Properties

Label 9576.2.a.bd.1.2
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
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] = [9576,2,Mod(1,9576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9576, 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("9576.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.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: \(76.4647449756\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-2.00000 q^{5} -1.00000 q^{7} +2.00000 q^{11} +5.12311 q^{13} +5.12311 q^{17} -1.00000 q^{19} +1.12311 q^{23} -1.00000 q^{25} +0.876894 q^{29} +7.12311 q^{31} +2.00000 q^{35} -9.12311 q^{37} +8.24621 q^{41} +4.00000 q^{43} +1.00000 q^{49} -3.12311 q^{53} -4.00000 q^{55} -10.2462 q^{59} -2.00000 q^{61} -10.2462 q^{65} +2.24621 q^{67} +15.3693 q^{71} -10.0000 q^{73} -2.00000 q^{77} +4.87689 q^{79} -0.876894 q^{83} -10.2462 q^{85} +16.2462 q^{89} -5.12311 q^{91} +2.00000 q^{95} -8.24621 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{5} - 2 q^{7} + 4 q^{11} + 2 q^{13} + 2 q^{17} - 2 q^{19} - 6 q^{23} - 2 q^{25} + 10 q^{29} + 6 q^{31} + 4 q^{35} - 10 q^{37} + 8 q^{43} + 2 q^{49} + 2 q^{53} - 8 q^{55} - 4 q^{59} - 4 q^{61} - 4 q^{65} - 12 q^{67} + 6 q^{71} - 20 q^{73} - 4 q^{77} + 18 q^{79} - 10 q^{83} - 4 q^{85} + 16 q^{89} - 2 q^{91} + 4 q^{95}+O(q^{100}) \) 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
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 5.12311 1.42089 0.710447 0.703751i \(-0.248493\pi\)
0.710447 + 0.703751i \(0.248493\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.12311 1.24254 0.621268 0.783598i \(-0.286618\pi\)
0.621268 + 0.783598i \(0.286618\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.12311 0.234184 0.117092 0.993121i \(-0.462643\pi\)
0.117092 + 0.993121i \(0.462643\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.876894 0.162835 0.0814176 0.996680i \(-0.474055\pi\)
0.0814176 + 0.996680i \(0.474055\pi\)
\(30\) 0 0
\(31\) 7.12311 1.27935 0.639674 0.768647i \(-0.279069\pi\)
0.639674 + 0.768647i \(0.279069\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) −9.12311 −1.49983 −0.749915 0.661535i \(-0.769905\pi\)
−0.749915 + 0.661535i \(0.769905\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.24621 1.28784 0.643921 0.765092i \(-0.277307\pi\)
0.643921 + 0.765092i \(0.277307\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.12311 −0.428992 −0.214496 0.976725i \(-0.568811\pi\)
−0.214496 + 0.976725i \(0.568811\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.2462 −1.33394 −0.666972 0.745083i \(-0.732410\pi\)
−0.666972 + 0.745083i \(0.732410\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −10.2462 −1.27089
\(66\) 0 0
\(67\) 2.24621 0.274418 0.137209 0.990542i \(-0.456187\pi\)
0.137209 + 0.990542i \(0.456187\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 15.3693 1.82400 0.912001 0.410188i \(-0.134537\pi\)
0.912001 + 0.410188i \(0.134537\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) 4.87689 0.548693 0.274347 0.961631i \(-0.411538\pi\)
0.274347 + 0.961631i \(0.411538\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.876894 −0.0962517 −0.0481258 0.998841i \(-0.515325\pi\)
−0.0481258 + 0.998841i \(0.515325\pi\)
\(84\) 0 0
\(85\) −10.2462 −1.11136
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.2462 1.72209 0.861047 0.508525i \(-0.169809\pi\)
0.861047 + 0.508525i \(0.169809\pi\)
\(90\) 0 0
\(91\) −5.12311 −0.537047
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 0.205196
\(96\) 0 0
\(97\) −8.24621 −0.837276 −0.418638 0.908153i \(-0.637492\pi\)
−0.418638 + 0.908153i \(0.637492\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) −8.87689 −0.874666 −0.437333 0.899300i \(-0.644077\pi\)
−0.437333 + 0.899300i \(0.644077\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.12311 −0.495269 −0.247635 0.968853i \(-0.579653\pi\)
−0.247635 + 0.968853i \(0.579653\pi\)
\(108\) 0 0
\(109\) −9.12311 −0.873835 −0.436918 0.899502i \(-0.643930\pi\)
−0.436918 + 0.899502i \(0.643930\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.876894 0.0824913 0.0412456 0.999149i \(-0.486867\pi\)
0.0412456 + 0.999149i \(0.486867\pi\)
\(114\) 0 0
\(115\) −2.24621 −0.209460
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.12311 −0.469634
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 12.8769 1.14264 0.571320 0.820728i \(-0.306432\pi\)
0.571320 + 0.820728i \(0.306432\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −19.6155 −1.71382 −0.856908 0.515469i \(-0.827618\pi\)
−0.856908 + 0.515469i \(0.827618\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.2462 −1.55888 −0.779440 0.626477i \(-0.784496\pi\)
−0.779440 + 0.626477i \(0.784496\pi\)
\(138\) 0 0
\(139\) 14.2462 1.20835 0.604174 0.796852i \(-0.293503\pi\)
0.604174 + 0.796852i \(0.293503\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.2462 0.856831
\(144\) 0 0
\(145\) −1.75379 −0.145644
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.87689 0.727224 0.363612 0.931551i \(-0.381543\pi\)
0.363612 + 0.931551i \(0.381543\pi\)
\(150\) 0 0
\(151\) 4.87689 0.396876 0.198438 0.980113i \(-0.436413\pi\)
0.198438 + 0.980113i \(0.436413\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −14.2462 −1.14428
\(156\) 0 0
\(157\) −24.2462 −1.93506 −0.967529 0.252759i \(-0.918662\pi\)
−0.967529 + 0.252759i \(0.918662\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.12311 −0.0885131
\(162\) 0 0
\(163\) 8.49242 0.665178 0.332589 0.943072i \(-0.392078\pi\)
0.332589 + 0.943072i \(0.392078\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 18.2462 1.41193 0.705967 0.708245i \(-0.250513\pi\)
0.705967 + 0.708245i \(0.250513\pi\)
\(168\) 0 0
\(169\) 13.2462 1.01894
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.2462 0.931062 0.465531 0.885032i \(-0.345863\pi\)
0.465531 + 0.885032i \(0.345863\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.3693 0.849783 0.424891 0.905244i \(-0.360312\pi\)
0.424891 + 0.905244i \(0.360312\pi\)
\(180\) 0 0
\(181\) 19.3693 1.43971 0.719855 0.694124i \(-0.244208\pi\)
0.719855 + 0.694124i \(0.244208\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 18.2462 1.34149
\(186\) 0 0
\(187\) 10.2462 0.749277
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −23.3693 −1.69094 −0.845472 0.534019i \(-0.820681\pi\)
−0.845472 + 0.534019i \(0.820681\pi\)
\(192\) 0 0
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.63068 0.187428 0.0937142 0.995599i \(-0.470126\pi\)
0.0937142 + 0.995599i \(0.470126\pi\)
\(198\) 0 0
\(199\) −22.2462 −1.57699 −0.788496 0.615040i \(-0.789140\pi\)
−0.788496 + 0.615040i \(0.789140\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.876894 −0.0615459
\(204\) 0 0
\(205\) −16.4924 −1.15188
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −24.4924 −1.68613 −0.843064 0.537813i \(-0.819251\pi\)
−0.843064 + 0.537813i \(0.819251\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −7.12311 −0.483548
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 26.2462 1.76551
\(222\) 0 0
\(223\) −9.36932 −0.627416 −0.313708 0.949520i \(-0.601571\pi\)
−0.313708 + 0.949520i \(0.601571\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.24621 −0.149086 −0.0745431 0.997218i \(-0.523750\pi\)
−0.0745431 + 0.997218i \(0.523750\pi\)
\(228\) 0 0
\(229\) 28.7386 1.89910 0.949551 0.313612i \(-0.101539\pi\)
0.949551 + 0.313612i \(0.101539\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.24621 −0.147154 −0.0735771 0.997290i \(-0.523441\pi\)
−0.0735771 + 0.997290i \(0.523441\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 17.1231 1.10760 0.553801 0.832649i \(-0.313177\pi\)
0.553801 + 0.832649i \(0.313177\pi\)
\(240\) 0 0
\(241\) −28.7386 −1.85122 −0.925609 0.378481i \(-0.876447\pi\)
−0.925609 + 0.378481i \(0.876447\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.00000 −0.127775
\(246\) 0 0
\(247\) −5.12311 −0.325975
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 25.3693 1.60130 0.800649 0.599134i \(-0.204488\pi\)
0.800649 + 0.599134i \(0.204488\pi\)
\(252\) 0 0
\(253\) 2.24621 0.141218
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.0000 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 0 0
\(259\) 9.12311 0.566882
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 29.6155 1.82617 0.913086 0.407767i \(-0.133693\pi\)
0.913086 + 0.407767i \(0.133693\pi\)
\(264\) 0 0
\(265\) 6.24621 0.383702
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 12.0000 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 −0.120605
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.8769 0.768171 0.384086 0.923298i \(-0.374517\pi\)
0.384086 + 0.923298i \(0.374517\pi\)
\(282\) 0 0
\(283\) 24.4924 1.45592 0.727962 0.685618i \(-0.240468\pi\)
0.727962 + 0.685618i \(0.240468\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.24621 −0.486758
\(288\) 0 0
\(289\) 9.24621 0.543895
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.246211 −0.0143838 −0.00719191 0.999974i \(-0.502289\pi\)
−0.00719191 + 0.999974i \(0.502289\pi\)
\(294\) 0 0
\(295\) 20.4924 1.19311
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.75379 0.332750
\(300\) 0 0
\(301\) −4.00000 −0.230556
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.00000 0.229039
\(306\) 0 0
\(307\) −8.49242 −0.484688 −0.242344 0.970190i \(-0.577916\pi\)
−0.242344 + 0.970190i \(0.577916\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 0 0
\(313\) 34.9848 1.97746 0.988730 0.149709i \(-0.0478335\pi\)
0.988730 + 0.149709i \(0.0478335\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.36932 0.526233 0.263117 0.964764i \(-0.415250\pi\)
0.263117 + 0.964764i \(0.415250\pi\)
\(318\) 0 0
\(319\) 1.75379 0.0981933
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.12311 −0.285057
\(324\) 0 0
\(325\) −5.12311 −0.284179
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4.49242 −0.245447
\(336\) 0 0
\(337\) 26.4924 1.44313 0.721567 0.692345i \(-0.243422\pi\)
0.721567 + 0.692345i \(0.243422\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 14.2462 0.771476
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.75379 0.416245 0.208123 0.978103i \(-0.433265\pi\)
0.208123 + 0.978103i \(0.433265\pi\)
\(348\) 0 0
\(349\) 20.2462 1.08375 0.541877 0.840458i \(-0.317714\pi\)
0.541877 + 0.840458i \(0.317714\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 27.3693 1.45672 0.728361 0.685194i \(-0.240282\pi\)
0.728361 + 0.685194i \(0.240282\pi\)
\(354\) 0 0
\(355\) −30.7386 −1.63144
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.36932 −0.388938 −0.194469 0.980909i \(-0.562298\pi\)
−0.194469 + 0.980909i \(0.562298\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 20.0000 1.04685
\(366\) 0 0
\(367\) −9.75379 −0.509144 −0.254572 0.967054i \(-0.581935\pi\)
−0.254572 + 0.967054i \(0.581935\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.12311 0.162144
\(372\) 0 0
\(373\) 29.6155 1.53343 0.766717 0.641985i \(-0.221889\pi\)
0.766717 + 0.641985i \(0.221889\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.49242 0.231372
\(378\) 0 0
\(379\) 24.4924 1.25809 0.629046 0.777368i \(-0.283446\pi\)
0.629046 + 0.777368i \(0.283446\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 32.0000 1.63512 0.817562 0.575841i \(-0.195325\pi\)
0.817562 + 0.575841i \(0.195325\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11.1231 0.563964 0.281982 0.959420i \(-0.409008\pi\)
0.281982 + 0.959420i \(0.409008\pi\)
\(390\) 0 0
\(391\) 5.75379 0.290982
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9.75379 −0.490766
\(396\) 0 0
\(397\) −28.7386 −1.44235 −0.721175 0.692753i \(-0.756398\pi\)
−0.721175 + 0.692753i \(0.756398\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 39.6155 1.97831 0.989153 0.146892i \(-0.0469270\pi\)
0.989153 + 0.146892i \(0.0469270\pi\)
\(402\) 0 0
\(403\) 36.4924 1.81782
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −18.2462 −0.904431
\(408\) 0 0
\(409\) −3.75379 −0.185613 −0.0928065 0.995684i \(-0.529584\pi\)
−0.0928065 + 0.995684i \(0.529584\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.2462 0.504183
\(414\) 0 0
\(415\) 1.75379 0.0860901
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.36932 0.0668955 0.0334478 0.999440i \(-0.489351\pi\)
0.0334478 + 0.999440i \(0.489351\pi\)
\(420\) 0 0
\(421\) 26.8769 1.30990 0.654950 0.755672i \(-0.272690\pi\)
0.654950 + 0.755672i \(0.272690\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5.12311 −0.248507
\(426\) 0 0
\(427\) 2.00000 0.0967868
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 26.8769 1.29461 0.647307 0.762229i \(-0.275895\pi\)
0.647307 + 0.762229i \(0.275895\pi\)
\(432\) 0 0
\(433\) −24.7386 −1.18886 −0.594431 0.804146i \(-0.702623\pi\)
−0.594431 + 0.804146i \(0.702623\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.12311 −0.0537254
\(438\) 0 0
\(439\) 14.6307 0.698284 0.349142 0.937070i \(-0.386473\pi\)
0.349142 + 0.937070i \(0.386473\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.2462 0.581835 0.290918 0.956748i \(-0.406039\pi\)
0.290918 + 0.956748i \(0.406039\pi\)
\(444\) 0 0
\(445\) −32.4924 −1.54029
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −24.8769 −1.17401 −0.587007 0.809582i \(-0.699694\pi\)
−0.587007 + 0.809582i \(0.699694\pi\)
\(450\) 0 0
\(451\) 16.4924 0.776598
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 10.2462 0.480350
\(456\) 0 0
\(457\) 15.7538 0.736931 0.368466 0.929641i \(-0.379883\pi\)
0.368466 + 0.929641i \(0.379883\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −15.7538 −0.733727 −0.366864 0.930275i \(-0.619568\pi\)
−0.366864 + 0.930275i \(0.619568\pi\)
\(462\) 0 0
\(463\) −18.7386 −0.870858 −0.435429 0.900223i \(-0.643403\pi\)
−0.435429 + 0.900223i \(0.643403\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.36932 0.0633644 0.0316822 0.999498i \(-0.489914\pi\)
0.0316822 + 0.999498i \(0.489914\pi\)
\(468\) 0 0
\(469\) −2.24621 −0.103720
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.00000 0.367840
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.50758 0.160265 0.0801327 0.996784i \(-0.474466\pi\)
0.0801327 + 0.996784i \(0.474466\pi\)
\(480\) 0 0
\(481\) −46.7386 −2.13110
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16.4924 0.748882
\(486\) 0 0
\(487\) −21.8617 −0.990650 −0.495325 0.868708i \(-0.664951\pi\)
−0.495325 + 0.868708i \(0.664951\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.00000 −0.0902587 −0.0451294 0.998981i \(-0.514370\pi\)
−0.0451294 + 0.998981i \(0.514370\pi\)
\(492\) 0 0
\(493\) 4.49242 0.202329
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −15.3693 −0.689408
\(498\) 0 0
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) −20.0000 −0.889988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −40.7386 −1.80571 −0.902854 0.429947i \(-0.858532\pi\)
−0.902854 + 0.429947i \(0.858532\pi\)
\(510\) 0 0
\(511\) 10.0000 0.442374
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 17.7538 0.782325
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.50758 0.0660482 0.0330241 0.999455i \(-0.489486\pi\)
0.0330241 + 0.999455i \(0.489486\pi\)
\(522\) 0 0
\(523\) −24.9848 −1.09251 −0.546255 0.837619i \(-0.683947\pi\)
−0.546255 + 0.837619i \(0.683947\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 36.4924 1.58963
\(528\) 0 0
\(529\) −21.7386 −0.945158
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 42.2462 1.82989
\(534\) 0 0
\(535\) 10.2462 0.442982
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) −32.2462 −1.38637 −0.693186 0.720758i \(-0.743794\pi\)
−0.693186 + 0.720758i \(0.743794\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.2462 0.781582
\(546\) 0 0
\(547\) 44.9848 1.92341 0.961707 0.274081i \(-0.0883737\pi\)
0.961707 + 0.274081i \(0.0883737\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.876894 −0.0373570
\(552\) 0 0
\(553\) −4.87689 −0.207387
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.63068 −0.111466 −0.0557328 0.998446i \(-0.517750\pi\)
−0.0557328 + 0.998446i \(0.517750\pi\)
\(558\) 0 0
\(559\) 20.4924 0.866737
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 24.4924 1.03223 0.516116 0.856519i \(-0.327377\pi\)
0.516116 + 0.856519i \(0.327377\pi\)
\(564\) 0 0
\(565\) −1.75379 −0.0737824
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.384472 0.0161179 0.00805895 0.999968i \(-0.497435\pi\)
0.00805895 + 0.999968i \(0.497435\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.12311 −0.0468367
\(576\) 0 0
\(577\) 0.246211 0.0102499 0.00512495 0.999987i \(-0.498369\pi\)
0.00512495 + 0.999987i \(0.498369\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.876894 0.0363797
\(582\) 0 0
\(583\) −6.24621 −0.258692
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.3693 −0.716908 −0.358454 0.933547i \(-0.616696\pi\)
−0.358454 + 0.933547i \(0.616696\pi\)
\(588\) 0 0
\(589\) −7.12311 −0.293502
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −27.8617 −1.14414 −0.572072 0.820203i \(-0.693860\pi\)
−0.572072 + 0.820203i \(0.693860\pi\)
\(594\) 0 0
\(595\) 10.2462 0.420054
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 39.3693 1.60859 0.804293 0.594232i \(-0.202544\pi\)
0.804293 + 0.594232i \(0.202544\pi\)
\(600\) 0 0
\(601\) −18.4924 −0.754322 −0.377161 0.926148i \(-0.623100\pi\)
−0.377161 + 0.926148i \(0.623100\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 14.0000 0.569181
\(606\) 0 0
\(607\) 47.6155 1.93265 0.966327 0.257316i \(-0.0828381\pi\)
0.966327 + 0.257316i \(0.0828381\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 24.7386 0.999184 0.499592 0.866261i \(-0.333483\pi\)
0.499592 + 0.866261i \(0.333483\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.492423 −0.0198242 −0.00991209 0.999951i \(-0.503155\pi\)
−0.00991209 + 0.999951i \(0.503155\pi\)
\(618\) 0 0
\(619\) −22.2462 −0.894151 −0.447075 0.894496i \(-0.647534\pi\)
−0.447075 + 0.894496i \(0.647534\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −16.2462 −0.650891
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −46.7386 −1.86359
\(630\) 0 0
\(631\) −22.2462 −0.885608 −0.442804 0.896619i \(-0.646016\pi\)
−0.442804 + 0.896619i \(0.646016\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −25.7538 −1.02201
\(636\) 0 0
\(637\) 5.12311 0.202985
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20.8769 −0.824588 −0.412294 0.911051i \(-0.635272\pi\)
−0.412294 + 0.911051i \(0.635272\pi\)
\(642\) 0 0
\(643\) −12.0000 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.75379 0.0689486 0.0344743 0.999406i \(-0.489024\pi\)
0.0344743 + 0.999406i \(0.489024\pi\)
\(648\) 0 0
\(649\) −20.4924 −0.804398
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −45.8617 −1.79471 −0.897354 0.441311i \(-0.854514\pi\)
−0.897354 + 0.441311i \(0.854514\pi\)
\(654\) 0 0
\(655\) 39.2311 1.53288
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 43.8617 1.70861 0.854305 0.519771i \(-0.173983\pi\)
0.854305 + 0.519771i \(0.173983\pi\)
\(660\) 0 0
\(661\) 5.61553 0.218419 0.109209 0.994019i \(-0.465168\pi\)
0.109209 + 0.994019i \(0.465168\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.00000 −0.0775567
\(666\) 0 0
\(667\) 0.984845 0.0381334
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) −13.5076 −0.520679 −0.260339 0.965517i \(-0.583834\pi\)
−0.260339 + 0.965517i \(0.583834\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.75379 −0.144270 −0.0721349 0.997395i \(-0.522981\pi\)
−0.0721349 + 0.997395i \(0.522981\pi\)
\(678\) 0 0
\(679\) 8.24621 0.316461
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.12311 −0.349086 −0.174543 0.984650i \(-0.555845\pi\)
−0.174543 + 0.984650i \(0.555845\pi\)
\(684\) 0 0
\(685\) 36.4924 1.39430
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16.0000 −0.609551
\(690\) 0 0
\(691\) −38.2462 −1.45495 −0.727477 0.686132i \(-0.759307\pi\)
−0.727477 + 0.686132i \(0.759307\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −28.4924 −1.08078
\(696\) 0 0
\(697\) 42.2462 1.60019
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −7.61553 −0.287635 −0.143817 0.989604i \(-0.545938\pi\)
−0.143817 + 0.989604i \(0.545938\pi\)
\(702\) 0 0
\(703\) 9.12311 0.344084
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.0000 −0.376089
\(708\) 0 0
\(709\) −37.2311 −1.39824 −0.699121 0.715004i \(-0.746425\pi\)
−0.699121 + 0.715004i \(0.746425\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 0 0
\(715\) −20.4924 −0.766373
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.2462 0.382119 0.191060 0.981578i \(-0.438808\pi\)
0.191060 + 0.981578i \(0.438808\pi\)
\(720\) 0 0
\(721\) 8.87689 0.330593
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.876894 −0.0325670
\(726\) 0 0
\(727\) 38.7386 1.43674 0.718368 0.695663i \(-0.244889\pi\)
0.718368 + 0.695663i \(0.244889\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 20.4924 0.757940
\(732\) 0 0
\(733\) −26.4924 −0.978520 −0.489260 0.872138i \(-0.662733\pi\)
−0.489260 + 0.872138i \(0.662733\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.49242 0.165481
\(738\) 0 0
\(739\) −0.492423 −0.0181141 −0.00905703 0.999959i \(-0.502883\pi\)
−0.00905703 + 0.999959i \(0.502883\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 47.3693 1.73781 0.868906 0.494977i \(-0.164824\pi\)
0.868906 + 0.494977i \(0.164824\pi\)
\(744\) 0 0
\(745\) −17.7538 −0.650448
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.12311 0.187194
\(750\) 0 0
\(751\) 17.3693 0.633815 0.316908 0.948456i \(-0.397355\pi\)
0.316908 + 0.948456i \(0.397355\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9.75379 −0.354977
\(756\) 0 0
\(757\) 6.49242 0.235971 0.117986 0.993015i \(-0.462356\pi\)
0.117986 + 0.993015i \(0.462356\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18.8769 0.684287 0.342143 0.939648i \(-0.388847\pi\)
0.342143 + 0.939648i \(0.388847\pi\)
\(762\) 0 0
\(763\) 9.12311 0.330279
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −52.4924 −1.89539
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.50758 0.341964 0.170982 0.985274i \(-0.445306\pi\)
0.170982 + 0.985274i \(0.445306\pi\)
\(774\) 0 0
\(775\) −7.12311 −0.255870
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.24621 −0.295451
\(780\) 0 0
\(781\) 30.7386 1.09991
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 48.4924 1.73077
\(786\) 0 0
\(787\) −50.7386 −1.80864 −0.904318 0.426858i \(-0.859620\pi\)
−0.904318 + 0.426858i \(0.859620\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.876894 −0.0311788
\(792\) 0 0
\(793\) −10.2462 −0.363854
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −42.9848 −1.52260 −0.761301 0.648399i \(-0.775439\pi\)
−0.761301 + 0.648399i \(0.775439\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −20.0000 −0.705785
\(804\) 0 0
\(805\) 2.24621 0.0791685
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −34.7386 −1.22135 −0.610673 0.791883i \(-0.709101\pi\)
−0.610673 + 0.791883i \(0.709101\pi\)
\(810\) 0 0
\(811\) 2.73863 0.0961664 0.0480832 0.998843i \(-0.484689\pi\)
0.0480832 + 0.998843i \(0.484689\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −16.9848 −0.594953
\(816\) 0 0
\(817\) −4.00000 −0.139942
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 24.1080 0.841373 0.420687 0.907206i \(-0.361789\pi\)
0.420687 + 0.907206i \(0.361789\pi\)
\(822\) 0 0
\(823\) 42.7386 1.48978 0.744888 0.667190i \(-0.232503\pi\)
0.744888 + 0.667190i \(0.232503\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −7.86174 −0.273379 −0.136690 0.990614i \(-0.543646\pi\)
−0.136690 + 0.990614i \(0.543646\pi\)
\(828\) 0 0
\(829\) −37.6155 −1.30644 −0.653221 0.757168i \(-0.726583\pi\)
−0.653221 + 0.757168i \(0.726583\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.12311 0.177505
\(834\) 0 0
\(835\) −36.4924 −1.26287
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −22.7386 −0.785025 −0.392512 0.919747i \(-0.628394\pi\)
−0.392512 + 0.919747i \(0.628394\pi\)
\(840\) 0 0
\(841\) −28.2311 −0.973485
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −26.4924 −0.911367
\(846\) 0 0
\(847\) 7.00000 0.240523
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −10.2462 −0.351236
\(852\) 0 0
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 36.7386 1.25497 0.627484 0.778630i \(-0.284085\pi\)
0.627484 + 0.778630i \(0.284085\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 9.61553 0.327316 0.163658 0.986517i \(-0.447671\pi\)
0.163658 + 0.986517i \(0.447671\pi\)
\(864\) 0 0
\(865\) −24.4924 −0.832767
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 9.75379 0.330875
\(870\) 0 0
\(871\) 11.5076 0.389919
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −12.0000 −0.405674
\(876\) 0 0
\(877\) 21.6155 0.729905 0.364952 0.931026i \(-0.381085\pi\)
0.364952 + 0.931026i \(0.381085\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −33.1231 −1.11595 −0.557973 0.829859i \(-0.688421\pi\)
−0.557973 + 0.829859i \(0.688421\pi\)
\(882\) 0 0
\(883\) −12.9848 −0.436975 −0.218487 0.975840i \(-0.570112\pi\)
−0.218487 + 0.975840i \(0.570112\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −26.2462 −0.881262 −0.440631 0.897688i \(-0.645245\pi\)
−0.440631 + 0.897688i \(0.645245\pi\)
\(888\) 0 0
\(889\) −12.8769 −0.431877
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −22.7386 −0.760069
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 6.24621 0.208323
\(900\) 0 0
\(901\) −16.0000 −0.533037
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −38.7386 −1.28772
\(906\) 0 0
\(907\) 10.2462 0.340220 0.170110 0.985425i \(-0.445588\pi\)
0.170110 + 0.985425i \(0.445588\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 59.8617 1.98331 0.991654 0.128928i \(-0.0411536\pi\)
0.991654 + 0.128928i \(0.0411536\pi\)
\(912\) 0 0
\(913\) −1.75379 −0.0580419
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 19.6155 0.647762
\(918\) 0 0
\(919\) −22.2462 −0.733835 −0.366917 0.930254i \(-0.619587\pi\)
−0.366917 + 0.930254i \(0.619587\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 78.7386 2.59171
\(924\) 0 0
\(925\) 9.12311 0.299966
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 45.6155 1.49660 0.748298 0.663362i \(-0.230871\pi\)
0.748298 + 0.663362i \(0.230871\pi\)
\(930\) 0 0
\(931\) −1.00000 −0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −20.4924 −0.670174
\(936\) 0 0
\(937\) −11.2614 −0.367893 −0.183946 0.982936i \(-0.558887\pi\)
−0.183946 + 0.982936i \(0.558887\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 33.2311 1.08330 0.541651 0.840604i \(-0.317800\pi\)
0.541651 + 0.840604i \(0.317800\pi\)
\(942\) 0 0
\(943\) 9.26137 0.301592
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −16.7386 −0.543933 −0.271966 0.962307i \(-0.587674\pi\)
−0.271966 + 0.962307i \(0.587674\pi\)
\(948\) 0 0
\(949\) −51.2311 −1.66303
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 32.1080 1.04008 0.520039 0.854142i \(-0.325917\pi\)
0.520039 + 0.854142i \(0.325917\pi\)
\(954\) 0 0
\(955\) 46.7386 1.51243
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18.2462 0.589201
\(960\) 0 0
\(961\) 19.7386 0.636730
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 4.00000 0.128765
\(966\) 0 0
\(967\) 24.0000 0.771788 0.385894 0.922543i \(-0.373893\pi\)
0.385894 + 0.922543i \(0.373893\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 12.4924 0.400901 0.200450 0.979704i \(-0.435759\pi\)
0.200450 + 0.979704i \(0.435759\pi\)
\(972\) 0 0
\(973\) −14.2462 −0.456713
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 23.6155 0.755528 0.377764 0.925902i \(-0.376693\pi\)
0.377764 + 0.925902i \(0.376693\pi\)
\(978\) 0 0
\(979\) 32.4924 1.03846
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −8.00000 −0.255160 −0.127580 0.991828i \(-0.540721\pi\)
−0.127580 + 0.991828i \(0.540721\pi\)
\(984\) 0 0
\(985\) −5.26137 −0.167641
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.49242 0.142851
\(990\) 0 0
\(991\) 9.36932 0.297626 0.148813 0.988865i \(-0.452455\pi\)
0.148813 + 0.988865i \(0.452455\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 44.4924 1.41050
\(996\) 0 0
\(997\) −11.7538 −0.372246 −0.186123 0.982526i \(-0.559592\pi\)
−0.186123 + 0.982526i \(0.559592\pi\)
\(998\) 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 9576.2.a.bd.1.2 2
3.2 odd 2 9576.2.a.bx.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.bd.1.2 2 1.1 even 1 trivial
9576.2.a.bx.1.2 yes 2 3.2 odd 2