Properties

Label 6012.2.a.j.1.5
Level $6012$
Weight $2$
Character 6012.1
Self dual yes
Analytic conductor $48.006$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6012,2,Mod(1,6012)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6012.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0060616952\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} - 26x^{8} + 82x^{7} + 211x^{6} - 340x^{5} - 593x^{4} + 192x^{3} + 423x^{2} + 126x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.19255\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.553287 q^{5} -1.19255 q^{7} +O(q^{10})\) \(q-0.553287 q^{5} -1.19255 q^{7} -0.843505 q^{11} +2.93872 q^{13} -3.89858 q^{17} -3.92245 q^{19} +3.42491 q^{23} -4.69387 q^{25} +8.30275 q^{29} +7.13278 q^{31} +0.659822 q^{35} +5.02924 q^{37} -8.17577 q^{41} +9.35576 q^{43} -6.99954 q^{47} -5.57783 q^{49} +4.65547 q^{53} +0.466701 q^{55} -5.45570 q^{59} +1.19050 q^{61} -1.62595 q^{65} -5.61950 q^{67} -10.1882 q^{71} +3.81452 q^{73} +1.00592 q^{77} +2.65506 q^{79} -7.17199 q^{83} +2.15703 q^{85} +0.0346287 q^{89} -3.50456 q^{91} +2.17024 q^{95} -16.0201 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 6 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 6 q^{5} + 4 q^{7} - 8 q^{11} - 2 q^{13} - 6 q^{17} - 20 q^{23} + 24 q^{25} - 8 q^{29} - 4 q^{31} - 4 q^{37} + 14 q^{41} + 20 q^{43} - 48 q^{47} - 2 q^{49} - 22 q^{53} - 6 q^{55} - 2 q^{59} - 8 q^{61} - 28 q^{65} - 6 q^{67} - 20 q^{71} + 20 q^{73} - 24 q^{77} - 4 q^{79} - 46 q^{83} - 18 q^{85} + 8 q^{89} + 28 q^{91} - 36 q^{95} - 34 q^{97}+O(q^{100}) \) 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
\(5\) −0.553287 −0.247438 −0.123719 0.992317i \(-0.539482\pi\)
−0.123719 + 0.992317i \(0.539482\pi\)
\(6\) 0 0
\(7\) −1.19255 −0.450741 −0.225370 0.974273i \(-0.572359\pi\)
−0.225370 + 0.974273i \(0.572359\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.843505 −0.254326 −0.127163 0.991882i \(-0.540587\pi\)
−0.127163 + 0.991882i \(0.540587\pi\)
\(12\) 0 0
\(13\) 2.93872 0.815054 0.407527 0.913193i \(-0.366391\pi\)
0.407527 + 0.913193i \(0.366391\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.89858 −0.945544 −0.472772 0.881185i \(-0.656747\pi\)
−0.472772 + 0.881185i \(0.656747\pi\)
\(18\) 0 0
\(19\) −3.92245 −0.899873 −0.449936 0.893061i \(-0.648553\pi\)
−0.449936 + 0.893061i \(0.648553\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.42491 0.714143 0.357072 0.934077i \(-0.383775\pi\)
0.357072 + 0.934077i \(0.383775\pi\)
\(24\) 0 0
\(25\) −4.69387 −0.938775
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.30275 1.54178 0.770891 0.636968i \(-0.219812\pi\)
0.770891 + 0.636968i \(0.219812\pi\)
\(30\) 0 0
\(31\) 7.13278 1.28109 0.640543 0.767923i \(-0.278709\pi\)
0.640543 + 0.767923i \(0.278709\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.659822 0.111530
\(36\) 0 0
\(37\) 5.02924 0.826802 0.413401 0.910549i \(-0.364341\pi\)
0.413401 + 0.910549i \(0.364341\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.17577 −1.27684 −0.638420 0.769688i \(-0.720412\pi\)
−0.638420 + 0.769688i \(0.720412\pi\)
\(42\) 0 0
\(43\) 9.35576 1.42674 0.713370 0.700788i \(-0.247168\pi\)
0.713370 + 0.700788i \(0.247168\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.99954 −1.02099 −0.510494 0.859881i \(-0.670537\pi\)
−0.510494 + 0.859881i \(0.670537\pi\)
\(48\) 0 0
\(49\) −5.57783 −0.796833
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.65547 0.639477 0.319739 0.947506i \(-0.396405\pi\)
0.319739 + 0.947506i \(0.396405\pi\)
\(54\) 0 0
\(55\) 0.466701 0.0629299
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.45570 −0.710272 −0.355136 0.934815i \(-0.615565\pi\)
−0.355136 + 0.934815i \(0.615565\pi\)
\(60\) 0 0
\(61\) 1.19050 0.152428 0.0762142 0.997091i \(-0.475717\pi\)
0.0762142 + 0.997091i \(0.475717\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.62595 −0.201675
\(66\) 0 0
\(67\) −5.61950 −0.686531 −0.343265 0.939238i \(-0.611533\pi\)
−0.343265 + 0.939238i \(0.611533\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.1882 −1.20912 −0.604560 0.796559i \(-0.706651\pi\)
−0.604560 + 0.796559i \(0.706651\pi\)
\(72\) 0 0
\(73\) 3.81452 0.446456 0.223228 0.974766i \(-0.428341\pi\)
0.223228 + 0.974766i \(0.428341\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.00592 0.114635
\(78\) 0 0
\(79\) 2.65506 0.298718 0.149359 0.988783i \(-0.452279\pi\)
0.149359 + 0.988783i \(0.452279\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.17199 −0.787228 −0.393614 0.919276i \(-0.628775\pi\)
−0.393614 + 0.919276i \(0.628775\pi\)
\(84\) 0 0
\(85\) 2.15703 0.233963
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.0346287 0.00367063 0.00183531 0.999998i \(-0.499416\pi\)
0.00183531 + 0.999998i \(0.499416\pi\)
\(90\) 0 0
\(91\) −3.50456 −0.367378
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.17024 0.222662
\(96\) 0 0
\(97\) −16.0201 −1.62659 −0.813296 0.581851i \(-0.802329\pi\)
−0.813296 + 0.581851i \(0.802329\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.26340 −0.324721 −0.162360 0.986732i \(-0.551911\pi\)
−0.162360 + 0.986732i \(0.551911\pi\)
\(102\) 0 0
\(103\) 3.52096 0.346930 0.173465 0.984840i \(-0.444504\pi\)
0.173465 + 0.984840i \(0.444504\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.0090 −1.25762 −0.628811 0.777558i \(-0.716458\pi\)
−0.628811 + 0.777558i \(0.716458\pi\)
\(108\) 0 0
\(109\) −5.62330 −0.538615 −0.269307 0.963054i \(-0.586795\pi\)
−0.269307 + 0.963054i \(0.586795\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.78699 −0.638466 −0.319233 0.947676i \(-0.603425\pi\)
−0.319233 + 0.947676i \(0.603425\pi\)
\(114\) 0 0
\(115\) −1.89496 −0.176706
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.64924 0.426196
\(120\) 0 0
\(121\) −10.2885 −0.935318
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.36350 0.479726
\(126\) 0 0
\(127\) −11.5685 −1.02654 −0.513268 0.858228i \(-0.671565\pi\)
−0.513268 + 0.858228i \(0.671565\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −10.6410 −0.929708 −0.464854 0.885387i \(-0.653893\pi\)
−0.464854 + 0.885387i \(0.653893\pi\)
\(132\) 0 0
\(133\) 4.67772 0.405609
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 21.4369 1.83147 0.915737 0.401777i \(-0.131607\pi\)
0.915737 + 0.401777i \(0.131607\pi\)
\(138\) 0 0
\(139\) 14.1597 1.20101 0.600506 0.799620i \(-0.294966\pi\)
0.600506 + 0.799620i \(0.294966\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.47882 −0.207290
\(144\) 0 0
\(145\) −4.59380 −0.381495
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.93561 −0.486264 −0.243132 0.969993i \(-0.578175\pi\)
−0.243132 + 0.969993i \(0.578175\pi\)
\(150\) 0 0
\(151\) −2.85158 −0.232058 −0.116029 0.993246i \(-0.537017\pi\)
−0.116029 + 0.993246i \(0.537017\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.94648 −0.316989
\(156\) 0 0
\(157\) 7.96471 0.635653 0.317827 0.948149i \(-0.397047\pi\)
0.317827 + 0.948149i \(0.397047\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.08437 −0.321894
\(162\) 0 0
\(163\) −7.00784 −0.548896 −0.274448 0.961602i \(-0.588495\pi\)
−0.274448 + 0.961602i \(0.588495\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −4.36394 −0.335688
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 25.6960 1.95363 0.976814 0.214092i \(-0.0686792\pi\)
0.976814 + 0.214092i \(0.0686792\pi\)
\(174\) 0 0
\(175\) 5.59767 0.423144
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.29160 −0.619743 −0.309872 0.950778i \(-0.600286\pi\)
−0.309872 + 0.950778i \(0.600286\pi\)
\(180\) 0 0
\(181\) 24.8881 1.84992 0.924960 0.380064i \(-0.124098\pi\)
0.924960 + 0.380064i \(0.124098\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.78261 −0.204582
\(186\) 0 0
\(187\) 3.28847 0.240477
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.1554 −1.74782 −0.873910 0.486088i \(-0.838424\pi\)
−0.873910 + 0.486088i \(0.838424\pi\)
\(192\) 0 0
\(193\) 5.74862 0.413794 0.206897 0.978363i \(-0.433663\pi\)
0.206897 + 0.978363i \(0.433663\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −21.1007 −1.50336 −0.751682 0.659526i \(-0.770757\pi\)
−0.751682 + 0.659526i \(0.770757\pi\)
\(198\) 0 0
\(199\) −7.63118 −0.540960 −0.270480 0.962726i \(-0.587182\pi\)
−0.270480 + 0.962726i \(0.587182\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −9.90143 −0.694944
\(204\) 0 0
\(205\) 4.52355 0.315938
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.30861 0.228861
\(210\) 0 0
\(211\) 8.88130 0.611414 0.305707 0.952126i \(-0.401107\pi\)
0.305707 + 0.952126i \(0.401107\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.17642 −0.353029
\(216\) 0 0
\(217\) −8.50619 −0.577438
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −11.4568 −0.770669
\(222\) 0 0
\(223\) 8.98927 0.601966 0.300983 0.953629i \(-0.402685\pi\)
0.300983 + 0.953629i \(0.402685\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −13.7375 −0.911791 −0.455895 0.890033i \(-0.650681\pi\)
−0.455895 + 0.890033i \(0.650681\pi\)
\(228\) 0 0
\(229\) 8.18243 0.540710 0.270355 0.962761i \(-0.412859\pi\)
0.270355 + 0.962761i \(0.412859\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −22.6304 −1.48256 −0.741282 0.671194i \(-0.765782\pi\)
−0.741282 + 0.671194i \(0.765782\pi\)
\(234\) 0 0
\(235\) 3.87275 0.252631
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −20.1846 −1.30563 −0.652817 0.757516i \(-0.726413\pi\)
−0.652817 + 0.757516i \(0.726413\pi\)
\(240\) 0 0
\(241\) 14.5196 0.935291 0.467646 0.883916i \(-0.345102\pi\)
0.467646 + 0.883916i \(0.345102\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.08614 0.197166
\(246\) 0 0
\(247\) −11.5270 −0.733445
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −16.5054 −1.04181 −0.520905 0.853615i \(-0.674405\pi\)
−0.520905 + 0.853615i \(0.674405\pi\)
\(252\) 0 0
\(253\) −2.88893 −0.181625
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −17.8128 −1.11113 −0.555566 0.831473i \(-0.687498\pi\)
−0.555566 + 0.831473i \(0.687498\pi\)
\(258\) 0 0
\(259\) −5.99761 −0.372673
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.29983 −0.141814 −0.0709068 0.997483i \(-0.522589\pi\)
−0.0709068 + 0.997483i \(0.522589\pi\)
\(264\) 0 0
\(265\) −2.57581 −0.158231
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.03212 0.306814 0.153407 0.988163i \(-0.450975\pi\)
0.153407 + 0.988163i \(0.450975\pi\)
\(270\) 0 0
\(271\) 4.85768 0.295083 0.147541 0.989056i \(-0.452864\pi\)
0.147541 + 0.989056i \(0.452864\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.95931 0.238755
\(276\) 0 0
\(277\) −12.6282 −0.758753 −0.379377 0.925242i \(-0.623862\pi\)
−0.379377 + 0.925242i \(0.623862\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −17.7600 −1.05948 −0.529738 0.848161i \(-0.677710\pi\)
−0.529738 + 0.848161i \(0.677710\pi\)
\(282\) 0 0
\(283\) −4.43500 −0.263633 −0.131817 0.991274i \(-0.542081\pi\)
−0.131817 + 0.991274i \(0.542081\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.75000 0.575524
\(288\) 0 0
\(289\) −1.80108 −0.105946
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.8983 −1.10405 −0.552025 0.833828i \(-0.686145\pi\)
−0.552025 + 0.833828i \(0.686145\pi\)
\(294\) 0 0
\(295\) 3.01857 0.175748
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10.0648 0.582065
\(300\) 0 0
\(301\) −11.1572 −0.643090
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.658690 −0.0377165
\(306\) 0 0
\(307\) −22.5138 −1.28493 −0.642467 0.766314i \(-0.722089\pi\)
−0.642467 + 0.766314i \(0.722089\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.5228 −1.39056 −0.695281 0.718738i \(-0.744720\pi\)
−0.695281 + 0.718738i \(0.744720\pi\)
\(312\) 0 0
\(313\) 15.8723 0.897153 0.448576 0.893744i \(-0.351931\pi\)
0.448576 + 0.893744i \(0.351931\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.97332 0.279329 0.139665 0.990199i \(-0.455398\pi\)
0.139665 + 0.990199i \(0.455398\pi\)
\(318\) 0 0
\(319\) −7.00341 −0.392116
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.2920 0.850869
\(324\) 0 0
\(325\) −13.7940 −0.765152
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8.34729 0.460201
\(330\) 0 0
\(331\) −28.1768 −1.54874 −0.774368 0.632736i \(-0.781932\pi\)
−0.774368 + 0.632736i \(0.781932\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.10920 0.169874
\(336\) 0 0
\(337\) −30.2227 −1.64633 −0.823167 0.567799i \(-0.807795\pi\)
−0.823167 + 0.567799i \(0.807795\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.01654 −0.325814
\(342\) 0 0
\(343\) 14.9997 0.809906
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.4230 1.09636 0.548182 0.836359i \(-0.315320\pi\)
0.548182 + 0.836359i \(0.315320\pi\)
\(348\) 0 0
\(349\) −7.59387 −0.406490 −0.203245 0.979128i \(-0.565149\pi\)
−0.203245 + 0.979128i \(0.565149\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −35.7547 −1.90303 −0.951517 0.307597i \(-0.900475\pi\)
−0.951517 + 0.307597i \(0.900475\pi\)
\(354\) 0 0
\(355\) 5.63702 0.299182
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5.91617 0.312244 0.156122 0.987738i \(-0.450101\pi\)
0.156122 + 0.987738i \(0.450101\pi\)
\(360\) 0 0
\(361\) −3.61435 −0.190229
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.11053 −0.110470
\(366\) 0 0
\(367\) 27.7218 1.44707 0.723534 0.690289i \(-0.242516\pi\)
0.723534 + 0.690289i \(0.242516\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.55187 −0.288239
\(372\) 0 0
\(373\) −7.77432 −0.402539 −0.201270 0.979536i \(-0.564507\pi\)
−0.201270 + 0.979536i \(0.564507\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 24.3994 1.25663
\(378\) 0 0
\(379\) −20.3173 −1.04363 −0.521816 0.853058i \(-0.674745\pi\)
−0.521816 + 0.853058i \(0.674745\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5.49960 0.281016 0.140508 0.990080i \(-0.455126\pi\)
0.140508 + 0.990080i \(0.455126\pi\)
\(384\) 0 0
\(385\) −0.556563 −0.0283651
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13.6983 0.694530 0.347265 0.937767i \(-0.387110\pi\)
0.347265 + 0.937767i \(0.387110\pi\)
\(390\) 0 0
\(391\) −13.3523 −0.675254
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.46901 −0.0739140
\(396\) 0 0
\(397\) 9.48233 0.475905 0.237952 0.971277i \(-0.423524\pi\)
0.237952 + 0.971277i \(0.423524\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.61248 0.230337 0.115168 0.993346i \(-0.463259\pi\)
0.115168 + 0.993346i \(0.463259\pi\)
\(402\) 0 0
\(403\) 20.9612 1.04415
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.24219 −0.210278
\(408\) 0 0
\(409\) 36.1759 1.78879 0.894393 0.447282i \(-0.147608\pi\)
0.894393 + 0.447282i \(0.147608\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.50619 0.320149
\(414\) 0 0
\(415\) 3.96817 0.194790
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.80836 −0.332610 −0.166305 0.986074i \(-0.553184\pi\)
−0.166305 + 0.986074i \(0.553184\pi\)
\(420\) 0 0
\(421\) −2.28706 −0.111464 −0.0557322 0.998446i \(-0.517749\pi\)
−0.0557322 + 0.998446i \(0.517749\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 18.2994 0.887653
\(426\) 0 0
\(427\) −1.41973 −0.0687057
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 18.1173 0.872681 0.436340 0.899782i \(-0.356274\pi\)
0.436340 + 0.899782i \(0.356274\pi\)
\(432\) 0 0
\(433\) 29.9195 1.43784 0.718920 0.695093i \(-0.244637\pi\)
0.718920 + 0.695093i \(0.244637\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −13.4341 −0.642638
\(438\) 0 0
\(439\) 36.9704 1.76450 0.882250 0.470780i \(-0.156028\pi\)
0.882250 + 0.470780i \(0.156028\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −32.0326 −1.52191 −0.760957 0.648803i \(-0.775270\pi\)
−0.760957 + 0.648803i \(0.775270\pi\)
\(444\) 0 0
\(445\) −0.0191596 −0.000908252 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 17.1504 0.809379 0.404690 0.914454i \(-0.367380\pi\)
0.404690 + 0.914454i \(0.367380\pi\)
\(450\) 0 0
\(451\) 6.89630 0.324734
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.93903 0.0909031
\(456\) 0 0
\(457\) −13.8100 −0.646005 −0.323002 0.946398i \(-0.604692\pi\)
−0.323002 + 0.946398i \(0.604692\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.0964 −0.749686 −0.374843 0.927088i \(-0.622303\pi\)
−0.374843 + 0.927088i \(0.622303\pi\)
\(462\) 0 0
\(463\) −36.1389 −1.67952 −0.839758 0.542961i \(-0.817303\pi\)
−0.839758 + 0.542961i \(0.817303\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −14.9562 −0.692092 −0.346046 0.938218i \(-0.612476\pi\)
−0.346046 + 0.938218i \(0.612476\pi\)
\(468\) 0 0
\(469\) 6.70152 0.309448
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −7.89163 −0.362858
\(474\) 0 0
\(475\) 18.4115 0.844778
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.11705 0.370878 0.185439 0.982656i \(-0.440629\pi\)
0.185439 + 0.982656i \(0.440629\pi\)
\(480\) 0 0
\(481\) 14.7795 0.673888
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.86370 0.402480
\(486\) 0 0
\(487\) −11.4148 −0.517256 −0.258628 0.965977i \(-0.583270\pi\)
−0.258628 + 0.965977i \(0.583270\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.17339 0.188342 0.0941712 0.995556i \(-0.469980\pi\)
0.0941712 + 0.995556i \(0.469980\pi\)
\(492\) 0 0
\(493\) −32.3689 −1.45782
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.1500 0.545000
\(498\) 0 0
\(499\) −18.7796 −0.840692 −0.420346 0.907364i \(-0.638091\pi\)
−0.420346 + 0.907364i \(0.638091\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14.6242 0.652063 0.326031 0.945359i \(-0.394289\pi\)
0.326031 + 0.945359i \(0.394289\pi\)
\(504\) 0 0
\(505\) 1.80560 0.0803481
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.72936 0.386922 0.193461 0.981108i \(-0.438029\pi\)
0.193461 + 0.981108i \(0.438029\pi\)
\(510\) 0 0
\(511\) −4.54900 −0.201236
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.94810 −0.0858436
\(516\) 0 0
\(517\) 5.90415 0.259664
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 37.8308 1.65740 0.828698 0.559696i \(-0.189082\pi\)
0.828698 + 0.559696i \(0.189082\pi\)
\(522\) 0 0
\(523\) 16.8820 0.738198 0.369099 0.929390i \(-0.379666\pi\)
0.369099 + 0.929390i \(0.379666\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −27.8077 −1.21132
\(528\) 0 0
\(529\) −11.2700 −0.490000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −24.0263 −1.04069
\(534\) 0 0
\(535\) 7.19769 0.311183
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.70493 0.202656
\(540\) 0 0
\(541\) 35.8584 1.54167 0.770836 0.637033i \(-0.219839\pi\)
0.770836 + 0.637033i \(0.219839\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.11130 0.133273
\(546\) 0 0
\(547\) −21.6738 −0.926703 −0.463352 0.886174i \(-0.653353\pi\)
−0.463352 + 0.886174i \(0.653353\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −32.5671 −1.38741
\(552\) 0 0
\(553\) −3.16629 −0.134644
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.434369 −0.0184048 −0.00920241 0.999958i \(-0.502929\pi\)
−0.00920241 + 0.999958i \(0.502929\pi\)
\(558\) 0 0
\(559\) 27.4939 1.16287
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.17536 0.302405 0.151203 0.988503i \(-0.451685\pi\)
0.151203 + 0.988503i \(0.451685\pi\)
\(564\) 0 0
\(565\) 3.75515 0.157980
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −41.8314 −1.75366 −0.876832 0.480796i \(-0.840348\pi\)
−0.876832 + 0.480796i \(0.840348\pi\)
\(570\) 0 0
\(571\) 3.69600 0.154673 0.0773364 0.997005i \(-0.475358\pi\)
0.0773364 + 0.997005i \(0.475358\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16.0761 −0.670419
\(576\) 0 0
\(577\) 32.3267 1.34578 0.672890 0.739743i \(-0.265053\pi\)
0.672890 + 0.739743i \(0.265053\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.55294 0.354836
\(582\) 0 0
\(583\) −3.92691 −0.162636
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.757694 −0.0312734 −0.0156367 0.999878i \(-0.504978\pi\)
−0.0156367 + 0.999878i \(0.504978\pi\)
\(588\) 0 0
\(589\) −27.9780 −1.15281
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 27.7840 1.14095 0.570475 0.821315i \(-0.306759\pi\)
0.570475 + 0.821315i \(0.306759\pi\)
\(594\) 0 0
\(595\) −2.57237 −0.105457
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −19.0577 −0.778679 −0.389339 0.921094i \(-0.627297\pi\)
−0.389339 + 0.921094i \(0.627297\pi\)
\(600\) 0 0
\(601\) −38.5642 −1.57307 −0.786533 0.617548i \(-0.788126\pi\)
−0.786533 + 0.617548i \(0.788126\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.69249 0.231433
\(606\) 0 0
\(607\) 5.93884 0.241050 0.120525 0.992710i \(-0.461542\pi\)
0.120525 + 0.992710i \(0.461542\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20.5697 −0.832160
\(612\) 0 0
\(613\) −9.21906 −0.372354 −0.186177 0.982516i \(-0.559610\pi\)
−0.186177 + 0.982516i \(0.559610\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.11101 −0.205761 −0.102881 0.994694i \(-0.532806\pi\)
−0.102881 + 0.994694i \(0.532806\pi\)
\(618\) 0 0
\(619\) −31.2033 −1.25417 −0.627083 0.778952i \(-0.715751\pi\)
−0.627083 + 0.778952i \(0.715751\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.0412963 −0.00165450
\(624\) 0 0
\(625\) 20.5018 0.820073
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −19.6069 −0.781778
\(630\) 0 0
\(631\) −1.51818 −0.0604378 −0.0302189 0.999543i \(-0.509620\pi\)
−0.0302189 + 0.999543i \(0.509620\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.40069 0.254004
\(636\) 0 0
\(637\) −16.3917 −0.649461
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 48.9404 1.93303 0.966515 0.256609i \(-0.0826053\pi\)
0.966515 + 0.256609i \(0.0826053\pi\)
\(642\) 0 0
\(643\) −13.0494 −0.514620 −0.257310 0.966329i \(-0.582836\pi\)
−0.257310 + 0.966329i \(0.582836\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.21609 0.283694 0.141847 0.989889i \(-0.454696\pi\)
0.141847 + 0.989889i \(0.454696\pi\)
\(648\) 0 0
\(649\) 4.60191 0.180641
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.8951 0.778556 0.389278 0.921120i \(-0.372724\pi\)
0.389278 + 0.921120i \(0.372724\pi\)
\(654\) 0 0
\(655\) 5.88752 0.230045
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −23.9877 −0.934430 −0.467215 0.884144i \(-0.654743\pi\)
−0.467215 + 0.884144i \(0.654743\pi\)
\(660\) 0 0
\(661\) −4.49867 −0.174978 −0.0874890 0.996165i \(-0.527884\pi\)
−0.0874890 + 0.996165i \(0.527884\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.58812 −0.100363
\(666\) 0 0
\(667\) 28.4362 1.10105
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.00420 −0.0387666
\(672\) 0 0
\(673\) 16.8519 0.649592 0.324796 0.945784i \(-0.394704\pi\)
0.324796 + 0.945784i \(0.394704\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −29.4746 −1.13280 −0.566401 0.824130i \(-0.691665\pi\)
−0.566401 + 0.824130i \(0.691665\pi\)
\(678\) 0 0
\(679\) 19.1047 0.733171
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 41.5730 1.59075 0.795373 0.606120i \(-0.207275\pi\)
0.795373 + 0.606120i \(0.207275\pi\)
\(684\) 0 0
\(685\) −11.8607 −0.453176
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 13.6811 0.521208
\(690\) 0 0
\(691\) 27.7341 1.05506 0.527528 0.849538i \(-0.323119\pi\)
0.527528 + 0.849538i \(0.323119\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.83439 −0.297175
\(696\) 0 0
\(697\) 31.8739 1.20731
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.66547 0.100673 0.0503367 0.998732i \(-0.483971\pi\)
0.0503367 + 0.998732i \(0.483971\pi\)
\(702\) 0 0
\(703\) −19.7270 −0.744016
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.89177 0.146365
\(708\) 0 0
\(709\) −35.3193 −1.32644 −0.663222 0.748423i \(-0.730811\pi\)
−0.663222 + 0.748423i \(0.730811\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.4291 0.914878
\(714\) 0 0
\(715\) 1.37150 0.0512912
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.5636 0.393954 0.196977 0.980408i \(-0.436888\pi\)
0.196977 + 0.980408i \(0.436888\pi\)
\(720\) 0 0
\(721\) −4.19891 −0.156376
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −38.9720 −1.44739
\(726\) 0 0
\(727\) 2.55384 0.0947167 0.0473584 0.998878i \(-0.484920\pi\)
0.0473584 + 0.998878i \(0.484920\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −36.4742 −1.34905
\(732\) 0 0
\(733\) −23.9050 −0.882953 −0.441476 0.897273i \(-0.645545\pi\)
−0.441476 + 0.897273i \(0.645545\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.74008 0.174603
\(738\) 0 0
\(739\) 45.2160 1.66330 0.831648 0.555303i \(-0.187398\pi\)
0.831648 + 0.555303i \(0.187398\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −42.3530 −1.55378 −0.776890 0.629636i \(-0.783204\pi\)
−0.776890 + 0.629636i \(0.783204\pi\)
\(744\) 0 0
\(745\) 3.28410 0.120320
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.5138 0.566862
\(750\) 0 0
\(751\) −8.78671 −0.320632 −0.160316 0.987066i \(-0.551251\pi\)
−0.160316 + 0.987066i \(0.551251\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.57774 0.0574198
\(756\) 0 0
\(757\) 25.5182 0.927474 0.463737 0.885973i \(-0.346508\pi\)
0.463737 + 0.885973i \(0.346508\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −33.7547 −1.22361 −0.611804 0.791010i \(-0.709556\pi\)
−0.611804 + 0.791010i \(0.709556\pi\)
\(762\) 0 0
\(763\) 6.70606 0.242776
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −16.0328 −0.578910
\(768\) 0 0
\(769\) −44.3898 −1.60074 −0.800369 0.599507i \(-0.795363\pi\)
−0.800369 + 0.599507i \(0.795363\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.30404 0.154806 0.0774028 0.997000i \(-0.475337\pi\)
0.0774028 + 0.997000i \(0.475337\pi\)
\(774\) 0 0
\(775\) −33.4804 −1.20265
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 32.0691 1.14899
\(780\) 0 0
\(781\) 8.59382 0.307511
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.40677 −0.157284
\(786\) 0 0
\(787\) 0.0547106 0.00195022 0.000975112 1.00000i \(-0.499690\pi\)
0.000975112 1.00000i \(0.499690\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.09381 0.287783
\(792\) 0 0
\(793\) 3.49855 0.124237
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11.0615 −0.391818 −0.195909 0.980622i \(-0.562766\pi\)
−0.195909 + 0.980622i \(0.562766\pi\)
\(798\) 0 0
\(799\) 27.2883 0.965389
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3.21757 −0.113546
\(804\) 0 0
\(805\) 2.25983 0.0796485
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 45.3733 1.59524 0.797620 0.603160i \(-0.206092\pi\)
0.797620 + 0.603160i \(0.206092\pi\)
\(810\) 0 0
\(811\) −23.8301 −0.836787 −0.418394 0.908266i \(-0.637407\pi\)
−0.418394 + 0.908266i \(0.637407\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3.87735 0.135818
\(816\) 0 0
\(817\) −36.6975 −1.28388
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 49.6841 1.73399 0.866994 0.498319i \(-0.166049\pi\)
0.866994 + 0.498319i \(0.166049\pi\)
\(822\) 0 0
\(823\) −26.8208 −0.934916 −0.467458 0.884015i \(-0.654830\pi\)
−0.467458 + 0.884015i \(0.654830\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −53.8347 −1.87202 −0.936009 0.351977i \(-0.885509\pi\)
−0.936009 + 0.351977i \(0.885509\pi\)
\(828\) 0 0
\(829\) 5.71959 0.198649 0.0993247 0.995055i \(-0.468332\pi\)
0.0993247 + 0.995055i \(0.468332\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 21.7456 0.753441
\(834\) 0 0
\(835\) −0.553287 −0.0191473
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 17.3026 0.597352 0.298676 0.954355i \(-0.403455\pi\)
0.298676 + 0.954355i \(0.403455\pi\)
\(840\) 0 0
\(841\) 39.9356 1.37709
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.41451 0.0830617
\(846\) 0 0
\(847\) 12.2695 0.421586
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 17.2247 0.590455
\(852\) 0 0
\(853\) 1.07488 0.0368033 0.0184016 0.999831i \(-0.494142\pi\)
0.0184016 + 0.999831i \(0.494142\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 17.7863 0.607568 0.303784 0.952741i \(-0.401750\pi\)
0.303784 + 0.952741i \(0.401750\pi\)
\(858\) 0 0
\(859\) 51.4455 1.75530 0.877649 0.479305i \(-0.159111\pi\)
0.877649 + 0.479305i \(0.159111\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 18.2535 0.621357 0.310678 0.950515i \(-0.399444\pi\)
0.310678 + 0.950515i \(0.399444\pi\)
\(864\) 0 0
\(865\) −14.2172 −0.483401
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.23956 −0.0759719
\(870\) 0 0
\(871\) −16.5141 −0.559560
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6.39623 −0.216232
\(876\) 0 0
\(877\) −16.1122 −0.544072 −0.272036 0.962287i \(-0.587697\pi\)
−0.272036 + 0.962287i \(0.587697\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 20.2142 0.681034 0.340517 0.940238i \(-0.389398\pi\)
0.340517 + 0.940238i \(0.389398\pi\)
\(882\) 0 0
\(883\) −13.6929 −0.460803 −0.230401 0.973096i \(-0.574004\pi\)
−0.230401 + 0.973096i \(0.574004\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −57.0860 −1.91676 −0.958380 0.285495i \(-0.907842\pi\)
−0.958380 + 0.285495i \(0.907842\pi\)
\(888\) 0 0
\(889\) 13.7960 0.462702
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 27.4554 0.918759
\(894\) 0 0
\(895\) 4.58763 0.153348
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 59.2217 1.97515
\(900\) 0 0
\(901\) −18.1497 −0.604654
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −13.7703 −0.457740
\(906\) 0 0
\(907\) 15.6389 0.519280 0.259640 0.965706i \(-0.416396\pi\)
0.259640 + 0.965706i \(0.416396\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 57.7626 1.91376 0.956880 0.290483i \(-0.0938159\pi\)
0.956880 + 0.290483i \(0.0938159\pi\)
\(912\) 0 0
\(913\) 6.04961 0.200213
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 12.6899 0.419057
\(918\) 0 0
\(919\) −29.3839 −0.969284 −0.484642 0.874713i \(-0.661050\pi\)
−0.484642 + 0.874713i \(0.661050\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −29.9403 −0.985498
\(924\) 0 0
\(925\) −23.6066 −0.776181
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −22.9096 −0.751639 −0.375820 0.926693i \(-0.622639\pi\)
−0.375820 + 0.926693i \(0.622639\pi\)
\(930\) 0 0
\(931\) 21.8788 0.717048
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.81947 −0.0595030
\(936\) 0 0
\(937\) −13.5414 −0.442377 −0.221189 0.975231i \(-0.570994\pi\)
−0.221189 + 0.975231i \(0.570994\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 26.8442 0.875094 0.437547 0.899195i \(-0.355847\pi\)
0.437547 + 0.899195i \(0.355847\pi\)
\(942\) 0 0
\(943\) −28.0013 −0.911847
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 32.9637 1.07118 0.535588 0.844480i \(-0.320090\pi\)
0.535588 + 0.844480i \(0.320090\pi\)
\(948\) 0 0
\(949\) 11.2098 0.363886
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 56.8888 1.84281 0.921404 0.388606i \(-0.127043\pi\)
0.921404 + 0.388606i \(0.127043\pi\)
\(954\) 0 0
\(955\) 13.3648 0.432476
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −25.5645 −0.825521
\(960\) 0 0
\(961\) 19.8766 0.641180
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3.18064 −0.102388
\(966\) 0 0
\(967\) −53.0993 −1.70756 −0.853778 0.520636i \(-0.825695\pi\)
−0.853778 + 0.520636i \(0.825695\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −39.0178 −1.25214 −0.626070 0.779767i \(-0.715338\pi\)
−0.626070 + 0.779767i \(0.715338\pi\)
\(972\) 0 0
\(973\) −16.8862 −0.541345
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 25.7115 0.822584 0.411292 0.911504i \(-0.365078\pi\)
0.411292 + 0.911504i \(0.365078\pi\)
\(978\) 0 0
\(979\) −0.0292094 −0.000933538 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −52.9445 −1.68867 −0.844334 0.535817i \(-0.820004\pi\)
−0.844334 + 0.535817i \(0.820004\pi\)
\(984\) 0 0
\(985\) 11.6748 0.371989
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 32.0426 1.01890
\(990\) 0 0
\(991\) 32.1464 1.02117 0.510583 0.859829i \(-0.329430\pi\)
0.510583 + 0.859829i \(0.329430\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4.22224 0.133854
\(996\) 0 0
\(997\) 41.5417 1.31564 0.657819 0.753176i \(-0.271479\pi\)
0.657819 + 0.753176i \(0.271479\pi\)
\(998\) 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 6012.2.a.j.1.5 10
3.2 odd 2 6012.2.a.k.1.6 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6012.2.a.j.1.5 10 1.1 even 1 trivial
6012.2.a.k.1.6 yes 10 3.2 odd 2