i \(-0.419410\pi\)
0.250483 + 0.968121i \(0.419410\pi\)
\(594\) 0 0
\(595\) −8.54983 −0.350509
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 23.2749 0.950987 0.475494 0.879719i \(-0.342269\pi\)
0.475494 + 0.879719i \(0.342269\pi\)
\(600\) 0 0
\(601\) −32.0997 −1.30937 −0.654686 0.755901i \(-0.727199\pi\)
−0.654686 + 0.755901i \(0.727199\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.37459 −0.381131
\(606\) 0 0
\(607\) 24.0000 0.974130 0.487065 0.873366i \(-0.338067\pi\)
0.487065 + 0.873366i \(0.338067\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −39.3746 −1.59293
\(612\) 0 0
\(613\) 37.0241 1.49539 0.747694 0.664043i \(-0.231161\pi\)
0.747694 + 0.664043i \(0.231161\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.64950 0.0664065 0.0332033 0.999449i \(-0.489429\pi\)
0.0332033 + 0.999449i \(0.489429\pi\)
\(618\) 0 0
\(619\) −19.3746 −0.778730 −0.389365 0.921083i \(-0.627306\pi\)
−0.389365 + 0.921083i \(0.627306\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 42.0000 1.68269
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.09967 0.362828
\(630\) 0 0
\(631\) 43.4743 1.73068 0.865341 0.501183i \(-0.167102\pi\)
0.865341 + 0.501183i \(0.167102\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.72508 −0.147825
\(636\) 0 0
\(637\) 70.7492 2.80318
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.9244 −0.747470 −0.373735 0.927536i \(-0.621923\pi\)
−0.373735 + 0.927536i \(0.621923\pi\)
\(642\) 0 0
\(643\) 2.90033 0.114378 0.0571889 0.998363i \(-0.481786\pi\)
0.0571889 + 0.998363i \(0.481786\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13.4502 0.528781 0.264390 0.964416i \(-0.414829\pi\)
0.264390 + 0.964416i \(0.414829\pi\)
\(648\) 0 0
\(649\) 16.5739 0.650583
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24.5498 0.960709 0.480355 0.877074i \(-0.340508\pi\)
0.480355 + 0.877074i \(0.340508\pi\)
\(654\) 0 0
\(655\) 13.5498 0.529436
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.72508 0.378835 0.189418 0.981897i \(-0.439340\pi\)
0.189418 + 0.981897i \(0.439340\pi\)
\(660\) 0 0
\(661\) 12.9244 0.502702 0.251351 0.967896i \(-0.419125\pi\)
0.251351 + 0.967896i \(0.419125\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.27492 0.165774
\(666\) 0 0
\(667\) 0.350497 0.0135713
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.35050 −0.322367
\(672\) 0 0
\(673\) −39.0997 −1.50718 −0.753591 0.657344i \(-0.771680\pi\)
−0.753591 + 0.657344i \(0.771680\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 25.9244 0.996356 0.498178 0.867075i \(-0.334003\pi\)
0.498178 + 0.867075i \(0.334003\pi\)
\(678\) 0 0
\(679\) −68.3987 −2.62490
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16.5498 0.633262 0.316631 0.948549i \(-0.397448\pi\)
0.316631 + 0.948549i \(0.397448\pi\)
\(684\) 0 0
\(685\) −0.549834 −0.0210081
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 51.9244 1.97816
\(690\) 0 0
\(691\) −14.8248 −0.563960 −0.281980 0.959420i \(-0.590991\pi\)
−0.281980 + 0.959420i \(0.590991\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.00000 0.341389
\(696\) 0 0
\(697\) −15.0997 −0.571941
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4.37459 0.165226 0.0826129 0.996582i \(-0.473673\pi\)
0.0826129 + 0.996582i \(0.473673\pi\)
\(702\) 0 0
\(703\) −4.54983 −0.171600
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −73.8488 −2.77737
\(708\) 0 0
\(709\) −31.0997 −1.16797 −0.583986 0.811764i \(-0.698508\pi\)
−0.583986 + 0.811764i \(0.698508\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.350497 −0.0131262
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 22.1752 0.826997 0.413499 0.910505i \(-0.364307\pi\)
0.413499 + 0.910505i \(0.364307\pi\)
\(720\) 0 0
\(721\) 71.9244 2.67861
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.27492 −0.0473492
\(726\) 0 0
\(727\) −7.37459 −0.273508 −0.136754 0.990605i \(-0.543667\pi\)
−0.136754 + 0.990605i \(0.543667\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18.5498 0.683292
\(738\) 0 0
\(739\) 36.9244 1.35829 0.679143 0.734006i \(-0.262351\pi\)
0.679143 + 0.734006i \(0.262351\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13.4502 0.493439 0.246719 0.969087i \(-0.420647\pi\)
0.246719 + 0.969087i \(0.420647\pi\)
\(744\) 0 0
\(745\) 2.00000 0.0732743
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −64.5498 −2.35860
\(750\) 0 0
\(751\) −19.4502 −0.709747 −0.354873 0.934914i \(-0.615476\pi\)
−0.354873 + 0.934914i \(0.615476\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.72508 0.171963
\(756\) 0 0
\(757\) −3.37459 −0.122651 −0.0613257 0.998118i \(-0.519533\pi\)
−0.0613257 + 0.998118i \(0.519533\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34.4502 1.24882 0.624409 0.781098i \(-0.285340\pi\)
0.624409 + 0.781098i \(0.285340\pi\)
\(762\) 0 0
\(763\) −5.45017 −0.197309
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 81.5739 2.94546
\(768\) 0 0
\(769\) −8.72508 −0.314635 −0.157317 0.987548i \(-0.550285\pi\)
−0.157317 + 0.987548i \(0.550285\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −13.6495 −0.490939 −0.245469 0.969404i \(-0.578942\pi\)
−0.245469 + 0.969404i \(0.578942\pi\)
\(774\) 0 0
\(775\) 1.27492 0.0457964
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.54983 0.270501
\(780\) 0 0
\(781\) 0.924421 0.0330784
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 18.2749 0.652260
\(786\) 0 0
\(787\) 34.0000 1.21197 0.605985 0.795476i \(-0.292779\pi\)
0.605985 + 0.795476i \(0.292779\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 25.6495 0.911991
\(792\) 0 0
\(793\) −41.0997 −1.45949
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −40.5498 −1.43635 −0.718174 0.695863i \(-0.755022\pi\)
−0.718174 + 0.695863i \(0.755022\pi\)
\(798\) 0 0
\(799\) −12.5498 −0.443981
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −19.2508 −0.679347
\(804\) 0 0
\(805\) 1.17525 0.0414221
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −28.6495 −1.00726 −0.503631 0.863919i \(-0.668003\pi\)
−0.503631 + 0.863919i \(0.668003\pi\)
\(810\) 0 0
\(811\) −35.8248 −1.25798 −0.628989 0.777415i \(-0.716531\pi\)
−0.628989 + 0.777415i \(0.716531\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.45017 −0.190911
\(816\) 0 0
\(817\) 4.00000 0.139942
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −17.8248 −0.622088 −0.311044 0.950395i \(-0.600679\pi\)
−0.311044 + 0.950395i \(0.600679\pi\)
\(822\) 0 0
\(823\) −38.5498 −1.34376 −0.671881 0.740659i \(-0.734514\pi\)
−0.671881 + 0.740659i \(0.734514\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.09967 0.316426 0.158213 0.987405i \(-0.449427\pi\)
0.158213 + 0.987405i \(0.449427\pi\)
\(828\) 0 0
\(829\) −35.8248 −1.24425 −0.622123 0.782920i \(-0.713729\pi\)
−0.622123 + 0.782920i \(0.713729\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 22.5498 0.781305
\(834\) 0 0
\(835\) 22.5498 0.780369
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15.4743 0.534231 0.267115 0.963665i \(-0.413930\pi\)
0.267115 + 0.963665i \(0.413930\pi\)
\(840\) 0 0
\(841\) −27.3746 −0.943951
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 26.3746 0.907313
\(846\) 0 0
\(847\) 40.0756 1.37701
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.25083 −0.0428778
\(852\) 0 0
\(853\) 41.2990 1.41405 0.707026 0.707188i \(-0.250037\pi\)
0.707026 + 0.707188i \(0.250037\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 22.7492 0.777097 0.388548 0.921428i \(-0.372977\pi\)
0.388548 + 0.921428i \(0.372977\pi\)
\(858\) 0 0
\(859\) 15.4743 0.527975 0.263987 0.964526i \(-0.414962\pi\)
0.263987 + 0.964526i \(0.414962\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −15.7251 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(864\) 0 0
\(865\) 16.2749 0.553364
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.80066 0.196774
\(870\) 0 0
\(871\) 91.2990 3.09355
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.27492 −0.144519
\(876\) 0 0
\(877\) −5.72508 −0.193322 −0.0966612 0.995317i \(-0.530816\pi\)
−0.0966612 + 0.995317i \(0.530816\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 56.3746 1.89931 0.949654 0.313301i \(-0.101435\pi\)
0.949654 + 0.313301i \(0.101435\pi\)
\(882\) 0 0
\(883\) 28.1993 0.948983 0.474492 0.880260i \(-0.342632\pi\)
0.474492 + 0.880260i \(0.342632\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −22.8248 −0.766380 −0.383190 0.923670i \(-0.625175\pi\)
−0.383190 + 0.923670i \(0.625175\pi\)
\(888\) 0 0
\(889\) 15.9244 0.534088
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 6.27492 0.209982
\(894\) 0 0
\(895\) −3.54983 −0.118658
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.62541 −0.0542106
\(900\) 0 0
\(901\) 16.5498 0.551355
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8.72508 0.290032
\(906\) 0 0
\(907\) −20.9003 −0.693984 −0.346992 0.937868i \(-0.612797\pi\)
−0.346992 + 0.937868i \(0.612797\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −56.0241 −1.85616 −0.928080 0.372380i \(-0.878542\pi\)
−0.928080 + 0.372380i \(0.878542\pi\)
\(912\) 0 0
\(913\) −16.0000 −0.529523
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −57.9244 −1.91283
\(918\) 0 0
\(919\) 40.9244 1.34997 0.674986 0.737831i \(-0.264150\pi\)
0.674986 + 0.737831i \(0.264150\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4.54983 0.149760
\(924\) 0 0
\(925\) 4.54983 0.149598
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 53.1238 1.74293 0.871467 0.490454i \(-0.163169\pi\)
0.871467 + 0.490454i \(0.163169\pi\)
\(930\) 0 0
\(931\) −11.2749 −0.369520
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.54983 0.0833885
\(936\) 0 0
\(937\) 14.5498 0.475322 0.237661 0.971348i \(-0.423619\pi\)
0.237661 + 0.971348i \(0.423619\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −23.0997 −0.753028 −0.376514 0.926411i \(-0.622877\pi\)
−0.376514 + 0.926411i \(0.622877\pi\)
\(942\) 0 0
\(943\) 2.07558 0.0675902
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 42.5498 1.38268 0.691342 0.722528i \(-0.257020\pi\)
0.691342 + 0.722528i \(0.257020\pi\)
\(948\) 0 0
\(949\) −94.7492 −3.07569
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.90033 −0.0939509 −0.0469755 0.998896i \(-0.514958\pi\)
−0.0469755 + 0.998896i \(0.514958\pi\)
\(954\) 0 0
\(955\) 18.3746 0.594588
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.35050 0.0759015
\(960\) 0 0
\(961\) −29.3746 −0.947567
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 4.00000 0.128765
\(966\) 0 0
\(967\) −55.6495 −1.78957 −0.894784 0.446500i \(-0.852670\pi\)
−0.894784 + 0.446500i \(0.852670\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 8.64950 0.277576 0.138788 0.990322i \(-0.455679\pi\)
0.138788 + 0.990322i \(0.455679\pi\)
\(972\) 0 0
\(973\) −38.4743 −1.23343
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −41.6495 −1.33249 −0.666243 0.745735i \(-0.732099\pi\)
−0.666243 + 0.745735i \(0.732099\pi\)
\(978\) 0 0
\(979\) −12.5257 −0.400325
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −28.7492 −0.916956 −0.458478 0.888706i \(-0.651605\pi\)
−0.458478 + 0.888706i \(0.651605\pi\)
\(984\) 0 0
\(985\) 15.3746 0.489875
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.09967 0.0349674
\(990\) 0 0
\(991\) 9.27492 0.294627 0.147314 0.989090i \(-0.452937\pi\)
0.147314 + 0.989090i \(0.452937\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8.00000 −0.253617
\(996\) 0 0
\(997\) −29.3746 −0.930302 −0.465151 0.885231i \(-0.654000\pi\)
−0.465151 + 0.885231i \(0.654000\pi\)
\(998\) 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 6480.2.a.bm.1.1 2
3.2 odd 2 6480.2.a.bf.1.1 2
4.3 odd 2 3240.2.a.n.1.2 yes 2
12.11 even 2 3240.2.a.h.1.2 2
36.7 odd 6 3240.2.q.y.1081.1 4
36.11 even 6 3240.2.q.be.1081.1 4
36.23 even 6 3240.2.q.be.2161.1 4
36.31 odd 6 3240.2.q.y.2161.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3240.2.a.h.1.2 2 12.11 even 2
3240.2.a.n.1.2 yes 2 4.3 odd 2
3240.2.q.y.1081.1 4 36.7 odd 6
3240.2.q.y.2161.1 4 36.31 odd 6
3240.2.q.be.1081.1 4 36.11 even 6
3240.2.q.be.2161.1 4 36.23 even 6
6480.2.a.bf.1.1 2 3.2 odd 2
6480.2.a.bm.1.1 2 1.1 even 1 trivial