Properties

Label 1008.4.a.be.1.2
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{19}) \)
Defining polynomial: \(x^{2} - 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 63)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(4.35890\) of defining polynomial
Character \(\chi\) \(=\) 1008.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.71780 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q+8.71780 q^{5} +7.00000 q^{7} +43.5890 q^{11} +82.0000 q^{13} -78.4602 q^{17} +20.0000 q^{19} +130.767 q^{23} -49.0000 q^{25} +244.098 q^{29} -156.000 q^{31} +61.0246 q^{35} +186.000 q^{37} -165.638 q^{41} -164.000 q^{43} -470.761 q^{47} +49.0000 q^{49} -156.920 q^{53} +380.000 q^{55} -156.920 q^{59} +790.000 q^{61} +714.859 q^{65} +44.0000 q^{67} -444.608 q^{71} +126.000 q^{73} +305.123 q^{77} +712.000 q^{79} +1464.59 q^{83} -684.000 q^{85} -1455.87 q^{89} +574.000 q^{91} +174.356 q^{95} +798.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 14q^{7} + O(q^{10}) \) \( 2q + 14q^{7} + 164q^{13} + 40q^{19} - 98q^{25} - 312q^{31} + 372q^{37} - 328q^{43} + 98q^{49} + 760q^{55} + 1580q^{61} + 88q^{67} + 252q^{73} + 1424q^{79} - 1368q^{85} + 1148q^{91} + 1596q^{97} + O(q^{100}) \)

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
\(5\) 8.71780 0.779744 0.389872 0.920869i \(-0.372519\pi\)
0.389872 + 0.920869i \(0.372519\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 43.5890 1.19478 0.597390 0.801951i \(-0.296205\pi\)
0.597390 + 0.801951i \(0.296205\pi\)
\(12\) 0 0
\(13\) 82.0000 1.74944 0.874720 0.484629i \(-0.161046\pi\)
0.874720 + 0.484629i \(0.161046\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −78.4602 −1.11938 −0.559688 0.828703i \(-0.689079\pi\)
−0.559688 + 0.828703i \(0.689079\pi\)
\(18\) 0 0
\(19\) 20.0000 0.241490 0.120745 0.992684i \(-0.461472\pi\)
0.120745 + 0.992684i \(0.461472\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 130.767 1.18551 0.592756 0.805382i \(-0.298040\pi\)
0.592756 + 0.805382i \(0.298040\pi\)
\(24\) 0 0
\(25\) −49.0000 −0.392000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 244.098 1.56303 0.781516 0.623885i \(-0.214447\pi\)
0.781516 + 0.623885i \(0.214447\pi\)
\(30\) 0 0
\(31\) −156.000 −0.903820 −0.451910 0.892063i \(-0.649257\pi\)
−0.451910 + 0.892063i \(0.649257\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 61.0246 0.294715
\(36\) 0 0
\(37\) 186.000 0.826438 0.413219 0.910632i \(-0.364404\pi\)
0.413219 + 0.910632i \(0.364404\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −165.638 −0.630935 −0.315467 0.948936i \(-0.602161\pi\)
−0.315467 + 0.948936i \(0.602161\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −470.761 −1.46101 −0.730506 0.682906i \(-0.760716\pi\)
−0.730506 + 0.682906i \(0.760716\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −156.920 −0.406692 −0.203346 0.979107i \(-0.565182\pi\)
−0.203346 + 0.979107i \(0.565182\pi\)
\(54\) 0 0
\(55\) 380.000 0.931622
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −156.920 −0.346259 −0.173130 0.984899i \(-0.555388\pi\)
−0.173130 + 0.984899i \(0.555388\pi\)
\(60\) 0 0
\(61\) 790.000 1.65818 0.829091 0.559113i \(-0.188858\pi\)
0.829091 + 0.559113i \(0.188858\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 714.859 1.36411
\(66\) 0 0
\(67\) 44.0000 0.0802307 0.0401153 0.999195i \(-0.487227\pi\)
0.0401153 + 0.999195i \(0.487227\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −444.608 −0.743172 −0.371586 0.928398i \(-0.621186\pi\)
−0.371586 + 0.928398i \(0.621186\pi\)
\(72\) 0 0
\(73\) 126.000 0.202016 0.101008 0.994886i \(-0.467793\pi\)
0.101008 + 0.994886i \(0.467793\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 305.123 0.451584
\(78\) 0 0
\(79\) 712.000 1.01400 0.507002 0.861945i \(-0.330754\pi\)
0.507002 + 0.861945i \(0.330754\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1464.59 1.93686 0.968432 0.249280i \(-0.0801938\pi\)
0.968432 + 0.249280i \(0.0801938\pi\)
\(84\) 0 0
\(85\) −684.000 −0.872826
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1455.87 −1.73396 −0.866978 0.498346i \(-0.833941\pi\)
−0.866978 + 0.498346i \(0.833941\pi\)
\(90\) 0 0
\(91\) 574.000 0.661226
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 174.356 0.188300
\(96\) 0 0
\(97\) 798.000 0.835305 0.417653 0.908607i \(-0.362853\pi\)
0.417653 + 0.908607i \(0.362853\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 409.737 0.403666 0.201833 0.979420i \(-0.435310\pi\)
0.201833 + 0.979420i \(0.435310\pi\)
\(102\) 0 0
\(103\) 916.000 0.876273 0.438137 0.898908i \(-0.355639\pi\)
0.438137 + 0.898908i \(0.355639\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −897.933 −0.811275 −0.405638 0.914034i \(-0.632951\pi\)
−0.405638 + 0.914034i \(0.632951\pi\)
\(108\) 0 0
\(109\) −342.000 −0.300529 −0.150264 0.988646i \(-0.548013\pi\)
−0.150264 + 0.988646i \(0.548013\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −488.197 −0.406422 −0.203211 0.979135i \(-0.565138\pi\)
−0.203211 + 0.979135i \(0.565138\pi\)
\(114\) 0 0
\(115\) 1140.00 0.924396
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −549.221 −0.423084
\(120\) 0 0
\(121\) 569.000 0.427498
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1516.90 −1.08540
\(126\) 0 0
\(127\) −456.000 −0.318610 −0.159305 0.987229i \(-0.550925\pi\)
−0.159305 + 0.987229i \(0.550925\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1499.46 −1.00007 −0.500033 0.866007i \(-0.666679\pi\)
−0.500033 + 0.866007i \(0.666679\pi\)
\(132\) 0 0
\(133\) 140.000 0.0912747
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −889.215 −0.554531 −0.277266 0.960793i \(-0.589428\pi\)
−0.277266 + 0.960793i \(0.589428\pi\)
\(138\) 0 0
\(139\) 768.000 0.468640 0.234320 0.972160i \(-0.424714\pi\)
0.234320 + 0.972160i \(0.424714\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3574.30 2.09019
\(144\) 0 0
\(145\) 2128.00 1.21876
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 993.829 0.546427 0.273214 0.961953i \(-0.411913\pi\)
0.273214 + 0.961953i \(0.411913\pi\)
\(150\) 0 0
\(151\) 3496.00 1.88411 0.942054 0.335460i \(-0.108892\pi\)
0.942054 + 0.335460i \(0.108892\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1359.98 −0.704748
\(156\) 0 0
\(157\) −506.000 −0.257218 −0.128609 0.991695i \(-0.541051\pi\)
−0.128609 + 0.991695i \(0.541051\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 915.369 0.448082
\(162\) 0 0
\(163\) 2564.00 1.23207 0.616037 0.787717i \(-0.288737\pi\)
0.616037 + 0.787717i \(0.288737\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 645.117 0.298926 0.149463 0.988767i \(-0.452245\pi\)
0.149463 + 0.988767i \(0.452245\pi\)
\(168\) 0 0
\(169\) 4527.00 2.06054
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3861.98 1.69723 0.848616 0.529009i \(-0.177436\pi\)
0.848616 + 0.529009i \(0.177436\pi\)
\(174\) 0 0
\(175\) −343.000 −0.148162
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 270.252 0.112847 0.0564234 0.998407i \(-0.482030\pi\)
0.0564234 + 0.998407i \(0.482030\pi\)
\(180\) 0 0
\(181\) 418.000 0.171656 0.0858279 0.996310i \(-0.472646\pi\)
0.0858279 + 0.996310i \(0.472646\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1621.51 0.644410
\(186\) 0 0
\(187\) −3420.00 −1.33741
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1525.61 −0.577956 −0.288978 0.957336i \(-0.593315\pi\)
−0.288978 + 0.957336i \(0.593315\pi\)
\(192\) 0 0
\(193\) 1358.00 0.506482 0.253241 0.967403i \(-0.418503\pi\)
0.253241 + 0.967403i \(0.418503\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3748.65 1.35574 0.677869 0.735183i \(-0.262904\pi\)
0.677869 + 0.735183i \(0.262904\pi\)
\(198\) 0 0
\(199\) 1056.00 0.376170 0.188085 0.982153i \(-0.439772\pi\)
0.188085 + 0.982153i \(0.439772\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1708.69 0.590771
\(204\) 0 0
\(205\) −1444.00 −0.491967
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 871.780 0.288528
\(210\) 0 0
\(211\) 3620.00 1.18110 0.590548 0.807003i \(-0.298912\pi\)
0.590548 + 0.807003i \(0.298912\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1429.72 −0.453516
\(216\) 0 0
\(217\) −1092.00 −0.341612
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6433.73 −1.95828
\(222\) 0 0
\(223\) −5368.00 −1.61196 −0.805982 0.591940i \(-0.798362\pi\)
−0.805982 + 0.591940i \(0.798362\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1621.51 −0.474112 −0.237056 0.971496i \(-0.576182\pi\)
−0.237056 + 0.971496i \(0.576182\pi\)
\(228\) 0 0
\(229\) 2186.00 0.630808 0.315404 0.948958i \(-0.397860\pi\)
0.315404 + 0.948958i \(0.397860\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4132.24 −1.16185 −0.580927 0.813956i \(-0.697310\pi\)
−0.580927 + 0.813956i \(0.697310\pi\)
\(234\) 0 0
\(235\) −4104.00 −1.13921
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4838.38 1.30949 0.654746 0.755849i \(-0.272776\pi\)
0.654746 + 0.755849i \(0.272776\pi\)
\(240\) 0 0
\(241\) 1286.00 0.343728 0.171864 0.985121i \(-0.445021\pi\)
0.171864 + 0.985121i \(0.445021\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 427.172 0.111392
\(246\) 0 0
\(247\) 1640.00 0.422472
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1795.87 0.451610 0.225805 0.974173i \(-0.427499\pi\)
0.225805 + 0.974173i \(0.427499\pi\)
\(252\) 0 0
\(253\) 5700.00 1.41643
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1944.07 −0.471859 −0.235929 0.971770i \(-0.575813\pi\)
−0.235929 + 0.971770i \(0.575813\pi\)
\(258\) 0 0
\(259\) 1302.00 0.312364
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5344.01 −1.25295 −0.626475 0.779442i \(-0.715503\pi\)
−0.626475 + 0.779442i \(0.715503\pi\)
\(264\) 0 0
\(265\) −1368.00 −0.317115
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4001.47 −0.906966 −0.453483 0.891265i \(-0.649819\pi\)
−0.453483 + 0.891265i \(0.649819\pi\)
\(270\) 0 0
\(271\) −2788.00 −0.624941 −0.312470 0.949928i \(-0.601156\pi\)
−0.312470 + 0.949928i \(0.601156\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2135.86 −0.468354
\(276\) 0 0
\(277\) −4562.00 −0.989545 −0.494773 0.869022i \(-0.664749\pi\)
−0.494773 + 0.869022i \(0.664749\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1551.77 −0.329433 −0.164717 0.986341i \(-0.552671\pi\)
−0.164717 + 0.986341i \(0.552671\pi\)
\(282\) 0 0
\(283\) 6788.00 1.42581 0.712906 0.701260i \(-0.247379\pi\)
0.712906 + 0.701260i \(0.247379\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1159.47 −0.238471
\(288\) 0 0
\(289\) 1243.00 0.253002
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1142.03 0.227707 0.113854 0.993498i \(-0.463681\pi\)
0.113854 + 0.993498i \(0.463681\pi\)
\(294\) 0 0
\(295\) −1368.00 −0.269993
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10722.9 2.07398
\(300\) 0 0
\(301\) −1148.00 −0.219833
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6887.06 1.29296
\(306\) 0 0
\(307\) −532.000 −0.0989018 −0.0494509 0.998777i \(-0.515747\pi\)
−0.0494509 + 0.998777i \(0.515747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6538.35 −1.19214 −0.596070 0.802932i \(-0.703272\pi\)
−0.596070 + 0.802932i \(0.703272\pi\)
\(312\) 0 0
\(313\) 4994.00 0.901845 0.450923 0.892563i \(-0.351095\pi\)
0.450923 + 0.892563i \(0.351095\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −470.761 −0.0834088 −0.0417044 0.999130i \(-0.513279\pi\)
−0.0417044 + 0.999130i \(0.513279\pi\)
\(318\) 0 0
\(319\) 10640.0 1.86748
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1569.20 −0.270318
\(324\) 0 0
\(325\) −4018.00 −0.685780
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3295.33 −0.552211
\(330\) 0 0
\(331\) −2588.00 −0.429756 −0.214878 0.976641i \(-0.568935\pi\)
−0.214878 + 0.976641i \(0.568935\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 383.583 0.0625594
\(336\) 0 0
\(337\) 238.000 0.0384709 0.0192354 0.999815i \(-0.493877\pi\)
0.0192354 + 0.999815i \(0.493877\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6799.88 −1.07987
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7052.70 −1.09109 −0.545546 0.838081i \(-0.683678\pi\)
−0.545546 + 0.838081i \(0.683678\pi\)
\(348\) 0 0
\(349\) −10850.0 −1.66415 −0.832073 0.554666i \(-0.812846\pi\)
−0.832073 + 0.554666i \(0.812846\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5291.70 0.797872 0.398936 0.916979i \(-0.369379\pi\)
0.398936 + 0.916979i \(0.369379\pi\)
\(354\) 0 0
\(355\) −3876.00 −0.579484
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4820.94 0.708745 0.354373 0.935104i \(-0.384694\pi\)
0.354373 + 0.935104i \(0.384694\pi\)
\(360\) 0 0
\(361\) −6459.00 −0.941682
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1098.44 0.157521
\(366\) 0 0
\(367\) −11712.0 −1.66583 −0.832917 0.553397i \(-0.813331\pi\)
−0.832917 + 0.553397i \(0.813331\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1098.44 −0.153715
\(372\) 0 0
\(373\) −10450.0 −1.45062 −0.725309 0.688423i \(-0.758303\pi\)
−0.725309 + 0.688423i \(0.758303\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 20016.1 2.73443
\(378\) 0 0
\(379\) 756.000 0.102462 0.0512310 0.998687i \(-0.483686\pi\)
0.0512310 + 0.998687i \(0.483686\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6381.43 −0.851373 −0.425686 0.904871i \(-0.639967\pi\)
−0.425686 + 0.904871i \(0.639967\pi\)
\(384\) 0 0
\(385\) 2660.00 0.352120
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −418.454 −0.0545411 −0.0272705 0.999628i \(-0.508682\pi\)
−0.0272705 + 0.999628i \(0.508682\pi\)
\(390\) 0 0
\(391\) −10260.0 −1.32703
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6207.07 0.790663
\(396\) 0 0
\(397\) −5802.00 −0.733486 −0.366743 0.930322i \(-0.619527\pi\)
−0.366743 + 0.930322i \(0.619527\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4132.24 −0.514599 −0.257299 0.966332i \(-0.582833\pi\)
−0.257299 + 0.966332i \(0.582833\pi\)
\(402\) 0 0
\(403\) −12792.0 −1.58118
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8107.55 0.987411
\(408\) 0 0
\(409\) −1330.00 −0.160793 −0.0803964 0.996763i \(-0.525619\pi\)
−0.0803964 + 0.996763i \(0.525619\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1098.44 −0.130874
\(414\) 0 0
\(415\) 12768.0 1.51026
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10409.1 −1.21364 −0.606820 0.794839i \(-0.707555\pi\)
−0.606820 + 0.794839i \(0.707555\pi\)
\(420\) 0 0
\(421\) −12274.0 −1.42090 −0.710449 0.703749i \(-0.751508\pi\)
−0.710449 + 0.703749i \(0.751508\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3844.55 0.438795
\(426\) 0 0
\(427\) 5530.00 0.626734
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4681.46 0.523197 0.261598 0.965177i \(-0.415750\pi\)
0.261598 + 0.965177i \(0.415750\pi\)
\(432\) 0 0
\(433\) 5770.00 0.640389 0.320195 0.947352i \(-0.396252\pi\)
0.320195 + 0.947352i \(0.396252\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2615.34 0.286290
\(438\) 0 0
\(439\) 1872.00 0.203521 0.101760 0.994809i \(-0.467552\pi\)
0.101760 + 0.994809i \(0.467552\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11115.2 1.19210 0.596048 0.802949i \(-0.296737\pi\)
0.596048 + 0.802949i \(0.296737\pi\)
\(444\) 0 0
\(445\) −12692.0 −1.35204
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7636.79 −0.802678 −0.401339 0.915930i \(-0.631455\pi\)
−0.401339 + 0.915930i \(0.631455\pi\)
\(450\) 0 0
\(451\) −7220.00 −0.753828
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5004.02 0.515587
\(456\) 0 0
\(457\) 15142.0 1.54992 0.774959 0.632011i \(-0.217770\pi\)
0.774959 + 0.632011i \(0.217770\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −13190.0 −1.33258 −0.666292 0.745691i \(-0.732119\pi\)
−0.666292 + 0.745691i \(0.732119\pi\)
\(462\) 0 0
\(463\) −9328.00 −0.936304 −0.468152 0.883648i \(-0.655080\pi\)
−0.468152 + 0.883648i \(0.655080\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3399.94 −0.336896 −0.168448 0.985711i \(-0.553876\pi\)
−0.168448 + 0.985711i \(0.553876\pi\)
\(468\) 0 0
\(469\) 308.000 0.0303243
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −7148.59 −0.694911
\(474\) 0 0
\(475\) −980.000 −0.0946642
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3574.30 −0.340947 −0.170474 0.985362i \(-0.554530\pi\)
−0.170474 + 0.985362i \(0.554530\pi\)
\(480\) 0 0
\(481\) 15252.0 1.44580
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6956.80 0.651324
\(486\) 0 0
\(487\) −8968.00 −0.834454 −0.417227 0.908802i \(-0.636998\pi\)
−0.417227 + 0.908802i \(0.636998\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5169.65 −0.475159 −0.237580 0.971368i \(-0.576354\pi\)
−0.237580 + 0.971368i \(0.576354\pi\)
\(492\) 0 0
\(493\) −19152.0 −1.74962
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3112.25 −0.280893
\(498\) 0 0
\(499\) −3940.00 −0.353464 −0.176732 0.984259i \(-0.556553\pi\)
−0.176732 + 0.984259i \(0.556553\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10252.1 −0.908787 −0.454394 0.890801i \(-0.650144\pi\)
−0.454394 + 0.890801i \(0.650144\pi\)
\(504\) 0 0
\(505\) 3572.00 0.314756
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9772.65 0.851012 0.425506 0.904956i \(-0.360096\pi\)
0.425506 + 0.904956i \(0.360096\pi\)
\(510\) 0 0
\(511\) 882.000 0.0763550
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7985.50 0.683269
\(516\) 0 0
\(517\) −20520.0 −1.74559
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7401.41 −0.622383 −0.311192 0.950347i \(-0.600728\pi\)
−0.311192 + 0.950347i \(0.600728\pi\)
\(522\) 0 0
\(523\) 2768.00 0.231427 0.115713 0.993283i \(-0.463085\pi\)
0.115713 + 0.993283i \(0.463085\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12239.8 1.01171
\(528\) 0 0
\(529\) 4933.00 0.405441
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −13582.3 −1.10378
\(534\) 0 0
\(535\) −7828.00 −0.632587
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2135.86 0.170683
\(540\) 0 0
\(541\) 16310.0 1.29616 0.648079 0.761573i \(-0.275573\pi\)
0.648079 + 0.761573i \(0.275573\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2981.49 −0.234336
\(546\) 0 0
\(547\) −11140.0 −0.870771 −0.435386 0.900244i \(-0.643388\pi\)
−0.435386 + 0.900244i \(0.643388\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4881.97 0.377457
\(552\) 0 0
\(553\) 4984.00 0.383257
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22788.3 1.73352 0.866761 0.498723i \(-0.166197\pi\)
0.866761 + 0.498723i \(0.166197\pi\)
\(558\) 0 0
\(559\) −13448.0 −1.01751
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 11524.9 0.862732 0.431366 0.902177i \(-0.358032\pi\)
0.431366 + 0.902177i \(0.358032\pi\)
\(564\) 0 0
\(565\) −4256.00 −0.316905
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1691.25 −0.124606 −0.0623032 0.998057i \(-0.519845\pi\)
−0.0623032 + 0.998057i \(0.519845\pi\)
\(570\) 0 0
\(571\) −11228.0 −0.822902 −0.411451 0.911432i \(-0.634978\pi\)
−0.411451 + 0.911432i \(0.634978\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6407.58 −0.464721
\(576\) 0 0
\(577\) 2050.00 0.147907 0.0739537 0.997262i \(-0.476438\pi\)
0.0739537 + 0.997262i \(0.476438\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10252.1 0.732065
\(582\) 0 0
\(583\) −6840.00 −0.485907
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18394.6 −1.29340 −0.646699 0.762745i \(-0.723851\pi\)
−0.646699 + 0.762745i \(0.723851\pi\)
\(588\) 0 0
\(589\) −3120.00 −0.218264
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12632.1 −0.874769 −0.437384 0.899275i \(-0.644095\pi\)
−0.437384 + 0.899275i \(0.644095\pi\)
\(594\) 0 0
\(595\) −4788.00 −0.329897
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9598.30 0.654717 0.327359 0.944900i \(-0.393841\pi\)
0.327359 + 0.944900i \(0.393841\pi\)
\(600\) 0 0
\(601\) −10758.0 −0.730163 −0.365082 0.930976i \(-0.618959\pi\)
−0.365082 + 0.930976i \(0.618959\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4960.43 0.333339
\(606\) 0 0
\(607\) 21352.0 1.42776 0.713881 0.700268i \(-0.246936\pi\)
0.713881 + 0.700268i \(0.246936\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −38602.4 −2.55595
\(612\) 0 0
\(613\) −5714.00 −0.376487 −0.188243 0.982122i \(-0.560279\pi\)
−0.188243 + 0.982122i \(0.560279\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6747.58 0.440271 0.220135 0.975469i \(-0.429350\pi\)
0.220135 + 0.975469i \(0.429350\pi\)
\(618\) 0 0
\(619\) 1880.00 0.122074 0.0610368 0.998136i \(-0.480559\pi\)
0.0610368 + 0.998136i \(0.480559\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −10191.1 −0.655374
\(624\) 0 0
\(625\) −7099.00 −0.454336
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −14593.6 −0.925095
\(630\) 0 0
\(631\) 28888.0 1.82252 0.911262 0.411826i \(-0.135109\pi\)
0.911262 + 0.411826i \(0.135109\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3975.32 −0.248434
\(636\) 0 0
\(637\) 4018.00 0.249920
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 25996.5 1.60187 0.800935 0.598751i \(-0.204336\pi\)
0.800935 + 0.598751i \(0.204336\pi\)
\(642\) 0 0
\(643\) −24788.0 −1.52029 −0.760143 0.649756i \(-0.774871\pi\)
−0.760143 + 0.649756i \(0.774871\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28472.3 −1.73008 −0.865041 0.501702i \(-0.832708\pi\)
−0.865041 + 0.501702i \(0.832708\pi\)
\(648\) 0 0
\(649\) −6840.00 −0.413703
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3243.02 0.194348 0.0971740 0.995267i \(-0.469020\pi\)
0.0971740 + 0.995267i \(0.469020\pi\)
\(654\) 0 0
\(655\) −13072.0 −0.779794
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1176.90 −0.0695685 −0.0347842 0.999395i \(-0.511074\pi\)
−0.0347842 + 0.999395i \(0.511074\pi\)
\(660\) 0 0
\(661\) 11590.0 0.681995 0.340998 0.940064i \(-0.389235\pi\)
0.340998 + 0.940064i \(0.389235\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1220.49 0.0711709
\(666\) 0 0
\(667\) 31920.0 1.85299
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 34435.3 1.98116
\(672\) 0 0
\(673\) 23062.0 1.32091 0.660457 0.750864i \(-0.270363\pi\)
0.660457 + 0.750864i \(0.270363\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −22884.2 −1.29913 −0.649566 0.760305i \(-0.725049\pi\)
−0.649566 + 0.760305i \(0.725049\pi\)
\(678\) 0 0
\(679\) 5586.00 0.315716
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24715.0 1.38461 0.692307 0.721603i \(-0.256594\pi\)
0.692307 + 0.721603i \(0.256594\pi\)
\(684\) 0 0
\(685\) −7752.00 −0.432392
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −12867.5 −0.711483
\(690\) 0 0
\(691\) 10600.0 0.583564 0.291782 0.956485i \(-0.405752\pi\)
0.291782 + 0.956485i \(0.405752\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6695.27 0.365419
\(696\) 0 0
\(697\) 12996.0 0.706253
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12449.0 0.670746 0.335373 0.942085i \(-0.391138\pi\)
0.335373 + 0.942085i \(0.391138\pi\)
\(702\) 0 0
\(703\) 3720.00 0.199577
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2868.16 0.152572
\(708\) 0 0
\(709\) −13710.0 −0.726220 −0.363110 0.931746i \(-0.618285\pi\)
−0.363110 + 0.931746i \(0.618285\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −20399.6 −1.07149
\(714\) 0 0
\(715\) 31160.0 1.62982
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2510.73 0.130228 0.0651142 0.997878i \(-0.479259\pi\)
0.0651142 + 0.997878i \(0.479259\pi\)
\(720\) 0 0
\(721\) 6412.00 0.331200
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −11960.8 −0.612708
\(726\) 0 0
\(727\) −620.000 −0.0316293 −0.0158147 0.999875i \(-0.505034\pi\)
−0.0158147 + 0.999875i \(0.505034\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 12867.5 0.651054
\(732\) 0 0
\(733\) −20214.0 −1.01858 −0.509291 0.860594i \(-0.670092\pi\)
−0.509291 + 0.860594i \(0.670092\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1917.92 0.0958580
\(738\) 0 0
\(739\) 12324.0 0.613458 0.306729 0.951797i \(-0.400765\pi\)
0.306729 + 0.951797i \(0.400765\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −29736.4 −1.46827 −0.734134 0.679005i \(-0.762412\pi\)
−0.734134 + 0.679005i \(0.762412\pi\)
\(744\) 0 0
\(745\) 8664.00 0.426073
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6285.53 −0.306633
\(750\) 0 0
\(751\) −19336.0 −0.939522 −0.469761 0.882794i \(-0.655660\pi\)
−0.469761 + 0.882794i \(0.655660\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 30477.4 1.46912
\(756\) 0 0
\(757\) 15986.0 0.767531 0.383766 0.923431i \(-0.374627\pi\)
0.383766 + 0.923431i \(0.374627\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 37007.1 1.76282 0.881409 0.472354i \(-0.156596\pi\)
0.881409 + 0.472354i \(0.156596\pi\)
\(762\) 0 0
\(763\) −2394.00 −0.113589
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12867.5 −0.605759
\(768\) 0 0
\(769\) −36070.0 −1.69144 −0.845720 0.533627i \(-0.820829\pi\)
−0.845720 + 0.533627i \(0.820829\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −531.786 −0.0247439 −0.0123719 0.999923i \(-0.503938\pi\)
−0.0123719 + 0.999923i \(0.503938\pi\)
\(774\) 0 0
\(775\) 7644.00 0.354298
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3312.76 −0.152365
\(780\) 0 0
\(781\) −19380.0 −0.887927
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4411.21 −0.200564
\(786\) 0 0
\(787\) 1136.00 0.0514537 0.0257268 0.999669i \(-0.491810\pi\)
0.0257268 + 0.999669i \(0.491810\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3417.38 −0.153613
\(792\) 0 0
\(793\) 64780.0 2.90089
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18054.6 0.802416 0.401208 0.915987i \(-0.368591\pi\)
0.401208 + 0.915987i \(0.368591\pi\)
\(798\) 0 0
\(799\) 36936.0 1.63542
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5492.21 0.241365
\(804\) 0 0
\(805\) 7980.00 0.349389
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −38707.0 −1.68216 −0.841079 0.540912i \(-0.818079\pi\)
−0.841079 + 0.540912i \(0.818079\pi\)
\(810\) 0 0
\(811\) −17936.0 −0.776595 −0.388297 0.921534i \(-0.626937\pi\)
−0.388297 + 0.921534i \(0.626937\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 22352.4 0.960701
\(816\) 0 0
\(817\) −3280.00 −0.140456
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 24915.5 1.05914 0.529571 0.848266i \(-0.322353\pi\)
0.529571 + 0.848266i \(0.322353\pi\)
\(822\) 0 0
\(823\) −23424.0 −0.992113 −0.496057 0.868290i \(-0.665219\pi\)
−0.496057 + 0.868290i \(0.665219\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 26650.3 1.12058 0.560291 0.828296i \(-0.310689\pi\)
0.560291 + 0.828296i \(0.310689\pi\)
\(828\) 0 0
\(829\) −26254.0 −1.09993 −0.549963 0.835189i \(-0.685358\pi\)
−0.549963 + 0.835189i \(0.685358\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3844.55 −0.159911
\(834\) 0 0
\(835\) 5624.00 0.233086
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 6189.64 0.254696 0.127348 0.991858i \(-0.459353\pi\)
0.127348 + 0.991858i \(0.459353\pi\)
\(840\) 0 0
\(841\) 35195.0 1.44307
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 39465.5 1.60669
\(846\) 0 0
\(847\) 3983.00 0.161579
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 24322.7 0.979753
\(852\) 0 0
\(853\) −45322.0 −1.81922 −0.909611 0.415462i \(-0.863620\pi\)
−0.909611 + 0.415462i \(0.863620\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 8691.64 0.346442 0.173221 0.984883i \(-0.444582\pi\)
0.173221 + 0.984883i \(0.444582\pi\)
\(858\) 0 0
\(859\) 43252.0 1.71797 0.858987 0.511998i \(-0.171094\pi\)
0.858987 + 0.511998i \(0.171094\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 29318.0 1.15642 0.578212 0.815886i \(-0.303750\pi\)
0.578212 + 0.815886i \(0.303750\pi\)
\(864\) 0 0
\(865\) 33668.0 1.32341
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 31035.4 1.21151
\(870\) 0 0
\(871\) 3608.00 0.140359
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −10618.3 −0.410244
\(876\) 0 0
\(877\) 47110.0 1.81390 0.906951 0.421237i \(-0.138404\pi\)
0.906951 + 0.421237i \(0.138404\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −42133.1 −1.61124 −0.805619 0.592434i \(-0.798167\pi\)
−0.805619 + 0.592434i \(0.798167\pi\)
\(882\) 0 0
\(883\) 22732.0 0.866356 0.433178 0.901308i \(-0.357392\pi\)
0.433178 + 0.901308i \(0.357392\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −21463.2 −0.812474 −0.406237 0.913768i \(-0.633159\pi\)
−0.406237 + 0.913768i \(0.633159\pi\)
\(888\) 0 0
\(889\) −3192.00 −0.120423
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −9415.22 −0.352820
\(894\) 0 0
\(895\) 2356.00 0.0879915
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −38079.3 −1.41270
\(900\) 0 0
\(901\) 12312.0 0.455241
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3644.04 0.133847
\(906\) 0 0
\(907\) 6916.00 0.253189 0.126594 0.991955i \(-0.459595\pi\)
0.126594 + 0.991955i \(0.459595\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −38210.1 −1.38963 −0.694817 0.719186i \(-0.744515\pi\)
−0.694817 + 0.719186i \(0.744515\pi\)
\(912\) 0 0
\(913\) 63840.0 2.31412
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −10496.2 −0.377989
\(918\) 0 0
\(919\) 47632.0 1.70972 0.854861 0.518857i \(-0.173642\pi\)
0.854861 + 0.518857i \(0.173642\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −36457.8 −1.30013
\(924\) 0 0
\(925\) −9114.00 −0.323964
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3304.05 −0.116687 −0.0583435 0.998297i \(-0.518582\pi\)
−0.0583435 + 0.998297i \(0.518582\pi\)
\(930\) 0 0
\(931\) 980.000 0.0344986
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −29814.9 −1.04283
\(936\) 0 0
\(937\) 21858.0 0.762081 0.381040 0.924558i \(-0.375566\pi\)
0.381040 + 0.924558i \(0.375566\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −50380.2 −1.74532 −0.872660 0.488328i \(-0.837607\pi\)
−0.872660 + 0.488328i \(0.837607\pi\)
\(942\) 0 0
\(943\) −21660.0 −0.747982
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −31061.5 −1.06585 −0.532927 0.846161i \(-0.678908\pi\)
−0.532927 + 0.846161i \(0.678908\pi\)
\(948\) 0 0
\(949\) 10332.0 0.353415
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 22770.9 0.773999 0.387000 0.922080i \(-0.373511\pi\)
0.387000 + 0.922080i \(0.373511\pi\)
\(954\) 0 0
\(955\) −13300.0 −0.450657
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6224.51 −0.209593
\(960\) 0 0
\(961\) −5455.00 −0.183109
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 11838.8 0.394926
\(966\) 0 0
\(967\) 36416.0 1.21102 0.605512 0.795836i \(-0.292968\pi\)
0.605512 + 0.795836i \(0.292968\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 18621.2 0.615431 0.307715 0.951478i \(-0.400436\pi\)
0.307715 + 0.951478i \(0.400436\pi\)
\(972\) 0 0
\(973\) 5376.00 0.177129
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −5806.05 −0.190125 −0.0950625 0.995471i \(-0.530305\pi\)
−0.0950625 + 0.995471i \(0.530305\pi\)
\(978\) 0 0
\(979\) −63460.0 −2.07170
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3243.02 0.105225 0.0526126 0.998615i \(-0.483245\pi\)
0.0526126 + 0.998615i \(0.483245\pi\)
\(984\) 0 0
\(985\) 32680.0 1.05713
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −21445.8 −0.689521
\(990\) 0 0
\(991\) −49448.0 −1.58503 −0.792516 0.609851i \(-0.791229\pi\)
−0.792516 + 0.609851i \(0.791229\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 9205.99 0.293316
\(996\) 0 0
\(997\) 16294.0 0.517589 0.258794 0.965932i \(-0.416675\pi\)
0.258794 + 0.965932i \(0.416675\pi\)
\(998\) 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.be.1.2 2
3.2 odd 2 inner 1008.4.a.be.1.1 2
4.3 odd 2 63.4.a.d.1.2 yes 2
12.11 even 2 63.4.a.d.1.1 2
20.19 odd 2 1575.4.a.t.1.1 2
28.3 even 6 441.4.e.s.226.1 4
28.11 odd 6 441.4.e.r.226.1 4
28.19 even 6 441.4.e.s.361.1 4
28.23 odd 6 441.4.e.r.361.1 4
28.27 even 2 441.4.a.q.1.2 2
60.59 even 2 1575.4.a.t.1.2 2
84.11 even 6 441.4.e.r.226.2 4
84.23 even 6 441.4.e.r.361.2 4
84.47 odd 6 441.4.e.s.361.2 4
84.59 odd 6 441.4.e.s.226.2 4
84.83 odd 2 441.4.a.q.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.a.d.1.1 2 12.11 even 2
63.4.a.d.1.2 yes 2 4.3 odd 2
441.4.a.q.1.1 2 84.83 odd 2
441.4.a.q.1.2 2 28.27 even 2
441.4.e.r.226.1 4 28.11 odd 6
441.4.e.r.226.2 4 84.11 even 6
441.4.e.r.361.1 4 28.23 odd 6
441.4.e.r.361.2 4 84.23 even 6
441.4.e.s.226.1 4 28.3 even 6
441.4.e.s.226.2 4 84.59 odd 6
441.4.e.s.361.1 4 28.19 even 6
441.4.e.s.361.2 4 84.47 odd 6
1008.4.a.be.1.1 2 3.2 odd 2 inner
1008.4.a.be.1.2 2 1.1 even 1 trivial
1575.4.a.t.1.1 2 20.19 odd 2
1575.4.a.t.1.2 2 60.59 even 2