Properties

Label 225.4.a.a.1.1
Level $225$
Weight $4$
Character 225.1
Self dual yes
Analytic conductor $13.275$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 225.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.00000 q^{2} +17.0000 q^{4} +30.0000 q^{7} -45.0000 q^{8} +O(q^{10})\) \(q-5.00000 q^{2} +17.0000 q^{4} +30.0000 q^{7} -45.0000 q^{8} +50.0000 q^{11} +20.0000 q^{13} -150.000 q^{14} +89.0000 q^{16} +10.0000 q^{17} -44.0000 q^{19} -250.000 q^{22} -120.000 q^{23} -100.000 q^{26} +510.000 q^{28} -50.0000 q^{29} +108.000 q^{31} -85.0000 q^{32} -50.0000 q^{34} +40.0000 q^{37} +220.000 q^{38} +400.000 q^{41} -280.000 q^{43} +850.000 q^{44} +600.000 q^{46} +280.000 q^{47} +557.000 q^{49} +340.000 q^{52} +610.000 q^{53} -1350.00 q^{56} +250.000 q^{58} +50.0000 q^{59} -518.000 q^{61} -540.000 q^{62} -287.000 q^{64} +180.000 q^{67} +170.000 q^{68} +700.000 q^{71} +410.000 q^{73} -200.000 q^{74} -748.000 q^{76} +1500.00 q^{77} -516.000 q^{79} -2000.00 q^{82} -660.000 q^{83} +1400.00 q^{86} -2250.00 q^{88} -1500.00 q^{89} +600.000 q^{91} -2040.00 q^{92} -1400.00 q^{94} +1630.00 q^{97} -2785.00 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.00000 −1.76777 −0.883883 0.467707i \(-0.845080\pi\)
−0.883883 + 0.467707i \(0.845080\pi\)
\(3\) 0 0
\(4\) 17.0000 2.12500
\(5\) 0 0
\(6\) 0 0
\(7\) 30.0000 1.61985 0.809924 0.586535i \(-0.199508\pi\)
0.809924 + 0.586535i \(0.199508\pi\)
\(8\) −45.0000 −1.98874
\(9\) 0 0
\(10\) 0 0
\(11\) 50.0000 1.37051 0.685253 0.728305i \(-0.259692\pi\)
0.685253 + 0.728305i \(0.259692\pi\)
\(12\) 0 0
\(13\) 20.0000 0.426692 0.213346 0.976977i \(-0.431564\pi\)
0.213346 + 0.976977i \(0.431564\pi\)
\(14\) −150.000 −2.86351
\(15\) 0 0
\(16\) 89.0000 1.39062
\(17\) 10.0000 0.142668 0.0713340 0.997452i \(-0.477274\pi\)
0.0713340 + 0.997452i \(0.477274\pi\)
\(18\) 0 0
\(19\) −44.0000 −0.531279 −0.265639 0.964072i \(-0.585583\pi\)
−0.265639 + 0.964072i \(0.585583\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −250.000 −2.42274
\(23\) −120.000 −1.08790 −0.543951 0.839117i \(-0.683072\pi\)
−0.543951 + 0.839117i \(0.683072\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −100.000 −0.754293
\(27\) 0 0
\(28\) 510.000 3.44218
\(29\) −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 \(-0.398713\pi\)
0.312861 + 0.949799i \(0.398713\pi\)
\(32\) −85.0000 −0.469563
\(33\) 0 0
\(34\) −50.0000 −0.252204
\(35\) 0 0
\(36\) 0 0
\(37\) 40.0000 0.177729 0.0888643 0.996044i \(-0.471676\pi\)
0.0888643 + 0.996044i \(0.471676\pi\)
\(38\) 220.000 0.939177
\(39\) 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 \(0.665384\pi\)
\(44\) 850.000 2.91233
\(45\) 0 0
\(46\) 600.000 1.92316
\(47\) 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
\(52\) 340.000 0.906721
\(53\) 610.000 1.58094 0.790471 0.612499i \(-0.209836\pi\)
0.790471 + 0.612499i \(0.209836\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1350.00 −3.22145
\(57\) 0 0
\(58\) 250.000 0.565976
\(59\) 50.0000 0.110330 0.0551648 0.998477i \(-0.482432\pi\)
0.0551648 + 0.998477i \(0.482432\pi\)
\(60\) 0 0
\(61\) −518.000 −1.08726 −0.543632 0.839324i \(-0.682951\pi\)
−0.543632 + 0.839324i \(0.682951\pi\)
\(62\) −540.000 −1.10613
\(63\) 0 0
\(64\) −287.000 −0.560547
\(65\) 0 0
\(66\) 0 0
\(67\) 180.000 0.328216 0.164108 0.986442i \(-0.447525\pi\)
0.164108 + 0.986442i \(0.447525\pi\)
\(68\) 170.000 0.303170
\(69\) 0 0
\(70\) 0 0
\(71\) 700.000 1.17007 0.585033 0.811009i \(-0.301081\pi\)
0.585033 + 0.811009i \(0.301081\pi\)
\(72\) 0 0
\(73\) 410.000 0.657354 0.328677 0.944442i \(-0.393397\pi\)
0.328677 + 0.944442i \(0.393397\pi\)
\(74\) −200.000 −0.314183
\(75\) 0 0
\(76\) −748.000 −1.12897
\(77\) 1500.00 2.22001
\(78\) 0 0
\(79\) −516.000 −0.734868 −0.367434 0.930050i \(-0.619764\pi\)
−0.367434 + 0.930050i \(0.619764\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −2000.00 −2.69345
\(83\) −660.000 −0.872824 −0.436412 0.899747i \(-0.643751\pi\)
−0.436412 + 0.899747i \(0.643751\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1400.00 1.75542
\(87\) 0 0
\(88\) −2250.00 −2.72558
\(89\) −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
\(92\) −2040.00 −2.31179
\(93\) 0 0
\(94\) −1400.00 −1.53616
\(95\) 0 0
\(96\) 0 0
\(97\) 1630.00 1.70620 0.853100 0.521747i \(-0.174720\pi\)
0.853100 + 0.521747i \(0.174720\pi\)
\(98\) −2785.00 −2.87069
\(99\) 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 \(0.620061\pi\)
\(104\) −900.000 −0.848579
\(105\) 0 0
\(106\) −3050.00 −2.79474
\(107\) −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
\(112\) 2670.00 2.25260
\(113\) 310.000 0.258074 0.129037 0.991640i \(-0.458811\pi\)
0.129037 + 0.991640i \(0.458811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −850.000 −0.680349
\(117\) 0 0
\(118\) −250.000 −0.195037
\(119\) 300.000 0.231100
\(120\) 0 0
\(121\) 1169.00 0.878287
\(122\) 2590.00 1.92203
\(123\) 0 0
\(124\) 1836.00 1.32966
\(125\) 0 0
\(126\) 0 0
\(127\) 1070.00 0.747615 0.373808 0.927506i \(-0.378052\pi\)
0.373808 + 0.927506i \(0.378052\pi\)
\(128\) 2115.00 1.46048
\(129\) 0 0
\(130\) 0 0
\(131\) 1950.00 1.30055 0.650276 0.759698i \(-0.274653\pi\)
0.650276 + 0.759698i \(0.274653\pi\)
\(132\) 0 0
\(133\) −1320.00 −0.860590
\(134\) −900.000 −0.580210
\(135\) 0 0
\(136\) −450.000 −0.283729
\(137\) −1050.00 −0.654800 −0.327400 0.944886i \(-0.606172\pi\)
−0.327400 + 0.944886i \(0.606172\pi\)
\(138\) 0 0
\(139\) 1676.00 1.02271 0.511354 0.859370i \(-0.329144\pi\)
0.511354 + 0.859370i \(0.329144\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3500.00 −2.06840
\(143\) 1000.00 0.584785
\(144\) 0 0
\(145\) 0 0
\(146\) −2050.00 −1.16205
\(147\) 0 0
\(148\) 680.000 0.377673
\(149\) 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 \(-0.461479\pi\)
0.120721 + 0.992686i \(0.461479\pi\)
\(152\) 1980.00 1.05657
\(153\) 0 0
\(154\) −7500.00 −3.92446
\(155\) 0 0
\(156\) 0 0
\(157\) 100.000 0.0508336 0.0254168 0.999677i \(-0.491909\pi\)
0.0254168 + 0.999677i \(0.491909\pi\)
\(158\) 2580.00 1.29907
\(159\) 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 \(0.349102\pi\)
\(164\) 6800.00 3.23775
\(165\) 0 0
\(166\) 3300.00 1.54295
\(167\) −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
\(172\) −4760.00 −2.11015
\(173\) −2550.00 −1.12065 −0.560326 0.828272i \(-0.689324\pi\)
−0.560326 + 0.828272i \(0.689324\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4450.00 1.90586
\(177\) 0 0
\(178\) 7500.00 3.15814
\(179\) 3650.00 1.52410 0.762050 0.647518i \(-0.224193\pi\)
0.762050 + 0.647518i \(0.224193\pi\)
\(180\) 0 0
\(181\) −4342.00 −1.78308 −0.891542 0.452937i \(-0.850376\pi\)
−0.891542 + 0.452937i \(0.850376\pi\)
\(182\) −3000.00 −1.22184
\(183\) 0 0
\(184\) 5400.00 2.16355
\(185\) 0 0
\(186\) 0 0
\(187\) 500.000 0.195527
\(188\) 4760.00 1.84659
\(189\) 0 0
\(190\) 0 0
\(191\) −3500.00 −1.32592 −0.662961 0.748654i \(-0.730701\pi\)
−0.662961 + 0.748654i \(0.730701\pi\)
\(192\) 0 0
\(193\) −3350.00 −1.24942 −0.624711 0.780856i \(-0.714783\pi\)
−0.624711 + 0.780856i \(0.714783\pi\)
\(194\) −8150.00 −3.01616
\(195\) 0 0
\(196\) 9469.00 3.45080
\(197\) −90.0000 −0.0325494 −0.0162747 0.999868i \(-0.505181\pi\)
−0.0162747 + 0.999868i \(0.505181\pi\)
\(198\) 0 0
\(199\) 3664.00 1.30520 0.652598 0.757704i \(-0.273679\pi\)
0.652598 + 0.757704i \(0.273679\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2250.00 0.783710
\(203\) −1500.00 −0.518618
\(204\) 0 0
\(205\) 0 0
\(206\) 3850.00 1.30215
\(207\) 0 0
\(208\) 1780.00 0.593369
\(209\) −2200.00 −0.728120
\(210\) 0 0
\(211\) −268.000 −0.0874402 −0.0437201 0.999044i \(-0.513921\pi\)
−0.0437201 + 0.999044i \(0.513921\pi\)
\(212\) 10370.0 3.35950
\(213\) 0 0
\(214\) 3300.00 1.05413
\(215\) 0 0
\(216\) 0 0
\(217\) 3240.00 1.01357
\(218\) −8770.00 −2.72468
\(219\) 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 \(0.314233\pi\)
\(224\) −2550.00 −0.760621
\(225\) 0 0
\(226\) −1550.00 −0.456214
\(227\) −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
\(232\) 2250.00 0.636723
\(233\) 3450.00 0.970030 0.485015 0.874506i \(-0.338814\pi\)
0.485015 + 0.874506i \(0.338814\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 850.000 0.234450
\(237\) 0 0
\(238\) −1500.00 −0.408532
\(239\) −4900.00 −1.32617 −0.663085 0.748544i \(-0.730753\pi\)
−0.663085 + 0.748544i \(0.730753\pi\)
\(240\) 0 0
\(241\) 4822.00 1.28885 0.644424 0.764668i \(-0.277097\pi\)
0.644424 + 0.764668i \(0.277097\pi\)
\(242\) −5845.00 −1.55261
\(243\) 0 0
\(244\) −8806.00 −2.31044
\(245\) 0 0
\(246\) 0 0
\(247\) −880.000 −0.226693
\(248\) −4860.00 −1.24440
\(249\) 0 0
\(250\) 0 0
\(251\) −4650.00 −1.16934 −0.584672 0.811270i \(-0.698777\pi\)
−0.584672 + 0.811270i \(0.698777\pi\)
\(252\) 0 0
\(253\) −6000.00 −1.49098
\(254\) −5350.00 −1.32161
\(255\) 0 0
\(256\) −8279.00 −2.02124
\(257\) −5130.00 −1.24514 −0.622569 0.782565i \(-0.713911\pi\)
−0.622569 + 0.782565i \(0.713911\pi\)
\(258\) 0 0
\(259\) 1200.00 0.287893
\(260\) 0 0
\(261\) 0 0
\(262\) −9750.00 −2.29907
\(263\) 1280.00 0.300107 0.150054 0.988678i \(-0.452055\pi\)
0.150054 + 0.988678i \(0.452055\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6600.00 1.52132
\(267\) 0 0
\(268\) 3060.00 0.697460
\(269\) 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 \(-0.288037\pi\)
0.617768 + 0.786361i \(0.288037\pi\)
\(272\) 890.000 0.198398
\(273\) 0 0
\(274\) 5250.00 1.15753
\(275\) 0 0
\(276\) 0 0
\(277\) −4920.00 −1.06720 −0.533600 0.845737i \(-0.679161\pi\)
−0.533600 + 0.845737i \(0.679161\pi\)
\(278\) −8380.00 −1.80791
\(279\) 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 \(0.241993\pi\)
\(284\) 11900.0 2.48639
\(285\) 0 0
\(286\) −5000.00 −1.03376
\(287\) 12000.0 2.46808
\(288\) 0 0
\(289\) −4813.00 −0.979646
\(290\) 0 0
\(291\) 0 0
\(292\) 6970.00 1.39688
\(293\) −1530.00 −0.305063 −0.152532 0.988299i \(-0.548743\pi\)
−0.152532 + 0.988299i \(0.548743\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1800.00 −0.353456
\(297\) 0 0
\(298\) −10250.0 −1.99251
\(299\) −2400.00 −0.464199
\(300\) 0 0
\(301\) −8400.00 −1.60853
\(302\) −2240.00 −0.426813
\(303\) 0 0
\(304\) −3916.00 −0.738809
\(305\) 0 0
\(306\) 0 0
\(307\) −3040.00 −0.565153 −0.282576 0.959245i \(-0.591189\pi\)
−0.282576 + 0.959245i \(0.591189\pi\)
\(308\) 25500.0 4.71752
\(309\) 0 0
\(310\) 0 0
\(311\) −5700.00 −1.03928 −0.519642 0.854384i \(-0.673935\pi\)
−0.519642 + 0.854384i \(0.673935\pi\)
\(312\) 0 0
\(313\) −3110.00 −0.561622 −0.280811 0.959763i \(-0.590603\pi\)
−0.280811 + 0.959763i \(0.590603\pi\)
\(314\) −500.000 −0.0898619
\(315\) 0 0
\(316\) −8772.00 −1.56159
\(317\) 950.000 0.168320 0.0841598 0.996452i \(-0.473179\pi\)
0.0841598 + 0.996452i \(0.473179\pi\)
\(318\) 0 0
\(319\) −2500.00 −0.438787
\(320\) 0 0
\(321\) 0 0
\(322\) 18000.0 3.11522
\(323\) −440.000 −0.0757965
\(324\) 0 0
\(325\) 0 0
\(326\) −9500.00 −1.61398
\(327\) 0 0
\(328\) −18000.0 −3.03013
\(329\) 8400.00 1.40762
\(330\) 0 0
\(331\) 2292.00 0.380603 0.190302 0.981726i \(-0.439053\pi\)
0.190302 + 0.981726i \(0.439053\pi\)
\(332\) −11220.0 −1.85475
\(333\) 0 0
\(334\) 9600.00 1.57272
\(335\) 0 0
\(336\) 0 0
\(337\) 7730.00 1.24950 0.624748 0.780827i \(-0.285202\pi\)
0.624748 + 0.780827i \(0.285202\pi\)
\(338\) 8985.00 1.44592
\(339\) 0 0
\(340\) 0 0
\(341\) 5400.00 0.857555
\(342\) 0 0
\(343\) 6420.00 1.01063
\(344\) 12600.0 1.97484
\(345\) 0 0
\(346\) 12750.0 1.98105
\(347\) 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
\(352\) −4250.00 −0.643539
\(353\) −3630.00 −0.547324 −0.273662 0.961826i \(-0.588235\pi\)
−0.273662 + 0.961826i \(0.588235\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −25500.0 −3.79634
\(357\) 0 0
\(358\) −18250.0 −2.69425
\(359\) −1800.00 −0.264625 −0.132312 0.991208i \(-0.542240\pi\)
−0.132312 + 0.991208i \(0.542240\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 21710.0 3.15208
\(363\) 0 0
\(364\) 10200.0 1.46875
\(365\) 0 0
\(366\) 0 0
\(367\) −8490.00 −1.20756 −0.603780 0.797151i \(-0.706339\pi\)
−0.603780 + 0.797151i \(0.706339\pi\)
\(368\) −10680.0 −1.51286
\(369\) 0 0
\(370\) 0 0
\(371\) 18300.0 2.56089
\(372\) 0 0
\(373\) −100.000 −0.0138815 −0.00694076 0.999976i \(-0.502209\pi\)
−0.00694076 + 0.999976i \(0.502209\pi\)
\(374\) −2500.00 −0.345647
\(375\) 0 0
\(376\) −12600.0 −1.72818
\(377\) −1000.00 −0.136612
\(378\) 0 0
\(379\) −8084.00 −1.09564 −0.547820 0.836597i \(-0.684542\pi\)
−0.547820 + 0.836597i \(0.684542\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 17500.0 2.34392
\(383\) 9480.00 1.26477 0.632383 0.774656i \(-0.282077\pi\)
0.632383 + 0.774656i \(0.282077\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 16750.0 2.20869
\(387\) 0 0
\(388\) 27710.0 3.62568
\(389\) −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
\(392\) −25065.0 −3.22952
\(393\) 0 0
\(394\) 450.000 0.0575398
\(395\) 0 0
\(396\) 0 0
\(397\) −13840.0 −1.74965 −0.874823 0.484442i \(-0.839023\pi\)
−0.874823 + 0.484442i \(0.839023\pi\)
\(398\) −18320.0 −2.30728
\(399\) 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
\(404\) −7650.00 −0.942083
\(405\) 0 0
\(406\) 7500.00 0.916795
\(407\) 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
\(412\) −13090.0 −1.56529
\(413\) 1500.00 0.178717
\(414\) 0 0
\(415\) 0 0
\(416\) −1700.00 −0.200359
\(417\) 0 0
\(418\) 11000.0 1.28715
\(419\) 1150.00 0.134084 0.0670420 0.997750i \(-0.478644\pi\)
0.0670420 + 0.997750i \(0.478644\pi\)
\(420\) 0 0
\(421\) −11162.0 −1.29217 −0.646084 0.763266i \(-0.723594\pi\)
−0.646084 + 0.763266i \(0.723594\pi\)
\(422\) 1340.00 0.154574
\(423\) 0 0
\(424\) −27450.0 −3.14408
\(425\) 0 0
\(426\) 0 0
\(427\) −15540.0 −1.76120
\(428\) −11220.0 −1.26715
\(429\) 0 0
\(430\) 0 0
\(431\) −1200.00 −0.134111 −0.0670556 0.997749i \(-0.521361\pi\)
−0.0670556 + 0.997749i \(0.521361\pi\)
\(432\) 0 0
\(433\) −1510.00 −0.167589 −0.0837944 0.996483i \(-0.526704\pi\)
−0.0837944 + 0.996483i \(0.526704\pi\)
\(434\) −16200.0 −1.79176
\(435\) 0 0
\(436\) 29818.0 3.27528
\(437\) 5280.00 0.577979
\(438\) 0 0
\(439\) 424.000 0.0460966 0.0230483 0.999734i \(-0.492663\pi\)
0.0230483 + 0.999734i \(0.492663\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1000.00 −0.107613
\(443\) −12360.0 −1.32560 −0.662801 0.748796i \(-0.730632\pi\)
−0.662801 + 0.748796i \(0.730632\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −18350.0 −1.94820
\(447\) 0 0
\(448\) −8610.00 −0.908001
\(449\) −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
\(452\) 5270.00 0.548407
\(453\) 0 0
\(454\) 18800.0 1.94345
\(455\) 0 0
\(456\) 0 0
\(457\) 7190.00 0.735961 0.367980 0.929834i \(-0.380049\pi\)
0.367980 + 0.929834i \(0.380049\pi\)
\(458\) 7170.00 0.731511
\(459\) 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 \(0.542783\pi\)
\(464\) −4450.00 −0.445229
\(465\) 0 0
\(466\) −17250.0 −1.71479
\(467\) −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
\(472\) −2250.00 −0.219417
\(473\) −14000.0 −1.36093
\(474\) 0 0
\(475\) 0 0
\(476\) 5100.00 0.491088
\(477\) 0 0
\(478\) 24500.0 2.34436
\(479\) −14100.0 −1.34498 −0.672490 0.740106i \(-0.734775\pi\)
−0.672490 + 0.740106i \(0.734775\pi\)
\(480\) 0 0
\(481\) 800.000 0.0758355
\(482\) −24110.0 −2.27838
\(483\) 0 0
\(484\) 19873.0 1.86636
\(485\) 0 0
\(486\) 0 0
\(487\) 9850.00 0.916522 0.458261 0.888818i \(-0.348473\pi\)
0.458261 + 0.888818i \(0.348473\pi\)
\(488\) 23310.0 2.16228
\(489\) 0 0
\(490\) 0 0
\(491\) −2450.00 −0.225187 −0.112594 0.993641i \(-0.535916\pi\)
−0.112594 + 0.993641i \(0.535916\pi\)
\(492\) 0 0
\(493\) −500.000 −0.0456772
\(494\) 4400.00 0.400740
\(495\) 0 0
\(496\) 9612.00 0.870144
\(497\) 21000.0 1.89533
\(498\) 0 0
\(499\) −17036.0 −1.52833 −0.764164 0.645021i \(-0.776848\pi\)
−0.764164 + 0.645021i \(0.776848\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 23250.0 2.06713
\(503\) 20600.0 1.82606 0.913030 0.407891i \(-0.133736\pi\)
0.913030 + 0.407891i \(0.133736\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 30000.0 2.63570
\(507\) 0 0
\(508\) 18190.0 1.58868
\(509\) 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
\(512\) 24475.0 2.11260
\(513\) 0 0
\(514\) 25650.0 2.20111
\(515\) 0 0
\(516\) 0 0
\(517\) 14000.0 1.19095
\(518\) −6000.00 −0.508928
\(519\) 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 \(0.301978\pi\)
\(524\) 33150.0 2.76367
\(525\) 0 0
\(526\) −6400.00 −0.530520
\(527\) 1080.00 0.0892705
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 0 0
\(531\) 0 0
\(532\) −22440.0 −1.82875
\(533\) 8000.00 0.650128
\(534\) 0 0
\(535\) 0 0
\(536\) −8100.00 −0.652736
\(537\) 0 0
\(538\) −16750.0 −1.34227
\(539\) 27850.0 2.22557
\(540\) 0 0
\(541\) −20478.0 −1.62739 −0.813695 0.581292i \(-0.802547\pi\)
−0.813695 + 0.581292i \(0.802547\pi\)
\(542\) −27560.0 −2.18414
\(543\) 0 0
\(544\) −850.000 −0.0669916
\(545\) 0 0
\(546\) 0 0
\(547\) −12040.0 −0.941121 −0.470561 0.882368i \(-0.655948\pi\)
−0.470561 + 0.882368i \(0.655948\pi\)
\(548\) −17850.0 −1.39145
\(549\) 0 0
\(550\) 0 0
\(551\) 2200.00 0.170096
\(552\) 0 0
\(553\) −15480.0 −1.19037
\(554\) 24600.0 1.88656
\(555\) 0 0
\(556\) 28492.0 2.17326
\(557\) −23550.0 −1.79146 −0.895732 0.444594i \(-0.853348\pi\)
−0.895732 + 0.444594i \(0.853348\pi\)
\(558\) 0 0
\(559\) −5600.00 −0.423712
\(560\) 0 0
\(561\) 0 0
\(562\) −22500.0 −1.68880
\(563\) 6120.00 0.458130 0.229065 0.973411i \(-0.426433\pi\)
0.229065 + 0.973411i \(0.426433\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −34500.0 −2.56209
\(567\) 0 0
\(568\) −31500.0 −2.32696
\(569\) −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 \(-0.597003\pi\)
−0.300050 + 0.953923i \(0.597003\pi\)
\(572\) 17000.0 1.24267
\(573\) 0 0
\(574\) −60000.0 −4.36298
\(575\) 0 0
\(576\) 0 0
\(577\) −11690.0 −0.843433 −0.421717 0.906728i \(-0.638572\pi\)
−0.421717 + 0.906728i \(0.638572\pi\)
\(578\) 24065.0 1.73179
\(579\) 0 0
\(580\) 0 0
\(581\) −19800.0 −1.41384
\(582\) 0 0
\(583\) 30500.0 2.16669
\(584\) −18450.0 −1.30731
\(585\) 0 0
\(586\) 7650.00 0.539281
\(587\) −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
\(592\) 3560.00 0.247154
\(593\) 22910.0 1.58651 0.793255 0.608889i \(-0.208385\pi\)
0.793255 + 0.608889i \(0.208385\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 34850.0 2.39515
\(597\) 0 0
\(598\) 12000.0 0.820596
\(599\) −1400.00 −0.0954966 −0.0477483 0.998859i \(-0.515205\pi\)
−0.0477483 + 0.998859i \(0.515205\pi\)
\(600\) 0 0
\(601\) −11002.0 −0.746724 −0.373362 0.927686i \(-0.621795\pi\)
−0.373362 + 0.927686i \(0.621795\pi\)
\(602\) 42000.0 2.84351
\(603\) 0 0
\(604\) 7616.00 0.513064
\(605\) 0 0
\(606\) 0 0
\(607\) −4630.00 −0.309598 −0.154799 0.987946i \(-0.549473\pi\)
−0.154799 + 0.987946i \(0.549473\pi\)
\(608\) 3740.00 0.249469
\(609\) 0 0
\(610\) 0 0
\(611\) 5600.00 0.370788
\(612\) 0 0
\(613\) −24040.0 −1.58396 −0.791979 0.610548i \(-0.790949\pi\)
−0.791979 + 0.610548i \(0.790949\pi\)
\(614\) 15200.0 0.999059
\(615\) 0 0
\(616\) −67500.0 −4.41502
\(617\) 1890.00 0.123320 0.0616601 0.998097i \(-0.480361\pi\)
0.0616601 + 0.998097i \(0.480361\pi\)
\(618\) 0 0
\(619\) 19244.0 1.24957 0.624783 0.780798i \(-0.285187\pi\)
0.624783 + 0.780798i \(0.285187\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 28500.0 1.83721
\(623\) −45000.0 −2.89388
\(624\) 0 0
\(625\) 0 0
\(626\) 15550.0 0.992816
\(627\) 0 0
\(628\) 1700.00 0.108021
\(629\) 400.000 0.0253562
\(630\) 0 0
\(631\) 15892.0 1.00262 0.501308 0.865269i \(-0.332852\pi\)
0.501308 + 0.865269i \(0.332852\pi\)
\(632\) 23220.0 1.46146
\(633\) 0 0
\(634\) −4750.00 −0.297550
\(635\) 0 0
\(636\) 0 0
\(637\) 11140.0 0.692909
\(638\) 12500.0 0.775674
\(639\) 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 \(0.571465\pi\)
\(644\) −61200.0 −3.74475
\(645\) 0 0
\(646\) 2200.00 0.133990
\(647\) −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
\(652\) 32300.0 1.94013
\(653\) 4790.00 0.287055 0.143528 0.989646i \(-0.454155\pi\)
0.143528 + 0.989646i \(0.454155\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 35600.0 2.11882
\(657\) 0 0
\(658\) −42000.0 −2.48834
\(659\) −1450.00 −0.0857117 −0.0428558 0.999081i \(-0.513646\pi\)
−0.0428558 + 0.999081i \(0.513646\pi\)
\(660\) 0 0
\(661\) 11818.0 0.695411 0.347706 0.937604i \(-0.386961\pi\)
0.347706 + 0.937604i \(0.386961\pi\)
\(662\) −11460.0 −0.672818
\(663\) 0 0
\(664\) 29700.0 1.73582
\(665\) 0 0
\(666\) 0 0
\(667\) 6000.00 0.348307
\(668\) −32640.0 −1.89054
\(669\) 0 0
\(670\) 0 0
\(671\) −25900.0 −1.49010
\(672\) 0 0
\(673\) −5550.00 −0.317885 −0.158943 0.987288i \(-0.550808\pi\)
−0.158943 + 0.987288i \(0.550808\pi\)
\(674\) −38650.0 −2.20882
\(675\) 0 0
\(676\) −30549.0 −1.73811
\(677\) −12930.0 −0.734033 −0.367016 0.930214i \(-0.619621\pi\)
−0.367016 + 0.930214i \(0.619621\pi\)
\(678\) 0 0
\(679\) 48900.0 2.76378
\(680\) 0 0
\(681\) 0 0
\(682\) −27000.0 −1.51596
\(683\) −32580.0 −1.82524 −0.912620 0.408809i \(-0.865944\pi\)
−0.912620 + 0.408809i \(0.865944\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −32100.0 −1.78657
\(687\) 0 0
\(688\) −24920.0 −1.38091
\(689\) 12200.0 0.674576
\(690\) 0 0
\(691\) 10228.0 0.563085 0.281542 0.959549i \(-0.409154\pi\)
0.281542 + 0.959549i \(0.409154\pi\)
\(692\) −43350.0 −2.38139
\(693\) 0 0
\(694\) −5600.00 −0.306301
\(695\) 0 0
\(696\) 0 0
\(697\) 4000.00 0.217376
\(698\) −5930.00 −0.321567
\(699\) 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
\(704\) −14350.0 −0.768233
\(705\) 0 0
\(706\) 18150.0 0.967541
\(707\) −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
\(712\) 67500.0 3.55291
\(713\) −12960.0 −0.680723
\(714\) 0 0
\(715\) 0 0
\(716\) 62050.0 3.23871
\(717\) 0 0
\(718\) 9000.00 0.467795
\(719\) 29400.0 1.52494 0.762472 0.647021i \(-0.223985\pi\)
0.762472 + 0.647021i \(0.223985\pi\)
\(720\) 0 0
\(721\) −23100.0 −1.19319
\(722\) 24615.0 1.26880
\(723\) 0 0
\(724\) −73814.0 −3.78905
\(725\) 0 0
\(726\) 0 0
\(727\) 16330.0 0.833076 0.416538 0.909118i \(-0.363243\pi\)
0.416538 + 0.909118i \(0.363243\pi\)
\(728\) −27000.0 −1.37457
\(729\) 0 0
\(730\) 0 0
\(731\) −2800.00 −0.141671
\(732\) 0 0
\(733\) −30800.0 −1.55201 −0.776005 0.630726i \(-0.782757\pi\)
−0.776005 + 0.630726i \(0.782757\pi\)
\(734\) 42450.0 2.13468
\(735\) 0 0
\(736\) 10200.0 0.510838
\(737\) 9000.00 0.449823
\(738\) 0 0
\(739\) −9524.00 −0.474081 −0.237041 0.971500i \(-0.576177\pi\)
−0.237041 + 0.971500i \(0.576177\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −91500.0 −4.52705
\(743\) 28600.0 1.41216 0.706078 0.708134i \(-0.250463\pi\)
0.706078 + 0.708134i \(0.250463\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 500.000 0.0245393
\(747\) 0 0
\(748\) 8500.00 0.415496
\(749\) −19800.0 −0.965923
\(750\) 0 0
\(751\) −8252.00 −0.400958 −0.200479 0.979698i \(-0.564250\pi\)
−0.200479 + 0.979698i \(0.564250\pi\)
\(752\) 24920.0 1.20843
\(753\) 0 0
\(754\) 5000.00 0.241498
\(755\) 0 0
\(756\) 0 0
\(757\) 24920.0 1.19648 0.598238 0.801318i \(-0.295868\pi\)
0.598238 + 0.801318i \(0.295868\pi\)
\(758\) 40420.0 1.93683
\(759\) 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
\(764\) −59500.0 −2.81758
\(765\) 0 0
\(766\) −47400.0 −2.23581
\(767\) 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
\(772\) −56950.0 −2.65502
\(773\) 12510.0 0.582087 0.291044 0.956710i \(-0.405998\pi\)
0.291044 + 0.956710i \(0.405998\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −73350.0 −3.39318
\(777\) 0 0
\(778\) 54750.0 2.52299
\(779\) −17600.0 −0.809481
\(780\) 0 0
\(781\) 35000.0 1.60358
\(782\) 6000.00 0.274373
\(783\) 0 0
\(784\) 49573.0 2.25825
\(785\) 0 0
\(786\) 0 0
\(787\) 1100.00 0.0498231 0.0249115 0.999690i \(-0.492070\pi\)
0.0249115 + 0.999690i \(0.492070\pi\)
\(788\) −1530.00 −0.0691675
\(789\) 0 0
\(790\) 0 0
\(791\) 9300.00 0.418040
\(792\) 0 0
\(793\) −10360.0 −0.463927
\(794\) 69200.0 3.09297
\(795\) 0 0
\(796\) 62288.0 2.77354
\(797\) 4490.00 0.199553 0.0997766 0.995010i \(-0.468187\pi\)
0.0997766 + 0.995010i \(0.468187\pi\)
\(798\) 0 0
\(799\) 2800.00 0.123976
\(800\) 0 0
\(801\) 0 0
\(802\) −46500.0 −2.04735
\(803\) 20500.0 0.900908
\(804\) 0 0
\(805\) 0 0
\(806\) −10800.0 −0.471977
\(807\) 0 0
\(808\) 20250.0 0.881674
\(809\) 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 \(-0.430059\pi\)
0.217963 + 0.975957i \(0.430059\pi\)
\(812\) −25500.0 −1.10206
\(813\) 0 0
\(814\) −10000.0 −0.430589
\(815\) 0 0
\(816\) 0 0
\(817\) 12320.0 0.527567
\(818\) 14270.0 0.609950
\(819\) 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 \(0.546203\pi\)
\(824\) 34650.0 1.46491
\(825\) 0 0
\(826\) −7500.00 −0.315930
\(827\) 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
\(832\) −5740.00 −0.239181
\(833\) 5570.00 0.231680
\(834\) 0 0
\(835\) 0 0
\(836\) −37400.0 −1.54726
\(837\) 0 0
\(838\) −5750.00 −0.237029
\(839\) −8000.00 −0.329190 −0.164595 0.986361i \(-0.552632\pi\)
−0.164595 + 0.986361i \(0.552632\pi\)
\(840\) 0 0
\(841\) −21889.0 −0.897495
\(842\) 55810.0 2.28425
\(843\) 0 0
\(844\) −4556.00 −0.185810
\(845\) 0 0
\(846\) 0 0
\(847\) 35070.0 1.42269
\(848\) 54290.0 2.19850
\(849\) 0 0
\(850\) 0 0
\(851\) −4800.00 −0.193351
\(852\) 0 0
\(853\) −5160.00 −0.207122 −0.103561 0.994623i \(-0.533024\pi\)
−0.103561 + 0.994623i \(0.533024\pi\)
\(854\) 77700.0 3.11339
\(855\) 0 0
\(856\) 29700.0 1.18589
\(857\) −7670.00 −0.305720 −0.152860 0.988248i \(-0.548848\pi\)
−0.152860 + 0.988248i \(0.548848\pi\)
\(858\) 0 0
\(859\) 25804.0 1.02494 0.512469 0.858706i \(-0.328731\pi\)
0.512469 + 0.858706i \(0.328731\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 6000.00 0.237078
\(863\) −400.000 −0.0157777 −0.00788885 0.999969i \(-0.502511\pi\)
−0.00788885 + 0.999969i \(0.502511\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 7550.00 0.296258
\(867\) 0 0
\(868\) 55080.0 2.15384
\(869\) −25800.0 −1.00714
\(870\) 0 0
\(871\) 3600.00 0.140047
\(872\) −78930.0 −3.06526
\(873\) 0 0
\(874\) −26400.0 −1.02173
\(875\) 0 0
\(876\) 0 0
\(877\) 35100.0 1.35147 0.675737 0.737143i \(-0.263825\pi\)
0.675737 + 0.737143i \(0.263825\pi\)
\(878\) −2120.00 −0.0814881
\(879\) 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 \(0.481915\pi\)
\(884\) 3400.00 0.129360
\(885\) 0 0
\(886\) 61800.0 2.34335
\(887\) 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
\(892\) 62390.0 2.34190
\(893\) −12320.0 −0.461672
\(894\) 0 0
\(895\) 0 0
\(896\) 63450.0 2.36575
\(897\) 0 0
\(898\) 6500.00 0.241545
\(899\) −5400.00 −0.200334
\(900\) 0 0
\(901\) 6100.00 0.225550
\(902\) −100000. −3.69139
\(903\) 0 0
\(904\) −13950.0 −0.513241
\(905\) 0 0
\(906\) 0 0
\(907\) −45240.0 −1.65620 −0.828098 0.560584i \(-0.810577\pi\)
−0.828098 + 0.560584i \(0.810577\pi\)
\(908\) −63920.0 −2.33619
\(909\) 0 0
\(910\) 0 0
\(911\) 33200.0 1.20743 0.603713 0.797202i \(-0.293687\pi\)
0.603713 + 0.797202i \(0.293687\pi\)
\(912\) 0 0
\(913\) −33000.0 −1.19621
\(914\) −35950.0 −1.30101
\(915\) 0 0
\(916\) −24378.0 −0.879336
\(917\) 58500.0 2.10670
\(918\) 0 0
\(919\) 35356.0 1.26908 0.634541 0.772889i \(-0.281189\pi\)
0.634541 + 0.772889i \(0.281189\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 750.000 0.0267895
\(923\) 14000.0 0.499259
\(924\) 0 0
\(925\) 0 0
\(926\) 13350.0 0.473767
\(927\) 0 0
\(928\) 4250.00 0.150337
\(929\) −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
\(932\) 58650.0 2.06131
\(933\) 0 0
\(934\) 5900.00 0.206696
\(935\) 0 0
\(936\) 0 0
\(937\) −52890.0 −1.84401 −0.922007 0.387173i \(-0.873451\pi\)
−0.922007 + 0.387173i \(0.873451\pi\)
\(938\) −27000.0 −0.939852
\(939\) 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
\(944\) 4450.00 0.153427
\(945\) 0 0
\(946\) 70000.0 2.40581
\(947\) 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
\(952\) −13500.0 −0.459598
\(953\) −15170.0 −0.515640 −0.257820 0.966193i \(-0.583004\pi\)
−0.257820 + 0.966193i \(0.583004\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −83300.0 −2.81811
\(957\) 0 0
\(958\) 70500.0 2.37761
\(959\) −31500.0 −1.06068
\(960\) 0 0
\(961\) −18127.0 −0.608472
\(962\) −4000.00 −0.134059
\(963\) 0 0
\(964\) 81974.0 2.73880
\(965\) 0 0
\(966\) 0 0
\(967\) 5470.00 0.181906 0.0909531 0.995855i \(-0.471009\pi\)
0.0909531 + 0.995855i \(0.471009\pi\)
\(968\) −52605.0 −1.74668
\(969\) 0 0
\(970\) 0 0
\(971\) 15150.0 0.500707 0.250354 0.968154i \(-0.419453\pi\)
0.250354 + 0.968154i \(0.419453\pi\)
\(972\) 0 0
\(973\) 50280.0 1.65663
\(974\) −49250.0 −1.62020
\(975\) 0 0
\(976\) −46102.0 −1.51198
\(977\) −31190.0 −1.02135 −0.510674 0.859775i \(-0.670604\pi\)
−0.510674 + 0.859775i \(0.670604\pi\)
\(978\) 0 0
\(979\) −75000.0 −2.44843
\(980\) 0 0
\(981\) 0 0
\(982\) 12250.0 0.398079
\(983\) 7560.00 0.245297 0.122648 0.992450i \(-0.460861\pi\)
0.122648 + 0.992450i \(0.460861\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 2500.00 0.0807467
\(987\) 0 0
\(988\) −14960.0 −0.481722
\(989\) 33600.0 1.08030
\(990\) 0 0
\(991\) 32672.0 1.04729 0.523643 0.851938i \(-0.324573\pi\)
0.523643 + 0.851938i \(0.324573\pi\)
\(992\) −9180.00 −0.293816
\(993\) 0 0
\(994\) −105000. −3.35050
\(995\) 0 0
\(996\) 0 0
\(997\) 4740.00 0.150569 0.0752845 0.997162i \(-0.476014\pi\)
0.0752845 + 0.997162i \(0.476014\pi\)
\(998\) 85180.0 2.70173
\(999\) 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 225.4.a.a.1.1 1
3.2 odd 2 225.4.a.h.1.1 1
5.2 odd 4 225.4.b.b.199.1 2
5.3 odd 4 225.4.b.b.199.2 2
5.4 even 2 45.4.a.e.1.1 yes 1
15.2 even 4 225.4.b.a.199.2 2
15.8 even 4 225.4.b.a.199.1 2
15.14 odd 2 45.4.a.a.1.1 1
20.19 odd 2 720.4.a.o.1.1 1
35.34 odd 2 2205.4.a.t.1.1 1
45.4 even 6 405.4.e.b.136.1 2
45.14 odd 6 405.4.e.n.136.1 2
45.29 odd 6 405.4.e.n.271.1 2
45.34 even 6 405.4.e.b.271.1 2
60.59 even 2 720.4.a.bc.1.1 1
105.104 even 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 15.14 odd 2
45.4.a.e.1.1 yes 1 5.4 even 2
225.4.a.a.1.1 1 1.1 even 1 trivial
225.4.a.h.1.1 1 3.2 odd 2
225.4.b.a.199.1 2 15.8 even 4
225.4.b.a.199.2 2 15.2 even 4
225.4.b.b.199.1 2 5.2 odd 4
225.4.b.b.199.2 2 5.3 odd 4
405.4.e.b.136.1 2 45.4 even 6
405.4.e.b.271.1 2 45.34 even 6
405.4.e.n.136.1 2 45.14 odd 6
405.4.e.n.271.1 2 45.29 odd 6
720.4.a.o.1.1 1 20.19 odd 2
720.4.a.bc.1.1 1 60.59 even 2
2205.4.a.a.1.1 1 105.104 even 2
2205.4.a.t.1.1 1 35.34 odd 2