Properties

Label 138.4.d.a.137.19
Level $138$
Weight $4$
Character 138.137
Analytic conductor $8.142$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [138,4,Mod(137,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.137");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 138.d (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(8.14226358079\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 137.19
Character \(\chi\) \(=\) 138.137
Dual form 138.4.d.a.137.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000i q^{2} +(2.34341 - 4.63772i) q^{3} -4.00000 q^{4} -10.8839 q^{5} +(9.27544 + 4.68682i) q^{6} +21.8179i q^{7} -8.00000i q^{8} +(-16.0169 - 21.7361i) q^{9} +O(q^{10})\) \(q+2.00000i q^{2} +(2.34341 - 4.63772i) q^{3} -4.00000 q^{4} -10.8839 q^{5} +(9.27544 + 4.68682i) q^{6} +21.8179i q^{7} -8.00000i q^{8} +(-16.0169 - 21.7361i) q^{9} -21.7678i q^{10} +10.5986 q^{11} +(-9.37363 + 18.5509i) q^{12} -57.2594 q^{13} -43.6358 q^{14} +(-25.5055 + 50.4766i) q^{15} +16.0000 q^{16} -114.219 q^{17} +(43.4723 - 32.0338i) q^{18} +113.444i q^{19} +43.5357 q^{20} +(101.185 + 51.1283i) q^{21} +21.1971i q^{22} +(-99.6450 + 47.3062i) q^{23} +(-37.1018 - 18.7473i) q^{24} -6.54035 q^{25} -114.519i q^{26} +(-138.340 + 23.3452i) q^{27} -87.2717i q^{28} -126.097i q^{29} +(-100.953 - 51.0109i) q^{30} +289.289 q^{31} +32.0000i q^{32} +(24.8368 - 49.1532i) q^{33} -228.439i q^{34} -237.464i q^{35} +(64.0675 + 86.9445i) q^{36} -84.7151i q^{37} -226.887 q^{38} +(-134.182 + 265.553i) q^{39} +87.0713i q^{40} +299.551i q^{41} +(-102.257 + 202.371i) q^{42} -365.488i q^{43} -42.3943 q^{44} +(174.326 + 236.574i) q^{45} +(-94.6123 - 199.290i) q^{46} -254.505i q^{47} +(37.4945 - 74.2035i) q^{48} -133.021 q^{49} -13.0807i q^{50} +(-267.663 + 529.718i) q^{51} +229.038 q^{52} +467.085 q^{53} +(-46.6904 - 276.680i) q^{54} -115.354 q^{55} +174.543 q^{56} +(526.120 + 265.845i) q^{57} +252.193 q^{58} +304.305i q^{59} +(102.022 - 201.906i) q^{60} -697.918i q^{61} +578.578i q^{62} +(474.237 - 349.455i) q^{63} -64.0000 q^{64} +623.206 q^{65} +(98.3063 + 49.6735i) q^{66} +671.692i q^{67} +456.878 q^{68} +(-14.1161 + 572.983i) q^{69} +474.929 q^{70} +354.578i q^{71} +(-173.889 + 128.135i) q^{72} -321.406 q^{73} +169.430 q^{74} +(-15.3267 + 30.3323i) q^{75} -453.774i q^{76} +231.239i q^{77} +(-531.106 - 268.364i) q^{78} -78.6582i q^{79} -174.143 q^{80} +(-215.919 + 696.290i) q^{81} -599.101 q^{82} -506.936 q^{83} +(-404.741 - 204.513i) q^{84} +1243.16 q^{85} +730.976 q^{86} +(-584.801 - 295.496i) q^{87} -84.7885i q^{88} -1122.44 q^{89} +(-473.149 + 348.653i) q^{90} -1249.28i q^{91} +(398.580 - 189.225i) q^{92} +(677.922 - 1341.64i) q^{93} +509.010 q^{94} -1234.71i q^{95} +(148.407 + 74.9890i) q^{96} +553.523i q^{97} -266.043i q^{98} +(-169.756 - 230.372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 2.34341 4.63772i 0.450989 0.892530i
\(4\) −4.00000 −0.500000
\(5\) −10.8839 −0.973487 −0.486744 0.873545i \(-0.661815\pi\)
−0.486744 + 0.873545i \(0.661815\pi\)
\(6\) 9.27544 + 4.68682i 0.631114 + 0.318897i
\(7\) 21.8179i 1.17806i 0.808112 + 0.589028i \(0.200489\pi\)
−0.808112 + 0.589028i \(0.799511\pi\)
\(8\) 8.00000i 0.353553i
\(9\) −16.0169 21.7361i −0.593218 0.805042i
\(10\) 21.7678i 0.688359i
\(11\) 10.5986 0.290508 0.145254 0.989394i \(-0.453600\pi\)
0.145254 + 0.989394i \(0.453600\pi\)
\(12\) −9.37363 + 18.5509i −0.225494 + 0.446265i
\(13\) −57.2594 −1.22161 −0.610804 0.791782i \(-0.709154\pi\)
−0.610804 + 0.791782i \(0.709154\pi\)
\(14\) −43.6358 −0.833012
\(15\) −25.5055 + 50.4766i −0.439032 + 0.868866i
\(16\) 16.0000 0.250000
\(17\) −114.219 −1.62955 −0.814773 0.579780i \(-0.803139\pi\)
−0.814773 + 0.579780i \(0.803139\pi\)
\(18\) 43.4723 32.0338i 0.569251 0.419468i
\(19\) 113.444i 1.36978i 0.728648 + 0.684888i \(0.240149\pi\)
−0.728648 + 0.684888i \(0.759851\pi\)
\(20\) 43.5357 0.486744
\(21\) 101.185 + 51.1283i 1.05145 + 0.531291i
\(22\) 21.1971i 0.205420i
\(23\) −99.6450 + 47.3062i −0.903366 + 0.428870i
\(24\) −37.1018 18.7473i −0.315557 0.159449i
\(25\) −6.54035 −0.0523228
\(26\) 114.519i 0.863807i
\(27\) −138.340 + 23.3452i −0.986058 + 0.166399i
\(28\) 87.2717i 0.589028i
\(29\) 126.097i 0.807433i −0.914884 0.403717i \(-0.867718\pi\)
0.914884 0.403717i \(-0.132282\pi\)
\(30\) −100.953 51.0109i −0.614381 0.310442i
\(31\) 289.289 1.67606 0.838030 0.545624i \(-0.183707\pi\)
0.838030 + 0.545624i \(0.183707\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 24.8368 49.1532i 0.131016 0.259287i
\(34\) 228.439i 1.15226i
\(35\) 237.464i 1.14682i
\(36\) 64.0675 + 86.9445i 0.296609 + 0.402521i
\(37\) 84.7151i 0.376408i −0.982130 0.188204i \(-0.939733\pi\)
0.982130 0.188204i \(-0.0602665\pi\)
\(38\) −226.887 −0.968578
\(39\) −134.182 + 265.553i −0.550932 + 1.09032i
\(40\) 87.0713i 0.344180i
\(41\) 299.551i 1.14102i 0.821290 + 0.570511i \(0.193255\pi\)
−0.821290 + 0.570511i \(0.806745\pi\)
\(42\) −102.257 + 202.371i −0.375679 + 0.743488i
\(43\) 365.488i 1.29619i −0.761558 0.648097i \(-0.775565\pi\)
0.761558 0.648097i \(-0.224435\pi\)
\(44\) −42.3943 −0.145254
\(45\) 174.326 + 236.574i 0.577490 + 0.783698i
\(46\) −94.6123 199.290i −0.303257 0.638776i
\(47\) 254.505i 0.789859i −0.918712 0.394929i \(-0.870769\pi\)
0.918712 0.394929i \(-0.129231\pi\)
\(48\) 37.4945 74.2035i 0.112747 0.223132i
\(49\) −133.021 −0.387817
\(50\) 13.0807i 0.0369978i
\(51\) −267.663 + 529.718i −0.734908 + 1.45442i
\(52\) 229.038 0.610804
\(53\) 467.085 1.21055 0.605274 0.796017i \(-0.293064\pi\)
0.605274 + 0.796017i \(0.293064\pi\)
\(54\) −46.6904 276.680i −0.117662 0.697249i
\(55\) −115.354 −0.282806
\(56\) 174.543 0.416506
\(57\) 526.120 + 265.845i 1.22257 + 0.617754i
\(58\) 252.193 0.570941
\(59\) 304.305i 0.671476i 0.941955 + 0.335738i \(0.108986\pi\)
−0.941955 + 0.335738i \(0.891014\pi\)
\(60\) 102.022 201.906i 0.219516 0.434433i
\(61\) 697.918i 1.46491i −0.680818 0.732453i \(-0.738375\pi\)
0.680818 0.732453i \(-0.261625\pi\)
\(62\) 578.578i 1.18515i
\(63\) 474.237 349.455i 0.948385 0.698844i
\(64\) −64.0000 −0.125000
\(65\) 623.206 1.18922
\(66\) 98.3063 + 49.6735i 0.183344 + 0.0926422i
\(67\) 671.692i 1.22478i 0.790556 + 0.612389i \(0.209792\pi\)
−0.790556 + 0.612389i \(0.790208\pi\)
\(68\) 456.878 0.814773
\(69\) −14.1161 + 572.983i −0.0246287 + 0.999697i
\(70\) 474.929 0.810926
\(71\) 354.578i 0.592685i 0.955082 + 0.296343i \(0.0957670\pi\)
−0.955082 + 0.296343i \(0.904233\pi\)
\(72\) −173.889 + 128.135i −0.284625 + 0.209734i
\(73\) −321.406 −0.515311 −0.257656 0.966237i \(-0.582950\pi\)
−0.257656 + 0.966237i \(0.582950\pi\)
\(74\) 169.430 0.266160
\(75\) −15.3267 + 30.3323i −0.0235970 + 0.0466996i
\(76\) 453.774i 0.684888i
\(77\) 231.239i 0.342235i
\(78\) −531.106 268.364i −0.770973 0.389567i
\(79\) 78.6582i 0.112022i −0.998430 0.0560110i \(-0.982162\pi\)
0.998430 0.0560110i \(-0.0178382\pi\)
\(80\) −174.143 −0.243372
\(81\) −215.919 + 696.290i −0.296185 + 0.955131i
\(82\) −599.101 −0.806825
\(83\) −506.936 −0.670404 −0.335202 0.942146i \(-0.608805\pi\)
−0.335202 + 0.942146i \(0.608805\pi\)
\(84\) −404.741 204.513i −0.525725 0.265645i
\(85\) 1243.16 1.58634
\(86\) 730.976 0.916548
\(87\) −584.801 295.496i −0.720658 0.364143i
\(88\) 84.7885i 0.102710i
\(89\) −1122.44 −1.33683 −0.668416 0.743788i \(-0.733027\pi\)
−0.668416 + 0.743788i \(0.733027\pi\)
\(90\) −473.149 + 348.653i −0.554158 + 0.408347i
\(91\) 1249.28i 1.43912i
\(92\) 398.580 189.225i 0.451683 0.214435i
\(93\) 677.922 1341.64i 0.755885 1.49593i
\(94\) 509.010 0.558514
\(95\) 1234.71i 1.33346i
\(96\) 148.407 + 74.9890i 0.157778 + 0.0797243i
\(97\) 553.523i 0.579399i 0.957118 + 0.289700i \(0.0935554\pi\)
−0.957118 + 0.289700i \(0.906445\pi\)
\(98\) 266.043i 0.274228i
\(99\) −169.756 230.372i −0.172334 0.233871i
\(100\) 26.1614 0.0261614
\(101\) 619.354i 0.610179i 0.952324 + 0.305089i \(0.0986863\pi\)
−0.952324 + 0.305089i \(0.901314\pi\)
\(102\) −1059.44 535.326i −1.02843 0.519658i
\(103\) 1232.74i 1.17928i −0.807667 0.589639i \(-0.799270\pi\)
0.807667 0.589639i \(-0.200730\pi\)
\(104\) 458.075i 0.431903i
\(105\) −1101.29 556.476i −1.02357 0.517205i
\(106\) 934.169i 0.855986i
\(107\) −998.586 −0.902215 −0.451107 0.892470i \(-0.648971\pi\)
−0.451107 + 0.892470i \(0.648971\pi\)
\(108\) 553.361 93.3808i 0.493029 0.0831997i
\(109\) 1042.56i 0.916140i 0.888916 + 0.458070i \(0.151459\pi\)
−0.888916 + 0.458070i \(0.848541\pi\)
\(110\) 230.708i 0.199974i
\(111\) −392.885 198.522i −0.335955 0.169756i
\(112\) 349.087i 0.294514i
\(113\) −1720.22 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(114\) −531.689 + 1052.24i −0.436818 + 0.864484i
\(115\) 1084.53 514.876i 0.879415 0.417500i
\(116\) 504.387i 0.403717i
\(117\) 917.117 + 1244.60i 0.724679 + 0.983445i
\(118\) −608.609 −0.474805
\(119\) 2492.03i 1.91970i
\(120\) 403.812 + 204.044i 0.307191 + 0.155221i
\(121\) −1218.67 −0.915605
\(122\) 1395.84 1.03584
\(123\) 1389.23 + 701.969i 1.01840 + 0.514589i
\(124\) −1157.16 −0.838030
\(125\) 1431.67 1.02442
\(126\) 698.910 + 948.474i 0.494157 + 0.670609i
\(127\) −417.436 −0.291665 −0.145833 0.989309i \(-0.546586\pi\)
−0.145833 + 0.989309i \(0.546586\pi\)
\(128\) 128.000i 0.0883883i
\(129\) −1695.03 856.487i −1.15689 0.584570i
\(130\) 1246.41i 0.840905i
\(131\) 994.475i 0.663265i 0.943409 + 0.331633i \(0.107599\pi\)
−0.943409 + 0.331633i \(0.892401\pi\)
\(132\) −99.3470 + 196.613i −0.0655079 + 0.129643i
\(133\) −2475.10 −1.61367
\(134\) −1343.38 −0.866049
\(135\) 1505.68 254.087i 0.959915 0.161988i
\(136\) 913.756i 0.576132i
\(137\) 1322.32 0.824624 0.412312 0.911043i \(-0.364721\pi\)
0.412312 + 0.911043i \(0.364721\pi\)
\(138\) −1145.97 28.2322i −0.706892 0.0174151i
\(139\) 642.320 0.391949 0.195974 0.980609i \(-0.437213\pi\)
0.195974 + 0.980609i \(0.437213\pi\)
\(140\) 949.857i 0.573411i
\(141\) −1180.32 596.409i −0.704972 0.356217i
\(142\) −709.156 −0.419092
\(143\) −606.867 −0.354887
\(144\) −256.270 347.778i −0.148304 0.201260i
\(145\) 1372.43i 0.786026i
\(146\) 642.812i 0.364380i
\(147\) −311.723 + 616.916i −0.174901 + 0.346138i
\(148\) 338.860i 0.188204i
\(149\) −69.6174 −0.0382770 −0.0191385 0.999817i \(-0.506092\pi\)
−0.0191385 + 0.999817i \(0.506092\pi\)
\(150\) −60.6646 30.6534i −0.0330216 0.0166856i
\(151\) 1839.55 0.991394 0.495697 0.868496i \(-0.334913\pi\)
0.495697 + 0.868496i \(0.334913\pi\)
\(152\) 907.549 0.484289
\(153\) 1829.44 + 2482.69i 0.966676 + 1.31185i
\(154\) −462.477 −0.241997
\(155\) −3148.60 −1.63162
\(156\) 536.728 1062.21i 0.275466 0.545160i
\(157\) 686.113i 0.348776i 0.984677 + 0.174388i \(0.0557947\pi\)
−0.984677 + 0.174388i \(0.944205\pi\)
\(158\) 157.316 0.0792115
\(159\) 1094.57 2166.21i 0.545943 1.08045i
\(160\) 348.285i 0.172090i
\(161\) −1032.12 2174.05i −0.505234 1.06422i
\(162\) −1392.58 431.838i −0.675379 0.209435i
\(163\) 2558.16 1.22927 0.614633 0.788813i \(-0.289304\pi\)
0.614633 + 0.788813i \(0.289304\pi\)
\(164\) 1198.20i 0.570511i
\(165\) −270.321 + 534.979i −0.127542 + 0.252412i
\(166\) 1013.87i 0.474047i
\(167\) 722.148i 0.334620i 0.985904 + 0.167310i \(0.0535080\pi\)
−0.985904 + 0.167310i \(0.946492\pi\)
\(168\) 409.026 809.483i 0.187840 0.371744i
\(169\) 1081.64 0.492325
\(170\) 2486.31i 1.12171i
\(171\) 2465.83 1817.01i 1.10273 0.812576i
\(172\) 1461.95i 0.648097i
\(173\) 2672.05i 1.17429i 0.809482 + 0.587145i \(0.199748\pi\)
−0.809482 + 0.587145i \(0.800252\pi\)
\(174\) 590.992 1169.60i 0.257488 0.509582i
\(175\) 142.697i 0.0616392i
\(176\) 169.577 0.0726270
\(177\) 1411.28 + 713.109i 0.599312 + 0.302828i
\(178\) 2244.87i 0.945283i
\(179\) 1537.45i 0.641982i −0.947082 0.320991i \(-0.895984\pi\)
0.947082 0.320991i \(-0.104016\pi\)
\(180\) −697.306 946.297i −0.288745 0.391849i
\(181\) 2480.61i 1.01869i 0.860563 + 0.509344i \(0.170112\pi\)
−0.860563 + 0.509344i \(0.829888\pi\)
\(182\) 2498.56 1.01761
\(183\) −3236.75 1635.51i −1.30747 0.660656i
\(184\) 378.449 + 797.160i 0.151629 + 0.319388i
\(185\) 922.032i 0.366428i
\(186\) 2683.28 + 1355.84i 1.05778 + 0.534491i
\(187\) −1210.56 −0.473396
\(188\) 1018.02i 0.394929i
\(189\) −509.343 3018.29i −0.196028 1.16163i
\(190\) 2469.42 0.942898
\(191\) −2283.68 −0.865139 −0.432570 0.901601i \(-0.642393\pi\)
−0.432570 + 0.901601i \(0.642393\pi\)
\(192\) −149.978 + 296.814i −0.0563736 + 0.111566i
\(193\) −3711.80 −1.38436 −0.692179 0.721726i \(-0.743349\pi\)
−0.692179 + 0.721726i \(0.743349\pi\)
\(194\) −1107.05 −0.409697
\(195\) 1460.43 2890.26i 0.536325 1.06141i
\(196\) 532.085 0.193909
\(197\) 3550.99i 1.28425i −0.766600 0.642125i \(-0.778053\pi\)
0.766600 0.642125i \(-0.221947\pi\)
\(198\) 460.744 339.512i 0.165372 0.121859i
\(199\) 501.412i 0.178614i −0.996004 0.0893070i \(-0.971535\pi\)
0.996004 0.0893070i \(-0.0284652\pi\)
\(200\) 52.3228i 0.0184989i
\(201\) 3115.12 + 1574.05i 1.09315 + 0.552362i
\(202\) −1238.71 −0.431462
\(203\) 2751.17 0.951202
\(204\) 1070.65 2118.87i 0.367454 0.727209i
\(205\) 3260.28i 1.11077i
\(206\) 2465.48 0.833875
\(207\) 2624.26 + 1408.20i 0.881152 + 0.472834i
\(208\) −916.150 −0.305402
\(209\) 1202.34i 0.397931i
\(210\) 1112.95 2202.59i 0.365719 0.723776i
\(211\) −5985.97 −1.95304 −0.976520 0.215429i \(-0.930885\pi\)
−0.976520 + 0.215429i \(0.930885\pi\)
\(212\) −1868.34 −0.605274
\(213\) 1644.43 + 830.920i 0.528989 + 0.267294i
\(214\) 1997.17i 0.637962i
\(215\) 3977.94i 1.26183i
\(216\) 186.762 + 1106.72i 0.0588311 + 0.348624i
\(217\) 6311.68i 1.97449i
\(218\) −2085.12 −0.647809
\(219\) −753.185 + 1490.59i −0.232400 + 0.459930i
\(220\) 461.416 0.141403
\(221\) 6540.14 1.99067
\(222\) 397.044 785.770i 0.120035 0.237556i
\(223\) 3360.05 1.00899 0.504496 0.863414i \(-0.331678\pi\)
0.504496 + 0.863414i \(0.331678\pi\)
\(224\) −698.173 −0.208253
\(225\) 104.756 + 142.162i 0.0310388 + 0.0421220i
\(226\) 3440.44i 1.01263i
\(227\) 864.868 0.252878 0.126439 0.991974i \(-0.459645\pi\)
0.126439 + 0.991974i \(0.459645\pi\)
\(228\) −2104.48 1063.38i −0.611283 0.308877i
\(229\) 644.141i 0.185878i 0.995672 + 0.0929390i \(0.0296262\pi\)
−0.995672 + 0.0929390i \(0.970374\pi\)
\(230\) 1029.75 + 2169.06i 0.295217 + 0.621840i
\(231\) 1072.42 + 541.886i 0.305455 + 0.154344i
\(232\) −1008.77 −0.285471
\(233\) 5314.43i 1.49425i −0.664685 0.747124i \(-0.731434\pi\)
0.664685 0.747124i \(-0.268566\pi\)
\(234\) −2489.20 + 1834.23i −0.695401 + 0.512426i
\(235\) 2770.01i 0.768917i
\(236\) 1217.22i 0.335738i
\(237\) −364.795 184.328i −0.0999830 0.0505207i
\(238\) 4984.06 1.35743
\(239\) 3518.25i 0.952204i 0.879390 + 0.476102i \(0.157951\pi\)
−0.879390 + 0.476102i \(0.842049\pi\)
\(240\) −408.087 + 807.625i −0.109758 + 0.217217i
\(241\) 4742.64i 1.26763i 0.773483 + 0.633817i \(0.218513\pi\)
−0.773483 + 0.633817i \(0.781487\pi\)
\(242\) 2437.34i 0.647431i
\(243\) 2723.21 + 2633.06i 0.718906 + 0.695107i
\(244\) 2791.67i 0.732453i
\(245\) 1447.79 0.377535
\(246\) −1403.94 + 2778.46i −0.363869 + 0.720115i
\(247\) 6495.71i 1.67333i
\(248\) 2314.31i 0.592577i
\(249\) −1187.96 + 2351.03i −0.302345 + 0.598355i
\(250\) 2863.35i 0.724376i
\(251\) 930.257 0.233933 0.116967 0.993136i \(-0.462683\pi\)
0.116967 + 0.993136i \(0.462683\pi\)
\(252\) −1896.95 + 1397.82i −0.474193 + 0.349422i
\(253\) −1056.09 + 501.377i −0.262435 + 0.124590i
\(254\) 834.873i 0.206238i
\(255\) 2913.22 5765.41i 0.715423 1.41586i
\(256\) 256.000 0.0625000
\(257\) 1399.11i 0.339588i −0.985480 0.169794i \(-0.945690\pi\)
0.985480 0.169794i \(-0.0543102\pi\)
\(258\) 1712.97 3390.06i 0.413353 0.818046i
\(259\) 1848.31 0.443429
\(260\) −2492.83 −0.594610
\(261\) −2740.85 + 2019.68i −0.650017 + 0.478984i
\(262\) −1988.95 −0.468999
\(263\) −4854.60 −1.13820 −0.569101 0.822267i \(-0.692709\pi\)
−0.569101 + 0.822267i \(0.692709\pi\)
\(264\) −393.225 198.694i −0.0916718 0.0463211i
\(265\) −5083.71 −1.17845
\(266\) 4950.21i 1.14104i
\(267\) −2630.33 + 5205.55i −0.602896 + 1.19316i
\(268\) 2686.77i 0.612389i
\(269\) 4990.97i 1.13124i 0.824665 + 0.565622i \(0.191364\pi\)
−0.824665 + 0.565622i \(0.808636\pi\)
\(270\) 508.174 + 3011.37i 0.114543 + 0.678763i
\(271\) −5973.67 −1.33902 −0.669510 0.742803i \(-0.733496\pi\)
−0.669510 + 0.742803i \(0.733496\pi\)
\(272\) −1827.51 −0.407387
\(273\) −5793.81 2927.57i −1.28446 0.649029i
\(274\) 2644.64i 0.583097i
\(275\) −69.3183 −0.0152002
\(276\) 56.4643 2291.93i 0.0123143 0.499848i
\(277\) 2759.86 0.598642 0.299321 0.954152i \(-0.403240\pi\)
0.299321 + 0.954152i \(0.403240\pi\)
\(278\) 1284.64i 0.277150i
\(279\) −4633.51 6288.03i −0.994269 1.34930i
\(280\) −1899.71 −0.405463
\(281\) 902.764 0.191653 0.0958263 0.995398i \(-0.469451\pi\)
0.0958263 + 0.995398i \(0.469451\pi\)
\(282\) 1192.82 2360.64i 0.251884 0.498491i
\(283\) 7168.41i 1.50572i 0.658183 + 0.752858i \(0.271325\pi\)
−0.658183 + 0.752858i \(0.728675\pi\)
\(284\) 1418.31i 0.296343i
\(285\) −5726.24 2893.43i −1.19015 0.601376i
\(286\) 1213.73i 0.250943i
\(287\) −6535.57 −1.34419
\(288\) 695.556 512.540i 0.142313 0.104867i
\(289\) 8133.09 1.65542
\(290\) −2744.85 −0.555804
\(291\) 2567.08 + 1297.13i 0.517131 + 0.261303i
\(292\) 1285.62 0.257656
\(293\) −601.951 −0.120022 −0.0600109 0.998198i \(-0.519114\pi\)
−0.0600109 + 0.998198i \(0.519114\pi\)
\(294\) −1233.83 623.447i −0.244757 0.123674i
\(295\) 3312.03i 0.653673i
\(296\) −677.721 −0.133080
\(297\) −1466.21 + 247.425i −0.286458 + 0.0483403i
\(298\) 139.235i 0.0270660i
\(299\) 5705.61 2708.72i 1.10356 0.523911i
\(300\) 61.3068 121.329i 0.0117985 0.0233498i
\(301\) 7974.18 1.52699
\(302\) 3679.10i 0.701021i
\(303\) 2872.39 + 1451.40i 0.544603 + 0.275184i
\(304\) 1815.10i 0.342444i
\(305\) 7596.08i 1.42607i
\(306\) −4965.38 + 3658.88i −0.927620 + 0.683543i
\(307\) −9095.26 −1.69086 −0.845429 0.534087i \(-0.820655\pi\)
−0.845429 + 0.534087i \(0.820655\pi\)
\(308\) 924.954i 0.171117i
\(309\) −5717.11 2888.82i −1.05254 0.531841i
\(310\) 6297.20i 1.15373i
\(311\) 2085.16i 0.380188i 0.981766 + 0.190094i \(0.0608793\pi\)
−0.981766 + 0.190094i \(0.939121\pi\)
\(312\) 2124.42 + 1073.46i 0.385487 + 0.194784i
\(313\) 7530.75i 1.35995i −0.733237 0.679973i \(-0.761992\pi\)
0.733237 0.679973i \(-0.238008\pi\)
\(314\) −1372.23 −0.246622
\(315\) −5161.56 + 3803.44i −0.923241 + 0.680316i
\(316\) 314.633i 0.0560110i
\(317\) 5822.34i 1.03159i 0.856711 + 0.515797i \(0.172504\pi\)
−0.856711 + 0.515797i \(0.827496\pi\)
\(318\) 4332.41 + 2189.14i 0.763993 + 0.386040i
\(319\) 1336.44i 0.234566i
\(320\) 696.571 0.121686
\(321\) −2340.09 + 4631.16i −0.406889 + 0.805253i
\(322\) 4348.09 2064.24i 0.752515 0.357254i
\(323\) 12957.5i 2.23211i
\(324\) 863.676 2785.16i 0.148093 0.477565i
\(325\) 374.496 0.0639179
\(326\) 5116.31i 0.869222i
\(327\) 4835.11 + 2443.15i 0.817682 + 0.413169i
\(328\) 2396.40 0.403413
\(329\) 5552.77 0.930498
\(330\) −1069.96 540.642i −0.178483 0.0901860i
\(331\) 9020.57 1.49793 0.748965 0.662609i \(-0.230551\pi\)
0.748965 + 0.662609i \(0.230551\pi\)
\(332\) 2027.75 0.335202
\(333\) −1841.38 + 1356.87i −0.303024 + 0.223292i
\(334\) −1444.30 −0.236612
\(335\) 7310.64i 1.19231i
\(336\) 1618.97 + 818.052i 0.262863 + 0.132823i
\(337\) 7456.58i 1.20530i −0.798006 0.602649i \(-0.794112\pi\)
0.798006 0.602649i \(-0.205888\pi\)
\(338\) 2163.28i 0.348126i
\(339\) −4031.18 + 7977.90i −0.645851 + 1.27817i
\(340\) −4972.62 −0.793171
\(341\) 3066.05 0.486909
\(342\) 3634.03 + 4931.65i 0.574578 + 0.779746i
\(343\) 4581.30i 0.721186i
\(344\) −2923.90 −0.458274
\(345\) 153.638 6236.30i 0.0239757 0.973192i
\(346\) −5344.10 −0.830348
\(347\) 4527.76i 0.700469i −0.936662 0.350235i \(-0.886102\pi\)
0.936662 0.350235i \(-0.113898\pi\)
\(348\) 2339.20 + 1181.98i 0.360329 + 0.182072i
\(349\) 1114.89 0.170999 0.0854993 0.996338i \(-0.472751\pi\)
0.0854993 + 0.996338i \(0.472751\pi\)
\(350\) 285.393 0.0435855
\(351\) 7921.27 1336.73i 1.20458 0.203275i
\(352\) 339.154i 0.0513550i
\(353\) 817.597i 0.123276i 0.998099 + 0.0616378i \(0.0196324\pi\)
−0.998099 + 0.0616378i \(0.980368\pi\)
\(354\) −1426.22 + 2822.56i −0.214132 + 0.423778i
\(355\) 3859.20i 0.576971i
\(356\) 4489.75 0.668416
\(357\) −11557.3 5839.84i −1.71339 0.865763i
\(358\) 3074.91 0.453950
\(359\) −5448.72 −0.801038 −0.400519 0.916288i \(-0.631170\pi\)
−0.400519 + 0.916288i \(0.631170\pi\)
\(360\) 1892.59 1394.61i 0.277079 0.204174i
\(361\) −6010.45 −0.876287
\(362\) −4961.22 −0.720321
\(363\) −2855.84 + 5651.85i −0.412928 + 0.817205i
\(364\) 4997.12i 0.719561i
\(365\) 3498.15 0.501649
\(366\) 3271.01 6473.50i 0.467155 0.924522i
\(367\) 168.276i 0.0239345i 0.999928 + 0.0119672i \(0.00380938\pi\)
−0.999928 + 0.0119672i \(0.996191\pi\)
\(368\) −1594.32 + 756.899i −0.225842 + 0.107218i
\(369\) 6511.07 4797.87i 0.918571 0.676875i
\(370\) −1844.06 −0.259104
\(371\) 10190.8i 1.42609i
\(372\) −2711.69 + 5366.57i −0.377942 + 0.747966i
\(373\) 8526.68i 1.18363i −0.806073 0.591816i \(-0.798411\pi\)
0.806073 0.591816i \(-0.201589\pi\)
\(374\) 2421.12i 0.334742i
\(375\) 3355.00 6639.70i 0.462003 0.914327i
\(376\) −2036.04 −0.279257
\(377\) 7220.22i 0.986366i
\(378\) 6036.59 1018.69i 0.821398 0.138613i
\(379\) 1545.20i 0.209423i 0.994503 + 0.104712i \(0.0333920\pi\)
−0.994503 + 0.104712i \(0.966608\pi\)
\(380\) 4938.84i 0.666730i
\(381\) −978.223 + 1935.95i −0.131538 + 0.260320i
\(382\) 4567.37i 0.611746i
\(383\) −5941.15 −0.792633 −0.396316 0.918114i \(-0.629712\pi\)
−0.396316 + 0.918114i \(0.629712\pi\)
\(384\) −593.628 299.956i −0.0788892 0.0398622i
\(385\) 2516.78i 0.333161i
\(386\) 7423.60i 0.978889i
\(387\) −7944.29 + 5853.98i −1.04349 + 0.768926i
\(388\) 2214.09i 0.289700i
\(389\) 8342.65 1.08738 0.543688 0.839288i \(-0.317028\pi\)
0.543688 + 0.839288i \(0.317028\pi\)
\(390\) 5780.51 + 2920.85i 0.750532 + 0.379239i
\(391\) 11381.4 5403.29i 1.47208 0.698864i
\(392\) 1064.17i 0.137114i
\(393\) 4612.10 + 2330.46i 0.591984 + 0.299125i
\(394\) 7101.97 0.908102
\(395\) 856.110i 0.109052i
\(396\) 679.024 + 921.487i 0.0861672 + 0.116936i
\(397\) 12254.3 1.54918 0.774591 0.632462i \(-0.217956\pi\)
0.774591 + 0.632462i \(0.217956\pi\)
\(398\) 1002.82 0.126299
\(399\) −5800.17 + 11478.8i −0.727749 + 1.44025i
\(400\) −104.646 −0.0130807
\(401\) 5605.08 0.698016 0.349008 0.937120i \(-0.386519\pi\)
0.349008 + 0.937120i \(0.386519\pi\)
\(402\) −3148.09 + 6230.23i −0.390579 + 0.772975i
\(403\) −16564.5 −2.04749
\(404\) 2477.42i 0.305089i
\(405\) 2350.04 7578.36i 0.288332 0.929807i
\(406\) 5502.33i 0.672601i
\(407\) 897.859i 0.109349i
\(408\) 4237.74 + 2141.30i 0.514215 + 0.259829i
\(409\) −5378.51 −0.650245 −0.325123 0.945672i \(-0.605406\pi\)
−0.325123 + 0.945672i \(0.605406\pi\)
\(410\) 6520.57 0.785434
\(411\) 3098.74 6132.55i 0.371896 0.736001i
\(412\) 4930.97i 0.589639i
\(413\) −6639.29 −0.791037
\(414\) −2816.40 + 5248.51i −0.334344 + 0.623068i
\(415\) 5517.45 0.652629
\(416\) 1832.30i 0.215952i
\(417\) 1505.22 2978.90i 0.176765 0.349826i
\(418\) −2404.68 −0.281380
\(419\) 8349.36 0.973491 0.486746 0.873544i \(-0.338184\pi\)
0.486746 + 0.873544i \(0.338184\pi\)
\(420\) 4405.17 + 2225.90i 0.511787 + 0.258602i
\(421\) 9197.86i 1.06479i −0.846496 0.532395i \(-0.821292\pi\)
0.846496 0.532395i \(-0.178708\pi\)
\(422\) 11971.9i 1.38101i
\(423\) −5531.95 + 4076.37i −0.635869 + 0.468558i
\(424\) 3736.68i 0.427993i
\(425\) 747.035 0.0852624
\(426\) −1661.84 + 3288.87i −0.189006 + 0.374052i
\(427\) 15227.1 1.72574
\(428\) 3994.34 0.451107
\(429\) −1422.14 + 2814.48i −0.160050 + 0.316747i
\(430\) −7955.88 −0.892248
\(431\) 14207.2 1.58779 0.793896 0.608053i \(-0.208049\pi\)
0.793896 + 0.608053i \(0.208049\pi\)
\(432\) −2213.44 + 373.523i −0.246515 + 0.0415999i
\(433\) 3114.44i 0.345659i −0.984952 0.172829i \(-0.944709\pi\)
0.984952 0.172829i \(-0.0552910\pi\)
\(434\) −12623.4 −1.39618
\(435\) 6364.92 + 3216.15i 0.701551 + 0.354489i
\(436\) 4170.25i 0.458070i
\(437\) −5366.58 11304.1i −0.587456 1.23741i
\(438\) −2981.18 1506.37i −0.325220 0.164331i
\(439\) −8269.58 −0.899055 −0.449528 0.893266i \(-0.648408\pi\)
−0.449528 + 0.893266i \(0.648408\pi\)
\(440\) 922.831i 0.0999869i
\(441\) 2130.59 + 2891.37i 0.230060 + 0.312209i
\(442\) 13080.3i 1.40761i
\(443\) 5073.97i 0.544179i −0.962272 0.272090i \(-0.912285\pi\)
0.962272 0.272090i \(-0.0877147\pi\)
\(444\) 1571.54 + 794.088i 0.167977 + 0.0848778i
\(445\) 12216.5 1.30139
\(446\) 6720.09i 0.713466i
\(447\) −163.142 + 322.866i −0.0172625 + 0.0341634i
\(448\) 1396.35i 0.147257i
\(449\) 3625.22i 0.381035i −0.981684 0.190518i \(-0.938983\pi\)
0.981684 0.190518i \(-0.0610166\pi\)
\(450\) −284.324 + 209.512i −0.0297848 + 0.0219477i
\(451\) 3174.81i 0.331476i
\(452\) 6880.89 0.716039
\(453\) 4310.81 8531.32i 0.447108 0.884848i
\(454\) 1729.74i 0.178812i
\(455\) 13597.1i 1.40097i
\(456\) 2126.76 4208.96i 0.218409 0.432242i
\(457\) 2136.11i 0.218650i −0.994006 0.109325i \(-0.965131\pi\)
0.994006 0.109325i \(-0.0348689\pi\)
\(458\) −1288.28 −0.131436
\(459\) 15801.1 2666.48i 1.60683 0.271156i
\(460\) −4338.11 + 2059.51i −0.439708 + 0.208750i
\(461\) 16072.6i 1.62381i 0.583789 + 0.811905i \(0.301570\pi\)
−0.583789 + 0.811905i \(0.698430\pi\)
\(462\) −1083.77 + 2144.84i −0.109138 + 0.215989i
\(463\) 5419.34 0.543970 0.271985 0.962302i \(-0.412320\pi\)
0.271985 + 0.962302i \(0.412320\pi\)
\(464\) 2017.55i 0.201858i
\(465\) −7378.45 + 14602.3i −0.735844 + 1.45627i
\(466\) 10628.9 1.05659
\(467\) −11598.4 −1.14927 −0.574635 0.818410i \(-0.694856\pi\)
−0.574635 + 0.818410i \(0.694856\pi\)
\(468\) −3668.47 4978.39i −0.362340 0.491723i
\(469\) −14654.9 −1.44286
\(470\) −5540.02 −0.543707
\(471\) 3182.00 + 1607.84i 0.311293 + 0.157294i
\(472\) 2434.44 0.237403
\(473\) 3873.65i 0.376555i
\(474\) 368.657 729.590i 0.0357235 0.0706986i
\(475\) 741.960i 0.0716705i
\(476\) 9968.12i 0.959849i
\(477\) −7481.24 10152.6i −0.718118 0.974541i
\(478\) −7036.51 −0.673310
\(479\) −5374.35 −0.512652 −0.256326 0.966590i \(-0.582512\pi\)
−0.256326 + 0.966590i \(0.582512\pi\)
\(480\) −1615.25 816.175i −0.153595 0.0776106i
\(481\) 4850.74i 0.459822i
\(482\) −9485.27 −0.896353
\(483\) −12501.3 307.984i −1.17770 0.0290139i
\(484\) 4874.68 0.457803
\(485\) 6024.50i 0.564038i
\(486\) −5266.13 + 5446.42i −0.491515 + 0.508343i
\(487\) −6983.42 −0.649792 −0.324896 0.945750i \(-0.605329\pi\)
−0.324896 + 0.945750i \(0.605329\pi\)
\(488\) −5583.34 −0.517922
\(489\) 5994.80 11864.0i 0.554385 1.09716i
\(490\) 2895.59i 0.266958i
\(491\) 8559.41i 0.786723i −0.919384 0.393361i \(-0.871312\pi\)
0.919384 0.393361i \(-0.128688\pi\)
\(492\) −5556.93 2807.88i −0.509198 0.257294i
\(493\) 14402.7i 1.31575i
\(494\) 12991.4 1.18322
\(495\) 1847.61 + 2507.35i 0.167765 + 0.227670i
\(496\) 4628.63 0.419015
\(497\) −7736.15 −0.698217
\(498\) −4702.06 2375.92i −0.423101 0.213790i
\(499\) −18995.8 −1.70415 −0.852073 0.523423i \(-0.824655\pi\)
−0.852073 + 0.523423i \(0.824655\pi\)
\(500\) −5726.70 −0.512211
\(501\) 3349.12 + 1692.29i 0.298658 + 0.150910i
\(502\) 1860.51i 0.165416i
\(503\) 11330.9 1.00441 0.502206 0.864748i \(-0.332522\pi\)
0.502206 + 0.864748i \(0.332522\pi\)
\(504\) −2795.64 3793.90i −0.247079 0.335305i
\(505\) 6741.00i 0.594001i
\(506\) −1002.75 2112.19i −0.0880986 0.185570i
\(507\) 2534.72 5016.33i 0.222033 0.439414i
\(508\) 1669.75 0.145833
\(509\) 8569.51i 0.746242i 0.927783 + 0.373121i \(0.121712\pi\)
−0.927783 + 0.373121i \(0.878288\pi\)
\(510\) 11530.8 + 5826.44i 1.00116 + 0.505881i
\(511\) 7012.40i 0.607066i
\(512\) 512.000i 0.0441942i
\(513\) −2648.36 15693.8i −0.227930 1.35068i
\(514\) 2798.22 0.240125
\(515\) 13417.1i 1.14801i
\(516\) 6780.12 + 3425.95i 0.578446 + 0.292285i
\(517\) 2697.39i 0.229460i
\(518\) 3696.61i 0.313552i
\(519\) 12392.2 + 6261.70i 1.04809 + 0.529592i
\(520\) 4985.65i 0.420452i
\(521\) −4048.12 −0.340405 −0.170203 0.985409i \(-0.554442\pi\)
−0.170203 + 0.985409i \(0.554442\pi\)
\(522\) −4039.35 5481.71i −0.338693 0.459632i
\(523\) 23230.1i 1.94222i 0.238631 + 0.971110i \(0.423301\pi\)
−0.238631 + 0.971110i \(0.576699\pi\)
\(524\) 3977.90i 0.331633i
\(525\) −661.787 334.397i −0.0550148 0.0277986i
\(526\) 9709.19i 0.804831i
\(527\) −33042.5 −2.73122
\(528\) 397.388 786.451i 0.0327540 0.0648217i
\(529\) 7691.25 9427.65i 0.632140 0.774854i
\(530\) 10167.4i 0.833292i
\(531\) 6614.40 4874.01i 0.540566 0.398331i
\(532\) 9900.41 0.806837
\(533\) 17152.1i 1.39388i
\(534\) −10411.1 5260.65i −0.843693 0.426312i
\(535\) 10868.5 0.878294
\(536\) 5373.53 0.433025
\(537\) −7130.28 3602.88i −0.572988 0.289527i
\(538\) −9981.93 −0.799910
\(539\) −1409.84 −0.112664
\(540\) −6022.73 + 1016.35i −0.479958 + 0.0809938i
\(541\) −24127.3 −1.91740 −0.958699 0.284423i \(-0.908198\pi\)
−0.958699 + 0.284423i \(0.908198\pi\)
\(542\) 11947.3i 0.946831i
\(543\) 11504.4 + 5813.08i 0.909208 + 0.459417i
\(544\) 3655.02i 0.288066i
\(545\) 11347.2i 0.891851i
\(546\) 5855.15 11587.6i 0.458932 0.908250i
\(547\) −13147.0 −1.02765 −0.513825 0.857895i \(-0.671772\pi\)
−0.513825 + 0.857895i \(0.671772\pi\)
\(548\) −5289.28 −0.412312
\(549\) −15170.0 + 11178.5i −1.17931 + 0.869008i
\(550\) 138.637i 0.0107482i
\(551\) 14304.9 1.10600
\(552\) 4583.87 + 112.929i 0.353446 + 0.00870754i
\(553\) 1716.16 0.131968
\(554\) 5519.72i 0.423304i
\(555\) 4276.13 + 2160.70i 0.327048 + 0.165255i
\(556\) −2569.28 −0.195974
\(557\) −17149.8 −1.30460 −0.652299 0.757962i \(-0.726195\pi\)
−0.652299 + 0.757962i \(0.726195\pi\)
\(558\) 12576.1 9267.02i 0.954098 0.703054i
\(559\) 20927.6i 1.58344i
\(560\) 3799.43i 0.286706i
\(561\) −2836.84 + 5614.25i −0.213496 + 0.422520i
\(562\) 1805.53i 0.135519i
\(563\) 11494.3 0.860439 0.430220 0.902724i \(-0.358436\pi\)
0.430220 + 0.902724i \(0.358436\pi\)
\(564\) 4721.29 + 2385.63i 0.352486 + 0.178109i
\(565\) 18722.7 1.39411
\(566\) −14336.8 −1.06470
\(567\) −15191.6 4710.90i −1.12520 0.348923i
\(568\) 2836.62 0.209546
\(569\) 17741.2 1.30712 0.653559 0.756876i \(-0.273275\pi\)
0.653559 + 0.756876i \(0.273275\pi\)
\(570\) 5786.86 11452.5i 0.425237 0.841565i
\(571\) 4401.50i 0.322587i 0.986906 + 0.161293i \(0.0515665\pi\)
−0.986906 + 0.161293i \(0.948433\pi\)
\(572\) 2427.47 0.177443
\(573\) −5351.60 + 10591.1i −0.390168 + 0.772162i
\(574\) 13071.1i 0.950486i
\(575\) 651.713 309.399i 0.0472666 0.0224397i
\(576\) 1025.08 + 1391.11i 0.0741522 + 0.100630i
\(577\) −19288.4 −1.39165 −0.695827 0.718209i \(-0.744962\pi\)
−0.695827 + 0.718209i \(0.744962\pi\)
\(578\) 16266.2i 1.17056i
\(579\) −8698.25 + 17214.3i −0.624330 + 1.23558i
\(580\) 5489.70i 0.393013i
\(581\) 11060.3i 0.789773i
\(582\) −2594.26 + 5134.17i −0.184769 + 0.365667i
\(583\) 4950.43 0.351674
\(584\) 2571.25i 0.182190i
\(585\) −9981.82 13546.1i −0.705466 0.957371i
\(586\) 1203.90i 0.0848682i
\(587\) 15199.2i 1.06872i −0.845258 0.534359i \(-0.820553\pi\)
0.845258 0.534359i \(-0.179447\pi\)
\(588\) 1246.89 2467.66i 0.0874507 0.173069i
\(589\) 32818.0i 2.29583i
\(590\) 6624.05 0.462217
\(591\) −16468.5 8321.41i −1.14623 0.579183i
\(592\) 1355.44i 0.0941019i
\(593\) 28258.0i 1.95686i 0.206582 + 0.978429i \(0.433766\pi\)
−0.206582 + 0.978429i \(0.566234\pi\)
\(594\) −494.851 2932.41i −0.0341818 0.202556i
\(595\) 27123.1i 1.86880i
\(596\) 278.470 0.0191385
\(597\) −2325.41 1175.01i −0.159418 0.0805529i
\(598\) 5417.45 + 11411.2i 0.370461 + 0.780334i
\(599\) 12584.5i 0.858413i 0.903206 + 0.429207i \(0.141207\pi\)
−0.903206 + 0.429207i \(0.858793\pi\)
\(600\) 242.658 + 122.614i 0.0165108 + 0.00834280i
\(601\) 11623.5 0.788907 0.394453 0.918916i \(-0.370934\pi\)
0.394453 + 0.918916i \(0.370934\pi\)
\(602\) 15948.4i 1.07975i
\(603\) 14600.0 10758.4i 0.985998 0.726561i
\(604\) −7358.20 −0.495697
\(605\) 13263.9 0.891330
\(606\) −2902.80 + 5744.78i −0.194584 + 0.385092i
\(607\) −356.633 −0.0238473 −0.0119236 0.999929i \(-0.503796\pi\)
−0.0119236 + 0.999929i \(0.503796\pi\)
\(608\) −3630.20 −0.242145
\(609\) 6447.10 12759.1i 0.428982 0.848976i
\(610\) −15192.2 −1.00838
\(611\) 14572.8i 0.964897i
\(612\) −7317.76 9930.76i −0.483338 0.655927i
\(613\) 27137.1i 1.78802i 0.448047 + 0.894010i \(0.352120\pi\)
−0.448047 + 0.894010i \(0.647880\pi\)
\(614\) 18190.5i 1.19562i
\(615\) −15120.3 7640.17i −0.991396 0.500946i
\(616\) 1849.91 0.120998
\(617\) −4164.50 −0.271728 −0.135864 0.990727i \(-0.543381\pi\)
−0.135864 + 0.990727i \(0.543381\pi\)
\(618\) 5777.63 11434.2i 0.376069 0.744258i
\(619\) 15299.4i 0.993434i −0.867913 0.496717i \(-0.834539\pi\)
0.867913 0.496717i \(-0.165461\pi\)
\(620\) 12594.4 0.815811
\(621\) 12680.5 8870.58i 0.819408 0.573211i
\(622\) −4170.32 −0.268834
\(623\) 24489.2i 1.57486i
\(624\) −2146.91 + 4248.85i −0.137733 + 0.272580i
\(625\) −14764.7 −0.944940
\(626\) 15061.5 0.961627
\(627\) 5576.11 + 2817.57i 0.355165 + 0.179462i
\(628\) 2744.45i 0.174388i
\(629\) 9676.12i 0.613374i
\(630\) −7606.88 10323.1i −0.481056 0.652830i
\(631\) 19697.8i 1.24272i −0.783524 0.621361i \(-0.786580\pi\)
0.783524 0.621361i \(-0.213420\pi\)
\(632\) −629.266 −0.0396058
\(633\) −14027.6 + 27761.3i −0.880799 + 1.74315i
\(634\) −11644.7 −0.729447
\(635\) 4543.34 0.283932
\(636\) −4378.28 + 8664.83i −0.272972 + 0.540225i
\(637\) 7616.72 0.473761
\(638\) 2672.89 0.165863
\(639\) 7707.15 5679.23i 0.477136 0.351591i
\(640\) 1393.14i 0.0860449i
\(641\) 16305.2 1.00471 0.502353 0.864663i \(-0.332468\pi\)
0.502353 + 0.864663i \(0.332468\pi\)
\(642\) −9262.32 4680.19i −0.569400 0.287714i
\(643\) 27798.7i 1.70494i 0.522777 + 0.852469i \(0.324896\pi\)
−0.522777 + 0.852469i \(0.675104\pi\)
\(644\) 4128.49 + 8696.18i 0.252617 + 0.532108i
\(645\) 18448.6 + 9321.93i 1.12622 + 0.569071i
\(646\) 25914.9 1.57834
\(647\) 27022.7i 1.64200i −0.570929 0.820999i \(-0.693417\pi\)
0.570929 0.820999i \(-0.306583\pi\)
\(648\) 5570.32 + 1727.35i 0.337690 + 0.104717i
\(649\) 3225.19i 0.195069i
\(650\) 748.992i 0.0451968i
\(651\) 29271.8 + 14790.8i 1.76229 + 0.890475i
\(652\) −10232.6 −0.614633
\(653\) 10675.4i 0.639757i 0.947459 + 0.319878i \(0.103642\pi\)
−0.947459 + 0.319878i \(0.896358\pi\)
\(654\) −4886.29 + 9670.21i −0.292155 + 0.578188i
\(655\) 10823.8i 0.645680i
\(656\) 4792.81i 0.285256i
\(657\) 5147.92 + 6986.12i 0.305692 + 0.414847i
\(658\) 11105.5i 0.657961i
\(659\) 11027.6 0.651856 0.325928 0.945395i \(-0.394323\pi\)
0.325928 + 0.945395i \(0.394323\pi\)
\(660\) 1081.28 2139.92i 0.0637711 0.126206i
\(661\) 32451.1i 1.90953i −0.297361 0.954765i \(-0.596106\pi\)
0.297361 0.954765i \(-0.403894\pi\)
\(662\) 18041.1i 1.05920i
\(663\) 15326.2 30331.3i 0.897769 1.77673i
\(664\) 4055.49i 0.237023i
\(665\) 26938.8 1.57089
\(666\) −2713.74 3682.76i −0.157891 0.214270i
\(667\) 5965.15 + 12564.9i 0.346284 + 0.729408i
\(668\) 2888.59i 0.167310i
\(669\) 7873.96 15583.0i 0.455045 0.900556i
\(670\) 14621.3 0.843088
\(671\) 7396.93i 0.425567i
\(672\) −1636.10 + 3237.93i −0.0939198 + 0.185872i
\(673\) −11825.2 −0.677306 −0.338653 0.940911i \(-0.609971\pi\)
−0.338653 + 0.940911i \(0.609971\pi\)
\(674\) 14913.2 0.852275
\(675\) 904.793 152.686i 0.0515933 0.00870648i
\(676\) −4326.55 −0.246162
\(677\) 20118.7 1.14213 0.571066 0.820904i \(-0.306530\pi\)
0.571066 + 0.820904i \(0.306530\pi\)
\(678\) −15955.8 8062.36i −0.903804 0.456686i
\(679\) −12076.7 −0.682565
\(680\) 9945.24i 0.560857i
\(681\) 2026.74 4011.01i 0.114045 0.225701i
\(682\) 6132.10i 0.344296i
\(683\) 21040.7i 1.17877i 0.807852 + 0.589386i \(0.200630\pi\)
−0.807852 + 0.589386i \(0.799370\pi\)
\(684\) −9863.30 + 7268.05i −0.551364 + 0.406288i
\(685\) −14392.0 −0.802761
\(686\) −9162.59 −0.509955
\(687\) 2987.35 + 1509.49i 0.165902 + 0.0838289i
\(688\) 5847.81i 0.324049i
\(689\) −26745.0 −1.47881
\(690\) 12472.6 + 307.277i 0.688151 + 0.0169534i
\(691\) 18617.3 1.02495 0.512473 0.858703i \(-0.328730\pi\)
0.512473 + 0.858703i \(0.328730\pi\)
\(692\) 10688.2i 0.587145i
\(693\) 5026.23 3703.72i 0.275513 0.203020i
\(694\) 9055.52 0.495307
\(695\) −6990.96 −0.381557
\(696\) −2363.97 + 4678.41i −0.128744 + 0.254791i
\(697\) 34214.5i 1.85935i
\(698\) 2229.77i 0.120914i
\(699\) −24646.8 12453.9i −1.33366 0.673889i
\(700\) 570.787i 0.0308196i
\(701\) −9866.96 −0.531626 −0.265813 0.964025i \(-0.585640\pi\)
−0.265813 + 0.964025i \(0.585640\pi\)
\(702\) 2673.46 + 15842.5i 0.143737 + 0.851764i
\(703\) 9610.39 0.515594
\(704\) −678.308 −0.0363135
\(705\) 12846.5 + 6491.26i 0.686281 + 0.346773i
\(706\) −1635.19 −0.0871690
\(707\) −13513.0 −0.718825
\(708\) −5645.12 2852.44i −0.299656 0.151414i
\(709\) 33.7969i 0.00179022i 1.00000 0.000895112i \(0.000284923\pi\)
−1.00000 0.000895112i \(0.999715\pi\)
\(710\) 7718.39 0.407980
\(711\) −1709.73 + 1259.86i −0.0901824 + 0.0664535i
\(712\) 8979.49i 0.472641i
\(713\) −28826.2 + 13685.2i −1.51410 + 0.718812i
\(714\) 11679.7 23114.7i 0.612187 1.21155i
\(715\) 6605.09 0.345478
\(716\) 6149.82i 0.320991i
\(717\) 16316.7 + 8244.70i 0.849871 + 0.429434i
\(718\) 10897.4i 0.566419i
\(719\) 899.131i 0.0466369i −0.999728 0.0233184i \(-0.992577\pi\)
0.999728 0.0233184i \(-0.00742316\pi\)
\(720\) 2789.22 + 3785.19i 0.144372 + 0.195925i
\(721\) 26895.8 1.38926
\(722\) 12020.9i 0.619628i
\(723\) 21995.0 + 11113.9i 1.13140 + 0.571689i
\(724\) 9922.44i 0.509344i
\(725\) 824.716i 0.0422471i
\(726\) −11303.7 5711.68i −0.577851 0.291984i
\(727\) 21188.1i 1.08091i −0.841372 0.540456i \(-0.818252\pi\)
0.841372 0.540456i \(-0.181748\pi\)
\(728\) −9994.24 −0.508807
\(729\) 18593.0 6459.15i 0.944622 0.328159i
\(730\) 6996.31i 0.354719i
\(731\) 41745.8i 2.11221i
\(732\) 12947.0 + 6542.03i 0.653736 + 0.330328i
\(733\) 22353.8i 1.12641i −0.826318 0.563204i \(-0.809569\pi\)
0.826318 0.563204i \(-0.190431\pi\)
\(734\) −336.553 −0.0169242
\(735\) 3392.77 6714.46i 0.170264 0.336961i
\(736\) −1513.80 3188.64i −0.0758143 0.159694i
\(737\) 7118.97i 0.355808i
\(738\) 9595.73 + 13022.1i 0.478623 + 0.649528i
\(739\) 923.698 0.0459794 0.0229897 0.999736i \(-0.492682\pi\)
0.0229897 + 0.999736i \(0.492682\pi\)
\(740\) 3688.13i 0.183214i
\(741\) −30125.3 15222.1i −1.49350 0.754653i
\(742\) −20381.6 −1.00840
\(743\) −33416.4 −1.64997 −0.824986 0.565153i \(-0.808817\pi\)
−0.824986 + 0.565153i \(0.808817\pi\)
\(744\) −10733.1 5423.38i −0.528892 0.267246i
\(745\) 757.710 0.0372622
\(746\) 17053.4 0.836954
\(747\) 8119.54 + 11018.8i 0.397695 + 0.539703i
\(748\) 4842.25 0.236698
\(749\) 21787.1i 1.06286i
\(750\) 13279.4 + 6709.99i 0.646527 + 0.326686i
\(751\) 29846.4i 1.45022i −0.688635 0.725108i \(-0.741790\pi\)
0.688635 0.725108i \(-0.258210\pi\)
\(752\) 4072.08i 0.197465i
\(753\) 2179.97 4314.27i 0.105501 0.208792i
\(754\) −14440.4 −0.697466
\(755\) −20021.5 −0.965109
\(756\) 2037.37 + 12073.2i 0.0980140 + 0.580816i
\(757\) 18544.8i 0.890387i −0.895434 0.445194i \(-0.853135\pi\)
0.895434 0.445194i \(-0.146865\pi\)
\(758\) −3090.39 −0.148085
\(759\) −149.610 + 6072.80i −0.00715482 + 0.290420i
\(760\) −9877.69 −0.471449
\(761\) 19671.3i 0.937035i −0.883454 0.468518i \(-0.844788\pi\)
0.883454 0.468518i \(-0.155212\pi\)
\(762\) −3871.90 1956.45i −0.184074 0.0930113i
\(763\) −22746.5 −1.07926
\(764\) 9134.74 0.432570
\(765\) −19911.5 27021.4i −0.941047 1.27707i
\(766\) 11882.3i 0.560476i
\(767\) 17424.3i 0.820280i
\(768\) 599.912 1187.26i 0.0281868 0.0557831i
\(769\) 5569.11i 0.261154i −0.991438 0.130577i \(-0.958317\pi\)
0.991438 0.130577i \(-0.0416829\pi\)
\(770\) 5033.56 0.235581
\(771\) −6488.68 3278.69i −0.303092 0.153150i
\(772\) 14847.2 0.692179
\(773\) 22579.3 1.05061 0.525304 0.850914i \(-0.323951\pi\)
0.525304 + 0.850914i \(0.323951\pi\)
\(774\) −11708.0 15888.6i −0.543713 0.737860i
\(775\) −1892.05 −0.0876961
\(776\) 4428.18 0.204849
\(777\) 4331.34 8571.93i 0.199982 0.395774i
\(778\) 16685.3i 0.768890i
\(779\) −33982.1 −1.56295
\(780\) −5841.71 + 11561.0i −0.268162 + 0.530707i
\(781\) 3758.02i 0.172180i
\(782\) 10806.6 + 22762.8i 0.494172 + 1.04092i
\(783\) 2943.75 + 17444.2i 0.134356 + 0.796176i
\(784\) −2128.34 −0.0969543
\(785\) 7467.60i 0.339529i
\(786\) −4660.92 + 9224.20i −0.211513 + 0.418596i
\(787\) 12325.7i 0.558279i 0.960251 + 0.279139i \(0.0900491\pi\)
−0.960251 + 0.279139i \(0.909951\pi\)
\(788\) 14203.9i 0.642125i
\(789\) −11376.3 + 22514.3i −0.513317 + 1.01588i
\(790\) −1712.22 −0.0771114
\(791\) 37531.6i 1.68707i
\(792\) −1842.97 + 1358.05i −0.0826859 + 0.0609294i
\(793\) 39962.4i 1.78954i
\(794\) 24508.6i 1.09544i
\(795\) −11913.2 + 23576.8i −0.531469 + 1.05180i
\(796\) 2005.65i 0.0893070i
\(797\) 10368.6 0.460820 0.230410 0.973094i \(-0.425993\pi\)
0.230410 + 0.973094i \(0.425993\pi\)
\(798\) −22957.7 11600.3i −1.01841 0.514596i
\(799\) 29069.4i 1.28711i
\(800\) 209.291i 0.00924945i
\(801\) 17977.9 + 24397.4i 0.793033 + 1.07621i
\(802\) 11210.2i 0.493572i
\(803\) −3406.44 −0.149702
\(804\) −12460.5 6296.19i −0.546576 0.276181i
\(805\) 11233.5 + 23662.1i 0.491838 + 1.03600i
\(806\) 33129.0i 1.44779i
\(807\) 23146.7 + 11695.9i 1.00967 + 0.510179i
\(808\) 4954.83 0.215731
\(809\) 29964.1i 1.30220i −0.758991 0.651102i \(-0.774307\pi\)
0.758991 0.651102i \(-0.225693\pi\)
\(810\) 15156.7 + 4700.09i 0.657473 + 0.203882i
\(811\) −13277.9 −0.574906 −0.287453 0.957795i \(-0.592809\pi\)
−0.287453 + 0.957795i \(0.592809\pi\)
\(812\) −11004.7 −0.475601
\(813\) −13998.7 + 27704.2i −0.603884 + 1.19512i
\(814\) 1795.72 0.0773217
\(815\) −27842.8 −1.19667
\(816\) −4282.60 + 8475.49i −0.183727 + 0.363605i
\(817\) 41462.3 1.77550
\(818\) 10757.0i 0.459793i
\(819\) −27154.5 + 20009.6i −1.15855 + 0.853713i
\(820\) 13041.1i 0.555386i
\(821\) 23294.6i 0.990238i 0.868825 + 0.495119i \(0.164876\pi\)
−0.868825 + 0.495119i \(0.835124\pi\)
\(822\) 12265.1 + 6197.47i 0.520431 + 0.262970i
\(823\) 11000.7 0.465928 0.232964 0.972485i \(-0.425158\pi\)
0.232964 + 0.972485i \(0.425158\pi\)
\(824\) −9861.93 −0.416938
\(825\) −162.441 + 321.479i −0.00685511 + 0.0135666i
\(826\) 13278.6i 0.559347i
\(827\) 259.872 0.0109270 0.00546350 0.999985i \(-0.498261\pi\)
0.00546350 + 0.999985i \(0.498261\pi\)
\(828\) −10497.0 5632.80i −0.440576 0.236417i
\(829\) −10639.1 −0.445732 −0.222866 0.974849i \(-0.571541\pi\)
−0.222866 + 0.974849i \(0.571541\pi\)
\(830\) 11034.9i 0.461479i
\(831\) 6467.47 12799.5i 0.269981 0.534306i
\(832\) 3664.60 0.152701
\(833\) 15193.6 0.631966
\(834\) 5957.80 + 3010.43i 0.247364 + 0.124991i
\(835\) 7859.80i 0.325748i
\(836\) 4809.36i 0.198965i
\(837\) −40020.3 + 6753.51i −1.65269 + 0.278895i
\(838\) 16698.7i 0.688362i
\(839\) −11414.8 −0.469706 −0.234853 0.972031i \(-0.575461\pi\)
−0.234853 + 0.972031i \(0.575461\pi\)
\(840\) −4451.81 + 8810.34i −0.182859 + 0.361888i
\(841\) 8488.64 0.348052
\(842\) 18395.7 0.752920
\(843\) 2115.54 4186.76i 0.0864332 0.171056i
\(844\) 23943.9 0.976520
\(845\) −11772.5 −0.479272
\(846\) −8152.75 11063.9i −0.331321 0.449627i
\(847\) 26588.8i 1.07863i
\(848\) 7473.35 0.302637
\(849\) 33245.1 + 16798.5i 1.34390 + 0.679062i
\(850\) 1494.07i 0.0602896i
\(851\) 4007.55 + 8441.44i 0.161430 + 0.340034i
\(852\) −6577.73 3323.68i −0.264495 0.133647i
\(853\) −15505.0 −0.622369 −0.311185 0.950349i \(-0.600726\pi\)
−0.311185 + 0.950349i \(0.600726\pi\)
\(854\) 30454.2i 1.22028i
\(855\) −26837.8 + 19776.2i −1.07349 + 0.791032i
\(856\) 7988.69i 0.318981i
\(857\) 12174.6i 0.485270i −0.970118 0.242635i \(-0.921988\pi\)
0.970118 0.242635i \(-0.0780118\pi\)
\(858\) −5628.96 2844.27i −0.223974 0.113172i
\(859\) −389.206 −0.0154593 −0.00772966 0.999970i \(-0.502460\pi\)
−0.00772966 + 0.999970i \(0.502460\pi\)
\(860\) 15911.8i 0.630914i
\(861\) −15315.5 + 30310.1i −0.606215 + 1.19973i
\(862\) 28414.5i 1.12274i
\(863\) 23693.5i 0.934574i −0.884106 0.467287i \(-0.845231\pi\)
0.884106 0.467287i \(-0.154769\pi\)
\(864\) −747.046 4426.89i −0.0294155 0.174312i
\(865\) 29082.3i 1.14316i
\(866\) 6228.88 0.244418
\(867\) 19059.1 37719.0i 0.746577 1.47751i
\(868\) 25246.7i 0.987247i
\(869\) 833.664i 0.0325433i
\(870\) −6432.30 + 12729.8i −0.250662 + 0.496072i
\(871\) 38460.6i 1.49620i
\(872\) 8340.49 0.323904
\(873\) 12031.4 8865.71i 0.466441 0.343710i
\(874\) 22608.2 10733.2i 0.874980 0.415394i
\(875\) 31236.1i 1.20683i
\(876\) 3012.74 5962.36i 0.116200 0.229965i
\(877\) −13683.0 −0.526843 −0.263422 0.964681i \(-0.584851\pi\)
−0.263422 + 0.964681i \(0.584851\pi\)
\(878\) 16539.2i 0.635728i
\(879\) −1410.62 + 2791.68i −0.0541285 + 0.107123i
\(880\) −1845.66 −0.0707014
\(881\) −36403.5 −1.39213 −0.696065 0.717979i \(-0.745067\pi\)
−0.696065 + 0.717979i \(0.745067\pi\)
\(882\) −5782.74 + 4261.17i −0.220765 + 0.162677i
\(883\) 13924.0 0.530669 0.265335 0.964156i \(-0.414518\pi\)
0.265335 + 0.964156i \(0.414518\pi\)
\(884\) −26160.5 −0.995333
\(885\) −15360.2 7761.42i −0.583423 0.294799i
\(886\) 10147.9 0.384793
\(887\) 3666.91i 0.138808i −0.997589 0.0694041i \(-0.977890\pi\)
0.997589 0.0694041i \(-0.0221098\pi\)
\(888\) −1588.18 + 3143.08i −0.0600177 + 0.118778i
\(889\) 9107.59i 0.343598i
\(890\) 24433.0i 0.920221i
\(891\) −2288.43 + 7379.68i −0.0860441 + 0.277473i
\(892\) −13440.2 −0.504496
\(893\) 28871.9 1.08193
\(894\) −645.732 326.284i −0.0241572 0.0122064i
\(895\) 16733.5i 0.624961i
\(896\) 2792.69 0.104126
\(897\) 808.278 32808.7i 0.0300865 1.22124i
\(898\) 7250.44 0.269432
\(899\) 36478.4i 1.35331i
\(900\) −419.024 568.647i −0.0155194 0.0210610i
\(901\) −53350.2 −1.97264
\(902\) −6349.61 −0.234389
\(903\) 18686.8 36982.0i 0.688656 1.36288i
\(904\) 13761.8i 0.506316i
\(905\) 26998.8i 0.991679i
\(906\) 17062.6 + 8621.63i 0.625682 + 0.316153i
\(907\) 20915.3i 0.765691i −0.923812 0.382845i \(-0.874944\pi\)
0.923812 0.382845i \(-0.125056\pi\)
\(908\) −3459.47 −0.126439
\(909\) 13462.4 9920.12i 0.491220 0.361969i
\(910\) −27194.1 −0.990634
\(911\) −18080.6 −0.657561 −0.328781 0.944406i \(-0.606638\pi\)
−0.328781 + 0.944406i \(0.606638\pi\)
\(912\) 8417.91 + 4253.51i 0.305641 + 0.154438i
\(913\) −5372.80 −0.194758
\(914\) 4272.22 0.154609
\(915\) 35228.5 + 17800.7i 1.27281 + 0.643140i
\(916\) 2576.57i 0.0929390i
\(917\) −21697.4 −0.781364
\(918\) 5332.95 + 31602.3i 0.191736 + 1.13620i
\(919\) 21465.5i 0.770491i −0.922814 0.385245i \(-0.874117\pi\)
0.922814 0.385245i \(-0.125883\pi\)
\(920\) −4119.01 8676.22i −0.147608 0.310920i
\(921\) −21313.9 + 42181.2i −0.762559 + 1.50914i
\(922\) −32145.2 −1.14821
\(923\) 20302.9i 0.724029i
\(924\) −4289.68 2167.54i −0.152727 0.0771721i
\(925\) 554.066i 0.0196947i
\(926\) 10838.7i 0.384645i
\(927\) −26795.0 + 19744.7i −0.949368 + 0.699569i
\(928\) 4035.09 0.142735
\(929\) 44128.4i 1.55846i 0.626740 + 0.779229i \(0.284389\pi\)
−0.626740 + 0.779229i \(0.715611\pi\)
\(930\) −29204.6 14756.9i −1.02974 0.520320i
\(931\) 15090.4i 0.531223i
\(932\) 21257.7i 0.747124i
\(933\) 9670.38 + 4886.38i 0.339329 + 0.171461i
\(934\) 23196.8i 0.812656i
\(935\) 13175.7 0.460845
\(936\) 9956.78 7336.94i 0.347700 0.256213i
\(937\) 27758.5i 0.967803i 0.875122 + 0.483902i \(0.160781\pi\)
−0.875122 + 0.483902i \(0.839219\pi\)
\(938\) 29309.8i 1.02026i
\(939\) −34925.5 17647.6i −1.21379 0.613321i
\(940\) 11080.0i 0.384459i
\(941\) −18461.1 −0.639549 −0.319774 0.947494i \(-0.603607\pi\)
−0.319774 + 0.947494i \(0.603607\pi\)
\(942\) −3215.69 + 6364.00i −0.111224 + 0.220117i
\(943\) −14170.6 29848.7i −0.489351 1.03076i
\(944\) 4868.87i 0.167869i
\(945\) 5543.65 + 32850.9i 0.190831 + 1.13083i
\(946\) 7747.29 0.266264
\(947\) 3695.82i 0.126819i −0.997988 0.0634097i \(-0.979803\pi\)
0.997988 0.0634097i \(-0.0201975\pi\)
\(948\) 1459.18 + 737.313i 0.0499915 + 0.0252604i
\(949\) 18403.5 0.629508
\(950\) 1483.92 0.0506787
\(951\) 27002.4 + 13644.1i 0.920728 + 0.465237i
\(952\) −19936.2 −0.678716
\(953\) 10904.7 0.370658 0.185329 0.982677i \(-0.440665\pi\)
0.185329 + 0.982677i \(0.440665\pi\)
\(954\) 20305.2 14962.5i 0.689105 0.507786i
\(955\) 24855.4 0.842202
\(956\) 14073.0i 0.476102i
\(957\) −6198.05 3131.83i −0.209357 0.105787i
\(958\) 10748.7i 0.362500i
\(959\) 28850.3i 0.971454i
\(960\) 1632.35 3230.50i 0.0548790 0.108608i
\(961\) 53897.2 1.80918
\(962\) −9701.47 −0.325143
\(963\) 15994.2 + 21705.4i 0.535210 + 0.726321i
\(964\) 18970.5i 0.633817i
\(965\) 40398.9 1.34765
\(966\) 615.967 25002.6i 0.0205160 0.832759i
\(967\) 34528.8 1.14827 0.574133 0.818762i \(-0.305339\pi\)
0.574133 + 0.818762i \(0.305339\pi\)
\(968\) 9749.36i 0.323715i
\(969\) −60093.1 30364.6i −1.99223 1.00666i
\(970\) 12049.0 0.398835
\(971\) 41579.1 1.37419 0.687094 0.726568i \(-0.258886\pi\)
0.687094 + 0.726568i \(0.258886\pi\)
\(972\) −10892.8 10532.3i −0.359453 0.347554i
\(973\) 14014.1i 0.461738i
\(974\) 13966.8i 0.459473i
\(975\) 877.597 1736.81i 0.0288263 0.0570486i
\(976\) 11166.7i 0.366226i
\(977\) 4631.39 0.151660 0.0758298 0.997121i \(-0.475839\pi\)
0.0758298 + 0.997121i \(0.475839\pi\)
\(978\) 23728.0 + 11989.6i 0.775806 + 0.392009i
\(979\) −11896.2 −0.388360
\(980\) −5791.17 −0.188768
\(981\) 22661.3 16698.6i 0.737531 0.543471i
\(982\) 17118.8 0.556297
\(983\) 11223.2 0.364155 0.182077 0.983284i \(-0.441718\pi\)
0.182077 + 0.983284i \(0.441718\pi\)
\(984\) 5615.75 11113.9i 0.181935 0.360058i
\(985\) 38648.6i 1.25020i
\(986\) −28805.4 −0.930376
\(987\) 13012.4 25752.2i 0.419644 0.830497i
\(988\) 25982.8i 0.836664i
\(989\) 17289.8 + 36419.0i 0.555900 + 1.17094i
\(990\) −5014.69 + 3695.22i −0.160987 + 0.118628i
\(991\) 19975.4 0.640304 0.320152 0.947366i \(-0.396266\pi\)
0.320152 + 0.947366i \(0.396266\pi\)
\(992\) 9257.25i 0.296288i
\(993\) 21138.9 41834.9i 0.675550 1.33695i
\(994\) 15472.3i 0.493714i
\(995\) 5457.33i 0.173878i
\(996\) 4751.83 9404.12i 0.151172 0.299178i
\(997\) 22337.7 0.709571 0.354785 0.934948i \(-0.384554\pi\)
0.354785 + 0.934948i \(0.384554\pi\)
\(998\) 37991.6i 1.20501i
\(999\) 1977.69 + 11719.5i 0.0626340 + 0.371160i
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 138.4.d.a.137.19 yes 24
3.2 odd 2 inner 138.4.d.a.137.8 yes 24
23.22 odd 2 inner 138.4.d.a.137.20 yes 24
69.68 even 2 inner 138.4.d.a.137.7 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.4.d.a.137.7 24 69.68 even 2 inner
138.4.d.a.137.8 yes 24 3.2 odd 2 inner
138.4.d.a.137.19 yes 24 1.1 even 1 trivial
138.4.d.a.137.20 yes 24 23.22 odd 2 inner