Properties

Label 4011.2.a.m.1.13
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $29$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.223362 q^{2} +1.00000 q^{3} -1.95011 q^{4} +1.64565 q^{5} -0.223362 q^{6} -1.00000 q^{7} +0.882304 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.223362 q^{2} +1.00000 q^{3} -1.95011 q^{4} +1.64565 q^{5} -0.223362 q^{6} -1.00000 q^{7} +0.882304 q^{8} +1.00000 q^{9} -0.367576 q^{10} +4.86719 q^{11} -1.95011 q^{12} +4.77509 q^{13} +0.223362 q^{14} +1.64565 q^{15} +3.70315 q^{16} +2.25251 q^{17} -0.223362 q^{18} -1.51705 q^{19} -3.20920 q^{20} -1.00000 q^{21} -1.08714 q^{22} -1.56513 q^{23} +0.882304 q^{24} -2.29184 q^{25} -1.06657 q^{26} +1.00000 q^{27} +1.95011 q^{28} +5.30592 q^{29} -0.367576 q^{30} -5.90322 q^{31} -2.59175 q^{32} +4.86719 q^{33} -0.503126 q^{34} -1.64565 q^{35} -1.95011 q^{36} +9.20145 q^{37} +0.338851 q^{38} +4.77509 q^{39} +1.45196 q^{40} -6.69771 q^{41} +0.223362 q^{42} +9.36637 q^{43} -9.49155 q^{44} +1.64565 q^{45} +0.349590 q^{46} -2.53680 q^{47} +3.70315 q^{48} +1.00000 q^{49} +0.511909 q^{50} +2.25251 q^{51} -9.31195 q^{52} +6.61461 q^{53} -0.223362 q^{54} +8.00969 q^{55} -0.882304 q^{56} -1.51705 q^{57} -1.18514 q^{58} -6.16906 q^{59} -3.20920 q^{60} +7.37451 q^{61} +1.31856 q^{62} -1.00000 q^{63} -6.82739 q^{64} +7.85812 q^{65} -1.08714 q^{66} -0.551822 q^{67} -4.39265 q^{68} -1.56513 q^{69} +0.367576 q^{70} -10.5578 q^{71} +0.882304 q^{72} +3.39844 q^{73} -2.05525 q^{74} -2.29184 q^{75} +2.95841 q^{76} -4.86719 q^{77} -1.06657 q^{78} -11.4131 q^{79} +6.09408 q^{80} +1.00000 q^{81} +1.49601 q^{82} -8.33903 q^{83} +1.95011 q^{84} +3.70685 q^{85} -2.09209 q^{86} +5.30592 q^{87} +4.29434 q^{88} -11.6275 q^{89} -0.367576 q^{90} -4.77509 q^{91} +3.05217 q^{92} -5.90322 q^{93} +0.566624 q^{94} -2.49653 q^{95} -2.59175 q^{96} +5.63135 q^{97} -0.223362 q^{98} +4.86719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.223362 −0.157941 −0.0789704 0.996877i \(-0.525163\pi\)
−0.0789704 + 0.996877i \(0.525163\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.95011 −0.975055
\(5\) 1.64565 0.735957 0.367979 0.929834i \(-0.380050\pi\)
0.367979 + 0.929834i \(0.380050\pi\)
\(6\) −0.223362 −0.0911871
\(7\) −1.00000 −0.377964
\(8\) 0.882304 0.311942
\(9\) 1.00000 0.333333
\(10\) −0.367576 −0.116238
\(11\) 4.86719 1.46751 0.733756 0.679413i \(-0.237765\pi\)
0.733756 + 0.679413i \(0.237765\pi\)
\(12\) −1.95011 −0.562948
\(13\) 4.77509 1.32437 0.662186 0.749340i \(-0.269629\pi\)
0.662186 + 0.749340i \(0.269629\pi\)
\(14\) 0.223362 0.0596960
\(15\) 1.64565 0.424905
\(16\) 3.70315 0.925786
\(17\) 2.25251 0.546315 0.273157 0.961969i \(-0.411932\pi\)
0.273157 + 0.961969i \(0.411932\pi\)
\(18\) −0.223362 −0.0526469
\(19\) −1.51705 −0.348035 −0.174018 0.984743i \(-0.555675\pi\)
−0.174018 + 0.984743i \(0.555675\pi\)
\(20\) −3.20920 −0.717598
\(21\) −1.00000 −0.218218
\(22\) −1.08714 −0.231780
\(23\) −1.56513 −0.326352 −0.163176 0.986597i \(-0.552174\pi\)
−0.163176 + 0.986597i \(0.552174\pi\)
\(24\) 0.882304 0.180100
\(25\) −2.29184 −0.458367
\(26\) −1.06657 −0.209172
\(27\) 1.00000 0.192450
\(28\) 1.95011 0.368536
\(29\) 5.30592 0.985285 0.492642 0.870232i \(-0.336031\pi\)
0.492642 + 0.870232i \(0.336031\pi\)
\(30\) −0.367576 −0.0671098
\(31\) −5.90322 −1.06025 −0.530125 0.847919i \(-0.677855\pi\)
−0.530125 + 0.847919i \(0.677855\pi\)
\(32\) −2.59175 −0.458161
\(33\) 4.86719 0.847269
\(34\) −0.503126 −0.0862853
\(35\) −1.64565 −0.278166
\(36\) −1.95011 −0.325018
\(37\) 9.20145 1.51271 0.756354 0.654162i \(-0.226979\pi\)
0.756354 + 0.654162i \(0.226979\pi\)
\(38\) 0.338851 0.0549689
\(39\) 4.77509 0.764626
\(40\) 1.45196 0.229576
\(41\) −6.69771 −1.04601 −0.523004 0.852330i \(-0.675189\pi\)
−0.523004 + 0.852330i \(0.675189\pi\)
\(42\) 0.223362 0.0344655
\(43\) 9.36637 1.42836 0.714179 0.699963i \(-0.246800\pi\)
0.714179 + 0.699963i \(0.246800\pi\)
\(44\) −9.49155 −1.43091
\(45\) 1.64565 0.245319
\(46\) 0.349590 0.0515442
\(47\) −2.53680 −0.370030 −0.185015 0.982736i \(-0.559233\pi\)
−0.185015 + 0.982736i \(0.559233\pi\)
\(48\) 3.70315 0.534503
\(49\) 1.00000 0.142857
\(50\) 0.511909 0.0723949
\(51\) 2.25251 0.315415
\(52\) −9.31195 −1.29133
\(53\) 6.61461 0.908587 0.454294 0.890852i \(-0.349892\pi\)
0.454294 + 0.890852i \(0.349892\pi\)
\(54\) −0.223362 −0.0303957
\(55\) 8.00969 1.08003
\(56\) −0.882304 −0.117903
\(57\) −1.51705 −0.200938
\(58\) −1.18514 −0.155617
\(59\) −6.16906 −0.803143 −0.401571 0.915828i \(-0.631536\pi\)
−0.401571 + 0.915828i \(0.631536\pi\)
\(60\) −3.20920 −0.414306
\(61\) 7.37451 0.944209 0.472105 0.881543i \(-0.343494\pi\)
0.472105 + 0.881543i \(0.343494\pi\)
\(62\) 1.31856 0.167457
\(63\) −1.00000 −0.125988
\(64\) −6.82739 −0.853424
\(65\) 7.85812 0.974680
\(66\) −1.08714 −0.133818
\(67\) −0.551822 −0.0674158 −0.0337079 0.999432i \(-0.510732\pi\)
−0.0337079 + 0.999432i \(0.510732\pi\)
\(68\) −4.39265 −0.532687
\(69\) −1.56513 −0.188419
\(70\) 0.367576 0.0439337
\(71\) −10.5578 −1.25298 −0.626492 0.779428i \(-0.715510\pi\)
−0.626492 + 0.779428i \(0.715510\pi\)
\(72\) 0.882304 0.103981
\(73\) 3.39844 0.397758 0.198879 0.980024i \(-0.436270\pi\)
0.198879 + 0.980024i \(0.436270\pi\)
\(74\) −2.05525 −0.238918
\(75\) −2.29184 −0.264638
\(76\) 2.95841 0.339353
\(77\) −4.86719 −0.554668
\(78\) −1.06657 −0.120766
\(79\) −11.4131 −1.28408 −0.642038 0.766673i \(-0.721911\pi\)
−0.642038 + 0.766673i \(0.721911\pi\)
\(80\) 6.09408 0.681339
\(81\) 1.00000 0.111111
\(82\) 1.49601 0.165207
\(83\) −8.33903 −0.915327 −0.457664 0.889125i \(-0.651314\pi\)
−0.457664 + 0.889125i \(0.651314\pi\)
\(84\) 1.95011 0.212774
\(85\) 3.70685 0.402064
\(86\) −2.09209 −0.225596
\(87\) 5.30592 0.568854
\(88\) 4.29434 0.457778
\(89\) −11.6275 −1.23251 −0.616254 0.787547i \(-0.711351\pi\)
−0.616254 + 0.787547i \(0.711351\pi\)
\(90\) −0.367576 −0.0387459
\(91\) −4.77509 −0.500565
\(92\) 3.05217 0.318211
\(93\) −5.90322 −0.612136
\(94\) 0.566624 0.0584428
\(95\) −2.49653 −0.256139
\(96\) −2.59175 −0.264519
\(97\) 5.63135 0.571777 0.285889 0.958263i \(-0.407711\pi\)
0.285889 + 0.958263i \(0.407711\pi\)
\(98\) −0.223362 −0.0225630
\(99\) 4.86719 0.489171
\(100\) 4.46933 0.446933
\(101\) 9.56571 0.951824 0.475912 0.879493i \(-0.342118\pi\)
0.475912 + 0.879493i \(0.342118\pi\)
\(102\) −0.503126 −0.0498168
\(103\) −9.20767 −0.907259 −0.453629 0.891190i \(-0.649871\pi\)
−0.453629 + 0.891190i \(0.649871\pi\)
\(104\) 4.21308 0.413127
\(105\) −1.64565 −0.160599
\(106\) −1.47745 −0.143503
\(107\) 18.5977 1.79791 0.898955 0.438040i \(-0.144327\pi\)
0.898955 + 0.438040i \(0.144327\pi\)
\(108\) −1.95011 −0.187649
\(109\) −10.0096 −0.958750 −0.479375 0.877610i \(-0.659137\pi\)
−0.479375 + 0.877610i \(0.659137\pi\)
\(110\) −1.78906 −0.170580
\(111\) 9.20145 0.873363
\(112\) −3.70315 −0.349914
\(113\) 12.1724 1.14509 0.572543 0.819875i \(-0.305957\pi\)
0.572543 + 0.819875i \(0.305957\pi\)
\(114\) 0.338851 0.0317363
\(115\) −2.57565 −0.240181
\(116\) −10.3471 −0.960706
\(117\) 4.77509 0.441457
\(118\) 1.37793 0.126849
\(119\) −2.25251 −0.206487
\(120\) 1.45196 0.132546
\(121\) 12.6895 1.15359
\(122\) −1.64718 −0.149129
\(123\) −6.69771 −0.603913
\(124\) 11.5119 1.03380
\(125\) −11.9998 −1.07330
\(126\) 0.223362 0.0198987
\(127\) 21.4700 1.90515 0.952577 0.304298i \(-0.0984220\pi\)
0.952577 + 0.304298i \(0.0984220\pi\)
\(128\) 6.70848 0.592951
\(129\) 9.36637 0.824663
\(130\) −1.75521 −0.153942
\(131\) −0.303802 −0.0265433 −0.0132717 0.999912i \(-0.504225\pi\)
−0.0132717 + 0.999912i \(0.504225\pi\)
\(132\) −9.49155 −0.826134
\(133\) 1.51705 0.131545
\(134\) 0.123256 0.0106477
\(135\) 1.64565 0.141635
\(136\) 1.98740 0.170418
\(137\) −0.770104 −0.0657944 −0.0328972 0.999459i \(-0.510473\pi\)
−0.0328972 + 0.999459i \(0.510473\pi\)
\(138\) 0.349590 0.0297591
\(139\) −7.08197 −0.600685 −0.300343 0.953831i \(-0.597101\pi\)
−0.300343 + 0.953831i \(0.597101\pi\)
\(140\) 3.20920 0.271227
\(141\) −2.53680 −0.213637
\(142\) 2.35822 0.197897
\(143\) 23.2413 1.94353
\(144\) 3.70315 0.308595
\(145\) 8.73169 0.725127
\(146\) −0.759083 −0.0628222
\(147\) 1.00000 0.0824786
\(148\) −17.9438 −1.47497
\(149\) 11.3047 0.926120 0.463060 0.886327i \(-0.346751\pi\)
0.463060 + 0.886327i \(0.346751\pi\)
\(150\) 0.511909 0.0417972
\(151\) 8.18096 0.665757 0.332879 0.942970i \(-0.391980\pi\)
0.332879 + 0.942970i \(0.391980\pi\)
\(152\) −1.33850 −0.108567
\(153\) 2.25251 0.182105
\(154\) 1.08714 0.0876046
\(155\) −9.71464 −0.780298
\(156\) −9.31195 −0.745552
\(157\) −8.21090 −0.655301 −0.327651 0.944799i \(-0.606257\pi\)
−0.327651 + 0.944799i \(0.606257\pi\)
\(158\) 2.54926 0.202808
\(159\) 6.61461 0.524573
\(160\) −4.26511 −0.337187
\(161\) 1.56513 0.123349
\(162\) −0.223362 −0.0175490
\(163\) 13.7864 1.07984 0.539918 0.841718i \(-0.318455\pi\)
0.539918 + 0.841718i \(0.318455\pi\)
\(164\) 13.0613 1.01991
\(165\) 8.00969 0.623553
\(166\) 1.86262 0.144567
\(167\) 9.64070 0.746020 0.373010 0.927827i \(-0.378326\pi\)
0.373010 + 0.927827i \(0.378326\pi\)
\(168\) −0.882304 −0.0680712
\(169\) 9.80148 0.753960
\(170\) −0.827968 −0.0635023
\(171\) −1.51705 −0.116012
\(172\) −18.2655 −1.39273
\(173\) 6.30279 0.479192 0.239596 0.970873i \(-0.422985\pi\)
0.239596 + 0.970873i \(0.422985\pi\)
\(174\) −1.18514 −0.0898453
\(175\) 2.29184 0.173247
\(176\) 18.0239 1.35860
\(177\) −6.16906 −0.463695
\(178\) 2.59713 0.194663
\(179\) −7.80163 −0.583121 −0.291561 0.956552i \(-0.594175\pi\)
−0.291561 + 0.956552i \(0.594175\pi\)
\(180\) −3.20920 −0.239199
\(181\) 25.2714 1.87841 0.939204 0.343360i \(-0.111565\pi\)
0.939204 + 0.343360i \(0.111565\pi\)
\(182\) 1.06657 0.0790597
\(183\) 7.37451 0.545139
\(184\) −1.38092 −0.101803
\(185\) 15.1424 1.11329
\(186\) 1.31856 0.0966812
\(187\) 10.9634 0.801724
\(188\) 4.94704 0.360800
\(189\) −1.00000 −0.0727393
\(190\) 0.557631 0.0404548
\(191\) −1.00000 −0.0723575
\(192\) −6.82739 −0.492725
\(193\) 23.5978 1.69861 0.849303 0.527906i \(-0.177023\pi\)
0.849303 + 0.527906i \(0.177023\pi\)
\(194\) −1.25783 −0.0903069
\(195\) 7.85812 0.562732
\(196\) −1.95011 −0.139294
\(197\) −14.6505 −1.04381 −0.521904 0.853004i \(-0.674778\pi\)
−0.521904 + 0.853004i \(0.674778\pi\)
\(198\) −1.08714 −0.0772600
\(199\) −21.1058 −1.49615 −0.748076 0.663614i \(-0.769022\pi\)
−0.748076 + 0.663614i \(0.769022\pi\)
\(200\) −2.02210 −0.142984
\(201\) −0.551822 −0.0389225
\(202\) −2.13662 −0.150332
\(203\) −5.30592 −0.372403
\(204\) −4.39265 −0.307547
\(205\) −11.0221 −0.769816
\(206\) 2.05664 0.143293
\(207\) −1.56513 −0.108784
\(208\) 17.6829 1.22609
\(209\) −7.38377 −0.510746
\(210\) 0.367576 0.0253651
\(211\) −5.58343 −0.384379 −0.192190 0.981358i \(-0.561559\pi\)
−0.192190 + 0.981358i \(0.561559\pi\)
\(212\) −12.8992 −0.885922
\(213\) −10.5578 −0.723411
\(214\) −4.15403 −0.283963
\(215\) 15.4138 1.05121
\(216\) 0.882304 0.0600332
\(217\) 5.90322 0.400737
\(218\) 2.23577 0.151426
\(219\) 3.39844 0.229646
\(220\) −15.6198 −1.05308
\(221\) 10.7559 0.723523
\(222\) −2.05525 −0.137940
\(223\) 23.8421 1.59658 0.798292 0.602271i \(-0.205737\pi\)
0.798292 + 0.602271i \(0.205737\pi\)
\(224\) 2.59175 0.173169
\(225\) −2.29184 −0.152789
\(226\) −2.71886 −0.180856
\(227\) 13.9517 0.926005 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(228\) 2.95841 0.195926
\(229\) −0.970158 −0.0641099 −0.0320549 0.999486i \(-0.510205\pi\)
−0.0320549 + 0.999486i \(0.510205\pi\)
\(230\) 0.575303 0.0379343
\(231\) −4.86719 −0.320238
\(232\) 4.68143 0.307351
\(233\) 12.6698 0.830027 0.415013 0.909815i \(-0.363777\pi\)
0.415013 + 0.909815i \(0.363777\pi\)
\(234\) −1.06657 −0.0697241
\(235\) −4.17468 −0.272326
\(236\) 12.0303 0.783108
\(237\) −11.4131 −0.741362
\(238\) 0.503126 0.0326128
\(239\) −6.15618 −0.398210 −0.199105 0.979978i \(-0.563804\pi\)
−0.199105 + 0.979978i \(0.563804\pi\)
\(240\) 6.09408 0.393371
\(241\) 10.2118 0.657798 0.328899 0.944365i \(-0.393322\pi\)
0.328899 + 0.944365i \(0.393322\pi\)
\(242\) −2.83436 −0.182199
\(243\) 1.00000 0.0641500
\(244\) −14.3811 −0.920656
\(245\) 1.64565 0.105137
\(246\) 1.49601 0.0953824
\(247\) −7.24405 −0.460928
\(248\) −5.20844 −0.330736
\(249\) −8.33903 −0.528464
\(250\) 2.68030 0.169517
\(251\) 7.90110 0.498713 0.249356 0.968412i \(-0.419781\pi\)
0.249356 + 0.968412i \(0.419781\pi\)
\(252\) 1.95011 0.122845
\(253\) −7.61777 −0.478925
\(254\) −4.79558 −0.300901
\(255\) 3.70685 0.232132
\(256\) 12.1564 0.759773
\(257\) −28.0298 −1.74845 −0.874227 0.485518i \(-0.838631\pi\)
−0.874227 + 0.485518i \(0.838631\pi\)
\(258\) −2.09209 −0.130248
\(259\) −9.20145 −0.571750
\(260\) −15.3242 −0.950367
\(261\) 5.30592 0.328428
\(262\) 0.0678578 0.00419227
\(263\) −15.3246 −0.944954 −0.472477 0.881343i \(-0.656640\pi\)
−0.472477 + 0.881343i \(0.656640\pi\)
\(264\) 4.29434 0.264298
\(265\) 10.8853 0.668681
\(266\) −0.338851 −0.0207763
\(267\) −11.6275 −0.711589
\(268\) 1.07611 0.0657341
\(269\) 2.50287 0.152603 0.0763014 0.997085i \(-0.475689\pi\)
0.0763014 + 0.997085i \(0.475689\pi\)
\(270\) −0.367576 −0.0223699
\(271\) −6.89447 −0.418809 −0.209405 0.977829i \(-0.567153\pi\)
−0.209405 + 0.977829i \(0.567153\pi\)
\(272\) 8.34138 0.505771
\(273\) −4.77509 −0.289002
\(274\) 0.172012 0.0103916
\(275\) −11.1548 −0.672660
\(276\) 3.05217 0.183719
\(277\) −24.9943 −1.50176 −0.750882 0.660436i \(-0.770371\pi\)
−0.750882 + 0.660436i \(0.770371\pi\)
\(278\) 1.58184 0.0948726
\(279\) −5.90322 −0.353417
\(280\) −1.45196 −0.0867714
\(281\) 21.3653 1.27455 0.637273 0.770638i \(-0.280062\pi\)
0.637273 + 0.770638i \(0.280062\pi\)
\(282\) 0.566624 0.0337420
\(283\) −9.44217 −0.561279 −0.280639 0.959813i \(-0.590547\pi\)
−0.280639 + 0.959813i \(0.590547\pi\)
\(284\) 20.5889 1.22173
\(285\) −2.49653 −0.147882
\(286\) −5.19121 −0.306963
\(287\) 6.69771 0.395354
\(288\) −2.59175 −0.152720
\(289\) −11.9262 −0.701540
\(290\) −1.95033 −0.114527
\(291\) 5.63135 0.330116
\(292\) −6.62734 −0.387836
\(293\) −3.95148 −0.230848 −0.115424 0.993316i \(-0.536823\pi\)
−0.115424 + 0.993316i \(0.536823\pi\)
\(294\) −0.223362 −0.0130267
\(295\) −10.1521 −0.591079
\(296\) 8.11847 0.471877
\(297\) 4.86719 0.282423
\(298\) −2.52505 −0.146272
\(299\) −7.47362 −0.432211
\(300\) 4.46933 0.258037
\(301\) −9.36637 −0.539869
\(302\) −1.82732 −0.105150
\(303\) 9.56571 0.549536
\(304\) −5.61786 −0.322206
\(305\) 12.1359 0.694897
\(306\) −0.503126 −0.0287618
\(307\) 23.8890 1.36342 0.681708 0.731624i \(-0.261237\pi\)
0.681708 + 0.731624i \(0.261237\pi\)
\(308\) 9.49155 0.540831
\(309\) −9.20767 −0.523806
\(310\) 2.16988 0.123241
\(311\) −7.71261 −0.437342 −0.218671 0.975799i \(-0.570172\pi\)
−0.218671 + 0.975799i \(0.570172\pi\)
\(312\) 4.21308 0.238519
\(313\) −12.5329 −0.708402 −0.354201 0.935169i \(-0.615247\pi\)
−0.354201 + 0.935169i \(0.615247\pi\)
\(314\) 1.83400 0.103499
\(315\) −1.64565 −0.0927219
\(316\) 22.2568 1.25204
\(317\) 0.316613 0.0177828 0.00889138 0.999960i \(-0.497170\pi\)
0.00889138 + 0.999960i \(0.497170\pi\)
\(318\) −1.47745 −0.0828514
\(319\) 25.8249 1.44592
\(320\) −11.2355 −0.628083
\(321\) 18.5977 1.03802
\(322\) −0.349590 −0.0194819
\(323\) −3.41718 −0.190137
\(324\) −1.95011 −0.108339
\(325\) −10.9437 −0.607049
\(326\) −3.07936 −0.170550
\(327\) −10.0096 −0.553535
\(328\) −5.90942 −0.326293
\(329\) 2.53680 0.139858
\(330\) −1.78906 −0.0984845
\(331\) 1.81798 0.0999254 0.0499627 0.998751i \(-0.484090\pi\)
0.0499627 + 0.998751i \(0.484090\pi\)
\(332\) 16.2620 0.892494
\(333\) 9.20145 0.504236
\(334\) −2.15337 −0.117827
\(335\) −0.908106 −0.0496151
\(336\) −3.70315 −0.202023
\(337\) −3.17086 −0.172728 −0.0863638 0.996264i \(-0.527525\pi\)
−0.0863638 + 0.996264i \(0.527525\pi\)
\(338\) −2.18928 −0.119081
\(339\) 12.1724 0.661116
\(340\) −7.22876 −0.392034
\(341\) −28.7321 −1.55593
\(342\) 0.338851 0.0183230
\(343\) −1.00000 −0.0539949
\(344\) 8.26399 0.445564
\(345\) −2.57565 −0.138668
\(346\) −1.40780 −0.0756840
\(347\) −25.3635 −1.36158 −0.680791 0.732478i \(-0.738364\pi\)
−0.680791 + 0.732478i \(0.738364\pi\)
\(348\) −10.3471 −0.554664
\(349\) −1.31709 −0.0705023 −0.0352511 0.999378i \(-0.511223\pi\)
−0.0352511 + 0.999378i \(0.511223\pi\)
\(350\) −0.511909 −0.0273627
\(351\) 4.77509 0.254875
\(352\) −12.6145 −0.672357
\(353\) 16.2871 0.866877 0.433438 0.901183i \(-0.357300\pi\)
0.433438 + 0.901183i \(0.357300\pi\)
\(354\) 1.37793 0.0732363
\(355\) −17.3745 −0.922143
\(356\) 22.6748 1.20176
\(357\) −2.25251 −0.119216
\(358\) 1.74259 0.0920986
\(359\) 15.9051 0.839437 0.419719 0.907654i \(-0.362129\pi\)
0.419719 + 0.907654i \(0.362129\pi\)
\(360\) 1.45196 0.0765252
\(361\) −16.6986 −0.878871
\(362\) −5.64467 −0.296677
\(363\) 12.6895 0.666028
\(364\) 9.31195 0.488079
\(365\) 5.59265 0.292733
\(366\) −1.64718 −0.0860997
\(367\) −8.20766 −0.428436 −0.214218 0.976786i \(-0.568720\pi\)
−0.214218 + 0.976786i \(0.568720\pi\)
\(368\) −5.79590 −0.302132
\(369\) −6.69771 −0.348669
\(370\) −3.38223 −0.175834
\(371\) −6.61461 −0.343414
\(372\) 11.5119 0.596866
\(373\) 17.8290 0.923150 0.461575 0.887101i \(-0.347285\pi\)
0.461575 + 0.887101i \(0.347285\pi\)
\(374\) −2.44881 −0.126625
\(375\) −11.9998 −0.619668
\(376\) −2.23823 −0.115428
\(377\) 25.3362 1.30488
\(378\) 0.223362 0.0114885
\(379\) −6.32961 −0.325130 −0.162565 0.986698i \(-0.551977\pi\)
−0.162565 + 0.986698i \(0.551977\pi\)
\(380\) 4.86851 0.249750
\(381\) 21.4700 1.09994
\(382\) 0.223362 0.0114282
\(383\) 29.0791 1.48587 0.742936 0.669363i \(-0.233433\pi\)
0.742936 + 0.669363i \(0.233433\pi\)
\(384\) 6.70848 0.342341
\(385\) −8.00969 −0.408212
\(386\) −5.27084 −0.268279
\(387\) 9.36637 0.476119
\(388\) −10.9818 −0.557514
\(389\) 0.0476793 0.00241744 0.00120872 0.999999i \(-0.499615\pi\)
0.00120872 + 0.999999i \(0.499615\pi\)
\(390\) −1.75521 −0.0888783
\(391\) −3.52547 −0.178291
\(392\) 0.882304 0.0445631
\(393\) −0.303802 −0.0153248
\(394\) 3.27237 0.164860
\(395\) −18.7820 −0.945025
\(396\) −9.49155 −0.476968
\(397\) 1.71013 0.0858287 0.0429144 0.999079i \(-0.486336\pi\)
0.0429144 + 0.999079i \(0.486336\pi\)
\(398\) 4.71423 0.236303
\(399\) 1.51705 0.0759475
\(400\) −8.48700 −0.424350
\(401\) 25.3818 1.26751 0.633753 0.773535i \(-0.281513\pi\)
0.633753 + 0.773535i \(0.281513\pi\)
\(402\) 0.123256 0.00614745
\(403\) −28.1884 −1.40416
\(404\) −18.6542 −0.928080
\(405\) 1.64565 0.0817730
\(406\) 1.18514 0.0588175
\(407\) 44.7852 2.21992
\(408\) 1.98740 0.0983910
\(409\) 22.7962 1.12720 0.563600 0.826048i \(-0.309416\pi\)
0.563600 + 0.826048i \(0.309416\pi\)
\(410\) 2.46192 0.121585
\(411\) −0.770104 −0.0379864
\(412\) 17.9560 0.884627
\(413\) 6.16906 0.303559
\(414\) 0.349590 0.0171814
\(415\) −13.7231 −0.673642
\(416\) −12.3758 −0.606775
\(417\) −7.08197 −0.346806
\(418\) 1.64925 0.0806676
\(419\) 32.0283 1.56469 0.782343 0.622848i \(-0.214025\pi\)
0.782343 + 0.622848i \(0.214025\pi\)
\(420\) 3.20920 0.156593
\(421\) −30.1308 −1.46849 −0.734243 0.678887i \(-0.762463\pi\)
−0.734243 + 0.678887i \(0.762463\pi\)
\(422\) 1.24713 0.0607092
\(423\) −2.53680 −0.123343
\(424\) 5.83610 0.283426
\(425\) −5.16239 −0.250413
\(426\) 2.35822 0.114256
\(427\) −7.37451 −0.356878
\(428\) −36.2676 −1.75306
\(429\) 23.2413 1.12210
\(430\) −3.44285 −0.166029
\(431\) 24.2478 1.16798 0.583988 0.811762i \(-0.301492\pi\)
0.583988 + 0.811762i \(0.301492\pi\)
\(432\) 3.70315 0.178168
\(433\) −27.5399 −1.32348 −0.661741 0.749733i \(-0.730182\pi\)
−0.661741 + 0.749733i \(0.730182\pi\)
\(434\) −1.31856 −0.0632927
\(435\) 8.73169 0.418652
\(436\) 19.5199 0.934834
\(437\) 2.37438 0.113582
\(438\) −0.759083 −0.0362704
\(439\) −20.3765 −0.972519 −0.486260 0.873814i \(-0.661639\pi\)
−0.486260 + 0.873814i \(0.661639\pi\)
\(440\) 7.06698 0.336905
\(441\) 1.00000 0.0476190
\(442\) −2.40247 −0.114274
\(443\) 15.4318 0.733189 0.366594 0.930381i \(-0.380524\pi\)
0.366594 + 0.930381i \(0.380524\pi\)
\(444\) −17.9438 −0.851576
\(445\) −19.1347 −0.907073
\(446\) −5.32541 −0.252166
\(447\) 11.3047 0.534696
\(448\) 6.82739 0.322564
\(449\) 38.3342 1.80910 0.904551 0.426366i \(-0.140207\pi\)
0.904551 + 0.426366i \(0.140207\pi\)
\(450\) 0.511909 0.0241316
\(451\) −32.5990 −1.53503
\(452\) −23.7376 −1.11652
\(453\) 8.18096 0.384375
\(454\) −3.11627 −0.146254
\(455\) −7.85812 −0.368395
\(456\) −1.33850 −0.0626810
\(457\) −29.0968 −1.36109 −0.680545 0.732707i \(-0.738257\pi\)
−0.680545 + 0.732707i \(0.738257\pi\)
\(458\) 0.216696 0.0101256
\(459\) 2.25251 0.105138
\(460\) 5.02280 0.234189
\(461\) 0.713652 0.0332381 0.0166190 0.999862i \(-0.494710\pi\)
0.0166190 + 0.999862i \(0.494710\pi\)
\(462\) 1.08714 0.0505785
\(463\) −29.8664 −1.38801 −0.694005 0.719970i \(-0.744155\pi\)
−0.694005 + 0.719970i \(0.744155\pi\)
\(464\) 19.6486 0.912163
\(465\) −9.71464 −0.450506
\(466\) −2.82995 −0.131095
\(467\) −14.8655 −0.687895 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(468\) −9.31195 −0.430445
\(469\) 0.551822 0.0254808
\(470\) 0.932465 0.0430114
\(471\) −8.21090 −0.378338
\(472\) −5.44298 −0.250534
\(473\) 45.5879 2.09613
\(474\) 2.54926 0.117091
\(475\) 3.47683 0.159528
\(476\) 4.39265 0.201337
\(477\) 6.61461 0.302862
\(478\) 1.37506 0.0628936
\(479\) 31.6472 1.44600 0.722998 0.690850i \(-0.242764\pi\)
0.722998 + 0.690850i \(0.242764\pi\)
\(480\) −4.26511 −0.194675
\(481\) 43.9377 2.00339
\(482\) −2.28092 −0.103893
\(483\) 1.56513 0.0712158
\(484\) −24.7460 −1.12482
\(485\) 9.26724 0.420804
\(486\) −0.223362 −0.0101319
\(487\) −21.2101 −0.961120 −0.480560 0.876962i \(-0.659567\pi\)
−0.480560 + 0.876962i \(0.659567\pi\)
\(488\) 6.50656 0.294538
\(489\) 13.7864 0.623444
\(490\) −0.367576 −0.0166054
\(491\) −12.4276 −0.560848 −0.280424 0.959876i \(-0.590475\pi\)
−0.280424 + 0.959876i \(0.590475\pi\)
\(492\) 13.0613 0.588848
\(493\) 11.9517 0.538275
\(494\) 1.61805 0.0727993
\(495\) 8.00969 0.360009
\(496\) −21.8605 −0.981565
\(497\) 10.5578 0.473584
\(498\) 1.86262 0.0834661
\(499\) −12.9368 −0.579131 −0.289566 0.957158i \(-0.593511\pi\)
−0.289566 + 0.957158i \(0.593511\pi\)
\(500\) 23.4009 1.04652
\(501\) 9.64070 0.430715
\(502\) −1.76480 −0.0787671
\(503\) 30.0964 1.34193 0.670967 0.741487i \(-0.265879\pi\)
0.670967 + 0.741487i \(0.265879\pi\)
\(504\) −0.882304 −0.0393009
\(505\) 15.7418 0.700501
\(506\) 1.70152 0.0756418
\(507\) 9.80148 0.435299
\(508\) −41.8688 −1.85763
\(509\) −19.1384 −0.848296 −0.424148 0.905593i \(-0.639426\pi\)
−0.424148 + 0.905593i \(0.639426\pi\)
\(510\) −0.827968 −0.0366631
\(511\) −3.39844 −0.150338
\(512\) −16.1322 −0.712951
\(513\) −1.51705 −0.0669794
\(514\) 6.26080 0.276152
\(515\) −15.1526 −0.667703
\(516\) −18.2655 −0.804092
\(517\) −12.3471 −0.543024
\(518\) 2.05525 0.0903026
\(519\) 6.30279 0.276662
\(520\) 6.93326 0.304043
\(521\) −16.2645 −0.712560 −0.356280 0.934379i \(-0.615955\pi\)
−0.356280 + 0.934379i \(0.615955\pi\)
\(522\) −1.18514 −0.0518722
\(523\) −21.4200 −0.936629 −0.468315 0.883562i \(-0.655139\pi\)
−0.468315 + 0.883562i \(0.655139\pi\)
\(524\) 0.592447 0.0258812
\(525\) 2.29184 0.100024
\(526\) 3.42293 0.149247
\(527\) −13.2971 −0.579230
\(528\) 18.0239 0.784390
\(529\) −20.5504 −0.893495
\(530\) −2.43137 −0.105612
\(531\) −6.16906 −0.267714
\(532\) −2.95841 −0.128264
\(533\) −31.9822 −1.38530
\(534\) 2.59713 0.112389
\(535\) 30.6054 1.32319
\(536\) −0.486875 −0.0210298
\(537\) −7.80163 −0.336665
\(538\) −0.559047 −0.0241022
\(539\) 4.86719 0.209645
\(540\) −3.20920 −0.138102
\(541\) 4.31352 0.185453 0.0927264 0.995692i \(-0.470442\pi\)
0.0927264 + 0.995692i \(0.470442\pi\)
\(542\) 1.53996 0.0661470
\(543\) 25.2714 1.08450
\(544\) −5.83795 −0.250300
\(545\) −16.4724 −0.705599
\(546\) 1.06657 0.0456451
\(547\) −26.3839 −1.12809 −0.564047 0.825743i \(-0.690756\pi\)
−0.564047 + 0.825743i \(0.690756\pi\)
\(548\) 1.50179 0.0641532
\(549\) 7.37451 0.314736
\(550\) 2.49156 0.106240
\(551\) −8.04935 −0.342914
\(552\) −1.38092 −0.0587758
\(553\) 11.4131 0.485335
\(554\) 5.58278 0.237190
\(555\) 15.1424 0.642757
\(556\) 13.8106 0.585701
\(557\) −46.9422 −1.98901 −0.994503 0.104707i \(-0.966610\pi\)
−0.994503 + 0.104707i \(0.966610\pi\)
\(558\) 1.31856 0.0558189
\(559\) 44.7253 1.89168
\(560\) −6.09408 −0.257522
\(561\) 10.9634 0.462875
\(562\) −4.77219 −0.201303
\(563\) −3.83498 −0.161625 −0.0808126 0.996729i \(-0.525752\pi\)
−0.0808126 + 0.996729i \(0.525752\pi\)
\(564\) 4.94704 0.208308
\(565\) 20.0316 0.842734
\(566\) 2.10902 0.0886488
\(567\) −1.00000 −0.0419961
\(568\) −9.31522 −0.390858
\(569\) −13.3813 −0.560972 −0.280486 0.959858i \(-0.590496\pi\)
−0.280486 + 0.959858i \(0.590496\pi\)
\(570\) 0.557631 0.0233566
\(571\) −43.0700 −1.80242 −0.901211 0.433381i \(-0.857320\pi\)
−0.901211 + 0.433381i \(0.857320\pi\)
\(572\) −45.3230 −1.89505
\(573\) −1.00000 −0.0417756
\(574\) −1.49601 −0.0624424
\(575\) 3.58702 0.149589
\(576\) −6.82739 −0.284475
\(577\) 44.5747 1.85567 0.927834 0.372993i \(-0.121669\pi\)
0.927834 + 0.372993i \(0.121669\pi\)
\(578\) 2.66386 0.110802
\(579\) 23.5978 0.980690
\(580\) −17.0277 −0.707039
\(581\) 8.33903 0.345961
\(582\) −1.25783 −0.0521387
\(583\) 32.1946 1.33336
\(584\) 2.99846 0.124077
\(585\) 7.85812 0.324893
\(586\) 0.882609 0.0364602
\(587\) −13.2505 −0.546906 −0.273453 0.961885i \(-0.588166\pi\)
−0.273453 + 0.961885i \(0.588166\pi\)
\(588\) −1.95011 −0.0804212
\(589\) 8.95549 0.369004
\(590\) 2.26759 0.0933554
\(591\) −14.6505 −0.602643
\(592\) 34.0743 1.40045
\(593\) −40.2704 −1.65371 −0.826853 0.562418i \(-0.809871\pi\)
−0.826853 + 0.562418i \(0.809871\pi\)
\(594\) −1.08714 −0.0446061
\(595\) −3.70685 −0.151966
\(596\) −22.0455 −0.903018
\(597\) −21.1058 −0.863803
\(598\) 1.66932 0.0682637
\(599\) −21.3921 −0.874055 −0.437028 0.899448i \(-0.643969\pi\)
−0.437028 + 0.899448i \(0.643969\pi\)
\(600\) −2.02210 −0.0825517
\(601\) −21.7809 −0.888463 −0.444231 0.895912i \(-0.646523\pi\)
−0.444231 + 0.895912i \(0.646523\pi\)
\(602\) 2.09209 0.0852673
\(603\) −0.551822 −0.0224719
\(604\) −15.9538 −0.649150
\(605\) 20.8825 0.848995
\(606\) −2.13662 −0.0867941
\(607\) −11.5745 −0.469794 −0.234897 0.972020i \(-0.575475\pi\)
−0.234897 + 0.972020i \(0.575475\pi\)
\(608\) 3.93182 0.159456
\(609\) −5.30592 −0.215007
\(610\) −2.71069 −0.109753
\(611\) −12.1134 −0.490057
\(612\) −4.39265 −0.177562
\(613\) 12.9157 0.521660 0.260830 0.965385i \(-0.416004\pi\)
0.260830 + 0.965385i \(0.416004\pi\)
\(614\) −5.33589 −0.215339
\(615\) −11.0221 −0.444454
\(616\) −4.29434 −0.173024
\(617\) −34.5405 −1.39055 −0.695274 0.718745i \(-0.744717\pi\)
−0.695274 + 0.718745i \(0.744717\pi\)
\(618\) 2.05664 0.0827303
\(619\) −10.4591 −0.420386 −0.210193 0.977660i \(-0.567409\pi\)
−0.210193 + 0.977660i \(0.567409\pi\)
\(620\) 18.9446 0.760834
\(621\) −1.56513 −0.0628064
\(622\) 1.72270 0.0690741
\(623\) 11.6275 0.465844
\(624\) 17.6829 0.707881
\(625\) −8.28830 −0.331532
\(626\) 2.79938 0.111886
\(627\) −7.38377 −0.294879
\(628\) 16.0122 0.638955
\(629\) 20.7264 0.826415
\(630\) 0.367576 0.0146446
\(631\) −42.9499 −1.70981 −0.854904 0.518786i \(-0.826384\pi\)
−0.854904 + 0.518786i \(0.826384\pi\)
\(632\) −10.0698 −0.400557
\(633\) −5.58343 −0.221922
\(634\) −0.0707193 −0.00280862
\(635\) 35.3321 1.40211
\(636\) −12.8992 −0.511487
\(637\) 4.77509 0.189196
\(638\) −5.76830 −0.228369
\(639\) −10.5578 −0.417662
\(640\) 11.0398 0.436387
\(641\) 5.36544 0.211922 0.105961 0.994370i \(-0.466208\pi\)
0.105961 + 0.994370i \(0.466208\pi\)
\(642\) −4.15403 −0.163946
\(643\) 13.3645 0.527045 0.263522 0.964653i \(-0.415116\pi\)
0.263522 + 0.964653i \(0.415116\pi\)
\(644\) −3.05217 −0.120272
\(645\) 15.4138 0.606917
\(646\) 0.763267 0.0300303
\(647\) −44.0694 −1.73255 −0.866274 0.499569i \(-0.833492\pi\)
−0.866274 + 0.499569i \(0.833492\pi\)
\(648\) 0.882304 0.0346602
\(649\) −30.0260 −1.17862
\(650\) 2.44441 0.0958777
\(651\) 5.90322 0.231366
\(652\) −26.8850 −1.05290
\(653\) 5.13038 0.200767 0.100384 0.994949i \(-0.467993\pi\)
0.100384 + 0.994949i \(0.467993\pi\)
\(654\) 2.23577 0.0874257
\(655\) −0.499952 −0.0195347
\(656\) −24.8026 −0.968379
\(657\) 3.39844 0.132586
\(658\) −0.566624 −0.0220893
\(659\) 21.5484 0.839408 0.419704 0.907661i \(-0.362134\pi\)
0.419704 + 0.907661i \(0.362134\pi\)
\(660\) −15.6198 −0.607999
\(661\) −25.6285 −0.996833 −0.498416 0.866938i \(-0.666085\pi\)
−0.498416 + 0.866938i \(0.666085\pi\)
\(662\) −0.406068 −0.0157823
\(663\) 10.7559 0.417726
\(664\) −7.35756 −0.285529
\(665\) 2.49653 0.0968114
\(666\) −2.05525 −0.0796394
\(667\) −8.30444 −0.321549
\(668\) −18.8004 −0.727410
\(669\) 23.8421 0.921788
\(670\) 0.202836 0.00783625
\(671\) 35.8931 1.38564
\(672\) 2.59175 0.0999789
\(673\) 36.1879 1.39494 0.697470 0.716614i \(-0.254309\pi\)
0.697470 + 0.716614i \(0.254309\pi\)
\(674\) 0.708248 0.0272807
\(675\) −2.29184 −0.0882128
\(676\) −19.1139 −0.735152
\(677\) −24.8477 −0.954976 −0.477488 0.878638i \(-0.658453\pi\)
−0.477488 + 0.878638i \(0.658453\pi\)
\(678\) −2.71886 −0.104417
\(679\) −5.63135 −0.216112
\(680\) 3.27057 0.125420
\(681\) 13.9517 0.534629
\(682\) 6.41766 0.245745
\(683\) 22.5038 0.861085 0.430542 0.902570i \(-0.358322\pi\)
0.430542 + 0.902570i \(0.358322\pi\)
\(684\) 2.95841 0.113118
\(685\) −1.26732 −0.0484219
\(686\) 0.223362 0.00852800
\(687\) −0.970158 −0.0370138
\(688\) 34.6850 1.32235
\(689\) 31.5854 1.20331
\(690\) 0.575303 0.0219014
\(691\) −17.4227 −0.662792 −0.331396 0.943492i \(-0.607520\pi\)
−0.331396 + 0.943492i \(0.607520\pi\)
\(692\) −12.2911 −0.467239
\(693\) −4.86719 −0.184889
\(694\) 5.66523 0.215049
\(695\) −11.6544 −0.442078
\(696\) 4.68143 0.177449
\(697\) −15.0867 −0.571449
\(698\) 0.294188 0.0111352
\(699\) 12.6698 0.479216
\(700\) −4.46933 −0.168925
\(701\) 37.3696 1.41143 0.705715 0.708496i \(-0.250626\pi\)
0.705715 + 0.708496i \(0.250626\pi\)
\(702\) −1.06657 −0.0402552
\(703\) −13.9591 −0.526476
\(704\) −33.2302 −1.25241
\(705\) −4.17468 −0.157228
\(706\) −3.63793 −0.136915
\(707\) −9.56571 −0.359756
\(708\) 12.0303 0.452128
\(709\) −41.8739 −1.57261 −0.786303 0.617840i \(-0.788008\pi\)
−0.786303 + 0.617840i \(0.788008\pi\)
\(710\) 3.88080 0.145644
\(711\) −11.4131 −0.428025
\(712\) −10.2590 −0.384471
\(713\) 9.23930 0.346014
\(714\) 0.503126 0.0188290
\(715\) 38.2470 1.43036
\(716\) 15.2140 0.568575
\(717\) −6.15618 −0.229907
\(718\) −3.55259 −0.132581
\(719\) 41.4719 1.54664 0.773320 0.634015i \(-0.218594\pi\)
0.773320 + 0.634015i \(0.218594\pi\)
\(720\) 6.09408 0.227113
\(721\) 9.20767 0.342912
\(722\) 3.72982 0.138810
\(723\) 10.2118 0.379780
\(724\) −49.2820 −1.83155
\(725\) −12.1603 −0.451622
\(726\) −2.83436 −0.105193
\(727\) 21.9046 0.812396 0.406198 0.913785i \(-0.366854\pi\)
0.406198 + 0.913785i \(0.366854\pi\)
\(728\) −4.21308 −0.156147
\(729\) 1.00000 0.0370370
\(730\) −1.24918 −0.0462344
\(731\) 21.0979 0.780333
\(732\) −14.3811 −0.531541
\(733\) 31.6650 1.16957 0.584787 0.811187i \(-0.301178\pi\)
0.584787 + 0.811187i \(0.301178\pi\)
\(734\) 1.83328 0.0676676
\(735\) 1.64565 0.0607007
\(736\) 4.05642 0.149522
\(737\) −2.68582 −0.0989336
\(738\) 1.49601 0.0550691
\(739\) −24.3883 −0.897139 −0.448569 0.893748i \(-0.648066\pi\)
−0.448569 + 0.893748i \(0.648066\pi\)
\(740\) −29.5293 −1.08552
\(741\) −7.24405 −0.266117
\(742\) 1.47745 0.0542390
\(743\) −13.2264 −0.485230 −0.242615 0.970123i \(-0.578005\pi\)
−0.242615 + 0.970123i \(0.578005\pi\)
\(744\) −5.20844 −0.190951
\(745\) 18.6036 0.681585
\(746\) −3.98232 −0.145803
\(747\) −8.33903 −0.305109
\(748\) −21.3798 −0.781724
\(749\) −18.5977 −0.679546
\(750\) 2.68030 0.0978707
\(751\) 51.3872 1.87515 0.937573 0.347789i \(-0.113068\pi\)
0.937573 + 0.347789i \(0.113068\pi\)
\(752\) −9.39414 −0.342569
\(753\) 7.90110 0.287932
\(754\) −5.65915 −0.206094
\(755\) 13.4630 0.489969
\(756\) 1.95011 0.0709248
\(757\) 54.2128 1.97040 0.985199 0.171412i \(-0.0548330\pi\)
0.985199 + 0.171412i \(0.0548330\pi\)
\(758\) 1.41379 0.0513513
\(759\) −7.61777 −0.276508
\(760\) −2.20270 −0.0799004
\(761\) 16.0740 0.582684 0.291342 0.956619i \(-0.405898\pi\)
0.291342 + 0.956619i \(0.405898\pi\)
\(762\) −4.79558 −0.173725
\(763\) 10.0096 0.362374
\(764\) 1.95011 0.0705525
\(765\) 3.70685 0.134021
\(766\) −6.49516 −0.234680
\(767\) −29.4578 −1.06366
\(768\) 12.1564 0.438655
\(769\) 9.19946 0.331741 0.165871 0.986148i \(-0.446957\pi\)
0.165871 + 0.986148i \(0.446957\pi\)
\(770\) 1.78906 0.0644732
\(771\) −28.0298 −1.00947
\(772\) −46.0182 −1.65623
\(773\) −29.0805 −1.04595 −0.522976 0.852348i \(-0.675178\pi\)
−0.522976 + 0.852348i \(0.675178\pi\)
\(774\) −2.09209 −0.0751987
\(775\) 13.5292 0.485984
\(776\) 4.96857 0.178361
\(777\) −9.20145 −0.330100
\(778\) −0.0106497 −0.000381811 0
\(779\) 10.1608 0.364047
\(780\) −15.3242 −0.548694
\(781\) −51.3870 −1.83877
\(782\) 0.787456 0.0281594
\(783\) 5.30592 0.189618
\(784\) 3.70315 0.132255
\(785\) −13.5123 −0.482274
\(786\) 0.0678578 0.00242041
\(787\) −0.755113 −0.0269169 −0.0134584 0.999909i \(-0.504284\pi\)
−0.0134584 + 0.999909i \(0.504284\pi\)
\(788\) 28.5702 1.01777
\(789\) −15.3246 −0.545570
\(790\) 4.19518 0.149258
\(791\) −12.1724 −0.432802
\(792\) 4.29434 0.152593
\(793\) 35.2139 1.25048
\(794\) −0.381977 −0.0135559
\(795\) 10.8853 0.386063
\(796\) 41.1586 1.45883
\(797\) 24.2393 0.858601 0.429301 0.903162i \(-0.358760\pi\)
0.429301 + 0.903162i \(0.358760\pi\)
\(798\) −0.338851 −0.0119952
\(799\) −5.71417 −0.202153
\(800\) 5.93987 0.210006
\(801\) −11.6275 −0.410836
\(802\) −5.66933 −0.200191
\(803\) 16.5409 0.583715
\(804\) 1.07611 0.0379516
\(805\) 2.57565 0.0907798
\(806\) 6.29622 0.221775
\(807\) 2.50287 0.0881053
\(808\) 8.43986 0.296913
\(809\) −4.06154 −0.142796 −0.0713981 0.997448i \(-0.522746\pi\)
−0.0713981 + 0.997448i \(0.522746\pi\)
\(810\) −0.367576 −0.0129153
\(811\) −15.8676 −0.557185 −0.278593 0.960409i \(-0.589868\pi\)
−0.278593 + 0.960409i \(0.589868\pi\)
\(812\) 10.3471 0.363113
\(813\) −6.89447 −0.241800
\(814\) −10.0033 −0.350616
\(815\) 22.6876 0.794713
\(816\) 8.34138 0.292007
\(817\) −14.2093 −0.497119
\(818\) −5.09180 −0.178031
\(819\) −4.77509 −0.166855
\(820\) 21.4943 0.750613
\(821\) 7.32970 0.255808 0.127904 0.991787i \(-0.459175\pi\)
0.127904 + 0.991787i \(0.459175\pi\)
\(822\) 0.172012 0.00599960
\(823\) −48.1052 −1.67684 −0.838421 0.545023i \(-0.816521\pi\)
−0.838421 + 0.545023i \(0.816521\pi\)
\(824\) −8.12397 −0.283012
\(825\) −11.1548 −0.388360
\(826\) −1.37793 −0.0479444
\(827\) 6.84983 0.238192 0.119096 0.992883i \(-0.462000\pi\)
0.119096 + 0.992883i \(0.462000\pi\)
\(828\) 3.05217 0.106070
\(829\) −27.3764 −0.950821 −0.475410 0.879764i \(-0.657700\pi\)
−0.475410 + 0.879764i \(0.657700\pi\)
\(830\) 3.06522 0.106395
\(831\) −24.9943 −0.867044
\(832\) −32.6014 −1.13025
\(833\) 2.25251 0.0780449
\(834\) 1.58184 0.0547747
\(835\) 15.8652 0.549038
\(836\) 14.3992 0.498005
\(837\) −5.90322 −0.204045
\(838\) −7.15390 −0.247128
\(839\) 14.8460 0.512541 0.256271 0.966605i \(-0.417506\pi\)
0.256271 + 0.966605i \(0.417506\pi\)
\(840\) −1.45196 −0.0500975
\(841\) −0.847214 −0.0292143
\(842\) 6.73007 0.231934
\(843\) 21.3653 0.735860
\(844\) 10.8883 0.374791
\(845\) 16.1298 0.554882
\(846\) 0.566624 0.0194809
\(847\) −12.6895 −0.436017
\(848\) 24.4949 0.841158
\(849\) −9.44217 −0.324055
\(850\) 1.15308 0.0395504
\(851\) −14.4014 −0.493675
\(852\) 20.5889 0.705365
\(853\) −21.5697 −0.738532 −0.369266 0.929324i \(-0.620391\pi\)
−0.369266 + 0.929324i \(0.620391\pi\)
\(854\) 1.64718 0.0563655
\(855\) −2.49653 −0.0853797
\(856\) 16.4089 0.560843
\(857\) −13.5451 −0.462692 −0.231346 0.972871i \(-0.574313\pi\)
−0.231346 + 0.972871i \(0.574313\pi\)
\(858\) −5.19121 −0.177225
\(859\) 1.46474 0.0499762 0.0249881 0.999688i \(-0.492045\pi\)
0.0249881 + 0.999688i \(0.492045\pi\)
\(860\) −30.0585 −1.02499
\(861\) 6.69771 0.228258
\(862\) −5.41604 −0.184471
\(863\) 46.0152 1.56638 0.783188 0.621785i \(-0.213592\pi\)
0.783188 + 0.621785i \(0.213592\pi\)
\(864\) −2.59175 −0.0881731
\(865\) 10.3722 0.352665
\(866\) 6.15136 0.209032
\(867\) −11.9262 −0.405035
\(868\) −11.5119 −0.390740
\(869\) −55.5498 −1.88440
\(870\) −1.95033 −0.0661223
\(871\) −2.63500 −0.0892836
\(872\) −8.83155 −0.299074
\(873\) 5.63135 0.190592
\(874\) −0.530346 −0.0179392
\(875\) 11.9998 0.405668
\(876\) −6.62734 −0.223917
\(877\) 42.6501 1.44019 0.720096 0.693875i \(-0.244098\pi\)
0.720096 + 0.693875i \(0.244098\pi\)
\(878\) 4.55134 0.153600
\(879\) −3.95148 −0.133280
\(880\) 29.6610 0.999874
\(881\) −36.3417 −1.22438 −0.612191 0.790710i \(-0.709712\pi\)
−0.612191 + 0.790710i \(0.709712\pi\)
\(882\) −0.223362 −0.00752099
\(883\) 33.8777 1.14008 0.570038 0.821619i \(-0.306929\pi\)
0.570038 + 0.821619i \(0.306929\pi\)
\(884\) −20.9753 −0.705475
\(885\) −10.1521 −0.341259
\(886\) −3.44689 −0.115800
\(887\) −27.3629 −0.918755 −0.459378 0.888241i \(-0.651928\pi\)
−0.459378 + 0.888241i \(0.651928\pi\)
\(888\) 8.11847 0.272438
\(889\) −21.4700 −0.720080
\(890\) 4.27397 0.143264
\(891\) 4.86719 0.163057
\(892\) −46.4947 −1.55676
\(893\) 3.84845 0.128784
\(894\) −2.52505 −0.0844502
\(895\) −12.8388 −0.429152
\(896\) −6.70848 −0.224115
\(897\) −7.47362 −0.249537
\(898\) −8.56239 −0.285731
\(899\) −31.3220 −1.04465
\(900\) 4.46933 0.148978
\(901\) 14.8995 0.496374
\(902\) 7.28138 0.242444
\(903\) −9.36637 −0.311693
\(904\) 10.7398 0.357200
\(905\) 41.5879 1.38243
\(906\) −1.82732 −0.0607085
\(907\) −13.8138 −0.458681 −0.229340 0.973346i \(-0.573657\pi\)
−0.229340 + 0.973346i \(0.573657\pi\)
\(908\) −27.2073 −0.902905
\(909\) 9.56571 0.317275
\(910\) 1.75521 0.0581845
\(911\) 0.348944 0.0115610 0.00578051 0.999983i \(-0.498160\pi\)
0.00578051 + 0.999983i \(0.498160\pi\)
\(912\) −5.61786 −0.186026
\(913\) −40.5876 −1.34325
\(914\) 6.49911 0.214971
\(915\) 12.1359 0.401199
\(916\) 1.89191 0.0625106
\(917\) 0.303802 0.0100324
\(918\) −0.503126 −0.0166056
\(919\) −12.2068 −0.402665 −0.201333 0.979523i \(-0.564527\pi\)
−0.201333 + 0.979523i \(0.564527\pi\)
\(920\) −2.27251 −0.0749224
\(921\) 23.8890 0.787169
\(922\) −0.159403 −0.00524965
\(923\) −50.4146 −1.65942
\(924\) 9.49155 0.312249
\(925\) −21.0882 −0.693376
\(926\) 6.67102 0.219223
\(927\) −9.20767 −0.302420
\(928\) −13.7516 −0.451419
\(929\) 16.4967 0.541238 0.270619 0.962686i \(-0.412772\pi\)
0.270619 + 0.962686i \(0.412772\pi\)
\(930\) 2.16988 0.0711532
\(931\) −1.51705 −0.0497193
\(932\) −24.7075 −0.809322
\(933\) −7.71261 −0.252500
\(934\) 3.32039 0.108647
\(935\) 18.0419 0.590034
\(936\) 4.21308 0.137709
\(937\) −54.8587 −1.79216 −0.896078 0.443898i \(-0.853595\pi\)
−0.896078 + 0.443898i \(0.853595\pi\)
\(938\) −0.123256 −0.00402445
\(939\) −12.5329 −0.408996
\(940\) 8.14109 0.265533
\(941\) 19.7793 0.644788 0.322394 0.946606i \(-0.395512\pi\)
0.322394 + 0.946606i \(0.395512\pi\)
\(942\) 1.83400 0.0597551
\(943\) 10.4828 0.341366
\(944\) −22.8449 −0.743539
\(945\) −1.64565 −0.0535330
\(946\) −10.1826 −0.331065
\(947\) 51.3059 1.66722 0.833609 0.552355i \(-0.186271\pi\)
0.833609 + 0.552355i \(0.186271\pi\)
\(948\) 22.2568 0.722868
\(949\) 16.2279 0.526779
\(950\) −0.776592 −0.0251960
\(951\) 0.316613 0.0102669
\(952\) −1.98740 −0.0644120
\(953\) −24.3952 −0.790239 −0.395120 0.918630i \(-0.629297\pi\)
−0.395120 + 0.918630i \(0.629297\pi\)
\(954\) −1.47745 −0.0478343
\(955\) −1.64565 −0.0532520
\(956\) 12.0052 0.388277
\(957\) 25.8249 0.834801
\(958\) −7.06877 −0.228382
\(959\) 0.770104 0.0248680
\(960\) −11.2355 −0.362624
\(961\) 3.84804 0.124130
\(962\) −9.81401 −0.316417
\(963\) 18.5977 0.599304
\(964\) −19.9141 −0.641389
\(965\) 38.8337 1.25010
\(966\) −0.349590 −0.0112479
\(967\) −34.8517 −1.12075 −0.560377 0.828238i \(-0.689344\pi\)
−0.560377 + 0.828238i \(0.689344\pi\)
\(968\) 11.1960 0.359854
\(969\) −3.41718 −0.109775
\(970\) −2.06995 −0.0664620
\(971\) −11.6094 −0.372564 −0.186282 0.982496i \(-0.559644\pi\)
−0.186282 + 0.982496i \(0.559644\pi\)
\(972\) −1.95011 −0.0625498
\(973\) 7.08197 0.227038
\(974\) 4.73752 0.151800
\(975\) −10.9437 −0.350480
\(976\) 27.3089 0.874136
\(977\) −48.7283 −1.55896 −0.779478 0.626430i \(-0.784515\pi\)
−0.779478 + 0.626430i \(0.784515\pi\)
\(978\) −3.07936 −0.0984672
\(979\) −56.5930 −1.80872
\(980\) −3.20920 −0.102514
\(981\) −10.0096 −0.319583
\(982\) 2.77584 0.0885808
\(983\) −46.4993 −1.48310 −0.741548 0.670900i \(-0.765908\pi\)
−0.741548 + 0.670900i \(0.765908\pi\)
\(984\) −5.90942 −0.188385
\(985\) −24.1097 −0.768198
\(986\) −2.66954 −0.0850156
\(987\) 2.53680 0.0807472
\(988\) 14.1267 0.449430
\(989\) −14.6596 −0.466147
\(990\) −1.78906 −0.0568600
\(991\) 42.8927 1.36253 0.681266 0.732036i \(-0.261430\pi\)
0.681266 + 0.732036i \(0.261430\pi\)
\(992\) 15.2997 0.485765
\(993\) 1.81798 0.0576919
\(994\) −2.35822 −0.0747981
\(995\) −34.7328 −1.10110
\(996\) 16.2620 0.515282
\(997\) −39.6127 −1.25455 −0.627273 0.778799i \(-0.715829\pi\)
−0.627273 + 0.778799i \(0.715829\pi\)
\(998\) 2.88959 0.0914684
\(999\) 9.20145 0.291121
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 4011.2.a.m.1.13 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.m.1.13 29 1.1 even 1 trivial