Properties

Label 1008.4.a.y.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{177}) \)
Defining polynomial: \(x^{2} - x - 44\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(7.15207\) of defining polynomial
Character \(\chi\) \(=\) 1008.1

$q$-expansion

\(f(q)\) \(=\) \(q-20.3041 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q-20.3041 q^{5} -7.00000 q^{7} -30.9124 q^{11} +50.6083 q^{13} +102.737 q^{17} +61.2165 q^{19} +148.129 q^{23} +287.258 q^{25} -159.217 q^{29} +121.217 q^{31} +142.129 q^{35} -357.908 q^{37} -466.737 q^{41} +185.567 q^{43} -131.392 q^{47} +49.0000 q^{49} -200.175 q^{53} +627.650 q^{55} -591.908 q^{59} +70.5158 q^{61} -1027.56 q^{65} +643.041 q^{67} -522.397 q^{71} -576.175 q^{73} +216.387 q^{77} -280.774 q^{79} -557.732 q^{83} -2085.99 q^{85} +1228.89 q^{89} -354.258 q^{91} -1242.95 q^{95} +65.0413 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 14q^{5} - 14q^{7} + O(q^{10}) \) \( 2q - 14q^{5} - 14q^{7} + 18q^{11} + 48q^{13} - 34q^{17} + 16q^{19} + 110q^{23} + 202q^{25} - 212q^{29} + 136q^{31} + 98q^{35} - 24q^{37} - 694q^{41} + 584q^{43} - 316q^{47} + 98q^{49} - 560q^{53} + 936q^{55} - 492q^{59} - 604q^{61} - 1044q^{65} + 1020q^{67} - 1710q^{71} - 1312q^{73} - 126q^{77} + 556q^{79} - 264q^{83} - 2948q^{85} - 70q^{89} - 336q^{91} - 1528q^{95} - 136q^{97} + O(q^{100}) \)

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
\(5\) −20.3041 −1.81606 −0.908029 0.418908i \(-0.862413\pi\)
−0.908029 + 0.418908i \(0.862413\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −30.9124 −0.847313 −0.423656 0.905823i \(-0.639254\pi\)
−0.423656 + 0.905823i \(0.639254\pi\)
\(12\) 0 0
\(13\) 50.6083 1.07971 0.539854 0.841759i \(-0.318479\pi\)
0.539854 + 0.841759i \(0.318479\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 102.737 1.46573 0.732866 0.680373i \(-0.238182\pi\)
0.732866 + 0.680373i \(0.238182\pi\)
\(18\) 0 0
\(19\) 61.2165 0.739160 0.369580 0.929199i \(-0.379502\pi\)
0.369580 + 0.929199i \(0.379502\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 148.129 1.34291 0.671457 0.741044i \(-0.265669\pi\)
0.671457 + 0.741044i \(0.265669\pi\)
\(24\) 0 0
\(25\) 287.258 2.29806
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −159.217 −1.01951 −0.509755 0.860320i \(-0.670264\pi\)
−0.509755 + 0.860320i \(0.670264\pi\)
\(30\) 0 0
\(31\) 121.217 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 142.129 0.686405
\(36\) 0 0
\(37\) −357.908 −1.59026 −0.795130 0.606439i \(-0.792598\pi\)
−0.795130 + 0.606439i \(0.792598\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −466.737 −1.77786 −0.888928 0.458047i \(-0.848549\pi\)
−0.888928 + 0.458047i \(0.848549\pi\)
\(42\) 0 0
\(43\) 185.567 0.658109 0.329055 0.944311i \(-0.393270\pi\)
0.329055 + 0.944311i \(0.393270\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −131.392 −0.407776 −0.203888 0.978994i \(-0.565358\pi\)
−0.203888 + 0.978994i \(0.565358\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −200.175 −0.518796 −0.259398 0.965771i \(-0.583524\pi\)
−0.259398 + 0.965771i \(0.583524\pi\)
\(54\) 0 0
\(55\) 627.650 1.53877
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −591.908 −1.30610 −0.653049 0.757316i \(-0.726510\pi\)
−0.653049 + 0.757316i \(0.726510\pi\)
\(60\) 0 0
\(61\) 70.5158 0.148010 0.0740051 0.997258i \(-0.476422\pi\)
0.0740051 + 0.997258i \(0.476422\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1027.56 −1.96081
\(66\) 0 0
\(67\) 643.041 1.17254 0.586269 0.810117i \(-0.300596\pi\)
0.586269 + 0.810117i \(0.300596\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −522.397 −0.873198 −0.436599 0.899656i \(-0.643817\pi\)
−0.436599 + 0.899656i \(0.643817\pi\)
\(72\) 0 0
\(73\) −576.175 −0.923784 −0.461892 0.886936i \(-0.652829\pi\)
−0.461892 + 0.886936i \(0.652829\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 216.387 0.320254
\(78\) 0 0
\(79\) −280.774 −0.399867 −0.199934 0.979809i \(-0.564073\pi\)
−0.199934 + 0.979809i \(0.564073\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −557.732 −0.737579 −0.368790 0.929513i \(-0.620228\pi\)
−0.368790 + 0.929513i \(0.620228\pi\)
\(84\) 0 0
\(85\) −2085.99 −2.66185
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1228.89 1.46362 0.731811 0.681508i \(-0.238675\pi\)
0.731811 + 0.681508i \(0.238675\pi\)
\(90\) 0 0
\(91\) −354.258 −0.408091
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1242.95 −1.34236
\(96\) 0 0
\(97\) 65.0413 0.0680819 0.0340410 0.999420i \(-0.489162\pi\)
0.0340410 + 0.999420i \(0.489162\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −303.511 −0.299014 −0.149507 0.988761i \(-0.547769\pi\)
−0.149507 + 0.988761i \(0.547769\pi\)
\(102\) 0 0
\(103\) −174.268 −0.166710 −0.0833549 0.996520i \(-0.526564\pi\)
−0.0833549 + 0.996520i \(0.526564\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1945.42 1.75767 0.878835 0.477126i \(-0.158321\pi\)
0.878835 + 0.477126i \(0.158321\pi\)
\(108\) 0 0
\(109\) −1102.87 −0.969132 −0.484566 0.874755i \(-0.661023\pi\)
−0.484566 + 0.874755i \(0.661023\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −80.0827 −0.0666685 −0.0333343 0.999444i \(-0.510613\pi\)
−0.0333343 + 0.999444i \(0.510613\pi\)
\(114\) 0 0
\(115\) −3007.63 −2.43881
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −719.160 −0.553994
\(120\) 0 0
\(121\) −375.423 −0.282061
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3294.51 −2.35736
\(126\) 0 0
\(127\) 1981.12 1.38422 0.692112 0.721791i \(-0.256681\pi\)
0.692112 + 0.721791i \(0.256681\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2854.25 1.90364 0.951820 0.306658i \(-0.0992107\pi\)
0.951820 + 0.306658i \(0.0992107\pi\)
\(132\) 0 0
\(133\) −428.516 −0.279376
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 535.474 0.333932 0.166966 0.985963i \(-0.446603\pi\)
0.166966 + 0.985963i \(0.446603\pi\)
\(138\) 0 0
\(139\) −2326.43 −1.41961 −0.709804 0.704399i \(-0.751216\pi\)
−0.709804 + 0.704399i \(0.751216\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1564.42 −0.914851
\(144\) 0 0
\(145\) 3232.75 1.85149
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2061.04 −1.13320 −0.566601 0.823992i \(-0.691742\pi\)
−0.566601 + 0.823992i \(0.691742\pi\)
\(150\) 0 0
\(151\) 1113.03 0.599849 0.299925 0.953963i \(-0.403038\pi\)
0.299925 + 0.953963i \(0.403038\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2461.20 −1.27541
\(156\) 0 0
\(157\) −1537.30 −0.781464 −0.390732 0.920505i \(-0.627778\pi\)
−0.390732 + 0.920505i \(0.627778\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1036.90 −0.507574
\(162\) 0 0
\(163\) 2043.52 0.981967 0.490984 0.871169i \(-0.336637\pi\)
0.490984 + 0.871169i \(0.336637\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2513.44 1.16464 0.582322 0.812958i \(-0.302144\pi\)
0.582322 + 0.812958i \(0.302144\pi\)
\(168\) 0 0
\(169\) 364.197 0.165770
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1591.00 −0.699197 −0.349599 0.936900i \(-0.613682\pi\)
−0.349599 + 0.936900i \(0.613682\pi\)
\(174\) 0 0
\(175\) −2010.81 −0.868586
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2552.27 1.06573 0.532866 0.846200i \(-0.321115\pi\)
0.532866 + 0.846200i \(0.321115\pi\)
\(180\) 0 0
\(181\) −3361.33 −1.38036 −0.690182 0.723636i \(-0.742470\pi\)
−0.690182 + 0.723636i \(0.742470\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7267.00 2.88800
\(186\) 0 0
\(187\) −3175.85 −1.24193
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3868.64 −1.46558 −0.732789 0.680456i \(-0.761782\pi\)
−0.732789 + 0.680456i \(0.761782\pi\)
\(192\) 0 0
\(193\) 2693.17 1.00445 0.502224 0.864738i \(-0.332515\pi\)
0.502224 + 0.864738i \(0.332515\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1064.86 0.385116 0.192558 0.981286i \(-0.438322\pi\)
0.192558 + 0.981286i \(0.438322\pi\)
\(198\) 0 0
\(199\) −1625.92 −0.579187 −0.289594 0.957150i \(-0.593520\pi\)
−0.289594 + 0.957150i \(0.593520\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1114.52 0.385338
\(204\) 0 0
\(205\) 9476.70 3.22869
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1892.35 −0.626300
\(210\) 0 0
\(211\) −1138.04 −0.371309 −0.185654 0.982615i \(-0.559440\pi\)
−0.185654 + 0.982615i \(0.559440\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3767.78 −1.19516
\(216\) 0 0
\(217\) −848.516 −0.265442
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5199.35 1.58256
\(222\) 0 0
\(223\) −3535.78 −1.06176 −0.530881 0.847446i \(-0.678139\pi\)
−0.530881 + 0.847446i \(0.678139\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3055.21 −0.893309 −0.446655 0.894706i \(-0.647385\pi\)
−0.446655 + 0.894706i \(0.647385\pi\)
\(228\) 0 0
\(229\) −321.703 −0.0928329 −0.0464164 0.998922i \(-0.514780\pi\)
−0.0464164 + 0.998922i \(0.514780\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 906.939 0.255002 0.127501 0.991838i \(-0.459304\pi\)
0.127501 + 0.991838i \(0.459304\pi\)
\(234\) 0 0
\(235\) 2667.80 0.740544
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4290.84 −1.16130 −0.580651 0.814152i \(-0.697202\pi\)
−0.580651 + 0.814152i \(0.697202\pi\)
\(240\) 0 0
\(241\) −6985.64 −1.86716 −0.933579 0.358373i \(-0.883332\pi\)
−0.933579 + 0.358373i \(0.883332\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −994.903 −0.259437
\(246\) 0 0
\(247\) 3098.06 0.798077
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5666.63 −1.42500 −0.712499 0.701673i \(-0.752437\pi\)
−0.712499 + 0.701673i \(0.752437\pi\)
\(252\) 0 0
\(253\) −4579.02 −1.13787
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −840.596 −0.204027 −0.102013 0.994783i \(-0.532528\pi\)
−0.102013 + 0.994783i \(0.532528\pi\)
\(258\) 0 0
\(259\) 2505.35 0.601062
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3386.69 0.794039 0.397019 0.917810i \(-0.370045\pi\)
0.397019 + 0.917810i \(0.370045\pi\)
\(264\) 0 0
\(265\) 4064.38 0.942163
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7929.42 −1.79727 −0.898635 0.438698i \(-0.855440\pi\)
−0.898635 + 0.438698i \(0.855440\pi\)
\(270\) 0 0
\(271\) −5080.25 −1.13876 −0.569379 0.822075i \(-0.692816\pi\)
−0.569379 + 0.822075i \(0.692816\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8879.83 −1.94718
\(276\) 0 0
\(277\) −195.329 −0.0423688 −0.0211844 0.999776i \(-0.506744\pi\)
−0.0211844 + 0.999776i \(0.506744\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4029.83 −0.855514 −0.427757 0.903894i \(-0.640696\pi\)
−0.427757 + 0.903894i \(0.640696\pi\)
\(282\) 0 0
\(283\) −6927.28 −1.45507 −0.727534 0.686072i \(-0.759333\pi\)
−0.727534 + 0.686072i \(0.759333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3267.16 0.671967
\(288\) 0 0
\(289\) 5641.93 1.14837
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 911.009 0.181644 0.0908221 0.995867i \(-0.471051\pi\)
0.0908221 + 0.995867i \(0.471051\pi\)
\(294\) 0 0
\(295\) 12018.2 2.37195
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7496.55 1.44996
\(300\) 0 0
\(301\) −1298.97 −0.248742
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1431.76 −0.268795
\(306\) 0 0
\(307\) −3310.72 −0.615482 −0.307741 0.951470i \(-0.599573\pi\)
−0.307741 + 0.951470i \(0.599573\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4979.13 0.907847 0.453924 0.891041i \(-0.350024\pi\)
0.453924 + 0.891041i \(0.350024\pi\)
\(312\) 0 0
\(313\) −5116.19 −0.923911 −0.461955 0.886903i \(-0.652852\pi\)
−0.461955 + 0.886903i \(0.652852\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −978.317 −0.173337 −0.0866684 0.996237i \(-0.527622\pi\)
−0.0866684 + 0.996237i \(0.527622\pi\)
\(318\) 0 0
\(319\) 4921.77 0.863843
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6289.22 1.08341
\(324\) 0 0
\(325\) 14537.6 2.48124
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 919.742 0.154125
\(330\) 0 0
\(331\) −9092.36 −1.50985 −0.754926 0.655810i \(-0.772327\pi\)
−0.754926 + 0.655810i \(0.772327\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13056.4 −2.12939
\(336\) 0 0
\(337\) −621.406 −0.100445 −0.0502227 0.998738i \(-0.515993\pi\)
−0.0502227 + 0.998738i \(0.515993\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3747.09 −0.595063
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4276.85 0.661652 0.330826 0.943692i \(-0.392673\pi\)
0.330826 + 0.943692i \(0.392673\pi\)
\(348\) 0 0
\(349\) −7497.41 −1.14993 −0.574967 0.818177i \(-0.694985\pi\)
−0.574967 + 0.818177i \(0.694985\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2295.77 0.346151 0.173076 0.984909i \(-0.444629\pi\)
0.173076 + 0.984909i \(0.444629\pi\)
\(354\) 0 0
\(355\) 10606.8 1.58578
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 681.808 0.100235 0.0501176 0.998743i \(-0.484040\pi\)
0.0501176 + 0.998743i \(0.484040\pi\)
\(360\) 0 0
\(361\) −3111.54 −0.453643
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11698.7 1.67764
\(366\) 0 0
\(367\) −8497.77 −1.20867 −0.604333 0.796732i \(-0.706560\pi\)
−0.604333 + 0.796732i \(0.706560\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1401.23 0.196086
\(372\) 0 0
\(373\) 12306.1 1.70828 0.854138 0.520046i \(-0.174085\pi\)
0.854138 + 0.520046i \(0.174085\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8057.67 −1.10077
\(378\) 0 0
\(379\) −7064.19 −0.957423 −0.478711 0.877972i \(-0.658896\pi\)
−0.478711 + 0.877972i \(0.658896\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3082.91 0.411304 0.205652 0.978625i \(-0.434069\pi\)
0.205652 + 0.978625i \(0.434069\pi\)
\(384\) 0 0
\(385\) −4393.55 −0.581600
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9990.11 −1.30210 −0.651052 0.759033i \(-0.725672\pi\)
−0.651052 + 0.759033i \(0.725672\pi\)
\(390\) 0 0
\(391\) 15218.4 1.96835
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5700.87 0.726182
\(396\) 0 0
\(397\) 8327.91 1.05281 0.526405 0.850234i \(-0.323540\pi\)
0.526405 + 0.850234i \(0.323540\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9715.82 1.20994 0.604969 0.796249i \(-0.293185\pi\)
0.604969 + 0.796249i \(0.293185\pi\)
\(402\) 0 0
\(403\) 6134.56 0.758273
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11063.8 1.34745
\(408\) 0 0
\(409\) 13341.8 1.61299 0.806493 0.591244i \(-0.201363\pi\)
0.806493 + 0.591244i \(0.201363\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4143.35 0.493659
\(414\) 0 0
\(415\) 11324.3 1.33949
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4281.34 0.499181 0.249591 0.968351i \(-0.419704\pi\)
0.249591 + 0.968351i \(0.419704\pi\)
\(420\) 0 0
\(421\) −3296.60 −0.381631 −0.190815 0.981626i \(-0.561113\pi\)
−0.190815 + 0.981626i \(0.561113\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 29512.1 3.36834
\(426\) 0 0
\(427\) −493.610 −0.0559426
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4122.73 0.460754 0.230377 0.973101i \(-0.426004\pi\)
0.230377 + 0.973101i \(0.426004\pi\)
\(432\) 0 0
\(433\) 1070.60 0.118822 0.0594110 0.998234i \(-0.481078\pi\)
0.0594110 + 0.998234i \(0.481078\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9067.94 0.992628
\(438\) 0 0
\(439\) −6.22847 −0.000677150 0 −0.000338575 1.00000i \(-0.500108\pi\)
−0.000338575 1.00000i \(0.500108\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6835.85 −0.733140 −0.366570 0.930390i \(-0.619468\pi\)
−0.366570 + 0.930390i \(0.619468\pi\)
\(444\) 0 0
\(445\) −24951.6 −2.65802
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5590.94 −0.587646 −0.293823 0.955860i \(-0.594928\pi\)
−0.293823 + 0.955860i \(0.594928\pi\)
\(450\) 0 0
\(451\) 14428.0 1.50640
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 7192.90 0.741117
\(456\) 0 0
\(457\) −7615.65 −0.779530 −0.389765 0.920914i \(-0.627444\pi\)
−0.389765 + 0.920914i \(0.627444\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12191.7 −1.23172 −0.615860 0.787855i \(-0.711192\pi\)
−0.615860 + 0.787855i \(0.711192\pi\)
\(462\) 0 0
\(463\) −4210.28 −0.422610 −0.211305 0.977420i \(-0.567771\pi\)
−0.211305 + 0.977420i \(0.567771\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16128.2 1.59812 0.799062 0.601248i \(-0.205330\pi\)
0.799062 + 0.601248i \(0.205330\pi\)
\(468\) 0 0
\(469\) −4501.29 −0.443177
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5736.32 −0.557624
\(474\) 0 0
\(475\) 17584.9 1.69864
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3736.70 −0.356438 −0.178219 0.983991i \(-0.557034\pi\)
−0.178219 + 0.983991i \(0.557034\pi\)
\(480\) 0 0
\(481\) −18113.1 −1.71702
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1320.61 −0.123641
\(486\) 0 0
\(487\) −15812.5 −1.47132 −0.735661 0.677350i \(-0.763128\pi\)
−0.735661 + 0.677350i \(0.763128\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2564.56 0.235717 0.117858 0.993030i \(-0.462397\pi\)
0.117858 + 0.993030i \(0.462397\pi\)
\(492\) 0 0
\(493\) −16357.5 −1.49433
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3656.78 0.330038
\(498\) 0 0
\(499\) 8511.36 0.763569 0.381784 0.924251i \(-0.375310\pi\)
0.381784 + 0.924251i \(0.375310\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6486.89 0.575022 0.287511 0.957777i \(-0.407172\pi\)
0.287511 + 0.957777i \(0.407172\pi\)
\(504\) 0 0
\(505\) 6162.53 0.543027
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13980.3 1.21742 0.608710 0.793393i \(-0.291687\pi\)
0.608710 + 0.793393i \(0.291687\pi\)
\(510\) 0 0
\(511\) 4033.23 0.349157
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3538.35 0.302754
\(516\) 0 0
\(517\) 4061.63 0.345513
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10684.8 0.898485 0.449242 0.893410i \(-0.351694\pi\)
0.449242 + 0.893410i \(0.351694\pi\)
\(522\) 0 0
\(523\) −2500.29 −0.209044 −0.104522 0.994523i \(-0.533331\pi\)
−0.104522 + 0.994523i \(0.533331\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12453.4 1.02938
\(528\) 0 0
\(529\) 9775.18 0.803418
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −23620.8 −1.91957
\(534\) 0 0
\(535\) −39500.0 −3.19203
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1514.71 −0.121045
\(540\) 0 0
\(541\) −8780.94 −0.697823 −0.348911 0.937156i \(-0.613449\pi\)
−0.348911 + 0.937156i \(0.613449\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 22392.7 1.76000
\(546\) 0 0
\(547\) 10965.6 0.857140 0.428570 0.903509i \(-0.359018\pi\)
0.428570 + 0.903509i \(0.359018\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9746.69 −0.753580
\(552\) 0 0
\(553\) 1965.42 0.151136
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3156.31 −0.240103 −0.120051 0.992768i \(-0.538306\pi\)
−0.120051 + 0.992768i \(0.538306\pi\)
\(558\) 0 0
\(559\) 9391.22 0.710566
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −16805.3 −1.25801 −0.629003 0.777403i \(-0.716536\pi\)
−0.629003 + 0.777403i \(0.716536\pi\)
\(564\) 0 0
\(565\) 1626.01 0.121074
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16899.6 1.24511 0.622557 0.782575i \(-0.286094\pi\)
0.622557 + 0.782575i \(0.286094\pi\)
\(570\) 0 0
\(571\) 7998.44 0.586207 0.293104 0.956081i \(-0.405312\pi\)
0.293104 + 0.956081i \(0.405312\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 42551.2 3.08610
\(576\) 0 0
\(577\) 23385.2 1.68724 0.843619 0.536942i \(-0.180421\pi\)
0.843619 + 0.536942i \(0.180421\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3904.13 0.278779
\(582\) 0 0
\(583\) 6187.90 0.439582
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7583.02 −0.533194 −0.266597 0.963808i \(-0.585899\pi\)
−0.266597 + 0.963808i \(0.585899\pi\)
\(588\) 0 0
\(589\) 7420.46 0.519108
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10593.1 −0.733567 −0.366783 0.930306i \(-0.619541\pi\)
−0.366783 + 0.930306i \(0.619541\pi\)
\(594\) 0 0
\(595\) 14601.9 1.00609
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −22125.1 −1.50919 −0.754597 0.656188i \(-0.772168\pi\)
−0.754597 + 0.656188i \(0.772168\pi\)
\(600\) 0 0
\(601\) −19841.6 −1.34669 −0.673343 0.739331i \(-0.735142\pi\)
−0.673343 + 0.739331i \(0.735142\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7622.64 0.512239
\(606\) 0 0
\(607\) −15507.5 −1.03695 −0.518475 0.855093i \(-0.673500\pi\)
−0.518475 + 0.855093i \(0.673500\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6649.51 −0.440279
\(612\) 0 0
\(613\) −14042.8 −0.925255 −0.462628 0.886553i \(-0.653093\pi\)
−0.462628 + 0.886553i \(0.653093\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13175.9 −0.859708 −0.429854 0.902898i \(-0.641435\pi\)
−0.429854 + 0.902898i \(0.641435\pi\)
\(618\) 0 0
\(619\) −10828.3 −0.703109 −0.351555 0.936167i \(-0.614347\pi\)
−0.351555 + 0.936167i \(0.614347\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8602.25 −0.553197
\(624\) 0 0
\(625\) 30984.9 1.98303
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −36770.4 −2.33089
\(630\) 0 0
\(631\) 23922.2 1.50923 0.754617 0.656166i \(-0.227823\pi\)
0.754617 + 0.656166i \(0.227823\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −40225.0 −2.51383
\(636\) 0 0
\(637\) 2479.81 0.154244
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21962.6 1.35331 0.676654 0.736301i \(-0.263429\pi\)
0.676654 + 0.736301i \(0.263429\pi\)
\(642\) 0 0
\(643\) −17927.1 −1.09950 −0.549749 0.835330i \(-0.685276\pi\)
−0.549749 + 0.835330i \(0.685276\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 850.926 0.0517054 0.0258527 0.999666i \(-0.491770\pi\)
0.0258527 + 0.999666i \(0.491770\pi\)
\(648\) 0 0
\(649\) 18297.3 1.10667
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −18674.9 −1.11915 −0.559575 0.828780i \(-0.689036\pi\)
−0.559575 + 0.828780i \(0.689036\pi\)
\(654\) 0 0
\(655\) −57953.0 −3.45712
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −777.121 −0.0459368 −0.0229684 0.999736i \(-0.507312\pi\)
−0.0229684 + 0.999736i \(0.507312\pi\)
\(660\) 0 0
\(661\) 21963.4 1.29240 0.646201 0.763167i \(-0.276357\pi\)
0.646201 + 0.763167i \(0.276357\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 8700.64 0.507363
\(666\) 0 0
\(667\) −23584.6 −1.36911
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2179.81 −0.125411
\(672\) 0 0
\(673\) 29380.0 1.68279 0.841393 0.540423i \(-0.181736\pi\)
0.841393 + 0.540423i \(0.181736\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7898.58 −0.448400 −0.224200 0.974543i \(-0.571977\pi\)
−0.224200 + 0.974543i \(0.571977\pi\)
\(678\) 0 0
\(679\) −455.289 −0.0257326
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3097.04 0.173507 0.0867533 0.996230i \(-0.472351\pi\)
0.0867533 + 0.996230i \(0.472351\pi\)
\(684\) 0 0
\(685\) −10872.3 −0.606439
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −10130.5 −0.560148
\(690\) 0 0
\(691\) −26926.3 −1.48238 −0.741189 0.671296i \(-0.765738\pi\)
−0.741189 + 0.671296i \(0.765738\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 47236.2 2.57809
\(696\) 0 0
\(697\) −47951.3 −2.60586
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 16209.3 0.873347 0.436674 0.899620i \(-0.356156\pi\)
0.436674 + 0.899620i \(0.356156\pi\)
\(702\) 0 0
\(703\) −21909.9 −1.17546
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2124.58 0.113017
\(708\) 0 0
\(709\) −8277.60 −0.438465 −0.219233 0.975673i \(-0.570355\pi\)
−0.219233 + 0.975673i \(0.570355\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 17955.7 0.943121
\(714\) 0 0
\(715\) 31764.3 1.66142
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2334.31 −0.121078 −0.0605389 0.998166i \(-0.519282\pi\)
−0.0605389 + 0.998166i \(0.519282\pi\)
\(720\) 0 0
\(721\) 1219.87 0.0630104
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −45736.2 −2.34290
\(726\) 0 0
\(727\) 18885.8 0.963462 0.481731 0.876319i \(-0.340008\pi\)
0.481731 + 0.876319i \(0.340008\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 19064.6 0.964611
\(732\) 0 0
\(733\) 3071.96 0.154796 0.0773980 0.997000i \(-0.475339\pi\)
0.0773980 + 0.997000i \(0.475339\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −19878.0 −0.993506
\(738\) 0 0
\(739\) 27388.4 1.36333 0.681663 0.731666i \(-0.261257\pi\)
0.681663 + 0.731666i \(0.261257\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30541.6 −1.50803 −0.754013 0.656859i \(-0.771885\pi\)
−0.754013 + 0.656859i \(0.771885\pi\)
\(744\) 0 0
\(745\) 41847.7 2.05796
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13617.9 −0.664337
\(750\) 0 0
\(751\) 36868.0 1.79139 0.895695 0.444670i \(-0.146679\pi\)
0.895695 + 0.444670i \(0.146679\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −22599.1 −1.08936
\(756\) 0 0
\(757\) 1804.07 0.0866184 0.0433092 0.999062i \(-0.486210\pi\)
0.0433092 + 0.999062i \(0.486210\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17838.8 0.849746 0.424873 0.905253i \(-0.360319\pi\)
0.424873 + 0.905253i \(0.360319\pi\)
\(762\) 0 0
\(763\) 7720.06 0.366298
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −29955.4 −1.41021
\(768\) 0 0
\(769\) 6804.58 0.319089 0.159544 0.987191i \(-0.448997\pi\)
0.159544 + 0.987191i \(0.448997\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 23600.9 1.09814 0.549072 0.835775i \(-0.314981\pi\)
0.549072 + 0.835775i \(0.314981\pi\)
\(774\) 0 0
\(775\) 34820.4 1.61392
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −28572.0 −1.31412
\(780\) 0 0
\(781\) 16148.5 0.739872
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 31213.5 1.41918
\(786\) 0 0
\(787\) −9183.98 −0.415977 −0.207988 0.978131i \(-0.566692\pi\)
−0.207988 + 0.978131i \(0.566692\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 560.579 0.0251983
\(792\) 0 0
\(793\) 3568.68 0.159808
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11076.9 −0.492302 −0.246151 0.969231i \(-0.579166\pi\)
−0.246151 + 0.969231i \(0.579166\pi\)
\(798\) 0 0
\(799\) −13498.8 −0.597690
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 17811.0 0.782734
\(804\) 0 0
\(805\) 21053.4 0.921783
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −32258.3 −1.40190 −0.700952 0.713209i \(-0.747241\pi\)
−0.700952 + 0.713209i \(0.747241\pi\)
\(810\) 0 0
\(811\) −17693.9 −0.766114 −0.383057 0.923725i \(-0.625129\pi\)
−0.383057 + 0.923725i \(0.625129\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −41491.9 −1.78331
\(816\) 0 0
\(817\) 11359.8 0.486448
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 18430.7 0.783480 0.391740 0.920076i \(-0.371873\pi\)
0.391740 + 0.920076i \(0.371873\pi\)
\(822\) 0 0
\(823\) 32285.9 1.36746 0.683729 0.729736i \(-0.260357\pi\)
0.683729 + 0.729736i \(0.260357\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 36266.1 1.52491 0.762453 0.647044i \(-0.223995\pi\)
0.762453 + 0.647044i \(0.223995\pi\)
\(828\) 0 0
\(829\) −31156.2 −1.30531 −0.652654 0.757656i \(-0.726345\pi\)
−0.652654 + 0.757656i \(0.726345\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5034.12 0.209390
\(834\) 0 0
\(835\) −51033.1 −2.11506
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −85.5051 −0.00351843 −0.00175922 0.999998i \(-0.500560\pi\)
−0.00175922 + 0.999998i \(0.500560\pi\)
\(840\) 0 0
\(841\) 960.906 0.0393992
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7394.70 −0.301048
\(846\) 0 0
\(847\) 2627.96 0.106609
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −53016.5 −2.13558
\(852\) 0 0
\(853\) 1148.37 0.0460956 0.0230478 0.999734i \(-0.492663\pi\)
0.0230478 + 0.999734i \(0.492663\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 11674.6 0.465340 0.232670 0.972556i \(-0.425254\pi\)
0.232670 + 0.972556i \(0.425254\pi\)
\(858\) 0 0
\(859\) 47503.1 1.88683 0.943413 0.331619i \(-0.107595\pi\)
0.943413 + 0.331619i \(0.107595\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −10361.9 −0.408717 −0.204359 0.978896i \(-0.565511\pi\)
−0.204359 + 0.978896i \(0.565511\pi\)
\(864\) 0 0
\(865\) 32303.8 1.26978
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 8679.39 0.338813
\(870\) 0 0
\(871\) 32543.2 1.26600
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 23061.5 0.890997
\(876\) 0 0
\(877\) −26153.1 −1.00699 −0.503493 0.863999i \(-0.667952\pi\)
−0.503493 + 0.863999i \(0.667952\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −35711.7 −1.36567 −0.682837 0.730571i \(-0.739254\pi\)
−0.682837 + 0.730571i \(0.739254\pi\)
\(882\) 0 0
\(883\) −5654.75 −0.215513 −0.107756 0.994177i \(-0.534367\pi\)
−0.107756 + 0.994177i \(0.534367\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8344.44 0.315873 0.157936 0.987449i \(-0.449516\pi\)
0.157936 + 0.987449i \(0.449516\pi\)
\(888\) 0 0
\(889\) −13867.9 −0.523187
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −8043.35 −0.301411
\(894\) 0 0
\(895\) −51821.7 −1.93543
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −19299.7 −0.715996
\(900\) 0 0
\(901\) −20565.4 −0.760415
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 68249.0 2.50682
\(906\) 0 0
\(907\) −52612.1 −1.92608 −0.963040 0.269358i \(-0.913188\pi\)
−0.963040 + 0.269358i \(0.913188\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24706.6 −0.898536 −0.449268 0.893397i \(-0.648315\pi\)
−0.449268 + 0.893397i \(0.648315\pi\)
\(912\) 0 0
\(913\) 17240.8 0.624960
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −19979.7 −0.719508
\(918\) 0 0
\(919\) −42479.2 −1.52477 −0.762383 0.647127i \(-0.775970\pi\)
−0.762383 + 0.647127i \(0.775970\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −26437.6 −0.942799
\(924\) 0 0
\(925\) −102812. −3.65452
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −9423.54 −0.332805 −0.166403 0.986058i \(-0.553215\pi\)
−0.166403 + 0.986058i \(0.553215\pi\)
\(930\) 0 0
\(931\) 2999.61 0.105594
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 64483.0 2.25542
\(936\) 0 0
\(937\) −33158.7 −1.15608 −0.578041 0.816008i \(-0.696183\pi\)
−0.578041 + 0.816008i \(0.696183\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −15005.1 −0.519822 −0.259911 0.965633i \(-0.583693\pi\)
−0.259911 + 0.965633i \(0.583693\pi\)
\(942\) 0 0
\(943\) −69137.3 −2.38751
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 7631.38 0.261865 0.130933 0.991391i \(-0.458203\pi\)
0.130933 + 0.991391i \(0.458203\pi\)
\(948\) 0 0
\(949\) −29159.2 −0.997417
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 42615.3 1.44853 0.724263 0.689524i \(-0.242180\pi\)
0.724263 + 0.689524i \(0.242180\pi\)
\(954\) 0 0
\(955\) 78549.5 2.66157
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −3748.32 −0.126214
\(960\) 0 0
\(961\) −15097.6 −0.506782
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −54682.4 −1.82413
\(966\) 0 0
\(967\) −34795.1 −1.15712 −0.578559 0.815640i \(-0.696385\pi\)
−0.578559 + 0.815640i \(0.696385\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 7714.99 0.254980 0.127490 0.991840i \(-0.459308\pi\)
0.127490 + 0.991840i \(0.459308\pi\)
\(972\) 0 0
\(973\) 16285.0 0.536561
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −22817.7 −0.747188 −0.373594 0.927592i \(-0.621875\pi\)
−0.373594 + 0.927592i \(0.621875\pi\)
\(978\) 0 0
\(979\) −37988.0 −1.24015
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −10924.8 −0.354473 −0.177237 0.984168i \(-0.556716\pi\)
−0.177237 + 0.984168i \(0.556716\pi\)
\(984\) 0 0
\(985\) −21621.0 −0.699393
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 27487.8 0.883784
\(990\) 0 0
\(991\) 49279.5 1.57963 0.789816 0.613343i \(-0.210176\pi\)
0.789816 + 0.613343i \(0.210176\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 33012.8 1.05184
\(996\) 0 0
\(997\) −49601.6 −1.57563 −0.787813 0.615914i \(-0.788787\pi\)
−0.787813 + 0.615914i \(0.788787\pi\)
\(998\) 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 1008.4.a.y.1.1 2
3.2 odd 2 336.4.a.n.1.2 2
4.3 odd 2 504.4.a.j.1.1 2
12.11 even 2 168.4.a.h.1.2 2
21.20 even 2 2352.4.a.bv.1.1 2
24.5 odd 2 1344.4.a.bl.1.1 2
24.11 even 2 1344.4.a.bd.1.1 2
84.83 odd 2 1176.4.a.p.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.4.a.h.1.2 2 12.11 even 2
336.4.a.n.1.2 2 3.2 odd 2
504.4.a.j.1.1 2 4.3 odd 2
1008.4.a.y.1.1 2 1.1 even 1 trivial
1176.4.a.p.1.1 2 84.83 odd 2
1344.4.a.bd.1.1 2 24.11 even 2
1344.4.a.bl.1.1 2 24.5 odd 2
2352.4.a.bv.1.1 2 21.20 even 2