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Properties

Label 800.4.a.h.1.1
Level $800$
Weight $4$
Character 800.1
Self dual yes
Analytic conductor $47.202$
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] = [800,4,Mod(1,800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("800.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 800.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: \(47.2015280046\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{3} -6.00000 q^{7} -23.0000 q^{9} +60.0000 q^{11} -50.0000 q^{13} +30.0000 q^{17} +40.0000 q^{19} -12.0000 q^{21} -178.000 q^{23} -100.000 q^{27} +166.000 q^{29} +20.0000 q^{31} +120.000 q^{33} -10.0000 q^{37} -100.000 q^{39} -250.000 q^{41} -142.000 q^{43} -214.000 q^{47} -307.000 q^{49} +60.0000 q^{51} -490.000 q^{53} +80.0000 q^{57} -800.000 q^{59} +250.000 q^{61} +138.000 q^{63} +774.000 q^{67} -356.000 q^{69} +100.000 q^{71} +230.000 q^{73} -360.000 q^{77} -1320.00 q^{79} +421.000 q^{81} -982.000 q^{83} +332.000 q^{87} +874.000 q^{89} +300.000 q^{91} +40.0000 q^{93} +310.000 q^{97} -1380.00 q^{99} +O(q^{100})\)

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
\(3\) 2.00000 0.384900 0.192450 − 0.981307i \(-0.438357\pi\)
0.192450 + 0.981307i \(0.438357\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −6.00000 −0.323970 −0.161985 − 0.986793i \(-0.551790\pi\)
−0.161985 + 0.986793i \(0.551790\pi\)
\(8\) 0 0
\(9\) −23.0000 −0.851852
\(10\) 0 0
\(11\) 60.0000 1.64461 0.822304 − 0.569049i \(-0.192689\pi\)
0.822304 + 0.569049i \(0.192689\pi\)
\(12\) 0 0
\(13\) −50.0000 −1.06673 −0.533366 − 0.845885i \(-0.679073\pi\)
−0.533366 + 0.845885i \(0.679073\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 30.0000 0.428004 0.214002 − 0.976833i \(-0.431350\pi\)
0.214002 + 0.976833i \(0.431350\pi\)
\(18\) 0 0
\(19\) 40.0000 0.482980 0.241490 − 0.970403i \(-0.422364\pi\)
0.241490 + 0.970403i \(0.422364\pi\)
\(20\) 0 0
\(21\) −12.0000 −0.124696
\(22\) 0 0
\(23\) −178.000 −1.61372 −0.806860 − 0.590743i \(-0.798835\pi\)
−0.806860 + 0.590743i \(0.798835\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −100.000 −0.712778
\(28\) 0 0
\(29\) 166.000 1.06295 0.531473 − 0.847075i \(-0.321639\pi\)
0.531473 + 0.847075i \(0.321639\pi\)
\(30\) 0 0
\(31\) 20.0000 0.115874 0.0579372 − 0.998320i \(-0.481548\pi\)
0.0579372 + 0.998320i \(0.481548\pi\)
\(32\) 0 0
\(33\) 120.000 0.633010
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0000 −0.0444322 −0.0222161 − 0.999753i \(-0.507072\pi\)
−0.0222161 + 0.999753i \(0.507072\pi\)
\(38\) 0 0
\(39\) −100.000 −0.410585
\(40\) 0 0
\(41\) −250.000 −0.952279 −0.476140 − 0.879370i \(-0.657964\pi\)
−0.476140 + 0.879370i \(0.657964\pi\)
\(42\) 0 0
\(43\) −142.000 −0.503600 −0.251800 − 0.967779i \(-0.581023\pi\)
−0.251800 + 0.967779i \(0.581023\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −214.000 −0.664151 −0.332076 − 0.943253i \(-0.607749\pi\)
−0.332076 + 0.943253i \(0.607749\pi\)
\(48\) 0 0
\(49\) −307.000 −0.895044
\(50\) 0 0
\(51\) 60.0000 0.164739
\(52\) 0 0
\(53\) −490.000 −1.26994 −0.634969 − 0.772538i \(-0.718987\pi\)
−0.634969 + 0.772538i \(0.718987\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 80.0000 0.185899
\(58\) 0 0
\(59\) −800.000 −1.76527 −0.882637 − 0.470056i \(-0.844234\pi\)
−0.882637 + 0.470056i \(0.844234\pi\)
\(60\) 0 0
\(61\) 250.000 0.524741 0.262371 − 0.964967i \(-0.415496\pi\)
0.262371 + 0.964967i \(0.415496\pi\)
\(62\) 0 0
\(63\) 138.000 0.275974
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 774.000 1.41133 0.705665 − 0.708545i \(-0.250648\pi\)
0.705665 + 0.708545i \(0.250648\pi\)
\(68\) 0 0
\(69\) −356.000 −0.621121
\(70\) 0 0
\(71\) 100.000 0.167152 0.0835762 − 0.996501i \(-0.473366\pi\)
0.0835762 + 0.996501i \(0.473366\pi\)
\(72\) 0 0
\(73\) 230.000 0.368760 0.184380 − 0.982855i \(-0.440972\pi\)
0.184380 + 0.982855i \(0.440972\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −360.000 −0.532803
\(78\) 0 0
\(79\) −1320.00 −1.87989 −0.939947 − 0.341321i \(-0.889126\pi\)
−0.939947 + 0.341321i \(0.889126\pi\)
\(80\) 0 0
\(81\) 421.000 0.577503
\(82\) 0 0
\(83\) −982.000 −1.29866 −0.649328 − 0.760508i \(-0.724950\pi\)
−0.649328 + 0.760508i \(0.724950\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 332.000 0.409128
\(88\) 0 0
\(89\) 874.000 1.04094 0.520471 − 0.853879i \(-0.325756\pi\)
0.520471 + 0.853879i \(0.325756\pi\)
\(90\) 0 0
\(91\) 300.000 0.345588
\(92\) 0 0
\(93\) 40.0000 0.0446001
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 310.000 0.324492 0.162246 − 0.986750i \(-0.448126\pi\)
0.162246 + 0.986750i \(0.448126\pi\)
\(98\) 0 0
\(99\) −1380.00 −1.40096
\(100\) 0 0
\(101\) −1498.00 −1.47581 −0.737904 − 0.674906i \(-0.764184\pi\)
−0.737904 + 0.674906i \(0.764184\pi\)
\(102\) 0 0
\(103\) −1402.00 −1.34120 −0.670598 − 0.741821i \(-0.733962\pi\)
−0.670598 + 0.741821i \(0.733962\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1194.00 −1.07877 −0.539385 − 0.842059i \(-0.681343\pi\)
−0.539385 + 0.842059i \(0.681343\pi\)
\(108\) 0 0
\(109\) 650.000 0.571181 0.285590 − 0.958352i \(-0.407810\pi\)
0.285590 + 0.958352i \(0.407810\pi\)
\(110\) 0 0
\(111\) −20.0000 −0.0171019
\(112\) 0 0
\(113\) 1510.00 1.25707 0.628535 − 0.777782i \(-0.283655\pi\)
0.628535 + 0.777782i \(0.283655\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1150.00 0.908697
\(118\) 0 0
\(119\) −180.000 −0.138660
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) 0 0
\(123\) −500.000 −0.366532
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1246.00 −0.870588 −0.435294 − 0.900288i \(-0.643355\pi\)
−0.435294 + 0.900288i \(0.643355\pi\)
\(128\) 0 0
\(129\) −284.000 −0.193836
\(130\) 0 0
\(131\) 2660.00 1.77409 0.887043 − 0.461687i \(-0.152756\pi\)
0.887043 + 0.461687i \(0.152756\pi\)
\(132\) 0 0
\(133\) −240.000 −0.156471
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2770.00 −1.72742 −0.863712 − 0.503986i \(-0.831866\pi\)
−0.863712 + 0.503986i \(0.831866\pi\)
\(138\) 0 0
\(139\) −560.000 −0.341716 −0.170858 − 0.985296i \(-0.554654\pi\)
−0.170858 + 0.985296i \(0.554654\pi\)
\(140\) 0 0
\(141\) −428.000 −0.255632
\(142\) 0 0
\(143\) −3000.00 −1.75435
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −614.000 −0.344502
\(148\) 0 0
\(149\) −2350.00 −1.29208 −0.646039 − 0.763305i \(-0.723576\pi\)
−0.646039 + 0.763305i \(0.723576\pi\)
\(150\) 0 0
\(151\) 580.000 0.312581 0.156290 − 0.987711i \(-0.450046\pi\)
0.156290 + 0.987711i \(0.450046\pi\)
\(152\) 0 0
\(153\) −690.000 −0.364596
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1310.00 0.665920 0.332960 − 0.942941i \(-0.391953\pi\)
0.332960 + 0.942941i \(0.391953\pi\)
\(158\) 0 0
\(159\) −980.000 −0.488799
\(160\) 0 0
\(161\) 1068.00 0.522796
\(162\) 0 0
\(163\) −1862.00 −0.894743 −0.447371 − 0.894348i \(-0.647640\pi\)
−0.447371 + 0.894348i \(0.647640\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −726.000 −0.336405 −0.168202 − 0.985752i \(-0.553796\pi\)
−0.168202 + 0.985752i \(0.553796\pi\)
\(168\) 0 0
\(169\) 303.000 0.137915
\(170\) 0 0
\(171\) −920.000 −0.411428
\(172\) 0 0
\(173\) −3250.00 −1.42828 −0.714141 − 0.700001i \(-0.753183\pi\)
−0.714141 + 0.700001i \(0.753183\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1600.00 −0.679454
\(178\) 0 0
\(179\) −1120.00 −0.467669 −0.233834 − 0.972276i \(-0.575127\pi\)
−0.233834 + 0.972276i \(0.575127\pi\)
\(180\) 0 0
\(181\) −2842.00 −1.16710 −0.583548 − 0.812079i \(-0.698336\pi\)
−0.583548 + 0.812079i \(0.698336\pi\)
\(182\) 0 0
\(183\) 500.000 0.201973
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1800.00 0.703899
\(188\) 0 0
\(189\) 600.000 0.230918
\(190\) 0 0
\(191\) 3180.00 1.20469 0.602347 − 0.798234i \(-0.294232\pi\)
0.602347 + 0.798234i \(0.294232\pi\)
\(192\) 0 0
\(193\) 4670.00 1.74173 0.870865 − 0.491522i \(-0.163559\pi\)
0.870865 + 0.491522i \(0.163559\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2990.00 1.08136 0.540682 − 0.841227i \(-0.318166\pi\)
0.540682 + 0.841227i \(0.318166\pi\)
\(198\) 0 0
\(199\) −4240.00 −1.51038 −0.755190 − 0.655506i \(-0.772455\pi\)
−0.755190 + 0.655506i \(0.772455\pi\)
\(200\) 0 0
\(201\) 1548.00 0.543221
\(202\) 0 0
\(203\) −996.000 −0.344362
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4094.00 1.37465
\(208\) 0 0
\(209\) 2400.00 0.794313
\(210\) 0 0
\(211\) −4060.00 −1.32465 −0.662327 − 0.749215i \(-0.730431\pi\)
−0.662327 + 0.749215i \(0.730431\pi\)
\(212\) 0 0
\(213\) 200.000 0.0643370
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −120.000 −0.0375398
\(218\) 0 0
\(219\) 460.000 0.141936
\(220\) 0 0
\(221\) −1500.00 −0.456565
\(222\) 0 0
\(223\) 5622.00 1.68824 0.844119 − 0.536156i \(-0.180124\pi\)
0.844119 + 0.536156i \(0.180124\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1554.00 −0.454373 −0.227186 − 0.973851i \(-0.572953\pi\)
−0.227186 + 0.973851i \(0.572953\pi\)
\(228\) 0 0
\(229\) 1134.00 0.327235 0.163618 − 0.986524i \(-0.447684\pi\)
0.163618 + 0.986524i \(0.447684\pi\)
\(230\) 0 0
\(231\) −720.000 −0.205076
\(232\) 0 0
\(233\) 1710.00 0.480798 0.240399 − 0.970674i \(-0.422722\pi\)
0.240399 + 0.970674i \(0.422722\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2640.00 −0.723571
\(238\) 0 0
\(239\) 4440.00 1.20167 0.600836 − 0.799372i \(-0.294834\pi\)
0.600836 + 0.799372i \(0.294834\pi\)
\(240\) 0 0
\(241\) −850.000 −0.227192 −0.113596 − 0.993527i \(-0.536237\pi\)
−0.113596 + 0.993527i \(0.536237\pi\)
\(242\) 0 0
\(243\) 3542.00 0.935059
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2000.00 −0.515210
\(248\) 0 0
\(249\) −1964.00 −0.499853
\(250\) 0 0
\(251\) −660.000 −0.165971 −0.0829857 − 0.996551i \(-0.526446\pi\)
−0.0829857 + 0.996551i \(0.526446\pi\)
\(252\) 0 0
\(253\) −10680.0 −2.65394
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7590.00 1.84222 0.921111 − 0.389299i \(-0.127283\pi\)
0.921111 + 0.389299i \(0.127283\pi\)
\(258\) 0 0
\(259\) 60.0000 0.0143947
\(260\) 0 0
\(261\) −3818.00 −0.905472
\(262\) 0 0
\(263\) −762.000 −0.178658 −0.0893288 − 0.996002i \(-0.528472\pi\)
−0.0893288 + 0.996002i \(0.528472\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1748.00 0.400659
\(268\) 0 0
\(269\) −150.000 −0.0339987 −0.0169994 − 0.999856i \(-0.505411\pi\)
−0.0169994 + 0.999856i \(0.505411\pi\)
\(270\) 0 0
\(271\) −6580.00 −1.47493 −0.737466 − 0.675384i \(-0.763978\pi\)
−0.737466 + 0.675384i \(0.763978\pi\)
\(272\) 0 0
\(273\) 600.000 0.133017
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −4530.00 −0.982604 −0.491302 − 0.870989i \(-0.663479\pi\)
−0.491302 + 0.870989i \(0.663479\pi\)
\(278\) 0 0
\(279\) −460.000 −0.0987078
\(280\) 0 0
\(281\) 6950.00 1.47545 0.737726 − 0.675100i \(-0.235899\pi\)
0.737726 + 0.675100i \(0.235899\pi\)
\(282\) 0 0
\(283\) 3882.00 0.815410 0.407705 − 0.913114i \(-0.366329\pi\)
0.407705 + 0.913114i \(0.366329\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1500.00 0.308509
\(288\) 0 0
\(289\) −4013.00 −0.816813
\(290\) 0 0
\(291\) 620.000 0.124897
\(292\) 0 0
\(293\) −1370.00 −0.273161 −0.136581 − 0.990629i \(-0.543611\pi\)
−0.136581 + 0.990629i \(0.543611\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −6000.00 −1.17224
\(298\) 0 0
\(299\) 8900.00 1.72141
\(300\) 0 0
\(301\) 852.000 0.163151
\(302\) 0 0
\(303\) −2996.00 −0.568039
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4106.00 −0.763328 −0.381664 − 0.924301i \(-0.624649\pi\)
−0.381664 + 0.924301i \(0.624649\pi\)
\(308\) 0 0
\(309\) −2804.00 −0.516226
\(310\) 0 0
\(311\) 2220.00 0.404774 0.202387 − 0.979306i \(-0.435130\pi\)
0.202387 + 0.979306i \(0.435130\pi\)
\(312\) 0 0
\(313\) 9430.00 1.70292 0.851462 − 0.524417i \(-0.175717\pi\)
0.851462 + 0.524417i \(0.175717\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6470.00 1.14635 0.573173 − 0.819435i \(-0.305712\pi\)
0.573173 + 0.819435i \(0.305712\pi\)
\(318\) 0 0
\(319\) 9960.00 1.74813
\(320\) 0 0
\(321\) −2388.00 −0.415219
\(322\) 0 0
\(323\) 1200.00 0.206718
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1300.00 0.219848
\(328\) 0 0
\(329\) 1284.00 0.215165
\(330\) 0 0
\(331\) 900.000 0.149452 0.0747258 − 0.997204i \(-0.476192\pi\)
0.0747258 + 0.997204i \(0.476192\pi\)
\(332\) 0 0
\(333\) 230.000 0.0378496
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −530.000 −0.0856704 −0.0428352 − 0.999082i \(-0.513639\pi\)
−0.0428352 + 0.999082i \(0.513639\pi\)
\(338\) 0 0
\(339\) 3020.00 0.483846
\(340\) 0 0
\(341\) 1200.00 0.190568
\(342\) 0 0
\(343\) 3900.00 0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 414.000 0.0640481 0.0320240 − 0.999487i \(-0.489805\pi\)
0.0320240 + 0.999487i \(0.489805\pi\)
\(348\) 0 0
\(349\) 8614.00 1.32119 0.660597 − 0.750741i \(-0.270303\pi\)
0.660597 + 0.750741i \(0.270303\pi\)
\(350\) 0 0
\(351\) 5000.00 0.760343
\(352\) 0 0
\(353\) 2270.00 0.342266 0.171133 − 0.985248i \(-0.445257\pi\)
0.171133 + 0.985248i \(0.445257\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −360.000 −0.0533704
\(358\) 0 0
\(359\) 8080.00 1.18787 0.593936 − 0.804512i \(-0.297573\pi\)
0.593936 + 0.804512i \(0.297573\pi\)
\(360\) 0 0
\(361\) −5259.00 −0.766730
\(362\) 0 0
\(363\) 4538.00 0.656152
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −2374.00 −0.337662 −0.168831 − 0.985645i \(-0.553999\pi\)
−0.168831 + 0.985645i \(0.553999\pi\)
\(368\) 0 0
\(369\) 5750.00 0.811201
\(370\) 0 0
\(371\) 2940.00 0.411421
\(372\) 0 0
\(373\) −1810.00 −0.251255 −0.125628 − 0.992077i \(-0.540094\pi\)
−0.125628 + 0.992077i \(0.540094\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8300.00 −1.13388
\(378\) 0 0
\(379\) 8120.00 1.10052 0.550259 − 0.834994i \(-0.314529\pi\)
0.550259 + 0.834994i \(0.314529\pi\)
\(380\) 0 0
\(381\) −2492.00 −0.335089
\(382\) 0 0
\(383\) 11782.0 1.57189 0.785943 − 0.618299i \(-0.212178\pi\)
0.785943 + 0.618299i \(0.212178\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3266.00 0.428993
\(388\) 0 0
\(389\) −4350.00 −0.566976 −0.283488 − 0.958976i \(-0.591492\pi\)
−0.283488 + 0.958976i \(0.591492\pi\)
\(390\) 0 0
\(391\) −5340.00 −0.690679
\(392\) 0 0
\(393\) 5320.00 0.682846
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 7470.00 0.944354 0.472177 − 0.881504i \(-0.343468\pi\)
0.472177 + 0.881504i \(0.343468\pi\)
\(398\) 0 0
\(399\) −480.000 −0.0602257
\(400\) 0 0
\(401\) 11698.0 1.45678 0.728392 − 0.685161i \(-0.240268\pi\)
0.728392 + 0.685161i \(0.240268\pi\)
\(402\) 0 0
\(403\) −1000.00 −0.123607
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −600.000 −0.0730735
\(408\) 0 0
\(409\) −3650.00 −0.441274 −0.220637 − 0.975356i \(-0.570814\pi\)
−0.220637 + 0.975356i \(0.570814\pi\)
\(410\) 0 0
\(411\) −5540.00 −0.664886
\(412\) 0 0
\(413\) 4800.00 0.571895
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1120.00 −0.131527
\(418\) 0 0
\(419\) −1120.00 −0.130586 −0.0652931 − 0.997866i \(-0.520798\pi\)
−0.0652931 + 0.997866i \(0.520798\pi\)
\(420\) 0 0
\(421\) 4850.00 0.561460 0.280730 − 0.959787i \(-0.409424\pi\)
0.280730 + 0.959787i \(0.409424\pi\)
\(422\) 0 0
\(423\) 4922.00 0.565758
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1500.00 −0.170000
\(428\) 0 0
\(429\) −6000.00 −0.675251
\(430\) 0 0
\(431\) −12580.0 −1.40593 −0.702967 − 0.711223i \(-0.748142\pi\)
−0.702967 + 0.711223i \(0.748142\pi\)
\(432\) 0 0
\(433\) −13130.0 −1.45725 −0.728623 − 0.684915i \(-0.759839\pi\)
−0.728623 + 0.684915i \(0.759839\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7120.00 −0.779395
\(438\) 0 0
\(439\) 8560.00 0.930630 0.465315 − 0.885145i \(-0.345941\pi\)
0.465315 + 0.885145i \(0.345941\pi\)
\(440\) 0 0
\(441\) 7061.00 0.762445
\(442\) 0 0
\(443\) 4258.00 0.456667 0.228334 − 0.973583i \(-0.426672\pi\)
0.228334 + 0.973583i \(0.426672\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4700.00 −0.497321
\(448\) 0 0
\(449\) 2550.00 0.268022 0.134011 − 0.990980i \(-0.457214\pi\)
0.134011 + 0.990980i \(0.457214\pi\)
\(450\) 0 0
\(451\) −15000.0 −1.56613
\(452\) 0 0
\(453\) 1160.00 0.120312
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6710.00 0.686828 0.343414 − 0.939184i \(-0.388417\pi\)
0.343414 + 0.939184i \(0.388417\pi\)
\(458\) 0 0
\(459\) −3000.00 −0.305072
\(460\) 0 0
\(461\) −14482.0 −1.46311 −0.731555 − 0.681782i \(-0.761205\pi\)
−0.731555 + 0.681782i \(0.761205\pi\)
\(462\) 0 0
\(463\) −162.000 −0.0162609 −0.00813043 − 0.999967i \(-0.502588\pi\)
−0.00813043 + 0.999967i \(0.502588\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15974.0 1.58284 0.791422 − 0.611270i \(-0.209341\pi\)
0.791422 + 0.611270i \(0.209341\pi\)
\(468\) 0 0
\(469\) −4644.00 −0.457228
\(470\) 0 0
\(471\) 2620.00 0.256313
\(472\) 0 0
\(473\) −8520.00 −0.828224
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 11270.0 1.08180
\(478\) 0 0
\(479\) −10760.0 −1.02638 −0.513191 − 0.858274i \(-0.671537\pi\)
−0.513191 + 0.858274i \(0.671537\pi\)
\(480\) 0 0
\(481\) 500.000 0.0473972
\(482\) 0 0
\(483\) 2136.00 0.201224
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 9266.00 0.862182 0.431091 − 0.902309i \(-0.358129\pi\)
0.431091 + 0.902309i \(0.358129\pi\)
\(488\) 0 0
\(489\) −3724.00 −0.344387
\(490\) 0 0
\(491\) 2860.00 0.262872 0.131436 − 0.991325i \(-0.458041\pi\)
0.131436 + 0.991325i \(0.458041\pi\)
\(492\) 0 0
\(493\) 4980.00 0.454945
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −600.000 −0.0541523
\(498\) 0 0
\(499\) 7160.00 0.642336 0.321168 − 0.947022i \(-0.395925\pi\)
0.321168 + 0.947022i \(0.395925\pi\)
\(500\) 0 0
\(501\) −1452.00 −0.129482
\(502\) 0 0
\(503\) 1398.00 0.123924 0.0619620 − 0.998079i \(-0.480264\pi\)
0.0619620 + 0.998079i \(0.480264\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 606.000 0.0530836
\(508\) 0 0
\(509\) 7446.00 0.648405 0.324203 − 0.945988i \(-0.394904\pi\)
0.324203 + 0.945988i \(0.394904\pi\)
\(510\) 0 0
\(511\) −1380.00 −0.119467
\(512\) 0 0
\(513\) −4000.00 −0.344258
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −12840.0 −1.09227
\(518\) 0 0
\(519\) −6500.00 −0.549746
\(520\) 0 0
\(521\) −16438.0 −1.38227 −0.691134 − 0.722726i \(-0.742889\pi\)
−0.691134 + 0.722726i \(0.742889\pi\)
\(522\) 0 0
\(523\) 7322.00 0.612177 0.306089 − 0.952003i \(-0.400980\pi\)
0.306089 + 0.952003i \(0.400980\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 600.000 0.0495947
\(528\) 0 0
\(529\) 19517.0 1.60409
\(530\) 0 0
\(531\) 18400.0 1.50375
\(532\) 0 0
\(533\) 12500.0 1.01583
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2240.00 −0.180006
\(538\) 0 0
\(539\) −18420.0 −1.47200
\(540\) 0 0
\(541\) 10878.0 0.864476 0.432238 − 0.901759i \(-0.357724\pi\)
0.432238 + 0.901759i \(0.357724\pi\)
\(542\) 0 0
\(543\) −5684.00 −0.449215
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −16114.0 −1.25957 −0.629785 − 0.776769i \(-0.716857\pi\)
−0.629785 + 0.776769i \(0.716857\pi\)
\(548\) 0 0
\(549\) −5750.00 −0.447002
\(550\) 0 0
\(551\) 6640.00 0.513382
\(552\) 0 0
\(553\) 7920.00 0.609028
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3690.00 −0.280701 −0.140350 − 0.990102i \(-0.544823\pi\)
−0.140350 + 0.990102i \(0.544823\pi\)
\(558\) 0 0
\(559\) 7100.00 0.537206
\(560\) 0 0
\(561\) 3600.00 0.270931
\(562\) 0 0
\(563\) 2562.00 0.191786 0.0958929 − 0.995392i \(-0.469429\pi\)
0.0958929 + 0.995392i \(0.469429\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2526.00 −0.187094
\(568\) 0 0
\(569\) −6050.00 −0.445746 −0.222873 − 0.974848i \(-0.571543\pi\)
−0.222873 + 0.974848i \(0.571543\pi\)
\(570\) 0 0
\(571\) 8260.00 0.605377 0.302688 − 0.953090i \(-0.402116\pi\)
0.302688 + 0.953090i \(0.402116\pi\)
\(572\) 0 0
\(573\) 6360.00 0.463687
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 16870.0 1.21717 0.608585 − 0.793489i \(-0.291737\pi\)
0.608585 + 0.793489i \(0.291737\pi\)
\(578\) 0 0
\(579\) 9340.00 0.670392
\(580\) 0 0
\(581\) 5892.00 0.420725
\(582\) 0 0
\(583\) −29400.0 −2.08855
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 966.000 0.0679235 0.0339617 − 0.999423i \(-0.489188\pi\)
0.0339617 + 0.999423i \(0.489188\pi\)
\(588\) 0 0
\(589\) 800.000 0.0559651
\(590\) 0 0
\(591\) 5980.00 0.416217
\(592\) 0 0
\(593\) −26290.0 −1.82057 −0.910287 − 0.413977i \(-0.864139\pi\)
−0.910287 + 0.413977i \(0.864139\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8480.00 −0.581346
\(598\) 0 0
\(599\) −11640.0 −0.793986 −0.396993 − 0.917822i \(-0.629946\pi\)
−0.396993 + 0.917822i \(0.629946\pi\)
\(600\) 0 0
\(601\) −25450.0 −1.72733 −0.863667 − 0.504064i \(-0.831838\pi\)
−0.863667 + 0.504064i \(0.831838\pi\)
\(602\) 0 0
\(603\) −17802.0 −1.20224
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −16694.0 −1.11629 −0.558145 − 0.829743i \(-0.688487\pi\)
−0.558145 + 0.829743i \(0.688487\pi\)
\(608\) 0 0
\(609\) −1992.00 −0.132545
\(610\) 0 0
\(611\) 10700.0 0.708471
\(612\) 0 0
\(613\) −15890.0 −1.04697 −0.523484 − 0.852036i \(-0.675368\pi\)
−0.523484 + 0.852036i \(0.675368\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1230.00 0.0802560 0.0401280 − 0.999195i \(-0.487223\pi\)
0.0401280 + 0.999195i \(0.487223\pi\)
\(618\) 0 0
\(619\) −10840.0 −0.703871 −0.351936 − 0.936024i \(-0.614476\pi\)
−0.351936 + 0.936024i \(0.614476\pi\)
\(620\) 0 0
\(621\) 17800.0 1.15022
\(622\) 0 0
\(623\) −5244.00 −0.337233
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 4800.00 0.305731
\(628\) 0 0
\(629\) −300.000 −0.0190171
\(630\) 0 0
\(631\) −14060.0 −0.887036 −0.443518 − 0.896265i \(-0.646270\pi\)
−0.443518 + 0.896265i \(0.646270\pi\)
\(632\) 0 0
\(633\) −8120.00 −0.509859
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 15350.0 0.954771
\(638\) 0 0
\(639\) −2300.00 −0.142389
\(640\) 0 0
\(641\) −17650.0 −1.08757 −0.543786 − 0.839224i \(-0.683010\pi\)
−0.543786 + 0.839224i \(0.683010\pi\)
\(642\) 0 0
\(643\) −27358.0 −1.67791 −0.838953 − 0.544203i \(-0.816832\pi\)
−0.838953 + 0.544203i \(0.816832\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6786.00 0.412342 0.206171 − 0.978516i \(-0.433900\pi\)
0.206171 + 0.978516i \(0.433900\pi\)
\(648\) 0 0
\(649\) −48000.0 −2.90318
\(650\) 0 0
\(651\) −240.000 −0.0144491
\(652\) 0 0
\(653\) 9030.00 0.541150 0.270575 − 0.962699i \(-0.412786\pi\)
0.270575 + 0.962699i \(0.412786\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5290.00 −0.314129
\(658\) 0 0
\(659\) −15600.0 −0.922139 −0.461070 − 0.887364i \(-0.652534\pi\)
−0.461070 + 0.887364i \(0.652534\pi\)
\(660\) 0 0
\(661\) 16850.0 0.991511 0.495756 − 0.868462i \(-0.334891\pi\)
0.495756 + 0.868462i \(0.334891\pi\)
\(662\) 0 0
\(663\) −3000.00 −0.175732
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −29548.0 −1.71530
\(668\) 0 0
\(669\) 11244.0 0.649803
\(670\) 0 0
\(671\) 15000.0 0.862993
\(672\) 0 0
\(673\) 7990.00 0.457640 0.228820 − 0.973469i \(-0.426513\pi\)
0.228820 + 0.973469i \(0.426513\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18690.0 −1.06103 −0.530513 − 0.847677i \(-0.678001\pi\)
−0.530513 + 0.847677i \(0.678001\pi\)
\(678\) 0 0
\(679\) −1860.00 −0.105126
\(680\) 0 0
\(681\) −3108.00 −0.174888
\(682\) 0 0
\(683\) −19182.0 −1.07464 −0.537320 − 0.843379i \(-0.680563\pi\)
−0.537320 + 0.843379i \(0.680563\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2268.00 0.125953
\(688\) 0 0
\(689\) 24500.0 1.35468
\(690\) 0 0
\(691\) −23380.0 −1.28714 −0.643572 − 0.765385i \(-0.722548\pi\)
−0.643572 + 0.765385i \(0.722548\pi\)
\(692\) 0 0
\(693\) 8280.00 0.453869
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −7500.00 −0.407579
\(698\) 0 0
\(699\) 3420.00 0.185059
\(700\) 0 0
\(701\) 11850.0 0.638471 0.319236 − 0.947675i \(-0.396574\pi\)
0.319236 + 0.947675i \(0.396574\pi\)
\(702\) 0 0
\(703\) −400.000 −0.0214599
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8988.00 0.478117
\(708\) 0 0
\(709\) 25646.0 1.35847 0.679235 − 0.733921i \(-0.262312\pi\)
0.679235 + 0.733921i \(0.262312\pi\)
\(710\) 0 0
\(711\) 30360.0 1.60139
\(712\) 0 0
\(713\) −3560.00 −0.186989
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 8880.00 0.462524
\(718\) 0 0
\(719\) −30280.0 −1.57059 −0.785294 − 0.619122i \(-0.787488\pi\)
−0.785294 + 0.619122i \(0.787488\pi\)
\(720\) 0 0
\(721\) 8412.00 0.434507
\(722\) 0 0
\(723\) −1700.00 −0.0874463
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −17446.0 −0.890009 −0.445004 − 0.895528i \(-0.646798\pi\)
−0.445004 + 0.895528i \(0.646798\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 0 0
\(731\) −4260.00 −0.215543
\(732\) 0 0
\(733\) 16750.0 0.844032 0.422016 − 0.906588i \(-0.361323\pi\)
0.422016 + 0.906588i \(0.361323\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 46440.0 2.32108
\(738\) 0 0
\(739\) −36560.0 −1.81987 −0.909933 − 0.414755i \(-0.863867\pi\)
−0.909933 + 0.414755i \(0.863867\pi\)
\(740\) 0 0
\(741\) −4000.00 −0.198305
\(742\) 0 0
\(743\) 30142.0 1.48829 0.744147 − 0.668016i \(-0.232856\pi\)
0.744147 + 0.668016i \(0.232856\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 22586.0 1.10626
\(748\) 0 0
\(749\) 7164.00 0.349488
\(750\) 0 0
\(751\) 11860.0 0.576268 0.288134 − 0.957590i \(-0.406965\pi\)
0.288134 + 0.957590i \(0.406965\pi\)
\(752\) 0 0
\(753\) −1320.00 −0.0638824
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −37010.0 −1.77695 −0.888475 − 0.458925i \(-0.848235\pi\)
−0.888475 + 0.458925i \(0.848235\pi\)
\(758\) 0 0
\(759\) −21360.0 −1.02150
\(760\) 0 0
\(761\) −11718.0 −0.558183 −0.279091 − 0.960265i \(-0.590033\pi\)
−0.279091 + 0.960265i \(0.590033\pi\)
\(762\) 0 0
\(763\) −3900.00 −0.185045
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 40000.0 1.88307
\(768\) 0 0
\(769\) 4706.00 0.220680 0.110340 − 0.993894i \(-0.464806\pi\)
0.110340 + 0.993894i \(0.464806\pi\)
\(770\) 0 0
\(771\) 15180.0 0.709072
\(772\) 0 0
\(773\) 28670.0 1.33401 0.667004 − 0.745054i \(-0.267576\pi\)
0.667004 + 0.745054i \(0.267576\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 120.000 0.00554051
\(778\) 0 0
\(779\) −10000.0 −0.459932
\(780\) 0 0
\(781\) 6000.00 0.274900
\(782\) 0 0
\(783\) −16600.0 −0.757644
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −20434.0 −0.925532 −0.462766 − 0.886481i \(-0.653143\pi\)
−0.462766 + 0.886481i \(0.653143\pi\)
\(788\) 0 0
\(789\) −1524.00 −0.0687653
\(790\) 0 0
\(791\) −9060.00 −0.407252
\(792\) 0 0
\(793\) −12500.0 −0.559758
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3930.00 −0.174665 −0.0873323 − 0.996179i \(-0.527834\pi\)
−0.0873323 + 0.996179i \(0.527834\pi\)
\(798\) 0 0
\(799\) −6420.00 −0.284259
\(800\) 0 0
\(801\) −20102.0 −0.886728
\(802\) 0 0
\(803\) 13800.0 0.606465
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −300.000 −0.0130861
\(808\) 0 0
\(809\) −4854.00 −0.210949 −0.105474 − 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 0 0
\(811\) −13140.0 −0.568937 −0.284468 − 0.958685i \(-0.591817\pi\)
−0.284468 + 0.958685i \(0.591817\pi\)
\(812\) 0 0
\(813\) −13160.0 −0.567702
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −5680.00 −0.243229
\(818\) 0 0
\(819\) −6900.00 −0.294390
\(820\) 0 0
\(821\) 22050.0 0.937333 0.468666 − 0.883375i \(-0.344735\pi\)
0.468666 + 0.883375i \(0.344735\pi\)
\(822\) 0 0
\(823\) −14578.0 −0.617445 −0.308722 − 0.951152i \(-0.599901\pi\)
−0.308722 + 0.951152i \(0.599901\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 37054.0 1.55803 0.779017 − 0.627003i \(-0.215719\pi\)
0.779017 + 0.627003i \(0.215719\pi\)
\(828\) 0 0
\(829\) −6150.00 −0.257658 −0.128829 − 0.991667i \(-0.541122\pi\)
−0.128829 + 0.991667i \(0.541122\pi\)
\(830\) 0 0
\(831\) −9060.00 −0.378204
\(832\) 0 0
\(833\) −9210.00 −0.383082
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2000.00 −0.0825927
\(838\) 0 0
\(839\) −8200.00 −0.337420 −0.168710 − 0.985666i \(-0.553960\pi\)
−0.168710 + 0.985666i \(0.553960\pi\)
\(840\) 0 0
\(841\) 3167.00 0.129854
\(842\) 0 0
\(843\) 13900.0 0.567902
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −13614.0 −0.552282
\(848\) 0 0
\(849\) 7764.00 0.313851
\(850\) 0 0
\(851\) 1780.00 0.0717011
\(852\) 0 0
\(853\) 42990.0 1.72561 0.862807 − 0.505533i \(-0.168704\pi\)
0.862807 + 0.505533i \(0.168704\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −32130.0 −1.28068 −0.640338 − 0.768093i \(-0.721206\pi\)
−0.640338 + 0.768093i \(0.721206\pi\)
\(858\) 0 0
\(859\) 15440.0 0.613278 0.306639 − 0.951826i \(-0.400796\pi\)
0.306639 + 0.951826i \(0.400796\pi\)
\(860\) 0 0
\(861\) 3000.00 0.118745
\(862\) 0 0
\(863\) −46938.0 −1.85143 −0.925717 − 0.378216i \(-0.876538\pi\)
−0.925717 + 0.378216i \(0.876538\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8026.00 −0.314391
\(868\) 0 0
\(869\) −79200.0 −3.09169
\(870\) 0 0
\(871\) −38700.0 −1.50551
\(872\) 0 0
\(873\) −7130.00 −0.276419
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 31230.0 1.20247 0.601233 − 0.799074i \(-0.294676\pi\)
0.601233 + 0.799074i \(0.294676\pi\)
\(878\) 0 0
\(879\) −2740.00 −0.105140
\(880\) 0 0
\(881\) 25550.0 0.977073 0.488537 − 0.872543i \(-0.337531\pi\)
0.488537 + 0.872543i \(0.337531\pi\)
\(882\) 0 0
\(883\) −4318.00 −0.164567 −0.0822833 − 0.996609i \(-0.526221\pi\)
−0.0822833 + 0.996609i \(0.526221\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1766.00 −0.0668506 −0.0334253 − 0.999441i \(-0.510642\pi\)
−0.0334253 + 0.999441i \(0.510642\pi\)
\(888\) 0 0
\(889\) 7476.00 0.282044
\(890\) 0 0
\(891\) 25260.0 0.949766
\(892\) 0 0
\(893\) −8560.00 −0.320772
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 17800.0 0.662569
\(898\) 0 0
\(899\) 3320.00 0.123168
\(900\) 0 0
\(901\) −14700.0 −0.543538
\(902\) 0 0
\(903\) 1704.00 0.0627969
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −41906.0 −1.53414 −0.767071 − 0.641563i \(-0.778286\pi\)
−0.767071 + 0.641563i \(0.778286\pi\)
\(908\) 0 0
\(909\) 34454.0 1.25717
\(910\) 0 0
\(911\) 25140.0 0.914298 0.457149 − 0.889390i \(-0.348871\pi\)
0.457149 + 0.889390i \(0.348871\pi\)
\(912\) 0 0
\(913\) −58920.0 −2.13578
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15960.0 −0.574750
\(918\) 0 0
\(919\) 32920.0 1.18164 0.590822 − 0.806802i \(-0.298804\pi\)
0.590822 + 0.806802i \(0.298804\pi\)
\(920\) 0 0
\(921\) −8212.00 −0.293805
\(922\) 0 0
\(923\) −5000.00 −0.178307
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 32246.0 1.14250
\(928\) 0 0
\(929\) 10150.0 0.358461 0.179231 − 0.983807i \(-0.442639\pi\)
0.179231 + 0.983807i \(0.442639\pi\)
\(930\) 0 0
\(931\) −12280.0 −0.432289
\(932\) 0 0
\(933\) 4440.00 0.155798
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −28530.0 −0.994701 −0.497350 − 0.867550i \(-0.665694\pi\)
−0.497350 + 0.867550i \(0.665694\pi\)
\(938\) 0 0
\(939\) 18860.0 0.655456
\(940\) 0 0
\(941\) 9678.00 0.335275 0.167638 − 0.985849i \(-0.446386\pi\)
0.167638 + 0.985849i \(0.446386\pi\)
\(942\) 0 0
\(943\) 44500.0 1.53671
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36986.0 −1.26915 −0.634574 − 0.772862i \(-0.718824\pi\)
−0.634574 + 0.772862i \(0.718824\pi\)
\(948\) 0 0
\(949\) −11500.0 −0.393368
\(950\) 0 0
\(951\) 12940.0 0.441228
\(952\) 0 0
\(953\) 3350.00 0.113869 0.0569345 − 0.998378i \(-0.481867\pi\)
0.0569345 + 0.998378i \(0.481867\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 19920.0 0.672855
\(958\) 0 0
\(959\) 16620.0 0.559633
\(960\) 0 0
\(961\) −29391.0 −0.986573
\(962\) 0 0
\(963\) 27462.0 0.918952
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −43774.0 −1.45572 −0.727858 − 0.685728i \(-0.759484\pi\)
−0.727858 + 0.685728i \(0.759484\pi\)
\(968\) 0 0
\(969\) 2400.00 0.0795656
\(970\) 0 0
\(971\) 8740.00 0.288857 0.144428 − 0.989515i \(-0.453866\pi\)
0.144428 + 0.989515i \(0.453866\pi\)
\(972\) 0 0
\(973\) 3360.00 0.110706
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 48310.0 1.58196 0.790979 − 0.611843i \(-0.209571\pi\)
0.790979 + 0.611843i \(0.209571\pi\)
\(978\) 0 0
\(979\) 52440.0 1.71194
\(980\) 0 0
\(981\) −14950.0 −0.486561
\(982\) 0 0
\(983\) −2282.00 −0.0740432 −0.0370216 − 0.999314i \(-0.511787\pi\)
−0.0370216 + 0.999314i \(0.511787\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2568.00 0.0828170
\(988\) 0 0
\(989\) 25276.0 0.812669
\(990\) 0 0
\(991\) −31580.0 −1.01228 −0.506141 − 0.862451i \(-0.668929\pi\)
−0.506141 + 0.862451i \(0.668929\pi\)
\(992\) 0 0
\(993\) 1800.00 0.0575239
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 2790.00 0.0886261 0.0443130 − 0.999018i \(-0.485890\pi\)
0.0443130 + 0.999018i \(0.485890\pi\)
\(998\) 0 0
\(999\) 1000.00 0.0316703
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 800.4.a.h.1.1 1
4.3 odd 2 800.4.a.d.1.1 1
5.2 odd 4 800.4.c.f.449.1 2
5.3 odd 4 800.4.c.f.449.2 2
5.4 even 2 160.4.a.a.1.1 ✓ 1
8.3 odd 2 1600.4.a.bj.1.1 1
8.5 even 2 1600.4.a.r.1.1 1
15.14 odd 2 1440.4.a.o.1.1 1
20.3 even 4 800.4.c.e.449.1 2
20.7 even 4 800.4.c.e.449.2 2
20.19 odd 2 160.4.a.b.1.1 yes 1
40.19 odd 2 320.4.a.f.1.1 1
40.29 even 2 320.4.a.i.1.1 1
60.59 even 2 1440.4.a.n.1.1 1
80.19 odd 4 1280.4.d.k.641.2 2
80.29 even 4 1280.4.d.f.641.1 2
80.59 odd 4 1280.4.d.k.641.1 2
80.69 even 4 1280.4.d.f.641.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.4.a.a.1.1 ✓ 1 5.4 even 2
160.4.a.b.1.1 yes 1 20.19 odd 2
320.4.a.f.1.1 1 40.19 odd 2
320.4.a.i.1.1 1 40.29 even 2
800.4.a.d.1.1 1 4.3 odd 2
800.4.a.h.1.1 1 1.1 even 1 trivial
800.4.c.e.449.1 2 20.3 even 4
800.4.c.e.449.2 2 20.7 even 4
800.4.c.f.449.1 2 5.2 odd 4
800.4.c.f.449.2 2 5.3 odd 4
1280.4.d.f.641.1 2 80.29 even 4
1280.4.d.f.641.2 2 80.69 even 4
1280.4.d.k.641.1 2 80.59 odd 4
1280.4.d.k.641.2 2 80.19 odd 4
1440.4.a.n.1.1 1 60.59 even 2
1440.4.a.o.1.1 1 15.14 odd 2
1600.4.a.r.1.1 1 8.5 even 2
1600.4.a.bj.1.1 1 8.3 odd 2