Properties

Label 720.4.a.o.1.1
Level $720$
Weight $4$
Character 720.1
Self dual yes
Analytic conductor $42.481$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.4813752041\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 720.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.00000 q^{5} +30.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +30.0000 q^{7} -50.0000 q^{11} -20.0000 q^{13} -10.0000 q^{17} +44.0000 q^{19} -120.000 q^{23} +25.0000 q^{25} -50.0000 q^{29} -108.000 q^{31} -150.000 q^{35} -40.0000 q^{37} +400.000 q^{41} -280.000 q^{43} +280.000 q^{47} +557.000 q^{49} -610.000 q^{53} +250.000 q^{55} -50.0000 q^{59} -518.000 q^{61} +100.000 q^{65} +180.000 q^{67} -700.000 q^{71} -410.000 q^{73} -1500.00 q^{77} +516.000 q^{79} -660.000 q^{83} +50.0000 q^{85} -1500.00 q^{89} -600.000 q^{91} -220.000 q^{95} -1630.00 q^{97} +O(q^{100})\)

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 \(-0.199508\pi\)
0.809924 + 0.586535i \(0.199508\pi\)
\(8\) 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
\(13\) −20.0000 −0.426692 −0.213346 0.976977i \(-0.568436\pi\)
−0.213346 + 0.976977i \(0.568436\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −10.0000 −0.142668 −0.0713340 0.997452i \(-0.522726\pi\)
−0.0713340 + 0.997452i \(0.522726\pi\)
\(18\) 0 0
\(19\) 44.0000 0.531279 0.265639 0.964072i \(-0.414417\pi\)
0.265639 + 0.964072i \(0.414417\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −120.000 −1.08790 −0.543951 0.839117i \(-0.683072\pi\)
−0.543951 + 0.839117i \(0.683072\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −50.0000 −0.320164 −0.160082 0.987104i \(-0.551176\pi\)
−0.160082 + 0.987104i \(0.551176\pi\)
\(30\) 0 0
\(31\) −108.000 −0.625722 −0.312861 0.949799i \(-0.601287\pi\)
−0.312861 + 0.949799i \(0.601287\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −150.000 −0.724418
\(36\) 0 0
\(37\) −40.0000 −0.177729 −0.0888643 0.996044i \(-0.528324\pi\)
−0.0888643 + 0.996044i \(0.528324\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 400.000 1.52365 0.761823 0.647785i \(-0.224304\pi\)
0.761823 + 0.647785i \(0.224304\pi\)
\(42\) 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
\(47\) 280.000 0.868983 0.434491 0.900676i \(-0.356928\pi\)
0.434491 + 0.900676i \(0.356928\pi\)
\(48\) 0 0
\(49\) 557.000 1.62391
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −610.000 −1.58094 −0.790471 0.612499i \(-0.790164\pi\)
−0.790471 + 0.612499i \(0.790164\pi\)
\(54\) 0 0
\(55\) 250.000 0.612909
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −50.0000 −0.110330 −0.0551648 0.998477i \(-0.517568\pi\)
−0.0551648 + 0.998477i \(0.517568\pi\)
\(60\) 0 0
\(61\) −518.000 −1.08726 −0.543632 0.839324i \(-0.682951\pi\)
−0.543632 + 0.839324i \(0.682951\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 100.000 0.190823
\(66\) 0 0
\(67\) 180.000 0.328216 0.164108 0.986442i \(-0.447525\pi\)
0.164108 + 0.986442i \(0.447525\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −700.000 −1.17007 −0.585033 0.811009i \(-0.698919\pi\)
−0.585033 + 0.811009i \(0.698919\pi\)
\(72\) 0 0
\(73\) −410.000 −0.657354 −0.328677 0.944442i \(-0.606603\pi\)
−0.328677 + 0.944442i \(0.606603\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1500.00 −2.22001
\(78\) 0 0
\(79\) 516.000 0.734868 0.367434 0.930050i \(-0.380236\pi\)
0.367434 + 0.930050i \(0.380236\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −660.000 −0.872824 −0.436412 0.899747i \(-0.643751\pi\)
−0.436412 + 0.899747i \(0.643751\pi\)
\(84\) 0 0
\(85\) 50.0000 0.0638031
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1500.00 −1.78651 −0.893257 0.449547i \(-0.851585\pi\)
−0.893257 + 0.449547i \(0.851585\pi\)
\(90\) 0 0
\(91\) −600.000 −0.691177
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −220.000 −0.237595
\(96\) 0 0
\(97\) −1630.00 −1.70620 −0.853100 0.521747i \(-0.825280\pi\)
−0.853100 + 0.521747i \(0.825280\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −450.000 −0.443333 −0.221667 0.975122i \(-0.571150\pi\)
−0.221667 + 0.975122i \(0.571150\pi\)
\(102\) 0 0
\(103\) −770.000 −0.736605 −0.368303 0.929706i \(-0.620061\pi\)
−0.368303 + 0.929706i \(0.620061\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −660.000 −0.596305 −0.298152 0.954518i \(-0.596370\pi\)
−0.298152 + 0.954518i \(0.596370\pi\)
\(108\) 0 0
\(109\) 1754.00 1.54131 0.770655 0.637253i \(-0.219929\pi\)
0.770655 + 0.637253i \(0.219929\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −310.000 −0.258074 −0.129037 0.991640i \(-0.541189\pi\)
−0.129037 + 0.991640i \(0.541189\pi\)
\(114\) 0 0
\(115\) 600.000 0.486524
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −300.000 −0.231100
\(120\) 0 0
\(121\) 1169.00 0.878287
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1070.00 0.747615 0.373808 0.927506i \(-0.378052\pi\)
0.373808 + 0.927506i \(0.378052\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1950.00 −1.30055 −0.650276 0.759698i \(-0.725347\pi\)
−0.650276 + 0.759698i \(0.725347\pi\)
\(132\) 0 0
\(133\) 1320.00 0.860590
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1050.00 0.654800 0.327400 0.944886i \(-0.393828\pi\)
0.327400 + 0.944886i \(0.393828\pi\)
\(138\) 0 0
\(139\) −1676.00 −1.02271 −0.511354 0.859370i \(-0.670856\pi\)
−0.511354 + 0.859370i \(0.670856\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1000.00 0.584785
\(144\) 0 0
\(145\) 250.000 0.143182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2050.00 1.12713 0.563566 0.826071i \(-0.309429\pi\)
0.563566 + 0.826071i \(0.309429\pi\)
\(150\) 0 0
\(151\) −448.000 −0.241442 −0.120721 0.992686i \(-0.538521\pi\)
−0.120721 + 0.992686i \(0.538521\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 540.000 0.279831
\(156\) 0 0
\(157\) −100.000 −0.0508336 −0.0254168 0.999677i \(-0.508091\pi\)
−0.0254168 + 0.999677i \(0.508091\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3600.00 −1.76223
\(162\) 0 0
\(163\) 1900.00 0.913003 0.456501 0.889723i \(-0.349102\pi\)
0.456501 + 0.889723i \(0.349102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1920.00 −0.889665 −0.444833 0.895614i \(-0.646737\pi\)
−0.444833 + 0.895614i \(0.646737\pi\)
\(168\) 0 0
\(169\) −1797.00 −0.817934
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2550.00 1.12065 0.560326 0.828272i \(-0.310676\pi\)
0.560326 + 0.828272i \(0.310676\pi\)
\(174\) 0 0
\(175\) 750.000 0.323970
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3650.00 −1.52410 −0.762050 0.647518i \(-0.775807\pi\)
−0.762050 + 0.647518i \(0.775807\pi\)
\(180\) 0 0
\(181\) −4342.00 −1.78308 −0.891542 0.452937i \(-0.850376\pi\)
−0.891542 + 0.452937i \(0.850376\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 200.000 0.0794827
\(186\) 0 0
\(187\) 500.000 0.195527
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3500.00 1.32592 0.662961 0.748654i \(-0.269299\pi\)
0.662961 + 0.748654i \(0.269299\pi\)
\(192\) 0 0
\(193\) 3350.00 1.24942 0.624711 0.780856i \(-0.285217\pi\)
0.624711 + 0.780856i \(0.285217\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 90.0000 0.0325494 0.0162747 0.999868i \(-0.494819\pi\)
0.0162747 + 0.999868i \(0.494819\pi\)
\(198\) 0 0
\(199\) −3664.00 −1.30520 −0.652598 0.757704i \(-0.726321\pi\)
−0.652598 + 0.757704i \(0.726321\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1500.00 −0.518618
\(204\) 0 0
\(205\) −2000.00 −0.681395
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2200.00 −0.728120
\(210\) 0 0
\(211\) 268.000 0.0874402 0.0437201 0.999044i \(-0.486079\pi\)
0.0437201 + 0.999044i \(0.486079\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1400.00 0.444089
\(216\) 0 0
\(217\) −3240.00 −1.01357
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 200.000 0.0608754
\(222\) 0 0
\(223\) 3670.00 1.10207 0.551034 0.834482i \(-0.314233\pi\)
0.551034 + 0.834482i \(0.314233\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3760.00 −1.09938 −0.549692 0.835368i \(-0.685255\pi\)
−0.549692 + 0.835368i \(0.685255\pi\)
\(228\) 0 0
\(229\) −1434.00 −0.413805 −0.206903 0.978362i \(-0.566338\pi\)
−0.206903 + 0.978362i \(0.566338\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3450.00 −0.970030 −0.485015 0.874506i \(-0.661186\pi\)
−0.485015 + 0.874506i \(0.661186\pi\)
\(234\) 0 0
\(235\) −1400.00 −0.388621
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4900.00 1.32617 0.663085 0.748544i \(-0.269247\pi\)
0.663085 + 0.748544i \(0.269247\pi\)
\(240\) 0 0
\(241\) 4822.00 1.28885 0.644424 0.764668i \(-0.277097\pi\)
0.644424 + 0.764668i \(0.277097\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2785.00 −0.726233
\(246\) 0 0
\(247\) −880.000 −0.226693
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4650.00 1.16934 0.584672 0.811270i \(-0.301223\pi\)
0.584672 + 0.811270i \(0.301223\pi\)
\(252\) 0 0
\(253\) 6000.00 1.49098
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5130.00 1.24514 0.622569 0.782565i \(-0.286089\pi\)
0.622569 + 0.782565i \(0.286089\pi\)
\(258\) 0 0
\(259\) −1200.00 −0.287893
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1280.00 0.300107 0.150054 0.988678i \(-0.452055\pi\)
0.150054 + 0.988678i \(0.452055\pi\)
\(264\) 0 0
\(265\) 3050.00 0.707019
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3350.00 0.759305 0.379653 0.925129i \(-0.376044\pi\)
0.379653 + 0.925129i \(0.376044\pi\)
\(270\) 0 0
\(271\) −5512.00 −1.23554 −0.617768 0.786361i \(-0.711963\pi\)
−0.617768 + 0.786361i \(0.711963\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1250.00 −0.274101
\(276\) 0 0
\(277\) 4920.00 1.06720 0.533600 0.845737i \(-0.320839\pi\)
0.533600 + 0.845737i \(0.320839\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4500.00 0.955329 0.477665 0.878542i \(-0.341483\pi\)
0.477665 + 0.878542i \(0.341483\pi\)
\(282\) 0 0
\(283\) 6900.00 1.44934 0.724669 0.689098i \(-0.241993\pi\)
0.724669 + 0.689098i \(0.241993\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12000.0 2.46808
\(288\) 0 0
\(289\) −4813.00 −0.979646
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1530.00 0.305063 0.152532 0.988299i \(-0.451257\pi\)
0.152532 + 0.988299i \(0.451257\pi\)
\(294\) 0 0
\(295\) 250.000 0.0493409
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2400.00 0.464199
\(300\) 0 0
\(301\) −8400.00 −1.60853
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2590.00 0.486239
\(306\) 0 0
\(307\) −3040.00 −0.565153 −0.282576 0.959245i \(-0.591189\pi\)
−0.282576 + 0.959245i \(0.591189\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5700.00 1.03928 0.519642 0.854384i \(-0.326065\pi\)
0.519642 + 0.854384i \(0.326065\pi\)
\(312\) 0 0
\(313\) 3110.00 0.561622 0.280811 0.959763i \(-0.409397\pi\)
0.280811 + 0.959763i \(0.409397\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −950.000 −0.168320 −0.0841598 0.996452i \(-0.526821\pi\)
−0.0841598 + 0.996452i \(0.526821\pi\)
\(318\) 0 0
\(319\) 2500.00 0.438787
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −440.000 −0.0757965
\(324\) 0 0
\(325\) −500.000 −0.0853385
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8400.00 1.40762
\(330\) 0 0
\(331\) −2292.00 −0.380603 −0.190302 0.981726i \(-0.560947\pi\)
−0.190302 + 0.981726i \(0.560947\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −900.000 −0.146783
\(336\) 0 0
\(337\) −7730.00 −1.24950 −0.624748 0.780827i \(-0.714798\pi\)
−0.624748 + 0.780827i \(0.714798\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5400.00 0.857555
\(342\) 0 0
\(343\) 6420.00 1.01063
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1120.00 0.173270 0.0866351 0.996240i \(-0.472389\pi\)
0.0866351 + 0.996240i \(0.472389\pi\)
\(348\) 0 0
\(349\) 1186.00 0.181906 0.0909529 0.995855i \(-0.471009\pi\)
0.0909529 + 0.995855i \(0.471009\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3630.00 0.547324 0.273662 0.961826i \(-0.411765\pi\)
0.273662 + 0.961826i \(0.411765\pi\)
\(354\) 0 0
\(355\) 3500.00 0.523270
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1800.00 0.264625 0.132312 0.991208i \(-0.457760\pi\)
0.132312 + 0.991208i \(0.457760\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2050.00 0.293978
\(366\) 0 0
\(367\) −8490.00 −1.20756 −0.603780 0.797151i \(-0.706339\pi\)
−0.603780 + 0.797151i \(0.706339\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −18300.0 −2.56089
\(372\) 0 0
\(373\) 100.000 0.0138815 0.00694076 0.999976i \(-0.497791\pi\)
0.00694076 + 0.999976i \(0.497791\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1000.00 0.136612
\(378\) 0 0
\(379\) 8084.00 1.09564 0.547820 0.836597i \(-0.315458\pi\)
0.547820 + 0.836597i \(0.315458\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9480.00 1.26477 0.632383 0.774656i \(-0.282077\pi\)
0.632383 + 0.774656i \(0.282077\pi\)
\(384\) 0 0
\(385\) 7500.00 0.992819
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −10950.0 −1.42722 −0.713608 0.700545i \(-0.752940\pi\)
−0.713608 + 0.700545i \(0.752940\pi\)
\(390\) 0 0
\(391\) 1200.00 0.155209
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2580.00 −0.328643
\(396\) 0 0
\(397\) 13840.0 1.74965 0.874823 0.484442i \(-0.160977\pi\)
0.874823 + 0.484442i \(0.160977\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9300.00 1.15815 0.579077 0.815273i \(-0.303413\pi\)
0.579077 + 0.815273i \(0.303413\pi\)
\(402\) 0 0
\(403\) 2160.00 0.266991
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2000.00 0.243578
\(408\) 0 0
\(409\) −2854.00 −0.345040 −0.172520 0.985006i \(-0.555191\pi\)
−0.172520 + 0.985006i \(0.555191\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1500.00 −0.178717
\(414\) 0 0
\(415\) 3300.00 0.390339
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1150.00 −0.134084 −0.0670420 0.997750i \(-0.521356\pi\)
−0.0670420 + 0.997750i \(0.521356\pi\)
\(420\) 0 0
\(421\) −11162.0 −1.29217 −0.646084 0.763266i \(-0.723594\pi\)
−0.646084 + 0.763266i \(0.723594\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −250.000 −0.0285336
\(426\) 0 0
\(427\) −15540.0 −1.76120
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1200.00 0.134111 0.0670556 0.997749i \(-0.478639\pi\)
0.0670556 + 0.997749i \(0.478639\pi\)
\(432\) 0 0
\(433\) 1510.00 0.167589 0.0837944 0.996483i \(-0.473296\pi\)
0.0837944 + 0.996483i \(0.473296\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5280.00 −0.577979
\(438\) 0 0
\(439\) −424.000 −0.0460966 −0.0230483 0.999734i \(-0.507337\pi\)
−0.0230483 + 0.999734i \(0.507337\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12360.0 −1.32560 −0.662801 0.748796i \(-0.730632\pi\)
−0.662801 + 0.748796i \(0.730632\pi\)
\(444\) 0 0
\(445\) 7500.00 0.798953
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1300.00 −0.136639 −0.0683194 0.997664i \(-0.521764\pi\)
−0.0683194 + 0.997664i \(0.521764\pi\)
\(450\) 0 0
\(451\) −20000.0 −2.08817
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3000.00 0.309104
\(456\) 0 0
\(457\) −7190.00 −0.735961 −0.367980 0.929834i \(-0.619951\pi\)
−0.367980 + 0.929834i \(0.619951\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −150.000 −0.0151544 −0.00757722 0.999971i \(-0.502412\pi\)
−0.00757722 + 0.999971i \(0.502412\pi\)
\(462\) 0 0
\(463\) −2670.00 −0.268003 −0.134002 0.990981i \(-0.542783\pi\)
−0.134002 + 0.990981i \(0.542783\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1180.00 −0.116925 −0.0584624 0.998290i \(-0.518620\pi\)
−0.0584624 + 0.998290i \(0.518620\pi\)
\(468\) 0 0
\(469\) 5400.00 0.531661
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 14000.0 1.36093
\(474\) 0 0
\(475\) 1100.00 0.106256
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14100.0 1.34498 0.672490 0.740106i \(-0.265225\pi\)
0.672490 + 0.740106i \(0.265225\pi\)
\(480\) 0 0
\(481\) 800.000 0.0758355
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8150.00 0.763036
\(486\) 0 0
\(487\) 9850.00 0.916522 0.458261 0.888818i \(-0.348473\pi\)
0.458261 + 0.888818i \(0.348473\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2450.00 0.225187 0.112594 0.993641i \(-0.464084\pi\)
0.112594 + 0.993641i \(0.464084\pi\)
\(492\) 0 0
\(493\) 500.000 0.0456772
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −21000.0 −1.89533
\(498\) 0 0
\(499\) 17036.0 1.52833 0.764164 0.645021i \(-0.223152\pi\)
0.764164 + 0.645021i \(0.223152\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 20600.0 1.82606 0.913030 0.407891i \(-0.133736\pi\)
0.913030 + 0.407891i \(0.133736\pi\)
\(504\) 0 0
\(505\) 2250.00 0.198265
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5750.00 0.500716 0.250358 0.968153i \(-0.419452\pi\)
0.250358 + 0.968153i \(0.419452\pi\)
\(510\) 0 0
\(511\) −12300.0 −1.06481
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3850.00 0.329420
\(516\) 0 0
\(517\) −14000.0 −1.19095
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15500.0 −1.30339 −0.651696 0.758480i \(-0.725942\pi\)
−0.651696 + 0.758480i \(0.725942\pi\)
\(522\) 0 0
\(523\) 13940.0 1.16549 0.582747 0.812653i \(-0.301978\pi\)
0.582747 + 0.812653i \(0.301978\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1080.00 0.0892705
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −8000.00 −0.650128
\(534\) 0 0
\(535\) 3300.00 0.266676
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −27850.0 −2.22557
\(540\) 0 0
\(541\) −20478.0 −1.62739 −0.813695 0.581292i \(-0.802547\pi\)
−0.813695 + 0.581292i \(0.802547\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8770.00 −0.689295
\(546\) 0 0
\(547\) −12040.0 −0.941121 −0.470561 0.882368i \(-0.655948\pi\)
−0.470561 + 0.882368i \(0.655948\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2200.00 −0.170096
\(552\) 0 0
\(553\) 15480.0 1.19037
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 23550.0 1.79146 0.895732 0.444594i \(-0.146652\pi\)
0.895732 + 0.444594i \(0.146652\pi\)
\(558\) 0 0
\(559\) 5600.00 0.423712
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6120.00 0.458130 0.229065 0.973411i \(-0.426433\pi\)
0.229065 + 0.973411i \(0.426433\pi\)
\(564\) 0 0
\(565\) 1550.00 0.115414
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11700.0 −0.862020 −0.431010 0.902347i \(-0.641843\pi\)
−0.431010 + 0.902347i \(0.641843\pi\)
\(570\) 0 0
\(571\) 8188.00 0.600100 0.300050 0.953923i \(-0.402997\pi\)
0.300050 + 0.953923i \(0.402997\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3000.00 −0.217580
\(576\) 0 0
\(577\) 11690.0 0.843433 0.421717 0.906728i \(-0.361428\pi\)
0.421717 + 0.906728i \(0.361428\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −19800.0 −1.41384
\(582\) 0 0
\(583\) 30500.0 2.16669
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −21060.0 −1.48082 −0.740408 0.672157i \(-0.765368\pi\)
−0.740408 + 0.672157i \(0.765368\pi\)
\(588\) 0 0
\(589\) −4752.00 −0.332433
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −22910.0 −1.58651 −0.793255 0.608889i \(-0.791615\pi\)
−0.793255 + 0.608889i \(0.791615\pi\)
\(594\) 0 0
\(595\) 1500.00 0.103351
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1400.00 0.0954966 0.0477483 0.998859i \(-0.484795\pi\)
0.0477483 + 0.998859i \(0.484795\pi\)
\(600\) 0 0
\(601\) −11002.0 −0.746724 −0.373362 0.927686i \(-0.621795\pi\)
−0.373362 + 0.927686i \(0.621795\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5845.00 −0.392782
\(606\) 0 0
\(607\) −4630.00 −0.309598 −0.154799 0.987946i \(-0.549473\pi\)
−0.154799 + 0.987946i \(0.549473\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5600.00 −0.370788
\(612\) 0 0
\(613\) 24040.0 1.58396 0.791979 0.610548i \(-0.209051\pi\)
0.791979 + 0.610548i \(0.209051\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1890.00 −0.123320 −0.0616601 0.998097i \(-0.519639\pi\)
−0.0616601 + 0.998097i \(0.519639\pi\)
\(618\) 0 0
\(619\) −19244.0 −1.24957 −0.624783 0.780798i \(-0.714813\pi\)
−0.624783 + 0.780798i \(0.714813\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −45000.0 −2.89388
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 400.000 0.0253562
\(630\) 0 0
\(631\) −15892.0 −1.00262 −0.501308 0.865269i \(-0.667148\pi\)
−0.501308 + 0.865269i \(0.667148\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5350.00 −0.334344
\(636\) 0 0
\(637\) −11140.0 −0.692909
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12600.0 −0.776396 −0.388198 0.921576i \(-0.626902\pi\)
−0.388198 + 0.921576i \(0.626902\pi\)
\(642\) 0 0
\(643\) −7260.00 −0.445267 −0.222633 0.974902i \(-0.571465\pi\)
−0.222633 + 0.974902i \(0.571465\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7400.00 −0.449651 −0.224825 0.974399i \(-0.572181\pi\)
−0.224825 + 0.974399i \(0.572181\pi\)
\(648\) 0 0
\(649\) 2500.00 0.151207
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4790.00 −0.287055 −0.143528 0.989646i \(-0.545845\pi\)
−0.143528 + 0.989646i \(0.545845\pi\)
\(654\) 0 0
\(655\) 9750.00 0.581624
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1450.00 0.0857117 0.0428558 0.999081i \(-0.486354\pi\)
0.0428558 + 0.999081i \(0.486354\pi\)
\(660\) 0 0
\(661\) 11818.0 0.695411 0.347706 0.937604i \(-0.386961\pi\)
0.347706 + 0.937604i \(0.386961\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6600.00 −0.384868
\(666\) 0 0
\(667\) 6000.00 0.348307
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 25900.0 1.49010
\(672\) 0 0
\(673\) 5550.00 0.317885 0.158943 0.987288i \(-0.449192\pi\)
0.158943 + 0.987288i \(0.449192\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12930.0 0.734033 0.367016 0.930214i \(-0.380379\pi\)
0.367016 + 0.930214i \(0.380379\pi\)
\(678\) 0 0
\(679\) −48900.0 −2.76378
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −32580.0 −1.82524 −0.912620 0.408809i \(-0.865944\pi\)
−0.912620 + 0.408809i \(0.865944\pi\)
\(684\) 0 0
\(685\) −5250.00 −0.292835
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12200.0 0.674576
\(690\) 0 0
\(691\) −10228.0 −0.563085 −0.281542 0.959549i \(-0.590846\pi\)
−0.281542 + 0.959549i \(0.590846\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8380.00 0.457369
\(696\) 0 0
\(697\) −4000.00 −0.217376
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8350.00 0.449893 0.224947 0.974371i \(-0.427779\pi\)
0.224947 + 0.974371i \(0.427779\pi\)
\(702\) 0 0
\(703\) −1760.00 −0.0944234
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −13500.0 −0.718133
\(708\) 0 0
\(709\) −14954.0 −0.792115 −0.396057 0.918226i \(-0.629622\pi\)
−0.396057 + 0.918226i \(0.629622\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 12960.0 0.680723
\(714\) 0 0
\(715\) −5000.00 −0.261524
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −29400.0 −1.52494 −0.762472 0.647021i \(-0.776015\pi\)
−0.762472 + 0.647021i \(0.776015\pi\)
\(720\) 0 0
\(721\) −23100.0 −1.19319
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1250.00 −0.0640329
\(726\) 0 0
\(727\) 16330.0 0.833076 0.416538 0.909118i \(-0.363243\pi\)
0.416538 + 0.909118i \(0.363243\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2800.00 0.141671
\(732\) 0 0
\(733\) 30800.0 1.55201 0.776005 0.630726i \(-0.217243\pi\)
0.776005 + 0.630726i \(0.217243\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9000.00 −0.449823
\(738\) 0 0
\(739\) 9524.00 0.474081 0.237041 0.971500i \(-0.423823\pi\)
0.237041 + 0.971500i \(0.423823\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 28600.0 1.41216 0.706078 0.708134i \(-0.250463\pi\)
0.706078 + 0.708134i \(0.250463\pi\)
\(744\) 0 0
\(745\) −10250.0 −0.504068
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −19800.0 −0.965923
\(750\) 0 0
\(751\) 8252.00 0.400958 0.200479 0.979698i \(-0.435750\pi\)
0.200479 + 0.979698i \(0.435750\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2240.00 0.107976
\(756\) 0 0
\(757\) −24920.0 −1.19648 −0.598238 0.801318i \(-0.704132\pi\)
−0.598238 + 0.801318i \(0.704132\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27900.0 1.32901 0.664503 0.747285i \(-0.268643\pi\)
0.664503 + 0.747285i \(0.268643\pi\)
\(762\) 0 0
\(763\) 52620.0 2.49669
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1000.00 0.0470768
\(768\) 0 0
\(769\) −11506.0 −0.539554 −0.269777 0.962923i \(-0.586950\pi\)
−0.269777 + 0.962923i \(0.586950\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12510.0 −0.582087 −0.291044 0.956710i \(-0.594002\pi\)
−0.291044 + 0.956710i \(0.594002\pi\)
\(774\) 0 0
\(775\) −2700.00 −0.125144
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 17600.0 0.809481
\(780\) 0 0
\(781\) 35000.0 1.60358
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 500.000 0.0227335
\(786\) 0 0
\(787\) 1100.00 0.0498231 0.0249115 0.999690i \(-0.492070\pi\)
0.0249115 + 0.999690i \(0.492070\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9300.00 −0.418040
\(792\) 0 0
\(793\) 10360.0 0.463927
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4490.00 −0.199553 −0.0997766 0.995010i \(-0.531813\pi\)
−0.0997766 + 0.995010i \(0.531813\pi\)
\(798\) 0 0
\(799\) −2800.00 −0.123976
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 20500.0 0.900908
\(804\) 0 0
\(805\) 18000.0 0.788095
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 28600.0 1.24292 0.621460 0.783446i \(-0.286540\pi\)
0.621460 + 0.783446i \(0.286540\pi\)
\(810\) 0 0
\(811\) −10068.0 −0.435925 −0.217963 0.975957i \(-0.569941\pi\)
−0.217963 + 0.975957i \(0.569941\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −9500.00 −0.408307
\(816\) 0 0
\(817\) −12320.0 −0.527567
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −14250.0 −0.605759 −0.302880 0.953029i \(-0.597948\pi\)
−0.302880 + 0.953029i \(0.597948\pi\)
\(822\) 0 0
\(823\) −6830.00 −0.289282 −0.144641 0.989484i \(-0.546203\pi\)
−0.144641 + 0.989484i \(0.546203\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 8920.00 0.375065 0.187533 0.982258i \(-0.439951\pi\)
0.187533 + 0.982258i \(0.439951\pi\)
\(828\) 0 0
\(829\) −3534.00 −0.148059 −0.0740295 0.997256i \(-0.523586\pi\)
−0.0740295 + 0.997256i \(0.523586\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5570.00 −0.231680
\(834\) 0 0
\(835\) 9600.00 0.397870
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 8000.00 0.329190 0.164595 0.986361i \(-0.447368\pi\)
0.164595 + 0.986361i \(0.447368\pi\)
\(840\) 0 0
\(841\) −21889.0 −0.897495
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8985.00 0.365791
\(846\) 0 0
\(847\) 35070.0 1.42269
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4800.00 0.193351
\(852\) 0 0
\(853\) 5160.00 0.207122 0.103561 0.994623i \(-0.466976\pi\)
0.103561 + 0.994623i \(0.466976\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 7670.00 0.305720 0.152860 0.988248i \(-0.451152\pi\)
0.152860 + 0.988248i \(0.451152\pi\)
\(858\) 0 0
\(859\) −25804.0 −1.02494 −0.512469 0.858706i \(-0.671269\pi\)
−0.512469 + 0.858706i \(0.671269\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −400.000 −0.0157777 −0.00788885 0.999969i \(-0.502511\pi\)
−0.00788885 + 0.999969i \(0.502511\pi\)
\(864\) 0 0
\(865\) −12750.0 −0.501171
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −25800.0 −1.00714
\(870\) 0 0
\(871\) −3600.00 −0.140047
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3750.00 −0.144884
\(876\) 0 0
\(877\) −35100.0 −1.35147 −0.675737 0.737143i \(-0.736175\pi\)
−0.675737 + 0.737143i \(0.736175\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −18700.0 −0.715118 −0.357559 0.933891i \(-0.616391\pi\)
−0.357559 + 0.933891i \(0.616391\pi\)
\(882\) 0 0
\(883\) 2980.00 0.113573 0.0567865 0.998386i \(-0.481915\pi\)
0.0567865 + 0.998386i \(0.481915\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 35880.0 1.35821 0.679105 0.734041i \(-0.262368\pi\)
0.679105 + 0.734041i \(0.262368\pi\)
\(888\) 0 0
\(889\) 32100.0 1.21102
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 12320.0 0.461672
\(894\) 0 0
\(895\) 18250.0 0.681598
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 5400.00 0.200334
\(900\) 0 0
\(901\) 6100.00 0.225550
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 21710.0 0.797420
\(906\) 0 0
\(907\) −45240.0 −1.65620 −0.828098 0.560584i \(-0.810577\pi\)
−0.828098 + 0.560584i \(0.810577\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −33200.0 −1.20743 −0.603713 0.797202i \(-0.706313\pi\)
−0.603713 + 0.797202i \(0.706313\pi\)
\(912\) 0 0
\(913\) 33000.0 1.19621
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −58500.0 −2.10670
\(918\) 0 0
\(919\) −35356.0 −1.26908 −0.634541 0.772889i \(-0.718811\pi\)
−0.634541 + 0.772889i \(0.718811\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 14000.0 0.499259
\(924\) 0 0
\(925\) −1000.00 −0.0355457
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −25700.0 −0.907631 −0.453816 0.891096i \(-0.649938\pi\)
−0.453816 + 0.891096i \(0.649938\pi\)
\(930\) 0 0
\(931\) 24508.0 0.862747
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2500.00 −0.0874425
\(936\) 0 0
\(937\) 52890.0 1.84401 0.922007 0.387173i \(-0.126549\pi\)
0.922007 + 0.387173i \(0.126549\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 38050.0 1.31817 0.659083 0.752070i \(-0.270945\pi\)
0.659083 + 0.752070i \(0.270945\pi\)
\(942\) 0 0
\(943\) −48000.0 −1.65758
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 29640.0 1.01708 0.508538 0.861040i \(-0.330186\pi\)
0.508538 + 0.861040i \(0.330186\pi\)
\(948\) 0 0
\(949\) 8200.00 0.280488
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 15170.0 0.515640 0.257820 0.966193i \(-0.416996\pi\)
0.257820 + 0.966193i \(0.416996\pi\)
\(954\) 0 0
\(955\) −17500.0 −0.592970
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 31500.0 1.06068
\(960\) 0 0
\(961\) −18127.0 −0.608472
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −16750.0 −0.558758
\(966\) 0 0
\(967\) 5470.00 0.181906 0.0909531 0.995855i \(-0.471009\pi\)
0.0909531 + 0.995855i \(0.471009\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −15150.0 −0.500707 −0.250354 0.968154i \(-0.580547\pi\)
−0.250354 + 0.968154i \(0.580547\pi\)
\(972\) 0 0
\(973\) −50280.0 −1.65663
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 31190.0 1.02135 0.510674 0.859775i \(-0.329396\pi\)
0.510674 + 0.859775i \(0.329396\pi\)
\(978\) 0 0
\(979\) 75000.0 2.44843
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 7560.00 0.245297 0.122648 0.992450i \(-0.460861\pi\)
0.122648 + 0.992450i \(0.460861\pi\)
\(984\) 0 0
\(985\) −450.000 −0.0145565
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 33600.0 1.08030
\(990\) 0 0
\(991\) −32672.0 −1.04729 −0.523643 0.851938i \(-0.675427\pi\)
−0.523643 + 0.851938i \(0.675427\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 18320.0 0.583702
\(996\) 0 0
\(997\) −4740.00 −0.150569 −0.0752845 0.997162i \(-0.523986\pi\)
−0.0752845 + 0.997162i \(0.523986\pi\)
\(998\) 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 720.4.a.o.1.1 1
3.2 odd 2 720.4.a.bc.1.1 1
4.3 odd 2 45.4.a.e.1.1 yes 1
12.11 even 2 45.4.a.a.1.1 1
20.3 even 4 225.4.b.b.199.1 2
20.7 even 4 225.4.b.b.199.2 2
20.19 odd 2 225.4.a.a.1.1 1
28.27 even 2 2205.4.a.t.1.1 1
36.7 odd 6 405.4.e.b.271.1 2
36.11 even 6 405.4.e.n.271.1 2
36.23 even 6 405.4.e.n.136.1 2
36.31 odd 6 405.4.e.b.136.1 2
60.23 odd 4 225.4.b.a.199.2 2
60.47 odd 4 225.4.b.a.199.1 2
60.59 even 2 225.4.a.h.1.1 1
84.83 odd 2 2205.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.a.a.1.1 1 12.11 even 2
45.4.a.e.1.1 yes 1 4.3 odd 2
225.4.a.a.1.1 1 20.19 odd 2
225.4.a.h.1.1 1 60.59 even 2
225.4.b.a.199.1 2 60.47 odd 4
225.4.b.a.199.2 2 60.23 odd 4
225.4.b.b.199.1 2 20.3 even 4
225.4.b.b.199.2 2 20.7 even 4
405.4.e.b.136.1 2 36.31 odd 6
405.4.e.b.271.1 2 36.7 odd 6
405.4.e.n.136.1 2 36.23 even 6
405.4.e.n.271.1 2 36.11 even 6
720.4.a.o.1.1 1 1.1 even 1 trivial
720.4.a.bc.1.1 1 3.2 odd 2
2205.4.a.a.1.1 1 84.83 odd 2
2205.4.a.t.1.1 1 28.27 even 2