Properties

Label 6160.2.a.w.1.2
Level $6160$
Weight $2$
Character 6160.1
Self dual yes
Analytic conductor $49.188$
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] = [6160,2,Mod(1,6160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6160.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6160.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: \(49.1878476451\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 3080)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 6160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{9} +1.00000 q^{11} +4.47214 q^{13} +4.47214 q^{17} +2.47214 q^{19} -6.47214 q^{23} +1.00000 q^{25} -4.47214 q^{29} +6.47214 q^{31} +1.00000 q^{35} -4.47214 q^{37} -2.00000 q^{41} -4.00000 q^{43} +3.00000 q^{45} +2.47214 q^{47} +1.00000 q^{49} +8.47214 q^{53} -1.00000 q^{55} -1.52786 q^{59} -4.47214 q^{61} +3.00000 q^{63} -4.47214 q^{65} -12.9443 q^{67} +7.52786 q^{73} -1.00000 q^{77} -10.4721 q^{79} +9.00000 q^{81} -4.47214 q^{85} +14.9443 q^{89} -4.47214 q^{91} -2.47214 q^{95} +4.47214 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} - 2 q^{7} - 6 q^{9} + 2 q^{11} - 4 q^{19} - 4 q^{23} + 2 q^{25} + 4 q^{31} + 2 q^{35} - 4 q^{41} - 8 q^{43} + 6 q^{45} - 4 q^{47} + 2 q^{49} + 8 q^{53} - 2 q^{55} - 12 q^{59} + 6 q^{63} - 8 q^{67} + 24 q^{73} - 2 q^{77} - 12 q^{79} + 18 q^{81} + 12 q^{89} + 4 q^{95} - 6 q^{99}+O(q^{100}) \) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 4.47214 1.24035 0.620174 0.784465i \(-0.287062\pi\)
0.620174 + 0.784465i \(0.287062\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.47214 1.08465 0.542326 0.840168i \(-0.317544\pi\)
0.542326 + 0.840168i \(0.317544\pi\)
\(18\) 0 0
\(19\) 2.47214 0.567147 0.283573 0.958951i \(-0.408480\pi\)
0.283573 + 0.958951i \(0.408480\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.47214 −1.34953 −0.674767 0.738031i \(-0.735756\pi\)
−0.674767 + 0.738031i \(0.735756\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) 0 0
\(31\) 6.47214 1.16243 0.581215 0.813750i \(-0.302578\pi\)
0.581215 + 0.813750i \(0.302578\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 3.00000 0.447214
\(46\) 0 0
\(47\) 2.47214 0.360598 0.180299 0.983612i \(-0.442293\pi\)
0.180299 + 0.983612i \(0.442293\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.52786 −0.198911 −0.0994555 0.995042i \(-0.531710\pi\)
−0.0994555 + 0.995042i \(0.531710\pi\)
\(60\) 0 0
\(61\) −4.47214 −0.572598 −0.286299 0.958140i \(-0.592425\pi\)
−0.286299 + 0.958140i \(0.592425\pi\)
\(62\) 0 0
\(63\) 3.00000 0.377964
\(64\) 0 0
\(65\) −4.47214 −0.554700
\(66\) 0 0
\(67\) −12.9443 −1.58139 −0.790697 0.612207i \(-0.790282\pi\)
−0.790697 + 0.612207i \(0.790282\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 7.52786 0.881070 0.440535 0.897735i \(-0.354789\pi\)
0.440535 + 0.897735i \(0.354789\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −10.4721 −1.17821 −0.589104 0.808057i \(-0.700519\pi\)
−0.589104 + 0.808057i \(0.700519\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −4.47214 −0.485071
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.9443 1.58409 0.792045 0.610463i \(-0.209017\pi\)
0.792045 + 0.610463i \(0.209017\pi\)
\(90\) 0 0
\(91\) −4.47214 −0.468807
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.47214 −0.253636
\(96\) 0 0
\(97\) 4.47214 0.454077 0.227038 0.973886i \(-0.427096\pi\)
0.227038 + 0.973886i \(0.427096\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 8.47214 0.843009 0.421505 0.906826i \(-0.361502\pi\)
0.421505 + 0.906826i \(0.361502\pi\)
\(102\) 0 0
\(103\) −10.4721 −1.03185 −0.515925 0.856634i \(-0.672552\pi\)
−0.515925 + 0.856634i \(0.672552\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.944272 −0.0912862 −0.0456431 0.998958i \(-0.514534\pi\)
−0.0456431 + 0.998958i \(0.514534\pi\)
\(108\) 0 0
\(109\) 3.52786 0.337908 0.168954 0.985624i \(-0.445961\pi\)
0.168954 + 0.985624i \(0.445961\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 6.47214 0.603530
\(116\) 0 0
\(117\) −13.4164 −1.24035
\(118\) 0 0
\(119\) −4.47214 −0.409960
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 18.4721 1.61392 0.806959 0.590607i \(-0.201112\pi\)
0.806959 + 0.590607i \(0.201112\pi\)
\(132\) 0 0
\(133\) −2.47214 −0.214361
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) −10.4721 −0.888235 −0.444117 0.895969i \(-0.646483\pi\)
−0.444117 + 0.895969i \(0.646483\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.47214 0.373979
\(144\) 0 0
\(145\) 4.47214 0.371391
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.472136 0.0386789 0.0193394 0.999813i \(-0.493844\pi\)
0.0193394 + 0.999813i \(0.493844\pi\)
\(150\) 0 0
\(151\) −2.47214 −0.201180 −0.100590 0.994928i \(-0.532073\pi\)
−0.100590 + 0.994928i \(0.532073\pi\)
\(152\) 0 0
\(153\) −13.4164 −1.08465
\(154\) 0 0
\(155\) −6.47214 −0.519854
\(156\) 0 0
\(157\) 14.9443 1.19268 0.596341 0.802731i \(-0.296620\pi\)
0.596341 + 0.802731i \(0.296620\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.47214 0.510076
\(162\) 0 0
\(163\) 20.9443 1.64048 0.820241 0.572018i \(-0.193839\pi\)
0.820241 + 0.572018i \(0.193839\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 17.8885 1.38426 0.692129 0.721774i \(-0.256673\pi\)
0.692129 + 0.721774i \(0.256673\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) −7.41641 −0.567147
\(172\) 0 0
\(173\) 12.4721 0.948239 0.474119 0.880461i \(-0.342766\pi\)
0.474119 + 0.880461i \(0.342766\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.94427 0.668526 0.334263 0.942480i \(-0.391513\pi\)
0.334263 + 0.942480i \(0.391513\pi\)
\(180\) 0 0
\(181\) 14.9443 1.11080 0.555399 0.831584i \(-0.312565\pi\)
0.555399 + 0.831584i \(0.312565\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.47214 0.328798
\(186\) 0 0
\(187\) 4.47214 0.327035
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 17.8885 1.29437 0.647185 0.762333i \(-0.275946\pi\)
0.647185 + 0.762333i \(0.275946\pi\)
\(192\) 0 0
\(193\) 22.0000 1.58359 0.791797 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.94427 0.494759 0.247379 0.968919i \(-0.420431\pi\)
0.247379 + 0.968919i \(0.420431\pi\)
\(198\) 0 0
\(199\) −9.52786 −0.675412 −0.337706 0.941252i \(-0.609651\pi\)
−0.337706 + 0.941252i \(0.609651\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.47214 0.313882
\(204\) 0 0
\(205\) 2.00000 0.139686
\(206\) 0 0
\(207\) 19.4164 1.34953
\(208\) 0 0
\(209\) 2.47214 0.171001
\(210\) 0 0
\(211\) −21.8885 −1.50687 −0.753435 0.657523i \(-0.771604\pi\)
−0.753435 + 0.657523i \(0.771604\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) −6.47214 −0.439357
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 20.0000 1.34535
\(222\) 0 0
\(223\) −18.4721 −1.23699 −0.618493 0.785790i \(-0.712256\pi\)
−0.618493 + 0.785790i \(0.712256\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) 14.9443 0.987545 0.493773 0.869591i \(-0.335618\pi\)
0.493773 + 0.869591i \(0.335618\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −22.9443 −1.50313 −0.751565 0.659659i \(-0.770701\pi\)
−0.751565 + 0.659659i \(0.770701\pi\)
\(234\) 0 0
\(235\) −2.47214 −0.161264
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 15.4164 0.997205 0.498602 0.866831i \(-0.333847\pi\)
0.498602 + 0.866831i \(0.333847\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 11.0557 0.703459
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.4164 1.73051 0.865254 0.501333i \(-0.167157\pi\)
0.865254 + 0.501333i \(0.167157\pi\)
\(252\) 0 0
\(253\) −6.47214 −0.406900
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.52786 0.469575 0.234788 0.972047i \(-0.424561\pi\)
0.234788 + 0.972047i \(0.424561\pi\)
\(258\) 0 0
\(259\) 4.47214 0.277885
\(260\) 0 0
\(261\) 13.4164 0.830455
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −8.47214 −0.520439
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 22.9443 1.39894 0.699468 0.714663i \(-0.253420\pi\)
0.699468 + 0.714663i \(0.253420\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) −15.8885 −0.954650 −0.477325 0.878727i \(-0.658394\pi\)
−0.477325 + 0.878727i \(0.658394\pi\)
\(278\) 0 0
\(279\) −19.4164 −1.16243
\(280\) 0 0
\(281\) −15.8885 −0.947831 −0.473916 0.880570i \(-0.657160\pi\)
−0.473916 + 0.880570i \(0.657160\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.00000 0.118056
\(288\) 0 0
\(289\) 3.00000 0.176471
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.3607 −1.07264 −0.536321 0.844014i \(-0.680186\pi\)
−0.536321 + 0.844014i \(0.680186\pi\)
\(294\) 0 0
\(295\) 1.52786 0.0889557
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −28.9443 −1.67389
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.47214 0.256074
\(306\) 0 0
\(307\) −4.94427 −0.282185 −0.141092 0.989996i \(-0.545061\pi\)
−0.141092 + 0.989996i \(0.545061\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −14.4721 −0.820640 −0.410320 0.911942i \(-0.634583\pi\)
−0.410320 + 0.911942i \(0.634583\pi\)
\(312\) 0 0
\(313\) 17.4164 0.984434 0.492217 0.870473i \(-0.336187\pi\)
0.492217 + 0.870473i \(0.336187\pi\)
\(314\) 0 0
\(315\) −3.00000 −0.169031
\(316\) 0 0
\(317\) −2.58359 −0.145109 −0.0725545 0.997364i \(-0.523115\pi\)
−0.0725545 + 0.997364i \(0.523115\pi\)
\(318\) 0 0
\(319\) −4.47214 −0.250392
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11.0557 0.615157
\(324\) 0 0
\(325\) 4.47214 0.248069
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.47214 −0.136293
\(330\) 0 0
\(331\) 26.8328 1.47486 0.737432 0.675421i \(-0.236038\pi\)
0.737432 + 0.675421i \(0.236038\pi\)
\(332\) 0 0
\(333\) 13.4164 0.735215
\(334\) 0 0
\(335\) 12.9443 0.707221
\(336\) 0 0
\(337\) 28.8328 1.57062 0.785312 0.619100i \(-0.212503\pi\)
0.785312 + 0.619100i \(0.212503\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.47214 0.350486
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.0000 1.07366 0.536828 0.843692i \(-0.319622\pi\)
0.536828 + 0.843692i \(0.319622\pi\)
\(348\) 0 0
\(349\) −17.4164 −0.932279 −0.466139 0.884711i \(-0.654356\pi\)
−0.466139 + 0.884711i \(0.654356\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −18.3607 −0.977240 −0.488620 0.872497i \(-0.662500\pi\)
−0.488620 + 0.872497i \(0.662500\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.3607 −1.07460 −0.537298 0.843393i \(-0.680555\pi\)
−0.537298 + 0.843393i \(0.680555\pi\)
\(360\) 0 0
\(361\) −12.8885 −0.678344
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.52786 −0.394026
\(366\) 0 0
\(367\) −10.4721 −0.546641 −0.273321 0.961923i \(-0.588122\pi\)
−0.273321 + 0.961923i \(0.588122\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) −8.47214 −0.439851
\(372\) 0 0
\(373\) 32.8328 1.70002 0.850009 0.526768i \(-0.176596\pi\)
0.850009 + 0.526768i \(0.176596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −20.0000 −1.03005
\(378\) 0 0
\(379\) 8.94427 0.459436 0.229718 0.973257i \(-0.426220\pi\)
0.229718 + 0.973257i \(0.426220\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −25.3050 −1.29302 −0.646511 0.762904i \(-0.723773\pi\)
−0.646511 + 0.762904i \(0.723773\pi\)
\(384\) 0 0
\(385\) 1.00000 0.0509647
\(386\) 0 0
\(387\) 12.0000 0.609994
\(388\) 0 0
\(389\) −6.94427 −0.352089 −0.176044 0.984382i \(-0.556330\pi\)
−0.176044 + 0.984382i \(0.556330\pi\)
\(390\) 0 0
\(391\) −28.9443 −1.46377
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 10.4721 0.526910
\(396\) 0 0
\(397\) 5.05573 0.253740 0.126870 0.991919i \(-0.459507\pi\)
0.126870 + 0.991919i \(0.459507\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) 28.9443 1.44182
\(404\) 0 0
\(405\) −9.00000 −0.447214
\(406\) 0 0
\(407\) −4.47214 −0.221676
\(408\) 0 0
\(409\) −32.8328 −1.62348 −0.811739 0.584020i \(-0.801479\pi\)
−0.811739 + 0.584020i \(0.801479\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.52786 0.0751813
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.41641 −0.166902 −0.0834512 0.996512i \(-0.526594\pi\)
−0.0834512 + 0.996512i \(0.526594\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 0 0
\(423\) −7.41641 −0.360598
\(424\) 0 0
\(425\) 4.47214 0.216930
\(426\) 0 0
\(427\) 4.47214 0.216422
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.58359 −0.413457 −0.206729 0.978398i \(-0.566282\pi\)
−0.206729 + 0.978398i \(0.566282\pi\)
\(432\) 0 0
\(433\) 35.3050 1.69665 0.848324 0.529478i \(-0.177612\pi\)
0.848324 + 0.529478i \(0.177612\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −16.0000 −0.765384
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 0 0
\(445\) −14.9443 −0.708426
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 0 0
\(451\) −2.00000 −0.0941763
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4.47214 0.209657
\(456\) 0 0
\(457\) −35.8885 −1.67880 −0.839398 0.543518i \(-0.817092\pi\)
−0.839398 + 0.543518i \(0.817092\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.58359 0.306628 0.153314 0.988177i \(-0.451005\pi\)
0.153314 + 0.988177i \(0.451005\pi\)
\(462\) 0 0
\(463\) 3.41641 0.158774 0.0793870 0.996844i \(-0.474704\pi\)
0.0793870 + 0.996844i \(0.474704\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.11146 0.282804 0.141402 0.989952i \(-0.454839\pi\)
0.141402 + 0.989952i \(0.454839\pi\)
\(468\) 0 0
\(469\) 12.9443 0.597711
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.00000 −0.183920
\(474\) 0 0
\(475\) 2.47214 0.113429
\(476\) 0 0
\(477\) −25.4164 −1.16374
\(478\) 0 0
\(479\) −28.9443 −1.32250 −0.661249 0.750167i \(-0.729973\pi\)
−0.661249 + 0.750167i \(0.729973\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.47214 −0.203069
\(486\) 0 0
\(487\) 27.4164 1.24236 0.621178 0.783669i \(-0.286654\pi\)
0.621178 + 0.783669i \(0.286654\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 32.9443 1.48675 0.743377 0.668873i \(-0.233223\pi\)
0.743377 + 0.668873i \(0.233223\pi\)
\(492\) 0 0
\(493\) −20.0000 −0.900755
\(494\) 0 0
\(495\) 3.00000 0.134840
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 13.8885 0.621737 0.310868 0.950453i \(-0.399380\pi\)
0.310868 + 0.950453i \(0.399380\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.94427 0.220454 0.110227 0.993906i \(-0.464842\pi\)
0.110227 + 0.993906i \(0.464842\pi\)
\(504\) 0 0
\(505\) −8.47214 −0.377005
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −12.8328 −0.568805 −0.284402 0.958705i \(-0.591795\pi\)
−0.284402 + 0.958705i \(0.591795\pi\)
\(510\) 0 0
\(511\) −7.52786 −0.333013
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.4721 0.461457
\(516\) 0 0
\(517\) 2.47214 0.108724
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 19.8885 0.871333 0.435666 0.900108i \(-0.356513\pi\)
0.435666 + 0.900108i \(0.356513\pi\)
\(522\) 0 0
\(523\) 22.8328 0.998409 0.499205 0.866484i \(-0.333626\pi\)
0.499205 + 0.866484i \(0.333626\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 28.9443 1.26083
\(528\) 0 0
\(529\) 18.8885 0.821241
\(530\) 0 0
\(531\) 4.58359 0.198911
\(532\) 0 0
\(533\) −8.94427 −0.387419
\(534\) 0 0
\(535\) 0.944272 0.0408244
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 3.52786 0.151675 0.0758374 0.997120i \(-0.475837\pi\)
0.0758374 + 0.997120i \(0.475837\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.52786 −0.151117
\(546\) 0 0
\(547\) 37.8885 1.62000 0.809999 0.586432i \(-0.199468\pi\)
0.809999 + 0.586432i \(0.199468\pi\)
\(548\) 0 0
\(549\) 13.4164 0.572598
\(550\) 0 0
\(551\) −11.0557 −0.470990
\(552\) 0 0
\(553\) 10.4721 0.445321
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 24.8328 1.05220 0.526100 0.850423i \(-0.323654\pi\)
0.526100 + 0.850423i \(0.323654\pi\)
\(558\) 0 0
\(559\) −17.8885 −0.756605
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 20.9443 0.882696 0.441348 0.897336i \(-0.354500\pi\)
0.441348 + 0.897336i \(0.354500\pi\)
\(564\) 0 0
\(565\) −10.0000 −0.420703
\(566\) 0 0
\(567\) −9.00000 −0.377964
\(568\) 0 0
\(569\) −34.9443 −1.46494 −0.732470 0.680799i \(-0.761633\pi\)
−0.732470 + 0.680799i \(0.761633\pi\)
\(570\) 0 0
\(571\) −18.8328 −0.788129 −0.394064 0.919083i \(-0.628931\pi\)
−0.394064 + 0.919083i \(0.628931\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.47214 −0.269907
\(576\) 0 0
\(577\) −23.3050 −0.970198 −0.485099 0.874459i \(-0.661216\pi\)
−0.485099 + 0.874459i \(0.661216\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 8.47214 0.350880
\(584\) 0 0
\(585\) 13.4164 0.554700
\(586\) 0 0
\(587\) −9.88854 −0.408144 −0.204072 0.978956i \(-0.565418\pi\)
−0.204072 + 0.978956i \(0.565418\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 41.4164 1.70077 0.850384 0.526163i \(-0.176370\pi\)
0.850384 + 0.526163i \(0.176370\pi\)
\(594\) 0 0
\(595\) 4.47214 0.183340
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 41.8885 1.71152 0.855760 0.517373i \(-0.173090\pi\)
0.855760 + 0.517373i \(0.173090\pi\)
\(600\) 0 0
\(601\) 20.8328 0.849788 0.424894 0.905243i \(-0.360311\pi\)
0.424894 + 0.905243i \(0.360311\pi\)
\(602\) 0 0
\(603\) 38.8328 1.58139
\(604\) 0 0
\(605\) −1.00000 −0.0406558
\(606\) 0 0
\(607\) −38.8328 −1.57618 −0.788088 0.615563i \(-0.788929\pi\)
−0.788088 + 0.615563i \(0.788929\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11.0557 0.447267
\(612\) 0 0
\(613\) 43.8885 1.77264 0.886321 0.463072i \(-0.153253\pi\)
0.886321 + 0.463072i \(0.153253\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16.8328 0.677664 0.338832 0.940847i \(-0.389968\pi\)
0.338832 + 0.940847i \(0.389968\pi\)
\(618\) 0 0
\(619\) −12.5836 −0.505777 −0.252889 0.967495i \(-0.581381\pi\)
−0.252889 + 0.967495i \(0.581381\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −14.9443 −0.598730
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) −17.8885 −0.712132 −0.356066 0.934461i \(-0.615882\pi\)
−0.356066 + 0.934461i \(0.615882\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.47214 0.177192
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.88854 −0.311579 −0.155789 0.987790i \(-0.549792\pi\)
−0.155789 + 0.987790i \(0.549792\pi\)
\(642\) 0 0
\(643\) 28.9443 1.14145 0.570725 0.821141i \(-0.306662\pi\)
0.570725 + 0.821141i \(0.306662\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.4721 1.04073 0.520364 0.853945i \(-0.325796\pi\)
0.520364 + 0.853945i \(0.325796\pi\)
\(648\) 0 0
\(649\) −1.52786 −0.0599739
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.47214 0.331540 0.165770 0.986164i \(-0.446989\pi\)
0.165770 + 0.986164i \(0.446989\pi\)
\(654\) 0 0
\(655\) −18.4721 −0.721766
\(656\) 0 0
\(657\) −22.5836 −0.881070
\(658\) 0 0
\(659\) −37.8885 −1.47593 −0.737964 0.674840i \(-0.764213\pi\)
−0.737964 + 0.674840i \(0.764213\pi\)
\(660\) 0 0
\(661\) −31.8885 −1.24032 −0.620160 0.784475i \(-0.712932\pi\)
−0.620160 + 0.784475i \(0.712932\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.47214 0.0958653
\(666\) 0 0
\(667\) 28.9443 1.12073
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.47214 −0.172645
\(672\) 0 0
\(673\) 44.8328 1.72818 0.864089 0.503339i \(-0.167895\pi\)
0.864089 + 0.503339i \(0.167895\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.58359 0.0992955 0.0496478 0.998767i \(-0.484190\pi\)
0.0496478 + 0.998767i \(0.484190\pi\)
\(678\) 0 0
\(679\) −4.47214 −0.171625
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −40.7214 −1.55816 −0.779080 0.626925i \(-0.784313\pi\)
−0.779080 + 0.626925i \(0.784313\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 37.8885 1.44344
\(690\) 0 0
\(691\) 19.4164 0.738635 0.369317 0.929303i \(-0.379591\pi\)
0.369317 + 0.929303i \(0.379591\pi\)
\(692\) 0 0
\(693\) 3.00000 0.113961
\(694\) 0 0
\(695\) 10.4721 0.397231
\(696\) 0 0
\(697\) −8.94427 −0.338788
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −9.41641 −0.355653 −0.177826 0.984062i \(-0.556907\pi\)
−0.177826 + 0.984062i \(0.556907\pi\)
\(702\) 0 0
\(703\) −11.0557 −0.416975
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.47214 −0.318627
\(708\) 0 0
\(709\) −16.8328 −0.632170 −0.316085 0.948731i \(-0.602368\pi\)
−0.316085 + 0.948731i \(0.602368\pi\)
\(710\) 0 0
\(711\) 31.4164 1.17821
\(712\) 0 0
\(713\) −41.8885 −1.56874
\(714\) 0 0
\(715\) −4.47214 −0.167248
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −12.5836 −0.469289 −0.234644 0.972081i \(-0.575393\pi\)
−0.234644 + 0.972081i \(0.575393\pi\)
\(720\) 0 0
\(721\) 10.4721 0.390003
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.47214 −0.166091
\(726\) 0 0
\(727\) 15.4164 0.571763 0.285881 0.958265i \(-0.407714\pi\)
0.285881 + 0.958265i \(0.407714\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −17.8885 −0.661632
\(732\) 0 0
\(733\) −18.3607 −0.678167 −0.339084 0.940756i \(-0.610117\pi\)
−0.339084 + 0.940756i \(0.610117\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.9443 −0.476808
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.88854 0.0692840 0.0346420 0.999400i \(-0.488971\pi\)
0.0346420 + 0.999400i \(0.488971\pi\)
\(744\) 0 0
\(745\) −0.472136 −0.0172977
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.944272 0.0345029
\(750\) 0 0
\(751\) −9.88854 −0.360838 −0.180419 0.983590i \(-0.557745\pi\)
−0.180419 + 0.983590i \(0.557745\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.47214 0.0899702
\(756\) 0 0
\(757\) −39.5279 −1.43666 −0.718332 0.695700i \(-0.755094\pi\)
−0.718332 + 0.695700i \(0.755094\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18.9443 0.686729 0.343365 0.939202i \(-0.388433\pi\)
0.343365 + 0.939202i \(0.388433\pi\)
\(762\) 0 0
\(763\) −3.52786 −0.127717
\(764\) 0 0
\(765\) 13.4164 0.485071
\(766\) 0 0
\(767\) −6.83282 −0.246719
\(768\) 0 0
\(769\) −21.7771 −0.785302 −0.392651 0.919688i \(-0.628442\pi\)
−0.392651 + 0.919688i \(0.628442\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −10.9443 −0.393638 −0.196819 0.980440i \(-0.563061\pi\)
−0.196819 + 0.980440i \(0.563061\pi\)
\(774\) 0 0
\(775\) 6.47214 0.232486
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.94427 −0.177147
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −14.9443 −0.533384
\(786\) 0 0
\(787\) 3.05573 0.108925 0.0544625 0.998516i \(-0.482655\pi\)
0.0544625 + 0.998516i \(0.482655\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −10.0000 −0.355559
\(792\) 0 0
\(793\) −20.0000 −0.710221
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30.9443 1.09610 0.548051 0.836445i \(-0.315370\pi\)
0.548051 + 0.836445i \(0.315370\pi\)
\(798\) 0 0
\(799\) 11.0557 0.391124
\(800\) 0 0
\(801\) −44.8328 −1.58409
\(802\) 0 0
\(803\) 7.52786 0.265653
\(804\) 0 0
\(805\) −6.47214 −0.228113
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 48.8328 1.71687 0.858435 0.512922i \(-0.171437\pi\)
0.858435 + 0.512922i \(0.171437\pi\)
\(810\) 0 0
\(811\) 34.4721 1.21048 0.605240 0.796043i \(-0.293077\pi\)
0.605240 + 0.796043i \(0.293077\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −20.9443 −0.733646
\(816\) 0 0
\(817\) −9.88854 −0.345956
\(818\) 0 0
\(819\) 13.4164 0.468807
\(820\) 0 0
\(821\) −28.4721 −0.993684 −0.496842 0.867841i \(-0.665507\pi\)
−0.496842 + 0.867841i \(0.665507\pi\)
\(822\) 0 0
\(823\) −35.4164 −1.23454 −0.617269 0.786752i \(-0.711761\pi\)
−0.617269 + 0.786752i \(0.711761\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0.944272 0.0328356 0.0164178 0.999865i \(-0.494774\pi\)
0.0164178 + 0.999865i \(0.494774\pi\)
\(828\) 0 0
\(829\) −14.0000 −0.486240 −0.243120 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.47214 0.154950
\(834\) 0 0
\(835\) −17.8885 −0.619059
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 50.2492 1.73480 0.867398 0.497615i \(-0.165791\pi\)
0.867398 + 0.497615i \(0.165791\pi\)
\(840\) 0 0
\(841\) −9.00000 −0.310345
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7.00000 −0.240807
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 28.9443 0.992197
\(852\) 0 0
\(853\) 46.3607 1.58736 0.793680 0.608336i \(-0.208163\pi\)
0.793680 + 0.608336i \(0.208163\pi\)
\(854\) 0 0
\(855\) 7.41641 0.253636
\(856\) 0 0
\(857\) 19.3050 0.659445 0.329722 0.944078i \(-0.393045\pi\)
0.329722 + 0.944078i \(0.393045\pi\)
\(858\) 0 0
\(859\) 21.3050 0.726916 0.363458 0.931611i \(-0.381596\pi\)
0.363458 + 0.931611i \(0.381596\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 46.4721 1.58193 0.790965 0.611861i \(-0.209579\pi\)
0.790965 + 0.611861i \(0.209579\pi\)
\(864\) 0 0
\(865\) −12.4721 −0.424065
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −10.4721 −0.355243
\(870\) 0 0
\(871\) −57.8885 −1.96148
\(872\) 0 0
\(873\) −13.4164 −0.454077
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −47.8885 −1.61708 −0.808541 0.588440i \(-0.799742\pi\)
−0.808541 + 0.588440i \(0.799742\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −33.0557 −1.11368 −0.556838 0.830621i \(-0.687986\pi\)
−0.556838 + 0.830621i \(0.687986\pi\)
\(882\) 0 0
\(883\) −4.94427 −0.166388 −0.0831940 0.996533i \(-0.526512\pi\)
−0.0831940 + 0.996533i \(0.526512\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 30.8328 1.03526 0.517632 0.855603i \(-0.326814\pi\)
0.517632 + 0.855603i \(0.326814\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 9.00000 0.301511
\(892\) 0 0
\(893\) 6.11146 0.204512
\(894\) 0 0
\(895\) −8.94427 −0.298974
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −28.9443 −0.965346
\(900\) 0 0
\(901\) 37.8885 1.26225
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14.9443 −0.496764
\(906\) 0 0
\(907\) 32.0000 1.06254 0.531271 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 0 0
\(909\) −25.4164 −0.843009
\(910\) 0 0
\(911\) −43.7771 −1.45040 −0.725200 0.688538i \(-0.758253\pi\)
−0.725200 + 0.688538i \(0.758253\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −18.4721 −0.610004
\(918\) 0 0
\(919\) −13.5279 −0.446243 −0.223122 0.974791i \(-0.571625\pi\)
−0.223122 + 0.974791i \(0.571625\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −4.47214 −0.147043
\(926\) 0 0
\(927\) 31.4164 1.03185
\(928\) 0 0
\(929\) 2.00000 0.0656179 0.0328089 0.999462i \(-0.489555\pi\)
0.0328089 + 0.999462i \(0.489555\pi\)
\(930\) 0 0
\(931\) 2.47214 0.0810210
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4.47214 −0.146254
\(936\) 0 0
\(937\) −53.4164 −1.74504 −0.872519 0.488580i \(-0.837515\pi\)
−0.872519 + 0.488580i \(0.837515\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 13.4164 0.437362 0.218681 0.975796i \(-0.429825\pi\)
0.218681 + 0.975796i \(0.429825\pi\)
\(942\) 0 0
\(943\) 12.9443 0.421523
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.05573 0.0992978 0.0496489 0.998767i \(-0.484190\pi\)
0.0496489 + 0.998767i \(0.484190\pi\)
\(948\) 0 0
\(949\) 33.6656 1.09283
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 38.0000 1.23094 0.615470 0.788160i \(-0.288966\pi\)
0.615470 + 0.788160i \(0.288966\pi\)
\(954\) 0 0
\(955\) −17.8885 −0.578860
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2.00000 −0.0645834
\(960\) 0 0
\(961\) 10.8885 0.351243
\(962\) 0 0
\(963\) 2.83282 0.0912862
\(964\) 0 0
\(965\) −22.0000 −0.708205
\(966\) 0 0
\(967\) −27.0557 −0.870054 −0.435027 0.900418i \(-0.643261\pi\)
−0.435027 + 0.900418i \(0.643261\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 7.63932 0.245157 0.122579 0.992459i \(-0.460884\pi\)
0.122579 + 0.992459i \(0.460884\pi\)
\(972\) 0 0
\(973\) 10.4721 0.335721
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0.111456 0.00356580 0.00178290 0.999998i \(-0.499432\pi\)
0.00178290 + 0.999998i \(0.499432\pi\)
\(978\) 0 0
\(979\) 14.9443 0.477621
\(980\) 0 0
\(981\) −10.5836 −0.337908
\(982\) 0 0
\(983\) −10.4721 −0.334009 −0.167005 0.985956i \(-0.553409\pi\)
−0.167005 + 0.985956i \(0.553409\pi\)
\(984\) 0 0
\(985\) −6.94427 −0.221263
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 25.8885 0.823208
\(990\) 0 0
\(991\) −27.0557 −0.859454 −0.429727 0.902959i \(-0.641390\pi\)
−0.429727 + 0.902959i \(0.641390\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 9.52786 0.302054
\(996\) 0 0
\(997\) 2.58359 0.0818232 0.0409116 0.999163i \(-0.486974\pi\)
0.0409116 + 0.999163i \(0.486974\pi\)
\(998\) 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 6160.2.a.w.1.2 2
4.3 odd 2 3080.2.a.f.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3080.2.a.f.1.2 2 4.3 odd 2
6160.2.a.w.1.2 2 1.1 even 1 trivial