Properties

Label 8280.2.a.bt.1.6
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(1\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.85512\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +3.20659 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +3.20659 q^{7} +5.11246 q^{11} +0.597792 q^{13} -5.98790 q^{17} -3.11246 q^{19} -1.00000 q^{23} +1.00000 q^{25} -4.64671 q^{29} +3.39011 q^{31} -3.20659 q^{35} -6.51188 q^{37} -11.4767 q^{41} -3.71025 q^{43} +1.80717 q^{47} +3.28222 q^{49} -8.13553 q^{53} -5.11246 q^{55} +3.80438 q^{59} -7.07454 q^{61} -0.597792 q^{65} +0.0987010 q^{67} -9.51463 q^{71} -7.41593 q^{73} +16.3936 q^{77} -5.96209 q^{79} +4.55235 q^{83} +5.98790 q^{85} -10.9776 q^{89} +1.91687 q^{91} +3.11246 q^{95} +10.4630 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{5} - 2 q^{7} + 4 q^{11} - 4 q^{17} + 8 q^{19} - 6 q^{23} + 6 q^{25} - 18 q^{29} - 8 q^{31} + 2 q^{35} + 6 q^{37} - 6 q^{41} + 8 q^{43} + 8 q^{47} + 10 q^{49} - 8 q^{53} - 4 q^{55} - 2 q^{59} - 8 q^{61} - 2 q^{67} - 2 q^{71} + 8 q^{73} - 16 q^{77} - 28 q^{79} - 24 q^{83} + 4 q^{85} - 4 q^{89} - 8 q^{91} - 8 q^{95} + 24 q^{97}+O(q^{100}) \) 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
\(7\) 3.20659 1.21198 0.605989 0.795473i \(-0.292778\pi\)
0.605989 + 0.795473i \(0.292778\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.11246 1.54146 0.770732 0.637160i \(-0.219891\pi\)
0.770732 + 0.637160i \(0.219891\pi\)
\(12\) 0 0
\(13\) 0.597792 0.165798 0.0828988 0.996558i \(-0.473582\pi\)
0.0828988 + 0.996558i \(0.473582\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.98790 −1.45228 −0.726140 0.687547i \(-0.758688\pi\)
−0.726140 + 0.687547i \(0.758688\pi\)
\(18\) 0 0
\(19\) −3.11246 −0.714047 −0.357023 0.934095i \(-0.616208\pi\)
−0.357023 + 0.934095i \(0.616208\pi\)
\(20\) 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
\(29\) −4.64671 −0.862873 −0.431436 0.902143i \(-0.641993\pi\)
−0.431436 + 0.902143i \(0.641993\pi\)
\(30\) 0 0
\(31\) 3.39011 0.608882 0.304441 0.952531i \(-0.401530\pi\)
0.304441 + 0.952531i \(0.401530\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.20659 −0.542013
\(36\) 0 0
\(37\) −6.51188 −1.07055 −0.535273 0.844679i \(-0.679791\pi\)
−0.535273 + 0.844679i \(0.679791\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −11.4767 −1.79236 −0.896181 0.443688i \(-0.853670\pi\)
−0.896181 + 0.443688i \(0.853670\pi\)
\(42\) 0 0
\(43\) −3.71025 −0.565808 −0.282904 0.959148i \(-0.591298\pi\)
−0.282904 + 0.959148i \(0.591298\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.80717 0.263602 0.131801 0.991276i \(-0.457924\pi\)
0.131801 + 0.991276i \(0.457924\pi\)
\(48\) 0 0
\(49\) 3.28222 0.468889
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.13553 −1.11750 −0.558750 0.829336i \(-0.688719\pi\)
−0.558750 + 0.829336i \(0.688719\pi\)
\(54\) 0 0
\(55\) −5.11246 −0.689364
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.80438 0.495288 0.247644 0.968851i \(-0.420344\pi\)
0.247644 + 0.968851i \(0.420344\pi\)
\(60\) 0 0
\(61\) −7.07454 −0.905802 −0.452901 0.891561i \(-0.649611\pi\)
−0.452901 + 0.891561i \(0.649611\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.597792 −0.0741470
\(66\) 0 0
\(67\) 0.0987010 0.0120583 0.00602913 0.999982i \(-0.498081\pi\)
0.00602913 + 0.999982i \(0.498081\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.51463 −1.12918 −0.564590 0.825372i \(-0.690966\pi\)
−0.564590 + 0.825372i \(0.690966\pi\)
\(72\) 0 0
\(73\) −7.41593 −0.867969 −0.433985 0.900920i \(-0.642893\pi\)
−0.433985 + 0.900920i \(0.642893\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 16.3936 1.86822
\(78\) 0 0
\(79\) −5.96209 −0.670787 −0.335394 0.942078i \(-0.608869\pi\)
−0.335394 + 0.942078i \(0.608869\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.55235 0.499685 0.249843 0.968286i \(-0.419621\pi\)
0.249843 + 0.968286i \(0.419621\pi\)
\(84\) 0 0
\(85\) 5.98790 0.649479
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.9776 −1.16363 −0.581813 0.813323i \(-0.697656\pi\)
−0.581813 + 0.813323i \(0.697656\pi\)
\(90\) 0 0
\(91\) 1.91687 0.200943
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.11246 0.319331
\(96\) 0 0
\(97\) 10.4630 1.06235 0.531176 0.847261i \(-0.321750\pi\)
0.531176 + 0.847261i \(0.321750\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −13.4905 −1.34236 −0.671178 0.741296i \(-0.734211\pi\)
−0.671178 + 0.741296i \(0.734211\pi\)
\(102\) 0 0
\(103\) 15.2949 1.50705 0.753525 0.657419i \(-0.228352\pi\)
0.753525 + 0.657419i \(0.228352\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.09761 −0.782826 −0.391413 0.920215i \(-0.628014\pi\)
−0.391413 + 0.920215i \(0.628014\pi\)
\(108\) 0 0
\(109\) −2.51010 −0.240424 −0.120212 0.992748i \(-0.538357\pi\)
−0.120212 + 0.992748i \(0.538357\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −14.9075 −1.40238 −0.701191 0.712973i \(-0.747348\pi\)
−0.701191 + 0.712973i \(0.747348\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −19.2008 −1.76013
\(120\) 0 0
\(121\) 15.1372 1.37611
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 7.26008 0.644228 0.322114 0.946701i \(-0.395607\pi\)
0.322114 + 0.946701i \(0.395607\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.66229 0.232605 0.116303 0.993214i \(-0.462896\pi\)
0.116303 + 0.993214i \(0.462896\pi\)
\(132\) 0 0
\(133\) −9.98038 −0.865408
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19.5439 1.66975 0.834875 0.550439i \(-0.185540\pi\)
0.834875 + 0.550439i \(0.185540\pi\)
\(138\) 0 0
\(139\) −1.08664 −0.0921675 −0.0460838 0.998938i \(-0.514674\pi\)
−0.0460838 + 0.998938i \(0.514674\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.05619 0.255571
\(144\) 0 0
\(145\) 4.64671 0.385888
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.33223 −0.191064 −0.0955320 0.995426i \(-0.530455\pi\)
−0.0955320 + 0.995426i \(0.530455\pi\)
\(150\) 0 0
\(151\) 3.71847 0.302605 0.151303 0.988488i \(-0.451653\pi\)
0.151303 + 0.988488i \(0.451653\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.39011 −0.272300
\(156\) 0 0
\(157\) 6.97219 0.556441 0.278221 0.960517i \(-0.410255\pi\)
0.278221 + 0.960517i \(0.410255\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.20659 −0.252715
\(162\) 0 0
\(163\) −9.58464 −0.750727 −0.375364 0.926878i \(-0.622482\pi\)
−0.375364 + 0.926878i \(0.622482\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.78479 0.679788 0.339894 0.940464i \(-0.389609\pi\)
0.339894 + 0.940464i \(0.389609\pi\)
\(168\) 0 0
\(169\) −12.6426 −0.972511
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −20.2193 −1.53725 −0.768624 0.639700i \(-0.779058\pi\)
−0.768624 + 0.639700i \(0.779058\pi\)
\(174\) 0 0
\(175\) 3.20659 0.242395
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.66502 0.498167 0.249083 0.968482i \(-0.419871\pi\)
0.249083 + 0.968482i \(0.419871\pi\)
\(180\) 0 0
\(181\) 20.2331 1.50392 0.751959 0.659210i \(-0.229109\pi\)
0.751959 + 0.659210i \(0.229109\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.51188 0.478763
\(186\) 0 0
\(187\) −30.6129 −2.23864
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.9169 −1.00699 −0.503495 0.863998i \(-0.667953\pi\)
−0.503495 + 0.863998i \(0.667953\pi\)
\(192\) 0 0
\(193\) −26.8113 −1.92992 −0.964960 0.262397i \(-0.915487\pi\)
−0.964960 + 0.262397i \(0.915487\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.4183 1.52599 0.762996 0.646403i \(-0.223728\pi\)
0.762996 + 0.646403i \(0.223728\pi\)
\(198\) 0 0
\(199\) 16.1628 1.14575 0.572876 0.819642i \(-0.305828\pi\)
0.572876 + 0.819642i \(0.305828\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −14.9001 −1.04578
\(204\) 0 0
\(205\) 11.4767 0.801569
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −15.9123 −1.10068
\(210\) 0 0
\(211\) 23.7247 1.63327 0.816637 0.577152i \(-0.195836\pi\)
0.816637 + 0.577152i \(0.195836\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.71025 0.253037
\(216\) 0 0
\(217\) 10.8707 0.737951
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.57952 −0.240785
\(222\) 0 0
\(223\) 26.4339 1.77014 0.885071 0.465456i \(-0.154110\pi\)
0.885071 + 0.465456i \(0.154110\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 18.4119 1.22204 0.611021 0.791614i \(-0.290759\pi\)
0.611021 + 0.791614i \(0.290759\pi\)
\(228\) 0 0
\(229\) 7.94703 0.525155 0.262577 0.964911i \(-0.415428\pi\)
0.262577 + 0.964911i \(0.415428\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.2711 0.934928 0.467464 0.884012i \(-0.345168\pi\)
0.467464 + 0.884012i \(0.345168\pi\)
\(234\) 0 0
\(235\) −1.80717 −0.117886
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.53665 0.616874 0.308437 0.951245i \(-0.400194\pi\)
0.308437 + 0.951245i \(0.400194\pi\)
\(240\) 0 0
\(241\) 6.05344 0.389936 0.194968 0.980810i \(-0.437540\pi\)
0.194968 + 0.980810i \(0.437540\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.28222 −0.209694
\(246\) 0 0
\(247\) −1.86060 −0.118387
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −11.1956 −0.706659 −0.353329 0.935499i \(-0.614951\pi\)
−0.353329 + 0.935499i \(0.614951\pi\)
\(252\) 0 0
\(253\) −5.11246 −0.321417
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.2002 −0.823403 −0.411701 0.911319i \(-0.635065\pi\)
−0.411701 + 0.911319i \(0.635065\pi\)
\(258\) 0 0
\(259\) −20.8809 −1.29748
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.8787 −1.16411 −0.582057 0.813148i \(-0.697752\pi\)
−0.582057 + 0.813148i \(0.697752\pi\)
\(264\) 0 0
\(265\) 8.13553 0.499761
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −14.8862 −0.907629 −0.453815 0.891096i \(-0.649937\pi\)
−0.453815 + 0.891096i \(0.649937\pi\)
\(270\) 0 0
\(271\) −10.5368 −0.640067 −0.320033 0.947406i \(-0.603694\pi\)
−0.320033 + 0.947406i \(0.603694\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.11246 0.308293
\(276\) 0 0
\(277\) −20.0724 −1.20603 −0.603016 0.797729i \(-0.706035\pi\)
−0.603016 + 0.797729i \(0.706035\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.2597 1.08928 0.544642 0.838669i \(-0.316666\pi\)
0.544642 + 0.838669i \(0.316666\pi\)
\(282\) 0 0
\(283\) −12.8395 −0.763232 −0.381616 0.924321i \(-0.624632\pi\)
−0.381616 + 0.924321i \(0.624632\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −36.8011 −2.17230
\(288\) 0 0
\(289\) 18.8550 1.10912
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.4701 0.845355 0.422678 0.906280i \(-0.361090\pi\)
0.422678 + 0.906280i \(0.361090\pi\)
\(294\) 0 0
\(295\) −3.80438 −0.221500
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.597792 −0.0345712
\(300\) 0 0
\(301\) −11.8973 −0.685746
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.07454 0.405087
\(306\) 0 0
\(307\) −12.2424 −0.698708 −0.349354 0.936991i \(-0.613599\pi\)
−0.349354 + 0.936991i \(0.613599\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 6.98585 0.396131 0.198066 0.980189i \(-0.436534\pi\)
0.198066 + 0.980189i \(0.436534\pi\)
\(312\) 0 0
\(313\) 9.99868 0.565159 0.282579 0.959244i \(-0.408810\pi\)
0.282579 + 0.959244i \(0.408810\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.244471 0.0137308 0.00686542 0.999976i \(-0.497815\pi\)
0.00686542 + 0.999976i \(0.497815\pi\)
\(318\) 0 0
\(319\) −23.7561 −1.33009
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 18.6371 1.03700
\(324\) 0 0
\(325\) 0.597792 0.0331595
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.79484 0.319480
\(330\) 0 0
\(331\) 17.5908 0.966880 0.483440 0.875378i \(-0.339387\pi\)
0.483440 + 0.875378i \(0.339387\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.0987010 −0.00539261
\(336\) 0 0
\(337\) 21.6226 1.17786 0.588928 0.808186i \(-0.299550\pi\)
0.588928 + 0.808186i \(0.299550\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 17.3318 0.938570
\(342\) 0 0
\(343\) −11.9214 −0.643694
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.4205 −0.827816 −0.413908 0.910319i \(-0.635836\pi\)
−0.413908 + 0.910319i \(0.635836\pi\)
\(348\) 0 0
\(349\) −27.4998 −1.47203 −0.736014 0.676966i \(-0.763294\pi\)
−0.736014 + 0.676966i \(0.763294\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.36248 0.232191 0.116096 0.993238i \(-0.462962\pi\)
0.116096 + 0.993238i \(0.462962\pi\)
\(354\) 0 0
\(355\) 9.51463 0.504984
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −25.5106 −1.34640 −0.673199 0.739462i \(-0.735080\pi\)
−0.673199 + 0.739462i \(0.735080\pi\)
\(360\) 0 0
\(361\) −9.31261 −0.490137
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.41593 0.388168
\(366\) 0 0
\(367\) −11.6833 −0.609865 −0.304933 0.952374i \(-0.598634\pi\)
−0.304933 + 0.952374i \(0.598634\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −26.0873 −1.35439
\(372\) 0 0
\(373\) 27.7597 1.43734 0.718672 0.695350i \(-0.244750\pi\)
0.718672 + 0.695350i \(0.244750\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.77777 −0.143062
\(378\) 0 0
\(379\) −33.8557 −1.73905 −0.869525 0.493889i \(-0.835575\pi\)
−0.869525 + 0.493889i \(0.835575\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −18.7690 −0.959053 −0.479527 0.877527i \(-0.659192\pi\)
−0.479527 + 0.877527i \(0.659192\pi\)
\(384\) 0 0
\(385\) −16.3936 −0.835493
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −24.8319 −1.25903 −0.629513 0.776990i \(-0.716745\pi\)
−0.629513 + 0.776990i \(0.716745\pi\)
\(390\) 0 0
\(391\) 5.98790 0.302821
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5.96209 0.299985
\(396\) 0 0
\(397\) 4.27232 0.214421 0.107211 0.994236i \(-0.465808\pi\)
0.107211 + 0.994236i \(0.465808\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.4425 −0.970913 −0.485456 0.874261i \(-0.661347\pi\)
−0.485456 + 0.874261i \(0.661347\pi\)
\(402\) 0 0
\(403\) 2.02658 0.100951
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −33.2917 −1.65021
\(408\) 0 0
\(409\) 18.1621 0.898058 0.449029 0.893517i \(-0.351770\pi\)
0.449029 + 0.893517i \(0.351770\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 12.1991 0.600278
\(414\) 0 0
\(415\) −4.55235 −0.223466
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.91499 0.337819 0.168910 0.985632i \(-0.445975\pi\)
0.168910 + 0.985632i \(0.445975\pi\)
\(420\) 0 0
\(421\) 6.97855 0.340114 0.170057 0.985434i \(-0.445605\pi\)
0.170057 + 0.985434i \(0.445605\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5.98790 −0.290456
\(426\) 0 0
\(427\) −22.6852 −1.09781
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.04796 −0.243151 −0.121576 0.992582i \(-0.538795\pi\)
−0.121576 + 0.992582i \(0.538795\pi\)
\(432\) 0 0
\(433\) −19.1582 −0.920685 −0.460342 0.887741i \(-0.652273\pi\)
−0.460342 + 0.887741i \(0.652273\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.11246 0.148889
\(438\) 0 0
\(439\) −22.0192 −1.05092 −0.525460 0.850818i \(-0.676107\pi\)
−0.525460 + 0.850818i \(0.676107\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.0174 −0.665989 −0.332994 0.942929i \(-0.608059\pi\)
−0.332994 + 0.942929i \(0.608059\pi\)
\(444\) 0 0
\(445\) 10.9776 0.520389
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −22.6121 −1.06713 −0.533566 0.845758i \(-0.679148\pi\)
−0.533566 + 0.845758i \(0.679148\pi\)
\(450\) 0 0
\(451\) −58.6742 −2.76286
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.91687 −0.0898644
\(456\) 0 0
\(457\) −1.90826 −0.0892645 −0.0446322 0.999003i \(-0.514212\pi\)
−0.0446322 + 0.999003i \(0.514212\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −20.0302 −0.932898 −0.466449 0.884548i \(-0.654467\pi\)
−0.466449 + 0.884548i \(0.654467\pi\)
\(462\) 0 0
\(463\) −12.1824 −0.566166 −0.283083 0.959095i \(-0.591357\pi\)
−0.283083 + 0.959095i \(0.591357\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.39322 −0.249568 −0.124784 0.992184i \(-0.539824\pi\)
−0.124784 + 0.992184i \(0.539824\pi\)
\(468\) 0 0
\(469\) 0.316494 0.0146143
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −18.9685 −0.872172
\(474\) 0 0
\(475\) −3.11246 −0.142809
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 19.2098 0.877720 0.438860 0.898555i \(-0.355382\pi\)
0.438860 + 0.898555i \(0.355382\pi\)
\(480\) 0 0
\(481\) −3.89275 −0.177494
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.4630 −0.475099
\(486\) 0 0
\(487\) −16.6289 −0.753526 −0.376763 0.926310i \(-0.622963\pi\)
−0.376763 + 0.926310i \(0.622963\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 40.5038 1.82791 0.913956 0.405814i \(-0.133012\pi\)
0.913956 + 0.405814i \(0.133012\pi\)
\(492\) 0 0
\(493\) 27.8241 1.25313
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −30.5095 −1.36854
\(498\) 0 0
\(499\) −27.0798 −1.21226 −0.606129 0.795366i \(-0.707279\pi\)
−0.606129 + 0.795366i \(0.707279\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 11.7892 0.525656 0.262828 0.964843i \(-0.415345\pi\)
0.262828 + 0.964843i \(0.415345\pi\)
\(504\) 0 0
\(505\) 13.4905 0.600320
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −31.2798 −1.38645 −0.693227 0.720719i \(-0.743812\pi\)
−0.693227 + 0.720719i \(0.743812\pi\)
\(510\) 0 0
\(511\) −23.7799 −1.05196
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −15.2949 −0.673973
\(516\) 0 0
\(517\) 9.23906 0.406333
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −22.7282 −0.995740 −0.497870 0.867252i \(-0.665884\pi\)
−0.497870 + 0.867252i \(0.665884\pi\)
\(522\) 0 0
\(523\) −8.44196 −0.369141 −0.184571 0.982819i \(-0.559089\pi\)
−0.184571 + 0.982819i \(0.559089\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.2997 −0.884267
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.86069 −0.297169
\(534\) 0 0
\(535\) 8.09761 0.350090
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 16.7802 0.722775
\(540\) 0 0
\(541\) 40.3987 1.73687 0.868437 0.495799i \(-0.165125\pi\)
0.868437 + 0.495799i \(0.165125\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.51010 0.107521
\(546\) 0 0
\(547\) 37.7337 1.61337 0.806687 0.590978i \(-0.201258\pi\)
0.806687 + 0.590978i \(0.201258\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 14.4627 0.616132
\(552\) 0 0
\(553\) −19.1180 −0.812979
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −39.0703 −1.65546 −0.827732 0.561124i \(-0.810369\pi\)
−0.827732 + 0.561124i \(0.810369\pi\)
\(558\) 0 0
\(559\) −2.21796 −0.0938096
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −29.5551 −1.24560 −0.622800 0.782381i \(-0.714005\pi\)
−0.622800 + 0.782381i \(0.714005\pi\)
\(564\) 0 0
\(565\) 14.9075 0.627164
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15.2322 0.638568 0.319284 0.947659i \(-0.396558\pi\)
0.319284 + 0.947659i \(0.396558\pi\)
\(570\) 0 0
\(571\) 0.389436 0.0162974 0.00814869 0.999967i \(-0.497406\pi\)
0.00814869 + 0.999967i \(0.497406\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 42.1490 1.75469 0.877343 0.479863i \(-0.159314\pi\)
0.877343 + 0.479863i \(0.159314\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 14.5975 0.605607
\(582\) 0 0
\(583\) −41.5925 −1.72259
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.46664 0.390730 0.195365 0.980731i \(-0.437411\pi\)
0.195365 + 0.980731i \(0.437411\pi\)
\(588\) 0 0
\(589\) −10.5516 −0.434770
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 36.9855 1.51881 0.759407 0.650616i \(-0.225489\pi\)
0.759407 + 0.650616i \(0.225489\pi\)
\(594\) 0 0
\(595\) 19.2008 0.787154
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12.5153 0.511360 0.255680 0.966762i \(-0.417701\pi\)
0.255680 + 0.966762i \(0.417701\pi\)
\(600\) 0 0
\(601\) 5.92898 0.241848 0.120924 0.992662i \(-0.461414\pi\)
0.120924 + 0.992662i \(0.461414\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −15.1372 −0.615416
\(606\) 0 0
\(607\) 32.7076 1.32756 0.663781 0.747927i \(-0.268951\pi\)
0.663781 + 0.747927i \(0.268951\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.08031 0.0437046
\(612\) 0 0
\(613\) 22.6704 0.915651 0.457825 0.889042i \(-0.348629\pi\)
0.457825 + 0.889042i \(0.348629\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.19087 −0.249235 −0.124618 0.992205i \(-0.539770\pi\)
−0.124618 + 0.992205i \(0.539770\pi\)
\(618\) 0 0
\(619\) −9.30848 −0.374139 −0.187070 0.982347i \(-0.559899\pi\)
−0.187070 + 0.982347i \(0.559899\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −35.2008 −1.41029
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 38.9925 1.55473
\(630\) 0 0
\(631\) −33.1998 −1.32166 −0.660832 0.750534i \(-0.729797\pi\)
−0.660832 + 0.750534i \(0.729797\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.26008 −0.288107
\(636\) 0 0
\(637\) 1.96209 0.0777407
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 43.4347 1.71557 0.857784 0.514011i \(-0.171841\pi\)
0.857784 + 0.514011i \(0.171841\pi\)
\(642\) 0 0
\(643\) 4.13171 0.162939 0.0814694 0.996676i \(-0.474039\pi\)
0.0814694 + 0.996676i \(0.474039\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.95836 0.0769912 0.0384956 0.999259i \(-0.487743\pi\)
0.0384956 + 0.999259i \(0.487743\pi\)
\(648\) 0 0
\(649\) 19.4497 0.763469
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.0317 −1.21436 −0.607181 0.794563i \(-0.707700\pi\)
−0.607181 + 0.794563i \(0.707700\pi\)
\(654\) 0 0
\(655\) −2.66229 −0.104024
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −36.1084 −1.40658 −0.703292 0.710901i \(-0.748287\pi\)
−0.703292 + 0.710901i \(0.748287\pi\)
\(660\) 0 0
\(661\) −35.9247 −1.39731 −0.698654 0.715459i \(-0.746217\pi\)
−0.698654 + 0.715459i \(0.746217\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9.98038 0.387022
\(666\) 0 0
\(667\) 4.64671 0.179921
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −36.1683 −1.39626
\(672\) 0 0
\(673\) 32.1463 1.23915 0.619574 0.784938i \(-0.287305\pi\)
0.619574 + 0.784938i \(0.287305\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17.1407 −0.658769 −0.329385 0.944196i \(-0.606841\pi\)
−0.329385 + 0.944196i \(0.606841\pi\)
\(678\) 0 0
\(679\) 33.5504 1.28755
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 29.8878 1.14362 0.571812 0.820385i \(-0.306241\pi\)
0.571812 + 0.820385i \(0.306241\pi\)
\(684\) 0 0
\(685\) −19.5439 −0.746735
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.86335 −0.185279
\(690\) 0 0
\(691\) 19.9726 0.759794 0.379897 0.925029i \(-0.375959\pi\)
0.379897 + 0.925029i \(0.375959\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.08664 0.0412186
\(696\) 0 0
\(697\) 68.7215 2.60301
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6.92969 −0.261731 −0.130865 0.991400i \(-0.541776\pi\)
−0.130865 + 0.991400i \(0.541776\pi\)
\(702\) 0 0
\(703\) 20.2680 0.764420
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −43.2585 −1.62690
\(708\) 0 0
\(709\) −16.9233 −0.635567 −0.317784 0.948163i \(-0.602939\pi\)
−0.317784 + 0.948163i \(0.602939\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.39011 −0.126961
\(714\) 0 0
\(715\) −3.05619 −0.114295
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 45.0448 1.67989 0.839944 0.542672i \(-0.182587\pi\)
0.839944 + 0.542672i \(0.182587\pi\)
\(720\) 0 0
\(721\) 49.0445 1.82651
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.64671 −0.172575
\(726\) 0 0
\(727\) 39.0659 1.44887 0.724437 0.689341i \(-0.242100\pi\)
0.724437 + 0.689341i \(0.242100\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 22.2166 0.821711
\(732\) 0 0
\(733\) 10.3959 0.383980 0.191990 0.981397i \(-0.438506\pi\)
0.191990 + 0.981397i \(0.438506\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.504605 0.0185874
\(738\) 0 0
\(739\) −36.2681 −1.33414 −0.667072 0.744993i \(-0.732453\pi\)
−0.667072 + 0.744993i \(0.732453\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.4179 1.33604 0.668021 0.744142i \(-0.267141\pi\)
0.668021 + 0.744142i \(0.267141\pi\)
\(744\) 0 0
\(745\) 2.33223 0.0854464
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −25.9657 −0.948767
\(750\) 0 0
\(751\) 28.5873 1.04317 0.521583 0.853201i \(-0.325342\pi\)
0.521583 + 0.853201i \(0.325342\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.71847 −0.135329
\(756\) 0 0
\(757\) −18.4091 −0.669091 −0.334546 0.942380i \(-0.608583\pi\)
−0.334546 + 0.942380i \(0.608583\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 19.3926 0.702981 0.351490 0.936191i \(-0.385675\pi\)
0.351490 + 0.936191i \(0.385675\pi\)
\(762\) 0 0
\(763\) −8.04886 −0.291388
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.27423 0.0821176
\(768\) 0 0
\(769\) 0.205159 0.00739823 0.00369912 0.999993i \(-0.498823\pi\)
0.00369912 + 0.999993i \(0.498823\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −28.1930 −1.01403 −0.507015 0.861937i \(-0.669251\pi\)
−0.507015 + 0.861937i \(0.669251\pi\)
\(774\) 0 0
\(775\) 3.39011 0.121776
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 35.7208 1.27983
\(780\) 0 0
\(781\) −48.6431 −1.74059
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.97219 −0.248848
\(786\) 0 0
\(787\) 25.3346 0.903081 0.451541 0.892251i \(-0.350875\pi\)
0.451541 + 0.892251i \(0.350875\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −47.8023 −1.69966
\(792\) 0 0
\(793\) −4.22910 −0.150180
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.56341 −0.232488 −0.116244 0.993221i \(-0.537085\pi\)
−0.116244 + 0.993221i \(0.537085\pi\)
\(798\) 0 0
\(799\) −10.8211 −0.382824
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −37.9136 −1.33794
\(804\) 0 0
\(805\) 3.20659 0.113017
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 13.0910 0.460254 0.230127 0.973161i \(-0.426086\pi\)
0.230127 + 0.973161i \(0.426086\pi\)
\(810\) 0 0
\(811\) 36.0233 1.26495 0.632475 0.774581i \(-0.282039\pi\)
0.632475 + 0.774581i \(0.282039\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9.58464 0.335735
\(816\) 0 0
\(817\) 11.5480 0.404013
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 11.4828 0.400753 0.200376 0.979719i \(-0.435784\pi\)
0.200376 + 0.979719i \(0.435784\pi\)
\(822\) 0 0
\(823\) −55.5316 −1.93571 −0.967855 0.251509i \(-0.919073\pi\)
−0.967855 + 0.251509i \(0.919073\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −25.3188 −0.880420 −0.440210 0.897895i \(-0.645096\pi\)
−0.440210 + 0.897895i \(0.645096\pi\)
\(828\) 0 0
\(829\) 4.70766 0.163504 0.0817519 0.996653i \(-0.473948\pi\)
0.0817519 + 0.996653i \(0.473948\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −19.6536 −0.680958
\(834\) 0 0
\(835\) −8.78479 −0.304010
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 19.9612 0.689138 0.344569 0.938761i \(-0.388025\pi\)
0.344569 + 0.938761i \(0.388025\pi\)
\(840\) 0 0
\(841\) −7.40806 −0.255450
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 12.6426 0.434920
\(846\) 0 0
\(847\) 48.5389 1.66782
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 6.51188 0.223224
\(852\) 0 0
\(853\) −24.6148 −0.842795 −0.421398 0.906876i \(-0.638460\pi\)
−0.421398 + 0.906876i \(0.638460\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 22.4111 0.765548 0.382774 0.923842i \(-0.374969\pi\)
0.382774 + 0.923842i \(0.374969\pi\)
\(858\) 0 0
\(859\) 6.46831 0.220696 0.110348 0.993893i \(-0.464803\pi\)
0.110348 + 0.993893i \(0.464803\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.58867 0.0540789 0.0270395 0.999634i \(-0.491392\pi\)
0.0270395 + 0.999634i \(0.491392\pi\)
\(864\) 0 0
\(865\) 20.2193 0.687478
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −30.4809 −1.03399
\(870\) 0 0
\(871\) 0.0590027 0.00199923
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3.20659 −0.108403
\(876\) 0 0
\(877\) −17.7991 −0.601032 −0.300516 0.953777i \(-0.597159\pi\)
−0.300516 + 0.953777i \(0.597159\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4.56857 0.153919 0.0769595 0.997034i \(-0.475479\pi\)
0.0769595 + 0.997034i \(0.475479\pi\)
\(882\) 0 0
\(883\) 8.86016 0.298168 0.149084 0.988825i \(-0.452367\pi\)
0.149084 + 0.988825i \(0.452367\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −45.0417 −1.51235 −0.756176 0.654368i \(-0.772935\pi\)
−0.756176 + 0.654368i \(0.772935\pi\)
\(888\) 0 0
\(889\) 23.2801 0.780790
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.62473 −0.188224
\(894\) 0 0
\(895\) −6.66502 −0.222787
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −15.7529 −0.525388
\(900\) 0 0
\(901\) 48.7148 1.62292
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −20.2331 −0.672572
\(906\) 0 0
\(907\) −45.8393 −1.52207 −0.761035 0.648711i \(-0.775308\pi\)
−0.761035 + 0.648711i \(0.775308\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 48.0322 1.59138 0.795689 0.605705i \(-0.207109\pi\)
0.795689 + 0.605705i \(0.207109\pi\)
\(912\) 0 0
\(913\) 23.2737 0.770247
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.53687 0.281912
\(918\) 0 0
\(919\) −25.0155 −0.825187 −0.412593 0.910915i \(-0.635377\pi\)
−0.412593 + 0.910915i \(0.635377\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5.68777 −0.187215
\(924\) 0 0
\(925\) −6.51188 −0.214109
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −53.0509 −1.74054 −0.870272 0.492572i \(-0.836057\pi\)
−0.870272 + 0.492572i \(0.836057\pi\)
\(930\) 0 0
\(931\) −10.2158 −0.334809
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 30.6129 1.00115
\(936\) 0 0
\(937\) 39.2729 1.28299 0.641494 0.767128i \(-0.278315\pi\)
0.641494 + 0.767128i \(0.278315\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −11.6157 −0.378661 −0.189331 0.981913i \(-0.560632\pi\)
−0.189331 + 0.981913i \(0.560632\pi\)
\(942\) 0 0
\(943\) 11.4767 0.373733
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.4740 −0.600323 −0.300161 0.953888i \(-0.597041\pi\)
−0.300161 + 0.953888i \(0.597041\pi\)
\(948\) 0 0
\(949\) −4.43318 −0.143907
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 29.4785 0.954903 0.477451 0.878658i \(-0.341561\pi\)
0.477451 + 0.878658i \(0.341561\pi\)
\(954\) 0 0
\(955\) 13.9169 0.450339
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 62.6694 2.02370
\(960\) 0 0
\(961\) −19.5071 −0.629263
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 26.8113 0.863086
\(966\) 0 0
\(967\) 9.25644 0.297667 0.148834 0.988862i \(-0.452448\pi\)
0.148834 + 0.988862i \(0.452448\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −27.2356 −0.874031 −0.437015 0.899454i \(-0.643964\pi\)
−0.437015 + 0.899454i \(0.643964\pi\)
\(972\) 0 0
\(973\) −3.48441 −0.111705
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 33.2495 1.06374 0.531872 0.846825i \(-0.321489\pi\)
0.531872 + 0.846825i \(0.321489\pi\)
\(978\) 0 0
\(979\) −56.1227 −1.79369
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 12.5093 0.398983 0.199492 0.979900i \(-0.436071\pi\)
0.199492 + 0.979900i \(0.436071\pi\)
\(984\) 0 0
\(985\) −21.4183 −0.682444
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.71025 0.117979
\(990\) 0 0
\(991\) −27.8833 −0.885743 −0.442871 0.896585i \(-0.646040\pi\)
−0.442871 + 0.896585i \(0.646040\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −16.1628 −0.512396
\(996\) 0 0
\(997\) 44.3248 1.40378 0.701890 0.712285i \(-0.252340\pi\)
0.701890 + 0.712285i \(0.252340\pi\)
\(998\) 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.bt.1.6 6
3.2 odd 2 8280.2.a.bu.1.6 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bt.1.6 6 1.1 even 1 trivial
8280.2.a.bu.1.6 yes 6 3.2 odd 2