Properties

Label 363.2.f.b.239.2
Level $363$
Weight $2$
Character 363.239
Analytic conductor $2.899$
Analytic rank $0$
Dimension $8$
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] = [363,2,Mod(161,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.f (of order \(10\), degree \(4\), 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 239.2
Root \(-0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 363.239
Dual form 363.2.f.b.161.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.951057 - 0.690983i) q^{2} +(1.34786 - 1.08779i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.224514 + 0.309017i) q^{5} +(0.530249 - 1.96589i) q^{6} +(2.92705 + 0.951057i) q^{7} +(0.951057 + 2.92705i) q^{8} +(0.633446 - 2.93236i) q^{9} +O(q^{10})\) \(q+(0.951057 - 0.690983i) q^{2} +(1.34786 - 1.08779i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.224514 + 0.309017i) q^{5} +(0.530249 - 1.96589i) q^{6} +(2.92705 + 0.951057i) q^{7} +(0.951057 + 2.92705i) q^{8} +(0.633446 - 2.93236i) q^{9} +0.449028i q^{10} +(0.381966 + 1.00000i) q^{12} +(-0.427051 - 0.587785i) q^{13} +(3.44095 - 1.11803i) q^{14} +(0.0335310 + 0.660734i) q^{15} +(1.92705 + 1.40008i) q^{16} +(-3.44095 - 2.50000i) q^{17} +(-1.42377 - 3.22654i) q^{18} +(-2.50000 + 0.812299i) q^{19} +(-0.138757 - 0.190983i) q^{20} +(4.97980 - 1.90211i) q^{21} -6.23607i q^{23} +(4.46589 + 2.91071i) q^{24} +(1.50000 + 4.61653i) q^{25} +(-0.812299 - 0.263932i) q^{26} +(-2.33598 - 4.64146i) q^{27} +(-1.11803 + 1.53884i) q^{28} +(0.726543 - 2.23607i) q^{29} +(0.488446 + 0.605226i) q^{30} +(-4.73607 + 3.44095i) q^{31} -3.35520 q^{32} -5.00000 q^{34} +(-0.951057 + 0.690983i) q^{35} +(1.60262 + 0.932362i) q^{36} +(0.927051 - 2.85317i) q^{37} +(-1.81636 + 2.50000i) q^{38} +(-1.21499 - 0.327712i) q^{39} +(-1.11803 - 0.363271i) q^{40} +(-0.224514 - 0.690983i) q^{41} +(3.42174 - 5.24997i) q^{42} +6.88191i q^{43} +(0.763932 + 0.854102i) q^{45} +(-4.30902 - 5.93085i) q^{46} +(-7.91872 + 2.57295i) q^{47} +(4.12038 - 0.209101i) q^{48} +(2.00000 + 1.45309i) q^{49} +(4.61653 + 3.35410i) q^{50} +(-7.35738 + 0.373373i) q^{51} +(0.427051 - 0.138757i) q^{52} +(1.08981 + 1.50000i) q^{53} +(-5.42882 - 2.80017i) q^{54} +9.47214i q^{56} +(-2.48604 + 3.81433i) q^{57} +(-0.854102 - 2.62866i) q^{58} +(-0.363271 - 0.118034i) q^{59} +(-0.394774 - 0.106480i) q^{60} +(-1.54508 + 2.12663i) q^{61} +(-2.12663 + 6.54508i) q^{62} +(4.64297 - 7.98073i) q^{63} +(-7.04508 + 5.11855i) q^{64} +0.277515 q^{65} +7.32624 q^{67} +(2.12663 - 1.54508i) q^{68} +(-6.78350 - 8.40534i) q^{69} +(-0.427051 + 1.31433i) q^{70} +(3.13068 - 4.30902i) q^{71} +(9.18562 - 0.934712i) q^{72} +(8.94427 + 2.90617i) q^{73} +(-1.08981 - 3.35410i) q^{74} +(7.04358 + 4.59075i) q^{75} -1.62460i q^{76} +(-1.38197 + 0.527864i) q^{78} +(-2.33688 - 3.21644i) q^{79} +(-0.865300 + 0.281153i) q^{80} +(-8.19749 - 3.71499i) q^{81} +(-0.690983 - 0.502029i) q^{82} +(5.11855 + 3.71885i) q^{83} +(0.166977 + 3.29032i) q^{84} +(1.54508 - 0.502029i) q^{85} +(4.75528 + 6.54508i) q^{86} +(-1.45309 - 3.80423i) q^{87} +0.527864i q^{89} +(1.31671 + 0.284435i) q^{90} +(-0.690983 - 2.12663i) q^{91} +(3.66547 + 1.19098i) q^{92} +(-2.64053 + 9.78975i) q^{93} +(-5.75329 + 7.91872i) q^{94} +(0.310271 - 0.954915i) q^{95} +(-4.52233 + 3.64973i) q^{96} +(3.54508 - 2.57565i) q^{97} +2.90617 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9} + 12 q^{12} + 10 q^{13} - 6 q^{15} + 2 q^{16} - 20 q^{19} + 10 q^{24} + 12 q^{25} - 12 q^{27} + 20 q^{30} - 20 q^{31} - 40 q^{34} - 10 q^{36} - 6 q^{37} - 20 q^{39} + 20 q^{42} + 24 q^{45} - 30 q^{46} + 26 q^{48} + 16 q^{49} - 30 q^{51} - 10 q^{52} + 30 q^{57} + 20 q^{58} + 2 q^{60} + 10 q^{61} + 30 q^{63} - 34 q^{64} - 4 q^{67} - 16 q^{69} + 10 q^{70} + 20 q^{72} + 6 q^{75} - 20 q^{78} - 50 q^{79} - 2 q^{81} - 10 q^{82} - 10 q^{85} - 40 q^{90} - 10 q^{91} + 10 q^{93} + 30 q^{94} - 10 q^{96} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.951057 0.690983i 0.672499 0.488599i −0.198362 0.980129i \(-0.563562\pi\)
0.870861 + 0.491530i \(0.163562\pi\)
\(3\) 1.34786 1.08779i 0.778187 0.628033i
\(4\) −0.190983 + 0.587785i −0.0954915 + 0.293893i
\(5\) −0.224514 + 0.309017i −0.100406 + 0.138197i −0.856264 0.516539i \(-0.827220\pi\)
0.755858 + 0.654736i \(0.227220\pi\)
\(6\) 0.530249 1.96589i 0.216473 0.802572i
\(7\) 2.92705 + 0.951057i 1.10632 + 0.359466i 0.804532 0.593909i \(-0.202416\pi\)
0.301789 + 0.953375i \(0.402416\pi\)
\(8\) 0.951057 + 2.92705i 0.336249 + 1.03487i
\(9\) 0.633446 2.93236i 0.211149 0.977454i
\(10\) 0.449028i 0.141995i
\(11\) 0 0
\(12\) 0.381966 + 1.00000i 0.110264 + 0.288675i
\(13\) −0.427051 0.587785i −0.118443 0.163022i 0.745679 0.666305i \(-0.232125\pi\)
−0.864122 + 0.503283i \(0.832125\pi\)
\(14\) 3.44095 1.11803i 0.919634 0.298807i
\(15\) 0.0335310 + 0.660734i 0.00865766 + 0.170601i
\(16\) 1.92705 + 1.40008i 0.481763 + 0.350021i
\(17\) −3.44095 2.50000i −0.834554 0.606339i 0.0862900 0.996270i \(-0.472499\pi\)
−0.920844 + 0.389931i \(0.872499\pi\)
\(18\) −1.42377 3.22654i −0.335586 0.760503i
\(19\) −2.50000 + 0.812299i −0.573539 + 0.186354i −0.581404 0.813615i \(-0.697496\pi\)
0.00786490 + 0.999969i \(0.497496\pi\)
\(20\) −0.138757 0.190983i −0.0310271 0.0427051i
\(21\) 4.97980 1.90211i 1.08668 0.415075i
\(22\) 0 0
\(23\) 6.23607i 1.30031i −0.759802 0.650155i \(-0.774704\pi\)
0.759802 0.650155i \(-0.225296\pi\)
\(24\) 4.46589 + 2.91071i 0.911597 + 0.594145i
\(25\) 1.50000 + 4.61653i 0.300000 + 0.923305i
\(26\) −0.812299 0.263932i −0.159305 0.0517613i
\(27\) −2.33598 4.64146i −0.449560 0.893250i
\(28\) −1.11803 + 1.53884i −0.211289 + 0.290814i
\(29\) 0.726543 2.23607i 0.134916 0.415227i −0.860661 0.509178i \(-0.829950\pi\)
0.995577 + 0.0939505i \(0.0299495\pi\)
\(30\) 0.488446 + 0.605226i 0.0891776 + 0.110499i
\(31\) −4.73607 + 3.44095i −0.850623 + 0.618014i −0.925318 0.379193i \(-0.876202\pi\)
0.0746948 + 0.997206i \(0.476202\pi\)
\(32\) −3.35520 −0.593121
\(33\) 0 0
\(34\) −5.00000 −0.857493
\(35\) −0.951057 + 0.690983i −0.160758 + 0.116797i
\(36\) 1.60262 + 0.932362i 0.267104 + 0.155394i
\(37\) 0.927051 2.85317i 0.152406 0.469058i −0.845483 0.534003i \(-0.820687\pi\)
0.997889 + 0.0649448i \(0.0206871\pi\)
\(38\) −1.81636 + 2.50000i −0.294652 + 0.405554i
\(39\) −1.21499 0.327712i −0.194554 0.0524759i
\(40\) −1.11803 0.363271i −0.176777 0.0574382i
\(41\) −0.224514 0.690983i −0.0350632 0.107913i 0.931993 0.362476i \(-0.118069\pi\)
−0.967056 + 0.254563i \(0.918069\pi\)
\(42\) 3.42174 5.24997i 0.527986 0.810088i
\(43\) 6.88191i 1.04948i 0.851262 + 0.524741i \(0.175838\pi\)
−0.851262 + 0.524741i \(0.824162\pi\)
\(44\) 0 0
\(45\) 0.763932 + 0.854102i 0.113880 + 0.127322i
\(46\) −4.30902 5.93085i −0.635330 0.874457i
\(47\) −7.91872 + 2.57295i −1.15506 + 0.375303i −0.823049 0.567971i \(-0.807729\pi\)
−0.332016 + 0.943274i \(0.607729\pi\)
\(48\) 4.12038 0.209101i 0.594726 0.0301812i
\(49\) 2.00000 + 1.45309i 0.285714 + 0.207584i
\(50\) 4.61653 + 3.35410i 0.652875 + 0.474342i
\(51\) −7.35738 + 0.373373i −1.03024 + 0.0522827i
\(52\) 0.427051 0.138757i 0.0592213 0.0192422i
\(53\) 1.08981 + 1.50000i 0.149697 + 0.206041i 0.877280 0.479980i \(-0.159356\pi\)
−0.727582 + 0.686021i \(0.759356\pi\)
\(54\) −5.42882 2.80017i −0.738769 0.381055i
\(55\) 0 0
\(56\) 9.47214i 1.26577i
\(57\) −2.48604 + 3.81433i −0.329284 + 0.505220i
\(58\) −0.854102 2.62866i −0.112149 0.345159i
\(59\) −0.363271 0.118034i −0.0472939 0.0153667i 0.285275 0.958446i \(-0.407915\pi\)
−0.332568 + 0.943079i \(0.607915\pi\)
\(60\) −0.394774 0.106480i −0.0509651 0.0137465i
\(61\) −1.54508 + 2.12663i −0.197828 + 0.272287i −0.896393 0.443259i \(-0.853822\pi\)
0.698566 + 0.715546i \(0.253822\pi\)
\(62\) −2.12663 + 6.54508i −0.270082 + 0.831227i
\(63\) 4.64297 7.98073i 0.584959 1.00548i
\(64\) −7.04508 + 5.11855i −0.880636 + 0.639819i
\(65\) 0.277515 0.0344214
\(66\) 0 0
\(67\) 7.32624 0.895042 0.447521 0.894273i \(-0.352307\pi\)
0.447521 + 0.894273i \(0.352307\pi\)
\(68\) 2.12663 1.54508i 0.257891 0.187369i
\(69\) −6.78350 8.40534i −0.816638 1.01188i
\(70\) −0.427051 + 1.31433i −0.0510424 + 0.157092i
\(71\) 3.13068 4.30902i 0.371544 0.511386i −0.581776 0.813349i \(-0.697642\pi\)
0.953320 + 0.301963i \(0.0976419\pi\)
\(72\) 9.18562 0.934712i 1.08254 0.110157i
\(73\) 8.94427 + 2.90617i 1.04685 + 0.340141i 0.781431 0.623992i \(-0.214490\pi\)
0.265417 + 0.964134i \(0.414490\pi\)
\(74\) −1.08981 3.35410i −0.126688 0.389906i
\(75\) 7.04358 + 4.59075i 0.813322 + 0.530094i
\(76\) 1.62460i 0.186354i
\(77\) 0 0
\(78\) −1.38197 + 0.527864i −0.156477 + 0.0597688i
\(79\) −2.33688 3.21644i −0.262920 0.361878i 0.657064 0.753835i \(-0.271798\pi\)
−0.919984 + 0.391957i \(0.871798\pi\)
\(80\) −0.865300 + 0.281153i −0.0967435 + 0.0314339i
\(81\) −8.19749 3.71499i −0.910832 0.412777i
\(82\) −0.690983 0.502029i −0.0763063 0.0554398i
\(83\) 5.11855 + 3.71885i 0.561834 + 0.408196i 0.832130 0.554581i \(-0.187121\pi\)
−0.270296 + 0.962777i \(0.587121\pi\)
\(84\) 0.166977 + 3.29032i 0.0182187 + 0.359004i
\(85\) 1.54508 0.502029i 0.167588 0.0544526i
\(86\) 4.75528 + 6.54508i 0.512775 + 0.705775i
\(87\) −1.45309 3.80423i −0.155787 0.407856i
\(88\) 0 0
\(89\) 0.527864i 0.0559535i 0.999609 + 0.0279767i \(0.00890643\pi\)
−0.999609 + 0.0279767i \(0.991094\pi\)
\(90\) 1.31671 + 0.284435i 0.138794 + 0.0299821i
\(91\) −0.690983 2.12663i −0.0724347 0.222931i
\(92\) 3.66547 + 1.19098i 0.382152 + 0.124169i
\(93\) −2.64053 + 9.78975i −0.273810 + 1.01515i
\(94\) −5.75329 + 7.91872i −0.593406 + 0.816754i
\(95\) 0.310271 0.954915i 0.0318331 0.0979722i
\(96\) −4.52233 + 3.64973i −0.461559 + 0.372500i
\(97\) 3.54508 2.57565i 0.359949 0.261518i −0.393082 0.919503i \(-0.628591\pi\)
0.753031 + 0.657985i \(0.228591\pi\)
\(98\) 2.90617 0.293568
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) −12.8985 + 9.37132i −1.28345 + 0.932481i −0.999651 0.0264022i \(-0.991595\pi\)
−0.283799 + 0.958884i \(0.591595\pi\)
\(102\) −6.73929 + 5.43893i −0.667290 + 0.538534i
\(103\) −3.47214 + 10.6861i −0.342120 + 1.05294i 0.620988 + 0.783820i \(0.286732\pi\)
−0.963108 + 0.269116i \(0.913268\pi\)
\(104\) 1.31433 1.80902i 0.128880 0.177389i
\(105\) −0.530249 + 1.96589i −0.0517470 + 0.191851i
\(106\) 2.07295 + 0.673542i 0.201343 + 0.0654202i
\(107\) −4.02874 12.3992i −0.389473 1.19867i −0.933183 0.359402i \(-0.882981\pi\)
0.543710 0.839273i \(-0.317019\pi\)
\(108\) 3.17432 0.486616i 0.305449 0.0468247i
\(109\) 4.70228i 0.450397i −0.974313 0.225198i \(-0.927697\pi\)
0.974313 0.225198i \(-0.0723030\pi\)
\(110\) 0 0
\(111\) −1.85410 4.85410i −0.175984 0.460731i
\(112\) 4.30902 + 5.93085i 0.407164 + 0.560413i
\(113\) −1.95511 + 0.635255i −0.183922 + 0.0597598i −0.399530 0.916720i \(-0.630827\pi\)
0.215608 + 0.976480i \(0.430827\pi\)
\(114\) 0.271271 + 5.34545i 0.0254069 + 0.500647i
\(115\) 1.92705 + 1.40008i 0.179698 + 0.130559i
\(116\) 1.17557 + 0.854102i 0.109149 + 0.0793014i
\(117\) −1.99411 + 0.879937i −0.184356 + 0.0813502i
\(118\) −0.427051 + 0.138757i −0.0393132 + 0.0127736i
\(119\) −7.69421 10.5902i −0.705327 0.970799i
\(120\) −1.90211 + 0.726543i −0.173638 + 0.0663240i
\(121\) 0 0
\(122\) 3.09017i 0.279771i
\(123\) −1.05425 0.687124i −0.0950589 0.0619559i
\(124\) −1.11803 3.44095i −0.100402 0.309007i
\(125\) −3.57971 1.16312i −0.320179 0.104033i
\(126\) −1.09882 10.7983i −0.0978906 0.961992i
\(127\) 7.56231 10.4086i 0.671046 0.923616i −0.328737 0.944421i \(-0.606623\pi\)
0.999784 + 0.0208056i \(0.00662311\pi\)
\(128\) −1.08981 + 3.35410i −0.0963268 + 0.296464i
\(129\) 7.48604 + 9.27584i 0.659109 + 0.816692i
\(130\) 0.263932 0.191758i 0.0231484 0.0168183i
\(131\) 10.4086 0.909405 0.454703 0.890643i \(-0.349746\pi\)
0.454703 + 0.890643i \(0.349746\pi\)
\(132\) 0 0
\(133\) −8.09017 −0.701507
\(134\) 6.96767 5.06231i 0.601915 0.437317i
\(135\) 1.95875 + 0.320215i 0.168583 + 0.0275597i
\(136\) 4.04508 12.4495i 0.346863 1.06754i
\(137\) −2.76741 + 3.80902i −0.236436 + 0.325426i −0.910703 0.413061i \(-0.864460\pi\)
0.674267 + 0.738487i \(0.264460\pi\)
\(138\) −12.2594 3.30667i −1.04359 0.281482i
\(139\) −13.5172 4.39201i −1.14652 0.372526i −0.326686 0.945133i \(-0.605932\pi\)
−0.819830 + 0.572607i \(0.805932\pi\)
\(140\) −0.224514 0.690983i −0.0189749 0.0583987i
\(141\) −7.87450 + 12.0818i −0.663153 + 1.01747i
\(142\) 6.26137i 0.525442i
\(143\) 0 0
\(144\) 5.32624 4.76393i 0.443853 0.396994i
\(145\) 0.527864 + 0.726543i 0.0438367 + 0.0603361i
\(146\) 10.5146 3.41641i 0.870196 0.282744i
\(147\) 4.27636 0.217017i 0.352708 0.0178993i
\(148\) 1.50000 + 1.08981i 0.123299 + 0.0895821i
\(149\) −10.5474 7.66312i −0.864075 0.627787i 0.0649156 0.997891i \(-0.479322\pi\)
−0.928990 + 0.370104i \(0.879322\pi\)
\(150\) 9.87097 0.500932i 0.805961 0.0409010i
\(151\) −5.32624 + 1.73060i −0.433443 + 0.140834i −0.517608 0.855618i \(-0.673178\pi\)
0.0841654 + 0.996452i \(0.473178\pi\)
\(152\) −4.75528 6.54508i −0.385704 0.530876i
\(153\) −9.51057 + 8.50651i −0.768884 + 0.687710i
\(154\) 0 0
\(155\) 2.23607i 0.179605i
\(156\) 0.424666 0.651565i 0.0340005 0.0521669i
\(157\) 3.00000 + 9.23305i 0.239426 + 0.736878i 0.996503 + 0.0835524i \(0.0266266\pi\)
−0.757077 + 0.653325i \(0.773373\pi\)
\(158\) −4.44501 1.44427i −0.353626 0.114900i
\(159\) 3.10059 + 0.836305i 0.245893 + 0.0663233i
\(160\) 0.753289 1.03681i 0.0595527 0.0819673i
\(161\) 5.93085 18.2533i 0.467417 1.43856i
\(162\) −10.3633 + 2.13116i −0.814215 + 0.167440i
\(163\) 11.8262 8.59226i 0.926302 0.672998i −0.0187823 0.999824i \(-0.505979\pi\)
0.945085 + 0.326825i \(0.105979\pi\)
\(164\) 0.449028 0.0350632
\(165\) 0 0
\(166\) 7.43769 0.577277
\(167\) 17.0660 12.3992i 1.32061 0.959478i 0.320684 0.947186i \(-0.396087\pi\)
0.999924 0.0122915i \(-0.00391261\pi\)
\(168\) 10.3036 + 12.7671i 0.794944 + 0.985003i
\(169\) 3.85410 11.8617i 0.296469 0.912439i
\(170\) 1.12257 1.54508i 0.0860972 0.118503i
\(171\) 0.798339 + 7.84545i 0.0610505 + 0.599957i
\(172\) −4.04508 1.31433i −0.308435 0.100217i
\(173\) 7.13918 + 21.9721i 0.542782 + 1.67051i 0.726206 + 0.687477i \(0.241282\pi\)
−0.183425 + 0.983034i \(0.558718\pi\)
\(174\) −4.01062 2.61398i −0.304044 0.198165i
\(175\) 14.9394i 1.12931i
\(176\) 0 0
\(177\) −0.618034 + 0.236068i −0.0464543 + 0.0177440i
\(178\) 0.364745 + 0.502029i 0.0273388 + 0.0376286i
\(179\) 13.2618 4.30902i 0.991233 0.322071i 0.231876 0.972745i \(-0.425514\pi\)
0.759357 + 0.650674i \(0.225514\pi\)
\(180\) −0.647927 + 0.285909i −0.0482936 + 0.0213104i
\(181\) −6.28115 4.56352i −0.466874 0.339204i 0.329348 0.944209i \(-0.393171\pi\)
−0.796222 + 0.605005i \(0.793171\pi\)
\(182\) −2.12663 1.54508i −0.157636 0.114529i
\(183\) 0.230757 + 4.54711i 0.0170581 + 0.336132i
\(184\) 18.2533 5.93085i 1.34565 0.437228i
\(185\) 0.673542 + 0.927051i 0.0495198 + 0.0681581i
\(186\) 4.25325 + 11.1352i 0.311864 + 0.816470i
\(187\) 0 0
\(188\) 5.14590i 0.375303i
\(189\) −2.42325 15.8075i −0.176265 1.14982i
\(190\) −0.364745 1.12257i −0.0264614 0.0814398i
\(191\) 23.0499 + 7.48936i 1.66783 + 0.541911i 0.982490 0.186313i \(-0.0596538\pi\)
0.685340 + 0.728224i \(0.259654\pi\)
\(192\) −3.92789 + 14.5626i −0.283471 + 1.05097i
\(193\) 5.79180 7.97172i 0.416903 0.573817i −0.547982 0.836490i \(-0.684604\pi\)
0.964885 + 0.262673i \(0.0846039\pi\)
\(194\) 1.59184 4.89919i 0.114288 0.351741i
\(195\) 0.374050 0.301876i 0.0267863 0.0216178i
\(196\) −1.23607 + 0.898056i −0.0882906 + 0.0641469i
\(197\) −8.61251 −0.613616 −0.306808 0.951771i \(-0.599261\pi\)
−0.306808 + 0.951771i \(0.599261\pi\)
\(198\) 0 0
\(199\) 2.23607 0.158511 0.0792553 0.996854i \(-0.474746\pi\)
0.0792553 + 0.996854i \(0.474746\pi\)
\(200\) −12.0862 + 8.78115i −0.854625 + 0.620921i
\(201\) 9.87473 7.96937i 0.696510 0.562116i
\(202\) −5.79180 + 17.8253i −0.407509 + 1.25418i
\(203\) 4.25325 5.85410i 0.298520 0.410877i
\(204\) 1.18567 4.39587i 0.0830137 0.307772i
\(205\) 0.263932 + 0.0857567i 0.0184338 + 0.00598951i
\(206\) 4.08174 + 12.5623i 0.284388 + 0.875257i
\(207\) −18.2864 3.95022i −1.27099 0.274559i
\(208\) 1.73060i 0.119995i
\(209\) 0 0
\(210\) 0.854102 + 2.23607i 0.0589386 + 0.154303i
\(211\) 11.4443 + 15.7517i 0.787856 + 1.08439i 0.994372 + 0.105948i \(0.0337876\pi\)
−0.206516 + 0.978443i \(0.566212\pi\)
\(212\) −1.08981 + 0.354102i −0.0748487 + 0.0243198i
\(213\) −0.467565 9.21346i −0.0320370 0.631296i
\(214\) −12.3992 9.00854i −0.847591 0.615811i
\(215\) −2.12663 1.54508i −0.145035 0.105374i
\(216\) 11.3641 11.2518i 0.773232 0.765591i
\(217\) −17.1353 + 5.56758i −1.16322 + 0.377952i
\(218\) −3.24920 4.47214i −0.220063 0.302891i
\(219\) 15.2169 5.81234i 1.02826 0.392762i
\(220\) 0 0
\(221\) 3.09017i 0.207867i
\(222\) −5.11746 3.33537i −0.343461 0.223856i
\(223\) 0.545085 + 1.67760i 0.0365016 + 0.112340i 0.967647 0.252307i \(-0.0811894\pi\)
−0.931146 + 0.364648i \(0.881189\pi\)
\(224\) −9.82084 3.19098i −0.656182 0.213207i
\(225\) 14.4875 1.47422i 0.965833 0.0982814i
\(226\) −1.42047 + 1.95511i −0.0944885 + 0.130052i
\(227\) −4.47777 + 13.7812i −0.297200 + 0.914687i 0.685274 + 0.728286i \(0.259683\pi\)
−0.982474 + 0.186402i \(0.940317\pi\)
\(228\) −1.76721 2.18973i −0.117037 0.145018i
\(229\) 12.2361 8.89002i 0.808582 0.587469i −0.104837 0.994489i \(-0.533432\pi\)
0.913419 + 0.407020i \(0.133432\pi\)
\(230\) 2.80017 0.184638
\(231\) 0 0
\(232\) 7.23607 0.475071
\(233\) 7.83297 5.69098i 0.513155 0.372829i −0.300864 0.953667i \(-0.597275\pi\)
0.814019 + 0.580838i \(0.197275\pi\)
\(234\) −1.28849 + 2.21477i −0.0842314 + 0.144784i
\(235\) 0.982779 3.02468i 0.0641094 0.197309i
\(236\) 0.138757 0.190983i 0.00903233 0.0124319i
\(237\) −6.64858 1.79328i −0.431872 0.116486i
\(238\) −14.6353 4.75528i −0.948663 0.308239i
\(239\) −2.38390 7.33688i −0.154201 0.474583i 0.843878 0.536536i \(-0.180267\pi\)
−0.998079 + 0.0619523i \(0.980267\pi\)
\(240\) −0.860468 + 1.32021i −0.0555430 + 0.0852195i
\(241\) 27.8707i 1.79531i −0.440702 0.897654i \(-0.645270\pi\)
0.440702 0.897654i \(-0.354730\pi\)
\(242\) 0 0
\(243\) −15.0902 + 3.90983i −0.968035 + 0.250816i
\(244\) −0.954915 1.31433i −0.0611322 0.0841412i
\(245\) −0.898056 + 0.291796i −0.0573747 + 0.0186422i
\(246\) −1.47745 + 0.0749776i −0.0941986 + 0.00478039i
\(247\) 1.54508 + 1.12257i 0.0983114 + 0.0714274i
\(248\) −14.5761 10.5902i −0.925584 0.672476i
\(249\) 10.9444 0.555407i 0.693573 0.0351975i
\(250\) −4.20820 + 1.36733i −0.266150 + 0.0864774i
\(251\) 11.9475 + 16.4443i 0.754117 + 1.03795i 0.997681 + 0.0680683i \(0.0216836\pi\)
−0.243563 + 0.969885i \(0.578316\pi\)
\(252\) 3.80423 + 4.25325i 0.239644 + 0.267930i
\(253\) 0 0
\(254\) 15.1246i 0.949003i
\(255\) 1.53646 2.35738i 0.0962167 0.147625i
\(256\) −4.10081 12.6210i −0.256301 0.788813i
\(257\) −21.1805 6.88197i −1.32120 0.429285i −0.438296 0.898831i \(-0.644418\pi\)
−0.882908 + 0.469546i \(0.844418\pi\)
\(258\) 13.5291 + 3.64912i 0.842285 + 0.227185i
\(259\) 5.42705 7.46969i 0.337221 0.464144i
\(260\) −0.0530006 + 0.163119i −0.00328696 + 0.0101162i
\(261\) −6.09673 3.54691i −0.377378 0.219549i
\(262\) 9.89919 7.19218i 0.611574 0.444334i
\(263\) −9.12705 −0.562798 −0.281399 0.959591i \(-0.590798\pi\)
−0.281399 + 0.959591i \(0.590798\pi\)
\(264\) 0 0
\(265\) −0.708204 −0.0435046
\(266\) −7.69421 + 5.59017i −0.471762 + 0.342755i
\(267\) 0.574203 + 0.711486i 0.0351406 + 0.0435422i
\(268\) −1.39919 + 4.30625i −0.0854689 + 0.263046i
\(269\) −11.0292 + 15.1803i −0.672460 + 0.925562i −0.999813 0.0193404i \(-0.993843\pi\)
0.327353 + 0.944902i \(0.393843\pi\)
\(270\) 2.08415 1.04892i 0.126837 0.0638354i
\(271\) 16.1180 + 5.23707i 0.979101 + 0.318129i 0.754484 0.656318i \(-0.227887\pi\)
0.224617 + 0.974447i \(0.427887\pi\)
\(272\) −3.13068 9.63525i −0.189826 0.584223i
\(273\) −3.24466 2.11475i −0.196376 0.127991i
\(274\) 5.53483i 0.334371i
\(275\) 0 0
\(276\) 6.23607 2.38197i 0.375367 0.143378i
\(277\) 9.53444 + 13.1230i 0.572869 + 0.788487i 0.992891 0.119027i \(-0.0379776\pi\)
−0.420022 + 0.907514i \(0.637978\pi\)
\(278\) −15.8904 + 5.16312i −0.953046 + 0.309663i
\(279\) 7.09008 + 16.0675i 0.424472 + 0.961938i
\(280\) −2.92705 2.12663i −0.174925 0.127090i
\(281\) 21.5438 + 15.6525i 1.28519 + 0.933748i 0.999697 0.0246309i \(-0.00784106\pi\)
0.285498 + 0.958379i \(0.407841\pi\)
\(282\) 0.859249 + 16.9317i 0.0511675 + 1.00827i
\(283\) 20.3262 6.60440i 1.20827 0.392591i 0.365472 0.930822i \(-0.380907\pi\)
0.842797 + 0.538232i \(0.180907\pi\)
\(284\) 1.93487 + 2.66312i 0.114813 + 0.158027i
\(285\) −0.620541 1.62460i −0.0367577 0.0962329i
\(286\) 0 0
\(287\) 2.23607i 0.131991i
\(288\) −2.12534 + 9.83865i −0.125237 + 0.579748i
\(289\) 0.336881 + 1.03681i 0.0198165 + 0.0609890i
\(290\) 1.00406 + 0.326238i 0.0589603 + 0.0191574i
\(291\) 1.97651 7.32791i 0.115865 0.429570i
\(292\) −3.41641 + 4.70228i −0.199930 + 0.275180i
\(293\) −4.30625 + 13.2533i −0.251574 + 0.774265i 0.742911 + 0.669390i \(0.233444\pi\)
−0.994485 + 0.104876i \(0.966556\pi\)
\(294\) 3.91711 3.16129i 0.228450 0.184370i
\(295\) 0.118034 0.0857567i 0.00687220 0.00499295i
\(296\) 9.23305 0.536660
\(297\) 0 0
\(298\) −15.3262 −0.887825
\(299\) −3.66547 + 2.66312i −0.211980 + 0.154012i
\(300\) −4.04358 + 3.26336i −0.233456 + 0.188410i
\(301\) −6.54508 + 20.1437i −0.377252 + 1.16106i
\(302\) −3.86974 + 5.32624i −0.222678 + 0.306491i
\(303\) −7.19140 + 26.6620i −0.413135 + 1.53169i
\(304\) −5.95492 1.93487i −0.341538 0.110972i
\(305\) −0.310271 0.954915i −0.0177660 0.0546783i
\(306\) −3.16723 + 14.6618i −0.181059 + 0.838160i
\(307\) 9.51057i 0.542797i −0.962467 0.271398i \(-0.912514\pi\)
0.962467 0.271398i \(-0.0874861\pi\)
\(308\) 0 0
\(309\) 6.94427 + 18.1803i 0.395046 + 1.03424i
\(310\) −1.54508 2.12663i −0.0877549 0.120784i
\(311\) −4.75528 + 1.54508i −0.269647 + 0.0876137i −0.440720 0.897645i \(-0.645277\pi\)
0.171072 + 0.985258i \(0.445277\pi\)
\(312\) −0.196294 3.86801i −0.0111129 0.218983i
\(313\) −8.89919 6.46564i −0.503012 0.365459i 0.307154 0.951660i \(-0.400623\pi\)
−0.810166 + 0.586200i \(0.800623\pi\)
\(314\) 9.23305 + 6.70820i 0.521051 + 0.378566i
\(315\) 1.42377 + 3.22654i 0.0802203 + 0.181795i
\(316\) 2.33688 0.759299i 0.131460 0.0427139i
\(317\) −2.48990 3.42705i −0.139847 0.192482i 0.733349 0.679853i \(-0.237956\pi\)
−0.873195 + 0.487370i \(0.837956\pi\)
\(318\) 3.52671 1.34708i 0.197768 0.0755407i
\(319\) 0 0
\(320\) 3.32624i 0.185942i
\(321\) −18.9178 12.3299i −1.05589 0.688191i
\(322\) −6.97214 21.4580i −0.388542 1.19581i
\(323\) 10.6331 + 3.45492i 0.591643 + 0.192237i
\(324\) 3.74920 4.10886i 0.208289 0.228270i
\(325\) 2.07295 2.85317i 0.114987 0.158265i
\(326\) 5.31031 16.3435i 0.294111 0.905180i
\(327\) −5.11507 6.33801i −0.282864 0.350493i
\(328\) 1.80902 1.31433i 0.0998863 0.0725716i
\(329\) −25.6255 −1.41278
\(330\) 0 0
\(331\) 12.8885 0.708418 0.354209 0.935166i \(-0.384750\pi\)
0.354209 + 0.935166i \(0.384750\pi\)
\(332\) −3.16344 + 2.29837i −0.173616 + 0.126140i
\(333\) −7.77929 4.52578i −0.426302 0.248011i
\(334\) 7.66312 23.5847i 0.419307 1.29049i
\(335\) −1.64484 + 2.26393i −0.0898674 + 0.123692i
\(336\) 12.2594 + 3.30667i 0.668807 + 0.180393i
\(337\) −23.9443 7.77997i −1.30433 0.423802i −0.427243 0.904137i \(-0.640515\pi\)
−0.877085 + 0.480335i \(0.840515\pi\)
\(338\) −4.53077 13.9443i −0.246441 0.758468i
\(339\) −1.94420 + 2.98298i −0.105594 + 0.162013i
\(340\) 1.00406i 0.0544526i
\(341\) 0 0
\(342\) 6.18034 + 6.90983i 0.334195 + 0.373641i
\(343\) −8.19098 11.2739i −0.442272 0.608735i
\(344\) −20.1437 + 6.54508i −1.08608 + 0.352887i
\(345\) 4.12038 0.209101i 0.221834 0.0112576i
\(346\) 21.9721 + 15.9637i 1.18123 + 0.858213i
\(347\) 5.87785 + 4.27051i 0.315540 + 0.229253i 0.734270 0.678858i \(-0.237525\pi\)
−0.418730 + 0.908111i \(0.637525\pi\)
\(348\) 2.51358 0.127559i 0.134742 0.00683790i
\(349\) −12.9271 + 4.20025i −0.691969 + 0.224834i −0.633828 0.773474i \(-0.718517\pi\)
−0.0581411 + 0.998308i \(0.518517\pi\)
\(350\) 10.3229 + 14.2082i 0.551780 + 0.759460i
\(351\) −1.73060 + 3.35520i −0.0923726 + 0.179087i
\(352\) 0 0
\(353\) 33.5967i 1.78817i 0.447893 + 0.894087i \(0.352175\pi\)
−0.447893 + 0.894087i \(0.647825\pi\)
\(354\) −0.424666 + 0.651565i −0.0225708 + 0.0346303i
\(355\) 0.628677 + 1.93487i 0.0333667 + 0.102692i
\(356\) −0.310271 0.100813i −0.0164443 0.00534308i
\(357\) −21.8905 5.90441i −1.15857 0.312494i
\(358\) 9.63525 13.2618i 0.509239 0.700907i
\(359\) −9.85359 + 30.3262i −0.520053 + 1.60056i 0.253844 + 0.967245i \(0.418305\pi\)
−0.773896 + 0.633312i \(0.781695\pi\)
\(360\) −1.77346 + 3.04837i −0.0934694 + 0.160663i
\(361\) −9.78115 + 7.10642i −0.514798 + 0.374022i
\(362\) −9.12705 −0.479707
\(363\) 0 0
\(364\) 1.38197 0.0724347
\(365\) −2.90617 + 2.11146i −0.152116 + 0.110519i
\(366\) 3.36144 + 4.16511i 0.175705 + 0.217714i
\(367\) 7.40983 22.8051i 0.386790 1.19042i −0.548383 0.836227i \(-0.684757\pi\)
0.935173 0.354190i \(-0.115243\pi\)
\(368\) 8.73102 12.0172i 0.455136 0.626441i
\(369\) −2.16843 + 0.220655i −0.112884 + 0.0114869i
\(370\) 1.28115 + 0.416272i 0.0666040 + 0.0216409i
\(371\) 1.76336 + 5.42705i 0.0915489 + 0.281758i
\(372\) −5.24997 3.42174i −0.272198 0.177409i
\(373\) 27.3561i 1.41645i 0.705989 + 0.708223i \(0.250503\pi\)
−0.705989 + 0.708223i \(0.749497\pi\)
\(374\) 0 0
\(375\) −6.09017 + 2.32624i −0.314495 + 0.120126i
\(376\) −15.0623 20.7315i −0.776779 1.06914i
\(377\) −1.62460 + 0.527864i −0.0836711 + 0.0271864i
\(378\) −13.2273 13.3594i −0.680340 0.687131i
\(379\) −2.33688 1.69784i −0.120038 0.0872124i 0.526147 0.850394i \(-0.323636\pi\)
−0.646184 + 0.763181i \(0.723636\pi\)
\(380\) 0.502029 + 0.364745i 0.0257535 + 0.0187110i
\(381\) −1.12942 22.2555i −0.0578622 1.14018i
\(382\) 27.0967 8.80427i 1.38639 0.450465i
\(383\) 7.29818 + 10.0451i 0.372920 + 0.513280i 0.953691 0.300787i \(-0.0972492\pi\)
−0.580772 + 0.814066i \(0.697249\pi\)
\(384\) 2.17963 + 5.70634i 0.111229 + 0.291200i
\(385\) 0 0
\(386\) 11.5836i 0.589589i
\(387\) 20.1802 + 4.35932i 1.02582 + 0.221597i
\(388\) 0.836881 + 2.57565i 0.0424862 + 0.130759i
\(389\) −7.02067 2.28115i −0.355962 0.115659i 0.125577 0.992084i \(-0.459922\pi\)
−0.481539 + 0.876425i \(0.659922\pi\)
\(390\) 0.147152 0.545564i 0.00745132 0.0276257i
\(391\) −15.5902 + 21.4580i −0.788429 + 1.08518i
\(392\) −2.35114 + 7.23607i −0.118751 + 0.365477i
\(393\) 14.0294 11.3223i 0.707687 0.571137i
\(394\) −8.19098 + 5.95110i −0.412656 + 0.299812i
\(395\) 1.51860 0.0764089
\(396\) 0 0
\(397\) −23.0000 −1.15434 −0.577168 0.816625i \(-0.695842\pi\)
−0.577168 + 0.816625i \(0.695842\pi\)
\(398\) 2.12663 1.54508i 0.106598 0.0774481i
\(399\) −10.9044 + 8.80037i −0.545903 + 0.440569i
\(400\) −3.57295 + 10.9964i −0.178647 + 0.549820i
\(401\) 16.3722 22.5344i 0.817590 1.12532i −0.172517 0.985006i \(-0.555190\pi\)
0.990108 0.140310i \(-0.0448099\pi\)
\(402\) 3.88473 14.4026i 0.193753 0.718336i
\(403\) 4.04508 + 1.31433i 0.201500 + 0.0654713i
\(404\) −3.04493 9.37132i −0.151491 0.466241i
\(405\) 2.98845 1.69910i 0.148497 0.0844288i
\(406\) 8.50651i 0.422171i
\(407\) 0 0
\(408\) −8.09017 21.1803i −0.400523 1.04858i
\(409\) 12.4377 + 17.1190i 0.615004 + 0.846481i 0.996977 0.0776926i \(-0.0247553\pi\)
−0.381973 + 0.924173i \(0.624755\pi\)
\(410\) 0.310271 0.100813i 0.0153232 0.00497880i
\(411\) 0.413311 + 8.14437i 0.0203871 + 0.401732i
\(412\) −5.61803 4.08174i −0.276781 0.201093i
\(413\) −0.951057 0.690983i −0.0467984 0.0340011i
\(414\) −20.1209 + 8.87872i −0.988890 + 0.436365i
\(415\) −2.29837 + 0.746787i −0.112823 + 0.0366583i
\(416\) 1.43284 + 1.97214i 0.0702508 + 0.0966919i
\(417\) −22.9969 + 8.78402i −1.12616 + 0.430155i
\(418\) 0 0
\(419\) 0.854102i 0.0417256i −0.999782 0.0208628i \(-0.993359\pi\)
0.999782 0.0208628i \(-0.00664132\pi\)
\(420\) −1.05425 0.687124i −0.0514423 0.0335282i
\(421\) 5.91641 + 18.2088i 0.288348 + 0.887444i 0.985375 + 0.170399i \(0.0545057\pi\)
−0.697027 + 0.717045i \(0.745494\pi\)
\(422\) 21.7683 + 7.07295i 1.05966 + 0.344306i
\(423\) 2.52873 + 24.8504i 0.122951 + 1.20827i
\(424\) −3.35410 + 4.61653i −0.162890 + 0.224198i
\(425\) 6.37988 19.6353i 0.309470 0.952450i
\(426\) −6.81102 8.43944i −0.329995 0.408892i
\(427\) −6.54508 + 4.75528i −0.316739 + 0.230124i
\(428\) 8.05748 0.389473
\(429\) 0 0
\(430\) −3.09017 −0.149021
\(431\) −4.89404 + 3.55573i −0.235738 + 0.171273i −0.699382 0.714748i \(-0.746541\pi\)
0.463645 + 0.886021i \(0.346541\pi\)
\(432\) 1.99688 12.2149i 0.0960750 0.587690i
\(433\) −1.85410 + 5.70634i −0.0891025 + 0.274229i −0.985672 0.168674i \(-0.946051\pi\)
0.896569 + 0.442903i \(0.146051\pi\)
\(434\) −12.4495 + 17.1353i −0.597595 + 0.822519i
\(435\) 1.50181 + 0.405074i 0.0720062 + 0.0194218i
\(436\) 2.76393 + 0.898056i 0.132368 + 0.0430091i
\(437\) 5.06555 + 15.5902i 0.242318 + 0.745779i
\(438\) 10.4559 16.0425i 0.499603 0.766540i
\(439\) 2.73466i 0.130518i −0.997868 0.0652590i \(-0.979213\pi\)
0.997868 0.0652590i \(-0.0207874\pi\)
\(440\) 0 0
\(441\) 5.52786 4.94427i 0.263232 0.235442i
\(442\) 2.13525 + 2.93893i 0.101564 + 0.139790i
\(443\) 1.45309 0.472136i 0.0690382 0.0224319i −0.274294 0.961646i \(-0.588444\pi\)
0.343332 + 0.939214i \(0.388444\pi\)
\(444\) 3.20727 0.162763i 0.152210 0.00772438i
\(445\) −0.163119 0.118513i −0.00773258 0.00561805i
\(446\) 1.67760 + 1.21885i 0.0794366 + 0.0577141i
\(447\) −22.5522 + 1.14448i −1.06668 + 0.0541321i
\(448\) −25.4894 + 8.28199i −1.20426 + 0.391287i
\(449\) −16.3925 22.5623i −0.773609 1.06478i −0.995959 0.0898141i \(-0.971373\pi\)
0.222350 0.974967i \(-0.428627\pi\)
\(450\) 12.7598 11.4127i 0.601501 0.537999i
\(451\) 0 0
\(452\) 1.27051i 0.0597598i
\(453\) −5.29650 + 8.12641i −0.248851 + 0.381812i
\(454\) 5.26393 + 16.2007i 0.247049 + 0.760337i
\(455\) 0.812299 + 0.263932i 0.0380812 + 0.0123733i
\(456\) −13.5291 3.64912i −0.633558 0.170886i
\(457\) −14.7361 + 20.2825i −0.689324 + 0.948773i −0.999998 0.00174308i \(-0.999445\pi\)
0.310674 + 0.950516i \(0.399445\pi\)
\(458\) 5.49434 16.9098i 0.256734 0.790144i
\(459\) −3.56564 + 21.8110i −0.166430 + 1.01805i
\(460\) −1.19098 + 0.865300i −0.0555299 + 0.0403448i
\(461\) 30.7113 1.43037 0.715184 0.698936i \(-0.246343\pi\)
0.715184 + 0.698936i \(0.246343\pi\)
\(462\) 0 0
\(463\) 33.2705 1.54621 0.773106 0.634277i \(-0.218702\pi\)
0.773106 + 0.634277i \(0.218702\pi\)
\(464\) 4.53077 3.29180i 0.210336 0.152818i
\(465\) −2.43236 3.01390i −0.112798 0.139766i
\(466\) 3.51722 10.8249i 0.162932 0.501453i
\(467\) −4.49801 + 6.19098i −0.208143 + 0.286485i −0.900307 0.435256i \(-0.856658\pi\)
0.692163 + 0.721741i \(0.256658\pi\)
\(468\) −0.136373 1.34016i −0.00630382 0.0619491i
\(469\) 21.4443 + 6.96767i 0.990204 + 0.321737i
\(470\) −1.15533 3.55573i −0.0532912 0.164014i
\(471\) 14.0872 + 9.18149i 0.649102 + 0.423061i
\(472\) 1.17557i 0.0541100i
\(473\) 0 0
\(474\) −7.56231 + 2.88854i −0.347348 + 0.132675i
\(475\) −7.50000 10.3229i −0.344124 0.473646i
\(476\) 7.69421 2.50000i 0.352663 0.114587i
\(477\) 5.08888 2.24556i 0.233004 0.102817i
\(478\) −7.33688 5.33056i −0.335581 0.243814i
\(479\) −16.2007 11.7705i −0.740230 0.537808i 0.152553 0.988295i \(-0.451250\pi\)
−0.892783 + 0.450487i \(0.851250\pi\)
\(480\) −0.112503 2.21689i −0.00513504 0.101187i
\(481\) −2.07295 + 0.673542i −0.0945183 + 0.0307109i
\(482\) −19.2582 26.5066i −0.877185 1.20734i
\(483\) −11.8617 31.0543i −0.539726 1.41302i
\(484\) 0 0
\(485\) 1.67376i 0.0760016i
\(486\) −11.6500 + 14.1455i −0.528454 + 0.641654i
\(487\) 0.454915 + 1.40008i 0.0206142 + 0.0634439i 0.960834 0.277123i \(-0.0893810\pi\)
−0.940220 + 0.340567i \(0.889381\pi\)
\(488\) −7.69421 2.50000i −0.348300 0.113170i
\(489\) 6.59356 24.4456i 0.298171 1.10547i
\(490\) −0.652476 + 0.898056i −0.0294759 + 0.0405700i
\(491\) 5.46158 16.8090i 0.246478 0.758580i −0.748912 0.662669i \(-0.769424\pi\)
0.995390 0.0959111i \(-0.0305765\pi\)
\(492\) 0.605226 0.488446i 0.0272857 0.0220208i
\(493\) −8.09017 + 5.87785i −0.364363 + 0.264725i
\(494\) 2.24514 0.101014
\(495\) 0 0
\(496\) −13.9443 −0.626116
\(497\) 13.2618 9.63525i 0.594873 0.432200i
\(498\) 10.0250 8.09061i 0.449229 0.362549i
\(499\) −11.1180 + 34.2178i −0.497712 + 1.53180i 0.314976 + 0.949100i \(0.398003\pi\)
−0.812688 + 0.582699i \(0.801997\pi\)
\(500\) 1.36733 1.88197i 0.0611488 0.0841641i
\(501\) 9.51493 35.2765i 0.425096 1.57604i
\(502\) 22.7254 + 7.38394i 1.01429 + 0.329561i
\(503\) −2.62866 8.09017i −0.117206 0.360723i 0.875195 0.483771i \(-0.160733\pi\)
−0.992401 + 0.123048i \(0.960733\pi\)
\(504\) 27.7757 + 6.00009i 1.23723 + 0.267265i
\(505\) 6.08985i 0.270995i
\(506\) 0 0
\(507\) −7.70820 20.1803i −0.342333 0.896240i
\(508\) 4.67376 + 6.43288i 0.207365 + 0.285413i
\(509\) 31.6421 10.2812i 1.40251 0.455704i 0.492510 0.870307i \(-0.336079\pi\)
0.910003 + 0.414602i \(0.136079\pi\)
\(510\) −0.167655 3.30367i −0.00742388 0.146289i
\(511\) 23.4164 + 17.0130i 1.03588 + 0.752612i
\(512\) −18.3273 13.3156i −0.809962 0.588472i
\(513\) 9.61022 + 9.70614i 0.424301 + 0.428537i
\(514\) −24.8992 + 8.09024i −1.09826 + 0.356845i
\(515\) −2.52265 3.47214i −0.111161 0.153001i
\(516\) −6.88191 + 2.62866i −0.302959 + 0.115720i
\(517\) 0 0
\(518\) 10.8541i 0.476902i
\(519\) 33.5236 + 21.8494i 1.47152 + 0.959084i
\(520\) 0.263932 + 0.812299i 0.0115742 + 0.0356217i
\(521\) −32.0584 10.4164i −1.40450 0.456351i −0.493860 0.869542i \(-0.664414\pi\)
−0.910645 + 0.413190i \(0.864414\pi\)
\(522\) −8.24920 + 0.839423i −0.361058 + 0.0367406i
\(523\) 11.9721 16.4782i 0.523505 0.720543i −0.462618 0.886558i \(-0.653090\pi\)
0.986123 + 0.166015i \(0.0530900\pi\)
\(524\) −1.98787 + 6.11803i −0.0868405 + 0.267268i
\(525\) 16.2508 + 20.1362i 0.709245 + 0.878815i
\(526\) −8.68034 + 6.30664i −0.378481 + 0.274982i
\(527\) 24.8990 1.08462
\(528\) 0 0
\(529\) −15.8885 −0.690806
\(530\) −0.673542 + 0.489357i −0.0292568 + 0.0212563i
\(531\) −0.576231 + 0.990475i −0.0250063 + 0.0429829i
\(532\) 1.54508 4.75528i 0.0669879 0.206168i
\(533\) −0.310271 + 0.427051i −0.0134393 + 0.0184976i
\(534\) 1.03772 + 0.279899i 0.0449067 + 0.0121124i
\(535\) 4.73607 + 1.53884i 0.204758 + 0.0665299i
\(536\) 6.96767 + 21.4443i 0.300957 + 0.926251i
\(537\) 13.1877 20.2339i 0.569093 0.873158i
\(538\) 22.0583i 0.951002i
\(539\) 0 0
\(540\) −0.562306 + 1.09017i −0.0241978 + 0.0469134i
\(541\) −8.98278 12.3637i −0.386200 0.531558i 0.571014 0.820940i \(-0.306550\pi\)
−0.957214 + 0.289382i \(0.906550\pi\)
\(542\) 18.9479 6.15654i 0.813881 0.264446i
\(543\) −13.4302 + 0.681559i −0.576347 + 0.0292485i
\(544\) 11.5451 + 8.38800i 0.494991 + 0.359632i
\(545\) 1.45309 + 1.05573i 0.0622433 + 0.0452224i
\(546\) −4.54711 + 0.230757i −0.194598 + 0.00987550i
\(547\) 25.5517 8.30224i 1.09251 0.354978i 0.293294 0.956022i \(-0.405248\pi\)
0.799216 + 0.601044i \(0.205248\pi\)
\(548\) −1.71036 2.35410i −0.0730628 0.100562i
\(549\) 5.25731 + 5.87785i 0.224377 + 0.250861i
\(550\) 0 0
\(551\) 6.18034i 0.263291i
\(552\) 18.1514 27.8496i 0.772573 1.18536i
\(553\) −3.78115 11.6372i −0.160791 0.494864i
\(554\) 18.1356 + 5.89261i 0.770507 + 0.250353i
\(555\) 1.91627 + 0.516865i 0.0813412 + 0.0219397i
\(556\) 5.16312 7.10642i 0.218965 0.301379i
\(557\) −0.0857567 + 0.263932i −0.00363363 + 0.0111832i −0.952857 0.303420i \(-0.901871\pi\)
0.949223 + 0.314603i \(0.101871\pi\)
\(558\) 17.8455 + 10.3820i 0.755458 + 0.439505i
\(559\) 4.04508 2.93893i 0.171089 0.124303i
\(560\) −2.80017 −0.118329
\(561\) 0 0
\(562\) 31.3050 1.32052
\(563\) 0.865300 0.628677i 0.0364680 0.0264956i −0.569402 0.822059i \(-0.692825\pi\)
0.605870 + 0.795564i \(0.292825\pi\)
\(564\) −5.59763 6.93594i −0.235703 0.292056i
\(565\) 0.242646 0.746787i 0.0102082 0.0314176i
\(566\) 14.7679 20.3262i 0.620740 0.854376i
\(567\) −20.4613 18.6702i −0.859294 0.784076i
\(568\) 15.5902 + 5.06555i 0.654149 + 0.212546i
\(569\) −6.43288 19.7984i −0.269680 0.829991i −0.990578 0.136949i \(-0.956270\pi\)
0.720898 0.693042i \(-0.243730\pi\)
\(570\) −1.71274 1.11630i −0.0717388 0.0467567i
\(571\) 22.5478i 0.943598i 0.881706 + 0.471799i \(0.156395\pi\)
−0.881706 + 0.471799i \(0.843605\pi\)
\(572\) 0 0
\(573\) 39.2148 14.9787i 1.63822 0.625745i
\(574\) −1.54508 2.12663i −0.0644906 0.0887637i
\(575\) 28.7890 9.35410i 1.20058 0.390093i
\(576\) 10.5468 + 23.9011i 0.439449 + 0.995878i
\(577\) 6.47214 + 4.70228i 0.269439 + 0.195759i 0.714298 0.699842i \(-0.246746\pi\)
−0.444859 + 0.895601i \(0.646746\pi\)
\(578\) 1.03681 + 0.753289i 0.0431257 + 0.0313327i
\(579\) −0.865000 17.0450i −0.0359482 0.708366i
\(580\) −0.527864 + 0.171513i −0.0219184 + 0.00712171i
\(581\) 11.4454 + 15.7533i 0.474837 + 0.653557i
\(582\) −3.18368 8.33499i −0.131968 0.345497i
\(583\) 0 0
\(584\) 28.9443i 1.19772i
\(585\) 0.175791 0.813773i 0.00726805 0.0336454i
\(586\) 5.06231 + 15.5802i 0.209122 + 0.643611i
\(587\) 11.3597 + 3.69098i 0.468864 + 0.152343i 0.533914 0.845539i \(-0.320721\pi\)
−0.0650498 + 0.997882i \(0.520721\pi\)
\(588\) −0.689153 + 2.55503i −0.0284202 + 0.105368i
\(589\) 9.04508 12.4495i 0.372696 0.512972i
\(590\) 0.0530006 0.163119i 0.00218200 0.00671550i
\(591\) −11.6084 + 9.36856i −0.477508 + 0.385371i
\(592\) 5.78115 4.20025i 0.237604 0.172629i
\(593\) −7.33094 −0.301046 −0.150523 0.988607i \(-0.548096\pi\)
−0.150523 + 0.988607i \(0.548096\pi\)
\(594\) 0 0
\(595\) 5.00000 0.204980
\(596\) 6.51864 4.73607i 0.267014 0.193997i
\(597\) 3.01390 2.43236i 0.123351 0.0995499i
\(598\) −1.64590 + 5.06555i −0.0673058 + 0.207146i
\(599\) −12.7598 + 17.5623i −0.521350 + 0.717576i −0.985781 0.168033i \(-0.946259\pi\)
0.464432 + 0.885609i \(0.346259\pi\)
\(600\) −6.73851 + 24.9830i −0.275098 + 1.01993i
\(601\) 17.7254 + 5.75934i 0.723035 + 0.234928i 0.647339 0.762203i \(-0.275882\pi\)
0.0756965 + 0.997131i \(0.475882\pi\)
\(602\) 7.69421 + 23.6803i 0.313593 + 0.965139i
\(603\) 4.64078 21.4832i 0.188987 0.874863i
\(604\) 3.46120i 0.140834i
\(605\) 0 0
\(606\) 11.5836 + 30.3262i 0.470551 + 1.23192i
\(607\) −21.7705 29.9645i −0.883638 1.21622i −0.975400 0.220442i \(-0.929250\pi\)
0.0917623 0.995781i \(-0.470750\pi\)
\(608\) 8.38800 2.72542i 0.340178 0.110531i
\(609\) −0.635220 12.5171i −0.0257404 0.507220i
\(610\) −0.954915 0.693786i −0.0386634 0.0280906i
\(611\) 4.89404 + 3.55573i 0.197992 + 0.143849i
\(612\) −3.18364 7.21477i −0.128691 0.291640i
\(613\) −36.1803 + 11.7557i −1.46131 + 0.474808i −0.928470 0.371407i \(-0.878875\pi\)
−0.532840 + 0.846216i \(0.678875\pi\)
\(614\) −6.57164 9.04508i −0.265210 0.365030i
\(615\) 0.449028 0.171513i 0.0181066 0.00691609i
\(616\) 0 0
\(617\) 15.7639i 0.634632i −0.948320 0.317316i \(-0.897218\pi\)
0.948320 0.317316i \(-0.102782\pi\)
\(618\) 19.1667 + 12.4922i 0.770998 + 0.502508i
\(619\) −4.45492 13.7108i −0.179058 0.551084i 0.820737 0.571306i \(-0.193563\pi\)
−0.999796 + 0.0202213i \(0.993563\pi\)
\(620\) 1.31433 + 0.427051i 0.0527847 + 0.0171508i
\(621\) −28.9445 + 14.5674i −1.16150 + 0.584568i
\(622\) −3.45492 + 4.75528i −0.138529 + 0.190669i
\(623\) −0.502029 + 1.54508i −0.0201133 + 0.0619025i
\(624\) −1.88252 2.33260i −0.0753611 0.0933789i
\(625\) −18.4721 + 13.4208i −0.738885 + 0.536832i
\(626\) −12.9313 −0.516838
\(627\) 0 0
\(628\) −6.00000 −0.239426
\(629\) −10.3229 + 7.50000i −0.411600 + 0.299045i
\(630\) 3.58357 + 2.08482i 0.142773 + 0.0830614i
\(631\) 13.4271 41.3242i 0.534522 1.64509i −0.210156 0.977668i \(-0.567397\pi\)
0.744679 0.667423i \(-0.232603\pi\)
\(632\) 7.19218 9.89919i 0.286090 0.393769i
\(633\) 32.5597 + 8.78214i 1.29413 + 0.349059i
\(634\) −4.73607 1.53884i −0.188093 0.0611152i
\(635\) 1.51860 + 4.67376i 0.0602637 + 0.185473i
\(636\) −1.08373 + 1.66276i −0.0429726 + 0.0659328i
\(637\) 1.79611i 0.0711645i
\(638\) 0 0
\(639\) −10.6525 11.9098i −0.421405 0.471146i
\(640\) −0.791796 1.08981i −0.0312985 0.0430787i
\(641\) −10.6004 + 3.44427i −0.418690 + 0.136041i −0.510783 0.859710i \(-0.670644\pi\)
0.0920929 + 0.995750i \(0.470644\pi\)
\(642\) −26.5117 + 1.34542i −1.04633 + 0.0530994i
\(643\) −15.4443 11.2209i −0.609063 0.442510i 0.240021 0.970768i \(-0.422846\pi\)
−0.849084 + 0.528258i \(0.822846\pi\)
\(644\) 9.59632 + 6.97214i 0.378148 + 0.274741i
\(645\) −4.54711 + 0.230757i −0.179042 + 0.00908606i
\(646\) 12.5000 4.06150i 0.491806 0.159797i
\(647\) −14.7881 20.3541i −0.581381 0.800202i 0.412465 0.910973i \(-0.364668\pi\)
−0.993846 + 0.110771i \(0.964668\pi\)
\(648\) 3.07768 27.5276i 0.120903 1.08139i
\(649\) 0 0
\(650\) 4.14590i 0.162615i
\(651\) −17.0396 + 26.1438i −0.667833 + 1.02466i
\(652\) 2.79180 + 8.59226i 0.109335 + 0.336499i
\(653\) 39.8056 + 12.9336i 1.55771 + 0.506132i 0.956196 0.292727i \(-0.0945628\pi\)
0.601518 + 0.798859i \(0.294563\pi\)
\(654\) −9.24418 2.49338i −0.361476 0.0974988i
\(655\) −2.33688 + 3.21644i −0.0913095 + 0.125677i
\(656\) 0.534785 1.64590i 0.0208798 0.0642615i
\(657\) 14.1877 24.3869i 0.553513 0.951425i
\(658\) −24.3713 + 17.7068i −0.950093 + 0.690283i
\(659\) 3.59222 0.139933 0.0699666 0.997549i \(-0.477711\pi\)
0.0699666 + 0.997549i \(0.477711\pi\)
\(660\) 0 0
\(661\) −23.4508 −0.912132 −0.456066 0.889946i \(-0.650742\pi\)
−0.456066 + 0.889946i \(0.650742\pi\)
\(662\) 12.2577 8.90576i 0.476410 0.346132i
\(663\) 3.36144 + 4.16511i 0.130548 + 0.161760i
\(664\) −6.01722 + 18.5191i −0.233513 + 0.718681i
\(665\) 1.81636 2.50000i 0.0704353 0.0969458i
\(666\) −10.5258 + 1.07108i −0.407866 + 0.0415037i
\(667\) −13.9443 4.53077i −0.539924 0.175432i
\(668\) 4.02874 + 12.3992i 0.155877 + 0.479739i
\(669\) 2.55957 + 1.66823i 0.0989585 + 0.0644975i
\(670\) 3.28969i 0.127092i
\(671\) 0 0
\(672\) −16.7082 + 6.38197i −0.644533 + 0.246190i
\(673\) −6.07953 8.36775i −0.234349 0.322553i 0.675605 0.737264i \(-0.263883\pi\)
−0.909953 + 0.414711i \(0.863883\pi\)
\(674\) −28.1482 + 9.14590i −1.08423 + 0.352287i
\(675\) 17.9235 17.7463i 0.689874 0.683056i
\(676\) 6.23607 + 4.53077i 0.239849 + 0.174260i
\(677\) −24.0009 17.4377i −0.922431 0.670185i 0.0216973 0.999765i \(-0.493093\pi\)
−0.944128 + 0.329580i \(0.893093\pi\)
\(678\) 0.212147 + 4.18039i 0.00814744 + 0.160547i
\(679\) 12.8262 4.16750i 0.492226 0.159934i
\(680\) 2.93893 + 4.04508i 0.112703 + 0.155122i
\(681\) 8.95554 + 23.4459i 0.343177 + 0.898449i
\(682\) 0 0
\(683\) 9.00000i 0.344375i −0.985064 0.172188i \(-0.944916\pi\)
0.985064 0.172188i \(-0.0550836\pi\)
\(684\) −4.76391 1.02910i −0.182153 0.0393485i
\(685\) −0.555728 1.71036i −0.0212333 0.0653493i
\(686\) −15.5802 5.06231i −0.594854 0.193280i
\(687\) 6.82205 25.2927i 0.260278 0.964977i
\(688\) −9.63525 + 13.2618i −0.367341 + 0.505601i
\(689\) 0.416272 1.28115i 0.0158587 0.0488080i
\(690\) 3.77423 3.04598i 0.143683 0.115959i
\(691\) 8.38197 6.08985i 0.318865 0.231669i −0.416826 0.908986i \(-0.636858\pi\)
0.735691 + 0.677317i \(0.236858\pi\)
\(692\) −14.2784 −0.542782
\(693\) 0 0
\(694\) 8.54102 0.324213
\(695\) 4.39201 3.19098i 0.166598 0.121041i
\(696\) 9.75320 7.87129i 0.369694 0.298360i
\(697\) −0.954915 + 2.93893i −0.0361700 + 0.111320i
\(698\) −9.39205 + 12.9271i −0.355494 + 0.489296i
\(699\) 4.36716 16.1912i 0.165181 0.612408i
\(700\) −8.78115 2.85317i −0.331896 0.107840i
\(701\) −4.78804 14.7361i −0.180842 0.556574i 0.819010 0.573779i \(-0.194523\pi\)
−0.999852 + 0.0172053i \(0.994523\pi\)
\(702\) 0.672487 + 4.38680i 0.0253814 + 0.165569i
\(703\) 7.88597i 0.297425i
\(704\) 0 0
\(705\) −1.96556 5.14590i −0.0740272 0.193806i
\(706\) 23.2148 + 31.9524i 0.873700 + 1.20254i
\(707\) −46.6673 + 15.1631i −1.75510 + 0.570268i
\(708\) −0.0207233 0.408356i −0.000778829 0.0153470i
\(709\) 16.5902 + 12.0535i 0.623057 + 0.452677i 0.853988 0.520293i \(-0.174177\pi\)
−0.230931 + 0.972970i \(0.574177\pi\)
\(710\) 1.93487 + 1.40576i 0.0726143 + 0.0527574i
\(711\) −10.9121 + 4.81514i −0.409234 + 0.180582i
\(712\) −1.54508 + 0.502029i −0.0579045 + 0.0188143i
\(713\) 21.4580 + 29.5344i 0.803609 + 1.10607i
\(714\) −24.8990 + 9.51057i −0.931821 + 0.355924i
\(715\) 0 0
\(716\) 8.61803i 0.322071i
\(717\) −11.1941 7.29591i −0.418052 0.272471i
\(718\) 11.5836 + 35.6506i 0.432296 + 1.33047i
\(719\) −28.6502 9.30902i −1.06847 0.347168i −0.278580 0.960413i \(-0.589864\pi\)
−0.789893 + 0.613245i \(0.789864\pi\)
\(720\) 0.276321 + 2.71547i 0.0102979 + 0.101199i
\(721\) −20.3262 + 27.9767i −0.756989 + 1.04191i
\(722\) −4.39201 + 13.5172i −0.163454 + 0.503059i
\(723\) −30.3173 37.5657i −1.12751 1.39708i
\(724\) 3.88197 2.82041i 0.144272 0.104820i
\(725\) 11.4127 0.423856
\(726\) 0 0
\(727\) −27.8541 −1.03305 −0.516526 0.856272i \(-0.672775\pi\)
−0.516526 + 0.856272i \(0.672775\pi\)
\(728\) 5.56758 4.04508i 0.206348 0.149921i
\(729\) −16.0864 + 21.6848i −0.595791 + 0.803139i
\(730\) −1.30495 + 4.01623i −0.0482984 + 0.148647i
\(731\) 17.2048 23.6803i 0.636342 0.875849i
\(732\) −2.71680 0.732786i −0.100416 0.0270845i
\(733\) −44.7984 14.5559i −1.65467 0.537633i −0.674922 0.737889i \(-0.735823\pi\)
−0.979744 + 0.200256i \(0.935823\pi\)
\(734\) −8.71078 26.8090i −0.321521 0.989539i
\(735\) −0.893041 + 1.37019i −0.0329403 + 0.0505403i
\(736\) 20.9232i 0.771241i
\(737\) 0 0
\(738\) −1.90983 + 1.70820i −0.0703018 + 0.0628799i
\(739\) −7.98936 10.9964i −0.293893 0.404509i 0.636381 0.771375i \(-0.280431\pi\)
−0.930274 + 0.366866i \(0.880431\pi\)
\(740\) −0.673542 + 0.218847i −0.0247599 + 0.00804498i
\(741\) 3.30367 0.167655i 0.121363 0.00615896i
\(742\) 5.42705 + 3.94298i 0.199233 + 0.144751i
\(743\) 23.7562 + 17.2599i 0.871529 + 0.633203i 0.930997 0.365027i \(-0.118940\pi\)
−0.0594676 + 0.998230i \(0.518940\pi\)
\(744\) −31.1664 + 1.58163i −1.14261 + 0.0579855i
\(745\) 4.73607 1.53884i 0.173516 0.0563788i
\(746\) 18.9026 + 26.0172i 0.692074 + 0.952558i
\(747\) 14.1473 12.6538i 0.517624 0.462977i
\(748\) 0 0
\(749\) 40.1246i 1.46612i
\(750\) −4.18470 + 6.42059i −0.152804 + 0.234447i
\(751\) −4.50000 13.8496i −0.164207 0.505378i 0.834770 0.550599i \(-0.185601\pi\)
−0.998977 + 0.0452211i \(0.985601\pi\)
\(752\) −18.8621 6.12868i −0.687831 0.223490i
\(753\) 33.9913 + 9.16828i 1.23871 + 0.334111i
\(754\) −1.18034 + 1.62460i −0.0429854 + 0.0591644i
\(755\) 0.661030 2.03444i 0.0240574 0.0740409i
\(756\) 9.75419 + 1.59460i 0.354756 + 0.0579952i
\(757\) −8.80902 + 6.40013i −0.320169 + 0.232617i −0.736248 0.676712i \(-0.763404\pi\)
0.416078 + 0.909329i \(0.363404\pi\)
\(758\) −3.39569 −0.123337
\(759\) 0 0
\(760\) 3.09017 0.112092
\(761\) −26.8339 + 19.4959i −0.972726 + 0.706727i −0.956071 0.293134i \(-0.905302\pi\)
−0.0166551 + 0.999861i \(0.505302\pi\)
\(762\) −16.4523 20.3858i −0.596005 0.738501i
\(763\) 4.47214 13.7638i 0.161902 0.498284i
\(764\) −8.80427 + 12.1180i −0.318527 + 0.438415i
\(765\) −0.493401 4.84876i −0.0178389 0.175307i
\(766\) 13.8820 + 4.51052i 0.501576 + 0.162972i
\(767\) 0.0857567 + 0.263932i 0.00309650 + 0.00953003i
\(768\) −19.2563 12.5505i −0.694850 0.452878i
\(769\) 30.7113i 1.10748i −0.832690 0.553739i \(-0.813200\pi\)
0.832690 0.553739i \(-0.186800\pi\)
\(770\) 0 0
\(771\) −36.0344 + 13.7639i −1.29775 + 0.495696i
\(772\) 3.57953 + 4.92680i 0.128830 + 0.177319i
\(773\) −43.5896 + 14.1631i −1.56781 + 0.509412i −0.958880 0.283813i \(-0.908401\pi\)
−0.608929 + 0.793225i \(0.708401\pi\)
\(774\) 22.2048 9.79825i 0.798134 0.352191i
\(775\) −22.9894 16.7027i −0.825802 0.599980i
\(776\) 10.9106 + 7.92705i 0.391669 + 0.284565i
\(777\) −0.810526 15.9716i −0.0290774 0.572977i
\(778\) −8.25329 + 2.68166i −0.295895 + 0.0961420i
\(779\) 1.12257 + 1.54508i 0.0402202 + 0.0553584i
\(780\) 0.106001 + 0.277515i 0.00379545 + 0.00993661i
\(781\) 0 0
\(782\) 31.1803i 1.11501i
\(783\) −12.0758 + 1.85120i −0.431555 + 0.0661564i
\(784\) 1.81966 + 5.60034i 0.0649879 + 0.200012i
\(785\) −3.52671 1.14590i −0.125874 0.0408989i
\(786\) 5.51916 20.4622i 0.196862 0.729864i
\(787\) −1.83282 + 2.52265i −0.0653328 + 0.0899229i −0.840433 0.541915i \(-0.817699\pi\)
0.775100 + 0.631838i \(0.217699\pi\)
\(788\) 1.64484 5.06231i 0.0585951 0.180337i
\(789\) −12.3020 + 9.92827i −0.437962 + 0.353456i
\(790\) 1.44427 1.04932i 0.0513849 0.0373333i
\(791\) −6.32688 −0.224958
\(792\) 0 0
\(793\) 1.90983 0.0678201
\(794\) −21.8743 + 15.8926i −0.776290 + 0.564008i
\(795\) −0.954559 + 0.770374i −0.0338547 + 0.0273223i
\(796\) −0.427051 + 1.31433i −0.0151364 + 0.0465851i
\(797\) −21.2008 + 29.1803i −0.750969 + 1.03362i 0.246942 + 0.969030i \(0.420574\pi\)
−0.997912 + 0.0645905i \(0.979426\pi\)
\(798\) −4.28980 + 15.9044i −0.151857 + 0.563010i
\(799\) 33.6803 + 10.9434i 1.19152 + 0.387150i
\(800\) −5.03280 15.4894i −0.177936 0.547631i
\(801\) 1.54789 + 0.334374i 0.0546919 + 0.0118145i
\(802\) 32.7445i 1.15625i
\(803\) 0 0
\(804\) 2.79837 + 7.32624i 0.0986910 + 0.258376i
\(805\) 4.30902 + 5.93085i 0.151873 + 0.209035i
\(806\) 4.75528 1.54508i 0.167498 0.0544233i
\(807\) 1.64720 + 32.4583i 0.0579841 + 1.14259i
\(808\) −39.6976 28.8420i −1.39656 1.01466i
\(809\) 17.3435 + 12.6008i 0.609766 + 0.443021i 0.849332 0.527859i \(-0.177005\pi\)
−0.239566 + 0.970880i \(0.577005\pi\)
\(810\) 1.66813 3.68090i 0.0586122 0.129334i
\(811\) 19.8992 6.46564i 0.698755 0.227039i 0.0619670 0.998078i \(-0.480263\pi\)
0.636788 + 0.771039i \(0.280263\pi\)
\(812\) 2.62866 + 3.61803i 0.0922477 + 0.126968i
\(813\) 27.4216 10.4741i 0.961719 0.367344i
\(814\) 0 0
\(815\) 5.58359i 0.195585i
\(816\) −14.7008 9.58145i −0.514631 0.335418i
\(817\) −5.59017 17.2048i −0.195575 0.601919i
\(818\) 23.6579 + 7.68692i 0.827179 + 0.268767i
\(819\) −6.67374 + 0.679108i −0.233199 + 0.0237299i
\(820\) −0.100813 + 0.138757i −0.00352054 + 0.00484561i
\(821\) −14.3718 + 44.2320i −0.501581 + 1.54371i 0.304863 + 0.952396i \(0.401389\pi\)
−0.806443 + 0.591311i \(0.798611\pi\)
\(822\) 6.02070 + 7.46016i 0.209996 + 0.260203i
\(823\) −21.1353 + 15.3557i −0.736729 + 0.535265i −0.891685 0.452657i \(-0.850476\pi\)
0.154956 + 0.987921i \(0.450476\pi\)
\(824\) −34.5811 −1.20469
\(825\) 0 0
\(826\) −1.38197 −0.0480847
\(827\) −21.0948 + 15.3262i −0.733537 + 0.532946i −0.890680 0.454630i \(-0.849771\pi\)
0.157144 + 0.987576i \(0.449771\pi\)
\(828\) 5.81427 9.99406i 0.202060 0.347317i
\(829\) −1.62868 + 5.01255i −0.0565663 + 0.174093i −0.975348 0.220673i \(-0.929175\pi\)
0.918781 + 0.394767i \(0.129175\pi\)
\(830\) −1.66987 + 2.29837i −0.0579619 + 0.0797777i
\(831\) 27.1261 + 7.31657i 0.940995 + 0.253809i
\(832\) 6.01722 + 1.95511i 0.208610 + 0.0677814i
\(833\) −3.24920 10.0000i −0.112578 0.346479i
\(834\) −15.8017 + 24.2445i −0.547169 + 0.839520i
\(835\) 8.05748i 0.278841i
\(836\) 0 0
\(837\) 27.0344 + 13.9443i 0.934447 + 0.481985i
\(838\) −0.590170 0.812299i −0.0203871 0.0280604i
\(839\) 1.57160 0.510643i 0.0542576 0.0176294i −0.281762 0.959484i \(-0.590919\pi\)
0.336020 + 0.941855i \(0.390919\pi\)
\(840\) −6.25856 + 0.317610i −0.215941 + 0.0109586i
\(841\) 18.9894 + 13.7966i 0.654805 + 0.475744i
\(842\) 18.2088 + 13.2295i 0.627518 + 0.455918i
\(843\) 46.0645 2.33768i 1.58655 0.0805141i
\(844\) −11.4443 + 3.71847i −0.393928 + 0.127995i
\(845\) 2.80017 + 3.85410i 0.0963287 + 0.132585i
\(846\) 19.5762 + 21.8868i 0.673042 + 0.752484i
\(847\) 0 0
\(848\) 4.41641i 0.151660i
\(849\) 20.2127 31.0124i 0.693699 1.06434i
\(850\) −7.50000 23.0826i −0.257248 0.791728i
\(851\) −17.7926 5.78115i −0.609921 0.198175i
\(852\) 5.50483 + 1.48479i 0.188592 + 0.0508679i
\(853\) 0.551663 0.759299i 0.0188886 0.0259979i −0.799468 0.600708i \(-0.794885\pi\)
0.818357 + 0.574710i \(0.194885\pi\)
\(854\) −2.93893 + 9.04508i −0.100568 + 0.309516i
\(855\) −2.60362 1.51471i −0.0890418 0.0518021i
\(856\) 32.4615 23.5847i 1.10951 0.806107i
\(857\) −34.9646 −1.19437 −0.597184 0.802105i \(-0.703714\pi\)
−0.597184 + 0.802105i \(0.703714\pi\)
\(858\) 0 0
\(859\) 43.4721 1.48325 0.741625 0.670815i \(-0.234055\pi\)
0.741625 + 0.670815i \(0.234055\pi\)
\(860\) 1.31433 0.954915i 0.0448182 0.0325623i
\(861\) −2.43236 3.01390i −0.0828947 0.102714i
\(862\) −2.19756 + 6.76340i −0.0748492 + 0.230362i
\(863\) 0.661030 0.909830i 0.0225017 0.0309710i −0.797618 0.603163i \(-0.793907\pi\)
0.820120 + 0.572192i \(0.193907\pi\)
\(864\) 7.83769 + 15.5730i 0.266644 + 0.529805i
\(865\) −8.39261 2.72692i −0.285357 0.0927182i
\(866\) 2.17963 + 6.70820i 0.0740668 + 0.227954i
\(867\) 1.58190 + 1.03102i 0.0537241 + 0.0350154i
\(868\) 11.1352i 0.377952i
\(869\) 0 0
\(870\) 1.70820 0.652476i 0.0579135 0.0221210i
\(871\) −3.12868 4.30625i −0.106011 0.145912i
\(872\) 13.7638 4.47214i 0.466102 0.151446i
\(873\) −5.30713 12.0270i −0.179619 0.407053i
\(874\) 15.5902 + 11.3269i 0.527345 + 0.383139i
\(875\) −9.37181 6.80902i −0.316825 0.230187i
\(876\) 0.510238 + 10.0543i 0.0172393 + 0.339704i
\(877\) 32.7254 10.6331i 1.10506 0.359055i 0.301012 0.953620i \(-0.402676\pi\)
0.804048 + 0.594565i \(0.202676\pi\)
\(878\) −1.88960 2.60081i −0.0637710 0.0877732i
\(879\) 8.61251 + 22.5478i 0.290493 + 0.760520i
\(880\) 0 0
\(881\) 29.9230i 1.00813i −0.863665 0.504066i \(-0.831837\pi\)
0.863665 0.504066i \(-0.168163\pi\)
\(882\) 1.84090 8.52194i 0.0619864 0.286949i
\(883\) −12.4164 38.2138i −0.417845 1.28600i −0.909681 0.415308i \(-0.863674\pi\)
0.491836 0.870688i \(-0.336326\pi\)
\(884\) −1.81636 0.590170i −0.0610907 0.0198496i
\(885\) 0.0658083 0.243984i 0.00221212 0.00820142i
\(886\) 1.05573 1.45309i 0.0354679 0.0488173i
\(887\) 4.30625 13.2533i 0.144590 0.445002i −0.852368 0.522942i \(-0.824834\pi\)
0.996958 + 0.0779403i \(0.0248344\pi\)
\(888\) 12.4448 10.0436i 0.417622 0.337040i
\(889\) 32.0344 23.2744i 1.07440 0.780598i
\(890\) −0.237026 −0.00794512
\(891\) 0 0
\(892\) −1.09017 −0.0365016
\(893\) 17.7068 12.8647i 0.592536 0.430502i
\(894\) −20.6576 + 16.6717i −0.690894 + 0.557584i
\(895\) −1.64590 + 5.06555i −0.0550163 + 0.169323i
\(896\) −6.37988 + 8.78115i −0.213137 + 0.293358i
\(897\) −2.04363 + 7.57675i −0.0682349 + 0.252980i
\(898\) −31.1803 10.1311i −1.04050 0.338079i
\(899\) 4.25325 + 13.0902i 0.141854 + 0.436582i
\(900\) −1.90034 + 8.79709i −0.0633446 + 0.293236i
\(901\) 7.88597i 0.262720i
\(902\) 0 0
\(903\) 13.0902 + 34.2705i 0.435614 + 1.14045i
\(904\) −3.71885 5.11855i −0.123687 0.170241i
\(905\) 2.82041 0.916408i 0.0937537 0.0304624i
\(906\) 0.577942 + 11.3885i 0.0192008 + 0.378356i
\(907\) 25.3992 + 18.4536i 0.843366 + 0.612741i 0.923309 0.384058i \(-0.125474\pi\)
−0.0799428 + 0.996799i \(0.525474\pi\)
\(908\) −7.24518 5.26393i −0.240440 0.174690i
\(909\) 19.3096 + 43.7594i 0.640459 + 1.45141i
\(910\) 0.954915 0.310271i 0.0316551 0.0102854i
\(911\) 18.6453 + 25.6631i 0.617748 + 0.850257i 0.997187 0.0749598i \(-0.0238829\pi\)
−0.379439 + 0.925217i \(0.623883\pi\)
\(912\) −10.1311 + 3.86974i −0.335474 + 0.128140i
\(913\) 0 0
\(914\) 29.4721i 0.974852i
\(915\) −1.45694 0.949583i −0.0481651 0.0313922i
\(916\) 2.88854 + 8.89002i 0.0954402 + 0.293735i
\(917\) 30.4666 + 9.89919i 1.00609 + 0.326900i
\(918\) 11.6799 + 23.2073i 0.385495 + 0.765956i
\(919\) 27.2599 37.5200i 0.899220 1.23767i −0.0714961 0.997441i \(-0.522777\pi\)
0.970716 0.240229i \(-0.0772226\pi\)
\(920\) −2.26538 + 6.97214i −0.0746875 + 0.229865i
\(921\) −10.3455 12.8189i −0.340894 0.422397i
\(922\) 29.2082 21.2210i 0.961921 0.698876i
\(923\) −3.86974 −0.127374
\(924\) 0 0
\(925\) 14.5623 0.478806
\(926\) 31.6421 22.9894i 1.03983 0.755477i
\(927\) 29.1362 + 16.9507i 0.956958 + 0.556733i
\(928\) −2.43769 + 7.50245i −0.0800212 + 0.246280i
\(929\) 18.9884 26.1353i 0.622988 0.857470i −0.374578 0.927195i \(-0.622212\pi\)
0.997566 + 0.0697256i \(0.0222124\pi\)
\(930\) −4.39587 1.18567i −0.144146 0.0388797i
\(931\) −6.18034 2.00811i −0.202552 0.0658133i
\(932\) 1.84911 + 5.69098i 0.0605697 + 0.186414i
\(933\) −4.72873 + 7.25528i −0.154812 + 0.237527i
\(934\) 8.99602i 0.294359i
\(935\) 0 0
\(936\) −4.47214 5.00000i −0.146176 0.163430i
\(937\) 21.4828 + 29.5685i 0.701812 + 0.965961i 0.999935 + 0.0114336i \(0.00363949\pi\)
−0.298123 + 0.954528i \(0.596361\pi\)
\(938\) 25.2093 8.19098i 0.823111 0.267445i
\(939\) −19.0281 + 0.965638i −0.620958 + 0.0315124i
\(940\) 1.59017 + 1.15533i 0.0518656 + 0.0376826i
\(941\) −28.9605 21.0410i −0.944085 0.685918i 0.00531578 0.999986i \(-0.498308\pi\)
−0.949400 + 0.314068i \(0.898308\pi\)
\(942\) 19.7419 1.00186i 0.643227 0.0326425i
\(943\) −4.30902 + 1.40008i −0.140321 + 0.0455930i
\(944\) −0.534785 0.736068i −0.0174058 0.0239570i
\(945\) 5.42882 + 2.80017i 0.176600 + 0.0910895i
\(946\) 0 0
\(947\) 17.1459i 0.557167i −0.960412 0.278583i \(-0.910135\pi\)
0.960412 0.278583i \(-0.0898649\pi\)
\(948\) 2.32383 3.56545i 0.0754745 0.115801i
\(949\) −2.11146 6.49839i −0.0685408 0.210947i
\(950\) −14.2658 4.63525i −0.462845 0.150388i
\(951\) −7.08393 1.91071i −0.229712 0.0619589i
\(952\) 23.6803 32.5932i 0.767484 1.05635i
\(953\) −1.24108 + 3.81966i −0.0402026 + 0.123731i −0.969144 0.246497i \(-0.920720\pi\)
0.928941 + 0.370228i \(0.120720\pi\)
\(954\) 3.28817 5.65198i 0.106458 0.182990i
\(955\) −7.48936 + 5.44134i −0.242350 + 0.176078i
\(956\) 4.76779 0.154201
\(957\) 0 0
\(958\) −23.5410 −0.760576
\(959\) −11.7229 + 8.51722i −0.378554 + 0.275035i
\(960\) −3.61823 4.48330i −0.116778 0.144698i
\(961\) 1.01064 3.11044i 0.0326014 0.100337i
\(962\) −1.50609 + 2.07295i −0.0485581 + 0.0668346i
\(963\) −38.9109 + 3.95950i −1.25389 + 0.127593i
\(964\) 16.3820 + 5.32282i 0.527628 + 0.171437i
\(965\) 1.16306 + 3.57953i 0.0374402 + 0.115229i
\(966\) −32.7392 21.3382i −1.05337 0.686545i
\(967\) 12.9313i 0.415842i 0.978146 + 0.207921i \(0.0666697\pi\)
−0.978146 + 0.207921i \(0.933330\pi\)
\(968\) 0 0
\(969\) 18.0902 6.90983i 0.581140 0.221976i
\(970\) 1.15654 + 1.59184i 0.0371343 + 0.0511110i
\(971\) 7.77997 2.52786i 0.249671 0.0811230i −0.181508 0.983389i \(-0.558098\pi\)
0.431179 + 0.902266i \(0.358098\pi\)
\(972\) 0.583826 9.61649i 0.0187262 0.308449i
\(973\) −35.3885 25.7113i −1.13450 0.824266i
\(974\) 1.40008 + 1.01722i 0.0448616 + 0.0325939i
\(975\) −0.309593 6.10059i −0.00991492 0.195375i
\(976\) −5.95492 + 1.93487i −0.190612 + 0.0619337i
\(977\) −20.0175 27.5517i −0.640415 0.881456i 0.358223 0.933636i \(-0.383383\pi\)
−0.998638 + 0.0521804i \(0.983383\pi\)
\(978\) −10.6206 27.8052i −0.339610 0.889111i
\(979\) 0 0
\(980\) 0.583592i 0.0186422i
\(981\) −13.7888 2.97864i −0.440242 0.0951008i
\(982\) −6.42047 19.7602i −0.204886 0.630573i
\(983\) −54.5002 17.7082i −1.73829 0.564804i −0.743682 0.668533i \(-0.766922\pi\)
−0.994606 + 0.103729i \(0.966922\pi\)
\(984\) 1.00859 3.73935i 0.0321528 0.119206i
\(985\) 1.93363 2.66141i 0.0616105 0.0847996i
\(986\) −3.63271 + 11.1803i −0.115689 + 0.356055i
\(987\) −34.5396 + 27.8751i −1.09941 + 0.887273i
\(988\) −0.954915 + 0.693786i −0.0303799 + 0.0220723i
\(989\) 42.9161 1.36465
\(990\) 0 0
\(991\) −12.5623 −0.399055 −0.199527 0.979892i \(-0.563941\pi\)
−0.199527 + 0.979892i \(0.563941\pi\)
\(992\) 15.8904 11.5451i 0.504522 0.366557i
\(993\) 17.3719 14.0200i 0.551282 0.444910i
\(994\) 5.95492 18.3273i 0.188878 0.581308i
\(995\) −0.502029 + 0.690983i −0.0159154 + 0.0219056i
\(996\) −1.76373 + 6.53903i −0.0558860 + 0.207197i
\(997\) −14.0066 4.55101i −0.443593 0.144132i 0.0786999 0.996898i \(-0.474923\pi\)
−0.522293 + 0.852766i \(0.674923\pi\)
\(998\) 13.0700 + 40.2254i 0.413725 + 1.27331i
\(999\) −15.4085 + 2.36208i −0.487502 + 0.0747330i
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 363.2.f.b.239.2 8
3.2 odd 2 inner 363.2.f.b.239.1 8
11.2 odd 10 363.2.d.f.362.5 8
11.3 even 5 363.2.f.e.215.1 8
11.4 even 5 33.2.f.a.29.2 yes 8
11.5 even 5 363.2.f.d.233.1 8
11.6 odd 10 363.2.f.e.233.2 8
11.7 odd 10 inner 363.2.f.b.161.1 8
11.8 odd 10 363.2.f.d.215.2 8
11.9 even 5 363.2.d.f.362.3 8
11.10 odd 2 33.2.f.a.8.1 8
33.2 even 10 363.2.d.f.362.4 8
33.5 odd 10 363.2.f.d.233.2 8
33.8 even 10 363.2.f.d.215.1 8
33.14 odd 10 363.2.f.e.215.2 8
33.17 even 10 363.2.f.e.233.1 8
33.20 odd 10 363.2.d.f.362.6 8
33.26 odd 10 33.2.f.a.29.1 yes 8
33.29 even 10 inner 363.2.f.b.161.2 8
33.32 even 2 33.2.f.a.8.2 yes 8
44.15 odd 10 528.2.bn.c.161.2 8
44.43 even 2 528.2.bn.c.305.1 8
55.4 even 10 825.2.bi.b.326.1 8
55.32 even 4 825.2.bs.a.74.1 8
55.37 odd 20 825.2.bs.a.524.2 8
55.43 even 4 825.2.bs.d.74.2 8
55.48 odd 20 825.2.bs.d.524.1 8
55.54 odd 2 825.2.bi.b.701.2 8
99.4 even 15 891.2.u.a.755.1 16
99.32 even 6 891.2.u.a.107.2 16
99.43 odd 6 891.2.u.a.701.2 16
99.59 odd 30 891.2.u.a.755.2 16
99.65 even 6 891.2.u.a.701.1 16
99.70 even 15 891.2.u.a.458.2 16
99.76 odd 6 891.2.u.a.107.1 16
99.92 odd 30 891.2.u.a.458.1 16
132.59 even 10 528.2.bn.c.161.1 8
132.131 odd 2 528.2.bn.c.305.2 8
165.32 odd 4 825.2.bs.d.74.1 8
165.59 odd 10 825.2.bi.b.326.2 8
165.92 even 20 825.2.bs.d.524.2 8
165.98 odd 4 825.2.bs.a.74.2 8
165.158 even 20 825.2.bs.a.524.1 8
165.164 even 2 825.2.bi.b.701.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.f.a.8.1 8 11.10 odd 2
33.2.f.a.8.2 yes 8 33.32 even 2
33.2.f.a.29.1 yes 8 33.26 odd 10
33.2.f.a.29.2 yes 8 11.4 even 5
363.2.d.f.362.3 8 11.9 even 5
363.2.d.f.362.4 8 33.2 even 10
363.2.d.f.362.5 8 11.2 odd 10
363.2.d.f.362.6 8 33.20 odd 10
363.2.f.b.161.1 8 11.7 odd 10 inner
363.2.f.b.161.2 8 33.29 even 10 inner
363.2.f.b.239.1 8 3.2 odd 2 inner
363.2.f.b.239.2 8 1.1 even 1 trivial
363.2.f.d.215.1 8 33.8 even 10
363.2.f.d.215.2 8 11.8 odd 10
363.2.f.d.233.1 8 11.5 even 5
363.2.f.d.233.2 8 33.5 odd 10
363.2.f.e.215.1 8 11.3 even 5
363.2.f.e.215.2 8 33.14 odd 10
363.2.f.e.233.1 8 33.17 even 10
363.2.f.e.233.2 8 11.6 odd 10
528.2.bn.c.161.1 8 132.59 even 10
528.2.bn.c.161.2 8 44.15 odd 10
528.2.bn.c.305.1 8 44.43 even 2
528.2.bn.c.305.2 8 132.131 odd 2
825.2.bi.b.326.1 8 55.4 even 10
825.2.bi.b.326.2 8 165.59 odd 10
825.2.bi.b.701.1 8 165.164 even 2
825.2.bi.b.701.2 8 55.54 odd 2
825.2.bs.a.74.1 8 55.32 even 4
825.2.bs.a.74.2 8 165.98 odd 4
825.2.bs.a.524.1 8 165.158 even 20
825.2.bs.a.524.2 8 55.37 odd 20
825.2.bs.d.74.1 8 165.32 odd 4
825.2.bs.d.74.2 8 55.43 even 4
825.2.bs.d.524.1 8 55.48 odd 20
825.2.bs.d.524.2 8 165.92 even 20
891.2.u.a.107.1 16 99.76 odd 6
891.2.u.a.107.2 16 99.32 even 6
891.2.u.a.458.1 16 99.92 odd 30
891.2.u.a.458.2 16 99.70 even 15
891.2.u.a.701.1 16 99.65 even 6
891.2.u.a.701.2 16 99.43 odd 6
891.2.u.a.755.1 16 99.4 even 15
891.2.u.a.755.2 16 99.59 odd 30