Properties

Label 5796.2.a.k.1.1
Level $5796$
Weight $2$
Character 5796.1
Self dual yes
Analytic conductor $46.281$
Analytic rank $1$
Dimension $2$
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] = [5796,2,Mod(1,5796)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5796, 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("5796.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5796.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: \(46.2812930115\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1932)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.30278\) of defining polynomial
Character \(\chi\) \(=\) 5796.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.30278 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-2.30278 q^{5} +1.00000 q^{7} +3.60555 q^{11} -0.697224 q^{13} +3.00000 q^{17} -7.60555 q^{19} +1.00000 q^{23} +0.302776 q^{25} -1.00000 q^{29} +1.00000 q^{31} -2.30278 q^{35} -8.21110 q^{37} +5.60555 q^{41} -7.90833 q^{43} +10.6056 q^{47} +1.00000 q^{49} -12.9083 q^{53} -8.30278 q^{55} -10.9083 q^{59} +8.51388 q^{61} +1.60555 q^{65} +10.1194 q^{67} +11.9083 q^{71} +10.8167 q^{73} +3.60555 q^{77} -6.39445 q^{79} +0.394449 q^{83} -6.90833 q^{85} -3.30278 q^{89} -0.697224 q^{91} +17.5139 q^{95} -11.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{5} + 2 q^{7} - 5 q^{13} + 6 q^{17} - 8 q^{19} + 2 q^{23} - 3 q^{25} - 2 q^{29} + 2 q^{31} - q^{35} - 2 q^{37} + 4 q^{41} - 5 q^{43} + 14 q^{47} + 2 q^{49} - 15 q^{53} - 13 q^{55} - 11 q^{59} - q^{61} - 4 q^{65} - 5 q^{67} + 13 q^{71} - 20 q^{79} + 8 q^{83} - 3 q^{85} - 3 q^{89} - 5 q^{91} + 17 q^{95} - 22 q^{97}+O(q^{100}) \) 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
\(5\) −2.30278 −1.02983 −0.514916 0.857240i \(-0.672177\pi\)
−0.514916 + 0.857240i \(0.672177\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.60555 1.08711 0.543557 0.839372i \(-0.317077\pi\)
0.543557 + 0.839372i \(0.317077\pi\)
\(12\) 0 0
\(13\) −0.697224 −0.193375 −0.0966876 0.995315i \(-0.530825\pi\)
−0.0966876 + 0.995315i \(0.530825\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −7.60555 −1.74483 −0.872417 0.488763i \(-0.837448\pi\)
−0.872417 + 0.488763i \(0.837448\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0.302776 0.0605551
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.30278 −0.389240
\(36\) 0 0
\(37\) −8.21110 −1.34990 −0.674948 0.737865i \(-0.735834\pi\)
−0.674948 + 0.737865i \(0.735834\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.60555 0.875440 0.437720 0.899111i \(-0.355786\pi\)
0.437720 + 0.899111i \(0.355786\pi\)
\(42\) 0 0
\(43\) −7.90833 −1.20601 −0.603004 0.797738i \(-0.706030\pi\)
−0.603004 + 0.797738i \(0.706030\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.6056 1.54698 0.773489 0.633809i \(-0.218510\pi\)
0.773489 + 0.633809i \(0.218510\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12.9083 −1.77310 −0.886548 0.462638i \(-0.846903\pi\)
−0.886548 + 0.462638i \(0.846903\pi\)
\(54\) 0 0
\(55\) −8.30278 −1.11955
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.9083 −1.42014 −0.710072 0.704129i \(-0.751337\pi\)
−0.710072 + 0.704129i \(0.751337\pi\)
\(60\) 0 0
\(61\) 8.51388 1.09009 0.545045 0.838407i \(-0.316512\pi\)
0.545045 + 0.838407i \(0.316512\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.60555 0.199144
\(66\) 0 0
\(67\) 10.1194 1.23629 0.618143 0.786066i \(-0.287885\pi\)
0.618143 + 0.786066i \(0.287885\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.9083 1.41326 0.706629 0.707584i \(-0.250215\pi\)
0.706629 + 0.707584i \(0.250215\pi\)
\(72\) 0 0
\(73\) 10.8167 1.26599 0.632997 0.774154i \(-0.281825\pi\)
0.632997 + 0.774154i \(0.281825\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.60555 0.410891
\(78\) 0 0
\(79\) −6.39445 −0.719432 −0.359716 0.933062i \(-0.617126\pi\)
−0.359716 + 0.933062i \(0.617126\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.394449 0.0432964 0.0216482 0.999766i \(-0.493109\pi\)
0.0216482 + 0.999766i \(0.493109\pi\)
\(84\) 0 0
\(85\) −6.90833 −0.749313
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.30278 −0.350094 −0.175047 0.984560i \(-0.556008\pi\)
−0.175047 + 0.984560i \(0.556008\pi\)
\(90\) 0 0
\(91\) −0.697224 −0.0730890
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 17.5139 1.79689
\(96\) 0 0
\(97\) −11.0000 −1.11688 −0.558440 0.829545i \(-0.688600\pi\)
−0.558440 + 0.829545i \(0.688600\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.51388 0.946666 0.473333 0.880884i \(-0.343051\pi\)
0.473333 + 0.880884i \(0.343051\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.5139 −1.20976 −0.604881 0.796316i \(-0.706779\pi\)
−0.604881 + 0.796316i \(0.706779\pi\)
\(108\) 0 0
\(109\) −10.9083 −1.04483 −0.522414 0.852692i \(-0.674968\pi\)
−0.522414 + 0.852692i \(0.674968\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.51388 −0.330558 −0.165279 0.986247i \(-0.552852\pi\)
−0.165279 + 0.986247i \(0.552852\pi\)
\(114\) 0 0
\(115\) −2.30278 −0.214735
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) 2.00000 0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.8167 0.967471
\(126\) 0 0
\(127\) 3.30278 0.293074 0.146537 0.989205i \(-0.453187\pi\)
0.146537 + 0.989205i \(0.453187\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.81665 −0.420833 −0.210416 0.977612i \(-0.567482\pi\)
−0.210416 + 0.977612i \(0.567482\pi\)
\(132\) 0 0
\(133\) −7.60555 −0.659485
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.0278 1.36934 0.684672 0.728851i \(-0.259946\pi\)
0.684672 + 0.728851i \(0.259946\pi\)
\(138\) 0 0
\(139\) −10.3028 −0.873870 −0.436935 0.899493i \(-0.643936\pi\)
−0.436935 + 0.899493i \(0.643936\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.51388 −0.210221
\(144\) 0 0
\(145\) 2.30278 0.191235
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −19.8167 −1.62344 −0.811722 0.584044i \(-0.801469\pi\)
−0.811722 + 0.584044i \(0.801469\pi\)
\(150\) 0 0
\(151\) −6.60555 −0.537552 −0.268776 0.963203i \(-0.586619\pi\)
−0.268776 + 0.963203i \(0.586619\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.30278 −0.184963
\(156\) 0 0
\(157\) 23.0278 1.83782 0.918908 0.394473i \(-0.129073\pi\)
0.918908 + 0.394473i \(0.129073\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −23.5139 −1.84175 −0.920875 0.389859i \(-0.872524\pi\)
−0.920875 + 0.389859i \(0.872524\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 16.8167 1.30131 0.650656 0.759373i \(-0.274494\pi\)
0.650656 + 0.759373i \(0.274494\pi\)
\(168\) 0 0
\(169\) −12.5139 −0.962606
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.0278 1.37062 0.685312 0.728249i \(-0.259666\pi\)
0.685312 + 0.728249i \(0.259666\pi\)
\(174\) 0 0
\(175\) 0.302776 0.0228877
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.908327 0.0678915 0.0339458 0.999424i \(-0.489193\pi\)
0.0339458 + 0.999424i \(0.489193\pi\)
\(180\) 0 0
\(181\) −9.42221 −0.700347 −0.350173 0.936685i \(-0.613877\pi\)
−0.350173 + 0.936685i \(0.613877\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 18.9083 1.39017
\(186\) 0 0
\(187\) 10.8167 0.790992
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −21.0278 −1.52152 −0.760758 0.649036i \(-0.775172\pi\)
−0.760758 + 0.649036i \(0.775172\pi\)
\(192\) 0 0
\(193\) 9.81665 0.706618 0.353309 0.935507i \(-0.385056\pi\)
0.353309 + 0.935507i \(0.385056\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.3028 −1.66025 −0.830127 0.557574i \(-0.811732\pi\)
−0.830127 + 0.557574i \(0.811732\pi\)
\(198\) 0 0
\(199\) 19.6972 1.39630 0.698150 0.715952i \(-0.254007\pi\)
0.698150 + 0.715952i \(0.254007\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.00000 −0.0701862
\(204\) 0 0
\(205\) −12.9083 −0.901557
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −27.4222 −1.89683
\(210\) 0 0
\(211\) −13.6056 −0.936645 −0.468322 0.883558i \(-0.655141\pi\)
−0.468322 + 0.883558i \(0.655141\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 18.2111 1.24199
\(216\) 0 0
\(217\) 1.00000 0.0678844
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.09167 −0.140701
\(222\) 0 0
\(223\) −27.5139 −1.84247 −0.921233 0.389012i \(-0.872817\pi\)
−0.921233 + 0.389012i \(0.872817\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −19.6972 −1.30735 −0.653675 0.756775i \(-0.726774\pi\)
−0.653675 + 0.756775i \(0.726774\pi\)
\(228\) 0 0
\(229\) −11.6972 −0.772974 −0.386487 0.922295i \(-0.626312\pi\)
−0.386487 + 0.922295i \(0.626312\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.3305 −1.39741 −0.698705 0.715410i \(-0.746240\pi\)
−0.698705 + 0.715410i \(0.746240\pi\)
\(234\) 0 0
\(235\) −24.4222 −1.59313
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −9.69722 −0.627261 −0.313631 0.949545i \(-0.601545\pi\)
−0.313631 + 0.949545i \(0.601545\pi\)
\(240\) 0 0
\(241\) 5.78890 0.372896 0.186448 0.982465i \(-0.440302\pi\)
0.186448 + 0.982465i \(0.440302\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.30278 −0.147119
\(246\) 0 0
\(247\) 5.30278 0.337408
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.39445 0.214256 0.107128 0.994245i \(-0.465835\pi\)
0.107128 + 0.994245i \(0.465835\pi\)
\(252\) 0 0
\(253\) 3.60555 0.226679
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.0278 −0.812649 −0.406325 0.913729i \(-0.633190\pi\)
−0.406325 + 0.913729i \(0.633190\pi\)
\(258\) 0 0
\(259\) −8.21110 −0.510213
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.6333 −1.14898 −0.574489 0.818512i \(-0.694799\pi\)
−0.574489 + 0.818512i \(0.694799\pi\)
\(264\) 0 0
\(265\) 29.7250 1.82599
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.72498 0.471000 0.235500 0.971874i \(-0.424327\pi\)
0.235500 + 0.971874i \(0.424327\pi\)
\(270\) 0 0
\(271\) −10.8167 −0.657065 −0.328532 0.944493i \(-0.606554\pi\)
−0.328532 + 0.944493i \(0.606554\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.09167 0.0658304
\(276\) 0 0
\(277\) −16.3305 −0.981207 −0.490603 0.871383i \(-0.663224\pi\)
−0.490603 + 0.871383i \(0.663224\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −17.8167 −1.06285 −0.531426 0.847105i \(-0.678344\pi\)
−0.531426 + 0.847105i \(0.678344\pi\)
\(282\) 0 0
\(283\) 5.69722 0.338665 0.169332 0.985559i \(-0.445839\pi\)
0.169332 + 0.985559i \(0.445839\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.60555 0.330885
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 13.2111 0.771801 0.385900 0.922540i \(-0.373891\pi\)
0.385900 + 0.922540i \(0.373891\pi\)
\(294\) 0 0
\(295\) 25.1194 1.46251
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.697224 −0.0403215
\(300\) 0 0
\(301\) −7.90833 −0.455828
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −19.6056 −1.12261
\(306\) 0 0
\(307\) 13.4222 0.766046 0.383023 0.923739i \(-0.374883\pi\)
0.383023 + 0.923739i \(0.374883\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.90833 −0.335030 −0.167515 0.985869i \(-0.553574\pi\)
−0.167515 + 0.985869i \(0.553574\pi\)
\(312\) 0 0
\(313\) −25.2111 −1.42502 −0.712508 0.701664i \(-0.752441\pi\)
−0.712508 + 0.701664i \(0.752441\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.30278 −0.129337 −0.0646684 0.997907i \(-0.520599\pi\)
−0.0646684 + 0.997907i \(0.520599\pi\)
\(318\) 0 0
\(319\) −3.60555 −0.201872
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −22.8167 −1.26955
\(324\) 0 0
\(325\) −0.211103 −0.0117099
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.6056 0.584703
\(330\) 0 0
\(331\) 19.2111 1.05594 0.527969 0.849264i \(-0.322954\pi\)
0.527969 + 0.849264i \(0.322954\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −23.3028 −1.27317
\(336\) 0 0
\(337\) 12.5139 0.681674 0.340837 0.940122i \(-0.389290\pi\)
0.340837 + 0.940122i \(0.389290\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.60555 0.195252
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −28.8167 −1.54696 −0.773480 0.633821i \(-0.781485\pi\)
−0.773480 + 0.633821i \(0.781485\pi\)
\(348\) 0 0
\(349\) −4.48612 −0.240137 −0.120068 0.992766i \(-0.538311\pi\)
−0.120068 + 0.992766i \(0.538311\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −11.6056 −0.617701 −0.308851 0.951111i \(-0.599944\pi\)
−0.308851 + 0.951111i \(0.599944\pi\)
\(354\) 0 0
\(355\) −27.4222 −1.45542
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.0917 0.585396 0.292698 0.956205i \(-0.405447\pi\)
0.292698 + 0.956205i \(0.405447\pi\)
\(360\) 0 0
\(361\) 38.8444 2.04444
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −24.9083 −1.30376
\(366\) 0 0
\(367\) −29.7250 −1.55163 −0.775816 0.630960i \(-0.782661\pi\)
−0.775816 + 0.630960i \(0.782661\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −12.9083 −0.670167
\(372\) 0 0
\(373\) 31.4222 1.62698 0.813490 0.581579i \(-0.197565\pi\)
0.813490 + 0.581579i \(0.197565\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.697224 0.0359089
\(378\) 0 0
\(379\) −5.21110 −0.267676 −0.133838 0.991003i \(-0.542730\pi\)
−0.133838 + 0.991003i \(0.542730\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 30.0278 1.53435 0.767173 0.641440i \(-0.221663\pi\)
0.767173 + 0.641440i \(0.221663\pi\)
\(384\) 0 0
\(385\) −8.30278 −0.423149
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −15.7889 −0.800529 −0.400264 0.916400i \(-0.631082\pi\)
−0.400264 + 0.916400i \(0.631082\pi\)
\(390\) 0 0
\(391\) 3.00000 0.151717
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 14.7250 0.740894
\(396\) 0 0
\(397\) −10.6056 −0.532277 −0.266139 0.963935i \(-0.585748\pi\)
−0.266139 + 0.963935i \(0.585748\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.4222 0.770148 0.385074 0.922886i \(-0.374176\pi\)
0.385074 + 0.922886i \(0.374176\pi\)
\(402\) 0 0
\(403\) −0.697224 −0.0347312
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −29.6056 −1.46749
\(408\) 0 0
\(409\) −21.4222 −1.05926 −0.529630 0.848229i \(-0.677669\pi\)
−0.529630 + 0.848229i \(0.677669\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.9083 −0.536764
\(414\) 0 0
\(415\) −0.908327 −0.0445880
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9.51388 −0.464783 −0.232392 0.972622i \(-0.574655\pi\)
−0.232392 + 0.972622i \(0.574655\pi\)
\(420\) 0 0
\(421\) 11.9083 0.580376 0.290188 0.956970i \(-0.406282\pi\)
0.290188 + 0.956970i \(0.406282\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.908327 0.0440603
\(426\) 0 0
\(427\) 8.51388 0.412015
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.09167 0.100752 0.0503762 0.998730i \(-0.483958\pi\)
0.0503762 + 0.998730i \(0.483958\pi\)
\(432\) 0 0
\(433\) −35.0278 −1.68333 −0.841663 0.540003i \(-0.818423\pi\)
−0.841663 + 0.540003i \(0.818423\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.60555 −0.363823
\(438\) 0 0
\(439\) 32.6333 1.55750 0.778751 0.627333i \(-0.215853\pi\)
0.778751 + 0.627333i \(0.215853\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 23.6333 1.12285 0.561426 0.827527i \(-0.310253\pi\)
0.561426 + 0.827527i \(0.310253\pi\)
\(444\) 0 0
\(445\) 7.60555 0.360538
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7.88057 −0.371907 −0.185954 0.982559i \(-0.559537\pi\)
−0.185954 + 0.982559i \(0.559537\pi\)
\(450\) 0 0
\(451\) 20.2111 0.951704
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.60555 0.0752694
\(456\) 0 0
\(457\) −0.724981 −0.0339132 −0.0169566 0.999856i \(-0.505398\pi\)
−0.0169566 + 0.999856i \(0.505398\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −28.5416 −1.32932 −0.664658 0.747148i \(-0.731423\pi\)
−0.664658 + 0.747148i \(0.731423\pi\)
\(462\) 0 0
\(463\) 26.2111 1.21813 0.609067 0.793119i \(-0.291544\pi\)
0.609067 + 0.793119i \(0.291544\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.6056 0.907237 0.453618 0.891196i \(-0.350133\pi\)
0.453618 + 0.891196i \(0.350133\pi\)
\(468\) 0 0
\(469\) 10.1194 0.467272
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −28.5139 −1.31107
\(474\) 0 0
\(475\) −2.30278 −0.105659
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.4222 0.704659 0.352329 0.935876i \(-0.385390\pi\)
0.352329 + 0.935876i \(0.385390\pi\)
\(480\) 0 0
\(481\) 5.72498 0.261037
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 25.3305 1.15020
\(486\) 0 0
\(487\) −19.7889 −0.896721 −0.448360 0.893853i \(-0.647992\pi\)
−0.448360 + 0.893853i \(0.647992\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.3305 0.556469 0.278235 0.960513i \(-0.410251\pi\)
0.278235 + 0.960513i \(0.410251\pi\)
\(492\) 0 0
\(493\) −3.00000 −0.135113
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 11.9083 0.534161
\(498\) 0 0
\(499\) 36.5416 1.63583 0.817914 0.575340i \(-0.195130\pi\)
0.817914 + 0.575340i \(0.195130\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16.3028 0.726905 0.363452 0.931613i \(-0.381598\pi\)
0.363452 + 0.931613i \(0.381598\pi\)
\(504\) 0 0
\(505\) −21.9083 −0.974908
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.39445 0.0618079 0.0309039 0.999522i \(-0.490161\pi\)
0.0309039 + 0.999522i \(0.490161\pi\)
\(510\) 0 0
\(511\) 10.8167 0.478501
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 36.8444 1.62356
\(516\) 0 0
\(517\) 38.2389 1.68174
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −24.7889 −1.08602 −0.543011 0.839726i \(-0.682716\pi\)
−0.543011 + 0.839726i \(0.682716\pi\)
\(522\) 0 0
\(523\) 2.00000 0.0874539 0.0437269 0.999044i \(-0.486077\pi\)
0.0437269 + 0.999044i \(0.486077\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.00000 0.130682
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.90833 −0.169288
\(534\) 0 0
\(535\) 28.8167 1.24585
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.60555 0.155302
\(540\) 0 0
\(541\) −1.39445 −0.0599520 −0.0299760 0.999551i \(-0.509543\pi\)
−0.0299760 + 0.999551i \(0.509543\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 25.1194 1.07600
\(546\) 0 0
\(547\) −1.51388 −0.0647288 −0.0323644 0.999476i \(-0.510304\pi\)
−0.0323644 + 0.999476i \(0.510304\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.60555 0.324007
\(552\) 0 0
\(553\) −6.39445 −0.271920
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 29.4500 1.24783 0.623917 0.781490i \(-0.285540\pi\)
0.623917 + 0.781490i \(0.285540\pi\)
\(558\) 0 0
\(559\) 5.51388 0.233212
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.11943 −0.300048 −0.150024 0.988682i \(-0.547935\pi\)
−0.150024 + 0.988682i \(0.547935\pi\)
\(564\) 0 0
\(565\) 8.09167 0.340419
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.00000 0.167689 0.0838444 0.996479i \(-0.473280\pi\)
0.0838444 + 0.996479i \(0.473280\pi\)
\(570\) 0 0
\(571\) 20.8167 0.871150 0.435575 0.900152i \(-0.356545\pi\)
0.435575 + 0.900152i \(0.356545\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.302776 0.0126266
\(576\) 0 0
\(577\) −17.6333 −0.734084 −0.367042 0.930204i \(-0.619630\pi\)
−0.367042 + 0.930204i \(0.619630\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.394449 0.0163645
\(582\) 0 0
\(583\) −46.5416 −1.92756
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.30278 0.0537713 0.0268857 0.999639i \(-0.491441\pi\)
0.0268857 + 0.999639i \(0.491441\pi\)
\(588\) 0 0
\(589\) −7.60555 −0.313381
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11.0278 −0.452856 −0.226428 0.974028i \(-0.572705\pi\)
−0.226428 + 0.974028i \(0.572705\pi\)
\(594\) 0 0
\(595\) −6.90833 −0.283214
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −17.7250 −0.724223 −0.362112 0.932135i \(-0.617944\pi\)
−0.362112 + 0.932135i \(0.617944\pi\)
\(600\) 0 0
\(601\) −35.9361 −1.46586 −0.732932 0.680302i \(-0.761849\pi\)
−0.732932 + 0.680302i \(0.761849\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.60555 −0.187242
\(606\) 0 0
\(607\) 2.88057 0.116919 0.0584594 0.998290i \(-0.481381\pi\)
0.0584594 + 0.998290i \(0.481381\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.39445 −0.299147
\(612\) 0 0
\(613\) −44.4500 −1.79532 −0.897659 0.440692i \(-0.854733\pi\)
−0.897659 + 0.440692i \(0.854733\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.11943 0.286617 0.143309 0.989678i \(-0.454226\pi\)
0.143309 + 0.989678i \(0.454226\pi\)
\(618\) 0 0
\(619\) 32.3305 1.29947 0.649737 0.760159i \(-0.274879\pi\)
0.649737 + 0.760159i \(0.274879\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.30278 −0.132323
\(624\) 0 0
\(625\) −26.4222 −1.05689
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24.6333 −0.982194
\(630\) 0 0
\(631\) 25.0000 0.995234 0.497617 0.867397i \(-0.334208\pi\)
0.497617 + 0.867397i \(0.334208\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.60555 −0.301817
\(636\) 0 0
\(637\) −0.697224 −0.0276250
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −22.1472 −0.874761 −0.437381 0.899276i \(-0.644094\pi\)
−0.437381 + 0.899276i \(0.644094\pi\)
\(642\) 0 0
\(643\) −49.7250 −1.96096 −0.980481 0.196614i \(-0.937005\pi\)
−0.980481 + 0.196614i \(0.937005\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.0917 0.907827 0.453914 0.891046i \(-0.350027\pi\)
0.453914 + 0.891046i \(0.350027\pi\)
\(648\) 0 0
\(649\) −39.3305 −1.54386
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.51388 0.294041 0.147020 0.989133i \(-0.453032\pi\)
0.147020 + 0.989133i \(0.453032\pi\)
\(654\) 0 0
\(655\) 11.0917 0.433388
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20.3944 −0.794455 −0.397227 0.917720i \(-0.630028\pi\)
−0.397227 + 0.917720i \(0.630028\pi\)
\(660\) 0 0
\(661\) −8.21110 −0.319375 −0.159687 0.987168i \(-0.551049\pi\)
−0.159687 + 0.987168i \(0.551049\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 17.5139 0.679159
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 30.6972 1.18505
\(672\) 0 0
\(673\) −4.57779 −0.176461 −0.0882305 0.996100i \(-0.528121\pi\)
−0.0882305 + 0.996100i \(0.528121\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30.6972 −1.17979 −0.589895 0.807480i \(-0.700831\pi\)
−0.589895 + 0.807480i \(0.700831\pi\)
\(678\) 0 0
\(679\) −11.0000 −0.422141
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 47.6056 1.82158 0.910788 0.412875i \(-0.135475\pi\)
0.910788 + 0.412875i \(0.135475\pi\)
\(684\) 0 0
\(685\) −36.9083 −1.41019
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.00000 0.342873
\(690\) 0 0
\(691\) −8.93608 −0.339945 −0.169972 0.985449i \(-0.554368\pi\)
−0.169972 + 0.985449i \(0.554368\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 23.7250 0.899940
\(696\) 0 0
\(697\) 16.8167 0.636976
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.88057 −0.0710282 −0.0355141 0.999369i \(-0.511307\pi\)
−0.0355141 + 0.999369i \(0.511307\pi\)
\(702\) 0 0
\(703\) 62.4500 2.35534
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.51388 0.357806
\(708\) 0 0
\(709\) 6.09167 0.228778 0.114389 0.993436i \(-0.463509\pi\)
0.114389 + 0.993436i \(0.463509\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.00000 0.0374503
\(714\) 0 0
\(715\) 5.78890 0.216492
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 25.0000 0.932343 0.466171 0.884694i \(-0.345633\pi\)
0.466171 + 0.884694i \(0.345633\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.302776 −0.0112448
\(726\) 0 0
\(727\) 3.60555 0.133722 0.0668612 0.997762i \(-0.478702\pi\)
0.0668612 + 0.997762i \(0.478702\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −23.7250 −0.877500
\(732\) 0 0
\(733\) 23.0278 0.850550 0.425275 0.905064i \(-0.360177\pi\)
0.425275 + 0.905064i \(0.360177\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 36.4861 1.34398
\(738\) 0 0
\(739\) 50.0278 1.84030 0.920150 0.391565i \(-0.128066\pi\)
0.920150 + 0.391565i \(0.128066\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6.72498 0.246716 0.123358 0.992362i \(-0.460634\pi\)
0.123358 + 0.992362i \(0.460634\pi\)
\(744\) 0 0
\(745\) 45.6333 1.67188
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.5139 −0.457247
\(750\) 0 0
\(751\) 35.5139 1.29592 0.647960 0.761674i \(-0.275622\pi\)
0.647960 + 0.761674i \(0.275622\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15.2111 0.553589
\(756\) 0 0
\(757\) 17.4222 0.633221 0.316610 0.948556i \(-0.397455\pi\)
0.316610 + 0.948556i \(0.397455\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.2111 0.478902 0.239451 0.970908i \(-0.423033\pi\)
0.239451 + 0.970908i \(0.423033\pi\)
\(762\) 0 0
\(763\) −10.9083 −0.394908
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.60555 0.274621
\(768\) 0 0
\(769\) −42.6611 −1.53840 −0.769199 0.639010i \(-0.779344\pi\)
−0.769199 + 0.639010i \(0.779344\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 24.0278 0.864218 0.432109 0.901821i \(-0.357770\pi\)
0.432109 + 0.901821i \(0.357770\pi\)
\(774\) 0 0
\(775\) 0.302776 0.0108760
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −42.6333 −1.52750
\(780\) 0 0
\(781\) 42.9361 1.53637
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −53.0278 −1.89264
\(786\) 0 0
\(787\) −34.3583 −1.22474 −0.612370 0.790571i \(-0.709784\pi\)
−0.612370 + 0.790571i \(0.709784\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.51388 −0.124939
\(792\) 0 0
\(793\) −5.93608 −0.210796
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14.6056 0.517355 0.258678 0.965964i \(-0.416713\pi\)
0.258678 + 0.965964i \(0.416713\pi\)
\(798\) 0 0
\(799\) 31.8167 1.12559
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 39.0000 1.37628
\(804\) 0 0
\(805\) −2.30278 −0.0811622
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −7.54163 −0.265150 −0.132575 0.991173i \(-0.542324\pi\)
−0.132575 + 0.991173i \(0.542324\pi\)
\(810\) 0 0
\(811\) 25.2389 0.886256 0.443128 0.896458i \(-0.353869\pi\)
0.443128 + 0.896458i \(0.353869\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 54.1472 1.89669
\(816\) 0 0
\(817\) 60.1472 2.10428
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7.81665 −0.272803 −0.136402 0.990654i \(-0.543554\pi\)
−0.136402 + 0.990654i \(0.543554\pi\)
\(822\) 0 0
\(823\) −51.3305 −1.78927 −0.894635 0.446798i \(-0.852564\pi\)
−0.894635 + 0.446798i \(0.852564\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −34.5416 −1.20113 −0.600565 0.799576i \(-0.705058\pi\)
−0.600565 + 0.799576i \(0.705058\pi\)
\(828\) 0 0
\(829\) 19.8444 0.689225 0.344612 0.938745i \(-0.388010\pi\)
0.344612 + 0.938745i \(0.388010\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.00000 0.103944
\(834\) 0 0
\(835\) −38.7250 −1.34013
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −30.6972 −1.05979 −0.529893 0.848065i \(-0.677768\pi\)
−0.529893 + 0.848065i \(0.677768\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 28.8167 0.991323
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −8.21110 −0.281473
\(852\) 0 0
\(853\) 21.8167 0.746988 0.373494 0.927633i \(-0.378160\pi\)
0.373494 + 0.927633i \(0.378160\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 25.8167 0.881880 0.440940 0.897537i \(-0.354645\pi\)
0.440940 + 0.897537i \(0.354645\pi\)
\(858\) 0 0
\(859\) 19.2111 0.655474 0.327737 0.944769i \(-0.393714\pi\)
0.327737 + 0.944769i \(0.393714\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 19.3944 0.660195 0.330097 0.943947i \(-0.392918\pi\)
0.330097 + 0.943947i \(0.392918\pi\)
\(864\) 0 0
\(865\) −41.5139 −1.41151
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −23.0555 −0.782105
\(870\) 0 0
\(871\) −7.05551 −0.239067
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 10.8167 0.365670
\(876\) 0 0
\(877\) −17.2111 −0.581178 −0.290589 0.956848i \(-0.593851\pi\)
−0.290589 + 0.956848i \(0.593851\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −46.6611 −1.57205 −0.786026 0.618194i \(-0.787865\pi\)
−0.786026 + 0.618194i \(0.787865\pi\)
\(882\) 0 0
\(883\) 13.1194 0.441504 0.220752 0.975330i \(-0.429149\pi\)
0.220752 + 0.975330i \(0.429149\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −35.4861 −1.19151 −0.595754 0.803167i \(-0.703147\pi\)
−0.595754 + 0.803167i \(0.703147\pi\)
\(888\) 0 0
\(889\) 3.30278 0.110772
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −80.6611 −2.69922
\(894\) 0 0
\(895\) −2.09167 −0.0699169
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.00000 −0.0333519
\(900\) 0 0
\(901\) −38.7250 −1.29012
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 21.6972 0.721240
\(906\) 0 0
\(907\) −7.27502 −0.241563 −0.120782 0.992679i \(-0.538540\pi\)
−0.120782 + 0.992679i \(0.538540\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 14.6056 0.483904 0.241952 0.970288i \(-0.422212\pi\)
0.241952 + 0.970288i \(0.422212\pi\)
\(912\) 0 0
\(913\) 1.42221 0.0470681
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.81665 −0.159060
\(918\) 0 0
\(919\) 52.2666 1.72412 0.862058 0.506809i \(-0.169175\pi\)
0.862058 + 0.506809i \(0.169175\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −8.30278 −0.273289
\(924\) 0 0
\(925\) −2.48612 −0.0817432
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 6.90833 0.226655 0.113327 0.993558i \(-0.463849\pi\)
0.113327 + 0.993558i \(0.463849\pi\)
\(930\) 0 0
\(931\) −7.60555 −0.249262
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −24.9083 −0.814589
\(936\) 0 0
\(937\) 48.8722 1.59658 0.798292 0.602271i \(-0.205737\pi\)
0.798292 + 0.602271i \(0.205737\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 48.8444 1.59228 0.796141 0.605111i \(-0.206871\pi\)
0.796141 + 0.605111i \(0.206871\pi\)
\(942\) 0 0
\(943\) 5.60555 0.182542
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 48.4222 1.57351 0.786755 0.617265i \(-0.211759\pi\)
0.786755 + 0.617265i \(0.211759\pi\)
\(948\) 0 0
\(949\) −7.54163 −0.244812
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 32.3305 1.04729 0.523644 0.851937i \(-0.324572\pi\)
0.523644 + 0.851937i \(0.324572\pi\)
\(954\) 0 0
\(955\) 48.4222 1.56691
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 16.0278 0.517563
\(960\) 0 0
\(961\) −30.0000 −0.967742
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −22.6056 −0.727698
\(966\) 0 0
\(967\) 6.36669 0.204739 0.102370 0.994746i \(-0.467358\pi\)
0.102370 + 0.994746i \(0.467358\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 22.2750 0.714839 0.357420 0.933944i \(-0.383657\pi\)
0.357420 + 0.933944i \(0.383657\pi\)
\(972\) 0 0
\(973\) −10.3028 −0.330292
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −46.5139 −1.48811 −0.744055 0.668118i \(-0.767100\pi\)
−0.744055 + 0.668118i \(0.767100\pi\)
\(978\) 0 0
\(979\) −11.9083 −0.380592
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.23886 −0.0395135 −0.0197567 0.999805i \(-0.506289\pi\)
−0.0197567 + 0.999805i \(0.506289\pi\)
\(984\) 0 0
\(985\) 53.6611 1.70978
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.90833 −0.251470
\(990\) 0 0
\(991\) 8.69722 0.276276 0.138138 0.990413i \(-0.455888\pi\)
0.138138 + 0.990413i \(0.455888\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −45.3583 −1.43795
\(996\) 0 0
\(997\) 12.5778 0.398343 0.199171 0.979965i \(-0.436175\pi\)
0.199171 + 0.979965i \(0.436175\pi\)
\(998\) 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 5796.2.a.k.1.1 2
3.2 odd 2 1932.2.a.e.1.2 2
12.11 even 2 7728.2.a.bk.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1932.2.a.e.1.2 2 3.2 odd 2
5796.2.a.k.1.1 2 1.1 even 1 trivial
7728.2.a.bk.1.2 2 12.11 even 2