Properties

Label 2300.2.a.o.1.1
Level $2300$
Weight $2$
Character 2300.1
Self dual yes
Analytic conductor $18.366$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2300.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.3655924649\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.143376304.1
Defining polynomial: \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 460)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.26443\) of defining polynomial
Character \(\chi\) \(=\) 2300.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.40050 q^{3} +4.41307 q^{7} +2.76241 q^{9} +O(q^{10})\) \(q-2.40050 q^{3} +4.41307 q^{7} +2.76241 q^{9} +2.29289 q^{11} +6.92936 q^{13} +1.51387 q^{17} +2.89920 q^{19} -10.5936 q^{21} +1.00000 q^{23} +0.570328 q^{27} -7.68764 q^{29} +3.85746 q^{31} -5.50408 q^{33} +8.62830 q^{37} -16.6340 q^{39} -6.44324 q^{41} -3.48497 q^{43} -6.19747 q^{47} +12.4752 q^{49} -3.63405 q^{51} +2.17710 q^{53} -6.95953 q^{57} -11.7637 q^{59} -5.11443 q^{61} +12.1907 q^{63} +9.94597 q^{67} -2.40050 q^{69} +3.41407 q^{71} -8.95307 q^{73} +10.1187 q^{77} -1.92694 q^{79} -9.65631 q^{81} +8.04131 q^{83} +18.4542 q^{87} -1.09273 q^{89} +30.5798 q^{91} -9.25985 q^{93} -16.9208 q^{97} +6.33390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 4 q^{3} + 9 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 4 q^{3} + 9 q^{7} + 10 q^{9} + 2 q^{11} + 8 q^{13} + 5 q^{17} + 4 q^{19} + 6 q^{23} + 22 q^{27} + 5 q^{29} + 9 q^{31} - 10 q^{33} + 21 q^{37} - 8 q^{39} - q^{41} + 16 q^{43} + 16 q^{47} + 19 q^{49} - 12 q^{51} - q^{53} + 12 q^{57} - 11 q^{59} - 4 q^{61} + 19 q^{63} + 25 q^{67} + 4 q^{69} - 17 q^{71} - 14 q^{73} + 20 q^{77} + 10 q^{79} + 14 q^{81} + 21 q^{83} + 64 q^{87} - 24 q^{89} - 4 q^{91} + 4 q^{97} - 16 q^{99}+O(q^{100}) \) 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
\(3\) −2.40050 −1.38593 −0.692965 0.720971i \(-0.743696\pi\)
−0.692965 + 0.720971i \(0.743696\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.41307 1.66798 0.833992 0.551777i \(-0.186050\pi\)
0.833992 + 0.551777i \(0.186050\pi\)
\(8\) 0 0
\(9\) 2.76241 0.920804
\(10\) 0 0
\(11\) 2.29289 0.691332 0.345666 0.938358i \(-0.387653\pi\)
0.345666 + 0.938358i \(0.387653\pi\)
\(12\) 0 0
\(13\) 6.92936 1.92186 0.960930 0.276792i \(-0.0892713\pi\)
0.960930 + 0.276792i \(0.0892713\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.51387 0.367168 0.183584 0.983004i \(-0.441230\pi\)
0.183584 + 0.983004i \(0.441230\pi\)
\(18\) 0 0
\(19\) 2.89920 0.665121 0.332561 0.943082i \(-0.392087\pi\)
0.332561 + 0.943082i \(0.392087\pi\)
\(20\) 0 0
\(21\) −10.5936 −2.31171
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.570328 0.109760
\(28\) 0 0
\(29\) −7.68764 −1.42756 −0.713779 0.700371i \(-0.753018\pi\)
−0.713779 + 0.700371i \(0.753018\pi\)
\(30\) 0 0
\(31\) 3.85746 0.692821 0.346410 0.938083i \(-0.387401\pi\)
0.346410 + 0.938083i \(0.387401\pi\)
\(32\) 0 0
\(33\) −5.50408 −0.958138
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.62830 1.41848 0.709242 0.704965i \(-0.249037\pi\)
0.709242 + 0.704965i \(0.249037\pi\)
\(38\) 0 0
\(39\) −16.6340 −2.66356
\(40\) 0 0
\(41\) −6.44324 −1.00626 −0.503132 0.864209i \(-0.667819\pi\)
−0.503132 + 0.864209i \(0.667819\pi\)
\(42\) 0 0
\(43\) −3.48497 −0.531453 −0.265727 0.964048i \(-0.585612\pi\)
−0.265727 + 0.964048i \(0.585612\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.19747 −0.903994 −0.451997 0.892019i \(-0.649288\pi\)
−0.451997 + 0.892019i \(0.649288\pi\)
\(48\) 0 0
\(49\) 12.4752 1.78217
\(50\) 0 0
\(51\) −3.63405 −0.508869
\(52\) 0 0
\(53\) 2.17710 0.299047 0.149524 0.988758i \(-0.452226\pi\)
0.149524 + 0.988758i \(0.452226\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −6.95953 −0.921812
\(58\) 0 0
\(59\) −11.7637 −1.53150 −0.765750 0.643138i \(-0.777632\pi\)
−0.765750 + 0.643138i \(0.777632\pi\)
\(60\) 0 0
\(61\) −5.11443 −0.654835 −0.327418 0.944880i \(-0.606178\pi\)
−0.327418 + 0.944880i \(0.606178\pi\)
\(62\) 0 0
\(63\) 12.1907 1.53589
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 9.94597 1.21509 0.607547 0.794284i \(-0.292154\pi\)
0.607547 + 0.794284i \(0.292154\pi\)
\(68\) 0 0
\(69\) −2.40050 −0.288987
\(70\) 0 0
\(71\) 3.41407 0.405175 0.202588 0.979264i \(-0.435065\pi\)
0.202588 + 0.979264i \(0.435065\pi\)
\(72\) 0 0
\(73\) −8.95307 −1.04788 −0.523939 0.851756i \(-0.675538\pi\)
−0.523939 + 0.851756i \(0.675538\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.1187 1.15313
\(78\) 0 0
\(79\) −1.92694 −0.216798 −0.108399 0.994107i \(-0.534572\pi\)
−0.108399 + 0.994107i \(0.534572\pi\)
\(80\) 0 0
\(81\) −9.65631 −1.07292
\(82\) 0 0
\(83\) 8.04131 0.882648 0.441324 0.897348i \(-0.354509\pi\)
0.441324 + 0.897348i \(0.354509\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 18.4542 1.97850
\(88\) 0 0
\(89\) −1.09273 −0.115829 −0.0579147 0.998322i \(-0.518445\pi\)
−0.0579147 + 0.998322i \(0.518445\pi\)
\(90\) 0 0
\(91\) 30.5798 3.20563
\(92\) 0 0
\(93\) −9.25985 −0.960201
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.9208 −1.71805 −0.859026 0.511933i \(-0.828930\pi\)
−0.859026 + 0.511933i \(0.828930\pi\)
\(98\) 0 0
\(99\) 6.33390 0.636581
\(100\) 0 0
\(101\) 12.9497 1.28855 0.644274 0.764795i \(-0.277160\pi\)
0.644274 + 0.764795i \(0.277160\pi\)
\(102\) 0 0
\(103\) 10.9754 1.08144 0.540721 0.841202i \(-0.318152\pi\)
0.540721 + 0.841202i \(0.318152\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 19.8821 1.92208 0.961040 0.276411i \(-0.0891450\pi\)
0.961040 + 0.276411i \(0.0891450\pi\)
\(108\) 0 0
\(109\) 0.427249 0.0409231 0.0204615 0.999791i \(-0.493486\pi\)
0.0204615 + 0.999791i \(0.493486\pi\)
\(110\) 0 0
\(111\) −20.7123 −1.96592
\(112\) 0 0
\(113\) −5.38533 −0.506609 −0.253304 0.967387i \(-0.581517\pi\)
−0.253304 + 0.967387i \(0.581517\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 19.1418 1.76966
\(118\) 0 0
\(119\) 6.68082 0.612430
\(120\) 0 0
\(121\) −5.74267 −0.522061
\(122\) 0 0
\(123\) 15.4670 1.39461
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 6.16014 0.546624 0.273312 0.961925i \(-0.411881\pi\)
0.273312 + 0.961925i \(0.411881\pi\)
\(128\) 0 0
\(129\) 8.36569 0.736558
\(130\) 0 0
\(131\) 14.6325 1.27845 0.639225 0.769020i \(-0.279255\pi\)
0.639225 + 0.769020i \(0.279255\pi\)
\(132\) 0 0
\(133\) 12.7944 1.10941
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.972256 0.0830654 0.0415327 0.999137i \(-0.486776\pi\)
0.0415327 + 0.999137i \(0.486776\pi\)
\(138\) 0 0
\(139\) 7.74312 0.656763 0.328382 0.944545i \(-0.393497\pi\)
0.328382 + 0.944545i \(0.393497\pi\)
\(140\) 0 0
\(141\) 14.8770 1.25287
\(142\) 0 0
\(143\) 15.8883 1.32864
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −29.9467 −2.46996
\(148\) 0 0
\(149\) −17.6823 −1.44859 −0.724293 0.689492i \(-0.757834\pi\)
−0.724293 + 0.689492i \(0.757834\pi\)
\(150\) 0 0
\(151\) −2.01286 −0.163804 −0.0819022 0.996640i \(-0.526100\pi\)
−0.0819022 + 0.996640i \(0.526100\pi\)
\(152\) 0 0
\(153\) 4.18194 0.338090
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −5.82703 −0.465048 −0.232524 0.972591i \(-0.574698\pi\)
−0.232524 + 0.972591i \(0.574698\pi\)
\(158\) 0 0
\(159\) −5.22612 −0.414459
\(160\) 0 0
\(161\) 4.41307 0.347799
\(162\) 0 0
\(163\) −6.75147 −0.528816 −0.264408 0.964411i \(-0.585177\pi\)
−0.264408 + 0.964411i \(0.585177\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −23.4541 −1.81493 −0.907466 0.420125i \(-0.861986\pi\)
−0.907466 + 0.420125i \(0.861986\pi\)
\(168\) 0 0
\(169\) 35.0161 2.69355
\(170\) 0 0
\(171\) 8.00878 0.612447
\(172\) 0 0
\(173\) −8.28850 −0.630163 −0.315081 0.949065i \(-0.602032\pi\)
−0.315081 + 0.949065i \(0.602032\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 28.2387 2.12255
\(178\) 0 0
\(179\) 1.04002 0.0777345 0.0388673 0.999244i \(-0.487625\pi\)
0.0388673 + 0.999244i \(0.487625\pi\)
\(180\) 0 0
\(181\) 2.71850 0.202065 0.101032 0.994883i \(-0.467785\pi\)
0.101032 + 0.994883i \(0.467785\pi\)
\(182\) 0 0
\(183\) 12.2772 0.907557
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.47114 0.253835
\(188\) 0 0
\(189\) 2.51690 0.183077
\(190\) 0 0
\(191\) 8.04858 0.582375 0.291187 0.956666i \(-0.405950\pi\)
0.291187 + 0.956666i \(0.405950\pi\)
\(192\) 0 0
\(193\) −16.0276 −1.15370 −0.576848 0.816852i \(-0.695717\pi\)
−0.576848 + 0.816852i \(0.695717\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.06316 0.289488 0.144744 0.989469i \(-0.453764\pi\)
0.144744 + 0.989469i \(0.453764\pi\)
\(198\) 0 0
\(199\) 18.7042 1.32590 0.662952 0.748662i \(-0.269303\pi\)
0.662952 + 0.748662i \(0.269303\pi\)
\(200\) 0 0
\(201\) −23.8753 −1.68404
\(202\) 0 0
\(203\) −33.9261 −2.38114
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.76241 0.192001
\(208\) 0 0
\(209\) 6.64753 0.459819
\(210\) 0 0
\(211\) 7.87839 0.542371 0.271185 0.962527i \(-0.412584\pi\)
0.271185 + 0.962527i \(0.412584\pi\)
\(212\) 0 0
\(213\) −8.19548 −0.561545
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 17.0232 1.15561
\(218\) 0 0
\(219\) 21.4919 1.45229
\(220\) 0 0
\(221\) 10.4902 0.705645
\(222\) 0 0
\(223\) −2.29263 −0.153526 −0.0767628 0.997049i \(-0.524458\pi\)
−0.0767628 + 0.997049i \(0.524458\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.8325 0.851725 0.425862 0.904788i \(-0.359971\pi\)
0.425862 + 0.904788i \(0.359971\pi\)
\(228\) 0 0
\(229\) −16.2528 −1.07401 −0.537007 0.843578i \(-0.680445\pi\)
−0.537007 + 0.843578i \(0.680445\pi\)
\(230\) 0 0
\(231\) −24.2899 −1.59816
\(232\) 0 0
\(233\) 21.5410 1.41120 0.705598 0.708613i \(-0.250679\pi\)
0.705598 + 0.708613i \(0.250679\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 4.62563 0.300467
\(238\) 0 0
\(239\) −11.0622 −0.715555 −0.357778 0.933807i \(-0.616465\pi\)
−0.357778 + 0.933807i \(0.616465\pi\)
\(240\) 0 0
\(241\) 18.2164 1.17342 0.586710 0.809797i \(-0.300423\pi\)
0.586710 + 0.809797i \(0.300423\pi\)
\(242\) 0 0
\(243\) 21.4690 1.37724
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 20.0896 1.27827
\(248\) 0 0
\(249\) −19.3032 −1.22329
\(250\) 0 0
\(251\) −10.0182 −0.632345 −0.316172 0.948702i \(-0.602398\pi\)
−0.316172 + 0.948702i \(0.602398\pi\)
\(252\) 0 0
\(253\) 2.29289 0.144153
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.3021 −0.892141 −0.446070 0.894998i \(-0.647177\pi\)
−0.446070 + 0.894998i \(0.647177\pi\)
\(258\) 0 0
\(259\) 38.0773 2.36601
\(260\) 0 0
\(261\) −21.2364 −1.31450
\(262\) 0 0
\(263\) −9.44361 −0.582318 −0.291159 0.956675i \(-0.594041\pi\)
−0.291159 + 0.956675i \(0.594041\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.62311 0.160531
\(268\) 0 0
\(269\) 23.7630 1.44886 0.724428 0.689350i \(-0.242104\pi\)
0.724428 + 0.689350i \(0.242104\pi\)
\(270\) 0 0
\(271\) −17.5939 −1.06875 −0.534375 0.845247i \(-0.679453\pi\)
−0.534375 + 0.845247i \(0.679453\pi\)
\(272\) 0 0
\(273\) −73.4068 −4.44278
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −29.6582 −1.78199 −0.890995 0.454014i \(-0.849992\pi\)
−0.890995 + 0.454014i \(0.849992\pi\)
\(278\) 0 0
\(279\) 10.6559 0.637952
\(280\) 0 0
\(281\) −8.25484 −0.492442 −0.246221 0.969214i \(-0.579189\pi\)
−0.246221 + 0.969214i \(0.579189\pi\)
\(282\) 0 0
\(283\) 9.21317 0.547666 0.273833 0.961777i \(-0.411708\pi\)
0.273833 + 0.961777i \(0.411708\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −28.4344 −1.67843
\(288\) 0 0
\(289\) −14.7082 −0.865188
\(290\) 0 0
\(291\) 40.6185 2.38110
\(292\) 0 0
\(293\) 11.1138 0.649277 0.324639 0.945838i \(-0.394757\pi\)
0.324639 + 0.945838i \(0.394757\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.30770 0.0758804
\(298\) 0 0
\(299\) 6.92936 0.400735
\(300\) 0 0
\(301\) −15.3794 −0.886455
\(302\) 0 0
\(303\) −31.0859 −1.78584
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 18.7800 1.07183 0.535916 0.844272i \(-0.319967\pi\)
0.535916 + 0.844272i \(0.319967\pi\)
\(308\) 0 0
\(309\) −26.3465 −1.49880
\(310\) 0 0
\(311\) 2.51258 0.142475 0.0712377 0.997459i \(-0.477305\pi\)
0.0712377 + 0.997459i \(0.477305\pi\)
\(312\) 0 0
\(313\) 19.9278 1.12638 0.563192 0.826326i \(-0.309573\pi\)
0.563192 + 0.826326i \(0.309573\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −27.8849 −1.56617 −0.783087 0.621912i \(-0.786356\pi\)
−0.783087 + 0.621912i \(0.786356\pi\)
\(318\) 0 0
\(319\) −17.6269 −0.986916
\(320\) 0 0
\(321\) −47.7271 −2.66387
\(322\) 0 0
\(323\) 4.38901 0.244211
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.02561 −0.0567165
\(328\) 0 0
\(329\) −27.3499 −1.50785
\(330\) 0 0
\(331\) −28.5409 −1.56875 −0.784375 0.620287i \(-0.787016\pi\)
−0.784375 + 0.620287i \(0.787016\pi\)
\(332\) 0 0
\(333\) 23.8349 1.30615
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.71371 0.202298 0.101149 0.994871i \(-0.467748\pi\)
0.101149 + 0.994871i \(0.467748\pi\)
\(338\) 0 0
\(339\) 12.9275 0.702125
\(340\) 0 0
\(341\) 8.84472 0.478969
\(342\) 0 0
\(343\) 24.1624 1.30464
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 14.1459 0.759393 0.379696 0.925111i \(-0.376028\pi\)
0.379696 + 0.925111i \(0.376028\pi\)
\(348\) 0 0
\(349\) −21.2802 −1.13910 −0.569550 0.821957i \(-0.692883\pi\)
−0.569550 + 0.821957i \(0.692883\pi\)
\(350\) 0 0
\(351\) 3.95201 0.210943
\(352\) 0 0
\(353\) 24.4641 1.30209 0.651046 0.759038i \(-0.274331\pi\)
0.651046 + 0.759038i \(0.274331\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −16.0373 −0.848786
\(358\) 0 0
\(359\) −23.0252 −1.21522 −0.607612 0.794234i \(-0.707872\pi\)
−0.607612 + 0.794234i \(0.707872\pi\)
\(360\) 0 0
\(361\) −10.5947 −0.557613
\(362\) 0 0
\(363\) 13.7853 0.723540
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.478057 0.0249544 0.0124772 0.999922i \(-0.496028\pi\)
0.0124772 + 0.999922i \(0.496028\pi\)
\(368\) 0 0
\(369\) −17.7989 −0.926573
\(370\) 0 0
\(371\) 9.60767 0.498806
\(372\) 0 0
\(373\) 27.3508 1.41617 0.708085 0.706127i \(-0.249559\pi\)
0.708085 + 0.706127i \(0.249559\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −53.2704 −2.74357
\(378\) 0 0
\(379\) −7.35358 −0.377728 −0.188864 0.982003i \(-0.560481\pi\)
−0.188864 + 0.982003i \(0.560481\pi\)
\(380\) 0 0
\(381\) −14.7874 −0.757583
\(382\) 0 0
\(383\) −3.34108 −0.170721 −0.0853606 0.996350i \(-0.527204\pi\)
−0.0853606 + 0.996350i \(0.527204\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −9.62693 −0.489364
\(388\) 0 0
\(389\) 0.366568 0.0185858 0.00929288 0.999957i \(-0.497042\pi\)
0.00929288 + 0.999957i \(0.497042\pi\)
\(390\) 0 0
\(391\) 1.51387 0.0765598
\(392\) 0 0
\(393\) −35.1254 −1.77184
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −11.3222 −0.568245 −0.284122 0.958788i \(-0.591702\pi\)
−0.284122 + 0.958788i \(0.591702\pi\)
\(398\) 0 0
\(399\) −30.7129 −1.53757
\(400\) 0 0
\(401\) 37.1673 1.85605 0.928024 0.372520i \(-0.121506\pi\)
0.928024 + 0.372520i \(0.121506\pi\)
\(402\) 0 0
\(403\) 26.7298 1.33150
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 19.7837 0.980643
\(408\) 0 0
\(409\) −13.7745 −0.681107 −0.340553 0.940225i \(-0.610614\pi\)
−0.340553 + 0.940225i \(0.610614\pi\)
\(410\) 0 0
\(411\) −2.33390 −0.115123
\(412\) 0 0
\(413\) −51.9139 −2.55452
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −18.5874 −0.910228
\(418\) 0 0
\(419\) 7.50726 0.366753 0.183377 0.983043i \(-0.441297\pi\)
0.183377 + 0.983043i \(0.441297\pi\)
\(420\) 0 0
\(421\) −7.65685 −0.373172 −0.186586 0.982439i \(-0.559742\pi\)
−0.186586 + 0.982439i \(0.559742\pi\)
\(422\) 0 0
\(423\) −17.1200 −0.832402
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −22.5703 −1.09225
\(428\) 0 0
\(429\) −38.1398 −1.84141
\(430\) 0 0
\(431\) 6.22764 0.299975 0.149987 0.988688i \(-0.452077\pi\)
0.149987 + 0.988688i \(0.452077\pi\)
\(432\) 0 0
\(433\) 0.704087 0.0338362 0.0169181 0.999857i \(-0.494615\pi\)
0.0169181 + 0.999857i \(0.494615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.89920 0.138687
\(438\) 0 0
\(439\) −34.8570 −1.66363 −0.831816 0.555052i \(-0.812699\pi\)
−0.831816 + 0.555052i \(0.812699\pi\)
\(440\) 0 0
\(441\) 34.4616 1.64103
\(442\) 0 0
\(443\) −24.8165 −1.17907 −0.589533 0.807745i \(-0.700688\pi\)
−0.589533 + 0.807745i \(0.700688\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 42.4463 2.00764
\(448\) 0 0
\(449\) 6.77738 0.319844 0.159922 0.987130i \(-0.448876\pi\)
0.159922 + 0.987130i \(0.448876\pi\)
\(450\) 0 0
\(451\) −14.7736 −0.695662
\(452\) 0 0
\(453\) 4.83188 0.227021
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.47169 0.0688429 0.0344214 0.999407i \(-0.489041\pi\)
0.0344214 + 0.999407i \(0.489041\pi\)
\(458\) 0 0
\(459\) 0.863404 0.0403003
\(460\) 0 0
\(461\) 25.8037 1.20180 0.600899 0.799325i \(-0.294809\pi\)
0.600899 + 0.799325i \(0.294809\pi\)
\(462\) 0 0
\(463\) −15.3469 −0.713231 −0.356616 0.934251i \(-0.616069\pi\)
−0.356616 + 0.934251i \(0.616069\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.2933 0.476315 0.238157 0.971227i \(-0.423457\pi\)
0.238157 + 0.971227i \(0.423457\pi\)
\(468\) 0 0
\(469\) 43.8922 2.02676
\(470\) 0 0
\(471\) 13.9878 0.644524
\(472\) 0 0
\(473\) −7.99065 −0.367410
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.01404 0.275364
\(478\) 0 0
\(479\) 4.50453 0.205817 0.102909 0.994691i \(-0.467185\pi\)
0.102909 + 0.994691i \(0.467185\pi\)
\(480\) 0 0
\(481\) 59.7886 2.72613
\(482\) 0 0
\(483\) −10.5936 −0.482025
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −27.2669 −1.23558 −0.617790 0.786343i \(-0.711972\pi\)
−0.617790 + 0.786343i \(0.711972\pi\)
\(488\) 0 0
\(489\) 16.2069 0.732902
\(490\) 0 0
\(491\) 24.4866 1.10507 0.552533 0.833491i \(-0.313661\pi\)
0.552533 + 0.833491i \(0.313661\pi\)
\(492\) 0 0
\(493\) −11.6381 −0.524154
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 15.0665 0.675826
\(498\) 0 0
\(499\) −24.1892 −1.08286 −0.541429 0.840746i \(-0.682117\pi\)
−0.541429 + 0.840746i \(0.682117\pi\)
\(500\) 0 0
\(501\) 56.3016 2.51537
\(502\) 0 0
\(503\) 30.6230 1.36541 0.682706 0.730693i \(-0.260803\pi\)
0.682706 + 0.730693i \(0.260803\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −84.0562 −3.73307
\(508\) 0 0
\(509\) −2.56826 −0.113836 −0.0569181 0.998379i \(-0.518127\pi\)
−0.0569181 + 0.998379i \(0.518127\pi\)
\(510\) 0 0
\(511\) −39.5105 −1.74784
\(512\) 0 0
\(513\) 1.65349 0.0730035
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −14.2101 −0.624960
\(518\) 0 0
\(519\) 19.8966 0.873362
\(520\) 0 0
\(521\) −44.1355 −1.93361 −0.966807 0.255509i \(-0.917757\pi\)
−0.966807 + 0.255509i \(0.917757\pi\)
\(522\) 0 0
\(523\) 42.2884 1.84914 0.924572 0.381008i \(-0.124423\pi\)
0.924572 + 0.381008i \(0.124423\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.83970 0.254381
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −32.4961 −1.41021
\(532\) 0 0
\(533\) −44.6475 −1.93390
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.49656 −0.107735
\(538\) 0 0
\(539\) 28.6042 1.23207
\(540\) 0 0
\(541\) 10.2776 0.441871 0.220935 0.975288i \(-0.429089\pi\)
0.220935 + 0.975288i \(0.429089\pi\)
\(542\) 0 0
\(543\) −6.52577 −0.280048
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.87305 −0.165600 −0.0827998 0.996566i \(-0.526386\pi\)
−0.0827998 + 0.996566i \(0.526386\pi\)
\(548\) 0 0
\(549\) −14.1282 −0.602975
\(550\) 0 0
\(551\) −22.2880 −0.949500
\(552\) 0 0
\(553\) −8.50373 −0.361615
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.62364 −0.407767 −0.203883 0.978995i \(-0.565356\pi\)
−0.203883 + 0.978995i \(0.565356\pi\)
\(558\) 0 0
\(559\) −24.1486 −1.02138
\(560\) 0 0
\(561\) −8.33248 −0.351797
\(562\) 0 0
\(563\) 3.35865 0.141550 0.0707751 0.997492i \(-0.477453\pi\)
0.0707751 + 0.997492i \(0.477453\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −42.6140 −1.78962
\(568\) 0 0
\(569\) −4.26939 −0.178982 −0.0894910 0.995988i \(-0.528524\pi\)
−0.0894910 + 0.995988i \(0.528524\pi\)
\(570\) 0 0
\(571\) 16.4567 0.688689 0.344345 0.938843i \(-0.388101\pi\)
0.344345 + 0.938843i \(0.388101\pi\)
\(572\) 0 0
\(573\) −19.3206 −0.807131
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.98780 0.0827530 0.0413765 0.999144i \(-0.486826\pi\)
0.0413765 + 0.999144i \(0.486826\pi\)
\(578\) 0 0
\(579\) 38.4744 1.59894
\(580\) 0 0
\(581\) 35.4869 1.47224
\(582\) 0 0
\(583\) 4.99184 0.206741
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −28.9720 −1.19580 −0.597900 0.801570i \(-0.703998\pi\)
−0.597900 + 0.801570i \(0.703998\pi\)
\(588\) 0 0
\(589\) 11.1835 0.460810
\(590\) 0 0
\(591\) −9.75363 −0.401211
\(592\) 0 0
\(593\) −19.4799 −0.799944 −0.399972 0.916527i \(-0.630980\pi\)
−0.399972 + 0.916527i \(0.630980\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −44.8994 −1.83761
\(598\) 0 0
\(599\) 37.8442 1.54627 0.773136 0.634240i \(-0.218687\pi\)
0.773136 + 0.634240i \(0.218687\pi\)
\(600\) 0 0
\(601\) −20.2347 −0.825389 −0.412695 0.910869i \(-0.635412\pi\)
−0.412695 + 0.910869i \(0.635412\pi\)
\(602\) 0 0
\(603\) 27.4749 1.11886
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 24.4075 0.990670 0.495335 0.868702i \(-0.335045\pi\)
0.495335 + 0.868702i \(0.335045\pi\)
\(608\) 0 0
\(609\) 81.4396 3.30010
\(610\) 0 0
\(611\) −42.9445 −1.73735
\(612\) 0 0
\(613\) 10.6964 0.432025 0.216012 0.976391i \(-0.430695\pi\)
0.216012 + 0.976391i \(0.430695\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −27.4738 −1.10605 −0.553026 0.833164i \(-0.686527\pi\)
−0.553026 + 0.833164i \(0.686527\pi\)
\(618\) 0 0
\(619\) −0.389330 −0.0156485 −0.00782425 0.999969i \(-0.502491\pi\)
−0.00782425 + 0.999969i \(0.502491\pi\)
\(620\) 0 0
\(621\) 0.570328 0.0228865
\(622\) 0 0
\(623\) −4.82230 −0.193201
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −15.9574 −0.637278
\(628\) 0 0
\(629\) 13.0621 0.520822
\(630\) 0 0
\(631\) −11.9330 −0.475047 −0.237523 0.971382i \(-0.576336\pi\)
−0.237523 + 0.971382i \(0.576336\pi\)
\(632\) 0 0
\(633\) −18.9121 −0.751689
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 86.4451 3.42508
\(638\) 0 0
\(639\) 9.43106 0.373087
\(640\) 0 0
\(641\) 22.8525 0.902621 0.451311 0.892367i \(-0.350957\pi\)
0.451311 + 0.892367i \(0.350957\pi\)
\(642\) 0 0
\(643\) 34.9279 1.37742 0.688711 0.725036i \(-0.258177\pi\)
0.688711 + 0.725036i \(0.258177\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.3738 1.03686 0.518430 0.855120i \(-0.326517\pi\)
0.518430 + 0.855120i \(0.326517\pi\)
\(648\) 0 0
\(649\) −26.9728 −1.05877
\(650\) 0 0
\(651\) −40.8643 −1.60160
\(652\) 0 0
\(653\) −2.17022 −0.0849274 −0.0424637 0.999098i \(-0.513521\pi\)
−0.0424637 + 0.999098i \(0.513521\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −24.7321 −0.964891
\(658\) 0 0
\(659\) 19.7820 0.770596 0.385298 0.922792i \(-0.374099\pi\)
0.385298 + 0.922792i \(0.374099\pi\)
\(660\) 0 0
\(661\) 45.7505 1.77949 0.889743 0.456461i \(-0.150883\pi\)
0.889743 + 0.456461i \(0.150883\pi\)
\(662\) 0 0
\(663\) −25.1817 −0.977976
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7.68764 −0.297666
\(668\) 0 0
\(669\) 5.50346 0.212776
\(670\) 0 0
\(671\) −11.7268 −0.452708
\(672\) 0 0
\(673\) 6.99940 0.269807 0.134904 0.990859i \(-0.456928\pi\)
0.134904 + 0.990859i \(0.456928\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 26.7178 1.02685 0.513425 0.858134i \(-0.328376\pi\)
0.513425 + 0.858134i \(0.328376\pi\)
\(678\) 0 0
\(679\) −74.6728 −2.86568
\(680\) 0 0
\(681\) −30.8045 −1.18043
\(682\) 0 0
\(683\) −19.8947 −0.761248 −0.380624 0.924730i \(-0.624291\pi\)
−0.380624 + 0.924730i \(0.624291\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 39.0148 1.48851
\(688\) 0 0
\(689\) 15.0859 0.574727
\(690\) 0 0
\(691\) 1.24438 0.0473385 0.0236693 0.999720i \(-0.492465\pi\)
0.0236693 + 0.999720i \(0.492465\pi\)
\(692\) 0 0
\(693\) 27.9520 1.06181
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.75424 −0.369468
\(698\) 0 0
\(699\) −51.7091 −1.95582
\(700\) 0 0
\(701\) −29.8454 −1.12724 −0.563622 0.826033i \(-0.690592\pi\)
−0.563622 + 0.826033i \(0.690592\pi\)
\(702\) 0 0
\(703\) 25.0151 0.943464
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 57.1481 2.14928
\(708\) 0 0
\(709\) 25.2255 0.947362 0.473681 0.880697i \(-0.342925\pi\)
0.473681 + 0.880697i \(0.342925\pi\)
\(710\) 0 0
\(711\) −5.32301 −0.199628
\(712\) 0 0
\(713\) 3.85746 0.144463
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 26.5549 0.991710
\(718\) 0 0
\(719\) −23.7787 −0.886797 −0.443398 0.896325i \(-0.646227\pi\)
−0.443398 + 0.896325i \(0.646227\pi\)
\(720\) 0 0
\(721\) 48.4353 1.80383
\(722\) 0 0
\(723\) −43.7285 −1.62628
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 36.5849 1.35686 0.678429 0.734666i \(-0.262661\pi\)
0.678429 + 0.734666i \(0.262661\pi\)
\(728\) 0 0
\(729\) −22.5675 −0.835833
\(730\) 0 0
\(731\) −5.27580 −0.195133
\(732\) 0 0
\(733\) −21.7593 −0.803698 −0.401849 0.915706i \(-0.631632\pi\)
−0.401849 + 0.915706i \(0.631632\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22.8050 0.840032
\(738\) 0 0
\(739\) 2.72303 0.100168 0.0500842 0.998745i \(-0.484051\pi\)
0.0500842 + 0.998745i \(0.484051\pi\)
\(740\) 0 0
\(741\) −48.2251 −1.77159
\(742\) 0 0
\(743\) −32.0161 −1.17456 −0.587278 0.809385i \(-0.699800\pi\)
−0.587278 + 0.809385i \(0.699800\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 22.2134 0.812746
\(748\) 0 0
\(749\) 87.7413 3.20600
\(750\) 0 0
\(751\) −36.0949 −1.31712 −0.658561 0.752527i \(-0.728835\pi\)
−0.658561 + 0.752527i \(0.728835\pi\)
\(752\) 0 0
\(753\) 24.0488 0.876386
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −46.8188 −1.70166 −0.850830 0.525442i \(-0.823900\pi\)
−0.850830 + 0.525442i \(0.823900\pi\)
\(758\) 0 0
\(759\) −5.50408 −0.199786
\(760\) 0 0
\(761\) −28.8182 −1.04466 −0.522330 0.852744i \(-0.674937\pi\)
−0.522330 + 0.852744i \(0.674937\pi\)
\(762\) 0 0
\(763\) 1.88548 0.0682590
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −81.5148 −2.94333
\(768\) 0 0
\(769\) 51.6243 1.86162 0.930811 0.365501i \(-0.119102\pi\)
0.930811 + 0.365501i \(0.119102\pi\)
\(770\) 0 0
\(771\) 34.3322 1.23645
\(772\) 0 0
\(773\) 25.9610 0.933753 0.466877 0.884322i \(-0.345379\pi\)
0.466877 + 0.884322i \(0.345379\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −91.4046 −3.27912
\(778\) 0 0
\(779\) −18.6802 −0.669288
\(780\) 0 0
\(781\) 7.82807 0.280110
\(782\) 0 0
\(783\) −4.38448 −0.156688
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 53.2258 1.89730 0.948648 0.316333i \(-0.102452\pi\)
0.948648 + 0.316333i \(0.102452\pi\)
\(788\) 0 0
\(789\) 22.6694 0.807053
\(790\) 0 0
\(791\) −23.7658 −0.845015
\(792\) 0 0
\(793\) −35.4397 −1.25850
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 31.1874 1.10471 0.552357 0.833608i \(-0.313729\pi\)
0.552357 + 0.833608i \(0.313729\pi\)
\(798\) 0 0
\(799\) −9.38218 −0.331918
\(800\) 0 0
\(801\) −3.01858 −0.106656
\(802\) 0 0
\(803\) −20.5284 −0.724431
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −57.0432 −2.00802
\(808\) 0 0
\(809\) −1.60251 −0.0563414 −0.0281707 0.999603i \(-0.508968\pi\)
−0.0281707 + 0.999603i \(0.508968\pi\)
\(810\) 0 0
\(811\) −36.9545 −1.29765 −0.648824 0.760938i \(-0.724739\pi\)
−0.648824 + 0.760938i \(0.724739\pi\)
\(812\) 0 0
\(813\) 42.2341 1.48121
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −10.1036 −0.353481
\(818\) 0 0
\(819\) 84.4739 2.95176
\(820\) 0 0
\(821\) −16.5583 −0.577890 −0.288945 0.957346i \(-0.593304\pi\)
−0.288945 + 0.957346i \(0.593304\pi\)
\(822\) 0 0
\(823\) −7.63201 −0.266035 −0.133018 0.991114i \(-0.542467\pi\)
−0.133018 + 0.991114i \(0.542467\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −19.1969 −0.667543 −0.333772 0.942654i \(-0.608321\pi\)
−0.333772 + 0.942654i \(0.608321\pi\)
\(828\) 0 0
\(829\) −6.32413 −0.219646 −0.109823 0.993951i \(-0.535028\pi\)
−0.109823 + 0.993951i \(0.535028\pi\)
\(830\) 0 0
\(831\) 71.1946 2.46971
\(832\) 0 0
\(833\) 18.8858 0.654355
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2.20002 0.0760438
\(838\) 0 0
\(839\) 23.1158 0.798046 0.399023 0.916941i \(-0.369349\pi\)
0.399023 + 0.916941i \(0.369349\pi\)
\(840\) 0 0
\(841\) 30.0997 1.03792
\(842\) 0 0
\(843\) 19.8158 0.682491
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −25.3428 −0.870789
\(848\) 0 0
\(849\) −22.1163 −0.759028
\(850\) 0 0
\(851\) 8.62830 0.295774
\(852\) 0 0
\(853\) −37.7049 −1.29099 −0.645496 0.763764i \(-0.723349\pi\)
−0.645496 + 0.763764i \(0.723349\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 19.7133 0.673395 0.336697 0.941613i \(-0.390690\pi\)
0.336697 + 0.941613i \(0.390690\pi\)
\(858\) 0 0
\(859\) 2.00609 0.0684471 0.0342235 0.999414i \(-0.489104\pi\)
0.0342235 + 0.999414i \(0.489104\pi\)
\(860\) 0 0
\(861\) 68.2570 2.32619
\(862\) 0 0
\(863\) 16.8127 0.572312 0.286156 0.958183i \(-0.407623\pi\)
0.286156 + 0.958183i \(0.407623\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 35.3071 1.19909
\(868\) 0 0
\(869\) −4.41826 −0.149879
\(870\) 0 0
\(871\) 68.9192 2.33524
\(872\) 0 0
\(873\) −46.7424 −1.58199
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 14.8922 0.502874 0.251437 0.967874i \(-0.419097\pi\)
0.251437 + 0.967874i \(0.419097\pi\)
\(878\) 0 0
\(879\) −26.6788 −0.899853
\(880\) 0 0
\(881\) −16.5218 −0.556632 −0.278316 0.960490i \(-0.589776\pi\)
−0.278316 + 0.960490i \(0.589776\pi\)
\(882\) 0 0
\(883\) 38.7254 1.30321 0.651607 0.758557i \(-0.274095\pi\)
0.651607 + 0.758557i \(0.274095\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.16364 0.0390711 0.0195355 0.999809i \(-0.493781\pi\)
0.0195355 + 0.999809i \(0.493781\pi\)
\(888\) 0 0
\(889\) 27.1851 0.911760
\(890\) 0 0
\(891\) −22.1408 −0.741746
\(892\) 0 0
\(893\) −17.9677 −0.601266
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −16.6340 −0.555392
\(898\) 0 0
\(899\) −29.6548 −0.989042
\(900\) 0 0
\(901\) 3.29584 0.109800
\(902\) 0 0
\(903\) 36.9183 1.22857
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 30.2796 1.00542 0.502709 0.864456i \(-0.332337\pi\)
0.502709 + 0.864456i \(0.332337\pi\)
\(908\) 0 0
\(909\) 35.7725 1.18650
\(910\) 0 0
\(911\) −28.2296 −0.935290 −0.467645 0.883916i \(-0.654897\pi\)
−0.467645 + 0.883916i \(0.654897\pi\)
\(912\) 0 0
\(913\) 18.4378 0.610203
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 64.5744 2.13243
\(918\) 0 0
\(919\) 3.28150 0.108247 0.0541233 0.998534i \(-0.482764\pi\)
0.0541233 + 0.998534i \(0.482764\pi\)
\(920\) 0 0
\(921\) −45.0814 −1.48548
\(922\) 0 0
\(923\) 23.6573 0.778690
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 30.3187 0.995796
\(928\) 0 0
\(929\) 7.64745 0.250905 0.125452 0.992100i \(-0.459962\pi\)
0.125452 + 0.992100i \(0.459962\pi\)
\(930\) 0 0
\(931\) 36.1680 1.18536
\(932\) 0 0
\(933\) −6.03146 −0.197461
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −4.95226 −0.161783 −0.0808917 0.996723i \(-0.525777\pi\)
−0.0808917 + 0.996723i \(0.525777\pi\)
\(938\) 0 0
\(939\) −47.8366 −1.56109
\(940\) 0 0
\(941\) −8.62677 −0.281225 −0.140612 0.990065i \(-0.544907\pi\)
−0.140612 + 0.990065i \(0.544907\pi\)
\(942\) 0 0
\(943\) −6.44324 −0.209821
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −46.6807 −1.51692 −0.758460 0.651720i \(-0.774048\pi\)
−0.758460 + 0.651720i \(0.774048\pi\)
\(948\) 0 0
\(949\) −62.0391 −2.01387
\(950\) 0 0
\(951\) 66.9378 2.17061
\(952\) 0 0
\(953\) −12.2343 −0.396307 −0.198154 0.980171i \(-0.563495\pi\)
−0.198154 + 0.980171i \(0.563495\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 42.3134 1.36780
\(958\) 0 0
\(959\) 4.29063 0.138552
\(960\) 0 0
\(961\) −16.1200 −0.520000
\(962\) 0 0
\(963\) 54.9227 1.76986
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −54.8318 −1.76327 −0.881635 0.471932i \(-0.843557\pi\)
−0.881635 + 0.471932i \(0.843557\pi\)
\(968\) 0 0
\(969\) −10.5358 −0.338460
\(970\) 0 0
\(971\) 40.3804 1.29587 0.647935 0.761696i \(-0.275633\pi\)
0.647935 + 0.761696i \(0.275633\pi\)
\(972\) 0 0
\(973\) 34.1709 1.09547
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −10.6700 −0.341363 −0.170681 0.985326i \(-0.554597\pi\)
−0.170681 + 0.985326i \(0.554597\pi\)
\(978\) 0 0
\(979\) −2.50551 −0.0800765
\(980\) 0 0
\(981\) 1.18024 0.0376821
\(982\) 0 0
\(983\) 6.27812 0.200241 0.100120 0.994975i \(-0.468077\pi\)
0.100120 + 0.994975i \(0.468077\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 65.6535 2.08977
\(988\) 0 0
\(989\) −3.48497 −0.110816
\(990\) 0 0
\(991\) 61.2864 1.94683 0.973413 0.229057i \(-0.0735643\pi\)
0.973413 + 0.229057i \(0.0735643\pi\)
\(992\) 0 0
\(993\) 68.5125 2.17418
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 39.9799 1.26618 0.633088 0.774080i \(-0.281787\pi\)
0.633088 + 0.774080i \(0.281787\pi\)
\(998\) 0 0
\(999\) 4.92096 0.155692
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 2300.2.a.o.1.1 6
4.3 odd 2 9200.2.a.cx.1.6 6
5.2 odd 4 460.2.c.a.369.10 yes 12
5.3 odd 4 460.2.c.a.369.3 12
5.4 even 2 2300.2.a.n.1.6 6
15.2 even 4 4140.2.f.b.829.7 12
15.8 even 4 4140.2.f.b.829.8 12
20.3 even 4 1840.2.e.f.369.10 12
20.7 even 4 1840.2.e.f.369.3 12
20.19 odd 2 9200.2.a.cy.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.c.a.369.3 12 5.3 odd 4
460.2.c.a.369.10 yes 12 5.2 odd 4
1840.2.e.f.369.3 12 20.7 even 4
1840.2.e.f.369.10 12 20.3 even 4
2300.2.a.n.1.6 6 5.4 even 2
2300.2.a.o.1.1 6 1.1 even 1 trivial
4140.2.f.b.829.7 12 15.2 even 4
4140.2.f.b.829.8 12 15.8 even 4
9200.2.a.cx.1.6 6 4.3 odd 2
9200.2.a.cy.1.1 6 20.19 odd 2