Properties

Label 8280.2.a.bv.1.7
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $7$
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: \(7\)
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 1.7
Root \(-1.44295\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +4.19500 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +4.19500 q^{7} +1.38918 q^{11} -6.52161 q^{13} +5.47124 q^{17} -3.72005 q^{19} -1.00000 q^{23} +1.00000 q^{25} -0.0800846 q^{29} +6.53599 q^{31} -4.19500 q^{35} -4.51480 q^{37} -8.32175 q^{41} +9.02002 q^{43} -0.818220 q^{47} +10.5980 q^{49} +9.55813 q^{53} -1.38918 q^{55} +1.34251 q^{59} -12.3566 q^{61} +6.52161 q^{65} +0.926124 q^{67} +13.6775 q^{71} +2.65805 q^{73} +5.82760 q^{77} +10.6365 q^{79} +10.2496 q^{83} -5.47124 q^{85} +5.66172 q^{89} -27.3581 q^{91} +3.72005 q^{95} -9.57250 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 7 q^{5} - 6 q^{7}+O(q^{10}) \) 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
\(7\) 4.19500 1.58556 0.792780 0.609508i \(-0.208633\pi\)
0.792780 + 0.609508i \(0.208633\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.38918 0.418853 0.209427 0.977824i \(-0.432840\pi\)
0.209427 + 0.977824i \(0.432840\pi\)
\(12\) 0 0
\(13\) −6.52161 −1.80877 −0.904384 0.426719i \(-0.859669\pi\)
−0.904384 + 0.426719i \(0.859669\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.47124 1.32697 0.663485 0.748189i \(-0.269077\pi\)
0.663485 + 0.748189i \(0.269077\pi\)
\(18\) 0 0
\(19\) −3.72005 −0.853439 −0.426719 0.904384i \(-0.640331\pi\)
−0.426719 + 0.904384i \(0.640331\pi\)
\(20\) 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
\(29\) −0.0800846 −0.0148713 −0.00743567 0.999972i \(-0.502367\pi\)
−0.00743567 + 0.999972i \(0.502367\pi\)
\(30\) 0 0
\(31\) 6.53599 1.17390 0.586949 0.809624i \(-0.300329\pi\)
0.586949 + 0.809624i \(0.300329\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.19500 −0.709084
\(36\) 0 0
\(37\) −4.51480 −0.742229 −0.371115 0.928587i \(-0.621024\pi\)
−0.371115 + 0.928587i \(0.621024\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.32175 −1.29964 −0.649819 0.760089i \(-0.725155\pi\)
−0.649819 + 0.760089i \(0.725155\pi\)
\(42\) 0 0
\(43\) 9.02002 1.37554 0.687770 0.725929i \(-0.258590\pi\)
0.687770 + 0.725929i \(0.258590\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.818220 −0.119350 −0.0596748 0.998218i \(-0.519006\pi\)
−0.0596748 + 0.998218i \(0.519006\pi\)
\(48\) 0 0
\(49\) 10.5980 1.51400
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.55813 1.31291 0.656455 0.754365i \(-0.272055\pi\)
0.656455 + 0.754365i \(0.272055\pi\)
\(54\) 0 0
\(55\) −1.38918 −0.187317
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.34251 0.174780 0.0873901 0.996174i \(-0.472147\pi\)
0.0873901 + 0.996174i \(0.472147\pi\)
\(60\) 0 0
\(61\) −12.3566 −1.58210 −0.791049 0.611753i \(-0.790464\pi\)
−0.791049 + 0.611753i \(0.790464\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.52161 0.808906
\(66\) 0 0
\(67\) 0.926124 0.113144 0.0565720 0.998399i \(-0.481983\pi\)
0.0565720 + 0.998399i \(0.481983\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.6775 1.62322 0.811611 0.584199i \(-0.198591\pi\)
0.811611 + 0.584199i \(0.198591\pi\)
\(72\) 0 0
\(73\) 2.65805 0.311101 0.155551 0.987828i \(-0.450285\pi\)
0.155551 + 0.987828i \(0.450285\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.82760 0.664116
\(78\) 0 0
\(79\) 10.6365 1.19670 0.598351 0.801234i \(-0.295823\pi\)
0.598351 + 0.801234i \(0.295823\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.2496 1.12504 0.562520 0.826784i \(-0.309832\pi\)
0.562520 + 0.826784i \(0.309832\pi\)
\(84\) 0 0
\(85\) −5.47124 −0.593439
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.66172 0.600141 0.300070 0.953917i \(-0.402990\pi\)
0.300070 + 0.953917i \(0.402990\pi\)
\(90\) 0 0
\(91\) −27.3581 −2.86791
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.72005 0.381669
\(96\) 0 0
\(97\) −9.57250 −0.971941 −0.485970 0.873975i \(-0.661534\pi\)
−0.485970 + 0.873975i \(0.661534\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.13666 −0.610620 −0.305310 0.952253i \(-0.598760\pi\)
−0.305310 + 0.952253i \(0.598760\pi\)
\(102\) 0 0
\(103\) −1.34469 −0.132497 −0.0662483 0.997803i \(-0.521103\pi\)
−0.0662483 + 0.997803i \(0.521103\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.2809 1.47726 0.738631 0.674110i \(-0.235472\pi\)
0.738631 + 0.674110i \(0.235472\pi\)
\(108\) 0 0
\(109\) 8.56884 0.820746 0.410373 0.911918i \(-0.365399\pi\)
0.410373 + 0.911918i \(0.365399\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.41466 0.321225 0.160612 0.987018i \(-0.448653\pi\)
0.160612 + 0.987018i \(0.448653\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 22.9518 2.10399
\(120\) 0 0
\(121\) −9.07018 −0.824562
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −10.6977 −0.949268 −0.474634 0.880183i \(-0.657420\pi\)
−0.474634 + 0.880183i \(0.657420\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.66916 0.407946 0.203973 0.978976i \(-0.434614\pi\)
0.203973 + 0.978976i \(0.434614\pi\)
\(132\) 0 0
\(133\) −15.6056 −1.35318
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.5224 1.49704 0.748521 0.663111i \(-0.230764\pi\)
0.748521 + 0.663111i \(0.230764\pi\)
\(138\) 0 0
\(139\) 4.10698 0.348349 0.174175 0.984715i \(-0.444274\pi\)
0.174175 + 0.984715i \(0.444274\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.05968 −0.757608
\(144\) 0 0
\(145\) 0.0800846 0.00665066
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.7539 1.12676 0.563381 0.826197i \(-0.309500\pi\)
0.563381 + 0.826197i \(0.309500\pi\)
\(150\) 0 0
\(151\) 5.77352 0.469843 0.234921 0.972014i \(-0.424517\pi\)
0.234921 + 0.972014i \(0.424517\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.53599 −0.524983
\(156\) 0 0
\(157\) −15.2428 −1.21651 −0.608253 0.793743i \(-0.708130\pi\)
−0.608253 + 0.793743i \(0.708130\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.19500 −0.330612
\(162\) 0 0
\(163\) −3.12599 −0.244846 −0.122423 0.992478i \(-0.539066\pi\)
−0.122423 + 0.992478i \(0.539066\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −22.4858 −1.74001 −0.870003 0.493047i \(-0.835883\pi\)
−0.870003 + 0.493047i \(0.835883\pi\)
\(168\) 0 0
\(169\) 29.5314 2.27164
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.11858 −0.237101 −0.118551 0.992948i \(-0.537825\pi\)
−0.118551 + 0.992948i \(0.537825\pi\)
\(174\) 0 0
\(175\) 4.19500 0.317112
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.8859 0.813650 0.406825 0.913506i \(-0.366636\pi\)
0.406825 + 0.913506i \(0.366636\pi\)
\(180\) 0 0
\(181\) −14.6206 −1.08674 −0.543370 0.839493i \(-0.682852\pi\)
−0.543370 + 0.839493i \(0.682852\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.51480 0.331935
\(186\) 0 0
\(187\) 7.60053 0.555806
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 25.1397 1.81904 0.909521 0.415658i \(-0.136449\pi\)
0.909521 + 0.415658i \(0.136449\pi\)
\(192\) 0 0
\(193\) 16.1194 1.16030 0.580151 0.814509i \(-0.302994\pi\)
0.580151 + 0.814509i \(0.302994\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.21932 −0.371861 −0.185931 0.982563i \(-0.559530\pi\)
−0.185931 + 0.982563i \(0.559530\pi\)
\(198\) 0 0
\(199\) 18.0160 1.27712 0.638560 0.769572i \(-0.279530\pi\)
0.638560 + 0.769572i \(0.279530\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.335954 −0.0235794
\(204\) 0 0
\(205\) 8.32175 0.581216
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.16782 −0.357466
\(210\) 0 0
\(211\) −19.4355 −1.33799 −0.668997 0.743265i \(-0.733276\pi\)
−0.668997 + 0.743265i \(0.733276\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −9.02002 −0.615160
\(216\) 0 0
\(217\) 27.4184 1.86128
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −35.6813 −2.40018
\(222\) 0 0
\(223\) −1.23063 −0.0824089 −0.0412045 0.999151i \(-0.513120\pi\)
−0.0412045 + 0.999151i \(0.513120\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 27.2664 1.80973 0.904867 0.425693i \(-0.139970\pi\)
0.904867 + 0.425693i \(0.139970\pi\)
\(228\) 0 0
\(229\) 6.71929 0.444023 0.222012 0.975044i \(-0.428738\pi\)
0.222012 + 0.975044i \(0.428738\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.35418 0.219740 0.109870 0.993946i \(-0.464957\pi\)
0.109870 + 0.993946i \(0.464957\pi\)
\(234\) 0 0
\(235\) 0.818220 0.0533748
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7.35598 −0.475819 −0.237909 0.971287i \(-0.576462\pi\)
−0.237909 + 0.971287i \(0.576462\pi\)
\(240\) 0 0
\(241\) −16.1874 −1.04273 −0.521363 0.853335i \(-0.674576\pi\)
−0.521363 + 0.853335i \(0.674576\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −10.5980 −0.677081
\(246\) 0 0
\(247\) 24.2607 1.54367
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −14.5288 −0.917052 −0.458526 0.888681i \(-0.651622\pi\)
−0.458526 + 0.888681i \(0.651622\pi\)
\(252\) 0 0
\(253\) −1.38918 −0.0873369
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.16352 −0.322092 −0.161046 0.986947i \(-0.551487\pi\)
−0.161046 + 0.986947i \(0.551487\pi\)
\(258\) 0 0
\(259\) −18.9396 −1.17685
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 20.1083 1.23993 0.619965 0.784629i \(-0.287147\pi\)
0.619965 + 0.784629i \(0.287147\pi\)
\(264\) 0 0
\(265\) −9.55813 −0.587151
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −14.1485 −0.862652 −0.431326 0.902196i \(-0.641954\pi\)
−0.431326 + 0.902196i \(0.641954\pi\)
\(270\) 0 0
\(271\) −29.7004 −1.80417 −0.902084 0.431560i \(-0.857963\pi\)
−0.902084 + 0.431560i \(0.857963\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.38918 0.0837706
\(276\) 0 0
\(277\) 27.4666 1.65031 0.825154 0.564908i \(-0.191089\pi\)
0.825154 + 0.564908i \(0.191089\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.1314 0.723697 0.361849 0.932237i \(-0.382146\pi\)
0.361849 + 0.932237i \(0.382146\pi\)
\(282\) 0 0
\(283\) −30.3898 −1.80649 −0.903243 0.429129i \(-0.858821\pi\)
−0.903243 + 0.429129i \(0.858821\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −34.9097 −2.06065
\(288\) 0 0
\(289\) 12.9344 0.760850
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.6470 0.680424 0.340212 0.940349i \(-0.389501\pi\)
0.340212 + 0.940349i \(0.389501\pi\)
\(294\) 0 0
\(295\) −1.34251 −0.0781641
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.52161 0.377154
\(300\) 0 0
\(301\) 37.8389 2.18100
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12.3566 0.707535
\(306\) 0 0
\(307\) 16.8549 0.961959 0.480979 0.876732i \(-0.340281\pi\)
0.480979 + 0.876732i \(0.340281\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.28068 0.242735 0.121368 0.992608i \(-0.461272\pi\)
0.121368 + 0.992608i \(0.461272\pi\)
\(312\) 0 0
\(313\) 6.32499 0.357510 0.178755 0.983894i \(-0.442793\pi\)
0.178755 + 0.983894i \(0.442793\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.02393 −0.113675 −0.0568376 0.998383i \(-0.518102\pi\)
−0.0568376 + 0.998383i \(0.518102\pi\)
\(318\) 0 0
\(319\) −0.111252 −0.00622890
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −20.3533 −1.13249
\(324\) 0 0
\(325\) −6.52161 −0.361754
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.43243 −0.189236
\(330\) 0 0
\(331\) 6.37187 0.350229 0.175115 0.984548i \(-0.443970\pi\)
0.175115 + 0.984548i \(0.443970\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.926124 −0.0505996
\(336\) 0 0
\(337\) −7.95253 −0.433202 −0.216601 0.976260i \(-0.569497\pi\)
−0.216601 + 0.976260i \(0.569497\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 9.07965 0.491691
\(342\) 0 0
\(343\) 15.0935 0.814975
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −27.2135 −1.46090 −0.730450 0.682967i \(-0.760689\pi\)
−0.730450 + 0.682967i \(0.760689\pi\)
\(348\) 0 0
\(349\) −6.30951 −0.337740 −0.168870 0.985638i \(-0.554012\pi\)
−0.168870 + 0.985638i \(0.554012\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 26.6301 1.41738 0.708690 0.705520i \(-0.249287\pi\)
0.708690 + 0.705520i \(0.249287\pi\)
\(354\) 0 0
\(355\) −13.6775 −0.725927
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 28.9743 1.52921 0.764603 0.644501i \(-0.222935\pi\)
0.764603 + 0.644501i \(0.222935\pi\)
\(360\) 0 0
\(361\) −5.16120 −0.271642
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.65805 −0.139129
\(366\) 0 0
\(367\) 1.00117 0.0522608 0.0261304 0.999659i \(-0.491681\pi\)
0.0261304 + 0.999659i \(0.491681\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 40.0963 2.08170
\(372\) 0 0
\(373\) 25.2755 1.30872 0.654359 0.756184i \(-0.272939\pi\)
0.654359 + 0.756184i \(0.272939\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.522280 0.0268988
\(378\) 0 0
\(379\) −16.1132 −0.827677 −0.413838 0.910350i \(-0.635812\pi\)
−0.413838 + 0.910350i \(0.635812\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −17.3135 −0.884677 −0.442338 0.896848i \(-0.645851\pi\)
−0.442338 + 0.896848i \(0.645851\pi\)
\(384\) 0 0
\(385\) −5.82760 −0.297002
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −25.0782 −1.27151 −0.635757 0.771889i \(-0.719312\pi\)
−0.635757 + 0.771889i \(0.719312\pi\)
\(390\) 0 0
\(391\) −5.47124 −0.276692
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −10.6365 −0.535181
\(396\) 0 0
\(397\) 5.62513 0.282317 0.141159 0.989987i \(-0.454917\pi\)
0.141159 + 0.989987i \(0.454917\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 33.7974 1.68776 0.843881 0.536530i \(-0.180265\pi\)
0.843881 + 0.536530i \(0.180265\pi\)
\(402\) 0 0
\(403\) −42.6251 −2.12331
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.27187 −0.310885
\(408\) 0 0
\(409\) 34.9871 1.73000 0.865001 0.501770i \(-0.167318\pi\)
0.865001 + 0.501770i \(0.167318\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.63183 0.277124
\(414\) 0 0
\(415\) −10.2496 −0.503133
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.54710 0.368700 0.184350 0.982861i \(-0.440982\pi\)
0.184350 + 0.982861i \(0.440982\pi\)
\(420\) 0 0
\(421\) 24.9315 1.21509 0.607544 0.794286i \(-0.292155\pi\)
0.607544 + 0.794286i \(0.292155\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.47124 0.265394
\(426\) 0 0
\(427\) −51.8358 −2.50851
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −36.4090 −1.75376 −0.876880 0.480709i \(-0.840379\pi\)
−0.876880 + 0.480709i \(0.840379\pi\)
\(432\) 0 0
\(433\) 31.4774 1.51271 0.756353 0.654163i \(-0.226979\pi\)
0.756353 + 0.654163i \(0.226979\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.72005 0.177954
\(438\) 0 0
\(439\) 28.4963 1.36006 0.680028 0.733186i \(-0.261968\pi\)
0.680028 + 0.733186i \(0.261968\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.45319 −0.116555 −0.0582774 0.998300i \(-0.518561\pi\)
−0.0582774 + 0.998300i \(0.518561\pi\)
\(444\) 0 0
\(445\) −5.66172 −0.268391
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −31.7979 −1.50064 −0.750318 0.661077i \(-0.770100\pi\)
−0.750318 + 0.661077i \(0.770100\pi\)
\(450\) 0 0
\(451\) −11.5604 −0.544358
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 27.3581 1.28257
\(456\) 0 0
\(457\) 9.85843 0.461158 0.230579 0.973054i \(-0.425938\pi\)
0.230579 + 0.973054i \(0.425938\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 22.7458 1.05938 0.529689 0.848192i \(-0.322309\pi\)
0.529689 + 0.848192i \(0.322309\pi\)
\(462\) 0 0
\(463\) −4.32054 −0.200793 −0.100396 0.994948i \(-0.532011\pi\)
−0.100396 + 0.994948i \(0.532011\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.9073 1.33767 0.668835 0.743411i \(-0.266793\pi\)
0.668835 + 0.743411i \(0.266793\pi\)
\(468\) 0 0
\(469\) 3.88509 0.179397
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.5304 0.576149
\(474\) 0 0
\(475\) −3.72005 −0.170688
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18.6190 0.850725 0.425363 0.905023i \(-0.360147\pi\)
0.425363 + 0.905023i \(0.360147\pi\)
\(480\) 0 0
\(481\) 29.4438 1.34252
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.57250 0.434665
\(486\) 0 0
\(487\) −11.7879 −0.534162 −0.267081 0.963674i \(-0.586059\pi\)
−0.267081 + 0.963674i \(0.586059\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.20818 0.280171 0.140086 0.990139i \(-0.455262\pi\)
0.140086 + 0.990139i \(0.455262\pi\)
\(492\) 0 0
\(493\) −0.438162 −0.0197338
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 57.3771 2.57371
\(498\) 0 0
\(499\) −9.59513 −0.429537 −0.214769 0.976665i \(-0.568900\pi\)
−0.214769 + 0.976665i \(0.568900\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.09477 −0.0934014 −0.0467007 0.998909i \(-0.514871\pi\)
−0.0467007 + 0.998909i \(0.514871\pi\)
\(504\) 0 0
\(505\) 6.13666 0.273078
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.79838 −0.0797116 −0.0398558 0.999205i \(-0.512690\pi\)
−0.0398558 + 0.999205i \(0.512690\pi\)
\(510\) 0 0
\(511\) 11.1505 0.493270
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.34469 0.0592543
\(516\) 0 0
\(517\) −1.13665 −0.0499899
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 34.0735 1.49279 0.746394 0.665505i \(-0.231784\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(522\) 0 0
\(523\) 9.17733 0.401297 0.200648 0.979663i \(-0.435695\pi\)
0.200648 + 0.979663i \(0.435695\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 35.7599 1.55773
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 54.2712 2.35075
\(534\) 0 0
\(535\) −15.2809 −0.660652
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.7225 0.634143
\(540\) 0 0
\(541\) −42.8568 −1.84256 −0.921278 0.388904i \(-0.872854\pi\)
−0.921278 + 0.388904i \(0.872854\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.56884 −0.367049
\(546\) 0 0
\(547\) −27.7808 −1.18782 −0.593910 0.804531i \(-0.702416\pi\)
−0.593910 + 0.804531i \(0.702416\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.297919 0.0126918
\(552\) 0 0
\(553\) 44.6202 1.89744
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 38.4609 1.62964 0.814821 0.579713i \(-0.196835\pi\)
0.814821 + 0.579713i \(0.196835\pi\)
\(558\) 0 0
\(559\) −58.8250 −2.48803
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.48037 0.0623900 0.0311950 0.999513i \(-0.490069\pi\)
0.0311950 + 0.999513i \(0.490069\pi\)
\(564\) 0 0
\(565\) −3.41466 −0.143656
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19.3434 0.810918 0.405459 0.914113i \(-0.367112\pi\)
0.405459 + 0.914113i \(0.367112\pi\)
\(570\) 0 0
\(571\) 22.6781 0.949049 0.474525 0.880242i \(-0.342620\pi\)
0.474525 + 0.880242i \(0.342620\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 39.1602 1.63026 0.815131 0.579277i \(-0.196665\pi\)
0.815131 + 0.579277i \(0.196665\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 42.9970 1.78382
\(582\) 0 0
\(583\) 13.2779 0.549916
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.46112 0.225405 0.112702 0.993629i \(-0.464049\pi\)
0.112702 + 0.993629i \(0.464049\pi\)
\(588\) 0 0
\(589\) −24.3142 −1.00185
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −37.4952 −1.53974 −0.769872 0.638199i \(-0.779680\pi\)
−0.769872 + 0.638199i \(0.779680\pi\)
\(594\) 0 0
\(595\) −22.9518 −0.940933
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 27.7667 1.13452 0.567258 0.823540i \(-0.308004\pi\)
0.567258 + 0.823540i \(0.308004\pi\)
\(600\) 0 0
\(601\) 22.6366 0.923368 0.461684 0.887044i \(-0.347245\pi\)
0.461684 + 0.887044i \(0.347245\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.07018 0.368755
\(606\) 0 0
\(607\) −23.4302 −0.951004 −0.475502 0.879715i \(-0.657734\pi\)
−0.475502 + 0.879715i \(0.657734\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.33611 0.215876
\(612\) 0 0
\(613\) 0.0416709 0.00168307 0.000841536 1.00000i \(-0.499732\pi\)
0.000841536 1.00000i \(0.499732\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.45842 0.139231 0.0696153 0.997574i \(-0.477823\pi\)
0.0696153 + 0.997574i \(0.477823\pi\)
\(618\) 0 0
\(619\) 40.4554 1.62604 0.813020 0.582236i \(-0.197822\pi\)
0.813020 + 0.582236i \(0.197822\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 23.7509 0.951559
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24.7016 −0.984916
\(630\) 0 0
\(631\) −1.62353 −0.0646316 −0.0323158 0.999478i \(-0.510288\pi\)
−0.0323158 + 0.999478i \(0.510288\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.6977 0.424526
\(636\) 0 0
\(637\) −69.1159 −2.73847
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −38.8215 −1.53336 −0.766679 0.642031i \(-0.778092\pi\)
−0.766679 + 0.642031i \(0.778092\pi\)
\(642\) 0 0
\(643\) 29.2735 1.15443 0.577216 0.816591i \(-0.304139\pi\)
0.577216 + 0.816591i \(0.304139\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.0574 −0.709910 −0.354955 0.934883i \(-0.615504\pi\)
−0.354955 + 0.934883i \(0.615504\pi\)
\(648\) 0 0
\(649\) 1.86499 0.0732072
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −15.4664 −0.605246 −0.302623 0.953110i \(-0.597862\pi\)
−0.302623 + 0.953110i \(0.597862\pi\)
\(654\) 0 0
\(655\) −4.66916 −0.182439
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −15.3613 −0.598392 −0.299196 0.954192i \(-0.596719\pi\)
−0.299196 + 0.954192i \(0.596719\pi\)
\(660\) 0 0
\(661\) 28.6455 1.11418 0.557090 0.830452i \(-0.311918\pi\)
0.557090 + 0.830452i \(0.311918\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 15.6056 0.605160
\(666\) 0 0
\(667\) 0.0800846 0.00310089
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −17.1655 −0.662666
\(672\) 0 0
\(673\) −41.6064 −1.60381 −0.801904 0.597453i \(-0.796179\pi\)
−0.801904 + 0.597453i \(0.796179\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −40.7994 −1.56805 −0.784024 0.620731i \(-0.786836\pi\)
−0.784024 + 0.620731i \(0.786836\pi\)
\(678\) 0 0
\(679\) −40.1566 −1.54107
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −11.7416 −0.449280 −0.224640 0.974442i \(-0.572121\pi\)
−0.224640 + 0.974442i \(0.572121\pi\)
\(684\) 0 0
\(685\) −17.5224 −0.669497
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −62.3344 −2.37475
\(690\) 0 0
\(691\) 39.3669 1.49759 0.748794 0.662803i \(-0.230633\pi\)
0.748794 + 0.662803i \(0.230633\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.10698 −0.155787
\(696\) 0 0
\(697\) −45.5303 −1.72458
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 37.6494 1.42200 0.710999 0.703193i \(-0.248243\pi\)
0.710999 + 0.703193i \(0.248243\pi\)
\(702\) 0 0
\(703\) 16.7953 0.633447
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −25.7433 −0.968175
\(708\) 0 0
\(709\) 24.7527 0.929607 0.464804 0.885414i \(-0.346125\pi\)
0.464804 + 0.885414i \(0.346125\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.53599 −0.244775
\(714\) 0 0
\(715\) 9.05968 0.338813
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 11.6759 0.435436 0.217718 0.976012i \(-0.430139\pi\)
0.217718 + 0.976012i \(0.430139\pi\)
\(720\) 0 0
\(721\) −5.64098 −0.210081
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.0800846 −0.00297427
\(726\) 0 0
\(727\) 6.13549 0.227553 0.113776 0.993506i \(-0.463705\pi\)
0.113776 + 0.993506i \(0.463705\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 49.3507 1.82530
\(732\) 0 0
\(733\) −16.4803 −0.608713 −0.304356 0.952558i \(-0.598441\pi\)
−0.304356 + 0.952558i \(0.598441\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.28655 0.0473907
\(738\) 0 0
\(739\) 5.31851 0.195644 0.0978222 0.995204i \(-0.468812\pi\)
0.0978222 + 0.995204i \(0.468812\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32.5739 1.19502 0.597509 0.801862i \(-0.296157\pi\)
0.597509 + 0.801862i \(0.296157\pi\)
\(744\) 0 0
\(745\) −13.7539 −0.503904
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 64.1034 2.34229
\(750\) 0 0
\(751\) 11.3057 0.412552 0.206276 0.978494i \(-0.433865\pi\)
0.206276 + 0.978494i \(0.433865\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.77352 −0.210120
\(756\) 0 0
\(757\) 34.9036 1.26859 0.634296 0.773090i \(-0.281290\pi\)
0.634296 + 0.773090i \(0.281290\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −11.4872 −0.416412 −0.208206 0.978085i \(-0.566763\pi\)
−0.208206 + 0.978085i \(0.566763\pi\)
\(762\) 0 0
\(763\) 35.9462 1.30134
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.75534 −0.316137
\(768\) 0 0
\(769\) 30.9891 1.11750 0.558749 0.829337i \(-0.311282\pi\)
0.558749 + 0.829337i \(0.311282\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −19.6586 −0.707070 −0.353535 0.935421i \(-0.615020\pi\)
−0.353535 + 0.935421i \(0.615020\pi\)
\(774\) 0 0
\(775\) 6.53599 0.234780
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 30.9573 1.10916
\(780\) 0 0
\(781\) 19.0005 0.679891
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15.2428 0.544038
\(786\) 0 0
\(787\) −25.8432 −0.921211 −0.460606 0.887605i \(-0.652368\pi\)
−0.460606 + 0.887605i \(0.652368\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14.3245 0.509321
\(792\) 0 0
\(793\) 80.5847 2.86165
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 41.4039 1.46660 0.733300 0.679905i \(-0.237979\pi\)
0.733300 + 0.679905i \(0.237979\pi\)
\(798\) 0 0
\(799\) −4.47667 −0.158373
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.69251 0.130306
\(804\) 0 0
\(805\) 4.19500 0.147854
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 22.7280 0.799074 0.399537 0.916717i \(-0.369171\pi\)
0.399537 + 0.916717i \(0.369171\pi\)
\(810\) 0 0
\(811\) −32.7765 −1.15094 −0.575469 0.817823i \(-0.695181\pi\)
−0.575469 + 0.817823i \(0.695181\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3.12599 0.109498
\(816\) 0 0
\(817\) −33.5550 −1.17394
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30.8895 −1.07805 −0.539025 0.842290i \(-0.681207\pi\)
−0.539025 + 0.842290i \(0.681207\pi\)
\(822\) 0 0
\(823\) 0.0656550 0.00228859 0.00114430 0.999999i \(-0.499636\pi\)
0.00114430 + 0.999999i \(0.499636\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −15.6009 −0.542498 −0.271249 0.962509i \(-0.587437\pi\)
−0.271249 + 0.962509i \(0.587437\pi\)
\(828\) 0 0
\(829\) 17.0003 0.590444 0.295222 0.955429i \(-0.404606\pi\)
0.295222 + 0.955429i \(0.404606\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 57.9841 2.00903
\(834\) 0 0
\(835\) 22.4858 0.778154
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −26.2506 −0.906270 −0.453135 0.891442i \(-0.649694\pi\)
−0.453135 + 0.891442i \(0.649694\pi\)
\(840\) 0 0
\(841\) −28.9936 −0.999779
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −29.5314 −1.01591
\(846\) 0 0
\(847\) −38.0494 −1.30739
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.51480 0.154766
\(852\) 0 0
\(853\) −17.1224 −0.586260 −0.293130 0.956073i \(-0.594697\pi\)
−0.293130 + 0.956073i \(0.594697\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.93396 −0.0660627 −0.0330314 0.999454i \(-0.510516\pi\)
−0.0330314 + 0.999454i \(0.510516\pi\)
\(858\) 0 0
\(859\) 21.3189 0.727391 0.363696 0.931518i \(-0.381515\pi\)
0.363696 + 0.931518i \(0.381515\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 20.8030 0.708144 0.354072 0.935218i \(-0.384797\pi\)
0.354072 + 0.935218i \(0.384797\pi\)
\(864\) 0 0
\(865\) 3.11858 0.106035
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 14.7760 0.501242
\(870\) 0 0
\(871\) −6.03982 −0.204651
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.19500 −0.141817
\(876\) 0 0
\(877\) −28.4013 −0.959044 −0.479522 0.877530i \(-0.659190\pi\)
−0.479522 + 0.877530i \(0.659190\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −9.48486 −0.319553 −0.159776 0.987153i \(-0.551077\pi\)
−0.159776 + 0.987153i \(0.551077\pi\)
\(882\) 0 0
\(883\) −4.62619 −0.155684 −0.0778418 0.996966i \(-0.524803\pi\)
−0.0778418 + 0.996966i \(0.524803\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.36560 −0.146582 −0.0732912 0.997311i \(-0.523350\pi\)
−0.0732912 + 0.997311i \(0.523350\pi\)
\(888\) 0 0
\(889\) −44.8768 −1.50512
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.04382 0.101858
\(894\) 0 0
\(895\) −10.8859 −0.363876
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −0.523432 −0.0174574
\(900\) 0 0
\(901\) 52.2948 1.74219
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.6206 0.486005
\(906\) 0 0
\(907\) −12.8413 −0.426389 −0.213194 0.977010i \(-0.568387\pi\)
−0.213194 + 0.977010i \(0.568387\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −58.4104 −1.93522 −0.967612 0.252442i \(-0.918766\pi\)
−0.967612 + 0.252442i \(0.918766\pi\)
\(912\) 0 0
\(913\) 14.2385 0.471226
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 19.5871 0.646823
\(918\) 0 0
\(919\) 35.6291 1.17530 0.587648 0.809117i \(-0.300054\pi\)
0.587648 + 0.809117i \(0.300054\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −89.1993 −2.93603
\(924\) 0 0
\(925\) −4.51480 −0.148446
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −54.3493 −1.78314 −0.891571 0.452881i \(-0.850396\pi\)
−0.891571 + 0.452881i \(0.850396\pi\)
\(930\) 0 0
\(931\) −39.4251 −1.29211
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −7.60053 −0.248564
\(936\) 0 0
\(937\) −36.0273 −1.17696 −0.588481 0.808511i \(-0.700274\pi\)
−0.588481 + 0.808511i \(0.700274\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −31.6004 −1.03014 −0.515072 0.857147i \(-0.672235\pi\)
−0.515072 + 0.857147i \(0.672235\pi\)
\(942\) 0 0
\(943\) 8.32175 0.270993
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 9.97970 0.324297 0.162148 0.986766i \(-0.448158\pi\)
0.162148 + 0.986766i \(0.448158\pi\)
\(948\) 0 0
\(949\) −17.3348 −0.562710
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −49.2845 −1.59648 −0.798240 0.602339i \(-0.794236\pi\)
−0.798240 + 0.602339i \(0.794236\pi\)
\(954\) 0 0
\(955\) −25.1397 −0.813500
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 73.5065 2.37365
\(960\) 0 0
\(961\) 11.7191 0.378036
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −16.1194 −0.518903
\(966\) 0 0
\(967\) −38.5827 −1.24074 −0.620368 0.784311i \(-0.713017\pi\)
−0.620368 + 0.784311i \(0.713017\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −29.8162 −0.956849 −0.478424 0.878129i \(-0.658792\pi\)
−0.478424 + 0.878129i \(0.658792\pi\)
\(972\) 0 0
\(973\) 17.2288 0.552328
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −14.0676 −0.450063 −0.225031 0.974351i \(-0.572248\pi\)
−0.225031 + 0.974351i \(0.572248\pi\)
\(978\) 0 0
\(979\) 7.86514 0.251371
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −28.8527 −0.920258 −0.460129 0.887852i \(-0.652197\pi\)
−0.460129 + 0.887852i \(0.652197\pi\)
\(984\) 0 0
\(985\) 5.21932 0.166301
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9.02002 −0.286820
\(990\) 0 0
\(991\) −9.52333 −0.302518 −0.151259 0.988494i \(-0.548333\pi\)
−0.151259 + 0.988494i \(0.548333\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −18.0160 −0.571146
\(996\) 0 0
\(997\) 42.3081 1.33991 0.669956 0.742401i \(-0.266313\pi\)
0.669956 + 0.742401i \(0.266313\pi\)
\(998\) 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.bv.1.7 7
3.2 odd 2 8280.2.a.bw.1.7 yes 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bv.1.7 7 1.1 even 1 trivial
8280.2.a.bw.1.7 yes 7 3.2 odd 2