Properties

Label 2592.2.a.x.1.2
Level $2592$
Weight $2$
Character 2592.1
Self dual yes
Analytic conductor $20.697$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2592,2,Mod(1,2592)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2592, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("2592.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.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: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.13068.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 6x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 288)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.04374\) of defining polynomial
Character \(\chi\) \(=\) 2592.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.37228 q^{5} +2.20979 q^{7} +O(q^{10})\) \(q-2.37228 q^{5} +2.20979 q^{7} +5.93580 q^{11} +4.37228 q^{13} -3.37228 q^{17} -3.72601 q^{19} -2.20979 q^{23} +0.627719 q^{25} -0.372281 q^{29} +9.66181 q^{31} -5.24224 q^{35} +4.00000 q^{37} -1.00000 q^{41} +5.93580 q^{43} -2.20979 q^{47} -2.11684 q^{49} +4.00000 q^{53} -14.0814 q^{55} -10.3554 q^{59} +15.1168 q^{61} -10.3723 q^{65} -10.3554 q^{67} -4.41957 q^{71} +4.62772 q^{73} +13.1168 q^{77} -9.66181 q^{79} +14.0814 q^{83} +8.00000 q^{85} -1.25544 q^{89} +9.66181 q^{91} +8.83915 q^{95} +9.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{5} + 6 q^{13} - 2 q^{17} + 14 q^{25} + 10 q^{29} + 16 q^{37} - 4 q^{41} + 26 q^{49} + 16 q^{53} + 26 q^{61} - 30 q^{65} + 30 q^{73} + 18 q^{77} + 32 q^{85} - 28 q^{89} + 36 q^{97}+O(q^{100}) \) 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
\(5\) −2.37228 −1.06092 −0.530458 0.847711i \(-0.677980\pi\)
−0.530458 + 0.847711i \(0.677980\pi\)
\(6\) 0 0
\(7\) 2.20979 0.835221 0.417610 0.908626i \(-0.362868\pi\)
0.417610 + 0.908626i \(0.362868\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.93580 1.78971 0.894855 0.446357i \(-0.147279\pi\)
0.894855 + 0.446357i \(0.147279\pi\)
\(12\) 0 0
\(13\) 4.37228 1.21265 0.606326 0.795216i \(-0.292643\pi\)
0.606326 + 0.795216i \(0.292643\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.37228 −0.817898 −0.408949 0.912557i \(-0.634105\pi\)
−0.408949 + 0.912557i \(0.634105\pi\)
\(18\) 0 0
\(19\) −3.72601 −0.854805 −0.427403 0.904061i \(-0.640571\pi\)
−0.427403 + 0.904061i \(0.640571\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.20979 −0.460772 −0.230386 0.973099i \(-0.573999\pi\)
−0.230386 + 0.973099i \(0.573999\pi\)
\(24\) 0 0
\(25\) 0.627719 0.125544
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.372281 −0.0691309 −0.0345655 0.999402i \(-0.511005\pi\)
−0.0345655 + 0.999402i \(0.511005\pi\)
\(30\) 0 0
\(31\) 9.66181 1.73531 0.867656 0.497165i \(-0.165626\pi\)
0.867656 + 0.497165i \(0.165626\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −5.24224 −0.886099
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −0.156174 −0.0780869 0.996947i \(-0.524881\pi\)
−0.0780869 + 0.996947i \(0.524881\pi\)
\(42\) 0 0
\(43\) 5.93580 0.905201 0.452600 0.891714i \(-0.350496\pi\)
0.452600 + 0.891714i \(0.350496\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.20979 −0.322330 −0.161165 0.986927i \(-0.551525\pi\)
−0.161165 + 0.986927i \(0.551525\pi\)
\(48\) 0 0
\(49\) −2.11684 −0.302406
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 0 0
\(55\) −14.0814 −1.89873
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.3554 −1.34815 −0.674077 0.738661i \(-0.735458\pi\)
−0.674077 + 0.738661i \(0.735458\pi\)
\(60\) 0 0
\(61\) 15.1168 1.93551 0.967757 0.251887i \(-0.0810510\pi\)
0.967757 + 0.251887i \(0.0810510\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −10.3723 −1.28652
\(66\) 0 0
\(67\) −10.3554 −1.26511 −0.632555 0.774516i \(-0.717994\pi\)
−0.632555 + 0.774516i \(0.717994\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.41957 −0.524507 −0.262253 0.964999i \(-0.584466\pi\)
−0.262253 + 0.964999i \(0.584466\pi\)
\(72\) 0 0
\(73\) 4.62772 0.541634 0.270817 0.962631i \(-0.412706\pi\)
0.270817 + 0.962631i \(0.412706\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13.1168 1.49480
\(78\) 0 0
\(79\) −9.66181 −1.08704 −0.543519 0.839397i \(-0.682908\pi\)
−0.543519 + 0.839397i \(0.682908\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 14.0814 1.54563 0.772816 0.634630i \(-0.218847\pi\)
0.772816 + 0.634630i \(0.218847\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.25544 −0.133076 −0.0665380 0.997784i \(-0.521195\pi\)
−0.0665380 + 0.997784i \(0.521195\pi\)
\(90\) 0 0
\(91\) 9.66181 1.01283
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.83915 0.906877
\(96\) 0 0
\(97\) 9.00000 0.913812 0.456906 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.1168 1.50418 0.752091 0.659059i \(-0.229045\pi\)
0.752091 + 0.659059i \(0.229045\pi\)
\(102\) 0 0
\(103\) −2.20979 −0.217737 −0.108868 0.994056i \(-0.534723\pi\)
−0.108868 + 0.994056i \(0.534723\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.72601 0.360207 0.180104 0.983648i \(-0.442357\pi\)
0.180104 + 0.983648i \(0.442357\pi\)
\(108\) 0 0
\(109\) 17.4891 1.67515 0.837577 0.546319i \(-0.183971\pi\)
0.837577 + 0.546319i \(0.183971\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.6277 −1.09384 −0.546922 0.837184i \(-0.684201\pi\)
−0.546922 + 0.837184i \(0.684201\pi\)
\(114\) 0 0
\(115\) 5.24224 0.488841
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.45202 −0.683126
\(120\) 0 0
\(121\) 24.2337 2.20306
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.3723 0.927725
\(126\) 0 0
\(127\) 7.45202 0.661260 0.330630 0.943760i \(-0.392739\pi\)
0.330630 + 0.943760i \(0.392739\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.66181 0.844156 0.422078 0.906560i \(-0.361301\pi\)
0.422078 + 0.906560i \(0.361301\pi\)
\(132\) 0 0
\(133\) −8.23369 −0.713951
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.4891 1.06702 0.533509 0.845794i \(-0.320873\pi\)
0.533509 + 0.845794i \(0.320873\pi\)
\(138\) 0 0
\(139\) 2.90335 0.246259 0.123129 0.992391i \(-0.460707\pi\)
0.123129 + 0.992391i \(0.460707\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 25.9530 2.17030
\(144\) 0 0
\(145\) 0.883156 0.0733421
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.6277 0.952580 0.476290 0.879288i \(-0.341981\pi\)
0.476290 + 0.879288i \(0.341981\pi\)
\(150\) 0 0
\(151\) −2.20979 −0.179830 −0.0899149 0.995949i \(-0.528660\pi\)
−0.0899149 + 0.995949i \(0.528660\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −22.9205 −1.84102
\(156\) 0 0
\(157\) −3.11684 −0.248751 −0.124376 0.992235i \(-0.539693\pi\)
−0.124376 + 0.992235i \(0.539693\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.88316 −0.384847
\(162\) 0 0
\(163\) 8.83915 0.692335 0.346168 0.938173i \(-0.387483\pi\)
0.346168 + 0.938173i \(0.387483\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.66181 0.747653 0.373827 0.927499i \(-0.378046\pi\)
0.373827 + 0.927499i \(0.378046\pi\)
\(168\) 0 0
\(169\) 6.11684 0.470526
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.372281 0.0283040 0.0141520 0.999900i \(-0.495495\pi\)
0.0141520 + 0.999900i \(0.495495\pi\)
\(174\) 0 0
\(175\) 1.38712 0.104857
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.83915 −0.660669 −0.330334 0.943864i \(-0.607162\pi\)
−0.330334 + 0.943864i \(0.607162\pi\)
\(180\) 0 0
\(181\) −8.23369 −0.612005 −0.306003 0.952031i \(-0.598992\pi\)
−0.306003 + 0.952031i \(0.598992\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −9.48913 −0.697654
\(186\) 0 0
\(187\) −20.0172 −1.46380
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.1138 −1.23831 −0.619157 0.785268i \(-0.712525\pi\)
−0.619157 + 0.785268i \(0.712525\pi\)
\(192\) 0 0
\(193\) 1.00000 0.0719816 0.0359908 0.999352i \(-0.488541\pi\)
0.0359908 + 0.999352i \(0.488541\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.744563 −0.0530479 −0.0265239 0.999648i \(-0.508444\pi\)
−0.0265239 + 0.999648i \(0.508444\pi\)
\(198\) 0 0
\(199\) 20.7107 1.46815 0.734073 0.679071i \(-0.237617\pi\)
0.734073 + 0.679071i \(0.237617\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.822662 −0.0577396
\(204\) 0 0
\(205\) 2.37228 0.165687
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −22.1168 −1.52985
\(210\) 0 0
\(211\) −5.24224 −0.360890 −0.180445 0.983585i \(-0.557754\pi\)
−0.180445 + 0.983585i \(0.557754\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −14.0814 −0.960342
\(216\) 0 0
\(217\) 21.3505 1.44937
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −14.7446 −0.991827
\(222\) 0 0
\(223\) 2.20979 0.147978 0.0739891 0.997259i \(-0.476427\pi\)
0.0739891 + 0.997259i \(0.476427\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.96825 −0.595243 −0.297622 0.954684i \(-0.596193\pi\)
−0.297622 + 0.954684i \(0.596193\pi\)
\(228\) 0 0
\(229\) −4.37228 −0.288928 −0.144464 0.989510i \(-0.546146\pi\)
−0.144464 + 0.989510i \(0.546146\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.86141 −0.187457 −0.0937285 0.995598i \(-0.529879\pi\)
−0.0937285 + 0.995598i \(0.529879\pi\)
\(234\) 0 0
\(235\) 5.24224 0.341966
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −17.1138 −1.10700 −0.553501 0.832849i \(-0.686708\pi\)
−0.553501 + 0.832849i \(0.686708\pi\)
\(240\) 0 0
\(241\) 0.255437 0.0164542 0.00822708 0.999966i \(-0.497381\pi\)
0.00822708 + 0.999966i \(0.497381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.02175 0.320828
\(246\) 0 0
\(247\) −16.2912 −1.03658
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.1780 0.705551 0.352776 0.935708i \(-0.385238\pi\)
0.352776 + 0.935708i \(0.385238\pi\)
\(252\) 0 0
\(253\) −13.1168 −0.824649
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.48913 0.404781 0.202390 0.979305i \(-0.435129\pi\)
0.202390 + 0.979305i \(0.435129\pi\)
\(258\) 0 0
\(259\) 8.83915 0.549238
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 17.1138 1.05528 0.527642 0.849467i \(-0.323076\pi\)
0.527642 + 0.849467i \(0.323076\pi\)
\(264\) 0 0
\(265\) −9.48913 −0.582912
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.48913 −0.578562 −0.289281 0.957244i \(-0.593416\pi\)
−0.289281 + 0.957244i \(0.593416\pi\)
\(270\) 0 0
\(271\) 14.9040 0.905356 0.452678 0.891674i \(-0.350469\pi\)
0.452678 + 0.891674i \(0.350469\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.72601 0.224687
\(276\) 0 0
\(277\) 13.1168 0.788115 0.394057 0.919086i \(-0.371071\pi\)
0.394057 + 0.919086i \(0.371071\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −25.8614 −1.54276 −0.771381 0.636373i \(-0.780434\pi\)
−0.771381 + 0.636373i \(0.780434\pi\)
\(282\) 0 0
\(283\) 5.24224 0.311619 0.155809 0.987787i \(-0.450201\pi\)
0.155809 + 0.987787i \(0.450201\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.20979 −0.130440
\(288\) 0 0
\(289\) −5.62772 −0.331042
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 20.3723 1.19016 0.595081 0.803666i \(-0.297120\pi\)
0.595081 + 0.803666i \(0.297120\pi\)
\(294\) 0 0
\(295\) 24.5659 1.43028
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.66181 −0.558757
\(300\) 0 0
\(301\) 13.1168 0.756042
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −35.8614 −2.05342
\(306\) 0 0
\(307\) −28.8563 −1.64692 −0.823459 0.567376i \(-0.807959\pi\)
−0.823459 + 0.567376i \(0.807959\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.6943 0.719825 0.359913 0.932986i \(-0.382806\pi\)
0.359913 + 0.932986i \(0.382806\pi\)
\(312\) 0 0
\(313\) 19.2337 1.08715 0.543576 0.839360i \(-0.317070\pi\)
0.543576 + 0.839360i \(0.317070\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.37228 −0.470234 −0.235117 0.971967i \(-0.575547\pi\)
−0.235117 + 0.971967i \(0.575547\pi\)
\(318\) 0 0
\(319\) −2.20979 −0.123724
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.5652 0.699144
\(324\) 0 0
\(325\) 2.74456 0.152241
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.88316 −0.269217
\(330\) 0 0
\(331\) −33.4050 −1.83610 −0.918052 0.396459i \(-0.870239\pi\)
−0.918052 + 0.396459i \(0.870239\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 24.5659 1.34218
\(336\) 0 0
\(337\) −9.00000 −0.490261 −0.245131 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 57.3505 3.10571
\(342\) 0 0
\(343\) −20.1463 −1.08780
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.3554 0.555905 0.277953 0.960595i \(-0.410344\pi\)
0.277953 + 0.960595i \(0.410344\pi\)
\(348\) 0 0
\(349\) −23.1168 −1.23742 −0.618708 0.785621i \(-0.712344\pi\)
−0.618708 + 0.785621i \(0.712344\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 19.2337 1.02371 0.511853 0.859073i \(-0.328959\pi\)
0.511853 + 0.859073i \(0.328959\pi\)
\(354\) 0 0
\(355\) 10.4845 0.556458
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −22.3561 −1.17991 −0.589954 0.807437i \(-0.700854\pi\)
−0.589954 + 0.807437i \(0.700854\pi\)
\(360\) 0 0
\(361\) −5.11684 −0.269308
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −10.9783 −0.574628
\(366\) 0 0
\(367\) −27.3401 −1.42714 −0.713571 0.700583i \(-0.752923\pi\)
−0.713571 + 0.700583i \(0.752923\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.83915 0.458906
\(372\) 0 0
\(373\) −17.1168 −0.886277 −0.443138 0.896453i \(-0.646135\pi\)
−0.443138 + 0.896453i \(0.646135\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.62772 −0.0838318
\(378\) 0 0
\(379\) −8.14558 −0.418411 −0.209205 0.977872i \(-0.567088\pi\)
−0.209205 + 0.977872i \(0.567088\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −22.9205 −1.17118 −0.585592 0.810606i \(-0.699138\pi\)
−0.585592 + 0.810606i \(0.699138\pi\)
\(384\) 0 0
\(385\) −31.1168 −1.58586
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 19.3505 0.981111 0.490555 0.871410i \(-0.336794\pi\)
0.490555 + 0.871410i \(0.336794\pi\)
\(390\) 0 0
\(391\) 7.45202 0.376865
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 22.9205 1.15326
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −27.9783 −1.39717 −0.698584 0.715528i \(-0.746186\pi\)
−0.698584 + 0.715528i \(0.746186\pi\)
\(402\) 0 0
\(403\) 42.2441 2.10433
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 23.7432 1.17691
\(408\) 0 0
\(409\) −18.2554 −0.902673 −0.451337 0.892354i \(-0.649053\pi\)
−0.451337 + 0.892354i \(0.649053\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −22.8832 −1.12601
\(414\) 0 0
\(415\) −33.4050 −1.63979
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.24224 0.256100 0.128050 0.991768i \(-0.459128\pi\)
0.128050 + 0.991768i \(0.459128\pi\)
\(420\) 0 0
\(421\) −22.3723 −1.09036 −0.545179 0.838320i \(-0.683538\pi\)
−0.545179 + 0.838320i \(0.683538\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.11684 −0.102682
\(426\) 0 0
\(427\) 33.4050 1.61658
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.45202 −0.358951 −0.179476 0.983762i \(-0.557440\pi\)
−0.179476 + 0.983762i \(0.557440\pi\)
\(432\) 0 0
\(433\) −18.1168 −0.870640 −0.435320 0.900276i \(-0.643365\pi\)
−0.435320 + 0.900276i \(0.643365\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.23369 0.393871
\(438\) 0 0
\(439\) 22.9205 1.09394 0.546969 0.837153i \(-0.315782\pi\)
0.546969 + 0.837153i \(0.315782\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.96825 0.426094 0.213047 0.977042i \(-0.431661\pi\)
0.213047 + 0.977042i \(0.431661\pi\)
\(444\) 0 0
\(445\) 2.97825 0.141183
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 18.1168 0.854987 0.427493 0.904018i \(-0.359397\pi\)
0.427493 + 0.904018i \(0.359397\pi\)
\(450\) 0 0
\(451\) −5.93580 −0.279506
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −22.9205 −1.07453
\(456\) 0 0
\(457\) −25.9783 −1.21521 −0.607606 0.794239i \(-0.707870\pi\)
−0.607606 + 0.794239i \(0.707870\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 29.1168 1.35611 0.678053 0.735013i \(-0.262824\pi\)
0.678053 + 0.735013i \(0.262824\pi\)
\(462\) 0 0
\(463\) −37.8246 −1.75786 −0.878928 0.476954i \(-0.841741\pi\)
−0.878928 + 0.476954i \(0.841741\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −36.3083 −1.68015 −0.840075 0.542470i \(-0.817489\pi\)
−0.840075 + 0.542470i \(0.817489\pi\)
\(468\) 0 0
\(469\) −22.8832 −1.05665
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 35.2337 1.62005
\(474\) 0 0
\(475\) −2.33889 −0.107315
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.20979 0.100968 0.0504839 0.998725i \(-0.483924\pi\)
0.0504839 + 0.998725i \(0.483924\pi\)
\(480\) 0 0
\(481\) 17.4891 0.797435
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −21.3505 −0.969478
\(486\) 0 0
\(487\) 7.45202 0.337683 0.168842 0.985643i \(-0.445997\pi\)
0.168842 + 0.985643i \(0.445997\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.129100 −0.00582621 −0.00291310 0.999996i \(-0.500927\pi\)
−0.00291310 + 0.999996i \(0.500927\pi\)
\(492\) 0 0
\(493\) 1.25544 0.0565421
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.76631 −0.438079
\(498\) 0 0
\(499\) 25.2594 1.13077 0.565383 0.824828i \(-0.308728\pi\)
0.565383 + 0.824828i \(0.308728\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10.4845 −0.467479 −0.233740 0.972299i \(-0.575096\pi\)
−0.233740 + 0.972299i \(0.575096\pi\)
\(504\) 0 0
\(505\) −35.8614 −1.59581
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13.3505 0.591752 0.295876 0.955226i \(-0.404388\pi\)
0.295876 + 0.955226i \(0.404388\pi\)
\(510\) 0 0
\(511\) 10.2263 0.452384
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.24224 0.231000
\(516\) 0 0
\(517\) −13.1168 −0.576878
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16.3505 0.716330 0.358165 0.933658i \(-0.383403\pi\)
0.358165 + 0.933658i \(0.383403\pi\)
\(522\) 0 0
\(523\) −19.3236 −0.844963 −0.422481 0.906372i \(-0.638841\pi\)
−0.422481 + 0.906372i \(0.638841\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −32.5823 −1.41931
\(528\) 0 0
\(529\) −18.1168 −0.787689
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.37228 −0.189385
\(534\) 0 0
\(535\) −8.83915 −0.382150
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −12.5652 −0.541220
\(540\) 0 0
\(541\) 8.74456 0.375958 0.187979 0.982173i \(-0.439806\pi\)
0.187979 + 0.982173i \(0.439806\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −41.4891 −1.77720
\(546\) 0 0
\(547\) 1.51622 0.0648291 0.0324145 0.999475i \(-0.489680\pi\)
0.0324145 + 0.999475i \(0.489680\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.38712 0.0590935
\(552\) 0 0
\(553\) −21.3505 −0.907917
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.7446 0.794233 0.397116 0.917768i \(-0.370011\pi\)
0.397116 + 0.917768i \(0.370011\pi\)
\(558\) 0 0
\(559\) 25.9530 1.09769
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22.2270 −0.936755 −0.468377 0.883528i \(-0.655161\pi\)
−0.468377 + 0.883528i \(0.655161\pi\)
\(564\) 0 0
\(565\) 27.5842 1.16048
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 39.7446 1.66618 0.833089 0.553138i \(-0.186570\pi\)
0.833089 + 0.553138i \(0.186570\pi\)
\(570\) 0 0
\(571\) −0.129100 −0.00540267 −0.00270134 0.999996i \(-0.500860\pi\)
−0.00270134 + 0.999996i \(0.500860\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.38712 −0.0578471
\(576\) 0 0
\(577\) 18.1168 0.754214 0.377107 0.926170i \(-0.376919\pi\)
0.377107 + 0.926170i \(0.376919\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 31.1168 1.29094
\(582\) 0 0
\(583\) 23.7432 0.983342
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.7425 0.484665 0.242332 0.970193i \(-0.422088\pi\)
0.242332 + 0.970193i \(0.422088\pi\)
\(588\) 0 0
\(589\) −36.0000 −1.48335
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 17.7228 0.727789 0.363894 0.931440i \(-0.381447\pi\)
0.363894 + 0.931440i \(0.381447\pi\)
\(594\) 0 0
\(595\) 17.6783 0.724739
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 27.3401 1.11709 0.558543 0.829476i \(-0.311361\pi\)
0.558543 + 0.829476i \(0.311361\pi\)
\(600\) 0 0
\(601\) −2.76631 −0.112840 −0.0564201 0.998407i \(-0.517969\pi\)
−0.0564201 + 0.998407i \(0.517969\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −57.4891 −2.33727
\(606\) 0 0
\(607\) 37.8246 1.53525 0.767626 0.640898i \(-0.221438\pi\)
0.767626 + 0.640898i \(0.221438\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −9.66181 −0.390875
\(612\) 0 0
\(613\) 36.4674 1.47290 0.736452 0.676490i \(-0.236500\pi\)
0.736452 + 0.676490i \(0.236500\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.7446 1.51954 0.759769 0.650193i \(-0.225312\pi\)
0.759769 + 0.650193i \(0.225312\pi\)
\(618\) 0 0
\(619\) 1.51622 0.0609422 0.0304711 0.999536i \(-0.490299\pi\)
0.0304711 + 0.999536i \(0.490299\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.77425 −0.111148
\(624\) 0 0
\(625\) −27.7446 −1.10978
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −13.4891 −0.537847
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −17.6783 −0.701542
\(636\) 0 0
\(637\) −9.25544 −0.366714
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −13.7446 −0.542878 −0.271439 0.962456i \(-0.587499\pi\)
−0.271439 + 0.962456i \(0.587499\pi\)
\(642\) 0 0
\(643\) −17.8074 −0.702255 −0.351127 0.936328i \(-0.614202\pi\)
−0.351127 + 0.936328i \(0.614202\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 40.0344 1.57391 0.786956 0.617009i \(-0.211656\pi\)
0.786956 + 0.617009i \(0.211656\pi\)
\(648\) 0 0
\(649\) −61.4674 −2.41281
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −41.1168 −1.60903 −0.804513 0.593935i \(-0.797574\pi\)
−0.804513 + 0.593935i \(0.797574\pi\)
\(654\) 0 0
\(655\) −22.9205 −0.895579
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −31.7597 −1.23718 −0.618591 0.785713i \(-0.712296\pi\)
−0.618591 + 0.785713i \(0.712296\pi\)
\(660\) 0 0
\(661\) −3.11684 −0.121231 −0.0606156 0.998161i \(-0.519306\pi\)
−0.0606156 + 0.998161i \(0.519306\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 19.5326 0.757443
\(666\) 0 0
\(667\) 0.822662 0.0318536
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 89.7305 3.46401
\(672\) 0 0
\(673\) 23.3505 0.900097 0.450048 0.893004i \(-0.351407\pi\)
0.450048 + 0.893004i \(0.351407\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.35053 −0.0519052 −0.0259526 0.999663i \(-0.508262\pi\)
−0.0259526 + 0.999663i \(0.508262\pi\)
\(678\) 0 0
\(679\) 19.8881 0.763234
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 36.3083 1.38930 0.694650 0.719348i \(-0.255559\pi\)
0.694650 + 0.719348i \(0.255559\pi\)
\(684\) 0 0
\(685\) −29.6277 −1.13202
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 17.4891 0.666283
\(690\) 0 0
\(691\) −46.6637 −1.77517 −0.887586 0.460643i \(-0.847619\pi\)
−0.887586 + 0.460643i \(0.847619\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6.88756 −0.261260
\(696\) 0 0
\(697\) 3.37228 0.127734
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −34.7446 −1.31228 −0.656142 0.754637i \(-0.727813\pi\)
−0.656142 + 0.754637i \(0.727813\pi\)
\(702\) 0 0
\(703\) −14.9040 −0.562117
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 33.4050 1.25632
\(708\) 0 0
\(709\) −12.6060 −0.473427 −0.236714 0.971579i \(-0.576070\pi\)
−0.236714 + 0.971579i \(0.576070\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −21.3505 −0.799584
\(714\) 0 0
\(715\) −61.5678 −2.30250
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32.5823 1.21512 0.607558 0.794275i \(-0.292149\pi\)
0.607558 + 0.794275i \(0.292149\pi\)
\(720\) 0 0
\(721\) −4.88316 −0.181858
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.233688 −0.00867895
\(726\) 0 0
\(727\) −34.7921 −1.29037 −0.645184 0.764027i \(-0.723219\pi\)
−0.645184 + 0.764027i \(0.723219\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −20.0172 −0.740362
\(732\) 0 0
\(733\) 22.8832 0.845209 0.422604 0.906314i \(-0.361116\pi\)
0.422604 + 0.906314i \(0.361116\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −61.4674 −2.26418
\(738\) 0 0
\(739\) 15.5976 0.573767 0.286884 0.957965i \(-0.407381\pi\)
0.286884 + 0.957965i \(0.407381\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27.5983 −1.01248 −0.506242 0.862392i \(-0.668966\pi\)
−0.506242 + 0.862392i \(0.668966\pi\)
\(744\) 0 0
\(745\) −27.5842 −1.01061
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.23369 0.300852
\(750\) 0 0
\(751\) 22.9205 0.836382 0.418191 0.908359i \(-0.362664\pi\)
0.418191 + 0.908359i \(0.362664\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.24224 0.190784
\(756\) 0 0
\(757\) −34.4674 −1.25274 −0.626369 0.779527i \(-0.715460\pi\)
−0.626369 + 0.779527i \(0.715460\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −20.3723 −0.738495 −0.369247 0.929331i \(-0.620384\pi\)
−0.369247 + 0.929331i \(0.620384\pi\)
\(762\) 0 0
\(763\) 38.6472 1.39912
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −45.2766 −1.63484
\(768\) 0 0
\(769\) −14.8832 −0.536700 −0.268350 0.963321i \(-0.586478\pi\)
−0.268350 + 0.963321i \(0.586478\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 18.7446 0.674195 0.337098 0.941470i \(-0.390555\pi\)
0.337098 + 0.941470i \(0.390555\pi\)
\(774\) 0 0
\(775\) 6.06490 0.217858
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.72601 0.133498
\(780\) 0 0
\(781\) −26.2337 −0.938715
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.39403 0.263904
\(786\) 0 0
\(787\) −42.2441 −1.50584 −0.752921 0.658111i \(-0.771356\pi\)
−0.752921 + 0.658111i \(0.771356\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −25.6948 −0.913601
\(792\) 0 0
\(793\) 66.0951 2.34711
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −46.0951 −1.63277 −0.816386 0.577507i \(-0.804026\pi\)
−0.816386 + 0.577507i \(0.804026\pi\)
\(798\) 0 0
\(799\) 7.45202 0.263634
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 27.4692 0.969367
\(804\) 0 0
\(805\) 11.5842 0.408290
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 12.6277 0.443967 0.221983 0.975050i \(-0.428747\pi\)
0.221983 + 0.975050i \(0.428747\pi\)
\(810\) 0 0
\(811\) 33.5341 1.17754 0.588771 0.808300i \(-0.299612\pi\)
0.588771 + 0.808300i \(0.299612\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −20.9689 −0.734510
\(816\) 0 0
\(817\) −22.1168 −0.773770
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −8.37228 −0.292195 −0.146097 0.989270i \(-0.546671\pi\)
−0.146097 + 0.989270i \(0.546671\pi\)
\(822\) 0 0
\(823\) −22.9205 −0.798959 −0.399480 0.916742i \(-0.630809\pi\)
−0.399480 + 0.916742i \(0.630809\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −8.83915 −0.307367 −0.153684 0.988120i \(-0.549114\pi\)
−0.153684 + 0.988120i \(0.549114\pi\)
\(828\) 0 0
\(829\) −8.23369 −0.285968 −0.142984 0.989725i \(-0.545670\pi\)
−0.142984 + 0.989725i \(0.545670\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 7.13859 0.247338
\(834\) 0 0
\(835\) −22.9205 −0.793198
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −9.66181 −0.333563 −0.166781 0.985994i \(-0.553337\pi\)
−0.166781 + 0.985994i \(0.553337\pi\)
\(840\) 0 0
\(841\) −28.8614 −0.995221
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −14.5109 −0.499189
\(846\) 0 0
\(847\) 53.5513 1.84004
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −8.83915 −0.303002
\(852\) 0 0
\(853\) −21.1168 −0.723027 −0.361513 0.932367i \(-0.617740\pi\)
−0.361513 + 0.932367i \(0.617740\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 44.0951 1.50626 0.753130 0.657872i \(-0.228543\pi\)
0.753130 + 0.657872i \(0.228543\pi\)
\(858\) 0 0
\(859\) −17.8074 −0.607580 −0.303790 0.952739i \(-0.598252\pi\)
−0.303790 + 0.952739i \(0.598252\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −17.6783 −0.601776 −0.300888 0.953659i \(-0.597283\pi\)
−0.300888 + 0.953659i \(0.597283\pi\)
\(864\) 0 0
\(865\) −0.883156 −0.0300282
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −57.3505 −1.94548
\(870\) 0 0
\(871\) −45.2766 −1.53414
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 22.9205 0.774855
\(876\) 0 0
\(877\) −13.3505 −0.450815 −0.225408 0.974265i \(-0.572371\pi\)
−0.225408 + 0.974265i \(0.572371\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −4.23369 −0.142637 −0.0713183 0.997454i \(-0.522721\pi\)
−0.0713183 + 0.997454i \(0.522721\pi\)
\(882\) 0 0
\(883\) 21.4043 0.720312 0.360156 0.932892i \(-0.382723\pi\)
0.360156 + 0.932892i \(0.382723\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 22.9205 0.769596 0.384798 0.923001i \(-0.374271\pi\)
0.384798 + 0.923001i \(0.374271\pi\)
\(888\) 0 0
\(889\) 16.4674 0.552298
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8.23369 0.275530
\(894\) 0 0
\(895\) 20.9689 0.700914
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.59691 −0.119964
\(900\) 0 0
\(901\) −13.4891 −0.449388
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 19.5326 0.649286
\(906\) 0 0
\(907\) 28.2919 0.939416 0.469708 0.882822i \(-0.344359\pi\)
0.469708 + 0.882822i \(0.344359\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −52.7286 −1.74698 −0.873488 0.486845i \(-0.838148\pi\)
−0.873488 + 0.486845i \(0.838148\pi\)
\(912\) 0 0
\(913\) 83.5842 2.76623
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 21.3505 0.705057
\(918\) 0 0
\(919\) −25.1303 −0.828973 −0.414486 0.910056i \(-0.636039\pi\)
−0.414486 + 0.910056i \(0.636039\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −19.3236 −0.636045
\(924\) 0 0
\(925\) 2.51087 0.0825571
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −36.3723 −1.19334 −0.596668 0.802488i \(-0.703509\pi\)
−0.596668 + 0.802488i \(0.703509\pi\)
\(930\) 0 0
\(931\) 7.88738 0.258499
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 47.4864 1.55297
\(936\) 0 0
\(937\) 12.2337 0.399657 0.199829 0.979831i \(-0.435961\pi\)
0.199829 + 0.979831i \(0.435961\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 46.0951 1.50266 0.751329 0.659928i \(-0.229413\pi\)
0.751329 + 0.659928i \(0.229413\pi\)
\(942\) 0 0
\(943\) 2.20979 0.0719605
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −34.0986 −1.10805 −0.554027 0.832499i \(-0.686910\pi\)
−0.554027 + 0.832499i \(0.686910\pi\)
\(948\) 0 0
\(949\) 20.2337 0.656813
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 31.6060 1.02382 0.511909 0.859040i \(-0.328939\pi\)
0.511909 + 0.859040i \(0.328939\pi\)
\(954\) 0 0
\(955\) 40.5988 1.31375
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 27.5983 0.891196
\(960\) 0 0
\(961\) 62.3505 2.01131
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.37228 −0.0763664
\(966\) 0 0
\(967\) −27.5983 −0.887501 −0.443751 0.896150i \(-0.646352\pi\)
−0.443751 + 0.896150i \(0.646352\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −49.1317 −1.57671 −0.788356 0.615220i \(-0.789067\pi\)
−0.788356 + 0.615220i \(0.789067\pi\)
\(972\) 0 0
\(973\) 6.41578 0.205680
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −10.7663 −0.344445 −0.172222 0.985058i \(-0.555095\pi\)
−0.172222 + 0.985058i \(0.555095\pi\)
\(978\) 0 0
\(979\) −7.45202 −0.238168
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −40.5988 −1.29490 −0.647451 0.762107i \(-0.724165\pi\)
−0.647451 + 0.762107i \(0.724165\pi\)
\(984\) 0 0
\(985\) 1.76631 0.0562794
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −13.1168 −0.417091
\(990\) 0 0
\(991\) −47.4864 −1.50845 −0.754227 0.656613i \(-0.771988\pi\)
−0.754227 + 0.656613i \(0.771988\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −49.1317 −1.55758
\(996\) 0 0
\(997\) 41.3505 1.30958 0.654792 0.755809i \(-0.272756\pi\)
0.654792 + 0.755809i \(0.272756\pi\)
\(998\) 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 2592.2.a.x.1.2 4
3.2 odd 2 2592.2.a.u.1.4 4
4.3 odd 2 inner 2592.2.a.x.1.1 4
8.3 odd 2 5184.2.a.cc.1.3 4
8.5 even 2 5184.2.a.cc.1.4 4
9.2 odd 6 288.2.i.f.193.1 yes 8
9.4 even 3 864.2.i.f.289.3 8
9.5 odd 6 288.2.i.f.97.1 8
9.7 even 3 864.2.i.f.577.3 8
12.11 even 2 2592.2.a.u.1.3 4
24.5 odd 2 5184.2.a.cf.1.2 4
24.11 even 2 5184.2.a.cf.1.1 4
36.7 odd 6 864.2.i.f.577.4 8
36.11 even 6 288.2.i.f.193.4 yes 8
36.23 even 6 288.2.i.f.97.4 yes 8
36.31 odd 6 864.2.i.f.289.4 8
72.5 odd 6 576.2.i.n.385.4 8
72.11 even 6 576.2.i.n.193.1 8
72.13 even 6 1728.2.i.n.1153.1 8
72.29 odd 6 576.2.i.n.193.4 8
72.43 odd 6 1728.2.i.n.577.2 8
72.59 even 6 576.2.i.n.385.1 8
72.61 even 6 1728.2.i.n.577.1 8
72.67 odd 6 1728.2.i.n.1153.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.i.f.97.1 8 9.5 odd 6
288.2.i.f.97.4 yes 8 36.23 even 6
288.2.i.f.193.1 yes 8 9.2 odd 6
288.2.i.f.193.4 yes 8 36.11 even 6
576.2.i.n.193.1 8 72.11 even 6
576.2.i.n.193.4 8 72.29 odd 6
576.2.i.n.385.1 8 72.59 even 6
576.2.i.n.385.4 8 72.5 odd 6
864.2.i.f.289.3 8 9.4 even 3
864.2.i.f.289.4 8 36.31 odd 6
864.2.i.f.577.3 8 9.7 even 3
864.2.i.f.577.4 8 36.7 odd 6
1728.2.i.n.577.1 8 72.61 even 6
1728.2.i.n.577.2 8 72.43 odd 6
1728.2.i.n.1153.1 8 72.13 even 6
1728.2.i.n.1153.2 8 72.67 odd 6
2592.2.a.u.1.3 4 12.11 even 2
2592.2.a.u.1.4 4 3.2 odd 2
2592.2.a.x.1.1 4 4.3 odd 2 inner
2592.2.a.x.1.2 4 1.1 even 1 trivial
5184.2.a.cc.1.3 4 8.3 odd 2
5184.2.a.cc.1.4 4 8.5 even 2
5184.2.a.cf.1.1 4 24.11 even 2
5184.2.a.cf.1.2 4 24.5 odd 2