Properties

Label 5054.2.a.z.1.4
Level $5054$
Weight $2$
Character 5054.1
Self dual yes
Analytic conductor $40.356$
Analytic rank $1$
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] = [5054,2,Mod(1,5054)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5054, 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("5054.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5054.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: \(40.3563931816\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.36538000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 \) 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 1.4
Root \(0.479869\) of defining polynomial
Character \(\chi\) \(=\) 5054.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.479869 q^{3} +1.00000 q^{4} -2.85512 q^{5} -0.479869 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.76973 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.479869 q^{3} +1.00000 q^{4} -2.85512 q^{5} -0.479869 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.76973 q^{9} +2.85512 q^{10} +5.13981 q^{11} +0.479869 q^{12} -0.235441 q^{13} -1.00000 q^{14} -1.37008 q^{15} +1.00000 q^{16} -4.72430 q^{17} +2.76973 q^{18} -2.85512 q^{20} +0.479869 q^{21} -5.13981 q^{22} +6.09954 q^{23} -0.479869 q^{24} +3.15169 q^{25} +0.235441 q^{26} -2.76871 q^{27} +1.00000 q^{28} -5.85159 q^{29} +1.37008 q^{30} +5.68999 q^{31} -1.00000 q^{32} +2.46643 q^{33} +4.72430 q^{34} -2.85512 q^{35} -2.76973 q^{36} -2.94785 q^{37} -0.112981 q^{39} +2.85512 q^{40} +3.33146 q^{41} -0.479869 q^{42} -6.50989 q^{43} +5.13981 q^{44} +7.90789 q^{45} -6.09954 q^{46} -0.589626 q^{47} +0.479869 q^{48} +1.00000 q^{49} -3.15169 q^{50} -2.26704 q^{51} -0.235441 q^{52} +8.65809 q^{53} +2.76871 q^{54} -14.6748 q^{55} -1.00000 q^{56} +5.85159 q^{58} +8.79576 q^{59} -1.37008 q^{60} -5.43170 q^{61} -5.68999 q^{62} -2.76973 q^{63} +1.00000 q^{64} +0.672211 q^{65} -2.46643 q^{66} -11.1291 q^{67} -4.72430 q^{68} +2.92698 q^{69} +2.85512 q^{70} -3.04026 q^{71} +2.76973 q^{72} +10.8507 q^{73} +2.94785 q^{74} +1.51240 q^{75} +5.13981 q^{77} +0.112981 q^{78} -10.2573 q^{79} -2.85512 q^{80} +6.98056 q^{81} -3.33146 q^{82} +12.1326 q^{83} +0.479869 q^{84} +13.4884 q^{85} +6.50989 q^{86} -2.80800 q^{87} -5.13981 q^{88} -15.2958 q^{89} -7.90789 q^{90} -0.235441 q^{91} +6.09954 q^{92} +2.73045 q^{93} +0.589626 q^{94} -0.479869 q^{96} -10.2497 q^{97} -1.00000 q^{98} -14.2359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} - 6 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 15 q^{13} - 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 8 q^{18} - q^{20} - 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} + 12 q^{27} + 6 q^{28} - 7 q^{29} + 6 q^{30} - 4 q^{31} - 6 q^{32} - 28 q^{33} + 9 q^{34} - q^{35} + 8 q^{36} - 3 q^{37} - 8 q^{39} + q^{40} - 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} - 4 q^{46} + 12 q^{47} + 6 q^{49} - q^{50} - 44 q^{51} - 15 q^{52} + 5 q^{53} - 12 q^{54} - 8 q^{55} - 6 q^{56} + 7 q^{58} - 4 q^{59} - 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} + 20 q^{65} + 28 q^{66} - 14 q^{67} - 9 q^{68} + 24 q^{69} + q^{70} - 24 q^{71} - 8 q^{72} - 21 q^{73} + 3 q^{74} - 12 q^{75} + 4 q^{77} + 8 q^{78} - 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} + 10 q^{86} - 8 q^{87} - 4 q^{88} - 7 q^{89} - 19 q^{90} - 15 q^{91} + 4 q^{92} - 22 q^{93} - 12 q^{94} - 7 q^{97} - 6 q^{98} - 26 q^{99}+O(q^{100}) \) 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
\(3\) 0.479869 0.277052 0.138526 0.990359i \(-0.455763\pi\)
0.138526 + 0.990359i \(0.455763\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.85512 −1.27685 −0.638424 0.769685i \(-0.720413\pi\)
−0.638424 + 0.769685i \(0.720413\pi\)
\(6\) −0.479869 −0.195906
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.76973 −0.923242
\(10\) 2.85512 0.902867
\(11\) 5.13981 1.54971 0.774855 0.632139i \(-0.217823\pi\)
0.774855 + 0.632139i \(0.217823\pi\)
\(12\) 0.479869 0.138526
\(13\) −0.235441 −0.0652995 −0.0326498 0.999467i \(-0.510395\pi\)
−0.0326498 + 0.999467i \(0.510395\pi\)
\(14\) −1.00000 −0.267261
\(15\) −1.37008 −0.353753
\(16\) 1.00000 0.250000
\(17\) −4.72430 −1.14581 −0.572905 0.819622i \(-0.694184\pi\)
−0.572905 + 0.819622i \(0.694184\pi\)
\(18\) 2.76973 0.652831
\(19\) 0 0
\(20\) −2.85512 −0.638424
\(21\) 0.479869 0.104716
\(22\) −5.13981 −1.09581
\(23\) 6.09954 1.27184 0.635922 0.771754i \(-0.280620\pi\)
0.635922 + 0.771754i \(0.280620\pi\)
\(24\) −0.479869 −0.0979528
\(25\) 3.15169 0.630338
\(26\) 0.235441 0.0461737
\(27\) −2.76871 −0.532839
\(28\) 1.00000 0.188982
\(29\) −5.85159 −1.08661 −0.543307 0.839534i \(-0.682828\pi\)
−0.543307 + 0.839534i \(0.682828\pi\)
\(30\) 1.37008 0.250141
\(31\) 5.68999 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.46643 0.429351
\(34\) 4.72430 0.810210
\(35\) −2.85512 −0.482603
\(36\) −2.76973 −0.461621
\(37\) −2.94785 −0.484624 −0.242312 0.970198i \(-0.577906\pi\)
−0.242312 + 0.970198i \(0.577906\pi\)
\(38\) 0 0
\(39\) −0.112981 −0.0180914
\(40\) 2.85512 0.451434
\(41\) 3.33146 0.520287 0.260143 0.965570i \(-0.416230\pi\)
0.260143 + 0.965570i \(0.416230\pi\)
\(42\) −0.479869 −0.0740454
\(43\) −6.50989 −0.992749 −0.496374 0.868109i \(-0.665336\pi\)
−0.496374 + 0.868109i \(0.665336\pi\)
\(44\) 5.13981 0.774855
\(45\) 7.90789 1.17884
\(46\) −6.09954 −0.899329
\(47\) −0.589626 −0.0860057 −0.0430029 0.999075i \(-0.513692\pi\)
−0.0430029 + 0.999075i \(0.513692\pi\)
\(48\) 0.479869 0.0692631
\(49\) 1.00000 0.142857
\(50\) −3.15169 −0.445717
\(51\) −2.26704 −0.317449
\(52\) −0.235441 −0.0326498
\(53\) 8.65809 1.18928 0.594640 0.803992i \(-0.297295\pi\)
0.594640 + 0.803992i \(0.297295\pi\)
\(54\) 2.76871 0.376774
\(55\) −14.6748 −1.97874
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 5.85159 0.768352
\(59\) 8.79576 1.14511 0.572556 0.819866i \(-0.305952\pi\)
0.572556 + 0.819866i \(0.305952\pi\)
\(60\) −1.37008 −0.176877
\(61\) −5.43170 −0.695458 −0.347729 0.937595i \(-0.613047\pi\)
−0.347729 + 0.937595i \(0.613047\pi\)
\(62\) −5.68999 −0.722629
\(63\) −2.76973 −0.348953
\(64\) 1.00000 0.125000
\(65\) 0.672211 0.0833775
\(66\) −2.46643 −0.303597
\(67\) −11.1291 −1.35964 −0.679818 0.733380i \(-0.737941\pi\)
−0.679818 + 0.733380i \(0.737941\pi\)
\(68\) −4.72430 −0.572905
\(69\) 2.92698 0.352367
\(70\) 2.85512 0.341252
\(71\) −3.04026 −0.360813 −0.180406 0.983592i \(-0.557741\pi\)
−0.180406 + 0.983592i \(0.557741\pi\)
\(72\) 2.76973 0.326415
\(73\) 10.8507 1.26997 0.634987 0.772523i \(-0.281005\pi\)
0.634987 + 0.772523i \(0.281005\pi\)
\(74\) 2.94785 0.342681
\(75\) 1.51240 0.174637
\(76\) 0 0
\(77\) 5.13981 0.585735
\(78\) 0.112981 0.0127925
\(79\) −10.2573 −1.15404 −0.577020 0.816730i \(-0.695784\pi\)
−0.577020 + 0.816730i \(0.695784\pi\)
\(80\) −2.85512 −0.319212
\(81\) 6.98056 0.775618
\(82\) −3.33146 −0.367898
\(83\) 12.1326 1.33173 0.665863 0.746074i \(-0.268063\pi\)
0.665863 + 0.746074i \(0.268063\pi\)
\(84\) 0.479869 0.0523580
\(85\) 13.4884 1.46302
\(86\) 6.50989 0.701979
\(87\) −2.80800 −0.301049
\(88\) −5.13981 −0.547905
\(89\) −15.2958 −1.62135 −0.810673 0.585499i \(-0.800899\pi\)
−0.810673 + 0.585499i \(0.800899\pi\)
\(90\) −7.90789 −0.833565
\(91\) −0.235441 −0.0246809
\(92\) 6.09954 0.635922
\(93\) 2.73045 0.283134
\(94\) 0.589626 0.0608152
\(95\) 0 0
\(96\) −0.479869 −0.0489764
\(97\) −10.2497 −1.04070 −0.520352 0.853952i \(-0.674199\pi\)
−0.520352 + 0.853952i \(0.674199\pi\)
\(98\) −1.00000 −0.101015
\(99\) −14.2359 −1.43076
\(100\) 3.15169 0.315169
\(101\) 13.6679 1.36001 0.680003 0.733209i \(-0.261978\pi\)
0.680003 + 0.733209i \(0.261978\pi\)
\(102\) 2.26704 0.224471
\(103\) −6.38388 −0.629022 −0.314511 0.949254i \(-0.601841\pi\)
−0.314511 + 0.949254i \(0.601841\pi\)
\(104\) 0.235441 0.0230869
\(105\) −1.37008 −0.133706
\(106\) −8.65809 −0.840948
\(107\) 8.23814 0.796411 0.398206 0.917296i \(-0.369633\pi\)
0.398206 + 0.917296i \(0.369633\pi\)
\(108\) −2.76871 −0.266419
\(109\) −12.8636 −1.23211 −0.616056 0.787703i \(-0.711270\pi\)
−0.616056 + 0.787703i \(0.711270\pi\)
\(110\) 14.6748 1.39918
\(111\) −1.41458 −0.134266
\(112\) 1.00000 0.0944911
\(113\) −1.48774 −0.139955 −0.0699775 0.997549i \(-0.522293\pi\)
−0.0699775 + 0.997549i \(0.522293\pi\)
\(114\) 0 0
\(115\) −17.4149 −1.62395
\(116\) −5.85159 −0.543307
\(117\) 0.652106 0.0602873
\(118\) −8.79576 −0.809716
\(119\) −4.72430 −0.433076
\(120\) 1.37008 0.125071
\(121\) 15.4176 1.40160
\(122\) 5.43170 0.491763
\(123\) 1.59866 0.144147
\(124\) 5.68999 0.510976
\(125\) 5.27714 0.472001
\(126\) 2.76973 0.246747
\(127\) −0.603911 −0.0535884 −0.0267942 0.999641i \(-0.508530\pi\)
−0.0267942 + 0.999641i \(0.508530\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.12389 −0.275043
\(130\) −0.672211 −0.0589568
\(131\) 14.9371 1.30506 0.652529 0.757764i \(-0.273708\pi\)
0.652529 + 0.757764i \(0.273708\pi\)
\(132\) 2.46643 0.214675
\(133\) 0 0
\(134\) 11.1291 0.961409
\(135\) 7.90499 0.680354
\(136\) 4.72430 0.405105
\(137\) 16.1532 1.38006 0.690029 0.723781i \(-0.257598\pi\)
0.690029 + 0.723781i \(0.257598\pi\)
\(138\) −2.92698 −0.249161
\(139\) −20.8094 −1.76503 −0.882514 0.470285i \(-0.844151\pi\)
−0.882514 + 0.470285i \(0.844151\pi\)
\(140\) −2.85512 −0.241301
\(141\) −0.282943 −0.0238281
\(142\) 3.04026 0.255133
\(143\) −1.21012 −0.101195
\(144\) −2.76973 −0.230810
\(145\) 16.7070 1.38744
\(146\) −10.8507 −0.898008
\(147\) 0.479869 0.0395789
\(148\) −2.94785 −0.242312
\(149\) −17.3680 −1.42284 −0.711420 0.702767i \(-0.751948\pi\)
−0.711420 + 0.702767i \(0.751948\pi\)
\(150\) −1.51240 −0.123487
\(151\) −15.6190 −1.27106 −0.635528 0.772078i \(-0.719217\pi\)
−0.635528 + 0.772078i \(0.719217\pi\)
\(152\) 0 0
\(153\) 13.0850 1.05786
\(154\) −5.13981 −0.414177
\(155\) −16.2456 −1.30488
\(156\) −0.112981 −0.00904569
\(157\) 13.7329 1.09601 0.548003 0.836477i \(-0.315388\pi\)
0.548003 + 0.836477i \(0.315388\pi\)
\(158\) 10.2573 0.816029
\(159\) 4.15475 0.329493
\(160\) 2.85512 0.225717
\(161\) 6.09954 0.480711
\(162\) −6.98056 −0.548445
\(163\) −2.13899 −0.167539 −0.0837693 0.996485i \(-0.526696\pi\)
−0.0837693 + 0.996485i \(0.526696\pi\)
\(164\) 3.33146 0.260143
\(165\) −7.04195 −0.548215
\(166\) −12.1326 −0.941673
\(167\) 6.26600 0.484877 0.242439 0.970167i \(-0.422053\pi\)
0.242439 + 0.970167i \(0.422053\pi\)
\(168\) −0.479869 −0.0370227
\(169\) −12.9446 −0.995736
\(170\) −13.4884 −1.03451
\(171\) 0 0
\(172\) −6.50989 −0.496374
\(173\) 6.18843 0.470498 0.235249 0.971935i \(-0.424410\pi\)
0.235249 + 0.971935i \(0.424410\pi\)
\(174\) 2.80800 0.212874
\(175\) 3.15169 0.238246
\(176\) 5.13981 0.387428
\(177\) 4.22081 0.317256
\(178\) 15.2958 1.14646
\(179\) −25.3882 −1.89761 −0.948803 0.315870i \(-0.897704\pi\)
−0.948803 + 0.315870i \(0.897704\pi\)
\(180\) 7.90789 0.589419
\(181\) 7.26993 0.540370 0.270185 0.962808i \(-0.412915\pi\)
0.270185 + 0.962808i \(0.412915\pi\)
\(182\) 0.235441 0.0174520
\(183\) −2.60650 −0.192678
\(184\) −6.09954 −0.449664
\(185\) 8.41646 0.618791
\(186\) −2.73045 −0.200206
\(187\) −24.2820 −1.77567
\(188\) −0.589626 −0.0430029
\(189\) −2.76871 −0.201394
\(190\) 0 0
\(191\) −18.6408 −1.34880 −0.674400 0.738366i \(-0.735598\pi\)
−0.674400 + 0.738366i \(0.735598\pi\)
\(192\) 0.479869 0.0346315
\(193\) −21.7466 −1.56535 −0.782676 0.622429i \(-0.786146\pi\)
−0.782676 + 0.622429i \(0.786146\pi\)
\(194\) 10.2497 0.735889
\(195\) 0.322573 0.0230999
\(196\) 1.00000 0.0714286
\(197\) −21.8153 −1.55427 −0.777137 0.629331i \(-0.783329\pi\)
−0.777137 + 0.629331i \(0.783329\pi\)
\(198\) 14.2359 1.01170
\(199\) −3.08558 −0.218731 −0.109366 0.994002i \(-0.534882\pi\)
−0.109366 + 0.994002i \(0.534882\pi\)
\(200\) −3.15169 −0.222858
\(201\) −5.34051 −0.376691
\(202\) −13.6679 −0.961670
\(203\) −5.85159 −0.410701
\(204\) −2.26704 −0.158725
\(205\) −9.51171 −0.664327
\(206\) 6.38388 0.444786
\(207\) −16.8941 −1.17422
\(208\) −0.235441 −0.0163249
\(209\) 0 0
\(210\) 1.37008 0.0945446
\(211\) 10.5582 0.726860 0.363430 0.931622i \(-0.381606\pi\)
0.363430 + 0.931622i \(0.381606\pi\)
\(212\) 8.65809 0.594640
\(213\) −1.45893 −0.0999640
\(214\) −8.23814 −0.563148
\(215\) 18.5865 1.26759
\(216\) 2.76871 0.188387
\(217\) 5.68999 0.386262
\(218\) 12.8636 0.871234
\(219\) 5.20690 0.351849
\(220\) −14.6748 −0.989371
\(221\) 1.11229 0.0748209
\(222\) 1.41458 0.0949406
\(223\) −12.5217 −0.838513 −0.419256 0.907868i \(-0.637709\pi\)
−0.419256 + 0.907868i \(0.637709\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −8.72932 −0.581955
\(226\) 1.48774 0.0989631
\(227\) −26.7753 −1.77714 −0.888569 0.458743i \(-0.848300\pi\)
−0.888569 + 0.458743i \(0.848300\pi\)
\(228\) 0 0
\(229\) 18.8086 1.24291 0.621454 0.783451i \(-0.286542\pi\)
0.621454 + 0.783451i \(0.286542\pi\)
\(230\) 17.4149 1.14831
\(231\) 2.46643 0.162279
\(232\) 5.85159 0.384176
\(233\) −10.2268 −0.669981 −0.334991 0.942221i \(-0.608733\pi\)
−0.334991 + 0.942221i \(0.608733\pi\)
\(234\) −0.652106 −0.0426295
\(235\) 1.68345 0.109816
\(236\) 8.79576 0.572556
\(237\) −4.92217 −0.319729
\(238\) 4.72430 0.306231
\(239\) −16.8837 −1.09212 −0.546058 0.837747i \(-0.683872\pi\)
−0.546058 + 0.837747i \(0.683872\pi\)
\(240\) −1.37008 −0.0884384
\(241\) −21.5302 −1.38688 −0.693442 0.720513i \(-0.743907\pi\)
−0.693442 + 0.720513i \(0.743907\pi\)
\(242\) −15.4176 −0.991082
\(243\) 11.6559 0.747725
\(244\) −5.43170 −0.347729
\(245\) −2.85512 −0.182407
\(246\) −1.59866 −0.101927
\(247\) 0 0
\(248\) −5.68999 −0.361315
\(249\) 5.82206 0.368958
\(250\) −5.27714 −0.333755
\(251\) 4.88717 0.308476 0.154238 0.988034i \(-0.450708\pi\)
0.154238 + 0.988034i \(0.450708\pi\)
\(252\) −2.76973 −0.174476
\(253\) 31.3505 1.97099
\(254\) 0.603911 0.0378927
\(255\) 6.47267 0.405334
\(256\) 1.00000 0.0625000
\(257\) 28.1725 1.75736 0.878678 0.477416i \(-0.158426\pi\)
0.878678 + 0.477416i \(0.158426\pi\)
\(258\) 3.12389 0.194485
\(259\) −2.94785 −0.183171
\(260\) 0.672211 0.0416888
\(261\) 16.2073 1.00321
\(262\) −14.9371 −0.922816
\(263\) −2.20491 −0.135961 −0.0679803 0.997687i \(-0.521656\pi\)
−0.0679803 + 0.997687i \(0.521656\pi\)
\(264\) −2.46643 −0.151798
\(265\) −24.7198 −1.51853
\(266\) 0 0
\(267\) −7.33995 −0.449198
\(268\) −11.1291 −0.679818
\(269\) −9.96810 −0.607766 −0.303883 0.952709i \(-0.598283\pi\)
−0.303883 + 0.952709i \(0.598283\pi\)
\(270\) −7.90499 −0.481083
\(271\) 19.2204 1.16755 0.583777 0.811914i \(-0.301574\pi\)
0.583777 + 0.811914i \(0.301574\pi\)
\(272\) −4.72430 −0.286453
\(273\) −0.112981 −0.00683790
\(274\) −16.1532 −0.975849
\(275\) 16.1991 0.976842
\(276\) 2.92698 0.176184
\(277\) 8.70088 0.522785 0.261392 0.965233i \(-0.415818\pi\)
0.261392 + 0.965233i \(0.415818\pi\)
\(278\) 20.8094 1.24806
\(279\) −15.7597 −0.943509
\(280\) 2.85512 0.170626
\(281\) −26.5023 −1.58100 −0.790498 0.612464i \(-0.790178\pi\)
−0.790498 + 0.612464i \(0.790178\pi\)
\(282\) 0.282943 0.0168490
\(283\) −32.3219 −1.92134 −0.960670 0.277694i \(-0.910430\pi\)
−0.960670 + 0.277694i \(0.910430\pi\)
\(284\) −3.04026 −0.180406
\(285\) 0 0
\(286\) 1.21012 0.0715559
\(287\) 3.33146 0.196650
\(288\) 2.76973 0.163208
\(289\) 5.31898 0.312881
\(290\) −16.7070 −0.981068
\(291\) −4.91853 −0.288329
\(292\) 10.8507 0.634987
\(293\) −32.3512 −1.88998 −0.944988 0.327106i \(-0.893926\pi\)
−0.944988 + 0.327106i \(0.893926\pi\)
\(294\) −0.479869 −0.0279865
\(295\) −25.1129 −1.46213
\(296\) 2.94785 0.171340
\(297\) −14.2306 −0.825746
\(298\) 17.3680 1.00610
\(299\) −1.43608 −0.0830507
\(300\) 1.51240 0.0873184
\(301\) −6.50989 −0.375224
\(302\) 15.6190 0.898772
\(303\) 6.55879 0.376793
\(304\) 0 0
\(305\) 15.5081 0.887994
\(306\) −13.0850 −0.748020
\(307\) 5.06829 0.289263 0.144631 0.989486i \(-0.453800\pi\)
0.144631 + 0.989486i \(0.453800\pi\)
\(308\) 5.13981 0.292868
\(309\) −3.06342 −0.174272
\(310\) 16.2456 0.922687
\(311\) −15.9316 −0.903398 −0.451699 0.892170i \(-0.649182\pi\)
−0.451699 + 0.892170i \(0.649182\pi\)
\(312\) 0.112981 0.00639627
\(313\) 2.20536 0.124654 0.0623271 0.998056i \(-0.480148\pi\)
0.0623271 + 0.998056i \(0.480148\pi\)
\(314\) −13.7329 −0.774993
\(315\) 7.90789 0.445559
\(316\) −10.2573 −0.577020
\(317\) −18.1717 −1.02063 −0.510313 0.859989i \(-0.670471\pi\)
−0.510313 + 0.859989i \(0.670471\pi\)
\(318\) −4.15475 −0.232987
\(319\) −30.0761 −1.68394
\(320\) −2.85512 −0.159606
\(321\) 3.95323 0.220648
\(322\) −6.09954 −0.339914
\(323\) 0 0
\(324\) 6.98056 0.387809
\(325\) −0.742037 −0.0411608
\(326\) 2.13899 0.118468
\(327\) −6.17285 −0.341359
\(328\) −3.33146 −0.183949
\(329\) −0.589626 −0.0325071
\(330\) 7.04195 0.387647
\(331\) −1.92750 −0.105945 −0.0529724 0.998596i \(-0.516870\pi\)
−0.0529724 + 0.998596i \(0.516870\pi\)
\(332\) 12.1326 0.665863
\(333\) 8.16474 0.447425
\(334\) −6.26600 −0.342860
\(335\) 31.7749 1.73605
\(336\) 0.479869 0.0261790
\(337\) 4.91677 0.267833 0.133917 0.990993i \(-0.457245\pi\)
0.133917 + 0.990993i \(0.457245\pi\)
\(338\) 12.9446 0.704092
\(339\) −0.713921 −0.0387749
\(340\) 13.4884 0.731512
\(341\) 29.2454 1.58373
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 6.50989 0.350990
\(345\) −8.35687 −0.449919
\(346\) −6.18843 −0.332692
\(347\) −11.1668 −0.599465 −0.299732 0.954023i \(-0.596897\pi\)
−0.299732 + 0.954023i \(0.596897\pi\)
\(348\) −2.80800 −0.150524
\(349\) −17.6629 −0.945472 −0.472736 0.881204i \(-0.656733\pi\)
−0.472736 + 0.881204i \(0.656733\pi\)
\(350\) −3.15169 −0.168465
\(351\) 0.651867 0.0347941
\(352\) −5.13981 −0.273953
\(353\) 7.02213 0.373750 0.186875 0.982384i \(-0.440164\pi\)
0.186875 + 0.982384i \(0.440164\pi\)
\(354\) −4.22081 −0.224334
\(355\) 8.68030 0.460703
\(356\) −15.2958 −0.810673
\(357\) −2.26704 −0.119985
\(358\) 25.3882 1.34181
\(359\) 1.31686 0.0695014 0.0347507 0.999396i \(-0.488936\pi\)
0.0347507 + 0.999396i \(0.488936\pi\)
\(360\) −7.90789 −0.416782
\(361\) 0 0
\(362\) −7.26993 −0.382099
\(363\) 7.39843 0.388317
\(364\) −0.235441 −0.0123404
\(365\) −30.9799 −1.62156
\(366\) 2.60650 0.136244
\(367\) 17.2226 0.899012 0.449506 0.893277i \(-0.351600\pi\)
0.449506 + 0.893277i \(0.351600\pi\)
\(368\) 6.09954 0.317961
\(369\) −9.22723 −0.480351
\(370\) −8.41646 −0.437551
\(371\) 8.65809 0.449505
\(372\) 2.73045 0.141567
\(373\) 11.1310 0.576341 0.288171 0.957579i \(-0.406953\pi\)
0.288171 + 0.957579i \(0.406953\pi\)
\(374\) 24.2820 1.25559
\(375\) 2.53233 0.130769
\(376\) 0.589626 0.0304076
\(377\) 1.37770 0.0709553
\(378\) 2.76871 0.142407
\(379\) 13.0836 0.672059 0.336030 0.941851i \(-0.390916\pi\)
0.336030 + 0.941851i \(0.390916\pi\)
\(380\) 0 0
\(381\) −0.289798 −0.0148468
\(382\) 18.6408 0.953746
\(383\) 34.8408 1.78028 0.890141 0.455686i \(-0.150606\pi\)
0.890141 + 0.455686i \(0.150606\pi\)
\(384\) −0.479869 −0.0244882
\(385\) −14.6748 −0.747895
\(386\) 21.7466 1.10687
\(387\) 18.0306 0.916547
\(388\) −10.2497 −0.520352
\(389\) −9.69653 −0.491634 −0.245817 0.969316i \(-0.579056\pi\)
−0.245817 + 0.969316i \(0.579056\pi\)
\(390\) −0.322573 −0.0163341
\(391\) −28.8161 −1.45729
\(392\) −1.00000 −0.0505076
\(393\) 7.16783 0.361569
\(394\) 21.8153 1.09904
\(395\) 29.2859 1.47353
\(396\) −14.2359 −0.715379
\(397\) −6.18850 −0.310592 −0.155296 0.987868i \(-0.549633\pi\)
−0.155296 + 0.987868i \(0.549633\pi\)
\(398\) 3.08558 0.154666
\(399\) 0 0
\(400\) 3.15169 0.157585
\(401\) −31.9390 −1.59496 −0.797478 0.603348i \(-0.793833\pi\)
−0.797478 + 0.603348i \(0.793833\pi\)
\(402\) 5.34051 0.266360
\(403\) −1.33966 −0.0667330
\(404\) 13.6679 0.680003
\(405\) −19.9303 −0.990345
\(406\) 5.85159 0.290410
\(407\) −15.1514 −0.751027
\(408\) 2.26704 0.112235
\(409\) −1.74937 −0.0865009 −0.0432504 0.999064i \(-0.513771\pi\)
−0.0432504 + 0.999064i \(0.513771\pi\)
\(410\) 9.51171 0.469750
\(411\) 7.75140 0.382349
\(412\) −6.38388 −0.314511
\(413\) 8.79576 0.432811
\(414\) 16.8941 0.830298
\(415\) −34.6400 −1.70041
\(416\) 0.235441 0.0115434
\(417\) −9.98577 −0.489005
\(418\) 0 0
\(419\) 15.7702 0.770427 0.385213 0.922828i \(-0.374128\pi\)
0.385213 + 0.922828i \(0.374128\pi\)
\(420\) −1.37008 −0.0668531
\(421\) −12.0823 −0.588853 −0.294427 0.955674i \(-0.595129\pi\)
−0.294427 + 0.955674i \(0.595129\pi\)
\(422\) −10.5582 −0.513967
\(423\) 1.63310 0.0794041
\(424\) −8.65809 −0.420474
\(425\) −14.8895 −0.722248
\(426\) 1.45893 0.0706852
\(427\) −5.43170 −0.262859
\(428\) 8.23814 0.398206
\(429\) −0.580699 −0.0280364
\(430\) −18.5865 −0.896320
\(431\) 10.5216 0.506807 0.253403 0.967361i \(-0.418450\pi\)
0.253403 + 0.967361i \(0.418450\pi\)
\(432\) −2.76871 −0.133210
\(433\) 24.6468 1.18445 0.592226 0.805772i \(-0.298249\pi\)
0.592226 + 0.805772i \(0.298249\pi\)
\(434\) −5.68999 −0.273128
\(435\) 8.01716 0.384393
\(436\) −12.8636 −0.616056
\(437\) 0 0
\(438\) −5.20690 −0.248795
\(439\) −8.56215 −0.408649 −0.204325 0.978903i \(-0.565500\pi\)
−0.204325 + 0.978903i \(0.565500\pi\)
\(440\) 14.6748 0.699591
\(441\) −2.76973 −0.131892
\(442\) −1.11229 −0.0529063
\(443\) 0.396798 0.0188524 0.00942621 0.999956i \(-0.496999\pi\)
0.00942621 + 0.999956i \(0.496999\pi\)
\(444\) −1.41458 −0.0671331
\(445\) 43.6712 2.07021
\(446\) 12.5217 0.592918
\(447\) −8.33435 −0.394201
\(448\) 1.00000 0.0472456
\(449\) 39.6700 1.87214 0.936070 0.351813i \(-0.114435\pi\)
0.936070 + 0.351813i \(0.114435\pi\)
\(450\) 8.72932 0.411504
\(451\) 17.1231 0.806294
\(452\) −1.48774 −0.0699775
\(453\) −7.49507 −0.352149
\(454\) 26.7753 1.25663
\(455\) 0.672211 0.0315137
\(456\) 0 0
\(457\) 5.26900 0.246474 0.123237 0.992377i \(-0.460673\pi\)
0.123237 + 0.992377i \(0.460673\pi\)
\(458\) −18.8086 −0.878868
\(459\) 13.0802 0.610532
\(460\) −17.4149 −0.811974
\(461\) −7.92353 −0.369036 −0.184518 0.982829i \(-0.559072\pi\)
−0.184518 + 0.982829i \(0.559072\pi\)
\(462\) −2.46643 −0.114749
\(463\) 16.7306 0.777538 0.388769 0.921335i \(-0.372900\pi\)
0.388769 + 0.921335i \(0.372900\pi\)
\(464\) −5.85159 −0.271653
\(465\) −7.79575 −0.361519
\(466\) 10.2268 0.473748
\(467\) −9.87110 −0.456780 −0.228390 0.973570i \(-0.573346\pi\)
−0.228390 + 0.973570i \(0.573346\pi\)
\(468\) 0.652106 0.0301436
\(469\) −11.1291 −0.513894
\(470\) −1.68345 −0.0776518
\(471\) 6.58999 0.303651
\(472\) −8.79576 −0.404858
\(473\) −33.4596 −1.53847
\(474\) 4.92217 0.226083
\(475\) 0 0
\(476\) −4.72430 −0.216538
\(477\) −23.9805 −1.09799
\(478\) 16.8837 0.772243
\(479\) 3.43432 0.156918 0.0784591 0.996917i \(-0.475000\pi\)
0.0784591 + 0.996917i \(0.475000\pi\)
\(480\) 1.37008 0.0625354
\(481\) 0.694045 0.0316457
\(482\) 21.5302 0.980675
\(483\) 2.92698 0.133182
\(484\) 15.4176 0.700801
\(485\) 29.2642 1.32882
\(486\) −11.6559 −0.528722
\(487\) −18.6872 −0.846799 −0.423399 0.905943i \(-0.639163\pi\)
−0.423399 + 0.905943i \(0.639163\pi\)
\(488\) 5.43170 0.245882
\(489\) −1.02643 −0.0464169
\(490\) 2.85512 0.128981
\(491\) 31.2379 1.40975 0.704873 0.709333i \(-0.251004\pi\)
0.704873 + 0.709333i \(0.251004\pi\)
\(492\) 1.59866 0.0720733
\(493\) 27.6447 1.24505
\(494\) 0 0
\(495\) 40.6450 1.82686
\(496\) 5.68999 0.255488
\(497\) −3.04026 −0.136374
\(498\) −5.82206 −0.260893
\(499\) −11.4120 −0.510870 −0.255435 0.966826i \(-0.582219\pi\)
−0.255435 + 0.966826i \(0.582219\pi\)
\(500\) 5.27714 0.236001
\(501\) 3.00686 0.134336
\(502\) −4.88717 −0.218125
\(503\) −36.2498 −1.61630 −0.808150 0.588976i \(-0.799531\pi\)
−0.808150 + 0.588976i \(0.799531\pi\)
\(504\) 2.76973 0.123373
\(505\) −39.0234 −1.73652
\(506\) −31.3505 −1.39370
\(507\) −6.21169 −0.275871
\(508\) −0.603911 −0.0267942
\(509\) 20.7401 0.919288 0.459644 0.888103i \(-0.347977\pi\)
0.459644 + 0.888103i \(0.347977\pi\)
\(510\) −6.47267 −0.286615
\(511\) 10.8507 0.480005
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −28.1725 −1.24264
\(515\) 18.2267 0.803165
\(516\) −3.12389 −0.137522
\(517\) −3.03056 −0.133284
\(518\) 2.94785 0.129521
\(519\) 2.96963 0.130352
\(520\) −0.672211 −0.0294784
\(521\) −39.0045 −1.70882 −0.854409 0.519602i \(-0.826080\pi\)
−0.854409 + 0.519602i \(0.826080\pi\)
\(522\) −16.2073 −0.709375
\(523\) −42.6216 −1.86371 −0.931856 0.362827i \(-0.881812\pi\)
−0.931856 + 0.362827i \(0.881812\pi\)
\(524\) 14.9371 0.652529
\(525\) 1.51240 0.0660065
\(526\) 2.20491 0.0961387
\(527\) −26.8812 −1.17096
\(528\) 2.46643 0.107338
\(529\) 14.2044 0.617585
\(530\) 24.7198 1.07376
\(531\) −24.3619 −1.05721
\(532\) 0 0
\(533\) −0.784362 −0.0339745
\(534\) 7.33995 0.317631
\(535\) −23.5209 −1.01690
\(536\) 11.1291 0.480704
\(537\) −12.1830 −0.525736
\(538\) 9.96810 0.429755
\(539\) 5.13981 0.221387
\(540\) 7.90499 0.340177
\(541\) −12.4210 −0.534019 −0.267010 0.963694i \(-0.586036\pi\)
−0.267010 + 0.963694i \(0.586036\pi\)
\(542\) −19.2204 −0.825585
\(543\) 3.48861 0.149711
\(544\) 4.72430 0.202553
\(545\) 36.7271 1.57322
\(546\) 0.112981 0.00483513
\(547\) −21.6915 −0.927461 −0.463731 0.885976i \(-0.653489\pi\)
−0.463731 + 0.885976i \(0.653489\pi\)
\(548\) 16.1532 0.690029
\(549\) 15.0443 0.642076
\(550\) −16.1991 −0.690731
\(551\) 0 0
\(552\) −2.92698 −0.124581
\(553\) −10.2573 −0.436186
\(554\) −8.70088 −0.369665
\(555\) 4.03880 0.171437
\(556\) −20.8094 −0.882514
\(557\) 18.1866 0.770593 0.385296 0.922793i \(-0.374099\pi\)
0.385296 + 0.922793i \(0.374099\pi\)
\(558\) 15.7597 0.667162
\(559\) 1.53269 0.0648260
\(560\) −2.85512 −0.120651
\(561\) −11.6522 −0.491955
\(562\) 26.5023 1.11793
\(563\) −24.5873 −1.03623 −0.518116 0.855310i \(-0.673366\pi\)
−0.518116 + 0.855310i \(0.673366\pi\)
\(564\) −0.282943 −0.0119140
\(565\) 4.24768 0.178701
\(566\) 32.3219 1.35859
\(567\) 6.98056 0.293156
\(568\) 3.04026 0.127567
\(569\) 33.1071 1.38792 0.693960 0.720013i \(-0.255864\pi\)
0.693960 + 0.720013i \(0.255864\pi\)
\(570\) 0 0
\(571\) −9.83997 −0.411790 −0.205895 0.978574i \(-0.566011\pi\)
−0.205895 + 0.978574i \(0.566011\pi\)
\(572\) −1.21012 −0.0505977
\(573\) −8.94514 −0.373688
\(574\) −3.33146 −0.139052
\(575\) 19.2239 0.801691
\(576\) −2.76973 −0.115405
\(577\) −4.66787 −0.194326 −0.0971630 0.995268i \(-0.530977\pi\)
−0.0971630 + 0.995268i \(0.530977\pi\)
\(578\) −5.31898 −0.221240
\(579\) −10.4355 −0.433684
\(580\) 16.7070 0.693720
\(581\) 12.1326 0.503345
\(582\) 4.91853 0.203880
\(583\) 44.5009 1.84304
\(584\) −10.8507 −0.449004
\(585\) −1.86184 −0.0769776
\(586\) 32.3512 1.33641
\(587\) −22.0622 −0.910603 −0.455302 0.890337i \(-0.650469\pi\)
−0.455302 + 0.890337i \(0.650469\pi\)
\(588\) 0.479869 0.0197895
\(589\) 0 0
\(590\) 25.1129 1.03388
\(591\) −10.4685 −0.430615
\(592\) −2.94785 −0.121156
\(593\) −37.7846 −1.55163 −0.775814 0.630962i \(-0.782660\pi\)
−0.775814 + 0.630962i \(0.782660\pi\)
\(594\) 14.2306 0.583890
\(595\) 13.4884 0.552971
\(596\) −17.3680 −0.711420
\(597\) −1.48067 −0.0605999
\(598\) 1.43608 0.0587257
\(599\) −17.0576 −0.696956 −0.348478 0.937317i \(-0.613301\pi\)
−0.348478 + 0.937317i \(0.613301\pi\)
\(600\) −1.51240 −0.0617434
\(601\) −20.7601 −0.846822 −0.423411 0.905938i \(-0.639167\pi\)
−0.423411 + 0.905938i \(0.639167\pi\)
\(602\) 6.50989 0.265323
\(603\) 30.8246 1.25527
\(604\) −15.6190 −0.635528
\(605\) −44.0191 −1.78963
\(606\) −6.55879 −0.266433
\(607\) −1.83551 −0.0745009 −0.0372504 0.999306i \(-0.511860\pi\)
−0.0372504 + 0.999306i \(0.511860\pi\)
\(608\) 0 0
\(609\) −2.80800 −0.113786
\(610\) −15.5081 −0.627906
\(611\) 0.138822 0.00561613
\(612\) 13.0850 0.528930
\(613\) 17.4650 0.705406 0.352703 0.935735i \(-0.385263\pi\)
0.352703 + 0.935735i \(0.385263\pi\)
\(614\) −5.06829 −0.204540
\(615\) −4.56437 −0.184053
\(616\) −5.13981 −0.207089
\(617\) −42.3214 −1.70379 −0.851897 0.523709i \(-0.824548\pi\)
−0.851897 + 0.523709i \(0.824548\pi\)
\(618\) 3.06342 0.123229
\(619\) 45.8999 1.84487 0.922437 0.386147i \(-0.126194\pi\)
0.922437 + 0.386147i \(0.126194\pi\)
\(620\) −16.2456 −0.652438
\(621\) −16.8879 −0.677687
\(622\) 15.9316 0.638799
\(623\) −15.2958 −0.612811
\(624\) −0.112981 −0.00452285
\(625\) −30.8253 −1.23301
\(626\) −2.20536 −0.0881439
\(627\) 0 0
\(628\) 13.7329 0.548003
\(629\) 13.9265 0.555287
\(630\) −7.90789 −0.315058
\(631\) −24.0296 −0.956604 −0.478302 0.878195i \(-0.658748\pi\)
−0.478302 + 0.878195i \(0.658748\pi\)
\(632\) 10.2573 0.408015
\(633\) 5.06657 0.201378
\(634\) 18.1717 0.721692
\(635\) 1.72424 0.0684242
\(636\) 4.15475 0.164746
\(637\) −0.235441 −0.00932850
\(638\) 30.0761 1.19072
\(639\) 8.42069 0.333118
\(640\) 2.85512 0.112858
\(641\) 6.16026 0.243316 0.121658 0.992572i \(-0.461179\pi\)
0.121658 + 0.992572i \(0.461179\pi\)
\(642\) −3.95323 −0.156021
\(643\) 0.690101 0.0272149 0.0136075 0.999907i \(-0.495668\pi\)
0.0136075 + 0.999907i \(0.495668\pi\)
\(644\) 6.09954 0.240356
\(645\) 8.91908 0.351188
\(646\) 0 0
\(647\) −16.2484 −0.638791 −0.319396 0.947621i \(-0.603480\pi\)
−0.319396 + 0.947621i \(0.603480\pi\)
\(648\) −6.98056 −0.274222
\(649\) 45.2085 1.77459
\(650\) 0.742037 0.0291051
\(651\) 2.73045 0.107015
\(652\) −2.13899 −0.0837693
\(653\) −16.6598 −0.651947 −0.325974 0.945379i \(-0.605692\pi\)
−0.325974 + 0.945379i \(0.605692\pi\)
\(654\) 6.17285 0.241377
\(655\) −42.6471 −1.66636
\(656\) 3.33146 0.130072
\(657\) −30.0534 −1.17249
\(658\) 0.589626 0.0229860
\(659\) −10.9663 −0.427186 −0.213593 0.976923i \(-0.568517\pi\)
−0.213593 + 0.976923i \(0.568517\pi\)
\(660\) −7.04195 −0.274108
\(661\) −30.6314 −1.19142 −0.595711 0.803199i \(-0.703130\pi\)
−0.595711 + 0.803199i \(0.703130\pi\)
\(662\) 1.92750 0.0749144
\(663\) 0.533754 0.0207293
\(664\) −12.1326 −0.470836
\(665\) 0 0
\(666\) −8.16474 −0.316377
\(667\) −35.6920 −1.38200
\(668\) 6.26600 0.242439
\(669\) −6.00875 −0.232312
\(670\) −31.7749 −1.22757
\(671\) −27.9179 −1.07776
\(672\) −0.479869 −0.0185113
\(673\) 7.30454 0.281569 0.140785 0.990040i \(-0.455037\pi\)
0.140785 + 0.990040i \(0.455037\pi\)
\(674\) −4.91677 −0.189387
\(675\) −8.72612 −0.335869
\(676\) −12.9446 −0.497868
\(677\) 40.0820 1.54048 0.770238 0.637757i \(-0.220138\pi\)
0.770238 + 0.637757i \(0.220138\pi\)
\(678\) 0.713921 0.0274180
\(679\) −10.2497 −0.393349
\(680\) −13.4884 −0.517257
\(681\) −12.8486 −0.492360
\(682\) −29.2454 −1.11987
\(683\) −22.6845 −0.867998 −0.433999 0.900913i \(-0.642898\pi\)
−0.433999 + 0.900913i \(0.642898\pi\)
\(684\) 0 0
\(685\) −46.1192 −1.76212
\(686\) −1.00000 −0.0381802
\(687\) 9.02566 0.344350
\(688\) −6.50989 −0.248187
\(689\) −2.03847 −0.0776594
\(690\) 8.35687 0.318141
\(691\) −35.5384 −1.35195 −0.675973 0.736926i \(-0.736276\pi\)
−0.675973 + 0.736926i \(0.736276\pi\)
\(692\) 6.18843 0.235249
\(693\) −14.2359 −0.540776
\(694\) 11.1668 0.423886
\(695\) 59.4132 2.25367
\(696\) 2.80800 0.106437
\(697\) −15.7388 −0.596150
\(698\) 17.6629 0.668549
\(699\) −4.90753 −0.185620
\(700\) 3.15169 0.119123
\(701\) 25.0390 0.945711 0.472855 0.881140i \(-0.343223\pi\)
0.472855 + 0.881140i \(0.343223\pi\)
\(702\) −0.651867 −0.0246032
\(703\) 0 0
\(704\) 5.13981 0.193714
\(705\) 0.807835 0.0304248
\(706\) −7.02213 −0.264281
\(707\) 13.6679 0.514034
\(708\) 4.22081 0.158628
\(709\) 13.5044 0.507170 0.253585 0.967313i \(-0.418390\pi\)
0.253585 + 0.967313i \(0.418390\pi\)
\(710\) −8.68030 −0.325766
\(711\) 28.4100 1.06546
\(712\) 15.2958 0.573232
\(713\) 34.7063 1.29976
\(714\) 2.26704 0.0848419
\(715\) 3.45503 0.129211
\(716\) −25.3882 −0.948803
\(717\) −8.10196 −0.302573
\(718\) −1.31686 −0.0491449
\(719\) 0.0885629 0.00330284 0.00165142 0.999999i \(-0.499474\pi\)
0.00165142 + 0.999999i \(0.499474\pi\)
\(720\) 7.90789 0.294710
\(721\) −6.38388 −0.237748
\(722\) 0 0
\(723\) −10.3317 −0.384239
\(724\) 7.26993 0.270185
\(725\) −18.4424 −0.684934
\(726\) −7.39843 −0.274582
\(727\) 33.2385 1.23275 0.616373 0.787454i \(-0.288601\pi\)
0.616373 + 0.787454i \(0.288601\pi\)
\(728\) 0.235441 0.00872602
\(729\) −15.3484 −0.568459
\(730\) 30.9799 1.14662
\(731\) 30.7546 1.13750
\(732\) −2.60650 −0.0963392
\(733\) 4.68980 0.173222 0.0866109 0.996242i \(-0.472396\pi\)
0.0866109 + 0.996242i \(0.472396\pi\)
\(734\) −17.2226 −0.635698
\(735\) −1.37008 −0.0505362
\(736\) −6.09954 −0.224832
\(737\) −57.2015 −2.10704
\(738\) 9.22723 0.339659
\(739\) −19.1478 −0.704365 −0.352182 0.935931i \(-0.614560\pi\)
−0.352182 + 0.935931i \(0.614560\pi\)
\(740\) 8.41646 0.309395
\(741\) 0 0
\(742\) −8.65809 −0.317848
\(743\) 31.3894 1.15156 0.575782 0.817603i \(-0.304698\pi\)
0.575782 + 0.817603i \(0.304698\pi\)
\(744\) −2.73045 −0.100103
\(745\) 49.5876 1.81675
\(746\) −11.1310 −0.407535
\(747\) −33.6040 −1.22951
\(748\) −24.2820 −0.887837
\(749\) 8.23814 0.301015
\(750\) −2.53233 −0.0924677
\(751\) −15.7249 −0.573811 −0.286905 0.957959i \(-0.592627\pi\)
−0.286905 + 0.957959i \(0.592627\pi\)
\(752\) −0.589626 −0.0215014
\(753\) 2.34520 0.0854639
\(754\) −1.37770 −0.0501730
\(755\) 44.5940 1.62294
\(756\) −2.76871 −0.100697
\(757\) 31.8058 1.15600 0.578000 0.816037i \(-0.303833\pi\)
0.578000 + 0.816037i \(0.303833\pi\)
\(758\) −13.0836 −0.475218
\(759\) 15.0441 0.546067
\(760\) 0 0
\(761\) −8.99189 −0.325956 −0.162978 0.986630i \(-0.552110\pi\)
−0.162978 + 0.986630i \(0.552110\pi\)
\(762\) 0.289798 0.0104983
\(763\) −12.8636 −0.465694
\(764\) −18.6408 −0.674400
\(765\) −37.3592 −1.35073
\(766\) −34.8408 −1.25885
\(767\) −2.07088 −0.0747752
\(768\) 0.479869 0.0173158
\(769\) −3.50825 −0.126511 −0.0632554 0.997997i \(-0.520148\pi\)
−0.0632554 + 0.997997i \(0.520148\pi\)
\(770\) 14.6748 0.528841
\(771\) 13.5191 0.486879
\(772\) −21.7466 −0.782676
\(773\) 41.4008 1.48908 0.744542 0.667576i \(-0.232668\pi\)
0.744542 + 0.667576i \(0.232668\pi\)
\(774\) −18.0306 −0.648097
\(775\) 17.9331 0.644176
\(776\) 10.2497 0.367944
\(777\) −1.41458 −0.0507479
\(778\) 9.69653 0.347637
\(779\) 0 0
\(780\) 0.322573 0.0115500
\(781\) −15.6264 −0.559155
\(782\) 28.8161 1.03046
\(783\) 16.2014 0.578990
\(784\) 1.00000 0.0357143
\(785\) −39.2091 −1.39943
\(786\) −7.16783 −0.255668
\(787\) −24.0635 −0.857770 −0.428885 0.903359i \(-0.641093\pi\)
−0.428885 + 0.903359i \(0.641093\pi\)
\(788\) −21.8153 −0.777137
\(789\) −1.05807 −0.0376682
\(790\) −29.2859 −1.04194
\(791\) −1.48774 −0.0528980
\(792\) 14.2359 0.505849
\(793\) 1.27884 0.0454131
\(794\) 6.18850 0.219621
\(795\) −11.8623 −0.420712
\(796\) −3.08558 −0.109366
\(797\) 37.4880 1.32789 0.663947 0.747780i \(-0.268880\pi\)
0.663947 + 0.747780i \(0.268880\pi\)
\(798\) 0 0
\(799\) 2.78557 0.0985463
\(800\) −3.15169 −0.111429
\(801\) 42.3650 1.49690
\(802\) 31.9390 1.12780
\(803\) 55.7703 1.96809
\(804\) −5.34051 −0.188345
\(805\) −17.4149 −0.613795
\(806\) 1.33966 0.0471873
\(807\) −4.78338 −0.168383
\(808\) −13.6679 −0.480835
\(809\) −12.7505 −0.448285 −0.224143 0.974556i \(-0.571958\pi\)
−0.224143 + 0.974556i \(0.571958\pi\)
\(810\) 19.9303 0.700280
\(811\) 2.56267 0.0899876 0.0449938 0.998987i \(-0.485673\pi\)
0.0449938 + 0.998987i \(0.485673\pi\)
\(812\) −5.85159 −0.205351
\(813\) 9.22325 0.323474
\(814\) 15.1514 0.531056
\(815\) 6.10706 0.213921
\(816\) −2.26704 −0.0793624
\(817\) 0 0
\(818\) 1.74937 0.0611654
\(819\) 0.652106 0.0227864
\(820\) −9.51171 −0.332163
\(821\) 42.7932 1.49349 0.746746 0.665109i \(-0.231615\pi\)
0.746746 + 0.665109i \(0.231615\pi\)
\(822\) −7.75140 −0.270361
\(823\) 3.98657 0.138963 0.0694816 0.997583i \(-0.477865\pi\)
0.0694816 + 0.997583i \(0.477865\pi\)
\(824\) 6.38388 0.222393
\(825\) 7.77344 0.270636
\(826\) −8.79576 −0.306044
\(827\) 50.3618 1.75125 0.875625 0.482991i \(-0.160450\pi\)
0.875625 + 0.482991i \(0.160450\pi\)
\(828\) −16.8941 −0.587109
\(829\) −45.1081 −1.56667 −0.783335 0.621600i \(-0.786483\pi\)
−0.783335 + 0.621600i \(0.786483\pi\)
\(830\) 34.6400 1.20237
\(831\) 4.17528 0.144839
\(832\) −0.235441 −0.00816244
\(833\) −4.72430 −0.163687
\(834\) 9.98577 0.345779
\(835\) −17.8902 −0.619114
\(836\) 0 0
\(837\) −15.7539 −0.544536
\(838\) −15.7702 −0.544774
\(839\) 20.3105 0.701196 0.350598 0.936526i \(-0.385978\pi\)
0.350598 + 0.936526i \(0.385978\pi\)
\(840\) 1.37008 0.0472723
\(841\) 5.24113 0.180729
\(842\) 12.0823 0.416382
\(843\) −12.7176 −0.438019
\(844\) 10.5582 0.363430
\(845\) 36.9583 1.27140
\(846\) −1.63310 −0.0561472
\(847\) 15.4176 0.529756
\(848\) 8.65809 0.297320
\(849\) −15.5103 −0.532312
\(850\) 14.8895 0.510707
\(851\) −17.9806 −0.616366
\(852\) −1.45893 −0.0499820
\(853\) 13.1846 0.451433 0.225717 0.974193i \(-0.427528\pi\)
0.225717 + 0.974193i \(0.427528\pi\)
\(854\) 5.43170 0.185869
\(855\) 0 0
\(856\) −8.23814 −0.281574
\(857\) 40.8695 1.39608 0.698038 0.716061i \(-0.254057\pi\)
0.698038 + 0.716061i \(0.254057\pi\)
\(858\) 0.580699 0.0198247
\(859\) −53.6037 −1.82894 −0.914468 0.404658i \(-0.867390\pi\)
−0.914468 + 0.404658i \(0.867390\pi\)
\(860\) 18.5865 0.633794
\(861\) 1.59866 0.0544823
\(862\) −10.5216 −0.358366
\(863\) −24.0938 −0.820162 −0.410081 0.912049i \(-0.634500\pi\)
−0.410081 + 0.912049i \(0.634500\pi\)
\(864\) 2.76871 0.0941935
\(865\) −17.6687 −0.600753
\(866\) −24.6468 −0.837534
\(867\) 2.55241 0.0866845
\(868\) 5.68999 0.193131
\(869\) −52.7207 −1.78843
\(870\) −8.01716 −0.271807
\(871\) 2.62025 0.0887836
\(872\) 12.8636 0.435617
\(873\) 28.3890 0.960821
\(874\) 0 0
\(875\) 5.27714 0.178400
\(876\) 5.20690 0.175925
\(877\) −51.6182 −1.74302 −0.871512 0.490375i \(-0.836860\pi\)
−0.871512 + 0.490375i \(0.836860\pi\)
\(878\) 8.56215 0.288959
\(879\) −15.5243 −0.523622
\(880\) −14.6748 −0.494686
\(881\) 3.82731 0.128945 0.0644726 0.997919i \(-0.479463\pi\)
0.0644726 + 0.997919i \(0.479463\pi\)
\(882\) 2.76973 0.0932615
\(883\) 18.1829 0.611903 0.305952 0.952047i \(-0.401025\pi\)
0.305952 + 0.952047i \(0.401025\pi\)
\(884\) 1.11229 0.0374104
\(885\) −12.0509 −0.405087
\(886\) −0.396798 −0.0133307
\(887\) −8.09769 −0.271894 −0.135947 0.990716i \(-0.543408\pi\)
−0.135947 + 0.990716i \(0.543408\pi\)
\(888\) 1.41458 0.0474703
\(889\) −0.603911 −0.0202545
\(890\) −43.6712 −1.46386
\(891\) 35.8787 1.20198
\(892\) −12.5217 −0.419256
\(893\) 0 0
\(894\) 8.33435 0.278742
\(895\) 72.4864 2.42295
\(896\) −1.00000 −0.0334077
\(897\) −0.689131 −0.0230094
\(898\) −39.6700 −1.32380
\(899\) −33.2955 −1.11047
\(900\) −8.72932 −0.290977
\(901\) −40.9034 −1.36269
\(902\) −17.1231 −0.570136
\(903\) −3.12389 −0.103957
\(904\) 1.48774 0.0494816
\(905\) −20.7565 −0.689969
\(906\) 7.49507 0.249007
\(907\) 32.6030 1.08256 0.541282 0.840841i \(-0.317939\pi\)
0.541282 + 0.840841i \(0.317939\pi\)
\(908\) −26.7753 −0.888569
\(909\) −37.8563 −1.25561
\(910\) −0.672211 −0.0222836
\(911\) −6.09389 −0.201900 −0.100950 0.994892i \(-0.532188\pi\)
−0.100950 + 0.994892i \(0.532188\pi\)
\(912\) 0 0
\(913\) 62.3592 2.06379
\(914\) −5.26900 −0.174283
\(915\) 7.44187 0.246021
\(916\) 18.8086 0.621454
\(917\) 14.9371 0.493266
\(918\) −13.0802 −0.431711
\(919\) −30.8160 −1.01653 −0.508263 0.861202i \(-0.669712\pi\)
−0.508263 + 0.861202i \(0.669712\pi\)
\(920\) 17.4149 0.574153
\(921\) 2.43211 0.0801409
\(922\) 7.92353 0.260948
\(923\) 0.715802 0.0235609
\(924\) 2.46643 0.0811397
\(925\) −9.29072 −0.305477
\(926\) −16.7306 −0.549803
\(927\) 17.6816 0.580740
\(928\) 5.85159 0.192088
\(929\) 43.0248 1.41160 0.705798 0.708413i \(-0.250589\pi\)
0.705798 + 0.708413i \(0.250589\pi\)
\(930\) 7.79575 0.255633
\(931\) 0 0
\(932\) −10.2268 −0.334991
\(933\) −7.64508 −0.250289
\(934\) 9.87110 0.322992
\(935\) 69.3279 2.26726
\(936\) −0.652106 −0.0213148
\(937\) −27.1469 −0.886852 −0.443426 0.896311i \(-0.646237\pi\)
−0.443426 + 0.896311i \(0.646237\pi\)
\(938\) 11.1291 0.363378
\(939\) 1.05828 0.0345358
\(940\) 1.68345 0.0549081
\(941\) 45.0495 1.46857 0.734287 0.678840i \(-0.237517\pi\)
0.734287 + 0.678840i \(0.237517\pi\)
\(942\) −6.58999 −0.214714
\(943\) 20.3204 0.661723
\(944\) 8.79576 0.286278
\(945\) 7.90499 0.257149
\(946\) 33.4596 1.08786
\(947\) 22.0222 0.715626 0.357813 0.933793i \(-0.383523\pi\)
0.357813 + 0.933793i \(0.383523\pi\)
\(948\) −4.92217 −0.159865
\(949\) −2.55469 −0.0829287
\(950\) 0 0
\(951\) −8.72005 −0.282767
\(952\) 4.72430 0.153115
\(953\) 31.3488 1.01549 0.507744 0.861508i \(-0.330480\pi\)
0.507744 + 0.861508i \(0.330480\pi\)
\(954\) 23.9805 0.776398
\(955\) 53.2217 1.72221
\(956\) −16.8837 −0.546058
\(957\) −14.4326 −0.466538
\(958\) −3.43432 −0.110958
\(959\) 16.1532 0.521613
\(960\) −1.37008 −0.0442192
\(961\) 1.37597 0.0443863
\(962\) −0.694045 −0.0223769
\(963\) −22.8174 −0.735280
\(964\) −21.5302 −0.693442
\(965\) 62.0890 1.99872
\(966\) −2.92698 −0.0941741
\(967\) 48.3616 1.55521 0.777603 0.628756i \(-0.216436\pi\)
0.777603 + 0.628756i \(0.216436\pi\)
\(968\) −15.4176 −0.495541
\(969\) 0 0
\(970\) −29.2642 −0.939617
\(971\) 28.9214 0.928131 0.464065 0.885801i \(-0.346390\pi\)
0.464065 + 0.885801i \(0.346390\pi\)
\(972\) 11.6559 0.373863
\(973\) −20.8094 −0.667118
\(974\) 18.6872 0.598777
\(975\) −0.356080 −0.0114037
\(976\) −5.43170 −0.173865
\(977\) 60.4037 1.93249 0.966243 0.257631i \(-0.0829419\pi\)
0.966243 + 0.257631i \(0.0829419\pi\)
\(978\) 1.02643 0.0328217
\(979\) −78.6172 −2.51262
\(980\) −2.85512 −0.0912034
\(981\) 35.6287 1.13754
\(982\) −31.2379 −0.996841
\(983\) 6.35674 0.202748 0.101374 0.994848i \(-0.467676\pi\)
0.101374 + 0.994848i \(0.467676\pi\)
\(984\) −1.59866 −0.0509635
\(985\) 62.2852 1.98457
\(986\) −27.6447 −0.880385
\(987\) −0.282943 −0.00900617
\(988\) 0 0
\(989\) −39.7074 −1.26262
\(990\) −40.6450 −1.29178
\(991\) 53.6557 1.70443 0.852215 0.523192i \(-0.175259\pi\)
0.852215 + 0.523192i \(0.175259\pi\)
\(992\) −5.68999 −0.180657
\(993\) −0.924946 −0.0293523
\(994\) 3.04026 0.0964313
\(995\) 8.80969 0.279286
\(996\) 5.82206 0.184479
\(997\) −26.8958 −0.851798 −0.425899 0.904771i \(-0.640042\pi\)
−0.425899 + 0.904771i \(0.640042\pi\)
\(998\) 11.4120 0.361240
\(999\) 8.16175 0.258226
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 5054.2.a.z.1.4 6
19.18 odd 2 5054.2.a.be.1.3 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5054.2.a.z.1.4 6 1.1 even 1 trivial
5054.2.a.be.1.3 yes 6 19.18 odd 2