Properties

Label 2200.4.a.c.1.1
Level $2200$
Weight $4$
Character 2200.1
Self dual yes
Analytic conductor $129.804$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2200,4,Mod(1,2200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2200, 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("2200.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2200.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: \(129.804202013\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{3} -13.0000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q-5.00000 q^{3} -13.0000 q^{7} -2.00000 q^{9} -11.0000 q^{11} +12.0000 q^{13} +67.0000 q^{17} +151.000 q^{19} +65.0000 q^{21} -12.0000 q^{23} +145.000 q^{27} -143.000 q^{29} -337.000 q^{31} +55.0000 q^{33} +125.000 q^{37} -60.0000 q^{39} -240.000 q^{41} -270.000 q^{43} -448.000 q^{47} -174.000 q^{49} -335.000 q^{51} +45.0000 q^{53} -755.000 q^{57} +704.000 q^{59} -217.000 q^{61} +26.0000 q^{63} -284.000 q^{67} +60.0000 q^{69} -515.000 q^{71} +1162.00 q^{73} +143.000 q^{77} -944.000 q^{79} -671.000 q^{81} +124.000 q^{83} +715.000 q^{87} +361.000 q^{89} -156.000 q^{91} +1685.00 q^{93} +916.000 q^{97} +22.0000 q^{99} +O(q^{100})\)

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
\(3\) −5.00000 −0.962250 −0.481125 0.876652i \(-0.659772\pi\)
−0.481125 + 0.876652i \(0.659772\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −13.0000 −0.701934 −0.350967 0.936388i \(-0.614147\pi\)
−0.350967 + 0.936388i \(0.614147\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.0740741
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 12.0000 0.256015 0.128008 0.991773i \(-0.459142\pi\)
0.128008 + 0.991773i \(0.459142\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 67.0000 0.955876 0.477938 0.878394i \(-0.341384\pi\)
0.477938 + 0.878394i \(0.341384\pi\)
\(18\) 0 0
\(19\) 151.000 1.82325 0.911626 0.411021i \(-0.134828\pi\)
0.911626 + 0.411021i \(0.134828\pi\)
\(20\) 0 0
\(21\) 65.0000 0.675436
\(22\) 0 0
\(23\) −12.0000 −0.108790 −0.0543951 0.998519i \(-0.517323\pi\)
−0.0543951 + 0.998519i \(0.517323\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 145.000 1.03353
\(28\) 0 0
\(29\) −143.000 −0.915670 −0.457835 0.889037i \(-0.651375\pi\)
−0.457835 + 0.889037i \(0.651375\pi\)
\(30\) 0 0
\(31\) −337.000 −1.95248 −0.976242 0.216684i \(-0.930476\pi\)
−0.976242 + 0.216684i \(0.930476\pi\)
\(32\) 0 0
\(33\) 55.0000 0.290129
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 125.000 0.555402 0.277701 0.960668i \(-0.410428\pi\)
0.277701 + 0.960668i \(0.410428\pi\)
\(38\) 0 0
\(39\) −60.0000 −0.246351
\(40\) 0 0
\(41\) −240.000 −0.914188 −0.457094 0.889418i \(-0.651110\pi\)
−0.457094 + 0.889418i \(0.651110\pi\)
\(42\) 0 0
\(43\) −270.000 −0.957549 −0.478775 0.877938i \(-0.658919\pi\)
−0.478775 + 0.877938i \(0.658919\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −448.000 −1.39037 −0.695186 0.718830i \(-0.744678\pi\)
−0.695186 + 0.718830i \(0.744678\pi\)
\(48\) 0 0
\(49\) −174.000 −0.507289
\(50\) 0 0
\(51\) −335.000 −0.919792
\(52\) 0 0
\(53\) 45.0000 0.116627 0.0583134 0.998298i \(-0.481428\pi\)
0.0583134 + 0.998298i \(0.481428\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −755.000 −1.75442
\(58\) 0 0
\(59\) 704.000 1.55344 0.776720 0.629846i \(-0.216882\pi\)
0.776720 + 0.629846i \(0.216882\pi\)
\(60\) 0 0
\(61\) −217.000 −0.455475 −0.227738 0.973723i \(-0.573133\pi\)
−0.227738 + 0.973723i \(0.573133\pi\)
\(62\) 0 0
\(63\) 26.0000 0.0519951
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −284.000 −0.517853 −0.258926 0.965897i \(-0.583369\pi\)
−0.258926 + 0.965897i \(0.583369\pi\)
\(68\) 0 0
\(69\) 60.0000 0.104683
\(70\) 0 0
\(71\) −515.000 −0.860835 −0.430417 0.902630i \(-0.641634\pi\)
−0.430417 + 0.902630i \(0.641634\pi\)
\(72\) 0 0
\(73\) 1162.00 1.86304 0.931519 0.363692i \(-0.118484\pi\)
0.931519 + 0.363692i \(0.118484\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 143.000 0.211641
\(78\) 0 0
\(79\) −944.000 −1.34441 −0.672204 0.740366i \(-0.734652\pi\)
−0.672204 + 0.740366i \(0.734652\pi\)
\(80\) 0 0
\(81\) −671.000 −0.920439
\(82\) 0 0
\(83\) 124.000 0.163985 0.0819926 0.996633i \(-0.473872\pi\)
0.0819926 + 0.996633i \(0.473872\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 715.000 0.881104
\(88\) 0 0
\(89\) 361.000 0.429954 0.214977 0.976619i \(-0.431032\pi\)
0.214977 + 0.976619i \(0.431032\pi\)
\(90\) 0 0
\(91\) −156.000 −0.179706
\(92\) 0 0
\(93\) 1685.00 1.87878
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 916.000 0.958822 0.479411 0.877591i \(-0.340850\pi\)
0.479411 + 0.877591i \(0.340850\pi\)
\(98\) 0 0
\(99\) 22.0000 0.0223342
\(100\) 0 0
\(101\) −1190.00 −1.17237 −0.586185 0.810177i \(-0.699371\pi\)
−0.586185 + 0.810177i \(0.699371\pi\)
\(102\) 0 0
\(103\) −1460.00 −1.39668 −0.698340 0.715766i \(-0.746078\pi\)
−0.698340 + 0.715766i \(0.746078\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1124.00 1.01553 0.507763 0.861497i \(-0.330473\pi\)
0.507763 + 0.861497i \(0.330473\pi\)
\(108\) 0 0
\(109\) 1582.00 1.39017 0.695083 0.718929i \(-0.255368\pi\)
0.695083 + 0.718929i \(0.255368\pi\)
\(110\) 0 0
\(111\) −625.000 −0.534436
\(112\) 0 0
\(113\) 914.000 0.760902 0.380451 0.924801i \(-0.375769\pi\)
0.380451 + 0.924801i \(0.375769\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −24.0000 −0.0189641
\(118\) 0 0
\(119\) −871.000 −0.670962
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 1200.00 0.879678
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 40.0000 0.0279482 0.0139741 0.999902i \(-0.495552\pi\)
0.0139741 + 0.999902i \(0.495552\pi\)
\(128\) 0 0
\(129\) 1350.00 0.921402
\(130\) 0 0
\(131\) −1005.00 −0.670284 −0.335142 0.942168i \(-0.608784\pi\)
−0.335142 + 0.942168i \(0.608784\pi\)
\(132\) 0 0
\(133\) −1963.00 −1.27980
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1692.00 1.05516 0.527581 0.849504i \(-0.323099\pi\)
0.527581 + 0.849504i \(0.323099\pi\)
\(138\) 0 0
\(139\) 564.000 0.344157 0.172079 0.985083i \(-0.444952\pi\)
0.172079 + 0.985083i \(0.444952\pi\)
\(140\) 0 0
\(141\) 2240.00 1.33789
\(142\) 0 0
\(143\) −132.000 −0.0771916
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 870.000 0.488139
\(148\) 0 0
\(149\) −2681.00 −1.47407 −0.737034 0.675856i \(-0.763774\pi\)
−0.737034 + 0.675856i \(0.763774\pi\)
\(150\) 0 0
\(151\) 970.000 0.522765 0.261382 0.965235i \(-0.415822\pi\)
0.261382 + 0.965235i \(0.415822\pi\)
\(152\) 0 0
\(153\) −134.000 −0.0708056
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2551.00 −1.29676 −0.648382 0.761315i \(-0.724554\pi\)
−0.648382 + 0.761315i \(0.724554\pi\)
\(158\) 0 0
\(159\) −225.000 −0.112224
\(160\) 0 0
\(161\) 156.000 0.0763635
\(162\) 0 0
\(163\) −2377.00 −1.14221 −0.571107 0.820875i \(-0.693486\pi\)
−0.571107 + 0.820875i \(0.693486\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1113.00 −0.515728 −0.257864 0.966181i \(-0.583019\pi\)
−0.257864 + 0.966181i \(0.583019\pi\)
\(168\) 0 0
\(169\) −2053.00 −0.934456
\(170\) 0 0
\(171\) −302.000 −0.135056
\(172\) 0 0
\(173\) 2222.00 0.976506 0.488253 0.872702i \(-0.337634\pi\)
0.488253 + 0.872702i \(0.337634\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3520.00 −1.49480
\(178\) 0 0
\(179\) 2986.00 1.24684 0.623419 0.781888i \(-0.285743\pi\)
0.623419 + 0.781888i \(0.285743\pi\)
\(180\) 0 0
\(181\) 302.000 0.124019 0.0620096 0.998076i \(-0.480249\pi\)
0.0620096 + 0.998076i \(0.480249\pi\)
\(182\) 0 0
\(183\) 1085.00 0.438281
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −737.000 −0.288207
\(188\) 0 0
\(189\) −1885.00 −0.725469
\(190\) 0 0
\(191\) −1416.00 −0.536430 −0.268215 0.963359i \(-0.586434\pi\)
−0.268215 + 0.963359i \(0.586434\pi\)
\(192\) 0 0
\(193\) 4655.00 1.73614 0.868068 0.496445i \(-0.165362\pi\)
0.868068 + 0.496445i \(0.165362\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4146.00 1.49944 0.749721 0.661753i \(-0.230187\pi\)
0.749721 + 0.661753i \(0.230187\pi\)
\(198\) 0 0
\(199\) −3703.00 −1.31909 −0.659544 0.751666i \(-0.729251\pi\)
−0.659544 + 0.751666i \(0.729251\pi\)
\(200\) 0 0
\(201\) 1420.00 0.498304
\(202\) 0 0
\(203\) 1859.00 0.642740
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 24.0000 0.00805853
\(208\) 0 0
\(209\) −1661.00 −0.549731
\(210\) 0 0
\(211\) 5231.00 1.70672 0.853358 0.521326i \(-0.174562\pi\)
0.853358 + 0.521326i \(0.174562\pi\)
\(212\) 0 0
\(213\) 2575.00 0.828338
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4381.00 1.37051
\(218\) 0 0
\(219\) −5810.00 −1.79271
\(220\) 0 0
\(221\) 804.000 0.244719
\(222\) 0 0
\(223\) 3742.00 1.12369 0.561845 0.827243i \(-0.310092\pi\)
0.561845 + 0.827243i \(0.310092\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1260.00 −0.368410 −0.184205 0.982888i \(-0.558971\pi\)
−0.184205 + 0.982888i \(0.558971\pi\)
\(228\) 0 0
\(229\) 1704.00 0.491718 0.245859 0.969306i \(-0.420930\pi\)
0.245859 + 0.969306i \(0.420930\pi\)
\(230\) 0 0
\(231\) −715.000 −0.203652
\(232\) 0 0
\(233\) 4939.00 1.38869 0.694345 0.719643i \(-0.255694\pi\)
0.694345 + 0.719643i \(0.255694\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 4720.00 1.29366
\(238\) 0 0
\(239\) 5224.00 1.41386 0.706930 0.707284i \(-0.250080\pi\)
0.706930 + 0.707284i \(0.250080\pi\)
\(240\) 0 0
\(241\) 1128.00 0.301497 0.150749 0.988572i \(-0.451832\pi\)
0.150749 + 0.988572i \(0.451832\pi\)
\(242\) 0 0
\(243\) −560.000 −0.147835
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1812.00 0.466781
\(248\) 0 0
\(249\) −620.000 −0.157795
\(250\) 0 0
\(251\) −4110.00 −1.03355 −0.516775 0.856121i \(-0.672868\pi\)
−0.516775 + 0.856121i \(0.672868\pi\)
\(252\) 0 0
\(253\) 132.000 0.0328015
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1356.00 0.329124 0.164562 0.986367i \(-0.447379\pi\)
0.164562 + 0.986367i \(0.447379\pi\)
\(258\) 0 0
\(259\) −1625.00 −0.389856
\(260\) 0 0
\(261\) 286.000 0.0678274
\(262\) 0 0
\(263\) −3063.00 −0.718147 −0.359074 0.933309i \(-0.616907\pi\)
−0.359074 + 0.933309i \(0.616907\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1805.00 −0.413724
\(268\) 0 0
\(269\) −344.000 −0.0779704 −0.0389852 0.999240i \(-0.512413\pi\)
−0.0389852 + 0.999240i \(0.512413\pi\)
\(270\) 0 0
\(271\) 7086.00 1.58835 0.794177 0.607687i \(-0.207902\pi\)
0.794177 + 0.607687i \(0.207902\pi\)
\(272\) 0 0
\(273\) 780.000 0.172922
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1156.00 −0.250748 −0.125374 0.992110i \(-0.540013\pi\)
−0.125374 + 0.992110i \(0.540013\pi\)
\(278\) 0 0
\(279\) 674.000 0.144628
\(280\) 0 0
\(281\) 7174.00 1.52301 0.761503 0.648161i \(-0.224462\pi\)
0.761503 + 0.648161i \(0.224462\pi\)
\(282\) 0 0
\(283\) 2072.00 0.435221 0.217611 0.976036i \(-0.430174\pi\)
0.217611 + 0.976036i \(0.430174\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3120.00 0.641700
\(288\) 0 0
\(289\) −424.000 −0.0863016
\(290\) 0 0
\(291\) −4580.00 −0.922627
\(292\) 0 0
\(293\) −4736.00 −0.944301 −0.472150 0.881518i \(-0.656522\pi\)
−0.472150 + 0.881518i \(0.656522\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1595.00 −0.311620
\(298\) 0 0
\(299\) −144.000 −0.0278520
\(300\) 0 0
\(301\) 3510.00 0.672136
\(302\) 0 0
\(303\) 5950.00 1.12811
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4216.00 0.783778 0.391889 0.920013i \(-0.371822\pi\)
0.391889 + 0.920013i \(0.371822\pi\)
\(308\) 0 0
\(309\) 7300.00 1.34396
\(310\) 0 0
\(311\) −6605.00 −1.20429 −0.602147 0.798386i \(-0.705688\pi\)
−0.602147 + 0.798386i \(0.705688\pi\)
\(312\) 0 0
\(313\) −4842.00 −0.874396 −0.437198 0.899365i \(-0.644029\pi\)
−0.437198 + 0.899365i \(0.644029\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7211.00 1.27763 0.638817 0.769359i \(-0.279424\pi\)
0.638817 + 0.769359i \(0.279424\pi\)
\(318\) 0 0
\(319\) 1573.00 0.276085
\(320\) 0 0
\(321\) −5620.00 −0.977189
\(322\) 0 0
\(323\) 10117.0 1.74280
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −7910.00 −1.33769
\(328\) 0 0
\(329\) 5824.00 0.975950
\(330\) 0 0
\(331\) −4426.00 −0.734970 −0.367485 0.930030i \(-0.619781\pi\)
−0.367485 + 0.930030i \(0.619781\pi\)
\(332\) 0 0
\(333\) −250.000 −0.0411409
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1751.00 −0.283036 −0.141518 0.989936i \(-0.545198\pi\)
−0.141518 + 0.989936i \(0.545198\pi\)
\(338\) 0 0
\(339\) −4570.00 −0.732178
\(340\) 0 0
\(341\) 3707.00 0.588696
\(342\) 0 0
\(343\) 6721.00 1.05802
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1494.00 −0.231130 −0.115565 0.993300i \(-0.536868\pi\)
−0.115565 + 0.993300i \(0.536868\pi\)
\(348\) 0 0
\(349\) 1822.00 0.279454 0.139727 0.990190i \(-0.455378\pi\)
0.139727 + 0.990190i \(0.455378\pi\)
\(350\) 0 0
\(351\) 1740.00 0.264599
\(352\) 0 0
\(353\) 1390.00 0.209581 0.104791 0.994494i \(-0.466583\pi\)
0.104791 + 0.994494i \(0.466583\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 4355.00 0.645633
\(358\) 0 0
\(359\) −224.000 −0.0329311 −0.0164656 0.999864i \(-0.505241\pi\)
−0.0164656 + 0.999864i \(0.505241\pi\)
\(360\) 0 0
\(361\) 15942.0 2.32425
\(362\) 0 0
\(363\) −605.000 −0.0874773
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8256.00 −1.17428 −0.587139 0.809486i \(-0.699746\pi\)
−0.587139 + 0.809486i \(0.699746\pi\)
\(368\) 0 0
\(369\) 480.000 0.0677176
\(370\) 0 0
\(371\) −585.000 −0.0818644
\(372\) 0 0
\(373\) 11348.0 1.57527 0.787637 0.616140i \(-0.211304\pi\)
0.787637 + 0.616140i \(0.211304\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1716.00 −0.234426
\(378\) 0 0
\(379\) 3710.00 0.502823 0.251411 0.967880i \(-0.419105\pi\)
0.251411 + 0.967880i \(0.419105\pi\)
\(380\) 0 0
\(381\) −200.000 −0.0268932
\(382\) 0 0
\(383\) 14370.0 1.91716 0.958581 0.284822i \(-0.0919344\pi\)
0.958581 + 0.284822i \(0.0919344\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 540.000 0.0709296
\(388\) 0 0
\(389\) 6186.00 0.806279 0.403140 0.915138i \(-0.367919\pi\)
0.403140 + 0.915138i \(0.367919\pi\)
\(390\) 0 0
\(391\) −804.000 −0.103990
\(392\) 0 0
\(393\) 5025.00 0.644981
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 13634.0 1.72360 0.861802 0.507245i \(-0.169336\pi\)
0.861802 + 0.507245i \(0.169336\pi\)
\(398\) 0 0
\(399\) 9815.00 1.23149
\(400\) 0 0
\(401\) −7237.00 −0.901243 −0.450622 0.892715i \(-0.648798\pi\)
−0.450622 + 0.892715i \(0.648798\pi\)
\(402\) 0 0
\(403\) −4044.00 −0.499866
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1375.00 −0.167460
\(408\) 0 0
\(409\) −2420.00 −0.292570 −0.146285 0.989242i \(-0.546732\pi\)
−0.146285 + 0.989242i \(0.546732\pi\)
\(410\) 0 0
\(411\) −8460.00 −1.01533
\(412\) 0 0
\(413\) −9152.00 −1.09041
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2820.00 −0.331165
\(418\) 0 0
\(419\) −9140.00 −1.06568 −0.532838 0.846217i \(-0.678874\pi\)
−0.532838 + 0.846217i \(0.678874\pi\)
\(420\) 0 0
\(421\) −10884.0 −1.25999 −0.629993 0.776601i \(-0.716942\pi\)
−0.629993 + 0.776601i \(0.716942\pi\)
\(422\) 0 0
\(423\) 896.000 0.102991
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2821.00 0.319714
\(428\) 0 0
\(429\) 660.000 0.0742776
\(430\) 0 0
\(431\) 1752.00 0.195802 0.0979012 0.995196i \(-0.468787\pi\)
0.0979012 + 0.995196i \(0.468787\pi\)
\(432\) 0 0
\(433\) 5302.00 0.588448 0.294224 0.955737i \(-0.404939\pi\)
0.294224 + 0.955737i \(0.404939\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1812.00 −0.198352
\(438\) 0 0
\(439\) −3502.00 −0.380732 −0.190366 0.981713i \(-0.560967\pi\)
−0.190366 + 0.981713i \(0.560967\pi\)
\(440\) 0 0
\(441\) 348.000 0.0375769
\(442\) 0 0
\(443\) 7508.00 0.805228 0.402614 0.915370i \(-0.368102\pi\)
0.402614 + 0.915370i \(0.368102\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 13405.0 1.41842
\(448\) 0 0
\(449\) 12062.0 1.26780 0.633899 0.773416i \(-0.281454\pi\)
0.633899 + 0.773416i \(0.281454\pi\)
\(450\) 0 0
\(451\) 2640.00 0.275638
\(452\) 0 0
\(453\) −4850.00 −0.503031
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4691.00 −0.480166 −0.240083 0.970752i \(-0.577175\pi\)
−0.240083 + 0.970752i \(0.577175\pi\)
\(458\) 0 0
\(459\) 9715.00 0.987925
\(460\) 0 0
\(461\) 951.000 0.0960791 0.0480396 0.998845i \(-0.484703\pi\)
0.0480396 + 0.998845i \(0.484703\pi\)
\(462\) 0 0
\(463\) 5784.00 0.580573 0.290286 0.956940i \(-0.406249\pi\)
0.290286 + 0.956940i \(0.406249\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9233.00 −0.914887 −0.457444 0.889239i \(-0.651235\pi\)
−0.457444 + 0.889239i \(0.651235\pi\)
\(468\) 0 0
\(469\) 3692.00 0.363498
\(470\) 0 0
\(471\) 12755.0 1.24781
\(472\) 0 0
\(473\) 2970.00 0.288712
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −90.0000 −0.00863903
\(478\) 0 0
\(479\) −7562.00 −0.721329 −0.360665 0.932696i \(-0.617450\pi\)
−0.360665 + 0.932696i \(0.617450\pi\)
\(480\) 0 0
\(481\) 1500.00 0.142192
\(482\) 0 0
\(483\) −780.000 −0.0734808
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8346.00 0.776578 0.388289 0.921538i \(-0.373066\pi\)
0.388289 + 0.921538i \(0.373066\pi\)
\(488\) 0 0
\(489\) 11885.0 1.09910
\(490\) 0 0
\(491\) −6045.00 −0.555615 −0.277808 0.960637i \(-0.589608\pi\)
−0.277808 + 0.960637i \(0.589608\pi\)
\(492\) 0 0
\(493\) −9581.00 −0.875267
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6695.00 0.604249
\(498\) 0 0
\(499\) 11056.0 0.991853 0.495926 0.868365i \(-0.334829\pi\)
0.495926 + 0.868365i \(0.334829\pi\)
\(500\) 0 0
\(501\) 5565.00 0.496259
\(502\) 0 0
\(503\) −936.000 −0.0829705 −0.0414853 0.999139i \(-0.513209\pi\)
−0.0414853 + 0.999139i \(0.513209\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 10265.0 0.899181
\(508\) 0 0
\(509\) 1684.00 0.146644 0.0733222 0.997308i \(-0.476640\pi\)
0.0733222 + 0.997308i \(0.476640\pi\)
\(510\) 0 0
\(511\) −15106.0 −1.30773
\(512\) 0 0
\(513\) 21895.0 1.88438
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 4928.00 0.419213
\(518\) 0 0
\(519\) −11110.0 −0.939643
\(520\) 0 0
\(521\) 13190.0 1.10914 0.554572 0.832136i \(-0.312882\pi\)
0.554572 + 0.832136i \(0.312882\pi\)
\(522\) 0 0
\(523\) −5432.00 −0.454158 −0.227079 0.973876i \(-0.572918\pi\)
−0.227079 + 0.973876i \(0.572918\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −22579.0 −1.86633
\(528\) 0 0
\(529\) −12023.0 −0.988165
\(530\) 0 0
\(531\) −1408.00 −0.115070
\(532\) 0 0
\(533\) −2880.00 −0.234046
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −14930.0 −1.19977
\(538\) 0 0
\(539\) 1914.00 0.152953
\(540\) 0 0
\(541\) 6237.00 0.495655 0.247828 0.968804i \(-0.420283\pi\)
0.247828 + 0.968804i \(0.420283\pi\)
\(542\) 0 0
\(543\) −1510.00 −0.119338
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −11400.0 −0.891095 −0.445547 0.895258i \(-0.646991\pi\)
−0.445547 + 0.895258i \(0.646991\pi\)
\(548\) 0 0
\(549\) 434.000 0.0337389
\(550\) 0 0
\(551\) −21593.0 −1.66950
\(552\) 0 0
\(553\) 12272.0 0.943686
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2588.00 0.196871 0.0984354 0.995143i \(-0.468616\pi\)
0.0984354 + 0.995143i \(0.468616\pi\)
\(558\) 0 0
\(559\) −3240.00 −0.245147
\(560\) 0 0
\(561\) 3685.00 0.277328
\(562\) 0 0
\(563\) −12708.0 −0.951294 −0.475647 0.879636i \(-0.657786\pi\)
−0.475647 + 0.879636i \(0.657786\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 8723.00 0.646087
\(568\) 0 0
\(569\) 9828.00 0.724097 0.362049 0.932159i \(-0.382077\pi\)
0.362049 + 0.932159i \(0.382077\pi\)
\(570\) 0 0
\(571\) 16585.0 1.21552 0.607759 0.794122i \(-0.292069\pi\)
0.607759 + 0.794122i \(0.292069\pi\)
\(572\) 0 0
\(573\) 7080.00 0.516180
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −2992.00 −0.215873 −0.107936 0.994158i \(-0.534424\pi\)
−0.107936 + 0.994158i \(0.534424\pi\)
\(578\) 0 0
\(579\) −23275.0 −1.67060
\(580\) 0 0
\(581\) −1612.00 −0.115107
\(582\) 0 0
\(583\) −495.000 −0.0351643
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20325.0 1.42914 0.714568 0.699566i \(-0.246623\pi\)
0.714568 + 0.699566i \(0.246623\pi\)
\(588\) 0 0
\(589\) −50887.0 −3.55987
\(590\) 0 0
\(591\) −20730.0 −1.44284
\(592\) 0 0
\(593\) 5226.00 0.361899 0.180949 0.983492i \(-0.442083\pi\)
0.180949 + 0.983492i \(0.442083\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 18515.0 1.26929
\(598\) 0 0
\(599\) 2171.00 0.148088 0.0740440 0.997255i \(-0.476409\pi\)
0.0740440 + 0.997255i \(0.476409\pi\)
\(600\) 0 0
\(601\) 20786.0 1.41078 0.705390 0.708820i \(-0.250772\pi\)
0.705390 + 0.708820i \(0.250772\pi\)
\(602\) 0 0
\(603\) 568.000 0.0383594
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 11841.0 0.791781 0.395891 0.918298i \(-0.370436\pi\)
0.395891 + 0.918298i \(0.370436\pi\)
\(608\) 0 0
\(609\) −9295.00 −0.618477
\(610\) 0 0
\(611\) −5376.00 −0.355957
\(612\) 0 0
\(613\) −21782.0 −1.43518 −0.717591 0.696465i \(-0.754755\pi\)
−0.717591 + 0.696465i \(0.754755\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −25604.0 −1.67063 −0.835315 0.549772i \(-0.814715\pi\)
−0.835315 + 0.549772i \(0.814715\pi\)
\(618\) 0 0
\(619\) −3492.00 −0.226745 −0.113373 0.993553i \(-0.536165\pi\)
−0.113373 + 0.993553i \(0.536165\pi\)
\(620\) 0 0
\(621\) −1740.00 −0.112438
\(622\) 0 0
\(623\) −4693.00 −0.301799
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 8305.00 0.528979
\(628\) 0 0
\(629\) 8375.00 0.530895
\(630\) 0 0
\(631\) −6027.00 −0.380239 −0.190120 0.981761i \(-0.560888\pi\)
−0.190120 + 0.981761i \(0.560888\pi\)
\(632\) 0 0
\(633\) −26155.0 −1.64229
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −2088.00 −0.129874
\(638\) 0 0
\(639\) 1030.00 0.0637655
\(640\) 0 0
\(641\) −25937.0 −1.59821 −0.799103 0.601194i \(-0.794692\pi\)
−0.799103 + 0.601194i \(0.794692\pi\)
\(642\) 0 0
\(643\) 2827.00 0.173384 0.0866921 0.996235i \(-0.472370\pi\)
0.0866921 + 0.996235i \(0.472370\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −228.000 −0.0138541 −0.00692705 0.999976i \(-0.502205\pi\)
−0.00692705 + 0.999976i \(0.502205\pi\)
\(648\) 0 0
\(649\) −7744.00 −0.468380
\(650\) 0 0
\(651\) −21905.0 −1.31878
\(652\) 0 0
\(653\) −7377.00 −0.442089 −0.221045 0.975264i \(-0.570947\pi\)
−0.221045 + 0.975264i \(0.570947\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2324.00 −0.138003
\(658\) 0 0
\(659\) −6879.00 −0.406628 −0.203314 0.979114i \(-0.565171\pi\)
−0.203314 + 0.979114i \(0.565171\pi\)
\(660\) 0 0
\(661\) 20260.0 1.19217 0.596084 0.802922i \(-0.296723\pi\)
0.596084 + 0.802922i \(0.296723\pi\)
\(662\) 0 0
\(663\) −4020.00 −0.235481
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1716.00 0.0996159
\(668\) 0 0
\(669\) −18710.0 −1.08127
\(670\) 0 0
\(671\) 2387.00 0.137331
\(672\) 0 0
\(673\) −1489.00 −0.0852849 −0.0426424 0.999090i \(-0.513578\pi\)
−0.0426424 + 0.999090i \(0.513578\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5640.00 0.320181 0.160091 0.987102i \(-0.448821\pi\)
0.160091 + 0.987102i \(0.448821\pi\)
\(678\) 0 0
\(679\) −11908.0 −0.673030
\(680\) 0 0
\(681\) 6300.00 0.354503
\(682\) 0 0
\(683\) −8019.00 −0.449251 −0.224626 0.974445i \(-0.572116\pi\)
−0.224626 + 0.974445i \(0.572116\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −8520.00 −0.473156
\(688\) 0 0
\(689\) 540.000 0.0298583
\(690\) 0 0
\(691\) 20440.0 1.12529 0.562644 0.826699i \(-0.309784\pi\)
0.562644 + 0.826699i \(0.309784\pi\)
\(692\) 0 0
\(693\) −286.000 −0.0156771
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −16080.0 −0.873850
\(698\) 0 0
\(699\) −24695.0 −1.33627
\(700\) 0 0
\(701\) 10911.0 0.587878 0.293939 0.955824i \(-0.405034\pi\)
0.293939 + 0.955824i \(0.405034\pi\)
\(702\) 0 0
\(703\) 18875.0 1.01264
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15470.0 0.822927
\(708\) 0 0
\(709\) 24666.0 1.30656 0.653280 0.757116i \(-0.273392\pi\)
0.653280 + 0.757116i \(0.273392\pi\)
\(710\) 0 0
\(711\) 1888.00 0.0995858
\(712\) 0 0
\(713\) 4044.00 0.212411
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −26120.0 −1.36049
\(718\) 0 0
\(719\) 17399.0 0.902466 0.451233 0.892406i \(-0.350984\pi\)
0.451233 + 0.892406i \(0.350984\pi\)
\(720\) 0 0
\(721\) 18980.0 0.980377
\(722\) 0 0
\(723\) −5640.00 −0.290116
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 19794.0 1.00979 0.504896 0.863180i \(-0.331531\pi\)
0.504896 + 0.863180i \(0.331531\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 0 0
\(731\) −18090.0 −0.915298
\(732\) 0 0
\(733\) 32454.0 1.63536 0.817678 0.575676i \(-0.195261\pi\)
0.817678 + 0.575676i \(0.195261\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3124.00 0.156138
\(738\) 0 0
\(739\) 8024.00 0.399415 0.199707 0.979856i \(-0.436001\pi\)
0.199707 + 0.979856i \(0.436001\pi\)
\(740\) 0 0
\(741\) −9060.00 −0.449160
\(742\) 0 0
\(743\) 24159.0 1.19288 0.596439 0.802659i \(-0.296582\pi\)
0.596439 + 0.802659i \(0.296582\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −248.000 −0.0121470
\(748\) 0 0
\(749\) −14612.0 −0.712832
\(750\) 0 0
\(751\) −38477.0 −1.86957 −0.934784 0.355216i \(-0.884407\pi\)
−0.934784 + 0.355216i \(0.884407\pi\)
\(752\) 0 0
\(753\) 20550.0 0.994533
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −5014.00 −0.240736 −0.120368 0.992729i \(-0.538407\pi\)
−0.120368 + 0.992729i \(0.538407\pi\)
\(758\) 0 0
\(759\) −660.000 −0.0315632
\(760\) 0 0
\(761\) 15764.0 0.750913 0.375456 0.926840i \(-0.377486\pi\)
0.375456 + 0.926840i \(0.377486\pi\)
\(762\) 0 0
\(763\) −20566.0 −0.975805
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8448.00 0.397705
\(768\) 0 0
\(769\) 614.000 0.0287925 0.0143962 0.999896i \(-0.495417\pi\)
0.0143962 + 0.999896i \(0.495417\pi\)
\(770\) 0 0
\(771\) −6780.00 −0.316700
\(772\) 0 0
\(773\) −5943.00 −0.276526 −0.138263 0.990396i \(-0.544152\pi\)
−0.138263 + 0.990396i \(0.544152\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 8125.00 0.375139
\(778\) 0 0
\(779\) −36240.0 −1.66679
\(780\) 0 0
\(781\) 5665.00 0.259551
\(782\) 0 0
\(783\) −20735.0 −0.946371
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −26154.0 −1.18461 −0.592306 0.805713i \(-0.701782\pi\)
−0.592306 + 0.805713i \(0.701782\pi\)
\(788\) 0 0
\(789\) 15315.0 0.691037
\(790\) 0 0
\(791\) −11882.0 −0.534103
\(792\) 0 0
\(793\) −2604.00 −0.116609
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3270.00 −0.145332 −0.0726658 0.997356i \(-0.523151\pi\)
−0.0726658 + 0.997356i \(0.523151\pi\)
\(798\) 0 0
\(799\) −30016.0 −1.32902
\(800\) 0 0
\(801\) −722.000 −0.0318485
\(802\) 0 0
\(803\) −12782.0 −0.561727
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1720.00 0.0750271
\(808\) 0 0
\(809\) 14306.0 0.621721 0.310860 0.950456i \(-0.399383\pi\)
0.310860 + 0.950456i \(0.399383\pi\)
\(810\) 0 0
\(811\) −959.000 −0.0415229 −0.0207614 0.999784i \(-0.506609\pi\)
−0.0207614 + 0.999784i \(0.506609\pi\)
\(812\) 0 0
\(813\) −35430.0 −1.52839
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −40770.0 −1.74585
\(818\) 0 0
\(819\) 312.000 0.0133116
\(820\) 0 0
\(821\) 14190.0 0.603209 0.301604 0.953433i \(-0.402478\pi\)
0.301604 + 0.953433i \(0.402478\pi\)
\(822\) 0 0
\(823\) −34010.0 −1.44048 −0.720239 0.693726i \(-0.755968\pi\)
−0.720239 + 0.693726i \(0.755968\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14218.0 0.597833 0.298917 0.954279i \(-0.403375\pi\)
0.298917 + 0.954279i \(0.403375\pi\)
\(828\) 0 0
\(829\) 33172.0 1.38976 0.694880 0.719126i \(-0.255457\pi\)
0.694880 + 0.719126i \(0.255457\pi\)
\(830\) 0 0
\(831\) 5780.00 0.241283
\(832\) 0 0
\(833\) −11658.0 −0.484905
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −48865.0 −2.01795
\(838\) 0 0
\(839\) 28656.0 1.17916 0.589580 0.807710i \(-0.299293\pi\)
0.589580 + 0.807710i \(0.299293\pi\)
\(840\) 0 0
\(841\) −3940.00 −0.161548
\(842\) 0 0
\(843\) −35870.0 −1.46551
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1573.00 −0.0638122
\(848\) 0 0
\(849\) −10360.0 −0.418792
\(850\) 0 0
\(851\) −1500.00 −0.0604223
\(852\) 0 0
\(853\) −10244.0 −0.411193 −0.205597 0.978637i \(-0.565913\pi\)
−0.205597 + 0.978637i \(0.565913\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −11401.0 −0.454435 −0.227217 0.973844i \(-0.572963\pi\)
−0.227217 + 0.973844i \(0.572963\pi\)
\(858\) 0 0
\(859\) 26846.0 1.06633 0.533163 0.846013i \(-0.321003\pi\)
0.533163 + 0.846013i \(0.321003\pi\)
\(860\) 0 0
\(861\) −15600.0 −0.617476
\(862\) 0 0
\(863\) 40972.0 1.61611 0.808055 0.589107i \(-0.200520\pi\)
0.808055 + 0.589107i \(0.200520\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 2120.00 0.0830438
\(868\) 0 0
\(869\) 10384.0 0.405355
\(870\) 0 0
\(871\) −3408.00 −0.132578
\(872\) 0 0
\(873\) −1832.00 −0.0710238
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 15614.0 0.601194 0.300597 0.953751i \(-0.402814\pi\)
0.300597 + 0.953751i \(0.402814\pi\)
\(878\) 0 0
\(879\) 23680.0 0.908654
\(880\) 0 0
\(881\) −39938.0 −1.52729 −0.763647 0.645634i \(-0.776593\pi\)
−0.763647 + 0.645634i \(0.776593\pi\)
\(882\) 0 0
\(883\) −48467.0 −1.84716 −0.923581 0.383403i \(-0.874752\pi\)
−0.923581 + 0.383403i \(0.874752\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 25776.0 0.975731 0.487865 0.872919i \(-0.337776\pi\)
0.487865 + 0.872919i \(0.337776\pi\)
\(888\) 0 0
\(889\) −520.000 −0.0196178
\(890\) 0 0
\(891\) 7381.00 0.277523
\(892\) 0 0
\(893\) −67648.0 −2.53500
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 720.000 0.0268006
\(898\) 0 0
\(899\) 48191.0 1.78783
\(900\) 0 0
\(901\) 3015.00 0.111481
\(902\) 0 0
\(903\) −17550.0 −0.646763
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −23701.0 −0.867672 −0.433836 0.900992i \(-0.642840\pi\)
−0.433836 + 0.900992i \(0.642840\pi\)
\(908\) 0 0
\(909\) 2380.00 0.0868423
\(910\) 0 0
\(911\) 24189.0 0.879712 0.439856 0.898068i \(-0.355030\pi\)
0.439856 + 0.898068i \(0.355030\pi\)
\(912\) 0 0
\(913\) −1364.00 −0.0494434
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 13065.0 0.470495
\(918\) 0 0
\(919\) −24590.0 −0.882643 −0.441322 0.897349i \(-0.645490\pi\)
−0.441322 + 0.897349i \(0.645490\pi\)
\(920\) 0 0
\(921\) −21080.0 −0.754191
\(922\) 0 0
\(923\) −6180.00 −0.220387
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 2920.00 0.103458
\(928\) 0 0
\(929\) 16575.0 0.585369 0.292685 0.956209i \(-0.405451\pi\)
0.292685 + 0.956209i \(0.405451\pi\)
\(930\) 0 0
\(931\) −26274.0 −0.924915
\(932\) 0 0
\(933\) 33025.0 1.15883
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 15542.0 0.541873 0.270937 0.962597i \(-0.412667\pi\)
0.270937 + 0.962597i \(0.412667\pi\)
\(938\) 0 0
\(939\) 24210.0 0.841388
\(940\) 0 0
\(941\) 10893.0 0.377366 0.188683 0.982038i \(-0.439578\pi\)
0.188683 + 0.982038i \(0.439578\pi\)
\(942\) 0 0
\(943\) 2880.00 0.0994546
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −23831.0 −0.817744 −0.408872 0.912592i \(-0.634078\pi\)
−0.408872 + 0.912592i \(0.634078\pi\)
\(948\) 0 0
\(949\) 13944.0 0.476967
\(950\) 0 0
\(951\) −36055.0 −1.22940
\(952\) 0 0
\(953\) −3771.00 −0.128179 −0.0640895 0.997944i \(-0.520414\pi\)
−0.0640895 + 0.997944i \(0.520414\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −7865.00 −0.265663
\(958\) 0 0
\(959\) −21996.0 −0.740655
\(960\) 0 0
\(961\) 83778.0 2.81219
\(962\) 0 0
\(963\) −2248.00 −0.0752241
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 50413.0 1.67650 0.838249 0.545288i \(-0.183580\pi\)
0.838249 + 0.545288i \(0.183580\pi\)
\(968\) 0 0
\(969\) −50585.0 −1.67701
\(970\) 0 0
\(971\) 492.000 0.0162606 0.00813029 0.999967i \(-0.497412\pi\)
0.00813029 + 0.999967i \(0.497412\pi\)
\(972\) 0 0
\(973\) −7332.00 −0.241576
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 56748.0 1.85827 0.929135 0.369741i \(-0.120554\pi\)
0.929135 + 0.369741i \(0.120554\pi\)
\(978\) 0 0
\(979\) −3971.00 −0.129636
\(980\) 0 0
\(981\) −3164.00 −0.102975
\(982\) 0 0
\(983\) 49302.0 1.59968 0.799842 0.600210i \(-0.204917\pi\)
0.799842 + 0.600210i \(0.204917\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −29120.0 −0.939108
\(988\) 0 0
\(989\) 3240.00 0.104172
\(990\) 0 0
\(991\) 5064.00 0.162324 0.0811621 0.996701i \(-0.474137\pi\)
0.0811621 + 0.996701i \(0.474137\pi\)
\(992\) 0 0
\(993\) 22130.0 0.707225
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −61018.0 −1.93827 −0.969137 0.246522i \(-0.920712\pi\)
−0.969137 + 0.246522i \(0.920712\pi\)
\(998\) 0 0
\(999\) 18125.0 0.574024
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 2200.4.a.c.1.1 1
5.2 odd 4 440.4.b.a.89.2 yes 2
5.3 odd 4 440.4.b.a.89.1 2
5.4 even 2 2200.4.a.j.1.1 1
20.3 even 4 880.4.b.c.529.2 2
20.7 even 4 880.4.b.c.529.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.4.b.a.89.1 2 5.3 odd 4
440.4.b.a.89.2 yes 2 5.2 odd 4
880.4.b.c.529.1 2 20.7 even 4
880.4.b.c.529.2 2 20.3 even 4
2200.4.a.c.1.1 1 1.1 even 1 trivial
2200.4.a.j.1.1 1 5.4 even 2