Properties

Label 720.4.a.u.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 5)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+5.00000 q^{5} -6.00000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -6.00000 q^{7} +32.0000 q^{11} -38.0000 q^{13} -26.0000 q^{17} -100.000 q^{19} -78.0000 q^{23} +25.0000 q^{25} +50.0000 q^{29} +108.000 q^{31} -30.0000 q^{35} +266.000 q^{37} -22.0000 q^{41} -442.000 q^{43} -514.000 q^{47} -307.000 q^{49} -2.00000 q^{53} +160.000 q^{55} +500.000 q^{59} -518.000 q^{61} -190.000 q^{65} -126.000 q^{67} +412.000 q^{71} -878.000 q^{73} -192.000 q^{77} -600.000 q^{79} +282.000 q^{83} -130.000 q^{85} +150.000 q^{89} +228.000 q^{91} -500.000 q^{95} +386.000 q^{97} +O(q^{100})\)

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
\(7\) −6.00000 −0.323970 −0.161985 0.986793i \(-0.551790\pi\)
−0.161985 + 0.986793i \(0.551790\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 32.0000 0.877124 0.438562 0.898701i \(-0.355488\pi\)
0.438562 + 0.898701i \(0.355488\pi\)
\(12\) 0 0
\(13\) −38.0000 −0.810716 −0.405358 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −26.0000 −0.370937 −0.185468 0.982650i \(-0.559380\pi\)
−0.185468 + 0.982650i \(0.559380\pi\)
\(18\) 0 0
\(19\) −100.000 −1.20745 −0.603726 0.797192i \(-0.706318\pi\)
−0.603726 + 0.797192i \(0.706318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −78.0000 −0.707136 −0.353568 0.935409i \(-0.615032\pi\)
−0.353568 + 0.935409i \(0.615032\pi\)
\(24\) 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 \(-0.448824\pi\)
0.160082 + 0.987104i \(0.448824\pi\)
\(30\) 0 0
\(31\) 108.000 0.625722 0.312861 0.949799i \(-0.398713\pi\)
0.312861 + 0.949799i \(0.398713\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −30.0000 −0.144884
\(36\) 0 0
\(37\) 266.000 1.18190 0.590948 0.806710i \(-0.298754\pi\)
0.590948 + 0.806710i \(0.298754\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −22.0000 −0.0838006 −0.0419003 0.999122i \(-0.513341\pi\)
−0.0419003 + 0.999122i \(0.513341\pi\)
\(42\) 0 0
\(43\) −442.000 −1.56754 −0.783772 0.621049i \(-0.786707\pi\)
−0.783772 + 0.621049i \(0.786707\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −514.000 −1.59520 −0.797602 0.603184i \(-0.793899\pi\)
−0.797602 + 0.603184i \(0.793899\pi\)
\(48\) 0 0
\(49\) −307.000 −0.895044
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.00000 −0.00518342 −0.00259171 0.999997i \(-0.500825\pi\)
−0.00259171 + 0.999997i \(0.500825\pi\)
\(54\) 0 0
\(55\) 160.000 0.392262
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 500.000 1.10330 0.551648 0.834077i \(-0.313999\pi\)
0.551648 + 0.834077i \(0.313999\pi\)
\(60\) 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
\(65\) −190.000 −0.362563
\(66\) 0 0
\(67\) −126.000 −0.229751 −0.114876 0.993380i \(-0.536647\pi\)
−0.114876 + 0.993380i \(0.536647\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 412.000 0.688668 0.344334 0.938847i \(-0.388105\pi\)
0.344334 + 0.938847i \(0.388105\pi\)
\(72\) 0 0
\(73\) −878.000 −1.40770 −0.703850 0.710348i \(-0.748537\pi\)
−0.703850 + 0.710348i \(0.748537\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −192.000 −0.284161
\(78\) 0 0
\(79\) −600.000 −0.854497 −0.427249 0.904134i \(-0.640517\pi\)
−0.427249 + 0.904134i \(0.640517\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 282.000 0.372934 0.186467 0.982461i \(-0.440296\pi\)
0.186467 + 0.982461i \(0.440296\pi\)
\(84\) 0 0
\(85\) −130.000 −0.165888
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 150.000 0.178651 0.0893257 0.996002i \(-0.471529\pi\)
0.0893257 + 0.996002i \(0.471529\pi\)
\(90\) 0 0
\(91\) 228.000 0.262647
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −500.000 −0.539989
\(96\) 0 0
\(97\) 386.000 0.404045 0.202022 0.979381i \(-0.435249\pi\)
0.202022 + 0.979381i \(0.435249\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −702.000 −0.691600 −0.345800 0.938308i \(-0.612392\pi\)
−0.345800 + 0.938308i \(0.612392\pi\)
\(102\) 0 0
\(103\) 598.000 0.572065 0.286032 0.958220i \(-0.407663\pi\)
0.286032 + 0.958220i \(0.407663\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1194.00 −1.07877 −0.539385 0.842059i \(-0.681343\pi\)
−0.539385 + 0.842059i \(0.681343\pi\)
\(108\) 0 0
\(109\) −550.000 −0.483307 −0.241653 0.970363i \(-0.577690\pi\)
−0.241653 + 0.970363i \(0.577690\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1562.00 −1.30036 −0.650180 0.759781i \(-0.725306\pi\)
−0.650180 + 0.759781i \(0.725306\pi\)
\(114\) 0 0
\(115\) −390.000 −0.316241
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 156.000 0.120172
\(120\) 0 0
\(121\) −307.000 −0.230654
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1846.00 −1.28981 −0.644906 0.764262i \(-0.723103\pi\)
−0.644906 + 0.764262i \(0.723103\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2208.00 −1.47262 −0.736312 0.676642i \(-0.763435\pi\)
−0.736312 + 0.676642i \(0.763435\pi\)
\(132\) 0 0
\(133\) 600.000 0.391177
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2334.00 1.45553 0.727763 0.685829i \(-0.240560\pi\)
0.727763 + 0.685829i \(0.240560\pi\)
\(138\) 0 0
\(139\) 700.000 0.427146 0.213573 0.976927i \(-0.431490\pi\)
0.213573 + 0.976927i \(0.431490\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1216.00 −0.711098
\(144\) 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 \(-0.690571\pi\)
−0.563566 + 0.826071i \(0.690571\pi\)
\(150\) 0 0
\(151\) −1852.00 −0.998103 −0.499052 0.866572i \(-0.666318\pi\)
−0.499052 + 0.866572i \(0.666318\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 540.000 0.279831
\(156\) 0 0
\(157\) −2494.00 −1.26779 −0.633894 0.773420i \(-0.718545\pi\)
−0.633894 + 0.773420i \(0.718545\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 468.000 0.229090
\(162\) 0 0
\(163\) −2762.00 −1.32722 −0.663609 0.748080i \(-0.730976\pi\)
−0.663609 + 0.748080i \(0.730976\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3126.00 1.44849 0.724243 0.689545i \(-0.242189\pi\)
0.724243 + 0.689545i \(0.242189\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 78.0000 0.0342788 0.0171394 0.999853i \(-0.494544\pi\)
0.0171394 + 0.999853i \(0.494544\pi\)
\(174\) 0 0
\(175\) −150.000 −0.0647939
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1300.00 −0.542830 −0.271415 0.962462i \(-0.587492\pi\)
−0.271415 + 0.962462i \(0.587492\pi\)
\(180\) 0 0
\(181\) 1742.00 0.715369 0.357685 0.933842i \(-0.383566\pi\)
0.357685 + 0.933842i \(0.383566\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1330.00 0.528560
\(186\) 0 0
\(187\) −832.000 −0.325358
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3772.00 1.42897 0.714483 0.699653i \(-0.246662\pi\)
0.714483 + 0.699653i \(0.246662\pi\)
\(192\) 0 0
\(193\) −358.000 −0.133520 −0.0667601 0.997769i \(-0.521266\pi\)
−0.0667601 + 0.997769i \(0.521266\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2214.00 0.800716 0.400358 0.916359i \(-0.368886\pi\)
0.400358 + 0.916359i \(0.368886\pi\)
\(198\) 0 0
\(199\) 2600.00 0.926176 0.463088 0.886312i \(-0.346741\pi\)
0.463088 + 0.886312i \(0.346741\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −300.000 −0.103724
\(204\) 0 0
\(205\) −110.000 −0.0374767
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3200.00 −1.05908
\(210\) 0 0
\(211\) 1168.00 0.381083 0.190541 0.981679i \(-0.438976\pi\)
0.190541 + 0.981679i \(0.438976\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2210.00 −0.701027
\(216\) 0 0
\(217\) −648.000 −0.202715
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 988.000 0.300724
\(222\) 0 0
\(223\) 6478.00 1.94529 0.972643 0.232303i \(-0.0746262\pi\)
0.972643 + 0.232303i \(0.0746262\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 646.000 0.188883 0.0944417 0.995530i \(-0.469893\pi\)
0.0944417 + 0.995530i \(0.469893\pi\)
\(228\) 0 0
\(229\) 3750.00 1.08213 0.541063 0.840982i \(-0.318022\pi\)
0.541063 + 0.840982i \(0.318022\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1482.00 −0.416691 −0.208346 0.978055i \(-0.566808\pi\)
−0.208346 + 0.978055i \(0.566808\pi\)
\(234\) 0 0
\(235\) −2570.00 −0.713397
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1400.00 0.378906 0.189453 0.981890i \(-0.439329\pi\)
0.189453 + 0.981890i \(0.439329\pi\)
\(240\) 0 0
\(241\) 3022.00 0.807735 0.403867 0.914817i \(-0.367666\pi\)
0.403867 + 0.914817i \(0.367666\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1535.00 −0.400276
\(246\) 0 0
\(247\) 3800.00 0.978900
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1248.00 −0.313837 −0.156918 0.987612i \(-0.550156\pi\)
−0.156918 + 0.987612i \(0.550156\pi\)
\(252\) 0 0
\(253\) −2496.00 −0.620246
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2106.00 −0.511162 −0.255581 0.966788i \(-0.582267\pi\)
−0.255581 + 0.966788i \(0.582267\pi\)
\(258\) 0 0
\(259\) −1596.00 −0.382898
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3638.00 −0.852961 −0.426480 0.904497i \(-0.640247\pi\)
−0.426480 + 0.904497i \(0.640247\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.00231809
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6550.00 1.48461 0.742306 0.670061i \(-0.233732\pi\)
0.742306 + 0.670061i \(0.233732\pi\)
\(270\) 0 0
\(271\) 4388.00 0.983587 0.491793 0.870712i \(-0.336342\pi\)
0.491793 + 0.870712i \(0.336342\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 800.000 0.175425
\(276\) 0 0
\(277\) 546.000 0.118433 0.0592165 0.998245i \(-0.481140\pi\)
0.0592165 + 0.998245i \(0.481140\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6858.00 1.45592 0.727961 0.685619i \(-0.240468\pi\)
0.727961 + 0.685619i \(0.240468\pi\)
\(282\) 0 0
\(283\) −9282.00 −1.94967 −0.974837 0.222920i \(-0.928441\pi\)
−0.974837 + 0.222920i \(0.928441\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 132.000 0.0271488
\(288\) 0 0
\(289\) −4237.00 −0.862406
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4842.00 −0.965436 −0.482718 0.875776i \(-0.660350\pi\)
−0.482718 + 0.875776i \(0.660350\pi\)
\(294\) 0 0
\(295\) 2500.00 0.493409
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2964.00 0.573286
\(300\) 0 0
\(301\) 2652.00 0.507836
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2590.00 −0.486239
\(306\) 0 0
\(307\) 2594.00 0.482239 0.241120 0.970495i \(-0.422485\pi\)
0.241120 + 0.970495i \(0.422485\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7332.00 1.33685 0.668424 0.743781i \(-0.266969\pi\)
0.668424 + 0.743781i \(0.266969\pi\)
\(312\) 0 0
\(313\) 1562.00 0.282075 0.141037 0.990004i \(-0.454956\pi\)
0.141037 + 0.990004i \(0.454956\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1426.00 −0.252657 −0.126328 0.991988i \(-0.540319\pi\)
−0.126328 + 0.991988i \(0.540319\pi\)
\(318\) 0 0
\(319\) 1600.00 0.280824
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2600.00 0.447888
\(324\) 0 0
\(325\) −950.000 −0.162143
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3084.00 0.516798
\(330\) 0 0
\(331\) 4008.00 0.665558 0.332779 0.943005i \(-0.392014\pi\)
0.332779 + 0.943005i \(0.392014\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −630.000 −0.102748
\(336\) 0 0
\(337\) 8866.00 1.43312 0.716561 0.697525i \(-0.245715\pi\)
0.716561 + 0.697525i \(0.245715\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3456.00 0.548835
\(342\) 0 0
\(343\) 3900.00 0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1714.00 −0.265165 −0.132583 0.991172i \(-0.542327\pi\)
−0.132583 + 0.991172i \(0.542327\pi\)
\(348\) 0 0
\(349\) 1150.00 0.176384 0.0881921 0.996103i \(-0.471891\pi\)
0.0881921 + 0.996103i \(0.471891\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4398.00 0.663122 0.331561 0.943434i \(-0.392425\pi\)
0.331561 + 0.943434i \(0.392425\pi\)
\(354\) 0 0
\(355\) 2060.00 0.307982
\(356\) 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
\(361\) 3141.00 0.457938
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4390.00 −0.629543
\(366\) 0 0
\(367\) 5874.00 0.835478 0.417739 0.908567i \(-0.362823\pi\)
0.417739 + 0.908567i \(0.362823\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.0000 0.00167927
\(372\) 0 0
\(373\) −2078.00 −0.288458 −0.144229 0.989544i \(-0.546070\pi\)
−0.144229 + 0.989544i \(0.546070\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1900.00 −0.259562
\(378\) 0 0
\(379\) −7900.00 −1.07070 −0.535351 0.844630i \(-0.679821\pi\)
−0.535351 + 0.844630i \(0.679821\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7518.00 −1.00301 −0.501504 0.865155i \(-0.667220\pi\)
−0.501504 + 0.865155i \(0.667220\pi\)
\(384\) 0 0
\(385\) −960.000 −0.127081
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1950.00 0.254162 0.127081 0.991892i \(-0.459439\pi\)
0.127081 + 0.991892i \(0.459439\pi\)
\(390\) 0 0
\(391\) 2028.00 0.262303
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3000.00 −0.382143
\(396\) 0 0
\(397\) 13786.0 1.74282 0.871410 0.490555i \(-0.163206\pi\)
0.871410 + 0.490555i \(0.163206\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6402.00 −0.797258 −0.398629 0.917112i \(-0.630514\pi\)
−0.398629 + 0.917112i \(0.630514\pi\)
\(402\) 0 0
\(403\) −4104.00 −0.507282
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8512.00 1.03667
\(408\) 0 0
\(409\) 11150.0 1.34800 0.674000 0.738731i \(-0.264575\pi\)
0.674000 + 0.738731i \(0.264575\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3000.00 −0.357434
\(414\) 0 0
\(415\) 1410.00 0.166781
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13700.0 −1.59735 −0.798674 0.601764i \(-0.794465\pi\)
−0.798674 + 0.601764i \(0.794465\pi\)
\(420\) 0 0
\(421\) −5438.00 −0.629529 −0.314765 0.949170i \(-0.601926\pi\)
−0.314765 + 0.949170i \(0.601926\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −650.000 −0.0741874
\(426\) 0 0
\(427\) 3108.00 0.352240
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7692.00 0.859653 0.429827 0.902911i \(-0.358575\pi\)
0.429827 + 0.902911i \(0.358575\pi\)
\(432\) 0 0
\(433\) −1118.00 −0.124082 −0.0620412 0.998074i \(-0.519761\pi\)
−0.0620412 + 0.998074i \(0.519761\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7800.00 0.853832
\(438\) 0 0
\(439\) 2600.00 0.282668 0.141334 0.989962i \(-0.454861\pi\)
0.141334 + 0.989962i \(0.454861\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11958.0 −1.28249 −0.641243 0.767337i \(-0.721581\pi\)
−0.641243 + 0.767337i \(0.721581\pi\)
\(444\) 0 0
\(445\) 750.000 0.0798953
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 17050.0 1.79207 0.896035 0.443984i \(-0.146435\pi\)
0.896035 + 0.443984i \(0.146435\pi\)
\(450\) 0 0
\(451\) −704.000 −0.0735035
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1140.00 0.117459
\(456\) 0 0
\(457\) −9494.00 −0.971796 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11418.0 1.15356 0.576778 0.816901i \(-0.304310\pi\)
0.576778 + 0.816901i \(0.304310\pi\)
\(462\) 0 0
\(463\) −7962.00 −0.799191 −0.399596 0.916692i \(-0.630849\pi\)
−0.399596 + 0.916692i \(0.630849\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6526.00 0.646654 0.323327 0.946287i \(-0.395199\pi\)
0.323327 + 0.946287i \(0.395199\pi\)
\(468\) 0 0
\(469\) 756.000 0.0744325
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −14144.0 −1.37493
\(474\) 0 0
\(475\) −2500.00 −0.241490
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17400.0 1.65976 0.829881 0.557940i \(-0.188408\pi\)
0.829881 + 0.557940i \(0.188408\pi\)
\(480\) 0 0
\(481\) −10108.0 −0.958181
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1930.00 0.180694
\(486\) 0 0
\(487\) −1166.00 −0.108494 −0.0542469 0.998528i \(-0.517276\pi\)
−0.0542469 + 0.998528i \(0.517276\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7072.00 0.650010 0.325005 0.945712i \(-0.394634\pi\)
0.325005 + 0.945712i \(0.394634\pi\)
\(492\) 0 0
\(493\) −1300.00 −0.118761
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2472.00 −0.223107
\(498\) 0 0
\(499\) −100.000 −0.00897117 −0.00448559 0.999990i \(-0.501428\pi\)
−0.00448559 + 0.999990i \(0.501428\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2602.00 0.230651 0.115325 0.993328i \(-0.463209\pi\)
0.115325 + 0.993328i \(0.463209\pi\)
\(504\) 0 0
\(505\) −3510.00 −0.309293
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11150.0 −0.970953 −0.485476 0.874250i \(-0.661354\pi\)
−0.485476 + 0.874250i \(0.661354\pi\)
\(510\) 0 0
\(511\) 5268.00 0.456052
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2990.00 0.255835
\(516\) 0 0
\(517\) −16448.0 −1.39919
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3638.00 0.305919 0.152959 0.988232i \(-0.451120\pi\)
0.152959 + 0.988232i \(0.451120\pi\)
\(522\) 0 0
\(523\) 2078.00 0.173737 0.0868686 0.996220i \(-0.472314\pi\)
0.0868686 + 0.996220i \(0.472314\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2808.00 −0.232103
\(528\) 0 0
\(529\) −6083.00 −0.499959
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 836.000 0.0679384
\(534\) 0 0
\(535\) −5970.00 −0.482440
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9824.00 −0.785064
\(540\) 0 0
\(541\) 5622.00 0.446781 0.223391 0.974729i \(-0.428287\pi\)
0.223391 + 0.974729i \(0.428287\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2750.00 −0.216141
\(546\) 0 0
\(547\) −16486.0 −1.28865 −0.644324 0.764753i \(-0.722861\pi\)
−0.644324 + 0.764753i \(0.722861\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5000.00 −0.386583
\(552\) 0 0
\(553\) 3600.00 0.276831
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11706.0 −0.890483 −0.445242 0.895410i \(-0.646882\pi\)
−0.445242 + 0.895410i \(0.646882\pi\)
\(558\) 0 0
\(559\) 16796.0 1.27083
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −25038.0 −1.87429 −0.937146 0.348939i \(-0.886542\pi\)
−0.937146 + 0.348939i \(0.886542\pi\)
\(564\) 0 0
\(565\) −7810.00 −0.581538
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17550.0 −1.29303 −0.646515 0.762901i \(-0.723774\pi\)
−0.646515 + 0.762901i \(0.723774\pi\)
\(570\) 0 0
\(571\) −10712.0 −0.785084 −0.392542 0.919734i \(-0.628404\pi\)
−0.392542 + 0.919734i \(0.628404\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1950.00 −0.141427
\(576\) 0 0
\(577\) −13654.0 −0.985136 −0.492568 0.870274i \(-0.663942\pi\)
−0.492568 + 0.870274i \(0.663942\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1692.00 −0.120819
\(582\) 0 0
\(583\) −64.0000 −0.00454650
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14166.0 0.996071 0.498035 0.867157i \(-0.334055\pi\)
0.498035 + 0.867157i \(0.334055\pi\)
\(588\) 0 0
\(589\) −10800.0 −0.755528
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −17842.0 −1.23555 −0.617777 0.786354i \(-0.711966\pi\)
−0.617777 + 0.786354i \(0.711966\pi\)
\(594\) 0 0
\(595\) 780.000 0.0537427
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −17600.0 −1.20053 −0.600264 0.799802i \(-0.704938\pi\)
−0.600264 + 0.799802i \(0.704938\pi\)
\(600\) 0 0
\(601\) 27302.0 1.85303 0.926516 0.376256i \(-0.122789\pi\)
0.926516 + 0.376256i \(0.122789\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1535.00 −0.103151
\(606\) 0 0
\(607\) 3794.00 0.253696 0.126848 0.991922i \(-0.459514\pi\)
0.126848 + 0.991922i \(0.459514\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 19532.0 1.29326
\(612\) 0 0
\(613\) −13238.0 −0.872231 −0.436116 0.899891i \(-0.643646\pi\)
−0.436116 + 0.899891i \(0.643646\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11574.0 0.755189 0.377595 0.925971i \(-0.376751\pi\)
0.377595 + 0.925971i \(0.376751\pi\)
\(618\) 0 0
\(619\) −8300.00 −0.538942 −0.269471 0.963008i \(-0.586849\pi\)
−0.269471 + 0.963008i \(0.586849\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −900.000 −0.0578776
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6916.00 −0.438409
\(630\) 0 0
\(631\) 7508.00 0.473675 0.236837 0.971549i \(-0.423889\pi\)
0.236837 + 0.971549i \(0.423889\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9230.00 −0.576821
\(636\) 0 0
\(637\) 11666.0 0.725626
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 27378.0 1.68700 0.843499 0.537130i \(-0.180492\pi\)
0.843499 + 0.537130i \(0.180492\pi\)
\(642\) 0 0
\(643\) −1842.00 −0.112973 −0.0564863 0.998403i \(-0.517990\pi\)
−0.0564863 + 0.998403i \(0.517990\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10114.0 −0.614563 −0.307282 0.951619i \(-0.599419\pi\)
−0.307282 + 0.951619i \(0.599419\pi\)
\(648\) 0 0
\(649\) 16000.0 0.967727
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −10402.0 −0.623372 −0.311686 0.950185i \(-0.600894\pi\)
−0.311686 + 0.950185i \(0.600894\pi\)
\(654\) 0 0
\(655\) −11040.0 −0.658578
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7100.00 0.419692 0.209846 0.977734i \(-0.432704\pi\)
0.209846 + 0.977734i \(0.432704\pi\)
\(660\) 0 0
\(661\) −7118.00 −0.418847 −0.209424 0.977825i \(-0.567159\pi\)
−0.209424 + 0.977825i \(0.567159\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3000.00 0.174940
\(666\) 0 0
\(667\) −3900.00 −0.226400
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −16576.0 −0.953665
\(672\) 0 0
\(673\) −31278.0 −1.79150 −0.895749 0.444560i \(-0.853360\pi\)
−0.895749 + 0.444560i \(0.853360\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30054.0 1.70616 0.853079 0.521782i \(-0.174732\pi\)
0.853079 + 0.521782i \(0.174732\pi\)
\(678\) 0 0
\(679\) −2316.00 −0.130898
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4518.00 −0.253113 −0.126557 0.991959i \(-0.540393\pi\)
−0.126557 + 0.991959i \(0.540393\pi\)
\(684\) 0 0
\(685\) 11670.0 0.650931
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 76.0000 0.00420228
\(690\) 0 0
\(691\) −29272.0 −1.61152 −0.805759 0.592243i \(-0.798242\pi\)
−0.805759 + 0.592243i \(0.798242\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3500.00 0.191025
\(696\) 0 0
\(697\) 572.000 0.0310847
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5798.00 0.312393 0.156196 0.987726i \(-0.450077\pi\)
0.156196 + 0.987726i \(0.450077\pi\)
\(702\) 0 0
\(703\) −26600.0 −1.42708
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4212.00 0.224057
\(708\) 0 0
\(709\) 8950.00 0.474082 0.237041 0.971500i \(-0.423822\pi\)
0.237041 + 0.971500i \(0.423822\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8424.00 −0.442470
\(714\) 0 0
\(715\) −6080.00 −0.318013
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7800.00 0.404577 0.202289 0.979326i \(-0.435162\pi\)
0.202289 + 0.979326i \(0.435162\pi\)
\(720\) 0 0
\(721\) −3588.00 −0.185332
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1250.00 0.0640329
\(726\) 0 0
\(727\) 8554.00 0.436383 0.218191 0.975906i \(-0.429984\pi\)
0.218191 + 0.975906i \(0.429984\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11492.0 0.581460
\(732\) 0 0
\(733\) 2882.00 0.145224 0.0726119 0.997360i \(-0.476867\pi\)
0.0726119 + 0.997360i \(0.476867\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4032.00 −0.201521
\(738\) 0 0
\(739\) −18700.0 −0.930840 −0.465420 0.885090i \(-0.654097\pi\)
−0.465420 + 0.885090i \(0.654097\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12242.0 0.604462 0.302231 0.953235i \(-0.402269\pi\)
0.302231 + 0.953235i \(0.402269\pi\)
\(744\) 0 0
\(745\) −10250.0 −0.504068
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7164.00 0.349488
\(750\) 0 0
\(751\) 31148.0 1.51346 0.756729 0.653729i \(-0.226796\pi\)
0.756729 + 0.653729i \(0.226796\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9260.00 −0.446365
\(756\) 0 0
\(757\) −7694.00 −0.369410 −0.184705 0.982794i \(-0.559133\pi\)
−0.184705 + 0.982794i \(0.559133\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4518.00 0.215213 0.107607 0.994194i \(-0.465681\pi\)
0.107607 + 0.994194i \(0.465681\pi\)
\(762\) 0 0
\(763\) 3300.00 0.156577
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −19000.0 −0.894459
\(768\) 0 0
\(769\) −39550.0 −1.85463 −0.927314 0.374283i \(-0.877889\pi\)
−0.927314 + 0.374283i \(0.877889\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −22122.0 −1.02933 −0.514666 0.857391i \(-0.672084\pi\)
−0.514666 + 0.857391i \(0.672084\pi\)
\(774\) 0 0
\(775\) 2700.00 0.125144
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2200.00 0.101185
\(780\) 0 0
\(781\) 13184.0 0.604047
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −12470.0 −0.566972
\(786\) 0 0
\(787\) 16634.0 0.753416 0.376708 0.926332i \(-0.377056\pi\)
0.376708 + 0.926332i \(0.377056\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9372.00 0.421277
\(792\) 0 0
\(793\) 19684.0 0.881462
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27586.0 −1.22603 −0.613015 0.790071i \(-0.710044\pi\)
−0.613015 + 0.790071i \(0.710044\pi\)
\(798\) 0 0
\(799\) 13364.0 0.591720
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −28096.0 −1.23473
\(804\) 0 0
\(805\) 2340.00 0.102452
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3850.00 −0.167316 −0.0836581 0.996495i \(-0.526660\pi\)
−0.0836581 + 0.996495i \(0.526660\pi\)
\(810\) 0 0
\(811\) −10032.0 −0.434366 −0.217183 0.976131i \(-0.569687\pi\)
−0.217183 + 0.976131i \(0.569687\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −13810.0 −0.593550
\(816\) 0 0
\(817\) 44200.0 1.89273
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −20562.0 −0.874079 −0.437039 0.899442i \(-0.643973\pi\)
−0.437039 + 0.899442i \(0.643973\pi\)
\(822\) 0 0
\(823\) −10322.0 −0.437184 −0.218592 0.975816i \(-0.570146\pi\)
−0.218592 + 0.975816i \(0.570146\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 8846.00 0.371954 0.185977 0.982554i \(-0.440455\pi\)
0.185977 + 0.982554i \(0.440455\pi\)
\(828\) 0 0
\(829\) −25350.0 −1.06205 −0.531026 0.847355i \(-0.678194\pi\)
−0.531026 + 0.847355i \(0.678194\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 7982.00 0.332005
\(834\) 0 0
\(835\) 15630.0 0.647783
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 46000.0 1.89284 0.946422 0.322932i \(-0.104669\pi\)
0.946422 + 0.322932i \(0.104669\pi\)
\(840\) 0 0
\(841\) −21889.0 −0.897495
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3765.00 −0.153278
\(846\) 0 0
\(847\) 1842.00 0.0747248
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −20748.0 −0.835761
\(852\) 0 0
\(853\) −16998.0 −0.682298 −0.341149 0.940009i \(-0.610816\pi\)
−0.341149 + 0.940009i \(0.610816\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 26494.0 1.05603 0.528015 0.849235i \(-0.322936\pi\)
0.528015 + 0.849235i \(0.322936\pi\)
\(858\) 0 0
\(859\) 21500.0 0.853982 0.426991 0.904256i \(-0.359574\pi\)
0.426991 + 0.904256i \(0.359574\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 25762.0 1.01616 0.508082 0.861309i \(-0.330355\pi\)
0.508082 + 0.861309i \(0.330355\pi\)
\(864\) 0 0
\(865\) 390.000 0.0153299
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −19200.0 −0.749500
\(870\) 0 0
\(871\) 4788.00 0.186263
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −750.000 −0.0289767
\(876\) 0 0
\(877\) 30546.0 1.17613 0.588064 0.808814i \(-0.299890\pi\)
0.588064 + 0.808814i \(0.299890\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −32942.0 −1.25976 −0.629878 0.776694i \(-0.716895\pi\)
−0.629878 + 0.776694i \(0.716895\pi\)
\(882\) 0 0
\(883\) 27118.0 1.03351 0.516757 0.856132i \(-0.327139\pi\)
0.516757 + 0.856132i \(0.327139\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −38634.0 −1.46246 −0.731230 0.682131i \(-0.761054\pi\)
−0.731230 + 0.682131i \(0.761054\pi\)
\(888\) 0 0
\(889\) 11076.0 0.417860
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 51400.0 1.92613
\(894\) 0 0
\(895\) −6500.00 −0.242761
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 5400.00 0.200334
\(900\) 0 0
\(901\) 52.0000 0.00192272
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8710.00 0.319923
\(906\) 0 0
\(907\) 1794.00 0.0656767 0.0328384 0.999461i \(-0.489545\pi\)
0.0328384 + 0.999461i \(0.489545\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 41732.0 1.51772 0.758860 0.651254i \(-0.225757\pi\)
0.758860 + 0.651254i \(0.225757\pi\)
\(912\) 0 0
\(913\) 9024.00 0.327109
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 13248.0 0.477086
\(918\) 0 0
\(919\) −29200.0 −1.04812 −0.524058 0.851682i \(-0.675583\pi\)
−0.524058 + 0.851682i \(0.675583\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −15656.0 −0.558314
\(924\) 0 0
\(925\) 6650.00 0.236379
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 48650.0 1.71814 0.859071 0.511856i \(-0.171042\pi\)
0.859071 + 0.511856i \(0.171042\pi\)
\(930\) 0 0
\(931\) 30700.0 1.08072
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4160.00 −0.145504
\(936\) 0 0
\(937\) −11334.0 −0.395161 −0.197580 0.980287i \(-0.563308\pi\)
−0.197580 + 0.980287i \(0.563308\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 31178.0 1.08010 0.540050 0.841633i \(-0.318405\pi\)
0.540050 + 0.841633i \(0.318405\pi\)
\(942\) 0 0
\(943\) 1716.00 0.0592584
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4686.00 0.160797 0.0803984 0.996763i \(-0.474381\pi\)
0.0803984 + 0.996763i \(0.474381\pi\)
\(948\) 0 0
\(949\) 33364.0 1.14124
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 598.000 0.0203265 0.0101632 0.999948i \(-0.496765\pi\)
0.0101632 + 0.999948i \(0.496765\pi\)
\(954\) 0 0
\(955\) 18860.0 0.639053
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −14004.0 −0.471546
\(960\) 0 0
\(961\) −18127.0 −0.608472
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1790.00 −0.0597121
\(966\) 0 0
\(967\) −41726.0 −1.38761 −0.693804 0.720163i \(-0.744067\pi\)
−0.693804 + 0.720163i \(0.744067\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 24312.0 0.803511 0.401756 0.915747i \(-0.368400\pi\)
0.401756 + 0.915747i \(0.368400\pi\)
\(972\) 0 0
\(973\) −4200.00 −0.138382
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −40946.0 −1.34082 −0.670409 0.741992i \(-0.733881\pi\)
−0.670409 + 0.741992i \(0.733881\pi\)
\(978\) 0 0
\(979\) 4800.00 0.156699
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 42282.0 1.37191 0.685954 0.727645i \(-0.259385\pi\)
0.685954 + 0.727645i \(0.259385\pi\)
\(984\) 0 0
\(985\) 11070.0 0.358091
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 34476.0 1.10847
\(990\) 0 0
\(991\) −1172.00 −0.0375679 −0.0187840 0.999824i \(-0.505979\pi\)
−0.0187840 + 0.999824i \(0.505979\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 13000.0 0.414199
\(996\) 0 0
\(997\) −31614.0 −1.00424 −0.502119 0.864798i \(-0.667446\pi\)
−0.502119 + 0.864798i \(0.667446\pi\)
\(998\) 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.u.1.1 1
3.2 odd 2 80.4.a.d.1.1 1
4.3 odd 2 45.4.a.d.1.1 1
12.11 even 2 5.4.a.a.1.1 1
15.2 even 4 400.4.c.k.49.2 2
15.8 even 4 400.4.c.k.49.1 2
15.14 odd 2 400.4.a.m.1.1 1
20.3 even 4 225.4.b.c.199.1 2
20.7 even 4 225.4.b.c.199.2 2
20.19 odd 2 225.4.a.b.1.1 1
24.5 odd 2 320.4.a.h.1.1 1
24.11 even 2 320.4.a.g.1.1 1
28.27 even 2 2205.4.a.q.1.1 1
36.7 odd 6 405.4.e.c.271.1 2
36.11 even 6 405.4.e.l.271.1 2
36.23 even 6 405.4.e.l.136.1 2
36.31 odd 6 405.4.e.c.136.1 2
48.5 odd 4 1280.4.d.l.641.2 2
48.11 even 4 1280.4.d.e.641.1 2
48.29 odd 4 1280.4.d.l.641.1 2
48.35 even 4 1280.4.d.e.641.2 2
60.23 odd 4 25.4.b.a.24.2 2
60.47 odd 4 25.4.b.a.24.1 2
60.59 even 2 25.4.a.c.1.1 1
84.11 even 6 245.4.e.f.226.1 2
84.23 even 6 245.4.e.f.116.1 2
84.47 odd 6 245.4.e.g.116.1 2
84.59 odd 6 245.4.e.g.226.1 2
84.83 odd 2 245.4.a.a.1.1 1
120.29 odd 2 1600.4.a.s.1.1 1
120.59 even 2 1600.4.a.bi.1.1 1
132.131 odd 2 605.4.a.d.1.1 1
156.155 even 2 845.4.a.b.1.1 1
204.203 even 2 1445.4.a.a.1.1 1
228.227 odd 2 1805.4.a.h.1.1 1
420.419 odd 2 1225.4.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.4.a.a.1.1 1 12.11 even 2
25.4.a.c.1.1 1 60.59 even 2
25.4.b.a.24.1 2 60.47 odd 4
25.4.b.a.24.2 2 60.23 odd 4
45.4.a.d.1.1 1 4.3 odd 2
80.4.a.d.1.1 1 3.2 odd 2
225.4.a.b.1.1 1 20.19 odd 2
225.4.b.c.199.1 2 20.3 even 4
225.4.b.c.199.2 2 20.7 even 4
245.4.a.a.1.1 1 84.83 odd 2
245.4.e.f.116.1 2 84.23 even 6
245.4.e.f.226.1 2 84.11 even 6
245.4.e.g.116.1 2 84.47 odd 6
245.4.e.g.226.1 2 84.59 odd 6
320.4.a.g.1.1 1 24.11 even 2
320.4.a.h.1.1 1 24.5 odd 2
400.4.a.m.1.1 1 15.14 odd 2
400.4.c.k.49.1 2 15.8 even 4
400.4.c.k.49.2 2 15.2 even 4
405.4.e.c.136.1 2 36.31 odd 6
405.4.e.c.271.1 2 36.7 odd 6
405.4.e.l.136.1 2 36.23 even 6
405.4.e.l.271.1 2 36.11 even 6
605.4.a.d.1.1 1 132.131 odd 2
720.4.a.u.1.1 1 1.1 even 1 trivial
845.4.a.b.1.1 1 156.155 even 2
1225.4.a.k.1.1 1 420.419 odd 2
1280.4.d.e.641.1 2 48.11 even 4
1280.4.d.e.641.2 2 48.35 even 4
1280.4.d.l.641.1 2 48.29 odd 4
1280.4.d.l.641.2 2 48.5 odd 4
1445.4.a.a.1.1 1 204.203 even 2
1600.4.a.s.1.1 1 120.29 odd 2
1600.4.a.bi.1.1 1 120.59 even 2
1805.4.a.h.1.1 1 228.227 odd 2
2205.4.a.q.1.1 1 28.27 even 2