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Properties

Label 1440.4.a.j.1.1
Level $1440$
Weight $4$
Character 1440.1
Self dual yes
Analytic conductor $84.963$
Analytic rank $0$
Dimension $1$
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] = [1440,4,Mod(1,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1440.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1440.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: \(84.9627504083\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 480)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1440.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} +32.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +32.0000 q^{7} -64.0000 q^{11} -6.00000 q^{13} -38.0000 q^{17} -116.000 q^{19} +120.000 q^{23} +25.0000 q^{25} +122.000 q^{29} +164.000 q^{31} -160.000 q^{35} +146.000 q^{37} +238.000 q^{41} -148.000 q^{43} +184.000 q^{47} +681.000 q^{49} -470.000 q^{53} +320.000 q^{55} +216.000 q^{59} +806.000 q^{61} +30.0000 q^{65} -732.000 q^{67} -264.000 q^{71} -638.000 q^{73} -2048.00 q^{77} +596.000 q^{79} +884.000 q^{83} +190.000 q^{85} -930.000 q^{89} -192.000 q^{91} +580.000 q^{95} +322.000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 32.0000 1.72784 0.863919 − 0.503631i \(-0.168003\pi\)
0.863919 + 0.503631i \(0.168003\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −64.0000 −1.75425 −0.877124 − 0.480264i \(-0.840541\pi\)
−0.877124 + 0.480264i \(0.840541\pi\)
\(12\) 0 0
\(13\) −6.00000 −0.128008 −0.0640039 − 0.997950i \(-0.520387\pi\)
−0.0640039 + 0.997950i \(0.520387\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −38.0000 −0.542138 −0.271069 − 0.962560i \(-0.587377\pi\)
−0.271069 + 0.962560i \(0.587377\pi\)
\(18\) 0 0
\(19\) −116.000 −1.40064 −0.700322 − 0.713827i \(-0.746960\pi\)
−0.700322 + 0.713827i \(0.746960\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 120.000 1.08790 0.543951 − 0.839117i \(-0.316928\pi\)
0.543951 + 0.839117i \(0.316928\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 122.000 0.781201 0.390601 − 0.920560i \(-0.372267\pi\)
0.390601 + 0.920560i \(0.372267\pi\)
\(30\) 0 0
\(31\) 164.000 0.950170 0.475085 − 0.879940i \(-0.342417\pi\)
0.475085 + 0.879940i \(0.342417\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −160.000 −0.772712
\(36\) 0 0
\(37\) 146.000 0.648710 0.324355 − 0.945936i \(-0.394853\pi\)
0.324355 + 0.945936i \(0.394853\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 238.000 0.906570 0.453285 − 0.891366i \(-0.350252\pi\)
0.453285 + 0.891366i \(0.350252\pi\)
\(42\) 0 0
\(43\) −148.000 −0.524879 −0.262439 − 0.964948i \(-0.584527\pi\)
−0.262439 + 0.964948i \(0.584527\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 184.000 0.571046 0.285523 − 0.958372i \(-0.407833\pi\)
0.285523 + 0.958372i \(0.407833\pi\)
\(48\) 0 0
\(49\) 681.000 1.98542
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −470.000 −1.21810 −0.609052 − 0.793131i \(-0.708450\pi\)
−0.609052 + 0.793131i \(0.708450\pi\)
\(54\) 0 0
\(55\) 320.000 0.784523
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 216.000 0.476624 0.238312 − 0.971189i \(-0.423406\pi\)
0.238312 + 0.971189i \(0.423406\pi\)
\(60\) 0 0
\(61\) 806.000 1.69177 0.845883 − 0.533369i \(-0.179074\pi\)
0.845883 + 0.533369i \(0.179074\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 30.0000 0.0572468
\(66\) 0 0
\(67\) −732.000 −1.33475 −0.667373 − 0.744723i \(-0.732581\pi\)
−0.667373 + 0.744723i \(0.732581\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −264.000 −0.441282 −0.220641 − 0.975355i \(-0.570815\pi\)
−0.220641 + 0.975355i \(0.570815\pi\)
\(72\) 0 0
\(73\) −638.000 −1.02291 −0.511454 − 0.859311i \(-0.670893\pi\)
−0.511454 + 0.859311i \(0.670893\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2048.00 −3.03106
\(78\) 0 0
\(79\) 596.000 0.848800 0.424400 − 0.905475i \(-0.360485\pi\)
0.424400 + 0.905475i \(0.360485\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 884.000 1.16906 0.584528 − 0.811374i \(-0.301280\pi\)
0.584528 + 0.811374i \(0.301280\pi\)
\(84\) 0 0
\(85\) 190.000 0.242452
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −930.000 −1.10764 −0.553819 − 0.832637i \(-0.686830\pi\)
−0.553819 + 0.832637i \(0.686830\pi\)
\(90\) 0 0
\(91\) −192.000 −0.221177
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 580.000 0.626387
\(96\) 0 0
\(97\) 322.000 0.337053 0.168527 − 0.985697i \(-0.446099\pi\)
0.168527 + 0.985697i \(0.446099\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 946.000 0.931985 0.465993 − 0.884789i \(-0.345697\pi\)
0.465993 + 0.884789i \(0.345697\pi\)
\(102\) 0 0
\(103\) 424.000 0.405611 0.202806 − 0.979219i \(-0.434994\pi\)
0.202806 + 0.979219i \(0.434994\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1668.00 1.50702 0.753512 − 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(108\) 0 0
\(109\) −1634.00 −1.43586 −0.717930 − 0.696115i \(-0.754910\pi\)
−0.717930 + 0.696115i \(0.754910\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1686.00 −1.40359 −0.701794 − 0.712380i \(-0.747617\pi\)
−0.701794 + 0.712380i \(0.747617\pi\)
\(114\) 0 0
\(115\) −600.000 −0.486524
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1216.00 −0.936727
\(120\) 0 0
\(121\) 2765.00 2.07739
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 2640.00 1.84458 0.922292 − 0.386494i \(-0.126314\pi\)
0.922292 + 0.386494i \(0.126314\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2536.00 1.69138 0.845692 − 0.533671i \(-0.179188\pi\)
0.845692 + 0.533671i \(0.179188\pi\)
\(132\) 0 0
\(133\) −3712.00 −2.42008
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 634.000 0.395374 0.197687 − 0.980265i \(-0.436657\pi\)
0.197687 + 0.980265i \(0.436657\pi\)
\(138\) 0 0
\(139\) 2980.00 1.81842 0.909210 − 0.416338i \(-0.136687\pi\)
0.909210 + 0.416338i \(0.136687\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 384.000 0.224557
\(144\) 0 0
\(145\) −610.000 −0.349364
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 338.000 0.185839 0.0929196 − 0.995674i \(-0.470380\pi\)
0.0929196 + 0.995674i \(0.470380\pi\)
\(150\) 0 0
\(151\) −428.000 −0.230663 −0.115332 − 0.993327i \(-0.536793\pi\)
−0.115332 + 0.993327i \(0.536793\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −820.000 −0.424929
\(156\) 0 0
\(157\) 3010.00 1.53009 0.765045 − 0.643977i \(-0.222717\pi\)
0.765045 + 0.643977i \(0.222717\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3840.00 1.87972
\(162\) 0 0
\(163\) −132.000 −0.0634297 −0.0317148 − 0.999497i \(-0.510097\pi\)
−0.0317148 + 0.999497i \(0.510097\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2176.00 −1.00829 −0.504144 − 0.863620i \(-0.668192\pi\)
−0.504144 + 0.863620i \(0.668192\pi\)
\(168\) 0 0
\(169\) −2161.00 −0.983614
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2778.00 1.22085 0.610426 − 0.792073i \(-0.290998\pi\)
0.610426 + 0.792073i \(0.290998\pi\)
\(174\) 0 0
\(175\) 800.000 0.345568
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3888.00 1.62348 0.811740 − 0.584020i \(-0.198521\pi\)
0.811740 + 0.584020i \(0.198521\pi\)
\(180\) 0 0
\(181\) 1350.00 0.554391 0.277195 − 0.960814i \(-0.410595\pi\)
0.277195 + 0.960814i \(0.410595\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −730.000 −0.290112
\(186\) 0 0
\(187\) 2432.00 0.951045
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4760.00 1.80325 0.901627 − 0.432514i \(-0.142374\pi\)
0.901627 + 0.432514i \(0.142374\pi\)
\(192\) 0 0
\(193\) 1034.00 0.385642 0.192821 − 0.981234i \(-0.438236\pi\)
0.192821 + 0.981234i \(0.438236\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1354.00 0.489688 0.244844 − 0.969563i \(-0.421263\pi\)
0.244844 + 0.969563i \(0.421263\pi\)
\(198\) 0 0
\(199\) −2324.00 −0.827859 −0.413930 − 0.910309i \(-0.635844\pi\)
−0.413930 + 0.910309i \(0.635844\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3904.00 1.34979
\(204\) 0 0
\(205\) −1190.00 −0.405430
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 7424.00 2.45708
\(210\) 0 0
\(211\) −3220.00 −1.05059 −0.525294 − 0.850921i \(-0.676045\pi\)
−0.525294 + 0.850921i \(0.676045\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 740.000 0.234733
\(216\) 0 0
\(217\) 5248.00 1.64174
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 228.000 0.0693979
\(222\) 0 0
\(223\) −32.0000 −0.00960932 −0.00480466 − 0.999988i \(-0.501529\pi\)
−0.00480466 + 0.999988i \(0.501529\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3996.00 1.16839 0.584193 − 0.811614i \(-0.301411\pi\)
0.584193 + 0.811614i \(0.301411\pi\)
\(228\) 0 0
\(229\) −3010.00 −0.868587 −0.434293 − 0.900771i \(-0.643002\pi\)
−0.434293 + 0.900771i \(0.643002\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2698.00 0.758592 0.379296 − 0.925275i \(-0.376166\pi\)
0.379296 + 0.925275i \(0.376166\pi\)
\(234\) 0 0
\(235\) −920.000 −0.255380
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2200.00 0.595423 0.297712 − 0.954656i \(-0.403777\pi\)
0.297712 + 0.954656i \(0.403777\pi\)
\(240\) 0 0
\(241\) −6174.00 −1.65022 −0.825109 − 0.564974i \(-0.808886\pi\)
−0.825109 + 0.564974i \(0.808886\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3405.00 −0.887908
\(246\) 0 0
\(247\) 696.000 0.179293
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4808.00 −1.20908 −0.604538 − 0.796576i \(-0.706642\pi\)
−0.604538 + 0.796576i \(0.706642\pi\)
\(252\) 0 0
\(253\) −7680.00 −1.90845
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3974.00 −0.964558 −0.482279 − 0.876018i \(-0.660191\pi\)
−0.482279 + 0.876018i \(0.660191\pi\)
\(258\) 0 0
\(259\) 4672.00 1.12086
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1408.00 −0.330118 −0.165059 − 0.986284i \(-0.552781\pi\)
−0.165059 + 0.986284i \(0.552781\pi\)
\(264\) 0 0
\(265\) 2350.00 0.544752
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3258.00 0.738453 0.369226 − 0.929340i \(-0.379623\pi\)
0.369226 + 0.929340i \(0.379623\pi\)
\(270\) 0 0
\(271\) 8612.00 1.93041 0.965206 − 0.261490i \(-0.0842139\pi\)
0.965206 + 0.261490i \(0.0842139\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1600.00 −0.350850
\(276\) 0 0
\(277\) −4006.00 −0.868943 −0.434472 − 0.900686i \(-0.643065\pi\)
−0.434472 + 0.900686i \(0.643065\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6194.00 −1.31496 −0.657479 − 0.753473i \(-0.728377\pi\)
−0.657479 + 0.753473i \(0.728377\pi\)
\(282\) 0 0
\(283\) 1724.00 0.362124 0.181062 − 0.983472i \(-0.442046\pi\)
0.181062 + 0.983472i \(0.442046\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7616.00 1.56641
\(288\) 0 0
\(289\) −3469.00 −0.706086
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2502.00 −0.498868 −0.249434 − 0.968392i \(-0.580245\pi\)
−0.249434 + 0.968392i \(0.580245\pi\)
\(294\) 0 0
\(295\) −1080.00 −0.213153
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −720.000 −0.139260
\(300\) 0 0
\(301\) −4736.00 −0.906905
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4030.00 −0.756581
\(306\) 0 0
\(307\) −6404.00 −1.19054 −0.595270 − 0.803526i \(-0.702955\pi\)
−0.595270 + 0.803526i \(0.702955\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −896.000 −0.163368 −0.0816841 − 0.996658i \(-0.526030\pi\)
−0.0816841 + 0.996658i \(0.526030\pi\)
\(312\) 0 0
\(313\) −4110.00 −0.742207 −0.371104 − 0.928591i \(-0.621021\pi\)
−0.371104 + 0.928591i \(0.621021\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6926.00 −1.22714 −0.613569 − 0.789641i \(-0.710267\pi\)
−0.613569 + 0.789641i \(0.710267\pi\)
\(318\) 0 0
\(319\) −7808.00 −1.37042
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4408.00 0.759343
\(324\) 0 0
\(325\) −150.000 −0.0256015
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5888.00 0.986675
\(330\) 0 0
\(331\) −2692.00 −0.447026 −0.223513 − 0.974701i \(-0.571753\pi\)
−0.223513 + 0.974701i \(0.571753\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3660.00 0.596917
\(336\) 0 0
\(337\) 11914.0 1.92581 0.962903 − 0.269846i \(-0.0869728\pi\)
0.962903 + 0.269846i \(0.0869728\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10496.0 −1.66683
\(342\) 0 0
\(343\) 10816.0 1.70265
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6660.00 1.03034 0.515169 − 0.857088i \(-0.327729\pi\)
0.515169 + 0.857088i \(0.327729\pi\)
\(348\) 0 0
\(349\) 3046.00 0.467188 0.233594 − 0.972334i \(-0.424951\pi\)
0.233594 + 0.972334i \(0.424951\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3522.00 0.531040 0.265520 − 0.964105i \(-0.414456\pi\)
0.265520 + 0.964105i \(0.414456\pi\)
\(354\) 0 0
\(355\) 1320.00 0.197347
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8656.00 1.27255 0.636276 − 0.771461i \(-0.280474\pi\)
0.636276 + 0.771461i \(0.280474\pi\)
\(360\) 0 0
\(361\) 6597.00 0.961802
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3190.00 0.457458
\(366\) 0 0
\(367\) 936.000 0.133130 0.0665651 − 0.997782i \(-0.478796\pi\)
0.0665651 + 0.997782i \(0.478796\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −15040.0 −2.10468
\(372\) 0 0
\(373\) 11578.0 1.60720 0.803601 − 0.595169i \(-0.202915\pi\)
0.803601 + 0.595169i \(0.202915\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −732.000 −0.0999998
\(378\) 0 0
\(379\) 9948.00 1.34827 0.674135 − 0.738608i \(-0.264517\pi\)
0.674135 + 0.738608i \(0.264517\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8336.00 −1.11214 −0.556070 − 0.831135i \(-0.687691\pi\)
−0.556070 + 0.831135i \(0.687691\pi\)
\(384\) 0 0
\(385\) 10240.0 1.35553
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6370.00 0.830262 0.415131 − 0.909762i \(-0.363736\pi\)
0.415131 + 0.909762i \(0.363736\pi\)
\(390\) 0 0
\(391\) −4560.00 −0.589793
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2980.00 −0.379595
\(396\) 0 0
\(397\) 10394.0 1.31400 0.657002 − 0.753888i \(-0.271824\pi\)
0.657002 + 0.753888i \(0.271824\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7470.00 0.930259 0.465130 − 0.885243i \(-0.346008\pi\)
0.465130 + 0.885243i \(0.346008\pi\)
\(402\) 0 0
\(403\) −984.000 −0.121629
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9344.00 −1.13800
\(408\) 0 0
\(409\) 2810.00 0.339720 0.169860 − 0.985468i \(-0.445668\pi\)
0.169860 + 0.985468i \(0.445668\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6912.00 0.823529
\(414\) 0 0
\(415\) −4420.00 −0.522818
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4320.00 0.503689 0.251845 − 0.967768i \(-0.418963\pi\)
0.251845 + 0.967768i \(0.418963\pi\)
\(420\) 0 0
\(421\) −15122.0 −1.75060 −0.875298 − 0.483583i \(-0.839335\pi\)
−0.875298 + 0.483583i \(0.839335\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −950.000 −0.108428
\(426\) 0 0
\(427\) 25792.0 2.92310
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12616.0 1.40996 0.704978 − 0.709229i \(-0.250957\pi\)
0.704978 + 0.709229i \(0.250957\pi\)
\(432\) 0 0
\(433\) 15098.0 1.67567 0.837833 − 0.545926i \(-0.183822\pi\)
0.837833 + 0.545926i \(0.183822\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −13920.0 −1.52376
\(438\) 0 0
\(439\) −2372.00 −0.257880 −0.128940 − 0.991652i \(-0.541157\pi\)
−0.128940 + 0.991652i \(0.541157\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 36.0000 0.00386097 0.00193049 − 0.999998i \(-0.499386\pi\)
0.00193049 + 0.999998i \(0.499386\pi\)
\(444\) 0 0
\(445\) 4650.00 0.495351
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7330.00 −0.770432 −0.385216 − 0.922826i \(-0.625873\pi\)
−0.385216 + 0.922826i \(0.625873\pi\)
\(450\) 0 0
\(451\) −15232.0 −1.59035
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 960.000 0.0989132
\(456\) 0 0
\(457\) 9642.00 0.986945 0.493472 − 0.869761i \(-0.335727\pi\)
0.493472 + 0.869761i \(0.335727\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9654.00 −0.975340 −0.487670 − 0.873028i \(-0.662153\pi\)
−0.487670 + 0.873028i \(0.662153\pi\)
\(462\) 0 0
\(463\) −13960.0 −1.40124 −0.700622 − 0.713532i \(-0.747094\pi\)
−0.700622 + 0.713532i \(0.747094\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9996.00 −0.990492 −0.495246 − 0.868753i \(-0.664922\pi\)
−0.495246 + 0.868753i \(0.664922\pi\)
\(468\) 0 0
\(469\) −23424.0 −2.30623
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9472.00 0.920767
\(474\) 0 0
\(475\) −2900.00 −0.280129
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8736.00 0.833315 0.416658 − 0.909063i \(-0.363201\pi\)
0.416658 + 0.909063i \(0.363201\pi\)
\(480\) 0 0
\(481\) −876.000 −0.0830398
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1610.00 −0.150735
\(486\) 0 0
\(487\) 6712.00 0.624537 0.312269 − 0.949994i \(-0.398911\pi\)
0.312269 + 0.949994i \(0.398911\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2512.00 0.230886 0.115443 − 0.993314i \(-0.463171\pi\)
0.115443 + 0.993314i \(0.463171\pi\)
\(492\) 0 0
\(493\) −4636.00 −0.423519
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8448.00 −0.762464
\(498\) 0 0
\(499\) −5708.00 −0.512074 −0.256037 − 0.966667i \(-0.582417\pi\)
−0.256037 + 0.966667i \(0.582417\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5440.00 0.482222 0.241111 − 0.970498i \(-0.422488\pi\)
0.241111 + 0.970498i \(0.422488\pi\)
\(504\) 0 0
\(505\) −4730.00 −0.416797
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3942.00 −0.343273 −0.171637 − 0.985160i \(-0.554905\pi\)
−0.171637 + 0.985160i \(0.554905\pi\)
\(510\) 0 0
\(511\) −20416.0 −1.76742
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2120.00 −0.181395
\(516\) 0 0
\(517\) −11776.0 −1.00176
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2310.00 0.194247 0.0971237 − 0.995272i \(-0.469036\pi\)
0.0971237 + 0.995272i \(0.469036\pi\)
\(522\) 0 0
\(523\) −2956.00 −0.247145 −0.123573 − 0.992336i \(-0.539435\pi\)
−0.123573 + 0.992336i \(0.539435\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6232.00 −0.515124
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1428.00 −0.116048
\(534\) 0 0
\(535\) −8340.00 −0.673962
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −43584.0 −3.48292
\(540\) 0 0
\(541\) 2078.00 0.165139 0.0825695 − 0.996585i \(-0.473687\pi\)
0.0825695 + 0.996585i \(0.473687\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 8170.00 0.642136
\(546\) 0 0
\(547\) 6164.00 0.481816 0.240908 − 0.970548i \(-0.422555\pi\)
0.240908 + 0.970548i \(0.422555\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −14152.0 −1.09418
\(552\) 0 0
\(553\) 19072.0 1.46659
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13526.0 −1.02893 −0.514466 − 0.857511i \(-0.672010\pi\)
−0.514466 + 0.857511i \(0.672010\pi\)
\(558\) 0 0
\(559\) 888.000 0.0671885
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −276.000 −0.0206608 −0.0103304 − 0.999947i \(-0.503288\pi\)
−0.0103304 + 0.999947i \(0.503288\pi\)
\(564\) 0 0
\(565\) 8430.00 0.627704
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 774.000 0.0570260 0.0285130 − 0.999593i \(-0.490923\pi\)
0.0285130 + 0.999593i \(0.490923\pi\)
\(570\) 0 0
\(571\) −6676.00 −0.489285 −0.244643 − 0.969613i \(-0.578671\pi\)
−0.244643 + 0.969613i \(0.578671\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3000.00 0.217580
\(576\) 0 0
\(577\) −11774.0 −0.849494 −0.424747 − 0.905312i \(-0.639637\pi\)
−0.424747 + 0.905312i \(0.639637\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 28288.0 2.01994
\(582\) 0 0
\(583\) 30080.0 2.13685
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12292.0 0.864302 0.432151 − 0.901801i \(-0.357755\pi\)
0.432151 + 0.901801i \(0.357755\pi\)
\(588\) 0 0
\(589\) −19024.0 −1.33085
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −7110.00 −0.492365 −0.246183 − 0.969223i \(-0.579176\pi\)
−0.246183 + 0.969223i \(0.579176\pi\)
\(594\) 0 0
\(595\) 6080.00 0.418917
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4416.00 −0.301223 −0.150612 − 0.988593i \(-0.548124\pi\)
−0.150612 + 0.988593i \(0.548124\pi\)
\(600\) 0 0
\(601\) 3850.00 0.261306 0.130653 − 0.991428i \(-0.458293\pi\)
0.130653 + 0.991428i \(0.458293\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −13825.0 −0.929035
\(606\) 0 0
\(607\) −21880.0 −1.46307 −0.731534 − 0.681805i \(-0.761195\pi\)
−0.731534 + 0.681805i \(0.761195\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1104.00 −0.0730983
\(612\) 0 0
\(613\) 2786.00 0.183565 0.0917826 − 0.995779i \(-0.470744\pi\)
0.0917826 + 0.995779i \(0.470744\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1014.00 −0.0661622 −0.0330811 − 0.999453i \(-0.510532\pi\)
−0.0330811 + 0.999453i \(0.510532\pi\)
\(618\) 0 0
\(619\) 10708.0 0.695300 0.347650 − 0.937624i \(-0.386980\pi\)
0.347650 + 0.937624i \(0.386980\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −29760.0 −1.91382
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −5548.00 −0.351690
\(630\) 0 0
\(631\) −6660.00 −0.420175 −0.210087 − 0.977683i \(-0.567375\pi\)
−0.210087 + 0.977683i \(0.567375\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −13200.0 −0.824923
\(636\) 0 0
\(637\) −4086.00 −0.254149
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −90.0000 −0.00554569 −0.00277284 − 0.999996i \(-0.500883\pi\)
−0.00277284 + 0.999996i \(0.500883\pi\)
\(642\) 0 0
\(643\) −21684.0 −1.32991 −0.664956 − 0.746882i \(-0.731550\pi\)
−0.664956 + 0.746882i \(0.731550\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1344.00 0.0816663 0.0408331 − 0.999166i \(-0.486999\pi\)
0.0408331 + 0.999166i \(0.486999\pi\)
\(648\) 0 0
\(649\) −13824.0 −0.836116
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9210.00 0.551937 0.275969 − 0.961167i \(-0.411001\pi\)
0.275969 + 0.961167i \(0.411001\pi\)
\(654\) 0 0
\(655\) −12680.0 −0.756410
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −184.000 −0.0108765 −0.00543826 − 0.999985i \(-0.501731\pi\)
−0.00543826 + 0.999985i \(0.501731\pi\)
\(660\) 0 0
\(661\) −12866.0 −0.757079 −0.378540 − 0.925585i \(-0.623574\pi\)
−0.378540 + 0.925585i \(0.623574\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 18560.0 1.08229
\(666\) 0 0
\(667\) 14640.0 0.849870
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −51584.0 −2.96778
\(672\) 0 0
\(673\) −26534.0 −1.51978 −0.759889 − 0.650053i \(-0.774747\pi\)
−0.759889 + 0.650053i \(0.774747\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30062.0 −1.70661 −0.853306 − 0.521410i \(-0.825406\pi\)
−0.853306 + 0.521410i \(0.825406\pi\)
\(678\) 0 0
\(679\) 10304.0 0.582373
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12724.0 −0.712841 −0.356420 − 0.934326i \(-0.616003\pi\)
−0.356420 + 0.934326i \(0.616003\pi\)
\(684\) 0 0
\(685\) −3170.00 −0.176817
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2820.00 0.155927
\(690\) 0 0
\(691\) −21972.0 −1.20963 −0.604815 − 0.796366i \(-0.706753\pi\)
−0.604815 + 0.796366i \(0.706753\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14900.0 −0.813222
\(696\) 0 0
\(697\) −9044.00 −0.491486
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15642.0 0.842782 0.421391 − 0.906879i \(-0.361542\pi\)
0.421391 + 0.906879i \(0.361542\pi\)
\(702\) 0 0
\(703\) −16936.0 −0.908611
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 30272.0 1.61032
\(708\) 0 0
\(709\) 36398.0 1.92801 0.964003 − 0.265893i \(-0.0856668\pi\)
0.964003 + 0.265893i \(0.0856668\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 19680.0 1.03369
\(714\) 0 0
\(715\) −1920.00 −0.100425
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 36248.0 1.88014 0.940071 − 0.340978i \(-0.110758\pi\)
0.940071 + 0.340978i \(0.110758\pi\)
\(720\) 0 0
\(721\) 13568.0 0.700830
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3050.00 0.156240
\(726\) 0 0
\(727\) −4936.00 −0.251810 −0.125905 − 0.992042i \(-0.540184\pi\)
−0.125905 + 0.992042i \(0.540184\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5624.00 0.284557
\(732\) 0 0
\(733\) −23838.0 −1.20120 −0.600598 − 0.799551i \(-0.705071\pi\)
−0.600598 + 0.799551i \(0.705071\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 46848.0 2.34148
\(738\) 0 0
\(739\) 31700.0 1.57795 0.788974 − 0.614427i \(-0.210613\pi\)
0.788974 + 0.614427i \(0.210613\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13128.0 0.648209 0.324105 − 0.946021i \(-0.394937\pi\)
0.324105 + 0.946021i \(0.394937\pi\)
\(744\) 0 0
\(745\) −1690.00 −0.0831098
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 53376.0 2.60389
\(750\) 0 0
\(751\) −15676.0 −0.761685 −0.380842 − 0.924640i \(-0.624366\pi\)
−0.380842 + 0.924640i \(0.624366\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2140.00 0.103156
\(756\) 0 0
\(757\) −13238.0 −0.635592 −0.317796 − 0.948159i \(-0.602943\pi\)
−0.317796 + 0.948159i \(0.602943\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5270.00 0.251035 0.125517 − 0.992091i \(-0.459941\pi\)
0.125517 + 0.992091i \(0.459941\pi\)
\(762\) 0 0
\(763\) −52288.0 −2.48093
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1296.00 −0.0610115
\(768\) 0 0
\(769\) −8526.00 −0.399812 −0.199906 − 0.979815i \(-0.564064\pi\)
−0.199906 + 0.979815i \(0.564064\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −13606.0 −0.633084 −0.316542 − 0.948579i \(-0.602522\pi\)
−0.316542 + 0.948579i \(0.602522\pi\)
\(774\) 0 0
\(775\) 4100.00 0.190034
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −27608.0 −1.26978
\(780\) 0 0
\(781\) 16896.0 0.774118
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −15050.0 −0.684277
\(786\) 0 0
\(787\) −8836.00 −0.400215 −0.200108 − 0.979774i \(-0.564129\pi\)
−0.200108 + 0.979774i \(0.564129\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −53952.0 −2.42517
\(792\) 0 0
\(793\) −4836.00 −0.216559
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 29082.0 1.29252 0.646259 − 0.763118i \(-0.276332\pi\)
0.646259 + 0.763118i \(0.276332\pi\)
\(798\) 0 0
\(799\) −6992.00 −0.309586
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 40832.0 1.79443
\(804\) 0 0
\(805\) −19200.0 −0.840635
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26994.0 −1.17313 −0.586563 − 0.809904i \(-0.699519\pi\)
−0.586563 + 0.809904i \(0.699519\pi\)
\(810\) 0 0
\(811\) −9268.00 −0.401287 −0.200643 − 0.979664i \(-0.564303\pi\)
−0.200643 + 0.979664i \(0.564303\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 660.000 0.0283666
\(816\) 0 0
\(817\) 17168.0 0.735168
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −6286.00 −0.267214 −0.133607 − 0.991034i \(-0.542656\pi\)
−0.133607 + 0.991034i \(0.542656\pi\)
\(822\) 0 0
\(823\) 44088.0 1.86733 0.933664 − 0.358150i \(-0.116592\pi\)
0.933664 + 0.358150i \(0.116592\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −30100.0 −1.26563 −0.632817 − 0.774301i \(-0.718102\pi\)
−0.632817 + 0.774301i \(0.718102\pi\)
\(828\) 0 0
\(829\) 18254.0 0.764762 0.382381 − 0.924005i \(-0.375104\pi\)
0.382381 + 0.924005i \(0.375104\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −25878.0 −1.07637
\(834\) 0 0
\(835\) 10880.0 0.450920
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −13008.0 −0.535263 −0.267632 − 0.963521i \(-0.586241\pi\)
−0.267632 + 0.963521i \(0.586241\pi\)
\(840\) 0 0
\(841\) −9505.00 −0.389725
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10805.0 0.439886
\(846\) 0 0
\(847\) 88480.0 3.58938
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 17520.0 0.705732
\(852\) 0 0
\(853\) −16094.0 −0.646012 −0.323006 − 0.946397i \(-0.604693\pi\)
−0.323006 + 0.946397i \(0.604693\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 25938.0 1.03387 0.516934 − 0.856025i \(-0.327073\pi\)
0.516934 + 0.856025i \(0.327073\pi\)
\(858\) 0 0
\(859\) −38564.0 −1.53177 −0.765883 − 0.642980i \(-0.777698\pi\)
−0.765883 + 0.642980i \(0.777698\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −10216.0 −0.402963 −0.201481 − 0.979492i \(-0.564576\pi\)
−0.201481 + 0.979492i \(0.564576\pi\)
\(864\) 0 0
\(865\) −13890.0 −0.545982
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −38144.0 −1.48901
\(870\) 0 0
\(871\) 4392.00 0.170858
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4000.00 −0.154542
\(876\) 0 0
\(877\) −17006.0 −0.654791 −0.327396 − 0.944887i \(-0.606171\pi\)
−0.327396 + 0.944887i \(0.606171\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −43898.0 −1.67873 −0.839365 − 0.543568i \(-0.817073\pi\)
−0.839365 + 0.543568i \(0.817073\pi\)
\(882\) 0 0
\(883\) 29180.0 1.11210 0.556051 − 0.831149i \(-0.312316\pi\)
0.556051 + 0.831149i \(0.312316\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14752.0 0.558426 0.279213 − 0.960229i \(-0.409926\pi\)
0.279213 + 0.960229i \(0.409926\pi\)
\(888\) 0 0
\(889\) 84480.0 3.18714
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −21344.0 −0.799832
\(894\) 0 0
\(895\) −19440.0 −0.726042
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 20008.0 0.742274
\(900\) 0 0
\(901\) 17860.0 0.660381
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6750.00 −0.247931
\(906\) 0 0
\(907\) −12020.0 −0.440041 −0.220021 − 0.975495i \(-0.570612\pi\)
−0.220021 + 0.975495i \(0.570612\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 18560.0 0.674995 0.337497 − 0.941326i \(-0.390420\pi\)
0.337497 + 0.941326i \(0.390420\pi\)
\(912\) 0 0
\(913\) −56576.0 −2.05081
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 81152.0 2.92244
\(918\) 0 0
\(919\) −10244.0 −0.367702 −0.183851 − 0.982954i \(-0.558856\pi\)
−0.183851 + 0.982954i \(0.558856\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1584.00 0.0564875
\(924\) 0 0
\(925\) 3650.00 0.129742
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1266.00 −0.0447106 −0.0223553 − 0.999750i \(-0.507116\pi\)
−0.0223553 + 0.999750i \(0.507116\pi\)
\(930\) 0 0
\(931\) −78996.0 −2.78087
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −12160.0 −0.425320
\(936\) 0 0
\(937\) 47626.0 1.66048 0.830242 − 0.557403i \(-0.188202\pi\)
0.830242 + 0.557403i \(0.188202\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −31958.0 −1.10712 −0.553561 − 0.832809i \(-0.686731\pi\)
−0.553561 + 0.832809i \(0.686731\pi\)
\(942\) 0 0
\(943\) 28560.0 0.986258
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −25196.0 −0.864583 −0.432291 − 0.901734i \(-0.642295\pi\)
−0.432291 + 0.901734i \(0.642295\pi\)
\(948\) 0 0
\(949\) 3828.00 0.130940
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −51574.0 −1.75304 −0.876519 − 0.481367i \(-0.840141\pi\)
−0.876519 + 0.481367i \(0.840141\pi\)
\(954\) 0 0
\(955\) −23800.0 −0.806440
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 20288.0 0.683143
\(960\) 0 0
\(961\) −2895.00 −0.0971770
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5170.00 −0.172464
\(966\) 0 0
\(967\) 48296.0 1.60610 0.803048 − 0.595914i \(-0.203210\pi\)
0.803048 + 0.595914i \(0.203210\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 27288.0 0.901868 0.450934 − 0.892557i \(-0.351091\pi\)
0.450934 + 0.892557i \(0.351091\pi\)
\(972\) 0 0
\(973\) 95360.0 3.14193
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −14406.0 −0.471739 −0.235869 − 0.971785i \(-0.575794\pi\)
−0.235869 + 0.971785i \(0.575794\pi\)
\(978\) 0 0
\(979\) 59520.0 1.94307
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −18952.0 −0.614929 −0.307464 − 0.951560i \(-0.599480\pi\)
−0.307464 + 0.951560i \(0.599480\pi\)
\(984\) 0 0
\(985\) −6770.00 −0.218995
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −17760.0 −0.571016
\(990\) 0 0
\(991\) −44308.0 −1.42027 −0.710136 − 0.704064i \(-0.751367\pi\)
−0.710136 + 0.704064i \(0.751367\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 11620.0 0.370230
\(996\) 0 0
\(997\) 954.000 0.0303044 0.0151522 − 0.999885i \(-0.495177\pi\)
0.0151522 + 0.999885i \(0.495177\pi\)
\(998\) 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 1440.4.a.j.1.1 1
3.2 odd 2 480.4.a.l.1.1 yes 1
4.3 odd 2 1440.4.a.a.1.1 1
12.11 even 2 480.4.a.c.1.1 ✓ 1
15.14 odd 2 2400.4.a.a.1.1 1
24.5 odd 2 960.4.a.i.1.1 1
24.11 even 2 960.4.a.t.1.1 1
60.59 even 2 2400.4.a.v.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
480.4.a.c.1.1 ✓ 1 12.11 even 2
480.4.a.l.1.1 yes 1 3.2 odd 2
960.4.a.i.1.1 1 24.5 odd 2
960.4.a.t.1.1 1 24.11 even 2
1440.4.a.a.1.1 1 4.3 odd 2
1440.4.a.j.1.1 1 1.1 even 1 trivial
2400.4.a.a.1.1 1 15.14 odd 2
2400.4.a.v.1.1 1 60.59 even 2