Properties

Label 6034.2.a.p.1.16
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $0$
Dimension $27$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.482352 q^{3} +1.00000 q^{4} +2.96654 q^{5} -0.482352 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.76734 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.482352 q^{3} +1.00000 q^{4} +2.96654 q^{5} -0.482352 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.76734 q^{9} -2.96654 q^{10} +2.13961 q^{11} +0.482352 q^{12} +3.23107 q^{13} -1.00000 q^{14} +1.43092 q^{15} +1.00000 q^{16} +0.239086 q^{17} +2.76734 q^{18} -1.99134 q^{19} +2.96654 q^{20} +0.482352 q^{21} -2.13961 q^{22} -0.0927620 q^{23} -0.482352 q^{24} +3.80035 q^{25} -3.23107 q^{26} -2.78189 q^{27} +1.00000 q^{28} +5.49601 q^{29} -1.43092 q^{30} -1.27192 q^{31} -1.00000 q^{32} +1.03205 q^{33} -0.239086 q^{34} +2.96654 q^{35} -2.76734 q^{36} +2.61566 q^{37} +1.99134 q^{38} +1.55851 q^{39} -2.96654 q^{40} -8.16295 q^{41} -0.482352 q^{42} +8.50523 q^{43} +2.13961 q^{44} -8.20941 q^{45} +0.0927620 q^{46} +9.39850 q^{47} +0.482352 q^{48} +1.00000 q^{49} -3.80035 q^{50} +0.115323 q^{51} +3.23107 q^{52} +12.5678 q^{53} +2.78189 q^{54} +6.34724 q^{55} -1.00000 q^{56} -0.960528 q^{57} -5.49601 q^{58} -11.2092 q^{59} +1.43092 q^{60} -13.1502 q^{61} +1.27192 q^{62} -2.76734 q^{63} +1.00000 q^{64} +9.58508 q^{65} -1.03205 q^{66} +9.29161 q^{67} +0.239086 q^{68} -0.0447439 q^{69} -2.96654 q^{70} +0.681386 q^{71} +2.76734 q^{72} -0.776701 q^{73} -2.61566 q^{74} +1.83311 q^{75} -1.99134 q^{76} +2.13961 q^{77} -1.55851 q^{78} +2.65766 q^{79} +2.96654 q^{80} +6.96016 q^{81} +8.16295 q^{82} +0.462264 q^{83} +0.482352 q^{84} +0.709257 q^{85} -8.50523 q^{86} +2.65101 q^{87} -2.13961 q^{88} -8.66555 q^{89} +8.20941 q^{90} +3.23107 q^{91} -0.0927620 q^{92} -0.613512 q^{93} -9.39850 q^{94} -5.90739 q^{95} -0.482352 q^{96} +8.48519 q^{97} -1.00000 q^{98} -5.92103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 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
\(3\) 0.482352 0.278486 0.139243 0.990258i \(-0.455533\pi\)
0.139243 + 0.990258i \(0.455533\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.96654 1.32668 0.663338 0.748320i \(-0.269139\pi\)
0.663338 + 0.748320i \(0.269139\pi\)
\(6\) −0.482352 −0.196919
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.76734 −0.922446
\(10\) −2.96654 −0.938102
\(11\) 2.13961 0.645117 0.322559 0.946549i \(-0.395457\pi\)
0.322559 + 0.946549i \(0.395457\pi\)
\(12\) 0.482352 0.139243
\(13\) 3.23107 0.896137 0.448068 0.893999i \(-0.352112\pi\)
0.448068 + 0.893999i \(0.352112\pi\)
\(14\) −1.00000 −0.267261
\(15\) 1.43092 0.369461
\(16\) 1.00000 0.250000
\(17\) 0.239086 0.0579868 0.0289934 0.999580i \(-0.490770\pi\)
0.0289934 + 0.999580i \(0.490770\pi\)
\(18\) 2.76734 0.652267
\(19\) −1.99134 −0.456845 −0.228423 0.973562i \(-0.573357\pi\)
−0.228423 + 0.973562i \(0.573357\pi\)
\(20\) 2.96654 0.663338
\(21\) 0.482352 0.105258
\(22\) −2.13961 −0.456167
\(23\) −0.0927620 −0.0193422 −0.00967110 0.999953i \(-0.503078\pi\)
−0.00967110 + 0.999953i \(0.503078\pi\)
\(24\) −0.482352 −0.0984597
\(25\) 3.80035 0.760070
\(26\) −3.23107 −0.633664
\(27\) −2.78189 −0.535374
\(28\) 1.00000 0.188982
\(29\) 5.49601 1.02058 0.510292 0.860001i \(-0.329537\pi\)
0.510292 + 0.860001i \(0.329537\pi\)
\(30\) −1.43092 −0.261248
\(31\) −1.27192 −0.228443 −0.114222 0.993455i \(-0.536437\pi\)
−0.114222 + 0.993455i \(0.536437\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.03205 0.179656
\(34\) −0.239086 −0.0410028
\(35\) 2.96654 0.501436
\(36\) −2.76734 −0.461223
\(37\) 2.61566 0.430012 0.215006 0.976613i \(-0.431023\pi\)
0.215006 + 0.976613i \(0.431023\pi\)
\(38\) 1.99134 0.323038
\(39\) 1.55851 0.249562
\(40\) −2.96654 −0.469051
\(41\) −8.16295 −1.27484 −0.637420 0.770517i \(-0.719998\pi\)
−0.637420 + 0.770517i \(0.719998\pi\)
\(42\) −0.482352 −0.0744285
\(43\) 8.50523 1.29704 0.648518 0.761200i \(-0.275389\pi\)
0.648518 + 0.761200i \(0.275389\pi\)
\(44\) 2.13961 0.322559
\(45\) −8.20941 −1.22379
\(46\) 0.0927620 0.0136770
\(47\) 9.39850 1.37091 0.685456 0.728114i \(-0.259603\pi\)
0.685456 + 0.728114i \(0.259603\pi\)
\(48\) 0.482352 0.0696215
\(49\) 1.00000 0.142857
\(50\) −3.80035 −0.537451
\(51\) 0.115323 0.0161485
\(52\) 3.23107 0.448068
\(53\) 12.5678 1.72633 0.863163 0.504925i \(-0.168480\pi\)
0.863163 + 0.504925i \(0.168480\pi\)
\(54\) 2.78189 0.378567
\(55\) 6.34724 0.855862
\(56\) −1.00000 −0.133631
\(57\) −0.960528 −0.127225
\(58\) −5.49601 −0.721662
\(59\) −11.2092 −1.45931 −0.729656 0.683814i \(-0.760320\pi\)
−0.729656 + 0.683814i \(0.760320\pi\)
\(60\) 1.43092 0.184730
\(61\) −13.1502 −1.68371 −0.841854 0.539705i \(-0.818536\pi\)
−0.841854 + 0.539705i \(0.818536\pi\)
\(62\) 1.27192 0.161534
\(63\) −2.76734 −0.348652
\(64\) 1.00000 0.125000
\(65\) 9.58508 1.18888
\(66\) −1.03205 −0.127036
\(67\) 9.29161 1.13515 0.567575 0.823321i \(-0.307882\pi\)
0.567575 + 0.823321i \(0.307882\pi\)
\(68\) 0.239086 0.0289934
\(69\) −0.0447439 −0.00538654
\(70\) −2.96654 −0.354569
\(71\) 0.681386 0.0808656 0.0404328 0.999182i \(-0.487126\pi\)
0.0404328 + 0.999182i \(0.487126\pi\)
\(72\) 2.76734 0.326134
\(73\) −0.776701 −0.0909059 −0.0454530 0.998966i \(-0.514473\pi\)
−0.0454530 + 0.998966i \(0.514473\pi\)
\(74\) −2.61566 −0.304064
\(75\) 1.83311 0.211669
\(76\) −1.99134 −0.228423
\(77\) 2.13961 0.243831
\(78\) −1.55851 −0.176467
\(79\) 2.65766 0.299010 0.149505 0.988761i \(-0.452232\pi\)
0.149505 + 0.988761i \(0.452232\pi\)
\(80\) 2.96654 0.331669
\(81\) 6.96016 0.773351
\(82\) 8.16295 0.901447
\(83\) 0.462264 0.0507401 0.0253700 0.999678i \(-0.491924\pi\)
0.0253700 + 0.999678i \(0.491924\pi\)
\(84\) 0.482352 0.0526289
\(85\) 0.709257 0.0769297
\(86\) −8.50523 −0.917142
\(87\) 2.65101 0.284218
\(88\) −2.13961 −0.228083
\(89\) −8.66555 −0.918547 −0.459273 0.888295i \(-0.651890\pi\)
−0.459273 + 0.888295i \(0.651890\pi\)
\(90\) 8.20941 0.865348
\(91\) 3.23107 0.338708
\(92\) −0.0927620 −0.00967110
\(93\) −0.613512 −0.0636182
\(94\) −9.39850 −0.969381
\(95\) −5.90739 −0.606086
\(96\) −0.482352 −0.0492298
\(97\) 8.48519 0.861541 0.430770 0.902462i \(-0.358242\pi\)
0.430770 + 0.902462i \(0.358242\pi\)
\(98\) −1.00000 −0.101015
\(99\) −5.92103 −0.595086
\(100\) 3.80035 0.380035
\(101\) 2.08371 0.207337 0.103668 0.994612i \(-0.466942\pi\)
0.103668 + 0.994612i \(0.466942\pi\)
\(102\) −0.115323 −0.0114187
\(103\) 4.69630 0.462741 0.231370 0.972866i \(-0.425679\pi\)
0.231370 + 0.972866i \(0.425679\pi\)
\(104\) −3.23107 −0.316832
\(105\) 1.43092 0.139643
\(106\) −12.5678 −1.22070
\(107\) −4.74890 −0.459094 −0.229547 0.973298i \(-0.573724\pi\)
−0.229547 + 0.973298i \(0.573724\pi\)
\(108\) −2.78189 −0.267687
\(109\) 13.9853 1.33955 0.669775 0.742565i \(-0.266391\pi\)
0.669775 + 0.742565i \(0.266391\pi\)
\(110\) −6.34724 −0.605186
\(111\) 1.26167 0.119752
\(112\) 1.00000 0.0944911
\(113\) 18.6168 1.75132 0.875661 0.482926i \(-0.160426\pi\)
0.875661 + 0.482926i \(0.160426\pi\)
\(114\) 0.960528 0.0899617
\(115\) −0.275182 −0.0256608
\(116\) 5.49601 0.510292
\(117\) −8.94145 −0.826637
\(118\) 11.2092 1.03189
\(119\) 0.239086 0.0219169
\(120\) −1.43092 −0.130624
\(121\) −6.42206 −0.583824
\(122\) 13.1502 1.19056
\(123\) −3.93742 −0.355025
\(124\) −1.27192 −0.114222
\(125\) −3.55881 −0.318310
\(126\) 2.76734 0.246534
\(127\) −0.713567 −0.0633188 −0.0316594 0.999499i \(-0.510079\pi\)
−0.0316594 + 0.999499i \(0.510079\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.10251 0.361206
\(130\) −9.58508 −0.840667
\(131\) 12.8879 1.12602 0.563012 0.826448i \(-0.309642\pi\)
0.563012 + 0.826448i \(0.309642\pi\)
\(132\) 1.03205 0.0898281
\(133\) −1.99134 −0.172671
\(134\) −9.29161 −0.802673
\(135\) −8.25257 −0.710268
\(136\) −0.239086 −0.0205014
\(137\) −3.85098 −0.329012 −0.164506 0.986376i \(-0.552603\pi\)
−0.164506 + 0.986376i \(0.552603\pi\)
\(138\) 0.0447439 0.00380886
\(139\) 14.2324 1.20718 0.603590 0.797295i \(-0.293736\pi\)
0.603590 + 0.797295i \(0.293736\pi\)
\(140\) 2.96654 0.250718
\(141\) 4.53339 0.381780
\(142\) −0.681386 −0.0571806
\(143\) 6.91323 0.578113
\(144\) −2.76734 −0.230611
\(145\) 16.3041 1.35398
\(146\) 0.776701 0.0642802
\(147\) 0.482352 0.0397837
\(148\) 2.61566 0.215006
\(149\) 3.30358 0.270640 0.135320 0.990802i \(-0.456794\pi\)
0.135320 + 0.990802i \(0.456794\pi\)
\(150\) −1.83311 −0.149673
\(151\) −6.56285 −0.534077 −0.267039 0.963686i \(-0.586045\pi\)
−0.267039 + 0.963686i \(0.586045\pi\)
\(152\) 1.99134 0.161519
\(153\) −0.661630 −0.0534896
\(154\) −2.13961 −0.172415
\(155\) −3.77319 −0.303070
\(156\) 1.55851 0.124781
\(157\) −9.37570 −0.748262 −0.374131 0.927376i \(-0.622059\pi\)
−0.374131 + 0.927376i \(0.622059\pi\)
\(158\) −2.65766 −0.211432
\(159\) 6.06213 0.480758
\(160\) −2.96654 −0.234525
\(161\) −0.0927620 −0.00731067
\(162\) −6.96016 −0.546842
\(163\) 14.2718 1.11786 0.558928 0.829216i \(-0.311213\pi\)
0.558928 + 0.829216i \(0.311213\pi\)
\(164\) −8.16295 −0.637420
\(165\) 3.06161 0.238346
\(166\) −0.462264 −0.0358786
\(167\) 13.5331 1.04722 0.523612 0.851957i \(-0.324584\pi\)
0.523612 + 0.851957i \(0.324584\pi\)
\(168\) −0.482352 −0.0372143
\(169\) −2.56021 −0.196939
\(170\) −0.709257 −0.0543975
\(171\) 5.51071 0.421415
\(172\) 8.50523 0.648518
\(173\) −10.7610 −0.818145 −0.409073 0.912502i \(-0.634148\pi\)
−0.409073 + 0.912502i \(0.634148\pi\)
\(174\) −2.65101 −0.200973
\(175\) 3.80035 0.287279
\(176\) 2.13961 0.161279
\(177\) −5.40678 −0.406398
\(178\) 8.66555 0.649511
\(179\) 2.13053 0.159243 0.0796216 0.996825i \(-0.474629\pi\)
0.0796216 + 0.996825i \(0.474629\pi\)
\(180\) −8.20941 −0.611893
\(181\) −0.133121 −0.00989477 −0.00494738 0.999988i \(-0.501575\pi\)
−0.00494738 + 0.999988i \(0.501575\pi\)
\(182\) −3.23107 −0.239503
\(183\) −6.34302 −0.468889
\(184\) 0.0927620 0.00683850
\(185\) 7.75946 0.570487
\(186\) 0.613512 0.0449849
\(187\) 0.511550 0.0374083
\(188\) 9.39850 0.685456
\(189\) −2.78189 −0.202352
\(190\) 5.90739 0.428567
\(191\) −3.11563 −0.225439 −0.112720 0.993627i \(-0.535956\pi\)
−0.112720 + 0.993627i \(0.535956\pi\)
\(192\) 0.482352 0.0348108
\(193\) 16.5168 1.18891 0.594453 0.804131i \(-0.297369\pi\)
0.594453 + 0.804131i \(0.297369\pi\)
\(194\) −8.48519 −0.609201
\(195\) 4.62338 0.331087
\(196\) 1.00000 0.0714286
\(197\) 2.22701 0.158668 0.0793338 0.996848i \(-0.474721\pi\)
0.0793338 + 0.996848i \(0.474721\pi\)
\(198\) 5.92103 0.420789
\(199\) 15.1913 1.07688 0.538442 0.842663i \(-0.319013\pi\)
0.538442 + 0.842663i \(0.319013\pi\)
\(200\) −3.80035 −0.268725
\(201\) 4.48183 0.316124
\(202\) −2.08371 −0.146609
\(203\) 5.49601 0.385745
\(204\) 0.115323 0.00807425
\(205\) −24.2157 −1.69130
\(206\) −4.69630 −0.327207
\(207\) 0.256704 0.0178421
\(208\) 3.23107 0.224034
\(209\) −4.26070 −0.294719
\(210\) −1.43092 −0.0987426
\(211\) −26.0216 −1.79140 −0.895699 0.444661i \(-0.853324\pi\)
−0.895699 + 0.444661i \(0.853324\pi\)
\(212\) 12.5678 0.863163
\(213\) 0.328668 0.0225199
\(214\) 4.74890 0.324628
\(215\) 25.2311 1.72075
\(216\) 2.78189 0.189283
\(217\) −1.27192 −0.0863434
\(218\) −13.9853 −0.947204
\(219\) −0.374643 −0.0253160
\(220\) 6.34724 0.427931
\(221\) 0.772501 0.0519641
\(222\) −1.26167 −0.0846777
\(223\) −23.9130 −1.60133 −0.800665 0.599112i \(-0.795520\pi\)
−0.800665 + 0.599112i \(0.795520\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −10.5168 −0.701123
\(226\) −18.6168 −1.23837
\(227\) 23.4759 1.55815 0.779075 0.626931i \(-0.215689\pi\)
0.779075 + 0.626931i \(0.215689\pi\)
\(228\) −0.960528 −0.0636125
\(229\) 16.6106 1.09766 0.548830 0.835934i \(-0.315073\pi\)
0.548830 + 0.835934i \(0.315073\pi\)
\(230\) 0.275182 0.0181450
\(231\) 1.03205 0.0679037
\(232\) −5.49601 −0.360831
\(233\) −9.15714 −0.599904 −0.299952 0.953954i \(-0.596971\pi\)
−0.299952 + 0.953954i \(0.596971\pi\)
\(234\) 8.94145 0.584521
\(235\) 27.8810 1.81876
\(236\) −11.2092 −0.729656
\(237\) 1.28193 0.0832701
\(238\) −0.239086 −0.0154976
\(239\) 9.43344 0.610198 0.305099 0.952321i \(-0.401310\pi\)
0.305099 + 0.952321i \(0.401310\pi\)
\(240\) 1.43092 0.0923652
\(241\) −19.6860 −1.26808 −0.634042 0.773298i \(-0.718605\pi\)
−0.634042 + 0.773298i \(0.718605\pi\)
\(242\) 6.42206 0.412826
\(243\) 11.7029 0.750742
\(244\) −13.1502 −0.841854
\(245\) 2.96654 0.189525
\(246\) 3.93742 0.251041
\(247\) −6.43416 −0.409396
\(248\) 1.27192 0.0807669
\(249\) 0.222974 0.0141304
\(250\) 3.55881 0.225079
\(251\) 29.2174 1.84419 0.922094 0.386966i \(-0.126477\pi\)
0.922094 + 0.386966i \(0.126477\pi\)
\(252\) −2.76734 −0.174326
\(253\) −0.198475 −0.0124780
\(254\) 0.713567 0.0447732
\(255\) 0.342111 0.0214238
\(256\) 1.00000 0.0625000
\(257\) −20.5388 −1.28118 −0.640588 0.767885i \(-0.721309\pi\)
−0.640588 + 0.767885i \(0.721309\pi\)
\(258\) −4.10251 −0.255411
\(259\) 2.61566 0.162529
\(260\) 9.58508 0.594442
\(261\) −15.2093 −0.941433
\(262\) −12.8879 −0.796220
\(263\) −16.6882 −1.02904 −0.514519 0.857479i \(-0.672029\pi\)
−0.514519 + 0.857479i \(0.672029\pi\)
\(264\) −1.03205 −0.0635181
\(265\) 37.2830 2.29028
\(266\) 1.99134 0.122097
\(267\) −4.17985 −0.255802
\(268\) 9.29161 0.567575
\(269\) −22.0360 −1.34356 −0.671778 0.740752i \(-0.734469\pi\)
−0.671778 + 0.740752i \(0.734469\pi\)
\(270\) 8.25257 0.502236
\(271\) −11.9667 −0.726924 −0.363462 0.931609i \(-0.618405\pi\)
−0.363462 + 0.931609i \(0.618405\pi\)
\(272\) 0.239086 0.0144967
\(273\) 1.55851 0.0943254
\(274\) 3.85098 0.232646
\(275\) 8.13127 0.490334
\(276\) −0.0447439 −0.00269327
\(277\) 4.88474 0.293495 0.146748 0.989174i \(-0.453119\pi\)
0.146748 + 0.989174i \(0.453119\pi\)
\(278\) −14.2324 −0.853606
\(279\) 3.51982 0.210726
\(280\) −2.96654 −0.177285
\(281\) 16.4054 0.978663 0.489331 0.872098i \(-0.337241\pi\)
0.489331 + 0.872098i \(0.337241\pi\)
\(282\) −4.53339 −0.269959
\(283\) −30.2586 −1.79869 −0.899344 0.437242i \(-0.855955\pi\)
−0.899344 + 0.437242i \(0.855955\pi\)
\(284\) 0.681386 0.0404328
\(285\) −2.84944 −0.168786
\(286\) −6.91323 −0.408788
\(287\) −8.16295 −0.481844
\(288\) 2.76734 0.163067
\(289\) −16.9428 −0.996638
\(290\) −16.3041 −0.957412
\(291\) 4.09285 0.239927
\(292\) −0.776701 −0.0454530
\(293\) 11.3651 0.663958 0.331979 0.943287i \(-0.392284\pi\)
0.331979 + 0.943287i \(0.392284\pi\)
\(294\) −0.482352 −0.0281313
\(295\) −33.2525 −1.93604
\(296\) −2.61566 −0.152032
\(297\) −5.95216 −0.345379
\(298\) −3.30358 −0.191371
\(299\) −0.299720 −0.0173333
\(300\) 1.83311 0.105834
\(301\) 8.50523 0.490233
\(302\) 6.56285 0.377650
\(303\) 1.00508 0.0577404
\(304\) −1.99134 −0.114211
\(305\) −39.0105 −2.23374
\(306\) 0.661630 0.0378229
\(307\) −17.4281 −0.994676 −0.497338 0.867557i \(-0.665689\pi\)
−0.497338 + 0.867557i \(0.665689\pi\)
\(308\) 2.13961 0.121916
\(309\) 2.26527 0.128867
\(310\) 3.77319 0.214303
\(311\) −12.7887 −0.725183 −0.362592 0.931948i \(-0.618108\pi\)
−0.362592 + 0.931948i \(0.618108\pi\)
\(312\) −1.55851 −0.0882333
\(313\) 22.2518 1.25775 0.628874 0.777507i \(-0.283516\pi\)
0.628874 + 0.777507i \(0.283516\pi\)
\(314\) 9.37570 0.529101
\(315\) −8.20941 −0.462548
\(316\) 2.65766 0.149505
\(317\) 6.60862 0.371177 0.185589 0.982628i \(-0.440581\pi\)
0.185589 + 0.982628i \(0.440581\pi\)
\(318\) −6.06213 −0.339947
\(319\) 11.7593 0.658397
\(320\) 2.96654 0.165835
\(321\) −2.29064 −0.127851
\(322\) 0.0927620 0.00516942
\(323\) −0.476101 −0.0264910
\(324\) 6.96016 0.386676
\(325\) 12.2792 0.681126
\(326\) −14.2718 −0.790444
\(327\) 6.74584 0.373046
\(328\) 8.16295 0.450724
\(329\) 9.39850 0.518156
\(330\) −3.06161 −0.168536
\(331\) 12.0841 0.664202 0.332101 0.943244i \(-0.392242\pi\)
0.332101 + 0.943244i \(0.392242\pi\)
\(332\) 0.462264 0.0253700
\(333\) −7.23842 −0.396663
\(334\) −13.5331 −0.740499
\(335\) 27.5639 1.50598
\(336\) 0.482352 0.0263145
\(337\) −17.3674 −0.946065 −0.473033 0.881045i \(-0.656841\pi\)
−0.473033 + 0.881045i \(0.656841\pi\)
\(338\) 2.56021 0.139257
\(339\) 8.97986 0.487719
\(340\) 0.709257 0.0384648
\(341\) −2.72141 −0.147373
\(342\) −5.51071 −0.297985
\(343\) 1.00000 0.0539949
\(344\) −8.50523 −0.458571
\(345\) −0.132735 −0.00714619
\(346\) 10.7610 0.578516
\(347\) 28.9006 1.55147 0.775734 0.631060i \(-0.217380\pi\)
0.775734 + 0.631060i \(0.217380\pi\)
\(348\) 2.65101 0.142109
\(349\) −12.0905 −0.647192 −0.323596 0.946195i \(-0.604892\pi\)
−0.323596 + 0.946195i \(0.604892\pi\)
\(350\) −3.80035 −0.203137
\(351\) −8.98846 −0.479768
\(352\) −2.13961 −0.114042
\(353\) −27.7700 −1.47805 −0.739024 0.673679i \(-0.764713\pi\)
−0.739024 + 0.673679i \(0.764713\pi\)
\(354\) 5.40678 0.287367
\(355\) 2.02136 0.107282
\(356\) −8.66555 −0.459273
\(357\) 0.115323 0.00610356
\(358\) −2.13053 −0.112602
\(359\) −32.5443 −1.71762 −0.858812 0.512290i \(-0.828797\pi\)
−0.858812 + 0.512290i \(0.828797\pi\)
\(360\) 8.20941 0.432674
\(361\) −15.0346 −0.791292
\(362\) 0.133121 0.00699666
\(363\) −3.09769 −0.162587
\(364\) 3.23107 0.169354
\(365\) −2.30411 −0.120603
\(366\) 6.34302 0.331555
\(367\) 1.36993 0.0715097 0.0357548 0.999361i \(-0.488616\pi\)
0.0357548 + 0.999361i \(0.488616\pi\)
\(368\) −0.0927620 −0.00483555
\(369\) 22.5896 1.17597
\(370\) −7.75946 −0.403395
\(371\) 12.5678 0.652490
\(372\) −0.613512 −0.0318091
\(373\) 27.5413 1.42603 0.713016 0.701147i \(-0.247328\pi\)
0.713016 + 0.701147i \(0.247328\pi\)
\(374\) −0.511550 −0.0264516
\(375\) −1.71660 −0.0886448
\(376\) −9.39850 −0.484691
\(377\) 17.7580 0.914583
\(378\) 2.78189 0.143085
\(379\) −2.55245 −0.131110 −0.0655552 0.997849i \(-0.520882\pi\)
−0.0655552 + 0.997849i \(0.520882\pi\)
\(380\) −5.90739 −0.303043
\(381\) −0.344190 −0.0176334
\(382\) 3.11563 0.159409
\(383\) −33.6175 −1.71777 −0.858887 0.512165i \(-0.828844\pi\)
−0.858887 + 0.512165i \(0.828844\pi\)
\(384\) −0.482352 −0.0246149
\(385\) 6.34724 0.323485
\(386\) −16.5168 −0.840683
\(387\) −23.5368 −1.19644
\(388\) 8.48519 0.430770
\(389\) 8.37623 0.424692 0.212346 0.977195i \(-0.431890\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(390\) −4.62338 −0.234114
\(391\) −0.0221780 −0.00112159
\(392\) −1.00000 −0.0505076
\(393\) 6.21653 0.313582
\(394\) −2.22701 −0.112195
\(395\) 7.88405 0.396690
\(396\) −5.92103 −0.297543
\(397\) 7.71781 0.387346 0.193673 0.981066i \(-0.437960\pi\)
0.193673 + 0.981066i \(0.437960\pi\)
\(398\) −15.1913 −0.761472
\(399\) −0.960528 −0.0480865
\(400\) 3.80035 0.190017
\(401\) 10.3982 0.519260 0.259630 0.965708i \(-0.416399\pi\)
0.259630 + 0.965708i \(0.416399\pi\)
\(402\) −4.48183 −0.223533
\(403\) −4.10965 −0.204716
\(404\) 2.08371 0.103668
\(405\) 20.6476 1.02599
\(406\) −5.49601 −0.272763
\(407\) 5.59650 0.277408
\(408\) −0.115323 −0.00570936
\(409\) 39.0810 1.93243 0.966215 0.257737i \(-0.0829768\pi\)
0.966215 + 0.257737i \(0.0829768\pi\)
\(410\) 24.2157 1.19593
\(411\) −1.85753 −0.0916252
\(412\) 4.69630 0.231370
\(413\) −11.2092 −0.551568
\(414\) −0.256704 −0.0126163
\(415\) 1.37132 0.0673156
\(416\) −3.23107 −0.158416
\(417\) 6.86505 0.336183
\(418\) 4.26070 0.208398
\(419\) 25.0634 1.22443 0.612213 0.790693i \(-0.290279\pi\)
0.612213 + 0.790693i \(0.290279\pi\)
\(420\) 1.43092 0.0698215
\(421\) −15.6053 −0.760558 −0.380279 0.924872i \(-0.624172\pi\)
−0.380279 + 0.924872i \(0.624172\pi\)
\(422\) 26.0216 1.26671
\(423\) −26.0088 −1.26459
\(424\) −12.5678 −0.610349
\(425\) 0.908609 0.0440740
\(426\) −0.328668 −0.0159240
\(427\) −13.1502 −0.636382
\(428\) −4.74890 −0.229547
\(429\) 3.33461 0.160997
\(430\) −25.2311 −1.21675
\(431\) −1.00000 −0.0481683
\(432\) −2.78189 −0.133844
\(433\) −18.6033 −0.894017 −0.447008 0.894530i \(-0.647511\pi\)
−0.447008 + 0.894530i \(0.647511\pi\)
\(434\) 1.27192 0.0610540
\(435\) 7.86433 0.377066
\(436\) 13.9853 0.669775
\(437\) 0.184721 0.00883639
\(438\) 0.374643 0.0179011
\(439\) 21.8233 1.04157 0.520785 0.853688i \(-0.325639\pi\)
0.520785 + 0.853688i \(0.325639\pi\)
\(440\) −6.34724 −0.302593
\(441\) −2.76734 −0.131778
\(442\) −0.772501 −0.0367441
\(443\) 17.6938 0.840656 0.420328 0.907372i \(-0.361915\pi\)
0.420328 + 0.907372i \(0.361915\pi\)
\(444\) 1.26167 0.0598762
\(445\) −25.7067 −1.21861
\(446\) 23.9130 1.13231
\(447\) 1.59349 0.0753694
\(448\) 1.00000 0.0472456
\(449\) −16.6261 −0.784636 −0.392318 0.919830i \(-0.628327\pi\)
−0.392318 + 0.919830i \(0.628327\pi\)
\(450\) 10.5168 0.495769
\(451\) −17.4656 −0.822421
\(452\) 18.6168 0.875661
\(453\) −3.16560 −0.148733
\(454\) −23.4759 −1.10178
\(455\) 9.58508 0.449356
\(456\) 0.960528 0.0449808
\(457\) 1.44455 0.0675730 0.0337865 0.999429i \(-0.489243\pi\)
0.0337865 + 0.999429i \(0.489243\pi\)
\(458\) −16.6106 −0.776163
\(459\) −0.665109 −0.0310446
\(460\) −0.275182 −0.0128304
\(461\) −3.80273 −0.177111 −0.0885554 0.996071i \(-0.528225\pi\)
−0.0885554 + 0.996071i \(0.528225\pi\)
\(462\) −1.03205 −0.0480151
\(463\) −11.8740 −0.551831 −0.275916 0.961182i \(-0.588981\pi\)
−0.275916 + 0.961182i \(0.588981\pi\)
\(464\) 5.49601 0.255146
\(465\) −1.82001 −0.0844008
\(466\) 9.15714 0.424196
\(467\) −23.2619 −1.07643 −0.538217 0.842806i \(-0.680902\pi\)
−0.538217 + 0.842806i \(0.680902\pi\)
\(468\) −8.94145 −0.413319
\(469\) 9.29161 0.429047
\(470\) −27.8810 −1.28606
\(471\) −4.52239 −0.208381
\(472\) 11.2092 0.515945
\(473\) 18.1979 0.836740
\(474\) −1.28193 −0.0588809
\(475\) −7.56780 −0.347234
\(476\) 0.239086 0.0109585
\(477\) −34.7795 −1.59244
\(478\) −9.43344 −0.431475
\(479\) 1.74403 0.0796870 0.0398435 0.999206i \(-0.487314\pi\)
0.0398435 + 0.999206i \(0.487314\pi\)
\(480\) −1.43092 −0.0653121
\(481\) 8.45138 0.385350
\(482\) 19.6860 0.896671
\(483\) −0.0447439 −0.00203592
\(484\) −6.42206 −0.291912
\(485\) 25.1716 1.14299
\(486\) −11.7029 −0.530855
\(487\) 17.9150 0.811808 0.405904 0.913916i \(-0.366957\pi\)
0.405904 + 0.913916i \(0.366957\pi\)
\(488\) 13.1502 0.595281
\(489\) 6.88405 0.311307
\(490\) −2.96654 −0.134015
\(491\) 15.3446 0.692491 0.346246 0.938144i \(-0.387456\pi\)
0.346246 + 0.938144i \(0.387456\pi\)
\(492\) −3.93742 −0.177512
\(493\) 1.31402 0.0591804
\(494\) 6.43416 0.289486
\(495\) −17.5650 −0.789486
\(496\) −1.27192 −0.0571108
\(497\) 0.681386 0.0305643
\(498\) −0.222974 −0.00999170
\(499\) 25.0219 1.12014 0.560068 0.828447i \(-0.310775\pi\)
0.560068 + 0.828447i \(0.310775\pi\)
\(500\) −3.55881 −0.159155
\(501\) 6.52772 0.291637
\(502\) −29.2174 −1.30404
\(503\) −8.07209 −0.359917 −0.179958 0.983674i \(-0.557596\pi\)
−0.179958 + 0.983674i \(0.557596\pi\)
\(504\) 2.76734 0.123267
\(505\) 6.18140 0.275069
\(506\) 0.198475 0.00882327
\(507\) −1.23492 −0.0548449
\(508\) −0.713567 −0.0316594
\(509\) 12.2895 0.544721 0.272361 0.962195i \(-0.412196\pi\)
0.272361 + 0.962195i \(0.412196\pi\)
\(510\) −0.342111 −0.0151489
\(511\) −0.776701 −0.0343592
\(512\) −1.00000 −0.0441942
\(513\) 5.53969 0.244583
\(514\) 20.5388 0.905928
\(515\) 13.9318 0.613907
\(516\) 4.10251 0.180603
\(517\) 20.1091 0.884399
\(518\) −2.61566 −0.114926
\(519\) −5.19060 −0.227842
\(520\) −9.58508 −0.420334
\(521\) 14.2891 0.626016 0.313008 0.949750i \(-0.398663\pi\)
0.313008 + 0.949750i \(0.398663\pi\)
\(522\) 15.2093 0.665694
\(523\) −33.4009 −1.46052 −0.730259 0.683170i \(-0.760601\pi\)
−0.730259 + 0.683170i \(0.760601\pi\)
\(524\) 12.8879 0.563012
\(525\) 1.83311 0.0800033
\(526\) 16.6882 0.727639
\(527\) −0.304097 −0.0132467
\(528\) 1.03205 0.0449141
\(529\) −22.9914 −0.999626
\(530\) −37.2830 −1.61947
\(531\) 31.0196 1.34614
\(532\) −1.99134 −0.0863356
\(533\) −26.3750 −1.14243
\(534\) 4.17985 0.180880
\(535\) −14.0878 −0.609069
\(536\) −9.29161 −0.401336
\(537\) 1.02767 0.0443470
\(538\) 22.0360 0.950038
\(539\) 2.13961 0.0921596
\(540\) −8.25257 −0.355134
\(541\) 12.6938 0.545751 0.272875 0.962049i \(-0.412025\pi\)
0.272875 + 0.962049i \(0.412025\pi\)
\(542\) 11.9667 0.514013
\(543\) −0.0642110 −0.00275556
\(544\) −0.239086 −0.0102507
\(545\) 41.4879 1.77715
\(546\) −1.55851 −0.0666981
\(547\) 32.6253 1.39496 0.697478 0.716606i \(-0.254305\pi\)
0.697478 + 0.716606i \(0.254305\pi\)
\(548\) −3.85098 −0.164506
\(549\) 36.3910 1.55313
\(550\) −8.13127 −0.346719
\(551\) −10.9444 −0.466249
\(552\) 0.0447439 0.00190443
\(553\) 2.65766 0.113015
\(554\) −4.88474 −0.207533
\(555\) 3.74279 0.158873
\(556\) 14.2324 0.603590
\(557\) −4.81152 −0.203871 −0.101935 0.994791i \(-0.532503\pi\)
−0.101935 + 0.994791i \(0.532503\pi\)
\(558\) −3.51982 −0.149006
\(559\) 27.4810 1.16232
\(560\) 2.96654 0.125359
\(561\) 0.246747 0.0104177
\(562\) −16.4054 −0.692019
\(563\) 37.7250 1.58992 0.794959 0.606663i \(-0.207492\pi\)
0.794959 + 0.606663i \(0.207492\pi\)
\(564\) 4.53339 0.190890
\(565\) 55.2275 2.32344
\(566\) 30.2586 1.27186
\(567\) 6.96016 0.292299
\(568\) −0.681386 −0.0285903
\(569\) −10.3231 −0.432767 −0.216384 0.976308i \(-0.569426\pi\)
−0.216384 + 0.976308i \(0.569426\pi\)
\(570\) 2.84944 0.119350
\(571\) −17.7888 −0.744438 −0.372219 0.928145i \(-0.621403\pi\)
−0.372219 + 0.928145i \(0.621403\pi\)
\(572\) 6.91323 0.289057
\(573\) −1.50283 −0.0627816
\(574\) 8.16295 0.340715
\(575\) −0.352528 −0.0147014
\(576\) −2.76734 −0.115306
\(577\) −1.19926 −0.0499259 −0.0249630 0.999688i \(-0.507947\pi\)
−0.0249630 + 0.999688i \(0.507947\pi\)
\(578\) 16.9428 0.704729
\(579\) 7.96691 0.331094
\(580\) 16.3041 0.676992
\(581\) 0.462264 0.0191779
\(582\) −4.09285 −0.169654
\(583\) 26.8903 1.11368
\(584\) 0.776701 0.0321401
\(585\) −26.5251 −1.09668
\(586\) −11.3651 −0.469489
\(587\) 28.2652 1.16663 0.583316 0.812246i \(-0.301755\pi\)
0.583316 + 0.812246i \(0.301755\pi\)
\(588\) 0.482352 0.0198919
\(589\) 2.53282 0.104363
\(590\) 33.2525 1.36898
\(591\) 1.07420 0.0441867
\(592\) 2.61566 0.107503
\(593\) −27.6786 −1.13663 −0.568313 0.822813i \(-0.692404\pi\)
−0.568313 + 0.822813i \(0.692404\pi\)
\(594\) 5.95216 0.244220
\(595\) 0.709257 0.0290767
\(596\) 3.30358 0.135320
\(597\) 7.32756 0.299897
\(598\) 0.299720 0.0122565
\(599\) −39.0073 −1.59380 −0.796898 0.604113i \(-0.793527\pi\)
−0.796898 + 0.604113i \(0.793527\pi\)
\(600\) −1.83311 −0.0748363
\(601\) 17.1496 0.699547 0.349773 0.936834i \(-0.386259\pi\)
0.349773 + 0.936834i \(0.386259\pi\)
\(602\) −8.50523 −0.346647
\(603\) −25.7130 −1.04711
\(604\) −6.56285 −0.267039
\(605\) −19.0513 −0.774545
\(606\) −1.00508 −0.0408286
\(607\) 31.1658 1.26498 0.632490 0.774569i \(-0.282033\pi\)
0.632490 + 0.774569i \(0.282033\pi\)
\(608\) 1.99134 0.0807596
\(609\) 2.65101 0.107424
\(610\) 39.0105 1.57949
\(611\) 30.3672 1.22852
\(612\) −0.661630 −0.0267448
\(613\) 25.6400 1.03559 0.517794 0.855505i \(-0.326753\pi\)
0.517794 + 0.855505i \(0.326753\pi\)
\(614\) 17.4281 0.703342
\(615\) −11.6805 −0.471003
\(616\) −2.13961 −0.0862074
\(617\) 40.9546 1.64877 0.824385 0.566029i \(-0.191521\pi\)
0.824385 + 0.566029i \(0.191521\pi\)
\(618\) −2.26527 −0.0911226
\(619\) 14.6410 0.588471 0.294235 0.955733i \(-0.404935\pi\)
0.294235 + 0.955733i \(0.404935\pi\)
\(620\) −3.77319 −0.151535
\(621\) 0.258053 0.0103553
\(622\) 12.7887 0.512782
\(623\) −8.66555 −0.347178
\(624\) 1.55851 0.0623904
\(625\) −29.5591 −1.18236
\(626\) −22.2518 −0.889362
\(627\) −2.05516 −0.0820751
\(628\) −9.37570 −0.374131
\(629\) 0.625367 0.0249350
\(630\) 8.20941 0.327071
\(631\) 20.1195 0.800946 0.400473 0.916309i \(-0.368846\pi\)
0.400473 + 0.916309i \(0.368846\pi\)
\(632\) −2.65766 −0.105716
\(633\) −12.5516 −0.498879
\(634\) −6.60862 −0.262462
\(635\) −2.11682 −0.0840036
\(636\) 6.06213 0.240379
\(637\) 3.23107 0.128020
\(638\) −11.7593 −0.465557
\(639\) −1.88562 −0.0745941
\(640\) −2.96654 −0.117263
\(641\) 39.1696 1.54710 0.773552 0.633732i \(-0.218478\pi\)
0.773552 + 0.633732i \(0.218478\pi\)
\(642\) 2.29064 0.0904045
\(643\) −2.87102 −0.113222 −0.0566109 0.998396i \(-0.518029\pi\)
−0.0566109 + 0.998396i \(0.518029\pi\)
\(644\) −0.0927620 −0.00365533
\(645\) 12.1703 0.479204
\(646\) 0.476101 0.0187319
\(647\) 12.2329 0.480927 0.240463 0.970658i \(-0.422701\pi\)
0.240463 + 0.970658i \(0.422701\pi\)
\(648\) −6.96016 −0.273421
\(649\) −23.9833 −0.941428
\(650\) −12.2792 −0.481629
\(651\) −0.613512 −0.0240454
\(652\) 14.2718 0.558928
\(653\) 31.5162 1.23332 0.616662 0.787228i \(-0.288485\pi\)
0.616662 + 0.787228i \(0.288485\pi\)
\(654\) −6.74584 −0.263783
\(655\) 38.2326 1.49387
\(656\) −8.16295 −0.318710
\(657\) 2.14939 0.0838558
\(658\) −9.39850 −0.366392
\(659\) 15.0682 0.586974 0.293487 0.955963i \(-0.405184\pi\)
0.293487 + 0.955963i \(0.405184\pi\)
\(660\) 3.06161 0.119173
\(661\) 11.3999 0.443405 0.221703 0.975114i \(-0.428839\pi\)
0.221703 + 0.975114i \(0.428839\pi\)
\(662\) −12.0841 −0.469662
\(663\) 0.372618 0.0144713
\(664\) −0.462264 −0.0179393
\(665\) −5.90739 −0.229079
\(666\) 7.23842 0.280483
\(667\) −0.509821 −0.0197403
\(668\) 13.5331 0.523612
\(669\) −11.5345 −0.445948
\(670\) −27.5639 −1.06489
\(671\) −28.1363 −1.08619
\(672\) −0.482352 −0.0186071
\(673\) −46.2126 −1.78137 −0.890683 0.454625i \(-0.849773\pi\)
−0.890683 + 0.454625i \(0.849773\pi\)
\(674\) 17.3674 0.668969
\(675\) −10.5721 −0.406922
\(676\) −2.56021 −0.0984696
\(677\) −16.8944 −0.649303 −0.324652 0.945834i \(-0.605247\pi\)
−0.324652 + 0.945834i \(0.605247\pi\)
\(678\) −8.97986 −0.344869
\(679\) 8.48519 0.325632
\(680\) −0.709257 −0.0271987
\(681\) 11.3236 0.433923
\(682\) 2.72141 0.104208
\(683\) −24.9338 −0.954063 −0.477032 0.878886i \(-0.658287\pi\)
−0.477032 + 0.878886i \(0.658287\pi\)
\(684\) 5.51071 0.210707
\(685\) −11.4241 −0.436492
\(686\) −1.00000 −0.0381802
\(687\) 8.01216 0.305683
\(688\) 8.50523 0.324259
\(689\) 40.6076 1.54702
\(690\) 0.132735 0.00505312
\(691\) −21.5010 −0.817935 −0.408968 0.912549i \(-0.634111\pi\)
−0.408968 + 0.912549i \(0.634111\pi\)
\(692\) −10.7610 −0.409073
\(693\) −5.92103 −0.224921
\(694\) −28.9006 −1.09705
\(695\) 42.2211 1.60154
\(696\) −2.65101 −0.100486
\(697\) −1.95164 −0.0739238
\(698\) 12.0905 0.457634
\(699\) −4.41697 −0.167065
\(700\) 3.80035 0.143640
\(701\) −18.6725 −0.705251 −0.352625 0.935765i \(-0.614711\pi\)
−0.352625 + 0.935765i \(0.614711\pi\)
\(702\) 8.98846 0.339248
\(703\) −5.20868 −0.196449
\(704\) 2.13961 0.0806397
\(705\) 13.4485 0.506498
\(706\) 27.7700 1.04514
\(707\) 2.08371 0.0783659
\(708\) −5.40678 −0.203199
\(709\) −1.31186 −0.0492679 −0.0246339 0.999697i \(-0.507842\pi\)
−0.0246339 + 0.999697i \(0.507842\pi\)
\(710\) −2.02136 −0.0758602
\(711\) −7.35464 −0.275820
\(712\) 8.66555 0.324755
\(713\) 0.117986 0.00441860
\(714\) −0.115323 −0.00431587
\(715\) 20.5084 0.766969
\(716\) 2.13053 0.0796216
\(717\) 4.55024 0.169932
\(718\) 32.5443 1.21454
\(719\) 12.0334 0.448770 0.224385 0.974501i \(-0.427963\pi\)
0.224385 + 0.974501i \(0.427963\pi\)
\(720\) −8.20941 −0.305947
\(721\) 4.69630 0.174899
\(722\) 15.0346 0.559528
\(723\) −9.49557 −0.353144
\(724\) −0.133121 −0.00494738
\(725\) 20.8868 0.775715
\(726\) 3.09769 0.114966
\(727\) 32.5309 1.20650 0.603251 0.797551i \(-0.293872\pi\)
0.603251 + 0.797551i \(0.293872\pi\)
\(728\) −3.23107 −0.119751
\(729\) −15.2356 −0.564280
\(730\) 2.30411 0.0852790
\(731\) 2.03348 0.0752109
\(732\) −6.34302 −0.234445
\(733\) −38.9318 −1.43798 −0.718989 0.695022i \(-0.755395\pi\)
−0.718989 + 0.695022i \(0.755395\pi\)
\(734\) −1.36993 −0.0505650
\(735\) 1.43092 0.0527801
\(736\) 0.0927620 0.00341925
\(737\) 19.8804 0.732305
\(738\) −22.5896 −0.831536
\(739\) 11.4812 0.422344 0.211172 0.977449i \(-0.432272\pi\)
0.211172 + 0.977449i \(0.432272\pi\)
\(740\) 7.75946 0.285243
\(741\) −3.10353 −0.114011
\(742\) −12.5678 −0.461380
\(743\) 33.0620 1.21293 0.606463 0.795112i \(-0.292588\pi\)
0.606463 + 0.795112i \(0.292588\pi\)
\(744\) 0.613512 0.0224924
\(745\) 9.80019 0.359051
\(746\) −27.5413 −1.00836
\(747\) −1.27924 −0.0468049
\(748\) 0.511550 0.0187041
\(749\) −4.74890 −0.173521
\(750\) 1.71660 0.0626813
\(751\) −25.2421 −0.921098 −0.460549 0.887634i \(-0.652347\pi\)
−0.460549 + 0.887634i \(0.652347\pi\)
\(752\) 9.39850 0.342728
\(753\) 14.0931 0.513581
\(754\) −17.7580 −0.646708
\(755\) −19.4689 −0.708548
\(756\) −2.78189 −0.101176
\(757\) −31.7867 −1.15531 −0.577653 0.816282i \(-0.696031\pi\)
−0.577653 + 0.816282i \(0.696031\pi\)
\(758\) 2.55245 0.0927091
\(759\) −0.0957346 −0.00347495
\(760\) 5.90739 0.214284
\(761\) 15.1575 0.549460 0.274730 0.961521i \(-0.411412\pi\)
0.274730 + 0.961521i \(0.411412\pi\)
\(762\) 0.344190 0.0124687
\(763\) 13.9853 0.506302
\(764\) −3.11563 −0.112720
\(765\) −1.96275 −0.0709634
\(766\) 33.6175 1.21465
\(767\) −36.2176 −1.30774
\(768\) 0.482352 0.0174054
\(769\) −47.5970 −1.71639 −0.858195 0.513324i \(-0.828414\pi\)
−0.858195 + 0.513324i \(0.828414\pi\)
\(770\) −6.34724 −0.228739
\(771\) −9.90693 −0.356789
\(772\) 16.5168 0.594453
\(773\) −11.0673 −0.398064 −0.199032 0.979993i \(-0.563780\pi\)
−0.199032 + 0.979993i \(0.563780\pi\)
\(774\) 23.5368 0.846014
\(775\) −4.83373 −0.173633
\(776\) −8.48519 −0.304601
\(777\) 1.26167 0.0452621
\(778\) −8.37623 −0.300302
\(779\) 16.2552 0.582404
\(780\) 4.62338 0.165544
\(781\) 1.45790 0.0521678
\(782\) 0.0221780 0.000793085 0
\(783\) −15.2893 −0.546394
\(784\) 1.00000 0.0357143
\(785\) −27.8134 −0.992702
\(786\) −6.21653 −0.221736
\(787\) 21.1935 0.755466 0.377733 0.925915i \(-0.376704\pi\)
0.377733 + 0.925915i \(0.376704\pi\)
\(788\) 2.22701 0.0793338
\(789\) −8.04958 −0.286573
\(790\) −7.88405 −0.280502
\(791\) 18.6168 0.661938
\(792\) 5.92103 0.210395
\(793\) −42.4891 −1.50883
\(794\) −7.71781 −0.273895
\(795\) 17.9835 0.637810
\(796\) 15.1913 0.538442
\(797\) −2.94749 −0.104406 −0.0522028 0.998637i \(-0.516624\pi\)
−0.0522028 + 0.998637i \(0.516624\pi\)
\(798\) 0.960528 0.0340023
\(799\) 2.24705 0.0794948
\(800\) −3.80035 −0.134363
\(801\) 23.9805 0.847309
\(802\) −10.3982 −0.367173
\(803\) −1.66184 −0.0586450
\(804\) 4.48183 0.158062
\(805\) −0.275182 −0.00969889
\(806\) 4.10965 0.144756
\(807\) −10.6291 −0.374162
\(808\) −2.08371 −0.0733046
\(809\) 51.4707 1.80961 0.904807 0.425821i \(-0.140015\pi\)
0.904807 + 0.425821i \(0.140015\pi\)
\(810\) −20.6476 −0.725482
\(811\) 6.07227 0.213226 0.106613 0.994301i \(-0.465999\pi\)
0.106613 + 0.994301i \(0.465999\pi\)
\(812\) 5.49601 0.192872
\(813\) −5.77215 −0.202438
\(814\) −5.59650 −0.196157
\(815\) 42.3379 1.48303
\(816\) 0.115323 0.00403713
\(817\) −16.9368 −0.592544
\(818\) −39.0810 −1.36643
\(819\) −8.94145 −0.312439
\(820\) −24.2157 −0.845649
\(821\) −25.4579 −0.888487 −0.444243 0.895906i \(-0.646527\pi\)
−0.444243 + 0.895906i \(0.646527\pi\)
\(822\) 1.85753 0.0647888
\(823\) −5.89889 −0.205623 −0.102811 0.994701i \(-0.532784\pi\)
−0.102811 + 0.994701i \(0.532784\pi\)
\(824\) −4.69630 −0.163603
\(825\) 3.92214 0.136551
\(826\) 11.2092 0.390018
\(827\) 48.7745 1.69606 0.848028 0.529952i \(-0.177790\pi\)
0.848028 + 0.529952i \(0.177790\pi\)
\(828\) 0.256704 0.00892107
\(829\) −3.12935 −0.108687 −0.0543434 0.998522i \(-0.517307\pi\)
−0.0543434 + 0.998522i \(0.517307\pi\)
\(830\) −1.37132 −0.0475993
\(831\) 2.35616 0.0817344
\(832\) 3.23107 0.112017
\(833\) 0.239086 0.00828382
\(834\) −6.86505 −0.237717
\(835\) 40.1465 1.38933
\(836\) −4.26070 −0.147359
\(837\) 3.53833 0.122303
\(838\) −25.0634 −0.865800
\(839\) −7.40192 −0.255543 −0.127771 0.991804i \(-0.540782\pi\)
−0.127771 + 0.991804i \(0.540782\pi\)
\(840\) −1.43092 −0.0493713
\(841\) 1.20616 0.0415918
\(842\) 15.6053 0.537796
\(843\) 7.91317 0.272544
\(844\) −26.0216 −0.895699
\(845\) −7.59496 −0.261275
\(846\) 26.0088 0.894201
\(847\) −6.42206 −0.220665
\(848\) 12.5678 0.431582
\(849\) −14.5953 −0.500910
\(850\) −0.908609 −0.0311650
\(851\) −0.242634 −0.00831738
\(852\) 0.328668 0.0112600
\(853\) 16.3931 0.561288 0.280644 0.959812i \(-0.409452\pi\)
0.280644 + 0.959812i \(0.409452\pi\)
\(854\) 13.1502 0.449990
\(855\) 16.3477 0.559081
\(856\) 4.74890 0.162314
\(857\) 5.74407 0.196214 0.0981068 0.995176i \(-0.468721\pi\)
0.0981068 + 0.995176i \(0.468721\pi\)
\(858\) −3.33461 −0.113842
\(859\) −24.8230 −0.846951 −0.423476 0.905907i \(-0.639190\pi\)
−0.423476 + 0.905907i \(0.639190\pi\)
\(860\) 25.2311 0.860373
\(861\) −3.93742 −0.134187
\(862\) 1.00000 0.0340601
\(863\) −19.1481 −0.651809 −0.325905 0.945403i \(-0.605669\pi\)
−0.325905 + 0.945403i \(0.605669\pi\)
\(864\) 2.78189 0.0946417
\(865\) −31.9230 −1.08541
\(866\) 18.6033 0.632165
\(867\) −8.17241 −0.277550
\(868\) −1.27192 −0.0431717
\(869\) 5.68636 0.192897
\(870\) −7.86433 −0.266626
\(871\) 30.0218 1.01725
\(872\) −13.9853 −0.473602
\(873\) −23.4814 −0.794724
\(874\) −0.184721 −0.00624827
\(875\) −3.55881 −0.120310
\(876\) −0.374643 −0.0126580
\(877\) −13.6165 −0.459796 −0.229898 0.973215i \(-0.573839\pi\)
−0.229898 + 0.973215i \(0.573839\pi\)
\(878\) −21.8233 −0.736501
\(879\) 5.48199 0.184903
\(880\) 6.34724 0.213965
\(881\) 40.1314 1.35206 0.676031 0.736873i \(-0.263699\pi\)
0.676031 + 0.736873i \(0.263699\pi\)
\(882\) 2.76734 0.0931811
\(883\) −7.47828 −0.251664 −0.125832 0.992052i \(-0.540160\pi\)
−0.125832 + 0.992052i \(0.540160\pi\)
\(884\) 0.772501 0.0259820
\(885\) −16.0394 −0.539159
\(886\) −17.6938 −0.594434
\(887\) −31.9660 −1.07331 −0.536657 0.843800i \(-0.680313\pi\)
−0.536657 + 0.843800i \(0.680313\pi\)
\(888\) −1.26167 −0.0423389
\(889\) −0.713567 −0.0239323
\(890\) 25.7067 0.861690
\(891\) 14.8920 0.498902
\(892\) −23.9130 −0.800665
\(893\) −18.7156 −0.626295
\(894\) −1.59349 −0.0532942
\(895\) 6.32030 0.211264
\(896\) −1.00000 −0.0334077
\(897\) −0.144571 −0.00482707
\(898\) 16.6261 0.554822
\(899\) −6.99048 −0.233145
\(900\) −10.5168 −0.350562
\(901\) 3.00479 0.100104
\(902\) 17.4656 0.581539
\(903\) 4.10251 0.136523
\(904\) −18.6168 −0.619186
\(905\) −0.394907 −0.0131272
\(906\) 3.16560 0.105170
\(907\) 30.3328 1.00718 0.503591 0.863942i \(-0.332012\pi\)
0.503591 + 0.863942i \(0.332012\pi\)
\(908\) 23.4759 0.779075
\(909\) −5.76632 −0.191257
\(910\) −9.58508 −0.317742
\(911\) 21.3856 0.708537 0.354268 0.935144i \(-0.384730\pi\)
0.354268 + 0.935144i \(0.384730\pi\)
\(912\) −0.960528 −0.0318063
\(913\) 0.989066 0.0327333
\(914\) −1.44455 −0.0477813
\(915\) −18.8168 −0.622064
\(916\) 16.6106 0.548830
\(917\) 12.8879 0.425597
\(918\) 0.665109 0.0219519
\(919\) −27.2282 −0.898176 −0.449088 0.893487i \(-0.648251\pi\)
−0.449088 + 0.893487i \(0.648251\pi\)
\(920\) 0.275182 0.00907248
\(921\) −8.40650 −0.277004
\(922\) 3.80273 0.125236
\(923\) 2.20160 0.0724666
\(924\) 1.03205 0.0339518
\(925\) 9.94043 0.326839
\(926\) 11.8740 0.390204
\(927\) −12.9963 −0.426853
\(928\) −5.49601 −0.180415
\(929\) −59.9752 −1.96772 −0.983861 0.178934i \(-0.942735\pi\)
−0.983861 + 0.178934i \(0.942735\pi\)
\(930\) 1.82001 0.0596804
\(931\) −1.99134 −0.0652636
\(932\) −9.15714 −0.299952
\(933\) −6.16868 −0.201953
\(934\) 23.2619 0.761154
\(935\) 1.51753 0.0496287
\(936\) 8.94145 0.292260
\(937\) −40.9136 −1.33659 −0.668295 0.743896i \(-0.732976\pi\)
−0.668295 + 0.743896i \(0.732976\pi\)
\(938\) −9.29161 −0.303382
\(939\) 10.7332 0.350265
\(940\) 27.8810 0.909378
\(941\) −45.0824 −1.46965 −0.734823 0.678259i \(-0.762735\pi\)
−0.734823 + 0.678259i \(0.762735\pi\)
\(942\) 4.52239 0.147347
\(943\) 0.757212 0.0246582
\(944\) −11.2092 −0.364828
\(945\) −8.25257 −0.268456
\(946\) −18.1979 −0.591665
\(947\) 16.1246 0.523977 0.261989 0.965071i \(-0.415622\pi\)
0.261989 + 0.965071i \(0.415622\pi\)
\(948\) 1.28193 0.0416351
\(949\) −2.50957 −0.0814641
\(950\) 7.56780 0.245532
\(951\) 3.18768 0.103368
\(952\) −0.239086 −0.00774881
\(953\) −12.4513 −0.403336 −0.201668 0.979454i \(-0.564636\pi\)
−0.201668 + 0.979454i \(0.564636\pi\)
\(954\) 34.7795 1.12603
\(955\) −9.24264 −0.299085
\(956\) 9.43344 0.305099
\(957\) 5.67214 0.183354
\(958\) −1.74403 −0.0563472
\(959\) −3.85098 −0.124355
\(960\) 1.43092 0.0461826
\(961\) −29.3822 −0.947814
\(962\) −8.45138 −0.272483
\(963\) 13.1418 0.423489
\(964\) −19.6860 −0.634042
\(965\) 48.9977 1.57729
\(966\) 0.0447439 0.00143961
\(967\) −11.3303 −0.364358 −0.182179 0.983265i \(-0.558315\pi\)
−0.182179 + 0.983265i \(0.558315\pi\)
\(968\) 6.42206 0.206413
\(969\) −0.229648 −0.00737737
\(970\) −25.1716 −0.808213
\(971\) 28.5218 0.915308 0.457654 0.889130i \(-0.348690\pi\)
0.457654 + 0.889130i \(0.348690\pi\)
\(972\) 11.7029 0.375371
\(973\) 14.2324 0.456271
\(974\) −17.9150 −0.574035
\(975\) 5.92289 0.189684
\(976\) −13.1502 −0.420927
\(977\) 18.0110 0.576222 0.288111 0.957597i \(-0.406973\pi\)
0.288111 + 0.957597i \(0.406973\pi\)
\(978\) −6.88405 −0.220128
\(979\) −18.5409 −0.592570
\(980\) 2.96654 0.0947626
\(981\) −38.7020 −1.23566
\(982\) −15.3446 −0.489665
\(983\) 22.1089 0.705164 0.352582 0.935781i \(-0.385304\pi\)
0.352582 + 0.935781i \(0.385304\pi\)
\(984\) 3.93742 0.125520
\(985\) 6.60650 0.210501
\(986\) −1.31402 −0.0418468
\(987\) 4.53339 0.144299
\(988\) −6.43416 −0.204698
\(989\) −0.788962 −0.0250875
\(990\) 17.5650 0.558251
\(991\) −53.2704 −1.69219 −0.846094 0.533033i \(-0.821052\pi\)
−0.846094 + 0.533033i \(0.821052\pi\)
\(992\) 1.27192 0.0403834
\(993\) 5.82879 0.184971
\(994\) −0.681386 −0.0216122
\(995\) 45.0656 1.42868
\(996\) 0.222974 0.00706520
\(997\) −43.5453 −1.37909 −0.689547 0.724241i \(-0.742190\pi\)
−0.689547 + 0.724241i \(0.742190\pi\)
\(998\) −25.0219 −0.792056
\(999\) −7.27647 −0.230217
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 6034.2.a.p.1.16 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.p.1.16 27 1.1 even 1 trivial