Properties

Label 8280.2.a.bu.1.5
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
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: \(0\)
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 1.5
Root \(-1.88788\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +2.71231 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +2.71231 q^{7} +2.76466 q^{11} -1.01111 q^{13} -4.50408 q^{17} +4.76466 q^{19} +1.00000 q^{23} +1.00000 q^{25} +8.08400 q^{29} -5.49297 q^{31} +2.71231 q^{35} -10.9865 q^{37} -2.43515 q^{41} +5.77576 q^{43} +11.0389 q^{47} +0.356621 q^{49} +8.15293 q^{53} +2.76466 q^{55} -1.70120 q^{59} +3.12524 q^{61} -1.01111 q^{65} +5.56190 q^{67} -2.07456 q^{71} +9.63646 q^{73} +7.49860 q^{77} -3.63942 q^{79} +11.7908 q^{83} -4.50408 q^{85} +4.13786 q^{89} -2.74244 q^{91} +4.76466 q^{95} +9.89141 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{5} - 2 q^{7}+O(q^{10}) \) 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
\(7\) 2.71231 1.02516 0.512578 0.858641i \(-0.328690\pi\)
0.512578 + 0.858641i \(0.328690\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.76466 0.833575 0.416787 0.909004i \(-0.363156\pi\)
0.416787 + 0.909004i \(0.363156\pi\)
\(12\) 0 0
\(13\) −1.01111 −0.280431 −0.140215 0.990121i \(-0.544780\pi\)
−0.140215 + 0.990121i \(0.544780\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.50408 −1.09240 −0.546199 0.837655i \(-0.683926\pi\)
−0.546199 + 0.837655i \(0.683926\pi\)
\(18\) 0 0
\(19\) 4.76466 1.09309 0.546543 0.837431i \(-0.315943\pi\)
0.546543 + 0.837431i \(0.315943\pi\)
\(20\) 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
\(29\) 8.08400 1.50116 0.750581 0.660779i \(-0.229774\pi\)
0.750581 + 0.660779i \(0.229774\pi\)
\(30\) 0 0
\(31\) −5.49297 −0.986566 −0.493283 0.869869i \(-0.664203\pi\)
−0.493283 + 0.869869i \(0.664203\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.71231 0.458464
\(36\) 0 0
\(37\) −10.9865 −1.80617 −0.903086 0.429460i \(-0.858704\pi\)
−0.903086 + 0.429460i \(0.858704\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.43515 −0.380306 −0.190153 0.981754i \(-0.560898\pi\)
−0.190153 + 0.981754i \(0.560898\pi\)
\(42\) 0 0
\(43\) 5.77576 0.880796 0.440398 0.897803i \(-0.354837\pi\)
0.440398 + 0.897803i \(0.354837\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.0389 1.61018 0.805092 0.593150i \(-0.202116\pi\)
0.805092 + 0.593150i \(0.202116\pi\)
\(48\) 0 0
\(49\) 0.356621 0.0509459
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.15293 1.11989 0.559946 0.828529i \(-0.310822\pi\)
0.559946 + 0.828529i \(0.310822\pi\)
\(54\) 0 0
\(55\) 2.76466 0.372786
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.70120 −0.221477 −0.110739 0.993850i \(-0.535322\pi\)
−0.110739 + 0.993850i \(0.535322\pi\)
\(60\) 0 0
\(61\) 3.12524 0.400146 0.200073 0.979781i \(-0.435882\pi\)
0.200073 + 0.979781i \(0.435882\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.01111 −0.125413
\(66\) 0 0
\(67\) 5.56190 0.679494 0.339747 0.940517i \(-0.389659\pi\)
0.339747 + 0.940517i \(0.389659\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.07456 −0.246205 −0.123103 0.992394i \(-0.539284\pi\)
−0.123103 + 0.992394i \(0.539284\pi\)
\(72\) 0 0
\(73\) 9.63646 1.12786 0.563931 0.825822i \(-0.309288\pi\)
0.563931 + 0.825822i \(0.309288\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.49860 0.854545
\(78\) 0 0
\(79\) −3.63942 −0.409466 −0.204733 0.978818i \(-0.565633\pi\)
−0.204733 + 0.978818i \(0.565633\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.7908 1.29421 0.647106 0.762400i \(-0.275979\pi\)
0.647106 + 0.762400i \(0.275979\pi\)
\(84\) 0 0
\(85\) −4.50408 −0.488536
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.13786 0.438612 0.219306 0.975656i \(-0.429621\pi\)
0.219306 + 0.975656i \(0.429621\pi\)
\(90\) 0 0
\(91\) −2.74244 −0.287486
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.76466 0.488843
\(96\) 0 0
\(97\) 9.89141 1.00432 0.502160 0.864775i \(-0.332539\pi\)
0.502160 + 0.864775i \(0.332539\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.44068 −0.839879 −0.419940 0.907552i \(-0.637949\pi\)
−0.419940 + 0.907552i \(0.637949\pi\)
\(102\) 0 0
\(103\) −8.73948 −0.861127 −0.430563 0.902560i \(-0.641685\pi\)
−0.430563 + 0.902560i \(0.641685\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.79235 0.559967 0.279984 0.960005i \(-0.409671\pi\)
0.279984 + 0.960005i \(0.409671\pi\)
\(108\) 0 0
\(109\) 1.83848 0.176094 0.0880472 0.996116i \(-0.471937\pi\)
0.0880472 + 0.996116i \(0.471937\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.3076 −1.53409 −0.767045 0.641594i \(-0.778274\pi\)
−0.767045 + 0.641594i \(0.778274\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −12.2164 −1.11988
\(120\) 0 0
\(121\) −3.35668 −0.305153
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 9.89235 0.877804 0.438902 0.898535i \(-0.355367\pi\)
0.438902 + 0.898535i \(0.355367\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.90346 −0.603158 −0.301579 0.953441i \(-0.597514\pi\)
−0.301579 + 0.953441i \(0.597514\pi\)
\(132\) 0 0
\(133\) 12.9232 1.12059
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.90267 0.846042 0.423021 0.906120i \(-0.360970\pi\)
0.423021 + 0.906120i \(0.360970\pi\)
\(138\) 0 0
\(139\) −1.37884 −0.116951 −0.0584757 0.998289i \(-0.518624\pi\)
−0.0584757 + 0.998289i \(0.518624\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.79537 −0.233760
\(144\) 0 0
\(145\) 8.08400 0.671340
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 12.2213 1.00121 0.500603 0.865677i \(-0.333112\pi\)
0.500603 + 0.865677i \(0.333112\pi\)
\(150\) 0 0
\(151\) 7.69883 0.626522 0.313261 0.949667i \(-0.398579\pi\)
0.313261 + 0.949667i \(0.398579\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.49297 −0.441206
\(156\) 0 0
\(157\) −24.0768 −1.92154 −0.960769 0.277351i \(-0.910543\pi\)
−0.960769 + 0.277351i \(0.910543\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.71231 0.213760
\(162\) 0 0
\(163\) 4.96372 0.388788 0.194394 0.980923i \(-0.437726\pi\)
0.194394 + 0.980923i \(0.437726\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.9010 0.843545 0.421772 0.906702i \(-0.361408\pi\)
0.421772 + 0.906702i \(0.361408\pi\)
\(168\) 0 0
\(169\) −11.9777 −0.921358
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 25.9508 1.97300 0.986502 0.163749i \(-0.0523588\pi\)
0.986502 + 0.163749i \(0.0523588\pi\)
\(174\) 0 0
\(175\) 2.71231 0.205031
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.8398 −0.959692 −0.479846 0.877353i \(-0.659307\pi\)
−0.479846 + 0.877353i \(0.659307\pi\)
\(180\) 0 0
\(181\) 17.9453 1.33386 0.666931 0.745119i \(-0.267608\pi\)
0.666931 + 0.745119i \(0.267608\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −10.9865 −0.807745
\(186\) 0 0
\(187\) −12.4522 −0.910596
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.25756 0.669854 0.334927 0.942244i \(-0.391288\pi\)
0.334927 + 0.942244i \(0.391288\pi\)
\(192\) 0 0
\(193\) −0.0109521 −0.000788349 0 −0.000394175 1.00000i \(-0.500125\pi\)
−0.000394175 1.00000i \(0.500125\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.0906 0.932669 0.466334 0.884609i \(-0.345574\pi\)
0.466334 + 0.884609i \(0.345574\pi\)
\(198\) 0 0
\(199\) −22.8980 −1.62320 −0.811600 0.584214i \(-0.801403\pi\)
−0.811600 + 0.584214i \(0.801403\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 21.9263 1.53893
\(204\) 0 0
\(205\) −2.43515 −0.170078
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 13.1726 0.911170
\(210\) 0 0
\(211\) −3.36789 −0.231855 −0.115927 0.993258i \(-0.536984\pi\)
−0.115927 + 0.993258i \(0.536984\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.77576 0.393904
\(216\) 0 0
\(217\) −14.8986 −1.01138
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.55411 0.306342
\(222\) 0 0
\(223\) −12.5922 −0.843235 −0.421617 0.906774i \(-0.638537\pi\)
−0.421617 + 0.906774i \(0.638537\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.4192 1.02341 0.511704 0.859162i \(-0.329014\pi\)
0.511704 + 0.859162i \(0.329014\pi\)
\(228\) 0 0
\(229\) −19.1989 −1.26870 −0.634348 0.773047i \(-0.718732\pi\)
−0.634348 + 0.773047i \(0.718732\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −14.3059 −0.937208 −0.468604 0.883408i \(-0.655243\pi\)
−0.468604 + 0.883408i \(0.655243\pi\)
\(234\) 0 0
\(235\) 11.0389 0.720096
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.39449 −0.219571 −0.109786 0.993955i \(-0.535016\pi\)
−0.109786 + 0.993955i \(0.535016\pi\)
\(240\) 0 0
\(241\) 21.8564 1.40790 0.703949 0.710251i \(-0.251418\pi\)
0.703949 + 0.710251i \(0.251418\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.356621 0.0227837
\(246\) 0 0
\(247\) −4.81758 −0.306535
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7.97778 0.503553 0.251777 0.967785i \(-0.418985\pi\)
0.251777 + 0.967785i \(0.418985\pi\)
\(252\) 0 0
\(253\) 2.76466 0.173812
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.06272 0.502938 0.251469 0.967865i \(-0.419086\pi\)
0.251469 + 0.967865i \(0.419086\pi\)
\(258\) 0 0
\(259\) −29.7988 −1.85161
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.4983 −1.14065 −0.570327 0.821418i \(-0.693184\pi\)
−0.570327 + 0.821418i \(0.693184\pi\)
\(264\) 0 0
\(265\) 8.15293 0.500831
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.59724 0.158356 0.0791781 0.996860i \(-0.474770\pi\)
0.0791781 + 0.996860i \(0.474770\pi\)
\(270\) 0 0
\(271\) 19.2867 1.17158 0.585792 0.810462i \(-0.300784\pi\)
0.585792 + 0.810462i \(0.300784\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.76466 0.166715
\(276\) 0 0
\(277\) 23.6618 1.42170 0.710849 0.703345i \(-0.248311\pi\)
0.710849 + 0.703345i \(0.248311\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.1611 1.44133 0.720666 0.693282i \(-0.243836\pi\)
0.720666 + 0.693282i \(0.243836\pi\)
\(282\) 0 0
\(283\) −29.1229 −1.73117 −0.865587 0.500758i \(-0.833055\pi\)
−0.865587 + 0.500758i \(0.833055\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.60487 −0.389873
\(288\) 0 0
\(289\) 3.28670 0.193335
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.92004 −0.404273 −0.202137 0.979357i \(-0.564789\pi\)
−0.202137 + 0.979357i \(0.564789\pi\)
\(294\) 0 0
\(295\) −1.70120 −0.0990477
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.01111 −0.0584739
\(300\) 0 0
\(301\) 15.6657 0.902953
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.12524 0.178951
\(306\) 0 0
\(307\) −3.85481 −0.220006 −0.110003 0.993931i \(-0.535086\pi\)
−0.110003 + 0.993931i \(0.535086\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −13.6124 −0.771891 −0.385946 0.922522i \(-0.626125\pi\)
−0.385946 + 0.922522i \(0.626125\pi\)
\(312\) 0 0
\(313\) −10.1674 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.24812 0.182433 0.0912164 0.995831i \(-0.470924\pi\)
0.0912164 + 0.995831i \(0.470924\pi\)
\(318\) 0 0
\(319\) 22.3495 1.25133
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −21.4604 −1.19409
\(324\) 0 0
\(325\) −1.01111 −0.0560862
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 29.9408 1.65069
\(330\) 0 0
\(331\) −28.0304 −1.54069 −0.770346 0.637626i \(-0.779916\pi\)
−0.770346 + 0.637626i \(0.779916\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.56190 0.303879
\(336\) 0 0
\(337\) 9.39686 0.511880 0.255940 0.966693i \(-0.417615\pi\)
0.255940 + 0.966693i \(0.417615\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −15.1862 −0.822377
\(342\) 0 0
\(343\) −18.0189 −0.972929
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.55153 −0.190656 −0.0953280 0.995446i \(-0.530390\pi\)
−0.0953280 + 0.995446i \(0.530390\pi\)
\(348\) 0 0
\(349\) −16.1614 −0.865101 −0.432551 0.901610i \(-0.642386\pi\)
−0.432551 + 0.901610i \(0.642386\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.4955 0.558618 0.279309 0.960201i \(-0.409895\pi\)
0.279309 + 0.960201i \(0.409895\pi\)
\(354\) 0 0
\(355\) −2.07456 −0.110106
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.17832 −0.431635 −0.215818 0.976434i \(-0.569242\pi\)
−0.215818 + 0.976434i \(0.569242\pi\)
\(360\) 0 0
\(361\) 3.70194 0.194839
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.63646 0.504395
\(366\) 0 0
\(367\) −2.59818 −0.135624 −0.0678119 0.997698i \(-0.521602\pi\)
−0.0678119 + 0.997698i \(0.521602\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 22.1133 1.14806
\(372\) 0 0
\(373\) −13.6018 −0.704277 −0.352139 0.935948i \(-0.614545\pi\)
−0.352139 + 0.935948i \(0.614545\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.17380 −0.420972
\(378\) 0 0
\(379\) −19.3421 −0.993539 −0.496770 0.867882i \(-0.665481\pi\)
−0.496770 + 0.867882i \(0.665481\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −26.7947 −1.36915 −0.684573 0.728944i \(-0.740011\pi\)
−0.684573 + 0.728944i \(0.740011\pi\)
\(384\) 0 0
\(385\) 7.49860 0.382164
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.27292 −0.470156 −0.235078 0.971977i \(-0.575535\pi\)
−0.235078 + 0.971977i \(0.575535\pi\)
\(390\) 0 0
\(391\) −4.50408 −0.227781
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.63942 −0.183119
\(396\) 0 0
\(397\) 37.1497 1.86449 0.932245 0.361829i \(-0.117848\pi\)
0.932245 + 0.361829i \(0.117848\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.91752 0.295507 0.147754 0.989024i \(-0.452796\pi\)
0.147754 + 0.989024i \(0.452796\pi\)
\(402\) 0 0
\(403\) 5.55399 0.276664
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −30.3739 −1.50558
\(408\) 0 0
\(409\) 21.7069 1.07334 0.536669 0.843793i \(-0.319682\pi\)
0.536669 + 0.843793i \(0.319682\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.61418 −0.227049
\(414\) 0 0
\(415\) 11.7908 0.578789
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 22.5305 1.10069 0.550343 0.834939i \(-0.314497\pi\)
0.550343 + 0.834939i \(0.314497\pi\)
\(420\) 0 0
\(421\) 13.5912 0.662393 0.331197 0.943562i \(-0.392548\pi\)
0.331197 + 0.943562i \(0.392548\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.50408 −0.218480
\(426\) 0 0
\(427\) 8.47661 0.410212
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 34.9812 1.68498 0.842492 0.538709i \(-0.181088\pi\)
0.842492 + 0.538709i \(0.181088\pi\)
\(432\) 0 0
\(433\) 23.3040 1.11992 0.559959 0.828520i \(-0.310817\pi\)
0.559959 + 0.828520i \(0.310817\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.76466 0.227924
\(438\) 0 0
\(439\) −14.8907 −0.710693 −0.355347 0.934735i \(-0.615637\pi\)
−0.355347 + 0.934735i \(0.615637\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 21.3841 1.01599 0.507995 0.861360i \(-0.330387\pi\)
0.507995 + 0.861360i \(0.330387\pi\)
\(444\) 0 0
\(445\) 4.13786 0.196153
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −23.9378 −1.12970 −0.564848 0.825195i \(-0.691065\pi\)
−0.564848 + 0.825195i \(0.691065\pi\)
\(450\) 0 0
\(451\) −6.73234 −0.317013
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.74244 −0.128567
\(456\) 0 0
\(457\) 22.9311 1.07267 0.536337 0.844004i \(-0.319808\pi\)
0.536337 + 0.844004i \(0.319808\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 28.3016 1.31814 0.659069 0.752083i \(-0.270951\pi\)
0.659069 + 0.752083i \(0.270951\pi\)
\(462\) 0 0
\(463\) 3.97483 0.184726 0.0923629 0.995725i \(-0.470558\pi\)
0.0923629 + 0.995725i \(0.470558\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.4994 1.17997 0.589987 0.807413i \(-0.299133\pi\)
0.589987 + 0.807413i \(0.299133\pi\)
\(468\) 0 0
\(469\) 15.0856 0.696588
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.9680 0.734209
\(474\) 0 0
\(475\) 4.76466 0.218617
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.37018 0.153987 0.0769936 0.997032i \(-0.475468\pi\)
0.0769936 + 0.997032i \(0.475468\pi\)
\(480\) 0 0
\(481\) 11.1086 0.506507
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.89141 0.449146
\(486\) 0 0
\(487\) −5.98578 −0.271242 −0.135621 0.990761i \(-0.543303\pi\)
−0.135621 + 0.990761i \(0.543303\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.1234 0.547120 0.273560 0.961855i \(-0.411799\pi\)
0.273560 + 0.961855i \(0.411799\pi\)
\(492\) 0 0
\(493\) −36.4109 −1.63987
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.62686 −0.252399
\(498\) 0 0
\(499\) 27.6453 1.23757 0.618786 0.785560i \(-0.287625\pi\)
0.618786 + 0.785560i \(0.287625\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 42.4717 1.89372 0.946860 0.321647i \(-0.104237\pi\)
0.946860 + 0.321647i \(0.104237\pi\)
\(504\) 0 0
\(505\) −8.44068 −0.375605
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −17.5778 −0.779121 −0.389560 0.921001i \(-0.627373\pi\)
−0.389560 + 0.921001i \(0.627373\pi\)
\(510\) 0 0
\(511\) 26.1371 1.15624
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.73948 −0.385108
\(516\) 0 0
\(517\) 30.5186 1.34221
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8.73149 −0.382533 −0.191267 0.981538i \(-0.561260\pi\)
−0.191267 + 0.981538i \(0.561260\pi\)
\(522\) 0 0
\(523\) −13.6153 −0.595357 −0.297679 0.954666i \(-0.596212\pi\)
−0.297679 + 0.954666i \(0.596212\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.7407 1.07772
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.46220 0.106650
\(534\) 0 0
\(535\) 5.79235 0.250425
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.985934 0.0424672
\(540\) 0 0
\(541\) 0.983574 0.0422872 0.0211436 0.999776i \(-0.493269\pi\)
0.0211436 + 0.999776i \(0.493269\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.83848 0.0787518
\(546\) 0 0
\(547\) −7.85622 −0.335908 −0.167954 0.985795i \(-0.553716\pi\)
−0.167954 + 0.985795i \(0.553716\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 38.5175 1.64090
\(552\) 0 0
\(553\) −9.87123 −0.419767
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −31.2056 −1.32223 −0.661113 0.750287i \(-0.729915\pi\)
−0.661113 + 0.750287i \(0.729915\pi\)
\(558\) 0 0
\(559\) −5.83992 −0.247002
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.9061 1.17610 0.588051 0.808823i \(-0.299895\pi\)
0.588051 + 0.808823i \(0.299895\pi\)
\(564\) 0 0
\(565\) −16.3076 −0.686066
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.5055 0.775789 0.387895 0.921704i \(-0.373202\pi\)
0.387895 + 0.921704i \(0.373202\pi\)
\(570\) 0 0
\(571\) −27.5458 −1.15276 −0.576379 0.817183i \(-0.695535\pi\)
−0.576379 + 0.817183i \(0.695535\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 11.1075 0.462411 0.231205 0.972905i \(-0.425733\pi\)
0.231205 + 0.972905i \(0.425733\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 31.9804 1.32677
\(582\) 0 0
\(583\) 22.5400 0.933513
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.28364 −0.259354 −0.129677 0.991556i \(-0.541394\pi\)
−0.129677 + 0.991556i \(0.541394\pi\)
\(588\) 0 0
\(589\) −26.1721 −1.07840
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 19.4385 0.798242 0.399121 0.916898i \(-0.369315\pi\)
0.399121 + 0.916898i \(0.369315\pi\)
\(594\) 0 0
\(595\) −12.2164 −0.500825
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 43.3511 1.77128 0.885640 0.464373i \(-0.153720\pi\)
0.885640 + 0.464373i \(0.153720\pi\)
\(600\) 0 0
\(601\) −31.8988 −1.30118 −0.650589 0.759430i \(-0.725478\pi\)
−0.650589 + 0.759430i \(0.725478\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.35668 −0.136469
\(606\) 0 0
\(607\) −35.1080 −1.42499 −0.712495 0.701677i \(-0.752435\pi\)
−0.712495 + 0.701677i \(0.752435\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −11.1615 −0.451545
\(612\) 0 0
\(613\) 29.7360 1.20103 0.600513 0.799615i \(-0.294963\pi\)
0.600513 + 0.799615i \(0.294963\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.8604 −0.598257 −0.299129 0.954213i \(-0.596696\pi\)
−0.299129 + 0.954213i \(0.596696\pi\)
\(618\) 0 0
\(619\) −41.0063 −1.64818 −0.824091 0.566458i \(-0.808313\pi\)
−0.824091 + 0.566458i \(0.808313\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.2232 0.449646
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 49.4841 1.97306
\(630\) 0 0
\(631\) 4.23016 0.168400 0.0842000 0.996449i \(-0.473167\pi\)
0.0842000 + 0.996449i \(0.473167\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.89235 0.392566
\(636\) 0 0
\(637\) −0.360583 −0.0142868
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.54152 0.218877 0.109438 0.993994i \(-0.465095\pi\)
0.109438 + 0.993994i \(0.465095\pi\)
\(642\) 0 0
\(643\) −49.2134 −1.94079 −0.970393 0.241532i \(-0.922350\pi\)
−0.970393 + 0.241532i \(0.922350\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.3923 1.03759 0.518794 0.854900i \(-0.326381\pi\)
0.518794 + 0.854900i \(0.326381\pi\)
\(648\) 0 0
\(649\) −4.70323 −0.184618
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.60329 −0.375806 −0.187903 0.982188i \(-0.560169\pi\)
−0.187903 + 0.982188i \(0.560169\pi\)
\(654\) 0 0
\(655\) −6.90346 −0.269740
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12.0918 −0.471030 −0.235515 0.971871i \(-0.575678\pi\)
−0.235515 + 0.971871i \(0.575678\pi\)
\(660\) 0 0
\(661\) −14.6996 −0.571749 −0.285874 0.958267i \(-0.592284\pi\)
−0.285874 + 0.958267i \(0.592284\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 12.9232 0.501141
\(666\) 0 0
\(667\) 8.08400 0.313014
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.64020 0.333551
\(672\) 0 0
\(673\) 29.9292 1.15369 0.576843 0.816855i \(-0.304285\pi\)
0.576843 + 0.816855i \(0.304285\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.3623 −0.628855 −0.314427 0.949282i \(-0.601813\pi\)
−0.314427 + 0.949282i \(0.601813\pi\)
\(678\) 0 0
\(679\) 26.8286 1.02959
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 13.2260 0.506080 0.253040 0.967456i \(-0.418570\pi\)
0.253040 + 0.967456i \(0.418570\pi\)
\(684\) 0 0
\(685\) 9.90267 0.378362
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −8.24350 −0.314052
\(690\) 0 0
\(691\) −27.7402 −1.05529 −0.527644 0.849466i \(-0.676924\pi\)
−0.527644 + 0.849466i \(0.676924\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.37884 −0.0523023
\(696\) 0 0
\(697\) 10.9681 0.415446
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −47.8407 −1.80692 −0.903460 0.428673i \(-0.858981\pi\)
−0.903460 + 0.428673i \(0.858981\pi\)
\(702\) 0 0
\(703\) −52.3470 −1.97430
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −22.8937 −0.861008
\(708\) 0 0
\(709\) −11.5861 −0.435127 −0.217563 0.976046i \(-0.569811\pi\)
−0.217563 + 0.976046i \(0.569811\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5.49297 −0.205713
\(714\) 0 0
\(715\) −2.79537 −0.104541
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22.6703 −0.845461 −0.422730 0.906255i \(-0.638928\pi\)
−0.422730 + 0.906255i \(0.638928\pi\)
\(720\) 0 0
\(721\) −23.7042 −0.882790
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 8.08400 0.300232
\(726\) 0 0
\(727\) 52.3465 1.94142 0.970712 0.240247i \(-0.0772286\pi\)
0.970712 + 0.240247i \(0.0772286\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −26.0145 −0.962180
\(732\) 0 0
\(733\) −12.8962 −0.476333 −0.238167 0.971224i \(-0.576546\pi\)
−0.238167 + 0.971224i \(0.576546\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15.3767 0.566409
\(738\) 0 0
\(739\) −9.06928 −0.333619 −0.166809 0.985989i \(-0.553346\pi\)
−0.166809 + 0.985989i \(0.553346\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.1257 0.371478 0.185739 0.982599i \(-0.440532\pi\)
0.185739 + 0.982599i \(0.440532\pi\)
\(744\) 0 0
\(745\) 12.2213 0.447753
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.7106 0.574054
\(750\) 0 0
\(751\) 30.9936 1.13097 0.565486 0.824758i \(-0.308689\pi\)
0.565486 + 0.824758i \(0.308689\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7.69883 0.280189
\(756\) 0 0
\(757\) 4.67914 0.170066 0.0850331 0.996378i \(-0.472900\pi\)
0.0850331 + 0.996378i \(0.472900\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −20.3875 −0.739045 −0.369523 0.929222i \(-0.620479\pi\)
−0.369523 + 0.929222i \(0.620479\pi\)
\(762\) 0 0
\(763\) 4.98653 0.180524
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.72010 0.0621092
\(768\) 0 0
\(769\) 35.9408 1.29606 0.648029 0.761615i \(-0.275593\pi\)
0.648029 + 0.761615i \(0.275593\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.59644 −0.0933873 −0.0466936 0.998909i \(-0.514868\pi\)
−0.0466936 + 0.998909i \(0.514868\pi\)
\(774\) 0 0
\(775\) −5.49297 −0.197313
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −11.6026 −0.415707
\(780\) 0 0
\(781\) −5.73545 −0.205231
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24.0768 −0.859338
\(786\) 0 0
\(787\) −0.456271 −0.0162643 −0.00813215 0.999967i \(-0.502589\pi\)
−0.00813215 + 0.999967i \(0.502589\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −44.2312 −1.57268
\(792\) 0 0
\(793\) −3.15995 −0.112213
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −19.7327 −0.698968 −0.349484 0.936942i \(-0.613643\pi\)
−0.349484 + 0.936942i \(0.613643\pi\)
\(798\) 0 0
\(799\) −49.7199 −1.75896
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 26.6415 0.940158
\(804\) 0 0
\(805\) 2.71231 0.0955963
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 37.1549 1.30630 0.653148 0.757230i \(-0.273448\pi\)
0.653148 + 0.757230i \(0.273448\pi\)
\(810\) 0 0
\(811\) −7.07310 −0.248370 −0.124185 0.992259i \(-0.539632\pi\)
−0.124185 + 0.992259i \(0.539632\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.96372 0.173871
\(816\) 0 0
\(817\) 27.5195 0.962786
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 47.9341 1.67291 0.836456 0.548034i \(-0.184624\pi\)
0.836456 + 0.548034i \(0.184624\pi\)
\(822\) 0 0
\(823\) −3.19538 −0.111384 −0.0556920 0.998448i \(-0.517737\pi\)
−0.0556920 + 0.998448i \(0.517737\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 42.8892 1.49140 0.745701 0.666280i \(-0.232115\pi\)
0.745701 + 0.666280i \(0.232115\pi\)
\(828\) 0 0
\(829\) 13.0412 0.452938 0.226469 0.974018i \(-0.427282\pi\)
0.226469 + 0.974018i \(0.427282\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.60625 −0.0556532
\(834\) 0 0
\(835\) 10.9010 0.377245
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.05070 0.0362741 0.0181371 0.999836i \(-0.494226\pi\)
0.0181371 + 0.999836i \(0.494226\pi\)
\(840\) 0 0
\(841\) 36.3511 1.25348
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −11.9777 −0.412044
\(846\) 0 0
\(847\) −9.10436 −0.312829
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −10.9865 −0.376613
\(852\) 0 0
\(853\) 30.4176 1.04148 0.520739 0.853716i \(-0.325657\pi\)
0.520739 + 0.853716i \(0.325657\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −16.5276 −0.564570 −0.282285 0.959331i \(-0.591092\pi\)
−0.282285 + 0.959331i \(0.591092\pi\)
\(858\) 0 0
\(859\) 2.77145 0.0945607 0.0472803 0.998882i \(-0.484945\pi\)
0.0472803 + 0.998882i \(0.484945\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −29.4820 −1.00358 −0.501790 0.864990i \(-0.667325\pi\)
−0.501790 + 0.864990i \(0.667325\pi\)
\(864\) 0 0
\(865\) 25.9508 0.882354
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −10.0617 −0.341321
\(870\) 0 0
\(871\) −5.62368 −0.190551
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.71231 0.0916928
\(876\) 0 0
\(877\) 52.1487 1.76094 0.880469 0.474104i \(-0.157228\pi\)
0.880469 + 0.474104i \(0.157228\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4.76177 0.160428 0.0802141 0.996778i \(-0.474440\pi\)
0.0802141 + 0.996778i \(0.474440\pi\)
\(882\) 0 0
\(883\) −30.9756 −1.04241 −0.521206 0.853431i \(-0.674518\pi\)
−0.521206 + 0.853431i \(0.674518\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −29.6405 −0.995231 −0.497616 0.867398i \(-0.665791\pi\)
−0.497616 + 0.867398i \(0.665791\pi\)
\(888\) 0 0
\(889\) 26.8311 0.899887
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 52.5964 1.76007
\(894\) 0 0
\(895\) −12.8398 −0.429187
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −44.4051 −1.48099
\(900\) 0 0
\(901\) −36.7214 −1.22337
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 17.9453 0.596521
\(906\) 0 0
\(907\) 13.6636 0.453691 0.226846 0.973931i \(-0.427159\pi\)
0.226846 + 0.973931i \(0.427159\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 24.2035 0.801897 0.400948 0.916101i \(-0.368681\pi\)
0.400948 + 0.916101i \(0.368681\pi\)
\(912\) 0 0
\(913\) 32.5976 1.07882
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −18.7243 −0.618331
\(918\) 0 0
\(919\) −20.4984 −0.676181 −0.338091 0.941114i \(-0.609781\pi\)
−0.338091 + 0.941114i \(0.609781\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.09761 0.0690436
\(924\) 0 0
\(925\) −10.9865 −0.361234
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 28.6058 0.938527 0.469263 0.883058i \(-0.344520\pi\)
0.469263 + 0.883058i \(0.344520\pi\)
\(930\) 0 0
\(931\) 1.69918 0.0556883
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −12.4522 −0.407231
\(936\) 0 0
\(937\) 9.79147 0.319873 0.159937 0.987127i \(-0.448871\pi\)
0.159937 + 0.987127i \(0.448871\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −42.7249 −1.39279 −0.696395 0.717658i \(-0.745214\pi\)
−0.696395 + 0.717658i \(0.745214\pi\)
\(942\) 0 0
\(943\) −2.43515 −0.0792992
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.69250 −0.0874945 −0.0437473 0.999043i \(-0.513930\pi\)
−0.0437473 + 0.999043i \(0.513930\pi\)
\(948\) 0 0
\(949\) −9.74351 −0.316288
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 19.2706 0.624235 0.312117 0.950044i \(-0.398962\pi\)
0.312117 + 0.950044i \(0.398962\pi\)
\(954\) 0 0
\(955\) 9.25756 0.299568
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 26.8591 0.867326
\(960\) 0 0
\(961\) −0.827311 −0.0266874
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.0109521 −0.000352561 0
\(966\) 0 0
\(967\) −16.3997 −0.527378 −0.263689 0.964608i \(-0.584939\pi\)
−0.263689 + 0.964608i \(0.584939\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −54.1667 −1.73829 −0.869146 0.494555i \(-0.835331\pi\)
−0.869146 + 0.494555i \(0.835331\pi\)
\(972\) 0 0
\(973\) −3.73983 −0.119894
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −25.2388 −0.807462 −0.403731 0.914878i \(-0.632287\pi\)
−0.403731 + 0.914878i \(0.632287\pi\)
\(978\) 0 0
\(979\) 11.4398 0.365616
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −29.4824 −0.940343 −0.470172 0.882575i \(-0.655808\pi\)
−0.470172 + 0.882575i \(0.655808\pi\)
\(984\) 0 0
\(985\) 13.0906 0.417102
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 5.77576 0.183659
\(990\) 0 0
\(991\) −37.3421 −1.18621 −0.593105 0.805125i \(-0.702098\pi\)
−0.593105 + 0.805125i \(0.702098\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −22.8980 −0.725917
\(996\) 0 0
\(997\) −41.8442 −1.32522 −0.662609 0.748965i \(-0.730551\pi\)
−0.662609 + 0.748965i \(0.730551\pi\)
\(998\) 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.1.5 yes 6
3.2 odd 2 8280.2.a.bt.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bt.1.5 6 3.2 odd 2
8280.2.a.bu.1.5 yes 6 1.1 even 1 trivial