Properties

Label 5733.2.a.bf.1.3
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $1$
Dimension $4$
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] = [5733,2,Mod(1,5733)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5733, 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("5733.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.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: \(45.7782354788\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.17428.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 6x^{2} + 4x + 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 273)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.52616\) of defining polynomial
Character \(\chi\) \(=\) 5733.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.670843 q^{2} -1.54997 q^{4} +2.54997 q^{5} -2.38147 q^{8} +O(q^{10})\) \(q+0.670843 q^{2} -1.54997 q^{4} +2.54997 q^{5} -2.38147 q^{8} +1.71063 q^{10} +3.05232 q^{11} -1.00000 q^{13} +1.50235 q^{16} +1.34169 q^{17} -7.60228 q^{19} -3.95238 q^{20} +2.04762 q^{22} -1.84403 q^{23} +1.50235 q^{25} -0.670843 q^{26} +5.60228 q^{29} -10.2857 q^{31} +5.77078 q^{32} +0.900061 q^{34} -9.20457 q^{37} -5.09994 q^{38} -6.07268 q^{40} -8.04762 q^{41} +1.49765 q^{43} -4.73100 q^{44} -1.23706 q^{46} -3.89166 q^{47} +1.00784 q^{50} +1.54997 q^{52} -0.502345 q^{53} +7.78331 q^{55} +3.75825 q^{58} -4.28937 q^{59} +0.683372 q^{61} -6.90006 q^{62} +0.866598 q^{64} -2.54997 q^{65} -7.68806 q^{67} -2.07957 q^{68} +14.2569 q^{71} +12.0189 q^{73} -6.17482 q^{74} +11.7833 q^{76} +4.91891 q^{79} +3.83094 q^{80} -5.39869 q^{82} -1.20828 q^{83} +3.42126 q^{85} +1.00469 q^{86} -7.26900 q^{88} +13.7545 q^{89} +2.85819 q^{92} -2.61069 q^{94} -19.3856 q^{95} +7.18572 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 9 q^{16} - 2 q^{17} - 7 q^{19} - 32 q^{20} - 8 q^{22} - 3 q^{23} + 9 q^{25} + q^{26} - q^{29} - 3 q^{31} - 7 q^{32} + 30 q^{34} + 10 q^{37} + 6 q^{38} + 14 q^{40} - 16 q^{41} + 3 q^{43} + 12 q^{44} - 18 q^{46} + 5 q^{47} - 13 q^{50} - 7 q^{52} - 5 q^{53} - 10 q^{55} - 4 q^{58} - 20 q^{59} - 12 q^{61} - 54 q^{62} + 5 q^{64} + 3 q^{65} - 22 q^{67} - 10 q^{68} + 13 q^{73} + 6 q^{74} + 6 q^{76} + 11 q^{79} - 42 q^{80} - 10 q^{82} + q^{83} + 8 q^{85} + 10 q^{86} - 60 q^{88} - 5 q^{89} - 34 q^{92} - 34 q^{94} - 13 q^{95} + 17 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.670843 0.474358 0.237179 0.971466i \(-0.423777\pi\)
0.237179 + 0.971466i \(0.423777\pi\)
\(3\) 0 0
\(4\) −1.54997 −0.774985
\(5\) 2.54997 1.14038 0.570191 0.821512i \(-0.306869\pi\)
0.570191 + 0.821512i \(0.306869\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.38147 −0.841978
\(9\) 0 0
\(10\) 1.71063 0.540948
\(11\) 3.05232 0.920308 0.460154 0.887839i \(-0.347794\pi\)
0.460154 + 0.887839i \(0.347794\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 1.50235 0.375586
\(17\) 1.34169 0.325407 0.162703 0.986675i \(-0.447979\pi\)
0.162703 + 0.986675i \(0.447979\pi\)
\(18\) 0 0
\(19\) −7.60228 −1.74408 −0.872042 0.489431i \(-0.837204\pi\)
−0.872042 + 0.489431i \(0.837204\pi\)
\(20\) −3.95238 −0.883778
\(21\) 0 0
\(22\) 2.04762 0.436555
\(23\) −1.84403 −0.384507 −0.192254 0.981345i \(-0.561580\pi\)
−0.192254 + 0.981345i \(0.561580\pi\)
\(24\) 0 0
\(25\) 1.50235 0.300469
\(26\) −0.670843 −0.131563
\(27\) 0 0
\(28\) 0 0
\(29\) 5.60228 1.04032 0.520159 0.854069i \(-0.325873\pi\)
0.520159 + 0.854069i \(0.325873\pi\)
\(30\) 0 0
\(31\) −10.2857 −1.84736 −0.923679 0.383167i \(-0.874834\pi\)
−0.923679 + 0.383167i \(0.874834\pi\)
\(32\) 5.77078 1.02014
\(33\) 0 0
\(34\) 0.900061 0.154359
\(35\) 0 0
\(36\) 0 0
\(37\) −9.20457 −1.51322 −0.756611 0.653865i \(-0.773146\pi\)
−0.756611 + 0.653865i \(0.773146\pi\)
\(38\) −5.09994 −0.827319
\(39\) 0 0
\(40\) −6.07268 −0.960175
\(41\) −8.04762 −1.25683 −0.628414 0.777879i \(-0.716296\pi\)
−0.628414 + 0.777879i \(0.716296\pi\)
\(42\) 0 0
\(43\) 1.49765 0.228390 0.114195 0.993458i \(-0.463571\pi\)
0.114195 + 0.993458i \(0.463571\pi\)
\(44\) −4.73100 −0.713224
\(45\) 0 0
\(46\) −1.23706 −0.182394
\(47\) −3.89166 −0.567656 −0.283828 0.958875i \(-0.591605\pi\)
−0.283828 + 0.958875i \(0.591605\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.00784 0.142530
\(51\) 0 0
\(52\) 1.54997 0.214942
\(53\) −0.502345 −0.0690025 −0.0345012 0.999405i \(-0.510984\pi\)
−0.0345012 + 0.999405i \(0.510984\pi\)
\(54\) 0 0
\(55\) 7.78331 1.04950
\(56\) 0 0
\(57\) 0 0
\(58\) 3.75825 0.493483
\(59\) −4.28937 −0.558429 −0.279214 0.960229i \(-0.590074\pi\)
−0.279214 + 0.960229i \(0.590074\pi\)
\(60\) 0 0
\(61\) 0.683372 0.0874968 0.0437484 0.999043i \(-0.486070\pi\)
0.0437484 + 0.999043i \(0.486070\pi\)
\(62\) −6.90006 −0.876309
\(63\) 0 0
\(64\) 0.866598 0.108325
\(65\) −2.54997 −0.316285
\(66\) 0 0
\(67\) −7.68806 −0.939246 −0.469623 0.882867i \(-0.655610\pi\)
−0.469623 + 0.882867i \(0.655610\pi\)
\(68\) −2.07957 −0.252185
\(69\) 0 0
\(70\) 0 0
\(71\) 14.2569 1.69198 0.845990 0.533198i \(-0.179010\pi\)
0.845990 + 0.533198i \(0.179010\pi\)
\(72\) 0 0
\(73\) 12.0189 1.40670 0.703350 0.710844i \(-0.251687\pi\)
0.703350 + 0.710844i \(0.251687\pi\)
\(74\) −6.17482 −0.717808
\(75\) 0 0
\(76\) 11.7833 1.35164
\(77\) 0 0
\(78\) 0 0
\(79\) 4.91891 0.553421 0.276710 0.960953i \(-0.410756\pi\)
0.276710 + 0.960953i \(0.410756\pi\)
\(80\) 3.83094 0.428312
\(81\) 0 0
\(82\) −5.39869 −0.596186
\(83\) −1.20828 −0.132626 −0.0663132 0.997799i \(-0.521124\pi\)
−0.0663132 + 0.997799i \(0.521124\pi\)
\(84\) 0 0
\(85\) 3.42126 0.371088
\(86\) 1.00469 0.108339
\(87\) 0 0
\(88\) −7.26900 −0.774878
\(89\) 13.7545 1.45798 0.728989 0.684525i \(-0.239990\pi\)
0.728989 + 0.684525i \(0.239990\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.85819 0.297987
\(93\) 0 0
\(94\) −2.61069 −0.269272
\(95\) −19.3856 −1.98892
\(96\) 0 0
\(97\) 7.18572 0.729599 0.364800 0.931086i \(-0.381138\pi\)
0.364800 + 0.931086i \(0.381138\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.32859 −0.232859
\(101\) −18.4416 −1.83501 −0.917505 0.397724i \(-0.869800\pi\)
−0.917505 + 0.397724i \(0.869800\pi\)
\(102\) 0 0
\(103\) −1.89537 −0.186756 −0.0933782 0.995631i \(-0.529767\pi\)
−0.0933782 + 0.995631i \(0.529767\pi\)
\(104\) 2.38147 0.233523
\(105\) 0 0
\(106\) −0.336995 −0.0327318
\(107\) −18.5463 −1.79293 −0.896467 0.443110i \(-0.853875\pi\)
−0.896467 + 0.443110i \(0.853875\pi\)
\(108\) 0 0
\(109\) −1.42126 −0.136132 −0.0680659 0.997681i \(-0.521683\pi\)
−0.0680659 + 0.997681i \(0.521683\pi\)
\(110\) 5.22138 0.497839
\(111\) 0 0
\(112\) 0 0
\(113\) −5.60228 −0.527019 −0.263509 0.964657i \(-0.584880\pi\)
−0.263509 + 0.964657i \(0.584880\pi\)
\(114\) 0 0
\(115\) −4.70222 −0.438485
\(116\) −8.68337 −0.806231
\(117\) 0 0
\(118\) −2.87749 −0.264895
\(119\) 0 0
\(120\) 0 0
\(121\) −1.68337 −0.153034
\(122\) 0.458435 0.0415048
\(123\) 0 0
\(124\) 15.9425 1.43167
\(125\) −8.91891 −0.797732
\(126\) 0 0
\(127\) 14.1046 1.25158 0.625792 0.779990i \(-0.284776\pi\)
0.625792 + 0.779990i \(0.284776\pi\)
\(128\) −10.9602 −0.968755
\(129\) 0 0
\(130\) −1.71063 −0.150032
\(131\) −8.78800 −0.767811 −0.383906 0.923372i \(-0.625421\pi\)
−0.383906 + 0.923372i \(0.625421\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.15748 −0.445539
\(135\) 0 0
\(136\) −3.19519 −0.273985
\(137\) 1.97743 0.168944 0.0844718 0.996426i \(-0.473080\pi\)
0.0844718 + 0.996426i \(0.473080\pi\)
\(138\) 0 0
\(139\) −13.0999 −1.11112 −0.555561 0.831476i \(-0.687497\pi\)
−0.555561 + 0.831476i \(0.687497\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 9.56413 0.802604
\(143\) −3.05232 −0.255247
\(144\) 0 0
\(145\) 14.2857 1.18636
\(146\) 8.06276 0.667279
\(147\) 0 0
\(148\) 14.2668 1.17272
\(149\) −14.5939 −1.19558 −0.597789 0.801654i \(-0.703954\pi\)
−0.597789 + 0.801654i \(0.703954\pi\)
\(150\) 0 0
\(151\) −5.41188 −0.440412 −0.220206 0.975453i \(-0.570673\pi\)
−0.220206 + 0.975453i \(0.570673\pi\)
\(152\) 18.1046 1.46848
\(153\) 0 0
\(154\) 0 0
\(155\) −26.2281 −2.10669
\(156\) 0 0
\(157\) −23.4044 −1.86788 −0.933939 0.357432i \(-0.883652\pi\)
−0.933939 + 0.357432i \(0.883652\pi\)
\(158\) 3.29982 0.262519
\(159\) 0 0
\(160\) 14.7153 1.16335
\(161\) 0 0
\(162\) 0 0
\(163\) −10.1046 −0.791456 −0.395728 0.918368i \(-0.629508\pi\)
−0.395728 + 0.918368i \(0.629508\pi\)
\(164\) 12.4736 0.974022
\(165\) 0 0
\(166\) −0.810569 −0.0629123
\(167\) −3.09623 −0.239593 −0.119797 0.992798i \(-0.538224\pi\)
−0.119797 + 0.992798i \(0.538224\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 2.29513 0.176028
\(171\) 0 0
\(172\) −2.32132 −0.176999
\(173\) 2.75356 0.209349 0.104675 0.994507i \(-0.466620\pi\)
0.104675 + 0.994507i \(0.466620\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.58563 0.345655
\(177\) 0 0
\(178\) 9.22714 0.691603
\(179\) 1.57723 0.117887 0.0589437 0.998261i \(-0.481227\pi\)
0.0589437 + 0.998261i \(0.481227\pi\)
\(180\) 0 0
\(181\) −9.51651 −0.707356 −0.353678 0.935367i \(-0.615069\pi\)
−0.353678 + 0.935367i \(0.615069\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.39151 0.323746
\(185\) −23.4714 −1.72565
\(186\) 0 0
\(187\) 4.09525 0.299474
\(188\) 6.03195 0.439925
\(189\) 0 0
\(190\) −13.0047 −0.943459
\(191\) 22.8508 1.65342 0.826712 0.562626i \(-0.190209\pi\)
0.826712 + 0.562626i \(0.190209\pi\)
\(192\) 0 0
\(193\) 19.5760 1.40911 0.704556 0.709649i \(-0.251146\pi\)
0.704556 + 0.709649i \(0.251146\pi\)
\(194\) 4.82049 0.346091
\(195\) 0 0
\(196\) 0 0
\(197\) 21.2271 1.51237 0.756185 0.654357i \(-0.227061\pi\)
0.756185 + 0.654357i \(0.227061\pi\)
\(198\) 0 0
\(199\) 6.68337 0.473772 0.236886 0.971537i \(-0.423873\pi\)
0.236886 + 0.971537i \(0.423873\pi\)
\(200\) −3.57779 −0.252988
\(201\) 0 0
\(202\) −12.3714 −0.870451
\(203\) 0 0
\(204\) 0 0
\(205\) −20.5212 −1.43326
\(206\) −1.27150 −0.0885893
\(207\) 0 0
\(208\) −1.50235 −0.104169
\(209\) −23.2046 −1.60509
\(210\) 0 0
\(211\) −4.60698 −0.317157 −0.158579 0.987346i \(-0.550691\pi\)
−0.158579 + 0.987346i \(0.550691\pi\)
\(212\) 0.778620 0.0534759
\(213\) 0 0
\(214\) −12.4416 −0.850492
\(215\) 3.81897 0.260452
\(216\) 0 0
\(217\) 0 0
\(218\) −0.953441 −0.0645752
\(219\) 0 0
\(220\) −12.0639 −0.813348
\(221\) −1.34169 −0.0902516
\(222\) 0 0
\(223\) −8.60698 −0.576366 −0.288183 0.957575i \(-0.593051\pi\)
−0.288183 + 0.957575i \(0.593051\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.75825 −0.249995
\(227\) −14.4892 −0.961685 −0.480843 0.876807i \(-0.659669\pi\)
−0.480843 + 0.876807i \(0.659669\pi\)
\(228\) 0 0
\(229\) 20.1999 1.33485 0.667423 0.744679i \(-0.267397\pi\)
0.667423 + 0.744679i \(0.267397\pi\)
\(230\) −3.15445 −0.207999
\(231\) 0 0
\(232\) −13.3417 −0.875925
\(233\) −7.28097 −0.476992 −0.238496 0.971143i \(-0.576654\pi\)
−0.238496 + 0.971143i \(0.576654\pi\)
\(234\) 0 0
\(235\) −9.92360 −0.647345
\(236\) 6.64839 0.432774
\(237\) 0 0
\(238\) 0 0
\(239\) −27.6688 −1.78974 −0.894872 0.446323i \(-0.852733\pi\)
−0.894872 + 0.446323i \(0.852733\pi\)
\(240\) 0 0
\(241\) 22.2187 1.43123 0.715617 0.698493i \(-0.246146\pi\)
0.715617 + 0.698493i \(0.246146\pi\)
\(242\) −1.12928 −0.0725928
\(243\) 0 0
\(244\) −1.05921 −0.0678087
\(245\) 0 0
\(246\) 0 0
\(247\) 7.60228 0.483722
\(248\) 24.4950 1.55543
\(249\) 0 0
\(250\) −5.98319 −0.378410
\(251\) 17.3092 1.09255 0.546274 0.837607i \(-0.316046\pi\)
0.546274 + 0.837607i \(0.316046\pi\)
\(252\) 0 0
\(253\) −5.62857 −0.353865
\(254\) 9.46199 0.593698
\(255\) 0 0
\(256\) −9.08578 −0.567861
\(257\) −5.55837 −0.346722 −0.173361 0.984858i \(-0.555463\pi\)
−0.173361 + 0.984858i \(0.555463\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.95238 0.245116
\(261\) 0 0
\(262\) −5.89537 −0.364217
\(263\) −25.0486 −1.54456 −0.772281 0.635281i \(-0.780884\pi\)
−0.772281 + 0.635281i \(0.780884\pi\)
\(264\) 0 0
\(265\) −1.28097 −0.0786891
\(266\) 0 0
\(267\) 0 0
\(268\) 11.9163 0.727902
\(269\) −4.55368 −0.277643 −0.138821 0.990317i \(-0.544331\pi\)
−0.138821 + 0.990317i \(0.544331\pi\)
\(270\) 0 0
\(271\) −8.88325 −0.539619 −0.269810 0.962914i \(-0.586961\pi\)
−0.269810 + 0.962914i \(0.586961\pi\)
\(272\) 2.01568 0.122218
\(273\) 0 0
\(274\) 1.32655 0.0801397
\(275\) 4.58563 0.276524
\(276\) 0 0
\(277\) −5.38560 −0.323589 −0.161795 0.986824i \(-0.551728\pi\)
−0.161795 + 0.986824i \(0.551728\pi\)
\(278\) −8.78800 −0.527069
\(279\) 0 0
\(280\) 0 0
\(281\) 12.9727 0.773889 0.386944 0.922103i \(-0.373531\pi\)
0.386944 + 0.922103i \(0.373531\pi\)
\(282\) 0 0
\(283\) 1.52589 0.0907047 0.0453523 0.998971i \(-0.485559\pi\)
0.0453523 + 0.998971i \(0.485559\pi\)
\(284\) −22.0977 −1.31126
\(285\) 0 0
\(286\) −2.04762 −0.121079
\(287\) 0 0
\(288\) 0 0
\(289\) −15.1999 −0.894111
\(290\) 9.58343 0.562759
\(291\) 0 0
\(292\) −18.6289 −1.09017
\(293\) 18.8545 1.10149 0.550745 0.834673i \(-0.314344\pi\)
0.550745 + 0.834673i \(0.314344\pi\)
\(294\) 0 0
\(295\) −10.9378 −0.636821
\(296\) 21.9204 1.27410
\(297\) 0 0
\(298\) −9.79020 −0.567131
\(299\) 1.84403 0.106643
\(300\) 0 0
\(301\) 0 0
\(302\) −3.63052 −0.208913
\(303\) 0 0
\(304\) −11.4213 −0.655054
\(305\) 1.74258 0.0997797
\(306\) 0 0
\(307\) −15.3856 −0.878102 −0.439051 0.898462i \(-0.644685\pi\)
−0.439051 + 0.898462i \(0.644685\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −17.5949 −0.999326
\(311\) −17.0999 −0.969649 −0.484824 0.874612i \(-0.661116\pi\)
−0.484824 + 0.874612i \(0.661116\pi\)
\(312\) 0 0
\(313\) −4.89263 −0.276548 −0.138274 0.990394i \(-0.544155\pi\)
−0.138274 + 0.990394i \(0.544155\pi\)
\(314\) −15.7007 −0.886042
\(315\) 0 0
\(316\) −7.62417 −0.428893
\(317\) −1.44382 −0.0810933 −0.0405466 0.999178i \(-0.512910\pi\)
−0.0405466 + 0.999178i \(0.512910\pi\)
\(318\) 0 0
\(319\) 17.0999 0.957413
\(320\) 2.20980 0.123531
\(321\) 0 0
\(322\) 0 0
\(323\) −10.1999 −0.567536
\(324\) 0 0
\(325\) −1.50235 −0.0833351
\(326\) −6.77862 −0.375433
\(327\) 0 0
\(328\) 19.1652 1.05822
\(329\) 0 0
\(330\) 0 0
\(331\) −14.9953 −0.824217 −0.412108 0.911135i \(-0.635207\pi\)
−0.412108 + 0.911135i \(0.635207\pi\)
\(332\) 1.87280 0.102783
\(333\) 0 0
\(334\) −2.07708 −0.113653
\(335\) −19.6043 −1.07110
\(336\) 0 0
\(337\) −14.9115 −0.812280 −0.406140 0.913811i \(-0.633126\pi\)
−0.406140 + 0.913811i \(0.633126\pi\)
\(338\) 0.670843 0.0364890
\(339\) 0 0
\(340\) −5.30285 −0.287587
\(341\) −31.3951 −1.70014
\(342\) 0 0
\(343\) 0 0
\(344\) −3.56662 −0.192299
\(345\) 0 0
\(346\) 1.84721 0.0993065
\(347\) −7.07488 −0.379800 −0.189900 0.981803i \(-0.560816\pi\)
−0.189900 + 0.981803i \(0.560816\pi\)
\(348\) 0 0
\(349\) −21.1188 −1.13046 −0.565232 0.824932i \(-0.691213\pi\)
−0.565232 + 0.824932i \(0.691213\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 17.6142 0.938843
\(353\) −17.3643 −0.924206 −0.462103 0.886826i \(-0.652905\pi\)
−0.462103 + 0.886826i \(0.652905\pi\)
\(354\) 0 0
\(355\) 36.3546 1.92950
\(356\) −21.3191 −1.12991
\(357\) 0 0
\(358\) 1.05807 0.0559208
\(359\) −18.3521 −0.968589 −0.484294 0.874905i \(-0.660924\pi\)
−0.484294 + 0.874905i \(0.660924\pi\)
\(360\) 0 0
\(361\) 38.7947 2.04183
\(362\) −6.38408 −0.335540
\(363\) 0 0
\(364\) 0 0
\(365\) 30.6477 1.60417
\(366\) 0 0
\(367\) −8.40719 −0.438852 −0.219426 0.975629i \(-0.570418\pi\)
−0.219426 + 0.975629i \(0.570418\pi\)
\(368\) −2.77037 −0.144416
\(369\) 0 0
\(370\) −15.7456 −0.818575
\(371\) 0 0
\(372\) 0 0
\(373\) 27.0925 1.40280 0.701399 0.712769i \(-0.252559\pi\)
0.701399 + 0.712769i \(0.252559\pi\)
\(374\) 2.74727 0.142058
\(375\) 0 0
\(376\) 9.26787 0.477954
\(377\) −5.60228 −0.288532
\(378\) 0 0
\(379\) −6.41657 −0.329597 −0.164798 0.986327i \(-0.552697\pi\)
−0.164798 + 0.986327i \(0.552697\pi\)
\(380\) 30.0471 1.54138
\(381\) 0 0
\(382\) 15.3293 0.784314
\(383\) 32.5939 1.66547 0.832735 0.553672i \(-0.186774\pi\)
0.832735 + 0.553672i \(0.186774\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13.1324 0.668423
\(387\) 0 0
\(388\) −11.1376 −0.565428
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) −2.47411 −0.125121
\(392\) 0 0
\(393\) 0 0
\(394\) 14.2401 0.717405
\(395\) 12.5431 0.631111
\(396\) 0 0
\(397\) −15.7520 −0.790573 −0.395286 0.918558i \(-0.629355\pi\)
−0.395286 + 0.918558i \(0.629355\pi\)
\(398\) 4.48349 0.224737
\(399\) 0 0
\(400\) 2.25704 0.112852
\(401\) −26.1867 −1.30770 −0.653851 0.756624i \(-0.726848\pi\)
−0.653851 + 0.756624i \(0.726848\pi\)
\(402\) 0 0
\(403\) 10.2857 0.512365
\(404\) 28.5840 1.42211
\(405\) 0 0
\(406\) 0 0
\(407\) −28.0952 −1.39263
\(408\) 0 0
\(409\) 17.3856 0.859662 0.429831 0.902909i \(-0.358573\pi\)
0.429831 + 0.902909i \(0.358573\pi\)
\(410\) −13.7665 −0.679879
\(411\) 0 0
\(412\) 2.93777 0.144733
\(413\) 0 0
\(414\) 0 0
\(415\) −3.08109 −0.151245
\(416\) −5.77078 −0.282936
\(417\) 0 0
\(418\) −15.5666 −0.761388
\(419\) −12.4761 −0.609496 −0.304748 0.952433i \(-0.598572\pi\)
−0.304748 + 0.952433i \(0.598572\pi\)
\(420\) 0 0
\(421\) 9.57405 0.466611 0.233305 0.972404i \(-0.425046\pi\)
0.233305 + 0.972404i \(0.425046\pi\)
\(422\) −3.09056 −0.150446
\(423\) 0 0
\(424\) 1.19632 0.0580985
\(425\) 2.01568 0.0977746
\(426\) 0 0
\(427\) 0 0
\(428\) 28.7461 1.38950
\(429\) 0 0
\(430\) 2.56193 0.123547
\(431\) −5.20208 −0.250575 −0.125288 0.992120i \(-0.539985\pi\)
−0.125288 + 0.992120i \(0.539985\pi\)
\(432\) 0 0
\(433\) 17.2547 0.829207 0.414604 0.910002i \(-0.363920\pi\)
0.414604 + 0.910002i \(0.363920\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.20291 0.105500
\(437\) 14.0189 0.670613
\(438\) 0 0
\(439\) 22.1925 1.05919 0.529594 0.848251i \(-0.322344\pi\)
0.529594 + 0.848251i \(0.322344\pi\)
\(440\) −18.5357 −0.883657
\(441\) 0 0
\(442\) −0.900061 −0.0428115
\(443\) 37.9319 1.80220 0.901098 0.433615i \(-0.142762\pi\)
0.901098 + 0.433615i \(0.142762\pi\)
\(444\) 0 0
\(445\) 35.0737 1.66265
\(446\) −5.77393 −0.273403
\(447\) 0 0
\(448\) 0 0
\(449\) 33.3150 1.57223 0.786115 0.618080i \(-0.212089\pi\)
0.786115 + 0.618080i \(0.212089\pi\)
\(450\) 0 0
\(451\) −24.5639 −1.15667
\(452\) 8.68337 0.408431
\(453\) 0 0
\(454\) −9.72001 −0.456183
\(455\) 0 0
\(456\) 0 0
\(457\) −7.79269 −0.364527 −0.182263 0.983250i \(-0.558342\pi\)
−0.182263 + 0.983250i \(0.558342\pi\)
\(458\) 13.5509 0.633194
\(459\) 0 0
\(460\) 7.28831 0.339819
\(461\) 30.4568 1.41851 0.709256 0.704951i \(-0.249031\pi\)
0.709256 + 0.704951i \(0.249031\pi\)
\(462\) 0 0
\(463\) 39.4639 1.83405 0.917023 0.398835i \(-0.130585\pi\)
0.917023 + 0.398835i \(0.130585\pi\)
\(464\) 8.41657 0.390729
\(465\) 0 0
\(466\) −4.88438 −0.226265
\(467\) −9.93307 −0.459648 −0.229824 0.973232i \(-0.573815\pi\)
−0.229824 + 0.973232i \(0.573815\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −6.65718 −0.307073
\(471\) 0 0
\(472\) 10.2150 0.470184
\(473\) 4.57131 0.210189
\(474\) 0 0
\(475\) −11.4213 −0.524043
\(476\) 0 0
\(477\) 0 0
\(478\) −18.5614 −0.848978
\(479\) −0.941479 −0.0430173 −0.0215086 0.999769i \(-0.506847\pi\)
−0.0215086 + 0.999769i \(0.506847\pi\)
\(480\) 0 0
\(481\) 9.20457 0.419692
\(482\) 14.9053 0.678917
\(483\) 0 0
\(484\) 2.60918 0.118599
\(485\) 18.3234 0.832021
\(486\) 0 0
\(487\) −39.3499 −1.78312 −0.891558 0.452907i \(-0.850387\pi\)
−0.891558 + 0.452907i \(0.850387\pi\)
\(488\) −1.62743 −0.0736703
\(489\) 0 0
\(490\) 0 0
\(491\) −5.45374 −0.246124 −0.123062 0.992399i \(-0.539271\pi\)
−0.123062 + 0.992399i \(0.539271\pi\)
\(492\) 0 0
\(493\) 7.51651 0.338526
\(494\) 5.09994 0.229457
\(495\) 0 0
\(496\) −15.4526 −0.693843
\(497\) 0 0
\(498\) 0 0
\(499\) −31.3574 −1.40375 −0.701874 0.712301i \(-0.747653\pi\)
−0.701874 + 0.712301i \(0.747653\pi\)
\(500\) 13.8240 0.618230
\(501\) 0 0
\(502\) 11.6118 0.518258
\(503\) 43.9926 1.96153 0.980766 0.195188i \(-0.0625316\pi\)
0.980766 + 0.195188i \(0.0625316\pi\)
\(504\) 0 0
\(505\) −47.0256 −2.09261
\(506\) −3.77588 −0.167858
\(507\) 0 0
\(508\) −21.8617 −0.969958
\(509\) −41.8498 −1.85496 −0.927480 0.373874i \(-0.878029\pi\)
−0.927480 + 0.373874i \(0.878029\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 15.8253 0.699386
\(513\) 0 0
\(514\) −3.72880 −0.164470
\(515\) −4.83314 −0.212973
\(516\) 0 0
\(517\) −11.8786 −0.522418
\(518\) 0 0
\(519\) 0 0
\(520\) 6.07268 0.266305
\(521\) 8.32957 0.364925 0.182462 0.983213i \(-0.441593\pi\)
0.182462 + 0.983213i \(0.441593\pi\)
\(522\) 0 0
\(523\) −25.3092 −1.10669 −0.553347 0.832951i \(-0.686650\pi\)
−0.553347 + 0.832951i \(0.686650\pi\)
\(524\) 13.6211 0.595042
\(525\) 0 0
\(526\) −16.8037 −0.732675
\(527\) −13.8001 −0.601143
\(528\) 0 0
\(529\) −19.5995 −0.852154
\(530\) −0.859327 −0.0373268
\(531\) 0 0
\(532\) 0 0
\(533\) 8.04762 0.348581
\(534\) 0 0
\(535\) −47.2924 −2.04463
\(536\) 18.3089 0.790824
\(537\) 0 0
\(538\) −3.05481 −0.131702
\(539\) 0 0
\(540\) 0 0
\(541\) 27.1501 1.16727 0.583636 0.812015i \(-0.301630\pi\)
0.583636 + 0.812015i \(0.301630\pi\)
\(542\) −5.95927 −0.255972
\(543\) 0 0
\(544\) 7.74258 0.331960
\(545\) −3.62417 −0.155242
\(546\) 0 0
\(547\) 27.5949 1.17987 0.589935 0.807450i \(-0.299153\pi\)
0.589935 + 0.807450i \(0.299153\pi\)
\(548\) −3.06496 −0.130929
\(549\) 0 0
\(550\) 3.07624 0.131171
\(551\) −42.5902 −1.81440
\(552\) 0 0
\(553\) 0 0
\(554\) −3.61289 −0.153497
\(555\) 0 0
\(556\) 20.3045 0.861103
\(557\) −7.19881 −0.305024 −0.152512 0.988302i \(-0.548736\pi\)
−0.152512 + 0.988302i \(0.548736\pi\)
\(558\) 0 0
\(559\) −1.49765 −0.0633440
\(560\) 0 0
\(561\) 0 0
\(562\) 8.70267 0.367100
\(563\) −20.2594 −0.853831 −0.426915 0.904292i \(-0.640400\pi\)
−0.426915 + 0.904292i \(0.640400\pi\)
\(564\) 0 0
\(565\) −14.2857 −0.601002
\(566\) 1.02363 0.0430265
\(567\) 0 0
\(568\) −33.9524 −1.42461
\(569\) −7.28097 −0.305234 −0.152617 0.988285i \(-0.548770\pi\)
−0.152617 + 0.988285i \(0.548770\pi\)
\(570\) 0 0
\(571\) −22.1141 −0.925446 −0.462723 0.886503i \(-0.653128\pi\)
−0.462723 + 0.886503i \(0.653128\pi\)
\(572\) 4.73100 0.197813
\(573\) 0 0
\(574\) 0 0
\(575\) −2.77037 −0.115533
\(576\) 0 0
\(577\) −20.3139 −0.845678 −0.422839 0.906205i \(-0.638966\pi\)
−0.422839 + 0.906205i \(0.638966\pi\)
\(578\) −10.1967 −0.424128
\(579\) 0 0
\(580\) −22.1423 −0.919410
\(581\) 0 0
\(582\) 0 0
\(583\) −1.53332 −0.0635035
\(584\) −28.6226 −1.18441
\(585\) 0 0
\(586\) 12.6484 0.522500
\(587\) 35.8842 1.48110 0.740550 0.672001i \(-0.234565\pi\)
0.740550 + 0.672001i \(0.234565\pi\)
\(588\) 0 0
\(589\) 78.1945 3.22195
\(590\) −7.33752 −0.302081
\(591\) 0 0
\(592\) −13.8284 −0.568346
\(593\) 20.2664 0.832239 0.416120 0.909310i \(-0.363390\pi\)
0.416120 + 0.909310i \(0.363390\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 22.6201 0.926554
\(597\) 0 0
\(598\) 1.23706 0.0505870
\(599\) −14.9365 −0.610291 −0.305145 0.952306i \(-0.598705\pi\)
−0.305145 + 0.952306i \(0.598705\pi\)
\(600\) 0 0
\(601\) −4.89263 −0.199575 −0.0997873 0.995009i \(-0.531816\pi\)
−0.0997873 + 0.995009i \(0.531816\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 8.38824 0.341313
\(605\) −4.29255 −0.174517
\(606\) 0 0
\(607\) −20.6164 −0.836796 −0.418398 0.908264i \(-0.637408\pi\)
−0.418398 + 0.908264i \(0.637408\pi\)
\(608\) −43.8711 −1.77921
\(609\) 0 0
\(610\) 1.16900 0.0473313
\(611\) 3.89166 0.157440
\(612\) 0 0
\(613\) −9.73818 −0.393321 −0.196661 0.980472i \(-0.563010\pi\)
−0.196661 + 0.980472i \(0.563010\pi\)
\(614\) −10.3213 −0.416535
\(615\) 0 0
\(616\) 0 0
\(617\) 0.763482 0.0307366 0.0153683 0.999882i \(-0.495108\pi\)
0.0153683 + 0.999882i \(0.495108\pi\)
\(618\) 0 0
\(619\) 41.0925 1.65165 0.825824 0.563928i \(-0.190711\pi\)
0.825824 + 0.563928i \(0.190711\pi\)
\(620\) 40.6528 1.63265
\(621\) 0 0
\(622\) −11.4714 −0.459960
\(623\) 0 0
\(624\) 0 0
\(625\) −30.2547 −1.21019
\(626\) −3.28219 −0.131183
\(627\) 0 0
\(628\) 36.2762 1.44758
\(629\) −12.3496 −0.492412
\(630\) 0 0
\(631\) −14.4667 −0.575910 −0.287955 0.957644i \(-0.592975\pi\)
−0.287955 + 0.957644i \(0.592975\pi\)
\(632\) −11.7143 −0.465968
\(633\) 0 0
\(634\) −0.968580 −0.0384672
\(635\) 35.9664 1.42728
\(636\) 0 0
\(637\) 0 0
\(638\) 11.4714 0.454156
\(639\) 0 0
\(640\) −27.9482 −1.10475
\(641\) −35.7069 −1.41034 −0.705169 0.709039i \(-0.749129\pi\)
−0.705169 + 0.709039i \(0.749129\pi\)
\(642\) 0 0
\(643\) 26.4091 1.04147 0.520737 0.853717i \(-0.325657\pi\)
0.520737 + 0.853717i \(0.325657\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.84252 −0.269215
\(647\) 37.3543 1.46855 0.734275 0.678852i \(-0.237522\pi\)
0.734275 + 0.678852i \(0.237522\pi\)
\(648\) 0 0
\(649\) −13.0925 −0.513926
\(650\) −1.00784 −0.0395307
\(651\) 0 0
\(652\) 15.6619 0.613366
\(653\) 0.987881 0.0386588 0.0193294 0.999813i \(-0.493847\pi\)
0.0193294 + 0.999813i \(0.493847\pi\)
\(654\) 0 0
\(655\) −22.4091 −0.875598
\(656\) −12.0903 −0.472047
\(657\) 0 0
\(658\) 0 0
\(659\) 1.24653 0.0485578 0.0242789 0.999705i \(-0.492271\pi\)
0.0242789 + 0.999705i \(0.492271\pi\)
\(660\) 0 0
\(661\) 33.8994 1.31853 0.659266 0.751910i \(-0.270867\pi\)
0.659266 + 0.751910i \(0.270867\pi\)
\(662\) −10.0595 −0.390973
\(663\) 0 0
\(664\) 2.87749 0.111668
\(665\) 0 0
\(666\) 0 0
\(667\) −10.3308 −0.400010
\(668\) 4.79906 0.185681
\(669\) 0 0
\(670\) −13.1514 −0.508084
\(671\) 2.08587 0.0805240
\(672\) 0 0
\(673\) 42.5808 1.64137 0.820684 0.571382i \(-0.193592\pi\)
0.820684 + 0.571382i \(0.193592\pi\)
\(674\) −10.0033 −0.385311
\(675\) 0 0
\(676\) −1.54997 −0.0596142
\(677\) −33.8629 −1.30146 −0.650728 0.759311i \(-0.725536\pi\)
−0.650728 + 0.759311i \(0.725536\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −8.14763 −0.312447
\(681\) 0 0
\(682\) −21.0612 −0.806473
\(683\) 34.5163 1.32073 0.660364 0.750946i \(-0.270402\pi\)
0.660364 + 0.750946i \(0.270402\pi\)
\(684\) 0 0
\(685\) 5.04240 0.192660
\(686\) 0 0
\(687\) 0 0
\(688\) 2.24999 0.0857802
\(689\) 0.502345 0.0191378
\(690\) 0 0
\(691\) 7.90679 0.300789 0.150394 0.988626i \(-0.451946\pi\)
0.150394 + 0.988626i \(0.451946\pi\)
\(692\) −4.26794 −0.162243
\(693\) 0 0
\(694\) −4.74613 −0.180161
\(695\) −33.4044 −1.26710
\(696\) 0 0
\(697\) −10.7974 −0.408980
\(698\) −14.1674 −0.536244
\(699\) 0 0
\(700\) 0 0
\(701\) 5.19510 0.196216 0.0981081 0.995176i \(-0.468721\pi\)
0.0981081 + 0.995176i \(0.468721\pi\)
\(702\) 0 0
\(703\) 69.9758 2.63919
\(704\) 2.64513 0.0996921
\(705\) 0 0
\(706\) −11.6487 −0.438404
\(707\) 0 0
\(708\) 0 0
\(709\) 33.1971 1.24674 0.623372 0.781925i \(-0.285762\pi\)
0.623372 + 0.781925i \(0.285762\pi\)
\(710\) 24.3882 0.915275
\(711\) 0 0
\(712\) −32.7561 −1.22759
\(713\) 18.9671 0.710323
\(714\) 0 0
\(715\) −7.78331 −0.291079
\(716\) −2.44465 −0.0913610
\(717\) 0 0
\(718\) −12.3114 −0.459457
\(719\) 30.7261 1.14589 0.572944 0.819594i \(-0.305801\pi\)
0.572944 + 0.819594i \(0.305801\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 26.0252 0.968557
\(723\) 0 0
\(724\) 14.7503 0.548190
\(725\) 8.41657 0.312583
\(726\) 0 0
\(727\) −1.83783 −0.0681612 −0.0340806 0.999419i \(-0.510850\pi\)
−0.0340806 + 0.999419i \(0.510850\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 20.5598 0.760952
\(731\) 2.00938 0.0743197
\(732\) 0 0
\(733\) 19.1857 0.708641 0.354320 0.935124i \(-0.384712\pi\)
0.354320 + 0.935124i \(0.384712\pi\)
\(734\) −5.63990 −0.208173
\(735\) 0 0
\(736\) −10.6415 −0.392251
\(737\) −23.4664 −0.864396
\(738\) 0 0
\(739\) −21.4882 −0.790456 −0.395228 0.918583i \(-0.629334\pi\)
−0.395228 + 0.918583i \(0.629334\pi\)
\(740\) 36.3799 1.33735
\(741\) 0 0
\(742\) 0 0
\(743\) −19.9430 −0.731637 −0.365819 0.930686i \(-0.619211\pi\)
−0.365819 + 0.930686i \(0.619211\pi\)
\(744\) 0 0
\(745\) −37.2140 −1.36341
\(746\) 18.1748 0.665427
\(747\) 0 0
\(748\) −6.34751 −0.232088
\(749\) 0 0
\(750\) 0 0
\(751\) 38.4498 1.40305 0.701526 0.712644i \(-0.252502\pi\)
0.701526 + 0.712644i \(0.252502\pi\)
\(752\) −5.84661 −0.213204
\(753\) 0 0
\(754\) −3.75825 −0.136868
\(755\) −13.8001 −0.502238
\(756\) 0 0
\(757\) −16.2931 −0.592182 −0.296091 0.955160i \(-0.595683\pi\)
−0.296091 + 0.955160i \(0.595683\pi\)
\(758\) −4.30451 −0.156347
\(759\) 0 0
\(760\) 46.1663 1.67463
\(761\) 35.3380 1.28100 0.640500 0.767958i \(-0.278727\pi\)
0.640500 + 0.767958i \(0.278727\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −35.4180 −1.28138
\(765\) 0 0
\(766\) 21.8654 0.790028
\(767\) 4.28937 0.154880
\(768\) 0 0
\(769\) 11.5428 0.416244 0.208122 0.978103i \(-0.433265\pi\)
0.208122 + 0.978103i \(0.433265\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −30.3422 −1.09204
\(773\) −5.89786 −0.212131 −0.106066 0.994359i \(-0.533825\pi\)
−0.106066 + 0.994359i \(0.533825\pi\)
\(774\) 0 0
\(775\) −15.4526 −0.555074
\(776\) −17.1126 −0.614306
\(777\) 0 0
\(778\) −4.02506 −0.144305
\(779\) 61.1803 2.19201
\(780\) 0 0
\(781\) 43.5165 1.55714
\(782\) −1.65974 −0.0593522
\(783\) 0 0
\(784\) 0 0
\(785\) −59.6806 −2.13009
\(786\) 0 0
\(787\) −6.33079 −0.225668 −0.112834 0.993614i \(-0.535993\pi\)
−0.112834 + 0.993614i \(0.535993\pi\)
\(788\) −32.9014 −1.17206
\(789\) 0 0
\(790\) 8.41444 0.299372
\(791\) 0 0
\(792\) 0 0
\(793\) −0.683372 −0.0242672
\(794\) −10.5672 −0.375014
\(795\) 0 0
\(796\) −10.3590 −0.367166
\(797\) −22.0721 −0.781835 −0.390918 0.920426i \(-0.627842\pi\)
−0.390918 + 0.920426i \(0.627842\pi\)
\(798\) 0 0
\(799\) −5.22138 −0.184719
\(800\) 8.66971 0.306520
\(801\) 0 0
\(802\) −17.5672 −0.620318
\(803\) 36.6853 1.29460
\(804\) 0 0
\(805\) 0 0
\(806\) 6.90006 0.243044
\(807\) 0 0
\(808\) 43.9182 1.54504
\(809\) −36.2019 −1.27279 −0.636396 0.771363i \(-0.719576\pi\)
−0.636396 + 0.771363i \(0.719576\pi\)
\(810\) 0 0
\(811\) 52.4950 1.84335 0.921674 0.387964i \(-0.126822\pi\)
0.921674 + 0.387964i \(0.126822\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −18.8475 −0.660605
\(815\) −25.7665 −0.902561
\(816\) 0 0
\(817\) −11.3856 −0.398332
\(818\) 11.6630 0.407787
\(819\) 0 0
\(820\) 31.8072 1.11076
\(821\) 0.972743 0.0339490 0.0169745 0.999856i \(-0.494597\pi\)
0.0169745 + 0.999856i \(0.494597\pi\)
\(822\) 0 0
\(823\) −29.5572 −1.03030 −0.515150 0.857100i \(-0.672264\pi\)
−0.515150 + 0.857100i \(0.672264\pi\)
\(824\) 4.51377 0.157245
\(825\) 0 0
\(826\) 0 0
\(827\) −15.3191 −0.532698 −0.266349 0.963877i \(-0.585817\pi\)
−0.266349 + 0.963877i \(0.585817\pi\)
\(828\) 0 0
\(829\) −27.0236 −0.938570 −0.469285 0.883047i \(-0.655488\pi\)
−0.469285 + 0.883047i \(0.655488\pi\)
\(830\) −2.06693 −0.0717440
\(831\) 0 0
\(832\) −0.866598 −0.0300439
\(833\) 0 0
\(834\) 0 0
\(835\) −7.89528 −0.273227
\(836\) 35.9664 1.24392
\(837\) 0 0
\(838\) −8.36948 −0.289119
\(839\) 46.2200 1.59569 0.797846 0.602862i \(-0.205973\pi\)
0.797846 + 0.602862i \(0.205973\pi\)
\(840\) 0 0
\(841\) 2.38560 0.0822619
\(842\) 6.42268 0.221340
\(843\) 0 0
\(844\) 7.14067 0.245792
\(845\) 2.54997 0.0877216
\(846\) 0 0
\(847\) 0 0
\(848\) −0.754696 −0.0259164
\(849\) 0 0
\(850\) 1.35220 0.0463801
\(851\) 16.9735 0.581845
\(852\) 0 0
\(853\) 15.1094 0.517336 0.258668 0.965966i \(-0.416716\pi\)
0.258668 + 0.965966i \(0.416716\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 44.1674 1.50961
\(857\) −0.191631 −0.00654599 −0.00327299 0.999995i \(-0.501042\pi\)
−0.00327299 + 0.999995i \(0.501042\pi\)
\(858\) 0 0
\(859\) −7.06419 −0.241027 −0.120514 0.992712i \(-0.538454\pi\)
−0.120514 + 0.992712i \(0.538454\pi\)
\(860\) −5.91929 −0.201846
\(861\) 0 0
\(862\) −3.48978 −0.118862
\(863\) −41.6142 −1.41657 −0.708283 0.705929i \(-0.750530\pi\)
−0.708283 + 0.705929i \(0.750530\pi\)
\(864\) 0 0
\(865\) 7.02150 0.238738
\(866\) 11.5752 0.393341
\(867\) 0 0
\(868\) 0 0
\(869\) 15.0141 0.509318
\(870\) 0 0
\(871\) 7.68806 0.260500
\(872\) 3.38469 0.114620
\(873\) 0 0
\(874\) 9.40445 0.318110
\(875\) 0 0
\(876\) 0 0
\(877\) −52.5471 −1.77439 −0.887194 0.461396i \(-0.847349\pi\)
−0.887194 + 0.461396i \(0.847349\pi\)
\(878\) 14.8876 0.502434
\(879\) 0 0
\(880\) 11.6932 0.394178
\(881\) 0.934500 0.0314841 0.0157421 0.999876i \(-0.494989\pi\)
0.0157421 + 0.999876i \(0.494989\pi\)
\(882\) 0 0
\(883\) −42.6448 −1.43511 −0.717555 0.696501i \(-0.754739\pi\)
−0.717555 + 0.696501i \(0.754739\pi\)
\(884\) 2.07957 0.0699436
\(885\) 0 0
\(886\) 25.4463 0.854886
\(887\) 24.8833 0.835498 0.417749 0.908563i \(-0.362819\pi\)
0.417749 + 0.908563i \(0.362819\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 23.5289 0.788691
\(891\) 0 0
\(892\) 13.3406 0.446675
\(893\) 29.5855 0.990040
\(894\) 0 0
\(895\) 4.02188 0.134437
\(896\) 0 0
\(897\) 0 0
\(898\) 22.3491 0.745799
\(899\) −57.6232 −1.92184
\(900\) 0 0
\(901\) −0.673990 −0.0224539
\(902\) −16.4785 −0.548674
\(903\) 0 0
\(904\) 13.3417 0.443738
\(905\) −24.2668 −0.806656
\(906\) 0 0
\(907\) 42.2207 1.40191 0.700957 0.713203i \(-0.252756\pi\)
0.700957 + 0.713203i \(0.252756\pi\)
\(908\) 22.4579 0.745292
\(909\) 0 0
\(910\) 0 0
\(911\) −14.1108 −0.467513 −0.233756 0.972295i \(-0.575102\pi\)
−0.233756 + 0.972295i \(0.575102\pi\)
\(912\) 0 0
\(913\) −3.68806 −0.122057
\(914\) −5.22767 −0.172916
\(915\) 0 0
\(916\) −31.3092 −1.03449
\(917\) 0 0
\(918\) 0 0
\(919\) −18.1547 −0.598870 −0.299435 0.954117i \(-0.596798\pi\)
−0.299435 + 0.954117i \(0.596798\pi\)
\(920\) 11.1982 0.369194
\(921\) 0 0
\(922\) 20.4317 0.672882
\(923\) −14.2569 −0.469271
\(924\) 0 0
\(925\) −13.8284 −0.454676
\(926\) 26.4741 0.869993
\(927\) 0 0
\(928\) 32.3296 1.06127
\(929\) −8.24741 −0.270589 −0.135294 0.990805i \(-0.543198\pi\)
−0.135294 + 0.990805i \(0.543198\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 11.2853 0.369662
\(933\) 0 0
\(934\) −6.66353 −0.218037
\(935\) 10.4428 0.341515
\(936\) 0 0
\(937\) 21.6693 0.707905 0.353953 0.935263i \(-0.384837\pi\)
0.353953 + 0.935263i \(0.384837\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 15.3813 0.501682
\(941\) 42.5238 1.38624 0.693118 0.720824i \(-0.256237\pi\)
0.693118 + 0.720824i \(0.256237\pi\)
\(942\) 0 0
\(943\) 14.8401 0.483259
\(944\) −6.44412 −0.209738
\(945\) 0 0
\(946\) 3.06663 0.0997049
\(947\) 6.79792 0.220903 0.110451 0.993882i \(-0.464770\pi\)
0.110451 + 0.993882i \(0.464770\pi\)
\(948\) 0 0
\(949\) −12.0189 −0.390148
\(950\) −7.66187 −0.248584
\(951\) 0 0
\(952\) 0 0
\(953\) −57.3782 −1.85866 −0.929331 0.369249i \(-0.879615\pi\)
−0.929331 + 0.369249i \(0.879615\pi\)
\(954\) 0 0
\(955\) 58.2688 1.88553
\(956\) 42.8857 1.38702
\(957\) 0 0
\(958\) −0.631585 −0.0204056
\(959\) 0 0
\(960\) 0 0
\(961\) 74.7947 2.41273
\(962\) 6.17482 0.199084
\(963\) 0 0
\(964\) −34.4384 −1.10918
\(965\) 49.9182 1.60692
\(966\) 0 0
\(967\) 7.52393 0.241953 0.120977 0.992655i \(-0.461397\pi\)
0.120977 + 0.992655i \(0.461397\pi\)
\(968\) 4.00890 0.128851
\(969\) 0 0
\(970\) 12.2921 0.394675
\(971\) −18.5807 −0.596283 −0.298141 0.954522i \(-0.596367\pi\)
−0.298141 + 0.954522i \(0.596367\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −26.3976 −0.845835
\(975\) 0 0
\(976\) 1.02666 0.0328626
\(977\) 38.5939 1.23473 0.617364 0.786678i \(-0.288201\pi\)
0.617364 + 0.786678i \(0.288201\pi\)
\(978\) 0 0
\(979\) 41.9832 1.34179
\(980\) 0 0
\(981\) 0 0
\(982\) −3.65861 −0.116751
\(983\) −0.591837 −0.0188767 −0.00943834 0.999955i \(-0.503004\pi\)
−0.00943834 + 0.999955i \(0.503004\pi\)
\(984\) 0 0
\(985\) 54.1286 1.72468
\(986\) 5.04240 0.160583
\(987\) 0 0
\(988\) −11.7833 −0.374877
\(989\) −2.76172 −0.0878177
\(990\) 0 0
\(991\) 9.41686 0.299136 0.149568 0.988751i \(-0.452212\pi\)
0.149568 + 0.988751i \(0.452212\pi\)
\(992\) −59.3563 −1.88456
\(993\) 0 0
\(994\) 0 0
\(995\) 17.0424 0.540280
\(996\) 0 0
\(997\) −22.1716 −0.702180 −0.351090 0.936342i \(-0.614189\pi\)
−0.351090 + 0.936342i \(0.614189\pi\)
\(998\) −21.0359 −0.665879
\(999\) 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 5733.2.a.bf.1.3 4
3.2 odd 2 1911.2.a.s.1.2 4
7.6 odd 2 819.2.a.k.1.3 4
21.20 even 2 273.2.a.e.1.2 4
84.83 odd 2 4368.2.a.br.1.4 4
105.104 even 2 6825.2.a.bg.1.3 4
273.272 even 2 3549.2.a.w.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.a.e.1.2 4 21.20 even 2
819.2.a.k.1.3 4 7.6 odd 2
1911.2.a.s.1.2 4 3.2 odd 2
3549.2.a.w.1.3 4 273.272 even 2
4368.2.a.br.1.4 4 84.83 odd 2
5733.2.a.bf.1.3 4 1.1 even 1 trivial
6825.2.a.bg.1.3 4 105.104 even 2