Properties

Label 8280.2.a.bp.1.1
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \( x^{3} - x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.76156\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} -0.761557 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -0.761557 q^{7} +2.86464 q^{11} +0.864641 q^{13} -0.761557 q^{17} +6.38776 q^{19} -1.00000 q^{23} +1.00000 q^{25} +1.62620 q^{29} -3.62620 q^{31} -0.761557 q^{35} +2.76156 q^{37} +7.62620 q^{41} +1.72928 q^{43} +10.3878 q^{47} -6.42003 q^{49} -0.761557 q^{53} +2.86464 q^{55} -3.35548 q^{59} -2.11704 q^{61} +0.864641 q^{65} -7.74324 q^{67} -13.9248 q^{71} +4.92919 q^{73} -2.18159 q^{77} +10.5048 q^{79} -0.490839 q^{83} -0.761557 q^{85} -16.7755 q^{89} -0.658473 q^{91} +6.38776 q^{95} +6.77551 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{5} + 4 q^{7} + 6 q^{11} + 4 q^{17} + 4 q^{19} - 3 q^{23} + 3 q^{25} - 4 q^{29} - 2 q^{31} + 4 q^{35} + 2 q^{37} + 14 q^{41} + 16 q^{47} - 3 q^{49} + 4 q^{53} + 6 q^{55} + 4 q^{59} + 14 q^{61} + 6 q^{67} + 10 q^{71} + 10 q^{73} + 16 q^{77} - 4 q^{79} + 10 q^{83} + 4 q^{85} - 20 q^{89} + 8 q^{91} + 4 q^{95} - 10 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.761557 −0.287842 −0.143921 0.989589i \(-0.545971\pi\)
−0.143921 + 0.989589i \(0.545971\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.86464 0.863722 0.431861 0.901940i \(-0.357857\pi\)
0.431861 + 0.901940i \(0.357857\pi\)
\(12\) 0 0
\(13\) 0.864641 0.239808 0.119904 0.992785i \(-0.461741\pi\)
0.119904 + 0.992785i \(0.461741\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.761557 −0.184705 −0.0923524 0.995726i \(-0.529439\pi\)
−0.0923524 + 0.995726i \(0.529439\pi\)
\(18\) 0 0
\(19\) 6.38776 1.46545 0.732726 0.680524i \(-0.238248\pi\)
0.732726 + 0.680524i \(0.238248\pi\)
\(20\) 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
\(29\) 1.62620 0.301977 0.150989 0.988535i \(-0.451754\pi\)
0.150989 + 0.988535i \(0.451754\pi\)
\(30\) 0 0
\(31\) −3.62620 −0.651284 −0.325642 0.945493i \(-0.605580\pi\)
−0.325642 + 0.945493i \(0.605580\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.761557 −0.128727
\(36\) 0 0
\(37\) 2.76156 0.453997 0.226999 0.973895i \(-0.427109\pi\)
0.226999 + 0.973895i \(0.427109\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.62620 1.19101 0.595506 0.803351i \(-0.296952\pi\)
0.595506 + 0.803351i \(0.296952\pi\)
\(42\) 0 0
\(43\) 1.72928 0.263713 0.131856 0.991269i \(-0.457906\pi\)
0.131856 + 0.991269i \(0.457906\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.3878 1.51521 0.757605 0.652713i \(-0.226369\pi\)
0.757605 + 0.652713i \(0.226369\pi\)
\(48\) 0 0
\(49\) −6.42003 −0.917147
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.761557 −0.104608 −0.0523040 0.998631i \(-0.516656\pi\)
−0.0523040 + 0.998631i \(0.516656\pi\)
\(54\) 0 0
\(55\) 2.86464 0.386268
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.35548 −0.436846 −0.218423 0.975854i \(-0.570091\pi\)
−0.218423 + 0.975854i \(0.570091\pi\)
\(60\) 0 0
\(61\) −2.11704 −0.271059 −0.135529 0.990773i \(-0.543274\pi\)
−0.135529 + 0.990773i \(0.543274\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.864641 0.107246
\(66\) 0 0
\(67\) −7.74324 −0.945987 −0.472993 0.881066i \(-0.656827\pi\)
−0.472993 + 0.881066i \(0.656827\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −13.9248 −1.65257 −0.826286 0.563250i \(-0.809551\pi\)
−0.826286 + 0.563250i \(0.809551\pi\)
\(72\) 0 0
\(73\) 4.92919 0.576918 0.288459 0.957492i \(-0.406857\pi\)
0.288459 + 0.957492i \(0.406857\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.18159 −0.248615
\(78\) 0 0
\(79\) 10.5048 1.18188 0.590941 0.806715i \(-0.298757\pi\)
0.590941 + 0.806715i \(0.298757\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.490839 −0.0538766 −0.0269383 0.999637i \(-0.508576\pi\)
−0.0269383 + 0.999637i \(0.508576\pi\)
\(84\) 0 0
\(85\) −0.761557 −0.0826025
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −16.7755 −1.77820 −0.889100 0.457712i \(-0.848669\pi\)
−0.889100 + 0.457712i \(0.848669\pi\)
\(90\) 0 0
\(91\) −0.658473 −0.0690268
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.38776 0.655370
\(96\) 0 0
\(97\) 6.77551 0.687949 0.343974 0.938979i \(-0.388227\pi\)
0.343974 + 0.938979i \(0.388227\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.89692 0.785773 0.392886 0.919587i \(-0.371477\pi\)
0.392886 + 0.919587i \(0.371477\pi\)
\(102\) 0 0
\(103\) 16.8401 1.65930 0.829650 0.558283i \(-0.188540\pi\)
0.829650 + 0.558283i \(0.188540\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.74324 0.748567 0.374283 0.927314i \(-0.377889\pi\)
0.374283 + 0.927314i \(0.377889\pi\)
\(108\) 0 0
\(109\) 0.593923 0.0568875 0.0284437 0.999595i \(-0.490945\pi\)
0.0284437 + 0.999595i \(0.490945\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 20.7895 1.95571 0.977854 0.209288i \(-0.0671145\pi\)
0.977854 + 0.209288i \(0.0671145\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.579969 0.0531657
\(120\) 0 0
\(121\) −2.79383 −0.253985
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 14.6864 1.30321 0.651603 0.758560i \(-0.274097\pi\)
0.651603 + 0.758560i \(0.274097\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.72928 −0.675310 −0.337655 0.941270i \(-0.609634\pi\)
−0.337655 + 0.941270i \(0.609634\pi\)
\(132\) 0 0
\(133\) −4.86464 −0.421818
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.98168 −0.254742 −0.127371 0.991855i \(-0.540654\pi\)
−0.127371 + 0.991855i \(0.540654\pi\)
\(138\) 0 0
\(139\) −19.8603 −1.68453 −0.842263 0.539067i \(-0.818777\pi\)
−0.842263 + 0.539067i \(0.818777\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.47689 0.207128
\(144\) 0 0
\(145\) 1.62620 0.135048
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.92919 0.403815 0.201908 0.979405i \(-0.435286\pi\)
0.201908 + 0.979405i \(0.435286\pi\)
\(150\) 0 0
\(151\) 7.25240 0.590192 0.295096 0.955468i \(-0.404648\pi\)
0.295096 + 0.955468i \(0.404648\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.62620 −0.291263
\(156\) 0 0
\(157\) −13.2663 −1.05877 −0.529385 0.848382i \(-0.677577\pi\)
−0.529385 + 0.848382i \(0.677577\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.761557 0.0600191
\(162\) 0 0
\(163\) −16.0279 −1.25540 −0.627701 0.778454i \(-0.716004\pi\)
−0.627701 + 0.778454i \(0.716004\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.7047 1.52480 0.762398 0.647109i \(-0.224022\pi\)
0.762398 + 0.647109i \(0.224022\pi\)
\(168\) 0 0
\(169\) −12.2524 −0.942492
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −11.7572 −0.893882 −0.446941 0.894563i \(-0.647487\pi\)
−0.446941 + 0.894563i \(0.647487\pi\)
\(174\) 0 0
\(175\) −0.761557 −0.0575683
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.8401 1.55766 0.778830 0.627235i \(-0.215814\pi\)
0.778830 + 0.627235i \(0.215814\pi\)
\(180\) 0 0
\(181\) −26.0279 −1.93464 −0.967320 0.253560i \(-0.918398\pi\)
−0.967320 + 0.253560i \(0.918398\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.76156 0.203034
\(186\) 0 0
\(187\) −2.18159 −0.159534
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.40608 0.391170 0.195585 0.980687i \(-0.437339\pi\)
0.195585 + 0.980687i \(0.437339\pi\)
\(192\) 0 0
\(193\) −10.7476 −0.773629 −0.386815 0.922157i \(-0.626425\pi\)
−0.386815 + 0.922157i \(0.626425\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.9634 1.13734 0.568671 0.822565i \(-0.307458\pi\)
0.568671 + 0.822565i \(0.307458\pi\)
\(198\) 0 0
\(199\) −4.20617 −0.298167 −0.149084 0.988825i \(-0.547632\pi\)
−0.149084 + 0.988825i \(0.547632\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.23844 −0.0869216
\(204\) 0 0
\(205\) 7.62620 0.532637
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 18.2986 1.26574
\(210\) 0 0
\(211\) 16.4017 1.12914 0.564570 0.825385i \(-0.309042\pi\)
0.564570 + 0.825385i \(0.309042\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.72928 0.117936
\(216\) 0 0
\(217\) 2.76156 0.187467
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.658473 −0.0442937
\(222\) 0 0
\(223\) 14.7755 0.989441 0.494721 0.869052i \(-0.335270\pi\)
0.494721 + 0.869052i \(0.335270\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.54144 0.301426 0.150713 0.988578i \(-0.451843\pi\)
0.150713 + 0.988578i \(0.451843\pi\)
\(228\) 0 0
\(229\) 27.3449 1.80700 0.903499 0.428589i \(-0.140989\pi\)
0.903499 + 0.428589i \(0.140989\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0279 −1.18105 −0.590524 0.807020i \(-0.701079\pi\)
−0.590524 + 0.807020i \(0.701079\pi\)
\(234\) 0 0
\(235\) 10.3878 0.677622
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.81404 0.570133 0.285067 0.958508i \(-0.407984\pi\)
0.285067 + 0.958508i \(0.407984\pi\)
\(240\) 0 0
\(241\) −22.6864 −1.46136 −0.730679 0.682721i \(-0.760796\pi\)
−0.730679 + 0.682721i \(0.760796\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.42003 −0.410161
\(246\) 0 0
\(247\) 5.52311 0.351427
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.7293 0.740346 0.370173 0.928963i \(-0.379298\pi\)
0.370173 + 0.928963i \(0.379298\pi\)
\(252\) 0 0
\(253\) −2.86464 −0.180098
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 21.9109 1.36676 0.683381 0.730062i \(-0.260509\pi\)
0.683381 + 0.730062i \(0.260509\pi\)
\(258\) 0 0
\(259\) −2.10308 −0.130679
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 27.9773 1.72515 0.862577 0.505925i \(-0.168849\pi\)
0.862577 + 0.505925i \(0.168849\pi\)
\(264\) 0 0
\(265\) −0.761557 −0.0467821
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.21386 0.0740105 0.0370053 0.999315i \(-0.488218\pi\)
0.0370053 + 0.999315i \(0.488218\pi\)
\(270\) 0 0
\(271\) −22.7003 −1.37895 −0.689474 0.724311i \(-0.742158\pi\)
−0.689474 + 0.724311i \(0.742158\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.86464 0.172744
\(276\) 0 0
\(277\) 5.52311 0.331852 0.165926 0.986138i \(-0.446939\pi\)
0.165926 + 0.986138i \(0.446939\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.3511 1.45267 0.726333 0.687343i \(-0.241223\pi\)
0.726333 + 0.687343i \(0.241223\pi\)
\(282\) 0 0
\(283\) 14.9956 0.891398 0.445699 0.895183i \(-0.352955\pi\)
0.445699 + 0.895183i \(0.352955\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.80779 −0.342823
\(288\) 0 0
\(289\) −16.4200 −0.965884
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.5833 1.43617 0.718086 0.695955i \(-0.245019\pi\)
0.718086 + 0.695955i \(0.245019\pi\)
\(294\) 0 0
\(295\) −3.35548 −0.195364
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.864641 −0.0500035
\(300\) 0 0
\(301\) −1.31695 −0.0759076
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.11704 −0.121221
\(306\) 0 0
\(307\) 30.1816 1.72255 0.861277 0.508136i \(-0.169665\pi\)
0.861277 + 0.508136i \(0.169665\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 19.0741 1.08159 0.540797 0.841153i \(-0.318123\pi\)
0.540797 + 0.841153i \(0.318123\pi\)
\(312\) 0 0
\(313\) −23.3955 −1.32239 −0.661195 0.750214i \(-0.729950\pi\)
−0.661195 + 0.750214i \(0.729950\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −17.4985 −0.982816 −0.491408 0.870930i \(-0.663518\pi\)
−0.491408 + 0.870930i \(0.663518\pi\)
\(318\) 0 0
\(319\) 4.65847 0.260824
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.86464 −0.270676
\(324\) 0 0
\(325\) 0.864641 0.0479616
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7.91087 −0.436140
\(330\) 0 0
\(331\) 2.07518 0.114062 0.0570310 0.998372i \(-0.481837\pi\)
0.0570310 + 0.998372i \(0.481837\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7.74324 −0.423058
\(336\) 0 0
\(337\) 2.02791 0.110467 0.0552336 0.998473i \(-0.482410\pi\)
0.0552336 + 0.998473i \(0.482410\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10.3878 −0.562528
\(342\) 0 0
\(343\) 10.2201 0.551835
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) −10.1676 −0.544261 −0.272130 0.962260i \(-0.587728\pi\)
−0.272130 + 0.962260i \(0.587728\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.9937 0.585138 0.292569 0.956244i \(-0.405490\pi\)
0.292569 + 0.956244i \(0.405490\pi\)
\(354\) 0 0
\(355\) −13.9248 −0.739053
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 31.9109 1.68419 0.842096 0.539328i \(-0.181322\pi\)
0.842096 + 0.539328i \(0.181322\pi\)
\(360\) 0 0
\(361\) 21.8034 1.14755
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.92919 0.258006
\(366\) 0 0
\(367\) 27.2663 1.42329 0.711646 0.702538i \(-0.247950\pi\)
0.711646 + 0.702538i \(0.247950\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.579969 0.0301105
\(372\) 0 0
\(373\) −32.6743 −1.69181 −0.845906 0.533332i \(-0.820940\pi\)
−0.845906 + 0.533332i \(0.820940\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.40608 0.0724167
\(378\) 0 0
\(379\) −22.6339 −1.16263 −0.581313 0.813680i \(-0.697461\pi\)
−0.581313 + 0.813680i \(0.697461\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.46293 0.432436 0.216218 0.976345i \(-0.430628\pi\)
0.216218 + 0.976345i \(0.430628\pi\)
\(384\) 0 0
\(385\) −2.18159 −0.111184
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −35.7851 −1.81438 −0.907188 0.420725i \(-0.861776\pi\)
−0.907188 + 0.420725i \(0.861776\pi\)
\(390\) 0 0
\(391\) 0.761557 0.0385136
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 10.5048 0.528553
\(396\) 0 0
\(397\) 28.5972 1.43525 0.717627 0.696427i \(-0.245228\pi\)
0.717627 + 0.696427i \(0.245228\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.0279066 −0.00139359 −0.000696795 1.00000i \(-0.500222\pi\)
−0.000696795 1.00000i \(0.500222\pi\)
\(402\) 0 0
\(403\) −3.13536 −0.156183
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.91087 0.392127
\(408\) 0 0
\(409\) 5.65410 0.279577 0.139789 0.990181i \(-0.455358\pi\)
0.139789 + 0.990181i \(0.455358\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.55539 0.125743
\(414\) 0 0
\(415\) −0.490839 −0.0240943
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.54769 0.271023 0.135511 0.990776i \(-0.456732\pi\)
0.135511 + 0.990776i \(0.456732\pi\)
\(420\) 0 0
\(421\) 20.0033 0.974903 0.487451 0.873150i \(-0.337927\pi\)
0.487451 + 0.873150i \(0.337927\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.761557 −0.0369409
\(426\) 0 0
\(427\) 1.61224 0.0780220
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.58767 0.365485 0.182742 0.983161i \(-0.441503\pi\)
0.182742 + 0.983161i \(0.441503\pi\)
\(432\) 0 0
\(433\) −4.19221 −0.201465 −0.100732 0.994914i \(-0.532119\pi\)
−0.100732 + 0.994914i \(0.532119\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.38776 −0.305568
\(438\) 0 0
\(439\) −10.4769 −0.500034 −0.250017 0.968241i \(-0.580436\pi\)
−0.250017 + 0.968241i \(0.580436\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −29.6681 −1.40957 −0.704786 0.709420i \(-0.748957\pi\)
−0.704786 + 0.709420i \(0.748957\pi\)
\(444\) 0 0
\(445\) −16.7755 −0.795235
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8.81404 0.415960 0.207980 0.978133i \(-0.433311\pi\)
0.207980 + 0.978133i \(0.433311\pi\)
\(450\) 0 0
\(451\) 21.8463 1.02870
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.658473 −0.0308697
\(456\) 0 0
\(457\) −19.4725 −0.910886 −0.455443 0.890265i \(-0.650519\pi\)
−0.455443 + 0.890265i \(0.650519\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.98168 0.325169 0.162585 0.986695i \(-0.448017\pi\)
0.162585 + 0.986695i \(0.448017\pi\)
\(462\) 0 0
\(463\) −40.9850 −1.90473 −0.952367 0.304953i \(-0.901359\pi\)
−0.952367 + 0.304953i \(0.901359\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.09683 −0.328402 −0.164201 0.986427i \(-0.552505\pi\)
−0.164201 + 0.986427i \(0.552505\pi\)
\(468\) 0 0
\(469\) 5.89692 0.272294
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.95377 0.227775
\(474\) 0 0
\(475\) 6.38776 0.293090
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −19.7326 −0.901606 −0.450803 0.892623i \(-0.648862\pi\)
−0.450803 + 0.892623i \(0.648862\pi\)
\(480\) 0 0
\(481\) 2.38776 0.108872
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.77551 0.307660
\(486\) 0 0
\(487\) 3.04290 0.137887 0.0689435 0.997621i \(-0.478037\pi\)
0.0689435 + 0.997621i \(0.478037\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −22.8420 −1.03084 −0.515421 0.856937i \(-0.672365\pi\)
−0.515421 + 0.856937i \(0.672365\pi\)
\(492\) 0 0
\(493\) −1.23844 −0.0557767
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.6045 0.475679
\(498\) 0 0
\(499\) −8.57997 −0.384092 −0.192046 0.981386i \(-0.561512\pi\)
−0.192046 + 0.981386i \(0.561512\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.4138 −0.553503 −0.276751 0.960942i \(-0.589258\pi\)
−0.276751 + 0.960942i \(0.589258\pi\)
\(504\) 0 0
\(505\) 7.89692 0.351408
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 40.5606 1.79782 0.898909 0.438136i \(-0.144361\pi\)
0.898909 + 0.438136i \(0.144361\pi\)
\(510\) 0 0
\(511\) −3.75386 −0.166061
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 16.8401 0.742062
\(516\) 0 0
\(517\) 29.7572 1.30872
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 33.2557 1.45696 0.728480 0.685067i \(-0.240227\pi\)
0.728480 + 0.685067i \(0.240227\pi\)
\(522\) 0 0
\(523\) −9.34485 −0.408622 −0.204311 0.978906i \(-0.565495\pi\)
−0.204311 + 0.978906i \(0.565495\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.76156 0.120295
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.59392 0.285614
\(534\) 0 0
\(535\) 7.74324 0.334769
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −18.3911 −0.792160
\(540\) 0 0
\(541\) 12.5327 0.538823 0.269411 0.963025i \(-0.413171\pi\)
0.269411 + 0.963025i \(0.413171\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.593923 0.0254409
\(546\) 0 0
\(547\) 25.9634 1.11011 0.555056 0.831813i \(-0.312697\pi\)
0.555056 + 0.831813i \(0.312697\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 10.3878 0.442533
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.11515 0.174364 0.0871822 0.996192i \(-0.472214\pi\)
0.0871822 + 0.996192i \(0.472214\pi\)
\(558\) 0 0
\(559\) 1.49521 0.0632405
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.7616 0.453546 0.226773 0.973948i \(-0.427183\pi\)
0.226773 + 0.973948i \(0.427183\pi\)
\(564\) 0 0
\(565\) 20.7895 0.874619
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11.2524 0.471725 0.235862 0.971786i \(-0.424209\pi\)
0.235862 + 0.971786i \(0.424209\pi\)
\(570\) 0 0
\(571\) 38.2866 1.60224 0.801121 0.598502i \(-0.204237\pi\)
0.801121 + 0.598502i \(0.204237\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −43.9913 −1.83138 −0.915690 0.401885i \(-0.868355\pi\)
−0.915690 + 0.401885i \(0.868355\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.373802 0.0155079
\(582\) 0 0
\(583\) −2.18159 −0.0903521
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.8401 0.777613 0.388806 0.921320i \(-0.372888\pi\)
0.388806 + 0.921320i \(0.372888\pi\)
\(588\) 0 0
\(589\) −23.1633 −0.954426
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.81841 0.321064 0.160532 0.987031i \(-0.448679\pi\)
0.160532 + 0.987031i \(0.448679\pi\)
\(594\) 0 0
\(595\) 0.579969 0.0237764
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −17.6281 −0.720264 −0.360132 0.932901i \(-0.617268\pi\)
−0.360132 + 0.932901i \(0.617268\pi\)
\(600\) 0 0
\(601\) 2.40171 0.0979677 0.0489839 0.998800i \(-0.484402\pi\)
0.0489839 + 0.998800i \(0.484402\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.79383 −0.113585
\(606\) 0 0
\(607\) 11.9475 0.484935 0.242467 0.970160i \(-0.422043\pi\)
0.242467 + 0.970160i \(0.422043\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.98168 0.363360
\(612\) 0 0
\(613\) 0.234074 0.00945416 0.00472708 0.999989i \(-0.498495\pi\)
0.00472708 + 0.999989i \(0.498495\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.1835 −0.571005 −0.285503 0.958378i \(-0.592161\pi\)
−0.285503 + 0.958378i \(0.592161\pi\)
\(618\) 0 0
\(619\) 0.129102 0.00518903 0.00259452 0.999997i \(-0.499174\pi\)
0.00259452 + 0.999997i \(0.499174\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.7755 0.511840
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.10308 −0.0838554
\(630\) 0 0
\(631\) −15.6035 −0.621166 −0.310583 0.950546i \(-0.600524\pi\)
−0.310583 + 0.950546i \(0.600524\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14.6864 0.582811
\(636\) 0 0
\(637\) −5.55102 −0.219939
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10.6218 −0.419537 −0.209769 0.977751i \(-0.567271\pi\)
−0.209769 + 0.977751i \(0.567271\pi\)
\(642\) 0 0
\(643\) 8.82611 0.348068 0.174034 0.984740i \(-0.444320\pi\)
0.174034 + 0.984740i \(0.444320\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.49853 0.294798 0.147399 0.989077i \(-0.452910\pi\)
0.147399 + 0.989077i \(0.452910\pi\)
\(648\) 0 0
\(649\) −9.61224 −0.377314
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.34153 0.209030 0.104515 0.994523i \(-0.466671\pi\)
0.104515 + 0.994523i \(0.466671\pi\)
\(654\) 0 0
\(655\) −7.72928 −0.302008
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 35.6402 1.38834 0.694172 0.719810i \(-0.255771\pi\)
0.694172 + 0.719810i \(0.255771\pi\)
\(660\) 0 0
\(661\) −33.5144 −1.30356 −0.651779 0.758409i \(-0.725977\pi\)
−0.651779 + 0.758409i \(0.725977\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.86464 −0.188643
\(666\) 0 0
\(667\) −1.62620 −0.0629666
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.06455 −0.234119
\(672\) 0 0
\(673\) −28.0525 −1.08134 −0.540672 0.841234i \(-0.681830\pi\)
−0.540672 + 0.841234i \(0.681830\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 32.7616 1.25913 0.629564 0.776948i \(-0.283233\pi\)
0.629564 + 0.776948i \(0.283233\pi\)
\(678\) 0 0
\(679\) −5.15994 −0.198020
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.88296 −0.301633 −0.150817 0.988562i \(-0.548190\pi\)
−0.150817 + 0.988562i \(0.548190\pi\)
\(684\) 0 0
\(685\) −2.98168 −0.113924
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.658473 −0.0250858
\(690\) 0 0
\(691\) −10.4277 −0.396689 −0.198345 0.980132i \(-0.563557\pi\)
−0.198345 + 0.980132i \(0.563557\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −19.8603 −0.753343
\(696\) 0 0
\(697\) −5.80779 −0.219986
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 14.5294 0.548767 0.274383 0.961620i \(-0.411526\pi\)
0.274383 + 0.961620i \(0.411526\pi\)
\(702\) 0 0
\(703\) 17.6402 0.665311
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.01395 −0.226178
\(708\) 0 0
\(709\) −35.9754 −1.35109 −0.675543 0.737321i \(-0.736091\pi\)
−0.675543 + 0.737321i \(0.736091\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.62620 0.135802
\(714\) 0 0
\(715\) 2.47689 0.0926303
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −26.4942 −0.988066 −0.494033 0.869443i \(-0.664478\pi\)
−0.494033 + 0.869443i \(0.664478\pi\)
\(720\) 0 0
\(721\) −12.8247 −0.477616
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.62620 0.0603955
\(726\) 0 0
\(727\) 21.2018 0.786331 0.393166 0.919468i \(-0.371380\pi\)
0.393166 + 0.919468i \(0.371380\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.31695 −0.0487090
\(732\) 0 0
\(733\) 3.74324 0.138260 0.0691298 0.997608i \(-0.477978\pi\)
0.0691298 + 0.997608i \(0.477978\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −22.1816 −0.817069
\(738\) 0 0
\(739\) 25.1493 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.0925 0.517002 0.258501 0.966011i \(-0.416771\pi\)
0.258501 + 0.966011i \(0.416771\pi\)
\(744\) 0 0
\(745\) 4.92919 0.180592
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.89692 −0.215469
\(750\) 0 0
\(751\) 25.6681 0.936641 0.468320 0.883559i \(-0.344859\pi\)
0.468320 + 0.883559i \(0.344859\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7.25240 0.263942
\(756\) 0 0
\(757\) 22.2201 0.807604 0.403802 0.914846i \(-0.367688\pi\)
0.403802 + 0.914846i \(0.367688\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 23.4200 0.848975 0.424488 0.905434i \(-0.360454\pi\)
0.424488 + 0.905434i \(0.360454\pi\)
\(762\) 0 0
\(763\) −0.452306 −0.0163746
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.90129 −0.104759
\(768\) 0 0
\(769\) −14.7634 −0.532383 −0.266192 0.963920i \(-0.585765\pi\)
−0.266192 + 0.963920i \(0.585765\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −22.3632 −0.804348 −0.402174 0.915563i \(-0.631745\pi\)
−0.402174 + 0.915563i \(0.631745\pi\)
\(774\) 0 0
\(775\) −3.62620 −0.130257
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 48.7143 1.74537
\(780\) 0 0
\(781\) −39.8896 −1.42736
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −13.2663 −0.473496
\(786\) 0 0
\(787\) −8.72491 −0.311010 −0.155505 0.987835i \(-0.549700\pi\)
−0.155505 + 0.987835i \(0.549700\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.8324 −0.562934
\(792\) 0 0
\(793\) −1.83048 −0.0650021
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.8386 0.454767 0.227384 0.973805i \(-0.426983\pi\)
0.227384 + 0.973805i \(0.426983\pi\)
\(798\) 0 0
\(799\) −7.91087 −0.279866
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 14.1204 0.498297
\(804\) 0 0
\(805\) 0.761557 0.0268414
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3.18596 −0.112012 −0.0560061 0.998430i \(-0.517837\pi\)
−0.0560061 + 0.998430i \(0.517837\pi\)
\(810\) 0 0
\(811\) 34.4663 1.21027 0.605137 0.796121i \(-0.293118\pi\)
0.605137 + 0.796121i \(0.293118\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −16.0279 −0.561433
\(816\) 0 0
\(817\) 11.0462 0.386459
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −19.4219 −0.677830 −0.338915 0.940817i \(-0.610060\pi\)
−0.338915 + 0.940817i \(0.610060\pi\)
\(822\) 0 0
\(823\) 32.5327 1.13402 0.567009 0.823711i \(-0.308100\pi\)
0.567009 + 0.823711i \(0.308100\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32.1835 −1.11913 −0.559565 0.828787i \(-0.689032\pi\)
−0.559565 + 0.828787i \(0.689032\pi\)
\(828\) 0 0
\(829\) −46.6637 −1.62070 −0.810348 0.585948i \(-0.800722\pi\)
−0.810348 + 0.585948i \(0.800722\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.88922 0.169401
\(834\) 0 0
\(835\) 19.7047 0.681909
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15.2524 0.526571 0.263286 0.964718i \(-0.415194\pi\)
0.263286 + 0.964718i \(0.415194\pi\)
\(840\) 0 0
\(841\) −26.3555 −0.908810
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −12.2524 −0.421495
\(846\) 0 0
\(847\) 2.12766 0.0731074
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.76156 −0.0946650
\(852\) 0 0
\(853\) 26.2986 0.900448 0.450224 0.892916i \(-0.351344\pi\)
0.450224 + 0.892916i \(0.351344\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −23.7293 −0.810577 −0.405288 0.914189i \(-0.632829\pi\)
−0.405288 + 0.914189i \(0.632829\pi\)
\(858\) 0 0
\(859\) 33.3834 1.13903 0.569513 0.821982i \(-0.307132\pi\)
0.569513 + 0.821982i \(0.307132\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.38150 0.115108 0.0575538 0.998342i \(-0.481670\pi\)
0.0575538 + 0.998342i \(0.481670\pi\)
\(864\) 0 0
\(865\) −11.7572 −0.399756
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 30.0925 1.02082
\(870\) 0 0
\(871\) −6.69512 −0.226855
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.761557 −0.0257453
\(876\) 0 0
\(877\) 6.65515 0.224728 0.112364 0.993667i \(-0.464158\pi\)
0.112364 + 0.993667i \(0.464158\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −16.9205 −0.570065 −0.285032 0.958518i \(-0.592004\pi\)
−0.285032 + 0.958518i \(0.592004\pi\)
\(882\) 0 0
\(883\) 10.7509 0.361798 0.180899 0.983502i \(-0.442099\pi\)
0.180899 + 0.983502i \(0.442099\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −53.7572 −1.80499 −0.902495 0.430701i \(-0.858266\pi\)
−0.902495 + 0.430701i \(0.858266\pi\)
\(888\) 0 0
\(889\) −11.1845 −0.375117
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 66.3544 2.22047
\(894\) 0 0
\(895\) 20.8401 0.696606
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.89692 −0.196673
\(900\) 0 0
\(901\) 0.579969 0.0193216
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −26.0279 −0.865197
\(906\) 0 0
\(907\) 51.1526 1.69850 0.849248 0.527995i \(-0.177056\pi\)
0.849248 + 0.527995i \(0.177056\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24.9046 −0.825127 −0.412563 0.910929i \(-0.635366\pi\)
−0.412563 + 0.910929i \(0.635366\pi\)
\(912\) 0 0
\(913\) −1.40608 −0.0465344
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5.88629 0.194382
\(918\) 0 0
\(919\) −20.4923 −0.675978 −0.337989 0.941150i \(-0.609747\pi\)
−0.337989 + 0.941150i \(0.609747\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −12.0400 −0.396300
\(924\) 0 0
\(925\) 2.76156 0.0907994
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.97979 −0.0977637 −0.0488819 0.998805i \(-0.515566\pi\)
−0.0488819 + 0.998805i \(0.515566\pi\)
\(930\) 0 0
\(931\) −41.0096 −1.34403
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.18159 −0.0713456
\(936\) 0 0
\(937\) 41.1512 1.34435 0.672176 0.740392i \(-0.265360\pi\)
0.672176 + 0.740392i \(0.265360\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −22.1170 −0.720995 −0.360497 0.932760i \(-0.617393\pi\)
−0.360497 + 0.932760i \(0.617393\pi\)
\(942\) 0 0
\(943\) −7.62620 −0.248343
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −51.3361 −1.66820 −0.834100 0.551614i \(-0.814012\pi\)
−0.834100 + 0.551614i \(0.814012\pi\)
\(948\) 0 0
\(949\) 4.26198 0.138350
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 54.0558 1.75104 0.875520 0.483182i \(-0.160519\pi\)
0.875520 + 0.483182i \(0.160519\pi\)
\(954\) 0 0
\(955\) 5.40608 0.174937
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.27072 0.0733253
\(960\) 0 0
\(961\) −17.8507 −0.575829
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −10.7476 −0.345978
\(966\) 0 0
\(967\) −12.0033 −0.386001 −0.193000 0.981199i \(-0.561822\pi\)
−0.193000 + 0.981199i \(0.561822\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −24.0646 −0.772268 −0.386134 0.922443i \(-0.626190\pi\)
−0.386134 + 0.922443i \(0.626190\pi\)
\(972\) 0 0
\(973\) 15.1247 0.484877
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 43.3222 1.38600 0.692999 0.720938i \(-0.256289\pi\)
0.692999 + 0.720938i \(0.256289\pi\)
\(978\) 0 0
\(979\) −48.0558 −1.53587
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −59.3867 −1.89414 −0.947071 0.321024i \(-0.895973\pi\)
−0.947071 + 0.321024i \(0.895973\pi\)
\(984\) 0 0
\(985\) 15.9634 0.508635
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.72928 −0.0549880
\(990\) 0 0
\(991\) 26.0260 0.826744 0.413372 0.910562i \(-0.364351\pi\)
0.413372 + 0.910562i \(0.364351\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −4.20617 −0.133344
\(996\) 0 0
\(997\) 34.5048 1.09278 0.546389 0.837532i \(-0.316002\pi\)
0.546389 + 0.837532i \(0.316002\pi\)
\(998\) 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.bp.1.1 yes 3
3.2 odd 2 8280.2.a.bk.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bk.1.1 3 3.2 odd 2
8280.2.a.bp.1.1 yes 3 1.1 even 1 trivial