Properties

Label 4840.2.a.r.1.2
Level $4840$
Weight $2$
Character 4840.1
Self dual yes
Analytic conductor $38.648$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4840,2,Mod(1,4840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4840, 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("4840.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4840.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: \(38.6475945783\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.12489\) of defining polynomial
Character \(\chi\) \(=\) 4840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.484862 q^{3} +1.00000 q^{5} +0.484862 q^{7} -2.76491 q^{9} +O(q^{10})\) \(q-0.484862 q^{3} +1.00000 q^{5} +0.484862 q^{7} -2.76491 q^{9} -5.28005 q^{13} -0.484862 q^{15} -2.48486 q^{17} +4.73463 q^{19} -0.235091 q^{21} +4.24977 q^{23} +1.00000 q^{25} +2.79518 q^{27} +3.76491 q^{29} -0.235091 q^{31} +0.484862 q^{35} +5.76491 q^{37} +2.56009 q^{39} +0.969724 q^{41} +0.249771 q^{43} -2.76491 q^{45} +3.28005 q^{47} -6.76491 q^{49} +1.20482 q^{51} +5.76491 q^{53} -2.29564 q^{57} -12.4995 q^{59} -9.70436 q^{61} -1.34060 q^{63} -5.28005 q^{65} -10.3103 q^{67} -2.06055 q^{69} -5.70436 q^{71} +1.75023 q^{73} -0.484862 q^{75} -12.0000 q^{79} +6.93945 q^{81} -16.7493 q^{83} -2.48486 q^{85} -1.82546 q^{87} +3.82546 q^{89} -2.56009 q^{91} +0.113987 q^{93} +4.73463 q^{95} +6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} + 3 q^{5} + q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{3} + 3 q^{5} + q^{7} + 8 q^{9} - q^{15} - 7 q^{17} - 3 q^{19} - 17 q^{21} - 4 q^{23} + 3 q^{25} - 7 q^{27} - 5 q^{29} - 17 q^{31} + q^{35} + q^{37} - 24 q^{39} + 2 q^{41} - 16 q^{43} + 8 q^{45} - 6 q^{47} - 4 q^{49} + 19 q^{51} + q^{53} - 25 q^{57} - 4 q^{59} - 11 q^{61} + 10 q^{63} - 16 q^{67} - 8 q^{69} + q^{71} + 22 q^{73} - q^{75} - 36 q^{79} + 19 q^{81} - 7 q^{85} + 9 q^{87} - 3 q^{89} + 24 q^{91} + 13 q^{93} - 3 q^{95} + 18 q^{97}+O(q^{100}) \) 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
\(3\) −0.484862 −0.279935 −0.139968 0.990156i \(-0.544700\pi\)
−0.139968 + 0.990156i \(0.544700\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.484862 0.183261 0.0916303 0.995793i \(-0.470792\pi\)
0.0916303 + 0.995793i \(0.470792\pi\)
\(8\) 0 0
\(9\) −2.76491 −0.921636
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −5.28005 −1.46442 −0.732211 0.681078i \(-0.761511\pi\)
−0.732211 + 0.681078i \(0.761511\pi\)
\(14\) 0 0
\(15\) −0.484862 −0.125191
\(16\) 0 0
\(17\) −2.48486 −0.602668 −0.301334 0.953519i \(-0.597432\pi\)
−0.301334 + 0.953519i \(0.597432\pi\)
\(18\) 0 0
\(19\) 4.73463 1.08620 0.543100 0.839668i \(-0.317251\pi\)
0.543100 + 0.839668i \(0.317251\pi\)
\(20\) 0 0
\(21\) −0.235091 −0.0513011
\(22\) 0 0
\(23\) 4.24977 0.886138 0.443069 0.896487i \(-0.353890\pi\)
0.443069 + 0.896487i \(0.353890\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 2.79518 0.537934
\(28\) 0 0
\(29\) 3.76491 0.699126 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(30\) 0 0
\(31\) −0.235091 −0.0422236 −0.0211118 0.999777i \(-0.506721\pi\)
−0.0211118 + 0.999777i \(0.506721\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.484862 0.0819566
\(36\) 0 0
\(37\) 5.76491 0.947745 0.473873 0.880593i \(-0.342856\pi\)
0.473873 + 0.880593i \(0.342856\pi\)
\(38\) 0 0
\(39\) 2.56009 0.409943
\(40\) 0 0
\(41\) 0.969724 0.151445 0.0757227 0.997129i \(-0.475874\pi\)
0.0757227 + 0.997129i \(0.475874\pi\)
\(42\) 0 0
\(43\) 0.249771 0.0380897 0.0190448 0.999819i \(-0.493937\pi\)
0.0190448 + 0.999819i \(0.493937\pi\)
\(44\) 0 0
\(45\) −2.76491 −0.412168
\(46\) 0 0
\(47\) 3.28005 0.478444 0.239222 0.970965i \(-0.423108\pi\)
0.239222 + 0.970965i \(0.423108\pi\)
\(48\) 0 0
\(49\) −6.76491 −0.966416
\(50\) 0 0
\(51\) 1.20482 0.168708
\(52\) 0 0
\(53\) 5.76491 0.791871 0.395936 0.918278i \(-0.370420\pi\)
0.395936 + 0.918278i \(0.370420\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.29564 −0.304065
\(58\) 0 0
\(59\) −12.4995 −1.62730 −0.813651 0.581354i \(-0.802523\pi\)
−0.813651 + 0.581354i \(0.802523\pi\)
\(60\) 0 0
\(61\) −9.70436 −1.24252 −0.621258 0.783606i \(-0.713378\pi\)
−0.621258 + 0.783606i \(0.713378\pi\)
\(62\) 0 0
\(63\) −1.34060 −0.168900
\(64\) 0 0
\(65\) −5.28005 −0.654909
\(66\) 0 0
\(67\) −10.3103 −1.25961 −0.629803 0.776755i \(-0.716864\pi\)
−0.629803 + 0.776755i \(0.716864\pi\)
\(68\) 0 0
\(69\) −2.06055 −0.248061
\(70\) 0 0
\(71\) −5.70436 −0.676983 −0.338491 0.940970i \(-0.609917\pi\)
−0.338491 + 0.940970i \(0.609917\pi\)
\(72\) 0 0
\(73\) 1.75023 0.204849 0.102424 0.994741i \(-0.467340\pi\)
0.102424 + 0.994741i \(0.467340\pi\)
\(74\) 0 0
\(75\) −0.484862 −0.0559870
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 0 0
\(81\) 6.93945 0.771050
\(82\) 0 0
\(83\) −16.7493 −1.83848 −0.919238 0.393702i \(-0.871194\pi\)
−0.919238 + 0.393702i \(0.871194\pi\)
\(84\) 0 0
\(85\) −2.48486 −0.269521
\(86\) 0 0
\(87\) −1.82546 −0.195710
\(88\) 0 0
\(89\) 3.82546 0.405498 0.202749 0.979231i \(-0.435012\pi\)
0.202749 + 0.979231i \(0.435012\pi\)
\(90\) 0 0
\(91\) −2.56009 −0.268371
\(92\) 0 0
\(93\) 0.113987 0.0118199
\(94\) 0 0
\(95\) 4.73463 0.485763
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.03028 −0.301524 −0.150762 0.988570i \(-0.548173\pi\)
−0.150762 + 0.988570i \(0.548173\pi\)
\(102\) 0 0
\(103\) −4.71995 −0.465071 −0.232535 0.972588i \(-0.574702\pi\)
−0.232535 + 0.972588i \(0.574702\pi\)
\(104\) 0 0
\(105\) −0.235091 −0.0229425
\(106\) 0 0
\(107\) −1.21949 −0.117893 −0.0589465 0.998261i \(-0.518774\pi\)
−0.0589465 + 0.998261i \(0.518774\pi\)
\(108\) 0 0
\(109\) −16.0294 −1.53533 −0.767667 0.640849i \(-0.778583\pi\)
−0.767667 + 0.640849i \(0.778583\pi\)
\(110\) 0 0
\(111\) −2.79518 −0.265307
\(112\) 0 0
\(113\) −11.4693 −1.07894 −0.539469 0.842006i \(-0.681375\pi\)
−0.539469 + 0.842006i \(0.681375\pi\)
\(114\) 0 0
\(115\) 4.24977 0.396293
\(116\) 0 0
\(117\) 14.5988 1.34966
\(118\) 0 0
\(119\) −1.20482 −0.110445
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) −0.470182 −0.0423949
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.24977 −0.377106 −0.188553 0.982063i \(-0.560380\pi\)
−0.188553 + 0.982063i \(0.560380\pi\)
\(128\) 0 0
\(129\) −0.121104 −0.0106626
\(130\) 0 0
\(131\) −15.7649 −1.37739 −0.688693 0.725053i \(-0.741815\pi\)
−0.688693 + 0.725053i \(0.741815\pi\)
\(132\) 0 0
\(133\) 2.29564 0.199058
\(134\) 0 0
\(135\) 2.79518 0.240571
\(136\) 0 0
\(137\) 13.5298 1.15593 0.577965 0.816061i \(-0.303847\pi\)
0.577965 + 0.816061i \(0.303847\pi\)
\(138\) 0 0
\(139\) 16.6206 1.40974 0.704872 0.709334i \(-0.251004\pi\)
0.704872 + 0.709334i \(0.251004\pi\)
\(140\) 0 0
\(141\) −1.59037 −0.133933
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 3.76491 0.312659
\(146\) 0 0
\(147\) 3.28005 0.270534
\(148\) 0 0
\(149\) −5.20482 −0.426395 −0.213198 0.977009i \(-0.568388\pi\)
−0.213198 + 0.977009i \(0.568388\pi\)
\(150\) 0 0
\(151\) −22.5601 −1.83591 −0.917957 0.396679i \(-0.870162\pi\)
−0.917957 + 0.396679i \(0.870162\pi\)
\(152\) 0 0
\(153\) 6.87042 0.555440
\(154\) 0 0
\(155\) −0.235091 −0.0188830
\(156\) 0 0
\(157\) 3.70436 0.295640 0.147820 0.989014i \(-0.452774\pi\)
0.147820 + 0.989014i \(0.452774\pi\)
\(158\) 0 0
\(159\) −2.79518 −0.221673
\(160\) 0 0
\(161\) 2.06055 0.162394
\(162\) 0 0
\(163\) −15.5445 −1.21754 −0.608770 0.793347i \(-0.708337\pi\)
−0.608770 + 0.793347i \(0.708337\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −22.0752 −1.70823 −0.854116 0.520082i \(-0.825901\pi\)
−0.854116 + 0.520082i \(0.825901\pi\)
\(168\) 0 0
\(169\) 14.8789 1.14453
\(170\) 0 0
\(171\) −13.0908 −1.00108
\(172\) 0 0
\(173\) −2.24977 −0.171047 −0.0855235 0.996336i \(-0.527256\pi\)
−0.0855235 + 0.996336i \(0.527256\pi\)
\(174\) 0 0
\(175\) 0.484862 0.0366521
\(176\) 0 0
\(177\) 6.06055 0.455539
\(178\) 0 0
\(179\) 5.09083 0.380506 0.190253 0.981735i \(-0.439069\pi\)
0.190253 + 0.981735i \(0.439069\pi\)
\(180\) 0 0
\(181\) 7.46927 0.555186 0.277593 0.960699i \(-0.410463\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(182\) 0 0
\(183\) 4.70527 0.347824
\(184\) 0 0
\(185\) 5.76491 0.423845
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.35528 0.0985820
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −2.48486 −0.178864 −0.0894321 0.995993i \(-0.528505\pi\)
−0.0894321 + 0.995993i \(0.528505\pi\)
\(194\) 0 0
\(195\) 2.56009 0.183332
\(196\) 0 0
\(197\) 16.6888 1.18902 0.594512 0.804086i \(-0.297345\pi\)
0.594512 + 0.804086i \(0.297345\pi\)
\(198\) 0 0
\(199\) 4.73463 0.335629 0.167815 0.985819i \(-0.446329\pi\)
0.167815 + 0.985819i \(0.446329\pi\)
\(200\) 0 0
\(201\) 4.99908 0.352608
\(202\) 0 0
\(203\) 1.82546 0.128122
\(204\) 0 0
\(205\) 0.969724 0.0677285
\(206\) 0 0
\(207\) −11.7502 −0.816697
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0.235091 0.0161843 0.00809217 0.999967i \(-0.497424\pi\)
0.00809217 + 0.999967i \(0.497424\pi\)
\(212\) 0 0
\(213\) 2.76583 0.189511
\(214\) 0 0
\(215\) 0.249771 0.0170342
\(216\) 0 0
\(217\) −0.113987 −0.00773792
\(218\) 0 0
\(219\) −0.848620 −0.0573444
\(220\) 0 0
\(221\) 13.1202 0.882559
\(222\) 0 0
\(223\) 19.7796 1.32454 0.662270 0.749266i \(-0.269593\pi\)
0.662270 + 0.749266i \(0.269593\pi\)
\(224\) 0 0
\(225\) −2.76491 −0.184327
\(226\) 0 0
\(227\) 17.2195 1.14290 0.571449 0.820638i \(-0.306381\pi\)
0.571449 + 0.820638i \(0.306381\pi\)
\(228\) 0 0
\(229\) 9.40871 0.621745 0.310873 0.950452i \(-0.399379\pi\)
0.310873 + 0.950452i \(0.399379\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −24.9239 −1.63282 −0.816408 0.577476i \(-0.804038\pi\)
−0.816408 + 0.577476i \(0.804038\pi\)
\(234\) 0 0
\(235\) 3.28005 0.213967
\(236\) 0 0
\(237\) 5.81834 0.377942
\(238\) 0 0
\(239\) 11.5298 0.745802 0.372901 0.927871i \(-0.378363\pi\)
0.372901 + 0.927871i \(0.378363\pi\)
\(240\) 0 0
\(241\) −15.0303 −0.968185 −0.484093 0.875017i \(-0.660850\pi\)
−0.484093 + 0.875017i \(0.660850\pi\)
\(242\) 0 0
\(243\) −11.7502 −0.753778
\(244\) 0 0
\(245\) −6.76491 −0.432194
\(246\) 0 0
\(247\) −24.9991 −1.59065
\(248\) 0 0
\(249\) 8.12110 0.514654
\(250\) 0 0
\(251\) 5.93945 0.374895 0.187447 0.982275i \(-0.439979\pi\)
0.187447 + 0.982275i \(0.439979\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 1.20482 0.0754484
\(256\) 0 0
\(257\) −3.59037 −0.223961 −0.111981 0.993710i \(-0.535719\pi\)
−0.111981 + 0.993710i \(0.535719\pi\)
\(258\) 0 0
\(259\) 2.79518 0.173684
\(260\) 0 0
\(261\) −10.4096 −0.644340
\(262\) 0 0
\(263\) −16.9844 −1.04730 −0.523652 0.851933i \(-0.675431\pi\)
−0.523652 + 0.851933i \(0.675431\pi\)
\(264\) 0 0
\(265\) 5.76491 0.354136
\(266\) 0 0
\(267\) −1.85482 −0.113513
\(268\) 0 0
\(269\) 7.59037 0.462793 0.231397 0.972860i \(-0.425671\pi\)
0.231397 + 0.972860i \(0.425671\pi\)
\(270\) 0 0
\(271\) 14.5601 0.884463 0.442231 0.896901i \(-0.354187\pi\)
0.442231 + 0.896901i \(0.354187\pi\)
\(272\) 0 0
\(273\) 1.24129 0.0751264
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −28.8099 −1.73102 −0.865509 0.500894i \(-0.833005\pi\)
−0.865509 + 0.500894i \(0.833005\pi\)
\(278\) 0 0
\(279\) 0.650006 0.0389148
\(280\) 0 0
\(281\) −16.9697 −1.01233 −0.506164 0.862437i \(-0.668937\pi\)
−0.506164 + 0.862437i \(0.668937\pi\)
\(282\) 0 0
\(283\) −9.68968 −0.575992 −0.287996 0.957632i \(-0.592989\pi\)
−0.287996 + 0.957632i \(0.592989\pi\)
\(284\) 0 0
\(285\) −2.29564 −0.135982
\(286\) 0 0
\(287\) 0.470182 0.0277540
\(288\) 0 0
\(289\) −10.8255 −0.636792
\(290\) 0 0
\(291\) −2.90917 −0.170539
\(292\) 0 0
\(293\) 6.37088 0.372191 0.186095 0.982532i \(-0.440417\pi\)
0.186095 + 0.982532i \(0.440417\pi\)
\(294\) 0 0
\(295\) −12.4995 −0.727751
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −22.4390 −1.29768
\(300\) 0 0
\(301\) 0.121104 0.00698034
\(302\) 0 0
\(303\) 1.46927 0.0844071
\(304\) 0 0
\(305\) −9.70436 −0.555670
\(306\) 0 0
\(307\) 27.6585 1.57855 0.789277 0.614038i \(-0.210456\pi\)
0.789277 + 0.614038i \(0.210456\pi\)
\(308\) 0 0
\(309\) 2.28853 0.130190
\(310\) 0 0
\(311\) 13.7044 0.777103 0.388551 0.921427i \(-0.372976\pi\)
0.388551 + 0.921427i \(0.372976\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) −1.34060 −0.0755342
\(316\) 0 0
\(317\) 12.1745 0.683790 0.341895 0.939738i \(-0.388931\pi\)
0.341895 + 0.939738i \(0.388931\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.591287 0.0330024
\(322\) 0 0
\(323\) −11.7649 −0.654617
\(324\) 0 0
\(325\) −5.28005 −0.292884
\(326\) 0 0
\(327\) 7.77203 0.429794
\(328\) 0 0
\(329\) 1.59037 0.0876799
\(330\) 0 0
\(331\) −29.1202 −1.60059 −0.800295 0.599606i \(-0.795324\pi\)
−0.800295 + 0.599606i \(0.795324\pi\)
\(332\) 0 0
\(333\) −15.9394 −0.873476
\(334\) 0 0
\(335\) −10.3103 −0.563313
\(336\) 0 0
\(337\) 16.9239 0.921901 0.460950 0.887426i \(-0.347509\pi\)
0.460950 + 0.887426i \(0.347509\pi\)
\(338\) 0 0
\(339\) 5.56101 0.302033
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −6.67408 −0.360366
\(344\) 0 0
\(345\) −2.06055 −0.110936
\(346\) 0 0
\(347\) 7.77959 0.417630 0.208815 0.977955i \(-0.433039\pi\)
0.208815 + 0.977955i \(0.433039\pi\)
\(348\) 0 0
\(349\) −7.52982 −0.403062 −0.201531 0.979482i \(-0.564592\pi\)
−0.201531 + 0.979482i \(0.564592\pi\)
\(350\) 0 0
\(351\) −14.7587 −0.787762
\(352\) 0 0
\(353\) −22.5289 −1.19909 −0.599546 0.800340i \(-0.704652\pi\)
−0.599546 + 0.800340i \(0.704652\pi\)
\(354\) 0 0
\(355\) −5.70436 −0.302756
\(356\) 0 0
\(357\) 0.584169 0.0309175
\(358\) 0 0
\(359\) −17.3482 −0.915601 −0.457800 0.889055i \(-0.651363\pi\)
−0.457800 + 0.889055i \(0.651363\pi\)
\(360\) 0 0
\(361\) 3.41675 0.179829
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.75023 0.0916112
\(366\) 0 0
\(367\) −27.3094 −1.42554 −0.712770 0.701398i \(-0.752560\pi\)
−0.712770 + 0.701398i \(0.752560\pi\)
\(368\) 0 0
\(369\) −2.68120 −0.139578
\(370\) 0 0
\(371\) 2.79518 0.145119
\(372\) 0 0
\(373\) −2.24977 −0.116489 −0.0582444 0.998302i \(-0.518550\pi\)
−0.0582444 + 0.998302i \(0.518550\pi\)
\(374\) 0 0
\(375\) −0.484862 −0.0250382
\(376\) 0 0
\(377\) −19.8789 −1.02382
\(378\) 0 0
\(379\) 22.4390 1.15261 0.576307 0.817233i \(-0.304493\pi\)
0.576307 + 0.817233i \(0.304493\pi\)
\(380\) 0 0
\(381\) 2.06055 0.105565
\(382\) 0 0
\(383\) 5.21949 0.266704 0.133352 0.991069i \(-0.457426\pi\)
0.133352 + 0.991069i \(0.457426\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.690594 −0.0351048
\(388\) 0 0
\(389\) 27.5904 1.39889 0.699444 0.714688i \(-0.253431\pi\)
0.699444 + 0.714688i \(0.253431\pi\)
\(390\) 0 0
\(391\) −10.5601 −0.534047
\(392\) 0 0
\(393\) 7.64380 0.385579
\(394\) 0 0
\(395\) −12.0000 −0.603786
\(396\) 0 0
\(397\) 32.9385 1.65314 0.826569 0.562836i \(-0.190290\pi\)
0.826569 + 0.562836i \(0.190290\pi\)
\(398\) 0 0
\(399\) −1.11307 −0.0557232
\(400\) 0 0
\(401\) 0.295643 0.0147637 0.00738186 0.999973i \(-0.497650\pi\)
0.00738186 + 0.999973i \(0.497650\pi\)
\(402\) 0 0
\(403\) 1.24129 0.0618332
\(404\) 0 0
\(405\) 6.93945 0.344824
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −31.4087 −1.55306 −0.776530 0.630080i \(-0.783022\pi\)
−0.776530 + 0.630080i \(0.783022\pi\)
\(410\) 0 0
\(411\) −6.56009 −0.323586
\(412\) 0 0
\(413\) −6.06055 −0.298220
\(414\) 0 0
\(415\) −16.7493 −0.822191
\(416\) 0 0
\(417\) −8.05872 −0.394637
\(418\) 0 0
\(419\) −32.0294 −1.56474 −0.782368 0.622816i \(-0.785988\pi\)
−0.782368 + 0.622816i \(0.785988\pi\)
\(420\) 0 0
\(421\) −28.9385 −1.41038 −0.705189 0.709020i \(-0.749138\pi\)
−0.705189 + 0.709020i \(0.749138\pi\)
\(422\) 0 0
\(423\) −9.06903 −0.440951
\(424\) 0 0
\(425\) −2.48486 −0.120534
\(426\) 0 0
\(427\) −4.70527 −0.227704
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 33.6197 1.61941 0.809703 0.586840i \(-0.199628\pi\)
0.809703 + 0.586840i \(0.199628\pi\)
\(432\) 0 0
\(433\) 29.0596 1.39652 0.698258 0.715846i \(-0.253959\pi\)
0.698258 + 0.715846i \(0.253959\pi\)
\(434\) 0 0
\(435\) −1.82546 −0.0875242
\(436\) 0 0
\(437\) 20.1211 0.962523
\(438\) 0 0
\(439\) 15.5298 0.741198 0.370599 0.928793i \(-0.379152\pi\)
0.370599 + 0.928793i \(0.379152\pi\)
\(440\) 0 0
\(441\) 18.7044 0.890684
\(442\) 0 0
\(443\) 24.6282 1.17012 0.585061 0.810989i \(-0.301071\pi\)
0.585061 + 0.810989i \(0.301071\pi\)
\(444\) 0 0
\(445\) 3.82546 0.181344
\(446\) 0 0
\(447\) 2.52362 0.119363
\(448\) 0 0
\(449\) −8.06055 −0.380401 −0.190200 0.981745i \(-0.560914\pi\)
−0.190200 + 0.981745i \(0.560914\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 10.9385 0.513937
\(454\) 0 0
\(455\) −2.56009 −0.120019
\(456\) 0 0
\(457\) 10.4849 0.490461 0.245231 0.969465i \(-0.421136\pi\)
0.245231 + 0.969465i \(0.421136\pi\)
\(458\) 0 0
\(459\) −6.94565 −0.324195
\(460\) 0 0
\(461\) −36.3856 −1.69464 −0.847322 0.531079i \(-0.821787\pi\)
−0.847322 + 0.531079i \(0.821787\pi\)
\(462\) 0 0
\(463\) 27.3094 1.26918 0.634588 0.772851i \(-0.281170\pi\)
0.634588 + 0.772851i \(0.281170\pi\)
\(464\) 0 0
\(465\) 0.113987 0.00528601
\(466\) 0 0
\(467\) −12.6060 −0.583335 −0.291667 0.956520i \(-0.594210\pi\)
−0.291667 + 0.956520i \(0.594210\pi\)
\(468\) 0 0
\(469\) −4.99908 −0.230836
\(470\) 0 0
\(471\) −1.79610 −0.0827600
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 4.73463 0.217240
\(476\) 0 0
\(477\) −15.9394 −0.729817
\(478\) 0 0
\(479\) −20.5289 −0.937989 −0.468995 0.883201i \(-0.655384\pi\)
−0.468995 + 0.883201i \(0.655384\pi\)
\(480\) 0 0
\(481\) −30.4390 −1.38790
\(482\) 0 0
\(483\) −0.999083 −0.0454599
\(484\) 0 0
\(485\) 6.00000 0.272446
\(486\) 0 0
\(487\) 6.68876 0.303097 0.151548 0.988450i \(-0.451574\pi\)
0.151548 + 0.988450i \(0.451574\pi\)
\(488\) 0 0
\(489\) 7.53694 0.340832
\(490\) 0 0
\(491\) −40.8851 −1.84512 −0.922559 0.385855i \(-0.873906\pi\)
−0.922559 + 0.385855i \(0.873906\pi\)
\(492\) 0 0
\(493\) −9.35528 −0.421341
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.76583 −0.124064
\(498\) 0 0
\(499\) −20.0294 −0.896637 −0.448319 0.893874i \(-0.647977\pi\)
−0.448319 + 0.893874i \(0.647977\pi\)
\(500\) 0 0
\(501\) 10.7034 0.478194
\(502\) 0 0
\(503\) 17.8108 0.794143 0.397072 0.917788i \(-0.370026\pi\)
0.397072 + 0.917788i \(0.370026\pi\)
\(504\) 0 0
\(505\) −3.03028 −0.134846
\(506\) 0 0
\(507\) −7.21421 −0.320394
\(508\) 0 0
\(509\) 8.93853 0.396193 0.198097 0.980182i \(-0.436524\pi\)
0.198097 + 0.980182i \(0.436524\pi\)
\(510\) 0 0
\(511\) 0.848620 0.0375407
\(512\) 0 0
\(513\) 13.2342 0.584303
\(514\) 0 0
\(515\) −4.71995 −0.207986
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.09083 0.0478820
\(520\) 0 0
\(521\) 29.0596 1.27313 0.636563 0.771225i \(-0.280356\pi\)
0.636563 + 0.771225i \(0.280356\pi\)
\(522\) 0 0
\(523\) 32.2791 1.41147 0.705734 0.708477i \(-0.250617\pi\)
0.705734 + 0.708477i \(0.250617\pi\)
\(524\) 0 0
\(525\) −0.235091 −0.0102602
\(526\) 0 0
\(527\) 0.584169 0.0254468
\(528\) 0 0
\(529\) −4.93945 −0.214759
\(530\) 0 0
\(531\) 34.5601 1.49978
\(532\) 0 0
\(533\) −5.12019 −0.221780
\(534\) 0 0
\(535\) −1.21949 −0.0527234
\(536\) 0 0
\(537\) −2.46835 −0.106517
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 38.3250 1.64772 0.823860 0.566793i \(-0.191816\pi\)
0.823860 + 0.566793i \(0.191816\pi\)
\(542\) 0 0
\(543\) −3.62156 −0.155416
\(544\) 0 0
\(545\) −16.0294 −0.686622
\(546\) 0 0
\(547\) −9.71904 −0.415556 −0.207778 0.978176i \(-0.566623\pi\)
−0.207778 + 0.978176i \(0.566623\pi\)
\(548\) 0 0
\(549\) 26.8317 1.14515
\(550\) 0 0
\(551\) 17.8255 0.759390
\(552\) 0 0
\(553\) −5.81834 −0.247421
\(554\) 0 0
\(555\) −2.79518 −0.118649
\(556\) 0 0
\(557\) −16.7805 −0.711013 −0.355506 0.934674i \(-0.615692\pi\)
−0.355506 + 0.934674i \(0.615692\pi\)
\(558\) 0 0
\(559\) −1.31880 −0.0557794
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −25.7190 −1.08393 −0.541964 0.840402i \(-0.682319\pi\)
−0.541964 + 0.840402i \(0.682319\pi\)
\(564\) 0 0
\(565\) −11.4693 −0.482516
\(566\) 0 0
\(567\) 3.36467 0.141303
\(568\) 0 0
\(569\) 39.4087 1.65210 0.826050 0.563597i \(-0.190583\pi\)
0.826050 + 0.563597i \(0.190583\pi\)
\(570\) 0 0
\(571\) −40.4149 −1.69131 −0.845656 0.533729i \(-0.820790\pi\)
−0.845656 + 0.533729i \(0.820790\pi\)
\(572\) 0 0
\(573\) 5.81834 0.243065
\(574\) 0 0
\(575\) 4.24977 0.177228
\(576\) 0 0
\(577\) −7.34816 −0.305908 −0.152954 0.988233i \(-0.548879\pi\)
−0.152954 + 0.988233i \(0.548879\pi\)
\(578\) 0 0
\(579\) 1.20482 0.0500704
\(580\) 0 0
\(581\) −8.12110 −0.336920
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 14.5988 0.603588
\(586\) 0 0
\(587\) 41.9835 1.73284 0.866422 0.499312i \(-0.166414\pi\)
0.866422 + 0.499312i \(0.166414\pi\)
\(588\) 0 0
\(589\) −1.11307 −0.0458633
\(590\) 0 0
\(591\) −8.09174 −0.332850
\(592\) 0 0
\(593\) −19.3700 −0.795429 −0.397714 0.917509i \(-0.630197\pi\)
−0.397714 + 0.917509i \(0.630197\pi\)
\(594\) 0 0
\(595\) −1.20482 −0.0493926
\(596\) 0 0
\(597\) −2.29564 −0.0939544
\(598\) 0 0
\(599\) 4.14335 0.169293 0.0846463 0.996411i \(-0.473024\pi\)
0.0846463 + 0.996411i \(0.473024\pi\)
\(600\) 0 0
\(601\) −15.0303 −0.613098 −0.306549 0.951855i \(-0.599174\pi\)
−0.306549 + 0.951855i \(0.599174\pi\)
\(602\) 0 0
\(603\) 28.5071 1.16090
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −12.6060 −0.511660 −0.255830 0.966722i \(-0.582349\pi\)
−0.255830 + 0.966722i \(0.582349\pi\)
\(608\) 0 0
\(609\) −0.885097 −0.0358659
\(610\) 0 0
\(611\) −17.3188 −0.700644
\(612\) 0 0
\(613\) 14.2791 0.576729 0.288364 0.957521i \(-0.406889\pi\)
0.288364 + 0.957521i \(0.406889\pi\)
\(614\) 0 0
\(615\) −0.470182 −0.0189596
\(616\) 0 0
\(617\) 8.18166 0.329381 0.164691 0.986345i \(-0.447337\pi\)
0.164691 + 0.986345i \(0.447337\pi\)
\(618\) 0 0
\(619\) 39.0890 1.57112 0.785560 0.618786i \(-0.212375\pi\)
0.785560 + 0.618786i \(0.212375\pi\)
\(620\) 0 0
\(621\) 11.8789 0.476684
\(622\) 0 0
\(623\) 1.85482 0.0743118
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −14.3250 −0.571175
\(630\) 0 0
\(631\) −23.8860 −0.950887 −0.475444 0.879746i \(-0.657712\pi\)
−0.475444 + 0.879746i \(0.657712\pi\)
\(632\) 0 0
\(633\) −0.113987 −0.00453057
\(634\) 0 0
\(635\) −4.24977 −0.168647
\(636\) 0 0
\(637\) 35.7190 1.41524
\(638\) 0 0
\(639\) 15.7720 0.623932
\(640\) 0 0
\(641\) −9.64380 −0.380907 −0.190454 0.981696i \(-0.560996\pi\)
−0.190454 + 0.981696i \(0.560996\pi\)
\(642\) 0 0
\(643\) 39.5151 1.55832 0.779162 0.626822i \(-0.215645\pi\)
0.779162 + 0.626822i \(0.215645\pi\)
\(644\) 0 0
\(645\) −0.121104 −0.00476848
\(646\) 0 0
\(647\) −41.8695 −1.64606 −0.823030 0.567998i \(-0.807718\pi\)
−0.823030 + 0.567998i \(0.807718\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.0552678 0.00216612
\(652\) 0 0
\(653\) 9.41583 0.368470 0.184235 0.982882i \(-0.441019\pi\)
0.184235 + 0.982882i \(0.441019\pi\)
\(654\) 0 0
\(655\) −15.7649 −0.615986
\(656\) 0 0
\(657\) −4.83922 −0.188796
\(658\) 0 0
\(659\) 12.1433 0.473038 0.236519 0.971627i \(-0.423994\pi\)
0.236519 + 0.971627i \(0.423994\pi\)
\(660\) 0 0
\(661\) −26.0587 −1.01357 −0.506783 0.862073i \(-0.669166\pi\)
−0.506783 + 0.862073i \(0.669166\pi\)
\(662\) 0 0
\(663\) −6.36148 −0.247059
\(664\) 0 0
\(665\) 2.29564 0.0890212
\(666\) 0 0
\(667\) 16.0000 0.619522
\(668\) 0 0
\(669\) −9.59037 −0.370785
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 34.6353 1.33509 0.667547 0.744568i \(-0.267344\pi\)
0.667547 + 0.744568i \(0.267344\pi\)
\(674\) 0 0
\(675\) 2.79518 0.107587
\(676\) 0 0
\(677\) 22.3709 0.859783 0.429891 0.902881i \(-0.358552\pi\)
0.429891 + 0.902881i \(0.358552\pi\)
\(678\) 0 0
\(679\) 2.90917 0.111644
\(680\) 0 0
\(681\) −8.34908 −0.319937
\(682\) 0 0
\(683\) −28.6353 −1.09570 −0.547850 0.836576i \(-0.684554\pi\)
−0.547850 + 0.836576i \(0.684554\pi\)
\(684\) 0 0
\(685\) 13.5298 0.516948
\(686\) 0 0
\(687\) −4.56193 −0.174048
\(688\) 0 0
\(689\) −30.4390 −1.15963
\(690\) 0 0
\(691\) 7.65092 0.291055 0.145527 0.989354i \(-0.453512\pi\)
0.145527 + 0.989354i \(0.453512\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 16.6206 0.630457
\(696\) 0 0
\(697\) −2.40963 −0.0912712
\(698\) 0 0
\(699\) 12.0846 0.457083
\(700\) 0 0
\(701\) −28.8851 −1.09098 −0.545488 0.838119i \(-0.683655\pi\)
−0.545488 + 0.838119i \(0.683655\pi\)
\(702\) 0 0
\(703\) 27.2947 1.02944
\(704\) 0 0
\(705\) −1.59037 −0.0598968
\(706\) 0 0
\(707\) −1.46927 −0.0552574
\(708\) 0 0
\(709\) −42.9991 −1.61486 −0.807432 0.589960i \(-0.799143\pi\)
−0.807432 + 0.589960i \(0.799143\pi\)
\(710\) 0 0
\(711\) 33.1789 1.24431
\(712\) 0 0
\(713\) −0.999083 −0.0374160
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −5.59037 −0.208776
\(718\) 0 0
\(719\) −42.6741 −1.59147 −0.795737 0.605642i \(-0.792916\pi\)
−0.795737 + 0.605642i \(0.792916\pi\)
\(720\) 0 0
\(721\) −2.28853 −0.0852291
\(722\) 0 0
\(723\) 7.28761 0.271029
\(724\) 0 0
\(725\) 3.76491 0.139825
\(726\) 0 0
\(727\) −39.9301 −1.48092 −0.740462 0.672098i \(-0.765393\pi\)
−0.740462 + 0.672098i \(0.765393\pi\)
\(728\) 0 0
\(729\) −15.1211 −0.560041
\(730\) 0 0
\(731\) −0.620646 −0.0229554
\(732\) 0 0
\(733\) −17.7796 −0.656704 −0.328352 0.944555i \(-0.606493\pi\)
−0.328352 + 0.944555i \(0.606493\pi\)
\(734\) 0 0
\(735\) 3.28005 0.120986
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 22.4390 0.825432 0.412716 0.910860i \(-0.364580\pi\)
0.412716 + 0.910860i \(0.364580\pi\)
\(740\) 0 0
\(741\) 12.1211 0.445280
\(742\) 0 0
\(743\) 11.6656 0.427969 0.213985 0.976837i \(-0.431356\pi\)
0.213985 + 0.976837i \(0.431356\pi\)
\(744\) 0 0
\(745\) −5.20482 −0.190690
\(746\) 0 0
\(747\) 46.3103 1.69441
\(748\) 0 0
\(749\) −0.591287 −0.0216051
\(750\) 0 0
\(751\) −50.3544 −1.83746 −0.918728 0.394890i \(-0.870783\pi\)
−0.918728 + 0.394890i \(0.870783\pi\)
\(752\) 0 0
\(753\) −2.87981 −0.104946
\(754\) 0 0
\(755\) −22.5601 −0.821046
\(756\) 0 0
\(757\) 50.1798 1.82382 0.911908 0.410394i \(-0.134609\pi\)
0.911908 + 0.410394i \(0.134609\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 35.4087 1.28356 0.641782 0.766887i \(-0.278195\pi\)
0.641782 + 0.766887i \(0.278195\pi\)
\(762\) 0 0
\(763\) −7.77203 −0.281366
\(764\) 0 0
\(765\) 6.87042 0.248400
\(766\) 0 0
\(767\) 65.9982 2.38306
\(768\) 0 0
\(769\) 54.9679 1.98219 0.991096 0.133146i \(-0.0425080\pi\)
0.991096 + 0.133146i \(0.0425080\pi\)
\(770\) 0 0
\(771\) 1.74083 0.0626946
\(772\) 0 0
\(773\) −25.2947 −0.909788 −0.454894 0.890546i \(-0.650323\pi\)
−0.454894 + 0.890546i \(0.650323\pi\)
\(774\) 0 0
\(775\) −0.235091 −0.00844472
\(776\) 0 0
\(777\) −1.35528 −0.0486204
\(778\) 0 0
\(779\) 4.59129 0.164500
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 10.5236 0.376083
\(784\) 0 0
\(785\) 3.70436 0.132214
\(786\) 0 0
\(787\) 33.9612 1.21059 0.605294 0.796002i \(-0.293056\pi\)
0.605294 + 0.796002i \(0.293056\pi\)
\(788\) 0 0
\(789\) 8.23509 0.293177
\(790\) 0 0
\(791\) −5.56101 −0.197727
\(792\) 0 0
\(793\) 51.2395 1.81957
\(794\) 0 0
\(795\) −2.79518 −0.0991350
\(796\) 0 0
\(797\) 48.9385 1.73349 0.866746 0.498750i \(-0.166207\pi\)
0.866746 + 0.498750i \(0.166207\pi\)
\(798\) 0 0
\(799\) −8.15046 −0.288343
\(800\) 0 0
\(801\) −10.5771 −0.373722
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 2.06055 0.0726249
\(806\) 0 0
\(807\) −3.68028 −0.129552
\(808\) 0 0
\(809\) 39.6803 1.39508 0.697542 0.716544i \(-0.254277\pi\)
0.697542 + 0.716544i \(0.254277\pi\)
\(810\) 0 0
\(811\) 6.70344 0.235390 0.117695 0.993050i \(-0.462450\pi\)
0.117695 + 0.993050i \(0.462450\pi\)
\(812\) 0 0
\(813\) −7.05964 −0.247592
\(814\) 0 0
\(815\) −15.5445 −0.544500
\(816\) 0 0
\(817\) 1.18257 0.0413730
\(818\) 0 0
\(819\) 7.07843 0.247340
\(820\) 0 0
\(821\) −22.4096 −0.782101 −0.391051 0.920369i \(-0.627888\pi\)
−0.391051 + 0.920369i \(0.627888\pi\)
\(822\) 0 0
\(823\) 11.0378 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20.4002 −0.709386 −0.354693 0.934983i \(-0.615415\pi\)
−0.354693 + 0.934983i \(0.615415\pi\)
\(828\) 0 0
\(829\) 21.5298 0.747761 0.373881 0.927477i \(-0.378027\pi\)
0.373881 + 0.927477i \(0.378027\pi\)
\(830\) 0 0
\(831\) 13.9688 0.484573
\(832\) 0 0
\(833\) 16.8099 0.582427
\(834\) 0 0
\(835\) −22.0752 −0.763945
\(836\) 0 0
\(837\) −0.657123 −0.0227135
\(838\) 0 0
\(839\) −23.5592 −0.813353 −0.406677 0.913572i \(-0.633312\pi\)
−0.406677 + 0.913572i \(0.633312\pi\)
\(840\) 0 0
\(841\) −14.8255 −0.511223
\(842\) 0 0
\(843\) 8.22797 0.283386
\(844\) 0 0
\(845\) 14.8789 0.511850
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 4.69816 0.161240
\(850\) 0 0
\(851\) 24.4995 0.839833
\(852\) 0 0
\(853\) 19.3406 0.662210 0.331105 0.943594i \(-0.392579\pi\)
0.331105 + 0.943594i \(0.392579\pi\)
\(854\) 0 0
\(855\) −13.0908 −0.447697
\(856\) 0 0
\(857\) 37.5739 1.28350 0.641749 0.766915i \(-0.278209\pi\)
0.641749 + 0.766915i \(0.278209\pi\)
\(858\) 0 0
\(859\) −10.4390 −0.356174 −0.178087 0.984015i \(-0.556991\pi\)
−0.178087 + 0.984015i \(0.556991\pi\)
\(860\) 0 0
\(861\) −0.227973 −0.00776932
\(862\) 0 0
\(863\) −43.7796 −1.49027 −0.745137 0.666911i \(-0.767616\pi\)
−0.745137 + 0.666911i \(0.767616\pi\)
\(864\) 0 0
\(865\) −2.24977 −0.0764945
\(866\) 0 0
\(867\) 5.24885 0.178260
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 54.4390 1.84459
\(872\) 0 0
\(873\) −16.5895 −0.561468
\(874\) 0 0
\(875\) 0.484862 0.0163913
\(876\) 0 0
\(877\) 35.6273 1.20305 0.601524 0.798855i \(-0.294560\pi\)
0.601524 + 0.798855i \(0.294560\pi\)
\(878\) 0 0
\(879\) −3.08899 −0.104189
\(880\) 0 0
\(881\) −8.18166 −0.275647 −0.137824 0.990457i \(-0.544011\pi\)
−0.137824 + 0.990457i \(0.544011\pi\)
\(882\) 0 0
\(883\) 4.86330 0.163663 0.0818315 0.996646i \(-0.473923\pi\)
0.0818315 + 0.996646i \(0.473923\pi\)
\(884\) 0 0
\(885\) 6.06055 0.203723
\(886\) 0 0
\(887\) −11.2507 −0.377761 −0.188881 0.982000i \(-0.560486\pi\)
−0.188881 + 0.982000i \(0.560486\pi\)
\(888\) 0 0
\(889\) −2.06055 −0.0691087
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 15.5298 0.519686
\(894\) 0 0
\(895\) 5.09083 0.170168
\(896\) 0 0
\(897\) 10.8798 0.363266
\(898\) 0 0
\(899\) −0.885097 −0.0295196
\(900\) 0 0
\(901\) −14.3250 −0.477235
\(902\) 0 0
\(903\) −0.0587189 −0.00195404
\(904\) 0 0
\(905\) 7.46927 0.248287
\(906\) 0 0
\(907\) 9.69679 0.321977 0.160988 0.986956i \(-0.448532\pi\)
0.160988 + 0.986956i \(0.448532\pi\)
\(908\) 0 0
\(909\) 8.37844 0.277895
\(910\) 0 0
\(911\) −39.8236 −1.31942 −0.659708 0.751522i \(-0.729320\pi\)
−0.659708 + 0.751522i \(0.729320\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 4.70527 0.155552
\(916\) 0 0
\(917\) −7.64380 −0.252421
\(918\) 0 0
\(919\) −1.93945 −0.0639765 −0.0319882 0.999488i \(-0.510184\pi\)
−0.0319882 + 0.999488i \(0.510184\pi\)
\(920\) 0 0
\(921\) −13.4105 −0.441893
\(922\) 0 0
\(923\) 30.1193 0.991388
\(924\) 0 0
\(925\) 5.76491 0.189549
\(926\) 0 0
\(927\) 13.0502 0.428626
\(928\) 0 0
\(929\) −48.5823 −1.59393 −0.796967 0.604022i \(-0.793564\pi\)
−0.796967 + 0.604022i \(0.793564\pi\)
\(930\) 0 0
\(931\) −32.0294 −1.04972
\(932\) 0 0
\(933\) −6.64472 −0.217538
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −8.80986 −0.287806 −0.143903 0.989592i \(-0.545965\pi\)
−0.143903 + 0.989592i \(0.545965\pi\)
\(938\) 0 0
\(939\) −0.969724 −0.0316457
\(940\) 0 0
\(941\) −44.9145 −1.46417 −0.732085 0.681214i \(-0.761452\pi\)
−0.732085 + 0.681214i \(0.761452\pi\)
\(942\) 0 0
\(943\) 4.12110 0.134202
\(944\) 0 0
\(945\) 1.35528 0.0440872
\(946\) 0 0
\(947\) −13.0761 −0.424918 −0.212459 0.977170i \(-0.568147\pi\)
−0.212459 + 0.977170i \(0.568147\pi\)
\(948\) 0 0
\(949\) −9.24129 −0.299985
\(950\) 0 0
\(951\) −5.90297 −0.191417
\(952\) 0 0
\(953\) −25.6362 −0.830439 −0.415220 0.909721i \(-0.636295\pi\)
−0.415220 + 0.909721i \(0.636295\pi\)
\(954\) 0 0
\(955\) −12.0000 −0.388311
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.56009 0.211836
\(960\) 0 0
\(961\) −30.9447 −0.998217
\(962\) 0 0
\(963\) 3.37179 0.108654
\(964\) 0 0
\(965\) −2.48486 −0.0799905
\(966\) 0 0
\(967\) 41.4546 1.33309 0.666545 0.745465i \(-0.267773\pi\)
0.666545 + 0.745465i \(0.267773\pi\)
\(968\) 0 0
\(969\) 5.70436 0.183250
\(970\) 0 0
\(971\) 36.4078 1.16838 0.584191 0.811616i \(-0.301412\pi\)
0.584191 + 0.811616i \(0.301412\pi\)
\(972\) 0 0
\(973\) 8.05872 0.258351
\(974\) 0 0
\(975\) 2.56009 0.0819886
\(976\) 0 0
\(977\) 30.0587 0.961664 0.480832 0.876813i \(-0.340335\pi\)
0.480832 + 0.876813i \(0.340335\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 44.3197 1.41502
\(982\) 0 0
\(983\) −26.3103 −0.839169 −0.419584 0.907716i \(-0.637824\pi\)
−0.419584 + 0.907716i \(0.637824\pi\)
\(984\) 0 0
\(985\) 16.6888 0.531748
\(986\) 0 0
\(987\) −0.771110 −0.0245447
\(988\) 0 0
\(989\) 1.06147 0.0337527
\(990\) 0 0
\(991\) 11.0596 0.351321 0.175660 0.984451i \(-0.443794\pi\)
0.175660 + 0.984451i \(0.443794\pi\)
\(992\) 0 0
\(993\) 14.1193 0.448062
\(994\) 0 0
\(995\) 4.73463 0.150098
\(996\) 0 0
\(997\) 24.4608 0.774681 0.387340 0.921937i \(-0.373394\pi\)
0.387340 + 0.921937i \(0.373394\pi\)
\(998\) 0 0
\(999\) 16.1140 0.509824
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 4840.2.a.r.1.2 yes 3
4.3 odd 2 9680.2.a.cg.1.2 3
11.10 odd 2 4840.2.a.q.1.2 3
44.43 even 2 9680.2.a.ch.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4840.2.a.q.1.2 3 11.10 odd 2
4840.2.a.r.1.2 yes 3 1.1 even 1 trivial
9680.2.a.cg.1.2 3 4.3 odd 2
9680.2.a.ch.1.2 3 44.43 even 2