Properties

Label 4284.2.a.n.1.2
Level $4284$
Weight $2$
Character 4284.1
Self dual yes
Analytic conductor $34.208$
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] = [4284,2,Mod(1,4284)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4284, 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("4284.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4284.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: \(34.2079122259\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 476)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.30278\) of defining polynomial
Character \(\chi\) \(=\) 4284.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.30278 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+2.30278 q^{5} +1.00000 q^{7} +6.60555 q^{13} -1.00000 q^{17} +6.60555 q^{19} +0.302776 q^{25} +4.30278 q^{31} +2.30278 q^{35} -2.60555 q^{37} -3.90833 q^{41} +7.30278 q^{43} -4.60555 q^{47} +1.00000 q^{49} +3.69722 q^{53} -9.21110 q^{59} -7.90833 q^{61} +15.2111 q^{65} -1.69722 q^{67} +7.81665 q^{71} -7.90833 q^{73} +12.6056 q^{79} -6.00000 q^{83} -2.30278 q^{85} +16.6056 q^{89} +6.60555 q^{91} +15.2111 q^{95} -6.30278 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{5} + 2 q^{7} + 6 q^{13} - 2 q^{17} + 6 q^{19} - 3 q^{25} + 5 q^{31} + q^{35} + 2 q^{37} + 3 q^{41} + 11 q^{43} - 2 q^{47} + 2 q^{49} + 11 q^{53} - 4 q^{59} - 5 q^{61} + 16 q^{65} - 7 q^{67} - 6 q^{71} - 5 q^{73} + 18 q^{79} - 12 q^{83} - q^{85} + 26 q^{89} + 6 q^{91} + 16 q^{95} - 9 q^{97}+O(q^{100}) \) 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
\(5\) 2.30278 1.02983 0.514916 0.857240i \(-0.327823\pi\)
0.514916 + 0.857240i \(0.327823\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 6.60555 1.83205 0.916025 0.401121i \(-0.131379\pi\)
0.916025 + 0.401121i \(0.131379\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 6.60555 1.51542 0.757709 0.652593i \(-0.226319\pi\)
0.757709 + 0.652593i \(0.226319\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0.302776 0.0605551
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 4.30278 0.772801 0.386401 0.922331i \(-0.373718\pi\)
0.386401 + 0.922331i \(0.373718\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.30278 0.389240
\(36\) 0 0
\(37\) −2.60555 −0.428350 −0.214175 0.976795i \(-0.568706\pi\)
−0.214175 + 0.976795i \(0.568706\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.90833 −0.610378 −0.305189 0.952292i \(-0.598720\pi\)
−0.305189 + 0.952292i \(0.598720\pi\)
\(42\) 0 0
\(43\) 7.30278 1.11366 0.556831 0.830626i \(-0.312017\pi\)
0.556831 + 0.830626i \(0.312017\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.60555 −0.671789 −0.335894 0.941900i \(-0.609039\pi\)
−0.335894 + 0.941900i \(0.609039\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.69722 0.507853 0.253926 0.967224i \(-0.418278\pi\)
0.253926 + 0.967224i \(0.418278\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.21110 −1.19918 −0.599592 0.800306i \(-0.704670\pi\)
−0.599592 + 0.800306i \(0.704670\pi\)
\(60\) 0 0
\(61\) −7.90833 −1.01256 −0.506279 0.862370i \(-0.668979\pi\)
−0.506279 + 0.862370i \(0.668979\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 15.2111 1.88671
\(66\) 0 0
\(67\) −1.69722 −0.207349 −0.103674 0.994611i \(-0.533060\pi\)
−0.103674 + 0.994611i \(0.533060\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.81665 0.927666 0.463833 0.885923i \(-0.346474\pi\)
0.463833 + 0.885923i \(0.346474\pi\)
\(72\) 0 0
\(73\) −7.90833 −0.925600 −0.462800 0.886463i \(-0.653155\pi\)
−0.462800 + 0.886463i \(0.653155\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 12.6056 1.41824 0.709118 0.705090i \(-0.249093\pi\)
0.709118 + 0.705090i \(0.249093\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) −2.30278 −0.249771
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.6056 1.76018 0.880092 0.474802i \(-0.157480\pi\)
0.880092 + 0.474802i \(0.157480\pi\)
\(90\) 0 0
\(91\) 6.60555 0.692450
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 15.2111 1.56063
\(96\) 0 0
\(97\) −6.30278 −0.639950 −0.319975 0.947426i \(-0.603675\pi\)
−0.319975 + 0.947426i \(0.603675\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −19.8167 −1.97183 −0.985915 0.167245i \(-0.946513\pi\)
−0.985915 + 0.167245i \(0.946513\pi\)
\(102\) 0 0
\(103\) −7.21110 −0.710531 −0.355266 0.934765i \(-0.615610\pi\)
−0.355266 + 0.934765i \(0.615610\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.39445 0.134806 0.0674032 0.997726i \(-0.478529\pi\)
0.0674032 + 0.997726i \(0.478529\pi\)
\(108\) 0 0
\(109\) 8.42221 0.806701 0.403350 0.915046i \(-0.367846\pi\)
0.403350 + 0.915046i \(0.367846\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.60555 −0.433254 −0.216627 0.976254i \(-0.569506\pi\)
−0.216627 + 0.976254i \(0.569506\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.00000 −0.0916698
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.8167 −0.967471
\(126\) 0 0
\(127\) 14.9083 1.32290 0.661450 0.749989i \(-0.269941\pi\)
0.661450 + 0.749989i \(0.269941\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 21.2111 1.85322 0.926611 0.376021i \(-0.122708\pi\)
0.926611 + 0.376021i \(0.122708\pi\)
\(132\) 0 0
\(133\) 6.60555 0.572774
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.6972 1.08480 0.542399 0.840121i \(-0.317516\pi\)
0.542399 + 0.840121i \(0.317516\pi\)
\(138\) 0 0
\(139\) 7.09167 0.601508 0.300754 0.953702i \(-0.402762\pi\)
0.300754 + 0.953702i \(0.402762\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −17.7250 −1.45209 −0.726044 0.687649i \(-0.758643\pi\)
−0.726044 + 0.687649i \(0.758643\pi\)
\(150\) 0 0
\(151\) −11.1194 −0.904886 −0.452443 0.891793i \(-0.649447\pi\)
−0.452443 + 0.891793i \(0.649447\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.90833 0.795856
\(156\) 0 0
\(157\) −7.21110 −0.575509 −0.287754 0.957704i \(-0.592909\pi\)
−0.287754 + 0.957704i \(0.592909\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.6056 0.987343 0.493671 0.869648i \(-0.335655\pi\)
0.493671 + 0.869648i \(0.335655\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 23.7250 1.83589 0.917947 0.396703i \(-0.129846\pi\)
0.917947 + 0.396703i \(0.129846\pi\)
\(168\) 0 0
\(169\) 30.6333 2.35641
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −17.3028 −1.31551 −0.657753 0.753234i \(-0.728493\pi\)
−0.657753 + 0.753234i \(0.728493\pi\)
\(174\) 0 0
\(175\) 0.302776 0.0228877
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.90833 −0.740583 −0.370292 0.928916i \(-0.620742\pi\)
−0.370292 + 0.928916i \(0.620742\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 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
\(191\) −20.7250 −1.49961 −0.749803 0.661661i \(-0.769852\pi\)
−0.749803 + 0.661661i \(0.769852\pi\)
\(192\) 0 0
\(193\) −11.8167 −0.850581 −0.425291 0.905057i \(-0.639828\pi\)
−0.425291 + 0.905057i \(0.639828\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.60555 0.328132 0.164066 0.986449i \(-0.447539\pi\)
0.164066 + 0.986449i \(0.447539\pi\)
\(198\) 0 0
\(199\) 21.1194 1.49712 0.748558 0.663069i \(-0.230746\pi\)
0.748558 + 0.663069i \(0.230746\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −9.00000 −0.628587
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −21.0278 −1.44761 −0.723805 0.690004i \(-0.757609\pi\)
−0.723805 + 0.690004i \(0.757609\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 16.8167 1.14689
\(216\) 0 0
\(217\) 4.30278 0.292091
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.60555 −0.444337
\(222\) 0 0
\(223\) −9.02776 −0.604543 −0.302272 0.953222i \(-0.597745\pi\)
−0.302272 + 0.953222i \(0.597745\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.51388 −0.365969 −0.182984 0.983116i \(-0.558576\pi\)
−0.182984 + 0.983116i \(0.558576\pi\)
\(228\) 0 0
\(229\) 10.7889 0.712950 0.356475 0.934305i \(-0.383978\pi\)
0.356475 + 0.934305i \(0.383978\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.8167 0.905159 0.452580 0.891724i \(-0.350504\pi\)
0.452580 + 0.891724i \(0.350504\pi\)
\(234\) 0 0
\(235\) −10.6056 −0.691830
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.3028 −0.731116 −0.365558 0.930789i \(-0.619122\pi\)
−0.365558 + 0.930789i \(0.619122\pi\)
\(240\) 0 0
\(241\) 8.48612 0.546639 0.273320 0.961923i \(-0.411878\pi\)
0.273320 + 0.961923i \(0.411878\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.30278 0.147119
\(246\) 0 0
\(247\) 43.6333 2.77632
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.18335 −0.264050 −0.132025 0.991246i \(-0.542148\pi\)
−0.132025 + 0.991246i \(0.542148\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.21110 −0.200303 −0.100152 0.994972i \(-0.531933\pi\)
−0.100152 + 0.994972i \(0.531933\pi\)
\(258\) 0 0
\(259\) −2.60555 −0.161901
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.4222 1.13596 0.567981 0.823042i \(-0.307725\pi\)
0.567981 + 0.823042i \(0.307725\pi\)
\(264\) 0 0
\(265\) 8.51388 0.523003
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −15.2111 −0.927437 −0.463719 0.885983i \(-0.653485\pi\)
−0.463719 + 0.885983i \(0.653485\pi\)
\(270\) 0 0
\(271\) −1.21110 −0.0735692 −0.0367846 0.999323i \(-0.511712\pi\)
−0.0367846 + 0.999323i \(0.511712\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −22.4222 −1.34722 −0.673610 0.739087i \(-0.735257\pi\)
−0.673610 + 0.739087i \(0.735257\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.69722 −0.220558 −0.110279 0.993901i \(-0.535174\pi\)
−0.110279 + 0.993901i \(0.535174\pi\)
\(282\) 0 0
\(283\) −9.51388 −0.565541 −0.282771 0.959188i \(-0.591254\pi\)
−0.282771 + 0.959188i \(0.591254\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.90833 −0.230701
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.6333 1.26383 0.631916 0.775037i \(-0.282269\pi\)
0.631916 + 0.775037i \(0.282269\pi\)
\(294\) 0 0
\(295\) −21.2111 −1.23496
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 7.30278 0.420925
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −18.2111 −1.04276
\(306\) 0 0
\(307\) −1.21110 −0.0691213 −0.0345606 0.999403i \(-0.511003\pi\)
−0.0345606 + 0.999403i \(0.511003\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.88057 0.106637 0.0533187 0.998578i \(-0.483020\pi\)
0.0533187 + 0.998578i \(0.483020\pi\)
\(312\) 0 0
\(313\) 33.3305 1.88395 0.941977 0.335679i \(-0.108966\pi\)
0.941977 + 0.335679i \(0.108966\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.60555 −0.367543
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.60555 −0.253912
\(330\) 0 0
\(331\) 5.69722 0.313148 0.156574 0.987666i \(-0.449955\pi\)
0.156574 + 0.987666i \(0.449955\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.90833 −0.213535
\(336\) 0 0
\(337\) −16.0000 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 30.0000 1.61048 0.805242 0.592946i \(-0.202035\pi\)
0.805242 + 0.592946i \(0.202035\pi\)
\(348\) 0 0
\(349\) 29.2111 1.56363 0.781817 0.623508i \(-0.214293\pi\)
0.781817 + 0.623508i \(0.214293\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.6333 0.832077 0.416039 0.909347i \(-0.363418\pi\)
0.416039 + 0.909347i \(0.363418\pi\)
\(354\) 0 0
\(355\) 18.0000 0.955341
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.90833 −0.364608 −0.182304 0.983242i \(-0.558355\pi\)
−0.182304 + 0.983242i \(0.558355\pi\)
\(360\) 0 0
\(361\) 24.6333 1.29649
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −18.2111 −0.953213
\(366\) 0 0
\(367\) 6.33053 0.330451 0.165226 0.986256i \(-0.447165\pi\)
0.165226 + 0.986256i \(0.447165\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.69722 0.191950
\(372\) 0 0
\(373\) −30.9361 −1.60181 −0.800905 0.598792i \(-0.795648\pi\)
−0.800905 + 0.598792i \(0.795648\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −6.78890 −0.348722 −0.174361 0.984682i \(-0.555786\pi\)
−0.174361 + 0.984682i \(0.555786\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −18.4222 −0.941331 −0.470665 0.882312i \(-0.655986\pi\)
−0.470665 + 0.882312i \(0.655986\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.1194 0.513075 0.256538 0.966534i \(-0.417418\pi\)
0.256538 + 0.966534i \(0.417418\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 29.0278 1.46054
\(396\) 0 0
\(397\) −21.9361 −1.10094 −0.550470 0.834855i \(-0.685552\pi\)
−0.550470 + 0.834855i \(0.685552\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.6056 0.829242 0.414621 0.909994i \(-0.363914\pi\)
0.414621 + 0.909994i \(0.363914\pi\)
\(402\) 0 0
\(403\) 28.4222 1.41581
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −26.6056 −1.31556 −0.657780 0.753210i \(-0.728504\pi\)
−0.657780 + 0.753210i \(0.728504\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −9.21110 −0.453249
\(414\) 0 0
\(415\) −13.8167 −0.678233
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 17.5139 0.855609 0.427804 0.903871i \(-0.359287\pi\)
0.427804 + 0.903871i \(0.359287\pi\)
\(420\) 0 0
\(421\) −30.9361 −1.50773 −0.753866 0.657028i \(-0.771813\pi\)
−0.753866 + 0.657028i \(0.771813\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.302776 −0.0146868
\(426\) 0 0
\(427\) −7.90833 −0.382711
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.6333 0.753030 0.376515 0.926411i \(-0.377122\pi\)
0.376515 + 0.926411i \(0.377122\pi\)
\(432\) 0 0
\(433\) 3.81665 0.183417 0.0917083 0.995786i \(-0.470767\pi\)
0.0917083 + 0.995786i \(0.470767\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −7.90833 −0.377444 −0.188722 0.982031i \(-0.560434\pi\)
−0.188722 + 0.982031i \(0.560434\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 21.2111 1.00777 0.503885 0.863771i \(-0.331904\pi\)
0.503885 + 0.863771i \(0.331904\pi\)
\(444\) 0 0
\(445\) 38.2389 1.81270
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 32.2389 1.52145 0.760723 0.649077i \(-0.224845\pi\)
0.760723 + 0.649077i \(0.224845\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 15.2111 0.713107
\(456\) 0 0
\(457\) −3.09167 −0.144622 −0.0723112 0.997382i \(-0.523037\pi\)
−0.0723112 + 0.997382i \(0.523037\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 31.8167 1.48185 0.740925 0.671588i \(-0.234388\pi\)
0.740925 + 0.671588i \(0.234388\pi\)
\(462\) 0 0
\(463\) −16.6972 −0.775986 −0.387993 0.921662i \(-0.626832\pi\)
−0.387993 + 0.921662i \(0.626832\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 35.4500 1.64043 0.820214 0.572056i \(-0.193854\pi\)
0.820214 + 0.572056i \(0.193854\pi\)
\(468\) 0 0
\(469\) −1.69722 −0.0783705
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14.5139 −0.663156 −0.331578 0.943428i \(-0.607581\pi\)
−0.331578 + 0.943428i \(0.607581\pi\)
\(480\) 0 0
\(481\) −17.2111 −0.784759
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −14.5139 −0.659041
\(486\) 0 0
\(487\) 5.21110 0.236138 0.118069 0.993005i \(-0.462330\pi\)
0.118069 + 0.993005i \(0.462330\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 25.3305 1.14315 0.571575 0.820550i \(-0.306332\pi\)
0.571575 + 0.820550i \(0.306332\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.81665 0.350625
\(498\) 0 0
\(499\) 1.57779 0.0706318 0.0353159 0.999376i \(-0.488756\pi\)
0.0353159 + 0.999376i \(0.488756\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21.1472 −0.942906 −0.471453 0.881891i \(-0.656270\pi\)
−0.471453 + 0.881891i \(0.656270\pi\)
\(504\) 0 0
\(505\) −45.6333 −2.03066
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.0278 0.488797 0.244398 0.969675i \(-0.421410\pi\)
0.244398 + 0.969675i \(0.421410\pi\)
\(510\) 0 0
\(511\) −7.90833 −0.349844
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −16.6056 −0.731728
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −39.3583 −1.72432 −0.862159 0.506638i \(-0.830888\pi\)
−0.862159 + 0.506638i \(0.830888\pi\)
\(522\) 0 0
\(523\) 10.7889 0.471766 0.235883 0.971782i \(-0.424202\pi\)
0.235883 + 0.971782i \(0.424202\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.30278 −0.187432
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −25.8167 −1.11824
\(534\) 0 0
\(535\) 3.21110 0.138828
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 42.0555 1.80811 0.904054 0.427419i \(-0.140577\pi\)
0.904054 + 0.427419i \(0.140577\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 19.3944 0.830767
\(546\) 0 0
\(547\) −31.2111 −1.33449 −0.667245 0.744838i \(-0.732527\pi\)
−0.667245 + 0.744838i \(0.732527\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 12.6056 0.536043
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −33.6333 −1.42509 −0.712544 0.701627i \(-0.752457\pi\)
−0.712544 + 0.701627i \(0.752457\pi\)
\(558\) 0 0
\(559\) 48.2389 2.04029
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.6333 1.16461 0.582303 0.812972i \(-0.302152\pi\)
0.582303 + 0.812972i \(0.302152\pi\)
\(564\) 0 0
\(565\) −10.6056 −0.446179
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.88057 −0.204604 −0.102302 0.994753i \(-0.532621\pi\)
−0.102302 + 0.994753i \(0.532621\pi\)
\(570\) 0 0
\(571\) −9.02776 −0.377800 −0.188900 0.981996i \(-0.560492\pi\)
−0.188900 + 0.981996i \(0.560492\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 28.2389 1.17560 0.587800 0.809007i \(-0.299994\pi\)
0.587800 + 0.809007i \(0.299994\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.00000 −0.248922
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.6056 0.437738 0.218869 0.975754i \(-0.429763\pi\)
0.218869 + 0.975754i \(0.429763\pi\)
\(588\) 0 0
\(589\) 28.4222 1.17112
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −43.8167 −1.79933 −0.899667 0.436576i \(-0.856191\pi\)
−0.899667 + 0.436576i \(0.856191\pi\)
\(594\) 0 0
\(595\) −2.30278 −0.0944046
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −43.9638 −1.79631 −0.898157 0.439675i \(-0.855094\pi\)
−0.898157 + 0.439675i \(0.855094\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −25.3305 −1.02983
\(606\) 0 0
\(607\) −21.5139 −0.873221 −0.436611 0.899651i \(-0.643821\pi\)
−0.436611 + 0.899651i \(0.643821\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −30.4222 −1.23075
\(612\) 0 0
\(613\) 29.1472 1.17724 0.588622 0.808408i \(-0.299671\pi\)
0.588622 + 0.808408i \(0.299671\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.0000 0.966204 0.483102 0.875564i \(-0.339510\pi\)
0.483102 + 0.875564i \(0.339510\pi\)
\(618\) 0 0
\(619\) −43.6333 −1.75377 −0.876885 0.480700i \(-0.840383\pi\)
−0.876885 + 0.480700i \(0.840383\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 16.6056 0.665287
\(624\) 0 0
\(625\) −26.4222 −1.05689
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.60555 0.103890
\(630\) 0 0
\(631\) −8.11943 −0.323229 −0.161615 0.986854i \(-0.551670\pi\)
−0.161615 + 0.986854i \(0.551670\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 34.3305 1.36237
\(636\) 0 0
\(637\) 6.60555 0.261721
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12.8444 0.507324 0.253662 0.967293i \(-0.418365\pi\)
0.253662 + 0.967293i \(0.418365\pi\)
\(642\) 0 0
\(643\) 38.1472 1.50438 0.752189 0.658947i \(-0.228998\pi\)
0.752189 + 0.658947i \(0.228998\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.4222 −0.724252 −0.362126 0.932129i \(-0.617949\pi\)
−0.362126 + 0.932129i \(0.617949\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −28.0555 −1.09790 −0.548949 0.835856i \(-0.684972\pi\)
−0.548949 + 0.835856i \(0.684972\pi\)
\(654\) 0 0
\(655\) 48.8444 1.90851
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −38.3028 −1.49206 −0.746032 0.665910i \(-0.768043\pi\)
−0.746032 + 0.665910i \(0.768043\pi\)
\(660\) 0 0
\(661\) −14.1833 −0.551668 −0.275834 0.961205i \(-0.588954\pi\)
−0.275834 + 0.961205i \(0.588954\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 15.2111 0.589861
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −20.1833 −0.778011 −0.389005 0.921235i \(-0.627181\pi\)
−0.389005 + 0.921235i \(0.627181\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −48.4222 −1.86102 −0.930508 0.366271i \(-0.880634\pi\)
−0.930508 + 0.366271i \(0.880634\pi\)
\(678\) 0 0
\(679\) −6.30278 −0.241878
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −41.4500 −1.58604 −0.793019 0.609196i \(-0.791492\pi\)
−0.793019 + 0.609196i \(0.791492\pi\)
\(684\) 0 0
\(685\) 29.2389 1.11716
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 24.4222 0.930412
\(690\) 0 0
\(691\) 29.4861 1.12170 0.560852 0.827916i \(-0.310473\pi\)
0.560852 + 0.827916i \(0.310473\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 16.3305 0.619452
\(696\) 0 0
\(697\) 3.90833 0.148038
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 18.8444 0.711744 0.355872 0.934535i \(-0.384184\pi\)
0.355872 + 0.934535i \(0.384184\pi\)
\(702\) 0 0
\(703\) −17.2111 −0.649129
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −19.8167 −0.745282
\(708\) 0 0
\(709\) 12.1833 0.457555 0.228778 0.973479i \(-0.426527\pi\)
0.228778 + 0.973479i \(0.426527\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 29.3028 1.09281 0.546405 0.837521i \(-0.315996\pi\)
0.546405 + 0.837521i \(0.315996\pi\)
\(720\) 0 0
\(721\) −7.21110 −0.268555
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −22.4222 −0.831594 −0.415797 0.909458i \(-0.636497\pi\)
−0.415797 + 0.909458i \(0.636497\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7.30278 −0.270103
\(732\) 0 0
\(733\) −30.2389 −1.11690 −0.558449 0.829539i \(-0.688603\pi\)
−0.558449 + 0.829539i \(0.688603\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −25.3583 −0.932820 −0.466410 0.884569i \(-0.654453\pi\)
−0.466410 + 0.884569i \(0.654453\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.81665 −0.0666466 −0.0333233 0.999445i \(-0.510609\pi\)
−0.0333233 + 0.999445i \(0.510609\pi\)
\(744\) 0 0
\(745\) −40.8167 −1.49541
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.39445 0.0509520
\(750\) 0 0
\(751\) 18.6056 0.678926 0.339463 0.940619i \(-0.389755\pi\)
0.339463 + 0.940619i \(0.389755\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −25.6056 −0.931881
\(756\) 0 0
\(757\) −45.7250 −1.66190 −0.830951 0.556345i \(-0.812203\pi\)
−0.830951 + 0.556345i \(0.812203\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −37.8167 −1.37085 −0.685426 0.728142i \(-0.740384\pi\)
−0.685426 + 0.728142i \(0.740384\pi\)
\(762\) 0 0
\(763\) 8.42221 0.304904
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −60.8444 −2.19696
\(768\) 0 0
\(769\) −53.2666 −1.92084 −0.960422 0.278550i \(-0.910146\pi\)
−0.960422 + 0.278550i \(0.910146\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −25.8167 −0.928560 −0.464280 0.885688i \(-0.653687\pi\)
−0.464280 + 0.885688i \(0.653687\pi\)
\(774\) 0 0
\(775\) 1.30278 0.0467971
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −25.8167 −0.924978
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −16.6056 −0.592678
\(786\) 0 0
\(787\) 2.42221 0.0863423 0.0431711 0.999068i \(-0.486254\pi\)
0.0431711 + 0.999068i \(0.486254\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.60555 −0.163755
\(792\) 0 0
\(793\) −52.2389 −1.85506
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −0.422205 −0.0149553 −0.00747764 0.999972i \(-0.502380\pi\)
−0.00747764 + 0.999972i \(0.502380\pi\)
\(798\) 0 0
\(799\) 4.60555 0.162933
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −40.6056 −1.42762 −0.713808 0.700342i \(-0.753031\pi\)
−0.713808 + 0.700342i \(0.753031\pi\)
\(810\) 0 0
\(811\) 4.09167 0.143678 0.0718390 0.997416i \(-0.477113\pi\)
0.0718390 + 0.997416i \(0.477113\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 29.0278 1.01680
\(816\) 0 0
\(817\) 48.2389 1.68766
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 10.6056 0.370136 0.185068 0.982726i \(-0.440749\pi\)
0.185068 + 0.982726i \(0.440749\pi\)
\(822\) 0 0
\(823\) 43.8722 1.52929 0.764644 0.644453i \(-0.222915\pi\)
0.764644 + 0.644453i \(0.222915\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −27.6333 −0.960904 −0.480452 0.877021i \(-0.659527\pi\)
−0.480452 + 0.877021i \(0.659527\pi\)
\(828\) 0 0
\(829\) −26.6056 −0.924049 −0.462024 0.886867i \(-0.652877\pi\)
−0.462024 + 0.886867i \(0.652877\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00000 −0.0346479
\(834\) 0 0
\(835\) 54.6333 1.89066
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −18.4222 −0.636005 −0.318003 0.948090i \(-0.603012\pi\)
−0.318003 + 0.948090i \(0.603012\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 70.5416 2.42671
\(846\) 0 0
\(847\) −11.0000 −0.377964
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −16.4222 −0.562286 −0.281143 0.959666i \(-0.590713\pi\)
−0.281143 + 0.959666i \(0.590713\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 34.5416 1.17992 0.589960 0.807433i \(-0.299144\pi\)
0.589960 + 0.807433i \(0.299144\pi\)
\(858\) 0 0
\(859\) 37.4500 1.27778 0.638888 0.769300i \(-0.279395\pi\)
0.638888 + 0.769300i \(0.279395\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18.9083 −0.643647 −0.321823 0.946800i \(-0.604296\pi\)
−0.321823 + 0.946800i \(0.604296\pi\)
\(864\) 0 0
\(865\) −39.8444 −1.35475
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −11.2111 −0.379874
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −10.8167 −0.365670
\(876\) 0 0
\(877\) −32.6056 −1.10101 −0.550506 0.834831i \(-0.685565\pi\)
−0.550506 + 0.834831i \(0.685565\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 9.69722 0.326708 0.163354 0.986568i \(-0.447769\pi\)
0.163354 + 0.986568i \(0.447769\pi\)
\(882\) 0 0
\(883\) −14.6695 −0.493667 −0.246833 0.969058i \(-0.579390\pi\)
−0.246833 + 0.969058i \(0.579390\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 48.9083 1.64218 0.821090 0.570798i \(-0.193366\pi\)
0.821090 + 0.570798i \(0.193366\pi\)
\(888\) 0 0
\(889\) 14.9083 0.500009
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −30.4222 −1.01804
\(894\) 0 0
\(895\) −22.8167 −0.762677
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −3.69722 −0.123172
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 32.2389 1.07166
\(906\) 0 0
\(907\) −22.8444 −0.758536 −0.379268 0.925287i \(-0.623824\pi\)
−0.379268 + 0.925287i \(0.623824\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −37.8167 −1.25292 −0.626461 0.779453i \(-0.715497\pi\)
−0.626461 + 0.779453i \(0.715497\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 21.2111 0.700452
\(918\) 0 0
\(919\) 24.3305 0.802590 0.401295 0.915949i \(-0.368560\pi\)
0.401295 + 0.915949i \(0.368560\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 51.6333 1.69953
\(924\) 0 0
\(925\) −0.788897 −0.0259388
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −53.9361 −1.76959 −0.884793 0.465985i \(-0.845700\pi\)
−0.884793 + 0.465985i \(0.845700\pi\)
\(930\) 0 0
\(931\) 6.60555 0.216488
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −6.78890 −0.221784 −0.110892 0.993832i \(-0.535371\pi\)
−0.110892 + 0.993832i \(0.535371\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0.275019 0.00896537 0.00448269 0.999990i \(-0.498573\pi\)
0.00448269 + 0.999990i \(0.498573\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −48.8444 −1.58723 −0.793615 0.608420i \(-0.791804\pi\)
−0.793615 + 0.608420i \(0.791804\pi\)
\(948\) 0 0
\(949\) −52.2389 −1.69575
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −17.5139 −0.567330 −0.283665 0.958923i \(-0.591550\pi\)
−0.283665 + 0.958923i \(0.591550\pi\)
\(954\) 0 0
\(955\) −47.7250 −1.54434
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 12.6972 0.410015
\(960\) 0 0
\(961\) −12.4861 −0.402778
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −27.2111 −0.875956
\(966\) 0 0
\(967\) 16.5139 0.531051 0.265525 0.964104i \(-0.414455\pi\)
0.265525 + 0.964104i \(0.414455\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −36.8444 −1.18239 −0.591197 0.806527i \(-0.701344\pi\)
−0.591197 + 0.806527i \(0.701344\pi\)
\(972\) 0 0
\(973\) 7.09167 0.227349
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 33.1472 1.06047 0.530236 0.847850i \(-0.322103\pi\)
0.530236 + 0.847850i \(0.322103\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −23.0917 −0.736510 −0.368255 0.929725i \(-0.620045\pi\)
−0.368255 + 0.929725i \(0.620045\pi\)
\(984\) 0 0
\(985\) 10.6056 0.337921
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 14.0000 0.444725 0.222362 0.974964i \(-0.428623\pi\)
0.222362 + 0.974964i \(0.428623\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 48.6333 1.54178
\(996\) 0 0
\(997\) 14.1472 0.448046 0.224023 0.974584i \(-0.428081\pi\)
0.224023 + 0.974584i \(0.428081\pi\)
\(998\) 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 4284.2.a.n.1.2 2
3.2 odd 2 476.2.a.d.1.1 2
12.11 even 2 1904.2.a.h.1.2 2
21.20 even 2 3332.2.a.j.1.2 2
24.5 odd 2 7616.2.a.q.1.2 2
24.11 even 2 7616.2.a.v.1.1 2
51.50 odd 2 8092.2.a.k.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
476.2.a.d.1.1 2 3.2 odd 2
1904.2.a.h.1.2 2 12.11 even 2
3332.2.a.j.1.2 2 21.20 even 2
4284.2.a.n.1.2 2 1.1 even 1 trivial
7616.2.a.q.1.2 2 24.5 odd 2
7616.2.a.v.1.1 2 24.11 even 2
8092.2.a.k.1.2 2 51.50 odd 2