Properties

Label 8280.2.a.bu.1.1
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $6$
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: \(6\)
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 1.1
Root \(0.485614\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} -4.41777 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -4.41777 q^{7} -0.245598 q^{11} +0.725630 q^{13} -0.737339 q^{17} +1.75440 q^{19} +1.00000 q^{23} +1.00000 q^{25} -10.2258 q^{29} -3.46297 q^{31} -4.41777 q^{35} +0.273677 q^{37} +6.36154 q^{41} +1.02877 q^{43} +3.89849 q^{47} +12.5166 q^{49} -5.12696 q^{53} -0.245598 q^{55} +3.69214 q^{59} -9.32805 q^{61} +0.725630 q^{65} +8.56185 q^{67} -2.72091 q^{71} +13.2828 q^{73} +1.08499 q^{77} -13.0825 q^{79} -16.2960 q^{83} -0.737339 q^{85} +14.1978 q^{89} -3.20566 q^{91} +1.75440 q^{95} +18.6778 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{5} - 2 q^{7}+O(q^{10}) \) 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
\(7\) −4.41777 −1.66976 −0.834879 0.550433i \(-0.814463\pi\)
−0.834879 + 0.550433i \(0.814463\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.245598 −0.0740505 −0.0370253 0.999314i \(-0.511788\pi\)
−0.0370253 + 0.999314i \(0.511788\pi\)
\(12\) 0 0
\(13\) 0.725630 0.201253 0.100627 0.994924i \(-0.467915\pi\)
0.100627 + 0.994924i \(0.467915\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.737339 −0.178831 −0.0894155 0.995994i \(-0.528500\pi\)
−0.0894155 + 0.995994i \(0.528500\pi\)
\(18\) 0 0
\(19\) 1.75440 0.402487 0.201244 0.979541i \(-0.435502\pi\)
0.201244 + 0.979541i \(0.435502\pi\)
\(20\) 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
\(29\) −10.2258 −1.89889 −0.949446 0.313930i \(-0.898354\pi\)
−0.949446 + 0.313930i \(0.898354\pi\)
\(30\) 0 0
\(31\) −3.46297 −0.621968 −0.310984 0.950415i \(-0.600658\pi\)
−0.310984 + 0.950415i \(0.600658\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.41777 −0.746739
\(36\) 0 0
\(37\) 0.273677 0.0449923 0.0224961 0.999747i \(-0.492839\pi\)
0.0224961 + 0.999747i \(0.492839\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.36154 0.993506 0.496753 0.867892i \(-0.334525\pi\)
0.496753 + 0.867892i \(0.334525\pi\)
\(42\) 0 0
\(43\) 1.02877 0.156886 0.0784432 0.996919i \(-0.475005\pi\)
0.0784432 + 0.996919i \(0.475005\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.89849 0.568653 0.284327 0.958727i \(-0.408230\pi\)
0.284327 + 0.958727i \(0.408230\pi\)
\(48\) 0 0
\(49\) 12.5166 1.78809
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.12696 −0.704243 −0.352121 0.935954i \(-0.614540\pi\)
−0.352121 + 0.935954i \(0.614540\pi\)
\(54\) 0 0
\(55\) −0.245598 −0.0331164
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.69214 0.480675 0.240338 0.970689i \(-0.422742\pi\)
0.240338 + 0.970689i \(0.422742\pi\)
\(60\) 0 0
\(61\) −9.32805 −1.19433 −0.597167 0.802117i \(-0.703707\pi\)
−0.597167 + 0.802117i \(0.703707\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.725630 0.0900033
\(66\) 0 0
\(67\) 8.56185 1.04600 0.522998 0.852334i \(-0.324813\pi\)
0.522998 + 0.852334i \(0.324813\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.72091 −0.322912 −0.161456 0.986880i \(-0.551619\pi\)
−0.161456 + 0.986880i \(0.551619\pi\)
\(72\) 0 0
\(73\) 13.2828 1.55463 0.777315 0.629112i \(-0.216581\pi\)
0.777315 + 0.629112i \(0.216581\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.08499 0.123646
\(78\) 0 0
\(79\) −13.0825 −1.47189 −0.735945 0.677041i \(-0.763262\pi\)
−0.735945 + 0.677041i \(0.763262\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −16.2960 −1.78871 −0.894357 0.447354i \(-0.852366\pi\)
−0.894357 + 0.447354i \(0.852366\pi\)
\(84\) 0 0
\(85\) −0.737339 −0.0799757
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.1978 1.50496 0.752480 0.658615i \(-0.228857\pi\)
0.752480 + 0.658615i \(0.228857\pi\)
\(90\) 0 0
\(91\) −3.20566 −0.336045
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.75440 0.179998
\(96\) 0 0
\(97\) 18.6778 1.89644 0.948222 0.317610i \(-0.102880\pi\)
0.948222 + 0.317610i \(0.102880\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.28617 0.227482 0.113741 0.993510i \(-0.463717\pi\)
0.113741 + 0.993510i \(0.463717\pi\)
\(102\) 0 0
\(103\) −3.40597 −0.335600 −0.167800 0.985821i \(-0.553666\pi\)
−0.167800 + 0.985821i \(0.553666\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.95549 0.189044 0.0945221 0.995523i \(-0.469868\pi\)
0.0945221 + 0.995523i \(0.469868\pi\)
\(108\) 0 0
\(109\) 13.7052 1.31272 0.656362 0.754446i \(-0.272094\pi\)
0.656362 + 0.754446i \(0.272094\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.39023 −0.224854 −0.112427 0.993660i \(-0.535862\pi\)
−0.112427 + 0.993660i \(0.535862\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.25739 0.298605
\(120\) 0 0
\(121\) −10.9397 −0.994517
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.14403 −0.367723 −0.183861 0.982952i \(-0.558860\pi\)
−0.183861 + 0.982952i \(0.558860\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.86966 0.774945 0.387473 0.921881i \(-0.373348\pi\)
0.387473 + 0.921881i \(0.373348\pi\)
\(132\) 0 0
\(133\) −7.75054 −0.672057
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.92185 0.847681 0.423840 0.905737i \(-0.360682\pi\)
0.423840 + 0.905737i \(0.360682\pi\)
\(138\) 0 0
\(139\) −10.0654 −0.853735 −0.426868 0.904314i \(-0.640383\pi\)
−0.426868 + 0.904314i \(0.640383\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.178213 −0.0149029
\(144\) 0 0
\(145\) −10.2258 −0.849210
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.1715 0.915208 0.457604 0.889156i \(-0.348708\pi\)
0.457604 + 0.889156i \(0.348708\pi\)
\(150\) 0 0
\(151\) −10.6914 −0.870057 −0.435029 0.900417i \(-0.643262\pi\)
−0.435029 + 0.900417i \(0.643262\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.46297 −0.278152
\(156\) 0 0
\(157\) 21.6541 1.72818 0.864092 0.503334i \(-0.167893\pi\)
0.864092 + 0.503334i \(0.167893\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.41777 −0.348169
\(162\) 0 0
\(163\) 4.37720 0.342849 0.171424 0.985197i \(-0.445163\pi\)
0.171424 + 0.985197i \(0.445163\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.29928 −0.487453 −0.243726 0.969844i \(-0.578370\pi\)
−0.243726 + 0.969844i \(0.578370\pi\)
\(168\) 0 0
\(169\) −12.4735 −0.959497
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.90390 0.524894 0.262447 0.964946i \(-0.415470\pi\)
0.262447 + 0.964946i \(0.415470\pi\)
\(174\) 0 0
\(175\) −4.41777 −0.333952
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.27569 −0.244837 −0.122418 0.992479i \(-0.539065\pi\)
−0.122418 + 0.992479i \(0.539065\pi\)
\(180\) 0 0
\(181\) 0.828526 0.0615838 0.0307919 0.999526i \(-0.490197\pi\)
0.0307919 + 0.999526i \(0.490197\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.273677 0.0201212
\(186\) 0 0
\(187\) 0.181089 0.0132425
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.79434 0.636336 0.318168 0.948034i \(-0.396932\pi\)
0.318168 + 0.948034i \(0.396932\pi\)
\(192\) 0 0
\(193\) −5.30469 −0.381840 −0.190920 0.981606i \(-0.561147\pi\)
−0.190920 + 0.981606i \(0.561147\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.2703 1.23046 0.615228 0.788349i \(-0.289064\pi\)
0.615228 + 0.788349i \(0.289064\pi\)
\(198\) 0 0
\(199\) 0.0989687 0.00701571 0.00350785 0.999994i \(-0.498883\pi\)
0.00350785 + 0.999994i \(0.498883\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 45.1754 3.17069
\(204\) 0 0
\(205\) 6.36154 0.444310
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.430877 −0.0298044
\(210\) 0 0
\(211\) −6.76070 −0.465426 −0.232713 0.972546i \(-0.574760\pi\)
−0.232713 + 0.972546i \(0.574760\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.02877 0.0701617
\(216\) 0 0
\(217\) 15.2986 1.03854
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.535035 −0.0359904
\(222\) 0 0
\(223\) −16.1550 −1.08182 −0.540908 0.841082i \(-0.681919\pi\)
−0.540908 + 0.841082i \(0.681919\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.06484 −0.402538 −0.201269 0.979536i \(-0.564507\pi\)
−0.201269 + 0.979536i \(0.564507\pi\)
\(228\) 0 0
\(229\) 24.0582 1.58981 0.794905 0.606733i \(-0.207520\pi\)
0.794905 + 0.606733i \(0.207520\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.2539 0.802781 0.401391 0.915907i \(-0.368527\pi\)
0.401391 + 0.915907i \(0.368527\pi\)
\(234\) 0 0
\(235\) 3.89849 0.254309
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 18.4590 1.19401 0.597005 0.802237i \(-0.296357\pi\)
0.597005 + 0.802237i \(0.296357\pi\)
\(240\) 0 0
\(241\) 8.62544 0.555614 0.277807 0.960637i \(-0.410392\pi\)
0.277807 + 0.960637i \(0.410392\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 12.5166 0.799659
\(246\) 0 0
\(247\) 1.27305 0.0810020
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.4513 0.722797 0.361399 0.932411i \(-0.382299\pi\)
0.361399 + 0.932411i \(0.382299\pi\)
\(252\) 0 0
\(253\) −0.245598 −0.0154406
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 24.6765 1.53928 0.769638 0.638480i \(-0.220437\pi\)
0.769638 + 0.638480i \(0.220437\pi\)
\(258\) 0 0
\(259\) −1.20904 −0.0751263
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 31.1427 1.92034 0.960169 0.279420i \(-0.0901420\pi\)
0.960169 + 0.279420i \(0.0901420\pi\)
\(264\) 0 0
\(265\) −5.12696 −0.314947
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.0065 1.76856 0.884278 0.466961i \(-0.154651\pi\)
0.884278 + 0.466961i \(0.154651\pi\)
\(270\) 0 0
\(271\) −12.5881 −0.764670 −0.382335 0.924024i \(-0.624880\pi\)
−0.382335 + 0.924024i \(0.624880\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.245598 −0.0148101
\(276\) 0 0
\(277\) 20.4773 1.23036 0.615180 0.788387i \(-0.289083\pi\)
0.615180 + 0.788387i \(0.289083\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.22925 −0.0733310 −0.0366655 0.999328i \(-0.511674\pi\)
−0.0366655 + 0.999328i \(0.511674\pi\)
\(282\) 0 0
\(283\) −3.67264 −0.218316 −0.109158 0.994024i \(-0.534815\pi\)
−0.109158 + 0.994024i \(0.534815\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −28.1038 −1.65892
\(288\) 0 0
\(289\) −16.4563 −0.968019
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.94294 0.464031 0.232016 0.972712i \(-0.425468\pi\)
0.232016 + 0.972712i \(0.425468\pi\)
\(294\) 0 0
\(295\) 3.69214 0.214964
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.725630 0.0419642
\(300\) 0 0
\(301\) −4.54488 −0.261962
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −9.32805 −0.534123
\(306\) 0 0
\(307\) 24.4721 1.39669 0.698347 0.715759i \(-0.253919\pi\)
0.698347 + 0.715759i \(0.253919\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.535097 −0.0303426 −0.0151713 0.999885i \(-0.504829\pi\)
−0.0151713 + 0.999885i \(0.504829\pi\)
\(312\) 0 0
\(313\) 19.2521 1.08819 0.544096 0.839023i \(-0.316873\pi\)
0.544096 + 0.839023i \(0.316873\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.7411 1.22110 0.610551 0.791977i \(-0.290948\pi\)
0.610551 + 0.791977i \(0.290948\pi\)
\(318\) 0 0
\(319\) 2.51145 0.140614
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.29359 −0.0719773
\(324\) 0 0
\(325\) 0.725630 0.0402507
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −17.2226 −0.949513
\(330\) 0 0
\(331\) −12.4465 −0.684119 −0.342059 0.939678i \(-0.611124\pi\)
−0.342059 + 0.939678i \(0.611124\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8.56185 0.467784
\(336\) 0 0
\(337\) 0.540350 0.0294347 0.0147174 0.999892i \(-0.495315\pi\)
0.0147174 + 0.999892i \(0.495315\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.850498 0.0460570
\(342\) 0 0
\(343\) −24.3713 −1.31592
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.94246 0.319008 0.159504 0.987197i \(-0.449011\pi\)
0.159504 + 0.987197i \(0.449011\pi\)
\(348\) 0 0
\(349\) −6.74811 −0.361218 −0.180609 0.983555i \(-0.557807\pi\)
−0.180609 + 0.983555i \(0.557807\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5.31562 0.282922 0.141461 0.989944i \(-0.454820\pi\)
0.141461 + 0.989944i \(0.454820\pi\)
\(354\) 0 0
\(355\) −2.72091 −0.144411
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.3858 0.759255 0.379627 0.925140i \(-0.376052\pi\)
0.379627 + 0.925140i \(0.376052\pi\)
\(360\) 0 0
\(361\) −15.9221 −0.838004
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 13.2828 0.695251
\(366\) 0 0
\(367\) −6.18466 −0.322836 −0.161418 0.986886i \(-0.551607\pi\)
−0.161418 + 0.986886i \(0.551607\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 22.6497 1.17591
\(372\) 0 0
\(373\) −33.8811 −1.75430 −0.877148 0.480220i \(-0.840557\pi\)
−0.877148 + 0.480220i \(0.840557\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.42018 −0.382159
\(378\) 0 0
\(379\) 6.63112 0.340618 0.170309 0.985391i \(-0.445523\pi\)
0.170309 + 0.985391i \(0.445523\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 30.4498 1.55591 0.777957 0.628318i \(-0.216256\pi\)
0.777957 + 0.628318i \(0.216256\pi\)
\(384\) 0 0
\(385\) 1.08499 0.0552964
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −16.5655 −0.839905 −0.419953 0.907546i \(-0.637953\pi\)
−0.419953 + 0.907546i \(0.637953\pi\)
\(390\) 0 0
\(391\) −0.737339 −0.0372889
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −13.0825 −0.658250
\(396\) 0 0
\(397\) −25.1543 −1.26246 −0.631229 0.775596i \(-0.717449\pi\)
−0.631229 + 0.775596i \(0.717449\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.79559 −0.289418 −0.144709 0.989474i \(-0.546225\pi\)
−0.144709 + 0.989474i \(0.546225\pi\)
\(402\) 0 0
\(403\) −2.51283 −0.125173
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.0672146 −0.00333170
\(408\) 0 0
\(409\) 0.360203 0.0178109 0.00890546 0.999960i \(-0.497165\pi\)
0.00890546 + 0.999960i \(0.497165\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −16.3110 −0.802611
\(414\) 0 0
\(415\) −16.2960 −0.799937
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 29.3599 1.43432 0.717162 0.696907i \(-0.245441\pi\)
0.717162 + 0.696907i \(0.245441\pi\)
\(420\) 0 0
\(421\) −18.8355 −0.917985 −0.458992 0.888440i \(-0.651789\pi\)
−0.458992 + 0.888440i \(0.651789\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.737339 −0.0357662
\(426\) 0 0
\(427\) 41.2091 1.99425
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4.92732 0.237341 0.118670 0.992934i \(-0.462137\pi\)
0.118670 + 0.992934i \(0.462137\pi\)
\(432\) 0 0
\(433\) 15.3671 0.738497 0.369248 0.929331i \(-0.379615\pi\)
0.369248 + 0.929331i \(0.379615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.75440 0.0839244
\(438\) 0 0
\(439\) 16.3652 0.781066 0.390533 0.920589i \(-0.372291\pi\)
0.390533 + 0.920589i \(0.372291\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.9633 −0.615903 −0.307952 0.951402i \(-0.599644\pi\)
−0.307952 + 0.951402i \(0.599644\pi\)
\(444\) 0 0
\(445\) 14.1978 0.673039
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −25.2506 −1.19165 −0.595824 0.803115i \(-0.703175\pi\)
−0.595824 + 0.803115i \(0.703175\pi\)
\(450\) 0 0
\(451\) −1.56238 −0.0735697
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.20566 −0.150284
\(456\) 0 0
\(457\) 13.3241 0.623277 0.311639 0.950201i \(-0.399122\pi\)
0.311639 + 0.950201i \(0.399122\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −19.8825 −0.926019 −0.463010 0.886353i \(-0.653230\pi\)
−0.463010 + 0.886353i \(0.653230\pi\)
\(462\) 0 0
\(463\) 1.65157 0.0767549 0.0383774 0.999263i \(-0.487781\pi\)
0.0383774 + 0.999263i \(0.487781\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.28348 −0.0593922 −0.0296961 0.999559i \(-0.509454\pi\)
−0.0296961 + 0.999559i \(0.509454\pi\)
\(468\) 0 0
\(469\) −37.8243 −1.74656
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.252664 −0.0116175
\(474\) 0 0
\(475\) 1.75440 0.0804975
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −32.0595 −1.46484 −0.732419 0.680855i \(-0.761609\pi\)
−0.732419 + 0.680855i \(0.761609\pi\)
\(480\) 0 0
\(481\) 0.198588 0.00905486
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18.6778 0.848115
\(486\) 0 0
\(487\) −8.95626 −0.405847 −0.202923 0.979195i \(-0.565044\pi\)
−0.202923 + 0.979195i \(0.565044\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18.2930 0.825552 0.412776 0.910833i \(-0.364559\pi\)
0.412776 + 0.910833i \(0.364559\pi\)
\(492\) 0 0
\(493\) 7.53992 0.339581
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.0203 0.539186
\(498\) 0 0
\(499\) −42.2920 −1.89325 −0.946626 0.322335i \(-0.895532\pi\)
−0.946626 + 0.322335i \(0.895532\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.96067 0.399537 0.199768 0.979843i \(-0.435981\pi\)
0.199768 + 0.979843i \(0.435981\pi\)
\(504\) 0 0
\(505\) 2.28617 0.101733
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 21.5698 0.956064 0.478032 0.878342i \(-0.341350\pi\)
0.478032 + 0.878342i \(0.341350\pi\)
\(510\) 0 0
\(511\) −58.6801 −2.59586
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.40597 −0.150085
\(516\) 0 0
\(517\) −0.957461 −0.0421091
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.90097 −0.170905 −0.0854523 0.996342i \(-0.527234\pi\)
−0.0854523 + 0.996342i \(0.527234\pi\)
\(522\) 0 0
\(523\) 36.3684 1.59028 0.795140 0.606426i \(-0.207397\pi\)
0.795140 + 0.606426i \(0.207397\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.55338 0.111227
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.61613 0.199947
\(534\) 0 0
\(535\) 1.95549 0.0845432
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.07406 −0.132409
\(540\) 0 0
\(541\) 13.0728 0.562045 0.281023 0.959701i \(-0.409326\pi\)
0.281023 + 0.959701i \(0.409326\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 13.7052 0.587068
\(546\) 0 0
\(547\) 13.7971 0.589924 0.294962 0.955509i \(-0.404693\pi\)
0.294962 + 0.955509i \(0.404693\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −17.9402 −0.764280
\(552\) 0 0
\(553\) 57.7952 2.45770
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.70874 0.241887 0.120943 0.992659i \(-0.461408\pi\)
0.120943 + 0.992659i \(0.461408\pi\)
\(558\) 0 0
\(559\) 0.746508 0.0315739
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −25.2976 −1.06617 −0.533084 0.846063i \(-0.678967\pi\)
−0.533084 + 0.846063i \(0.678967\pi\)
\(564\) 0 0
\(565\) −2.39023 −0.100558
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11.2692 −0.472429 −0.236214 0.971701i \(-0.575907\pi\)
−0.236214 + 0.971701i \(0.575907\pi\)
\(570\) 0 0
\(571\) −14.8808 −0.622740 −0.311370 0.950289i \(-0.600788\pi\)
−0.311370 + 0.950289i \(0.600788\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 32.1743 1.33944 0.669718 0.742616i \(-0.266415\pi\)
0.669718 + 0.742616i \(0.266415\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 71.9917 2.98672
\(582\) 0 0
\(583\) 1.25917 0.0521495
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.8027 0.693520 0.346760 0.937954i \(-0.387282\pi\)
0.346760 + 0.937954i \(0.387282\pi\)
\(588\) 0 0
\(589\) −6.07544 −0.250334
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11.3158 −0.464684 −0.232342 0.972634i \(-0.574639\pi\)
−0.232342 + 0.972634i \(0.574639\pi\)
\(594\) 0 0
\(595\) 3.25739 0.133540
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 40.7326 1.66429 0.832144 0.554560i \(-0.187113\pi\)
0.832144 + 0.554560i \(0.187113\pi\)
\(600\) 0 0
\(601\) 14.4452 0.589234 0.294617 0.955615i \(-0.404808\pi\)
0.294617 + 0.955615i \(0.404808\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −10.9397 −0.444761
\(606\) 0 0
\(607\) 32.8828 1.33467 0.667336 0.744757i \(-0.267435\pi\)
0.667336 + 0.744757i \(0.267435\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.82886 0.114443
\(612\) 0 0
\(613\) −13.0141 −0.525634 −0.262817 0.964846i \(-0.584651\pi\)
−0.262817 + 0.964846i \(0.584651\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19.9737 0.804109 0.402055 0.915616i \(-0.368296\pi\)
0.402055 + 0.915616i \(0.368296\pi\)
\(618\) 0 0
\(619\) 29.4274 1.18279 0.591394 0.806382i \(-0.298578\pi\)
0.591394 + 0.806382i \(0.298578\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −62.7224 −2.51292
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.201793 −0.00804602
\(630\) 0 0
\(631\) 35.6892 1.42076 0.710382 0.703817i \(-0.248522\pi\)
0.710382 + 0.703817i \(0.248522\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.14403 −0.164451
\(636\) 0 0
\(637\) 9.08245 0.359860
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −32.0690 −1.26665 −0.633324 0.773887i \(-0.718310\pi\)
−0.633324 + 0.773887i \(0.718310\pi\)
\(642\) 0 0
\(643\) −24.9651 −0.984528 −0.492264 0.870446i \(-0.663831\pi\)
−0.492264 + 0.870446i \(0.663831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.4886 −0.608919 −0.304460 0.952525i \(-0.598476\pi\)
−0.304460 + 0.952525i \(0.598476\pi\)
\(648\) 0 0
\(649\) −0.906780 −0.0355942
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.4293 −0.447264 −0.223632 0.974674i \(-0.571791\pi\)
−0.223632 + 0.974674i \(0.571791\pi\)
\(654\) 0 0
\(655\) 8.86966 0.346566
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −29.1213 −1.13441 −0.567203 0.823578i \(-0.691974\pi\)
−0.567203 + 0.823578i \(0.691974\pi\)
\(660\) 0 0
\(661\) 19.4829 0.757799 0.378899 0.925438i \(-0.376303\pi\)
0.378899 + 0.925438i \(0.376303\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.75054 −0.300553
\(666\) 0 0
\(667\) −10.2258 −0.395946
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.29095 0.0884411
\(672\) 0 0
\(673\) −47.1173 −1.81624 −0.908120 0.418710i \(-0.862482\pi\)
−0.908120 + 0.418710i \(0.862482\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −19.5617 −0.751817 −0.375909 0.926657i \(-0.622669\pi\)
−0.375909 + 0.926657i \(0.622669\pi\)
\(678\) 0 0
\(679\) −82.5141 −3.16660
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26.0384 0.996332 0.498166 0.867082i \(-0.334007\pi\)
0.498166 + 0.867082i \(0.334007\pi\)
\(684\) 0 0
\(685\) 9.92185 0.379094
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.72028 −0.141731
\(690\) 0 0
\(691\) 46.0969 1.75361 0.876804 0.480849i \(-0.159671\pi\)
0.876804 + 0.480849i \(0.159671\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10.0654 −0.381802
\(696\) 0 0
\(697\) −4.69062 −0.177670
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.32214 −0.125475 −0.0627377 0.998030i \(-0.519983\pi\)
−0.0627377 + 0.998030i \(0.519983\pi\)
\(702\) 0 0
\(703\) 0.480140 0.0181088
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.0997 −0.379840
\(708\) 0 0
\(709\) 14.5408 0.546090 0.273045 0.962001i \(-0.411969\pi\)
0.273045 + 0.962001i \(0.411969\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.46297 −0.129689
\(714\) 0 0
\(715\) −0.178213 −0.00666479
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −23.9144 −0.891856 −0.445928 0.895069i \(-0.647126\pi\)
−0.445928 + 0.895069i \(0.647126\pi\)
\(720\) 0 0
\(721\) 15.0468 0.560371
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −10.2258 −0.379778
\(726\) 0 0
\(727\) 24.2960 0.901089 0.450544 0.892754i \(-0.351230\pi\)
0.450544 + 0.892754i \(0.351230\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.758555 −0.0280562
\(732\) 0 0
\(733\) −23.9750 −0.885537 −0.442768 0.896636i \(-0.646004\pi\)
−0.442768 + 0.896636i \(0.646004\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.10277 −0.0774566
\(738\) 0 0
\(739\) 28.7736 1.05845 0.529227 0.848480i \(-0.322482\pi\)
0.529227 + 0.848480i \(0.322482\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29.2923 1.07463 0.537315 0.843381i \(-0.319439\pi\)
0.537315 + 0.843381i \(0.319439\pi\)
\(744\) 0 0
\(745\) 11.1715 0.409293
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.63889 −0.315658
\(750\) 0 0
\(751\) −12.2197 −0.445905 −0.222952 0.974829i \(-0.571569\pi\)
−0.222952 + 0.974829i \(0.571569\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10.6914 −0.389101
\(756\) 0 0
\(757\) −4.27120 −0.155239 −0.0776197 0.996983i \(-0.524732\pi\)
−0.0776197 + 0.996983i \(0.524732\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.7938 −0.608775 −0.304388 0.952548i \(-0.598452\pi\)
−0.304388 + 0.952548i \(0.598452\pi\)
\(762\) 0 0
\(763\) −60.5466 −2.19193
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.67912 0.0967375
\(768\) 0 0
\(769\) −11.2226 −0.404698 −0.202349 0.979313i \(-0.564857\pi\)
−0.202349 + 0.979313i \(0.564857\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −27.7835 −0.999303 −0.499652 0.866226i \(-0.666539\pi\)
−0.499652 + 0.866226i \(0.666539\pi\)
\(774\) 0 0
\(775\) −3.46297 −0.124394
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.1607 0.399874
\(780\) 0 0
\(781\) 0.668249 0.0239118
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 21.6541 0.772867
\(786\) 0 0
\(787\) −45.2896 −1.61440 −0.807200 0.590277i \(-0.799018\pi\)
−0.807200 + 0.590277i \(0.799018\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10.5595 0.375452
\(792\) 0 0
\(793\) −6.76871 −0.240364
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 4.07523 0.144352 0.0721760 0.997392i \(-0.477006\pi\)
0.0721760 + 0.997392i \(0.477006\pi\)
\(798\) 0 0
\(799\) −2.87451 −0.101693
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3.26222 −0.115121
\(804\) 0 0
\(805\) −4.41777 −0.155706
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 17.9172 0.629935 0.314967 0.949102i \(-0.398006\pi\)
0.314967 + 0.949102i \(0.398006\pi\)
\(810\) 0 0
\(811\) −33.1654 −1.16459 −0.582297 0.812976i \(-0.697846\pi\)
−0.582297 + 0.812976i \(0.697846\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.37720 0.153327
\(816\) 0 0
\(817\) 1.80488 0.0631448
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −22.2808 −0.777605 −0.388802 0.921321i \(-0.627111\pi\)
−0.388802 + 0.921321i \(0.627111\pi\)
\(822\) 0 0
\(823\) −43.1993 −1.50583 −0.752916 0.658117i \(-0.771353\pi\)
−0.752916 + 0.658117i \(0.771353\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.5318 0.783509 0.391754 0.920070i \(-0.371868\pi\)
0.391754 + 0.920070i \(0.371868\pi\)
\(828\) 0 0
\(829\) −32.9217 −1.14342 −0.571710 0.820456i \(-0.693720\pi\)
−0.571710 + 0.820456i \(0.693720\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −9.22902 −0.319767
\(834\) 0 0
\(835\) −6.29928 −0.217995
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 32.2158 1.11221 0.556107 0.831111i \(-0.312295\pi\)
0.556107 + 0.831111i \(0.312295\pi\)
\(840\) 0 0
\(841\) 75.5679 2.60579
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −12.4735 −0.429100
\(846\) 0 0
\(847\) 48.3289 1.66060
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0.273677 0.00938154
\(852\) 0 0
\(853\) −18.2941 −0.626378 −0.313189 0.949691i \(-0.601397\pi\)
−0.313189 + 0.949691i \(0.601397\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 7.56651 0.258467 0.129233 0.991614i \(-0.458748\pi\)
0.129233 + 0.991614i \(0.458748\pi\)
\(858\) 0 0
\(859\) −19.0228 −0.649050 −0.324525 0.945877i \(-0.605204\pi\)
−0.324525 + 0.945877i \(0.605204\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 41.2309 1.40352 0.701759 0.712415i \(-0.252398\pi\)
0.701759 + 0.712415i \(0.252398\pi\)
\(864\) 0 0
\(865\) 6.90390 0.234740
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.21302 0.108994
\(870\) 0 0
\(871\) 6.21273 0.210510
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.41777 −0.149348
\(876\) 0 0
\(877\) 39.9178 1.34793 0.673964 0.738764i \(-0.264590\pi\)
0.673964 + 0.738764i \(0.264590\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 38.6579 1.30242 0.651209 0.758898i \(-0.274262\pi\)
0.651209 + 0.758898i \(0.274262\pi\)
\(882\) 0 0
\(883\) 39.8513 1.34110 0.670551 0.741864i \(-0.266058\pi\)
0.670551 + 0.741864i \(0.266058\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.90143 0.0974204 0.0487102 0.998813i \(-0.484489\pi\)
0.0487102 + 0.998813i \(0.484489\pi\)
\(888\) 0 0
\(889\) 18.3073 0.614008
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 6.83952 0.228876
\(894\) 0 0
\(895\) −3.27569 −0.109494
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 35.4118 1.18105
\(900\) 0 0
\(901\) 3.78031 0.125940
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.828526 0.0275411
\(906\) 0 0
\(907\) −23.5967 −0.783516 −0.391758 0.920068i \(-0.628133\pi\)
−0.391758 + 0.920068i \(0.628133\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 29.0893 0.963771 0.481886 0.876234i \(-0.339952\pi\)
0.481886 + 0.876234i \(0.339952\pi\)
\(912\) 0 0
\(913\) 4.00225 0.132455
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −39.1841 −1.29397
\(918\) 0 0
\(919\) −21.1153 −0.696530 −0.348265 0.937396i \(-0.613229\pi\)
−0.348265 + 0.937396i \(0.613229\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.97437 −0.0649872
\(924\) 0 0
\(925\) 0.273677 0.00899846
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −6.96102 −0.228384 −0.114192 0.993459i \(-0.536428\pi\)
−0.114192 + 0.993459i \(0.536428\pi\)
\(930\) 0 0
\(931\) 21.9592 0.719685
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.181089 0.00592224
\(936\) 0 0
\(937\) 36.3321 1.18692 0.593459 0.804864i \(-0.297762\pi\)
0.593459 + 0.804864i \(0.297762\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 50.9998 1.66254 0.831272 0.555865i \(-0.187613\pi\)
0.831272 + 0.555865i \(0.187613\pi\)
\(942\) 0 0
\(943\) 6.36154 0.207160
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.02468 −0.0657933 −0.0328967 0.999459i \(-0.510473\pi\)
−0.0328967 + 0.999459i \(0.510473\pi\)
\(948\) 0 0
\(949\) 9.63837 0.312875
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −40.7067 −1.31862 −0.659309 0.751872i \(-0.729151\pi\)
−0.659309 + 0.751872i \(0.729151\pi\)
\(954\) 0 0
\(955\) 8.79434 0.284578
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −43.8324 −1.41542
\(960\) 0 0
\(961\) −19.0078 −0.613156
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5.30469 −0.170764
\(966\) 0 0
\(967\) −35.4889 −1.14125 −0.570623 0.821212i \(-0.693298\pi\)
−0.570623 + 0.821212i \(0.693298\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −16.8380 −0.540357 −0.270179 0.962810i \(-0.587083\pi\)
−0.270179 + 0.962810i \(0.587083\pi\)
\(972\) 0 0
\(973\) 44.4665 1.42553
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 34.9820 1.11917 0.559586 0.828772i \(-0.310960\pi\)
0.559586 + 0.828772i \(0.310960\pi\)
\(978\) 0 0
\(979\) −3.48694 −0.111443
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 34.4075 1.09743 0.548715 0.836010i \(-0.315117\pi\)
0.548715 + 0.836010i \(0.315117\pi\)
\(984\) 0 0
\(985\) 17.2703 0.550277
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.02877 0.0327131
\(990\) 0 0
\(991\) −3.81411 −0.121159 −0.0605796 0.998163i \(-0.519295\pi\)
−0.0605796 + 0.998163i \(0.519295\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0.0989687 0.00313752
\(996\) 0 0
\(997\) −32.6186 −1.03304 −0.516520 0.856275i \(-0.672773\pi\)
−0.516520 + 0.856275i \(0.672773\pi\)
\(998\) 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.bu.1.1 yes 6
3.2 odd 2 8280.2.a.bt.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bt.1.1 6 3.2 odd 2
8280.2.a.bu.1.1 yes 6 1.1 even 1 trivial