Properties

Label 8036.2.a.k.1.1
Level $8036$
Weight $2$
Character 8036.1
Self dual yes
Analytic conductor $64.168$
Analytic rank $0$
Dimension $5$
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] = [8036,2,Mod(1,8036)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8036, 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("8036.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8036.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: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.287349.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 6x^{3} + 7x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1148)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.13797\) of defining polynomial
Character \(\chi\) \(=\) 8036.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.57090 q^{3} -0.350332 q^{5} +3.60954 q^{9} +O(q^{10})\) \(q-2.57090 q^{3} -0.350332 q^{5} +3.60954 q^{9} +1.25100 q^{11} -6.92944 q^{13} +0.900670 q^{15} +2.25921 q^{17} -5.55720 q^{19} -6.22344 q^{23} -4.87727 q^{25} -1.56706 q^{27} -5.45254 q^{29} -10.2015 q^{31} -3.21620 q^{33} +2.17277 q^{37} +17.8149 q^{39} +1.00000 q^{41} +1.54213 q^{43} -1.26454 q^{45} -5.11591 q^{47} -5.80820 q^{51} +10.0029 q^{53} -0.438266 q^{55} +14.2870 q^{57} +11.9497 q^{59} +1.51926 q^{61} +2.42760 q^{65} -12.6674 q^{67} +15.9999 q^{69} +16.5641 q^{71} -5.30087 q^{73} +12.5390 q^{75} -14.4987 q^{79} -6.79985 q^{81} -5.46607 q^{83} -0.791473 q^{85} +14.0179 q^{87} -6.80671 q^{89} +26.2272 q^{93} +1.94686 q^{95} +3.91406 q^{97} +4.51554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{3} + 3 q^{5} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{3} + 3 q^{5} + q^{9} + 6 q^{11} - 7 q^{13} + 9 q^{15} - q^{17} - 2 q^{19} + 4 q^{23} + 2 q^{25} - 8 q^{27} + 11 q^{29} - 13 q^{31} - 11 q^{33} + 5 q^{37} + 23 q^{39} + 5 q^{41} + 29 q^{43} - 11 q^{45} - 7 q^{47} - 3 q^{51} + 21 q^{53} - 19 q^{55} + 9 q^{57} - 3 q^{59} + 8 q^{61} - 5 q^{65} + 3 q^{67} - 10 q^{69} + 22 q^{71} + 16 q^{73} + 18 q^{75} + 4 q^{79} - 15 q^{81} + 6 q^{83} + 13 q^{85} - 6 q^{87} + 20 q^{89} - 5 q^{93} - 7 q^{95} + 24 q^{97} + 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.57090 −1.48431 −0.742156 0.670228i \(-0.766196\pi\)
−0.742156 + 0.670228i \(0.766196\pi\)
\(4\) 0 0
\(5\) −0.350332 −0.156673 −0.0783366 0.996927i \(-0.524961\pi\)
−0.0783366 + 0.996927i \(0.524961\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.60954 1.20318
\(10\) 0 0
\(11\) 1.25100 0.377191 0.188596 0.982055i \(-0.439606\pi\)
0.188596 + 0.982055i \(0.439606\pi\)
\(12\) 0 0
\(13\) −6.92944 −1.92188 −0.960940 0.276756i \(-0.910741\pi\)
−0.960940 + 0.276756i \(0.910741\pi\)
\(14\) 0 0
\(15\) 0.900670 0.232552
\(16\) 0 0
\(17\) 2.25921 0.547938 0.273969 0.961739i \(-0.411663\pi\)
0.273969 + 0.961739i \(0.411663\pi\)
\(18\) 0 0
\(19\) −5.55720 −1.27491 −0.637454 0.770488i \(-0.720013\pi\)
−0.637454 + 0.770488i \(0.720013\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.22344 −1.29768 −0.648839 0.760926i \(-0.724745\pi\)
−0.648839 + 0.760926i \(0.724745\pi\)
\(24\) 0 0
\(25\) −4.87727 −0.975453
\(26\) 0 0
\(27\) −1.56706 −0.301582
\(28\) 0 0
\(29\) −5.45254 −1.01251 −0.506255 0.862384i \(-0.668971\pi\)
−0.506255 + 0.862384i \(0.668971\pi\)
\(30\) 0 0
\(31\) −10.2015 −1.83225 −0.916125 0.400893i \(-0.868700\pi\)
−0.916125 + 0.400893i \(0.868700\pi\)
\(32\) 0 0
\(33\) −3.21620 −0.559869
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.17277 0.357200 0.178600 0.983922i \(-0.442843\pi\)
0.178600 + 0.983922i \(0.442843\pi\)
\(38\) 0 0
\(39\) 17.8149 2.85267
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 1.54213 0.235173 0.117586 0.993063i \(-0.462484\pi\)
0.117586 + 0.993063i \(0.462484\pi\)
\(44\) 0 0
\(45\) −1.26454 −0.188506
\(46\) 0 0
\(47\) −5.11591 −0.746232 −0.373116 0.927785i \(-0.621711\pi\)
−0.373116 + 0.927785i \(0.621711\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −5.80820 −0.813311
\(52\) 0 0
\(53\) 10.0029 1.37400 0.687000 0.726657i \(-0.258927\pi\)
0.687000 + 0.726657i \(0.258927\pi\)
\(54\) 0 0
\(55\) −0.438266 −0.0590958
\(56\) 0 0
\(57\) 14.2870 1.89236
\(58\) 0 0
\(59\) 11.9497 1.55572 0.777858 0.628440i \(-0.216306\pi\)
0.777858 + 0.628440i \(0.216306\pi\)
\(60\) 0 0
\(61\) 1.51926 0.194521 0.0972606 0.995259i \(-0.468992\pi\)
0.0972606 + 0.995259i \(0.468992\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.42760 0.301107
\(66\) 0 0
\(67\) −12.6674 −1.54757 −0.773784 0.633449i \(-0.781639\pi\)
−0.773784 + 0.633449i \(0.781639\pi\)
\(68\) 0 0
\(69\) 15.9999 1.92616
\(70\) 0 0
\(71\) 16.5641 1.96579 0.982896 0.184161i \(-0.0589569\pi\)
0.982896 + 0.184161i \(0.0589569\pi\)
\(72\) 0 0
\(73\) −5.30087 −0.620419 −0.310210 0.950668i \(-0.600399\pi\)
−0.310210 + 0.950668i \(0.600399\pi\)
\(74\) 0 0
\(75\) 12.5390 1.44788
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −14.4987 −1.63123 −0.815614 0.578596i \(-0.803601\pi\)
−0.815614 + 0.578596i \(0.803601\pi\)
\(80\) 0 0
\(81\) −6.79985 −0.755538
\(82\) 0 0
\(83\) −5.46607 −0.599979 −0.299990 0.953942i \(-0.596983\pi\)
−0.299990 + 0.953942i \(0.596983\pi\)
\(84\) 0 0
\(85\) −0.791473 −0.0858473
\(86\) 0 0
\(87\) 14.0179 1.50288
\(88\) 0 0
\(89\) −6.80671 −0.721509 −0.360755 0.932661i \(-0.617481\pi\)
−0.360755 + 0.932661i \(0.617481\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 26.2272 2.71963
\(94\) 0 0
\(95\) 1.94686 0.199744
\(96\) 0 0
\(97\) 3.91406 0.397412 0.198706 0.980059i \(-0.436326\pi\)
0.198706 + 0.980059i \(0.436326\pi\)
\(98\) 0 0
\(99\) 4.51554 0.453829
\(100\) 0 0
\(101\) 10.3873 1.03358 0.516788 0.856114i \(-0.327128\pi\)
0.516788 + 0.856114i \(0.327128\pi\)
\(102\) 0 0
\(103\) −12.7261 −1.25394 −0.626970 0.779044i \(-0.715705\pi\)
−0.626970 + 0.779044i \(0.715705\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.9590 −1.15612 −0.578061 0.815993i \(-0.696191\pi\)
−0.578061 + 0.815993i \(0.696191\pi\)
\(108\) 0 0
\(109\) −17.3813 −1.66483 −0.832413 0.554155i \(-0.813041\pi\)
−0.832413 + 0.554155i \(0.813041\pi\)
\(110\) 0 0
\(111\) −5.58597 −0.530197
\(112\) 0 0
\(113\) −6.91509 −0.650517 −0.325258 0.945625i \(-0.605451\pi\)
−0.325258 + 0.945625i \(0.605451\pi\)
\(114\) 0 0
\(115\) 2.18027 0.203311
\(116\) 0 0
\(117\) −25.0121 −2.31237
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −9.43499 −0.857727
\(122\) 0 0
\(123\) −2.57090 −0.231810
\(124\) 0 0
\(125\) 3.46032 0.309501
\(126\) 0 0
\(127\) 9.51170 0.844027 0.422013 0.906590i \(-0.361323\pi\)
0.422013 + 0.906590i \(0.361323\pi\)
\(128\) 0 0
\(129\) −3.96467 −0.349070
\(130\) 0 0
\(131\) 11.1283 0.972281 0.486141 0.873881i \(-0.338404\pi\)
0.486141 + 0.873881i \(0.338404\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.548993 0.0472498
\(136\) 0 0
\(137\) −20.0604 −1.71388 −0.856938 0.515419i \(-0.827636\pi\)
−0.856938 + 0.515419i \(0.827636\pi\)
\(138\) 0 0
\(139\) −6.12561 −0.519567 −0.259784 0.965667i \(-0.583651\pi\)
−0.259784 + 0.965667i \(0.583651\pi\)
\(140\) 0 0
\(141\) 13.1525 1.10764
\(142\) 0 0
\(143\) −8.66874 −0.724916
\(144\) 0 0
\(145\) 1.91020 0.158633
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.24615 0.102088 0.0510442 0.998696i \(-0.483745\pi\)
0.0510442 + 0.998696i \(0.483745\pi\)
\(150\) 0 0
\(151\) −2.13328 −0.173604 −0.0868020 0.996226i \(-0.527665\pi\)
−0.0868020 + 0.996226i \(0.527665\pi\)
\(152\) 0 0
\(153\) 8.15469 0.659268
\(154\) 0 0
\(155\) 3.57393 0.287065
\(156\) 0 0
\(157\) 8.15769 0.651054 0.325527 0.945533i \(-0.394458\pi\)
0.325527 + 0.945533i \(0.394458\pi\)
\(158\) 0 0
\(159\) −25.7164 −2.03944
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −12.8075 −1.00316 −0.501581 0.865111i \(-0.667248\pi\)
−0.501581 + 0.865111i \(0.667248\pi\)
\(164\) 0 0
\(165\) 1.12674 0.0877165
\(166\) 0 0
\(167\) 18.7837 1.45352 0.726762 0.686890i \(-0.241024\pi\)
0.726762 + 0.686890i \(0.241024\pi\)
\(168\) 0 0
\(169\) 35.0171 2.69363
\(170\) 0 0
\(171\) −20.0589 −1.53394
\(172\) 0 0
\(173\) −11.4467 −0.870275 −0.435137 0.900364i \(-0.643300\pi\)
−0.435137 + 0.900364i \(0.643300\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −30.7215 −2.30917
\(178\) 0 0
\(179\) 11.7864 0.880957 0.440479 0.897763i \(-0.354809\pi\)
0.440479 + 0.897763i \(0.354809\pi\)
\(180\) 0 0
\(181\) 1.11415 0.0828138 0.0414069 0.999142i \(-0.486816\pi\)
0.0414069 + 0.999142i \(0.486816\pi\)
\(182\) 0 0
\(183\) −3.90587 −0.288730
\(184\) 0 0
\(185\) −0.761189 −0.0559638
\(186\) 0 0
\(187\) 2.82627 0.206677
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −23.5893 −1.70686 −0.853432 0.521204i \(-0.825483\pi\)
−0.853432 + 0.521204i \(0.825483\pi\)
\(192\) 0 0
\(193\) −3.34661 −0.240894 −0.120447 0.992720i \(-0.538433\pi\)
−0.120447 + 0.992720i \(0.538433\pi\)
\(194\) 0 0
\(195\) −6.24114 −0.446937
\(196\) 0 0
\(197\) 3.00533 0.214121 0.107060 0.994253i \(-0.465856\pi\)
0.107060 + 0.994253i \(0.465856\pi\)
\(198\) 0 0
\(199\) −9.95284 −0.705538 −0.352769 0.935710i \(-0.614760\pi\)
−0.352769 + 0.935710i \(0.614760\pi\)
\(200\) 0 0
\(201\) 32.5666 2.29707
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.350332 −0.0244683
\(206\) 0 0
\(207\) −22.4638 −1.56134
\(208\) 0 0
\(209\) −6.95206 −0.480884
\(210\) 0 0
\(211\) 24.2907 1.67224 0.836120 0.548546i \(-0.184818\pi\)
0.836120 + 0.548546i \(0.184818\pi\)
\(212\) 0 0
\(213\) −42.5846 −2.91785
\(214\) 0 0
\(215\) −0.540258 −0.0368453
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 13.6280 0.920895
\(220\) 0 0
\(221\) −15.6550 −1.05307
\(222\) 0 0
\(223\) −6.28073 −0.420589 −0.210295 0.977638i \(-0.567442\pi\)
−0.210295 + 0.977638i \(0.567442\pi\)
\(224\) 0 0
\(225\) −17.6047 −1.17365
\(226\) 0 0
\(227\) −16.3484 −1.08508 −0.542539 0.840031i \(-0.682537\pi\)
−0.542539 + 0.840031i \(0.682537\pi\)
\(228\) 0 0
\(229\) 27.2276 1.79925 0.899626 0.436660i \(-0.143839\pi\)
0.899626 + 0.436660i \(0.143839\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.78533 0.444522 0.222261 0.974987i \(-0.428656\pi\)
0.222261 + 0.974987i \(0.428656\pi\)
\(234\) 0 0
\(235\) 1.79227 0.116915
\(236\) 0 0
\(237\) 37.2747 2.42125
\(238\) 0 0
\(239\) −18.4094 −1.19081 −0.595403 0.803427i \(-0.703007\pi\)
−0.595403 + 0.803427i \(0.703007\pi\)
\(240\) 0 0
\(241\) 16.3612 1.05392 0.526958 0.849891i \(-0.323332\pi\)
0.526958 + 0.849891i \(0.323332\pi\)
\(242\) 0 0
\(243\) 22.1829 1.42304
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 38.5083 2.45022
\(248\) 0 0
\(249\) 14.0527 0.890556
\(250\) 0 0
\(251\) 7.18246 0.453353 0.226677 0.973970i \(-0.427214\pi\)
0.226677 + 0.973970i \(0.427214\pi\)
\(252\) 0 0
\(253\) −7.78554 −0.489473
\(254\) 0 0
\(255\) 2.03480 0.127424
\(256\) 0 0
\(257\) 30.1418 1.88020 0.940098 0.340904i \(-0.110733\pi\)
0.940098 + 0.340904i \(0.110733\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −19.6811 −1.21823
\(262\) 0 0
\(263\) 11.7667 0.725567 0.362784 0.931873i \(-0.381826\pi\)
0.362784 + 0.931873i \(0.381826\pi\)
\(264\) 0 0
\(265\) −3.50433 −0.215269
\(266\) 0 0
\(267\) 17.4994 1.07094
\(268\) 0 0
\(269\) 21.7876 1.32842 0.664208 0.747548i \(-0.268769\pi\)
0.664208 + 0.747548i \(0.268769\pi\)
\(270\) 0 0
\(271\) −25.9648 −1.57725 −0.788623 0.614877i \(-0.789206\pi\)
−0.788623 + 0.614877i \(0.789206\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.10147 −0.367932
\(276\) 0 0
\(277\) 22.4372 1.34812 0.674059 0.738677i \(-0.264549\pi\)
0.674059 + 0.738677i \(0.264549\pi\)
\(278\) 0 0
\(279\) −36.8228 −2.20453
\(280\) 0 0
\(281\) 7.42259 0.442795 0.221397 0.975184i \(-0.428938\pi\)
0.221397 + 0.975184i \(0.428938\pi\)
\(282\) 0 0
\(283\) 5.14755 0.305990 0.152995 0.988227i \(-0.451108\pi\)
0.152995 + 0.988227i \(0.451108\pi\)
\(284\) 0 0
\(285\) −5.00520 −0.296482
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −11.8960 −0.699764
\(290\) 0 0
\(291\) −10.0627 −0.589883
\(292\) 0 0
\(293\) 12.0377 0.703248 0.351624 0.936141i \(-0.385630\pi\)
0.351624 + 0.936141i \(0.385630\pi\)
\(294\) 0 0
\(295\) −4.18636 −0.243739
\(296\) 0 0
\(297\) −1.96040 −0.113754
\(298\) 0 0
\(299\) 43.1250 2.49398
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −26.7048 −1.53415
\(304\) 0 0
\(305\) −0.532245 −0.0304763
\(306\) 0 0
\(307\) −28.2014 −1.60954 −0.804770 0.593587i \(-0.797711\pi\)
−0.804770 + 0.593587i \(0.797711\pi\)
\(308\) 0 0
\(309\) 32.7175 1.86124
\(310\) 0 0
\(311\) −16.5467 −0.938280 −0.469140 0.883124i \(-0.655436\pi\)
−0.469140 + 0.883124i \(0.655436\pi\)
\(312\) 0 0
\(313\) −8.91307 −0.503796 −0.251898 0.967754i \(-0.581055\pi\)
−0.251898 + 0.967754i \(0.581055\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.1314 0.906027 0.453014 0.891504i \(-0.350349\pi\)
0.453014 + 0.891504i \(0.350349\pi\)
\(318\) 0 0
\(319\) −6.82113 −0.381910
\(320\) 0 0
\(321\) 30.7455 1.71605
\(322\) 0 0
\(323\) −12.5549 −0.698571
\(324\) 0 0
\(325\) 33.7967 1.87471
\(326\) 0 0
\(327\) 44.6856 2.47112
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.805642 0.0442821 0.0221410 0.999755i \(-0.492952\pi\)
0.0221410 + 0.999755i \(0.492952\pi\)
\(332\) 0 0
\(333\) 7.84268 0.429776
\(334\) 0 0
\(335\) 4.43779 0.242463
\(336\) 0 0
\(337\) −14.3992 −0.784374 −0.392187 0.919885i \(-0.628281\pi\)
−0.392187 + 0.919885i \(0.628281\pi\)
\(338\) 0 0
\(339\) 17.7780 0.965569
\(340\) 0 0
\(341\) −12.7621 −0.691108
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −5.60527 −0.301777
\(346\) 0 0
\(347\) −10.2254 −0.548930 −0.274465 0.961597i \(-0.588501\pi\)
−0.274465 + 0.961597i \(0.588501\pi\)
\(348\) 0 0
\(349\) −6.18647 −0.331154 −0.165577 0.986197i \(-0.552949\pi\)
−0.165577 + 0.986197i \(0.552949\pi\)
\(350\) 0 0
\(351\) 10.8589 0.579604
\(352\) 0 0
\(353\) 21.1981 1.12826 0.564129 0.825687i \(-0.309212\pi\)
0.564129 + 0.825687i \(0.309212\pi\)
\(354\) 0 0
\(355\) −5.80292 −0.307987
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.54401 0.450936 0.225468 0.974251i \(-0.427609\pi\)
0.225468 + 0.974251i \(0.427609\pi\)
\(360\) 0 0
\(361\) 11.8824 0.625392
\(362\) 0 0
\(363\) 24.2565 1.27313
\(364\) 0 0
\(365\) 1.85706 0.0972031
\(366\) 0 0
\(367\) −17.9729 −0.938177 −0.469088 0.883151i \(-0.655417\pi\)
−0.469088 + 0.883151i \(0.655417\pi\)
\(368\) 0 0
\(369\) 3.60954 0.187905
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −35.5814 −1.84233 −0.921166 0.389169i \(-0.872762\pi\)
−0.921166 + 0.389169i \(0.872762\pi\)
\(374\) 0 0
\(375\) −8.89615 −0.459395
\(376\) 0 0
\(377\) 37.7830 1.94592
\(378\) 0 0
\(379\) 19.0487 0.978466 0.489233 0.872153i \(-0.337277\pi\)
0.489233 + 0.872153i \(0.337277\pi\)
\(380\) 0 0
\(381\) −24.4537 −1.25280
\(382\) 0 0
\(383\) −29.2921 −1.49676 −0.748378 0.663273i \(-0.769167\pi\)
−0.748378 + 0.663273i \(0.769167\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.56639 0.282955
\(388\) 0 0
\(389\) 11.6600 0.591188 0.295594 0.955314i \(-0.404482\pi\)
0.295594 + 0.955314i \(0.404482\pi\)
\(390\) 0 0
\(391\) −14.0600 −0.711047
\(392\) 0 0
\(393\) −28.6097 −1.44317
\(394\) 0 0
\(395\) 5.07935 0.255570
\(396\) 0 0
\(397\) 2.82656 0.141861 0.0709304 0.997481i \(-0.477403\pi\)
0.0709304 + 0.997481i \(0.477403\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.46635 −0.472727 −0.236364 0.971665i \(-0.575956\pi\)
−0.236364 + 0.971665i \(0.575956\pi\)
\(402\) 0 0
\(403\) 70.6909 3.52137
\(404\) 0 0
\(405\) 2.38220 0.118373
\(406\) 0 0
\(407\) 2.71813 0.134733
\(408\) 0 0
\(409\) −0.323971 −0.0160194 −0.00800968 0.999968i \(-0.502550\pi\)
−0.00800968 + 0.999968i \(0.502550\pi\)
\(410\) 0 0
\(411\) 51.5734 2.54393
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1.91494 0.0940007
\(416\) 0 0
\(417\) 15.7483 0.771199
\(418\) 0 0
\(419\) −4.52610 −0.221114 −0.110557 0.993870i \(-0.535264\pi\)
−0.110557 + 0.993870i \(0.535264\pi\)
\(420\) 0 0
\(421\) −3.43415 −0.167370 −0.0836851 0.996492i \(-0.526669\pi\)
−0.0836851 + 0.996492i \(0.526669\pi\)
\(422\) 0 0
\(423\) −18.4661 −0.897851
\(424\) 0 0
\(425\) −11.0188 −0.534488
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 22.2865 1.07600
\(430\) 0 0
\(431\) 31.9366 1.53833 0.769166 0.639048i \(-0.220672\pi\)
0.769166 + 0.639048i \(0.220672\pi\)
\(432\) 0 0
\(433\) −12.8577 −0.617904 −0.308952 0.951078i \(-0.599978\pi\)
−0.308952 + 0.951078i \(0.599978\pi\)
\(434\) 0 0
\(435\) −4.91093 −0.235461
\(436\) 0 0
\(437\) 34.5849 1.65442
\(438\) 0 0
\(439\) −6.62979 −0.316422 −0.158211 0.987405i \(-0.550573\pi\)
−0.158211 + 0.987405i \(0.550573\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8.36364 −0.397369 −0.198684 0.980064i \(-0.563667\pi\)
−0.198684 + 0.980064i \(0.563667\pi\)
\(444\) 0 0
\(445\) 2.38461 0.113041
\(446\) 0 0
\(447\) −3.20373 −0.151531
\(448\) 0 0
\(449\) 16.4022 0.774067 0.387034 0.922066i \(-0.373500\pi\)
0.387034 + 0.922066i \(0.373500\pi\)
\(450\) 0 0
\(451\) 1.25100 0.0589074
\(452\) 0 0
\(453\) 5.48446 0.257682
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 23.0384 1.07769 0.538844 0.842405i \(-0.318861\pi\)
0.538844 + 0.842405i \(0.318861\pi\)
\(458\) 0 0
\(459\) −3.54032 −0.165248
\(460\) 0 0
\(461\) −17.1948 −0.800843 −0.400422 0.916331i \(-0.631136\pi\)
−0.400422 + 0.916331i \(0.631136\pi\)
\(462\) 0 0
\(463\) 0.625032 0.0290477 0.0145239 0.999895i \(-0.495377\pi\)
0.0145239 + 0.999895i \(0.495377\pi\)
\(464\) 0 0
\(465\) −9.18821 −0.426093
\(466\) 0 0
\(467\) 27.5985 1.27711 0.638554 0.769577i \(-0.279533\pi\)
0.638554 + 0.769577i \(0.279533\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −20.9726 −0.966367
\(472\) 0 0
\(473\) 1.92921 0.0887052
\(474\) 0 0
\(475\) 27.1039 1.24361
\(476\) 0 0
\(477\) 36.1058 1.65317
\(478\) 0 0
\(479\) 1.39232 0.0636167 0.0318084 0.999494i \(-0.489873\pi\)
0.0318084 + 0.999494i \(0.489873\pi\)
\(480\) 0 0
\(481\) −15.0560 −0.686497
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.37122 −0.0622639
\(486\) 0 0
\(487\) −16.0344 −0.726587 −0.363293 0.931675i \(-0.618348\pi\)
−0.363293 + 0.931675i \(0.618348\pi\)
\(488\) 0 0
\(489\) 32.9269 1.48901
\(490\) 0 0
\(491\) −30.1447 −1.36041 −0.680206 0.733021i \(-0.738110\pi\)
−0.680206 + 0.733021i \(0.738110\pi\)
\(492\) 0 0
\(493\) −12.3184 −0.554793
\(494\) 0 0
\(495\) −1.58194 −0.0711028
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 7.06347 0.316204 0.158102 0.987423i \(-0.449462\pi\)
0.158102 + 0.987423i \(0.449462\pi\)
\(500\) 0 0
\(501\) −48.2910 −2.15748
\(502\) 0 0
\(503\) −39.6493 −1.76788 −0.883938 0.467604i \(-0.845117\pi\)
−0.883938 + 0.467604i \(0.845117\pi\)
\(504\) 0 0
\(505\) −3.63901 −0.161934
\(506\) 0 0
\(507\) −90.0256 −3.99818
\(508\) 0 0
\(509\) 17.7420 0.786401 0.393200 0.919453i \(-0.371368\pi\)
0.393200 + 0.919453i \(0.371368\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 8.70849 0.384489
\(514\) 0 0
\(515\) 4.45836 0.196459
\(516\) 0 0
\(517\) −6.40001 −0.281472
\(518\) 0 0
\(519\) 29.4283 1.29176
\(520\) 0 0
\(521\) 12.2800 0.537996 0.268998 0.963141i \(-0.413308\pi\)
0.268998 + 0.963141i \(0.413308\pi\)
\(522\) 0 0
\(523\) 15.1346 0.661790 0.330895 0.943668i \(-0.392649\pi\)
0.330895 + 0.943668i \(0.392649\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23.0474 −1.00396
\(528\) 0 0
\(529\) 15.7313 0.683968
\(530\) 0 0
\(531\) 43.1329 1.87181
\(532\) 0 0
\(533\) −6.92944 −0.300147
\(534\) 0 0
\(535\) 4.18963 0.181133
\(536\) 0 0
\(537\) −30.3017 −1.30761
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 35.3632 1.52038 0.760192 0.649699i \(-0.225105\pi\)
0.760192 + 0.649699i \(0.225105\pi\)
\(542\) 0 0
\(543\) −2.86436 −0.122922
\(544\) 0 0
\(545\) 6.08923 0.260834
\(546\) 0 0
\(547\) 10.3881 0.444164 0.222082 0.975028i \(-0.428715\pi\)
0.222082 + 0.975028i \(0.428715\pi\)
\(548\) 0 0
\(549\) 5.48383 0.234044
\(550\) 0 0
\(551\) 30.3008 1.29086
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.95694 0.0830676
\(556\) 0 0
\(557\) 26.6247 1.12813 0.564063 0.825732i \(-0.309237\pi\)
0.564063 + 0.825732i \(0.309237\pi\)
\(558\) 0 0
\(559\) −10.6861 −0.451974
\(560\) 0 0
\(561\) −7.26607 −0.306774
\(562\) 0 0
\(563\) −38.5864 −1.62622 −0.813111 0.582109i \(-0.802228\pi\)
−0.813111 + 0.582109i \(0.802228\pi\)
\(564\) 0 0
\(565\) 2.42258 0.101919
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 20.7060 0.868043 0.434021 0.900903i \(-0.357094\pi\)
0.434021 + 0.900903i \(0.357094\pi\)
\(570\) 0 0
\(571\) −2.83108 −0.118477 −0.0592386 0.998244i \(-0.518867\pi\)
−0.0592386 + 0.998244i \(0.518867\pi\)
\(572\) 0 0
\(573\) 60.6459 2.53352
\(574\) 0 0
\(575\) 30.3534 1.26582
\(576\) 0 0
\(577\) 25.6015 1.06580 0.532902 0.846177i \(-0.321102\pi\)
0.532902 + 0.846177i \(0.321102\pi\)
\(578\) 0 0
\(579\) 8.60381 0.357562
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 12.5136 0.518261
\(584\) 0 0
\(585\) 8.76253 0.362286
\(586\) 0 0
\(587\) −9.22208 −0.380636 −0.190318 0.981722i \(-0.560952\pi\)
−0.190318 + 0.981722i \(0.560952\pi\)
\(588\) 0 0
\(589\) 56.6920 2.33595
\(590\) 0 0
\(591\) −7.72641 −0.317822
\(592\) 0 0
\(593\) 5.03402 0.206722 0.103361 0.994644i \(-0.467040\pi\)
0.103361 + 0.994644i \(0.467040\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 25.5878 1.04724
\(598\) 0 0
\(599\) 42.7279 1.74582 0.872908 0.487885i \(-0.162231\pi\)
0.872908 + 0.487885i \(0.162231\pi\)
\(600\) 0 0
\(601\) 13.8634 0.565501 0.282750 0.959194i \(-0.408753\pi\)
0.282750 + 0.959194i \(0.408753\pi\)
\(602\) 0 0
\(603\) −45.7235 −1.86200
\(604\) 0 0
\(605\) 3.30538 0.134383
\(606\) 0 0
\(607\) −33.3140 −1.35217 −0.676086 0.736823i \(-0.736325\pi\)
−0.676086 + 0.736823i \(0.736325\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 35.4504 1.43417
\(612\) 0 0
\(613\) 20.5324 0.829296 0.414648 0.909982i \(-0.363905\pi\)
0.414648 + 0.909982i \(0.363905\pi\)
\(614\) 0 0
\(615\) 0.900670 0.0363185
\(616\) 0 0
\(617\) 33.4990 1.34862 0.674310 0.738448i \(-0.264441\pi\)
0.674310 + 0.738448i \(0.264441\pi\)
\(618\) 0 0
\(619\) 10.0499 0.403938 0.201969 0.979392i \(-0.435266\pi\)
0.201969 + 0.979392i \(0.435266\pi\)
\(620\) 0 0
\(621\) 9.75254 0.391356
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 23.1741 0.926963
\(626\) 0 0
\(627\) 17.8731 0.713782
\(628\) 0 0
\(629\) 4.90873 0.195724
\(630\) 0 0
\(631\) −4.66012 −0.185517 −0.0927583 0.995689i \(-0.529568\pi\)
−0.0927583 + 0.995689i \(0.529568\pi\)
\(632\) 0 0
\(633\) −62.4490 −2.48213
\(634\) 0 0
\(635\) −3.33225 −0.132236
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 59.7886 2.36520
\(640\) 0 0
\(641\) 32.4812 1.28293 0.641466 0.767152i \(-0.278327\pi\)
0.641466 + 0.767152i \(0.278327\pi\)
\(642\) 0 0
\(643\) 19.0063 0.749534 0.374767 0.927119i \(-0.377723\pi\)
0.374767 + 0.927119i \(0.377723\pi\)
\(644\) 0 0
\(645\) 1.38895 0.0546899
\(646\) 0 0
\(647\) −13.9845 −0.549787 −0.274893 0.961475i \(-0.588643\pi\)
−0.274893 + 0.961475i \(0.588643\pi\)
\(648\) 0 0
\(649\) 14.9491 0.586803
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.28550 −0.363370 −0.181685 0.983357i \(-0.558155\pi\)
−0.181685 + 0.983357i \(0.558155\pi\)
\(654\) 0 0
\(655\) −3.89859 −0.152331
\(656\) 0 0
\(657\) −19.1337 −0.746476
\(658\) 0 0
\(659\) 44.3849 1.72899 0.864495 0.502641i \(-0.167638\pi\)
0.864495 + 0.502641i \(0.167638\pi\)
\(660\) 0 0
\(661\) 10.5880 0.411826 0.205913 0.978570i \(-0.433984\pi\)
0.205913 + 0.978570i \(0.433984\pi\)
\(662\) 0 0
\(663\) 40.2476 1.56309
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 33.9336 1.31391
\(668\) 0 0
\(669\) 16.1472 0.624285
\(670\) 0 0
\(671\) 1.90060 0.0733717
\(672\) 0 0
\(673\) 4.47114 0.172350 0.0861749 0.996280i \(-0.472536\pi\)
0.0861749 + 0.996280i \(0.472536\pi\)
\(674\) 0 0
\(675\) 7.64299 0.294179
\(676\) 0 0
\(677\) −11.5640 −0.444439 −0.222219 0.974997i \(-0.571330\pi\)
−0.222219 + 0.974997i \(0.571330\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 42.0300 1.61059
\(682\) 0 0
\(683\) −5.45605 −0.208770 −0.104385 0.994537i \(-0.533287\pi\)
−0.104385 + 0.994537i \(0.533287\pi\)
\(684\) 0 0
\(685\) 7.02781 0.268519
\(686\) 0 0
\(687\) −69.9996 −2.67065
\(688\) 0 0
\(689\) −69.3143 −2.64067
\(690\) 0 0
\(691\) 4.81414 0.183139 0.0915694 0.995799i \(-0.470812\pi\)
0.0915694 + 0.995799i \(0.470812\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.14600 0.0814023
\(696\) 0 0
\(697\) 2.25921 0.0855736
\(698\) 0 0
\(699\) −17.4444 −0.659808
\(700\) 0 0
\(701\) 14.4352 0.545209 0.272604 0.962126i \(-0.412115\pi\)
0.272604 + 0.962126i \(0.412115\pi\)
\(702\) 0 0
\(703\) −12.0745 −0.455398
\(704\) 0 0
\(705\) −4.60774 −0.173538
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −31.1880 −1.17129 −0.585646 0.810567i \(-0.699159\pi\)
−0.585646 + 0.810567i \(0.699159\pi\)
\(710\) 0 0
\(711\) −52.3335 −1.96266
\(712\) 0 0
\(713\) 63.4887 2.37767
\(714\) 0 0
\(715\) 3.03694 0.113575
\(716\) 0 0
\(717\) 47.3288 1.76753
\(718\) 0 0
\(719\) 47.6718 1.77786 0.888930 0.458043i \(-0.151449\pi\)
0.888930 + 0.458043i \(0.151449\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −42.0630 −1.56434
\(724\) 0 0
\(725\) 26.5935 0.987657
\(726\) 0 0
\(727\) −0.960319 −0.0356163 −0.0178081 0.999841i \(-0.505669\pi\)
−0.0178081 + 0.999841i \(0.505669\pi\)
\(728\) 0 0
\(729\) −36.6306 −1.35669
\(730\) 0 0
\(731\) 3.48400 0.128860
\(732\) 0 0
\(733\) 29.4179 1.08657 0.543287 0.839547i \(-0.317180\pi\)
0.543287 + 0.839547i \(0.317180\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −15.8469 −0.583729
\(738\) 0 0
\(739\) −14.3624 −0.528330 −0.264165 0.964478i \(-0.585096\pi\)
−0.264165 + 0.964478i \(0.585096\pi\)
\(740\) 0 0
\(741\) −99.0010 −3.63689
\(742\) 0 0
\(743\) −25.1675 −0.923304 −0.461652 0.887061i \(-0.652743\pi\)
−0.461652 + 0.887061i \(0.652743\pi\)
\(744\) 0 0
\(745\) −0.436566 −0.0159945
\(746\) 0 0
\(747\) −19.7300 −0.721883
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −14.0272 −0.511861 −0.255931 0.966695i \(-0.582382\pi\)
−0.255931 + 0.966695i \(0.582382\pi\)
\(752\) 0 0
\(753\) −18.4654 −0.672917
\(754\) 0 0
\(755\) 0.747357 0.0271991
\(756\) 0 0
\(757\) 28.2649 1.02731 0.513653 0.857998i \(-0.328292\pi\)
0.513653 + 0.857998i \(0.328292\pi\)
\(758\) 0 0
\(759\) 20.0159 0.726530
\(760\) 0 0
\(761\) 0.807994 0.0292897 0.0146449 0.999893i \(-0.495338\pi\)
0.0146449 + 0.999893i \(0.495338\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −2.85685 −0.103290
\(766\) 0 0
\(767\) −82.8046 −2.98990
\(768\) 0 0
\(769\) 13.4595 0.485362 0.242681 0.970106i \(-0.421973\pi\)
0.242681 + 0.970106i \(0.421973\pi\)
\(770\) 0 0
\(771\) −77.4917 −2.79080
\(772\) 0 0
\(773\) 3.16587 0.113868 0.0569342 0.998378i \(-0.481867\pi\)
0.0569342 + 0.998378i \(0.481867\pi\)
\(774\) 0 0
\(775\) 49.7556 1.78727
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.55720 −0.199107
\(780\) 0 0
\(781\) 20.7217 0.741479
\(782\) 0 0
\(783\) 8.54448 0.305355
\(784\) 0 0
\(785\) −2.85790 −0.102003
\(786\) 0 0
\(787\) −6.32819 −0.225576 −0.112788 0.993619i \(-0.535978\pi\)
−0.112788 + 0.993619i \(0.535978\pi\)
\(788\) 0 0
\(789\) −30.2511 −1.07697
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −10.5276 −0.373847
\(794\) 0 0
\(795\) 9.00928 0.319526
\(796\) 0 0
\(797\) −35.7544 −1.26648 −0.633242 0.773954i \(-0.718276\pi\)
−0.633242 + 0.773954i \(0.718276\pi\)
\(798\) 0 0
\(799\) −11.5579 −0.408889
\(800\) 0 0
\(801\) −24.5691 −0.868105
\(802\) 0 0
\(803\) −6.63139 −0.234017
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −56.0139 −1.97178
\(808\) 0 0
\(809\) −10.1618 −0.357269 −0.178634 0.983916i \(-0.557168\pi\)
−0.178634 + 0.983916i \(0.557168\pi\)
\(810\) 0 0
\(811\) −35.3227 −1.24035 −0.620174 0.784465i \(-0.712938\pi\)
−0.620174 + 0.784465i \(0.712938\pi\)
\(812\) 0 0
\(813\) 66.7528 2.34112
\(814\) 0 0
\(815\) 4.48689 0.157169
\(816\) 0 0
\(817\) −8.56994 −0.299824
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −45.0837 −1.57343 −0.786716 0.617315i \(-0.788220\pi\)
−0.786716 + 0.617315i \(0.788220\pi\)
\(822\) 0 0
\(823\) −6.31875 −0.220258 −0.110129 0.993917i \(-0.535126\pi\)
−0.110129 + 0.993917i \(0.535126\pi\)
\(824\) 0 0
\(825\) 15.6863 0.546126
\(826\) 0 0
\(827\) 35.7160 1.24197 0.620983 0.783824i \(-0.286734\pi\)
0.620983 + 0.783824i \(0.286734\pi\)
\(828\) 0 0
\(829\) −23.5906 −0.819334 −0.409667 0.912235i \(-0.634355\pi\)
−0.409667 + 0.912235i \(0.634355\pi\)
\(830\) 0 0
\(831\) −57.6838 −2.00103
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −6.58052 −0.227728
\(836\) 0 0
\(837\) 15.9865 0.552573
\(838\) 0 0
\(839\) 4.93987 0.170543 0.0852716 0.996358i \(-0.472824\pi\)
0.0852716 + 0.996358i \(0.472824\pi\)
\(840\) 0 0
\(841\) 0.730160 0.0251779
\(842\) 0 0
\(843\) −19.0828 −0.657245
\(844\) 0 0
\(845\) −12.2676 −0.422019
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −13.2339 −0.454185
\(850\) 0 0
\(851\) −13.5221 −0.463531
\(852\) 0 0
\(853\) 14.5482 0.498123 0.249061 0.968488i \(-0.419878\pi\)
0.249061 + 0.968488i \(0.419878\pi\)
\(854\) 0 0
\(855\) 7.02728 0.240328
\(856\) 0 0
\(857\) 10.5690 0.361030 0.180515 0.983572i \(-0.442224\pi\)
0.180515 + 0.983572i \(0.442224\pi\)
\(858\) 0 0
\(859\) 3.75541 0.128133 0.0640664 0.997946i \(-0.479593\pi\)
0.0640664 + 0.997946i \(0.479593\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −47.7794 −1.62643 −0.813215 0.581964i \(-0.802285\pi\)
−0.813215 + 0.581964i \(0.802285\pi\)
\(864\) 0 0
\(865\) 4.01014 0.136349
\(866\) 0 0
\(867\) 30.5834 1.03867
\(868\) 0 0
\(869\) −18.1379 −0.615285
\(870\) 0 0
\(871\) 87.7779 2.97424
\(872\) 0 0
\(873\) 14.1279 0.478158
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −7.57739 −0.255870 −0.127935 0.991783i \(-0.540835\pi\)
−0.127935 + 0.991783i \(0.540835\pi\)
\(878\) 0 0
\(879\) −30.9477 −1.04384
\(880\) 0 0
\(881\) 53.4566 1.80100 0.900499 0.434857i \(-0.143201\pi\)
0.900499 + 0.434857i \(0.143201\pi\)
\(882\) 0 0
\(883\) 48.4484 1.63042 0.815209 0.579167i \(-0.196622\pi\)
0.815209 + 0.579167i \(0.196622\pi\)
\(884\) 0 0
\(885\) 10.7627 0.361785
\(886\) 0 0
\(887\) 21.3614 0.717246 0.358623 0.933483i \(-0.383246\pi\)
0.358623 + 0.933483i \(0.383246\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −8.50662 −0.284982
\(892\) 0 0
\(893\) 28.4301 0.951378
\(894\) 0 0
\(895\) −4.12916 −0.138022
\(896\) 0 0
\(897\) −110.870 −3.70185
\(898\) 0 0
\(899\) 55.6242 1.85517
\(900\) 0 0
\(901\) 22.5986 0.752867
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.390321 −0.0129747
\(906\) 0 0
\(907\) −21.6280 −0.718146 −0.359073 0.933310i \(-0.616907\pi\)
−0.359073 + 0.933310i \(0.616907\pi\)
\(908\) 0 0
\(909\) 37.4934 1.24358
\(910\) 0 0
\(911\) −48.3774 −1.60282 −0.801408 0.598118i \(-0.795915\pi\)
−0.801408 + 0.598118i \(0.795915\pi\)
\(912\) 0 0
\(913\) −6.83807 −0.226307
\(914\) 0 0
\(915\) 1.36835 0.0452363
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 50.2774 1.65850 0.829248 0.558880i \(-0.188769\pi\)
0.829248 + 0.558880i \(0.188769\pi\)
\(920\) 0 0
\(921\) 72.5031 2.38906
\(922\) 0 0
\(923\) −114.780 −3.77802
\(924\) 0 0
\(925\) −10.5972 −0.348432
\(926\) 0 0
\(927\) −45.9353 −1.50871
\(928\) 0 0
\(929\) −6.32962 −0.207668 −0.103834 0.994595i \(-0.533111\pi\)
−0.103834 + 0.994595i \(0.533111\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 42.5401 1.39270
\(934\) 0 0
\(935\) −0.990133 −0.0323808
\(936\) 0 0
\(937\) 3.72442 0.121672 0.0608358 0.998148i \(-0.480623\pi\)
0.0608358 + 0.998148i \(0.480623\pi\)
\(938\) 0 0
\(939\) 22.9146 0.747790
\(940\) 0 0
\(941\) −51.8875 −1.69149 −0.845743 0.533591i \(-0.820842\pi\)
−0.845743 + 0.533591i \(0.820842\pi\)
\(942\) 0 0
\(943\) −6.22344 −0.202663
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −20.6641 −0.671492 −0.335746 0.941953i \(-0.608988\pi\)
−0.335746 + 0.941953i \(0.608988\pi\)
\(948\) 0 0
\(949\) 36.7320 1.19237
\(950\) 0 0
\(951\) −41.4721 −1.34483
\(952\) 0 0
\(953\) −1.96240 −0.0635682 −0.0317841 0.999495i \(-0.510119\pi\)
−0.0317841 + 0.999495i \(0.510119\pi\)
\(954\) 0 0
\(955\) 8.26410 0.267420
\(956\) 0 0
\(957\) 17.5365 0.566873
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 73.0713 2.35714
\(962\) 0 0
\(963\) −43.1666 −1.39102
\(964\) 0 0
\(965\) 1.17243 0.0377417
\(966\) 0 0
\(967\) −30.4844 −0.980312 −0.490156 0.871635i \(-0.663060\pi\)
−0.490156 + 0.871635i \(0.663060\pi\)
\(968\) 0 0
\(969\) 32.2773 1.03690
\(970\) 0 0
\(971\) −18.2833 −0.586739 −0.293369 0.955999i \(-0.594777\pi\)
−0.293369 + 0.955999i \(0.594777\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −86.8881 −2.78265
\(976\) 0 0
\(977\) −28.2505 −0.903814 −0.451907 0.892065i \(-0.649256\pi\)
−0.451907 + 0.892065i \(0.649256\pi\)
\(978\) 0 0
\(979\) −8.51520 −0.272147
\(980\) 0 0
\(981\) −62.7385 −2.00309
\(982\) 0 0
\(983\) −37.1779 −1.18579 −0.592895 0.805280i \(-0.702015\pi\)
−0.592895 + 0.805280i \(0.702015\pi\)
\(984\) 0 0
\(985\) −1.05286 −0.0335470
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9.59738 −0.305179
\(990\) 0 0
\(991\) −10.7085 −0.340167 −0.170083 0.985430i \(-0.554404\pi\)
−0.170083 + 0.985430i \(0.554404\pi\)
\(992\) 0 0
\(993\) −2.07123 −0.0657284
\(994\) 0 0
\(995\) 3.48680 0.110539
\(996\) 0 0
\(997\) −13.6742 −0.433065 −0.216533 0.976275i \(-0.569475\pi\)
−0.216533 + 0.976275i \(0.569475\pi\)
\(998\) 0 0
\(999\) −3.40486 −0.107725
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 8036.2.a.k.1.1 5
7.6 odd 2 1148.2.a.d.1.5 5
28.27 even 2 4592.2.a.bc.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1148.2.a.d.1.5 5 7.6 odd 2
4592.2.a.bc.1.1 5 28.27 even 2
8036.2.a.k.1.1 5 1.1 even 1 trivial