Properties

Label 8280.2.a.bs.1.5
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.13955077.1
Defining polynomial: \(x^{5} - 14 x^{3} - x^{2} + 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.568386\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +4.73770 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +4.73770 q^{7} +0.360532 q^{11} +5.26123 q^{13} -0.370852 q^{17} -4.60586 q^{19} +1.00000 q^{23} +1.00000 q^{25} -0.939238 q^{29} +9.66662 q^{31} +4.73770 q^{35} +3.26862 q^{37} -5.29977 q^{41} +1.25491 q^{47} +15.4458 q^{49} -10.9278 q^{53} +0.360532 q^{55} +9.66955 q^{59} +9.71441 q^{61} +5.26123 q^{65} -7.07001 q^{67} -11.3747 q^{71} +0.745086 q^{73} +1.70809 q^{77} +0.415709 q^{79} +9.26862 q^{83} -0.370852 q^{85} -12.6122 q^{89} +24.9261 q^{91} -4.60586 q^{95} +14.0404 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 5q^{5} - 2q^{7} + O(q^{10}) \) \( 5q + 5q^{5} - 2q^{7} + q^{11} + 4q^{13} - 4q^{17} + 7q^{19} + 5q^{23} + 5q^{25} - 4q^{29} + 19q^{31} - 2q^{35} + 15q^{37} - 25q^{41} + 11q^{47} + 25q^{49} - 3q^{53} + q^{55} + q^{59} - 5q^{61} + 4q^{65} + 9q^{67} - q^{71} - q^{73} - 18q^{77} - 2q^{79} + 45q^{83} - 4q^{85} - 6q^{89} + 11q^{91} + 7q^{95} + 25q^{97} + O(q^{100}) \)

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
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 4.73770 1.79068 0.895341 0.445381i \(-0.146932\pi\)
0.895341 + 0.445381i \(0.146932\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.360532 0.108704 0.0543522 0.998522i \(-0.482691\pi\)
0.0543522 + 0.998522i \(0.482691\pi\)
\(12\) 0 0
\(13\) 5.26123 1.45920 0.729601 0.683873i \(-0.239706\pi\)
0.729601 + 0.683873i \(0.239706\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.370852 −0.0899449 −0.0449724 0.998988i \(-0.514320\pi\)
−0.0449724 + 0.998988i \(0.514320\pi\)
\(18\) 0 0
\(19\) −4.60586 −1.05666 −0.528328 0.849040i \(-0.677181\pi\)
−0.528328 + 0.849040i \(0.677181\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.939238 −0.174412 −0.0872061 0.996190i \(-0.527794\pi\)
−0.0872061 + 0.996190i \(0.527794\pi\)
\(30\) 0 0
\(31\) 9.66662 1.73618 0.868088 0.496411i \(-0.165349\pi\)
0.868088 + 0.496411i \(0.165349\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.73770 0.800817
\(36\) 0 0
\(37\) 3.26862 0.537357 0.268679 0.963230i \(-0.413413\pi\)
0.268679 + 0.963230i \(0.413413\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.29977 −0.827685 −0.413843 0.910348i \(-0.635814\pi\)
−0.413843 + 0.910348i \(0.635814\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.25491 0.183048 0.0915240 0.995803i \(-0.470826\pi\)
0.0915240 + 0.995803i \(0.470826\pi\)
\(48\) 0 0
\(49\) 15.4458 2.20654
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10.9278 −1.50106 −0.750528 0.660839i \(-0.770201\pi\)
−0.750528 + 0.660839i \(0.770201\pi\)
\(54\) 0 0
\(55\) 0.360532 0.0486141
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.66955 1.25887 0.629434 0.777054i \(-0.283287\pi\)
0.629434 + 0.777054i \(0.283287\pi\)
\(60\) 0 0
\(61\) 9.71441 1.24380 0.621901 0.783096i \(-0.286361\pi\)
0.621901 + 0.783096i \(0.286361\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.26123 0.652575
\(66\) 0 0
\(67\) −7.07001 −0.863739 −0.431870 0.901936i \(-0.642146\pi\)
−0.431870 + 0.901936i \(0.642146\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −11.3747 −1.34993 −0.674965 0.737850i \(-0.735841\pi\)
−0.674965 + 0.737850i \(0.735841\pi\)
\(72\) 0 0
\(73\) 0.745086 0.0872057 0.0436029 0.999049i \(-0.486116\pi\)
0.0436029 + 0.999049i \(0.486116\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.70809 0.194655
\(78\) 0 0
\(79\) 0.415709 0.0467709 0.0233854 0.999727i \(-0.492556\pi\)
0.0233854 + 0.999727i \(0.492556\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 9.26862 1.01736 0.508681 0.860955i \(-0.330133\pi\)
0.508681 + 0.860955i \(0.330133\pi\)
\(84\) 0 0
\(85\) −0.370852 −0.0402246
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −12.6122 −1.33689 −0.668444 0.743763i \(-0.733039\pi\)
−0.668444 + 0.743763i \(0.733039\pi\)
\(90\) 0 0
\(91\) 24.9261 2.61297
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.60586 −0.472551
\(96\) 0 0
\(97\) 14.0404 1.42559 0.712793 0.701374i \(-0.247430\pi\)
0.712793 + 0.701374i \(0.247430\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.7440 1.26808 0.634038 0.773302i \(-0.281396\pi\)
0.634038 + 0.773302i \(0.281396\pi\)
\(102\) 0 0
\(103\) −3.31347 −0.326486 −0.163243 0.986586i \(-0.552195\pi\)
−0.163243 + 0.986586i \(0.552195\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.13184 0.786135 0.393067 0.919510i \(-0.371414\pi\)
0.393067 + 0.919510i \(0.371414\pi\)
\(108\) 0 0
\(109\) −5.79508 −0.555068 −0.277534 0.960716i \(-0.589517\pi\)
−0.277534 + 0.960716i \(0.589517\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.60724 0.715629 0.357815 0.933793i \(-0.383522\pi\)
0.357815 + 0.933793i \(0.383522\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.75699 −0.161063
\(120\) 0 0
\(121\) −10.8700 −0.988183
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.13077 −0.366547 −0.183273 0.983062i \(-0.558669\pi\)
−0.183273 + 0.983062i \(0.558669\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 17.7582 1.55154 0.775770 0.631016i \(-0.217362\pi\)
0.775770 + 0.631016i \(0.217362\pi\)
\(132\) 0 0
\(133\) −21.8212 −1.89213
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.86954 −0.586905 −0.293452 0.955974i \(-0.594804\pi\)
−0.293452 + 0.955974i \(0.594804\pi\)
\(138\) 0 0
\(139\) 20.6635 1.75266 0.876330 0.481712i \(-0.159985\pi\)
0.876330 + 0.481712i \(0.159985\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.89684 0.158622
\(144\) 0 0
\(145\) −0.939238 −0.0779995
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 16.4763 1.34979 0.674896 0.737912i \(-0.264188\pi\)
0.674896 + 0.737912i \(0.264188\pi\)
\(150\) 0 0
\(151\) −8.89224 −0.723640 −0.361820 0.932248i \(-0.617844\pi\)
−0.361820 + 0.932248i \(0.617844\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.66662 0.776441
\(156\) 0 0
\(157\) −6.62249 −0.528532 −0.264266 0.964450i \(-0.585130\pi\)
−0.264266 + 0.964450i \(0.585130\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.73770 0.373383
\(162\) 0 0
\(163\) −16.0779 −1.25932 −0.629658 0.776872i \(-0.716805\pi\)
−0.629658 + 0.776872i \(0.716805\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −13.8763 −1.07378 −0.536891 0.843651i \(-0.680402\pi\)
−0.536891 + 0.843651i \(0.680402\pi\)
\(168\) 0 0
\(169\) 14.6805 1.12927
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.05518 0.156252 0.0781261 0.996943i \(-0.475106\pi\)
0.0781261 + 0.996943i \(0.475106\pi\)
\(174\) 0 0
\(175\) 4.73770 0.358136
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −17.6478 −1.31906 −0.659531 0.751678i \(-0.729245\pi\)
−0.659531 + 0.751678i \(0.729245\pi\)
\(180\) 0 0
\(181\) 2.85477 0.212193 0.106097 0.994356i \(-0.466165\pi\)
0.106097 + 0.994356i \(0.466165\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.26862 0.240313
\(186\) 0 0
\(187\) −0.133704 −0.00977741
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.13677 −0.0822540 −0.0411270 0.999154i \(-0.513095\pi\)
−0.0411270 + 0.999154i \(0.513095\pi\)
\(192\) 0 0
\(193\) −26.4694 −1.90531 −0.952654 0.304055i \(-0.901659\pi\)
−0.952654 + 0.304055i \(0.901659\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.44424 −0.387886 −0.193943 0.981013i \(-0.562128\pi\)
−0.193943 + 0.981013i \(0.562128\pi\)
\(198\) 0 0
\(199\) −18.6122 −1.31938 −0.659691 0.751537i \(-0.729313\pi\)
−0.659691 + 0.751537i \(0.729313\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.44983 −0.312317
\(204\) 0 0
\(205\) −5.29977 −0.370152
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.66056 −0.114863
\(210\) 0 0
\(211\) 6.10003 0.419944 0.209972 0.977707i \(-0.432663\pi\)
0.209972 + 0.977707i \(0.432663\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 45.7975 3.10894
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.95114 −0.131248
\(222\) 0 0
\(223\) −16.4136 −1.09913 −0.549567 0.835450i \(-0.685207\pi\)
−0.549567 + 0.835450i \(0.685207\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.21171 −0.0804240 −0.0402120 0.999191i \(-0.512803\pi\)
−0.0402120 + 0.999191i \(0.512803\pi\)
\(228\) 0 0
\(229\) −22.8293 −1.50860 −0.754300 0.656529i \(-0.772024\pi\)
−0.754300 + 0.656529i \(0.772024\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.9420 −1.43747 −0.718735 0.695284i \(-0.755278\pi\)
−0.718735 + 0.695284i \(0.755278\pi\)
\(234\) 0 0
\(235\) 1.25491 0.0818616
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.58274 0.555172 0.277586 0.960701i \(-0.410466\pi\)
0.277586 + 0.960701i \(0.410466\pi\)
\(240\) 0 0
\(241\) 15.3857 0.991079 0.495540 0.868585i \(-0.334970\pi\)
0.495540 + 0.868585i \(0.334970\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 15.4458 0.986795
\(246\) 0 0
\(247\) −24.2325 −1.54187
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.85477 0.558908 0.279454 0.960159i \(-0.409847\pi\)
0.279454 + 0.960159i \(0.409847\pi\)
\(252\) 0 0
\(253\) 0.360532 0.0226664
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.6008 1.40980 0.704899 0.709308i \(-0.250992\pi\)
0.704899 + 0.709308i \(0.250992\pi\)
\(258\) 0 0
\(259\) 15.4857 0.962236
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7.73590 0.477016 0.238508 0.971141i \(-0.423342\pi\)
0.238508 + 0.971141i \(0.423342\pi\)
\(264\) 0 0
\(265\) −10.9278 −0.671292
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.87154 0.236052 0.118026 0.993011i \(-0.462343\pi\)
0.118026 + 0.993011i \(0.462343\pi\)
\(270\) 0 0
\(271\) 4.24705 0.257990 0.128995 0.991645i \(-0.458825\pi\)
0.128995 + 0.991645i \(0.458825\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.360532 0.0217409
\(276\) 0 0
\(277\) −7.26754 −0.436664 −0.218332 0.975875i \(-0.570062\pi\)
−0.218332 + 0.975875i \(0.570062\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 13.0131 0.776297 0.388148 0.921597i \(-0.373115\pi\)
0.388148 + 0.921597i \(0.373115\pi\)
\(282\) 0 0
\(283\) 17.8342 1.06013 0.530067 0.847956i \(-0.322167\pi\)
0.530067 + 0.847956i \(0.322167\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −25.1087 −1.48212
\(288\) 0 0
\(289\) −16.8625 −0.991910
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.32291 −0.427809 −0.213905 0.976855i \(-0.568618\pi\)
−0.213905 + 0.976855i \(0.568618\pi\)
\(294\) 0 0
\(295\) 9.66955 0.562983
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.26123 0.304265
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.71441 0.556245
\(306\) 0 0
\(307\) −29.1127 −1.66155 −0.830775 0.556608i \(-0.812103\pi\)
−0.830775 + 0.556608i \(0.812103\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.458912 −0.0260225 −0.0130113 0.999915i \(-0.504142\pi\)
−0.0130113 + 0.999915i \(0.504142\pi\)
\(312\) 0 0
\(313\) −17.8279 −1.00769 −0.503846 0.863794i \(-0.668082\pi\)
−0.503846 + 0.863794i \(0.668082\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −23.8799 −1.34123 −0.670614 0.741807i \(-0.733969\pi\)
−0.670614 + 0.741807i \(0.733969\pi\)
\(318\) 0 0
\(319\) −0.338625 −0.0189594
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.70809 0.0950407
\(324\) 0 0
\(325\) 5.26123 0.291840
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.94540 0.327781
\(330\) 0 0
\(331\) 30.0214 1.65013 0.825063 0.565041i \(-0.191140\pi\)
0.825063 + 0.565041i \(0.191140\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7.07001 −0.386276
\(336\) 0 0
\(337\) 11.9440 0.650631 0.325316 0.945605i \(-0.394529\pi\)
0.325316 + 0.945605i \(0.394529\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.48512 0.188730
\(342\) 0 0
\(343\) 40.0136 2.16053
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.873132 0.0468722 0.0234361 0.999725i \(-0.492539\pi\)
0.0234361 + 0.999725i \(0.492539\pi\)
\(348\) 0 0
\(349\) −18.8868 −1.01099 −0.505493 0.862831i \(-0.668689\pi\)
−0.505493 + 0.862831i \(0.668689\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5.43875 0.289475 0.144738 0.989470i \(-0.453766\pi\)
0.144738 + 0.989470i \(0.453766\pi\)
\(354\) 0 0
\(355\) −11.3747 −0.603707
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 23.4229 1.23622 0.618108 0.786093i \(-0.287899\pi\)
0.618108 + 0.786093i \(0.287899\pi\)
\(360\) 0 0
\(361\) 2.21390 0.116521
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.745086 0.0389996
\(366\) 0 0
\(367\) 27.2014 1.41990 0.709951 0.704252i \(-0.248717\pi\)
0.709951 + 0.704252i \(0.248717\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −51.7728 −2.68791
\(372\) 0 0
\(373\) 20.0431 1.03779 0.518897 0.854837i \(-0.326343\pi\)
0.518897 + 0.854837i \(0.326343\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.94155 −0.254503
\(378\) 0 0
\(379\) −12.8364 −0.659362 −0.329681 0.944092i \(-0.606941\pi\)
−0.329681 + 0.944092i \(0.606941\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 30.5405 1.56055 0.780273 0.625439i \(-0.215080\pi\)
0.780273 + 0.625439i \(0.215080\pi\)
\(384\) 0 0
\(385\) 1.70809 0.0870524
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −32.3392 −1.63966 −0.819831 0.572605i \(-0.805933\pi\)
−0.819831 + 0.572605i \(0.805933\pi\)
\(390\) 0 0
\(391\) −0.370852 −0.0187548
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.415709 0.0209166
\(396\) 0 0
\(397\) 28.9147 1.45119 0.725594 0.688123i \(-0.241565\pi\)
0.725594 + 0.688123i \(0.241565\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −24.2862 −1.21279 −0.606397 0.795162i \(-0.707386\pi\)
−0.606397 + 0.795162i \(0.707386\pi\)
\(402\) 0 0
\(403\) 50.8583 2.53343
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.17844 0.0584131
\(408\) 0 0
\(409\) 31.8371 1.57424 0.787122 0.616797i \(-0.211570\pi\)
0.787122 + 0.616797i \(0.211570\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 45.8114 2.25423
\(414\) 0 0
\(415\) 9.26862 0.454978
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 21.4880 1.04976 0.524879 0.851177i \(-0.324110\pi\)
0.524879 + 0.851177i \(0.324110\pi\)
\(420\) 0 0
\(421\) −13.2930 −0.647859 −0.323930 0.946081i \(-0.605004\pi\)
−0.323930 + 0.946081i \(0.605004\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.370852 −0.0179890
\(426\) 0 0
\(427\) 46.0239 2.22725
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.534460 0.0257440 0.0128720 0.999917i \(-0.495903\pi\)
0.0128720 + 0.999917i \(0.495903\pi\)
\(432\) 0 0
\(433\) 16.3377 0.785140 0.392570 0.919722i \(-0.371586\pi\)
0.392570 + 0.919722i \(0.371586\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.60586 −0.220328
\(438\) 0 0
\(439\) 28.7573 1.37251 0.686255 0.727361i \(-0.259254\pi\)
0.686255 + 0.727361i \(0.259254\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 15.6542 0.743751 0.371876 0.928283i \(-0.378715\pi\)
0.371876 + 0.928283i \(0.378715\pi\)
\(444\) 0 0
\(445\) −12.6122 −0.597874
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −38.4302 −1.81363 −0.906817 0.421525i \(-0.861495\pi\)
−0.906817 + 0.421525i \(0.861495\pi\)
\(450\) 0 0
\(451\) −1.91074 −0.0899730
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 24.9261 1.16855
\(456\) 0 0
\(457\) −37.2199 −1.74107 −0.870536 0.492104i \(-0.836228\pi\)
−0.870536 + 0.492104i \(0.836228\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.25491 0.151596 0.0757982 0.997123i \(-0.475850\pi\)
0.0757982 + 0.997123i \(0.475850\pi\)
\(462\) 0 0
\(463\) 29.9534 1.39205 0.696027 0.718016i \(-0.254950\pi\)
0.696027 + 0.718016i \(0.254950\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 39.3302 1.81999 0.909993 0.414623i \(-0.136087\pi\)
0.909993 + 0.414623i \(0.136087\pi\)
\(468\) 0 0
\(469\) −33.4956 −1.54668
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −4.60586 −0.211331
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.18660 −0.374055 −0.187028 0.982355i \(-0.559885\pi\)
−0.187028 + 0.982355i \(0.559885\pi\)
\(480\) 0 0
\(481\) 17.1969 0.784113
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 14.0404 0.637542
\(486\) 0 0
\(487\) −31.9963 −1.44989 −0.724946 0.688806i \(-0.758135\pi\)
−0.724946 + 0.688806i \(0.758135\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.12584 0.321585 0.160792 0.986988i \(-0.448595\pi\)
0.160792 + 0.986988i \(0.448595\pi\)
\(492\) 0 0
\(493\) 0.348319 0.0156875
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −53.8899 −2.41729
\(498\) 0 0
\(499\) 23.4219 1.04851 0.524254 0.851562i \(-0.324344\pi\)
0.524254 + 0.851562i \(0.324344\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.94170 0.175752 0.0878758 0.996131i \(-0.471992\pi\)
0.0878758 + 0.996131i \(0.471992\pi\)
\(504\) 0 0
\(505\) 12.7440 0.567101
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −38.5237 −1.70753 −0.853766 0.520656i \(-0.825687\pi\)
−0.853766 + 0.520656i \(0.825687\pi\)
\(510\) 0 0
\(511\) 3.52999 0.156158
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.31347 −0.146009
\(516\) 0 0
\(517\) 0.452436 0.0198981
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 39.2428 1.71926 0.859630 0.510917i \(-0.170694\pi\)
0.859630 + 0.510917i \(0.170694\pi\)
\(522\) 0 0
\(523\) −39.0190 −1.70618 −0.853090 0.521763i \(-0.825274\pi\)
−0.853090 + 0.521763i \(0.825274\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.58489 −0.156160
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −27.8833 −1.20776
\(534\) 0 0
\(535\) 8.13184 0.351570
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.56870 0.239861
\(540\) 0 0
\(541\) 2.54061 0.109230 0.0546148 0.998508i \(-0.482607\pi\)
0.0546148 + 0.998508i \(0.482607\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.79508 −0.248234
\(546\) 0 0
\(547\) 6.78776 0.290224 0.145112 0.989415i \(-0.453646\pi\)
0.145112 + 0.989415i \(0.453646\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.32600 0.184294
\(552\) 0 0
\(553\) 1.96950 0.0837517
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 24.7086 1.04694 0.523468 0.852045i \(-0.324638\pi\)
0.523468 + 0.852045i \(0.324638\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 28.1423 1.18606 0.593029 0.805181i \(-0.297932\pi\)
0.593029 + 0.805181i \(0.297932\pi\)
\(564\) 0 0
\(565\) 7.60724 0.320039
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −41.1938 −1.72694 −0.863468 0.504404i \(-0.831712\pi\)
−0.863468 + 0.504404i \(0.831712\pi\)
\(570\) 0 0
\(571\) 32.4687 1.35877 0.679387 0.733780i \(-0.262246\pi\)
0.679387 + 0.733780i \(0.262246\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 6.61770 0.275498 0.137749 0.990467i \(-0.456013\pi\)
0.137749 + 0.990467i \(0.456013\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 43.9119 1.82177
\(582\) 0 0
\(583\) −3.93984 −0.163171
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.18008 0.337628 0.168814 0.985648i \(-0.446006\pi\)
0.168814 + 0.985648i \(0.446006\pi\)
\(588\) 0 0
\(589\) −44.5230 −1.83454
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −29.7489 −1.22164 −0.610821 0.791768i \(-0.709161\pi\)
−0.610821 + 0.791768i \(0.709161\pi\)
\(594\) 0 0
\(595\) −1.75699 −0.0720294
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −39.4069 −1.61012 −0.805061 0.593192i \(-0.797868\pi\)
−0.805061 + 0.593192i \(0.797868\pi\)
\(600\) 0 0
\(601\) −34.3183 −1.39987 −0.699937 0.714205i \(-0.746788\pi\)
−0.699937 + 0.714205i \(0.746788\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −10.8700 −0.441929
\(606\) 0 0
\(607\) −11.7570 −0.477200 −0.238600 0.971118i \(-0.576688\pi\)
−0.238600 + 0.971118i \(0.576688\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.60239 0.267104
\(612\) 0 0
\(613\) 5.86862 0.237031 0.118516 0.992952i \(-0.462186\pi\)
0.118516 + 0.992952i \(0.462186\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.45842 0.340523 0.170262 0.985399i \(-0.445539\pi\)
0.170262 + 0.985399i \(0.445539\pi\)
\(618\) 0 0
\(619\) 0.851047 0.0342065 0.0171032 0.999854i \(-0.494556\pi\)
0.0171032 + 0.999854i \(0.494556\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −59.7527 −2.39394
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.21217 −0.0483325
\(630\) 0 0
\(631\) 19.7131 0.784768 0.392384 0.919802i \(-0.371650\pi\)
0.392384 + 0.919802i \(0.371650\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.13077 −0.163925
\(636\) 0 0
\(637\) 81.2638 3.21979
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 34.3593 1.35711 0.678555 0.734550i \(-0.262607\pi\)
0.678555 + 0.734550i \(0.262607\pi\)
\(642\) 0 0
\(643\) −24.2817 −0.957578 −0.478789 0.877930i \(-0.658924\pi\)
−0.478789 + 0.877930i \(0.658924\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.1465 1.18518 0.592590 0.805504i \(-0.298105\pi\)
0.592590 + 0.805504i \(0.298105\pi\)
\(648\) 0 0
\(649\) 3.48618 0.136845
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.17298 0.280700 0.140350 0.990102i \(-0.455177\pi\)
0.140350 + 0.990102i \(0.455177\pi\)
\(654\) 0 0
\(655\) 17.7582 0.693870
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12.8521 0.500645 0.250323 0.968162i \(-0.419463\pi\)
0.250323 + 0.968162i \(0.419463\pi\)
\(660\) 0 0
\(661\) 3.72426 0.144857 0.0724285 0.997374i \(-0.476925\pi\)
0.0724285 + 0.997374i \(0.476925\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −21.8212 −0.846188
\(666\) 0 0
\(667\) −0.939238 −0.0363675
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.50235 0.135207
\(672\) 0 0
\(673\) 13.5204 0.521175 0.260587 0.965450i \(-0.416084\pi\)
0.260587 + 0.965450i \(0.416084\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17.8534 0.686161 0.343081 0.939306i \(-0.388530\pi\)
0.343081 + 0.939306i \(0.388530\pi\)
\(678\) 0 0
\(679\) 66.5192 2.55277
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −15.8200 −0.605337 −0.302669 0.953096i \(-0.597878\pi\)
−0.302669 + 0.953096i \(0.597878\pi\)
\(684\) 0 0
\(685\) −6.86954 −0.262472
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −57.4939 −2.19034
\(690\) 0 0
\(691\) 9.45476 0.359676 0.179838 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.6635 0.783813
\(696\) 0 0
\(697\) 1.96543 0.0744460
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −29.0096 −1.09568 −0.547838 0.836584i \(-0.684549\pi\)
−0.547838 + 0.836584i \(0.684549\pi\)
\(702\) 0 0
\(703\) −15.0548 −0.567801
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 60.3773 2.27072
\(708\) 0 0
\(709\) −8.22423 −0.308868 −0.154434 0.988003i \(-0.549355\pi\)
−0.154434 + 0.988003i \(0.549355\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9.66662 0.362018
\(714\) 0 0
\(715\) 1.89684 0.0709378
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12.5468 0.467917 0.233958 0.972247i \(-0.424832\pi\)
0.233958 + 0.972247i \(0.424832\pi\)
\(720\) 0 0
\(721\) −15.6982 −0.584633
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.939238 −0.0348824
\(726\) 0 0
\(727\) −29.1952 −1.08279 −0.541395 0.840768i \(-0.682104\pi\)
−0.541395 + 0.840768i \(0.682104\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −36.0414 −1.33122 −0.665611 0.746299i \(-0.731829\pi\)
−0.665611 + 0.746299i \(0.731829\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.54896 −0.0938923
\(738\) 0 0
\(739\) 0.728002 0.0267800 0.0133900 0.999910i \(-0.495738\pi\)
0.0133900 + 0.999910i \(0.495738\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32.8880 1.20655 0.603273 0.797535i \(-0.293863\pi\)
0.603273 + 0.797535i \(0.293863\pi\)
\(744\) 0 0
\(745\) 16.4763 0.603646
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 38.5262 1.40772
\(750\) 0 0
\(751\) 14.3337 0.523044 0.261522 0.965197i \(-0.415776\pi\)
0.261522 + 0.965197i \(0.415776\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8.89224 −0.323622
\(756\) 0 0
\(757\) −0.0587519 −0.00213537 −0.00106769 0.999999i \(-0.500340\pi\)
−0.00106769 + 0.999999i \(0.500340\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −45.7135 −1.65711 −0.828556 0.559906i \(-0.810837\pi\)
−0.828556 + 0.559906i \(0.810837\pi\)
\(762\) 0 0
\(763\) −27.4553 −0.993950
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 50.8737 1.83694
\(768\) 0 0
\(769\) −39.3949 −1.42061 −0.710307 0.703892i \(-0.751444\pi\)
−0.710307 + 0.703892i \(0.751444\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −21.1799 −0.761788 −0.380894 0.924619i \(-0.624384\pi\)
−0.380894 + 0.924619i \(0.624384\pi\)
\(774\) 0 0
\(775\) 9.66662 0.347235
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 24.4100 0.874578
\(780\) 0 0
\(781\) −4.10094 −0.146743
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.62249 −0.236367
\(786\) 0 0
\(787\) 21.5154 0.766941 0.383470 0.923553i \(-0.374729\pi\)
0.383470 + 0.923553i \(0.374729\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 36.0408 1.28146
\(792\) 0 0
\(793\) 51.1097 1.81496
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 54.7227 1.93838 0.969189 0.246320i \(-0.0792215\pi\)
0.969189 + 0.246320i \(0.0792215\pi\)
\(798\) 0 0
\(799\) −0.465388 −0.0164642
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0.268627 0.00947965
\(804\) 0 0
\(805\) 4.73770 0.166982
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 43.5554 1.53133 0.765663 0.643242i \(-0.222411\pi\)
0.765663 + 0.643242i \(0.222411\pi\)
\(810\) 0 0
\(811\) −13.1837 −0.462944 −0.231472 0.972842i \(-0.574354\pi\)
−0.231472 + 0.972842i \(0.574354\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −16.0779 −0.563183
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3.63328 0.126803 0.0634013 0.997988i \(-0.479805\pi\)
0.0634013 + 0.997988i \(0.479805\pi\)
\(822\) 0 0
\(823\) −39.5044 −1.37704 −0.688518 0.725220i \(-0.741738\pi\)
−0.688518 + 0.725220i \(0.741738\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −48.3819 −1.68240 −0.841202 0.540721i \(-0.818152\pi\)
−0.841202 + 0.540721i \(0.818152\pi\)
\(828\) 0 0
\(829\) −44.5864 −1.54855 −0.774275 0.632850i \(-0.781885\pi\)
−0.774275 + 0.632850i \(0.781885\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5.72810 −0.198467
\(834\) 0 0
\(835\) −13.8763 −0.480210
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 29.2324 1.00921 0.504606 0.863350i \(-0.331638\pi\)
0.504606 + 0.863350i \(0.331638\pi\)
\(840\) 0 0
\(841\) −28.1178 −0.969580
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 14.6805 0.505025
\(846\) 0 0
\(847\) −51.4989 −1.76952
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.26862 0.112047
\(852\) 0 0
\(853\) 50.5599 1.73114 0.865569 0.500790i \(-0.166957\pi\)
0.865569 + 0.500790i \(0.166957\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 21.9568 0.750030 0.375015 0.927019i \(-0.377638\pi\)
0.375015 + 0.927019i \(0.377638\pi\)
\(858\) 0 0
\(859\) 13.7671 0.469726 0.234863 0.972029i \(-0.424536\pi\)
0.234863 + 0.972029i \(0.424536\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 26.5748 0.904618 0.452309 0.891861i \(-0.350600\pi\)
0.452309 + 0.891861i \(0.350600\pi\)
\(864\) 0 0
\(865\) 2.05518 0.0698781
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.149876 0.00508420
\(870\) 0 0
\(871\) −37.1969 −1.26037
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 4.73770 0.160163
\(876\) 0 0
\(877\) 45.9414 1.55133 0.775665 0.631145i \(-0.217415\pi\)
0.775665 + 0.631145i \(0.217415\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 23.9054 0.805392 0.402696 0.915334i \(-0.368073\pi\)
0.402696 + 0.915334i \(0.368073\pi\)
\(882\) 0 0
\(883\) 52.4002 1.76341 0.881703 0.471804i \(-0.156397\pi\)
0.881703 + 0.471804i \(0.156397\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 32.7608 1.10000 0.550000 0.835165i \(-0.314628\pi\)
0.550000 + 0.835165i \(0.314628\pi\)
\(888\) 0 0
\(889\) −19.5703 −0.656368
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.77995 −0.193419
\(894\) 0 0
\(895\) −17.6478 −0.589902
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −9.07926 −0.302810
\(900\) 0 0
\(901\) 4.05262 0.135012
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.85477 0.0948957
\(906\) 0 0
\(907\) 20.9426 0.695388 0.347694 0.937608i \(-0.386965\pi\)
0.347694 + 0.937608i \(0.386965\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −40.6418 −1.34652 −0.673262 0.739404i \(-0.735107\pi\)
−0.673262 + 0.739404i \(0.735107\pi\)
\(912\) 0 0
\(913\) 3.34163 0.110592
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 84.1330 2.77831
\(918\) 0 0
\(919\) −50.3241 −1.66004 −0.830019 0.557735i \(-0.811670\pi\)
−0.830019 + 0.557735i \(0.811670\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −59.8449 −1.96982
\(924\) 0 0
\(925\) 3.26862 0.107471
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −24.1954 −0.793825 −0.396912 0.917856i \(-0.629918\pi\)
−0.396912 + 0.917856i \(0.629918\pi\)
\(930\) 0 0
\(931\) −71.1411 −2.33155
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −0.133704 −0.00437259
\(936\) 0 0
\(937\) −37.2988 −1.21850 −0.609250 0.792978i \(-0.708529\pi\)
−0.609250 + 0.792978i \(0.708529\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −16.6467 −0.542667 −0.271334 0.962485i \(-0.587465\pi\)
−0.271334 + 0.962485i \(0.587465\pi\)
\(942\) 0 0
\(943\) −5.29977 −0.172584
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 30.1868 0.980938 0.490469 0.871459i \(-0.336825\pi\)
0.490469 + 0.871459i \(0.336825\pi\)
\(948\) 0 0
\(949\) 3.92007 0.127251
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −34.6992 −1.12402 −0.562008 0.827132i \(-0.689971\pi\)
−0.562008 + 0.827132i \(0.689971\pi\)
\(954\) 0 0
\(955\) −1.13677 −0.0367851
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −32.5458 −1.05096
\(960\) 0 0
\(961\) 62.4435 2.01431
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −26.4694 −0.852080
\(966\) 0 0
\(967\) −11.4788 −0.369133 −0.184566 0.982820i \(-0.559088\pi\)
−0.184566 + 0.982820i \(0.559088\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 46.8441 1.50330 0.751650 0.659563i \(-0.229258\pi\)
0.751650 + 0.659563i \(0.229258\pi\)
\(972\) 0 0
\(973\) 97.8977 3.13846
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −39.3737 −1.25968 −0.629838 0.776727i \(-0.716879\pi\)
−0.629838 + 0.776727i \(0.716879\pi\)
\(978\) 0 0
\(979\) −4.54709 −0.145326
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −42.3505 −1.35077 −0.675385 0.737465i \(-0.736023\pi\)
−0.675385 + 0.737465i \(0.736023\pi\)
\(984\) 0 0
\(985\) −5.44424 −0.173468
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −2.00104 −0.0635652 −0.0317826 0.999495i \(-0.510118\pi\)
−0.0317826 + 0.999495i \(0.510118\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −18.6122 −0.590045
\(996\) 0 0
\(997\) 1.97936 0.0626869 0.0313435 0.999509i \(-0.490021\pi\)
0.0313435 + 0.999509i \(0.490021\pi\)
\(998\) 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 8280.2.a.bs.1.5 5
3.2 odd 2 920.2.a.j.1.3 5
12.11 even 2 1840.2.a.v.1.3 5
15.2 even 4 4600.2.e.u.4049.6 10
15.8 even 4 4600.2.e.u.4049.5 10
15.14 odd 2 4600.2.a.be.1.3 5
24.5 odd 2 7360.2.a.co.1.3 5
24.11 even 2 7360.2.a.cp.1.3 5
60.59 even 2 9200.2.a.cu.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.j.1.3 5 3.2 odd 2
1840.2.a.v.1.3 5 12.11 even 2
4600.2.a.be.1.3 5 15.14 odd 2
4600.2.e.u.4049.5 10 15.8 even 4
4600.2.e.u.4049.6 10 15.2 even 4
7360.2.a.co.1.3 5 24.5 odd 2
7360.2.a.cp.1.3 5 24.11 even 2
8280.2.a.bs.1.5 5 1.1 even 1 trivial
9200.2.a.cu.1.3 5 60.59 even 2