Properties

Label 2160.4.a.bt.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
Analytic rank $0$
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: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.697.1
Defining polynomial: \( x^{3} - 7x - 5 \) 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 1.1
Root \(-0.782816\) of defining polynomial
Character \(\chi\) \(=\) 2160.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.00000 q^{5} -11.6263 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -11.6263 q^{7} +47.4851 q^{11} +84.2727 q^{13} -26.9488 q^{17} +152.060 q^{19} +177.082 q^{23} +25.0000 q^{25} +60.0913 q^{29} +92.1613 q^{31} -58.1315 q^{35} -221.798 q^{37} +115.099 q^{41} -383.827 q^{43} -317.275 q^{47} -207.829 q^{49} -257.738 q^{53} +237.426 q^{55} +642.576 q^{59} -662.092 q^{61} +421.363 q^{65} -597.173 q^{67} +500.152 q^{71} +989.949 q^{73} -552.076 q^{77} +517.554 q^{79} +605.867 q^{83} -134.744 q^{85} -1519.15 q^{89} -979.780 q^{91} +760.301 q^{95} +742.835 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 15 q^{5} + 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 15 q^{5} + 24 q^{7} - 6 q^{11} + 48 q^{13} - 27 q^{17} + 195 q^{19} + 27 q^{23} + 75 q^{25} + 60 q^{29} + 279 q^{31} + 120 q^{35} - 138 q^{37} + 66 q^{41} - 222 q^{43} + 264 q^{47} - 237 q^{49} - 507 q^{53} - 30 q^{55} + 960 q^{59} + 543 q^{61} + 240 q^{65} + 1086 q^{67} + 1818 q^{71} + 1362 q^{73} - 1776 q^{77} + 129 q^{79} + 1569 q^{83} - 135 q^{85} - 1770 q^{89} - 1488 q^{91} + 975 q^{95} - 336 q^{97}+O(q^{100}) \) 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
\(7\) −11.6263 −0.627761 −0.313881 0.949462i \(-0.601629\pi\)
−0.313881 + 0.949462i \(0.601629\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 47.4851 1.30157 0.650787 0.759261i \(-0.274439\pi\)
0.650787 + 0.759261i \(0.274439\pi\)
\(12\) 0 0
\(13\) 84.2727 1.79793 0.898963 0.438024i \(-0.144322\pi\)
0.898963 + 0.438024i \(0.144322\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −26.9488 −0.384474 −0.192237 0.981349i \(-0.561574\pi\)
−0.192237 + 0.981349i \(0.561574\pi\)
\(18\) 0 0
\(19\) 152.060 1.83605 0.918027 0.396518i \(-0.129782\pi\)
0.918027 + 0.396518i \(0.129782\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 177.082 1.60539 0.802697 0.596387i \(-0.203397\pi\)
0.802697 + 0.596387i \(0.203397\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 60.0913 0.384782 0.192391 0.981318i \(-0.438376\pi\)
0.192391 + 0.981318i \(0.438376\pi\)
\(30\) 0 0
\(31\) 92.1613 0.533957 0.266978 0.963703i \(-0.413975\pi\)
0.266978 + 0.963703i \(0.413975\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −58.1315 −0.280743
\(36\) 0 0
\(37\) −221.798 −0.985496 −0.492748 0.870172i \(-0.664008\pi\)
−0.492748 + 0.870172i \(0.664008\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 115.099 0.438426 0.219213 0.975677i \(-0.429651\pi\)
0.219213 + 0.975677i \(0.429651\pi\)
\(42\) 0 0
\(43\) −383.827 −1.36123 −0.680617 0.732639i \(-0.738288\pi\)
−0.680617 + 0.732639i \(0.738288\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −317.275 −0.984666 −0.492333 0.870407i \(-0.663856\pi\)
−0.492333 + 0.870407i \(0.663856\pi\)
\(48\) 0 0
\(49\) −207.829 −0.605916
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −257.738 −0.667981 −0.333991 0.942576i \(-0.608395\pi\)
−0.333991 + 0.942576i \(0.608395\pi\)
\(54\) 0 0
\(55\) 237.426 0.582081
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 642.576 1.41790 0.708951 0.705257i \(-0.249169\pi\)
0.708951 + 0.705257i \(0.249169\pi\)
\(60\) 0 0
\(61\) −662.092 −1.38971 −0.694854 0.719150i \(-0.744531\pi\)
−0.694854 + 0.719150i \(0.744531\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 421.363 0.804057
\(66\) 0 0
\(67\) −597.173 −1.08890 −0.544450 0.838794i \(-0.683261\pi\)
−0.544450 + 0.838794i \(0.683261\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 500.152 0.836016 0.418008 0.908443i \(-0.362728\pi\)
0.418008 + 0.908443i \(0.362728\pi\)
\(72\) 0 0
\(73\) 989.949 1.58719 0.793594 0.608447i \(-0.208207\pi\)
0.793594 + 0.608447i \(0.208207\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −552.076 −0.817077
\(78\) 0 0
\(79\) 517.554 0.737081 0.368540 0.929612i \(-0.379858\pi\)
0.368540 + 0.929612i \(0.379858\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 605.867 0.801235 0.400617 0.916245i \(-0.368796\pi\)
0.400617 + 0.916245i \(0.368796\pi\)
\(84\) 0 0
\(85\) −134.744 −0.171942
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1519.15 −1.80932 −0.904658 0.426138i \(-0.859874\pi\)
−0.904658 + 0.426138i \(0.859874\pi\)
\(90\) 0 0
\(91\) −979.780 −1.12867
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 760.301 0.821108
\(96\) 0 0
\(97\) 742.835 0.777561 0.388781 0.921330i \(-0.372896\pi\)
0.388781 + 0.921330i \(0.372896\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1066.26 −1.05047 −0.525233 0.850959i \(-0.676022\pi\)
−0.525233 + 0.850959i \(0.676022\pi\)
\(102\) 0 0
\(103\) 471.508 0.451059 0.225529 0.974236i \(-0.427589\pi\)
0.225529 + 0.974236i \(0.427589\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1746.59 −1.57803 −0.789014 0.614375i \(-0.789408\pi\)
−0.789014 + 0.614375i \(0.789408\pi\)
\(108\) 0 0
\(109\) 1596.56 1.40296 0.701480 0.712689i \(-0.252523\pi\)
0.701480 + 0.712689i \(0.252523\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1622.95 1.35110 0.675550 0.737315i \(-0.263906\pi\)
0.675550 + 0.737315i \(0.263906\pi\)
\(114\) 0 0
\(115\) 885.408 0.717954
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 313.315 0.241358
\(120\) 0 0
\(121\) 923.837 0.694092
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1306.32 0.912730 0.456365 0.889793i \(-0.349151\pi\)
0.456365 + 0.889793i \(0.349151\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −539.259 −0.359659 −0.179829 0.983698i \(-0.557555\pi\)
−0.179829 + 0.983698i \(0.557555\pi\)
\(132\) 0 0
\(133\) −1767.90 −1.15260
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2877.22 −1.79429 −0.897144 0.441738i \(-0.854362\pi\)
−0.897144 + 0.441738i \(0.854362\pi\)
\(138\) 0 0
\(139\) 1479.89 0.903038 0.451519 0.892261i \(-0.350882\pi\)
0.451519 + 0.892261i \(0.350882\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4001.70 2.34013
\(144\) 0 0
\(145\) 300.457 0.172080
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1398.13 −0.768719 −0.384359 0.923184i \(-0.625578\pi\)
−0.384359 + 0.923184i \(0.625578\pi\)
\(150\) 0 0
\(151\) 2251.44 1.21337 0.606687 0.794941i \(-0.292498\pi\)
0.606687 + 0.794941i \(0.292498\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 460.806 0.238793
\(156\) 0 0
\(157\) 764.698 0.388723 0.194362 0.980930i \(-0.437736\pi\)
0.194362 + 0.980930i \(0.437736\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2058.81 −1.00780
\(162\) 0 0
\(163\) 1862.15 0.894817 0.447408 0.894330i \(-0.352347\pi\)
0.447408 + 0.894330i \(0.352347\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3324.33 1.54038 0.770192 0.637812i \(-0.220160\pi\)
0.770192 + 0.637812i \(0.220160\pi\)
\(168\) 0 0
\(169\) 4904.89 2.23254
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1344.67 −0.590943 −0.295471 0.955352i \(-0.595477\pi\)
−0.295471 + 0.955352i \(0.595477\pi\)
\(174\) 0 0
\(175\) −290.658 −0.125552
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2086.39 0.871195 0.435598 0.900142i \(-0.356537\pi\)
0.435598 + 0.900142i \(0.356537\pi\)
\(180\) 0 0
\(181\) 698.713 0.286933 0.143467 0.989655i \(-0.454175\pi\)
0.143467 + 0.989655i \(0.454175\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1108.99 −0.440727
\(186\) 0 0
\(187\) −1279.67 −0.500421
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2267.66 0.859067 0.429534 0.903051i \(-0.358678\pi\)
0.429534 + 0.903051i \(0.358678\pi\)
\(192\) 0 0
\(193\) −3747.64 −1.39772 −0.698862 0.715256i \(-0.746310\pi\)
−0.698862 + 0.715256i \(0.746310\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 293.859 0.106277 0.0531385 0.998587i \(-0.483078\pi\)
0.0531385 + 0.998587i \(0.483078\pi\)
\(198\) 0 0
\(199\) −2552.33 −0.909197 −0.454598 0.890697i \(-0.650217\pi\)
−0.454598 + 0.890697i \(0.650217\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −698.640 −0.241551
\(204\) 0 0
\(205\) 575.496 0.196070
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 7220.60 2.38976
\(210\) 0 0
\(211\) 5416.57 1.76726 0.883630 0.468185i \(-0.155092\pi\)
0.883630 + 0.468185i \(0.155092\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1919.14 −0.608763
\(216\) 0 0
\(217\) −1071.49 −0.335197
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2271.05 −0.691256
\(222\) 0 0
\(223\) −4739.25 −1.42316 −0.711578 0.702607i \(-0.752019\pi\)
−0.711578 + 0.702607i \(0.752019\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2489.12 0.727790 0.363895 0.931440i \(-0.381447\pi\)
0.363895 + 0.931440i \(0.381447\pi\)
\(228\) 0 0
\(229\) 4239.27 1.22331 0.611657 0.791123i \(-0.290503\pi\)
0.611657 + 0.791123i \(0.290503\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1200.46 −0.337531 −0.168765 0.985656i \(-0.553978\pi\)
−0.168765 + 0.985656i \(0.553978\pi\)
\(234\) 0 0
\(235\) −1586.37 −0.440356
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4609.67 −1.24759 −0.623796 0.781587i \(-0.714411\pi\)
−0.623796 + 0.781587i \(0.714411\pi\)
\(240\) 0 0
\(241\) −2121.92 −0.567157 −0.283578 0.958949i \(-0.591522\pi\)
−0.283578 + 0.958949i \(0.591522\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1039.15 −0.270974
\(246\) 0 0
\(247\) 12814.5 3.30109
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5032.56 −1.26555 −0.632773 0.774337i \(-0.718084\pi\)
−0.632773 + 0.774337i \(0.718084\pi\)
\(252\) 0 0
\(253\) 8408.74 2.08954
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5721.18 −1.38863 −0.694314 0.719672i \(-0.744292\pi\)
−0.694314 + 0.719672i \(0.744292\pi\)
\(258\) 0 0
\(259\) 2578.69 0.618657
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3348.24 −0.785025 −0.392512 0.919747i \(-0.628394\pi\)
−0.392512 + 0.919747i \(0.628394\pi\)
\(264\) 0 0
\(265\) −1288.69 −0.298730
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1726.71 −0.391373 −0.195686 0.980667i \(-0.562693\pi\)
−0.195686 + 0.980667i \(0.562693\pi\)
\(270\) 0 0
\(271\) −6347.21 −1.42275 −0.711375 0.702812i \(-0.751927\pi\)
−0.711375 + 0.702812i \(0.751927\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1187.13 0.260315
\(276\) 0 0
\(277\) −591.832 −0.128374 −0.0641872 0.997938i \(-0.520445\pi\)
−0.0641872 + 0.997938i \(0.520445\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1405.24 −0.298326 −0.149163 0.988813i \(-0.547658\pi\)
−0.149163 + 0.988813i \(0.547658\pi\)
\(282\) 0 0
\(283\) −1417.53 −0.297750 −0.148875 0.988856i \(-0.547565\pi\)
−0.148875 + 0.988856i \(0.547565\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1338.18 −0.275227
\(288\) 0 0
\(289\) −4186.76 −0.852180
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5127.59 −1.02238 −0.511189 0.859468i \(-0.670795\pi\)
−0.511189 + 0.859468i \(0.670795\pi\)
\(294\) 0 0
\(295\) 3212.88 0.634105
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 14923.2 2.88638
\(300\) 0 0
\(301\) 4462.49 0.854531
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3310.46 −0.621497
\(306\) 0 0
\(307\) −2481.35 −0.461296 −0.230648 0.973037i \(-0.574085\pi\)
−0.230648 + 0.973037i \(0.574085\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 201.357 0.0367135 0.0183567 0.999832i \(-0.494157\pi\)
0.0183567 + 0.999832i \(0.494157\pi\)
\(312\) 0 0
\(313\) 1850.89 0.334244 0.167122 0.985936i \(-0.446553\pi\)
0.167122 + 0.985936i \(0.446553\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2257.74 0.400024 0.200012 0.979793i \(-0.435902\pi\)
0.200012 + 0.979793i \(0.435902\pi\)
\(318\) 0 0
\(319\) 2853.44 0.500822
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4097.85 −0.705915
\(324\) 0 0
\(325\) 2106.82 0.359585
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3688.73 0.618135
\(330\) 0 0
\(331\) 4038.32 0.670592 0.335296 0.942113i \(-0.391164\pi\)
0.335296 + 0.942113i \(0.391164\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2985.86 −0.486971
\(336\) 0 0
\(337\) −3552.00 −0.574154 −0.287077 0.957908i \(-0.592684\pi\)
−0.287077 + 0.957908i \(0.592684\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4376.29 0.694983
\(342\) 0 0
\(343\) 6404.11 1.00813
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 781.347 0.120879 0.0604394 0.998172i \(-0.480750\pi\)
0.0604394 + 0.998172i \(0.480750\pi\)
\(348\) 0 0
\(349\) 2492.19 0.382246 0.191123 0.981566i \(-0.438787\pi\)
0.191123 + 0.981566i \(0.438787\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9230.11 1.39170 0.695849 0.718189i \(-0.255028\pi\)
0.695849 + 0.718189i \(0.255028\pi\)
\(354\) 0 0
\(355\) 2500.76 0.373878
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −925.350 −0.136039 −0.0680196 0.997684i \(-0.521668\pi\)
−0.0680196 + 0.997684i \(0.521668\pi\)
\(360\) 0 0
\(361\) 16263.3 2.37109
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4949.75 0.709812
\(366\) 0 0
\(367\) 9070.86 1.29018 0.645089 0.764108i \(-0.276820\pi\)
0.645089 + 0.764108i \(0.276820\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2996.54 0.419333
\(372\) 0 0
\(373\) 9388.07 1.30321 0.651603 0.758560i \(-0.274097\pi\)
0.651603 + 0.758560i \(0.274097\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5064.06 0.691810
\(378\) 0 0
\(379\) −10172.2 −1.37866 −0.689328 0.724449i \(-0.742094\pi\)
−0.689328 + 0.724449i \(0.742094\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1505.63 −0.200873 −0.100436 0.994943i \(-0.532024\pi\)
−0.100436 + 0.994943i \(0.532024\pi\)
\(384\) 0 0
\(385\) −2760.38 −0.365408
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3179.65 −0.414433 −0.207216 0.978295i \(-0.566440\pi\)
−0.207216 + 0.978295i \(0.566440\pi\)
\(390\) 0 0
\(391\) −4772.15 −0.617232
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2587.77 0.329632
\(396\) 0 0
\(397\) 5360.23 0.677638 0.338819 0.940852i \(-0.389973\pi\)
0.338819 + 0.940852i \(0.389973\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12550.4 1.56294 0.781468 0.623945i \(-0.214471\pi\)
0.781468 + 0.623945i \(0.214471\pi\)
\(402\) 0 0
\(403\) 7766.68 0.960015
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10532.1 −1.28270
\(408\) 0 0
\(409\) −5395.42 −0.652289 −0.326144 0.945320i \(-0.605750\pi\)
−0.326144 + 0.945320i \(0.605750\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7470.78 −0.890105
\(414\) 0 0
\(415\) 3029.33 0.358323
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4697.84 −0.547743 −0.273871 0.961766i \(-0.588304\pi\)
−0.273871 + 0.961766i \(0.588304\pi\)
\(420\) 0 0
\(421\) 8845.86 1.02404 0.512020 0.858974i \(-0.328897\pi\)
0.512020 + 0.858974i \(0.328897\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −673.721 −0.0768948
\(426\) 0 0
\(427\) 7697.69 0.872406
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5676.98 0.634456 0.317228 0.948349i \(-0.397248\pi\)
0.317228 + 0.948349i \(0.397248\pi\)
\(432\) 0 0
\(433\) 17273.3 1.91710 0.958549 0.284927i \(-0.0919695\pi\)
0.958549 + 0.284927i \(0.0919695\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 26927.1 2.94759
\(438\) 0 0
\(439\) 3583.55 0.389598 0.194799 0.980843i \(-0.437595\pi\)
0.194799 + 0.980843i \(0.437595\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6937.40 −0.744031 −0.372016 0.928227i \(-0.621333\pi\)
−0.372016 + 0.928227i \(0.621333\pi\)
\(444\) 0 0
\(445\) −7595.73 −0.809151
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12445.1 1.30806 0.654032 0.756467i \(-0.273076\pi\)
0.654032 + 0.756467i \(0.273076\pi\)
\(450\) 0 0
\(451\) 5465.50 0.570644
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4898.90 −0.504756
\(456\) 0 0
\(457\) −12112.2 −1.23979 −0.619896 0.784684i \(-0.712825\pi\)
−0.619896 + 0.784684i \(0.712825\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4932.76 0.498355 0.249178 0.968458i \(-0.419840\pi\)
0.249178 + 0.968458i \(0.419840\pi\)
\(462\) 0 0
\(463\) 12428.0 1.24747 0.623734 0.781637i \(-0.285615\pi\)
0.623734 + 0.781637i \(0.285615\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4549.10 −0.450765 −0.225383 0.974270i \(-0.572363\pi\)
−0.225383 + 0.974270i \(0.572363\pi\)
\(468\) 0 0
\(469\) 6942.91 0.683569
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −18226.1 −1.77175
\(474\) 0 0
\(475\) 3801.51 0.367211
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5122.02 −0.488583 −0.244292 0.969702i \(-0.578555\pi\)
−0.244292 + 0.969702i \(0.578555\pi\)
\(480\) 0 0
\(481\) −18691.5 −1.77185
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3714.17 0.347736
\(486\) 0 0
\(487\) 8650.25 0.804888 0.402444 0.915445i \(-0.368161\pi\)
0.402444 + 0.915445i \(0.368161\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −985.959 −0.0906226 −0.0453113 0.998973i \(-0.514428\pi\)
−0.0453113 + 0.998973i \(0.514428\pi\)
\(492\) 0 0
\(493\) −1619.39 −0.147939
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5814.92 −0.524819
\(498\) 0 0
\(499\) −3131.41 −0.280925 −0.140462 0.990086i \(-0.544859\pi\)
−0.140462 + 0.990086i \(0.544859\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −13765.8 −1.22025 −0.610126 0.792304i \(-0.708881\pi\)
−0.610126 + 0.792304i \(0.708881\pi\)
\(504\) 0 0
\(505\) −5331.31 −0.469783
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8241.51 −0.717679 −0.358839 0.933399i \(-0.616827\pi\)
−0.358839 + 0.933399i \(0.616827\pi\)
\(510\) 0 0
\(511\) −11509.4 −0.996376
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2357.54 0.201720
\(516\) 0 0
\(517\) −15065.8 −1.28161
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2556.69 0.214991 0.107496 0.994206i \(-0.465717\pi\)
0.107496 + 0.994206i \(0.465717\pi\)
\(522\) 0 0
\(523\) −8627.71 −0.721345 −0.360672 0.932693i \(-0.617453\pi\)
−0.360672 + 0.932693i \(0.617453\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2483.64 −0.205292
\(528\) 0 0
\(529\) 19190.9 1.57729
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9699.72 0.788258
\(534\) 0 0
\(535\) −8732.94 −0.705716
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9868.79 −0.788643
\(540\) 0 0
\(541\) 1265.74 0.100589 0.0502943 0.998734i \(-0.483984\pi\)
0.0502943 + 0.998734i \(0.483984\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7982.79 0.627423
\(546\) 0 0
\(547\) 6990.29 0.546405 0.273202 0.961957i \(-0.411917\pi\)
0.273202 + 0.961957i \(0.411917\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9137.50 0.706481
\(552\) 0 0
\(553\) −6017.24 −0.462711
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19679.0 −1.49699 −0.748496 0.663139i \(-0.769224\pi\)
−0.748496 + 0.663139i \(0.769224\pi\)
\(558\) 0 0
\(559\) −32346.2 −2.44740
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12913.2 −0.966652 −0.483326 0.875440i \(-0.660571\pi\)
−0.483326 + 0.875440i \(0.660571\pi\)
\(564\) 0 0
\(565\) 8114.74 0.604230
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19908.8 1.46682 0.733411 0.679786i \(-0.237927\pi\)
0.733411 + 0.679786i \(0.237927\pi\)
\(570\) 0 0
\(571\) 13278.9 0.973212 0.486606 0.873621i \(-0.338235\pi\)
0.486606 + 0.873621i \(0.338235\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4427.04 0.321079
\(576\) 0 0
\(577\) −2538.04 −0.183120 −0.0915598 0.995800i \(-0.529185\pi\)
−0.0915598 + 0.995800i \(0.529185\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7043.99 −0.502984
\(582\) 0 0
\(583\) −12238.7 −0.869426
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15312.4 −1.07668 −0.538341 0.842727i \(-0.680949\pi\)
−0.538341 + 0.842727i \(0.680949\pi\)
\(588\) 0 0
\(589\) 14014.1 0.980373
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −196.207 −0.0135873 −0.00679363 0.999977i \(-0.502162\pi\)
−0.00679363 + 0.999977i \(0.502162\pi\)
\(594\) 0 0
\(595\) 1566.58 0.107939
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13738.3 0.937113 0.468557 0.883433i \(-0.344774\pi\)
0.468557 + 0.883433i \(0.344774\pi\)
\(600\) 0 0
\(601\) 1702.20 0.115531 0.0577655 0.998330i \(-0.481602\pi\)
0.0577655 + 0.998330i \(0.481602\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4619.18 0.310408
\(606\) 0 0
\(607\) 11802.7 0.789223 0.394611 0.918848i \(-0.370879\pi\)
0.394611 + 0.918848i \(0.370879\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −26737.6 −1.77036
\(612\) 0 0
\(613\) 15365.9 1.01244 0.506218 0.862406i \(-0.331043\pi\)
0.506218 + 0.862406i \(0.331043\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17151.5 −1.11911 −0.559555 0.828793i \(-0.689028\pi\)
−0.559555 + 0.828793i \(0.689028\pi\)
\(618\) 0 0
\(619\) −10081.9 −0.654649 −0.327324 0.944912i \(-0.606147\pi\)
−0.327324 + 0.944912i \(0.606147\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 17662.1 1.13582
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5977.20 0.378898
\(630\) 0 0
\(631\) 15510.6 0.978554 0.489277 0.872128i \(-0.337261\pi\)
0.489277 + 0.872128i \(0.337261\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6531.58 0.408185
\(636\) 0 0
\(637\) −17514.3 −1.08939
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10534.8 0.649143 0.324571 0.945861i \(-0.394780\pi\)
0.324571 + 0.945861i \(0.394780\pi\)
\(642\) 0 0
\(643\) 627.807 0.0385044 0.0192522 0.999815i \(-0.493871\pi\)
0.0192522 + 0.999815i \(0.493871\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2880.41 0.175024 0.0875121 0.996163i \(-0.472108\pi\)
0.0875121 + 0.996163i \(0.472108\pi\)
\(648\) 0 0
\(649\) 30512.8 1.84550
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10664.9 0.639127 0.319564 0.947565i \(-0.396464\pi\)
0.319564 + 0.947565i \(0.396464\pi\)
\(654\) 0 0
\(655\) −2696.30 −0.160844
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4300.38 −0.254202 −0.127101 0.991890i \(-0.540567\pi\)
−0.127101 + 0.991890i \(0.540567\pi\)
\(660\) 0 0
\(661\) −10325.3 −0.607578 −0.303789 0.952739i \(-0.598252\pi\)
−0.303789 + 0.952739i \(0.598252\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8839.49 −0.515460
\(666\) 0 0
\(667\) 10641.1 0.617727
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −31439.5 −1.80881
\(672\) 0 0
\(673\) −13740.9 −0.787030 −0.393515 0.919318i \(-0.628741\pi\)
−0.393515 + 0.919318i \(0.628741\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 31303.5 1.77709 0.888547 0.458785i \(-0.151715\pi\)
0.888547 + 0.458785i \(0.151715\pi\)
\(678\) 0 0
\(679\) −8636.42 −0.488123
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8369.31 −0.468877 −0.234438 0.972131i \(-0.575325\pi\)
−0.234438 + 0.972131i \(0.575325\pi\)
\(684\) 0 0
\(685\) −14386.1 −0.802430
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −21720.3 −1.20098
\(690\) 0 0
\(691\) 24106.1 1.32712 0.663559 0.748124i \(-0.269045\pi\)
0.663559 + 0.748124i \(0.269045\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7399.43 0.403851
\(696\) 0 0
\(697\) −3101.79 −0.168563
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −30713.6 −1.65483 −0.827417 0.561589i \(-0.810190\pi\)
−0.827417 + 0.561589i \(0.810190\pi\)
\(702\) 0 0
\(703\) −33726.7 −1.80942
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12396.7 0.659442
\(708\) 0 0
\(709\) −518.034 −0.0274403 −0.0137201 0.999906i \(-0.504367\pi\)
−0.0137201 + 0.999906i \(0.504367\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 16320.1 0.857211
\(714\) 0 0
\(715\) 20008.5 1.04654
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1692.51 0.0877885 0.0438943 0.999036i \(-0.486024\pi\)
0.0438943 + 0.999036i \(0.486024\pi\)
\(720\) 0 0
\(721\) −5481.89 −0.283157
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1502.28 0.0769564
\(726\) 0 0
\(727\) 9191.77 0.468919 0.234459 0.972126i \(-0.424668\pi\)
0.234459 + 0.972126i \(0.424668\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 10343.7 0.523359
\(732\) 0 0
\(733\) −1047.13 −0.0527649 −0.0263824 0.999652i \(-0.508399\pi\)
−0.0263824 + 0.999652i \(0.508399\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −28356.8 −1.41728
\(738\) 0 0
\(739\) −21956.9 −1.09296 −0.546479 0.837473i \(-0.684032\pi\)
−0.546479 + 0.837473i \(0.684032\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −19304.1 −0.953160 −0.476580 0.879131i \(-0.658124\pi\)
−0.476580 + 0.879131i \(0.658124\pi\)
\(744\) 0 0
\(745\) −6990.64 −0.343781
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 20306.4 0.990625
\(750\) 0 0
\(751\) −21883.0 −1.06328 −0.531640 0.846970i \(-0.678424\pi\)
−0.531640 + 0.846970i \(0.678424\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 11257.2 0.542637
\(756\) 0 0
\(757\) 13738.5 0.659624 0.329812 0.944047i \(-0.393015\pi\)
0.329812 + 0.944047i \(0.393015\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −20167.9 −0.960689 −0.480345 0.877080i \(-0.659488\pi\)
−0.480345 + 0.877080i \(0.659488\pi\)
\(762\) 0 0
\(763\) −18562.1 −0.880724
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 54151.6 2.54928
\(768\) 0 0
\(769\) −28655.9 −1.34377 −0.671885 0.740655i \(-0.734515\pi\)
−0.671885 + 0.740655i \(0.734515\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −16224.0 −0.754898 −0.377449 0.926030i \(-0.623199\pi\)
−0.377449 + 0.926030i \(0.623199\pi\)
\(774\) 0 0
\(775\) 2304.03 0.106791
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 17502.0 0.804974
\(780\) 0 0
\(781\) 23749.8 1.08814
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3823.49 0.173842
\(786\) 0 0
\(787\) −3401.97 −0.154088 −0.0770440 0.997028i \(-0.524548\pi\)
−0.0770440 + 0.997028i \(0.524548\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18868.9 −0.848168
\(792\) 0 0
\(793\) −55796.3 −2.49859
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9328.18 0.414581 0.207290 0.978279i \(-0.433535\pi\)
0.207290 + 0.978279i \(0.433535\pi\)
\(798\) 0 0
\(799\) 8550.19 0.378578
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 47007.9 2.06584
\(804\) 0 0
\(805\) −10294.0 −0.450704
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21366.3 0.928552 0.464276 0.885690i \(-0.346314\pi\)
0.464276 + 0.885690i \(0.346314\pi\)
\(810\) 0 0
\(811\) −34119.9 −1.47733 −0.738664 0.674074i \(-0.764543\pi\)
−0.738664 + 0.674074i \(0.764543\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9310.77 0.400174
\(816\) 0 0
\(817\) −58364.9 −2.49930
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −21760.8 −0.925038 −0.462519 0.886609i \(-0.653054\pi\)
−0.462519 + 0.886609i \(0.653054\pi\)
\(822\) 0 0
\(823\) 3225.85 0.136629 0.0683147 0.997664i \(-0.478238\pi\)
0.0683147 + 0.997664i \(0.478238\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5208.23 −0.218994 −0.109497 0.993987i \(-0.534924\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(828\) 0 0
\(829\) 27899.5 1.16886 0.584432 0.811442i \(-0.301317\pi\)
0.584432 + 0.811442i \(0.301317\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5600.75 0.232959
\(834\) 0 0
\(835\) 16621.6 0.688881
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26244.4 1.07993 0.539964 0.841688i \(-0.318438\pi\)
0.539964 + 0.841688i \(0.318438\pi\)
\(840\) 0 0
\(841\) −20778.0 −0.851943
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 24524.4 0.998422
\(846\) 0 0
\(847\) −10740.8 −0.435724
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −39276.4 −1.58211
\(852\) 0 0
\(853\) 37048.2 1.48711 0.743556 0.668674i \(-0.233138\pi\)
0.743556 + 0.668674i \(0.233138\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16705.8 0.665879 0.332939 0.942948i \(-0.391960\pi\)
0.332939 + 0.942948i \(0.391960\pi\)
\(858\) 0 0
\(859\) −13768.5 −0.546887 −0.273443 0.961888i \(-0.588163\pi\)
−0.273443 + 0.961888i \(0.588163\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −37455.4 −1.47740 −0.738700 0.674034i \(-0.764560\pi\)
−0.738700 + 0.674034i \(0.764560\pi\)
\(864\) 0 0
\(865\) −6723.33 −0.264278
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 24576.1 0.959364
\(870\) 0 0
\(871\) −50325.4 −1.95776
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1453.29 −0.0561487
\(876\) 0 0
\(877\) −33351.2 −1.28414 −0.642070 0.766646i \(-0.721924\pi\)
−0.642070 + 0.766646i \(0.721924\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −45140.2 −1.72623 −0.863116 0.505005i \(-0.831491\pi\)
−0.863116 + 0.505005i \(0.831491\pi\)
\(882\) 0 0
\(883\) −47316.4 −1.80331 −0.901656 0.432454i \(-0.857648\pi\)
−0.901656 + 0.432454i \(0.857648\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 17513.8 0.662973 0.331487 0.943460i \(-0.392450\pi\)
0.331487 + 0.943460i \(0.392450\pi\)
\(888\) 0 0
\(889\) −15187.6 −0.572977
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −48244.9 −1.80790
\(894\) 0 0
\(895\) 10431.9 0.389610
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 5538.09 0.205457
\(900\) 0 0
\(901\) 6945.74 0.256821
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3493.57 0.128321
\(906\) 0 0
\(907\) 10576.5 0.387196 0.193598 0.981081i \(-0.437984\pi\)
0.193598 + 0.981081i \(0.437984\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 33191.6 1.20712 0.603560 0.797317i \(-0.293748\pi\)
0.603560 + 0.797317i \(0.293748\pi\)
\(912\) 0 0
\(913\) 28769.7 1.04287
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 6269.59 0.225780
\(918\) 0 0
\(919\) 51842.8 1.86087 0.930434 0.366460i \(-0.119430\pi\)
0.930434 + 0.366460i \(0.119430\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 42149.2 1.50310
\(924\) 0 0
\(925\) −5544.95 −0.197099
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 9039.52 0.319243 0.159622 0.987178i \(-0.448973\pi\)
0.159622 + 0.987178i \(0.448973\pi\)
\(930\) 0 0
\(931\) −31602.5 −1.11249
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6398.35 −0.223795
\(936\) 0 0
\(937\) −50041.7 −1.74471 −0.872353 0.488876i \(-0.837407\pi\)
−0.872353 + 0.488876i \(0.837407\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 12305.6 0.426304 0.213152 0.977019i \(-0.431627\pi\)
0.213152 + 0.977019i \(0.431627\pi\)
\(942\) 0 0
\(943\) 20382.0 0.703847
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −12109.2 −0.415519 −0.207759 0.978180i \(-0.566617\pi\)
−0.207759 + 0.978180i \(0.566617\pi\)
\(948\) 0 0
\(949\) 83425.7 2.85365
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −51371.2 −1.74615 −0.873073 0.487589i \(-0.837877\pi\)
−0.873073 + 0.487589i \(0.837877\pi\)
\(954\) 0 0
\(955\) 11338.3 0.384187
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 33451.4 1.12638
\(960\) 0 0
\(961\) −21297.3 −0.714890
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −18738.2 −0.625082
\(966\) 0 0
\(967\) 27271.5 0.906921 0.453460 0.891276i \(-0.350189\pi\)
0.453460 + 0.891276i \(0.350189\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 41605.1 1.37505 0.687524 0.726161i \(-0.258697\pi\)
0.687524 + 0.726161i \(0.258697\pi\)
\(972\) 0 0
\(973\) −17205.6 −0.566893
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −41821.2 −1.36948 −0.684738 0.728790i \(-0.740083\pi\)
−0.684738 + 0.728790i \(0.740083\pi\)
\(978\) 0 0
\(979\) −72136.8 −2.35496
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −37312.9 −1.21068 −0.605340 0.795967i \(-0.706963\pi\)
−0.605340 + 0.795967i \(0.706963\pi\)
\(984\) 0 0
\(985\) 1469.29 0.0475285
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −67968.8 −2.18532
\(990\) 0 0
\(991\) 32598.1 1.04492 0.522459 0.852664i \(-0.325015\pi\)
0.522459 + 0.852664i \(0.325015\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −12761.7 −0.406605
\(996\) 0 0
\(997\) 41856.8 1.32961 0.664804 0.747018i \(-0.268515\pi\)
0.664804 + 0.747018i \(0.268515\pi\)
\(998\) 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.bt.1.1 3
3.2 odd 2 2160.4.a.bl.1.1 3
4.3 odd 2 1080.4.a.i.1.3 yes 3
12.11 even 2 1080.4.a.c.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.4.a.c.1.3 3 12.11 even 2
1080.4.a.i.1.3 yes 3 4.3 odd 2
2160.4.a.bl.1.1 3 3.2 odd 2
2160.4.a.bt.1.1 3 1.1 even 1 trivial