Properties

Label 361.2.e.j.99.1
Level $361$
Weight $2$
Character 361.99
Analytic conductor $2.883$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $6$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [361,2,Mod(28,361)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(361, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("361.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 361.e (of order \(9\), degree \(6\), not 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: \(2.88259951297\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.6053445140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 99.1
Root \(1.52045 + 0.553400i\) of defining polynomial
Character \(\chi\) \(=\) 361.99
Dual form 361.2.e.j.62.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.52045 - 0.553400i) q^{2} +(0.0663277 + 0.376163i) q^{3} +(0.473442 + 0.397265i) q^{4} +(2.47897 - 2.08010i) q^{5} +(0.107320 - 0.608645i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(2.68198 - 0.976160i) q^{9} +O(q^{10})\) \(q+(-1.52045 - 0.553400i) q^{2} +(0.0663277 + 0.376163i) q^{3} +(0.473442 + 0.397265i) q^{4} +(2.47897 - 2.08010i) q^{5} +(0.107320 - 0.608645i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(2.68198 - 0.976160i) q^{9} +(-4.92029 + 1.79084i) q^{10} +(0.809017 + 1.40126i) q^{11} +(-0.118034 + 0.204441i) q^{12} +(-0.173648 + 0.984808i) q^{13} +(3.71846 - 3.12016i) q^{14} +(0.946883 + 0.794529i) q^{15} +(-0.842906 - 4.78036i) q^{16} +(-0.717861 - 0.261280i) q^{17} -4.61803 q^{18} +2.00000 q^{20} +(-1.07679 - 0.391920i) q^{21} +(-0.454617 - 2.57826i) q^{22} +(4.12283 + 3.45946i) q^{23} +(-0.654280 + 0.549006i) q^{24} +(0.950226 - 5.38900i) q^{25} +(0.809017 - 1.40126i) q^{26} +(1.11803 + 1.93649i) q^{27} +(-1.74229 + 0.634140i) q^{28} +(3.39984 - 1.23744i) q^{29} +(-1.00000 - 1.73205i) q^{30} +(4.42705 - 7.66788i) q^{31} +(-0.587272 + 3.33059i) q^{32} +(-0.473442 + 0.397265i) q^{33} +(0.946883 + 0.794529i) q^{34} +(1.68581 + 9.56071i) q^{35} +(1.65755 + 0.603300i) q^{36} +8.85410 q^{37} -0.381966 q^{39} +(6.79968 + 2.47488i) q^{40} +(-0.520945 - 2.95442i) q^{41} +(1.42032 + 1.19179i) q^{42} +(-0.111764 + 0.0937814i) q^{43} +(-0.173648 + 0.984808i) q^{44} +(4.61803 - 7.99867i) q^{45} +(-4.35410 - 7.54153i) q^{46} +(-2.81908 + 1.02606i) q^{47} +(1.74229 - 0.634140i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(-4.42705 + 7.66788i) q^{50} +(0.0506699 - 0.287363i) q^{51} +(-0.473442 + 0.397265i) q^{52} +(-4.84618 - 4.06643i) q^{53} +(-0.628265 - 3.56307i) q^{54} +(4.92029 + 1.79084i) q^{55} -6.70820 q^{56} -5.85410 q^{58} +(-0.306563 - 0.111580i) q^{59} +(0.132655 + 0.752326i) q^{60} +(-7.84128 - 6.57962i) q^{61} +(-10.9745 + 9.20873i) q^{62} +(-1.48683 + 8.43223i) q^{63} +(-2.11803 + 3.66854i) q^{64} +(1.61803 + 2.80252i) q^{65} +(0.939693 - 0.342020i) q^{66} +(6.57785 - 2.39414i) q^{67} +(-0.236068 - 0.408882i) q^{68} +(-1.02786 + 1.78031i) q^{69} +(2.72770 - 15.4696i) q^{70} +(-5.72399 + 4.80300i) q^{71} +(4.88887 + 4.10225i) q^{72} +(-0.470275 - 2.66706i) q^{73} +(-13.4623 - 4.89986i) q^{74} +2.09017 q^{75} -4.85410 q^{77} +(0.580762 + 0.211380i) q^{78} +(2.32973 + 13.2126i) q^{79} +(-12.0332 - 10.0970i) q^{80} +(5.90483 - 4.95474i) q^{81} +(-0.842906 + 4.78036i) q^{82} +(-4.23607 + 7.33708i) q^{83} +(-0.354102 - 0.613323i) q^{84} +(-2.32305 + 0.845520i) q^{85} +(0.221831 - 0.0807400i) q^{86} +(0.690983 + 1.19682i) q^{87} +(-1.80902 + 3.13331i) q^{88} +(-1.34819 + 7.64598i) q^{89} +(-11.4480 + 9.60599i) q^{90} +(-2.29813 - 1.92836i) q^{91} +(0.577595 + 3.27570i) q^{92} +(3.17801 + 1.15670i) q^{93} +4.85410 q^{94} -1.29180 q^{96} +(-13.0186 - 4.73838i) q^{97} +(0.561937 + 3.18690i) q^{98} +(3.53762 + 2.96842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 18 q^{7} + 3 q^{11} + 12 q^{12} - 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} + 33 q^{31} + 66 q^{37} - 18 q^{39} + 42 q^{45} - 12 q^{46} - 12 q^{49} - 33 q^{50} - 30 q^{58} - 12 q^{64} + 6 q^{65} + 24 q^{68} - 66 q^{69} - 42 q^{75} - 18 q^{77} - 24 q^{83} + 36 q^{84} + 15 q^{87} - 15 q^{88} + 18 q^{94} - 96 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.52045 0.553400i −1.07512 0.391313i −0.257033 0.966403i \(-0.582745\pi\)
−0.818090 + 0.575090i \(0.804967\pi\)
\(3\) 0.0663277 + 0.376163i 0.0382943 + 0.217178i 0.997950 0.0640004i \(-0.0203859\pi\)
−0.959656 + 0.281178i \(0.909275\pi\)
\(4\) 0.473442 + 0.397265i 0.236721 + 0.198632i
\(5\) 2.47897 2.08010i 1.10863 0.930251i 0.110655 0.993859i \(-0.464705\pi\)
0.997975 + 0.0636079i \(0.0202607\pi\)
\(6\) 0.107320 0.608645i 0.0438134 0.248478i
\(7\) −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i \(0.358542\pi\)
−0.996866 + 0.0791130i \(0.974791\pi\)
\(8\) 1.11803 + 1.93649i 0.395285 + 0.684653i
\(9\) 2.68198 0.976160i 0.893993 0.325387i
\(10\) −4.92029 + 1.79084i −1.55593 + 0.566314i
\(11\) 0.809017 + 1.40126i 0.243928 + 0.422495i 0.961830 0.273649i \(-0.0882307\pi\)
−0.717902 + 0.696144i \(0.754897\pi\)
\(12\) −0.118034 + 0.204441i −0.0340735 + 0.0590170i
\(13\) −0.173648 + 0.984808i −0.0481613 + 0.273137i −0.999373 0.0354021i \(-0.988729\pi\)
0.951212 + 0.308539i \(0.0998399\pi\)
\(14\) 3.71846 3.12016i 0.993800 0.833897i
\(15\) 0.946883 + 0.794529i 0.244484 + 0.205147i
\(16\) −0.842906 4.78036i −0.210726 1.19509i
\(17\) −0.717861 0.261280i −0.174107 0.0633697i 0.253496 0.967336i \(-0.418420\pi\)
−0.427603 + 0.903967i \(0.640642\pi\)
\(18\) −4.61803 −1.08848
\(19\) 0 0
\(20\) 2.00000 0.447214
\(21\) −1.07679 0.391920i −0.234975 0.0855240i
\(22\) −0.454617 2.57826i −0.0969246 0.549687i
\(23\) 4.12283 + 3.45946i 0.859668 + 0.721347i 0.961897 0.273413i \(-0.0881527\pi\)
−0.102228 + 0.994761i \(0.532597\pi\)
\(24\) −0.654280 + 0.549006i −0.133554 + 0.112065i
\(25\) 0.950226 5.38900i 0.190045 1.07780i
\(26\) 0.809017 1.40126i 0.158661 0.274809i
\(27\) 1.11803 + 1.93649i 0.215166 + 0.372678i
\(28\) −1.74229 + 0.634140i −0.329261 + 0.119841i
\(29\) 3.39984 1.23744i 0.631334 0.229787i −0.00647759 0.999979i \(-0.502062\pi\)
0.637812 + 0.770192i \(0.279840\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 4.42705 7.66788i 0.795122 1.37719i −0.127640 0.991821i \(-0.540740\pi\)
0.922762 0.385371i \(-0.125926\pi\)
\(32\) −0.587272 + 3.33059i −0.103816 + 0.588770i
\(33\) −0.473442 + 0.397265i −0.0824156 + 0.0691549i
\(34\) 0.946883 + 0.794529i 0.162389 + 0.136261i
\(35\) 1.68581 + 9.56071i 0.284954 + 1.61606i
\(36\) 1.65755 + 0.603300i 0.276259 + 0.100550i
\(37\) 8.85410 1.45561 0.727803 0.685787i \(-0.240542\pi\)
0.727803 + 0.685787i \(0.240542\pi\)
\(38\) 0 0
\(39\) −0.381966 −0.0611635
\(40\) 6.79968 + 2.47488i 1.07512 + 0.391313i
\(41\) −0.520945 2.95442i −0.0813579 0.461403i −0.998083 0.0618855i \(-0.980289\pi\)
0.916725 0.399518i \(-0.130822\pi\)
\(42\) 1.42032 + 1.19179i 0.219161 + 0.183898i
\(43\) −0.111764 + 0.0937814i −0.0170439 + 0.0143015i −0.651270 0.758846i \(-0.725763\pi\)
0.634226 + 0.773148i \(0.281319\pi\)
\(44\) −0.173648 + 0.984808i −0.0261784 + 0.148465i
\(45\) 4.61803 7.99867i 0.688416 1.19237i
\(46\) −4.35410 7.54153i −0.641977 1.11194i
\(47\) −2.81908 + 1.02606i −0.411205 + 0.149666i −0.539335 0.842091i \(-0.681325\pi\)
0.128131 + 0.991757i \(0.459102\pi\)
\(48\) 1.74229 0.634140i 0.251477 0.0915303i
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) −4.42705 + 7.66788i −0.626080 + 1.08440i
\(51\) 0.0506699 0.287363i 0.00709520 0.0402389i
\(52\) −0.473442 + 0.397265i −0.0656545 + 0.0550907i
\(53\) −4.84618 4.06643i −0.665674 0.558567i 0.246108 0.969243i \(-0.420848\pi\)
−0.911781 + 0.410676i \(0.865293\pi\)
\(54\) −0.628265 3.56307i −0.0854960 0.484872i
\(55\) 4.92029 + 1.79084i 0.663452 + 0.241477i
\(56\) −6.70820 −0.896421
\(57\) 0 0
\(58\) −5.85410 −0.768681
\(59\) −0.306563 0.111580i −0.0399112 0.0145265i 0.321987 0.946744i \(-0.395649\pi\)
−0.361899 + 0.932217i \(0.617871\pi\)
\(60\) 0.132655 + 0.752326i 0.0171257 + 0.0971249i
\(61\) −7.84128 6.57962i −1.00397 0.842434i −0.0164434 0.999865i \(-0.505234\pi\)
−0.987530 + 0.157431i \(0.949679\pi\)
\(62\) −10.9745 + 9.20873i −1.39377 + 1.16951i
\(63\) −1.48683 + 8.43223i −0.187323 + 1.06236i
\(64\) −2.11803 + 3.66854i −0.264754 + 0.458568i
\(65\) 1.61803 + 2.80252i 0.200692 + 0.347609i
\(66\) 0.939693 0.342020i 0.115668 0.0420998i
\(67\) 6.57785 2.39414i 0.803612 0.292491i 0.0926296 0.995701i \(-0.470473\pi\)
0.710982 + 0.703210i \(0.248251\pi\)
\(68\) −0.236068 0.408882i −0.0286274 0.0495842i
\(69\) −1.02786 + 1.78031i −0.123740 + 0.214324i
\(70\) 2.72770 15.4696i 0.326023 1.84897i
\(71\) −5.72399 + 4.80300i −0.679312 + 0.570011i −0.915805 0.401622i \(-0.868446\pi\)
0.236493 + 0.971633i \(0.424002\pi\)
\(72\) 4.88887 + 4.10225i 0.576159 + 0.483455i
\(73\) −0.470275 2.66706i −0.0550415 0.312156i 0.944840 0.327531i \(-0.106217\pi\)
−0.999882 + 0.0153756i \(0.995106\pi\)
\(74\) −13.4623 4.89986i −1.56496 0.569597i
\(75\) 2.09017 0.241352
\(76\) 0 0
\(77\) −4.85410 −0.553176
\(78\) 0.580762 + 0.211380i 0.0657583 + 0.0239341i
\(79\) 2.32973 + 13.2126i 0.262116 + 1.48653i 0.777125 + 0.629347i \(0.216678\pi\)
−0.515009 + 0.857185i \(0.672211\pi\)
\(80\) −12.0332 10.0970i −1.34535 1.12888i
\(81\) 5.90483 4.95474i 0.656092 0.550526i
\(82\) −0.842906 + 4.78036i −0.0930834 + 0.527902i
\(83\) −4.23607 + 7.33708i −0.464969 + 0.805350i −0.999200 0.0399887i \(-0.987268\pi\)
0.534231 + 0.845338i \(0.320601\pi\)
\(84\) −0.354102 0.613323i −0.0386357 0.0669190i
\(85\) −2.32305 + 0.845520i −0.251970 + 0.0917096i
\(86\) 0.221831 0.0807400i 0.0239207 0.00870642i
\(87\) 0.690983 + 1.19682i 0.0740812 + 0.128312i
\(88\) −1.80902 + 3.13331i −0.192842 + 0.334012i
\(89\) −1.34819 + 7.64598i −0.142908 + 0.810472i 0.826115 + 0.563502i \(0.190546\pi\)
−0.969023 + 0.246971i \(0.920565\pi\)
\(90\) −11.4480 + 9.60599i −1.20672 + 1.01256i
\(91\) −2.29813 1.92836i −0.240910 0.202147i
\(92\) 0.577595 + 3.27570i 0.0602185 + 0.341516i
\(93\) 3.17801 + 1.15670i 0.329544 + 0.119944i
\(94\) 4.85410 0.500662
\(95\) 0 0
\(96\) −1.29180 −0.131843
\(97\) −13.0186 4.73838i −1.32184 0.481110i −0.417791 0.908543i \(-0.637196\pi\)
−0.904047 + 0.427433i \(0.859418\pi\)
\(98\) 0.561937 + 3.18690i 0.0567642 + 0.321926i
\(99\) 3.53762 + 2.96842i 0.355544 + 0.298337i
\(100\) 2.59074 2.17389i 0.259074 0.217389i
\(101\) −1.59415 + 9.04087i −0.158624 + 0.899600i 0.796774 + 0.604278i \(0.206538\pi\)
−0.955398 + 0.295323i \(0.904573\pi\)
\(102\) −0.236068 + 0.408882i −0.0233742 + 0.0404853i
\(103\) −7.16312 12.4069i −0.705803 1.22249i −0.966401 0.257039i \(-0.917253\pi\)
0.260598 0.965447i \(-0.416080\pi\)
\(104\) −2.10122 + 0.764780i −0.206041 + 0.0749929i
\(105\) −3.48457 + 1.26828i −0.340059 + 0.123771i
\(106\) 5.11803 + 8.86469i 0.497107 + 0.861015i
\(107\) −8.20820 + 14.2170i −0.793517 + 1.37441i 0.130260 + 0.991480i \(0.458419\pi\)
−0.923777 + 0.382932i \(0.874914\pi\)
\(108\) −0.239976 + 1.36097i −0.0230917 + 0.130959i
\(109\) −2.52166 + 2.11593i −0.241531 + 0.202669i −0.755515 0.655131i \(-0.772613\pi\)
0.513984 + 0.857800i \(0.328169\pi\)
\(110\) −6.49003 5.44578i −0.618800 0.519235i
\(111\) 0.587272 + 3.33059i 0.0557414 + 0.316125i
\(112\) 13.6841 + 4.98060i 1.29303 + 0.470623i
\(113\) 6.76393 0.636297 0.318149 0.948041i \(-0.396939\pi\)
0.318149 + 0.948041i \(0.396939\pi\)
\(114\) 0 0
\(115\) 17.4164 1.62409
\(116\) 2.10122 + 0.764780i 0.195093 + 0.0710081i
\(117\) 0.495610 + 2.81074i 0.0458191 + 0.259853i
\(118\) 0.404367 + 0.339304i 0.0372250 + 0.0312355i
\(119\) 1.75562 1.47314i 0.160937 0.135042i
\(120\) −0.479952 + 2.72194i −0.0438134 + 0.248478i
\(121\) 4.19098 7.25900i 0.380998 0.659909i
\(122\) 8.28115 + 14.3434i 0.749740 + 1.29859i
\(123\) 1.07679 0.391920i 0.0970911 0.0353383i
\(124\) 5.14213 1.87158i 0.461777 0.168073i
\(125\) −0.763932 1.32317i −0.0683282 0.118348i
\(126\) 6.92705 11.9980i 0.617111 1.06887i
\(127\) 1.00090 5.67636i 0.0888152 0.503696i −0.907653 0.419722i \(-0.862128\pi\)
0.996468 0.0839740i \(-0.0267613\pi\)
\(128\) 10.4320 8.75350i 0.922069 0.773708i
\(129\) −0.0426902 0.0358213i −0.00375866 0.00315389i
\(130\) −0.909234 5.15652i −0.0797451 0.452257i
\(131\) −14.1801 5.16114i −1.23892 0.450931i −0.362279 0.932070i \(-0.618001\pi\)
−0.876644 + 0.481139i \(0.840223\pi\)
\(132\) −0.381966 −0.0332459
\(133\) 0 0
\(134\) −11.3262 −0.978438
\(135\) 6.79968 + 2.47488i 0.585223 + 0.213004i
\(136\) −0.296626 1.68225i −0.0254355 0.144252i
\(137\) 5.72399 + 4.80300i 0.489033 + 0.410348i 0.853680 0.520798i \(-0.174366\pi\)
−0.364646 + 0.931146i \(0.618810\pi\)
\(138\) 2.54805 2.13806i 0.216904 0.182004i
\(139\) 2.56971 14.5736i 0.217960 1.23611i −0.657736 0.753249i \(-0.728486\pi\)
0.875696 0.482864i \(-0.160403\pi\)
\(140\) −3.00000 + 5.19615i −0.253546 + 0.439155i
\(141\) −0.572949 0.992377i −0.0482510 0.0835732i
\(142\) 11.3610 4.13508i 0.953398 0.347008i
\(143\) −1.52045 + 0.553400i −0.127147 + 0.0462777i
\(144\) −6.92705 11.9980i −0.577254 0.999834i
\(145\) 5.85410 10.1396i 0.486157 0.842048i
\(146\) −0.760920 + 4.31539i −0.0629742 + 0.357145i
\(147\) 0.585206 0.491046i 0.0482670 0.0405008i
\(148\) 4.19190 + 3.51742i 0.344572 + 0.289130i
\(149\) −0.331639 1.88082i −0.0271689 0.154082i 0.968205 0.250157i \(-0.0804823\pi\)
−0.995374 + 0.0960748i \(0.969371\pi\)
\(150\) −3.17801 1.15670i −0.259483 0.0944442i
\(151\) −21.0902 −1.71629 −0.858147 0.513404i \(-0.828384\pi\)
−0.858147 + 0.513404i \(0.828384\pi\)
\(152\) 0 0
\(153\) −2.18034 −0.176270
\(154\) 7.38044 + 2.68626i 0.594733 + 0.216465i
\(155\) −4.97545 28.2172i −0.399638 2.26646i
\(156\) −0.180839 0.151742i −0.0144787 0.0121490i
\(157\) −13.6770 + 11.4764i −1.09155 + 0.915916i −0.996828 0.0795880i \(-0.974640\pi\)
−0.0947184 + 0.995504i \(0.530195\pi\)
\(158\) 3.76959 21.3784i 0.299892 1.70077i
\(159\) 1.20820 2.09267i 0.0958168 0.165960i
\(160\) 5.47214 + 9.47802i 0.432610 + 0.749303i
\(161\) −15.1722 + 5.52222i −1.19574 + 0.435212i
\(162\) −11.7200 + 4.26572i −0.920808 + 0.335147i
\(163\) −0.881966 1.52761i −0.0690809 0.119652i 0.829416 0.558631i \(-0.188673\pi\)
−0.898497 + 0.438980i \(0.855340\pi\)
\(164\) 0.927051 1.60570i 0.0723905 0.125384i
\(165\) −0.347296 + 1.96962i −0.0270370 + 0.153334i
\(166\) 10.5011 8.81146i 0.815043 0.683902i
\(167\) 15.5017 + 13.0075i 1.19956 + 1.00655i 0.999642 + 0.0267373i \(0.00851176\pi\)
0.199917 + 0.979813i \(0.435933\pi\)
\(168\) −0.444940 2.52338i −0.0343278 0.194683i
\(169\) 11.2763 + 4.10424i 0.867409 + 0.315711i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −0.0901699 −0.00687539
\(173\) 0.443663 + 0.161480i 0.0337310 + 0.0122771i 0.358831 0.933403i \(-0.383176\pi\)
−0.325100 + 0.945680i \(0.605398\pi\)
\(174\) −0.388289 2.20210i −0.0294361 0.166941i
\(175\) 12.5757 + 10.5523i 0.950633 + 0.797676i
\(176\) 6.01659 5.04852i 0.453518 0.380546i
\(177\) 0.0216386 0.122719i 0.00162646 0.00922410i
\(178\) 6.28115 10.8793i 0.470792 0.815436i
\(179\) −6.11803 10.5967i −0.457283 0.792038i 0.541533 0.840680i \(-0.317844\pi\)
−0.998816 + 0.0486416i \(0.984511\pi\)
\(180\) 5.36396 1.95232i 0.399806 0.145517i
\(181\) −11.2763 + 4.10424i −0.838162 + 0.305066i −0.725204 0.688534i \(-0.758255\pi\)
−0.112958 + 0.993600i \(0.536032\pi\)
\(182\) 2.42705 + 4.20378i 0.179905 + 0.311605i
\(183\) 1.95492 3.38601i 0.144511 0.250301i
\(184\) −2.08976 + 11.8516i −0.154059 + 0.873712i
\(185\) 21.9491 18.4175i 1.61373 1.35408i
\(186\) −4.19190 3.51742i −0.307365 0.257910i
\(187\) −0.214641 1.21729i −0.0156961 0.0890170i
\(188\) −1.74229 0.634140i −0.127069 0.0462494i
\(189\) −6.70820 −0.487950
\(190\) 0 0
\(191\) 14.2361 1.03009 0.515043 0.857164i \(-0.327776\pi\)
0.515043 + 0.857164i \(0.327776\pi\)
\(192\) −1.52045 0.553400i −0.109729 0.0399382i
\(193\) 0.877918 + 4.97892i 0.0631939 + 0.358391i 0.999964 + 0.00844596i \(0.00268847\pi\)
−0.936770 + 0.349945i \(0.886200\pi\)
\(194\) 17.1720 + 14.4090i 1.23288 + 1.03451i
\(195\) −0.946883 + 0.794529i −0.0678077 + 0.0568974i
\(196\) 0.214641 1.21729i 0.0153315 0.0869492i
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) −3.73607 6.47106i −0.265511 0.459878i
\(199\) 12.6073 4.58868i 0.893708 0.325283i 0.145979 0.989288i \(-0.453367\pi\)
0.747728 + 0.664005i \(0.231144\pi\)
\(200\) 11.4981 4.18498i 0.813041 0.295923i
\(201\) 1.33688 + 2.31555i 0.0942963 + 0.163326i
\(202\) 7.42705 12.8640i 0.522565 0.905110i
\(203\) −1.88480 + 10.6892i −0.132287 + 0.750235i
\(204\) 0.138148 0.115920i 0.00967232 0.00811604i
\(205\) −7.43692 6.24031i −0.519417 0.435842i
\(206\) 4.02522 + 22.8282i 0.280451 + 1.59051i
\(207\) 14.4343 + 5.25366i 1.00325 + 0.365155i
\(208\) 4.85410 0.336571
\(209\) 0 0
\(210\) 6.00000 0.414039
\(211\) 3.62167 + 1.31818i 0.249326 + 0.0907473i 0.463660 0.886013i \(-0.346536\pi\)
−0.214334 + 0.976760i \(0.568758\pi\)
\(212\) −0.678935 3.85043i −0.0466294 0.264449i
\(213\) −2.18637 1.83458i −0.149808 0.125703i
\(214\) 20.3479 17.0739i 1.39095 1.16715i
\(215\) −0.0819855 + 0.464963i −0.00559137 + 0.0317102i
\(216\) −2.50000 + 4.33013i −0.170103 + 0.294628i
\(217\) 13.2812 + 23.0036i 0.901583 + 1.56159i
\(218\) 5.00503 1.82168i 0.338983 0.123380i
\(219\) 0.972057 0.353800i 0.0656856 0.0239076i
\(220\) 1.61803 + 2.80252i 0.109088 + 0.188946i
\(221\) 0.381966 0.661585i 0.0256938 0.0445030i
\(222\) 0.950226 5.38900i 0.0637750 0.361686i
\(223\) −8.92631 + 7.49007i −0.597750 + 0.501572i −0.890722 0.454549i \(-0.849800\pi\)
0.292971 + 0.956121i \(0.405356\pi\)
\(224\) −7.77221 6.52166i −0.519303 0.435747i
\(225\) −2.71204 15.3808i −0.180803 1.02538i
\(226\) −10.2843 3.74316i −0.684098 0.248991i
\(227\) 16.4164 1.08960 0.544798 0.838568i \(-0.316606\pi\)
0.544798 + 0.838568i \(0.316606\pi\)
\(228\) 0 0
\(229\) −13.6180 −0.899905 −0.449953 0.893052i \(-0.648559\pi\)
−0.449953 + 0.893052i \(0.648559\pi\)
\(230\) −26.4809 9.63824i −1.74610 0.635527i
\(231\) −0.321961 1.82593i −0.0211835 0.120138i
\(232\) 6.19743 + 5.20026i 0.406881 + 0.341414i
\(233\) 3.46855 2.91045i 0.227232 0.190670i −0.522063 0.852907i \(-0.674837\pi\)
0.749294 + 0.662237i \(0.230393\pi\)
\(234\) 0.801913 4.54788i 0.0524227 0.297304i
\(235\) −4.85410 + 8.40755i −0.316647 + 0.548448i
\(236\) −0.100813 0.174613i −0.00656237 0.0113664i
\(237\) −4.81556 + 1.75272i −0.312804 + 0.113851i
\(238\) −3.48457 + 1.26828i −0.225871 + 0.0822104i
\(239\) 0.163119 + 0.282530i 0.0105513 + 0.0182754i 0.871253 0.490834i \(-0.163308\pi\)
−0.860702 + 0.509110i \(0.829975\pi\)
\(240\) 3.00000 5.19615i 0.193649 0.335410i
\(241\) 0.552260 3.13202i 0.0355742 0.201751i −0.961841 0.273610i \(-0.911782\pi\)
0.997415 + 0.0718591i \(0.0228932\pi\)
\(242\) −10.3893 + 8.71768i −0.667851 + 0.560394i
\(243\) 7.39423 + 6.20449i 0.474340 + 0.398018i
\(244\) −1.09854 6.23013i −0.0703268 0.398843i
\(245\) −6.08182 2.21360i −0.388553 0.141422i
\(246\) −1.85410 −0.118213
\(247\) 0 0
\(248\) 19.7984 1.25720
\(249\) −3.04091 1.10680i −0.192710 0.0701406i
\(250\) 0.429282 + 2.43458i 0.0271502 + 0.153976i
\(251\) −19.4274 16.3015i −1.22625 1.02894i −0.998474 0.0552293i \(-0.982411\pi\)
−0.227773 0.973714i \(-0.573145\pi\)
\(252\) −4.05375 + 3.40150i −0.255362 + 0.214274i
\(253\) −1.51216 + 8.57591i −0.0950689 + 0.539163i
\(254\) −4.66312 + 8.07676i −0.292590 + 0.506781i
\(255\) −0.472136 0.817763i −0.0295663 0.0512103i
\(256\) −12.7444 + 4.63858i −0.796525 + 0.289911i
\(257\) −19.1328 + 6.96376i −1.19347 + 0.434388i −0.860941 0.508705i \(-0.830124\pi\)
−0.332529 + 0.943093i \(0.607902\pi\)
\(258\) 0.0450850 + 0.0780895i 0.00280687 + 0.00486164i
\(259\) −13.2812 + 23.0036i −0.825251 + 1.42938i
\(260\) −0.347296 + 1.96962i −0.0215384 + 0.122150i
\(261\) 7.91036 6.63758i 0.489639 0.410856i
\(262\) 18.7041 + 15.6946i 1.15554 + 0.969613i
\(263\) −2.59505 14.7172i −0.160017 0.907504i −0.954054 0.299634i \(-0.903135\pi\)
0.794037 0.607870i \(-0.207976\pi\)
\(264\) −1.29862 0.472660i −0.0799247 0.0290902i
\(265\) −20.4721 −1.25759
\(266\) 0 0
\(267\) −2.96556 −0.181489
\(268\) 4.06533 + 1.47966i 0.248330 + 0.0903847i
\(269\) 5.26610 + 29.8655i 0.321080 + 1.82093i 0.535903 + 0.844280i \(0.319971\pi\)
−0.214823 + 0.976653i \(0.568918\pi\)
\(270\) −8.96900 7.52589i −0.545836 0.458011i
\(271\) 0.877809 0.736569i 0.0533231 0.0447434i −0.615737 0.787952i \(-0.711141\pi\)
0.669060 + 0.743209i \(0.266697\pi\)
\(272\) −0.643923 + 3.65187i −0.0390436 + 0.221427i
\(273\) 0.572949 0.992377i 0.0346765 0.0600614i
\(274\) −6.04508 10.4704i −0.365197 0.632540i
\(275\) 8.32013 3.02828i 0.501723 0.182612i
\(276\) −1.19389 + 0.434540i −0.0718637 + 0.0261562i
\(277\) −5.70820 9.88690i −0.342973 0.594046i 0.642011 0.766696i \(-0.278101\pi\)
−0.984983 + 0.172650i \(0.944767\pi\)
\(278\) −11.9721 + 20.7363i −0.718041 + 1.24368i
\(279\) 4.38818 24.8866i 0.262713 1.48992i
\(280\) −16.6294 + 13.9538i −0.993800 + 0.833897i
\(281\) −22.6033 18.9665i −1.34840 1.13144i −0.979381 0.202024i \(-0.935248\pi\)
−0.369022 0.929421i \(-0.620307\pi\)
\(282\) 0.321961 + 1.82593i 0.0191725 + 0.108733i
\(283\) −24.4644 8.90430i −1.45426 0.529306i −0.510479 0.859890i \(-0.670532\pi\)
−0.943777 + 0.330584i \(0.892754\pi\)
\(284\) −4.61803 −0.274030
\(285\) 0 0
\(286\) 2.61803 0.154808
\(287\) 8.45723 + 3.07818i 0.499215 + 0.181699i
\(288\) 1.67613 + 9.50583i 0.0987672 + 0.560137i
\(289\) −12.5757 10.5523i −0.739747 0.620721i
\(290\) −14.5122 + 12.1771i −0.852183 + 0.715066i
\(291\) 0.918911 5.21140i 0.0538675 0.305498i
\(292\) 0.836881 1.44952i 0.0489748 0.0848268i
\(293\) 5.07295 + 8.78661i 0.296365 + 0.513319i 0.975301 0.220878i \(-0.0708922\pi\)
−0.678937 + 0.734197i \(0.737559\pi\)
\(294\) −1.16152 + 0.422760i −0.0677415 + 0.0246559i
\(295\) −0.992060 + 0.361080i −0.0577600 + 0.0210229i
\(296\) 9.89919 + 17.1459i 0.575379 + 0.996585i
\(297\) −1.80902 + 3.13331i −0.104970 + 0.181813i
\(298\) −0.536602 + 3.04322i −0.0310845 + 0.176289i
\(299\) −4.12283 + 3.45946i −0.238429 + 0.200066i
\(300\) 0.989573 + 0.830351i 0.0571330 + 0.0479403i
\(301\) −0.0760048 0.431045i −0.00438084 0.0248450i
\(302\) 32.0666 + 11.6713i 1.84523 + 0.671608i
\(303\) −3.50658 −0.201448
\(304\) 0 0
\(305\) −33.1246 −1.89671
\(306\) 3.31511 + 1.20660i 0.189512 + 0.0689768i
\(307\) −3.00867 17.0630i −0.171714 0.973838i −0.941869 0.335981i \(-0.890932\pi\)
0.770155 0.637857i \(-0.220179\pi\)
\(308\) −2.29813 1.92836i −0.130948 0.109879i
\(309\) 4.19190 3.51742i 0.238469 0.200099i
\(310\) −8.05045 + 45.6564i −0.457235 + 2.59311i
\(311\) −6.32624 + 10.9574i −0.358728 + 0.621335i −0.987749 0.156053i \(-0.950123\pi\)
0.629021 + 0.777389i \(0.283456\pi\)
\(312\) −0.427051 0.739674i −0.0241770 0.0418758i
\(313\) 10.6432 3.87380i 0.601588 0.218960i −0.0232304 0.999730i \(-0.507395\pi\)
0.624819 + 0.780770i \(0.285173\pi\)
\(314\) 27.1464 9.88046i 1.53196 0.557587i
\(315\) 13.8541 + 23.9960i 0.780590 + 1.35202i
\(316\) −4.14590 + 7.18091i −0.233225 + 0.403958i
\(317\) 3.12567 17.7265i 0.175555 0.995622i −0.761946 0.647640i \(-0.775756\pi\)
0.937501 0.347982i \(-0.113133\pi\)
\(318\) −2.99510 + 2.51319i −0.167957 + 0.140933i
\(319\) 4.48450 + 3.76294i 0.251084 + 0.210684i
\(320\) 2.38040 + 13.4999i 0.133069 + 0.754670i
\(321\) −5.89235 2.14464i −0.328879 0.119702i
\(322\) 26.1246 1.45587
\(323\) 0 0
\(324\) 4.76393 0.264663
\(325\) 5.14213 + 1.87158i 0.285234 + 0.103817i
\(326\) 0.495610 + 2.81074i 0.0274493 + 0.155673i
\(327\) −0.963189 0.808212i −0.0532645 0.0446942i
\(328\) 5.13878 4.31195i 0.283742 0.238088i
\(329\) 1.56283 8.86327i 0.0861618 0.488648i
\(330\) 1.61803 2.80252i 0.0890698 0.154273i
\(331\) −5.47214 9.47802i −0.300776 0.520959i 0.675536 0.737327i \(-0.263912\pi\)
−0.976312 + 0.216368i \(0.930579\pi\)
\(332\) −4.92029 + 1.79084i −0.270036 + 0.0982852i
\(333\) 23.7465 8.64302i 1.30130 0.473635i
\(334\) −16.3713 28.3560i −0.895799 1.55157i
\(335\) 11.3262 19.6176i 0.618818 1.07183i
\(336\) −0.965884 + 5.47780i −0.0526933 + 0.298839i
\(337\) −13.1182 + 11.0075i −0.714595 + 0.599616i −0.925884 0.377807i \(-0.876678\pi\)
0.211290 + 0.977424i \(0.432234\pi\)
\(338\) −14.8738 12.4806i −0.809030 0.678857i
\(339\) 0.448636 + 2.54434i 0.0243666 + 0.138190i
\(340\) −1.43572 0.522560i −0.0778630 0.0283398i
\(341\) 14.3262 0.775809
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) −0.306563 0.111580i −0.0165288 0.00601599i
\(345\) 1.15519 + 6.55141i 0.0621934 + 0.352716i
\(346\) −0.585206 0.491046i −0.0314609 0.0263988i
\(347\) −19.4701 + 16.3374i −1.04521 + 0.877035i −0.992582 0.121579i \(-0.961204\pi\)
−0.0526279 + 0.998614i \(0.516760\pi\)
\(348\) −0.148313 + 0.841126i −0.00795042 + 0.0450891i
\(349\) 10.4894 18.1681i 0.561482 0.972516i −0.435885 0.900002i \(-0.643565\pi\)
0.997367 0.0725137i \(-0.0231021\pi\)
\(350\) −13.2812 23.0036i −0.709907 1.22960i
\(351\) −2.10122 + 0.764780i −0.112155 + 0.0408210i
\(352\) −5.14213 + 1.87158i −0.274076 + 0.0997556i
\(353\) −12.2254 21.1751i −0.650694 1.12703i −0.982955 0.183847i \(-0.941145\pi\)
0.332261 0.943187i \(-0.392188\pi\)
\(354\) −0.100813 + 0.174613i −0.00535815 + 0.00928059i
\(355\) −4.19887 + 23.8130i −0.222853 + 1.26386i
\(356\) −3.67577 + 3.08434i −0.194815 + 0.163469i
\(357\) 0.670586 + 0.562689i 0.0354912 + 0.0297806i
\(358\) 3.43795 + 19.4976i 0.181701 + 1.03048i
\(359\) −6.61021 2.40592i −0.348874 0.126980i 0.161639 0.986850i \(-0.448322\pi\)
−0.510512 + 0.859870i \(0.670544\pi\)
\(360\) 20.6525 1.08848
\(361\) 0 0
\(362\) 19.4164 1.02050
\(363\) 3.00854 + 1.09502i 0.157908 + 0.0574737i
\(364\) −0.321961 1.82593i −0.0168754 0.0957049i
\(365\) −6.71356 5.63335i −0.351404 0.294863i
\(366\) −4.84618 + 4.06643i −0.253314 + 0.212556i
\(367\) −2.76869 + 15.7020i −0.144525 + 0.819640i 0.823223 + 0.567718i \(0.192174\pi\)
−0.967748 + 0.251922i \(0.918937\pi\)
\(368\) 13.0623 22.6246i 0.680920 1.17939i
\(369\) −4.28115 7.41517i −0.222868 0.386019i
\(370\) −43.5648 + 15.8563i −2.26483 + 0.824329i
\(371\) 17.8342 6.49110i 0.925903 0.337001i
\(372\) 1.04508 + 1.81014i 0.0541851 + 0.0938514i
\(373\) 2.73607 4.73901i 0.141668 0.245377i −0.786457 0.617645i \(-0.788087\pi\)
0.928125 + 0.372269i \(0.121420\pi\)
\(374\) −0.347296 + 1.96962i −0.0179583 + 0.101846i
\(375\) 0.447058 0.375126i 0.0230860 0.0193714i
\(376\) −5.13878 4.31195i −0.265012 0.222372i
\(377\) 0.628265 + 3.56307i 0.0323573 + 0.183507i
\(378\) 10.1995 + 3.71232i 0.524607 + 0.190941i
\(379\) −15.1246 −0.776899 −0.388450 0.921470i \(-0.626989\pi\)
−0.388450 + 0.921470i \(0.626989\pi\)
\(380\) 0 0
\(381\) 2.20163 0.112793
\(382\) −21.6453 7.87824i −1.10747 0.403086i
\(383\) 0.0663277 + 0.376163i 0.00338919 + 0.0192210i 0.986455 0.164029i \(-0.0524492\pi\)
−0.983066 + 0.183250i \(0.941338\pi\)
\(384\) 3.98468 + 3.34354i 0.203342 + 0.170624i
\(385\) −12.0332 + 10.0970i −0.613268 + 0.514593i
\(386\) 1.42050 8.05606i 0.0723016 0.410043i
\(387\) −0.208204 + 0.360620i −0.0105836 + 0.0183313i
\(388\) −4.28115 7.41517i −0.217343 0.376448i
\(389\) −8.71143 + 3.17070i −0.441687 + 0.160761i −0.553284 0.832993i \(-0.686626\pi\)
0.111597 + 0.993754i \(0.464403\pi\)
\(390\) 1.87939 0.684040i 0.0951664 0.0346377i
\(391\) −2.05573 3.56063i −0.103963 0.180069i
\(392\) 2.23607 3.87298i 0.112938 0.195615i
\(393\) 1.00090 5.67636i 0.0504885 0.286335i
\(394\) 3.71846 3.12016i 0.187333 0.157191i
\(395\) 33.2589 + 27.9075i 1.67344 + 1.40418i
\(396\) 0.495610 + 2.81074i 0.0249053 + 0.141245i
\(397\) 10.7803 + 3.92370i 0.541047 + 0.196925i 0.598064 0.801448i \(-0.295937\pi\)
−0.0570173 + 0.998373i \(0.518159\pi\)
\(398\) −21.7082 −1.08813
\(399\) 0 0
\(400\) −26.5623 −1.32812
\(401\) 33.7242 + 12.2746i 1.68411 + 0.612965i 0.993864 0.110613i \(-0.0352815\pi\)
0.690243 + 0.723578i \(0.257504\pi\)
\(402\) −0.751243 4.26051i −0.0374686 0.212495i
\(403\) 6.78264 + 5.69131i 0.337867 + 0.283504i
\(404\) −4.34635 + 3.64702i −0.216239 + 0.181446i
\(405\) 4.33153 24.5653i 0.215235 1.22066i
\(406\) 8.78115 15.2094i 0.435801 0.754830i
\(407\) 7.16312 + 12.4069i 0.355063 + 0.614987i
\(408\) 0.613127 0.223160i 0.0303543 0.0110481i
\(409\) 7.79174 2.83596i 0.385277 0.140229i −0.142118 0.989850i \(-0.545391\pi\)
0.527395 + 0.849620i \(0.323169\pi\)
\(410\) 7.85410 + 13.6037i 0.387886 + 0.671839i
\(411\) −1.42705 + 2.47172i −0.0703912 + 0.121921i
\(412\) 1.53750 8.71959i 0.0757471 0.429583i
\(413\) 0.749738 0.629105i 0.0368922 0.0309562i
\(414\) −19.0393 15.9759i −0.935733 0.785173i
\(415\) 4.76081 + 26.9999i 0.233699 + 1.32537i
\(416\) −3.17801 1.15670i −0.155815 0.0567119i
\(417\) 5.65248 0.276803
\(418\) 0 0
\(419\) −8.94427 −0.436956 −0.218478 0.975842i \(-0.570109\pi\)
−0.218478 + 0.975842i \(0.570109\pi\)
\(420\) −2.15358 0.783840i −0.105084 0.0382475i
\(421\) −4.77049 27.0548i −0.232499 1.31857i −0.847817 0.530289i \(-0.822083\pi\)
0.615317 0.788279i \(-0.289028\pi\)
\(422\) −4.77711 4.00847i −0.232546 0.195129i
\(423\) −6.55911 + 5.50374i −0.318915 + 0.267601i
\(424\) 2.45641 13.9310i 0.119294 0.676549i
\(425\) −2.09017 + 3.62028i −0.101388 + 0.175609i
\(426\) 2.30902 + 3.99933i 0.111872 + 0.193768i
\(427\) 28.8563 10.5028i 1.39645 0.508267i
\(428\) −9.53403 + 3.47010i −0.460845 + 0.167734i
\(429\) −0.309017 0.535233i −0.0149195 0.0258413i
\(430\) 0.381966 0.661585i 0.0184200 0.0319044i
\(431\) 4.80180 27.2324i 0.231295 1.31174i −0.618984 0.785404i \(-0.712455\pi\)
0.850278 0.526333i \(-0.176434\pi\)
\(432\) 8.31472 6.97688i 0.400042 0.335675i
\(433\) −2.63343 2.20971i −0.126554 0.106192i 0.577314 0.816522i \(-0.304101\pi\)
−0.703868 + 0.710331i \(0.748545\pi\)
\(434\) −7.46318 42.3258i −0.358244 2.03170i
\(435\) 4.20243 + 1.52956i 0.201491 + 0.0733368i
\(436\) −2.03444 −0.0974321
\(437\) 0 0
\(438\) −1.67376 −0.0799754
\(439\) 32.5103 + 11.8328i 1.55163 + 0.564748i 0.968800 0.247844i \(-0.0797221\pi\)
0.582832 + 0.812592i \(0.301944\pi\)
\(440\) 2.03311 + 11.5303i 0.0969246 + 0.549687i
\(441\) −4.37274 3.66916i −0.208226 0.174722i
\(442\) −0.946883 + 0.794529i −0.0450386 + 0.0377919i
\(443\) −1.31688 + 7.46838i −0.0625667 + 0.354833i 0.937411 + 0.348224i \(0.113215\pi\)
−0.999978 + 0.00660970i \(0.997896\pi\)
\(444\) −1.04508 + 1.81014i −0.0495975 + 0.0859055i
\(445\) 12.5623 + 21.7586i 0.595510 + 1.03145i
\(446\) 17.7171 6.44848i 0.838927 0.305345i
\(447\) 0.685497 0.249500i 0.0324229 0.0118010i
\(448\) −6.35410 11.0056i −0.300203 0.519967i
\(449\) −1.44427 + 2.50155i −0.0681594 + 0.118056i −0.898091 0.439809i \(-0.855046\pi\)
0.829932 + 0.557865i \(0.188379\pi\)
\(450\) −4.38818 + 24.8866i −0.206861 + 1.17317i
\(451\) 3.71846 3.12016i 0.175095 0.146922i
\(452\) 3.20233 + 2.68707i 0.150625 + 0.126389i
\(453\) −1.39886 7.93334i −0.0657243 0.372741i
\(454\) −24.9604 9.08484i −1.17145 0.426373i
\(455\) −9.70820 −0.455128
\(456\) 0 0
\(457\) 19.7082 0.921911 0.460955 0.887423i \(-0.347507\pi\)
0.460955 + 0.887423i \(0.347507\pi\)
\(458\) 20.7056 + 7.53622i 0.967509 + 0.352145i
\(459\) −0.296626 1.68225i −0.0138453 0.0785208i
\(460\) 8.24565 + 6.91892i 0.384455 + 0.322596i
\(461\) 16.0442 13.4627i 0.747255 0.627021i −0.187520 0.982261i \(-0.560045\pi\)
0.934775 + 0.355239i \(0.115601\pi\)
\(462\) −0.520945 + 2.95442i −0.0242365 + 0.137452i
\(463\) −14.1353 + 24.4830i −0.656921 + 1.13782i 0.324487 + 0.945890i \(0.394808\pi\)
−0.981409 + 0.191931i \(0.938525\pi\)
\(464\) −8.78115 15.2094i −0.407655 0.706079i
\(465\) 10.2843 3.74316i 0.476921 0.173585i
\(466\) −6.88441 + 2.50572i −0.318914 + 0.116075i
\(467\) 7.97214 + 13.8081i 0.368906 + 0.638965i 0.989395 0.145251i \(-0.0463989\pi\)
−0.620488 + 0.784216i \(0.713066\pi\)
\(468\) −0.881966 + 1.52761i −0.0407689 + 0.0706138i
\(469\) −3.64661 + 20.6810i −0.168385 + 0.954958i
\(470\) 12.0332 10.0970i 0.555049 0.465742i
\(471\) −5.22416 4.38359i −0.240717 0.201985i
\(472\) −0.126675 0.718408i −0.00583067 0.0330674i
\(473\) −0.221831 0.0807400i −0.0101998 0.00371243i
\(474\) 8.29180 0.380855
\(475\) 0 0
\(476\) 1.41641 0.0649209
\(477\) −16.9668 6.17542i −0.776858 0.282753i
\(478\) −0.0916626 0.519845i −0.00419255 0.0237771i
\(479\) 17.6881 + 14.8421i 0.808190 + 0.678152i 0.950175 0.311717i \(-0.100904\pi\)
−0.141985 + 0.989869i \(0.545349\pi\)
\(480\) −3.20233 + 2.68707i −0.146166 + 0.122647i
\(481\) −1.53750 + 8.71959i −0.0701039 + 0.397579i
\(482\) −2.57295 + 4.45648i −0.117195 + 0.202987i
\(483\) −3.08359 5.34094i −0.140308 0.243021i
\(484\) 4.86793 1.77178i 0.221269 0.0805355i
\(485\) −42.1291 + 15.3337i −1.91298 + 0.696269i
\(486\) −7.80902 13.5256i −0.354224 0.613534i
\(487\) −2.09017 + 3.62028i −0.0947146 + 0.164051i −0.909489 0.415727i \(-0.863527\pi\)
0.814775 + 0.579778i \(0.196861\pi\)
\(488\) 3.97455 22.5408i 0.179920 1.02037i
\(489\) 0.516132 0.433086i 0.0233403 0.0195848i
\(490\) 8.02212 + 6.73136i 0.362403 + 0.304092i
\(491\) −3.68391 20.8925i −0.166252 0.942864i −0.947764 0.318973i \(-0.896662\pi\)
0.781511 0.623891i \(-0.214449\pi\)
\(492\) 0.665494 + 0.242220i 0.0300028 + 0.0109201i
\(493\) −2.76393 −0.124481
\(494\) 0 0
\(495\) 14.9443 0.671695
\(496\) −40.3868 14.6996i −1.81342 0.660031i
\(497\) −3.89257 22.0759i −0.174606 0.990237i
\(498\) 4.01106 + 3.36568i 0.179740 + 0.150820i
\(499\) 19.2466 16.1498i 0.861595 0.722964i −0.100716 0.994915i \(-0.532113\pi\)
0.962311 + 0.271951i \(0.0876690\pi\)
\(500\) 0.163971 0.929926i 0.00733301 0.0415876i
\(501\) −3.86475 + 6.69393i −0.172664 + 0.299063i
\(502\) 20.5172 + 35.5369i 0.915728 + 1.58609i
\(503\) −33.6718 + 12.2555i −1.50135 + 0.546448i −0.956410 0.292026i \(-0.905671\pi\)
−0.544942 + 0.838474i \(0.683448\pi\)
\(504\) −17.9913 + 6.54828i −0.801394 + 0.291684i
\(505\) 14.8541 + 25.7281i 0.660999 + 1.14488i
\(506\) 7.04508 12.2024i 0.313192 0.542465i
\(507\) −0.795932 + 4.51396i −0.0353486 + 0.200472i
\(508\) 2.72888 2.28981i 0.121075 0.101594i
\(509\) 1.55847 + 1.30771i 0.0690781 + 0.0579634i 0.676673 0.736284i \(-0.263421\pi\)
−0.607595 + 0.794247i \(0.707866\pi\)
\(510\) 0.265311 + 1.50465i 0.0117482 + 0.0666271i
\(511\) 7.63464 + 2.77878i 0.337736 + 0.122926i
\(512\) −5.29180 −0.233867
\(513\) 0 0
\(514\) 32.9443 1.45311
\(515\) −43.5648 15.8563i −1.91969 0.698711i
\(516\) −0.00598077 0.0339186i −0.000263289 0.00149318i
\(517\) −3.71846 3.12016i −0.163538 0.137224i
\(518\) 32.9236 27.6262i 1.44658 1.21382i
\(519\) −0.0313157 + 0.177600i −0.00137461 + 0.00779578i
\(520\) −3.61803 + 6.26662i −0.158661 + 0.274809i
\(521\) −3.13525 5.43042i −0.137358 0.237911i 0.789138 0.614216i \(-0.210528\pi\)
−0.926496 + 0.376305i \(0.877194\pi\)
\(522\) −15.7006 + 5.71454i −0.687196 + 0.250119i
\(523\) 4.15007 1.51050i 0.181470 0.0660496i −0.249687 0.968327i \(-0.580328\pi\)
0.431157 + 0.902277i \(0.358106\pi\)
\(524\) −4.66312 8.07676i −0.203709 0.352835i
\(525\) −3.13525 + 5.43042i −0.136834 + 0.237003i
\(526\) −4.19887 + 23.8130i −0.183080 + 1.03830i
\(527\) −5.18147 + 4.34777i −0.225708 + 0.189392i
\(528\) 2.29813 + 1.92836i 0.100013 + 0.0839212i
\(529\) 1.03591 + 5.87493i 0.0450395 + 0.255432i
\(530\) 31.1270 + 11.3293i 1.35207 + 0.492113i
\(531\) −0.931116 −0.0404070
\(532\) 0 0
\(533\) 3.00000 0.129944
\(534\) 4.50900 + 1.64114i 0.195123 + 0.0710191i
\(535\) 9.22499 + 52.3175i 0.398831 + 2.26188i
\(536\) 11.9905 + 10.0612i 0.517910 + 0.434578i
\(537\) 3.58031 3.00424i 0.154502 0.129642i
\(538\) 8.52072 48.3234i 0.367354 2.08337i
\(539\) 1.61803 2.80252i 0.0696937 0.120713i
\(540\) 2.23607 + 3.87298i 0.0962250 + 0.166667i
\(541\) 28.0337 10.2034i 1.20526 0.438679i 0.340204 0.940352i \(-0.389504\pi\)
0.865058 + 0.501672i \(0.167282\pi\)
\(542\) −1.74229 + 0.634140i −0.0748376 + 0.0272387i
\(543\) −2.29180 3.96951i −0.0983504 0.170348i
\(544\) 1.29180 2.23746i 0.0553853 0.0959302i
\(545\) −1.84978 + 10.4906i −0.0792360 + 0.449370i
\(546\) −1.42032 + 1.19179i −0.0607843 + 0.0510041i
\(547\) −20.6242 17.3058i −0.881827 0.739941i 0.0847267 0.996404i \(-0.472998\pi\)
−0.966554 + 0.256463i \(0.917443\pi\)
\(548\) 0.801913 + 4.54788i 0.0342560 + 0.194276i
\(549\) −27.4529 9.99204i −1.17166 0.426450i
\(550\) −14.3262 −0.610873
\(551\) 0 0
\(552\) −4.59675 −0.195651
\(553\) −37.8219 13.7660i −1.60835 0.585392i
\(554\) 3.20765 + 18.1915i 0.136280 + 0.772883i
\(555\) 8.38380 + 7.03484i 0.355872 + 0.298612i
\(556\) 7.00616 5.87887i 0.297128 0.249320i
\(557\) −0.142332 + 0.807208i −0.00603082 + 0.0342025i −0.987675 0.156521i \(-0.949972\pi\)
0.981644 + 0.190723i \(0.0610833\pi\)
\(558\) −20.4443 + 35.4105i −0.865475 + 1.49905i
\(559\) −0.0729490 0.126351i −0.00308541 0.00534409i
\(560\) 44.2826 16.1176i 1.87128 0.681091i
\(561\) 0.443663 0.161480i 0.0187315 0.00681769i
\(562\) 23.8713 + 41.3463i 1.00695 + 1.74409i
\(563\) 16.4164 28.4341i 0.691869 1.19835i −0.279356 0.960188i \(-0.590121\pi\)
0.971225 0.238165i \(-0.0765458\pi\)
\(564\) 0.122978 0.697445i 0.00517832 0.0293677i
\(565\) 16.7676 14.0697i 0.705418 0.591916i
\(566\) 32.2693 + 27.0772i 1.35638 + 1.13814i
\(567\) 4.01555 + 22.7733i 0.168637 + 0.956389i
\(568\) −15.7006 5.71454i −0.658782 0.239777i
\(569\) 16.9098 0.708897 0.354448 0.935076i \(-0.384669\pi\)
0.354448 + 0.935076i \(0.384669\pi\)
\(570\) 0 0
\(571\) 6.67376 0.279288 0.139644 0.990202i \(-0.455404\pi\)
0.139644 + 0.990202i \(0.455404\pi\)
\(572\) −0.939693 0.342020i −0.0392905 0.0143006i
\(573\) 0.944246 + 5.35508i 0.0394464 + 0.223712i
\(574\) −11.1554 9.36047i −0.465616 0.390698i
\(575\) 22.5607 18.9306i 0.940845 0.789462i
\(576\) −2.09944 + 11.9065i −0.0874765 + 0.496104i
\(577\) 6.06231 10.5002i 0.252377 0.437130i −0.711803 0.702379i \(-0.752121\pi\)
0.964180 + 0.265250i \(0.0854543\pi\)
\(578\) 13.2812 + 23.0036i 0.552423 + 0.956825i
\(579\) −1.81466 + 0.660481i −0.0754145 + 0.0274486i
\(580\) 6.79968 2.47488i 0.282341 0.102764i
\(581\) −12.7082 22.0113i −0.527225 0.913181i
\(582\) −4.28115 + 7.41517i −0.177459 + 0.307369i
\(583\) 1.77747 10.0806i 0.0736155 0.417494i
\(584\) 4.63896 3.89255i 0.191961 0.161075i
\(585\) 7.07524 + 5.93683i 0.292525 + 0.245458i
\(586\) −2.85068 16.1670i −0.117760 0.667853i
\(587\) 1.99648 + 0.726660i 0.0824036 + 0.0299925i 0.382893 0.923793i \(-0.374928\pi\)
−0.300489 + 0.953785i \(0.597150\pi\)
\(588\) 0.472136 0.0194706
\(589\) 0 0
\(590\) 1.70820 0.0703256
\(591\) −1.07679 0.391920i −0.0442933 0.0161214i
\(592\) −7.46318 42.3258i −0.306735 1.73958i
\(593\) 0.542516 + 0.455225i 0.0222784 + 0.0186938i 0.653859 0.756617i \(-0.273149\pi\)
−0.631580 + 0.775310i \(0.717593\pi\)
\(594\) 4.48450 3.76294i 0.184001 0.154395i
\(595\) 1.28785 7.30374i 0.0527965 0.299424i
\(596\) 0.590170 1.02220i 0.0241743 0.0418711i
\(597\) 2.56231 + 4.43804i 0.104868 + 0.181637i
\(598\) 8.18303 2.97838i 0.334629 0.121795i
\(599\) −26.7027 + 9.71898i −1.09104 + 0.397107i −0.824007 0.566580i \(-0.808266\pi\)
−0.267035 + 0.963687i \(0.586044\pi\)
\(600\) 2.33688 + 4.04760i 0.0954028 + 0.165242i
\(601\) −10.1459 + 17.5732i −0.413860 + 0.716826i −0.995308 0.0967572i \(-0.969153\pi\)
0.581448 + 0.813583i \(0.302486\pi\)
\(602\) −0.122978 + 0.697445i −0.00501222 + 0.0284257i
\(603\) 15.3046 12.8421i 0.623251 0.522970i
\(604\) −9.98496 8.37838i −0.406282 0.340911i
\(605\) −4.71014 26.7125i −0.191494 1.08602i
\(606\) 5.33159 + 1.94054i 0.216581 + 0.0788291i
\(607\) −6.27051 −0.254512 −0.127256 0.991870i \(-0.540617\pi\)
−0.127256 + 0.991870i \(0.540617\pi\)
\(608\) 0 0
\(609\) −4.14590 −0.168000
\(610\) 50.3645 + 18.3312i 2.03920 + 0.742207i
\(611\) −0.520945 2.95442i −0.0210752 0.119523i
\(612\) −1.03226 0.866172i −0.0417268 0.0350129i
\(613\) −15.2782 + 12.8199i −0.617081 + 0.517792i −0.896884 0.442265i \(-0.854175\pi\)
0.279804 + 0.960057i \(0.409731\pi\)
\(614\) −4.86813 + 27.6085i −0.196462 + 1.11419i
\(615\) 1.85410 3.21140i 0.0747646 0.129496i
\(616\) −5.42705 9.39993i −0.218662 0.378734i
\(617\) −7.21098 + 2.62458i −0.290303 + 0.105662i −0.483067 0.875584i \(-0.660477\pi\)
0.192764 + 0.981245i \(0.438255\pi\)
\(618\) −8.32013 + 3.02828i −0.334685 + 0.121815i
\(619\) −5.06231 8.76817i −0.203471 0.352423i 0.746173 0.665752i \(-0.231889\pi\)
−0.949645 + 0.313329i \(0.898556\pi\)
\(620\) 8.85410 15.3358i 0.355589 0.615899i
\(621\) −2.08976 + 11.8516i −0.0838591 + 0.475589i
\(622\) 15.6826 13.1592i 0.628814 0.527637i
\(623\) −17.8426 14.9717i −0.714847 0.599828i
\(624\) 0.321961 + 1.82593i 0.0128888 + 0.0730959i
\(625\) 21.0645 + 7.66686i 0.842581 + 0.306675i
\(626\) −18.3262 −0.732464
\(627\) 0 0
\(628\) −11.0344 −0.440322
\(629\) −6.35602 2.31340i −0.253431 0.0922413i
\(630\) −7.78514 44.1517i −0.310167 1.75905i
\(631\) 22.4916 + 18.8727i 0.895376 + 0.751310i 0.969281 0.245956i \(-0.0791018\pi\)
−0.0739052 + 0.997265i \(0.523546\pi\)
\(632\) −22.9813 + 19.2836i −0.914148 + 0.767062i
\(633\) −0.255634 + 1.44977i −0.0101605 + 0.0576232i
\(634\) −14.5623 + 25.2227i −0.578343 + 1.00172i
\(635\) −9.32624 16.1535i −0.370100 0.641033i
\(636\) 1.40336 0.510780i 0.0556468 0.0202538i
\(637\) 1.87939 0.684040i 0.0744640 0.0271027i
\(638\) −4.73607 8.20311i −0.187503 0.324764i
\(639\) −10.6631 + 18.4691i −0.421826 + 0.730625i
\(640\) 7.65248 43.3994i 0.302491 1.71551i
\(641\) −30.2638 + 25.3943i −1.19535 + 1.00302i −0.195597 + 0.980684i \(0.562665\pi\)
−0.999751 + 0.0223318i \(0.992891\pi\)
\(642\) 7.77221 + 6.52166i 0.306745 + 0.257389i
\(643\) −4.21823 23.9227i −0.166351 0.943421i −0.947661 0.319278i \(-0.896559\pi\)
0.781310 0.624143i \(-0.214552\pi\)
\(644\) −9.37692 3.41292i −0.369503 0.134488i
\(645\) −0.180340 −0.00710088
\(646\) 0 0
\(647\) 7.47214 0.293760 0.146880 0.989154i \(-0.453077\pi\)
0.146880 + 0.989154i \(0.453077\pi\)
\(648\) 16.1966 + 5.89508i 0.636263 + 0.231581i
\(649\) −0.0916626 0.519845i −0.00359807 0.0204057i
\(650\) −6.78264 5.69131i −0.266037 0.223231i
\(651\) −7.77221 + 6.52166i −0.304617 + 0.255604i
\(652\) 0.189306 1.07361i 0.00741380 0.0420457i
\(653\) 11.7812 20.4056i 0.461032 0.798531i −0.537981 0.842957i \(-0.680813\pi\)
0.999013 + 0.0444262i \(0.0141459\pi\)
\(654\) 1.01722 + 1.76188i 0.0397765 + 0.0688949i
\(655\) −45.8878 + 16.7018i −1.79299 + 0.652594i
\(656\) −13.6841 + 4.98060i −0.534274 + 0.194460i
\(657\) −3.86475 6.69393i −0.150778 0.261155i
\(658\) −7.28115 + 12.6113i −0.283849 + 0.491641i
\(659\) −4.47614 + 25.3855i −0.174366 + 0.988878i 0.764507 + 0.644615i \(0.222982\pi\)
−0.938873 + 0.344263i \(0.888129\pi\)
\(660\) −0.946883 + 0.794529i −0.0368574 + 0.0309270i
\(661\) 4.14921 + 3.48160i 0.161386 + 0.135419i 0.719904 0.694073i \(-0.244186\pi\)
−0.558519 + 0.829492i \(0.688630\pi\)
\(662\) 3.07500 + 17.4392i 0.119513 + 0.677793i
\(663\) 0.274199 + 0.0998001i 0.0106490 + 0.00387592i
\(664\) −18.9443 −0.735180
\(665\) 0 0
\(666\) −40.8885 −1.58440
\(667\) 18.2978 + 6.65986i 0.708495 + 0.257871i
\(668\) 2.17174 + 12.3166i 0.0840273 + 0.476543i
\(669\) −3.40955 2.86095i −0.131821 0.110611i
\(670\) −28.0774 + 23.5598i −1.08473 + 0.910193i
\(671\) 2.87601 16.3107i 0.111027 0.629667i
\(672\) 1.93769 3.35618i 0.0747482 0.129468i
\(673\) −17.0623 29.5528i −0.657704 1.13918i −0.981209 0.192950i \(-0.938195\pi\)
0.323505 0.946226i \(-0.395139\pi\)
\(674\) 26.0372 9.47676i 1.00292 0.365031i
\(675\) 11.4981 4.18498i 0.442564 0.161080i
\(676\) 3.70820 + 6.42280i 0.142623 + 0.247031i
\(677\) 15.3713 26.6239i 0.590768 1.02324i −0.403361 0.915041i \(-0.632158\pi\)
0.994129 0.108199i \(-0.0345085\pi\)
\(678\) 0.725908 4.11683i 0.0278783 0.158106i
\(679\) 31.8386 26.7157i 1.22185 1.02526i
\(680\) −4.23459 3.55324i −0.162389 0.136261i
\(681\) 1.08886 + 6.17525i 0.0417253 + 0.236636i
\(682\) −21.7824 7.92814i −0.834091 0.303584i
\(683\) 9.65248 0.369342 0.184671 0.982800i \(-0.440878\pi\)
0.184671 + 0.982800i \(0.440878\pi\)
\(684\) 0 0
\(685\) 24.1803 0.923883
\(686\) 22.8068 + 8.30100i 0.870768 + 0.316934i
\(687\) −0.903253 5.12260i −0.0344612 0.195439i
\(688\) 0.542516 + 0.455225i 0.0206832 + 0.0173553i
\(689\) 4.84618 4.06643i 0.184625 0.154919i
\(690\) 1.86914 10.6004i 0.0711568 0.403550i
\(691\) 19.5902 33.9312i 0.745245 1.29080i −0.204835 0.978797i \(-0.565666\pi\)
0.950080 0.312006i \(-0.101001\pi\)
\(692\) 0.145898 + 0.252703i 0.00554621 + 0.00960632i
\(693\) −13.0186 + 4.73838i −0.494536 + 0.179996i
\(694\) 38.6445 14.0654i 1.46692 0.533917i
\(695\) −23.9443 41.4727i −0.908258 1.57315i
\(696\) −1.54508 + 2.67617i −0.0585663 + 0.101440i
\(697\) −0.397966 + 2.25698i −0.0150740 + 0.0854892i
\(698\) −26.0028 + 21.8190i −0.984221 + 0.825860i
\(699\) 1.32487 + 1.11169i 0.0501110 + 0.0420482i
\(700\) 1.76182 + 9.99176i 0.0665904 + 0.377653i
\(701\) 37.2411 + 13.5547i 1.40658 + 0.511953i 0.930124 0.367246i \(-0.119699\pi\)
0.476455 + 0.879199i \(0.341922\pi\)
\(702\) 3.61803 0.136554
\(703\) 0 0
\(704\) −6.85410 −0.258324
\(705\) −3.48457 1.26828i −0.131237 0.0477662i
\(706\) 6.86992 + 38.9613i 0.258553 + 1.46633i
\(707\) −21.0976 17.7030i −0.793459 0.665791i
\(708\) 0.0589964 0.0495039i 0.00221722 0.00186047i
\(709\) 2.87971 16.3317i 0.108150 0.613348i −0.881766 0.471688i \(-0.843645\pi\)
0.989915 0.141660i \(-0.0452440\pi\)
\(710\) 19.5623 33.8829i 0.734160 1.27160i
\(711\) 19.1459 + 33.1617i 0.718027 + 1.24366i
\(712\) −16.3137 + 5.93770i −0.611382 + 0.222525i
\(713\) 44.7787 16.2981i 1.67697 0.610369i
\(714\) −0.708204 1.22665i −0.0265039 0.0459060i
\(715\) −2.61803 + 4.53457i −0.0979089 + 0.169583i
\(716\) 1.31318 7.44742i 0.0490759 0.278323i
\(717\) −0.0954582 + 0.0800989i −0.00356495 + 0.00299135i
\(718\) 8.71909 + 7.31619i 0.325394 + 0.273038i
\(719\) 8.16745 + 46.3199i 0.304594 + 1.72744i 0.625408 + 0.780298i \(0.284933\pi\)
−0.320814 + 0.947142i \(0.603956\pi\)
\(720\) −42.1291 15.3337i −1.57006 0.571454i
\(721\) 42.9787 1.60061
\(722\) 0 0
\(723\) 1.21478 0.0451782
\(724\) −6.96914 2.53656i −0.259006 0.0942705i
\(725\) −3.43795 19.4976i −0.127682 0.724122i
\(726\) −3.96837 3.32986i −0.147280 0.123583i
\(727\) −12.3095 + 10.3289i −0.456533 + 0.383077i −0.841854 0.539706i \(-0.818535\pi\)
0.385320 + 0.922783i \(0.374091\pi\)
\(728\) 1.16487 6.60629i 0.0431729 0.244845i
\(729\) 9.71885 16.8335i 0.359957 0.623464i
\(730\) 7.09017 + 12.2805i 0.262419 + 0.454523i
\(731\) 0.104735 0.0381203i 0.00387375 0.00140993i
\(732\) 2.27068 0.826460i 0.0839268 0.0305468i
\(733\) 26.4787 + 45.8625i 0.978014 + 1.69397i 0.669609 + 0.742714i \(0.266462\pi\)
0.308405 + 0.951255i \(0.400205\pi\)
\(734\) 12.8992 22.3420i 0.476118 0.824660i
\(735\) 0.429282 2.43458i 0.0158343 0.0898008i
\(736\) −13.9433 + 11.6998i −0.513955 + 0.431260i
\(737\) 8.67640 + 7.28037i 0.319599 + 0.268176i
\(738\) 2.40574 + 13.6436i 0.0885565 + 0.502229i
\(739\) 23.4923 + 8.55050i 0.864179 + 0.314535i 0.735807 0.677191i \(-0.236803\pi\)
0.128371 + 0.991726i \(0.459025\pi\)
\(740\) 17.7082 0.650967
\(741\) 0 0
\(742\) −30.7082 −1.12733
\(743\) 3.15801 + 1.14942i 0.115856 + 0.0421681i 0.399298 0.916821i \(-0.369254\pi\)
−0.283442 + 0.958989i \(0.591476\pi\)
\(744\) 1.31318 + 7.44742i 0.0481435 + 0.273036i
\(745\) −4.73442 3.97265i −0.173456 0.145546i
\(746\) −6.78264 + 5.69131i −0.248330 + 0.208374i
\(747\) −4.19887 + 23.8130i −0.153629 + 0.871272i
\(748\) 0.381966 0.661585i 0.0139661 0.0241899i
\(749\) −24.6246 42.6511i −0.899764 1.55844i
\(750\) −0.887325 + 0.322960i −0.0324005 + 0.0117928i
\(751\) 16.1119 5.86424i 0.587931 0.213989i −0.0308884 0.999523i \(-0.509834\pi\)
0.618819 + 0.785534i \(0.287611\pi\)
\(752\) 7.28115 + 12.6113i 0.265516 + 0.459888i
\(753\) 4.84346 8.38912i 0.176505 0.305716i
\(754\) 1.01655 5.76517i 0.0370207 0.209955i
\(755\) −52.2819 + 43.8698i −1.90273 + 1.59658i
\(756\) −3.17594 2.66493i −0.115508 0.0969226i
\(757\) 4.64381 + 26.3364i 0.168782 + 0.957211i 0.945079 + 0.326843i \(0.105985\pi\)
−0.776296 + 0.630368i \(0.782904\pi\)
\(758\) 22.9963 + 8.36996i 0.835263 + 0.304011i
\(759\) −3.32624 −0.120735
\(760\) 0 0
\(761\) 4.88854 0.177210 0.0886048 0.996067i \(-0.471759\pi\)
0.0886048 + 0.996067i \(0.471759\pi\)
\(762\) −3.34747 1.21838i −0.121266 0.0441373i
\(763\) −1.71484 9.72536i −0.0620815 0.352082i
\(764\) 6.73995 + 5.65549i 0.243843 + 0.204608i
\(765\) −5.40500 + 4.53533i −0.195418 + 0.163975i
\(766\) 0.107320 0.608645i 0.00387765 0.0219912i
\(767\) 0.163119 0.282530i 0.00588988 0.0102016i
\(768\) −2.59017 4.48631i −0.0934647 0.161886i
\(769\) −34.4221 + 12.5286i −1.24129 + 0.451793i −0.877450 0.479668i \(-0.840757\pi\)
−0.363841 + 0.931461i \(0.618535\pi\)
\(770\) 23.8836 8.69292i 0.860706 0.313271i
\(771\) −3.88854 6.73516i −0.140042 0.242561i
\(772\) −1.56231 + 2.70599i −0.0562286 + 0.0973908i
\(773\) −6.23796 + 35.3772i −0.224364 + 1.27243i 0.639534 + 0.768763i \(0.279127\pi\)
−0.863898 + 0.503668i \(0.831984\pi\)
\(774\) 0.516132 0.433086i 0.0185520 0.0155670i
\(775\) −37.1155 31.1436i −1.33323 1.11871i
\(776\) −5.37940 30.5081i −0.193109 1.09518i
\(777\) −9.53403 3.47010i −0.342031 0.124489i
\(778\) 15.0000 0.537776
\(779\) 0 0
\(780\) −0.763932 −0.0273532
\(781\) −11.3610 4.13508i −0.406530 0.147965i
\(782\) 1.15519 + 6.55141i 0.0413095 + 0.234278i
\(783\) 6.19743 + 5.20026i 0.221478 + 0.185842i
\(784\) −7.43692 + 6.24031i −0.265604 + 0.222868i
\(785\) −10.0329 + 56.8993i −0.358089 + 2.03082i
\(786\) −4.66312 + 8.07676i −0.166328 + 0.288088i
\(787\) −19.0000 32.9090i −0.677277 1.17308i −0.975798 0.218675i \(-0.929827\pi\)
0.298521 0.954403i \(-0.403507\pi\)
\(788\) −1.74229 + 0.634140i −0.0620664 + 0.0225903i
\(789\) 5.36396 1.95232i 0.190962 0.0695045i
\(790\) −35.1246 60.8376i −1.24968 2.16451i
\(791\) −10.1459 + 17.5732i −0.360747 + 0.624831i
\(792\) −1.79313 + 10.1694i −0.0637162 + 0.361352i
\(793\) 7.84128 6.57962i 0.278452 0.233649i
\(794\) −14.2196 11.9316i −0.504633 0.423437i
\(795\) −1.35787 7.70086i −0.0481587 0.273121i
\(796\) 7.79174 + 2.83596i 0.276171 + 0.100518i
\(797\) −20.2918 −0.718772 −0.359386 0.933189i \(-0.617014\pi\)
−0.359386 + 0.933189i \(0.617014\pi\)
\(798\) 0 0
\(799\) 2.29180 0.0810779
\(800\) 17.3905 + 6.32962i 0.614847 + 0.223786i
\(801\) 3.84788 + 21.8224i 0.135958 + 0.771057i
\(802\) −44.4833 37.3260i −1.57076 1.31803i
\(803\) 3.35678 2.81667i 0.118458 0.0993982i
\(804\) −0.286949 + 1.62737i −0.0101199 + 0.0573930i
\(805\) −26.1246 + 45.2492i −0.920772 + 1.59482i
\(806\) −7.16312 12.4069i −0.252310 0.437014i
\(807\) −10.8850 + 3.96182i −0.383171 + 0.139463i
\(808\) −19.2899 + 7.02094i −0.678616 + 0.246996i
\(809\) 12.3992 + 21.4760i 0.435932 + 0.755057i 0.997371 0.0724614i \(-0.0230854\pi\)
−0.561439 + 0.827518i \(0.689752\pi\)
\(810\) −20.1803 + 34.9534i −0.709065 + 1.22814i
\(811\) 3.99021 22.6296i 0.140115 0.794633i −0.831045 0.556205i \(-0.812257\pi\)
0.971160 0.238428i \(-0.0766321\pi\)
\(812\) −5.13878 + 4.31195i −0.180336 + 0.151320i
\(813\) 0.335293 + 0.281344i 0.0117592 + 0.00986718i
\(814\) −4.02522 22.8282i −0.141084 0.800127i
\(815\) −5.36396 1.95232i −0.187891 0.0683868i
\(816\) −1.41641 −0.0495842
\(817\) 0 0
\(818\) −13.4164 −0.469094
\(819\) −8.04594 2.92848i −0.281148 0.102329i
\(820\) −1.04189 5.90885i −0.0363843 0.206346i
\(821\) 39.8708 + 33.4556i 1.39150 + 1.16761i 0.964728 + 0.263247i \(0.0847935\pi\)
0.426771 + 0.904360i \(0.359651\pi\)
\(822\) 3.53762 2.96842i 0.123389 0.103535i
\(823\) −4.44483 + 25.2079i −0.154937 + 0.878691i 0.803906 + 0.594756i \(0.202751\pi\)
−0.958843 + 0.283935i \(0.908360\pi\)
\(824\) 16.0172 27.7426i 0.557986 0.966461i
\(825\) 1.69098 + 2.92887i 0.0588725 + 0.101970i
\(826\) −1.48809 + 0.541620i −0.0517773 + 0.0188454i
\(827\) −30.6309 + 11.1487i −1.06514 + 0.387680i −0.814358 0.580363i \(-0.802911\pi\)
−0.250784 + 0.968043i \(0.580688\pi\)
\(828\) 4.74671 + 8.22154i 0.164960 + 0.285718i
\(829\) −2.33688 + 4.04760i −0.0811632 + 0.140579i −0.903750 0.428061i \(-0.859197\pi\)
0.822587 + 0.568640i \(0.192530\pi\)
\(830\) 7.70315 43.6867i 0.267380 1.51639i
\(831\) 3.34047 2.80299i 0.115880 0.0972347i
\(832\) −3.24502 2.72289i −0.112501 0.0943993i
\(833\) 0.265311 + 1.50465i 0.00919247 + 0.0521331i
\(834\) −8.59433 3.12808i −0.297597 0.108317i
\(835\) 65.4853 2.26621
\(836\) 0 0
\(837\) 19.7984 0.684332
\(838\) 13.5994 + 4.94976i 0.469782 + 0.170987i
\(839\) 2.63973 + 14.9707i 0.0911338 + 0.516845i 0.995864 + 0.0908597i \(0.0289615\pi\)
−0.904730 + 0.425986i \(0.859927\pi\)
\(840\) −6.35188 5.32986i −0.219161 0.183898i
\(841\) −12.1876 + 10.2266i −0.420263 + 0.352643i
\(842\) −7.71881 + 43.7755i −0.266008 + 1.50860i
\(843\) 5.63525 9.76055i 0.194088 0.336171i
\(844\) 1.19098 + 2.06284i 0.0409953 + 0.0710060i
\(845\) 36.4909 13.2816i 1.25533 0.456901i
\(846\) 13.0186 4.73838i 0.447589 0.162909i
\(847\) 12.5729 + 21.7770i 0.432012 + 0.748266i
\(848\) −15.3541 + 26.5941i −0.527262 + 0.913245i
\(849\) 1.72680 9.79320i 0.0592638 0.336102i
\(850\) 5.18147 4.34777i 0.177723 0.149127i
\(851\) 36.5039 + 30.6304i 1.25134 + 1.05000i
\(852\) −0.306304 1.73713i −0.0104938 0.0595132i
\(853\) −28.8563 10.5028i −0.988020 0.359610i −0.203067 0.979165i \(-0.565091\pi\)
−0.784953 + 0.619555i \(0.787313\pi\)
\(854\) −49.6869 −1.70025
\(855\) 0 0
\(856\) −36.7082 −1.25466
\(857\) 9.97769 + 3.63158i 0.340831 + 0.124052i 0.506764 0.862085i \(-0.330841\pi\)
−0.165933 + 0.986137i \(0.553064\pi\)
\(858\) 0.173648 + 0.984808i 0.00592825 + 0.0336208i
\(859\) −37.1846 31.2016i −1.26872 1.06458i −0.994696 0.102861i \(-0.967200\pi\)
−0.274026 0.961722i \(-0.588355\pi\)
\(860\) −0.223529 + 0.187563i −0.00762227 + 0.00639584i
\(861\) −0.596949 + 3.38547i −0.0203440 + 0.115376i
\(862\) −22.3713 + 38.7483i −0.761970 + 1.31977i
\(863\) 13.5279 + 23.4309i 0.460494 + 0.797599i 0.998986 0.0450321i \(-0.0143390\pi\)
−0.538492 + 0.842631i \(0.681006\pi\)
\(864\) −7.10624 + 2.58646i −0.241759 + 0.0879932i
\(865\) 1.43572 0.522560i 0.0488160 0.0177676i
\(866\) 2.78115 + 4.81710i 0.0945074 + 0.163692i
\(867\) 3.13525 5.43042i 0.106479 0.184427i
\(868\) −2.85068 + 16.1670i −0.0967584 + 0.548744i
\(869\) −16.6294 + 13.9538i −0.564115 + 0.473349i
\(870\) −5.54315 4.65125i −0.187930 0.157692i
\(871\) 1.21554 + 6.89365i 0.0411869 + 0.233583i
\(872\) −6.91678 2.51750i −0.234232 0.0852533i
\(873\) −39.5410 −1.33826
\(874\) 0 0
\(875\) 4.58359 0.154954
\(876\) 0.600764 + 0.218660i 0.0202980 + 0.00738785i
\(877\) 2.05246 + 11.6401i 0.0693067 + 0.393058i 0.999652 + 0.0263737i \(0.00839598\pi\)
−0.930345 + 0.366684i \(0.880493\pi\)
\(878\) −42.8822 35.9824i −1.44720 1.21435i
\(879\) −2.96872 + 2.49105i −0.100132 + 0.0840211i
\(880\) 4.41351 25.0303i 0.148779 0.843770i
\(881\) −16.2254 + 28.1033i −0.546648 + 0.946823i 0.451853 + 0.892093i \(0.350763\pi\)
−0.998501 + 0.0547303i \(0.982570\pi\)
\(882\) 4.61803 + 7.99867i 0.155497 + 0.269329i
\(883\) 47.8520 17.4167i 1.61035 0.586118i 0.628838 0.777536i \(-0.283531\pi\)
0.981509 + 0.191418i \(0.0613087\pi\)
\(884\) 0.443663 0.161480i 0.0149220 0.00543116i
\(885\) −0.201626 0.349227i −0.00677759 0.0117391i
\(886\) 6.13525 10.6266i 0.206118 0.357007i
\(887\) 4.74885 26.9321i 0.159451 0.904290i −0.795153 0.606410i \(-0.792609\pi\)
0.954603 0.297880i \(-0.0962797\pi\)
\(888\) −5.79306 + 4.86096i −0.194402 + 0.163123i
\(889\) 13.2463 + 11.1150i 0.444266 + 0.372784i
\(890\) −7.05923 40.0349i −0.236626 1.34197i
\(891\) 11.7200 + 4.26572i 0.392634 + 0.142907i
\(892\) −7.20163 −0.241128
\(893\) 0 0
\(894\) −1.18034 −0.0394765
\(895\) −37.2088 13.5429i −1.24375 0.452689i
\(896\) 7.09424 + 40.2334i 0.237002 + 1.34410i
\(897\) −1.57478 1.32140i −0.0525803 0.0441201i
\(898\) 3.58031 3.00424i 0.119476 0.100253i
\(899\) 5.56272 31.5478i 0.185527 1.05218i
\(900\) 4.82624 8.35929i 0.160875 0.278643i
\(901\) 2.41641 + 4.18534i 0.0805022 + 0.139434i
\(902\) −7.38044 + 2.68626i −0.245742 + 0.0894427i
\(903\) 0.157102 0.0571804i 0.00522802 0.00190284i
\(904\) 7.56231 + 13.0983i 0.251519 + 0.435643i
\(905\) −19.4164 + 33.6302i −0.645423 + 1.11791i
\(906\) −2.26341 + 12.8364i −0.0751967 + 0.426461i
\(907\) −20.2788 + 17.0160i −0.673348 + 0.565006i −0.914054 0.405592i \(-0.867065\pi\)
0.240707 + 0.970598i \(0.422621\pi\)
\(908\) 7.77221 + 6.52166i 0.257930 + 0.216429i
\(909\) 4.54986 + 25.8036i 0.150909 + 0.855850i
\(910\) 14.7609 + 5.37252i 0.489319 + 0.178097i
\(911\) 3.38197 0.112050 0.0560248 0.998429i \(-0.482157\pi\)
0.0560248 + 0.998429i \(0.482157\pi\)
\(912\) 0 0
\(913\) −13.7082 −0.453675
\(914\) −29.9654 10.9065i −0.991168 0.360756i
\(915\) −2.19708 12.4603i −0.0726332 0.411923i
\(916\) −6.44734 5.40996i −0.213026 0.178750i
\(917\) 34.6792 29.0993i 1.14521 0.960944i
\(918\) −0.479952 + 2.72194i −0.0158408 + 0.0898375i
\(919\) −11.6459 + 20.1713i −0.384163 + 0.665389i −0.991653 0.128938i \(-0.958843\pi\)
0.607490 + 0.794327i \(0.292177\pi\)
\(920\) 19.4721 + 33.7267i 0.641977 + 1.11194i
\(921\) 6.21892 2.26350i 0.204920 0.0745849i
\(922\) −31.8448 + 11.5906i −1.04875 + 0.381715i
\(923\) −3.73607 6.47106i −0.122974 0.212998i
\(924\) 0.572949 0.992377i 0.0188486 0.0326468i
\(925\) 8.41340 47.7148i 0.276631 1.56885i
\(926\) 35.0409 29.4028i 1.15152 0.966236i
\(927\) −31.3224 26.2826i −1.02876 0.863235i
\(928\) 2.12477 + 12.0502i 0.0697490 + 0.395566i
\(929\) −15.3940 5.60296i −0.505061 0.183827i 0.0769078 0.997038i \(-0.475495\pi\)
−0.581969 + 0.813211i \(0.697718\pi\)
\(930\) −17.7082 −0.580675
\(931\) 0 0
\(932\) 2.79837 0.0916638
\(933\) −4.54136 1.65292i −0.148677 0.0541142i
\(934\) −4.47984 25.4064i −0.146585 0.831324i
\(935\) −3.06418 2.57115i −0.100209 0.0840856i
\(936\) −4.88887 + 4.10225i −0.159798 + 0.134086i
\(937\) 7.04357 39.9461i 0.230103 1.30498i −0.622581 0.782555i \(-0.713916\pi\)
0.852685 0.522426i \(-0.174973\pi\)
\(938\) 16.9894 29.4264i 0.554722 0.960807i
\(939\) 2.16312 + 3.74663i 0.0705907 + 0.122267i
\(940\) −5.63816 + 2.05212i −0.183896 + 0.0669328i
\(941\) 10.0424 3.65514i 0.327373 0.119154i −0.173105 0.984903i \(-0.555380\pi\)
0.500478 + 0.865749i \(0.333158\pi\)
\(942\) 5.51722 + 9.55611i 0.179761 + 0.311355i
\(943\) 8.07295 13.9828i 0.262891 0.455341i
\(944\) −0.274988 + 1.55953i −0.00895009 + 0.0507585i
\(945\) −16.6294 + 13.9538i −0.540956 + 0.453916i
\(946\) 0.292603 + 0.245523i 0.00951334 + 0.00798264i
\(947\) −5.67004 32.1564i −0.184252 1.04494i −0.926913 0.375276i \(-0.877548\pi\)
0.742661 0.669667i \(-0.233563\pi\)
\(948\) −2.97618 1.08324i −0.0966618 0.0351820i
\(949\) 2.70820 0.0879120
\(950\) 0 0
\(951\) 6.87539 0.222950
\(952\) 4.81556 + 1.75272i 0.156073 + 0.0568060i
\(953\) 3.00269 + 17.0291i 0.0972666 + 0.551626i 0.994029 + 0.109114i \(0.0348015\pi\)
−0.896763 + 0.442512i \(0.854087\pi\)
\(954\) 22.3798 + 18.7789i 0.724573 + 0.607989i
\(955\) 35.2908 29.6125i 1.14198 0.958238i
\(956\) −0.0350120 + 0.198563i −0.00113237 + 0.00642199i
\(957\) −1.11803 + 1.93649i −0.0361409 + 0.0625979i
\(958\) −18.6803 32.3553i −0.603534 1.04535i
\(959\) −21.0645 + 7.66686i −0.680209 + 0.247576i
\(960\) −4.92029 + 1.79084i −0.158802 + 0.0577991i
\(961\) −23.6976 41.0454i −0.764437 1.32404i
\(962\) 7.16312 12.4069i 0.230948 0.400014i
\(963\) −8.13613 + 46.1423i −0.262183 + 1.48691i
\(964\) 1.50570 1.26344i 0.0484955 0.0406925i
\(965\) 12.5330 + 10.5164i 0.403452 + 0.338536i
\(966\) 1.73279 + 9.82711i 0.0557515 + 0.316182i
\(967\) −6.14655 2.23716i −0.197660 0.0719422i 0.241293 0.970452i \(-0.422428\pi\)
−0.438953 + 0.898510i \(0.644651\pi\)
\(968\) 18.7426 0.602411
\(969\) 0 0
\(970\) 72.5410 2.32915
\(971\) −22.0890 8.03972i −0.708868 0.258007i −0.0376758 0.999290i \(-0.511995\pi\)
−0.671193 + 0.741283i \(0.734218\pi\)
\(972\) 1.03591 + 5.87493i 0.0332268 + 0.188438i
\(973\) 34.0086 + 28.5366i 1.09027 + 0.914842i
\(974\) 5.18147 4.34777i 0.166025 0.139312i
\(975\) −0.362954 + 2.05842i −0.0116238 + 0.0659221i
\(976\) −24.8435 + 43.0301i −0.795220 + 1.37736i
\(977\) −5.31966 9.21392i −0.170191 0.294779i 0.768296 0.640095i \(-0.221105\pi\)
−0.938487 + 0.345316i \(0.887772\pi\)
\(978\) −1.02442 + 0.372860i −0.0327575 + 0.0119228i
\(979\) −11.8047 + 4.29656i −0.377280 + 0.137319i
\(980\) −2.00000 3.46410i −0.0638877 0.110657i
\(981\) −4.69756 + 8.13641i −0.149982 + 0.259776i
\(982\) −5.96069 + 33.8047i −0.190213 + 1.07875i
\(983\) 24.9869 20.9665i 0.796957 0.668726i −0.150500 0.988610i \(-0.548088\pi\)
0.947457 + 0.319884i \(0.103644\pi\)
\(984\) 1.96284 + 1.64702i 0.0625731 + 0.0525050i
\(985\) 1.68581 + 9.56071i 0.0537144 + 0.304630i
\(986\) 4.20243 + 1.52956i 0.133833 + 0.0487111i
\(987\) 3.43769 0.109423
\(988\) 0 0
\(989\) −0.785218 −0.0249685
\(990\) −22.7221 8.27016i −0.722155 0.262843i
\(991\) 1.29383 + 7.33765i 0.0410998 + 0.233088i 0.998437 0.0558838i \(-0.0177976\pi\)
−0.957338 + 0.288972i \(0.906687\pi\)
\(992\) 22.9386 + 19.2478i 0.728303 + 0.611118i
\(993\) 3.20233 2.68707i 0.101623 0.0852716i
\(994\) −6.29831 + 35.7195i −0.199770 + 1.13295i
\(995\) 21.7082 37.5997i 0.688196 1.19199i
\(996\) −1.00000 1.73205i −0.0316862 0.0548821i
\(997\) −37.3135 + 13.5810i −1.18173 + 0.430115i −0.856813 0.515628i \(-0.827559\pi\)
−0.324918 + 0.945742i \(0.605337\pi\)
\(998\) −38.2008 + 13.9040i −1.20923 + 0.440122i
\(999\) 9.89919 + 17.1459i 0.313196 + 0.542472i
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 361.2.e.j.99.1 12
19.2 odd 18 361.2.e.i.54.1 12
19.3 odd 18 361.2.e.i.245.1 12
19.4 even 9 361.2.c.d.292.1 4
19.5 even 9 inner 361.2.e.j.62.1 12
19.6 even 9 361.2.c.d.68.1 4
19.7 even 3 inner 361.2.e.j.234.2 12
19.8 odd 6 361.2.e.i.28.1 12
19.9 even 9 361.2.a.f.1.2 yes 2
19.10 odd 18 361.2.a.c.1.1 2
19.11 even 3 inner 361.2.e.j.28.2 12
19.12 odd 6 361.2.e.i.234.1 12
19.13 odd 18 361.2.c.g.68.2 4
19.14 odd 18 361.2.e.i.62.2 12
19.15 odd 18 361.2.c.g.292.2 4
19.16 even 9 inner 361.2.e.j.245.2 12
19.17 even 9 inner 361.2.e.j.54.2 12
19.18 odd 2 361.2.e.i.99.2 12
57.29 even 18 3249.2.a.o.1.2 2
57.47 odd 18 3249.2.a.i.1.1 2
76.47 odd 18 5776.2.a.s.1.2 2
76.67 even 18 5776.2.a.bg.1.1 2
95.9 even 18 9025.2.a.n.1.1 2
95.29 odd 18 9025.2.a.s.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
361.2.a.c.1.1 2 19.10 odd 18
361.2.a.f.1.2 yes 2 19.9 even 9
361.2.c.d.68.1 4 19.6 even 9
361.2.c.d.292.1 4 19.4 even 9
361.2.c.g.68.2 4 19.13 odd 18
361.2.c.g.292.2 4 19.15 odd 18
361.2.e.i.28.1 12 19.8 odd 6
361.2.e.i.54.1 12 19.2 odd 18
361.2.e.i.62.2 12 19.14 odd 18
361.2.e.i.99.2 12 19.18 odd 2
361.2.e.i.234.1 12 19.12 odd 6
361.2.e.i.245.1 12 19.3 odd 18
361.2.e.j.28.2 12 19.11 even 3 inner
361.2.e.j.54.2 12 19.17 even 9 inner
361.2.e.j.62.1 12 19.5 even 9 inner
361.2.e.j.99.1 12 1.1 even 1 trivial
361.2.e.j.234.2 12 19.7 even 3 inner
361.2.e.j.245.2 12 19.16 even 9 inner
3249.2.a.i.1.1 2 57.47 odd 18
3249.2.a.o.1.2 2 57.29 even 18
5776.2.a.s.1.2 2 76.47 odd 18
5776.2.a.bg.1.1 2 76.67 even 18
9025.2.a.n.1.1 2 95.9 even 18
9025.2.a.s.1.2 2 95.29 odd 18