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Properties

Label 1440.4.a.b.1.1
Level $1440$
Weight $4$
Character 1440.1
Self dual yes
Analytic conductor $84.963$
Analytic rank $2$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1440,4,Mod(1,1440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://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);
 
Copy content sage: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")
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1440.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,-5,0,-30,0,0,0,-50,0,-88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(84.9627504083\)
Analytic rank: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} -30.0000 q^{7} -50.0000 q^{11} -88.0000 q^{13} +74.0000 q^{17} -140.000 q^{19} -80.0000 q^{23} +25.0000 q^{25} -234.000 q^{29} +150.000 q^{35} +116.000 q^{37} -72.0000 q^{41} -280.000 q^{43} -120.000 q^{47} +557.000 q^{49} -498.000 q^{53} +250.000 q^{55} +870.000 q^{59} +650.000 q^{61} +440.000 q^{65} -420.000 q^{67} -1020.00 q^{71} -322.000 q^{73} +1500.00 q^{77} -160.000 q^{79} +980.000 q^{83} -370.000 q^{85} -1124.00 q^{89} +2640.00 q^{91} +700.000 q^{95} +1114.00 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −30.0000 −1.61985 −0.809924 − 0.586535i \(-0.800492\pi\)
−0.809924 + 0.586535i \(0.800492\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −50.0000 −1.37051 −0.685253 − 0.728305i \(-0.740308\pi\)
−0.685253 + 0.728305i \(0.740308\pi\)
\(12\) 0 0
\(13\) −88.0000 −1.87745 −0.938723 − 0.344671i \(-0.887990\pi\)
−0.938723 + 0.344671i \(0.887990\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 74.0000 1.05574 0.527872 − 0.849324i \(-0.322990\pi\)
0.527872 + 0.849324i \(0.322990\pi\)
\(18\) 0 0
\(19\) −140.000 −1.69043 −0.845216 − 0.534425i \(-0.820528\pi\)
−0.845216 + 0.534425i \(0.820528\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −80.0000 −0.725268 −0.362634 − 0.931932i \(-0.618122\pi\)
−0.362634 + 0.931932i \(0.618122\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −234.000 −1.49837 −0.749185 − 0.662361i \(-0.769554\pi\)
−0.749185 + 0.662361i \(0.769554\pi\)
\(30\) 0 0
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 150.000 0.724418
\(36\) 0 0
\(37\) 116.000 0.515413 0.257707 − 0.966223i \(-0.417033\pi\)
0.257707 + 0.966223i \(0.417033\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −72.0000 −0.274256 −0.137128 − 0.990553i \(-0.543787\pi\)
−0.137128 + 0.990553i \(0.543787\pi\)
\(42\) 0 0
\(43\) −280.000 −0.993014 −0.496507 − 0.868033i \(-0.665384\pi\)
−0.496507 + 0.868033i \(0.665384\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −120.000 −0.372421 −0.186211 − 0.982510i \(-0.559621\pi\)
−0.186211 + 0.982510i \(0.559621\pi\)
\(48\) 0 0
\(49\) 557.000 1.62391
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −498.000 −1.29067 −0.645335 − 0.763899i \(-0.723282\pi\)
−0.645335 + 0.763899i \(0.723282\pi\)
\(54\) 0 0
\(55\) 250.000 0.612909
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 870.000 1.91973 0.959867 − 0.280454i \(-0.0904851\pi\)
0.959867 + 0.280454i \(0.0904851\pi\)
\(60\) 0 0
\(61\) 650.000 1.36433 0.682164 − 0.731199i \(-0.261039\pi\)
0.682164 + 0.731199i \(0.261039\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 440.000 0.839620
\(66\) 0 0
\(67\) −420.000 −0.765838 −0.382919 − 0.923782i \(-0.625081\pi\)
−0.382919 + 0.923782i \(0.625081\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1020.00 −1.70495 −0.852477 − 0.522765i \(-0.824901\pi\)
−0.852477 + 0.522765i \(0.824901\pi\)
\(72\) 0 0
\(73\) −322.000 −0.516264 −0.258132 − 0.966110i \(-0.583107\pi\)
−0.258132 + 0.966110i \(0.583107\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1500.00 2.22001
\(78\) 0 0
\(79\) −160.000 −0.227866 −0.113933 − 0.993488i \(-0.536345\pi\)
−0.113933 + 0.993488i \(0.536345\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 980.000 1.29601 0.648006 − 0.761635i \(-0.275603\pi\)
0.648006 + 0.761635i \(0.275603\pi\)
\(84\) 0 0
\(85\) −370.000 −0.472143
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1124.00 −1.33869 −0.669347 − 0.742950i \(-0.733426\pi\)
−0.669347 + 0.742950i \(0.733426\pi\)
\(90\) 0 0
\(91\) 2640.00 3.04118
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 700.000 0.755984
\(96\) 0 0
\(97\) 1114.00 1.16608 0.583039 − 0.812444i \(-0.301863\pi\)
0.583039 + 0.812444i \(0.301863\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −850.000 −0.837408 −0.418704 − 0.908123i \(-0.637515\pi\)
−0.418704 + 0.908123i \(0.637515\pi\)
\(102\) 0 0
\(103\) 1210.00 1.15752 0.578761 − 0.815497i \(-0.303536\pi\)
0.578761 + 0.815497i \(0.303536\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1620.00 −1.46366 −0.731829 − 0.681489i \(-0.761333\pi\)
−0.731829 + 0.681489i \(0.761333\pi\)
\(108\) 0 0
\(109\) −1054.00 −0.926192 −0.463096 − 0.886308i \(-0.653261\pi\)
−0.463096 + 0.886308i \(0.653261\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 462.000 0.384613 0.192307 − 0.981335i \(-0.438403\pi\)
0.192307 + 0.981335i \(0.438403\pi\)
\(114\) 0 0
\(115\) 400.000 0.324349
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2220.00 −1.71014
\(120\) 0 0
\(121\) 1169.00 0.878287
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1190.00 −0.831460 −0.415730 − 0.909488i \(-0.636474\pi\)
−0.415730 + 0.909488i \(0.636474\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2150.00 −1.43394 −0.716971 − 0.697103i \(-0.754472\pi\)
−0.716971 + 0.697103i \(0.754472\pi\)
\(132\) 0 0
\(133\) 4200.00 2.73824
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1334.00 0.831907 0.415954 − 0.909386i \(-0.363448\pi\)
0.415954 + 0.909386i \(0.363448\pi\)
\(138\) 0 0
\(139\) −220.000 −0.134246 −0.0671229 − 0.997745i \(-0.521382\pi\)
−0.0671229 + 0.997745i \(0.521382\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4400.00 2.57305
\(144\) 0 0
\(145\) 1170.00 0.670091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −150.000 −0.0824730 −0.0412365 − 0.999149i \(-0.513130\pi\)
−0.0412365 + 0.999149i \(0.513130\pi\)
\(150\) 0 0
\(151\) −2420.00 −1.30422 −0.652109 − 0.758126i \(-0.726115\pi\)
−0.652109 + 0.758126i \(0.726115\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1744.00 0.886537 0.443269 − 0.896389i \(-0.353819\pi\)
0.443269 + 0.896389i \(0.353819\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2400.00 1.17482
\(162\) 0 0
\(163\) −2620.00 −1.25898 −0.629492 − 0.777007i \(-0.716737\pi\)
−0.629492 + 0.777007i \(0.716737\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2160.00 1.00087 0.500437 − 0.865773i \(-0.333173\pi\)
0.500437 + 0.865773i \(0.333173\pi\)
\(168\) 0 0
\(169\) 5547.00 2.52481
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −322.000 −0.141510 −0.0707549 − 0.997494i \(-0.522541\pi\)
−0.0707549 + 0.997494i \(0.522541\pi\)
\(174\) 0 0
\(175\) −750.000 −0.323970
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1770.00 −0.739084 −0.369542 − 0.929214i \(-0.620485\pi\)
−0.369542 + 0.929214i \(0.620485\pi\)
\(180\) 0 0
\(181\) 1858.00 0.763006 0.381503 − 0.924368i \(-0.375407\pi\)
0.381503 + 0.924368i \(0.375407\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −580.000 −0.230500
\(186\) 0 0
\(187\) −3700.00 −1.44690
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −740.000 −0.280338 −0.140169 − 0.990128i \(-0.544765\pi\)
−0.140169 + 0.990128i \(0.544765\pi\)
\(192\) 0 0
\(193\) 758.000 0.282705 0.141352 − 0.989959i \(-0.454855\pi\)
0.141352 + 0.989959i \(0.454855\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4286.00 −1.55008 −0.775038 − 0.631915i \(-0.782269\pi\)
−0.775038 + 0.631915i \(0.782269\pi\)
\(198\) 0 0
\(199\) 740.000 0.263604 0.131802 − 0.991276i \(-0.457924\pi\)
0.131802 + 0.991276i \(0.457924\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7020.00 2.42713
\(204\) 0 0
\(205\) 360.000 0.122651
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 7000.00 2.31675
\(210\) 0 0
\(211\) 1340.00 0.437201 0.218600 − 0.975814i \(-0.429851\pi\)
0.218600 + 0.975814i \(0.429851\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1400.00 0.444089
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6512.00 −1.98210
\(222\) 0 0
\(223\) 210.000 0.0630612 0.0315306 − 0.999503i \(-0.489962\pi\)
0.0315306 + 0.999503i \(0.489962\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6520.00 −1.90638 −0.953189 − 0.302377i \(-0.902220\pi\)
−0.953189 + 0.302377i \(0.902220\pi\)
\(228\) 0 0
\(229\) 2550.00 0.735846 0.367923 − 0.929856i \(-0.380069\pi\)
0.367923 + 0.929856i \(0.380069\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1218.00 0.342463 0.171231 − 0.985231i \(-0.445225\pi\)
0.171231 + 0.985231i \(0.445225\pi\)
\(234\) 0 0
\(235\) 600.000 0.166552
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −380.000 −0.102846 −0.0514229 − 0.998677i \(-0.516376\pi\)
−0.0514229 + 0.998677i \(0.516376\pi\)
\(240\) 0 0
\(241\) −2650.00 −0.708305 −0.354153 − 0.935188i \(-0.615231\pi\)
−0.354153 + 0.935188i \(0.615231\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2785.00 −0.726233
\(246\) 0 0
\(247\) 12320.0 3.17370
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1830.00 −0.460194 −0.230097 − 0.973168i \(-0.573904\pi\)
−0.230097 + 0.973168i \(0.573904\pi\)
\(252\) 0 0
\(253\) 4000.00 0.993984
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1794.00 −0.435434 −0.217717 − 0.976012i \(-0.569861\pi\)
−0.217717 + 0.976012i \(0.569861\pi\)
\(258\) 0 0
\(259\) −3480.00 −0.834891
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5200.00 −1.21919 −0.609593 − 0.792715i \(-0.708667\pi\)
−0.609593 + 0.792715i \(0.708667\pi\)
\(264\) 0 0
\(265\) 2490.00 0.577206
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 350.000 0.0793304 0.0396652 − 0.999213i \(-0.487371\pi\)
0.0396652 + 0.999213i \(0.487371\pi\)
\(270\) 0 0
\(271\) −7940.00 −1.77978 −0.889890 − 0.456174i \(-0.849219\pi\)
−0.889890 + 0.456174i \(0.849219\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1250.00 −0.274101
\(276\) 0 0
\(277\) 5196.00 1.12707 0.563533 − 0.826093i \(-0.309442\pi\)
0.563533 + 0.826093i \(0.309442\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −308.000 −0.0653870 −0.0326935 − 0.999465i \(-0.510409\pi\)
−0.0326935 + 0.999465i \(0.510409\pi\)
\(282\) 0 0
\(283\) 7180.00 1.50815 0.754075 − 0.656788i \(-0.228085\pi\)
0.754075 + 0.656788i \(0.228085\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2160.00 0.444254
\(288\) 0 0
\(289\) 563.000 0.114594
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3442.00 0.686293 0.343146 − 0.939282i \(-0.388507\pi\)
0.343146 + 0.939282i \(0.388507\pi\)
\(294\) 0 0
\(295\) −4350.00 −0.858531
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7040.00 1.36165
\(300\) 0 0
\(301\) 8400.00 1.60853
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3250.00 −0.610146
\(306\) 0 0
\(307\) 2720.00 0.505663 0.252832 − 0.967510i \(-0.418638\pi\)
0.252832 + 0.967510i \(0.418638\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4140.00 −0.754848 −0.377424 − 0.926040i \(-0.623190\pi\)
−0.377424 + 0.926040i \(0.623190\pi\)
\(312\) 0 0
\(313\) 2038.00 0.368034 0.184017 − 0.982923i \(-0.441090\pi\)
0.184017 + 0.982923i \(0.441090\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4926.00 −0.872781 −0.436391 − 0.899757i \(-0.643743\pi\)
−0.436391 + 0.899757i \(0.643743\pi\)
\(318\) 0 0
\(319\) 11700.0 2.05352
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −10360.0 −1.78466
\(324\) 0 0
\(325\) −2200.00 −0.375489
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3600.00 0.603266
\(330\) 0 0
\(331\) 540.000 0.0896709 0.0448355 − 0.998994i \(-0.485724\pi\)
0.0448355 + 0.998994i \(0.485724\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2100.00 0.342493
\(336\) 0 0
\(337\) 9734.00 1.57343 0.786713 − 0.617319i \(-0.211781\pi\)
0.786713 + 0.617319i \(0.211781\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −6420.00 −1.01063
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9320.00 1.44186 0.720928 − 0.693010i \(-0.243716\pi\)
0.720928 + 0.693010i \(0.243716\pi\)
\(348\) 0 0
\(349\) 3250.00 0.498477 0.249239 − 0.968442i \(-0.419820\pi\)
0.249239 + 0.968442i \(0.419820\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8602.00 1.29699 0.648496 − 0.761218i \(-0.275398\pi\)
0.648496 + 0.761218i \(0.275398\pi\)
\(354\) 0 0
\(355\) 5100.00 0.762479
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3560.00 0.523369 0.261685 − 0.965153i \(-0.415722\pi\)
0.261685 + 0.965153i \(0.415722\pi\)
\(360\) 0 0
\(361\) 12741.0 1.85756
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1610.00 0.230880
\(366\) 0 0
\(367\) 3210.00 0.456568 0.228284 − 0.973595i \(-0.426688\pi\)
0.228284 + 0.973595i \(0.426688\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 14940.0 2.09069
\(372\) 0 0
\(373\) −3928.00 −0.545266 −0.272633 − 0.962118i \(-0.587894\pi\)
−0.272633 + 0.962118i \(0.587894\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 20592.0 2.81311
\(378\) 0 0
\(379\) 460.000 0.0623446 0.0311723 − 0.999514i \(-0.490076\pi\)
0.0311723 + 0.999514i \(0.490076\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9920.00 −1.32347 −0.661734 − 0.749739i \(-0.730179\pi\)
−0.661734 + 0.749739i \(0.730179\pi\)
\(384\) 0 0
\(385\) −7500.00 −0.992819
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4950.00 −0.645180 −0.322590 − 0.946539i \(-0.604553\pi\)
−0.322590 + 0.946539i \(0.604553\pi\)
\(390\) 0 0
\(391\) −5920.00 −0.765696
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 800.000 0.101905
\(396\) 0 0
\(397\) −13764.0 −1.74004 −0.870019 − 0.493018i \(-0.835894\pi\)
−0.870019 + 0.493018i \(0.835894\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11500.0 −1.43213 −0.716063 − 0.698036i \(-0.754058\pi\)
−0.716063 + 0.698036i \(0.754058\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5800.00 −0.706377
\(408\) 0 0
\(409\) −15046.0 −1.81901 −0.909507 − 0.415688i \(-0.863541\pi\)
−0.909507 + 0.415688i \(0.863541\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −26100.0 −3.10968
\(414\) 0 0
\(415\) −4900.00 −0.579594
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1650.00 0.192381 0.0961907 − 0.995363i \(-0.469334\pi\)
0.0961907 + 0.995363i \(0.469334\pi\)
\(420\) 0 0
\(421\) −11450.0 −1.32551 −0.662754 − 0.748837i \(-0.730612\pi\)
−0.662754 + 0.748837i \(0.730612\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1850.00 0.211149
\(426\) 0 0
\(427\) −19500.0 −2.21000
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10480.0 1.17124 0.585619 − 0.810586i \(-0.300851\pi\)
0.585619 + 0.810586i \(0.300851\pi\)
\(432\) 0 0
\(433\) −1618.00 −0.179575 −0.0897877 − 0.995961i \(-0.528619\pi\)
−0.0897877 + 0.995961i \(0.528619\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 11200.0 1.22602
\(438\) 0 0
\(439\) −17860.0 −1.94171 −0.970856 − 0.239665i \(-0.922962\pi\)
−0.970856 + 0.239665i \(0.922962\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5200.00 −0.557696 −0.278848 − 0.960335i \(-0.589953\pi\)
−0.278848 + 0.960335i \(0.589953\pi\)
\(444\) 0 0
\(445\) 5620.00 0.598682
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10700.0 1.12464 0.562321 − 0.826919i \(-0.309909\pi\)
0.562321 + 0.826919i \(0.309909\pi\)
\(450\) 0 0
\(451\) 3600.00 0.375870
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −13200.0 −1.36006
\(456\) 0 0
\(457\) −3694.00 −0.378114 −0.189057 − 0.981966i \(-0.560543\pi\)
−0.189057 + 0.981966i \(0.560543\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14350.0 −1.44977 −0.724887 − 0.688867i \(-0.758108\pi\)
−0.724887 + 0.688867i \(0.758108\pi\)
\(462\) 0 0
\(463\) −610.000 −0.0612292 −0.0306146 − 0.999531i \(-0.509746\pi\)
−0.0306146 + 0.999531i \(0.509746\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11580.0 1.14745 0.573724 − 0.819048i \(-0.305498\pi\)
0.573724 + 0.819048i \(0.305498\pi\)
\(468\) 0 0
\(469\) 12600.0 1.24054
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 14000.0 1.36093
\(474\) 0 0
\(475\) −3500.00 −0.338086
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −700.000 −0.0667721 −0.0333860 − 0.999443i \(-0.510629\pi\)
−0.0333860 + 0.999443i \(0.510629\pi\)
\(480\) 0 0
\(481\) −10208.0 −0.967661
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5570.00 −0.521486
\(486\) 0 0
\(487\) −1970.00 −0.183304 −0.0916522 − 0.995791i \(-0.529215\pi\)
−0.0916522 + 0.995791i \(0.529215\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6390.00 −0.587325 −0.293663 − 0.955909i \(-0.594874\pi\)
−0.293663 + 0.955909i \(0.594874\pi\)
\(492\) 0 0
\(493\) −17316.0 −1.58189
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 30600.0 2.76177
\(498\) 0 0
\(499\) 220.000 0.0197366 0.00986829 − 0.999951i \(-0.496859\pi\)
0.00986829 + 0.999951i \(0.496859\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5560.00 −0.492859 −0.246430 − 0.969161i \(-0.579257\pi\)
−0.246430 + 0.969161i \(0.579257\pi\)
\(504\) 0 0
\(505\) 4250.00 0.374500
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −17146.0 −1.49309 −0.746545 − 0.665335i \(-0.768289\pi\)
−0.746545 + 0.665335i \(0.768289\pi\)
\(510\) 0 0
\(511\) 9660.00 0.836269
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6050.00 −0.517660
\(516\) 0 0
\(517\) 6000.00 0.510406
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3900.00 −0.327950 −0.163975 − 0.986464i \(-0.552432\pi\)
−0.163975 + 0.986464i \(0.552432\pi\)
\(522\) 0 0
\(523\) −5780.00 −0.483254 −0.241627 − 0.970369i \(-0.577681\pi\)
−0.241627 + 0.970369i \(0.577681\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −5767.00 −0.473987
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6336.00 0.514902
\(534\) 0 0
\(535\) 8100.00 0.654567
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −27850.0 −2.22557
\(540\) 0 0
\(541\) −12678.0 −1.00752 −0.503761 − 0.863843i \(-0.668051\pi\)
−0.503761 + 0.863843i \(0.668051\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5270.00 0.414206
\(546\) 0 0
\(547\) 2120.00 0.165712 0.0828562 − 0.996562i \(-0.473596\pi\)
0.0828562 + 0.996562i \(0.473596\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 32760.0 2.53289
\(552\) 0 0
\(553\) 4800.00 0.369108
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12006.0 0.913304 0.456652 − 0.889645i \(-0.349048\pi\)
0.456652 + 0.889645i \(0.349048\pi\)
\(558\) 0 0
\(559\) 24640.0 1.86433
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −15600.0 −1.16778 −0.583891 − 0.811832i \(-0.698471\pi\)
−0.583891 + 0.811832i \(0.698471\pi\)
\(564\) 0 0
\(565\) −2310.00 −0.172004
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12100.0 −0.891491 −0.445746 − 0.895160i \(-0.647061\pi\)
−0.445746 + 0.895160i \(0.647061\pi\)
\(570\) 0 0
\(571\) 21580.0 1.58160 0.790801 − 0.612073i \(-0.209664\pi\)
0.790801 + 0.612073i \(0.209664\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2000.00 −0.145054
\(576\) 0 0
\(577\) −4846.00 −0.349639 −0.174819 − 0.984601i \(-0.555934\pi\)
−0.174819 + 0.984601i \(0.555934\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −29400.0 −2.09934
\(582\) 0 0
\(583\) 24900.0 1.76887
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7140.00 −0.502043 −0.251022 − 0.967981i \(-0.580767\pi\)
−0.251022 + 0.967981i \(0.580767\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14442.0 −1.00010 −0.500052 − 0.865995i \(-0.666686\pi\)
−0.500052 + 0.865995i \(0.666686\pi\)
\(594\) 0 0
\(595\) 11100.0 0.764799
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7480.00 0.510225 0.255112 − 0.966911i \(-0.417888\pi\)
0.255112 + 0.966911i \(0.417888\pi\)
\(600\) 0 0
\(601\) −3050.00 −0.207008 −0.103504 − 0.994629i \(-0.533006\pi\)
−0.103504 + 0.994629i \(0.533006\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5845.00 −0.392782
\(606\) 0 0
\(607\) −15050.0 −1.00636 −0.503180 − 0.864182i \(-0.667837\pi\)
−0.503180 + 0.864182i \(0.667837\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10560.0 0.699201
\(612\) 0 0
\(613\) −11612.0 −0.765097 −0.382548 − 0.923935i \(-0.624953\pi\)
−0.382548 + 0.923935i \(0.624953\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6726.00 −0.438863 −0.219432 − 0.975628i \(-0.570420\pi\)
−0.219432 + 0.975628i \(0.570420\pi\)
\(618\) 0 0
\(619\) −14300.0 −0.928539 −0.464269 − 0.885694i \(-0.653683\pi\)
−0.464269 + 0.885694i \(0.653683\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 33720.0 2.16848
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8584.00 0.544144
\(630\) 0 0
\(631\) 13400.0 0.845397 0.422699 − 0.906270i \(-0.361083\pi\)
0.422699 + 0.906270i \(0.361083\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5950.00 0.371840
\(636\) 0 0
\(637\) −49016.0 −3.04880
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7328.00 −0.451542 −0.225771 − 0.974180i \(-0.572490\pi\)
−0.225771 + 0.974180i \(0.572490\pi\)
\(642\) 0 0
\(643\) −22500.0 −1.37996 −0.689979 − 0.723829i \(-0.742380\pi\)
−0.689979 + 0.723829i \(0.742380\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 19640.0 1.19340 0.596699 − 0.802465i \(-0.296479\pi\)
0.596699 + 0.802465i \(0.296479\pi\)
\(648\) 0 0
\(649\) −43500.0 −2.63101
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13802.0 0.827127 0.413564 − 0.910475i \(-0.364284\pi\)
0.413564 + 0.910475i \(0.364284\pi\)
\(654\) 0 0
\(655\) 10750.0 0.641278
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6530.00 0.385998 0.192999 − 0.981199i \(-0.438179\pi\)
0.192999 + 0.981199i \(0.438179\pi\)
\(660\) 0 0
\(661\) −24950.0 −1.46814 −0.734072 − 0.679072i \(-0.762382\pi\)
−0.734072 + 0.679072i \(0.762382\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −21000.0 −1.22458
\(666\) 0 0
\(667\) 18720.0 1.08672
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −32500.0 −1.86982
\(672\) 0 0
\(673\) 8022.00 0.459473 0.229737 − 0.973253i \(-0.426214\pi\)
0.229737 + 0.973253i \(0.426214\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12546.0 0.712233 0.356117 − 0.934442i \(-0.384101\pi\)
0.356117 + 0.934442i \(0.384101\pi\)
\(678\) 0 0
\(679\) −33420.0 −1.88887
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6060.00 −0.339501 −0.169751 − 0.985487i \(-0.554296\pi\)
−0.169751 + 0.985487i \(0.554296\pi\)
\(684\) 0 0
\(685\) −6670.00 −0.372040
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 43824.0 2.42317
\(690\) 0 0
\(691\) 1940.00 0.106803 0.0534016 − 0.998573i \(-0.482994\pi\)
0.0534016 + 0.998573i \(0.482994\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1100.00 0.0600365
\(696\) 0 0
\(697\) −5328.00 −0.289544
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −35698.0 −1.92339 −0.961694 − 0.274126i \(-0.911612\pi\)
−0.961694 + 0.274126i \(0.911612\pi\)
\(702\) 0 0
\(703\) −16240.0 −0.871271
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 25500.0 1.35647
\(708\) 0 0
\(709\) −3050.00 −0.161559 −0.0807794 − 0.996732i \(-0.525741\pi\)
−0.0807794 + 0.996732i \(0.525741\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −22000.0 −1.15070
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5240.00 0.271793 0.135896 − 0.990723i \(-0.456609\pi\)
0.135896 + 0.990723i \(0.456609\pi\)
\(720\) 0 0
\(721\) −36300.0 −1.87501
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5850.00 −0.299674
\(726\) 0 0
\(727\) −7810.00 −0.398428 −0.199214 − 0.979956i \(-0.563839\pi\)
−0.199214 + 0.979956i \(0.563839\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −20720.0 −1.04837
\(732\) 0 0
\(733\) 17668.0 0.890290 0.445145 − 0.895459i \(-0.353152\pi\)
0.445145 + 0.895459i \(0.353152\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21000.0 1.04959
\(738\) 0 0
\(739\) 22580.0 1.12398 0.561988 − 0.827145i \(-0.310037\pi\)
0.561988 + 0.827145i \(0.310037\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15360.0 −0.758417 −0.379208 − 0.925311i \(-0.623804\pi\)
−0.379208 + 0.925311i \(0.623804\pi\)
\(744\) 0 0
\(745\) 750.000 0.0368831
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 48600.0 2.37090
\(750\) 0 0
\(751\) −25640.0 −1.24583 −0.622914 − 0.782290i \(-0.714051\pi\)
−0.622914 + 0.782290i \(0.714051\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12100.0 0.583264
\(756\) 0 0
\(757\) −644.000 −0.0309202 −0.0154601 − 0.999880i \(-0.504921\pi\)
−0.0154601 + 0.999880i \(0.504921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −21300.0 −1.01462 −0.507309 − 0.861764i \(-0.669360\pi\)
−0.507309 + 0.861764i \(0.669360\pi\)
\(762\) 0 0
\(763\) 31620.0 1.50029
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −76560.0 −3.60420
\(768\) 0 0
\(769\) −7250.00 −0.339976 −0.169988 − 0.985446i \(-0.554373\pi\)
−0.169988 + 0.985446i \(0.554373\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −22.0000 −0.00102365 −0.000511827 − 1.00000i \(-0.500163\pi\)
−0.000511827 1.00000i \(0.500163\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10080.0 0.463612
\(780\) 0 0
\(781\) 51000.0 2.33665
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8720.00 −0.396472
\(786\) 0 0
\(787\) 11620.0 0.526313 0.263156 − 0.964753i \(-0.415236\pi\)
0.263156 + 0.964753i \(0.415236\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −13860.0 −0.623015
\(792\) 0 0
\(793\) −57200.0 −2.56145
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12514.0 −0.556171 −0.278086 − 0.960556i \(-0.589700\pi\)
−0.278086 + 0.960556i \(0.589700\pi\)
\(798\) 0 0
\(799\) −8880.00 −0.393181
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 16100.0 0.707543
\(804\) 0 0
\(805\) −12000.0 −0.525397
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 11104.0 0.482566 0.241283 − 0.970455i \(-0.422432\pi\)
0.241283 + 0.970455i \(0.422432\pi\)
\(810\) 0 0
\(811\) −40140.0 −1.73799 −0.868993 − 0.494825i \(-0.835232\pi\)
−0.868993 + 0.494825i \(0.835232\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 13100.0 0.563034
\(816\) 0 0
\(817\) 39200.0 1.67862
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −24738.0 −1.05160 −0.525799 − 0.850609i \(-0.676234\pi\)
−0.525799 + 0.850609i \(0.676234\pi\)
\(822\) 0 0
\(823\) −6010.00 −0.254551 −0.127275 − 0.991867i \(-0.540623\pi\)
−0.127275 + 0.991867i \(0.540623\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18120.0 −0.761903 −0.380952 − 0.924595i \(-0.624404\pi\)
−0.380952 + 0.924595i \(0.624404\pi\)
\(828\) 0 0
\(829\) −22566.0 −0.945416 −0.472708 − 0.881219i \(-0.656723\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 41218.0 1.71443
\(834\) 0 0
\(835\) −10800.0 −0.447604
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 30000.0 1.23446 0.617232 − 0.786781i \(-0.288254\pi\)
0.617232 + 0.786781i \(0.288254\pi\)
\(840\) 0 0
\(841\) 30367.0 1.24511
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −27735.0 −1.12913
\(846\) 0 0
\(847\) −35070.0 −1.42269
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9280.00 −0.373812
\(852\) 0 0
\(853\) 15348.0 0.616067 0.308034 − 0.951375i \(-0.400329\pi\)
0.308034 + 0.951375i \(0.400329\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −17894.0 −0.713241 −0.356620 − 0.934249i \(-0.616071\pi\)
−0.356620 + 0.934249i \(0.616071\pi\)
\(858\) 0 0
\(859\) 2060.00 0.0818234 0.0409117 − 0.999163i \(-0.486974\pi\)
0.0409117 + 0.999163i \(0.486974\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 400.000 0.0157777 0.00788885 − 0.999969i \(-0.497489\pi\)
0.00788885 + 0.999969i \(0.497489\pi\)
\(864\) 0 0
\(865\) 1610.00 0.0632851
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 8000.00 0.312292
\(870\) 0 0
\(871\) 36960.0 1.43782
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3750.00 0.144884
\(876\) 0 0
\(877\) 9304.00 0.358237 0.179118 − 0.983828i \(-0.442675\pi\)
0.179118 + 0.983828i \(0.442675\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 19308.0 0.738369 0.369184 − 0.929356i \(-0.379637\pi\)
0.369184 + 0.929356i \(0.379637\pi\)
\(882\) 0 0
\(883\) −36500.0 −1.39108 −0.695540 − 0.718488i \(-0.744835\pi\)
−0.695540 + 0.718488i \(0.744835\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 19480.0 0.737401 0.368700 − 0.929548i \(-0.379803\pi\)
0.368700 + 0.929548i \(0.379803\pi\)
\(888\) 0 0
\(889\) 35700.0 1.34684
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 16800.0 0.629553
\(894\) 0 0
\(895\) 8850.00 0.330528
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −36852.0 −1.36262
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −9290.00 −0.341227
\(906\) 0 0
\(907\) 41160.0 1.50683 0.753415 − 0.657545i \(-0.228405\pi\)
0.753415 + 0.657545i \(0.228405\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −51440.0 −1.87078 −0.935391 − 0.353614i \(-0.884953\pi\)
−0.935391 + 0.353614i \(0.884953\pi\)
\(912\) 0 0
\(913\) −49000.0 −1.77619
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 64500.0 2.32277
\(918\) 0 0
\(919\) 25520.0 0.916025 0.458013 − 0.888946i \(-0.348561\pi\)
0.458013 + 0.888946i \(0.348561\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 89760.0 3.20096
\(924\) 0 0
\(925\) 2900.00 0.103083
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −10500.0 −0.370822 −0.185411 − 0.982661i \(-0.559362\pi\)
−0.185411 + 0.982661i \(0.559362\pi\)
\(930\) 0 0
\(931\) −77980.0 −2.74510
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 18500.0 0.647075
\(936\) 0 0
\(937\) −27366.0 −0.954118 −0.477059 − 0.878871i \(-0.658297\pi\)
−0.477059 + 0.878871i \(0.658297\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −51550.0 −1.78585 −0.892923 − 0.450208i \(-0.851350\pi\)
−0.892923 + 0.450208i \(0.851350\pi\)
\(942\) 0 0
\(943\) 5760.00 0.198909
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15160.0 −0.520205 −0.260102 − 0.965581i \(-0.583756\pi\)
−0.260102 + 0.965581i \(0.583756\pi\)
\(948\) 0 0
\(949\) 28336.0 0.969258
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −20898.0 −0.710339 −0.355169 − 0.934802i \(-0.615577\pi\)
−0.355169 + 0.934802i \(0.615577\pi\)
\(954\) 0 0
\(955\) 3700.00 0.125371
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −40020.0 −1.34756
\(960\) 0 0
\(961\) −29791.0 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3790.00 −0.126429
\(966\) 0 0
\(967\) 23450.0 0.779836 0.389918 − 0.920850i \(-0.372503\pi\)
0.389918 + 0.920850i \(0.372503\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −29150.0 −0.963407 −0.481703 − 0.876334i \(-0.659982\pi\)
−0.481703 + 0.876334i \(0.659982\pi\)
\(972\) 0 0
\(973\) 6600.00 0.217458
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 39546.0 1.29497 0.647487 − 0.762077i \(-0.275820\pi\)
0.647487 + 0.762077i \(0.275820\pi\)
\(978\) 0 0
\(979\) 56200.0 1.83469
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 17120.0 0.555486 0.277743 − 0.960655i \(-0.410414\pi\)
0.277743 + 0.960655i \(0.410414\pi\)
\(984\) 0 0
\(985\) 21430.0 0.693215
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 22400.0 0.720201
\(990\) 0 0
\(991\) 30620.0 0.981510 0.490755 − 0.871298i \(-0.336721\pi\)
0.490755 + 0.871298i \(0.336721\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3700.00 −0.117887
\(996\) 0 0
\(997\) −47136.0 −1.49730 −0.748652 − 0.662963i \(-0.769299\pi\)
−0.748652 + 0.662963i \(0.769299\pi\)
\(998\) 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.b.1.1 ✓ 1
3.2 odd 2 1440.4.a.k.1.1 yes 1
4.3 odd 2 1440.4.a.i.1.1 yes 1
12.11 even 2 1440.4.a.r.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1440.4.a.b.1.1 ✓ 1 1.1 even 1 trivial
1440.4.a.i.1.1 yes 1 4.3 odd 2
1440.4.a.k.1.1 yes 1 3.2 odd 2
1440.4.a.r.1.1 yes 1 12.11 even 2