Properties

Label 3240.2.a.o.1.1
Level $3240$
Weight $2$
Character 3240.1
Self dual yes
Analytic conductor $25.872$
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] = [3240,2,Mod(1,3240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3240, 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("3240.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.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: \(25.8715302549\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 360)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.44949\) of defining polynomial
Character \(\chi\) \(=\) 3240.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} -1.44949 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -1.44949 q^{7} +2.00000 q^{17} +2.89898 q^{19} +2.55051 q^{23} +1.00000 q^{25} -7.89898 q^{29} +10.8990 q^{31} -1.44949 q^{35} -6.00000 q^{37} +0.101021 q^{41} -7.79796 q^{43} +4.55051 q^{47} -4.89898 q^{49} +11.7980 q^{53} +10.8990 q^{59} -3.00000 q^{61} +11.2474 q^{67} +9.79796 q^{71} -5.79796 q^{73} +2.89898 q^{79} +0.550510 q^{83} +2.00000 q^{85} +16.7980 q^{89} +2.89898 q^{95} +2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} + 2 q^{7} + 4 q^{17} - 4 q^{19} + 10 q^{23} + 2 q^{25} - 6 q^{29} + 12 q^{31} + 2 q^{35} - 12 q^{37} + 10 q^{41} + 4 q^{43} + 14 q^{47} + 4 q^{53} + 12 q^{59} - 6 q^{61} - 2 q^{67} + 8 q^{73} - 4 q^{79} + 6 q^{83} + 4 q^{85} + 14 q^{89} - 4 q^{95} + 4 q^{97}+O(q^{100}) \) 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
\(7\) −1.44949 −0.547856 −0.273928 0.961750i \(-0.588323\pi\)
−0.273928 + 0.961750i \(0.588323\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 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
\(19\) 2.89898 0.665072 0.332536 0.943091i \(-0.392096\pi\)
0.332536 + 0.943091i \(0.392096\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.55051 0.531818 0.265909 0.963998i \(-0.414328\pi\)
0.265909 + 0.963998i \(0.414328\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7.89898 −1.46680 −0.733402 0.679795i \(-0.762069\pi\)
−0.733402 + 0.679795i \(0.762069\pi\)
\(30\) 0 0
\(31\) 10.8990 1.95751 0.978757 0.205023i \(-0.0657268\pi\)
0.978757 + 0.205023i \(0.0657268\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.44949 −0.245008
\(36\) 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
\(41\) 0.101021 0.0157768 0.00788838 0.999969i \(-0.497489\pi\)
0.00788838 + 0.999969i \(0.497489\pi\)
\(42\) 0 0
\(43\) −7.79796 −1.18918 −0.594589 0.804030i \(-0.702685\pi\)
−0.594589 + 0.804030i \(0.702685\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.55051 0.663760 0.331880 0.943322i \(-0.392317\pi\)
0.331880 + 0.943322i \(0.392317\pi\)
\(48\) 0 0
\(49\) −4.89898 −0.699854
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.7980 1.62057 0.810287 0.586033i \(-0.199311\pi\)
0.810287 + 0.586033i \(0.199311\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 10.8990 1.41893 0.709463 0.704743i \(-0.248937\pi\)
0.709463 + 0.704743i \(0.248937\pi\)
\(60\) 0 0
\(61\) −3.00000 −0.384111 −0.192055 0.981384i \(-0.561515\pi\)
−0.192055 + 0.981384i \(0.561515\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 11.2474 1.37409 0.687047 0.726613i \(-0.258907\pi\)
0.687047 + 0.726613i \(0.258907\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 9.79796 1.16280 0.581402 0.813617i \(-0.302504\pi\)
0.581402 + 0.813617i \(0.302504\pi\)
\(72\) 0 0
\(73\) −5.79796 −0.678600 −0.339300 0.940678i \(-0.610190\pi\)
−0.339300 + 0.940678i \(0.610190\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.89898 0.326161 0.163080 0.986613i \(-0.447857\pi\)
0.163080 + 0.986613i \(0.447857\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.550510 0.0604264 0.0302132 0.999543i \(-0.490381\pi\)
0.0302132 + 0.999543i \(0.490381\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.7980 1.78058 0.890290 0.455394i \(-0.150502\pi\)
0.890290 + 0.455394i \(0.150502\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.89898 0.297429
\(96\) 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
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.34847 −0.227035 −0.113518 0.993536i \(-0.536212\pi\)
−0.113518 + 0.993536i \(0.536212\pi\)
\(108\) 0 0
\(109\) 8.79796 0.842692 0.421346 0.906900i \(-0.361558\pi\)
0.421346 + 0.906900i \(0.361558\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.79796 −0.921714 −0.460857 0.887474i \(-0.652458\pi\)
−0.460857 + 0.887474i \(0.652458\pi\)
\(114\) 0 0
\(115\) 2.55051 0.237836
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.89898 −0.265749
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −14.3485 −1.27322 −0.636610 0.771186i \(-0.719664\pi\)
−0.636610 + 0.771186i \(0.719664\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.89898 0.602767 0.301383 0.953503i \(-0.402552\pi\)
0.301383 + 0.953503i \(0.402552\pi\)
\(132\) 0 0
\(133\) −4.20204 −0.364363
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19.5959 1.67419 0.837096 0.547056i \(-0.184251\pi\)
0.837096 + 0.547056i \(0.184251\pi\)
\(138\) 0 0
\(139\) −19.5959 −1.66210 −0.831052 0.556195i \(-0.812261\pi\)
−0.831052 + 0.556195i \(0.812261\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −7.89898 −0.655975
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 21.0000 1.72039 0.860194 0.509968i \(-0.170343\pi\)
0.860194 + 0.509968i \(0.170343\pi\)
\(150\) 0 0
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.8990 0.875427
\(156\) 0 0
\(157\) −4.20204 −0.335359 −0.167680 0.985842i \(-0.553627\pi\)
−0.167680 + 0.985842i \(0.553627\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.69694 −0.291360
\(162\) 0 0
\(163\) 11.7980 0.924087 0.462044 0.886857i \(-0.347116\pi\)
0.462044 + 0.886857i \(0.347116\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.34847 0.491259 0.245630 0.969364i \(-0.421005\pi\)
0.245630 + 0.969364i \(0.421005\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.0000 0.912343 0.456172 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) 0 0
\(175\) −1.44949 −0.109571
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −5.79796 −0.433360 −0.216680 0.976243i \(-0.569523\pi\)
−0.216680 + 0.976243i \(0.569523\pi\)
\(180\) 0 0
\(181\) 19.6969 1.46406 0.732031 0.681271i \(-0.238573\pi\)
0.732031 + 0.681271i \(0.238573\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.10102 0.369097 0.184548 0.982823i \(-0.440918\pi\)
0.184548 + 0.982823i \(0.440918\pi\)
\(192\) 0 0
\(193\) −21.7980 −1.56905 −0.784526 0.620096i \(-0.787094\pi\)
−0.784526 + 0.620096i \(0.787094\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.5959 −1.68114 −0.840570 0.541703i \(-0.817780\pi\)
−0.840570 + 0.541703i \(0.817780\pi\)
\(198\) 0 0
\(199\) 13.1010 0.928707 0.464353 0.885650i \(-0.346287\pi\)
0.464353 + 0.885650i \(0.346287\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 11.4495 0.803597
\(204\) 0 0
\(205\) 0.101021 0.00705558
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7.79796 −0.531816
\(216\) 0 0
\(217\) −15.7980 −1.07244
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.550510 0.0368649 0.0184324 0.999830i \(-0.494132\pi\)
0.0184324 + 0.999830i \(0.494132\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 27.7980 1.84502 0.922508 0.385979i \(-0.126136\pi\)
0.922508 + 0.385979i \(0.126136\pi\)
\(228\) 0 0
\(229\) −13.8990 −0.918470 −0.459235 0.888315i \(-0.651876\pi\)
−0.459235 + 0.888315i \(0.651876\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.202041 0.0132361 0.00661807 0.999978i \(-0.497893\pi\)
0.00661807 + 0.999978i \(0.497893\pi\)
\(234\) 0 0
\(235\) 4.55051 0.296843
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −21.7980 −1.40999 −0.704996 0.709211i \(-0.749051\pi\)
−0.704996 + 0.709211i \(0.749051\pi\)
\(240\) 0 0
\(241\) 25.6969 1.65529 0.827643 0.561255i \(-0.189681\pi\)
0.827643 + 0.561255i \(0.189681\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.89898 −0.312984
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.89898 0.435460 0.217730 0.976009i \(-0.430135\pi\)
0.217730 + 0.976009i \(0.430135\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.20204 −0.511629 −0.255815 0.966726i \(-0.582344\pi\)
−0.255815 + 0.966726i \(0.582344\pi\)
\(258\) 0 0
\(259\) 8.69694 0.540401
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) 11.7980 0.724743
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 16.5959 1.01187 0.505935 0.862571i \(-0.331147\pi\)
0.505935 + 0.862571i \(0.331147\pi\)
\(270\) 0 0
\(271\) 21.1010 1.28180 0.640898 0.767626i \(-0.278562\pi\)
0.640898 + 0.767626i \(0.278562\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 17.8990 1.06776 0.533882 0.845559i \(-0.320733\pi\)
0.533882 + 0.845559i \(0.320733\pi\)
\(282\) 0 0
\(283\) −18.3485 −1.09070 −0.545352 0.838207i \(-0.683604\pi\)
−0.545352 + 0.838207i \(0.683604\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.146428 −0.00864338
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.5959 1.26165 0.630823 0.775926i \(-0.282717\pi\)
0.630823 + 0.775926i \(0.282717\pi\)
\(294\) 0 0
\(295\) 10.8990 0.634563
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 11.3031 0.651498
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.00000 −0.171780
\(306\) 0 0
\(307\) −29.2474 −1.66924 −0.834620 0.550826i \(-0.814313\pi\)
−0.834620 + 0.550826i \(0.814313\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.89898 −0.164386 −0.0821930 0.996616i \(-0.526192\pi\)
−0.0821930 + 0.996616i \(0.526192\pi\)
\(312\) 0 0
\(313\) 23.5959 1.33372 0.666860 0.745183i \(-0.267638\pi\)
0.666860 + 0.745183i \(0.267638\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.20204 0.348341 0.174171 0.984715i \(-0.444276\pi\)
0.174171 + 0.984715i \(0.444276\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5.79796 0.322607
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.59592 −0.363645
\(330\) 0 0
\(331\) 2.89898 0.159342 0.0796712 0.996821i \(-0.474613\pi\)
0.0796712 + 0.996821i \(0.474613\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 11.2474 0.614514
\(336\) 0 0
\(337\) −10.2020 −0.555741 −0.277870 0.960619i \(-0.589629\pi\)
−0.277870 + 0.960619i \(0.589629\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 17.2474 0.931275
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.5959 −0.729867 −0.364934 0.931034i \(-0.618908\pi\)
−0.364934 + 0.931034i \(0.618908\pi\)
\(348\) 0 0
\(349\) −31.6969 −1.69670 −0.848349 0.529437i \(-0.822403\pi\)
−0.848349 + 0.529437i \(0.822403\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 9.79796 0.520022
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.696938 0.0367830 0.0183915 0.999831i \(-0.494145\pi\)
0.0183915 + 0.999831i \(0.494145\pi\)
\(360\) 0 0
\(361\) −10.5959 −0.557680
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.79796 −0.303479
\(366\) 0 0
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −17.1010 −0.887841
\(372\) 0 0
\(373\) −17.5959 −0.911082 −0.455541 0.890215i \(-0.650554\pi\)
−0.455541 + 0.890215i \(0.650554\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 17.1010 0.878420 0.439210 0.898384i \(-0.355258\pi\)
0.439210 + 0.898384i \(0.355258\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.00000 −0.102195 −0.0510976 0.998694i \(-0.516272\pi\)
−0.0510976 + 0.998694i \(0.516272\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −22.5959 −1.14566 −0.572829 0.819675i \(-0.694154\pi\)
−0.572829 + 0.819675i \(0.694154\pi\)
\(390\) 0 0
\(391\) 5.10102 0.257970
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.89898 0.145863
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.5959 0.678948 0.339474 0.940615i \(-0.389751\pi\)
0.339474 + 0.940615i \(0.389751\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 29.5959 1.46342 0.731712 0.681614i \(-0.238722\pi\)
0.731712 + 0.681614i \(0.238722\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −15.7980 −0.777367
\(414\) 0 0
\(415\) 0.550510 0.0270235
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) −13.5959 −0.662624 −0.331312 0.943521i \(-0.607491\pi\)
−0.331312 + 0.943521i \(0.607491\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) 4.34847 0.210437
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.10102 −0.245708 −0.122854 0.992425i \(-0.539205\pi\)
−0.122854 + 0.992425i \(0.539205\pi\)
\(432\) 0 0
\(433\) 7.79796 0.374746 0.187373 0.982289i \(-0.440003\pi\)
0.187373 + 0.982289i \(0.440003\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.39388 0.353697
\(438\) 0 0
\(439\) 1.79796 0.0858119 0.0429059 0.999079i \(-0.486338\pi\)
0.0429059 + 0.999079i \(0.486338\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −26.1464 −1.24225 −0.621127 0.783710i \(-0.713325\pi\)
−0.621127 + 0.783710i \(0.713325\pi\)
\(444\) 0 0
\(445\) 16.7980 0.796300
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 17.5959 0.830403 0.415201 0.909730i \(-0.363711\pi\)
0.415201 + 0.909730i \(0.363711\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −21.5959 −1.01021 −0.505107 0.863057i \(-0.668547\pi\)
−0.505107 + 0.863057i \(0.668547\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −21.8990 −1.01994 −0.509969 0.860193i \(-0.670343\pi\)
−0.509969 + 0.860193i \(0.670343\pi\)
\(462\) 0 0
\(463\) 31.7980 1.47778 0.738888 0.673828i \(-0.235351\pi\)
0.738888 + 0.673828i \(0.235351\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11.7980 0.545944 0.272972 0.962022i \(-0.411993\pi\)
0.272972 + 0.962022i \(0.411993\pi\)
\(468\) 0 0
\(469\) −16.3031 −0.752805
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 2.89898 0.133014
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18.4949 0.845053 0.422527 0.906350i \(-0.361143\pi\)
0.422527 + 0.906350i \(0.361143\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) 25.5959 1.15986 0.579931 0.814666i \(-0.303080\pi\)
0.579931 + 0.814666i \(0.303080\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.79796 −0.261658 −0.130829 0.991405i \(-0.541764\pi\)
−0.130829 + 0.991405i \(0.541764\pi\)
\(492\) 0 0
\(493\) −15.7980 −0.711504
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.2020 −0.637049
\(498\) 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
\(503\) 19.0454 0.849193 0.424596 0.905383i \(-0.360416\pi\)
0.424596 + 0.905383i \(0.360416\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13.8990 0.616061 0.308031 0.951376i \(-0.400330\pi\)
0.308031 + 0.951376i \(0.400330\pi\)
\(510\) 0 0
\(511\) 8.40408 0.371775
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.0000 0.440653
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −28.7980 −1.26166 −0.630831 0.775920i \(-0.717286\pi\)
−0.630831 + 0.775920i \(0.717286\pi\)
\(522\) 0 0
\(523\) −19.6515 −0.859301 −0.429651 0.902995i \(-0.641363\pi\)
−0.429651 + 0.902995i \(0.641363\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 21.7980 0.949534
\(528\) 0 0
\(529\) −16.4949 −0.717169
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −2.34847 −0.101533
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 21.8990 0.941511 0.470755 0.882264i \(-0.343981\pi\)
0.470755 + 0.882264i \(0.343981\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 8.79796 0.376863
\(546\) 0 0
\(547\) −41.2474 −1.76361 −0.881807 0.471611i \(-0.843673\pi\)
−0.881807 + 0.471611i \(0.843673\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −22.8990 −0.975529
\(552\) 0 0
\(553\) −4.20204 −0.178689
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −24.2020 −1.02547 −0.512737 0.858546i \(-0.671368\pi\)
−0.512737 + 0.858546i \(0.671368\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.34847 −0.183266 −0.0916331 0.995793i \(-0.529209\pi\)
−0.0916331 + 0.995793i \(0.529209\pi\)
\(564\) 0 0
\(565\) −9.79796 −0.412203
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.0000 −0.419222 −0.209611 0.977785i \(-0.567220\pi\)
−0.209611 + 0.977785i \(0.567220\pi\)
\(570\) 0 0
\(571\) 6.20204 0.259547 0.129774 0.991544i \(-0.458575\pi\)
0.129774 + 0.991544i \(0.458575\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.55051 0.106364
\(576\) 0 0
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.797959 −0.0331049
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −22.3485 −0.922420 −0.461210 0.887291i \(-0.652585\pi\)
−0.461210 + 0.887291i \(0.652585\pi\)
\(588\) 0 0
\(589\) 31.5959 1.30189
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −27.3939 −1.12493 −0.562466 0.826821i \(-0.690147\pi\)
−0.562466 + 0.826821i \(0.690147\pi\)
\(594\) 0 0
\(595\) −2.89898 −0.118847
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.69694 −0.191912 −0.0959559 0.995386i \(-0.530591\pi\)
−0.0959559 + 0.995386i \(0.530591\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.0000 −0.447214
\(606\) 0 0
\(607\) −32.1464 −1.30478 −0.652392 0.757882i \(-0.726234\pi\)
−0.652392 + 0.757882i \(0.726234\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 9.59592 0.387575 0.193788 0.981043i \(-0.437923\pi\)
0.193788 + 0.981043i \(0.437923\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −43.1918 −1.73884 −0.869419 0.494076i \(-0.835507\pi\)
−0.869419 + 0.494076i \(0.835507\pi\)
\(618\) 0 0
\(619\) 4.69694 0.188786 0.0943929 0.995535i \(-0.469909\pi\)
0.0943929 + 0.995535i \(0.469909\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −24.3485 −0.975501
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 23.5959 0.939339 0.469669 0.882842i \(-0.344373\pi\)
0.469669 + 0.882842i \(0.344373\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −14.3485 −0.569402
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.10102 0.161981 0.0809903 0.996715i \(-0.474192\pi\)
0.0809903 + 0.996715i \(0.474192\pi\)
\(642\) 0 0
\(643\) 14.1464 0.557881 0.278940 0.960308i \(-0.410017\pi\)
0.278940 + 0.960308i \(0.410017\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −11.4495 −0.450126 −0.225063 0.974344i \(-0.572259\pi\)
−0.225063 + 0.974344i \(0.572259\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.20204 −0.320971 −0.160485 0.987038i \(-0.551306\pi\)
−0.160485 + 0.987038i \(0.551306\pi\)
\(654\) 0 0
\(655\) 6.89898 0.269565
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −29.7980 −1.16076 −0.580382 0.814344i \(-0.697097\pi\)
−0.580382 + 0.814344i \(0.697097\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.20204 −0.162948
\(666\) 0 0
\(667\) −20.1464 −0.780073
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −33.7980 −1.29896 −0.649481 0.760378i \(-0.725014\pi\)
−0.649481 + 0.760378i \(0.725014\pi\)
\(678\) 0 0
\(679\) −2.89898 −0.111253
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 35.3939 1.35431 0.677155 0.735841i \(-0.263213\pi\)
0.677155 + 0.735841i \(0.263213\pi\)
\(684\) 0 0
\(685\) 19.5959 0.748722
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 29.1010 1.10705 0.553527 0.832831i \(-0.313281\pi\)
0.553527 + 0.832831i \(0.313281\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −19.5959 −0.743316
\(696\) 0 0
\(697\) 0.202041 0.00765285
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 28.3939 1.07242 0.536211 0.844084i \(-0.319855\pi\)
0.536211 + 0.844084i \(0.319855\pi\)
\(702\) 0 0
\(703\) −17.3939 −0.656022
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.89898 −0.109027
\(708\) 0 0
\(709\) −19.6969 −0.739734 −0.369867 0.929085i \(-0.620597\pi\)
−0.369867 + 0.929085i \(0.620597\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 27.7980 1.04104
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −40.2929 −1.50267 −0.751335 0.659921i \(-0.770590\pi\)
−0.751335 + 0.659921i \(0.770590\pi\)
\(720\) 0 0
\(721\) −14.4949 −0.539818
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.89898 −0.293361
\(726\) 0 0
\(727\) −6.75255 −0.250438 −0.125219 0.992129i \(-0.539963\pi\)
−0.125219 + 0.992129i \(0.539963\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −15.5959 −0.576836
\(732\) 0 0
\(733\) 9.59592 0.354433 0.177217 0.984172i \(-0.443291\pi\)
0.177217 + 0.984172i \(0.443291\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −42.8990 −1.57806 −0.789032 0.614352i \(-0.789418\pi\)
−0.789032 + 0.614352i \(0.789418\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −37.0454 −1.35906 −0.679532 0.733646i \(-0.737817\pi\)
−0.679532 + 0.733646i \(0.737817\pi\)
\(744\) 0 0
\(745\) 21.0000 0.769380
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.40408 0.124382
\(750\) 0 0
\(751\) 45.7980 1.67119 0.835596 0.549345i \(-0.185123\pi\)
0.835596 + 0.549345i \(0.185123\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) −7.59592 −0.276078 −0.138039 0.990427i \(-0.544080\pi\)
−0.138039 + 0.990427i \(0.544080\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −35.0000 −1.26875 −0.634375 0.773026i \(-0.718742\pi\)
−0.634375 + 0.773026i \(0.718742\pi\)
\(762\) 0 0
\(763\) −12.7526 −0.461673
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −24.7980 −0.894237 −0.447119 0.894475i \(-0.647550\pi\)
−0.447119 + 0.894475i \(0.647550\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −25.7980 −0.927888 −0.463944 0.885865i \(-0.653566\pi\)
−0.463944 + 0.885865i \(0.653566\pi\)
\(774\) 0 0
\(775\) 10.8990 0.391503
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.292856 0.0104927
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.20204 −0.149977
\(786\) 0 0
\(787\) −10.4041 −0.370865 −0.185433 0.982657i \(-0.559369\pi\)
−0.185433 + 0.982657i \(0.559369\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14.2020 0.504966
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.00000 0.283375 0.141687 0.989911i \(-0.454747\pi\)
0.141687 + 0.989911i \(0.454747\pi\)
\(798\) 0 0
\(799\) 9.10102 0.321971
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −3.69694 −0.130300
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 30.0000 1.05474 0.527372 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) 0 0
\(811\) 22.8990 0.804092 0.402046 0.915619i \(-0.368299\pi\)
0.402046 + 0.915619i \(0.368299\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 11.7980 0.413264
\(816\) 0 0
\(817\) −22.6061 −0.790888
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 16.7980 0.586253 0.293126 0.956074i \(-0.405304\pi\)
0.293126 + 0.956074i \(0.405304\pi\)
\(822\) 0 0
\(823\) 6.34847 0.221294 0.110647 0.993860i \(-0.464708\pi\)
0.110647 + 0.993860i \(0.464708\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 39.5403 1.37495 0.687476 0.726208i \(-0.258719\pi\)
0.687476 + 0.726208i \(0.258719\pi\)
\(828\) 0 0
\(829\) −28.1918 −0.979143 −0.489571 0.871963i \(-0.662847\pi\)
−0.489571 + 0.871963i \(0.662847\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −9.79796 −0.339479
\(834\) 0 0
\(835\) 6.34847 0.219698
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 24.6969 0.852633 0.426317 0.904574i \(-0.359811\pi\)
0.426317 + 0.904574i \(0.359811\pi\)
\(840\) 0 0
\(841\) 33.3939 1.15151
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −13.0000 −0.447214
\(846\) 0 0
\(847\) 15.9444 0.547856
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −15.3031 −0.524582
\(852\) 0 0
\(853\) 37.7980 1.29418 0.647089 0.762415i \(-0.275986\pi\)
0.647089 + 0.762415i \(0.275986\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −39.5959 −1.35257 −0.676285 0.736640i \(-0.736411\pi\)
−0.676285 + 0.736640i \(0.736411\pi\)
\(858\) 0 0
\(859\) −39.1918 −1.33721 −0.668604 0.743619i \(-0.733108\pi\)
−0.668604 + 0.743619i \(0.733108\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −52.5505 −1.78884 −0.894420 0.447228i \(-0.852411\pi\)
−0.894420 + 0.447228i \(0.852411\pi\)
\(864\) 0 0
\(865\) 12.0000 0.408012
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.44949 −0.0490017
\(876\) 0 0
\(877\) −39.5959 −1.33706 −0.668530 0.743686i \(-0.733076\pi\)
−0.668530 + 0.743686i \(0.733076\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −15.8990 −0.535650 −0.267825 0.963468i \(-0.586305\pi\)
−0.267825 + 0.963468i \(0.586305\pi\)
\(882\) 0 0
\(883\) −45.0454 −1.51590 −0.757949 0.652313i \(-0.773799\pi\)
−0.757949 + 0.652313i \(0.773799\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 37.5959 1.26235 0.631174 0.775642i \(-0.282574\pi\)
0.631174 + 0.775642i \(0.282574\pi\)
\(888\) 0 0
\(889\) 20.7980 0.697541
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 13.1918 0.441448
\(894\) 0 0
\(895\) −5.79796 −0.193804
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −86.0908 −2.87129
\(900\) 0 0
\(901\) 23.5959 0.786094
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 19.6969 0.654748
\(906\) 0 0
\(907\) −36.3485 −1.20693 −0.603466 0.797389i \(-0.706214\pi\)
−0.603466 + 0.797389i \(0.706214\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 38.4949 1.27539 0.637696 0.770288i \(-0.279887\pi\)
0.637696 + 0.770288i \(0.279887\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −10.0000 −0.330229
\(918\) 0 0
\(919\) −4.69694 −0.154938 −0.0774689 0.996995i \(-0.524684\pi\)
−0.0774689 + 0.996995i \(0.524684\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.59592 0.0523604 0.0261802 0.999657i \(-0.491666\pi\)
0.0261802 + 0.999657i \(0.491666\pi\)
\(930\) 0 0
\(931\) −14.2020 −0.465453
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 56.9898 1.86178 0.930888 0.365305i \(-0.119035\pi\)
0.930888 + 0.365305i \(0.119035\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −27.6969 −0.902894 −0.451447 0.892298i \(-0.649092\pi\)
−0.451447 + 0.892298i \(0.649092\pi\)
\(942\) 0 0
\(943\) 0.257654 0.00839036
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 46.1464 1.49956 0.749779 0.661689i \(-0.230160\pi\)
0.749779 + 0.661689i \(0.230160\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 33.7980 1.09482 0.547412 0.836863i \(-0.315613\pi\)
0.547412 + 0.836863i \(0.315613\pi\)
\(954\) 0 0
\(955\) 5.10102 0.165065
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −28.4041 −0.917216
\(960\) 0 0
\(961\) 87.7878 2.83186
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −21.7980 −0.701701
\(966\) 0 0
\(967\) −14.8434 −0.477330 −0.238665 0.971102i \(-0.576710\pi\)
−0.238665 + 0.971102i \(0.576710\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −60.6969 −1.94786 −0.973929 0.226854i \(-0.927156\pi\)
−0.973929 + 0.226854i \(0.927156\pi\)
\(972\) 0 0
\(973\) 28.4041 0.910593
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −45.3939 −1.45228 −0.726139 0.687548i \(-0.758687\pi\)
−0.726139 + 0.687548i \(0.758687\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 6.55051 0.208929 0.104464 0.994529i \(-0.466687\pi\)
0.104464 + 0.994529i \(0.466687\pi\)
\(984\) 0 0
\(985\) −23.5959 −0.751828
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −19.8888 −0.632426
\(990\) 0 0
\(991\) −0.696938 −0.0221390 −0.0110695 0.999939i \(-0.503524\pi\)
−0.0110695 + 0.999939i \(0.503524\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 13.1010 0.415330
\(996\) 0 0
\(997\) 35.3939 1.12094 0.560468 0.828176i \(-0.310621\pi\)
0.560468 + 0.828176i \(0.310621\pi\)
\(998\) 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 3240.2.a.o.1.1 2
3.2 odd 2 3240.2.a.j.1.1 2
4.3 odd 2 6480.2.a.bl.1.2 2
9.2 odd 6 360.2.q.c.121.2 4
9.4 even 3 1080.2.q.c.721.2 4
9.5 odd 6 360.2.q.c.241.2 yes 4
9.7 even 3 1080.2.q.c.361.2 4
12.11 even 2 6480.2.a.bc.1.2 2
36.7 odd 6 2160.2.q.g.1441.1 4
36.11 even 6 720.2.q.g.481.1 4
36.23 even 6 720.2.q.g.241.1 4
36.31 odd 6 2160.2.q.g.721.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.q.c.121.2 4 9.2 odd 6
360.2.q.c.241.2 yes 4 9.5 odd 6
720.2.q.g.241.1 4 36.23 even 6
720.2.q.g.481.1 4 36.11 even 6
1080.2.q.c.361.2 4 9.7 even 3
1080.2.q.c.721.2 4 9.4 even 3
2160.2.q.g.721.1 4 36.31 odd 6
2160.2.q.g.1441.1 4 36.7 odd 6
3240.2.a.j.1.1 2 3.2 odd 2
3240.2.a.o.1.1 2 1.1 even 1 trivial
6480.2.a.bc.1.2 2 12.11 even 2
6480.2.a.bl.1.2 2 4.3 odd 2