Properties

Label 8280.2.a.bw.1.5
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $7$
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: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \( x^{7} - 3x^{6} - 18x^{5} + 46x^{4} + 60x^{3} - 76x^{2} - 51x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(4.09437\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} -0.627340 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -0.627340 q^{7} -1.35025 q^{11} +2.31878 q^{13} +5.74602 q^{17} -8.04218 q^{19} +1.00000 q^{23} +1.00000 q^{25} -6.21116 q^{29} -7.91514 q^{31} -0.627340 q^{35} +10.0588 q^{37} -2.48776 q^{41} +4.42390 q^{43} -4.68883 q^{47} -6.60645 q^{49} +2.21712 q^{53} -1.35025 q^{55} -0.999511 q^{59} -9.30722 q^{61} +2.31878 q^{65} -11.0106 q^{67} -9.42438 q^{71} +9.73349 q^{73} +0.847065 q^{77} +3.26504 q^{79} +1.04553 q^{83} +5.74602 q^{85} +2.84494 q^{89} -1.45466 q^{91} -8.04218 q^{95} +7.81347 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 7 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 7 q^{5} - 6 q^{7} - 2 q^{11} - 6 q^{13} - 4 q^{17} - 8 q^{19} + 7 q^{23} + 7 q^{25} + 2 q^{29} - 8 q^{31} - 6 q^{35} - 16 q^{37} + 2 q^{41} - 10 q^{43} - 8 q^{47} + 19 q^{49} - 10 q^{53} - 2 q^{55} - 24 q^{59} + 8 q^{61} - 6 q^{65} - 20 q^{67} - 8 q^{71} + 2 q^{73} - 12 q^{77} - 2 q^{79} - 22 q^{83} - 4 q^{85} - 16 q^{89} - 20 q^{91} - 8 q^{95} + 4 q^{97}+O(q^{100}) \) 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
\(7\) −0.627340 −0.237112 −0.118556 0.992947i \(-0.537827\pi\)
−0.118556 + 0.992947i \(0.537827\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.35025 −0.407115 −0.203558 0.979063i \(-0.565250\pi\)
−0.203558 + 0.979063i \(0.565250\pi\)
\(12\) 0 0
\(13\) 2.31878 0.643114 0.321557 0.946890i \(-0.395794\pi\)
0.321557 + 0.946890i \(0.395794\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.74602 1.39362 0.696808 0.717258i \(-0.254603\pi\)
0.696808 + 0.717258i \(0.254603\pi\)
\(18\) 0 0
\(19\) −8.04218 −1.84500 −0.922501 0.385994i \(-0.873859\pi\)
−0.922501 + 0.385994i \(0.873859\pi\)
\(20\) 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
\(29\) −6.21116 −1.15338 −0.576692 0.816962i \(-0.695657\pi\)
−0.576692 + 0.816962i \(0.695657\pi\)
\(30\) 0 0
\(31\) −7.91514 −1.42160 −0.710800 0.703394i \(-0.751667\pi\)
−0.710800 + 0.703394i \(0.751667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.627340 −0.106040
\(36\) 0 0
\(37\) 10.0588 1.65366 0.826832 0.562449i \(-0.190141\pi\)
0.826832 + 0.562449i \(0.190141\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.48776 −0.388523 −0.194261 0.980950i \(-0.562231\pi\)
−0.194261 + 0.980950i \(0.562231\pi\)
\(42\) 0 0
\(43\) 4.42390 0.674638 0.337319 0.941390i \(-0.390480\pi\)
0.337319 + 0.941390i \(0.390480\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.68883 −0.683936 −0.341968 0.939712i \(-0.611093\pi\)
−0.341968 + 0.939712i \(0.611093\pi\)
\(48\) 0 0
\(49\) −6.60645 −0.943778
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.21712 0.304544 0.152272 0.988339i \(-0.451341\pi\)
0.152272 + 0.988339i \(0.451341\pi\)
\(54\) 0 0
\(55\) −1.35025 −0.182068
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.999511 −0.130125 −0.0650626 0.997881i \(-0.520725\pi\)
−0.0650626 + 0.997881i \(0.520725\pi\)
\(60\) 0 0
\(61\) −9.30722 −1.19167 −0.595833 0.803108i \(-0.703178\pi\)
−0.595833 + 0.803108i \(0.703178\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.31878 0.287609
\(66\) 0 0
\(67\) −11.0106 −1.34516 −0.672578 0.740026i \(-0.734813\pi\)
−0.672578 + 0.740026i \(0.734813\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.42438 −1.11847 −0.559234 0.829010i \(-0.688905\pi\)
−0.559234 + 0.829010i \(0.688905\pi\)
\(72\) 0 0
\(73\) 9.73349 1.13922 0.569609 0.821916i \(-0.307095\pi\)
0.569609 + 0.821916i \(0.307095\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.847065 0.0965320
\(78\) 0 0
\(79\) 3.26504 0.367345 0.183673 0.982987i \(-0.441201\pi\)
0.183673 + 0.982987i \(0.441201\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.04553 0.114761 0.0573807 0.998352i \(-0.481725\pi\)
0.0573807 + 0.998352i \(0.481725\pi\)
\(84\) 0 0
\(85\) 5.74602 0.623244
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.84494 0.301563 0.150782 0.988567i \(-0.451821\pi\)
0.150782 + 0.988567i \(0.451821\pi\)
\(90\) 0 0
\(91\) −1.45466 −0.152490
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.04218 −0.825110
\(96\) 0 0
\(97\) 7.81347 0.793338 0.396669 0.917962i \(-0.370166\pi\)
0.396669 + 0.917962i \(0.370166\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −11.5145 −1.14573 −0.572866 0.819649i \(-0.694168\pi\)
−0.572866 + 0.819649i \(0.694168\pi\)
\(102\) 0 0
\(103\) 6.21129 0.612017 0.306008 0.952029i \(-0.401006\pi\)
0.306008 + 0.952029i \(0.401006\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.34725 −0.710286 −0.355143 0.934812i \(-0.615568\pi\)
−0.355143 + 0.934812i \(0.615568\pi\)
\(108\) 0 0
\(109\) 6.76495 0.647965 0.323983 0.946063i \(-0.394978\pi\)
0.323983 + 0.946063i \(0.394978\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.55728 −0.334641 −0.167320 0.985903i \(-0.553511\pi\)
−0.167320 + 0.985903i \(0.553511\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.60471 −0.330443
\(120\) 0 0
\(121\) −9.17683 −0.834257
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −10.1787 −0.903210 −0.451605 0.892218i \(-0.649148\pi\)
−0.451605 + 0.892218i \(0.649148\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.5369 −1.53220 −0.766102 0.642719i \(-0.777806\pi\)
−0.766102 + 0.642719i \(0.777806\pi\)
\(132\) 0 0
\(133\) 5.04518 0.437472
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.923710 0.0789178 0.0394589 0.999221i \(-0.487437\pi\)
0.0394589 + 0.999221i \(0.487437\pi\)
\(138\) 0 0
\(139\) 12.3527 1.04775 0.523873 0.851796i \(-0.324487\pi\)
0.523873 + 0.851796i \(0.324487\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.13093 −0.261822
\(144\) 0 0
\(145\) −6.21116 −0.515809
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.56285 −0.128034 −0.0640169 0.997949i \(-0.520391\pi\)
−0.0640169 + 0.997949i \(0.520391\pi\)
\(150\) 0 0
\(151\) 16.1330 1.31288 0.656442 0.754377i \(-0.272061\pi\)
0.656442 + 0.754377i \(0.272061\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.91514 −0.635759
\(156\) 0 0
\(157\) −19.2721 −1.53808 −0.769039 0.639201i \(-0.779265\pi\)
−0.769039 + 0.639201i \(0.779265\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.627340 −0.0494413
\(162\) 0 0
\(163\) 6.84160 0.535875 0.267938 0.963436i \(-0.413658\pi\)
0.267938 + 0.963436i \(0.413658\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.1235 1.47982 0.739912 0.672704i \(-0.234867\pi\)
0.739912 + 0.672704i \(0.234867\pi\)
\(168\) 0 0
\(169\) −7.62325 −0.586404
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.9946 −0.835905 −0.417952 0.908469i \(-0.637252\pi\)
−0.417952 + 0.908469i \(0.637252\pi\)
\(174\) 0 0
\(175\) −0.627340 −0.0474224
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.188747 0.0141076 0.00705379 0.999975i \(-0.497755\pi\)
0.00705379 + 0.999975i \(0.497755\pi\)
\(180\) 0 0
\(181\) 13.6547 1.01495 0.507474 0.861667i \(-0.330579\pi\)
0.507474 + 0.861667i \(0.330579\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.0588 0.739541
\(186\) 0 0
\(187\) −7.75856 −0.567362
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.33019 0.675109 0.337555 0.941306i \(-0.390400\pi\)
0.337555 + 0.941306i \(0.390400\pi\)
\(192\) 0 0
\(193\) −15.9196 −1.14592 −0.572959 0.819584i \(-0.694204\pi\)
−0.572959 + 0.819584i \(0.694204\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.14012 −0.294972 −0.147486 0.989064i \(-0.547118\pi\)
−0.147486 + 0.989064i \(0.547118\pi\)
\(198\) 0 0
\(199\) −11.2974 −0.800852 −0.400426 0.916329i \(-0.631138\pi\)
−0.400426 + 0.916329i \(0.631138\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.89651 0.273481
\(204\) 0 0
\(205\) −2.48776 −0.173753
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 10.8589 0.751129
\(210\) 0 0
\(211\) −5.37625 −0.370116 −0.185058 0.982728i \(-0.559247\pi\)
−0.185058 + 0.982728i \(0.559247\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.42390 0.301707
\(216\) 0 0
\(217\) 4.96548 0.337079
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 13.3238 0.896254
\(222\) 0 0
\(223\) 0.171237 0.0114669 0.00573344 0.999984i \(-0.498175\pi\)
0.00573344 + 0.999984i \(0.498175\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.1906 0.875492 0.437746 0.899099i \(-0.355777\pi\)
0.437746 + 0.899099i \(0.355777\pi\)
\(228\) 0 0
\(229\) 7.06100 0.466604 0.233302 0.972404i \(-0.425047\pi\)
0.233302 + 0.972404i \(0.425047\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.5359 −1.01779 −0.508895 0.860829i \(-0.669946\pi\)
−0.508895 + 0.860829i \(0.669946\pi\)
\(234\) 0 0
\(235\) −4.68883 −0.305866
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −19.6546 −1.27135 −0.635675 0.771957i \(-0.719278\pi\)
−0.635675 + 0.771957i \(0.719278\pi\)
\(240\) 0 0
\(241\) 9.43078 0.607490 0.303745 0.952753i \(-0.401763\pi\)
0.303745 + 0.952753i \(0.401763\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.60645 −0.422070
\(246\) 0 0
\(247\) −18.6481 −1.18655
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −19.9799 −1.26112 −0.630561 0.776139i \(-0.717175\pi\)
−0.630561 + 0.776139i \(0.717175\pi\)
\(252\) 0 0
\(253\) −1.35025 −0.0848894
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −19.6706 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(258\) 0 0
\(259\) −6.31031 −0.392104
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 13.8941 0.856748 0.428374 0.903602i \(-0.359087\pi\)
0.428374 + 0.903602i \(0.359087\pi\)
\(264\) 0 0
\(265\) 2.21712 0.136196
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −24.5448 −1.49652 −0.748262 0.663404i \(-0.769111\pi\)
−0.748262 + 0.663404i \(0.769111\pi\)
\(270\) 0 0
\(271\) 1.96182 0.119172 0.0595859 0.998223i \(-0.481022\pi\)
0.0595859 + 0.998223i \(0.481022\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.35025 −0.0814231
\(276\) 0 0
\(277\) 1.86591 0.112112 0.0560560 0.998428i \(-0.482147\pi\)
0.0560560 + 0.998428i \(0.482147\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −19.0904 −1.13884 −0.569420 0.822046i \(-0.692832\pi\)
−0.569420 + 0.822046i \(0.692832\pi\)
\(282\) 0 0
\(283\) −12.4149 −0.737992 −0.368996 0.929431i \(-0.620298\pi\)
−0.368996 + 0.929431i \(0.620298\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.56067 0.0921235
\(288\) 0 0
\(289\) 16.0168 0.942165
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −25.6677 −1.49952 −0.749762 0.661708i \(-0.769832\pi\)
−0.749762 + 0.661708i \(0.769832\pi\)
\(294\) 0 0
\(295\) −0.999511 −0.0581938
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.31878 0.134099
\(300\) 0 0
\(301\) −2.77528 −0.159965
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −9.30722 −0.532930
\(306\) 0 0
\(307\) −28.4044 −1.62112 −0.810562 0.585653i \(-0.800838\pi\)
−0.810562 + 0.585653i \(0.800838\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.2898 0.753596 0.376798 0.926296i \(-0.377025\pi\)
0.376798 + 0.926296i \(0.377025\pi\)
\(312\) 0 0
\(313\) 16.2524 0.918638 0.459319 0.888271i \(-0.348094\pi\)
0.459319 + 0.888271i \(0.348094\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.3091 −1.36533 −0.682667 0.730730i \(-0.739180\pi\)
−0.682667 + 0.730730i \(0.739180\pi\)
\(318\) 0 0
\(319\) 8.38661 0.469560
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −46.2106 −2.57122
\(324\) 0 0
\(325\) 2.31878 0.128623
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.94149 0.162170
\(330\) 0 0
\(331\) 14.2774 0.784757 0.392379 0.919804i \(-0.371652\pi\)
0.392379 + 0.919804i \(0.371652\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −11.0106 −0.601572
\(336\) 0 0
\(337\) −7.07082 −0.385172 −0.192586 0.981280i \(-0.561687\pi\)
−0.192586 + 0.981280i \(0.561687\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10.6874 0.578756
\(342\) 0 0
\(343\) 8.53586 0.460893
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.50299 −0.295416 −0.147708 0.989031i \(-0.547190\pi\)
−0.147708 + 0.989031i \(0.547190\pi\)
\(348\) 0 0
\(349\) −2.21784 −0.118718 −0.0593592 0.998237i \(-0.518906\pi\)
−0.0593592 + 0.998237i \(0.518906\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 17.8763 0.951457 0.475729 0.879592i \(-0.342184\pi\)
0.475729 + 0.879592i \(0.342184\pi\)
\(354\) 0 0
\(355\) −9.42438 −0.500194
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.0365 −1.05748 −0.528742 0.848783i \(-0.677336\pi\)
−0.528742 + 0.848783i \(0.677336\pi\)
\(360\) 0 0
\(361\) 45.6767 2.40403
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.73349 0.509474
\(366\) 0 0
\(367\) −4.03743 −0.210752 −0.105376 0.994432i \(-0.533605\pi\)
−0.105376 + 0.994432i \(0.533605\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.39089 −0.0722112
\(372\) 0 0
\(373\) 21.4729 1.11182 0.555912 0.831241i \(-0.312369\pi\)
0.555912 + 0.831241i \(0.312369\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −14.4023 −0.741757
\(378\) 0 0
\(379\) 6.60661 0.339359 0.169679 0.985499i \(-0.445727\pi\)
0.169679 + 0.985499i \(0.445727\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −22.1012 −1.12932 −0.564660 0.825323i \(-0.690993\pi\)
−0.564660 + 0.825323i \(0.690993\pi\)
\(384\) 0 0
\(385\) 0.847065 0.0431704
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.49684 0.177297 0.0886485 0.996063i \(-0.471745\pi\)
0.0886485 + 0.996063i \(0.471745\pi\)
\(390\) 0 0
\(391\) 5.74602 0.290589
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.26504 0.164282
\(396\) 0 0
\(397\) −13.3465 −0.669844 −0.334922 0.942246i \(-0.608710\pi\)
−0.334922 + 0.942246i \(0.608710\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.1440 −1.30557 −0.652783 0.757545i \(-0.726399\pi\)
−0.652783 + 0.757545i \(0.726399\pi\)
\(402\) 0 0
\(403\) −18.3535 −0.914252
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −13.5819 −0.673232
\(408\) 0 0
\(409\) 26.0639 1.28877 0.644387 0.764699i \(-0.277112\pi\)
0.644387 + 0.764699i \(0.277112\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.627033 0.0308543
\(414\) 0 0
\(415\) 1.04553 0.0513229
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 22.1694 1.08305 0.541523 0.840686i \(-0.317848\pi\)
0.541523 + 0.840686i \(0.317848\pi\)
\(420\) 0 0
\(421\) −1.79226 −0.0873495 −0.0436748 0.999046i \(-0.513907\pi\)
−0.0436748 + 0.999046i \(0.513907\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.74602 0.278723
\(426\) 0 0
\(427\) 5.83879 0.282559
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.95997 0.0944085 0.0472042 0.998885i \(-0.484969\pi\)
0.0472042 + 0.998885i \(0.484969\pi\)
\(432\) 0 0
\(433\) −6.48430 −0.311616 −0.155808 0.987787i \(-0.549798\pi\)
−0.155808 + 0.987787i \(0.549798\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −8.04218 −0.384710
\(438\) 0 0
\(439\) 11.8824 0.567118 0.283559 0.958955i \(-0.408485\pi\)
0.283559 + 0.958955i \(0.408485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.4288 0.590508 0.295254 0.955419i \(-0.404596\pi\)
0.295254 + 0.955419i \(0.404596\pi\)
\(444\) 0 0
\(445\) 2.84494 0.134863
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −29.1634 −1.37631 −0.688154 0.725565i \(-0.741579\pi\)
−0.688154 + 0.725565i \(0.741579\pi\)
\(450\) 0 0
\(451\) 3.35910 0.158174
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.45466 −0.0681957
\(456\) 0 0
\(457\) 29.0382 1.35835 0.679175 0.733977i \(-0.262338\pi\)
0.679175 + 0.733977i \(0.262338\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 41.8601 1.94962 0.974810 0.223037i \(-0.0715971\pi\)
0.974810 + 0.223037i \(0.0715971\pi\)
\(462\) 0 0
\(463\) 18.6791 0.868093 0.434046 0.900890i \(-0.357085\pi\)
0.434046 + 0.900890i \(0.357085\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.6118 0.722426 0.361213 0.932483i \(-0.382363\pi\)
0.361213 + 0.932483i \(0.382363\pi\)
\(468\) 0 0
\(469\) 6.90737 0.318953
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.97336 −0.274655
\(474\) 0 0
\(475\) −8.04218 −0.369001
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −38.7467 −1.77038 −0.885191 0.465228i \(-0.845972\pi\)
−0.885191 + 0.465228i \(0.845972\pi\)
\(480\) 0 0
\(481\) 23.3243 1.06350
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.81347 0.354792
\(486\) 0 0
\(487\) −12.7078 −0.575844 −0.287922 0.957654i \(-0.592964\pi\)
−0.287922 + 0.957654i \(0.592964\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −22.7702 −1.02761 −0.513803 0.857908i \(-0.671764\pi\)
−0.513803 + 0.857908i \(0.671764\pi\)
\(492\) 0 0
\(493\) −35.6895 −1.60737
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.91229 0.265202
\(498\) 0 0
\(499\) 1.63295 0.0731007 0.0365503 0.999332i \(-0.488363\pi\)
0.0365503 + 0.999332i \(0.488363\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.34609 0.372134 0.186067 0.982537i \(-0.440426\pi\)
0.186067 + 0.982537i \(0.440426\pi\)
\(504\) 0 0
\(505\) −11.5145 −0.512387
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.87561 −0.127459 −0.0637295 0.997967i \(-0.520299\pi\)
−0.0637295 + 0.997967i \(0.520299\pi\)
\(510\) 0 0
\(511\) −6.10620 −0.270122
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.21129 0.273702
\(516\) 0 0
\(517\) 6.33109 0.278441
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.69979 −0.205902 −0.102951 0.994686i \(-0.532828\pi\)
−0.102951 + 0.994686i \(0.532828\pi\)
\(522\) 0 0
\(523\) −2.02492 −0.0885436 −0.0442718 0.999020i \(-0.514097\pi\)
−0.0442718 + 0.999020i \(0.514097\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −45.4806 −1.98117
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.76857 −0.249865
\(534\) 0 0
\(535\) −7.34725 −0.317650
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8.92034 0.384226
\(540\) 0 0
\(541\) −26.3432 −1.13258 −0.566292 0.824205i \(-0.691622\pi\)
−0.566292 + 0.824205i \(0.691622\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 6.76495 0.289779
\(546\) 0 0
\(547\) 43.8919 1.87668 0.938342 0.345708i \(-0.112361\pi\)
0.938342 + 0.345708i \(0.112361\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 49.9512 2.12799
\(552\) 0 0
\(553\) −2.04829 −0.0871020
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.91728 −0.250723 −0.125362 0.992111i \(-0.540009\pi\)
−0.125362 + 0.992111i \(0.540009\pi\)
\(558\) 0 0
\(559\) 10.2580 0.433869
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −26.9175 −1.13444 −0.567218 0.823568i \(-0.691980\pi\)
−0.567218 + 0.823568i \(0.691980\pi\)
\(564\) 0 0
\(565\) −3.55728 −0.149656
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12.1385 −0.508871 −0.254435 0.967090i \(-0.581890\pi\)
−0.254435 + 0.967090i \(0.581890\pi\)
\(570\) 0 0
\(571\) −42.2886 −1.76972 −0.884861 0.465855i \(-0.845747\pi\)
−0.884861 + 0.465855i \(0.845747\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −3.35667 −0.139740 −0.0698701 0.997556i \(-0.522258\pi\)
−0.0698701 + 0.997556i \(0.522258\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.655900 −0.0272113
\(582\) 0 0
\(583\) −2.99366 −0.123985
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −29.7175 −1.22657 −0.613286 0.789861i \(-0.710153\pi\)
−0.613286 + 0.789861i \(0.710153\pi\)
\(588\) 0 0
\(589\) 63.6550 2.62286
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 32.9653 1.35372 0.676861 0.736110i \(-0.263340\pi\)
0.676861 + 0.736110i \(0.263340\pi\)
\(594\) 0 0
\(595\) −3.60471 −0.147779
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.98074 −0.203508 −0.101754 0.994810i \(-0.532445\pi\)
−0.101754 + 0.994810i \(0.532445\pi\)
\(600\) 0 0
\(601\) 29.5795 1.20657 0.603286 0.797525i \(-0.293858\pi\)
0.603286 + 0.797525i \(0.293858\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.17683 −0.373091
\(606\) 0 0
\(607\) −8.66850 −0.351843 −0.175922 0.984404i \(-0.556291\pi\)
−0.175922 + 0.984404i \(0.556291\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10.8724 −0.439849
\(612\) 0 0
\(613\) 5.21499 0.210631 0.105316 0.994439i \(-0.466415\pi\)
0.105316 + 0.994439i \(0.466415\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −24.3664 −0.980956 −0.490478 0.871454i \(-0.663178\pi\)
−0.490478 + 0.871454i \(0.663178\pi\)
\(618\) 0 0
\(619\) −20.1629 −0.810417 −0.405209 0.914224i \(-0.632801\pi\)
−0.405209 + 0.914224i \(0.632801\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.78474 −0.0715043
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 57.7984 2.30457
\(630\) 0 0
\(631\) −44.6410 −1.77713 −0.888564 0.458752i \(-0.848297\pi\)
−0.888564 + 0.458752i \(0.848297\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10.1787 −0.403928
\(636\) 0 0
\(637\) −15.3189 −0.606957
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −24.4769 −0.966778 −0.483389 0.875406i \(-0.660594\pi\)
−0.483389 + 0.875406i \(0.660594\pi\)
\(642\) 0 0
\(643\) −16.8712 −0.665333 −0.332667 0.943044i \(-0.607948\pi\)
−0.332667 + 0.943044i \(0.607948\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 14.3206 0.563000 0.281500 0.959561i \(-0.409168\pi\)
0.281500 + 0.959561i \(0.409168\pi\)
\(648\) 0 0
\(649\) 1.34959 0.0529760
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −12.2996 −0.481320 −0.240660 0.970609i \(-0.577364\pi\)
−0.240660 + 0.970609i \(0.577364\pi\)
\(654\) 0 0
\(655\) −17.5369 −0.685222
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.80189 −0.0701916 −0.0350958 0.999384i \(-0.511174\pi\)
−0.0350958 + 0.999384i \(0.511174\pi\)
\(660\) 0 0
\(661\) −29.1017 −1.13192 −0.565962 0.824431i \(-0.691495\pi\)
−0.565962 + 0.824431i \(0.691495\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.04518 0.195644
\(666\) 0 0
\(667\) −6.21116 −0.240497
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.5671 0.485146
\(672\) 0 0
\(673\) 34.1899 1.31792 0.658962 0.752176i \(-0.270996\pi\)
0.658962 + 0.752176i \(0.270996\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.93105 0.266382 0.133191 0.991090i \(-0.457478\pi\)
0.133191 + 0.991090i \(0.457478\pi\)
\(678\) 0 0
\(679\) −4.90170 −0.188110
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 25.2446 0.965957 0.482978 0.875632i \(-0.339555\pi\)
0.482978 + 0.875632i \(0.339555\pi\)
\(684\) 0 0
\(685\) 0.923710 0.0352931
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5.14101 0.195857
\(690\) 0 0
\(691\) 9.81842 0.373510 0.186755 0.982406i \(-0.440203\pi\)
0.186755 + 0.982406i \(0.440203\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12.3527 0.468566
\(696\) 0 0
\(697\) −14.2947 −0.541452
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 26.5157 1.00149 0.500743 0.865596i \(-0.333060\pi\)
0.500743 + 0.865596i \(0.333060\pi\)
\(702\) 0 0
\(703\) −80.8951 −3.05101
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 7.22348 0.271667
\(708\) 0 0
\(709\) −15.0779 −0.566264 −0.283132 0.959081i \(-0.591373\pi\)
−0.283132 + 0.959081i \(0.591373\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.91514 −0.296424
\(714\) 0 0
\(715\) −3.13093 −0.117090
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.37151 −0.349499 −0.174749 0.984613i \(-0.555911\pi\)
−0.174749 + 0.984613i \(0.555911\pi\)
\(720\) 0 0
\(721\) −3.89659 −0.145117
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.21116 −0.230677
\(726\) 0 0
\(727\) −16.6604 −0.617900 −0.308950 0.951078i \(-0.599978\pi\)
−0.308950 + 0.951078i \(0.599978\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 25.4198 0.940186
\(732\) 0 0
\(733\) 10.2290 0.377817 0.188908 0.981995i \(-0.439505\pi\)
0.188908 + 0.981995i \(0.439505\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 14.8670 0.547634
\(738\) 0 0
\(739\) 21.9737 0.808316 0.404158 0.914689i \(-0.367565\pi\)
0.404158 + 0.914689i \(0.367565\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15.0976 0.553877 0.276938 0.960888i \(-0.410680\pi\)
0.276938 + 0.960888i \(0.410680\pi\)
\(744\) 0 0
\(745\) −1.56285 −0.0572584
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.60922 0.168417
\(750\) 0 0
\(751\) −19.1668 −0.699407 −0.349704 0.936860i \(-0.613718\pi\)
−0.349704 + 0.936860i \(0.613718\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.1330 0.587139
\(756\) 0 0
\(757\) −2.54988 −0.0926771 −0.0463385 0.998926i \(-0.514755\pi\)
−0.0463385 + 0.998926i \(0.514755\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −55.0184 −1.99442 −0.997208 0.0746748i \(-0.976208\pi\)
−0.997208 + 0.0746748i \(0.976208\pi\)
\(762\) 0 0
\(763\) −4.24392 −0.153640
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.31765 −0.0836854
\(768\) 0 0
\(769\) 30.3425 1.09418 0.547089 0.837074i \(-0.315736\pi\)
0.547089 + 0.837074i \(0.315736\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36.8692 1.32609 0.663047 0.748578i \(-0.269263\pi\)
0.663047 + 0.748578i \(0.269263\pi\)
\(774\) 0 0
\(775\) −7.91514 −0.284320
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20.0070 0.716826
\(780\) 0 0
\(781\) 12.7253 0.455346
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −19.2721 −0.687850
\(786\) 0 0
\(787\) −33.2534 −1.18536 −0.592678 0.805439i \(-0.701929\pi\)
−0.592678 + 0.805439i \(0.701929\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.23162 0.0793473
\(792\) 0 0
\(793\) −21.5814 −0.766378
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 25.8839 0.916854 0.458427 0.888732i \(-0.348413\pi\)
0.458427 + 0.888732i \(0.348413\pi\)
\(798\) 0 0
\(799\) −26.9421 −0.953144
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −13.1426 −0.463793
\(804\) 0 0
\(805\) −0.627340 −0.0221108
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −35.1660 −1.23637 −0.618186 0.786032i \(-0.712132\pi\)
−0.618186 + 0.786032i \(0.712132\pi\)
\(810\) 0 0
\(811\) 47.7014 1.67502 0.837512 0.546419i \(-0.184009\pi\)
0.837512 + 0.546419i \(0.184009\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6.84160 0.239651
\(816\) 0 0
\(817\) −35.5778 −1.24471
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −44.1313 −1.54019 −0.770097 0.637927i \(-0.779792\pi\)
−0.770097 + 0.637927i \(0.779792\pi\)
\(822\) 0 0
\(823\) 38.9463 1.35758 0.678791 0.734331i \(-0.262504\pi\)
0.678791 + 0.734331i \(0.262504\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −29.4861 −1.02533 −0.512666 0.858588i \(-0.671342\pi\)
−0.512666 + 0.858588i \(0.671342\pi\)
\(828\) 0 0
\(829\) 18.3170 0.636176 0.318088 0.948061i \(-0.396959\pi\)
0.318088 + 0.948061i \(0.396959\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −37.9608 −1.31526
\(834\) 0 0
\(835\) 19.1235 0.661797
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −31.4677 −1.08638 −0.543192 0.839608i \(-0.682785\pi\)
−0.543192 + 0.839608i \(0.682785\pi\)
\(840\) 0 0
\(841\) 9.57849 0.330293
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7.62325 −0.262248
\(846\) 0 0
\(847\) 5.75699 0.197812
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 10.0588 0.344813
\(852\) 0 0
\(853\) 27.6363 0.946250 0.473125 0.880995i \(-0.343126\pi\)
0.473125 + 0.880995i \(0.343126\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16.6011 0.567081 0.283541 0.958960i \(-0.408491\pi\)
0.283541 + 0.958960i \(0.408491\pi\)
\(858\) 0 0
\(859\) 16.0596 0.547947 0.273973 0.961737i \(-0.411662\pi\)
0.273973 + 0.961737i \(0.411662\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 49.7050 1.69198 0.845990 0.533199i \(-0.179010\pi\)
0.845990 + 0.533199i \(0.179010\pi\)
\(864\) 0 0
\(865\) −10.9946 −0.373828
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −4.40861 −0.149552
\(870\) 0 0
\(871\) −25.5311 −0.865089
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.627340 −0.0212079
\(876\) 0 0
\(877\) −26.7142 −0.902075 −0.451037 0.892505i \(-0.648946\pi\)
−0.451037 + 0.892505i \(0.648946\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.0231374 −0.000779520 0 −0.000389760 1.00000i \(-0.500124\pi\)
−0.000389760 1.00000i \(0.500124\pi\)
\(882\) 0 0
\(883\) 30.1060 1.01315 0.506574 0.862196i \(-0.330912\pi\)
0.506574 + 0.862196i \(0.330912\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8.48357 −0.284851 −0.142425 0.989806i \(-0.545490\pi\)
−0.142425 + 0.989806i \(0.545490\pi\)
\(888\) 0 0
\(889\) 6.38548 0.214162
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 37.7084 1.26186
\(894\) 0 0
\(895\) 0.188747 0.00630910
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 49.1622 1.63965
\(900\) 0 0
\(901\) 12.7396 0.424418
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 13.6547 0.453898
\(906\) 0 0
\(907\) −17.0547 −0.566292 −0.283146 0.959077i \(-0.591378\pi\)
−0.283146 + 0.959077i \(0.591378\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −36.2085 −1.19964 −0.599820 0.800135i \(-0.704761\pi\)
−0.599820 + 0.800135i \(0.704761\pi\)
\(912\) 0 0
\(913\) −1.41172 −0.0467212
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11.0016 0.363304
\(918\) 0 0
\(919\) −29.7478 −0.981290 −0.490645 0.871359i \(-0.663239\pi\)
−0.490645 + 0.871359i \(0.663239\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −21.8531 −0.719303
\(924\) 0 0
\(925\) 10.0588 0.330733
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 19.0832 0.626098 0.313049 0.949737i \(-0.398650\pi\)
0.313049 + 0.949737i \(0.398650\pi\)
\(930\) 0 0
\(931\) 53.1302 1.74127
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −7.75856 −0.253732
\(936\) 0 0
\(937\) 1.64285 0.0536694 0.0268347 0.999640i \(-0.491457\pi\)
0.0268347 + 0.999640i \(0.491457\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −35.4789 −1.15658 −0.578289 0.815832i \(-0.696280\pi\)
−0.578289 + 0.815832i \(0.696280\pi\)
\(942\) 0 0
\(943\) −2.48776 −0.0810126
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.50185 −0.113795 −0.0568975 0.998380i \(-0.518121\pi\)
−0.0568975 + 0.998380i \(0.518121\pi\)
\(948\) 0 0
\(949\) 22.5698 0.732648
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −21.3043 −0.690114 −0.345057 0.938582i \(-0.612140\pi\)
−0.345057 + 0.938582i \(0.612140\pi\)
\(954\) 0 0
\(955\) 9.33019 0.301918
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −0.579480 −0.0187124
\(960\) 0 0
\(961\) 31.6494 1.02095
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −15.9196 −0.512470
\(966\) 0 0
\(967\) −27.6522 −0.889234 −0.444617 0.895721i \(-0.646660\pi\)
−0.444617 + 0.895721i \(0.646660\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 55.1373 1.76944 0.884721 0.466121i \(-0.154349\pi\)
0.884721 + 0.466121i \(0.154349\pi\)
\(972\) 0 0
\(973\) −7.74937 −0.248433
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.73362 −0.0554635 −0.0277317 0.999615i \(-0.508828\pi\)
−0.0277317 + 0.999615i \(0.508828\pi\)
\(978\) 0 0
\(979\) −3.84138 −0.122771
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 22.0475 0.703205 0.351602 0.936149i \(-0.385637\pi\)
0.351602 + 0.936149i \(0.385637\pi\)
\(984\) 0 0
\(985\) −4.14012 −0.131915
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.42390 0.140672
\(990\) 0 0
\(991\) −17.4001 −0.552732 −0.276366 0.961052i \(-0.589130\pi\)
−0.276366 + 0.961052i \(0.589130\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −11.2974 −0.358152
\(996\) 0 0
\(997\) −9.32388 −0.295290 −0.147645 0.989040i \(-0.547169\pi\)
−0.147645 + 0.989040i \(0.547169\pi\)
\(998\) 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.bw.1.5 yes 7
3.2 odd 2 8280.2.a.bv.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bv.1.5 7 3.2 odd 2
8280.2.a.bw.1.5 yes 7 1.1 even 1 trivial