Properties

Label 2736.2.a.bc.1.1
Level $2736$
Weight $2$
Character 2736.1
Self dual yes
Analytic conductor $21.847$
Analytic rank $0$
Dimension $3$
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] = [2736,2,Mod(1,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2736.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.892.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 8x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1368)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.91729\) of defining polynomial
Character \(\chi\) \(=\) 2736.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.91729 q^{5} +4.32401 q^{7} +O(q^{10})\) \(q-3.91729 q^{5} +4.32401 q^{7} -0.0827140 q^{11} -7.02112 q^{13} +5.10383 q^{17} +1.00000 q^{19} -7.83457 q^{23} +10.3451 q^{25} +2.81346 q^{29} +6.00000 q^{31} -16.9384 q^{35} +4.00000 q^{37} -1.02112 q^{41} -0.324014 q^{43} -6.73074 q^{47} +11.6971 q^{49} -8.85569 q^{53} +0.324014 q^{55} +14.0422 q^{59} +9.34513 q^{61} +27.5037 q^{65} -1.62691 q^{67} +1.62691 q^{71} +3.30290 q^{73} -0.357657 q^{77} +13.0211 q^{79} -6.81346 q^{83} -19.9932 q^{85} +1.18654 q^{89} -30.3594 q^{91} -3.91729 q^{95} -5.66914 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{5} + 2 q^{7} - 10 q^{11} - 4 q^{13} + 8 q^{17} + 3 q^{19} - 4 q^{23} + 3 q^{25} + 6 q^{29} + 18 q^{31} - 24 q^{35} + 12 q^{37} + 14 q^{41} + 10 q^{43} - 8 q^{47} + 29 q^{49} + 10 q^{53} - 10 q^{55} + 8 q^{59} + 24 q^{65} + 16 q^{73} + 16 q^{77} + 22 q^{79} - 18 q^{83} - 10 q^{85} + 6 q^{89} + 4 q^{91} - 2 q^{95} + 22 q^{97}+O(q^{100}) \) 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
\(5\) −3.91729 −1.75186 −0.875932 0.482435i \(-0.839752\pi\)
−0.875932 + 0.482435i \(0.839752\pi\)
\(6\) 0 0
\(7\) 4.32401 1.63432 0.817162 0.576408i \(-0.195546\pi\)
0.817162 + 0.576408i \(0.195546\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.0827140 −0.0249392 −0.0124696 0.999922i \(-0.503969\pi\)
−0.0124696 + 0.999922i \(0.503969\pi\)
\(12\) 0 0
\(13\) −7.02112 −1.94731 −0.973653 0.228033i \(-0.926771\pi\)
−0.973653 + 0.228033i \(0.926771\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.10383 1.23786 0.618930 0.785446i \(-0.287566\pi\)
0.618930 + 0.785446i \(0.287566\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.83457 −1.63362 −0.816811 0.576906i \(-0.804260\pi\)
−0.816811 + 0.576906i \(0.804260\pi\)
\(24\) 0 0
\(25\) 10.3451 2.06903
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.81346 0.522446 0.261223 0.965279i \(-0.415874\pi\)
0.261223 + 0.965279i \(0.415874\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −16.9384 −2.86311
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.02112 −0.159471 −0.0797357 0.996816i \(-0.525408\pi\)
−0.0797357 + 0.996816i \(0.525408\pi\)
\(42\) 0 0
\(43\) −0.324014 −0.0494117 −0.0247059 0.999695i \(-0.507865\pi\)
−0.0247059 + 0.999695i \(0.507865\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.73074 −0.981780 −0.490890 0.871222i \(-0.663328\pi\)
−0.490890 + 0.871222i \(0.663328\pi\)
\(48\) 0 0
\(49\) 11.6971 1.67101
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.85569 −1.21642 −0.608211 0.793775i \(-0.708113\pi\)
−0.608211 + 0.793775i \(0.708113\pi\)
\(54\) 0 0
\(55\) 0.324014 0.0436901
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 14.0422 1.82814 0.914071 0.405553i \(-0.132921\pi\)
0.914071 + 0.405553i \(0.132921\pi\)
\(60\) 0 0
\(61\) 9.34513 1.19652 0.598261 0.801302i \(-0.295859\pi\)
0.598261 + 0.801302i \(0.295859\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 27.5037 3.41142
\(66\) 0 0
\(67\) −1.62691 −0.198759 −0.0993796 0.995050i \(-0.531686\pi\)
−0.0993796 + 0.995050i \(0.531686\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.62691 0.193079 0.0965396 0.995329i \(-0.469223\pi\)
0.0965396 + 0.995329i \(0.469223\pi\)
\(72\) 0 0
\(73\) 3.30290 0.386575 0.193288 0.981142i \(-0.438085\pi\)
0.193288 + 0.981142i \(0.438085\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.357657 −0.0407587
\(78\) 0 0
\(79\) 13.0211 1.46499 0.732495 0.680772i \(-0.238356\pi\)
0.732495 + 0.680772i \(0.238356\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.81346 −0.747874 −0.373937 0.927454i \(-0.621992\pi\)
−0.373937 + 0.927454i \(0.621992\pi\)
\(84\) 0 0
\(85\) −19.9932 −2.16856
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.18654 0.125773 0.0628867 0.998021i \(-0.479969\pi\)
0.0628867 + 0.998021i \(0.479969\pi\)
\(90\) 0 0
\(91\) −30.3594 −3.18253
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.91729 −0.401905
\(96\) 0 0
\(97\) −5.66914 −0.575614 −0.287807 0.957688i \(-0.592926\pi\)
−0.287807 + 0.957688i \(0.592926\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.02112 0.897635 0.448817 0.893624i \(-0.351845\pi\)
0.448817 + 0.893624i \(0.351845\pi\)
\(102\) 0 0
\(103\) −8.04223 −0.792424 −0.396212 0.918159i \(-0.629676\pi\)
−0.396212 + 0.918159i \(0.629676\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.46149 0.527982 0.263991 0.964525i \(-0.414961\pi\)
0.263991 + 0.964525i \(0.414961\pi\)
\(108\) 0 0
\(109\) 11.6691 1.11770 0.558851 0.829268i \(-0.311243\pi\)
0.558851 + 0.829268i \(0.311243\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.4826 0.986120 0.493060 0.869995i \(-0.335878\pi\)
0.493060 + 0.869995i \(0.335878\pi\)
\(114\) 0 0
\(115\) 30.6903 2.86188
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 22.0690 2.02306
\(120\) 0 0
\(121\) −10.9932 −0.999378
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −20.9384 −1.87279
\(126\) 0 0
\(127\) −0.373086 −0.0331061 −0.0165530 0.999863i \(-0.505269\pi\)
−0.0165530 + 0.999863i \(0.505269\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13.5442 1.18336 0.591681 0.806172i \(-0.298464\pi\)
0.591681 + 0.806172i \(0.298464\pi\)
\(132\) 0 0
\(133\) 4.32401 0.374940
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 18.5653 1.58614 0.793071 0.609129i \(-0.208481\pi\)
0.793071 + 0.609129i \(0.208481\pi\)
\(138\) 0 0
\(139\) 8.32401 0.706034 0.353017 0.935617i \(-0.385156\pi\)
0.353017 + 0.935617i \(0.385156\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.580745 0.0485643
\(144\) 0 0
\(145\) −11.0211 −0.915254
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.7519 0.962750 0.481375 0.876515i \(-0.340138\pi\)
0.481375 + 0.876515i \(0.340138\pi\)
\(150\) 0 0
\(151\) 13.0211 1.05964 0.529822 0.848109i \(-0.322259\pi\)
0.529822 + 0.848109i \(0.322259\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −23.5037 −1.88786
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −33.8768 −2.66987
\(162\) 0 0
\(163\) 10.0422 0.786568 0.393284 0.919417i \(-0.371339\pi\)
0.393284 + 0.919417i \(0.371339\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.16543 0.322330 0.161165 0.986927i \(-0.448475\pi\)
0.161165 + 0.986927i \(0.448475\pi\)
\(168\) 0 0
\(169\) 36.2961 2.79200
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 14.4826 1.10109 0.550546 0.834805i \(-0.314420\pi\)
0.550546 + 0.834805i \(0.314420\pi\)
\(174\) 0 0
\(175\) 44.7325 3.38146
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −17.4615 −1.30513 −0.652566 0.757732i \(-0.726308\pi\)
−0.652566 + 0.757732i \(0.726308\pi\)
\(180\) 0 0
\(181\) 1.39420 0.103630 0.0518151 0.998657i \(-0.483499\pi\)
0.0518151 + 0.998657i \(0.483499\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −15.6691 −1.15202
\(186\) 0 0
\(187\) −0.422158 −0.0308713
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.73074 0.487019 0.243510 0.969898i \(-0.421701\pi\)
0.243510 + 0.969898i \(0.421701\pi\)
\(192\) 0 0
\(193\) 13.0211 0.937280 0.468640 0.883389i \(-0.344744\pi\)
0.468640 + 0.883389i \(0.344744\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 25.0211 1.78268 0.891340 0.453335i \(-0.149766\pi\)
0.891340 + 0.453335i \(0.149766\pi\)
\(198\) 0 0
\(199\) −0.324014 −0.0229688 −0.0114844 0.999934i \(-0.503656\pi\)
−0.0114844 + 0.999934i \(0.503656\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.1654 0.853846
\(204\) 0 0
\(205\) 4.00000 0.279372
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.0827140 −0.00572145
\(210\) 0 0
\(211\) −19.6691 −1.35408 −0.677040 0.735946i \(-0.736738\pi\)
−0.677040 + 0.735946i \(0.736738\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.26926 0.0865626
\(216\) 0 0
\(217\) 25.9441 1.76120
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −35.8346 −2.41049
\(222\) 0 0
\(223\) −20.6903 −1.38552 −0.692761 0.721167i \(-0.743606\pi\)
−0.692761 + 0.721167i \(0.743606\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.16543 0.276469 0.138235 0.990400i \(-0.455857\pi\)
0.138235 + 0.990400i \(0.455857\pi\)
\(228\) 0 0
\(229\) 0.697101 0.0460657 0.0230329 0.999735i \(-0.492668\pi\)
0.0230329 + 0.999735i \(0.492668\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.9806 1.50551 0.752756 0.658300i \(-0.228724\pi\)
0.752756 + 0.658300i \(0.228724\pi\)
\(234\) 0 0
\(235\) 26.3662 1.71994
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −18.9806 −1.22775 −0.613877 0.789401i \(-0.710391\pi\)
−0.613877 + 0.789401i \(0.710391\pi\)
\(240\) 0 0
\(241\) −20.6903 −1.33278 −0.666388 0.745605i \(-0.732161\pi\)
−0.666388 + 0.745605i \(0.732161\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −45.8209 −2.92739
\(246\) 0 0
\(247\) −7.02112 −0.446743
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 26.1249 1.64899 0.824496 0.565868i \(-0.191459\pi\)
0.824496 + 0.565868i \(0.191459\pi\)
\(252\) 0 0
\(253\) 0.648029 0.0407412
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.02112 0.0636954 0.0318477 0.999493i \(-0.489861\pi\)
0.0318477 + 0.999493i \(0.489861\pi\)
\(258\) 0 0
\(259\) 17.2961 1.07472
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −14.8962 −0.918537 −0.459269 0.888297i \(-0.651888\pi\)
−0.459269 + 0.888297i \(0.651888\pi\)
\(264\) 0 0
\(265\) 34.6903 2.13101
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.81346 0.415424 0.207712 0.978190i \(-0.433398\pi\)
0.207712 + 0.978190i \(0.433398\pi\)
\(270\) 0 0
\(271\) −27.3383 −1.66068 −0.830341 0.557255i \(-0.811855\pi\)
−0.830341 + 0.557255i \(0.811855\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.855687 −0.0515999
\(276\) 0 0
\(277\) 1.99316 0.119757 0.0598786 0.998206i \(-0.480929\pi\)
0.0598786 + 0.998206i \(0.480929\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.1095 −0.722393 −0.361197 0.932490i \(-0.617632\pi\)
−0.361197 + 0.932490i \(0.617632\pi\)
\(282\) 0 0
\(283\) 1.63376 0.0971167 0.0485583 0.998820i \(-0.484537\pi\)
0.0485583 + 0.998820i \(0.484537\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.41532 −0.260628
\(288\) 0 0
\(289\) 9.04907 0.532298
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −11.3942 −0.665656 −0.332828 0.942987i \(-0.608003\pi\)
−0.332828 + 0.942987i \(0.608003\pi\)
\(294\) 0 0
\(295\) −55.0074 −3.20266
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 55.0074 3.18116
\(300\) 0 0
\(301\) −1.40104 −0.0807548
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −36.6075 −2.09614
\(306\) 0 0
\(307\) −19.6691 −1.12258 −0.561289 0.827620i \(-0.689694\pi\)
−0.561289 + 0.827620i \(0.689694\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.9384 0.960489 0.480244 0.877135i \(-0.340548\pi\)
0.480244 + 0.877135i \(0.340548\pi\)
\(312\) 0 0
\(313\) −21.3383 −1.20611 −0.603056 0.797699i \(-0.706050\pi\)
−0.603056 + 0.797699i \(0.706050\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.0211 −0.731339 −0.365669 0.930745i \(-0.619160\pi\)
−0.365669 + 0.930745i \(0.619160\pi\)
\(318\) 0 0
\(319\) −0.232712 −0.0130294
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5.10383 0.283985
\(324\) 0 0
\(325\) −72.6343 −4.02903
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −29.1038 −1.60455
\(330\) 0 0
\(331\) 25.7114 1.41322 0.706612 0.707601i \(-0.250222\pi\)
0.706612 + 0.707601i \(0.250222\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 6.37309 0.348199
\(336\) 0 0
\(337\) 13.6691 0.744606 0.372303 0.928111i \(-0.378568\pi\)
0.372303 + 0.928111i \(0.378568\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.496284 −0.0268753
\(342\) 0 0
\(343\) 20.3103 1.09665
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.58643 0.407261 0.203630 0.979048i \(-0.434726\pi\)
0.203630 + 0.979048i \(0.434726\pi\)
\(348\) 0 0
\(349\) −22.7393 −1.21721 −0.608604 0.793474i \(-0.708270\pi\)
−0.608604 + 0.793474i \(0.708270\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −13.2961 −0.707678 −0.353839 0.935306i \(-0.615124\pi\)
−0.353839 + 0.935306i \(0.615124\pi\)
\(354\) 0 0
\(355\) −6.37309 −0.338248
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.19223 −0.221257 −0.110629 0.993862i \(-0.535286\pi\)
−0.110629 + 0.993862i \(0.535286\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.9384 −0.677227
\(366\) 0 0
\(367\) 2.04223 0.106604 0.0533018 0.998578i \(-0.483025\pi\)
0.0533018 + 0.998578i \(0.483025\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −38.2921 −1.98803
\(372\) 0 0
\(373\) −19.3383 −1.00130 −0.500649 0.865650i \(-0.666905\pi\)
−0.500649 + 0.865650i \(0.666905\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −19.7536 −1.01736
\(378\) 0 0
\(379\) 4.64803 0.238753 0.119377 0.992849i \(-0.461910\pi\)
0.119377 + 0.992849i \(0.461910\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −33.8768 −1.73102 −0.865512 0.500888i \(-0.833007\pi\)
−0.865512 + 0.500888i \(0.833007\pi\)
\(384\) 0 0
\(385\) 1.40104 0.0714038
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 21.6287 1.09662 0.548308 0.836276i \(-0.315272\pi\)
0.548308 + 0.836276i \(0.315272\pi\)
\(390\) 0 0
\(391\) −39.9863 −2.02219
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −51.0074 −2.56646
\(396\) 0 0
\(397\) −2.65487 −0.133244 −0.0666221 0.997778i \(-0.521222\pi\)
−0.0666221 + 0.997778i \(0.521222\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.30974 −0.165281 −0.0826403 0.996579i \(-0.526335\pi\)
−0.0826403 + 0.996579i \(0.526335\pi\)
\(402\) 0 0
\(403\) −42.1267 −2.09848
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.330856 −0.0163999
\(408\) 0 0
\(409\) −1.25383 −0.0619978 −0.0309989 0.999519i \(-0.509869\pi\)
−0.0309989 + 0.999519i \(0.509869\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 60.7188 2.98778
\(414\) 0 0
\(415\) 26.6903 1.31017
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −22.4826 −1.09835 −0.549173 0.835708i \(-0.685057\pi\)
−0.549173 + 0.835708i \(0.685057\pi\)
\(420\) 0 0
\(421\) −33.9441 −1.65433 −0.827167 0.561957i \(-0.810049\pi\)
−0.827167 + 0.561957i \(0.810049\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 52.7998 2.56117
\(426\) 0 0
\(427\) 40.4085 1.95550
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.8346 1.34074 0.670372 0.742025i \(-0.266135\pi\)
0.670372 + 0.742025i \(0.266135\pi\)
\(432\) 0 0
\(433\) −3.62691 −0.174298 −0.0871492 0.996195i \(-0.527776\pi\)
−0.0871492 + 0.996195i \(0.527776\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.83457 −0.374778
\(438\) 0 0
\(439\) −16.9230 −0.807689 −0.403845 0.914828i \(-0.632326\pi\)
−0.403845 + 0.914828i \(0.632326\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 31.2556 1.48500 0.742499 0.669848i \(-0.233641\pi\)
0.742499 + 0.669848i \(0.233641\pi\)
\(444\) 0 0
\(445\) −4.64803 −0.220338
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.35197 0.0638035 0.0319017 0.999491i \(-0.489844\pi\)
0.0319017 + 0.999491i \(0.489844\pi\)
\(450\) 0 0
\(451\) 0.0844605 0.00397709
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 118.926 5.57536
\(456\) 0 0
\(457\) 31.2892 1.46365 0.731824 0.681494i \(-0.238669\pi\)
0.731824 + 0.681494i \(0.238669\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 27.7519 1.29253 0.646266 0.763112i \(-0.276329\pi\)
0.646266 + 0.763112i \(0.276329\pi\)
\(462\) 0 0
\(463\) 2.28178 0.106044 0.0530218 0.998593i \(-0.483115\pi\)
0.0530218 + 0.998593i \(0.483115\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.79803 −0.407124 −0.203562 0.979062i \(-0.565252\pi\)
−0.203562 + 0.979062i \(0.565252\pi\)
\(468\) 0 0
\(469\) −7.03480 −0.324837
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.0268005 0.00123229
\(474\) 0 0
\(475\) 10.3451 0.474667
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −25.8768 −1.18234 −0.591171 0.806547i \(-0.701334\pi\)
−0.591171 + 0.806547i \(0.701334\pi\)
\(480\) 0 0
\(481\) −28.0845 −1.28054
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 22.2077 1.00840
\(486\) 0 0
\(487\) −6.97888 −0.316243 −0.158122 0.987420i \(-0.550544\pi\)
−0.158122 + 0.987420i \(0.550544\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.77123 −0.215322 −0.107661 0.994188i \(-0.534336\pi\)
−0.107661 + 0.994188i \(0.534336\pi\)
\(492\) 0 0
\(493\) 14.3594 0.646715
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.03480 0.315554
\(498\) 0 0
\(499\) 23.0143 1.03026 0.515130 0.857112i \(-0.327744\pi\)
0.515130 + 0.857112i \(0.327744\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.41926 0.152457 0.0762285 0.997090i \(-0.475712\pi\)
0.0762285 + 0.997090i \(0.475712\pi\)
\(504\) 0 0
\(505\) −35.3383 −1.57253
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.2288 0.675004 0.337502 0.941325i \(-0.390418\pi\)
0.337502 + 0.941325i \(0.390418\pi\)
\(510\) 0 0
\(511\) 14.2818 0.631789
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 31.5037 1.38822
\(516\) 0 0
\(517\) 0.556727 0.0244848
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10.3172 −0.452004 −0.226002 0.974127i \(-0.572566\pi\)
−0.226002 + 0.974127i \(0.572566\pi\)
\(522\) 0 0
\(523\) −10.6058 −0.463759 −0.231880 0.972744i \(-0.574488\pi\)
−0.231880 + 0.972744i \(0.574488\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 30.6230 1.33396
\(528\) 0 0
\(529\) 38.3805 1.66872
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7.16937 0.310540
\(534\) 0 0
\(535\) −21.3942 −0.924952
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.967514 −0.0416738
\(540\) 0 0
\(541\) 10.7393 0.461720 0.230860 0.972987i \(-0.425846\pi\)
0.230860 + 0.972987i \(0.425846\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −45.7114 −1.95806
\(546\) 0 0
\(547\) −33.0633 −1.41369 −0.706843 0.707370i \(-0.749881\pi\)
−0.706843 + 0.707370i \(0.749881\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.81346 0.119857
\(552\) 0 0
\(553\) 56.3035 2.39427
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17.5442 0.743372 0.371686 0.928359i \(-0.378780\pi\)
0.371686 + 0.928359i \(0.378780\pi\)
\(558\) 0 0
\(559\) 2.27494 0.0962198
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.71137 −0.409286 −0.204643 0.978837i \(-0.565603\pi\)
−0.204643 + 0.978837i \(0.565603\pi\)
\(564\) 0 0
\(565\) −41.0633 −1.72755
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.8135 −0.788701 −0.394351 0.918960i \(-0.629030\pi\)
−0.394351 + 0.918960i \(0.629030\pi\)
\(570\) 0 0
\(571\) −18.0422 −0.755044 −0.377522 0.926001i \(-0.623224\pi\)
−0.377522 + 0.926001i \(0.623224\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −81.0497 −3.38000
\(576\) 0 0
\(577\) −17.2470 −0.718001 −0.359001 0.933337i \(-0.616882\pi\)
−0.359001 + 0.933337i \(0.616882\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −29.4615 −1.22227
\(582\) 0 0
\(583\) 0.732489 0.0303366
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.91729 −0.326781 −0.163391 0.986561i \(-0.552243\pi\)
−0.163391 + 0.986561i \(0.552243\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.25383 −0.133619 −0.0668093 0.997766i \(-0.521282\pi\)
−0.0668093 + 0.997766i \(0.521282\pi\)
\(594\) 0 0
\(595\) −86.4507 −3.54413
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −37.7114 −1.54084 −0.770422 0.637534i \(-0.779955\pi\)
−0.770422 + 0.637534i \(0.779955\pi\)
\(600\) 0 0
\(601\) 33.0211 1.34696 0.673480 0.739206i \(-0.264799\pi\)
0.673480 + 0.739206i \(0.264799\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 43.0633 1.75077
\(606\) 0 0
\(607\) 27.6269 1.12134 0.560671 0.828039i \(-0.310543\pi\)
0.560671 + 0.828039i \(0.310543\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 47.2573 1.91183
\(612\) 0 0
\(613\) 13.9932 0.565178 0.282589 0.959241i \(-0.408807\pi\)
0.282589 + 0.959241i \(0.408807\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.68457 0.0678184 0.0339092 0.999425i \(-0.489204\pi\)
0.0339092 + 0.999425i \(0.489204\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.13063 0.205554
\(624\) 0 0
\(625\) 30.2961 1.21184
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20.4153 0.814012
\(630\) 0 0
\(631\) 20.4085 0.812449 0.406224 0.913773i \(-0.366845\pi\)
0.406224 + 0.913773i \(0.366845\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.46149 0.0579973
\(636\) 0 0
\(637\) −82.1267 −3.25398
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 18.8135 0.743087 0.371543 0.928416i \(-0.378829\pi\)
0.371543 + 0.928416i \(0.378829\pi\)
\(642\) 0 0
\(643\) −31.6623 −1.24864 −0.624320 0.781169i \(-0.714624\pi\)
−0.624320 + 0.781169i \(0.714624\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25.1038 −0.986933 −0.493467 0.869765i \(-0.664271\pi\)
−0.493467 + 0.869765i \(0.664271\pi\)
\(648\) 0 0
\(649\) −1.16149 −0.0455924
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13.4632 −0.526857 −0.263428 0.964679i \(-0.584853\pi\)
−0.263428 + 0.964679i \(0.584853\pi\)
\(654\) 0 0
\(655\) −53.0565 −2.07309
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −37.1306 −1.44640 −0.723202 0.690637i \(-0.757330\pi\)
−0.723202 + 0.690637i \(0.757330\pi\)
\(660\) 0 0
\(661\) 18.0422 0.701761 0.350881 0.936420i \(-0.385882\pi\)
0.350881 + 0.936420i \(0.385882\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −16.9384 −0.656843
\(666\) 0 0
\(667\) −22.0422 −0.853479
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.772973 −0.0298403
\(672\) 0 0
\(673\) 30.3172 1.16864 0.584321 0.811523i \(-0.301361\pi\)
0.584321 + 0.811523i \(0.301361\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.10951 0.311674 0.155837 0.987783i \(-0.450193\pi\)
0.155837 + 0.987783i \(0.450193\pi\)
\(678\) 0 0
\(679\) −24.5135 −0.940740
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18.6230 −0.712588 −0.356294 0.934374i \(-0.615960\pi\)
−0.356294 + 0.934374i \(0.615960\pi\)
\(684\) 0 0
\(685\) −72.7256 −2.77870
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 62.1768 2.36875
\(690\) 0 0
\(691\) −10.9298 −0.415790 −0.207895 0.978151i \(-0.566661\pi\)
−0.207895 + 0.978151i \(0.566661\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −32.6075 −1.23687
\(696\) 0 0
\(697\) −5.21160 −0.197403
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 43.6132 1.64725 0.823624 0.567136i \(-0.191948\pi\)
0.823624 + 0.567136i \(0.191948\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 39.0074 1.46703
\(708\) 0 0
\(709\) −21.2538 −0.798204 −0.399102 0.916906i \(-0.630678\pi\)
−0.399102 + 0.916906i \(0.630678\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −47.0074 −1.76044
\(714\) 0 0
\(715\) −2.27494 −0.0850780
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −15.0616 −0.561703 −0.280851 0.959751i \(-0.590617\pi\)
−0.280851 + 0.959751i \(0.590617\pi\)
\(720\) 0 0
\(721\) −34.7747 −1.29508
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 29.1056 1.08095
\(726\) 0 0
\(727\) 17.0702 0.633098 0.316549 0.948576i \(-0.397476\pi\)
0.316549 + 0.948576i \(0.397476\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.65371 −0.0611648
\(732\) 0 0
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.134569 0.00495690
\(738\) 0 0
\(739\) 36.4085 1.33931 0.669654 0.742673i \(-0.266443\pi\)
0.669654 + 0.742673i \(0.266443\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 37.3805 1.37136 0.685679 0.727904i \(-0.259505\pi\)
0.685679 + 0.727904i \(0.259505\pi\)
\(744\) 0 0
\(745\) −46.0354 −1.68661
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 23.6155 0.862893
\(750\) 0 0
\(751\) −1.35197 −0.0493341 −0.0246671 0.999696i \(-0.507853\pi\)
−0.0246671 + 0.999696i \(0.507853\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −51.0074 −1.85635
\(756\) 0 0
\(757\) −4.61264 −0.167649 −0.0838246 0.996481i \(-0.526714\pi\)
−0.0838246 + 0.996481i \(0.526714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 43.7804 1.58704 0.793519 0.608545i \(-0.208247\pi\)
0.793519 + 0.608545i \(0.208247\pi\)
\(762\) 0 0
\(763\) 50.4575 1.82669
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −98.5921 −3.55995
\(768\) 0 0
\(769\) 27.3874 0.987613 0.493807 0.869572i \(-0.335605\pi\)
0.493807 + 0.869572i \(0.335605\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.9789 −0.682623 −0.341312 0.939950i \(-0.610871\pi\)
−0.341312 + 0.939950i \(0.610871\pi\)
\(774\) 0 0
\(775\) 62.0708 2.22965
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.02112 −0.0365852
\(780\) 0 0
\(781\) −0.134569 −0.00481524
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.83457 −0.279628
\(786\) 0 0
\(787\) 19.3383 0.689336 0.344668 0.938725i \(-0.387992\pi\)
0.344668 + 0.938725i \(0.387992\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 45.3269 1.61164
\(792\) 0 0
\(793\) −65.6132 −2.32999
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −26.6480 −0.943922 −0.471961 0.881620i \(-0.656454\pi\)
−0.471961 + 0.881620i \(0.656454\pi\)
\(798\) 0 0
\(799\) −34.3526 −1.21531
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −0.273196 −0.00964088
\(804\) 0 0
\(805\) 132.705 4.67724
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −30.4843 −1.07177 −0.535886 0.844290i \(-0.680022\pi\)
−0.535886 + 0.844290i \(0.680022\pi\)
\(810\) 0 0
\(811\) −39.5710 −1.38953 −0.694763 0.719239i \(-0.744491\pi\)
−0.694763 + 0.719239i \(0.744491\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −39.3383 −1.37796
\(816\) 0 0
\(817\) −0.324014 −0.0113358
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −12.0827 −0.421690 −0.210845 0.977520i \(-0.567621\pi\)
−0.210845 + 0.977520i \(0.567621\pi\)
\(822\) 0 0
\(823\) 45.7045 1.59316 0.796580 0.604533i \(-0.206640\pi\)
0.796580 + 0.604533i \(0.206640\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 42.6766 1.48401 0.742005 0.670394i \(-0.233875\pi\)
0.742005 + 0.670394i \(0.233875\pi\)
\(828\) 0 0
\(829\) 25.3805 0.881502 0.440751 0.897629i \(-0.354712\pi\)
0.440751 + 0.897629i \(0.354712\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 59.7000 2.06848
\(834\) 0 0
\(835\) −16.3172 −0.564679
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −45.1306 −1.55808 −0.779041 0.626973i \(-0.784294\pi\)
−0.779041 + 0.626973i \(0.784294\pi\)
\(840\) 0 0
\(841\) −21.0845 −0.727050
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −142.182 −4.89121
\(846\) 0 0
\(847\) −47.5346 −1.63331
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −31.3383 −1.07426
\(852\) 0 0
\(853\) −26.6343 −0.911943 −0.455971 0.889994i \(-0.650708\pi\)
−0.455971 + 0.889994i \(0.650708\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 24.2749 0.829216 0.414608 0.910000i \(-0.363919\pi\)
0.414608 + 0.910000i \(0.363919\pi\)
\(858\) 0 0
\(859\) −43.0987 −1.47051 −0.735255 0.677791i \(-0.762938\pi\)
−0.735255 + 0.677791i \(0.762938\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 26.5921 0.905206 0.452603 0.891712i \(-0.350495\pi\)
0.452603 + 0.891712i \(0.350495\pi\)
\(864\) 0 0
\(865\) −56.7325 −1.92896
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.07703 −0.0365357
\(870\) 0 0
\(871\) 11.4227 0.387045
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −90.5379 −3.06074
\(876\) 0 0
\(877\) −21.9441 −0.740999 −0.370500 0.928833i \(-0.620814\pi\)
−0.370500 + 0.928833i \(0.620814\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 9.68457 0.326282 0.163141 0.986603i \(-0.447838\pi\)
0.163141 + 0.986603i \(0.447838\pi\)
\(882\) 0 0
\(883\) −34.2681 −1.15321 −0.576607 0.817022i \(-0.695623\pi\)
−0.576607 + 0.817022i \(0.695623\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −10.7884 −0.362239 −0.181120 0.983461i \(-0.557972\pi\)
−0.181120 + 0.983461i \(0.557972\pi\)
\(888\) 0 0
\(889\) −1.61323 −0.0541060
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −6.73074 −0.225236
\(894\) 0 0
\(895\) 68.4016 2.28641
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 16.8807 0.563004
\(900\) 0 0
\(901\) −45.1979 −1.50576
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5.46149 −0.181546
\(906\) 0 0
\(907\) 3.43643 0.114105 0.0570524 0.998371i \(-0.481830\pi\)
0.0570524 + 0.998371i \(0.481830\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 53.1306 1.76030 0.880148 0.474699i \(-0.157443\pi\)
0.880148 + 0.474699i \(0.157443\pi\)
\(912\) 0 0
\(913\) 0.563568 0.0186514
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 58.5653 1.93400
\(918\) 0 0
\(919\) −17.3805 −0.573330 −0.286665 0.958031i \(-0.592547\pi\)
−0.286665 + 0.958031i \(0.592547\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −11.4227 −0.375984
\(924\) 0 0
\(925\) 41.3805 1.36058
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −13.6269 −0.447085 −0.223542 0.974694i \(-0.571762\pi\)
−0.223542 + 0.974694i \(0.571762\pi\)
\(930\) 0 0
\(931\) 11.6971 0.383357
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.65371 0.0540822
\(936\) 0 0
\(937\) 30.7256 1.00376 0.501882 0.864936i \(-0.332641\pi\)
0.501882 + 0.864936i \(0.332641\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −34.2362 −1.11607 −0.558034 0.829818i \(-0.688444\pi\)
−0.558034 + 0.829818i \(0.688444\pi\)
\(942\) 0 0
\(943\) 8.00000 0.260516
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −53.2710 −1.73108 −0.865538 0.500844i \(-0.833023\pi\)
−0.865538 + 0.500844i \(0.833023\pi\)
\(948\) 0 0
\(949\) −23.1900 −0.752780
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 55.0633 1.78368 0.891838 0.452354i \(-0.149416\pi\)
0.891838 + 0.452354i \(0.149416\pi\)
\(954\) 0 0
\(955\) −26.3662 −0.853192
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 80.2767 2.59227
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −51.0074 −1.64199
\(966\) 0 0
\(967\) 36.0845 1.16040 0.580199 0.814475i \(-0.302975\pi\)
0.580199 + 0.814475i \(0.302975\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 40.0000 1.28366 0.641831 0.766846i \(-0.278175\pi\)
0.641831 + 0.766846i \(0.278175\pi\)
\(972\) 0 0
\(973\) 35.9932 1.15389
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 8.85569 0.283319 0.141659 0.989915i \(-0.454756\pi\)
0.141659 + 0.989915i \(0.454756\pi\)
\(978\) 0 0
\(979\) −0.0981437 −0.00313669
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.92297 0.0932283 0.0466142 0.998913i \(-0.485157\pi\)
0.0466142 + 0.998913i \(0.485157\pi\)
\(984\) 0 0
\(985\) −98.0149 −3.12301
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.53851 0.0807201
\(990\) 0 0
\(991\) −36.7747 −1.16819 −0.584094 0.811686i \(-0.698550\pi\)
−0.584094 + 0.811686i \(0.698550\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.26926 0.0402382
\(996\) 0 0
\(997\) −10.8375 −0.343226 −0.171613 0.985164i \(-0.554898\pi\)
−0.171613 + 0.985164i \(0.554898\pi\)
\(998\) 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 2736.2.a.bc.1.1 3
3.2 odd 2 2736.2.a.be.1.3 3
4.3 odd 2 1368.2.a.m.1.1 3
12.11 even 2 1368.2.a.o.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.2.a.m.1.1 3 4.3 odd 2
1368.2.a.o.1.3 yes 3 12.11 even 2
2736.2.a.bc.1.1 3 1.1 even 1 trivial
2736.2.a.be.1.3 3 3.2 odd 2