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Properties

Label 1440.4.a.n.1.1
Level $1440$
Weight $4$
Character 1440.1
Self dual yes
Analytic conductor $84.963$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1440,4,Mod(1,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1440.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1440.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(84.9627504083\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -6.00000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -6.00000 q^{7} +60.0000 q^{11} +50.0000 q^{13} +30.0000 q^{17} -40.0000 q^{19} +178.000 q^{23} +25.0000 q^{25} -166.000 q^{29} -20.0000 q^{31} -30.0000 q^{35} +10.0000 q^{37} +250.000 q^{41} -142.000 q^{43} +214.000 q^{47} -307.000 q^{49} -490.000 q^{53} +300.000 q^{55} -800.000 q^{59} +250.000 q^{61} +250.000 q^{65} +774.000 q^{67} +100.000 q^{71} -230.000 q^{73} -360.000 q^{77} +1320.00 q^{79} +982.000 q^{83} +150.000 q^{85} -874.000 q^{89} -300.000 q^{91} -200.000 q^{95} -310.000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −6.00000 −0.323970 −0.161985 − 0.986793i \(-0.551790\pi\)
−0.161985 + 0.986793i \(0.551790\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 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 \(-0.320927\pi\)
0.533366 + 0.845885i \(0.320927\pi\)
\(14\) 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 \(-0.577636\pi\)
−0.241490 + 0.970403i \(0.577636\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 178.000 1.61372 0.806860 − 0.590743i \(-0.201165\pi\)
0.806860 + 0.590743i \(0.201165\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −166.000 −1.06295 −0.531473 − 0.847075i \(-0.678361\pi\)
−0.531473 + 0.847075i \(0.678361\pi\)
\(30\) 0 0
\(31\) −20.0000 −0.115874 −0.0579372 − 0.998320i \(-0.518452\pi\)
−0.0579372 + 0.998320i \(0.518452\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −30.0000 −0.144884
\(36\) 0 0
\(37\) 10.0000 0.0444322 0.0222161 − 0.999753i \(-0.492928\pi\)
0.0222161 + 0.999753i \(0.492928\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 250.000 0.952279 0.476140 − 0.879370i \(-0.342036\pi\)
0.476140 + 0.879370i \(0.342036\pi\)
\(42\) 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 \(-0.392251\pi\)
0.332076 + 0.943253i \(0.392251\pi\)
\(48\) 0 0
\(49\) −307.000 −0.895044
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −490.000 −1.26994 −0.634969 − 0.772538i \(-0.718987\pi\)
−0.634969 + 0.772538i \(0.718987\pi\)
\(54\) 0 0
\(55\) 300.000 0.735491
\(56\) 0 0
\(57\) 0 0
\(58\) 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
\(63\) 0 0
\(64\) 0 0
\(65\) 250.000 0.477057
\(66\) 0 0
\(67\) 774.000 1.41133 0.705665 − 0.708545i \(-0.250648\pi\)
0.705665 + 0.708545i \(0.250648\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 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 \(-0.559028\pi\)
−0.184380 + 0.982855i \(0.559028\pi\)
\(74\) 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 \(-0.110874\pi\)
0.939947 + 0.341321i \(0.110874\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 982.000 1.29866 0.649328 − 0.760508i \(-0.275050\pi\)
0.649328 + 0.760508i \(0.275050\pi\)
\(84\) 0 0
\(85\) 150.000 0.191409
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −874.000 −1.04094 −0.520471 − 0.853879i \(-0.674244\pi\)
−0.520471 + 0.853879i \(0.674244\pi\)
\(90\) 0 0
\(91\) −300.000 −0.345588
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −200.000 −0.215995
\(96\) 0 0
\(97\) −310.000 −0.324492 −0.162246 − 0.986750i \(-0.551874\pi\)
−0.162246 + 0.986750i \(0.551874\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1498.00 1.47581 0.737904 − 0.674906i \(-0.235816\pi\)
0.737904 + 0.674906i \(0.235816\pi\)
\(102\) 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 \(-0.318657\pi\)
0.539385 + 0.842059i \(0.318657\pi\)
\(108\) 0 0
\(109\) 650.000 0.571181 0.285590 − 0.958352i \(-0.407810\pi\)
0.285590 + 0.958352i \(0.407810\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1510.00 1.25707 0.628535 − 0.777782i \(-0.283655\pi\)
0.628535 + 0.777782i \(0.283655\pi\)
\(114\) 0 0
\(115\) 890.000 0.721678
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −180.000 −0.138660
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1246.00 −0.870588 −0.435294 − 0.900288i \(-0.643355\pi\)
−0.435294 + 0.900288i \(0.643355\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 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 \(-0.445346\pi\)
0.170858 + 0.985296i \(0.445346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3000.00 1.75435
\(144\) 0 0
\(145\) −830.000 −0.475364
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2350.00 1.29208 0.646039 − 0.763305i \(-0.276424\pi\)
0.646039 + 0.763305i \(0.276424\pi\)
\(150\) 0 0
\(151\) −580.000 −0.312581 −0.156290 − 0.987711i \(-0.549954\pi\)
−0.156290 + 0.987711i \(0.549954\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −100.000 −0.0518206
\(156\) 0 0
\(157\) −1310.00 −0.665920 −0.332960 − 0.942941i \(-0.608047\pi\)
−0.332960 + 0.942941i \(0.608047\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 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 \(-0.446204\pi\)
0.168202 + 0.985752i \(0.446204\pi\)
\(168\) 0 0
\(169\) 303.000 0.137915
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3250.00 −1.42828 −0.714141 − 0.700001i \(-0.753183\pi\)
−0.714141 + 0.700001i \(0.753183\pi\)
\(174\) 0 0
\(175\) −150.000 −0.0647939
\(176\) 0 0
\(177\) 0 0
\(178\) 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
\(183\) 0 0
\(184\) 0 0
\(185\) 50.0000 0.0198707
\(186\) 0 0
\(187\) 1800.00 0.703899
\(188\) 0 0
\(189\) 0 0
\(190\) 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 \(-0.836441\pi\)
−0.870865 + 0.491522i \(0.836441\pi\)
\(194\) 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 \(-0.227545\pi\)
0.755190 + 0.655506i \(0.227545\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 996.000 0.344362
\(204\) 0 0
\(205\) 1250.00 0.425872
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2400.00 −0.794313
\(210\) 0 0
\(211\) 4060.00 1.32465 0.662327 − 0.749215i \(-0.269569\pi\)
0.662327 + 0.749215i \(0.269569\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −710.000 −0.225217
\(216\) 0 0
\(217\) 120.000 0.0375398
\(218\) 0 0
\(219\) 0 0
\(220\) 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 \(-0.427047\pi\)
0.227186 + 0.973851i \(0.427047\pi\)
\(228\) 0 0
\(229\) 1134.00 0.327235 0.163618 − 0.986524i \(-0.447684\pi\)
0.163618 + 0.986524i \(0.447684\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1710.00 0.480798 0.240399 − 0.970674i \(-0.422722\pi\)
0.240399 + 0.970674i \(0.422722\pi\)
\(234\) 0 0
\(235\) 1070.00 0.297017
\(236\) 0 0
\(237\) 0 0
\(238\) 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
\(243\) 0 0
\(244\) 0 0
\(245\) −1535.00 −0.400276
\(246\) 0 0
\(247\) −2000.00 −0.515210
\(248\) 0 0
\(249\) 0 0
\(250\) 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
\(261\) 0 0
\(262\) 0 0
\(263\) 762.000 0.178658 0.0893288 − 0.996002i \(-0.471528\pi\)
0.0893288 + 0.996002i \(0.471528\pi\)
\(264\) 0 0
\(265\) −2450.00 −0.567933
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 150.000 0.0339987 0.0169994 − 0.999856i \(-0.494589\pi\)
0.0169994 + 0.999856i \(0.494589\pi\)
\(270\) 0 0
\(271\) 6580.00 1.47493 0.737466 − 0.675384i \(-0.236022\pi\)
0.737466 + 0.675384i \(0.236022\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1500.00 0.328921
\(276\) 0 0
\(277\) 4530.00 0.982604 0.491302 − 0.870989i \(-0.336521\pi\)
0.491302 + 0.870989i \(0.336521\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6950.00 −1.47545 −0.737726 − 0.675100i \(-0.764101\pi\)
−0.737726 + 0.675100i \(0.764101\pi\)
\(282\) 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
\(291\) 0 0
\(292\) 0 0
\(293\) −1370.00 −0.273161 −0.136581 − 0.990629i \(-0.543611\pi\)
−0.136581 + 0.990629i \(0.543611\pi\)
\(294\) 0 0
\(295\) −4000.00 −0.789454
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 8900.00 1.72141
\(300\) 0 0
\(301\) 852.000 0.163151
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1250.00 0.234671
\(306\) 0 0
\(307\) −4106.00 −0.763328 −0.381664 − 0.924301i \(-0.624649\pi\)
−0.381664 + 0.924301i \(0.624649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 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 \(-0.824283\pi\)
−0.851462 + 0.524417i \(0.824283\pi\)
\(314\) 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
\(321\) 0 0
\(322\) 0 0
\(323\) −1200.00 −0.206718
\(324\) 0 0
\(325\) 1250.00 0.213346
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1284.00 −0.215165
\(330\) 0 0
\(331\) −900.000 −0.149452 −0.0747258 − 0.997204i \(-0.523808\pi\)
−0.0747258 + 0.997204i \(0.523808\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3870.00 0.631166
\(336\) 0 0
\(337\) 530.000 0.0856704 0.0428352 − 0.999082i \(-0.486361\pi\)
0.0428352 + 0.999082i \(0.486361\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 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 \(-0.510195\pi\)
−0.0320240 + 0.999487i \(0.510195\pi\)
\(348\) 0 0
\(349\) 8614.00 1.32119 0.660597 − 0.750741i \(-0.270303\pi\)
0.660597 + 0.750741i \(0.270303\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2270.00 0.342266 0.171133 − 0.985248i \(-0.445257\pi\)
0.171133 + 0.985248i \(0.445257\pi\)
\(354\) 0 0
\(355\) 500.000 0.0747528
\(356\) 0 0
\(357\) 0 0
\(358\) 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
\(363\) 0 0
\(364\) 0 0
\(365\) −1150.00 −0.164914
\(366\) 0 0
\(367\) −2374.00 −0.337662 −0.168831 − 0.985645i \(-0.553999\pi\)
−0.168831 + 0.985645i \(0.553999\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2940.00 0.411421
\(372\) 0 0
\(373\) 1810.00 0.251255 0.125628 − 0.992077i \(-0.459906\pi\)
0.125628 + 0.992077i \(0.459906\pi\)
\(374\) 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 \(-0.685471\pi\)
−0.550259 + 0.834994i \(0.685471\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11782.0 −1.57189 −0.785943 − 0.618299i \(-0.787822\pi\)
−0.785943 + 0.618299i \(0.787822\pi\)
\(384\) 0 0
\(385\) −1800.00 −0.238277
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4350.00 0.566976 0.283488 − 0.958976i \(-0.408508\pi\)
0.283488 + 0.958976i \(0.408508\pi\)
\(390\) 0 0
\(391\) 5340.00 0.690679
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6600.00 0.840714
\(396\) 0 0
\(397\) −7470.00 −0.944354 −0.472177 − 0.881504i \(-0.656532\pi\)
−0.472177 + 0.881504i \(0.656532\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11698.0 −1.45678 −0.728392 − 0.685161i \(-0.759732\pi\)
−0.728392 + 0.685161i \(0.759732\pi\)
\(402\) 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
\(411\) 0 0
\(412\) 0 0
\(413\) 4800.00 0.571895
\(414\) 0 0
\(415\) 4910.00 0.580777
\(416\) 0 0
\(417\) 0 0
\(418\) 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
\(423\) 0 0
\(424\) 0 0
\(425\) 750.000 0.0856008
\(426\) 0 0
\(427\) −1500.00 −0.170000
\(428\) 0 0
\(429\) 0 0
\(430\) 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 \(-0.240161\pi\)
0.728623 + 0.684915i \(0.240161\pi\)
\(434\) 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 \(-0.654059\pi\)
−0.465315 + 0.885145i \(0.654059\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4258.00 −0.456667 −0.228334 − 0.973583i \(-0.573328\pi\)
−0.228334 + 0.973583i \(0.573328\pi\)
\(444\) 0 0
\(445\) −4370.00 −0.465523
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2550.00 −0.268022 −0.134011 − 0.990980i \(-0.542786\pi\)
−0.134011 + 0.990980i \(0.542786\pi\)
\(450\) 0 0
\(451\) 15000.0 1.56613
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1500.00 −0.154552
\(456\) 0 0
\(457\) −6710.00 −0.686828 −0.343414 − 0.939184i \(-0.611583\pi\)
−0.343414 + 0.939184i \(0.611583\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14482.0 1.46311 0.731555 − 0.681782i \(-0.238795\pi\)
0.731555 + 0.681782i \(0.238795\pi\)
\(462\) 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 \(-0.790659\pi\)
−0.791422 + 0.611270i \(0.790659\pi\)
\(468\) 0 0
\(469\) −4644.00 −0.457228
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8520.00 −0.828224
\(474\) 0 0
\(475\) −1000.00 −0.0965961
\(476\) 0 0
\(477\) 0 0
\(478\) 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
\(483\) 0 0
\(484\) 0 0
\(485\) −1550.00 −0.145117
\(486\) 0 0
\(487\) 9266.00 0.862182 0.431091 − 0.902309i \(-0.358129\pi\)
0.431091 + 0.902309i \(0.358129\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 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 \(-0.604075\pi\)
−0.321168 + 0.947022i \(0.604075\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1398.00 −0.123924 −0.0619620 − 0.998079i \(-0.519736\pi\)
−0.0619620 + 0.998079i \(0.519736\pi\)
\(504\) 0 0
\(505\) 7490.00 0.660001
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7446.00 −0.648405 −0.324203 − 0.945988i \(-0.605096\pi\)
−0.324203 + 0.945988i \(0.605096\pi\)
\(510\) 0 0
\(511\) 1380.00 0.119467
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7010.00 −0.599801
\(516\) 0 0
\(517\) 12840.0 1.09227
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16438.0 1.38227 0.691134 − 0.722726i \(-0.257111\pi\)
0.691134 + 0.722726i \(0.257111\pi\)
\(522\) 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
\(531\) 0 0
\(532\) 0 0
\(533\) 12500.0 1.01583
\(534\) 0 0
\(535\) 5970.00 0.482440
\(536\) 0 0
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) 0 0
\(545\) 3250.00 0.255440
\(546\) 0 0
\(547\) −16114.0 −1.25957 −0.629785 − 0.776769i \(-0.716857\pi\)
−0.629785 + 0.776769i \(0.716857\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 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
\(561\) 0 0
\(562\) 0 0
\(563\) −2562.00 −0.191786 −0.0958929 − 0.995392i \(-0.530571\pi\)
−0.0958929 + 0.995392i \(0.530571\pi\)
\(564\) 0 0
\(565\) 7550.00 0.562179
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6050.00 0.445746 0.222873 − 0.974848i \(-0.428457\pi\)
0.222873 + 0.974848i \(0.428457\pi\)
\(570\) 0 0
\(571\) −8260.00 −0.605377 −0.302688 − 0.953090i \(-0.597884\pi\)
−0.302688 + 0.953090i \(0.597884\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4450.00 0.322744
\(576\) 0 0
\(577\) −16870.0 −1.21717 −0.608585 − 0.793489i \(-0.708263\pi\)
−0.608585 + 0.793489i \(0.708263\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 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 \(-0.510812\pi\)
−0.0339617 + 0.999423i \(0.510812\pi\)
\(588\) 0 0
\(589\) 800.000 0.0559651
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −26290.0 −1.82057 −0.910287 − 0.413977i \(-0.864139\pi\)
−0.910287 + 0.413977i \(0.864139\pi\)
\(594\) 0 0
\(595\) −900.000 −0.0620108
\(596\) 0 0
\(597\) 0 0
\(598\) 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
\(603\) 0 0
\(604\) 0 0
\(605\) 11345.0 0.762380
\(606\) 0 0
\(607\) −16694.0 −1.11629 −0.558145 − 0.829743i \(-0.688487\pi\)
−0.558145 + 0.829743i \(0.688487\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10700.0 0.708471
\(612\) 0 0
\(613\) 15890.0 1.04697 0.523484 − 0.852036i \(-0.324632\pi\)
0.523484 + 0.852036i \(0.324632\pi\)
\(614\) 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 \(-0.385524\pi\)
0.351936 + 0.936024i \(0.385524\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5244.00 0.337233
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 300.000 0.0190171
\(630\) 0 0
\(631\) 14060.0 0.887036 0.443518 − 0.896265i \(-0.353730\pi\)
0.443518 + 0.896265i \(0.353730\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6230.00 −0.389339
\(636\) 0 0
\(637\) −15350.0 −0.954771
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 17650.0 1.08757 0.543786 − 0.839224i \(-0.316990\pi\)
0.543786 + 0.839224i \(0.316990\pi\)
\(642\) 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 \(-0.566100\pi\)
−0.206171 + 0.978516i \(0.566100\pi\)
\(648\) 0 0
\(649\) −48000.0 −2.90318
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9030.00 0.541150 0.270575 − 0.962699i \(-0.412786\pi\)
0.270575 + 0.962699i \(0.412786\pi\)
\(654\) 0 0
\(655\) 13300.0 0.793395
\(656\) 0 0
\(657\) 0 0
\(658\) 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
\(663\) 0 0
\(664\) 0 0
\(665\) 1200.00 0.0699759
\(666\) 0 0
\(667\) −29548.0 −1.71530
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15000.0 0.862993
\(672\) 0 0
\(673\) −7990.00 −0.457640 −0.228820 − 0.973469i \(-0.573487\pi\)
−0.228820 + 0.973469i \(0.573487\pi\)
\(674\) 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
\(681\) 0 0
\(682\) 0 0
\(683\) 19182.0 1.07464 0.537320 − 0.843379i \(-0.319437\pi\)
0.537320 + 0.843379i \(0.319437\pi\)
\(684\) 0 0
\(685\) −13850.0 −0.772527
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −24500.0 −1.35468
\(690\) 0 0
\(691\) 23380.0 1.28714 0.643572 − 0.765385i \(-0.277452\pi\)
0.643572 + 0.765385i \(0.277452\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2800.00 0.152820
\(696\) 0 0
\(697\) 7500.00 0.407579
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −11850.0 −0.638471 −0.319236 − 0.947675i \(-0.603426\pi\)
−0.319236 + 0.947675i \(0.603426\pi\)
\(702\) 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
\(711\) 0 0
\(712\) 0 0
\(713\) −3560.00 −0.186989
\(714\) 0 0
\(715\) 15000.0 0.784571
\(716\) 0 0
\(717\) 0 0
\(718\) 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
\(723\) 0 0
\(724\) 0 0
\(725\) −4150.00 −0.212589
\(726\) 0 0
\(727\) −17446.0 −0.890009 −0.445004 − 0.895528i \(-0.646798\pi\)
−0.445004 + 0.895528i \(0.646798\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4260.00 −0.215543
\(732\) 0 0
\(733\) −16750.0 −0.844032 −0.422016 − 0.906588i \(-0.638677\pi\)
−0.422016 + 0.906588i \(0.638677\pi\)
\(734\) 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 \(-0.136133\pi\)
0.909933 + 0.414755i \(0.136133\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30142.0 −1.48829 −0.744147 − 0.668016i \(-0.767144\pi\)
−0.744147 + 0.668016i \(0.767144\pi\)
\(744\) 0 0
\(745\) 11750.0 0.577834
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7164.00 −0.349488
\(750\) 0 0
\(751\) −11860.0 −0.576268 −0.288134 − 0.957590i \(-0.593035\pi\)
−0.288134 + 0.957590i \(0.593035\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2900.00 −0.139790
\(756\) 0 0
\(757\) 37010.0 1.77695 0.888475 − 0.458925i \(-0.151765\pi\)
0.888475 + 0.458925i \(0.151765\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11718.0 0.558183 0.279091 − 0.960265i \(-0.409967\pi\)
0.279091 + 0.960265i \(0.409967\pi\)
\(762\) 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
\(771\) 0 0
\(772\) 0 0
\(773\) 28670.0 1.33401 0.667004 − 0.745054i \(-0.267576\pi\)
0.667004 + 0.745054i \(0.267576\pi\)
\(774\) 0 0
\(775\) −500.000 −0.0231749
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10000.0 −0.459932
\(780\) 0 0
\(781\) 6000.00 0.274900
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6550.00 −0.297808
\(786\) 0 0
\(787\) −20434.0 −0.925532 −0.462766 − 0.886481i \(-0.653143\pi\)
−0.462766 + 0.886481i \(0.653143\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 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
\(801\) 0 0
\(802\) 0 0
\(803\) −13800.0 −0.606465
\(804\) 0 0
\(805\) −5340.00 −0.233802
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 4854.00 0.210949 0.105474 − 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) 13140.0 0.568937 0.284468 − 0.958685i \(-0.408183\pi\)
0.284468 + 0.958685i \(0.408183\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −9310.00 −0.400141
\(816\) 0 0
\(817\) 5680.00 0.243229
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −22050.0 −0.937333 −0.468666 − 0.883375i \(-0.655265\pi\)
−0.468666 + 0.883375i \(0.655265\pi\)
\(822\) 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 \(-0.784281\pi\)
−0.779017 + 0.627003i \(0.784281\pi\)
\(828\) 0 0
\(829\) −6150.00 −0.257658 −0.128829 − 0.991667i \(-0.541122\pi\)
−0.128829 + 0.991667i \(0.541122\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −9210.00 −0.383082
\(834\) 0 0
\(835\) 3630.00 0.150445
\(836\) 0 0
\(837\) 0 0
\(838\) 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
\(843\) 0 0
\(844\) 0 0
\(845\) 1515.00 0.0616776
\(846\) 0 0
\(847\) −13614.0 −0.552282
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1780.00 0.0717011
\(852\) 0 0
\(853\) −42990.0 −1.72561 −0.862807 − 0.505533i \(-0.831296\pi\)
−0.862807 + 0.505533i \(0.831296\pi\)
\(854\) 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 \(-0.599204\pi\)
−0.306639 + 0.951826i \(0.599204\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 46938.0 1.85143 0.925717 − 0.378216i \(-0.123462\pi\)
0.925717 + 0.378216i \(0.123462\pi\)
\(864\) 0 0
\(865\) −16250.0 −0.638747
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 79200.0 3.09169
\(870\) 0 0
\(871\) 38700.0 1.50551
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −750.000 −0.0289767
\(876\) 0 0
\(877\) −31230.0 −1.20247 −0.601233 − 0.799074i \(-0.705324\pi\)
−0.601233 + 0.799074i \(0.705324\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −25550.0 −0.977073 −0.488537 − 0.872543i \(-0.662469\pi\)
−0.488537 + 0.872543i \(0.662469\pi\)
\(882\) 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 \(-0.489358\pi\)
0.0334253 + 0.999441i \(0.489358\pi\)
\(888\) 0 0
\(889\) 7476.00 0.282044
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −8560.00 −0.320772
\(894\) 0 0
\(895\) −5600.00 −0.209148
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3320.00 0.123168
\(900\) 0 0
\(901\) −14700.0 −0.543538
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14210.0 −0.521941
\(906\) 0 0
\(907\) −41906.0 −1.53414 −0.767071 − 0.641563i \(-0.778286\pi\)
−0.767071 + 0.641563i \(0.778286\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 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 \(-0.701196\pi\)
−0.590822 + 0.806802i \(0.701196\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5000.00 0.178307
\(924\) 0 0
\(925\) 250.000 0.00888643
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −10150.0 −0.358461 −0.179231 − 0.983807i \(-0.557361\pi\)
−0.179231 + 0.983807i \(0.557361\pi\)
\(930\) 0 0
\(931\) 12280.0 0.432289
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 9000.00 0.314793
\(936\) 0 0
\(937\) 28530.0 0.994701 0.497350 − 0.867550i \(-0.334306\pi\)
0.497350 + 0.867550i \(0.334306\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −9678.00 −0.335275 −0.167638 − 0.985849i \(-0.553614\pi\)
−0.167638 + 0.985849i \(0.553614\pi\)
\(942\) 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 \(-0.281176\pi\)
0.634574 + 0.772862i \(0.281176\pi\)
\(948\) 0 0
\(949\) −11500.0 −0.393368
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3350.00 0.113869 0.0569345 − 0.998378i \(-0.481867\pi\)
0.0569345 + 0.998378i \(0.481867\pi\)
\(954\) 0 0
\(955\) 15900.0 0.538756
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 16620.0 0.559633
\(960\) 0 0
\(961\) −29391.0 −0.986573
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −23350.0 −0.778925
\(966\) 0 0
\(967\) −43774.0 −1.45572 −0.727858 − 0.685728i \(-0.759484\pi\)
−0.727858 + 0.685728i \(0.759484\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 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
\(981\) 0 0
\(982\) 0 0
\(983\) 2282.00 0.0740432 0.0370216 − 0.999314i \(-0.488213\pi\)
0.0370216 + 0.999314i \(0.488213\pi\)
\(984\) 0 0
\(985\) 14950.0 0.483601
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −25276.0 −0.812669
\(990\) 0 0
\(991\) 31580.0 1.01228 0.506141 − 0.862451i \(-0.331071\pi\)
0.506141 + 0.862451i \(0.331071\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 21200.0 0.675462
\(996\) 0 0
\(997\) −2790.00 −0.0886261 −0.0443130 − 0.999018i \(-0.514110\pi\)
−0.0443130 + 0.999018i \(0.514110\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1440.4.a.n.1.1 1
3.2 odd 2 160.4.a.b.1.1 yes 1
4.3 odd 2 1440.4.a.o.1.1 1
12.11 even 2 160.4.a.a.1.1 ✓ 1
15.2 even 4 800.4.c.e.449.1 2
15.8 even 4 800.4.c.e.449.2 2
15.14 odd 2 800.4.a.d.1.1 1
24.5 odd 2 320.4.a.f.1.1 1
24.11 even 2 320.4.a.i.1.1 1
48.5 odd 4 1280.4.d.k.641.1 2
48.11 even 4 1280.4.d.f.641.2 2
48.29 odd 4 1280.4.d.k.641.2 2
48.35 even 4 1280.4.d.f.641.1 2
60.23 odd 4 800.4.c.f.449.1 2
60.47 odd 4 800.4.c.f.449.2 2
60.59 even 2 800.4.a.h.1.1 1
120.29 odd 2 1600.4.a.bj.1.1 1
120.59 even 2 1600.4.a.r.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.4.a.a.1.1 ✓ 1 12.11 even 2
160.4.a.b.1.1 yes 1 3.2 odd 2
320.4.a.f.1.1 1 24.5 odd 2
320.4.a.i.1.1 1 24.11 even 2
800.4.a.d.1.1 1 15.14 odd 2
800.4.a.h.1.1 1 60.59 even 2
800.4.c.e.449.1 2 15.2 even 4
800.4.c.e.449.2 2 15.8 even 4
800.4.c.f.449.1 2 60.23 odd 4
800.4.c.f.449.2 2 60.47 odd 4
1280.4.d.f.641.1 2 48.35 even 4
1280.4.d.f.641.2 2 48.11 even 4
1280.4.d.k.641.1 2 48.5 odd 4
1280.4.d.k.641.2 2 48.29 odd 4
1440.4.a.n.1.1 1 1.1 even 1 trivial
1440.4.a.o.1.1 1 4.3 odd 2
1600.4.a.r.1.1 1 120.59 even 2
1600.4.a.bj.1.1 1 120.29 odd 2