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Properties

Label 2160.4.a.m.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
Analytic rank $1$
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] = [2160,4,Mod(1,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, 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("2160.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.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: \(127.444125612\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -8.00000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -8.00000 q^{7} -18.0000 q^{11} +8.00000 q^{13} +15.0000 q^{17} -23.0000 q^{19} -63.0000 q^{23} +25.0000 q^{25} +156.000 q^{29} +85.0000 q^{31} -40.0000 q^{35} +74.0000 q^{37} +246.000 q^{41} +190.000 q^{43} -288.000 q^{47} -279.000 q^{49} -177.000 q^{53} -90.0000 q^{55} -792.000 q^{59} -907.000 q^{61} +40.0000 q^{65} +322.000 q^{67} +270.000 q^{71} +254.000 q^{73} +144.000 q^{77} +1123.00 q^{79} +771.000 q^{83} +75.0000 q^{85} -198.000 q^{89} -64.0000 q^{91} -115.000 q^{95} -1192.00 q^{97} +O(q^{100})\)

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
\(7\) −8.00000 −0.431959 −0.215980 − 0.976398i \(-0.569295\pi\)
−0.215980 + 0.976398i \(0.569295\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −18.0000 −0.493382 −0.246691 − 0.969094i \(-0.579343\pi\)
−0.246691 + 0.969094i \(0.579343\pi\)
\(12\) 0 0
\(13\) 8.00000 0.170677 0.0853385 − 0.996352i \(-0.472803\pi\)
0.0853385 + 0.996352i \(0.472803\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 15.0000 0.214002 0.107001 − 0.994259i \(-0.465875\pi\)
0.107001 + 0.994259i \(0.465875\pi\)
\(18\) 0 0
\(19\) −23.0000 −0.277714 −0.138857 − 0.990312i \(-0.544343\pi\)
−0.138857 + 0.990312i \(0.544343\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −63.0000 −0.571148 −0.285574 − 0.958357i \(-0.592184\pi\)
−0.285574 + 0.958357i \(0.592184\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 156.000 0.998913 0.499456 − 0.866339i \(-0.333533\pi\)
0.499456 + 0.866339i \(0.333533\pi\)
\(30\) 0 0
\(31\) 85.0000 0.492466 0.246233 − 0.969211i \(-0.420807\pi\)
0.246233 + 0.969211i \(0.420807\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −40.0000 −0.193178
\(36\) 0 0
\(37\) 74.0000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 246.000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 190.000 0.673831 0.336915 − 0.941535i \(-0.390616\pi\)
0.336915 + 0.941535i \(0.390616\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −288.000 −0.893811 −0.446906 − 0.894581i \(-0.647474\pi\)
−0.446906 + 0.894581i \(0.647474\pi\)
\(48\) 0 0
\(49\) −279.000 −0.813411
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −177.000 −0.458732 −0.229366 − 0.973340i \(-0.573665\pi\)
−0.229366 + 0.973340i \(0.573665\pi\)
\(54\) 0 0
\(55\) −90.0000 −0.220647
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −792.000 −1.74762 −0.873810 − 0.486267i \(-0.838358\pi\)
−0.873810 + 0.486267i \(0.838358\pi\)
\(60\) 0 0
\(61\) −907.000 −1.90376 −0.951881 − 0.306469i \(-0.900853\pi\)
−0.951881 + 0.306469i \(0.900853\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 40.0000 0.0763291
\(66\) 0 0
\(67\) 322.000 0.587143 0.293571 − 0.955937i \(-0.405156\pi\)
0.293571 + 0.955937i \(0.405156\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 270.000 0.451311 0.225656 − 0.974207i \(-0.427548\pi\)
0.225656 + 0.974207i \(0.427548\pi\)
\(72\) 0 0
\(73\) 254.000 0.407239 0.203620 − 0.979050i \(-0.434729\pi\)
0.203620 + 0.979050i \(0.434729\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 144.000 0.213121
\(78\) 0 0
\(79\) 1123.00 1.59933 0.799667 − 0.600444i \(-0.205009\pi\)
0.799667 + 0.600444i \(0.205009\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 771.000 1.01962 0.509809 − 0.860288i \(-0.329716\pi\)
0.509809 + 0.860288i \(0.329716\pi\)
\(84\) 0 0
\(85\) 75.0000 0.0957046
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −198.000 −0.235820 −0.117910 − 0.993024i \(-0.537619\pi\)
−0.117910 + 0.993024i \(0.537619\pi\)
\(90\) 0 0
\(91\) −64.0000 −0.0737255
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −115.000 −0.124197
\(96\) 0 0
\(97\) −1192.00 −1.24772 −0.623862 − 0.781534i \(-0.714437\pi\)
−0.623862 + 0.781534i \(0.714437\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1692.00 −1.66693 −0.833467 − 0.552570i \(-0.813647\pi\)
−0.833467 + 0.552570i \(0.813647\pi\)
\(102\) 0 0
\(103\) −1748.00 −1.67219 −0.836095 − 0.548585i \(-0.815167\pi\)
−0.836095 + 0.548585i \(0.815167\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 948.000 0.856510 0.428255 − 0.903658i \(-0.359128\pi\)
0.428255 + 0.903658i \(0.359128\pi\)
\(108\) 0 0
\(109\) 593.000 0.521093 0.260546 − 0.965461i \(-0.416097\pi\)
0.260546 + 0.965461i \(0.416097\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1062.00 −0.884111 −0.442056 − 0.896988i \(-0.645751\pi\)
−0.442056 + 0.896988i \(0.645751\pi\)
\(114\) 0 0
\(115\) −315.000 −0.255425
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −120.000 −0.0924402
\(120\) 0 0
\(121\) −1007.00 −0.756574
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −326.000 −0.227778 −0.113889 − 0.993493i \(-0.536331\pi\)
−0.113889 + 0.993493i \(0.536331\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 990.000 0.660280 0.330140 − 0.943932i \(-0.392904\pi\)
0.330140 + 0.943932i \(0.392904\pi\)
\(132\) 0 0
\(133\) 184.000 0.119961
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −147.000 −0.0916720 −0.0458360 − 0.998949i \(-0.514595\pi\)
−0.0458360 + 0.998949i \(0.514595\pi\)
\(138\) 0 0
\(139\) −1604.00 −0.978773 −0.489387 − 0.872067i \(-0.662779\pi\)
−0.489387 + 0.872067i \(0.662779\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −144.000 −0.0842090
\(144\) 0 0
\(145\) 780.000 0.446727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1218.00 0.669681 0.334840 − 0.942275i \(-0.391318\pi\)
0.334840 + 0.942275i \(0.391318\pi\)
\(150\) 0 0
\(151\) 2248.00 1.21152 0.605760 − 0.795647i \(-0.292869\pi\)
0.605760 + 0.795647i \(0.292869\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 425.000 0.220238
\(156\) 0 0
\(157\) −2998.00 −1.52399 −0.761995 − 0.647583i \(-0.775780\pi\)
−0.761995 + 0.647583i \(0.775780\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 504.000 0.246713
\(162\) 0 0
\(163\) −3470.00 −1.66743 −0.833716 − 0.552194i \(-0.813791\pi\)
−0.833716 + 0.552194i \(0.813791\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −387.000 −0.179323 −0.0896616 − 0.995972i \(-0.528579\pi\)
−0.0896616 + 0.995972i \(0.528579\pi\)
\(168\) 0 0
\(169\) −2133.00 −0.970869
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −855.000 −0.375748 −0.187874 − 0.982193i \(-0.560160\pi\)
−0.187874 + 0.982193i \(0.560160\pi\)
\(174\) 0 0
\(175\) −200.000 −0.0863919
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 264.000 0.110236 0.0551181 − 0.998480i \(-0.482446\pi\)
0.0551181 + 0.998480i \(0.482446\pi\)
\(180\) 0 0
\(181\) −2551.00 −1.04759 −0.523797 − 0.851843i \(-0.675485\pi\)
−0.523797 + 0.851843i \(0.675485\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 370.000 0.147043
\(186\) 0 0
\(187\) −270.000 −0.105585
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2238.00 0.847832 0.423916 − 0.905701i \(-0.360655\pi\)
0.423916 + 0.905701i \(0.360655\pi\)
\(192\) 0 0
\(193\) 2180.00 0.813056 0.406528 − 0.913638i \(-0.366739\pi\)
0.406528 + 0.913638i \(0.366739\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2577.00 0.931998 0.465999 − 0.884785i \(-0.345695\pi\)
0.465999 + 0.884785i \(0.345695\pi\)
\(198\) 0 0
\(199\) −1412.00 −0.502985 −0.251493 − 0.967859i \(-0.580921\pi\)
−0.251493 + 0.967859i \(0.580921\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1248.00 −0.431490
\(204\) 0 0
\(205\) 1230.00 0.419058
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 414.000 0.137019
\(210\) 0 0
\(211\) 307.000 0.100165 0.0500823 − 0.998745i \(-0.484052\pi\)
0.0500823 + 0.998745i \(0.484052\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 950.000 0.301346
\(216\) 0 0
\(217\) −680.000 −0.212725
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 120.000 0.0365252
\(222\) 0 0
\(223\) −5234.00 −1.57172 −0.785862 − 0.618402i \(-0.787781\pi\)
−0.785862 + 0.618402i \(0.787781\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1509.00 −0.441215 −0.220608 − 0.975363i \(-0.570804\pi\)
−0.220608 + 0.975363i \(0.570804\pi\)
\(228\) 0 0
\(229\) 1211.00 0.349455 0.174727 − 0.984617i \(-0.444096\pi\)
0.174727 + 0.984617i \(0.444096\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6246.00 1.75618 0.878088 − 0.478499i \(-0.158819\pi\)
0.878088 + 0.478499i \(0.158819\pi\)
\(234\) 0 0
\(235\) −1440.00 −0.399724
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4650.00 −1.25851 −0.629254 − 0.777200i \(-0.716640\pi\)
−0.629254 + 0.777200i \(0.716640\pi\)
\(240\) 0 0
\(241\) −3145.00 −0.840611 −0.420306 − 0.907383i \(-0.638077\pi\)
−0.420306 + 0.907383i \(0.638077\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1395.00 −0.363768
\(246\) 0 0
\(247\) −184.000 −0.0473994
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1020.00 −0.256501 −0.128251 − 0.991742i \(-0.540936\pi\)
−0.128251 + 0.991742i \(0.540936\pi\)
\(252\) 0 0
\(253\) 1134.00 0.281794
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6741.00 1.63616 0.818078 − 0.575107i \(-0.195040\pi\)
0.818078 + 0.575107i \(0.195040\pi\)
\(258\) 0 0
\(259\) −592.000 −0.142027
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2340.00 −0.548633 −0.274317 − 0.961639i \(-0.588452\pi\)
−0.274317 + 0.961639i \(0.588452\pi\)
\(264\) 0 0
\(265\) −885.000 −0.205151
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6198.00 −1.40483 −0.702414 − 0.711769i \(-0.747894\pi\)
−0.702414 + 0.711769i \(0.747894\pi\)
\(270\) 0 0
\(271\) −875.000 −0.196135 −0.0980673 − 0.995180i \(-0.531266\pi\)
−0.0980673 + 0.995180i \(0.531266\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −450.000 −0.0986764
\(276\) 0 0
\(277\) 5486.00 1.18997 0.594985 − 0.803737i \(-0.297158\pi\)
0.594985 + 0.803737i \(0.297158\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3204.00 −0.680194 −0.340097 − 0.940390i \(-0.610460\pi\)
−0.340097 + 0.940390i \(0.610460\pi\)
\(282\) 0 0
\(283\) −7322.00 −1.53798 −0.768989 − 0.639262i \(-0.779240\pi\)
−0.768989 + 0.639262i \(0.779240\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1968.00 −0.404764
\(288\) 0 0
\(289\) −4688.00 −0.954203
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1353.00 0.269772 0.134886 − 0.990861i \(-0.456933\pi\)
0.134886 + 0.990861i \(0.456933\pi\)
\(294\) 0 0
\(295\) −3960.00 −0.781560
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −504.000 −0.0974818
\(300\) 0 0
\(301\) −1520.00 −0.291068
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4535.00 −0.851388
\(306\) 0 0
\(307\) −1658.00 −0.308231 −0.154116 − 0.988053i \(-0.549253\pi\)
−0.154116 + 0.988053i \(0.549253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1044.00 0.190353 0.0951765 − 0.995460i \(-0.469658\pi\)
0.0951765 + 0.995460i \(0.469658\pi\)
\(312\) 0 0
\(313\) 2588.00 0.467356 0.233678 − 0.972314i \(-0.424924\pi\)
0.233678 + 0.972314i \(0.424924\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1449.00 −0.256732 −0.128366 − 0.991727i \(-0.540973\pi\)
−0.128366 + 0.991727i \(0.540973\pi\)
\(318\) 0 0
\(319\) −2808.00 −0.492846
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −345.000 −0.0594313
\(324\) 0 0
\(325\) 200.000 0.0341354
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2304.00 0.386090
\(330\) 0 0
\(331\) −4880.00 −0.810360 −0.405180 − 0.914237i \(-0.632791\pi\)
−0.405180 + 0.914237i \(0.632791\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1610.00 0.262578
\(336\) 0 0
\(337\) −7744.00 −1.25176 −0.625879 − 0.779920i \(-0.715260\pi\)
−0.625879 + 0.779920i \(0.715260\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1530.00 −0.242974
\(342\) 0 0
\(343\) 4976.00 0.783320
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −804.000 −0.124383 −0.0621916 − 0.998064i \(-0.519809\pi\)
−0.0621916 + 0.998064i \(0.519809\pi\)
\(348\) 0 0
\(349\) −2815.00 −0.431758 −0.215879 − 0.976420i \(-0.569262\pi\)
−0.215879 + 0.976420i \(0.569262\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3738.00 −0.563608 −0.281804 − 0.959472i \(-0.590933\pi\)
−0.281804 + 0.959472i \(0.590933\pi\)
\(354\) 0 0
\(355\) 1350.00 0.201833
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11022.0 1.62039 0.810193 − 0.586163i \(-0.199362\pi\)
0.810193 + 0.586163i \(0.199362\pi\)
\(360\) 0 0
\(361\) −6330.00 −0.922875
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1270.00 0.182123
\(366\) 0 0
\(367\) −7544.00 −1.07301 −0.536504 − 0.843898i \(-0.680255\pi\)
−0.536504 + 0.843898i \(0.680255\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1416.00 0.198154
\(372\) 0 0
\(373\) −5404.00 −0.750157 −0.375078 − 0.926993i \(-0.622384\pi\)
−0.375078 + 0.926993i \(0.622384\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1248.00 0.170491
\(378\) 0 0
\(379\) 2335.00 0.316467 0.158233 − 0.987402i \(-0.449420\pi\)
0.158233 + 0.987402i \(0.449420\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6633.00 0.884936 0.442468 − 0.896784i \(-0.354103\pi\)
0.442468 + 0.896784i \(0.354103\pi\)
\(384\) 0 0
\(385\) 720.000 0.0953106
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7566.00 −0.986148 −0.493074 − 0.869987i \(-0.664127\pi\)
−0.493074 + 0.869987i \(0.664127\pi\)
\(390\) 0 0
\(391\) −945.000 −0.122227
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5615.00 0.715244
\(396\) 0 0
\(397\) −7420.00 −0.938033 −0.469017 − 0.883189i \(-0.655392\pi\)
−0.469017 + 0.883189i \(0.655392\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8502.00 −1.05878 −0.529389 − 0.848379i \(-0.677579\pi\)
−0.529389 + 0.848379i \(0.677579\pi\)
\(402\) 0 0
\(403\) 680.000 0.0840526
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1332.00 −0.162223
\(408\) 0 0
\(409\) −1903.00 −0.230067 −0.115033 − 0.993362i \(-0.536697\pi\)
−0.115033 + 0.993362i \(0.536697\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6336.00 0.754901
\(414\) 0 0
\(415\) 3855.00 0.455987
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13482.0 −1.57193 −0.785965 − 0.618271i \(-0.787834\pi\)
−0.785965 + 0.618271i \(0.787834\pi\)
\(420\) 0 0
\(421\) −1537.00 −0.177931 −0.0889653 − 0.996035i \(-0.528356\pi\)
−0.0889653 + 0.996035i \(0.528356\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 375.000 0.0428004
\(426\) 0 0
\(427\) 7256.00 0.822348
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10368.0 1.15872 0.579361 − 0.815071i \(-0.303302\pi\)
0.579361 + 0.815071i \(0.303302\pi\)
\(432\) 0 0
\(433\) −13168.0 −1.46146 −0.730732 − 0.682665i \(-0.760821\pi\)
−0.730732 + 0.682665i \(0.760821\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1449.00 0.158616
\(438\) 0 0
\(439\) −7319.00 −0.795710 −0.397855 − 0.917448i \(-0.630245\pi\)
−0.397855 + 0.917448i \(0.630245\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4119.00 0.441760 0.220880 − 0.975301i \(-0.429107\pi\)
0.220880 + 0.975301i \(0.429107\pi\)
\(444\) 0 0
\(445\) −990.000 −0.105462
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5388.00 −0.566315 −0.283158 − 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) −4428.00 −0.462320
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −320.000 −0.0329711
\(456\) 0 0
\(457\) −2752.00 −0.281692 −0.140846 − 0.990032i \(-0.544982\pi\)
−0.140846 + 0.990032i \(0.544982\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4314.00 −0.435842 −0.217921 − 0.975966i \(-0.569927\pi\)
−0.217921 + 0.975966i \(0.569927\pi\)
\(462\) 0 0
\(463\) 5794.00 0.581577 0.290788 − 0.956787i \(-0.406082\pi\)
0.290788 + 0.956787i \(0.406082\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6309.00 −0.625151 −0.312576 − 0.949893i \(-0.601192\pi\)
−0.312576 + 0.949893i \(0.601192\pi\)
\(468\) 0 0
\(469\) −2576.00 −0.253622
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3420.00 −0.332456
\(474\) 0 0
\(475\) −575.000 −0.0555428
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14826.0 −1.41423 −0.707116 − 0.707097i \(-0.750004\pi\)
−0.707116 + 0.707097i \(0.750004\pi\)
\(480\) 0 0
\(481\) 592.000 0.0561182
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5960.00 −0.557999
\(486\) 0 0
\(487\) −6758.00 −0.628818 −0.314409 − 0.949288i \(-0.601806\pi\)
−0.314409 + 0.949288i \(0.601806\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14574.0 1.33954 0.669771 − 0.742567i \(-0.266392\pi\)
0.669771 + 0.742567i \(0.266392\pi\)
\(492\) 0 0
\(493\) 2340.00 0.213769
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2160.00 −0.194948
\(498\) 0 0
\(499\) −12611.0 −1.13135 −0.565677 − 0.824627i \(-0.691385\pi\)
−0.565677 + 0.824627i \(0.691385\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −15639.0 −1.38630 −0.693150 − 0.720794i \(-0.743778\pi\)
−0.693150 + 0.720794i \(0.743778\pi\)
\(504\) 0 0
\(505\) −8460.00 −0.745475
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15420.0 1.34279 0.671394 − 0.741100i \(-0.265696\pi\)
0.671394 + 0.741100i \(0.265696\pi\)
\(510\) 0 0
\(511\) −2032.00 −0.175911
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8740.00 −0.747826
\(516\) 0 0
\(517\) 5184.00 0.440990
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10494.0 0.882439 0.441219 − 0.897399i \(-0.354546\pi\)
0.441219 + 0.897399i \(0.354546\pi\)
\(522\) 0 0
\(523\) 10708.0 0.895274 0.447637 − 0.894215i \(-0.352266\pi\)
0.447637 + 0.894215i \(0.352266\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1275.00 0.105389
\(528\) 0 0
\(529\) −8198.00 −0.673790
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1968.00 0.159932
\(534\) 0 0
\(535\) 4740.00 0.383043
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5022.00 0.401323
\(540\) 0 0
\(541\) 23030.0 1.83020 0.915099 − 0.403229i \(-0.132112\pi\)
0.915099 + 0.403229i \(0.132112\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2965.00 0.233040
\(546\) 0 0
\(547\) 3814.00 0.298126 0.149063 − 0.988828i \(-0.452374\pi\)
0.149063 + 0.988828i \(0.452374\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3588.00 −0.277412
\(552\) 0 0
\(553\) −8984.00 −0.690847
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22266.0 1.69379 0.846895 − 0.531761i \(-0.178469\pi\)
0.846895 + 0.531761i \(0.178469\pi\)
\(558\) 0 0
\(559\) 1520.00 0.115007
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23844.0 1.78491 0.892455 − 0.451136i \(-0.148981\pi\)
0.892455 + 0.451136i \(0.148981\pi\)
\(564\) 0 0
\(565\) −5310.00 −0.395387
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7488.00 0.551693 0.275846 − 0.961202i \(-0.411042\pi\)
0.275846 + 0.961202i \(0.411042\pi\)
\(570\) 0 0
\(571\) −5111.00 −0.374586 −0.187293 − 0.982304i \(-0.559971\pi\)
−0.187293 + 0.982304i \(0.559971\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1575.00 −0.114230
\(576\) 0 0
\(577\) 6986.00 0.504040 0.252020 − 0.967722i \(-0.418905\pi\)
0.252020 + 0.967722i \(0.418905\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6168.00 −0.440433
\(582\) 0 0
\(583\) 3186.00 0.226330
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20571.0 −1.44643 −0.723216 − 0.690622i \(-0.757337\pi\)
−0.723216 + 0.690622i \(0.757337\pi\)
\(588\) 0 0
\(589\) −1955.00 −0.136765
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 23241.0 1.60943 0.804716 − 0.593660i \(-0.202317\pi\)
0.804716 + 0.593660i \(0.202317\pi\)
\(594\) 0 0
\(595\) −600.000 −0.0413405
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20208.0 −1.37842 −0.689212 − 0.724559i \(-0.742043\pi\)
−0.689212 + 0.724559i \(0.742043\pi\)
\(600\) 0 0
\(601\) −9055.00 −0.614578 −0.307289 − 0.951616i \(-0.599422\pi\)
−0.307289 + 0.951616i \(0.599422\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5035.00 −0.338350
\(606\) 0 0
\(607\) −15554.0 −1.04006 −0.520031 − 0.854148i \(-0.674080\pi\)
−0.520031 + 0.854148i \(0.674080\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2304.00 −0.152553
\(612\) 0 0
\(613\) −5632.00 −0.371084 −0.185542 − 0.982636i \(-0.559404\pi\)
−0.185542 + 0.982636i \(0.559404\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9141.00 −0.596439 −0.298219 − 0.954497i \(-0.596393\pi\)
−0.298219 + 0.954497i \(0.596393\pi\)
\(618\) 0 0
\(619\) 13372.0 0.868281 0.434141 − 0.900845i \(-0.357052\pi\)
0.434141 + 0.900845i \(0.357052\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1584.00 0.101865
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1110.00 0.0703634
\(630\) 0 0
\(631\) −11165.0 −0.704392 −0.352196 − 0.935926i \(-0.614565\pi\)
−0.352196 + 0.935926i \(0.614565\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1630.00 −0.101865
\(636\) 0 0
\(637\) −2232.00 −0.138831
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −912.000 −0.0561963 −0.0280982 − 0.999605i \(-0.508945\pi\)
−0.0280982 + 0.999605i \(0.508945\pi\)
\(642\) 0 0
\(643\) 27952.0 1.71434 0.857169 − 0.515035i \(-0.172221\pi\)
0.857169 + 0.515035i \(0.172221\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6285.00 0.381899 0.190950 − 0.981600i \(-0.438843\pi\)
0.190950 + 0.981600i \(0.438843\pi\)
\(648\) 0 0
\(649\) 14256.0 0.862245
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −16497.0 −0.988633 −0.494317 − 0.869282i \(-0.664582\pi\)
−0.494317 + 0.869282i \(0.664582\pi\)
\(654\) 0 0
\(655\) 4950.00 0.295286
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −14844.0 −0.877451 −0.438725 − 0.898621i \(-0.644570\pi\)
−0.438725 + 0.898621i \(0.644570\pi\)
\(660\) 0 0
\(661\) 31934.0 1.87911 0.939553 − 0.342404i \(-0.111241\pi\)
0.939553 + 0.342404i \(0.111241\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 920.000 0.0536482
\(666\) 0 0
\(667\) −9828.00 −0.570527
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 16326.0 0.939282
\(672\) 0 0
\(673\) −24352.0 −1.39480 −0.697400 − 0.716682i \(-0.745660\pi\)
−0.697400 + 0.716682i \(0.745660\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10374.0 −0.588929 −0.294465 − 0.955662i \(-0.595141\pi\)
−0.294465 + 0.955662i \(0.595141\pi\)
\(678\) 0 0
\(679\) 9536.00 0.538966
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 7347.00 0.411603 0.205802 − 0.978594i \(-0.434020\pi\)
0.205802 + 0.978594i \(0.434020\pi\)
\(684\) 0 0
\(685\) −735.000 −0.0409969
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1416.00 −0.0782951
\(690\) 0 0
\(691\) 5371.00 0.295691 0.147845 − 0.989010i \(-0.452766\pi\)
0.147845 + 0.989010i \(0.452766\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8020.00 −0.437721
\(696\) 0 0
\(697\) 3690.00 0.200529
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7086.00 0.381790 0.190895 − 0.981610i \(-0.438861\pi\)
0.190895 + 0.981610i \(0.438861\pi\)
\(702\) 0 0
\(703\) −1702.00 −0.0913117
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13536.0 0.720048
\(708\) 0 0
\(709\) 17186.0 0.910344 0.455172 − 0.890404i \(-0.349578\pi\)
0.455172 + 0.890404i \(0.349578\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5355.00 −0.281271
\(714\) 0 0
\(715\) −720.000 −0.0376594
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 23814.0 1.23520 0.617602 − 0.786490i \(-0.288104\pi\)
0.617602 + 0.786490i \(0.288104\pi\)
\(720\) 0 0
\(721\) 13984.0 0.722318
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3900.00 0.199783
\(726\) 0 0
\(727\) 22732.0 1.15967 0.579837 − 0.814732i \(-0.303116\pi\)
0.579837 + 0.814732i \(0.303116\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2850.00 0.144201
\(732\) 0 0
\(733\) 4664.00 0.235019 0.117509 − 0.993072i \(-0.462509\pi\)
0.117509 + 0.993072i \(0.462509\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5796.00 −0.289686
\(738\) 0 0
\(739\) −5501.00 −0.273826 −0.136913 − 0.990583i \(-0.543718\pi\)
−0.136913 + 0.990583i \(0.543718\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 27096.0 1.33789 0.668947 − 0.743310i \(-0.266745\pi\)
0.668947 + 0.743310i \(0.266745\pi\)
\(744\) 0 0
\(745\) 6090.00 0.299490
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7584.00 −0.369978
\(750\) 0 0
\(751\) 5659.00 0.274967 0.137483 − 0.990504i \(-0.456099\pi\)
0.137483 + 0.990504i \(0.456099\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 11240.0 0.541809
\(756\) 0 0
\(757\) 37694.0 1.80979 0.904895 − 0.425634i \(-0.139949\pi\)
0.904895 + 0.425634i \(0.139949\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6588.00 −0.313817 −0.156909 − 0.987613i \(-0.550153\pi\)
−0.156909 + 0.987613i \(0.550153\pi\)
\(762\) 0 0
\(763\) −4744.00 −0.225091
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6336.00 −0.298279
\(768\) 0 0
\(769\) −19.0000 −0.000890972 0 −0.000445486 − 1.00000i \(-0.500142\pi\)
−0.000445486 1.00000i \(0.500142\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 33639.0 1.56521 0.782607 − 0.622516i \(-0.213889\pi\)
0.782607 + 0.622516i \(0.213889\pi\)
\(774\) 0 0
\(775\) 2125.00 0.0984932
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5658.00 −0.260230
\(780\) 0 0
\(781\) −4860.00 −0.222669
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −14990.0 −0.681549
\(786\) 0 0
\(787\) −23474.0 −1.06322 −0.531612 − 0.846988i \(-0.678414\pi\)
−0.531612 + 0.846988i \(0.678414\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8496.00 0.381900
\(792\) 0 0
\(793\) −7256.00 −0.324928
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7917.00 0.351863 0.175931 − 0.984402i \(-0.443706\pi\)
0.175931 + 0.984402i \(0.443706\pi\)
\(798\) 0 0
\(799\) −4320.00 −0.191277
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4572.00 −0.200925
\(804\) 0 0
\(805\) 2520.00 0.110333
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −41202.0 −1.79059 −0.895294 − 0.445476i \(-0.853034\pi\)
−0.895294 + 0.445476i \(0.853034\pi\)
\(810\) 0 0
\(811\) −35492.0 −1.53674 −0.768368 − 0.640008i \(-0.778931\pi\)
−0.768368 + 0.640008i \(0.778931\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −17350.0 −0.745698
\(816\) 0 0
\(817\) −4370.00 −0.187132
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7146.00 −0.303772 −0.151886 − 0.988398i \(-0.548535\pi\)
−0.151886 + 0.988398i \(0.548535\pi\)
\(822\) 0 0
\(823\) −8882.00 −0.376193 −0.188097 − 0.982151i \(-0.560232\pi\)
−0.188097 + 0.982151i \(0.560232\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 21705.0 0.912644 0.456322 − 0.889815i \(-0.349166\pi\)
0.456322 + 0.889815i \(0.349166\pi\)
\(828\) 0 0
\(829\) 29018.0 1.21573 0.607863 − 0.794042i \(-0.292027\pi\)
0.607863 + 0.794042i \(0.292027\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −4185.00 −0.174072
\(834\) 0 0
\(835\) −1935.00 −0.0801957
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −31164.0 −1.28236 −0.641180 − 0.767390i \(-0.721555\pi\)
−0.641180 + 0.767390i \(0.721555\pi\)
\(840\) 0 0
\(841\) −53.0000 −0.00217311
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10665.0 −0.434186
\(846\) 0 0
\(847\) 8056.00 0.326809
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4662.00 −0.187792
\(852\) 0 0
\(853\) 49160.0 1.97328 0.986639 − 0.162921i \(-0.0520916\pi\)
0.986639 + 0.162921i \(0.0520916\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2349.00 −0.0936293 −0.0468147 − 0.998904i \(-0.514907\pi\)
−0.0468147 + 0.998904i \(0.514907\pi\)
\(858\) 0 0
\(859\) 28195.0 1.11991 0.559954 − 0.828524i \(-0.310819\pi\)
0.559954 + 0.828524i \(0.310819\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 23997.0 0.946544 0.473272 − 0.880916i \(-0.343073\pi\)
0.473272 + 0.880916i \(0.343073\pi\)
\(864\) 0 0
\(865\) −4275.00 −0.168040
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −20214.0 −0.789083
\(870\) 0 0
\(871\) 2576.00 0.100212
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1000.00 −0.0386356
\(876\) 0 0
\(877\) 46286.0 1.78217 0.891087 − 0.453832i \(-0.149943\pi\)
0.891087 + 0.453832i \(0.149943\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 39636.0 1.51574 0.757872 − 0.652403i \(-0.226239\pi\)
0.757872 + 0.652403i \(0.226239\pi\)
\(882\) 0 0
\(883\) 16744.0 0.638143 0.319072 − 0.947731i \(-0.396629\pi\)
0.319072 + 0.947731i \(0.396629\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1251.00 −0.0473557 −0.0236778 − 0.999720i \(-0.507538\pi\)
−0.0236778 + 0.999720i \(0.507538\pi\)
\(888\) 0 0
\(889\) 2608.00 0.0983909
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 6624.00 0.248224
\(894\) 0 0
\(895\) 1320.00 0.0492991
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 13260.0 0.491931
\(900\) 0 0
\(901\) −2655.00 −0.0981697
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −12755.0 −0.468498
\(906\) 0 0
\(907\) 36988.0 1.35410 0.677049 − 0.735938i \(-0.263259\pi\)
0.677049 + 0.735938i \(0.263259\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −16404.0 −0.596585 −0.298292 − 0.954475i \(-0.596417\pi\)
−0.298292 + 0.954475i \(0.596417\pi\)
\(912\) 0 0
\(913\) −13878.0 −0.503061
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7920.00 −0.285214
\(918\) 0 0
\(919\) 664.000 0.0238339 0.0119169 − 0.999929i \(-0.496207\pi\)
0.0119169 + 0.999929i \(0.496207\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2160.00 0.0770285
\(924\) 0 0
\(925\) 1850.00 0.0657596
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −39642.0 −1.40001 −0.700006 − 0.714137i \(-0.746820\pi\)
−0.700006 + 0.714137i \(0.746820\pi\)
\(930\) 0 0
\(931\) 6417.00 0.225895
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1350.00 −0.0472190
\(936\) 0 0
\(937\) −36028.0 −1.25612 −0.628059 − 0.778165i \(-0.716151\pi\)
−0.628059 + 0.778165i \(0.716151\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 23058.0 0.798798 0.399399 − 0.916777i \(-0.369219\pi\)
0.399399 + 0.916777i \(0.369219\pi\)
\(942\) 0 0
\(943\) −15498.0 −0.535190
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −19953.0 −0.684673 −0.342337 − 0.939577i \(-0.611218\pi\)
−0.342337 + 0.939577i \(0.611218\pi\)
\(948\) 0 0
\(949\) 2032.00 0.0695063
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 25638.0 0.871455 0.435727 − 0.900079i \(-0.356491\pi\)
0.435727 + 0.900079i \(0.356491\pi\)
\(954\) 0 0
\(955\) 11190.0 0.379162
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1176.00 0.0395986
\(960\) 0 0
\(961\) −22566.0 −0.757477
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10900.0 0.363610
\(966\) 0 0
\(967\) 27034.0 0.899023 0.449511 − 0.893275i \(-0.351598\pi\)
0.449511 + 0.893275i \(0.351598\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −14802.0 −0.489206 −0.244603 − 0.969623i \(-0.578658\pi\)
−0.244603 + 0.969623i \(0.578658\pi\)
\(972\) 0 0
\(973\) 12832.0 0.422790
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −9186.00 −0.300805 −0.150402 − 0.988625i \(-0.548057\pi\)
−0.150402 + 0.988625i \(0.548057\pi\)
\(978\) 0 0
\(979\) 3564.00 0.116349
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −31647.0 −1.02684 −0.513419 − 0.858138i \(-0.671621\pi\)
−0.513419 + 0.858138i \(0.671621\pi\)
\(984\) 0 0
\(985\) 12885.0 0.416802
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −11970.0 −0.384857
\(990\) 0 0
\(991\) 48823.0 1.56500 0.782499 − 0.622651i \(-0.213945\pi\)
0.782499 + 0.622651i \(0.213945\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −7060.00 −0.224942
\(996\) 0 0
\(997\) −13066.0 −0.415050 −0.207525 − 0.978230i \(-0.566541\pi\)
−0.207525 + 0.978230i \(0.566541\pi\)
\(998\) 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 2160.4.a.m.1.1 1
3.2 odd 2 2160.4.a.c.1.1 1
4.3 odd 2 270.4.a.l.1.1 yes 1
12.11 even 2 270.4.a.b.1.1 ✓ 1
20.3 even 4 1350.4.c.n.649.1 2
20.7 even 4 1350.4.c.n.649.2 2
20.19 odd 2 1350.4.a.f.1.1 1
36.7 odd 6 810.4.e.b.271.1 2
36.11 even 6 810.4.e.v.271.1 2
36.23 even 6 810.4.e.v.541.1 2
36.31 odd 6 810.4.e.b.541.1 2
60.23 odd 4 1350.4.c.g.649.2 2
60.47 odd 4 1350.4.c.g.649.1 2
60.59 even 2 1350.4.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.b.1.1 ✓ 1 12.11 even 2
270.4.a.l.1.1 yes 1 4.3 odd 2
810.4.e.b.271.1 2 36.7 odd 6
810.4.e.b.541.1 2 36.31 odd 6
810.4.e.v.271.1 2 36.11 even 6
810.4.e.v.541.1 2 36.23 even 6
1350.4.a.f.1.1 1 20.19 odd 2
1350.4.a.t.1.1 1 60.59 even 2
1350.4.c.g.649.1 2 60.47 odd 4
1350.4.c.g.649.2 2 60.23 odd 4
1350.4.c.n.649.1 2 20.3 even 4
1350.4.c.n.649.2 2 20.7 even 4
2160.4.a.c.1.1 1 3.2 odd 2
2160.4.a.m.1.1 1 1.1 even 1 trivial