Properties

Label 2160.4.a.bo.1.2
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.444125612\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.985.1
Defining polynomial: \( x^{3} - x^{2} - 6x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 1080)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.93080\) of defining polynomial
Character \(\chi\) \(=\) 2160.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.00000 q^{5} +7.95278 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +7.95278 q^{7} +37.1224 q^{11} -35.1224 q^{13} -99.1976 q^{17} +44.6505 q^{19} -102.603 q^{23} +25.0000 q^{25} +285.404 q^{29} -238.593 q^{31} +39.7639 q^{35} +339.168 q^{37} -423.799 q^{41} -144.330 q^{43} -418.414 q^{47} -279.753 q^{49} +186.933 q^{53} +185.612 q^{55} -293.783 q^{59} -701.657 q^{61} -175.612 q^{65} +292.697 q^{67} -738.742 q^{71} +453.214 q^{73} +295.226 q^{77} -892.759 q^{79} +66.4113 q^{83} -495.988 q^{85} +868.816 q^{89} -279.321 q^{91} +223.253 q^{95} +112.488 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 15 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 15 q^{5} - 6 q^{7} - 12 q^{11} + 18 q^{13} - 21 q^{17} - 57 q^{19} - 87 q^{23} + 75 q^{25} + 138 q^{29} - 117 q^{31} - 30 q^{35} + 150 q^{37} - 180 q^{43} - 684 q^{47} - 81 q^{49} + 87 q^{53} - 60 q^{55} - 714 q^{59} - 513 q^{61} + 90 q^{65} + 174 q^{67} - 768 q^{71} - 252 q^{73} + 888 q^{77} - 207 q^{79} - 1689 q^{83} - 105 q^{85} + 312 q^{89} - 900 q^{91} - 285 q^{95} - 1080 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(7\) 7.95278 0.429410 0.214705 0.976679i \(-0.431121\pi\)
0.214705 + 0.976679i \(0.431121\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 37.1224 1.01753 0.508765 0.860906i \(-0.330102\pi\)
0.508765 + 0.860906i \(0.330102\pi\)
\(12\) 0 0
\(13\) −35.1224 −0.749323 −0.374662 0.927162i \(-0.622241\pi\)
−0.374662 + 0.927162i \(0.622241\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −99.1976 −1.41523 −0.707616 0.706597i \(-0.750229\pi\)
−0.707616 + 0.706597i \(0.750229\pi\)
\(18\) 0 0
\(19\) 44.6505 0.539133 0.269567 0.962982i \(-0.413120\pi\)
0.269567 + 0.962982i \(0.413120\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −102.603 −0.930186 −0.465093 0.885262i \(-0.653979\pi\)
−0.465093 + 0.885262i \(0.653979\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 285.404 1.82752 0.913762 0.406249i \(-0.133163\pi\)
0.913762 + 0.406249i \(0.133163\pi\)
\(30\) 0 0
\(31\) −238.593 −1.38234 −0.691171 0.722692i \(-0.742905\pi\)
−0.691171 + 0.722692i \(0.742905\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 39.7639 0.192038
\(36\) 0 0
\(37\) 339.168 1.50700 0.753498 0.657450i \(-0.228365\pi\)
0.753498 + 0.657450i \(0.228365\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −423.799 −1.61430 −0.807150 0.590346i \(-0.798991\pi\)
−0.807150 + 0.590346i \(0.798991\pi\)
\(42\) 0 0
\(43\) −144.330 −0.511863 −0.255931 0.966695i \(-0.582382\pi\)
−0.255931 + 0.966695i \(0.582382\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −418.414 −1.29855 −0.649276 0.760553i \(-0.724928\pi\)
−0.649276 + 0.760553i \(0.724928\pi\)
\(48\) 0 0
\(49\) −279.753 −0.815607
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 186.933 0.484476 0.242238 0.970217i \(-0.422118\pi\)
0.242238 + 0.970217i \(0.422118\pi\)
\(54\) 0 0
\(55\) 185.612 0.455053
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −293.783 −0.648259 −0.324129 0.946013i \(-0.605071\pi\)
−0.324129 + 0.946013i \(0.605071\pi\)
\(60\) 0 0
\(61\) −701.657 −1.47275 −0.736377 0.676571i \(-0.763465\pi\)
−0.736377 + 0.676571i \(0.763465\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −175.612 −0.335107
\(66\) 0 0
\(67\) 292.697 0.533710 0.266855 0.963737i \(-0.414016\pi\)
0.266855 + 0.963737i \(0.414016\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −738.742 −1.23482 −0.617412 0.786640i \(-0.711819\pi\)
−0.617412 + 0.786640i \(0.711819\pi\)
\(72\) 0 0
\(73\) 453.214 0.726639 0.363320 0.931665i \(-0.381643\pi\)
0.363320 + 0.931665i \(0.381643\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 295.226 0.436937
\(78\) 0 0
\(79\) −892.759 −1.27143 −0.635717 0.771922i \(-0.719295\pi\)
−0.635717 + 0.771922i \(0.719295\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 66.4113 0.0878264 0.0439132 0.999035i \(-0.486018\pi\)
0.0439132 + 0.999035i \(0.486018\pi\)
\(84\) 0 0
\(85\) −495.988 −0.632911
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 868.816 1.03477 0.517384 0.855753i \(-0.326906\pi\)
0.517384 + 0.855753i \(0.326906\pi\)
\(90\) 0 0
\(91\) −279.321 −0.321767
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 223.253 0.241108
\(96\) 0 0
\(97\) 112.488 0.117747 0.0588735 0.998265i \(-0.481249\pi\)
0.0588735 + 0.998265i \(0.481249\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1581.13 1.55770 0.778852 0.627207i \(-0.215802\pi\)
0.778852 + 0.627207i \(0.215802\pi\)
\(102\) 0 0
\(103\) 905.167 0.865910 0.432955 0.901416i \(-0.357471\pi\)
0.432955 + 0.901416i \(0.357471\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1127.93 1.01908 0.509539 0.860447i \(-0.329816\pi\)
0.509539 + 0.860447i \(0.329816\pi\)
\(108\) 0 0
\(109\) −1947.65 −1.71148 −0.855739 0.517408i \(-0.826897\pi\)
−0.855739 + 0.517408i \(0.826897\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1724.52 1.43566 0.717829 0.696220i \(-0.245136\pi\)
0.717829 + 0.696220i \(0.245136\pi\)
\(114\) 0 0
\(115\) −513.017 −0.415992
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −788.896 −0.607714
\(120\) 0 0
\(121\) 47.0724 0.0353662
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −645.720 −0.451168 −0.225584 0.974224i \(-0.572429\pi\)
−0.225584 + 0.974224i \(0.572429\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2055.92 −1.37119 −0.685597 0.727982i \(-0.740459\pi\)
−0.685597 + 0.727982i \(0.740459\pi\)
\(132\) 0 0
\(133\) 355.096 0.231509
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −244.549 −0.152505 −0.0762525 0.997089i \(-0.524296\pi\)
−0.0762525 + 0.997089i \(0.524296\pi\)
\(138\) 0 0
\(139\) −1068.67 −0.652111 −0.326056 0.945351i \(-0.605720\pi\)
−0.326056 + 0.945351i \(0.605720\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1303.83 −0.762458
\(144\) 0 0
\(145\) 1427.02 0.817294
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1295.84 −0.712481 −0.356240 0.934394i \(-0.615942\pi\)
−0.356240 + 0.934394i \(0.615942\pi\)
\(150\) 0 0
\(151\) 2727.32 1.46984 0.734921 0.678153i \(-0.237219\pi\)
0.734921 + 0.678153i \(0.237219\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1192.97 −0.618202
\(156\) 0 0
\(157\) 867.700 0.441083 0.220541 0.975378i \(-0.429218\pi\)
0.220541 + 0.975378i \(0.429218\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −815.981 −0.399431
\(162\) 0 0
\(163\) −1217.40 −0.584995 −0.292497 0.956266i \(-0.594486\pi\)
−0.292497 + 0.956266i \(0.594486\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3266.76 −1.51371 −0.756854 0.653583i \(-0.773265\pi\)
−0.756854 + 0.653583i \(0.773265\pi\)
\(168\) 0 0
\(169\) −963.417 −0.438515
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1421.71 0.624802 0.312401 0.949950i \(-0.398867\pi\)
0.312401 + 0.949950i \(0.398867\pi\)
\(174\) 0 0
\(175\) 198.819 0.0858819
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −949.492 −0.396471 −0.198236 0.980154i \(-0.563521\pi\)
−0.198236 + 0.980154i \(0.563521\pi\)
\(180\) 0 0
\(181\) 1748.25 0.717938 0.358969 0.933350i \(-0.383128\pi\)
0.358969 + 0.933350i \(0.383128\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1695.84 0.673950
\(186\) 0 0
\(187\) −3682.45 −1.44004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1418.37 0.537327 0.268664 0.963234i \(-0.413418\pi\)
0.268664 + 0.963234i \(0.413418\pi\)
\(192\) 0 0
\(193\) −3733.49 −1.39245 −0.696223 0.717825i \(-0.745138\pi\)
−0.696223 + 0.717825i \(0.745138\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2294.67 0.829889 0.414945 0.909847i \(-0.363801\pi\)
0.414945 + 0.909847i \(0.363801\pi\)
\(198\) 0 0
\(199\) −3713.93 −1.32298 −0.661492 0.749952i \(-0.730076\pi\)
−0.661492 + 0.749952i \(0.730076\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2269.76 0.784757
\(204\) 0 0
\(205\) −2119.00 −0.721937
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1657.53 0.548584
\(210\) 0 0
\(211\) 199.877 0.0652139 0.0326069 0.999468i \(-0.489619\pi\)
0.0326069 + 0.999468i \(0.489619\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −721.649 −0.228912
\(216\) 0 0
\(217\) −1897.48 −0.593591
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3484.06 1.06047
\(222\) 0 0
\(223\) −879.739 −0.264178 −0.132089 0.991238i \(-0.542168\pi\)
−0.132089 + 0.991238i \(0.542168\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4331.67 −1.26653 −0.633267 0.773934i \(-0.718286\pi\)
−0.633267 + 0.773934i \(0.718286\pi\)
\(228\) 0 0
\(229\) −2995.80 −0.864489 −0.432244 0.901757i \(-0.642278\pi\)
−0.432244 + 0.901757i \(0.642278\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2068.75 0.581666 0.290833 0.956774i \(-0.406068\pi\)
0.290833 + 0.956774i \(0.406068\pi\)
\(234\) 0 0
\(235\) −2092.07 −0.580730
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −311.612 −0.0843368 −0.0421684 0.999111i \(-0.513427\pi\)
−0.0421684 + 0.999111i \(0.513427\pi\)
\(240\) 0 0
\(241\) −4636.53 −1.23928 −0.619638 0.784888i \(-0.712720\pi\)
−0.619638 + 0.784888i \(0.712720\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1398.77 −0.364751
\(246\) 0 0
\(247\) −1568.23 −0.403985
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1243.61 −0.312732 −0.156366 0.987699i \(-0.549978\pi\)
−0.156366 + 0.987699i \(0.549978\pi\)
\(252\) 0 0
\(253\) −3808.88 −0.946491
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −687.895 −0.166964 −0.0834819 0.996509i \(-0.526604\pi\)
−0.0834819 + 0.996509i \(0.526604\pi\)
\(258\) 0 0
\(259\) 2697.33 0.647119
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2819.20 0.660986 0.330493 0.943808i \(-0.392785\pi\)
0.330493 + 0.943808i \(0.392785\pi\)
\(264\) 0 0
\(265\) 934.666 0.216664
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4208.33 0.953854 0.476927 0.878943i \(-0.341751\pi\)
0.476927 + 0.878943i \(0.341751\pi\)
\(270\) 0 0
\(271\) −8395.09 −1.88179 −0.940896 0.338696i \(-0.890014\pi\)
−0.940896 + 0.338696i \(0.890014\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 928.060 0.203506
\(276\) 0 0
\(277\) −1197.24 −0.259694 −0.129847 0.991534i \(-0.541449\pi\)
−0.129847 + 0.991534i \(0.541449\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2335.97 0.495916 0.247958 0.968771i \(-0.420241\pi\)
0.247958 + 0.968771i \(0.420241\pi\)
\(282\) 0 0
\(283\) 1028.83 0.216104 0.108052 0.994145i \(-0.465539\pi\)
0.108052 + 0.994145i \(0.465539\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3370.38 −0.693196
\(288\) 0 0
\(289\) 4927.16 1.00288
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3375.36 −0.673006 −0.336503 0.941682i \(-0.609244\pi\)
−0.336503 + 0.941682i \(0.609244\pi\)
\(294\) 0 0
\(295\) −1468.91 −0.289910
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3603.67 0.697010
\(300\) 0 0
\(301\) −1147.82 −0.219799
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3508.29 −0.658636
\(306\) 0 0
\(307\) −6518.27 −1.21178 −0.605892 0.795547i \(-0.707184\pi\)
−0.605892 + 0.795547i \(0.707184\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7327.27 1.33598 0.667992 0.744168i \(-0.267154\pi\)
0.667992 + 0.744168i \(0.267154\pi\)
\(312\) 0 0
\(313\) 1834.06 0.331206 0.165603 0.986193i \(-0.447043\pi\)
0.165603 + 0.986193i \(0.447043\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3431.64 0.608013 0.304006 0.952670i \(-0.401676\pi\)
0.304006 + 0.952670i \(0.401676\pi\)
\(318\) 0 0
\(319\) 10594.9 1.85956
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4429.22 −0.762999
\(324\) 0 0
\(325\) −878.060 −0.149865
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3327.55 −0.557611
\(330\) 0 0
\(331\) −7488.66 −1.24355 −0.621773 0.783197i \(-0.713588\pi\)
−0.621773 + 0.783197i \(0.713588\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1463.48 0.238682
\(336\) 0 0
\(337\) −6037.63 −0.975936 −0.487968 0.872862i \(-0.662262\pi\)
−0.487968 + 0.872862i \(0.662262\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −8857.15 −1.40657
\(342\) 0 0
\(343\) −4952.62 −0.779639
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4374.17 0.676708 0.338354 0.941019i \(-0.390130\pi\)
0.338354 + 0.941019i \(0.390130\pi\)
\(348\) 0 0
\(349\) −11777.8 −1.80645 −0.903223 0.429172i \(-0.858805\pi\)
−0.903223 + 0.429172i \(0.858805\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1548.39 −0.233463 −0.116732 0.993163i \(-0.537242\pi\)
−0.116732 + 0.993163i \(0.537242\pi\)
\(354\) 0 0
\(355\) −3693.71 −0.552230
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4793.75 0.704748 0.352374 0.935859i \(-0.385374\pi\)
0.352374 + 0.935859i \(0.385374\pi\)
\(360\) 0 0
\(361\) −4865.33 −0.709335
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2266.07 0.324963
\(366\) 0 0
\(367\) −7183.40 −1.02172 −0.510859 0.859665i \(-0.670673\pi\)
−0.510859 + 0.859665i \(0.670673\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1486.64 0.208039
\(372\) 0 0
\(373\) −6359.09 −0.882738 −0.441369 0.897326i \(-0.645507\pi\)
−0.441369 + 0.897326i \(0.645507\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10024.1 −1.36941
\(378\) 0 0
\(379\) 7598.86 1.02989 0.514944 0.857224i \(-0.327813\pi\)
0.514944 + 0.857224i \(0.327813\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11674.6 −1.55756 −0.778778 0.627300i \(-0.784160\pi\)
−0.778778 + 0.627300i \(0.784160\pi\)
\(384\) 0 0
\(385\) 1476.13 0.195404
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4324.51 −0.563653 −0.281827 0.959465i \(-0.590940\pi\)
−0.281827 + 0.959465i \(0.590940\pi\)
\(390\) 0 0
\(391\) 10178.0 1.31643
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4463.80 −0.568602
\(396\) 0 0
\(397\) 9834.45 1.24327 0.621633 0.783308i \(-0.286469\pi\)
0.621633 + 0.783308i \(0.286469\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2593.68 0.322998 0.161499 0.986873i \(-0.448367\pi\)
0.161499 + 0.986873i \(0.448367\pi\)
\(402\) 0 0
\(403\) 8379.96 1.03582
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12590.7 1.53341
\(408\) 0 0
\(409\) −12202.2 −1.47520 −0.737602 0.675236i \(-0.764042\pi\)
−0.737602 + 0.675236i \(0.764042\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2336.39 −0.278369
\(414\) 0 0
\(415\) 332.057 0.0392771
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13107.9 −1.52831 −0.764155 0.645033i \(-0.776844\pi\)
−0.764155 + 0.645033i \(0.776844\pi\)
\(420\) 0 0
\(421\) 624.409 0.0722846 0.0361423 0.999347i \(-0.488493\pi\)
0.0361423 + 0.999347i \(0.488493\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2479.94 −0.283046
\(426\) 0 0
\(427\) −5580.13 −0.632415
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6376.30 −0.712612 −0.356306 0.934369i \(-0.615964\pi\)
−0.356306 + 0.934369i \(0.615964\pi\)
\(432\) 0 0
\(433\) 11244.7 1.24800 0.624000 0.781424i \(-0.285506\pi\)
0.624000 + 0.781424i \(0.285506\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4581.29 −0.501494
\(438\) 0 0
\(439\) −11262.2 −1.22441 −0.612204 0.790700i \(-0.709717\pi\)
−0.612204 + 0.790700i \(0.709717\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14404.2 1.54485 0.772423 0.635109i \(-0.219045\pi\)
0.772423 + 0.635109i \(0.219045\pi\)
\(444\) 0 0
\(445\) 4344.08 0.462762
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −11709.3 −1.23073 −0.615365 0.788242i \(-0.710992\pi\)
−0.615365 + 0.788242i \(0.710992\pi\)
\(450\) 0 0
\(451\) −15732.4 −1.64260
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1396.60 −0.143898
\(456\) 0 0
\(457\) 15784.8 1.61572 0.807858 0.589377i \(-0.200627\pi\)
0.807858 + 0.589377i \(0.200627\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3956.19 0.399692 0.199846 0.979827i \(-0.435956\pi\)
0.199846 + 0.979827i \(0.435956\pi\)
\(462\) 0 0
\(463\) −9252.50 −0.928726 −0.464363 0.885645i \(-0.653717\pi\)
−0.464363 + 0.885645i \(0.653717\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9116.74 0.903367 0.451684 0.892178i \(-0.350824\pi\)
0.451684 + 0.892178i \(0.350824\pi\)
\(468\) 0 0
\(469\) 2327.75 0.229180
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5357.87 −0.520835
\(474\) 0 0
\(475\) 1116.26 0.107827
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2236.33 −0.213321 −0.106660 0.994296i \(-0.534016\pi\)
−0.106660 + 0.994296i \(0.534016\pi\)
\(480\) 0 0
\(481\) −11912.4 −1.12923
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 562.441 0.0526580
\(486\) 0 0
\(487\) −14371.9 −1.33728 −0.668638 0.743588i \(-0.733122\pi\)
−0.668638 + 0.743588i \(0.733122\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5423.17 0.498461 0.249230 0.968444i \(-0.419822\pi\)
0.249230 + 0.968444i \(0.419822\pi\)
\(492\) 0 0
\(493\) −28311.4 −2.58637
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5875.05 −0.530246
\(498\) 0 0
\(499\) 4920.24 0.441403 0.220701 0.975341i \(-0.429165\pi\)
0.220701 + 0.975341i \(0.429165\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16004.1 1.41866 0.709330 0.704876i \(-0.248998\pi\)
0.709330 + 0.704876i \(0.248998\pi\)
\(504\) 0 0
\(505\) 7905.64 0.696627
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −12973.0 −1.12970 −0.564852 0.825192i \(-0.691067\pi\)
−0.564852 + 0.825192i \(0.691067\pi\)
\(510\) 0 0
\(511\) 3604.31 0.312026
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4525.83 0.387247
\(516\) 0 0
\(517\) −15532.5 −1.32132
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1933.35 0.162575 0.0812877 0.996691i \(-0.474097\pi\)
0.0812877 + 0.996691i \(0.474097\pi\)
\(522\) 0 0
\(523\) −12275.0 −1.02629 −0.513144 0.858303i \(-0.671519\pi\)
−0.513144 + 0.858303i \(0.671519\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 23667.9 1.95633
\(528\) 0 0
\(529\) −1639.56 −0.134755
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 14884.8 1.20963
\(534\) 0 0
\(535\) 5639.67 0.455746
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10385.1 −0.829904
\(540\) 0 0
\(541\) 6956.43 0.552829 0.276414 0.961039i \(-0.410854\pi\)
0.276414 + 0.961039i \(0.410854\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −9738.25 −0.765396
\(546\) 0 0
\(547\) 16829.2 1.31547 0.657737 0.753247i \(-0.271514\pi\)
0.657737 + 0.753247i \(0.271514\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 12743.4 0.985280
\(552\) 0 0
\(553\) −7099.92 −0.545966
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1687.87 0.128398 0.0641988 0.997937i \(-0.479551\pi\)
0.0641988 + 0.997937i \(0.479551\pi\)
\(558\) 0 0
\(559\) 5069.21 0.383551
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19706.4 1.47518 0.737590 0.675249i \(-0.235964\pi\)
0.737590 + 0.675249i \(0.235964\pi\)
\(564\) 0 0
\(565\) 8622.61 0.642046
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19640.8 1.44707 0.723537 0.690286i \(-0.242515\pi\)
0.723537 + 0.690286i \(0.242515\pi\)
\(570\) 0 0
\(571\) 5247.74 0.384608 0.192304 0.981335i \(-0.438404\pi\)
0.192304 + 0.981335i \(0.438404\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2565.08 −0.186037
\(576\) 0 0
\(577\) 25474.3 1.83797 0.918985 0.394293i \(-0.129011\pi\)
0.918985 + 0.394293i \(0.129011\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 528.154 0.0377135
\(582\) 0 0
\(583\) 6939.41 0.492969
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −22502.7 −1.58226 −0.791129 0.611650i \(-0.790506\pi\)
−0.791129 + 0.611650i \(0.790506\pi\)
\(588\) 0 0
\(589\) −10653.3 −0.745266
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4175.65 −0.289163 −0.144581 0.989493i \(-0.546184\pi\)
−0.144581 + 0.989493i \(0.546184\pi\)
\(594\) 0 0
\(595\) −3944.48 −0.271778
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7096.57 0.484070 0.242035 0.970267i \(-0.422185\pi\)
0.242035 + 0.970267i \(0.422185\pi\)
\(600\) 0 0
\(601\) 9677.83 0.656850 0.328425 0.944530i \(-0.393482\pi\)
0.328425 + 0.944530i \(0.393482\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 235.362 0.0158162
\(606\) 0 0
\(607\) −24557.7 −1.64212 −0.821060 0.570842i \(-0.806617\pi\)
−0.821060 + 0.570842i \(0.806617\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14695.7 0.973035
\(612\) 0 0
\(613\) −22514.3 −1.48343 −0.741715 0.670716i \(-0.765987\pi\)
−0.741715 + 0.670716i \(0.765987\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14144.1 0.922882 0.461441 0.887171i \(-0.347333\pi\)
0.461441 + 0.887171i \(0.347333\pi\)
\(618\) 0 0
\(619\) 24650.9 1.60065 0.800324 0.599567i \(-0.204661\pi\)
0.800324 + 0.599567i \(0.204661\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6909.50 0.444339
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −33644.6 −2.13275
\(630\) 0 0
\(631\) 21513.3 1.35726 0.678630 0.734481i \(-0.262574\pi\)
0.678630 + 0.734481i \(0.262574\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3228.60 −0.201769
\(636\) 0 0
\(637\) 9825.61 0.611153
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17483.0 −1.07728 −0.538640 0.842536i \(-0.681062\pi\)
−0.538640 + 0.842536i \(0.681062\pi\)
\(642\) 0 0
\(643\) 25464.1 1.56175 0.780877 0.624685i \(-0.214773\pi\)
0.780877 + 0.624685i \(0.214773\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25974.4 −1.57830 −0.789148 0.614203i \(-0.789477\pi\)
−0.789148 + 0.614203i \(0.789477\pi\)
\(648\) 0 0
\(649\) −10905.9 −0.659622
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3532.46 −0.211694 −0.105847 0.994382i \(-0.533755\pi\)
−0.105847 + 0.994382i \(0.533755\pi\)
\(654\) 0 0
\(655\) −10279.6 −0.613216
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 29558.1 1.74723 0.873613 0.486622i \(-0.161771\pi\)
0.873613 + 0.486622i \(0.161771\pi\)
\(660\) 0 0
\(661\) −17632.5 −1.03755 −0.518777 0.854910i \(-0.673612\pi\)
−0.518777 + 0.854910i \(0.673612\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1775.48 0.103534
\(666\) 0 0
\(667\) −29283.4 −1.69994
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −26047.2 −1.49857
\(672\) 0 0
\(673\) 16119.9 0.923296 0.461648 0.887063i \(-0.347258\pi\)
0.461648 + 0.887063i \(0.347258\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8987.07 0.510194 0.255097 0.966915i \(-0.417893\pi\)
0.255097 + 0.966915i \(0.417893\pi\)
\(678\) 0 0
\(679\) 894.594 0.0505617
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16085.7 −0.901173 −0.450586 0.892733i \(-0.648785\pi\)
−0.450586 + 0.892733i \(0.648785\pi\)
\(684\) 0 0
\(685\) −1222.74 −0.0682023
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6565.54 −0.363029
\(690\) 0 0
\(691\) −2781.12 −0.153109 −0.0765547 0.997065i \(-0.524392\pi\)
−0.0765547 + 0.997065i \(0.524392\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5343.35 −0.291633
\(696\) 0 0
\(697\) 42039.9 2.28461
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19690.3 −1.06090 −0.530450 0.847716i \(-0.677977\pi\)
−0.530450 + 0.847716i \(0.677977\pi\)
\(702\) 0 0
\(703\) 15144.0 0.812472
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12574.4 0.668894
\(708\) 0 0
\(709\) −14455.3 −0.765699 −0.382849 0.923811i \(-0.625057\pi\)
−0.382849 + 0.923811i \(0.625057\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24480.4 1.28583
\(714\) 0 0
\(715\) −6519.14 −0.340982
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −20466.1 −1.06155 −0.530776 0.847512i \(-0.678100\pi\)
−0.530776 + 0.847512i \(0.678100\pi\)
\(720\) 0 0
\(721\) 7198.59 0.371830
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7135.10 0.365505
\(726\) 0 0
\(727\) −14551.8 −0.742362 −0.371181 0.928561i \(-0.621047\pi\)
−0.371181 + 0.928561i \(0.621047\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 14317.2 0.724405
\(732\) 0 0
\(733\) −7253.87 −0.365522 −0.182761 0.983157i \(-0.558503\pi\)
−0.182761 + 0.983157i \(0.558503\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10865.6 0.543066
\(738\) 0 0
\(739\) −19673.1 −0.979281 −0.489640 0.871925i \(-0.662872\pi\)
−0.489640 + 0.871925i \(0.662872\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16033.8 −0.791686 −0.395843 0.918318i \(-0.629547\pi\)
−0.395843 + 0.918318i \(0.629547\pi\)
\(744\) 0 0
\(745\) −6479.22 −0.318631
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8970.20 0.437602
\(750\) 0 0
\(751\) 4848.93 0.235606 0.117803 0.993037i \(-0.462415\pi\)
0.117803 + 0.993037i \(0.462415\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 13636.6 0.657333
\(756\) 0 0
\(757\) 31534.6 1.51406 0.757030 0.653380i \(-0.226650\pi\)
0.757030 + 0.653380i \(0.226650\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7873.75 0.375063 0.187532 0.982259i \(-0.439951\pi\)
0.187532 + 0.982259i \(0.439951\pi\)
\(762\) 0 0
\(763\) −15489.2 −0.734925
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10318.4 0.485755
\(768\) 0 0
\(769\) −7134.10 −0.334541 −0.167271 0.985911i \(-0.553495\pi\)
−0.167271 + 0.985911i \(0.553495\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9224.32 0.429205 0.214603 0.976701i \(-0.431154\pi\)
0.214603 + 0.976701i \(0.431154\pi\)
\(774\) 0 0
\(775\) −5964.83 −0.276468
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −18922.9 −0.870323
\(780\) 0 0
\(781\) −27423.9 −1.25647
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4338.50 0.197258
\(786\) 0 0
\(787\) 30384.7 1.37623 0.688117 0.725599i \(-0.258437\pi\)
0.688117 + 0.725599i \(0.258437\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 13714.7 0.616485
\(792\) 0 0
\(793\) 24643.9 1.10357
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −9064.89 −0.402879 −0.201440 0.979501i \(-0.564562\pi\)
−0.201440 + 0.979501i \(0.564562\pi\)
\(798\) 0 0
\(799\) 41505.7 1.83775
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 16824.4 0.739377
\(804\) 0 0
\(805\) −4079.91 −0.178631
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −11430.1 −0.496737 −0.248368 0.968666i \(-0.579894\pi\)
−0.248368 + 0.968666i \(0.579894\pi\)
\(810\) 0 0
\(811\) 27003.1 1.16918 0.584591 0.811328i \(-0.301255\pi\)
0.584591 + 0.811328i \(0.301255\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −6087.00 −0.261618
\(816\) 0 0
\(817\) −6444.40 −0.275962
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 32910.1 1.39899 0.699494 0.714638i \(-0.253409\pi\)
0.699494 + 0.714638i \(0.253409\pi\)
\(822\) 0 0
\(823\) 29489.1 1.24900 0.624499 0.781026i \(-0.285303\pi\)
0.624499 + 0.781026i \(0.285303\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18645.6 −0.784002 −0.392001 0.919965i \(-0.628217\pi\)
−0.392001 + 0.919965i \(0.628217\pi\)
\(828\) 0 0
\(829\) −4919.89 −0.206122 −0.103061 0.994675i \(-0.532864\pi\)
−0.103061 + 0.994675i \(0.532864\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 27750.9 1.15427
\(834\) 0 0
\(835\) −16333.8 −0.676951
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −45795.6 −1.88444 −0.942218 0.335001i \(-0.891263\pi\)
−0.942218 + 0.335001i \(0.891263\pi\)
\(840\) 0 0
\(841\) 57066.5 2.33985
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4817.09 −0.196110
\(846\) 0 0
\(847\) 374.356 0.0151866
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −34799.8 −1.40179
\(852\) 0 0
\(853\) 42136.7 1.69136 0.845681 0.533688i \(-0.179194\pi\)
0.845681 + 0.533688i \(0.179194\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 27884.1 1.11144 0.555720 0.831370i \(-0.312443\pi\)
0.555720 + 0.831370i \(0.312443\pi\)
\(858\) 0 0
\(859\) 28863.7 1.14647 0.573234 0.819392i \(-0.305689\pi\)
0.573234 + 0.819392i \(0.305689\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 13061.5 0.515203 0.257601 0.966251i \(-0.417068\pi\)
0.257601 + 0.966251i \(0.417068\pi\)
\(864\) 0 0
\(865\) 7108.56 0.279420
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −33141.4 −1.29372
\(870\) 0 0
\(871\) −10280.2 −0.399921
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 994.097 0.0384076
\(876\) 0 0
\(877\) 6501.20 0.250319 0.125160 0.992137i \(-0.460056\pi\)
0.125160 + 0.992137i \(0.460056\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 45486.0 1.73946 0.869729 0.493529i \(-0.164293\pi\)
0.869729 + 0.493529i \(0.164293\pi\)
\(882\) 0 0
\(883\) 5963.30 0.227272 0.113636 0.993522i \(-0.463750\pi\)
0.113636 + 0.993522i \(0.463750\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −14524.3 −0.549807 −0.274903 0.961472i \(-0.588646\pi\)
−0.274903 + 0.961472i \(0.588646\pi\)
\(888\) 0 0
\(889\) −5135.27 −0.193736
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −18682.4 −0.700093
\(894\) 0 0
\(895\) −4747.46 −0.177307
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −68095.5 −2.52626
\(900\) 0 0
\(901\) −18543.3 −0.685646
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8741.27 0.321072
\(906\) 0 0
\(907\) −25024.4 −0.916119 −0.458060 0.888921i \(-0.651455\pi\)
−0.458060 + 0.888921i \(0.651455\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 27898.0 1.01460 0.507300 0.861770i \(-0.330644\pi\)
0.507300 + 0.861770i \(0.330644\pi\)
\(912\) 0 0
\(913\) 2465.35 0.0893659
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −16350.3 −0.588804
\(918\) 0 0
\(919\) 19703.7 0.707253 0.353627 0.935387i \(-0.384948\pi\)
0.353627 + 0.935387i \(0.384948\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 25946.4 0.925283
\(924\) 0 0
\(925\) 8479.20 0.301399
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −17982.7 −0.635083 −0.317542 0.948244i \(-0.602857\pi\)
−0.317542 + 0.948244i \(0.602857\pi\)
\(930\) 0 0
\(931\) −12491.1 −0.439721
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −18412.3 −0.644006
\(936\) 0 0
\(937\) 25616.7 0.893128 0.446564 0.894752i \(-0.352647\pi\)
0.446564 + 0.894752i \(0.352647\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 18854.2 0.653166 0.326583 0.945169i \(-0.394103\pi\)
0.326583 + 0.945169i \(0.394103\pi\)
\(942\) 0 0
\(943\) 43483.2 1.50160
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 24298.8 0.833798 0.416899 0.908953i \(-0.363117\pi\)
0.416899 + 0.908953i \(0.363117\pi\)
\(948\) 0 0
\(949\) −15918.0 −0.544487
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −10472.4 −0.355963 −0.177982 0.984034i \(-0.556957\pi\)
−0.177982 + 0.984034i \(0.556957\pi\)
\(954\) 0 0
\(955\) 7091.84 0.240300
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1944.84 −0.0654871
\(960\) 0 0
\(961\) 27135.6 0.910867
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −18667.4 −0.622721
\(966\) 0 0
\(967\) −56840.3 −1.89024 −0.945120 0.326723i \(-0.894056\pi\)
−0.945120 + 0.326723i \(0.894056\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −52095.6 −1.72176 −0.860879 0.508810i \(-0.830086\pi\)
−0.860879 + 0.508810i \(0.830086\pi\)
\(972\) 0 0
\(973\) −8498.90 −0.280023
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −24247.8 −0.794017 −0.397008 0.917815i \(-0.629952\pi\)
−0.397008 + 0.917815i \(0.629952\pi\)
\(978\) 0 0
\(979\) 32252.5 1.05291
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3529.10 0.114508 0.0572538 0.998360i \(-0.481766\pi\)
0.0572538 + 0.998360i \(0.481766\pi\)
\(984\) 0 0
\(985\) 11473.3 0.371138
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 14808.7 0.476127
\(990\) 0 0
\(991\) −2131.22 −0.0683151 −0.0341576 0.999416i \(-0.510875\pi\)
−0.0341576 + 0.999416i \(0.510875\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −18569.7 −0.591656
\(996\) 0 0
\(997\) 20296.8 0.644739 0.322370 0.946614i \(-0.395521\pi\)
0.322370 + 0.946614i \(0.395521\pi\)
\(998\) 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 2160.4.a.bo.1.2 3
3.2 odd 2 2160.4.a.bg.1.2 3
4.3 odd 2 1080.4.a.m.1.2 yes 3
12.11 even 2 1080.4.a.g.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.4.a.g.1.2 3 12.11 even 2
1080.4.a.m.1.2 yes 3 4.3 odd 2
2160.4.a.bg.1.2 3 3.2 odd 2
2160.4.a.bo.1.2 3 1.1 even 1 trivial