Properties

Label 2200.4.a.i.1.1
Level $2200$
Weight $4$
Character 2200.1
Self dual yes
Analytic conductor $129.804$
Analytic rank $1$
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: \(1\)
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)
 
\(f(q)\) \(=\) \(q+5.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+5.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +11.0000 q^{11} -18.0000 q^{13} +113.000 q^{17} +55.0000 q^{19} -5.00000 q^{21} -190.000 q^{23} -145.000 q^{27} -69.0000 q^{29} -255.000 q^{31} +55.0000 q^{33} -51.0000 q^{37} -90.0000 q^{39} -314.000 q^{41} +484.000 q^{43} -470.000 q^{47} -342.000 q^{49} +565.000 q^{51} +545.000 q^{53} +275.000 q^{57} -102.000 q^{59} +129.000 q^{61} +2.00000 q^{63} +664.000 q^{67} -950.000 q^{69} -1029.00 q^{71} +758.000 q^{73} -11.0000 q^{77} +634.000 q^{79} -671.000 q^{81} +654.000 q^{83} -345.000 q^{87} -511.000 q^{89} +18.0000 q^{91} -1275.00 q^{93} -1736.00 q^{97} -22.0000 q^{99} +O(q^{100})\)

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 \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.0539949 −0.0269975 0.999636i \(-0.508595\pi\)
−0.0269975 + 0.999636i \(0.508595\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.0740741
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −18.0000 −0.384023 −0.192012 0.981393i \(-0.561501\pi\)
−0.192012 + 0.981393i \(0.561501\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 113.000 1.61215 0.806074 0.591814i \(-0.201588\pi\)
0.806074 + 0.591814i \(0.201588\pi\)
\(18\) 0 0
\(19\) 55.0000 0.664098 0.332049 0.943262i \(-0.392260\pi\)
0.332049 + 0.943262i \(0.392260\pi\)
\(20\) 0 0
\(21\) −5.00000 −0.0519566
\(22\) 0 0
\(23\) −190.000 −1.72251 −0.861255 0.508173i \(-0.830321\pi\)
−0.861255 + 0.508173i \(0.830321\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −145.000 −1.03353
\(28\) 0 0
\(29\) −69.0000 −0.441827 −0.220913 0.975293i \(-0.570904\pi\)
−0.220913 + 0.975293i \(0.570904\pi\)
\(30\) 0 0
\(31\) −255.000 −1.47740 −0.738699 0.674035i \(-0.764560\pi\)
−0.738699 + 0.674035i \(0.764560\pi\)
\(32\) 0 0
\(33\) 55.0000 0.290129
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −51.0000 −0.226604 −0.113302 0.993561i \(-0.536143\pi\)
−0.113302 + 0.993561i \(0.536143\pi\)
\(38\) 0 0
\(39\) −90.0000 −0.369527
\(40\) 0 0
\(41\) −314.000 −1.19606 −0.598031 0.801473i \(-0.704050\pi\)
−0.598031 + 0.801473i \(0.704050\pi\)
\(42\) 0 0
\(43\) 484.000 1.71650 0.858248 0.513236i \(-0.171553\pi\)
0.858248 + 0.513236i \(0.171553\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −470.000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) 0 0
\(49\) −342.000 −0.997085
\(50\) 0 0
\(51\) 565.000 1.55129
\(52\) 0 0
\(53\) 545.000 1.41248 0.706241 0.707972i \(-0.250390\pi\)
0.706241 + 0.707972i \(0.250390\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 275.000 0.639029
\(58\) 0 0
\(59\) −102.000 −0.225072 −0.112536 0.993648i \(-0.535897\pi\)
−0.112536 + 0.993648i \(0.535897\pi\)
\(60\) 0 0
\(61\) 129.000 0.270767 0.135383 0.990793i \(-0.456773\pi\)
0.135383 + 0.990793i \(0.456773\pi\)
\(62\) 0 0
\(63\) 2.00000 0.00399962
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 664.000 1.21075 0.605377 0.795939i \(-0.293022\pi\)
0.605377 + 0.795939i \(0.293022\pi\)
\(68\) 0 0
\(69\) −950.000 −1.65749
\(70\) 0 0
\(71\) −1029.00 −1.72000 −0.859999 0.510296i \(-0.829536\pi\)
−0.859999 + 0.510296i \(0.829536\pi\)
\(72\) 0 0
\(73\) 758.000 1.21530 0.607652 0.794203i \(-0.292112\pi\)
0.607652 + 0.794203i \(0.292112\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.0000 −0.0162801
\(78\) 0 0
\(79\) 634.000 0.902919 0.451459 0.892292i \(-0.350904\pi\)
0.451459 + 0.892292i \(0.350904\pi\)
\(80\) 0 0
\(81\) −671.000 −0.920439
\(82\) 0 0
\(83\) 654.000 0.864889 0.432445 0.901660i \(-0.357651\pi\)
0.432445 + 0.901660i \(0.357651\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −345.000 −0.425148
\(88\) 0 0
\(89\) −511.000 −0.608606 −0.304303 0.952575i \(-0.598423\pi\)
−0.304303 + 0.952575i \(0.598423\pi\)
\(90\) 0 0
\(91\) 18.0000 0.0207353
\(92\) 0 0
\(93\) −1275.00 −1.42163
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1736.00 −1.81716 −0.908578 0.417716i \(-0.862831\pi\)
−0.908578 + 0.417716i \(0.862831\pi\)
\(98\) 0 0
\(99\) −22.0000 −0.0223342
\(100\) 0 0
\(101\) −434.000 −0.427570 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(102\) 0 0
\(103\) 248.000 0.237244 0.118622 0.992939i \(-0.462152\pi\)
0.118622 + 0.992939i \(0.462152\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 92.0000 0.0831213 0.0415606 0.999136i \(-0.486767\pi\)
0.0415606 + 0.999136i \(0.486767\pi\)
\(108\) 0 0
\(109\) −1870.00 −1.64324 −0.821622 0.570033i \(-0.806930\pi\)
−0.821622 + 0.570033i \(0.806930\pi\)
\(110\) 0 0
\(111\) −255.000 −0.218050
\(112\) 0 0
\(113\) −432.000 −0.359638 −0.179819 0.983700i \(-0.557551\pi\)
−0.179819 + 0.983700i \(0.557551\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 36.0000 0.0284462
\(118\) 0 0
\(119\) −113.000 −0.0870478
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) −1570.00 −1.15091
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2696.00 −1.88371 −0.941856 0.336018i \(-0.890920\pi\)
−0.941856 + 0.336018i \(0.890920\pi\)
\(128\) 0 0
\(129\) 2420.00 1.65170
\(130\) 0 0
\(131\) −317.000 −0.211423 −0.105712 0.994397i \(-0.533712\pi\)
−0.105712 + 0.994397i \(0.533712\pi\)
\(132\) 0 0
\(133\) −55.0000 −0.0358579
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1908.00 1.18986 0.594932 0.803776i \(-0.297179\pi\)
0.594932 + 0.803776i \(0.297179\pi\)
\(138\) 0 0
\(139\) −2868.00 −1.75008 −0.875038 0.484054i \(-0.839164\pi\)
−0.875038 + 0.484054i \(0.839164\pi\)
\(140\) 0 0
\(141\) −2350.00 −1.40359
\(142\) 0 0
\(143\) −198.000 −0.115787
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1710.00 −0.959445
\(148\) 0 0
\(149\) 1953.00 1.07380 0.536899 0.843646i \(-0.319596\pi\)
0.536899 + 0.843646i \(0.319596\pi\)
\(150\) 0 0
\(151\) 1530.00 0.824567 0.412284 0.911056i \(-0.364731\pi\)
0.412284 + 0.911056i \(0.364731\pi\)
\(152\) 0 0
\(153\) −226.000 −0.119418
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3211.00 −1.63227 −0.816133 0.577864i \(-0.803886\pi\)
−0.816133 + 0.577864i \(0.803886\pi\)
\(158\) 0 0
\(159\) 2725.00 1.35916
\(160\) 0 0
\(161\) 190.000 0.0930068
\(162\) 0 0
\(163\) 1297.00 0.623245 0.311622 0.950206i \(-0.399128\pi\)
0.311622 + 0.950206i \(0.399128\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3673.00 −1.70195 −0.850974 0.525208i \(-0.823988\pi\)
−0.850974 + 0.525208i \(0.823988\pi\)
\(168\) 0 0
\(169\) −1873.00 −0.852526
\(170\) 0 0
\(171\) −110.000 −0.0491925
\(172\) 0 0
\(173\) 1062.00 0.466719 0.233359 0.972391i \(-0.425028\pi\)
0.233359 + 0.972391i \(0.425028\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −510.000 −0.216576
\(178\) 0 0
\(179\) 2780.00 1.16082 0.580410 0.814324i \(-0.302892\pi\)
0.580410 + 0.814324i \(0.302892\pi\)
\(180\) 0 0
\(181\) 182.000 0.0747401 0.0373700 0.999301i \(-0.488102\pi\)
0.0373700 + 0.999301i \(0.488102\pi\)
\(182\) 0 0
\(183\) 645.000 0.260545
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1243.00 0.486081
\(188\) 0 0
\(189\) 145.000 0.0558053
\(190\) 0 0
\(191\) −2764.00 −1.04710 −0.523550 0.851995i \(-0.675393\pi\)
−0.523550 + 0.851995i \(0.675393\pi\)
\(192\) 0 0
\(193\) 3261.00 1.21623 0.608114 0.793850i \(-0.291926\pi\)
0.608114 + 0.793850i \(0.291926\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 176.000 0.0636522 0.0318261 0.999493i \(-0.489868\pi\)
0.0318261 + 0.999493i \(0.489868\pi\)
\(198\) 0 0
\(199\) 1731.00 0.616620 0.308310 0.951286i \(-0.400237\pi\)
0.308310 + 0.951286i \(0.400237\pi\)
\(200\) 0 0
\(201\) 3320.00 1.16505
\(202\) 0 0
\(203\) 69.0000 0.0238564
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 380.000 0.127593
\(208\) 0 0
\(209\) 605.000 0.200233
\(210\) 0 0
\(211\) −2733.00 −0.891694 −0.445847 0.895109i \(-0.647097\pi\)
−0.445847 + 0.895109i \(0.647097\pi\)
\(212\) 0 0
\(213\) −5145.00 −1.65507
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 255.000 0.0797720
\(218\) 0 0
\(219\) 3790.00 1.16943
\(220\) 0 0
\(221\) −2034.00 −0.619102
\(222\) 0 0
\(223\) −1506.00 −0.452239 −0.226119 0.974100i \(-0.572604\pi\)
−0.226119 + 0.974100i \(0.572604\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5418.00 −1.58416 −0.792082 0.610415i \(-0.791003\pi\)
−0.792082 + 0.610415i \(0.791003\pi\)
\(228\) 0 0
\(229\) −4410.00 −1.27258 −0.636290 0.771450i \(-0.719532\pi\)
−0.636290 + 0.771450i \(0.719532\pi\)
\(230\) 0 0
\(231\) −55.0000 −0.0156655
\(232\) 0 0
\(233\) −5735.00 −1.61250 −0.806250 0.591575i \(-0.798506\pi\)
−0.806250 + 0.591575i \(0.798506\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 3170.00 0.868834
\(238\) 0 0
\(239\) 78.0000 0.0211105 0.0105552 0.999944i \(-0.496640\pi\)
0.0105552 + 0.999944i \(0.496640\pi\)
\(240\) 0 0
\(241\) −7030.00 −1.87901 −0.939506 0.342531i \(-0.888716\pi\)
−0.939506 + 0.342531i \(0.888716\pi\)
\(242\) 0 0
\(243\) 560.000 0.147835
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −990.000 −0.255029
\(248\) 0 0
\(249\) 3270.00 0.832240
\(250\) 0 0
\(251\) 670.000 0.168486 0.0842431 0.996445i \(-0.473153\pi\)
0.0842431 + 0.996445i \(0.473153\pi\)
\(252\) 0 0
\(253\) −2090.00 −0.519356
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4866.00 −1.18106 −0.590531 0.807015i \(-0.701082\pi\)
−0.590531 + 0.807015i \(0.701082\pi\)
\(258\) 0 0
\(259\) 51.0000 0.0122355
\(260\) 0 0
\(261\) 138.000 0.0327279
\(262\) 0 0
\(263\) −483.000 −0.113244 −0.0566218 0.998396i \(-0.518033\pi\)
−0.0566218 + 0.998396i \(0.518033\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2555.00 −0.585631
\(268\) 0 0
\(269\) −2364.00 −0.535820 −0.267910 0.963444i \(-0.586333\pi\)
−0.267910 + 0.963444i \(0.586333\pi\)
\(270\) 0 0
\(271\) −2200.00 −0.493138 −0.246569 0.969125i \(-0.579303\pi\)
−0.246569 + 0.969125i \(0.579303\pi\)
\(272\) 0 0
\(273\) 90.0000 0.0199526
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1064.00 0.230793 0.115396 0.993320i \(-0.463186\pi\)
0.115396 + 0.993320i \(0.463186\pi\)
\(278\) 0 0
\(279\) 510.000 0.109437
\(280\) 0 0
\(281\) 5114.00 1.08568 0.542839 0.839837i \(-0.317349\pi\)
0.542839 + 0.839837i \(0.317349\pi\)
\(282\) 0 0
\(283\) 2486.00 0.522181 0.261091 0.965314i \(-0.415918\pi\)
0.261091 + 0.965314i \(0.415918\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 314.000 0.0645813
\(288\) 0 0
\(289\) 7856.00 1.59902
\(290\) 0 0
\(291\) −8680.00 −1.74856
\(292\) 0 0
\(293\) 1706.00 0.340156 0.170078 0.985431i \(-0.445598\pi\)
0.170078 + 0.985431i \(0.445598\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1595.00 −0.311620
\(298\) 0 0
\(299\) 3420.00 0.661484
\(300\) 0 0
\(301\) −484.000 −0.0926820
\(302\) 0 0
\(303\) −2170.00 −0.411430
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2126.00 0.395235 0.197618 0.980279i \(-0.436680\pi\)
0.197618 + 0.980279i \(0.436680\pi\)
\(308\) 0 0
\(309\) 1240.00 0.228288
\(310\) 0 0
\(311\) 505.000 0.0920769 0.0460385 0.998940i \(-0.485340\pi\)
0.0460385 + 0.998940i \(0.485340\pi\)
\(312\) 0 0
\(313\) −7090.00 −1.28035 −0.640177 0.768228i \(-0.721139\pi\)
−0.640177 + 0.768228i \(0.721139\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7687.00 1.36197 0.680986 0.732297i \(-0.261552\pi\)
0.680986 + 0.732297i \(0.261552\pi\)
\(318\) 0 0
\(319\) −759.000 −0.133216
\(320\) 0 0
\(321\) 460.000 0.0799835
\(322\) 0 0
\(323\) 6215.00 1.07062
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −9350.00 −1.58121
\(328\) 0 0
\(329\) 470.000 0.0787597
\(330\) 0 0
\(331\) −5396.00 −0.896045 −0.448023 0.894022i \(-0.647872\pi\)
−0.448023 + 0.894022i \(0.647872\pi\)
\(332\) 0 0
\(333\) 102.000 0.0167855
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −2161.00 −0.349309 −0.174655 0.984630i \(-0.555881\pi\)
−0.174655 + 0.984630i \(0.555881\pi\)
\(338\) 0 0
\(339\) −2160.00 −0.346062
\(340\) 0 0
\(341\) −2805.00 −0.445452
\(342\) 0 0
\(343\) 685.000 0.107832
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5802.00 0.897601 0.448801 0.893632i \(-0.351851\pi\)
0.448801 + 0.893632i \(0.351851\pi\)
\(348\) 0 0
\(349\) 7234.00 1.10953 0.554767 0.832006i \(-0.312808\pi\)
0.554767 + 0.832006i \(0.312808\pi\)
\(350\) 0 0
\(351\) 2610.00 0.396899
\(352\) 0 0
\(353\) −3750.00 −0.565417 −0.282709 0.959206i \(-0.591233\pi\)
−0.282709 + 0.959206i \(0.591233\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −565.000 −0.0837618
\(358\) 0 0
\(359\) −2560.00 −0.376356 −0.188178 0.982135i \(-0.560258\pi\)
−0.188178 + 0.982135i \(0.560258\pi\)
\(360\) 0 0
\(361\) −3834.00 −0.558974
\(362\) 0 0
\(363\) 605.000 0.0874773
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8396.00 1.19419 0.597095 0.802171i \(-0.296322\pi\)
0.597095 + 0.802171i \(0.296322\pi\)
\(368\) 0 0
\(369\) 628.000 0.0885972
\(370\) 0 0
\(371\) −545.000 −0.0762668
\(372\) 0 0
\(373\) 6418.00 0.890915 0.445458 0.895303i \(-0.353041\pi\)
0.445458 + 0.895303i \(0.353041\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1242.00 0.169672
\(378\) 0 0
\(379\) 8134.00 1.10242 0.551208 0.834368i \(-0.314167\pi\)
0.551208 + 0.834368i \(0.314167\pi\)
\(380\) 0 0
\(381\) −13480.0 −1.81260
\(382\) 0 0
\(383\) 5734.00 0.764997 0.382498 0.923956i \(-0.375064\pi\)
0.382498 + 0.923956i \(0.375064\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −968.000 −0.127148
\(388\) 0 0
\(389\) 14814.0 1.93085 0.965424 0.260686i \(-0.0839487\pi\)
0.965424 + 0.260686i \(0.0839487\pi\)
\(390\) 0 0
\(391\) −21470.0 −2.77694
\(392\) 0 0
\(393\) −1585.00 −0.203442
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 10546.0 1.33322 0.666610 0.745406i \(-0.267745\pi\)
0.666610 + 0.745406i \(0.267745\pi\)
\(398\) 0 0
\(399\) −275.000 −0.0345043
\(400\) 0 0
\(401\) 3027.00 0.376961 0.188480 0.982077i \(-0.439644\pi\)
0.188480 + 0.982077i \(0.439644\pi\)
\(402\) 0 0
\(403\) 4590.00 0.567355
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −561.000 −0.0683237
\(408\) 0 0
\(409\) −5432.00 −0.656712 −0.328356 0.944554i \(-0.606495\pi\)
−0.328356 + 0.944554i \(0.606495\pi\)
\(410\) 0 0
\(411\) 9540.00 1.14495
\(412\) 0 0
\(413\) 102.000 0.0121528
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −14340.0 −1.68401
\(418\) 0 0
\(419\) −13132.0 −1.53112 −0.765561 0.643363i \(-0.777539\pi\)
−0.765561 + 0.643363i \(0.777539\pi\)
\(420\) 0 0
\(421\) 2724.00 0.315344 0.157672 0.987492i \(-0.449601\pi\)
0.157672 + 0.987492i \(0.449601\pi\)
\(422\) 0 0
\(423\) 940.000 0.108048
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −129.000 −0.0146200
\(428\) 0 0
\(429\) −990.000 −0.111416
\(430\) 0 0
\(431\) −152.000 −0.0169874 −0.00849372 0.999964i \(-0.502704\pi\)
−0.00849372 + 0.999964i \(0.502704\pi\)
\(432\) 0 0
\(433\) −11260.0 −1.24970 −0.624851 0.780744i \(-0.714840\pi\)
−0.624851 + 0.780744i \(0.714840\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10450.0 −1.14392
\(438\) 0 0
\(439\) −11432.0 −1.24287 −0.621435 0.783466i \(-0.713450\pi\)
−0.621435 + 0.783466i \(0.713450\pi\)
\(440\) 0 0
\(441\) 684.000 0.0738581
\(442\) 0 0
\(443\) −10164.0 −1.09008 −0.545041 0.838409i \(-0.683486\pi\)
−0.545041 + 0.838409i \(0.683486\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 9765.00 1.03326
\(448\) 0 0
\(449\) 5354.00 0.562741 0.281371 0.959599i \(-0.409211\pi\)
0.281371 + 0.959599i \(0.409211\pi\)
\(450\) 0 0
\(451\) −3454.00 −0.360626
\(452\) 0 0
\(453\) 7650.00 0.793440
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8675.00 0.887964 0.443982 0.896036i \(-0.353565\pi\)
0.443982 + 0.896036i \(0.353565\pi\)
\(458\) 0 0
\(459\) −16385.0 −1.66620
\(460\) 0 0
\(461\) −2323.00 −0.234692 −0.117346 0.993091i \(-0.537439\pi\)
−0.117346 + 0.993091i \(0.537439\pi\)
\(462\) 0 0
\(463\) 15722.0 1.57811 0.789053 0.614325i \(-0.210572\pi\)
0.789053 + 0.614325i \(0.210572\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8587.00 −0.850876 −0.425438 0.904988i \(-0.639880\pi\)
−0.425438 + 0.904988i \(0.639880\pi\)
\(468\) 0 0
\(469\) −664.000 −0.0653746
\(470\) 0 0
\(471\) −16055.0 −1.57065
\(472\) 0 0
\(473\) 5324.00 0.517543
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1090.00 −0.104628
\(478\) 0 0
\(479\) −420.000 −0.0400632 −0.0200316 0.999799i \(-0.506377\pi\)
−0.0200316 + 0.999799i \(0.506377\pi\)
\(480\) 0 0
\(481\) 918.000 0.0870212
\(482\) 0 0
\(483\) 950.000 0.0894959
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6132.00 −0.570570 −0.285285 0.958443i \(-0.592088\pi\)
−0.285285 + 0.958443i \(0.592088\pi\)
\(488\) 0 0
\(489\) 6485.00 0.599717
\(490\) 0 0
\(491\) −1033.00 −0.0949463 −0.0474732 0.998873i \(-0.515117\pi\)
−0.0474732 + 0.998873i \(0.515117\pi\)
\(492\) 0 0
\(493\) −7797.00 −0.712291
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1029.00 0.0928711
\(498\) 0 0
\(499\) −7984.00 −0.716258 −0.358129 0.933672i \(-0.616585\pi\)
−0.358129 + 0.933672i \(0.616585\pi\)
\(500\) 0 0
\(501\) −18365.0 −1.63770
\(502\) 0 0
\(503\) −16512.0 −1.46369 −0.731843 0.681474i \(-0.761339\pi\)
−0.731843 + 0.681474i \(0.761339\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −9365.00 −0.820344
\(508\) 0 0
\(509\) 9600.00 0.835977 0.417989 0.908452i \(-0.362735\pi\)
0.417989 + 0.908452i \(0.362735\pi\)
\(510\) 0 0
\(511\) −758.000 −0.0656202
\(512\) 0 0
\(513\) −7975.00 −0.686364
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −5170.00 −0.439799
\(518\) 0 0
\(519\) 5310.00 0.449100
\(520\) 0 0
\(521\) 10678.0 0.897911 0.448956 0.893554i \(-0.351796\pi\)
0.448956 + 0.893554i \(0.351796\pi\)
\(522\) 0 0
\(523\) 6492.00 0.542783 0.271391 0.962469i \(-0.412516\pi\)
0.271391 + 0.962469i \(0.412516\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −28815.0 −2.38179
\(528\) 0 0
\(529\) 23933.0 1.96704
\(530\) 0 0
\(531\) 204.000 0.0166720
\(532\) 0 0
\(533\) 5652.00 0.459316
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 13900.0 1.11700
\(538\) 0 0
\(539\) −3762.00 −0.300632
\(540\) 0 0
\(541\) −6241.00 −0.495973 −0.247987 0.968763i \(-0.579769\pi\)
−0.247987 + 0.968763i \(0.579769\pi\)
\(542\) 0 0
\(543\) 910.000 0.0719187
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −16756.0 −1.30975 −0.654876 0.755736i \(-0.727279\pi\)
−0.654876 + 0.755736i \(0.727279\pi\)
\(548\) 0 0
\(549\) −258.000 −0.0200568
\(550\) 0 0
\(551\) −3795.00 −0.293416
\(552\) 0 0
\(553\) −634.000 −0.0487530
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13862.0 1.05449 0.527246 0.849713i \(-0.323225\pi\)
0.527246 + 0.849713i \(0.323225\pi\)
\(558\) 0 0
\(559\) −8712.00 −0.659174
\(560\) 0 0
\(561\) 6215.00 0.467732
\(562\) 0 0
\(563\) −198.000 −0.0148219 −0.00741093 0.999973i \(-0.502359\pi\)
−0.00741093 + 0.999973i \(0.502359\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 671.000 0.0496990
\(568\) 0 0
\(569\) 5548.00 0.408760 0.204380 0.978892i \(-0.434482\pi\)
0.204380 + 0.978892i \(0.434482\pi\)
\(570\) 0 0
\(571\) 17089.0 1.25246 0.626228 0.779640i \(-0.284598\pi\)
0.626228 + 0.779640i \(0.284598\pi\)
\(572\) 0 0
\(573\) −13820.0 −1.00757
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 14294.0 1.03131 0.515656 0.856796i \(-0.327548\pi\)
0.515656 + 0.856796i \(0.327548\pi\)
\(578\) 0 0
\(579\) 16305.0 1.17032
\(580\) 0 0
\(581\) −654.000 −0.0466996
\(582\) 0 0
\(583\) 5995.00 0.425879
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15801.0 −1.11103 −0.555517 0.831505i \(-0.687480\pi\)
−0.555517 + 0.831505i \(0.687480\pi\)
\(588\) 0 0
\(589\) −14025.0 −0.981138
\(590\) 0 0
\(591\) 880.000 0.0612493
\(592\) 0 0
\(593\) −10714.0 −0.741941 −0.370971 0.928645i \(-0.620975\pi\)
−0.370971 + 0.928645i \(0.620975\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 8655.00 0.593343
\(598\) 0 0
\(599\) 3329.00 0.227077 0.113539 0.993534i \(-0.463781\pi\)
0.113539 + 0.993534i \(0.463781\pi\)
\(600\) 0 0
\(601\) 13718.0 0.931063 0.465532 0.885031i \(-0.345863\pi\)
0.465532 + 0.885031i \(0.345863\pi\)
\(602\) 0 0
\(603\) −1328.00 −0.0896855
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −9819.00 −0.656575 −0.328287 0.944578i \(-0.606471\pi\)
−0.328287 + 0.944578i \(0.606471\pi\)
\(608\) 0 0
\(609\) 345.000 0.0229558
\(610\) 0 0
\(611\) 8460.00 0.560155
\(612\) 0 0
\(613\) 16402.0 1.08070 0.540351 0.841440i \(-0.318291\pi\)
0.540351 + 0.841440i \(0.318291\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −24340.0 −1.58815 −0.794077 0.607817i \(-0.792046\pi\)
−0.794077 + 0.607817i \(0.792046\pi\)
\(618\) 0 0
\(619\) −2536.00 −0.164670 −0.0823348 0.996605i \(-0.526238\pi\)
−0.0823348 + 0.996605i \(0.526238\pi\)
\(620\) 0 0
\(621\) 27550.0 1.78026
\(622\) 0 0
\(623\) 511.000 0.0328616
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3025.00 0.192674
\(628\) 0 0
\(629\) −5763.00 −0.365319
\(630\) 0 0
\(631\) −3077.00 −0.194126 −0.0970629 0.995278i \(-0.530945\pi\)
−0.0970629 + 0.995278i \(0.530945\pi\)
\(632\) 0 0
\(633\) −13665.0 −0.858033
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6156.00 0.382904
\(638\) 0 0
\(639\) 2058.00 0.127407
\(640\) 0 0
\(641\) 12231.0 0.753659 0.376830 0.926283i \(-0.377014\pi\)
0.376830 + 0.926283i \(0.377014\pi\)
\(642\) 0 0
\(643\) −4911.00 −0.301199 −0.150599 0.988595i \(-0.548120\pi\)
−0.150599 + 0.988595i \(0.548120\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24426.0 −1.48421 −0.742106 0.670283i \(-0.766173\pi\)
−0.742106 + 0.670283i \(0.766173\pi\)
\(648\) 0 0
\(649\) −1122.00 −0.0678619
\(650\) 0 0
\(651\) 1275.00 0.0767607
\(652\) 0 0
\(653\) 15351.0 0.919956 0.459978 0.887930i \(-0.347857\pi\)
0.459978 + 0.887930i \(0.347857\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1516.00 −0.0900225
\(658\) 0 0
\(659\) −9907.00 −0.585617 −0.292809 0.956171i \(-0.594590\pi\)
−0.292809 + 0.956171i \(0.594590\pi\)
\(660\) 0 0
\(661\) 8626.00 0.507583 0.253792 0.967259i \(-0.418322\pi\)
0.253792 + 0.967259i \(0.418322\pi\)
\(662\) 0 0
\(663\) −10170.0 −0.595732
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 13110.0 0.761051
\(668\) 0 0
\(669\) −7530.00 −0.435167
\(670\) 0 0
\(671\) 1419.00 0.0816392
\(672\) 0 0
\(673\) 30205.0 1.73004 0.865020 0.501737i \(-0.167305\pi\)
0.865020 + 0.501737i \(0.167305\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 29160.0 1.65541 0.827703 0.561166i \(-0.189647\pi\)
0.827703 + 0.561166i \(0.189647\pi\)
\(678\) 0 0
\(679\) 1736.00 0.0981172
\(680\) 0 0
\(681\) −27090.0 −1.52436
\(682\) 0 0
\(683\) −13533.0 −0.758164 −0.379082 0.925363i \(-0.623760\pi\)
−0.379082 + 0.925363i \(0.623760\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −22050.0 −1.22454
\(688\) 0 0
\(689\) −9810.00 −0.542426
\(690\) 0 0
\(691\) 20002.0 1.10118 0.550588 0.834777i \(-0.314404\pi\)
0.550588 + 0.834777i \(0.314404\pi\)
\(692\) 0 0
\(693\) 22.0000 0.00120593
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −35482.0 −1.92823
\(698\) 0 0
\(699\) −28675.0 −1.55163
\(700\) 0 0
\(701\) −35903.0 −1.93443 −0.967217 0.253953i \(-0.918269\pi\)
−0.967217 + 0.253953i \(0.918269\pi\)
\(702\) 0 0
\(703\) −2805.00 −0.150487
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 434.000 0.0230866
\(708\) 0 0
\(709\) 31030.0 1.64366 0.821831 0.569732i \(-0.192953\pi\)
0.821831 + 0.569732i \(0.192953\pi\)
\(710\) 0 0
\(711\) −1268.00 −0.0668829
\(712\) 0 0
\(713\) 48450.0 2.54483
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 390.000 0.0203136
\(718\) 0 0
\(719\) −7275.00 −0.377346 −0.188673 0.982040i \(-0.560419\pi\)
−0.188673 + 0.982040i \(0.560419\pi\)
\(720\) 0 0
\(721\) −248.000 −0.0128100
\(722\) 0 0
\(723\) −35150.0 −1.80808
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −374.000 −0.0190796 −0.00953982 0.999954i \(-0.503037\pi\)
−0.00953982 + 0.999954i \(0.503037\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 0 0
\(731\) 54692.0 2.76725
\(732\) 0 0
\(733\) −1712.00 −0.0862676 −0.0431338 0.999069i \(-0.513734\pi\)
−0.0431338 + 0.999069i \(0.513734\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7304.00 0.365056
\(738\) 0 0
\(739\) −18056.0 −0.898783 −0.449392 0.893335i \(-0.648359\pi\)
−0.449392 + 0.893335i \(0.648359\pi\)
\(740\) 0 0
\(741\) −4950.00 −0.245402
\(742\) 0 0
\(743\) 17799.0 0.878845 0.439423 0.898280i \(-0.355183\pi\)
0.439423 + 0.898280i \(0.355183\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1308.00 −0.0640659
\(748\) 0 0
\(749\) −92.0000 −0.00448813
\(750\) 0 0
\(751\) −6051.00 −0.294013 −0.147007 0.989135i \(-0.546964\pi\)
−0.147007 + 0.989135i \(0.546964\pi\)
\(752\) 0 0
\(753\) 3350.00 0.162126
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 5562.00 0.267047 0.133523 0.991046i \(-0.457371\pi\)
0.133523 + 0.991046i \(0.457371\pi\)
\(758\) 0 0
\(759\) −10450.0 −0.499751
\(760\) 0 0
\(761\) −406.000 −0.0193397 −0.00966983 0.999953i \(-0.503078\pi\)
−0.00966983 + 0.999953i \(0.503078\pi\)
\(762\) 0 0
\(763\) 1870.00 0.0887268
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1836.00 0.0864330
\(768\) 0 0
\(769\) 7458.00 0.349730 0.174865 0.984592i \(-0.444051\pi\)
0.174865 + 0.984592i \(0.444051\pi\)
\(770\) 0 0
\(771\) −24330.0 −1.13648
\(772\) 0 0
\(773\) −36283.0 −1.68824 −0.844120 0.536155i \(-0.819876\pi\)
−0.844120 + 0.536155i \(0.819876\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 255.000 0.0117736
\(778\) 0 0
\(779\) −17270.0 −0.794303
\(780\) 0 0
\(781\) −11319.0 −0.518599
\(782\) 0 0
\(783\) 10005.0 0.456641
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 13368.0 0.605486 0.302743 0.953072i \(-0.402098\pi\)
0.302743 + 0.953072i \(0.402098\pi\)
\(788\) 0 0
\(789\) −2415.00 −0.108969
\(790\) 0 0
\(791\) 432.000 0.0194186
\(792\) 0 0
\(793\) −2322.00 −0.103981
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17894.0 0.795280 0.397640 0.917542i \(-0.369829\pi\)
0.397640 + 0.917542i \(0.369829\pi\)
\(798\) 0 0
\(799\) −53110.0 −2.35156
\(800\) 0 0
\(801\) 1022.00 0.0450819
\(802\) 0 0
\(803\) 8338.00 0.366428
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −11820.0 −0.515593
\(808\) 0 0
\(809\) −10662.0 −0.463357 −0.231679 0.972792i \(-0.574422\pi\)
−0.231679 + 0.972792i \(0.574422\pi\)
\(810\) 0 0
\(811\) 20805.0 0.900817 0.450408 0.892823i \(-0.351278\pi\)
0.450408 + 0.892823i \(0.351278\pi\)
\(812\) 0 0
\(813\) −11000.0 −0.474523
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 26620.0 1.13992
\(818\) 0 0
\(819\) −36.0000 −0.00153595
\(820\) 0 0
\(821\) 5834.00 0.248000 0.124000 0.992282i \(-0.460428\pi\)
0.124000 + 0.992282i \(0.460428\pi\)
\(822\) 0 0
\(823\) −8948.00 −0.378989 −0.189494 0.981882i \(-0.560685\pi\)
−0.189494 + 0.981882i \(0.560685\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14156.0 0.595227 0.297613 0.954687i \(-0.403809\pi\)
0.297613 + 0.954687i \(0.403809\pi\)
\(828\) 0 0
\(829\) −18940.0 −0.793502 −0.396751 0.917926i \(-0.629862\pi\)
−0.396751 + 0.917926i \(0.629862\pi\)
\(830\) 0 0
\(831\) 5320.00 0.222080
\(832\) 0 0
\(833\) −38646.0 −1.60745
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 36975.0 1.52693
\(838\) 0 0
\(839\) 17960.0 0.739032 0.369516 0.929224i \(-0.379523\pi\)
0.369516 + 0.929224i \(0.379523\pi\)
\(840\) 0 0
\(841\) −19628.0 −0.804789
\(842\) 0 0
\(843\) 25570.0 1.04469
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −121.000 −0.00490863
\(848\) 0 0
\(849\) 12430.0 0.502469
\(850\) 0 0
\(851\) 9690.00 0.390328
\(852\) 0 0
\(853\) 39698.0 1.59347 0.796737 0.604326i \(-0.206558\pi\)
0.796737 + 0.604326i \(0.206558\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 15865.0 0.632366 0.316183 0.948698i \(-0.397599\pi\)
0.316183 + 0.948698i \(0.397599\pi\)
\(858\) 0 0
\(859\) 29922.0 1.18850 0.594252 0.804279i \(-0.297448\pi\)
0.594252 + 0.804279i \(0.297448\pi\)
\(860\) 0 0
\(861\) 1570.00 0.0621434
\(862\) 0 0
\(863\) −41098.0 −1.62108 −0.810540 0.585683i \(-0.800826\pi\)
−0.810540 + 0.585683i \(0.800826\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 39280.0 1.53866
\(868\) 0 0
\(869\) 6974.00 0.272240
\(870\) 0 0
\(871\) −11952.0 −0.464958
\(872\) 0 0
\(873\) 3472.00 0.134604
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −562.000 −0.0216390 −0.0108195 0.999941i \(-0.503444\pi\)
−0.0108195 + 0.999941i \(0.503444\pi\)
\(878\) 0 0
\(879\) 8530.00 0.327315
\(880\) 0 0
\(881\) 31058.0 1.18771 0.593854 0.804573i \(-0.297606\pi\)
0.593854 + 0.804573i \(0.297606\pi\)
\(882\) 0 0
\(883\) 36251.0 1.38159 0.690795 0.723051i \(-0.257261\pi\)
0.690795 + 0.723051i \(0.257261\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40104.0 −1.51811 −0.759053 0.651028i \(-0.774338\pi\)
−0.759053 + 0.651028i \(0.774338\pi\)
\(888\) 0 0
\(889\) 2696.00 0.101711
\(890\) 0 0
\(891\) −7381.00 −0.277523
\(892\) 0 0
\(893\) −25850.0 −0.968687
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 17100.0 0.636513
\(898\) 0 0
\(899\) 17595.0 0.652754
\(900\) 0 0
\(901\) 61585.0 2.27713
\(902\) 0 0
\(903\) −2420.00 −0.0891833
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 25757.0 0.942941 0.471470 0.881882i \(-0.343723\pi\)
0.471470 + 0.881882i \(0.343723\pi\)
\(908\) 0 0
\(909\) 868.000 0.0316719
\(910\) 0 0
\(911\) 17623.0 0.640918 0.320459 0.947262i \(-0.396163\pi\)
0.320459 + 0.947262i \(0.396163\pi\)
\(912\) 0 0
\(913\) 7194.00 0.260774
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 317.000 0.0114158
\(918\) 0 0
\(919\) 12688.0 0.455428 0.227714 0.973728i \(-0.426875\pi\)
0.227714 + 0.973728i \(0.426875\pi\)
\(920\) 0 0
\(921\) 10630.0 0.380315
\(922\) 0 0
\(923\) 18522.0 0.660519
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −496.000 −0.0175737
\(928\) 0 0
\(929\) 20091.0 0.709542 0.354771 0.934953i \(-0.384559\pi\)
0.354771 + 0.934953i \(0.384559\pi\)
\(930\) 0 0
\(931\) −18810.0 −0.662162
\(932\) 0 0
\(933\) 2525.00 0.0886011
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 43222.0 1.50694 0.753469 0.657483i \(-0.228379\pi\)
0.753469 + 0.657483i \(0.228379\pi\)
\(938\) 0 0
\(939\) −35450.0 −1.23202
\(940\) 0 0
\(941\) 199.000 0.00689396 0.00344698 0.999994i \(-0.498903\pi\)
0.00344698 + 0.999994i \(0.498903\pi\)
\(942\) 0 0
\(943\) 59660.0 2.06023
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 26087.0 0.895157 0.447578 0.894245i \(-0.352287\pi\)
0.447578 + 0.894245i \(0.352287\pi\)
\(948\) 0 0
\(949\) −13644.0 −0.466705
\(950\) 0 0
\(951\) 38435.0 1.31056
\(952\) 0 0
\(953\) 40695.0 1.38325 0.691627 0.722255i \(-0.256894\pi\)
0.691627 + 0.722255i \(0.256894\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −3795.00 −0.128187
\(958\) 0 0
\(959\) −1908.00 −0.0642466
\(960\) 0 0
\(961\) 35234.0 1.18271
\(962\) 0 0
\(963\) −184.000 −0.00615713
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −34463.0 −1.14608 −0.573038 0.819529i \(-0.694235\pi\)
−0.573038 + 0.819529i \(0.694235\pi\)
\(968\) 0 0
\(969\) 31075.0 1.03021
\(970\) 0 0
\(971\) 9604.00 0.317412 0.158706 0.987326i \(-0.449268\pi\)
0.158706 + 0.987326i \(0.449268\pi\)
\(972\) 0 0
\(973\) 2868.00 0.0944952
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 22880.0 0.749228 0.374614 0.927181i \(-0.377775\pi\)
0.374614 + 0.927181i \(0.377775\pi\)
\(978\) 0 0
\(979\) −5621.00 −0.183501
\(980\) 0 0
\(981\) 3740.00 0.121722
\(982\) 0 0
\(983\) 1038.00 0.0336796 0.0168398 0.999858i \(-0.494639\pi\)
0.0168398 + 0.999858i \(0.494639\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2350.00 0.0757865
\(988\) 0 0
\(989\) −91960.0 −2.95668
\(990\) 0 0
\(991\) −12040.0 −0.385937 −0.192968 0.981205i \(-0.561811\pi\)
−0.192968 + 0.981205i \(0.561811\pi\)
\(992\) 0 0
\(993\) −26980.0 −0.862220
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 19368.0 0.615236 0.307618 0.951510i \(-0.400468\pi\)
0.307618 + 0.951510i \(0.400468\pi\)
\(998\) 0 0
\(999\) 7395.00 0.234202
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.i.1.1 1
5.4 even 2 440.4.a.a.1.1 1
20.19 odd 2 880.4.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.4.a.a.1.1 1 5.4 even 2
880.4.a.n.1.1 1 20.19 odd 2
2200.4.a.i.1.1 1 1.1 even 1 trivial