Properties

Label 1232.2.a.p.1.1
Level $1232$
Weight $2$
Character 1232.1
Self dual yes
Analytic conductor $9.838$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.83756952902\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 1232.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.23607 q^{3} -1.23607 q^{5} -1.00000 q^{7} -1.47214 q^{9} +O(q^{10})\) \(q-1.23607 q^{3} -1.23607 q^{5} -1.00000 q^{7} -1.47214 q^{9} -1.00000 q^{11} -3.23607 q^{13} +1.52786 q^{15} +2.47214 q^{17} +7.23607 q^{19} +1.23607 q^{21} -4.00000 q^{23} -3.47214 q^{25} +5.52786 q^{27} +4.47214 q^{29} -2.00000 q^{31} +1.23607 q^{33} +1.23607 q^{35} +6.94427 q^{37} +4.00000 q^{39} -2.47214 q^{41} +10.4721 q^{43} +1.81966 q^{45} +2.00000 q^{47} +1.00000 q^{49} -3.05573 q^{51} +8.47214 q^{53} +1.23607 q^{55} -8.94427 q^{57} -2.76393 q^{59} -0.763932 q^{61} +1.47214 q^{63} +4.00000 q^{65} -11.4164 q^{67} +4.94427 q^{69} -6.47214 q^{71} +12.9443 q^{73} +4.29180 q^{75} +1.00000 q^{77} -2.41641 q^{81} +12.1803 q^{83} -3.05573 q^{85} -5.52786 q^{87} +10.0000 q^{89} +3.23607 q^{91} +2.47214 q^{93} -8.94427 q^{95} +12.4721 q^{97} +1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 2 q^{5} - 2 q^{7} + 6 q^{9} - 2 q^{11} - 2 q^{13} + 12 q^{15} - 4 q^{17} + 10 q^{19} - 2 q^{21} - 8 q^{23} + 2 q^{25} + 20 q^{27} - 4 q^{31} - 2 q^{33} - 2 q^{35} - 4 q^{37} + 8 q^{39} + 4 q^{41} + 12 q^{43} + 26 q^{45} + 4 q^{47} + 2 q^{49} - 24 q^{51} + 8 q^{53} - 2 q^{55} - 10 q^{59} - 6 q^{61} - 6 q^{63} + 8 q^{65} + 4 q^{67} - 8 q^{69} - 4 q^{71} + 8 q^{73} + 22 q^{75} + 2 q^{77} + 22 q^{81} + 2 q^{83} - 24 q^{85} - 20 q^{87} + 20 q^{89} + 2 q^{91} - 4 q^{93} + 16 q^{97} - 6 q^{99}+O(q^{100}) \) 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
\(3\) −1.23607 −0.713644 −0.356822 0.934172i \(-0.616140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) 0 0
\(5\) −1.23607 −0.552786 −0.276393 0.961045i \(-0.589139\pi\)
−0.276393 + 0.961045i \(0.589139\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −1.47214 −0.490712
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −3.23607 −0.897524 −0.448762 0.893651i \(-0.648135\pi\)
−0.448762 + 0.893651i \(0.648135\pi\)
\(14\) 0 0
\(15\) 1.52786 0.394493
\(16\) 0 0
\(17\) 2.47214 0.599581 0.299791 0.954005i \(-0.403083\pi\)
0.299791 + 0.954005i \(0.403083\pi\)
\(18\) 0 0
\(19\) 7.23607 1.66007 0.830034 0.557713i \(-0.188321\pi\)
0.830034 + 0.557713i \(0.188321\pi\)
\(20\) 0 0
\(21\) 1.23607 0.269732
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −3.47214 −0.694427
\(26\) 0 0
\(27\) 5.52786 1.06384
\(28\) 0 0
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) 1.23607 0.215172
\(34\) 0 0
\(35\) 1.23607 0.208934
\(36\) 0 0
\(37\) 6.94427 1.14163 0.570816 0.821078i \(-0.306627\pi\)
0.570816 + 0.821078i \(0.306627\pi\)
\(38\) 0 0
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) −2.47214 −0.386083 −0.193041 0.981191i \(-0.561835\pi\)
−0.193041 + 0.981191i \(0.561835\pi\)
\(42\) 0 0
\(43\) 10.4721 1.59699 0.798493 0.602004i \(-0.205631\pi\)
0.798493 + 0.602004i \(0.205631\pi\)
\(44\) 0 0
\(45\) 1.81966 0.271259
\(46\) 0 0
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.05573 −0.427888
\(52\) 0 0
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) 0 0
\(55\) 1.23607 0.166671
\(56\) 0 0
\(57\) −8.94427 −1.18470
\(58\) 0 0
\(59\) −2.76393 −0.359833 −0.179917 0.983682i \(-0.557583\pi\)
−0.179917 + 0.983682i \(0.557583\pi\)
\(60\) 0 0
\(61\) −0.763932 −0.0978115 −0.0489057 0.998803i \(-0.515573\pi\)
−0.0489057 + 0.998803i \(0.515573\pi\)
\(62\) 0 0
\(63\) 1.47214 0.185472
\(64\) 0 0
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) −11.4164 −1.39474 −0.697368 0.716713i \(-0.745646\pi\)
−0.697368 + 0.716713i \(0.745646\pi\)
\(68\) 0 0
\(69\) 4.94427 0.595220
\(70\) 0 0
\(71\) −6.47214 −0.768101 −0.384051 0.923312i \(-0.625471\pi\)
−0.384051 + 0.923312i \(0.625471\pi\)
\(72\) 0 0
\(73\) 12.9443 1.51501 0.757506 0.652828i \(-0.226418\pi\)
0.757506 + 0.652828i \(0.226418\pi\)
\(74\) 0 0
\(75\) 4.29180 0.495574
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −2.41641 −0.268490
\(82\) 0 0
\(83\) 12.1803 1.33697 0.668483 0.743727i \(-0.266944\pi\)
0.668483 + 0.743727i \(0.266944\pi\)
\(84\) 0 0
\(85\) −3.05573 −0.331440
\(86\) 0 0
\(87\) −5.52786 −0.592649
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) 3.23607 0.339232
\(92\) 0 0
\(93\) 2.47214 0.256349
\(94\) 0 0
\(95\) −8.94427 −0.917663
\(96\) 0 0
\(97\) 12.4721 1.26635 0.633177 0.774007i \(-0.281751\pi\)
0.633177 + 0.774007i \(0.281751\pi\)
\(98\) 0 0
\(99\) 1.47214 0.147955
\(100\) 0 0
\(101\) 8.18034 0.813974 0.406987 0.913434i \(-0.366579\pi\)
0.406987 + 0.913434i \(0.366579\pi\)
\(102\) 0 0
\(103\) 14.9443 1.47250 0.736251 0.676708i \(-0.236594\pi\)
0.736251 + 0.676708i \(0.236594\pi\)
\(104\) 0 0
\(105\) −1.52786 −0.149104
\(106\) 0 0
\(107\) −2.47214 −0.238990 −0.119495 0.992835i \(-0.538128\pi\)
−0.119495 + 0.992835i \(0.538128\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −8.58359 −0.814719
\(112\) 0 0
\(113\) −0.472136 −0.0444148 −0.0222074 0.999753i \(-0.507069\pi\)
−0.0222074 + 0.999753i \(0.507069\pi\)
\(114\) 0 0
\(115\) 4.94427 0.461056
\(116\) 0 0
\(117\) 4.76393 0.440426
\(118\) 0 0
\(119\) −2.47214 −0.226620
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 3.05573 0.275526
\(124\) 0 0
\(125\) 10.4721 0.936656
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 0 0
\(129\) −12.9443 −1.13968
\(130\) 0 0
\(131\) −4.76393 −0.416227 −0.208113 0.978105i \(-0.566732\pi\)
−0.208113 + 0.978105i \(0.566732\pi\)
\(132\) 0 0
\(133\) −7.23607 −0.627447
\(134\) 0 0
\(135\) −6.83282 −0.588075
\(136\) 0 0
\(137\) −19.8885 −1.69919 −0.849596 0.527433i \(-0.823154\pi\)
−0.849596 + 0.527433i \(0.823154\pi\)
\(138\) 0 0
\(139\) 21.7082 1.84127 0.920633 0.390429i \(-0.127673\pi\)
0.920633 + 0.390429i \(0.127673\pi\)
\(140\) 0 0
\(141\) −2.47214 −0.208191
\(142\) 0 0
\(143\) 3.23607 0.270614
\(144\) 0 0
\(145\) −5.52786 −0.459064
\(146\) 0 0
\(147\) −1.23607 −0.101949
\(148\) 0 0
\(149\) −22.3607 −1.83186 −0.915929 0.401340i \(-0.868545\pi\)
−0.915929 + 0.401340i \(0.868545\pi\)
\(150\) 0 0
\(151\) −12.0000 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) 0 0
\(153\) −3.63932 −0.294222
\(154\) 0 0
\(155\) 2.47214 0.198567
\(156\) 0 0
\(157\) −12.6525 −1.00978 −0.504889 0.863184i \(-0.668466\pi\)
−0.504889 + 0.863184i \(0.668466\pi\)
\(158\) 0 0
\(159\) −10.4721 −0.830494
\(160\) 0 0
\(161\) 4.00000 0.315244
\(162\) 0 0
\(163\) 19.4164 1.52081 0.760405 0.649449i \(-0.225000\pi\)
0.760405 + 0.649449i \(0.225000\pi\)
\(164\) 0 0
\(165\) −1.52786 −0.118944
\(166\) 0 0
\(167\) −11.4164 −0.883428 −0.441714 0.897156i \(-0.645629\pi\)
−0.441714 + 0.897156i \(0.645629\pi\)
\(168\) 0 0
\(169\) −2.52786 −0.194451
\(170\) 0 0
\(171\) −10.6525 −0.814615
\(172\) 0 0
\(173\) −3.23607 −0.246034 −0.123017 0.992405i \(-0.539257\pi\)
−0.123017 + 0.992405i \(0.539257\pi\)
\(174\) 0 0
\(175\) 3.47214 0.262469
\(176\) 0 0
\(177\) 3.41641 0.256793
\(178\) 0 0
\(179\) 8.94427 0.668526 0.334263 0.942480i \(-0.391513\pi\)
0.334263 + 0.942480i \(0.391513\pi\)
\(180\) 0 0
\(181\) 9.23607 0.686512 0.343256 0.939242i \(-0.388470\pi\)
0.343256 + 0.939242i \(0.388470\pi\)
\(182\) 0 0
\(183\) 0.944272 0.0698026
\(184\) 0 0
\(185\) −8.58359 −0.631078
\(186\) 0 0
\(187\) −2.47214 −0.180780
\(188\) 0 0
\(189\) −5.52786 −0.402093
\(190\) 0 0
\(191\) 2.47214 0.178877 0.0894387 0.995992i \(-0.471493\pi\)
0.0894387 + 0.995992i \(0.471493\pi\)
\(192\) 0 0
\(193\) −14.9443 −1.07571 −0.537856 0.843037i \(-0.680766\pi\)
−0.537856 + 0.843037i \(0.680766\pi\)
\(194\) 0 0
\(195\) −4.94427 −0.354067
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −18.9443 −1.34292 −0.671462 0.741039i \(-0.734333\pi\)
−0.671462 + 0.741039i \(0.734333\pi\)
\(200\) 0 0
\(201\) 14.1115 0.995345
\(202\) 0 0
\(203\) −4.47214 −0.313882
\(204\) 0 0
\(205\) 3.05573 0.213421
\(206\) 0 0
\(207\) 5.88854 0.409282
\(208\) 0 0
\(209\) −7.23607 −0.500529
\(210\) 0 0
\(211\) 13.5279 0.931297 0.465648 0.884970i \(-0.345821\pi\)
0.465648 + 0.884970i \(0.345821\pi\)
\(212\) 0 0
\(213\) 8.00000 0.548151
\(214\) 0 0
\(215\) −12.9443 −0.882792
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) −16.0000 −1.08118
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 0.472136 0.0316166 0.0158083 0.999875i \(-0.494968\pi\)
0.0158083 + 0.999875i \(0.494968\pi\)
\(224\) 0 0
\(225\) 5.11146 0.340764
\(226\) 0 0
\(227\) 19.2361 1.27674 0.638371 0.769729i \(-0.279608\pi\)
0.638371 + 0.769729i \(0.279608\pi\)
\(228\) 0 0
\(229\) 17.2361 1.13899 0.569496 0.821994i \(-0.307139\pi\)
0.569496 + 0.821994i \(0.307139\pi\)
\(230\) 0 0
\(231\) −1.23607 −0.0813273
\(232\) 0 0
\(233\) −14.9443 −0.979032 −0.489516 0.871994i \(-0.662826\pi\)
−0.489516 + 0.871994i \(0.662826\pi\)
\(234\) 0 0
\(235\) −2.47214 −0.161264
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) 15.4164 0.993058 0.496529 0.868020i \(-0.334608\pi\)
0.496529 + 0.868020i \(0.334608\pi\)
\(242\) 0 0
\(243\) −13.5967 −0.872232
\(244\) 0 0
\(245\) −1.23607 −0.0789695
\(246\) 0 0
\(247\) −23.4164 −1.48995
\(248\) 0 0
\(249\) −15.0557 −0.954118
\(250\) 0 0
\(251\) −29.2361 −1.84536 −0.922682 0.385562i \(-0.874008\pi\)
−0.922682 + 0.385562i \(0.874008\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) 3.77709 0.236530
\(256\) 0 0
\(257\) 6.94427 0.433172 0.216586 0.976264i \(-0.430508\pi\)
0.216586 + 0.976264i \(0.430508\pi\)
\(258\) 0 0
\(259\) −6.94427 −0.431496
\(260\) 0 0
\(261\) −6.58359 −0.407514
\(262\) 0 0
\(263\) 4.94427 0.304877 0.152438 0.988313i \(-0.451287\pi\)
0.152438 + 0.988313i \(0.451287\pi\)
\(264\) 0 0
\(265\) −10.4721 −0.643298
\(266\) 0 0
\(267\) −12.3607 −0.756461
\(268\) 0 0
\(269\) −22.7639 −1.38794 −0.693971 0.720003i \(-0.744140\pi\)
−0.693971 + 0.720003i \(0.744140\pi\)
\(270\) 0 0
\(271\) −0.944272 −0.0573604 −0.0286802 0.999589i \(-0.509130\pi\)
−0.0286802 + 0.999589i \(0.509130\pi\)
\(272\) 0 0
\(273\) −4.00000 −0.242091
\(274\) 0 0
\(275\) 3.47214 0.209378
\(276\) 0 0
\(277\) 3.52786 0.211969 0.105984 0.994368i \(-0.466201\pi\)
0.105984 + 0.994368i \(0.466201\pi\)
\(278\) 0 0
\(279\) 2.94427 0.176269
\(280\) 0 0
\(281\) 28.8328 1.72002 0.860011 0.510276i \(-0.170457\pi\)
0.860011 + 0.510276i \(0.170457\pi\)
\(282\) 0 0
\(283\) −14.6525 −0.870999 −0.435500 0.900189i \(-0.643428\pi\)
−0.435500 + 0.900189i \(0.643428\pi\)
\(284\) 0 0
\(285\) 11.0557 0.654885
\(286\) 0 0
\(287\) 2.47214 0.145926
\(288\) 0 0
\(289\) −10.8885 −0.640503
\(290\) 0 0
\(291\) −15.4164 −0.903726
\(292\) 0 0
\(293\) −26.6525 −1.55705 −0.778527 0.627611i \(-0.784033\pi\)
−0.778527 + 0.627611i \(0.784033\pi\)
\(294\) 0 0
\(295\) 3.41641 0.198911
\(296\) 0 0
\(297\) −5.52786 −0.320759
\(298\) 0 0
\(299\) 12.9443 0.748587
\(300\) 0 0
\(301\) −10.4721 −0.603604
\(302\) 0 0
\(303\) −10.1115 −0.580888
\(304\) 0 0
\(305\) 0.944272 0.0540689
\(306\) 0 0
\(307\) 26.0689 1.48783 0.743915 0.668274i \(-0.232967\pi\)
0.743915 + 0.668274i \(0.232967\pi\)
\(308\) 0 0
\(309\) −18.4721 −1.05084
\(310\) 0 0
\(311\) 21.4164 1.21441 0.607207 0.794544i \(-0.292290\pi\)
0.607207 + 0.794544i \(0.292290\pi\)
\(312\) 0 0
\(313\) 19.5279 1.10378 0.551890 0.833917i \(-0.313907\pi\)
0.551890 + 0.833917i \(0.313907\pi\)
\(314\) 0 0
\(315\) −1.81966 −0.102526
\(316\) 0 0
\(317\) −30.9443 −1.73800 −0.869002 0.494809i \(-0.835238\pi\)
−0.869002 + 0.494809i \(0.835238\pi\)
\(318\) 0 0
\(319\) −4.47214 −0.250392
\(320\) 0 0
\(321\) 3.05573 0.170554
\(322\) 0 0
\(323\) 17.8885 0.995345
\(324\) 0 0
\(325\) 11.2361 0.623265
\(326\) 0 0
\(327\) 12.3607 0.683547
\(328\) 0 0
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) 16.9443 0.931341 0.465671 0.884958i \(-0.345813\pi\)
0.465671 + 0.884958i \(0.345813\pi\)
\(332\) 0 0
\(333\) −10.2229 −0.560212
\(334\) 0 0
\(335\) 14.1115 0.770991
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 0.583592 0.0316964
\(340\) 0 0
\(341\) 2.00000 0.108306
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −6.11146 −0.329030
\(346\) 0 0
\(347\) −2.47214 −0.132711 −0.0663556 0.997796i \(-0.521137\pi\)
−0.0663556 + 0.997796i \(0.521137\pi\)
\(348\) 0 0
\(349\) 21.7082 1.16201 0.581007 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(350\) 0 0
\(351\) −17.8885 −0.954820
\(352\) 0 0
\(353\) −17.0557 −0.907785 −0.453892 0.891056i \(-0.649965\pi\)
−0.453892 + 0.891056i \(0.649965\pi\)
\(354\) 0 0
\(355\) 8.00000 0.424596
\(356\) 0 0
\(357\) 3.05573 0.161726
\(358\) 0 0
\(359\) −26.8328 −1.41618 −0.708091 0.706121i \(-0.750443\pi\)
−0.708091 + 0.706121i \(0.750443\pi\)
\(360\) 0 0
\(361\) 33.3607 1.75583
\(362\) 0 0
\(363\) −1.23607 −0.0648767
\(364\) 0 0
\(365\) −16.0000 −0.837478
\(366\) 0 0
\(367\) 5.41641 0.282734 0.141367 0.989957i \(-0.454850\pi\)
0.141367 + 0.989957i \(0.454850\pi\)
\(368\) 0 0
\(369\) 3.63932 0.189455
\(370\) 0 0
\(371\) −8.47214 −0.439851
\(372\) 0 0
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) −12.9443 −0.668439
\(376\) 0 0
\(377\) −14.4721 −0.745353
\(378\) 0 0
\(379\) −14.4721 −0.743384 −0.371692 0.928356i \(-0.621222\pi\)
−0.371692 + 0.928356i \(0.621222\pi\)
\(380\) 0 0
\(381\) −14.8328 −0.759908
\(382\) 0 0
\(383\) 23.8885 1.22065 0.610324 0.792152i \(-0.291039\pi\)
0.610324 + 0.792152i \(0.291039\pi\)
\(384\) 0 0
\(385\) −1.23607 −0.0629959
\(386\) 0 0
\(387\) −15.4164 −0.783660
\(388\) 0 0
\(389\) 33.4164 1.69428 0.847140 0.531370i \(-0.178323\pi\)
0.847140 + 0.531370i \(0.178323\pi\)
\(390\) 0 0
\(391\) −9.88854 −0.500085
\(392\) 0 0
\(393\) 5.88854 0.297038
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −23.7082 −1.18988 −0.594940 0.803770i \(-0.702824\pi\)
−0.594940 + 0.803770i \(0.702824\pi\)
\(398\) 0 0
\(399\) 8.94427 0.447774
\(400\) 0 0
\(401\) 14.3607 0.717138 0.358569 0.933503i \(-0.383265\pi\)
0.358569 + 0.933503i \(0.383265\pi\)
\(402\) 0 0
\(403\) 6.47214 0.322400
\(404\) 0 0
\(405\) 2.98684 0.148417
\(406\) 0 0
\(407\) −6.94427 −0.344215
\(408\) 0 0
\(409\) 3.41641 0.168930 0.0844652 0.996426i \(-0.473082\pi\)
0.0844652 + 0.996426i \(0.473082\pi\)
\(410\) 0 0
\(411\) 24.5836 1.21262
\(412\) 0 0
\(413\) 2.76393 0.136004
\(414\) 0 0
\(415\) −15.0557 −0.739057
\(416\) 0 0
\(417\) −26.8328 −1.31401
\(418\) 0 0
\(419\) −17.2361 −0.842037 −0.421019 0.907052i \(-0.638327\pi\)
−0.421019 + 0.907052i \(0.638327\pi\)
\(420\) 0 0
\(421\) 16.4721 0.802803 0.401401 0.915902i \(-0.368523\pi\)
0.401401 + 0.915902i \(0.368523\pi\)
\(422\) 0 0
\(423\) −2.94427 −0.143155
\(424\) 0 0
\(425\) −8.58359 −0.416365
\(426\) 0 0
\(427\) 0.763932 0.0369693
\(428\) 0 0
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) −23.0557 −1.11056 −0.555278 0.831665i \(-0.687388\pi\)
−0.555278 + 0.831665i \(0.687388\pi\)
\(432\) 0 0
\(433\) 28.4721 1.36828 0.684142 0.729349i \(-0.260177\pi\)
0.684142 + 0.729349i \(0.260177\pi\)
\(434\) 0 0
\(435\) 6.83282 0.327608
\(436\) 0 0
\(437\) −28.9443 −1.38459
\(438\) 0 0
\(439\) −8.94427 −0.426887 −0.213443 0.976955i \(-0.568468\pi\)
−0.213443 + 0.976955i \(0.568468\pi\)
\(440\) 0 0
\(441\) −1.47214 −0.0701017
\(442\) 0 0
\(443\) 24.9443 1.18514 0.592569 0.805520i \(-0.298114\pi\)
0.592569 + 0.805520i \(0.298114\pi\)
\(444\) 0 0
\(445\) −12.3607 −0.585952
\(446\) 0 0
\(447\) 27.6393 1.30729
\(448\) 0 0
\(449\) 18.9443 0.894035 0.447018 0.894525i \(-0.352486\pi\)
0.447018 + 0.894525i \(0.352486\pi\)
\(450\) 0 0
\(451\) 2.47214 0.116408
\(452\) 0 0
\(453\) 14.8328 0.696906
\(454\) 0 0
\(455\) −4.00000 −0.187523
\(456\) 0 0
\(457\) 26.9443 1.26040 0.630200 0.776433i \(-0.282973\pi\)
0.630200 + 0.776433i \(0.282973\pi\)
\(458\) 0 0
\(459\) 13.6656 0.637857
\(460\) 0 0
\(461\) 24.7639 1.15337 0.576686 0.816966i \(-0.304346\pi\)
0.576686 + 0.816966i \(0.304346\pi\)
\(462\) 0 0
\(463\) 30.4721 1.41616 0.708080 0.706132i \(-0.249562\pi\)
0.708080 + 0.706132i \(0.249562\pi\)
\(464\) 0 0
\(465\) −3.05573 −0.141706
\(466\) 0 0
\(467\) 27.1246 1.25518 0.627589 0.778545i \(-0.284042\pi\)
0.627589 + 0.778545i \(0.284042\pi\)
\(468\) 0 0
\(469\) 11.4164 0.527161
\(470\) 0 0
\(471\) 15.6393 0.720622
\(472\) 0 0
\(473\) −10.4721 −0.481509
\(474\) 0 0
\(475\) −25.1246 −1.15280
\(476\) 0 0
\(477\) −12.4721 −0.571060
\(478\) 0 0
\(479\) −12.3607 −0.564774 −0.282387 0.959301i \(-0.591126\pi\)
−0.282387 + 0.959301i \(0.591126\pi\)
\(480\) 0 0
\(481\) −22.4721 −1.02464
\(482\) 0 0
\(483\) −4.94427 −0.224972
\(484\) 0 0
\(485\) −15.4164 −0.700023
\(486\) 0 0
\(487\) −16.9443 −0.767818 −0.383909 0.923371i \(-0.625422\pi\)
−0.383909 + 0.923371i \(0.625422\pi\)
\(488\) 0 0
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) 16.9443 0.764684 0.382342 0.924021i \(-0.375118\pi\)
0.382342 + 0.924021i \(0.375118\pi\)
\(492\) 0 0
\(493\) 11.0557 0.497925
\(494\) 0 0
\(495\) −1.81966 −0.0817876
\(496\) 0 0
\(497\) 6.47214 0.290315
\(498\) 0 0
\(499\) 32.3607 1.44866 0.724331 0.689452i \(-0.242149\pi\)
0.724331 + 0.689452i \(0.242149\pi\)
\(500\) 0 0
\(501\) 14.1115 0.630453
\(502\) 0 0
\(503\) −4.00000 −0.178351 −0.0891756 0.996016i \(-0.528423\pi\)
−0.0891756 + 0.996016i \(0.528423\pi\)
\(504\) 0 0
\(505\) −10.1115 −0.449954
\(506\) 0 0
\(507\) 3.12461 0.138769
\(508\) 0 0
\(509\) 24.0689 1.06683 0.533417 0.845852i \(-0.320908\pi\)
0.533417 + 0.845852i \(0.320908\pi\)
\(510\) 0 0
\(511\) −12.9443 −0.572621
\(512\) 0 0
\(513\) 40.0000 1.76604
\(514\) 0 0
\(515\) −18.4721 −0.813980
\(516\) 0 0
\(517\) −2.00000 −0.0879599
\(518\) 0 0
\(519\) 4.00000 0.175581
\(520\) 0 0
\(521\) −10.3607 −0.453910 −0.226955 0.973905i \(-0.572877\pi\)
−0.226955 + 0.973905i \(0.572877\pi\)
\(522\) 0 0
\(523\) 14.2918 0.624937 0.312468 0.949928i \(-0.398844\pi\)
0.312468 + 0.949928i \(0.398844\pi\)
\(524\) 0 0
\(525\) −4.29180 −0.187309
\(526\) 0 0
\(527\) −4.94427 −0.215376
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 4.06888 0.176575
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) 3.05573 0.132111
\(536\) 0 0
\(537\) −11.0557 −0.477090
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −26.9443 −1.15842 −0.579212 0.815177i \(-0.696640\pi\)
−0.579212 + 0.815177i \(0.696640\pi\)
\(542\) 0 0
\(543\) −11.4164 −0.489925
\(544\) 0 0
\(545\) 12.3607 0.529473
\(546\) 0 0
\(547\) 0.944272 0.0403742 0.0201871 0.999796i \(-0.493574\pi\)
0.0201871 + 0.999796i \(0.493574\pi\)
\(548\) 0 0
\(549\) 1.12461 0.0479973
\(550\) 0 0
\(551\) 32.3607 1.37861
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 10.6099 0.450365
\(556\) 0 0
\(557\) 24.8328 1.05220 0.526100 0.850423i \(-0.323654\pi\)
0.526100 + 0.850423i \(0.323654\pi\)
\(558\) 0 0
\(559\) −33.8885 −1.43333
\(560\) 0 0
\(561\) 3.05573 0.129013
\(562\) 0 0
\(563\) −31.2361 −1.31644 −0.658222 0.752824i \(-0.728691\pi\)
−0.658222 + 0.752824i \(0.728691\pi\)
\(564\) 0 0
\(565\) 0.583592 0.0245519
\(566\) 0 0
\(567\) 2.41641 0.101480
\(568\) 0 0
\(569\) −36.8328 −1.54411 −0.772056 0.635555i \(-0.780772\pi\)
−0.772056 + 0.635555i \(0.780772\pi\)
\(570\) 0 0
\(571\) 10.1115 0.423151 0.211576 0.977362i \(-0.432141\pi\)
0.211576 + 0.977362i \(0.432141\pi\)
\(572\) 0 0
\(573\) −3.05573 −0.127655
\(574\) 0 0
\(575\) 13.8885 0.579192
\(576\) 0 0
\(577\) 26.9443 1.12170 0.560852 0.827916i \(-0.310474\pi\)
0.560852 + 0.827916i \(0.310474\pi\)
\(578\) 0 0
\(579\) 18.4721 0.767676
\(580\) 0 0
\(581\) −12.1803 −0.505326
\(582\) 0 0
\(583\) −8.47214 −0.350880
\(584\) 0 0
\(585\) −5.88854 −0.243461
\(586\) 0 0
\(587\) 5.81966 0.240203 0.120102 0.992762i \(-0.461678\pi\)
0.120102 + 0.992762i \(0.461678\pi\)
\(588\) 0 0
\(589\) −14.4721 −0.596314
\(590\) 0 0
\(591\) −22.2492 −0.915211
\(592\) 0 0
\(593\) 24.0000 0.985562 0.492781 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(594\) 0 0
\(595\) 3.05573 0.125273
\(596\) 0 0
\(597\) 23.4164 0.958370
\(598\) 0 0
\(599\) 32.3607 1.32222 0.661111 0.750288i \(-0.270085\pi\)
0.661111 + 0.750288i \(0.270085\pi\)
\(600\) 0 0
\(601\) −34.8328 −1.42086 −0.710430 0.703768i \(-0.751500\pi\)
−0.710430 + 0.703768i \(0.751500\pi\)
\(602\) 0 0
\(603\) 16.8065 0.684414
\(604\) 0 0
\(605\) −1.23607 −0.0502533
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) 5.52786 0.224000
\(610\) 0 0
\(611\) −6.47214 −0.261835
\(612\) 0 0
\(613\) 28.4721 1.14998 0.574989 0.818161i \(-0.305006\pi\)
0.574989 + 0.818161i \(0.305006\pi\)
\(614\) 0 0
\(615\) −3.77709 −0.152307
\(616\) 0 0
\(617\) 21.4164 0.862192 0.431096 0.902306i \(-0.358127\pi\)
0.431096 + 0.902306i \(0.358127\pi\)
\(618\) 0 0
\(619\) −18.5410 −0.745227 −0.372613 0.927987i \(-0.621538\pi\)
−0.372613 + 0.927987i \(0.621538\pi\)
\(620\) 0 0
\(621\) −22.1115 −0.887302
\(622\) 0 0
\(623\) −10.0000 −0.400642
\(624\) 0 0
\(625\) 4.41641 0.176656
\(626\) 0 0
\(627\) 8.94427 0.357200
\(628\) 0 0
\(629\) 17.1672 0.684500
\(630\) 0 0
\(631\) 31.4164 1.25067 0.625334 0.780357i \(-0.284963\pi\)
0.625334 + 0.780357i \(0.284963\pi\)
\(632\) 0 0
\(633\) −16.7214 −0.664614
\(634\) 0 0
\(635\) −14.8328 −0.588622
\(636\) 0 0
\(637\) −3.23607 −0.128218
\(638\) 0 0
\(639\) 9.52786 0.376916
\(640\) 0 0
\(641\) 27.5279 1.08729 0.543643 0.839317i \(-0.317045\pi\)
0.543643 + 0.839317i \(0.317045\pi\)
\(642\) 0 0
\(643\) 18.7639 0.739977 0.369989 0.929036i \(-0.379362\pi\)
0.369989 + 0.929036i \(0.379362\pi\)
\(644\) 0 0
\(645\) 16.0000 0.629999
\(646\) 0 0
\(647\) 28.8328 1.13353 0.566767 0.823878i \(-0.308194\pi\)
0.566767 + 0.823878i \(0.308194\pi\)
\(648\) 0 0
\(649\) 2.76393 0.108494
\(650\) 0 0
\(651\) −2.47214 −0.0968906
\(652\) 0 0
\(653\) 46.3607 1.81423 0.907117 0.420879i \(-0.138278\pi\)
0.907117 + 0.420879i \(0.138278\pi\)
\(654\) 0 0
\(655\) 5.88854 0.230084
\(656\) 0 0
\(657\) −19.0557 −0.743435
\(658\) 0 0
\(659\) −16.5836 −0.646005 −0.323003 0.946398i \(-0.604692\pi\)
−0.323003 + 0.946398i \(0.604692\pi\)
\(660\) 0 0
\(661\) −3.12461 −0.121533 −0.0607667 0.998152i \(-0.519355\pi\)
−0.0607667 + 0.998152i \(0.519355\pi\)
\(662\) 0 0
\(663\) 9.88854 0.384039
\(664\) 0 0
\(665\) 8.94427 0.346844
\(666\) 0 0
\(667\) −17.8885 −0.692647
\(668\) 0 0
\(669\) −0.583592 −0.0225630
\(670\) 0 0
\(671\) 0.763932 0.0294913
\(672\) 0 0
\(673\) −3.88854 −0.149892 −0.0749462 0.997188i \(-0.523878\pi\)
−0.0749462 + 0.997188i \(0.523878\pi\)
\(674\) 0 0
\(675\) −19.1935 −0.738758
\(676\) 0 0
\(677\) −26.0689 −1.00191 −0.500954 0.865474i \(-0.667018\pi\)
−0.500954 + 0.865474i \(0.667018\pi\)
\(678\) 0 0
\(679\) −12.4721 −0.478637
\(680\) 0 0
\(681\) −23.7771 −0.911140
\(682\) 0 0
\(683\) −32.9443 −1.26058 −0.630289 0.776361i \(-0.717064\pi\)
−0.630289 + 0.776361i \(0.717064\pi\)
\(684\) 0 0
\(685\) 24.5836 0.939291
\(686\) 0 0
\(687\) −21.3050 −0.812835
\(688\) 0 0
\(689\) −27.4164 −1.04448
\(690\) 0 0
\(691\) −12.6525 −0.481323 −0.240661 0.970609i \(-0.577364\pi\)
−0.240661 + 0.970609i \(0.577364\pi\)
\(692\) 0 0
\(693\) −1.47214 −0.0559218
\(694\) 0 0
\(695\) −26.8328 −1.01783
\(696\) 0 0
\(697\) −6.11146 −0.231488
\(698\) 0 0
\(699\) 18.4721 0.698680
\(700\) 0 0
\(701\) −42.7214 −1.61356 −0.806782 0.590850i \(-0.798793\pi\)
−0.806782 + 0.590850i \(0.798793\pi\)
\(702\) 0 0
\(703\) 50.2492 1.89519
\(704\) 0 0
\(705\) 3.05573 0.115085
\(706\) 0 0
\(707\) −8.18034 −0.307653
\(708\) 0 0
\(709\) 4.47214 0.167955 0.0839773 0.996468i \(-0.473238\pi\)
0.0839773 + 0.996468i \(0.473238\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) 0 0
\(717\) 24.7214 0.923236
\(718\) 0 0
\(719\) −16.8328 −0.627758 −0.313879 0.949463i \(-0.601629\pi\)
−0.313879 + 0.949463i \(0.601629\pi\)
\(720\) 0 0
\(721\) −14.9443 −0.556554
\(722\) 0 0
\(723\) −19.0557 −0.708690
\(724\) 0 0
\(725\) −15.5279 −0.576690
\(726\) 0 0
\(727\) −18.0000 −0.667583 −0.333792 0.942647i \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 0 0
\(729\) 24.0557 0.890953
\(730\) 0 0
\(731\) 25.8885 0.957522
\(732\) 0 0
\(733\) 49.1246 1.81446 0.907229 0.420636i \(-0.138193\pi\)
0.907229 + 0.420636i \(0.138193\pi\)
\(734\) 0 0
\(735\) 1.52786 0.0563561
\(736\) 0 0
\(737\) 11.4164 0.420529
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 28.9443 1.06329
\(742\) 0 0
\(743\) −21.8885 −0.803013 −0.401506 0.915856i \(-0.631513\pi\)
−0.401506 + 0.915856i \(0.631513\pi\)
\(744\) 0 0
\(745\) 27.6393 1.01263
\(746\) 0 0
\(747\) −17.9311 −0.656065
\(748\) 0 0
\(749\) 2.47214 0.0903299
\(750\) 0 0
\(751\) 16.9443 0.618305 0.309153 0.951012i \(-0.399955\pi\)
0.309153 + 0.951012i \(0.399955\pi\)
\(752\) 0 0
\(753\) 36.1378 1.31693
\(754\) 0 0
\(755\) 14.8328 0.539821
\(756\) 0 0
\(757\) −23.3050 −0.847033 −0.423516 0.905888i \(-0.639204\pi\)
−0.423516 + 0.905888i \(0.639204\pi\)
\(758\) 0 0
\(759\) −4.94427 −0.179466
\(760\) 0 0
\(761\) −11.4164 −0.413844 −0.206922 0.978357i \(-0.566345\pi\)
−0.206922 + 0.978357i \(0.566345\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) 4.49845 0.162642
\(766\) 0 0
\(767\) 8.94427 0.322959
\(768\) 0 0
\(769\) −43.4164 −1.56564 −0.782818 0.622251i \(-0.786218\pi\)
−0.782818 + 0.622251i \(0.786218\pi\)
\(770\) 0 0
\(771\) −8.58359 −0.309131
\(772\) 0 0
\(773\) 15.7082 0.564985 0.282492 0.959270i \(-0.408839\pi\)
0.282492 + 0.959270i \(0.408839\pi\)
\(774\) 0 0
\(775\) 6.94427 0.249446
\(776\) 0 0
\(777\) 8.58359 0.307935
\(778\) 0 0
\(779\) −17.8885 −0.640924
\(780\) 0 0
\(781\) 6.47214 0.231591
\(782\) 0 0
\(783\) 24.7214 0.883469
\(784\) 0 0
\(785\) 15.6393 0.558191
\(786\) 0 0
\(787\) 28.1803 1.00452 0.502260 0.864716i \(-0.332502\pi\)
0.502260 + 0.864716i \(0.332502\pi\)
\(788\) 0 0
\(789\) −6.11146 −0.217574
\(790\) 0 0
\(791\) 0.472136 0.0167872
\(792\) 0 0
\(793\) 2.47214 0.0877881
\(794\) 0 0
\(795\) 12.9443 0.459086
\(796\) 0 0
\(797\) −41.5967 −1.47343 −0.736716 0.676202i \(-0.763625\pi\)
−0.736716 + 0.676202i \(0.763625\pi\)
\(798\) 0 0
\(799\) 4.94427 0.174916
\(800\) 0 0
\(801\) −14.7214 −0.520154
\(802\) 0 0
\(803\) −12.9443 −0.456793
\(804\) 0 0
\(805\) −4.94427 −0.174263
\(806\) 0 0
\(807\) 28.1378 0.990496
\(808\) 0 0
\(809\) −21.0557 −0.740280 −0.370140 0.928976i \(-0.620690\pi\)
−0.370140 + 0.928976i \(0.620690\pi\)
\(810\) 0 0
\(811\) −4.76393 −0.167284 −0.0836421 0.996496i \(-0.526655\pi\)
−0.0836421 + 0.996496i \(0.526655\pi\)
\(812\) 0 0
\(813\) 1.16718 0.0409349
\(814\) 0 0
\(815\) −24.0000 −0.840683
\(816\) 0 0
\(817\) 75.7771 2.65110
\(818\) 0 0
\(819\) −4.76393 −0.166465
\(820\) 0 0
\(821\) −1.41641 −0.0494330 −0.0247165 0.999695i \(-0.507868\pi\)
−0.0247165 + 0.999695i \(0.507868\pi\)
\(822\) 0 0
\(823\) 46.2492 1.61215 0.806073 0.591816i \(-0.201589\pi\)
0.806073 + 0.591816i \(0.201589\pi\)
\(824\) 0 0
\(825\) −4.29180 −0.149421
\(826\) 0 0
\(827\) −16.9443 −0.589210 −0.294605 0.955619i \(-0.595188\pi\)
−0.294605 + 0.955619i \(0.595188\pi\)
\(828\) 0 0
\(829\) 11.7082 0.406643 0.203321 0.979112i \(-0.434826\pi\)
0.203321 + 0.979112i \(0.434826\pi\)
\(830\) 0 0
\(831\) −4.36068 −0.151270
\(832\) 0 0
\(833\) 2.47214 0.0856544
\(834\) 0 0
\(835\) 14.1115 0.488347
\(836\) 0 0
\(837\) −11.0557 −0.382142
\(838\) 0 0
\(839\) −16.8328 −0.581133 −0.290567 0.956855i \(-0.593844\pi\)
−0.290567 + 0.956855i \(0.593844\pi\)
\(840\) 0 0
\(841\) −9.00000 −0.310345
\(842\) 0 0
\(843\) −35.6393 −1.22748
\(844\) 0 0
\(845\) 3.12461 0.107490
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 18.1115 0.621584
\(850\) 0 0
\(851\) −27.7771 −0.952186
\(852\) 0 0
\(853\) 32.5410 1.11418 0.557092 0.830451i \(-0.311917\pi\)
0.557092 + 0.830451i \(0.311917\pi\)
\(854\) 0 0
\(855\) 13.1672 0.450308
\(856\) 0 0
\(857\) −46.4721 −1.58746 −0.793729 0.608272i \(-0.791863\pi\)
−0.793729 + 0.608272i \(0.791863\pi\)
\(858\) 0 0
\(859\) −15.1246 −0.516045 −0.258023 0.966139i \(-0.583071\pi\)
−0.258023 + 0.966139i \(0.583071\pi\)
\(860\) 0 0
\(861\) −3.05573 −0.104139
\(862\) 0 0
\(863\) −0.583592 −0.0198657 −0.00993285 0.999951i \(-0.503162\pi\)
−0.00993285 + 0.999951i \(0.503162\pi\)
\(864\) 0 0
\(865\) 4.00000 0.136004
\(866\) 0 0
\(867\) 13.4590 0.457091
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 36.9443 1.25181
\(872\) 0 0
\(873\) −18.3607 −0.621415
\(874\) 0 0
\(875\) −10.4721 −0.354023
\(876\) 0 0
\(877\) 9.05573 0.305790 0.152895 0.988242i \(-0.451140\pi\)
0.152895 + 0.988242i \(0.451140\pi\)
\(878\) 0 0
\(879\) 32.9443 1.11118
\(880\) 0 0
\(881\) 28.8328 0.971402 0.485701 0.874125i \(-0.338564\pi\)
0.485701 + 0.874125i \(0.338564\pi\)
\(882\) 0 0
\(883\) 2.83282 0.0953318 0.0476659 0.998863i \(-0.484822\pi\)
0.0476659 + 0.998863i \(0.484822\pi\)
\(884\) 0 0
\(885\) −4.22291 −0.141952
\(886\) 0 0
\(887\) 44.3607 1.48949 0.744743 0.667351i \(-0.232572\pi\)
0.744743 + 0.667351i \(0.232572\pi\)
\(888\) 0 0
\(889\) −12.0000 −0.402467
\(890\) 0 0
\(891\) 2.41641 0.0809527
\(892\) 0 0
\(893\) 14.4721 0.484292
\(894\) 0 0
\(895\) −11.0557 −0.369552
\(896\) 0 0
\(897\) −16.0000 −0.534224
\(898\) 0 0
\(899\) −8.94427 −0.298308
\(900\) 0 0
\(901\) 20.9443 0.697755
\(902\) 0 0
\(903\) 12.9443 0.430758
\(904\) 0 0
\(905\) −11.4164 −0.379494
\(906\) 0 0
\(907\) 24.3607 0.808883 0.404442 0.914564i \(-0.367466\pi\)
0.404442 + 0.914564i \(0.367466\pi\)
\(908\) 0 0
\(909\) −12.0426 −0.399427
\(910\) 0 0
\(911\) 28.0000 0.927681 0.463841 0.885919i \(-0.346471\pi\)
0.463841 + 0.885919i \(0.346471\pi\)
\(912\) 0 0
\(913\) −12.1803 −0.403110
\(914\) 0 0
\(915\) −1.16718 −0.0385859
\(916\) 0 0
\(917\) 4.76393 0.157319
\(918\) 0 0
\(919\) 22.1115 0.729390 0.364695 0.931127i \(-0.381173\pi\)
0.364695 + 0.931127i \(0.381173\pi\)
\(920\) 0 0
\(921\) −32.2229 −1.06178
\(922\) 0 0
\(923\) 20.9443 0.689389
\(924\) 0 0
\(925\) −24.1115 −0.792780
\(926\) 0 0
\(927\) −22.0000 −0.722575
\(928\) 0 0
\(929\) 40.2492 1.32053 0.660267 0.751031i \(-0.270443\pi\)
0.660267 + 0.751031i \(0.270443\pi\)
\(930\) 0 0
\(931\) 7.23607 0.237153
\(932\) 0 0
\(933\) −26.4721 −0.866659
\(934\) 0 0
\(935\) 3.05573 0.0999330
\(936\) 0 0
\(937\) −3.05573 −0.0998263 −0.0499131 0.998754i \(-0.515894\pi\)
−0.0499131 + 0.998754i \(0.515894\pi\)
\(938\) 0 0
\(939\) −24.1378 −0.787706
\(940\) 0 0
\(941\) −11.8197 −0.385310 −0.192655 0.981267i \(-0.561710\pi\)
−0.192655 + 0.981267i \(0.561710\pi\)
\(942\) 0 0
\(943\) 9.88854 0.322015
\(944\) 0 0
\(945\) 6.83282 0.222272
\(946\) 0 0
\(947\) −16.9443 −0.550615 −0.275307 0.961356i \(-0.588780\pi\)
−0.275307 + 0.961356i \(0.588780\pi\)
\(948\) 0 0
\(949\) −41.8885 −1.35976
\(950\) 0 0
\(951\) 38.2492 1.24032
\(952\) 0 0
\(953\) 22.9443 0.743238 0.371619 0.928385i \(-0.378803\pi\)
0.371619 + 0.928385i \(0.378803\pi\)
\(954\) 0 0
\(955\) −3.05573 −0.0988810
\(956\) 0 0
\(957\) 5.52786 0.178690
\(958\) 0 0
\(959\) 19.8885 0.642235
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 3.63932 0.117275
\(964\) 0 0
\(965\) 18.4721 0.594639
\(966\) 0 0
\(967\) −45.8885 −1.47568 −0.737838 0.674978i \(-0.764153\pi\)
−0.737838 + 0.674978i \(0.764153\pi\)
\(968\) 0 0
\(969\) −22.1115 −0.710322
\(970\) 0 0
\(971\) −50.5410 −1.62194 −0.810969 0.585089i \(-0.801060\pi\)
−0.810969 + 0.585089i \(0.801060\pi\)
\(972\) 0 0
\(973\) −21.7082 −0.695933
\(974\) 0 0
\(975\) −13.8885 −0.444789
\(976\) 0 0
\(977\) −28.8328 −0.922443 −0.461222 0.887285i \(-0.652589\pi\)
−0.461222 + 0.887285i \(0.652589\pi\)
\(978\) 0 0
\(979\) −10.0000 −0.319601
\(980\) 0 0
\(981\) 14.7214 0.470017
\(982\) 0 0
\(983\) −14.0000 −0.446531 −0.223265 0.974758i \(-0.571672\pi\)
−0.223265 + 0.974758i \(0.571672\pi\)
\(984\) 0 0
\(985\) −22.2492 −0.708919
\(986\) 0 0
\(987\) 2.47214 0.0786890
\(988\) 0 0
\(989\) −41.8885 −1.33198
\(990\) 0 0
\(991\) 0.360680 0.0114574 0.00572869 0.999984i \(-0.498176\pi\)
0.00572869 + 0.999984i \(0.498176\pi\)
\(992\) 0 0
\(993\) −20.9443 −0.664646
\(994\) 0 0
\(995\) 23.4164 0.742350
\(996\) 0 0
\(997\) 24.1803 0.765799 0.382900 0.923790i \(-0.374926\pi\)
0.382900 + 0.923790i \(0.374926\pi\)
\(998\) 0 0
\(999\) 38.3870 1.21451
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 1232.2.a.p.1.1 2
4.3 odd 2 154.2.a.d.1.2 2
7.6 odd 2 8624.2.a.bf.1.2 2
8.3 odd 2 4928.2.a.bt.1.1 2
8.5 even 2 4928.2.a.bk.1.2 2
12.11 even 2 1386.2.a.m.1.2 2
20.3 even 4 3850.2.c.q.1849.2 4
20.7 even 4 3850.2.c.q.1849.3 4
20.19 odd 2 3850.2.a.bj.1.1 2
28.3 even 6 1078.2.e.n.177.2 4
28.11 odd 6 1078.2.e.q.177.1 4
28.19 even 6 1078.2.e.n.67.2 4
28.23 odd 6 1078.2.e.q.67.1 4
28.27 even 2 1078.2.a.w.1.1 2
44.43 even 2 1694.2.a.l.1.2 2
84.83 odd 2 9702.2.a.cu.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.a.d.1.2 2 4.3 odd 2
1078.2.a.w.1.1 2 28.27 even 2
1078.2.e.n.67.2 4 28.19 even 6
1078.2.e.n.177.2 4 28.3 even 6
1078.2.e.q.67.1 4 28.23 odd 6
1078.2.e.q.177.1 4 28.11 odd 6
1232.2.a.p.1.1 2 1.1 even 1 trivial
1386.2.a.m.1.2 2 12.11 even 2
1694.2.a.l.1.2 2 44.43 even 2
3850.2.a.bj.1.1 2 20.19 odd 2
3850.2.c.q.1849.2 4 20.3 even 4
3850.2.c.q.1849.3 4 20.7 even 4
4928.2.a.bk.1.2 2 8.5 even 2
4928.2.a.bt.1.1 2 8.3 odd 2
8624.2.a.bf.1.2 2 7.6 odd 2
9702.2.a.cu.1.1 2 84.83 odd 2