Properties

Label 4018.2.a.bq.1.3
Level $4018$
Weight $2$
Character 4018.1
Self dual yes
Analytic conductor $32.084$
Analytic rank $0$
Dimension $6$
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] = [4018,2,Mod(1,4018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.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: \(32.0838915322\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.5163008.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 5x^{2} - 6x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.56754\) of defining polynomial
Character \(\chi\) \(=\) 4018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.0387751 q^{3} +1.00000 q^{4} +2.61052 q^{5} +0.0387751 q^{6} +1.00000 q^{8} -2.99850 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.0387751 q^{3} +1.00000 q^{4} +2.61052 q^{5} +0.0387751 q^{6} +1.00000 q^{8} -2.99850 q^{9} +2.61052 q^{10} +3.07158 q^{11} +0.0387751 q^{12} -2.08825 q^{13} +0.101223 q^{15} +1.00000 q^{16} -0.761390 q^{17} -2.99850 q^{18} +7.09631 q^{19} +2.61052 q^{20} +3.07158 q^{22} +5.31219 q^{23} +0.0387751 q^{24} +1.81483 q^{25} -2.08825 q^{26} -0.232592 q^{27} +2.31533 q^{29} +0.101223 q^{30} +0.644105 q^{31} +1.00000 q^{32} +0.119101 q^{33} -0.761390 q^{34} -2.99850 q^{36} -9.45774 q^{37} +7.09631 q^{38} -0.0809720 q^{39} +2.61052 q^{40} -1.00000 q^{41} +4.79344 q^{43} +3.07158 q^{44} -7.82764 q^{45} +5.31219 q^{46} +4.61388 q^{47} +0.0387751 q^{48} +1.81483 q^{50} -0.0295230 q^{51} -2.08825 q^{52} -6.27441 q^{53} -0.232592 q^{54} +8.01842 q^{55} +0.275160 q^{57} +2.31533 q^{58} +14.3819 q^{59} +0.101223 q^{60} +3.84288 q^{61} +0.644105 q^{62} +1.00000 q^{64} -5.45142 q^{65} +0.119101 q^{66} +8.37335 q^{67} -0.761390 q^{68} +0.205981 q^{69} -10.8481 q^{71} -2.99850 q^{72} +3.35938 q^{73} -9.45774 q^{74} +0.0703702 q^{75} +7.09631 q^{76} -0.0809720 q^{78} -2.24510 q^{79} +2.61052 q^{80} +8.98647 q^{81} -1.00000 q^{82} +7.80581 q^{83} -1.98763 q^{85} +4.79344 q^{86} +0.0897774 q^{87} +3.07158 q^{88} -5.93525 q^{89} -7.82764 q^{90} +5.31219 q^{92} +0.0249753 q^{93} +4.61388 q^{94} +18.5251 q^{95} +0.0387751 q^{96} +16.7498 q^{97} -9.21011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9} + 12 q^{10} + 4 q^{12} + 8 q^{13} - 4 q^{15} + 6 q^{16} + 16 q^{17} + 18 q^{18} + 12 q^{19} + 12 q^{20} + 12 q^{23} + 4 q^{24} + 14 q^{25} + 8 q^{26} + 28 q^{27} - 4 q^{30} - 4 q^{31} + 6 q^{32} - 20 q^{33} + 16 q^{34} + 18 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{39} + 12 q^{40} - 6 q^{41} + 4 q^{43} + 28 q^{45} + 12 q^{46} - 16 q^{47} + 4 q^{48} + 14 q^{50} - 16 q^{51} + 8 q^{52} - 16 q^{53} + 28 q^{54} - 12 q^{55} - 28 q^{57} + 16 q^{59} - 4 q^{60} + 32 q^{61} - 4 q^{62} + 6 q^{64} - 4 q^{65} - 20 q^{66} - 20 q^{67} + 16 q^{68} + 56 q^{69} + 12 q^{71} + 18 q^{72} + 16 q^{73} - 24 q^{74} - 4 q^{75} + 12 q^{76} + 4 q^{78} + 12 q^{80} + 42 q^{81} - 6 q^{82} + 32 q^{83} + 48 q^{85} + 4 q^{86} + 20 q^{87} + 8 q^{89} + 28 q^{90} + 12 q^{92} - 12 q^{93} - 16 q^{94} + 28 q^{95} + 4 q^{96} + 8 q^{97} - 76 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.0387751 0.0223868 0.0111934 0.999937i \(-0.496437\pi\)
0.0111934 + 0.999937i \(0.496437\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.61052 1.16746 0.583731 0.811947i \(-0.301592\pi\)
0.583731 + 0.811947i \(0.301592\pi\)
\(6\) 0.0387751 0.0158299
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.99850 −0.999499
\(10\) 2.61052 0.825520
\(11\) 3.07158 0.926115 0.463057 0.886328i \(-0.346752\pi\)
0.463057 + 0.886328i \(0.346752\pi\)
\(12\) 0.0387751 0.0111934
\(13\) −2.08825 −0.579176 −0.289588 0.957151i \(-0.593518\pi\)
−0.289588 + 0.957151i \(0.593518\pi\)
\(14\) 0 0
\(15\) 0.101223 0.0261358
\(16\) 1.00000 0.250000
\(17\) −0.761390 −0.184664 −0.0923321 0.995728i \(-0.529432\pi\)
−0.0923321 + 0.995728i \(0.529432\pi\)
\(18\) −2.99850 −0.706752
\(19\) 7.09631 1.62801 0.814003 0.580861i \(-0.197284\pi\)
0.814003 + 0.580861i \(0.197284\pi\)
\(20\) 2.61052 0.583731
\(21\) 0 0
\(22\) 3.07158 0.654862
\(23\) 5.31219 1.10767 0.553835 0.832627i \(-0.313164\pi\)
0.553835 + 0.832627i \(0.313164\pi\)
\(24\) 0.0387751 0.00791494
\(25\) 1.81483 0.362966
\(26\) −2.08825 −0.409539
\(27\) −0.232592 −0.0447624
\(28\) 0 0
\(29\) 2.31533 0.429947 0.214973 0.976620i \(-0.431033\pi\)
0.214973 + 0.976620i \(0.431033\pi\)
\(30\) 0.101223 0.0184808
\(31\) 0.644105 0.115685 0.0578424 0.998326i \(-0.481578\pi\)
0.0578424 + 0.998326i \(0.481578\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.119101 0.0207328
\(34\) −0.761390 −0.130577
\(35\) 0 0
\(36\) −2.99850 −0.499749
\(37\) −9.45774 −1.55484 −0.777421 0.628980i \(-0.783473\pi\)
−0.777421 + 0.628980i \(0.783473\pi\)
\(38\) 7.09631 1.15117
\(39\) −0.0809720 −0.0129659
\(40\) 2.61052 0.412760
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 4.79344 0.730993 0.365497 0.930813i \(-0.380899\pi\)
0.365497 + 0.930813i \(0.380899\pi\)
\(44\) 3.07158 0.463057
\(45\) −7.82764 −1.16688
\(46\) 5.31219 0.783240
\(47\) 4.61388 0.673003 0.336501 0.941683i \(-0.390756\pi\)
0.336501 + 0.941683i \(0.390756\pi\)
\(48\) 0.0387751 0.00559671
\(49\) 0 0
\(50\) 1.81483 0.256656
\(51\) −0.0295230 −0.00413405
\(52\) −2.08825 −0.289588
\(53\) −6.27441 −0.861856 −0.430928 0.902386i \(-0.641814\pi\)
−0.430928 + 0.902386i \(0.641814\pi\)
\(54\) −0.232592 −0.0316518
\(55\) 8.01842 1.08120
\(56\) 0 0
\(57\) 0.275160 0.0364459
\(58\) 2.31533 0.304018
\(59\) 14.3819 1.87236 0.936181 0.351518i \(-0.114334\pi\)
0.936181 + 0.351518i \(0.114334\pi\)
\(60\) 0.101223 0.0130679
\(61\) 3.84288 0.492030 0.246015 0.969266i \(-0.420879\pi\)
0.246015 + 0.969266i \(0.420879\pi\)
\(62\) 0.644105 0.0818015
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −5.45142 −0.676165
\(66\) 0.119101 0.0146603
\(67\) 8.37335 1.02297 0.511484 0.859293i \(-0.329096\pi\)
0.511484 + 0.859293i \(0.329096\pi\)
\(68\) −0.761390 −0.0923321
\(69\) 0.205981 0.0247972
\(70\) 0 0
\(71\) −10.8481 −1.28744 −0.643718 0.765263i \(-0.722609\pi\)
−0.643718 + 0.765263i \(0.722609\pi\)
\(72\) −2.99850 −0.353376
\(73\) 3.35938 0.393185 0.196593 0.980485i \(-0.437012\pi\)
0.196593 + 0.980485i \(0.437012\pi\)
\(74\) −9.45774 −1.09944
\(75\) 0.0703702 0.00812565
\(76\) 7.09631 0.814003
\(77\) 0 0
\(78\) −0.0809720 −0.00916828
\(79\) −2.24510 −0.252594 −0.126297 0.991992i \(-0.540309\pi\)
−0.126297 + 0.991992i \(0.540309\pi\)
\(80\) 2.61052 0.291865
\(81\) 8.98647 0.998497
\(82\) −1.00000 −0.110432
\(83\) 7.80581 0.856799 0.428399 0.903589i \(-0.359078\pi\)
0.428399 + 0.903589i \(0.359078\pi\)
\(84\) 0 0
\(85\) −1.98763 −0.215588
\(86\) 4.79344 0.516890
\(87\) 0.0897774 0.00962515
\(88\) 3.07158 0.327431
\(89\) −5.93525 −0.629135 −0.314568 0.949235i \(-0.601860\pi\)
−0.314568 + 0.949235i \(0.601860\pi\)
\(90\) −7.82764 −0.825106
\(91\) 0 0
\(92\) 5.31219 0.553835
\(93\) 0.0249753 0.00258981
\(94\) 4.61388 0.475885
\(95\) 18.5251 1.90063
\(96\) 0.0387751 0.00395747
\(97\) 16.7498 1.70069 0.850345 0.526226i \(-0.176393\pi\)
0.850345 + 0.526226i \(0.176393\pi\)
\(98\) 0 0
\(99\) −9.21011 −0.925651
\(100\) 1.81483 0.181483
\(101\) 10.4656 1.04137 0.520683 0.853750i \(-0.325678\pi\)
0.520683 + 0.853750i \(0.325678\pi\)
\(102\) −0.0295230 −0.00292321
\(103\) −2.47421 −0.243791 −0.121896 0.992543i \(-0.538897\pi\)
−0.121896 + 0.992543i \(0.538897\pi\)
\(104\) −2.08825 −0.204770
\(105\) 0 0
\(106\) −6.27441 −0.609424
\(107\) −15.8124 −1.52864 −0.764320 0.644837i \(-0.776925\pi\)
−0.764320 + 0.644837i \(0.776925\pi\)
\(108\) −0.232592 −0.0223812
\(109\) 6.57783 0.630042 0.315021 0.949085i \(-0.397988\pi\)
0.315021 + 0.949085i \(0.397988\pi\)
\(110\) 8.01842 0.764526
\(111\) −0.366725 −0.0348080
\(112\) 0 0
\(113\) 3.34219 0.314407 0.157203 0.987566i \(-0.449752\pi\)
0.157203 + 0.987566i \(0.449752\pi\)
\(114\) 0.275160 0.0257711
\(115\) 13.8676 1.29316
\(116\) 2.31533 0.214973
\(117\) 6.26160 0.578885
\(118\) 14.3819 1.32396
\(119\) 0 0
\(120\) 0.101223 0.00924038
\(121\) −1.56542 −0.142311
\(122\) 3.84288 0.347918
\(123\) −0.0387751 −0.00349623
\(124\) 0.644105 0.0578424
\(125\) −8.31496 −0.743713
\(126\) 0 0
\(127\) −8.37867 −0.743487 −0.371743 0.928335i \(-0.621240\pi\)
−0.371743 + 0.928335i \(0.621240\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.185866 0.0163646
\(130\) −5.45142 −0.478121
\(131\) −12.7513 −1.11409 −0.557043 0.830483i \(-0.688064\pi\)
−0.557043 + 0.830483i \(0.688064\pi\)
\(132\) 0.119101 0.0103664
\(133\) 0 0
\(134\) 8.37335 0.723347
\(135\) −0.607188 −0.0522584
\(136\) −0.761390 −0.0652887
\(137\) 14.7866 1.26330 0.631651 0.775253i \(-0.282377\pi\)
0.631651 + 0.775253i \(0.282377\pi\)
\(138\) 0.205981 0.0175343
\(139\) 9.80861 0.831956 0.415978 0.909375i \(-0.363439\pi\)
0.415978 + 0.909375i \(0.363439\pi\)
\(140\) 0 0
\(141\) 0.178904 0.0150664
\(142\) −10.8481 −0.910355
\(143\) −6.41421 −0.536383
\(144\) −2.99850 −0.249875
\(145\) 6.04423 0.501946
\(146\) 3.35938 0.278024
\(147\) 0 0
\(148\) −9.45774 −0.777421
\(149\) −12.1994 −0.999412 −0.499706 0.866195i \(-0.666559\pi\)
−0.499706 + 0.866195i \(0.666559\pi\)
\(150\) 0.0703702 0.00574570
\(151\) −20.5621 −1.67332 −0.836660 0.547722i \(-0.815495\pi\)
−0.836660 + 0.547722i \(0.815495\pi\)
\(152\) 7.09631 0.575587
\(153\) 2.28303 0.184572
\(154\) 0 0
\(155\) 1.68145 0.135057
\(156\) −0.0809720 −0.00648295
\(157\) −4.63615 −0.370005 −0.185003 0.982738i \(-0.559229\pi\)
−0.185003 + 0.982738i \(0.559229\pi\)
\(158\) −2.24510 −0.178611
\(159\) −0.243291 −0.0192942
\(160\) 2.61052 0.206380
\(161\) 0 0
\(162\) 8.98647 0.706044
\(163\) 3.11486 0.243974 0.121987 0.992532i \(-0.461073\pi\)
0.121987 + 0.992532i \(0.461073\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0.310915 0.0242047
\(166\) 7.80581 0.605848
\(167\) −4.77073 −0.369170 −0.184585 0.982817i \(-0.559094\pi\)
−0.184585 + 0.982817i \(0.559094\pi\)
\(168\) 0 0
\(169\) −8.63922 −0.664556
\(170\) −1.98763 −0.152444
\(171\) −21.2783 −1.62719
\(172\) 4.79344 0.365497
\(173\) 2.15961 0.164192 0.0820959 0.996624i \(-0.473839\pi\)
0.0820959 + 0.996624i \(0.473839\pi\)
\(174\) 0.0897774 0.00680601
\(175\) 0 0
\(176\) 3.07158 0.231529
\(177\) 0.557659 0.0419163
\(178\) −5.93525 −0.444866
\(179\) −20.1667 −1.50733 −0.753663 0.657261i \(-0.771715\pi\)
−0.753663 + 0.657261i \(0.771715\pi\)
\(180\) −7.82764 −0.583438
\(181\) 7.51035 0.558240 0.279120 0.960256i \(-0.409957\pi\)
0.279120 + 0.960256i \(0.409957\pi\)
\(182\) 0 0
\(183\) 0.149008 0.0110150
\(184\) 5.31219 0.391620
\(185\) −24.6896 −1.81522
\(186\) 0.0249753 0.00183128
\(187\) −2.33867 −0.171020
\(188\) 4.61388 0.336501
\(189\) 0 0
\(190\) 18.5251 1.34395
\(191\) 4.24153 0.306907 0.153453 0.988156i \(-0.450961\pi\)
0.153453 + 0.988156i \(0.450961\pi\)
\(192\) 0.0387751 0.00279835
\(193\) 13.7705 0.991224 0.495612 0.868544i \(-0.334944\pi\)
0.495612 + 0.868544i \(0.334944\pi\)
\(194\) 16.7498 1.20257
\(195\) −0.211379 −0.0151372
\(196\) 0 0
\(197\) −2.68951 −0.191620 −0.0958100 0.995400i \(-0.530544\pi\)
−0.0958100 + 0.995400i \(0.530544\pi\)
\(198\) −9.21011 −0.654534
\(199\) −6.34370 −0.449693 −0.224847 0.974394i \(-0.572188\pi\)
−0.224847 + 0.974394i \(0.572188\pi\)
\(200\) 1.81483 0.128328
\(201\) 0.324678 0.0229010
\(202\) 10.4656 0.736356
\(203\) 0 0
\(204\) −0.0295230 −0.00206702
\(205\) −2.61052 −0.182327
\(206\) −2.47421 −0.172387
\(207\) −15.9286 −1.10711
\(208\) −2.08825 −0.144794
\(209\) 21.7969 1.50772
\(210\) 0 0
\(211\) −2.81048 −0.193481 −0.0967407 0.995310i \(-0.530842\pi\)
−0.0967407 + 0.995310i \(0.530842\pi\)
\(212\) −6.27441 −0.430928
\(213\) −0.420638 −0.0288216
\(214\) −15.8124 −1.08091
\(215\) 12.5134 0.853407
\(216\) −0.232592 −0.0158259
\(217\) 0 0
\(218\) 6.57783 0.445507
\(219\) 0.130260 0.00880217
\(220\) 8.01842 0.540602
\(221\) 1.58997 0.106953
\(222\) −0.366725 −0.0246130
\(223\) 19.0157 1.27338 0.636692 0.771118i \(-0.280302\pi\)
0.636692 + 0.771118i \(0.280302\pi\)
\(224\) 0 0
\(225\) −5.44176 −0.362784
\(226\) 3.34219 0.222319
\(227\) 9.23513 0.612957 0.306478 0.951878i \(-0.400849\pi\)
0.306478 + 0.951878i \(0.400849\pi\)
\(228\) 0.275160 0.0182229
\(229\) −19.7514 −1.30521 −0.652605 0.757698i \(-0.726324\pi\)
−0.652605 + 0.757698i \(0.726324\pi\)
\(230\) 13.8676 0.914403
\(231\) 0 0
\(232\) 2.31533 0.152009
\(233\) −19.5991 −1.28398 −0.641990 0.766713i \(-0.721891\pi\)
−0.641990 + 0.766713i \(0.721891\pi\)
\(234\) 6.26160 0.409334
\(235\) 12.0446 0.785705
\(236\) 14.3819 0.936181
\(237\) −0.0870541 −0.00565477
\(238\) 0 0
\(239\) −8.41493 −0.544317 −0.272158 0.962252i \(-0.587737\pi\)
−0.272158 + 0.962252i \(0.587737\pi\)
\(240\) 0.101223 0.00653394
\(241\) 3.36585 0.216813 0.108407 0.994107i \(-0.465425\pi\)
0.108407 + 0.994107i \(0.465425\pi\)
\(242\) −1.56542 −0.100629
\(243\) 1.04623 0.0671156
\(244\) 3.84288 0.246015
\(245\) 0 0
\(246\) −0.0387751 −0.00247221
\(247\) −14.8189 −0.942901
\(248\) 0.644105 0.0409007
\(249\) 0.302671 0.0191810
\(250\) −8.31496 −0.525884
\(251\) 2.97894 0.188029 0.0940144 0.995571i \(-0.470030\pi\)
0.0940144 + 0.995571i \(0.470030\pi\)
\(252\) 0 0
\(253\) 16.3168 1.02583
\(254\) −8.37867 −0.525725
\(255\) −0.0770704 −0.00482634
\(256\) 1.00000 0.0625000
\(257\) 6.74010 0.420436 0.210218 0.977655i \(-0.432583\pi\)
0.210218 + 0.977655i \(0.432583\pi\)
\(258\) 0.185866 0.0115715
\(259\) 0 0
\(260\) −5.45142 −0.338083
\(261\) −6.94252 −0.429731
\(262\) −12.7513 −0.787778
\(263\) 21.7936 1.34385 0.671926 0.740618i \(-0.265467\pi\)
0.671926 + 0.740618i \(0.265467\pi\)
\(264\) 0.119101 0.00733014
\(265\) −16.3795 −1.00618
\(266\) 0 0
\(267\) −0.230140 −0.0140843
\(268\) 8.37335 0.511484
\(269\) 26.2079 1.59793 0.798963 0.601380i \(-0.205382\pi\)
0.798963 + 0.601380i \(0.205382\pi\)
\(270\) −0.607188 −0.0369523
\(271\) −19.9240 −1.21030 −0.605149 0.796112i \(-0.706887\pi\)
−0.605149 + 0.796112i \(0.706887\pi\)
\(272\) −0.761390 −0.0461660
\(273\) 0 0
\(274\) 14.7866 0.893290
\(275\) 5.57438 0.336148
\(276\) 0.205981 0.0123986
\(277\) 20.0693 1.20585 0.602923 0.797799i \(-0.294003\pi\)
0.602923 + 0.797799i \(0.294003\pi\)
\(278\) 9.80861 0.588282
\(279\) −1.93135 −0.115627
\(280\) 0 0
\(281\) 22.8047 1.36041 0.680207 0.733020i \(-0.261890\pi\)
0.680207 + 0.733020i \(0.261890\pi\)
\(282\) 0.178904 0.0106536
\(283\) −20.5397 −1.22096 −0.610479 0.792033i \(-0.709023\pi\)
−0.610479 + 0.792033i \(0.709023\pi\)
\(284\) −10.8481 −0.643718
\(285\) 0.718312 0.0425491
\(286\) −6.41421 −0.379280
\(287\) 0 0
\(288\) −2.99850 −0.176688
\(289\) −16.4203 −0.965899
\(290\) 6.04423 0.354930
\(291\) 0.649477 0.0380730
\(292\) 3.35938 0.196593
\(293\) −26.9744 −1.57586 −0.787930 0.615764i \(-0.788847\pi\)
−0.787930 + 0.615764i \(0.788847\pi\)
\(294\) 0 0
\(295\) 37.5442 2.18591
\(296\) −9.45774 −0.549720
\(297\) −0.714425 −0.0414552
\(298\) −12.1994 −0.706691
\(299\) −11.0932 −0.641535
\(300\) 0.0703702 0.00406283
\(301\) 0 0
\(302\) −20.5621 −1.18322
\(303\) 0.405805 0.0233129
\(304\) 7.09631 0.407001
\(305\) 10.0319 0.574426
\(306\) 2.28303 0.130512
\(307\) 11.9580 0.682476 0.341238 0.939977i \(-0.389154\pi\)
0.341238 + 0.939977i \(0.389154\pi\)
\(308\) 0 0
\(309\) −0.0959379 −0.00545772
\(310\) 1.68145 0.0955001
\(311\) −17.8581 −1.01264 −0.506319 0.862346i \(-0.668994\pi\)
−0.506319 + 0.862346i \(0.668994\pi\)
\(312\) −0.0809720 −0.00458414
\(313\) 10.1352 0.572876 0.286438 0.958099i \(-0.407529\pi\)
0.286438 + 0.958099i \(0.407529\pi\)
\(314\) −4.63615 −0.261633
\(315\) 0 0
\(316\) −2.24510 −0.126297
\(317\) 11.6642 0.655127 0.327564 0.944829i \(-0.393772\pi\)
0.327564 + 0.944829i \(0.393772\pi\)
\(318\) −0.243291 −0.0136431
\(319\) 7.11173 0.398180
\(320\) 2.61052 0.145933
\(321\) −0.613127 −0.0342214
\(322\) 0 0
\(323\) −5.40306 −0.300634
\(324\) 8.98647 0.499248
\(325\) −3.78981 −0.210221
\(326\) 3.11486 0.172516
\(327\) 0.255056 0.0141046
\(328\) −1.00000 −0.0552158
\(329\) 0 0
\(330\) 0.310915 0.0171153
\(331\) −12.3608 −0.679413 −0.339707 0.940531i \(-0.610328\pi\)
−0.339707 + 0.940531i \(0.610328\pi\)
\(332\) 7.80581 0.428399
\(333\) 28.3590 1.55406
\(334\) −4.77073 −0.261043
\(335\) 21.8588 1.19428
\(336\) 0 0
\(337\) 27.7851 1.51355 0.756776 0.653675i \(-0.226774\pi\)
0.756776 + 0.653675i \(0.226774\pi\)
\(338\) −8.63922 −0.469912
\(339\) 0.129594 0.00703857
\(340\) −1.98763 −0.107794
\(341\) 1.97842 0.107137
\(342\) −21.2783 −1.15060
\(343\) 0 0
\(344\) 4.79344 0.258445
\(345\) 0.537718 0.0289498
\(346\) 2.15961 0.116101
\(347\) 2.25401 0.121002 0.0605008 0.998168i \(-0.480730\pi\)
0.0605008 + 0.998168i \(0.480730\pi\)
\(348\) 0.0897774 0.00481257
\(349\) −17.0144 −0.910762 −0.455381 0.890297i \(-0.650497\pi\)
−0.455381 + 0.890297i \(0.650497\pi\)
\(350\) 0 0
\(351\) 0.485711 0.0259253
\(352\) 3.07158 0.163716
\(353\) −17.9998 −0.958032 −0.479016 0.877806i \(-0.659006\pi\)
−0.479016 + 0.877806i \(0.659006\pi\)
\(354\) 0.557659 0.0296393
\(355\) −28.3193 −1.50303
\(356\) −5.93525 −0.314568
\(357\) 0 0
\(358\) −20.1667 −1.06584
\(359\) 9.57429 0.505312 0.252656 0.967556i \(-0.418696\pi\)
0.252656 + 0.967556i \(0.418696\pi\)
\(360\) −7.82764 −0.412553
\(361\) 31.3576 1.65040
\(362\) 7.51035 0.394735
\(363\) −0.0606995 −0.00318590
\(364\) 0 0
\(365\) 8.76973 0.459029
\(366\) 0.149008 0.00778877
\(367\) 13.8966 0.725396 0.362698 0.931907i \(-0.381856\pi\)
0.362698 + 0.931907i \(0.381856\pi\)
\(368\) 5.31219 0.276917
\(369\) 2.99850 0.156095
\(370\) −24.6896 −1.28355
\(371\) 0 0
\(372\) 0.0249753 0.00129491
\(373\) −30.4692 −1.57764 −0.788818 0.614627i \(-0.789307\pi\)
−0.788818 + 0.614627i \(0.789307\pi\)
\(374\) −2.33867 −0.120930
\(375\) −0.322414 −0.0166494
\(376\) 4.61388 0.237942
\(377\) −4.83499 −0.249015
\(378\) 0 0
\(379\) 12.9617 0.665799 0.332900 0.942962i \(-0.391973\pi\)
0.332900 + 0.942962i \(0.391973\pi\)
\(380\) 18.5251 0.950317
\(381\) −0.324884 −0.0166443
\(382\) 4.24153 0.217016
\(383\) −14.7064 −0.751460 −0.375730 0.926729i \(-0.622608\pi\)
−0.375730 + 0.926729i \(0.622608\pi\)
\(384\) 0.0387751 0.00197873
\(385\) 0 0
\(386\) 13.7705 0.700902
\(387\) −14.3731 −0.730627
\(388\) 16.7498 0.850345
\(389\) −27.1877 −1.37847 −0.689235 0.724537i \(-0.742053\pi\)
−0.689235 + 0.724537i \(0.742053\pi\)
\(390\) −0.211379 −0.0107036
\(391\) −4.04465 −0.204547
\(392\) 0 0
\(393\) −0.494433 −0.0249409
\(394\) −2.68951 −0.135496
\(395\) −5.86089 −0.294894
\(396\) −9.21011 −0.462825
\(397\) −35.1116 −1.76220 −0.881100 0.472930i \(-0.843196\pi\)
−0.881100 + 0.472930i \(0.843196\pi\)
\(398\) −6.34370 −0.317981
\(399\) 0 0
\(400\) 1.81483 0.0907414
\(401\) −13.7763 −0.687958 −0.343979 0.938977i \(-0.611775\pi\)
−0.343979 + 0.938977i \(0.611775\pi\)
\(402\) 0.324678 0.0161935
\(403\) −1.34505 −0.0670018
\(404\) 10.4656 0.520683
\(405\) 23.4594 1.16571
\(406\) 0 0
\(407\) −29.0502 −1.43996
\(408\) −0.0295230 −0.00146161
\(409\) 27.4007 1.35487 0.677437 0.735580i \(-0.263090\pi\)
0.677437 + 0.735580i \(0.263090\pi\)
\(410\) −2.61052 −0.128925
\(411\) 0.573351 0.0282813
\(412\) −2.47421 −0.121896
\(413\) 0 0
\(414\) −15.9286 −0.782848
\(415\) 20.3772 1.00028
\(416\) −2.08825 −0.102385
\(417\) 0.380330 0.0186248
\(418\) 21.7969 1.06612
\(419\) −29.5386 −1.44305 −0.721527 0.692386i \(-0.756559\pi\)
−0.721527 + 0.692386i \(0.756559\pi\)
\(420\) 0 0
\(421\) 5.26049 0.256380 0.128190 0.991750i \(-0.459083\pi\)
0.128190 + 0.991750i \(0.459083\pi\)
\(422\) −2.81048 −0.136812
\(423\) −13.8347 −0.672666
\(424\) −6.27441 −0.304712
\(425\) −1.38179 −0.0670268
\(426\) −0.420638 −0.0203800
\(427\) 0 0
\(428\) −15.8124 −0.764320
\(429\) −0.248712 −0.0120079
\(430\) 12.5134 0.603450
\(431\) −34.4649 −1.66012 −0.830059 0.557676i \(-0.811693\pi\)
−0.830059 + 0.557676i \(0.811693\pi\)
\(432\) −0.232592 −0.0111906
\(433\) −8.66488 −0.416408 −0.208204 0.978085i \(-0.566762\pi\)
−0.208204 + 0.978085i \(0.566762\pi\)
\(434\) 0 0
\(435\) 0.234366 0.0112370
\(436\) 6.57783 0.315021
\(437\) 37.6970 1.80329
\(438\) 0.130260 0.00622408
\(439\) 7.77642 0.371148 0.185574 0.982630i \(-0.440586\pi\)
0.185574 + 0.982630i \(0.440586\pi\)
\(440\) 8.01842 0.382263
\(441\) 0 0
\(442\) 1.58997 0.0756272
\(443\) −10.7928 −0.512782 −0.256391 0.966573i \(-0.582533\pi\)
−0.256391 + 0.966573i \(0.582533\pi\)
\(444\) −0.366725 −0.0174040
\(445\) −15.4941 −0.734491
\(446\) 19.0157 0.900419
\(447\) −0.473032 −0.0223737
\(448\) 0 0
\(449\) −17.4966 −0.825717 −0.412859 0.910795i \(-0.635470\pi\)
−0.412859 + 0.910795i \(0.635470\pi\)
\(450\) −5.44176 −0.256527
\(451\) −3.07158 −0.144635
\(452\) 3.34219 0.157203
\(453\) −0.797298 −0.0374603
\(454\) 9.23513 0.433426
\(455\) 0 0
\(456\) 0.275160 0.0128856
\(457\) 2.68726 0.125705 0.0628524 0.998023i \(-0.479980\pi\)
0.0628524 + 0.998023i \(0.479980\pi\)
\(458\) −19.7514 −0.922923
\(459\) 0.177094 0.00826602
\(460\) 13.8676 0.646580
\(461\) −8.15008 −0.379587 −0.189794 0.981824i \(-0.560782\pi\)
−0.189794 + 0.981824i \(0.560782\pi\)
\(462\) 0 0
\(463\) 11.1325 0.517372 0.258686 0.965961i \(-0.416711\pi\)
0.258686 + 0.965961i \(0.416711\pi\)
\(464\) 2.31533 0.107487
\(465\) 0.0651985 0.00302351
\(466\) −19.5991 −0.907911
\(467\) 33.9394 1.57053 0.785265 0.619160i \(-0.212527\pi\)
0.785265 + 0.619160i \(0.212527\pi\)
\(468\) 6.26160 0.289443
\(469\) 0 0
\(470\) 12.0446 0.555577
\(471\) −0.179767 −0.00828324
\(472\) 14.3819 0.661980
\(473\) 14.7234 0.676984
\(474\) −0.0870541 −0.00399853
\(475\) 12.8786 0.590910
\(476\) 0 0
\(477\) 18.8138 0.861424
\(478\) −8.41493 −0.384890
\(479\) −4.31877 −0.197329 −0.0986647 0.995121i \(-0.531457\pi\)
−0.0986647 + 0.995121i \(0.531457\pi\)
\(480\) 0.101223 0.00462019
\(481\) 19.7501 0.900527
\(482\) 3.36585 0.153310
\(483\) 0 0
\(484\) −1.56542 −0.0711556
\(485\) 43.7259 1.98549
\(486\) 1.04623 0.0474579
\(487\) 9.08302 0.411591 0.205795 0.978595i \(-0.434022\pi\)
0.205795 + 0.978595i \(0.434022\pi\)
\(488\) 3.84288 0.173959
\(489\) 0.120779 0.00546181
\(490\) 0 0
\(491\) −34.4075 −1.55279 −0.776393 0.630249i \(-0.782953\pi\)
−0.776393 + 0.630249i \(0.782953\pi\)
\(492\) −0.0387751 −0.00174812
\(493\) −1.76287 −0.0793958
\(494\) −14.8189 −0.666732
\(495\) −24.0432 −1.08066
\(496\) 0.644105 0.0289212
\(497\) 0 0
\(498\) 0.302671 0.0135630
\(499\) 13.8869 0.621665 0.310833 0.950465i \(-0.399392\pi\)
0.310833 + 0.950465i \(0.399392\pi\)
\(500\) −8.31496 −0.371856
\(501\) −0.184986 −0.00826455
\(502\) 2.97894 0.132956
\(503\) −16.1893 −0.721847 −0.360923 0.932595i \(-0.617538\pi\)
−0.360923 + 0.932595i \(0.617538\pi\)
\(504\) 0 0
\(505\) 27.3207 1.21575
\(506\) 16.3168 0.725371
\(507\) −0.334987 −0.0148773
\(508\) −8.37867 −0.371743
\(509\) 26.6050 1.17925 0.589623 0.807679i \(-0.299276\pi\)
0.589623 + 0.807679i \(0.299276\pi\)
\(510\) −0.0770704 −0.00341274
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −1.65055 −0.0728735
\(514\) 6.74010 0.297293
\(515\) −6.45899 −0.284617
\(516\) 0.185866 0.00818231
\(517\) 14.1719 0.623278
\(518\) 0 0
\(519\) 0.0837389 0.00367573
\(520\) −5.45142 −0.239060
\(521\) −21.8148 −0.955722 −0.477861 0.878436i \(-0.658588\pi\)
−0.477861 + 0.878436i \(0.658588\pi\)
\(522\) −6.94252 −0.303866
\(523\) −31.0649 −1.35838 −0.679188 0.733965i \(-0.737668\pi\)
−0.679188 + 0.733965i \(0.737668\pi\)
\(524\) −12.7513 −0.557043
\(525\) 0 0
\(526\) 21.7936 0.950247
\(527\) −0.490415 −0.0213628
\(528\) 0.119101 0.00518319
\(529\) 5.21941 0.226931
\(530\) −16.3795 −0.711479
\(531\) −43.1240 −1.87142
\(532\) 0 0
\(533\) 2.08825 0.0904520
\(534\) −0.230140 −0.00995914
\(535\) −41.2785 −1.78463
\(536\) 8.37335 0.361674
\(537\) −0.781964 −0.0337443
\(538\) 26.2079 1.12990
\(539\) 0 0
\(540\) −0.607188 −0.0261292
\(541\) 15.6807 0.674166 0.337083 0.941475i \(-0.390560\pi\)
0.337083 + 0.941475i \(0.390560\pi\)
\(542\) −19.9240 −0.855810
\(543\) 0.291215 0.0124972
\(544\) −0.761390 −0.0326443
\(545\) 17.1716 0.735549
\(546\) 0 0
\(547\) −5.18783 −0.221816 −0.110908 0.993831i \(-0.535376\pi\)
−0.110908 + 0.993831i \(0.535376\pi\)
\(548\) 14.7866 0.631651
\(549\) −11.5229 −0.491783
\(550\) 5.57438 0.237693
\(551\) 16.4303 0.699956
\(552\) 0.205981 0.00876713
\(553\) 0 0
\(554\) 20.0693 0.852662
\(555\) −0.957344 −0.0406370
\(556\) 9.80861 0.415978
\(557\) −20.5638 −0.871318 −0.435659 0.900112i \(-0.643485\pi\)
−0.435659 + 0.900112i \(0.643485\pi\)
\(558\) −1.93135 −0.0817605
\(559\) −10.0099 −0.423374
\(560\) 0 0
\(561\) −0.0906821 −0.00382860
\(562\) 22.8047 0.961957
\(563\) 30.8588 1.30054 0.650271 0.759702i \(-0.274655\pi\)
0.650271 + 0.759702i \(0.274655\pi\)
\(564\) 0.178904 0.00753320
\(565\) 8.72486 0.367058
\(566\) −20.5397 −0.863347
\(567\) 0 0
\(568\) −10.8481 −0.455178
\(569\) 34.7113 1.45517 0.727587 0.686016i \(-0.240642\pi\)
0.727587 + 0.686016i \(0.240642\pi\)
\(570\) 0.718312 0.0300868
\(571\) 8.47738 0.354767 0.177384 0.984142i \(-0.443237\pi\)
0.177384 + 0.984142i \(0.443237\pi\)
\(572\) −6.41421 −0.268192
\(573\) 0.164466 0.00687067
\(574\) 0 0
\(575\) 9.64072 0.402046
\(576\) −2.99850 −0.124937
\(577\) −16.7833 −0.698697 −0.349348 0.936993i \(-0.613597\pi\)
−0.349348 + 0.936993i \(0.613597\pi\)
\(578\) −16.4203 −0.682994
\(579\) 0.533954 0.0221904
\(580\) 6.04423 0.250973
\(581\) 0 0
\(582\) 0.649477 0.0269217
\(583\) −19.2723 −0.798178
\(584\) 3.35938 0.139012
\(585\) 16.3461 0.675826
\(586\) −26.9744 −1.11430
\(587\) −17.1051 −0.706003 −0.353001 0.935623i \(-0.614839\pi\)
−0.353001 + 0.935623i \(0.614839\pi\)
\(588\) 0 0
\(589\) 4.57077 0.188335
\(590\) 37.5442 1.54567
\(591\) −0.104286 −0.00428976
\(592\) −9.45774 −0.388711
\(593\) −23.4517 −0.963047 −0.481523 0.876433i \(-0.659916\pi\)
−0.481523 + 0.876433i \(0.659916\pi\)
\(594\) −0.714425 −0.0293132
\(595\) 0 0
\(596\) −12.1994 −0.499706
\(597\) −0.245978 −0.0100672
\(598\) −11.0932 −0.453634
\(599\) −20.3118 −0.829917 −0.414958 0.909840i \(-0.636204\pi\)
−0.414958 + 0.909840i \(0.636204\pi\)
\(600\) 0.0703702 0.00287285
\(601\) −21.9226 −0.894240 −0.447120 0.894474i \(-0.647550\pi\)
−0.447120 + 0.894474i \(0.647550\pi\)
\(602\) 0 0
\(603\) −25.1075 −1.02246
\(604\) −20.5621 −0.836660
\(605\) −4.08657 −0.166143
\(606\) 0.405805 0.0164847
\(607\) −0.152226 −0.00617865 −0.00308932 0.999995i \(-0.500983\pi\)
−0.00308932 + 0.999995i \(0.500983\pi\)
\(608\) 7.09631 0.287793
\(609\) 0 0
\(610\) 10.0319 0.406180
\(611\) −9.63491 −0.389787
\(612\) 2.28303 0.0922858
\(613\) 16.8306 0.679782 0.339891 0.940465i \(-0.389610\pi\)
0.339891 + 0.940465i \(0.389610\pi\)
\(614\) 11.9580 0.482584
\(615\) −0.101223 −0.00408172
\(616\) 0 0
\(617\) 41.5730 1.67366 0.836832 0.547459i \(-0.184405\pi\)
0.836832 + 0.547459i \(0.184405\pi\)
\(618\) −0.0959379 −0.00385919
\(619\) −1.19822 −0.0481604 −0.0240802 0.999710i \(-0.507666\pi\)
−0.0240802 + 0.999710i \(0.507666\pi\)
\(620\) 1.68145 0.0675287
\(621\) −1.23558 −0.0495820
\(622\) −17.8581 −0.716043
\(623\) 0 0
\(624\) −0.0809720 −0.00324148
\(625\) −30.7805 −1.23122
\(626\) 10.1352 0.405085
\(627\) 0.845176 0.0337531
\(628\) −4.63615 −0.185003
\(629\) 7.20103 0.287124
\(630\) 0 0
\(631\) 16.6115 0.661292 0.330646 0.943755i \(-0.392733\pi\)
0.330646 + 0.943755i \(0.392733\pi\)
\(632\) −2.24510 −0.0893054
\(633\) −0.108977 −0.00433143
\(634\) 11.6642 0.463245
\(635\) −21.8727 −0.867992
\(636\) −0.243291 −0.00964711
\(637\) 0 0
\(638\) 7.11173 0.281556
\(639\) 32.5281 1.28679
\(640\) 2.61052 0.103190
\(641\) −43.1532 −1.70445 −0.852225 0.523176i \(-0.824747\pi\)
−0.852225 + 0.523176i \(0.824747\pi\)
\(642\) −0.613127 −0.0241982
\(643\) −36.4417 −1.43712 −0.718559 0.695466i \(-0.755198\pi\)
−0.718559 + 0.695466i \(0.755198\pi\)
\(644\) 0 0
\(645\) 0.485208 0.0191051
\(646\) −5.40306 −0.212581
\(647\) 18.1008 0.711616 0.355808 0.934559i \(-0.384206\pi\)
0.355808 + 0.934559i \(0.384206\pi\)
\(648\) 8.98647 0.353022
\(649\) 44.1751 1.73402
\(650\) −3.78981 −0.148649
\(651\) 0 0
\(652\) 3.11486 0.121987
\(653\) −26.7064 −1.04510 −0.522551 0.852608i \(-0.675020\pi\)
−0.522551 + 0.852608i \(0.675020\pi\)
\(654\) 0.255056 0.00997348
\(655\) −33.2876 −1.30065
\(656\) −1.00000 −0.0390434
\(657\) −10.0731 −0.392988
\(658\) 0 0
\(659\) −49.7015 −1.93609 −0.968047 0.250767i \(-0.919317\pi\)
−0.968047 + 0.250767i \(0.919317\pi\)
\(660\) 0.310915 0.0121024
\(661\) 12.2909 0.478061 0.239030 0.971012i \(-0.423170\pi\)
0.239030 + 0.971012i \(0.423170\pi\)
\(662\) −12.3608 −0.480418
\(663\) 0.0616513 0.00239434
\(664\) 7.80581 0.302924
\(665\) 0 0
\(666\) 28.3590 1.09889
\(667\) 12.2995 0.476239
\(668\) −4.77073 −0.184585
\(669\) 0.737336 0.0285070
\(670\) 21.8588 0.844480
\(671\) 11.8037 0.455676
\(672\) 0 0
\(673\) 3.11146 0.119938 0.0599689 0.998200i \(-0.480900\pi\)
0.0599689 + 0.998200i \(0.480900\pi\)
\(674\) 27.7851 1.07024
\(675\) −0.422115 −0.0162472
\(676\) −8.63922 −0.332278
\(677\) 24.4512 0.939736 0.469868 0.882737i \(-0.344301\pi\)
0.469868 + 0.882737i \(0.344301\pi\)
\(678\) 0.129594 0.00497702
\(679\) 0 0
\(680\) −1.98763 −0.0762220
\(681\) 0.358093 0.0137222
\(682\) 1.97842 0.0757576
\(683\) 17.3445 0.663669 0.331834 0.943338i \(-0.392333\pi\)
0.331834 + 0.943338i \(0.392333\pi\)
\(684\) −21.2783 −0.813595
\(685\) 38.6007 1.47486
\(686\) 0 0
\(687\) −0.765863 −0.0292195
\(688\) 4.79344 0.182748
\(689\) 13.1025 0.499166
\(690\) 0.537718 0.0204706
\(691\) −43.8282 −1.66730 −0.833652 0.552290i \(-0.813754\pi\)
−0.833652 + 0.552290i \(0.813754\pi\)
\(692\) 2.15961 0.0820959
\(693\) 0 0
\(694\) 2.25401 0.0855610
\(695\) 25.6056 0.971276
\(696\) 0.0897774 0.00340300
\(697\) 0.761390 0.0288397
\(698\) −17.0144 −0.644006
\(699\) −0.759958 −0.0287442
\(700\) 0 0
\(701\) −46.1293 −1.74228 −0.871139 0.491036i \(-0.836618\pi\)
−0.871139 + 0.491036i \(0.836618\pi\)
\(702\) 0.485711 0.0183320
\(703\) −67.1151 −2.53129
\(704\) 3.07158 0.115764
\(705\) 0.467032 0.0175894
\(706\) −17.9998 −0.677431
\(707\) 0 0
\(708\) 0.557659 0.0209581
\(709\) −44.6646 −1.67741 −0.838707 0.544583i \(-0.816688\pi\)
−0.838707 + 0.544583i \(0.816688\pi\)
\(710\) −28.3193 −1.06280
\(711\) 6.73193 0.252467
\(712\) −5.93525 −0.222433
\(713\) 3.42161 0.128140
\(714\) 0 0
\(715\) −16.7444 −0.626207
\(716\) −20.1667 −0.753663
\(717\) −0.326290 −0.0121855
\(718\) 9.57429 0.357309
\(719\) −12.9542 −0.483110 −0.241555 0.970387i \(-0.577657\pi\)
−0.241555 + 0.970387i \(0.577657\pi\)
\(720\) −7.82764 −0.291719
\(721\) 0 0
\(722\) 31.3576 1.16701
\(723\) 0.130511 0.00485376
\(724\) 7.51035 0.279120
\(725\) 4.20194 0.156056
\(726\) −0.0606995 −0.00225277
\(727\) 24.3968 0.904827 0.452414 0.891808i \(-0.350563\pi\)
0.452414 + 0.891808i \(0.350563\pi\)
\(728\) 0 0
\(729\) −26.9188 −0.996994
\(730\) 8.76973 0.324582
\(731\) −3.64968 −0.134988
\(732\) 0.149008 0.00550749
\(733\) −25.5066 −0.942106 −0.471053 0.882105i \(-0.656126\pi\)
−0.471053 + 0.882105i \(0.656126\pi\)
\(734\) 13.8966 0.512932
\(735\) 0 0
\(736\) 5.31219 0.195810
\(737\) 25.7194 0.947386
\(738\) 2.99850 0.110376
\(739\) 50.7786 1.86792 0.933961 0.357376i \(-0.116328\pi\)
0.933961 + 0.357376i \(0.116328\pi\)
\(740\) −24.6896 −0.907609
\(741\) −0.574603 −0.0211086
\(742\) 0 0
\(743\) 7.81231 0.286606 0.143303 0.989679i \(-0.454228\pi\)
0.143303 + 0.989679i \(0.454228\pi\)
\(744\) 0.0249753 0.000915638 0
\(745\) −31.8468 −1.16677
\(746\) −30.4692 −1.11556
\(747\) −23.4057 −0.856370
\(748\) −2.33867 −0.0855101
\(749\) 0 0
\(750\) −0.322414 −0.0117729
\(751\) 27.5822 1.00649 0.503245 0.864144i \(-0.332139\pi\)
0.503245 + 0.864144i \(0.332139\pi\)
\(752\) 4.61388 0.168251
\(753\) 0.115509 0.00420937
\(754\) −4.83499 −0.176080
\(755\) −53.6778 −1.95354
\(756\) 0 0
\(757\) −39.6468 −1.44099 −0.720493 0.693462i \(-0.756085\pi\)
−0.720493 + 0.693462i \(0.756085\pi\)
\(758\) 12.9617 0.470791
\(759\) 0.632686 0.0229651
\(760\) 18.5251 0.671975
\(761\) −32.1470 −1.16533 −0.582665 0.812713i \(-0.697990\pi\)
−0.582665 + 0.812713i \(0.697990\pi\)
\(762\) −0.324884 −0.0117693
\(763\) 0 0
\(764\) 4.24153 0.153453
\(765\) 5.95989 0.215480
\(766\) −14.7064 −0.531362
\(767\) −30.0329 −1.08443
\(768\) 0.0387751 0.00139918
\(769\) 23.9039 0.861998 0.430999 0.902353i \(-0.358161\pi\)
0.430999 + 0.902353i \(0.358161\pi\)
\(770\) 0 0
\(771\) 0.261348 0.00941222
\(772\) 13.7705 0.495612
\(773\) 8.23647 0.296245 0.148123 0.988969i \(-0.452677\pi\)
0.148123 + 0.988969i \(0.452677\pi\)
\(774\) −14.3731 −0.516631
\(775\) 1.16894 0.0419896
\(776\) 16.7498 0.601284
\(777\) 0 0
\(778\) −27.1877 −0.974726
\(779\) −7.09631 −0.254252
\(780\) −0.211379 −0.00756860
\(781\) −33.3209 −1.19231
\(782\) −4.04465 −0.144636
\(783\) −0.538529 −0.0192455
\(784\) 0 0
\(785\) −12.1028 −0.431967
\(786\) −0.494433 −0.0176359
\(787\) −21.2691 −0.758163 −0.379082 0.925363i \(-0.623760\pi\)
−0.379082 + 0.925363i \(0.623760\pi\)
\(788\) −2.68951 −0.0958100
\(789\) 0.845050 0.0300846
\(790\) −5.86089 −0.208521
\(791\) 0 0
\(792\) −9.21011 −0.327267
\(793\) −8.02488 −0.284972
\(794\) −35.1116 −1.24606
\(795\) −0.635116 −0.0225253
\(796\) −6.34370 −0.224847
\(797\) 19.7091 0.698133 0.349067 0.937098i \(-0.386499\pi\)
0.349067 + 0.937098i \(0.386499\pi\)
\(798\) 0 0
\(799\) −3.51296 −0.124280
\(800\) 1.81483 0.0641639
\(801\) 17.7968 0.628820
\(802\) −13.7763 −0.486460
\(803\) 10.3186 0.364135
\(804\) 0.324678 0.0114505
\(805\) 0 0
\(806\) −1.34505 −0.0473774
\(807\) 1.01622 0.0357725
\(808\) 10.4656 0.368178
\(809\) −20.9287 −0.735813 −0.367907 0.929863i \(-0.619925\pi\)
−0.367907 + 0.929863i \(0.619925\pi\)
\(810\) 23.4594 0.824279
\(811\) −6.04921 −0.212417 −0.106208 0.994344i \(-0.533871\pi\)
−0.106208 + 0.994344i \(0.533871\pi\)
\(812\) 0 0
\(813\) −0.772557 −0.0270947
\(814\) −29.0502 −1.01821
\(815\) 8.13140 0.284831
\(816\) −0.0295230 −0.00103351
\(817\) 34.0158 1.19006
\(818\) 27.4007 0.958041
\(819\) 0 0
\(820\) −2.61052 −0.0911634
\(821\) 9.72428 0.339380 0.169690 0.985498i \(-0.445723\pi\)
0.169690 + 0.985498i \(0.445723\pi\)
\(822\) 0.573351 0.0199979
\(823\) −13.8729 −0.483578 −0.241789 0.970329i \(-0.577734\pi\)
−0.241789 + 0.970329i \(0.577734\pi\)
\(824\) −2.47421 −0.0861933
\(825\) 0.216147 0.00752529
\(826\) 0 0
\(827\) −28.1407 −0.978547 −0.489273 0.872130i \(-0.662738\pi\)
−0.489273 + 0.872130i \(0.662738\pi\)
\(828\) −15.9286 −0.553557
\(829\) −23.1463 −0.803904 −0.401952 0.915661i \(-0.631668\pi\)
−0.401952 + 0.915661i \(0.631668\pi\)
\(830\) 20.3772 0.707304
\(831\) 0.778189 0.0269951
\(832\) −2.08825 −0.0723970
\(833\) 0 0
\(834\) 0.380330 0.0131698
\(835\) −12.4541 −0.430992
\(836\) 21.7969 0.753860
\(837\) −0.149814 −0.00517833
\(838\) −29.5386 −1.02039
\(839\) −24.5774 −0.848508 −0.424254 0.905543i \(-0.639464\pi\)
−0.424254 + 0.905543i \(0.639464\pi\)
\(840\) 0 0
\(841\) −23.6392 −0.815146
\(842\) 5.26049 0.181288
\(843\) 0.884254 0.0304553
\(844\) −2.81048 −0.0967407
\(845\) −22.5529 −0.775843
\(846\) −13.8347 −0.475646
\(847\) 0 0
\(848\) −6.27441 −0.215464
\(849\) −0.796429 −0.0273334
\(850\) −1.38179 −0.0473951
\(851\) −50.2414 −1.72225
\(852\) −0.420638 −0.0144108
\(853\) −49.7805 −1.70445 −0.852225 0.523175i \(-0.824747\pi\)
−0.852225 + 0.523175i \(0.824747\pi\)
\(854\) 0 0
\(855\) −55.5474 −1.89968
\(856\) −15.8124 −0.540456
\(857\) 27.5930 0.942559 0.471280 0.881984i \(-0.343792\pi\)
0.471280 + 0.881984i \(0.343792\pi\)
\(858\) −0.248712 −0.00849088
\(859\) −26.1523 −0.892306 −0.446153 0.894957i \(-0.647206\pi\)
−0.446153 + 0.894957i \(0.647206\pi\)
\(860\) 12.5134 0.426703
\(861\) 0 0
\(862\) −34.4649 −1.17388
\(863\) 38.4067 1.30738 0.653689 0.756763i \(-0.273220\pi\)
0.653689 + 0.756763i \(0.273220\pi\)
\(864\) −0.232592 −0.00791295
\(865\) 5.63770 0.191687
\(866\) −8.66488 −0.294445
\(867\) −0.636699 −0.0216234
\(868\) 0 0
\(869\) −6.89600 −0.233931
\(870\) 0.234366 0.00794575
\(871\) −17.4856 −0.592478
\(872\) 6.57783 0.222753
\(873\) −50.2244 −1.69984
\(874\) 37.6970 1.27512
\(875\) 0 0
\(876\) 0.130260 0.00440109
\(877\) −5.62482 −0.189937 −0.0949683 0.995480i \(-0.530275\pi\)
−0.0949683 + 0.995480i \(0.530275\pi\)
\(878\) 7.77642 0.262441
\(879\) −1.04594 −0.0352785
\(880\) 8.01842 0.270301
\(881\) 49.5452 1.66922 0.834610 0.550841i \(-0.185693\pi\)
0.834610 + 0.550841i \(0.185693\pi\)
\(882\) 0 0
\(883\) −12.0172 −0.404409 −0.202205 0.979343i \(-0.564811\pi\)
−0.202205 + 0.979343i \(0.564811\pi\)
\(884\) 1.58997 0.0534765
\(885\) 1.45578 0.0489356
\(886\) −10.7928 −0.362592
\(887\) 44.5177 1.49476 0.747379 0.664398i \(-0.231312\pi\)
0.747379 + 0.664398i \(0.231312\pi\)
\(888\) −0.366725 −0.0123065
\(889\) 0 0
\(890\) −15.4941 −0.519364
\(891\) 27.6026 0.924723
\(892\) 19.0157 0.636692
\(893\) 32.7415 1.09565
\(894\) −0.473032 −0.0158206
\(895\) −52.6455 −1.75975
\(896\) 0 0
\(897\) −0.430139 −0.0143619
\(898\) −17.4966 −0.583870
\(899\) 1.49132 0.0497383
\(900\) −5.44176 −0.181392
\(901\) 4.77727 0.159154
\(902\) −3.07158 −0.102272
\(903\) 0 0
\(904\) 3.34219 0.111160
\(905\) 19.6059 0.651723
\(906\) −0.797298 −0.0264885
\(907\) 12.3361 0.409612 0.204806 0.978803i \(-0.434344\pi\)
0.204806 + 0.978803i \(0.434344\pi\)
\(908\) 9.23513 0.306478
\(909\) −31.3810 −1.04084
\(910\) 0 0
\(911\) 57.3470 1.89999 0.949996 0.312262i \(-0.101087\pi\)
0.949996 + 0.312262i \(0.101087\pi\)
\(912\) 0.275160 0.00911147
\(913\) 23.9761 0.793494
\(914\) 2.68726 0.0888867
\(915\) 0.388989 0.0128596
\(916\) −19.7514 −0.652605
\(917\) 0 0
\(918\) 0.177094 0.00584496
\(919\) 51.2205 1.68961 0.844804 0.535075i \(-0.179717\pi\)
0.844804 + 0.535075i \(0.179717\pi\)
\(920\) 13.8676 0.457201
\(921\) 0.463671 0.0152785
\(922\) −8.15008 −0.268409
\(923\) 22.6536 0.745652
\(924\) 0 0
\(925\) −17.1642 −0.564355
\(926\) 11.1325 0.365837
\(927\) 7.41892 0.243669
\(928\) 2.31533 0.0760046
\(929\) 21.9800 0.721140 0.360570 0.932732i \(-0.382582\pi\)
0.360570 + 0.932732i \(0.382582\pi\)
\(930\) 0.0651985 0.00213794
\(931\) 0 0
\(932\) −19.5991 −0.641990
\(933\) −0.692449 −0.0226698
\(934\) 33.9394 1.11053
\(935\) −6.10514 −0.199660
\(936\) 6.26160 0.204667
\(937\) 34.1101 1.11433 0.557164 0.830403i \(-0.311890\pi\)
0.557164 + 0.830403i \(0.311890\pi\)
\(938\) 0 0
\(939\) 0.392994 0.0128249
\(940\) 12.0446 0.392852
\(941\) 37.0147 1.20665 0.603323 0.797497i \(-0.293843\pi\)
0.603323 + 0.797497i \(0.293843\pi\)
\(942\) −0.179767 −0.00585713
\(943\) −5.31219 −0.172989
\(944\) 14.3819 0.468091
\(945\) 0 0
\(946\) 14.7234 0.478700
\(947\) 11.6847 0.379703 0.189851 0.981813i \(-0.439199\pi\)
0.189851 + 0.981813i \(0.439199\pi\)
\(948\) −0.0870541 −0.00282739
\(949\) −7.01521 −0.227723
\(950\) 12.8786 0.417837
\(951\) 0.452281 0.0146662
\(952\) 0 0
\(953\) −41.1180 −1.33194 −0.665971 0.745978i \(-0.731982\pi\)
−0.665971 + 0.745978i \(0.731982\pi\)
\(954\) 18.8138 0.609119
\(955\) 11.0726 0.358302
\(956\) −8.41493 −0.272158
\(957\) 0.275758 0.00891399
\(958\) −4.31877 −0.139533
\(959\) 0 0
\(960\) 0.101223 0.00326697
\(961\) −30.5851 −0.986617
\(962\) 19.7501 0.636769
\(963\) 47.4133 1.52787
\(964\) 3.36585 0.108407
\(965\) 35.9483 1.15722
\(966\) 0 0
\(967\) 22.6510 0.728407 0.364203 0.931319i \(-0.381341\pi\)
0.364203 + 0.931319i \(0.381341\pi\)
\(968\) −1.56542 −0.0503146
\(969\) −0.209504 −0.00673025
\(970\) 43.7259 1.40395
\(971\) 5.04506 0.161904 0.0809518 0.996718i \(-0.474204\pi\)
0.0809518 + 0.996718i \(0.474204\pi\)
\(972\) 1.04623 0.0335578
\(973\) 0 0
\(974\) 9.08302 0.291039
\(975\) −0.146950 −0.00470618
\(976\) 3.84288 0.123008
\(977\) 11.8207 0.378178 0.189089 0.981960i \(-0.439447\pi\)
0.189089 + 0.981960i \(0.439447\pi\)
\(978\) 0.120779 0.00386208
\(979\) −18.2306 −0.582652
\(980\) 0 0
\(981\) −19.7236 −0.629726
\(982\) −34.4075 −1.09799
\(983\) 44.6385 1.42375 0.711873 0.702308i \(-0.247847\pi\)
0.711873 + 0.702308i \(0.247847\pi\)
\(984\) −0.0387751 −0.00123611
\(985\) −7.02104 −0.223709
\(986\) −1.76287 −0.0561413
\(987\) 0 0
\(988\) −14.8189 −0.471451
\(989\) 25.4637 0.809699
\(990\) −24.0432 −0.764143
\(991\) 37.0298 1.17629 0.588146 0.808755i \(-0.299858\pi\)
0.588146 + 0.808755i \(0.299858\pi\)
\(992\) 0.644105 0.0204504
\(993\) −0.479293 −0.0152099
\(994\) 0 0
\(995\) −16.5604 −0.524999
\(996\) 0.302671 0.00959050
\(997\) −46.9480 −1.48686 −0.743429 0.668815i \(-0.766802\pi\)
−0.743429 + 0.668815i \(0.766802\pi\)
\(998\) 13.8869 0.439584
\(999\) 2.19980 0.0695986
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 4018.2.a.bq.1.3 yes 6
7.6 odd 2 4018.2.a.bp.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4018.2.a.bp.1.4 6 7.6 odd 2
4018.2.a.bq.1.3 yes 6 1.1 even 1 trivial