Properties

Label 363.2.f.e.215.1
Level $363$
Weight $2$
Character 363.215
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 215.1
Root \(0.951057 + 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 363.215
Dual form 363.2.f.e.233.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.363271 - 1.11803i) q^{2} +(-0.451057 + 1.67229i) q^{3} +(0.500000 - 0.363271i) q^{4} +(-0.363271 - 0.118034i) q^{5} +(2.03353 - 0.103198i) q^{6} +(-1.80902 - 2.48990i) q^{7} +(-2.48990 - 1.80902i) q^{8} +(-2.59310 - 1.50859i) q^{9} +O(q^{10})\) \(q+(-0.363271 - 1.11803i) q^{2} +(-0.451057 + 1.67229i) q^{3} +(0.500000 - 0.363271i) q^{4} +(-0.363271 - 0.118034i) q^{5} +(2.03353 - 0.103198i) q^{6} +(-1.80902 - 2.48990i) q^{7} +(-2.48990 - 1.80902i) q^{8} +(-2.59310 - 1.50859i) q^{9} +0.449028i q^{10} +(0.381966 + 1.00000i) q^{12} +(-0.690983 + 0.224514i) q^{13} +(-2.12663 + 2.92705i) q^{14} +(0.361243 - 0.554254i) q^{15} +(-0.736068 + 2.26538i) q^{16} +(1.31433 - 4.04508i) q^{17} +(-0.744661 + 3.44720i) q^{18} +(1.54508 - 2.12663i) q^{19} +(-0.224514 + 0.0729490i) q^{20} +(4.97980 - 1.90211i) q^{21} -6.23607i q^{23} +(4.14828 - 3.34786i) q^{24} +(-3.92705 - 2.85317i) q^{25} +(0.502029 + 0.690983i) q^{26} +(3.69244 - 3.65594i) q^{27} +(-1.80902 - 0.587785i) q^{28} +(-1.90211 + 1.38197i) q^{29} +(-0.750904 - 0.202537i) q^{30} +(1.80902 + 5.56758i) q^{31} -3.35520 q^{32} -5.00000 q^{34} +(0.363271 + 1.11803i) q^{35} +(-1.84458 + 0.187701i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(-2.93893 - 0.954915i) q^{38} +(-0.0637797 - 1.25679i) q^{39} +(0.690983 + 0.951057i) q^{40} +(0.587785 + 0.427051i) q^{41} +(-3.93564 - 4.87660i) q^{42} +6.88191i q^{43} +(0.763932 + 0.854102i) q^{45} +(-6.97214 + 2.26538i) q^{46} +(4.89404 - 6.73607i) q^{47} +(-3.45637 - 2.25273i) q^{48} +(-0.763932 + 2.35114i) q^{49} +(-1.76336 + 5.42705i) q^{50} +(6.17171 + 4.02250i) q^{51} +(-0.263932 + 0.363271i) q^{52} +(1.76336 - 0.572949i) q^{53} +(-5.42882 - 2.80017i) q^{54} +9.47214i q^{56} +(2.85941 + 3.54306i) q^{57} +(2.23607 + 1.62460i) q^{58} +(0.224514 + 0.309017i) q^{59} +(-0.0207233 - 0.408356i) q^{60} +(-2.50000 - 0.812299i) q^{61} +(5.56758 - 4.04508i) q^{62} +(0.934712 + 9.18562i) q^{63} +(2.69098 + 8.28199i) q^{64} +0.277515 q^{65} +7.32624 q^{67} +(-0.812299 - 2.50000i) q^{68} +(10.4285 + 2.81282i) q^{69} +(1.11803 - 0.812299i) q^{70} +(5.06555 + 1.64590i) q^{71} +(3.72747 + 8.44720i) q^{72} +(-5.52786 - 7.60845i) q^{73} +(2.85317 + 2.07295i) q^{74} +(6.54264 - 5.28022i) q^{75} -1.62460i q^{76} +(-1.38197 + 0.527864i) q^{78} +(-3.78115 + 1.22857i) q^{79} +(0.534785 - 0.736068i) q^{80} +(4.44829 + 7.82385i) q^{81} +(0.263932 - 0.812299i) q^{82} +(-1.95511 + 6.01722i) q^{83} +(1.79892 - 2.76007i) q^{84} +(-0.954915 + 1.31433i) q^{85} +(7.69421 - 2.50000i) q^{86} +(-1.45309 - 3.80423i) q^{87} +0.527864i q^{89} +(0.677400 - 1.16437i) q^{90} +(1.80902 + 1.31433i) q^{91} +(-2.26538 - 3.11803i) q^{92} +(-10.1266 + 0.513904i) q^{93} +(-9.30902 - 3.02468i) q^{94} +(-0.812299 + 0.590170i) q^{95} +(1.51338 - 5.61086i) q^{96} +(-1.35410 - 4.16750i) q^{97} +2.90617 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9} + 12 q^{12} - 10 q^{13} + 4 q^{15} + 12 q^{16} + 20 q^{18} - 10 q^{19} + 20 q^{24} - 18 q^{25} - 2 q^{27} - 10 q^{28} + 30 q^{30} + 10 q^{31} - 40 q^{34} - 6 q^{37} + 10 q^{39} + 10 q^{40} - 10 q^{42} + 24 q^{45} - 20 q^{46} - 14 q^{48} - 24 q^{49} + 10 q^{51} - 20 q^{52} - 10 q^{57} - 8 q^{60} - 20 q^{61} - 10 q^{63} + 26 q^{64} - 4 q^{67} + 34 q^{69} + 20 q^{72} - 80 q^{73} + 6 q^{75} - 20 q^{78} + 10 q^{79} - 2 q^{81} + 20 q^{82} - 10 q^{84} - 30 q^{85} + 30 q^{90} + 10 q^{91} - 70 q^{94} + 30 q^{96} + 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.363271 1.11803i −0.256872 0.790569i −0.993455 0.114223i \(-0.963562\pi\)
0.736584 0.676347i \(-0.236438\pi\)
\(3\) −0.451057 + 1.67229i −0.260418 + 0.965496i
\(4\) 0.500000 0.363271i 0.250000 0.181636i
\(5\) −0.363271 0.118034i −0.162460 0.0527864i 0.226658 0.973974i \(-0.427220\pi\)
−0.389118 + 0.921188i \(0.627220\pi\)
\(6\) 2.03353 0.103198i 0.830186 0.0421303i
\(7\) −1.80902 2.48990i −0.683744 0.941093i 0.316227 0.948684i \(-0.397584\pi\)
−0.999971 + 0.00759045i \(0.997584\pi\)
\(8\) −2.48990 1.80902i −0.880312 0.639584i
\(9\) −2.59310 1.50859i −0.864365 0.502864i
\(10\) 0.449028i 0.141995i
\(11\) 0 0
\(12\) 0.381966 + 1.00000i 0.110264 + 0.288675i
\(13\) −0.690983 + 0.224514i −0.191644 + 0.0622690i −0.403267 0.915083i \(-0.632125\pi\)
0.211622 + 0.977351i \(0.432125\pi\)
\(14\) −2.12663 + 2.92705i −0.568365 + 0.782287i
\(15\) 0.361243 0.554254i 0.0932725 0.143108i
\(16\) −0.736068 + 2.26538i −0.184017 + 0.566346i
\(17\) 1.31433 4.04508i 0.318771 0.981077i −0.655403 0.755279i \(-0.727501\pi\)
0.974174 0.225798i \(-0.0724989\pi\)
\(18\) −0.744661 + 3.44720i −0.175518 + 0.812512i
\(19\) 1.54508 2.12663i 0.354467 0.487882i −0.594130 0.804369i \(-0.702504\pi\)
0.948597 + 0.316487i \(0.102504\pi\)
\(20\) −0.224514 + 0.0729490i −0.0502029 + 0.0163119i
\(21\) 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 \(-0.225296\pi\)
\(24\) 4.14828 3.34786i 0.846765 0.683379i
\(25\) −3.92705 2.85317i −0.785410 0.570634i
\(26\) 0.502029 + 0.690983i 0.0984559 + 0.135513i
\(27\) 3.69244 3.65594i 0.710610 0.703587i
\(28\) −1.80902 0.587785i −0.341872 0.111081i
\(29\) −1.90211 + 1.38197i −0.353214 + 0.256625i −0.750216 0.661193i \(-0.770050\pi\)
0.397002 + 0.917818i \(0.370050\pi\)
\(30\) −0.750904 0.202537i −0.137096 0.0369780i
\(31\) 1.80902 + 5.56758i 0.324909 + 0.999967i 0.971482 + 0.237115i \(0.0762017\pi\)
−0.646573 + 0.762852i \(0.723798\pi\)
\(32\) −3.35520 −0.593121
\(33\) 0 0
\(34\) −5.00000 −0.857493
\(35\) 0.363271 + 1.11803i 0.0614041 + 0.188982i
\(36\) −1.84458 + 0.187701i −0.307429 + 0.0312835i
\(37\) −2.42705 + 1.76336i −0.399005 + 0.289894i −0.769135 0.639086i \(-0.779313\pi\)
0.370131 + 0.928980i \(0.379313\pi\)
\(38\) −2.93893 0.954915i −0.476757 0.154908i
\(39\) −0.0637797 1.25679i −0.0102129 0.201248i
\(40\) 0.690983 + 0.951057i 0.109254 + 0.150375i
\(41\) 0.587785 + 0.427051i 0.0917966 + 0.0666942i 0.632737 0.774367i \(-0.281931\pi\)
−0.540940 + 0.841061i \(0.681931\pi\)
\(42\) −3.93564 4.87660i −0.607283 0.752476i
\(43\) 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
\(46\) −6.97214 + 2.26538i −1.02799 + 0.334013i
\(47\) 4.89404 6.73607i 0.713869 0.982556i −0.285836 0.958279i \(-0.592271\pi\)
0.999705 0.0242780i \(-0.00772869\pi\)
\(48\) −3.45637 2.25273i −0.498884 0.325154i
\(49\) −0.763932 + 2.35114i −0.109133 + 0.335877i
\(50\) −1.76336 + 5.42705i −0.249376 + 0.767501i
\(51\) 6.17171 + 4.02250i 0.864213 + 0.563262i
\(52\) −0.263932 + 0.363271i −0.0366008 + 0.0503767i
\(53\) 1.76336 0.572949i 0.242216 0.0787006i −0.185394 0.982664i \(-0.559356\pi\)
0.427609 + 0.903964i \(0.359356\pi\)
\(54\) −5.42882 2.80017i −0.738769 0.381055i
\(55\) 0 0
\(56\) 9.47214i 1.26577i
\(57\) 2.85941 + 3.54306i 0.378738 + 0.469289i
\(58\) 2.23607 + 1.62460i 0.293610 + 0.213320i
\(59\) 0.224514 + 0.309017i 0.0292292 + 0.0402306i 0.823381 0.567488i \(-0.192085\pi\)
−0.794152 + 0.607719i \(0.792085\pi\)
\(60\) −0.0207233 0.408356i −0.00267536 0.0527186i
\(61\) −2.50000 0.812299i −0.320092 0.104004i 0.144564 0.989495i \(-0.453822\pi\)
−0.464656 + 0.885491i \(0.653822\pi\)
\(62\) 5.56758 4.04508i 0.707084 0.513726i
\(63\) 0.934712 + 9.18562i 0.117763 + 1.15728i
\(64\) 2.69098 + 8.28199i 0.336373 + 1.03525i
\(65\) 0.277515 0.0344214
\(66\) 0 0
\(67\) 7.32624 0.895042 0.447521 0.894273i \(-0.352307\pi\)
0.447521 + 0.894273i \(0.352307\pi\)
\(68\) −0.812299 2.50000i −0.0985058 0.303170i
\(69\) 10.4285 + 2.81282i 1.25544 + 0.338624i
\(70\) 1.11803 0.812299i 0.133631 0.0970883i
\(71\) 5.06555 + 1.64590i 0.601171 + 0.195332i 0.593762 0.804640i \(-0.297642\pi\)
0.00740814 + 0.999973i \(0.497642\pi\)
\(72\) 3.72747 + 8.44720i 0.439287 + 0.995512i
\(73\) −5.52786 7.60845i −0.646988 0.890502i 0.351976 0.936009i \(-0.385510\pi\)
−0.998964 + 0.0455069i \(0.985510\pi\)
\(74\) 2.85317 + 2.07295i 0.331674 + 0.240975i
\(75\) 6.54264 5.28022i 0.755479 0.609707i
\(76\) 1.62460i 0.186354i
\(77\) 0 0
\(78\) −1.38197 + 0.527864i −0.156477 + 0.0597688i
\(79\) −3.78115 + 1.22857i −0.425413 + 0.138225i −0.513896 0.857853i \(-0.671798\pi\)
0.0884828 + 0.996078i \(0.471798\pi\)
\(80\) 0.534785 0.736068i 0.0597907 0.0822949i
\(81\) 4.44829 + 7.82385i 0.494255 + 0.869317i
\(82\) 0.263932 0.812299i 0.0291464 0.0897034i
\(83\) −1.95511 + 6.01722i −0.214602 + 0.660476i 0.784580 + 0.620028i \(0.212879\pi\)
−0.999182 + 0.0404483i \(0.987121\pi\)
\(84\) 1.79892 2.76007i 0.196278 0.301149i
\(85\) −0.954915 + 1.31433i −0.103575 + 0.142559i
\(86\) 7.69421 2.50000i 0.829688 0.269582i
\(87\) −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 \(0.991094\pi\)
\(90\) 0.677400 1.16437i 0.0714043 0.122736i
\(91\) 1.80902 + 1.31433i 0.189637 + 0.137779i
\(92\) −2.26538 3.11803i −0.236183 0.325078i
\(93\) −10.1266 + 0.513904i −1.05008 + 0.0532893i
\(94\) −9.30902 3.02468i −0.960152 0.311972i
\(95\) −0.812299 + 0.590170i −0.0833401 + 0.0605502i
\(96\) 1.51338 5.61086i 0.154459 0.572656i
\(97\) −1.35410 4.16750i −0.137488 0.423145i 0.858481 0.512846i \(-0.171409\pi\)
−0.995969 + 0.0897009i \(0.971409\pi\)
\(98\) 2.90617 0.293568
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) 4.92680 + 15.1631i 0.490235 + 1.50879i 0.824254 + 0.566220i \(0.191595\pi\)
−0.334019 + 0.942566i \(0.608405\pi\)
\(102\) 2.25528 8.36144i 0.223306 0.827906i
\(103\) 9.09017 6.60440i 0.895681 0.650750i −0.0416720 0.999131i \(-0.513268\pi\)
0.937353 + 0.348381i \(0.113268\pi\)
\(104\) 2.12663 + 0.690983i 0.208533 + 0.0677565i
\(105\) −2.03353 + 0.103198i −0.198452 + 0.0100711i
\(106\) −1.28115 1.76336i −0.124437 0.171272i
\(107\) 10.5474 + 7.66312i 1.01965 + 0.740822i 0.966212 0.257749i \(-0.0829809\pi\)
0.0534417 + 0.998571i \(0.482981\pi\)
\(108\) 0.518118 3.16933i 0.0498560 0.304969i
\(109\) 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
\(112\) 6.97214 2.26538i 0.658805 0.214059i
\(113\) 1.20833 1.66312i 0.113670 0.156453i −0.748391 0.663258i \(-0.769173\pi\)
0.862061 + 0.506804i \(0.169173\pi\)
\(114\) 2.92252 4.48401i 0.273719 0.419966i
\(115\) −0.736068 + 2.26538i −0.0686387 + 0.211248i
\(116\) −0.449028 + 1.38197i −0.0416912 + 0.128312i
\(117\) 2.13049 + 0.460226i 0.196963 + 0.0425479i
\(118\) 0.263932 0.363271i 0.0242969 0.0334418i
\(119\) −12.4495 + 4.04508i −1.14124 + 0.370812i
\(120\) −1.90211 + 0.726543i −0.173638 + 0.0663240i
\(121\) 0 0
\(122\) 3.09017i 0.279771i
\(123\) −0.979277 + 0.790322i −0.0882984 + 0.0712610i
\(124\) 2.92705 + 2.12663i 0.262857 + 0.190977i
\(125\) 2.21238 + 3.04508i 0.197882 + 0.272361i
\(126\) 9.93028 4.38191i 0.884659 0.390372i
\(127\) 12.2361 + 3.97574i 1.08578 + 0.352790i 0.796613 0.604490i \(-0.206623\pi\)
0.289163 + 0.957280i \(0.406623\pi\)
\(128\) 2.85317 2.07295i 0.252187 0.183225i
\(129\) −11.5085 3.10413i −1.01327 0.273303i
\(130\) −0.100813 0.310271i −0.00884189 0.0272125i
\(131\) 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
\(134\) −2.66141 8.19098i −0.229911 0.707593i
\(135\) −1.77288 + 0.892266i −0.152585 + 0.0767941i
\(136\) −10.5902 + 7.69421i −0.908100 + 0.659773i
\(137\) −4.47777 1.45492i −0.382562 0.124302i 0.111422 0.993773i \(-0.464460\pi\)
−0.493983 + 0.869471i \(0.664460\pi\)
\(138\) −0.643548 12.6812i −0.0547825 1.07950i
\(139\) 8.35410 + 11.4984i 0.708586 + 0.975285i 0.999826 + 0.0186347i \(0.00593195\pi\)
−0.291241 + 0.956650i \(0.594068\pi\)
\(140\) 0.587785 + 0.427051i 0.0496769 + 0.0360924i
\(141\) 9.05716 + 11.2226i 0.762750 + 0.945113i
\(142\) 6.26137i 0.525442i
\(143\) 0 0
\(144\) 5.32624 4.76393i 0.443853 0.396994i
\(145\) 0.854102 0.277515i 0.0709293 0.0230463i
\(146\) −6.49839 + 8.94427i −0.537811 + 0.740233i
\(147\) −3.58721 2.33801i −0.295868 0.192836i
\(148\) −0.572949 + 1.76336i −0.0470961 + 0.144947i
\(149\) 4.02874 12.3992i 0.330047 1.01578i −0.639063 0.769154i \(-0.720678\pi\)
0.969111 0.246627i \(-0.0793222\pi\)
\(150\) −8.28022 5.39675i −0.676077 0.440642i
\(151\) 3.29180 4.53077i 0.267883 0.368709i −0.653791 0.756675i \(-0.726822\pi\)
0.921673 + 0.387967i \(0.126822\pi\)
\(152\) −7.69421 + 2.50000i −0.624083 + 0.202777i
\(153\) −9.51057 + 8.50651i −0.768884 + 0.687710i
\(154\) 0 0
\(155\) 2.23607i 0.179605i
\(156\) −0.488446 0.605226i −0.0391070 0.0484569i
\(157\) −7.85410 5.70634i −0.626826 0.455415i 0.228473 0.973550i \(-0.426627\pi\)
−0.855299 + 0.518135i \(0.826627\pi\)
\(158\) 2.74717 + 3.78115i 0.218553 + 0.300812i
\(159\) 0.162763 + 3.20727i 0.0129079 + 0.254353i
\(160\) 1.21885 + 0.396027i 0.0963583 + 0.0313087i
\(161\) −15.5272 + 11.2812i −1.22371 + 0.889079i
\(162\) 7.13140 7.81553i 0.560295 0.614046i
\(163\) −4.51722 13.9026i −0.353816 1.08893i −0.956693 0.291099i \(-0.905979\pi\)
0.602877 0.797834i \(-0.294021\pi\)
\(164\) 0.449028 0.0350632
\(165\) 0 0
\(166\) 7.43769 0.577277
\(167\) −6.51864 20.0623i −0.504427 1.55247i −0.801731 0.597685i \(-0.796087\pi\)
0.297304 0.954783i \(-0.403913\pi\)
\(168\) −15.8401 4.27247i −1.22209 0.329628i
\(169\) −10.0902 + 7.33094i −0.776167 + 0.563918i
\(170\) 1.81636 + 0.590170i 0.139308 + 0.0452640i
\(171\) −7.21477 + 3.18364i −0.551727 + 0.243459i
\(172\) 2.50000 + 3.44095i 0.190623 + 0.262370i
\(173\) −18.6906 13.5795i −1.42102 1.03243i −0.991602 0.129327i \(-0.958718\pi\)
−0.429419 0.903105i \(-0.641282\pi\)
\(174\) −3.72539 + 3.00656i −0.282421 + 0.227927i
\(175\) 14.9394i 1.12931i
\(176\) 0 0
\(177\) −0.618034 + 0.236068i −0.0464543 + 0.0177440i
\(178\) 0.590170 0.191758i 0.0442351 0.0143729i
\(179\) −8.19624 + 11.2812i −0.612616 + 0.843193i −0.996789 0.0800678i \(-0.974486\pi\)
0.384174 + 0.923261i \(0.374486\pi\)
\(180\) 0.692237 + 0.149536i 0.0515963 + 0.0111458i
\(181\) 2.39919 7.38394i 0.178330 0.548844i −0.821440 0.570295i \(-0.806829\pi\)
0.999770 + 0.0214515i \(0.00682876\pi\)
\(182\) 0.812299 2.50000i 0.0602116 0.185312i
\(183\) 2.48604 3.81433i 0.183773 0.281963i
\(184\) −11.2812 + 15.5272i −0.831658 + 1.14468i
\(185\) 1.08981 0.354102i 0.0801247 0.0260341i
\(186\) 4.25325 + 11.1352i 0.311864 + 0.816470i
\(187\) 0 0
\(188\) 5.14590i 0.375303i
\(189\) −15.7826 2.58012i −1.14802 0.187676i
\(190\) 0.954915 + 0.693786i 0.0692768 + 0.0503326i
\(191\) −14.2456 19.6074i −1.03078 1.41874i −0.904363 0.426763i \(-0.859654\pi\)
−0.126412 0.991978i \(-0.540346\pi\)
\(192\) −15.0637 + 0.764452i −1.08713 + 0.0551696i
\(193\) 9.37132 + 3.04493i 0.674563 + 0.219179i 0.626213 0.779652i \(-0.284604\pi\)
0.0483493 + 0.998830i \(0.484604\pi\)
\(194\) −4.16750 + 3.02786i −0.299209 + 0.217388i
\(195\) −0.125175 + 0.464084i −0.00896395 + 0.0332338i
\(196\) 0.472136 + 1.45309i 0.0337240 + 0.103792i
\(197\) −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 \(0.474746\pi\)
\(200\) 4.61653 + 14.2082i 0.326438 + 1.00467i
\(201\) −3.30455 + 12.2516i −0.233085 + 0.864160i
\(202\) 15.1631 11.0167i 1.06687 0.775129i
\(203\) 6.88191 + 2.23607i 0.483015 + 0.156941i
\(204\) 4.54711 0.230757i 0.318362 0.0161562i
\(205\) −0.163119 0.224514i −0.0113927 0.0156807i
\(206\) −10.6861 7.76393i −0.744538 0.540939i
\(207\) −9.40769 + 16.1707i −0.653880 + 1.12394i
\(208\) 1.73060i 0.119995i
\(209\) 0 0
\(210\) 0.854102 + 2.23607i 0.0589386 + 0.154303i
\(211\) 18.5172 6.01661i 1.27478 0.414201i 0.408040 0.912964i \(-0.366212\pi\)
0.866738 + 0.498764i \(0.166212\pi\)
\(212\) 0.673542 0.927051i 0.0462591 0.0636701i
\(213\) −5.03727 + 7.72867i −0.345148 + 0.529560i
\(214\) 4.73607 14.5761i 0.323751 0.996403i
\(215\) 0.812299 2.50000i 0.0553983 0.170499i
\(216\) −15.8075 + 2.42325i −1.07556 + 0.164881i
\(217\) 10.5902 14.5761i 0.718908 0.989491i
\(218\) −5.25731 + 1.70820i −0.356070 + 0.115694i
\(219\) 15.2169 5.81234i 1.02826 0.392762i
\(220\) 0 0
\(221\) 3.09017i 0.207867i
\(222\) −4.75351 + 3.83630i −0.319035 + 0.257476i
\(223\) −1.42705 1.03681i −0.0955624 0.0694301i 0.538978 0.842320i \(-0.318811\pi\)
−0.634540 + 0.772890i \(0.718811\pi\)
\(224\) 6.06961 + 8.35410i 0.405543 + 0.558182i
\(225\) 5.87895 + 13.3229i 0.391930 + 0.888191i
\(226\) −2.29837 0.746787i −0.152886 0.0496755i
\(227\) 11.7229 8.51722i 0.778079 0.565308i −0.126323 0.991989i \(-0.540317\pi\)
0.904402 + 0.426681i \(0.140317\pi\)
\(228\) 2.71680 + 0.732786i 0.179924 + 0.0485299i
\(229\) −4.67376 14.3844i −0.308851 0.950545i −0.978212 0.207608i \(-0.933432\pi\)
0.669361 0.742937i \(-0.266568\pi\)
\(230\) 2.80017 0.184638
\(231\) 0 0
\(232\) 7.23607 0.475071
\(233\) −2.99193 9.20820i −0.196008 0.603249i −0.999963 0.00856033i \(-0.997275\pi\)
0.803956 0.594689i \(-0.202725\pi\)
\(234\) −0.259396 2.54914i −0.0169573 0.166643i
\(235\) −2.57295 + 1.86936i −0.167841 + 0.121943i
\(236\) 0.224514 + 0.0729490i 0.0146146 + 0.00474858i
\(237\) −0.349011 6.87733i −0.0226707 0.446731i
\(238\) 9.04508 + 12.4495i 0.586306 + 0.806981i
\(239\) 6.24112 + 4.53444i 0.403705 + 0.293309i 0.771048 0.636777i \(-0.219733\pi\)
−0.367344 + 0.930085i \(0.619733\pi\)
\(240\) 0.989700 + 1.22632i 0.0638848 + 0.0791588i
\(241\) 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
\(244\) −1.54508 + 0.502029i −0.0989139 + 0.0321391i
\(245\) 0.555029 0.763932i 0.0354595 0.0488058i
\(246\) 1.23935 + 0.807763i 0.0790181 + 0.0515011i
\(247\) −0.590170 + 1.81636i −0.0375516 + 0.115572i
\(248\) 5.56758 17.1353i 0.353542 1.08809i
\(249\) −9.18066 5.98362i −0.581801 0.379197i
\(250\) 2.60081 3.57971i 0.164490 0.226401i
\(251\) 19.3314 6.28115i 1.22019 0.396463i 0.373037 0.927816i \(-0.378316\pi\)
0.847150 + 0.531354i \(0.178316\pi\)
\(252\) 3.80423 + 4.25325i 0.239644 + 0.267930i
\(253\) 0 0
\(254\) 15.1246i 0.949003i
\(255\) −1.76721 2.18973i −0.110667 0.137126i
\(256\) 10.7361 + 7.80021i 0.671004 + 0.487513i
\(257\) 13.0903 + 18.0172i 0.816549 + 1.12388i 0.990280 + 0.139090i \(0.0444178\pi\)
−0.173731 + 0.984793i \(0.555582\pi\)
\(258\) 0.710198 + 13.9946i 0.0442150 + 0.871264i
\(259\) 8.78115 + 2.85317i 0.545634 + 0.177287i
\(260\) 0.138757 0.100813i 0.00860536 0.00625216i
\(261\) 7.01719 0.714056i 0.434353 0.0441990i
\(262\) −3.78115 11.6372i −0.233600 0.718948i
\(263\) −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
\(266\) 2.93893 + 9.04508i 0.180197 + 0.554590i
\(267\) −0.882741 0.238097i −0.0540229 0.0145713i
\(268\) 3.66312 2.66141i 0.223761 0.162572i
\(269\) −17.8456 5.79837i −1.08806 0.353533i −0.290565 0.956855i \(-0.593843\pi\)
−0.797498 + 0.603322i \(0.793843\pi\)
\(270\) 1.64162 + 1.65801i 0.0999059 + 0.100903i
\(271\) −9.96149 13.7108i −0.605118 0.832873i 0.391047 0.920371i \(-0.372113\pi\)
−0.996165 + 0.0874977i \(0.972113\pi\)
\(272\) 8.19624 + 5.95492i 0.496970 + 0.361070i
\(273\) −3.01390 + 2.43236i −0.182410 + 0.147213i
\(274\) 5.53483i 0.334371i
\(275\) 0 0
\(276\) 6.23607 2.38197i 0.375367 0.143378i
\(277\) 15.4271 5.01255i 0.926922 0.301175i 0.193618 0.981077i \(-0.437978\pi\)
0.733303 + 0.679902i \(0.237978\pi\)
\(278\) 9.82084 13.5172i 0.589015 0.810709i
\(279\) 3.70826 17.1663i 0.222008 1.02772i
\(280\) 1.11803 3.44095i 0.0668153 0.205636i
\(281\) −8.22899 + 25.3262i −0.490901 + 1.51084i 0.332349 + 0.943157i \(0.392159\pi\)
−0.823249 + 0.567680i \(0.807841\pi\)
\(282\) 9.25703 14.2031i 0.551248 0.845780i
\(283\) −12.5623 + 17.2905i −0.746752 + 1.02782i 0.251450 + 0.967870i \(0.419093\pi\)
−0.998202 + 0.0599451i \(0.980907\pi\)
\(284\) 3.13068 1.01722i 0.185772 0.0603610i
\(285\) −0.620541 1.62460i −0.0367577 0.0962329i
\(286\) 0 0
\(287\) 2.23607i 0.131991i
\(288\) 8.70035 + 5.06163i 0.512673 + 0.298259i
\(289\) −0.881966 0.640786i −0.0518804 0.0376933i
\(290\) −0.620541 0.854102i −0.0364394 0.0501546i
\(291\) 7.58003 0.384672i 0.444349 0.0225499i
\(292\) −5.52786 1.79611i −0.323494 0.105109i
\(293\) 11.2739 8.19098i 0.658629 0.478522i −0.207570 0.978220i \(-0.566556\pi\)
0.866200 + 0.499698i \(0.166556\pi\)
\(294\) −1.31085 + 4.85995i −0.0764501 + 0.283438i
\(295\) −0.0450850 0.138757i −0.00262495 0.00807876i
\(296\) 9.23305 0.536660
\(297\) 0 0
\(298\) −15.3262 −0.887825
\(299\) 1.40008 + 4.30902i 0.0809690 + 0.249197i
\(300\) 1.35317 5.01686i 0.0781253 0.289649i
\(301\) 17.1353 12.4495i 0.987660 0.717577i
\(302\) −6.26137 2.03444i −0.360301 0.117069i
\(303\) −27.5794 + 1.39960i −1.58439 + 0.0804049i
\(304\) 3.68034 + 5.06555i 0.211082 + 0.290529i
\(305\) 0.812299 + 0.590170i 0.0465121 + 0.0337930i
\(306\) 12.9655 + 7.54297i 0.741187 + 0.431203i
\(307\) 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
\(310\) −2.50000 + 0.812299i −0.141990 + 0.0461355i
\(311\) 2.93893 4.04508i 0.166651 0.229376i −0.717521 0.696537i \(-0.754723\pi\)
0.884172 + 0.467161i \(0.154723\pi\)
\(312\) −2.11475 + 3.24466i −0.119724 + 0.183693i
\(313\) 3.39919 10.4616i 0.192133 0.591326i −0.807865 0.589368i \(-0.799377\pi\)
0.999998 0.00195780i \(-0.000623187\pi\)
\(314\) −3.52671 + 10.8541i −0.199024 + 0.612532i
\(315\) 0.744661 3.44720i 0.0419569 0.194228i
\(316\) −1.44427 + 1.98787i −0.0812466 + 0.111826i
\(317\) −4.02874 + 1.30902i −0.226277 + 0.0735217i −0.419961 0.907542i \(-0.637956\pi\)
0.193684 + 0.981064i \(0.437956\pi\)
\(318\) 3.52671 1.34708i 0.197768 0.0755407i
\(319\) 0 0
\(320\) 3.32624i 0.185942i
\(321\) −17.5724 + 14.1818i −0.980796 + 0.791549i
\(322\) 18.2533 + 13.2618i 1.01722 + 0.739051i
\(323\) −6.57164 9.04508i −0.365656 0.503282i
\(324\) 5.06633 + 2.29599i 0.281463 + 0.127555i
\(325\) 3.35410 + 1.08981i 0.186052 + 0.0604520i
\(326\) −13.9026 + 10.1008i −0.769992 + 0.559432i
\(327\) 7.86357 + 2.12099i 0.434856 + 0.117291i
\(328\) −0.690983 2.12663i −0.0381532 0.117423i
\(329\) −25.6255 −1.41278
\(330\) 0 0
\(331\) 12.8885 0.708418 0.354209 0.935166i \(-0.384750\pi\)
0.354209 + 0.935166i \(0.384750\pi\)
\(332\) 1.20833 + 3.71885i 0.0663155 + 0.204098i
\(333\) 8.95376 0.911119i 0.490663 0.0499290i
\(334\) −20.0623 + 14.5761i −1.09776 + 0.797570i
\(335\) −2.66141 0.864745i −0.145408 0.0472461i
\(336\) 0.643548 + 12.6812i 0.0351084 + 0.691818i
\(337\) 14.7984 + 20.3682i 0.806119 + 1.10953i 0.991911 + 0.126938i \(0.0405150\pi\)
−0.185792 + 0.982589i \(0.559485\pi\)
\(338\) 11.8617 + 8.61803i 0.645192 + 0.468759i
\(339\) 2.23619 + 2.77083i 0.121453 + 0.150491i
\(340\) 1.00406i 0.0544526i
\(341\) 0 0
\(342\) 6.18034 + 6.90983i 0.334195 + 0.373641i
\(343\) −13.2533 + 4.30625i −0.715610 + 0.232516i
\(344\) 12.4495 17.1353i 0.671232 0.923871i
\(345\) −3.45637 2.25273i −0.186085 0.121283i
\(346\) −8.39261 + 25.8298i −0.451189 + 1.38862i
\(347\) −2.24514 + 6.90983i −0.120525 + 0.370939i −0.993059 0.117614i \(-0.962475\pi\)
0.872534 + 0.488554i \(0.162475\pi\)
\(348\) −2.10851 1.37425i −0.113028 0.0736675i
\(349\) 7.98936 10.9964i 0.427660 0.588624i −0.539754 0.841823i \(-0.681483\pi\)
0.967414 + 0.253199i \(0.0814827\pi\)
\(350\) 16.7027 5.42705i 0.892799 0.290088i
\(351\) −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 \(0.647825\pi\)
\(354\) 0.488446 + 0.605226i 0.0259606 + 0.0321674i
\(355\) −1.64590 1.19581i −0.0873552 0.0634673i
\(356\) 0.191758 + 0.263932i 0.0101631 + 0.0139884i
\(357\) −1.14912 22.6437i −0.0608181 1.19843i
\(358\) 15.5902 + 5.06555i 0.823966 + 0.267723i
\(359\) 25.7970 18.7426i 1.36152 0.989199i 0.363169 0.931723i \(-0.381695\pi\)
0.998347 0.0574756i \(-0.0183051\pi\)
\(360\) −0.357028 3.50859i −0.0188170 0.184919i
\(361\) 3.73607 + 11.4984i 0.196635 + 0.605181i
\(362\) −9.12705 −0.479707
\(363\) 0 0
\(364\) 1.38197 0.0724347
\(365\) 1.11006 + 3.41641i 0.0581031 + 0.178823i
\(366\) −5.16765 1.39384i −0.270118 0.0728573i
\(367\) −19.3992 + 14.0943i −1.01263 + 0.735718i −0.964759 0.263135i \(-0.915243\pi\)
−0.0478704 + 0.998854i \(0.515243\pi\)
\(368\) 14.1271 + 4.59017i 0.736425 + 0.239279i
\(369\) −0.879937 1.99411i −0.0458077 0.103809i
\(370\) −0.791796 1.08981i −0.0411635 0.0566567i
\(371\) −4.61653 3.35410i −0.239678 0.174136i
\(372\) −4.87660 + 3.93564i −0.252840 + 0.204054i
\(373\) 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
\(376\) −24.3713 + 7.91872i −1.25686 + 0.408377i
\(377\) 1.00406 1.38197i 0.0517116 0.0711749i
\(378\) 2.84870 + 18.5828i 0.146521 + 0.955795i
\(379\) 0.892609 2.74717i 0.0458503 0.141113i −0.925511 0.378722i \(-0.876364\pi\)
0.971361 + 0.237609i \(0.0763637\pi\)
\(380\) −0.191758 + 0.590170i −0.00983697 + 0.0302751i
\(381\) −12.1677 + 18.6689i −0.623372 + 0.956439i
\(382\) −16.7467 + 23.0499i −0.856836 + 1.17933i
\(383\) 11.8087 3.83688i 0.603397 0.196055i 0.00864191 0.999963i \(-0.497249\pi\)
0.594755 + 0.803907i \(0.297249\pi\)
\(384\) 2.17963 + 5.70634i 0.111229 + 0.291200i
\(385\) 0 0
\(386\) 11.5836i 0.589589i
\(387\) 10.3820 17.8455i 0.527747 0.907135i
\(388\) −2.19098 1.59184i −0.111230 0.0808136i
\(389\) 4.33901 + 5.97214i 0.219997 + 0.302799i 0.904723 0.426001i \(-0.140078\pi\)
−0.684726 + 0.728801i \(0.740078\pi\)
\(390\) 0.564334 0.0286389i 0.0285762 0.00145019i
\(391\) −25.2254 8.19624i −1.27570 0.414502i
\(392\) 6.15537 4.47214i 0.310893 0.225877i
\(393\) −4.69488 + 17.4062i −0.236825 + 0.878027i
\(394\) 3.12868 + 9.62908i 0.157620 + 0.485106i
\(395\) 1.51860 0.0764089
\(396\) 0 0
\(397\) −23.0000 −1.15434 −0.577168 0.816625i \(-0.695842\pi\)
−0.577168 + 0.816625i \(0.695842\pi\)
\(398\) −0.812299 2.50000i −0.0407169 0.125314i
\(399\) 3.64912 13.5291i 0.182685 0.677302i
\(400\) 9.35410 6.79615i 0.467705 0.339808i
\(401\) 26.4908 + 8.60739i 1.32289 + 0.429833i 0.883486 0.468458i \(-0.155190\pi\)
0.439403 + 0.898290i \(0.355190\pi\)
\(402\) 14.8981 0.756051i 0.743051 0.0377084i
\(403\) −2.50000 3.44095i −0.124534 0.171406i
\(404\) 7.97172 + 5.79180i 0.396608 + 0.288153i
\(405\) −0.692457 3.36723i −0.0344085 0.167319i
\(406\) 8.50651i 0.422171i
\(407\) 0 0
\(408\) −8.09017 21.1803i −0.400523 1.04858i
\(409\) 20.1246 6.53888i 0.995098 0.323327i 0.234193 0.972190i \(-0.424755\pi\)
0.760905 + 0.648863i \(0.224755\pi\)
\(410\) −0.191758 + 0.263932i −0.00947024 + 0.0130347i
\(411\) 4.45276 6.83187i 0.219639 0.336991i
\(412\) 2.14590 6.60440i 0.105721 0.325375i
\(413\) 0.363271 1.11803i 0.0178754 0.0550149i
\(414\) 21.4970 + 4.64376i 1.05652 + 0.228228i
\(415\) 1.42047 1.95511i 0.0697283 0.0959728i
\(416\) 2.31838 0.753289i 0.113668 0.0369330i
\(417\) −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 \(-0.00664132\pi\)
\(420\) −0.979277 + 0.790322i −0.0477838 + 0.0385638i
\(421\) −15.4894 11.2537i −0.754905 0.548471i 0.142438 0.989804i \(-0.454506\pi\)
−0.897343 + 0.441333i \(0.854506\pi\)
\(422\) −13.4535 18.5172i −0.654908 0.901404i
\(423\) −22.8527 + 10.0842i −1.11114 + 0.490308i
\(424\) −5.42705 1.76336i −0.263561 0.0856361i
\(425\) −16.7027 + 12.1353i −0.810202 + 0.588646i
\(426\) 10.4708 + 2.82423i 0.507313 + 0.136834i
\(427\) 2.50000 + 7.69421i 0.120983 + 0.372349i
\(428\) 8.05748 0.389473
\(429\) 0 0
\(430\) −3.09017 −0.149021
\(431\) 1.86936 + 5.75329i 0.0900438 + 0.277126i 0.985930 0.167157i \(-0.0534586\pi\)
−0.895887 + 0.444283i \(0.853459\pi\)
\(432\) 5.56423 + 11.0558i 0.267709 + 0.531923i
\(433\) 4.85410 3.52671i 0.233273 0.169483i −0.465008 0.885307i \(-0.653949\pi\)
0.698281 + 0.715824i \(0.253949\pi\)
\(434\) −20.1437 6.54508i −0.966929 0.314174i
\(435\) 0.0788361 + 1.55348i 0.00377990 + 0.0744836i
\(436\) −1.70820 2.35114i −0.0818081 0.112599i
\(437\) −13.2618 9.63525i −0.634397 0.460917i
\(438\) −12.0263 14.9016i −0.574637 0.712024i
\(439\) 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
\(442\) 3.45492 1.12257i 0.164334 0.0533952i
\(443\) −0.898056 + 1.23607i −0.0426679 + 0.0587274i −0.829818 0.558034i \(-0.811556\pi\)
0.787150 + 0.616762i \(0.211556\pi\)
\(444\) −2.69041 1.75351i −0.127681 0.0832179i
\(445\) 0.0623059 0.191758i 0.00295358 0.00909019i
\(446\) −0.640786 + 1.97214i −0.0303421 + 0.0933833i
\(447\) 18.9178 + 12.3299i 0.894782 + 0.583187i
\(448\) 15.7533 21.6825i 0.744273 1.02440i
\(449\) −26.5236 + 8.61803i −1.25173 + 0.406710i −0.858539 0.512749i \(-0.828627\pi\)
−0.393186 + 0.919459i \(0.628627\pi\)
\(450\) 12.7598 11.4127i 0.601501 0.537999i
\(451\) 0 0
\(452\) 1.27051i 0.0597598i
\(453\) 6.09197 + 7.54846i 0.286225 + 0.354658i
\(454\) −13.7812 10.0126i −0.646782 0.469914i
\(455\) −0.502029 0.690983i −0.0235355 0.0323938i
\(456\) −0.710198 13.9946i −0.0332581 0.655356i
\(457\) −23.8435 7.74721i −1.11535 0.362399i −0.307359 0.951594i \(-0.599445\pi\)
−0.807991 + 0.589195i \(0.799445\pi\)
\(458\) −14.3844 + 10.4508i −0.672137 + 0.488336i
\(459\) −9.93553 19.7413i −0.463751 0.921446i
\(460\) 0.454915 + 1.40008i 0.0212105 + 0.0652793i
\(461\) 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 \(0.218702\pi\)
\(464\) −1.73060 5.32624i −0.0803411 0.247264i
\(465\) 3.73935 + 1.00859i 0.173408 + 0.0467724i
\(466\) −9.20820 + 6.69015i −0.426562 + 0.309915i
\(467\) −7.27794 2.36475i −0.336783 0.109427i 0.135743 0.990744i \(-0.456658\pi\)
−0.472526 + 0.881317i \(0.656658\pi\)
\(468\) 1.23243 0.543831i 0.0569691 0.0251386i
\(469\) −13.2533 18.2416i −0.611980 0.842318i
\(470\) 3.02468 + 2.19756i 0.139518 + 0.101366i
\(471\) 13.0853 10.5604i 0.602938 0.486599i
\(472\) 1.17557i 0.0541100i
\(473\) 0 0
\(474\) −7.56231 + 2.88854i −0.347348 + 0.132675i
\(475\) −12.1353 + 3.94298i −0.556804 + 0.180916i
\(476\) −4.75528 + 6.54508i −0.217958 + 0.299993i
\(477\) −5.43690 1.17447i −0.248938 0.0537755i
\(478\) 2.80244 8.62502i 0.128181 0.394499i
\(479\) 6.18812 19.0451i 0.282743 0.870192i −0.704324 0.709879i \(-0.748750\pi\)
0.987066 0.160313i \(-0.0512504\pi\)
\(480\) −1.21204 + 1.85963i −0.0553218 + 0.0848802i
\(481\) 1.28115 1.76336i 0.0584155 0.0804021i
\(482\) −31.1604 + 10.1246i −1.41932 + 0.461163i
\(483\) −11.8617 31.0543i −0.539726 1.41302i
\(484\) 0 0
\(485\) 1.67376i 0.0760016i
\(486\) 9.85315 + 15.4510i 0.446948 + 0.700871i
\(487\) −1.19098 0.865300i −0.0539686 0.0392105i 0.560474 0.828172i \(-0.310619\pi\)
−0.614442 + 0.788962i \(0.710619\pi\)
\(488\) 4.75528 + 6.54508i 0.215262 + 0.296282i
\(489\) 25.2866 1.28325i 1.14350 0.0580305i
\(490\) −1.05573 0.343027i −0.0476929 0.0154964i
\(491\) −14.2986 + 10.3885i −0.645287 + 0.468828i −0.861662 0.507482i \(-0.830576\pi\)
0.216376 + 0.976310i \(0.430576\pi\)
\(492\) −0.202537 + 0.750904i −0.00913107 + 0.0338534i
\(493\) 3.09017 + 9.51057i 0.139174 + 0.428334i
\(494\) 2.24514 0.101014
\(495\) 0 0
\(496\) −13.9443 −0.626116
\(497\) −5.06555 15.5902i −0.227221 0.699315i
\(498\) −3.35482 + 12.4380i −0.150333 + 0.557359i
\(499\) 29.1074 21.1478i 1.30303 0.946704i 0.303045 0.952976i \(-0.401997\pi\)
0.999980 + 0.00627247i \(0.00199660\pi\)
\(500\) 2.21238 + 0.718847i 0.0989408 + 0.0321478i
\(501\) 36.4902 1.85181i 1.63026 0.0827327i
\(502\) −14.0451 19.3314i −0.626863 0.862803i
\(503\) 6.88191 + 5.00000i 0.306849 + 0.222939i 0.730543 0.682866i \(-0.239267\pi\)
−0.423694 + 0.905805i \(0.639267\pi\)
\(504\) 14.2896 24.5622i 0.636509 1.09409i
\(505\) 6.08985i 0.270995i
\(506\) 0 0
\(507\) −7.70820 20.1803i −0.342333 0.896240i
\(508\) 7.56231 2.45714i 0.335523 0.109018i
\(509\) −19.5559 + 26.9164i −0.866801 + 1.19305i 0.113104 + 0.993583i \(0.463921\pi\)
−0.979905 + 0.199466i \(0.936079\pi\)
\(510\) −1.80621 + 2.77127i −0.0799805 + 0.122714i
\(511\) −8.94427 + 27.5276i −0.395671 + 1.21775i
\(512\) 7.00042 21.5451i 0.309378 0.952167i
\(513\) −2.06970 13.5012i −0.0913796 0.596091i
\(514\) 15.3885 21.1805i 0.678760 0.934232i
\(515\) −4.08174 + 1.32624i −0.179863 + 0.0584410i
\(516\) −6.88191 + 2.62866i −0.302959 + 0.115720i
\(517\) 0 0
\(518\) 10.8541i 0.476902i
\(519\) 31.1394 25.1310i 1.36687 1.10313i
\(520\) −0.690983 0.502029i −0.0303016 0.0220154i
\(521\) 19.8132 + 27.2705i 0.868031 + 1.19474i 0.979594 + 0.200985i \(0.0644144\pi\)
−0.111563 + 0.993757i \(0.535586\pi\)
\(522\) −3.34748 7.58606i −0.146515 0.332033i
\(523\) 19.3713 + 6.29412i 0.847049 + 0.275223i 0.700209 0.713938i \(-0.253090\pi\)
0.146839 + 0.989160i \(0.453090\pi\)
\(524\) 5.20431 3.78115i 0.227351 0.165180i
\(525\) −24.9830 6.73851i −1.09035 0.294093i
\(526\) 3.31559 + 10.2044i 0.144567 + 0.444931i
\(527\) 24.8990 1.08462
\(528\) 0 0
\(529\) −15.8885 −0.690806
\(530\) 0.257270 + 0.791796i 0.0111751 + 0.0343934i
\(531\) −0.116005 1.14001i −0.00503421 0.0494723i
\(532\) −4.04508 + 2.93893i −0.175377 + 0.127419i
\(533\) −0.502029 0.163119i −0.0217453 0.00706547i
\(534\) 0.0544744 + 1.07343i 0.00235734 + 0.0464518i
\(535\) −2.92705 4.02874i −0.126547 0.174178i
\(536\) −18.2416 13.2533i −0.787917 0.572455i
\(537\) −15.1684 18.7949i −0.654564 0.811060i
\(538\) 22.0583i 0.951002i
\(539\) 0 0
\(540\) −0.562306 + 1.09017i −0.0241978 + 0.0469134i
\(541\) −14.5344 + 4.72253i −0.624884 + 0.203037i −0.604308 0.796751i \(-0.706550\pi\)
−0.0205767 + 0.999788i \(0.506550\pi\)
\(542\) −11.7104 + 16.1180i −0.503006 + 0.692329i
\(543\) 11.2659 + 7.34271i 0.483466 + 0.315106i
\(544\) −4.40983 + 13.5721i −0.189070 + 0.581897i
\(545\) −0.555029 + 1.70820i −0.0237748 + 0.0731714i
\(546\) 3.81433 + 2.48604i 0.163238 + 0.106393i
\(547\) −15.7918 + 21.7355i −0.675208 + 0.929345i −0.999864 0.0164876i \(-0.994752\pi\)
0.324656 + 0.945832i \(0.394752\pi\)
\(548\) −2.76741 + 0.899187i −0.118218 + 0.0384114i
\(549\) 5.25731 + 5.87785i 0.224377 + 0.250861i
\(550\) 0 0
\(551\) 6.18034i 0.263291i
\(552\) −20.8775 25.8690i −0.888604 1.10106i
\(553\) 9.89919 + 7.19218i 0.420956 + 0.305843i
\(554\) −11.2084 15.4271i −0.476200 0.655433i
\(555\) 0.100593 + 1.98220i 0.00426993 + 0.0841398i
\(556\) 8.35410 + 2.71441i 0.354293 + 0.115117i
\(557\) 0.224514 0.163119i 0.00951296 0.00691157i −0.583019 0.812459i \(-0.698129\pi\)
0.592532 + 0.805547i \(0.298129\pi\)
\(558\) −20.5397 + 2.09008i −0.869513 + 0.0884801i
\(559\) −1.54508 4.75528i −0.0653501 0.201127i
\(560\) −2.80017 −0.118329
\(561\) 0 0
\(562\) 31.3050 1.32052
\(563\) −0.330515 1.01722i −0.0139296 0.0428708i 0.943850 0.330374i \(-0.107175\pi\)
−0.957780 + 0.287503i \(0.907175\pi\)
\(564\) 8.60542 + 2.32109i 0.362354 + 0.0977356i
\(565\) −0.635255 + 0.461540i −0.0267254 + 0.0194171i
\(566\) 23.8949 + 7.76393i 1.00438 + 0.326342i
\(567\) 11.4336 25.2293i 0.480164 1.05953i
\(568\) −9.63525 13.2618i −0.404286 0.556452i
\(569\) 16.8415 + 12.2361i 0.706033 + 0.512963i 0.881891 0.471453i \(-0.156270\pi\)
−0.175859 + 0.984415i \(0.556270\pi\)
\(570\) −1.59093 + 1.28396i −0.0666368 + 0.0537790i
\(571\) 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
\(574\) −2.50000 + 0.812299i −0.104348 + 0.0339047i
\(575\) −17.7926 + 24.4894i −0.742001 + 1.02128i
\(576\) 5.51618 25.5356i 0.229841 1.06398i
\(577\) −2.47214 + 7.60845i −0.102916 + 0.316744i −0.989236 0.146330i \(-0.953254\pi\)
0.886319 + 0.463074i \(0.153254\pi\)
\(578\) −0.396027 + 1.21885i −0.0164726 + 0.0506974i
\(579\) −9.31899 + 14.2981i −0.387284 + 0.594210i
\(580\) 0.326238 0.449028i 0.0135463 0.0186449i
\(581\) 18.5191 6.01722i 0.768302 0.249636i
\(582\) −3.18368 8.33499i −0.131968 0.345497i
\(583\) 0 0
\(584\) 28.9443i 1.19772i
\(585\) −0.719622 0.418657i −0.0297527 0.0173093i
\(586\) −13.2533 9.62908i −0.547488 0.397774i
\(587\) −7.02067 9.66312i −0.289774 0.398840i 0.639167 0.769068i \(-0.279279\pi\)
−0.928941 + 0.370229i \(0.879279\pi\)
\(588\) −2.64294 + 0.134124i −0.108993 + 0.00553118i
\(589\) 14.6353 + 4.75528i 0.603035 + 0.195938i
\(590\) −0.138757 + 0.100813i −0.00571255 + 0.00415041i
\(591\) 3.88473 14.4026i 0.159796 0.592444i
\(592\) −2.20820 6.79615i −0.0907566 0.279320i
\(593\) −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
\(596\) −2.48990 7.66312i −0.101990 0.313894i
\(597\) −1.00859 + 3.73935i −0.0412790 + 0.153041i
\(598\) 4.30902 3.13068i 0.176209 0.128023i
\(599\) −20.6457 6.70820i −0.843562 0.274090i −0.144815 0.989459i \(-0.546259\pi\)
−0.698747 + 0.715369i \(0.746259\pi\)
\(600\) −25.8425 + 1.31146i −1.05502 + 0.0535401i
\(601\) −10.9549 15.0781i −0.446860 0.615050i 0.524859 0.851189i \(-0.324118\pi\)
−0.971719 + 0.236139i \(0.924118\pi\)
\(602\) −20.1437 14.6353i −0.820996 0.596488i
\(603\) −18.9976 11.0523i −0.773644 0.450085i
\(604\) 3.46120i 0.140834i
\(605\) 0 0
\(606\) 11.5836 + 30.3262i 0.470551 + 1.23192i
\(607\) −35.2254 + 11.4454i −1.42976 + 0.464556i −0.918688 0.394984i \(-0.870750\pi\)
−0.511068 + 0.859540i \(0.670750\pi\)
\(608\) −5.18407 + 7.13525i −0.210242 + 0.289373i
\(609\) −6.84348 + 10.4999i −0.277312 + 0.425479i
\(610\) 0.364745 1.12257i 0.0147681 0.0454515i
\(611\) −1.86936 + 5.75329i −0.0756261 + 0.232753i
\(612\) −1.66511 + 7.70817i −0.0673082 + 0.311584i
\(613\) 22.3607 30.7768i 0.903139 1.24306i −0.0663165 0.997799i \(-0.521125\pi\)
0.969456 0.245266i \(-0.0788753\pi\)
\(614\) −10.6331 + 3.45492i −0.429118 + 0.139429i
\(615\) 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 \(-0.102782\pi\)
\(618\) 17.8036 14.3683i 0.716165 0.577979i
\(619\) 11.6631 + 8.47375i 0.468780 + 0.340589i 0.796966 0.604024i \(-0.206437\pi\)
−0.328185 + 0.944613i \(0.606437\pi\)
\(620\) −0.812299 1.11803i −0.0326227 0.0449013i
\(621\) −22.7987 23.0263i −0.914881 0.924013i
\(622\) −5.59017 1.81636i −0.224145 0.0728293i
\(623\) 1.31433 0.954915i 0.0526574 0.0382579i
\(624\) 2.89406 + 0.780598i 0.115855 + 0.0312489i
\(625\) 7.05573 + 21.7153i 0.282229 + 0.868612i
\(626\) −12.9313 −0.516838
\(627\) 0 0
\(628\) −6.00000 −0.239426
\(629\) 3.94298 + 12.1353i 0.157217 + 0.483864i
\(630\) −4.12460 + 0.419712i −0.164328 + 0.0167217i
\(631\) −35.1525 + 25.5398i −1.39940 + 1.01672i −0.404639 + 0.914477i \(0.632603\pi\)
−0.994759 + 0.102246i \(0.967397\pi\)
\(632\) 11.6372 + 3.78115i 0.462903 + 0.150406i
\(633\) 1.70919 + 33.6800i 0.0679343 + 1.33866i
\(634\) 2.92705 + 4.02874i 0.116248 + 0.160002i
\(635\) −3.97574 2.88854i −0.157772 0.114628i
\(636\) 1.24649 + 1.54451i 0.0494266 + 0.0612438i
\(637\) 1.79611i 0.0711645i
\(638\) 0 0
\(639\) −10.6525 11.9098i −0.421405 0.471146i
\(640\) −1.28115 + 0.416272i −0.0506420 + 0.0164546i
\(641\) 6.55139 9.01722i 0.258765 0.356159i −0.659792 0.751448i \(-0.729356\pi\)
0.918557 + 0.395289i \(0.129356\pi\)
\(642\) 22.2392 + 14.4947i 0.877713 + 0.572061i
\(643\) 5.89919 18.1558i 0.232641 0.715996i −0.764784 0.644286i \(-0.777154\pi\)
0.997426 0.0717097i \(-0.0228455\pi\)
\(644\) −3.66547 + 11.2812i −0.144440 + 0.444540i
\(645\) 3.81433 + 2.48604i 0.150189 + 0.0978877i
\(646\) −7.72542 + 10.6331i −0.303953 + 0.418355i
\(647\) −23.9277 + 7.77458i −0.940694 + 0.305650i −0.738929 0.673784i \(-0.764668\pi\)
−0.201766 + 0.979434i \(0.564668\pi\)
\(648\) 3.07768 27.5276i 0.120903 1.08139i
\(649\) 0 0
\(650\) 4.14590i 0.162615i
\(651\) 19.5987 + 24.2845i 0.768134 + 0.951783i
\(652\) −7.30902 5.31031i −0.286243 0.207968i
\(653\) −24.6012 33.8607i −0.962720 1.32507i −0.945640 0.325217i \(-0.894563\pi\)
−0.0170808 0.999854i \(-0.505437\pi\)
\(654\) −0.485265 9.56224i −0.0189754 0.373913i
\(655\) −3.78115 1.22857i −0.147742 0.0480042i
\(656\) −1.40008 + 1.01722i −0.0546641 + 0.0397158i
\(657\) 2.85622 + 28.0687i 0.111432 + 1.09507i
\(658\) 9.30902 + 28.6502i 0.362903 + 1.11690i
\(659\) 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 \(0.650742\pi\)
\(662\) −4.68204 14.4098i −0.181973 0.560054i
\(663\) −5.16765 1.39384i −0.200695 0.0541323i
\(664\) 15.7533 11.4454i 0.611346 0.444169i
\(665\) 2.93893 + 0.954915i 0.113967 + 0.0370300i
\(666\) −4.27131 9.67963i −0.165510 0.375078i
\(667\) 8.61803 + 11.8617i 0.333692 + 0.459287i
\(668\) −10.5474 7.66312i −0.408090 0.296495i
\(669\) 2.37753 1.91878i 0.0919207 0.0741843i
\(670\) 3.28969i 0.127092i
\(671\) 0 0
\(672\) −16.7082 + 6.38197i −0.644533 + 0.246190i
\(673\) −9.83688 + 3.19620i −0.379184 + 0.123204i −0.492407 0.870365i \(-0.663883\pi\)
0.113223 + 0.993570i \(0.463883\pi\)
\(674\) 17.3965 23.9443i 0.670089 0.922299i
\(675\) −24.9314 + 3.82193i −0.959610 + 0.147106i
\(676\) −2.38197 + 7.33094i −0.0916141 + 0.281959i
\(677\) 9.16754 28.2148i 0.352337 1.08438i −0.605200 0.796073i \(-0.706907\pi\)
0.957537 0.288309i \(-0.0930930\pi\)
\(678\) 2.28554 3.50670i 0.0877756 0.134674i
\(679\) −7.92705 + 10.9106i −0.304212 + 0.418712i
\(680\) 4.75528 1.54508i 0.182357 0.0592513i
\(681\) 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 \(-0.0550836\pi\)
\(684\) −2.45086 + 4.21274i −0.0937109 + 0.161078i
\(685\) 1.45492 + 1.05706i 0.0555894 + 0.0403881i
\(686\) 9.62908 + 13.2533i 0.367640 + 0.506013i
\(687\) 26.1629 1.32772i 0.998178 0.0506556i
\(688\) −15.5902 5.06555i −0.594370 0.193122i
\(689\) −1.08981 + 0.791796i −0.0415186 + 0.0301650i
\(690\) −1.26303 + 4.68269i −0.0480829 + 0.178267i
\(691\) −3.20163 9.85359i −0.121796 0.374848i 0.871508 0.490381i \(-0.163142\pi\)
−0.993304 + 0.115533i \(0.963142\pi\)
\(692\) −14.2784 −0.542782
\(693\) 0 0
\(694\) 8.54102 0.324213
\(695\) −1.67760 5.16312i −0.0636350 0.195848i
\(696\) −3.26388 + 12.1008i −0.123717 + 0.458679i
\(697\) 2.50000 1.81636i 0.0946943 0.0687994i
\(698\) −15.1967 4.93769i −0.575202 0.186894i
\(699\) 16.7483 0.849944i 0.633479 0.0321478i
\(700\) 5.42705 + 7.46969i 0.205123 + 0.282328i
\(701\) 12.5352 + 9.10739i 0.473450 + 0.343981i 0.798784 0.601618i \(-0.205477\pi\)
−0.325334 + 0.945599i \(0.605477\pi\)
\(702\) 4.37990 + 0.716022i 0.165309 + 0.0270245i
\(703\) 7.88597i 0.297425i
\(704\) 0 0
\(705\) −1.96556 5.14590i −0.0740272 0.193806i
\(706\) 37.5623 12.2047i 1.41368 0.459331i
\(707\) 28.8420 39.6976i 1.08471 1.49298i
\(708\) −0.223260 + 0.342548i −0.00839064 + 0.0128737i
\(709\) −6.33688 + 19.5029i −0.237987 + 0.732447i 0.758725 + 0.651411i \(0.225823\pi\)
−0.996711 + 0.0810358i \(0.974177\pi\)
\(710\) −0.739054 + 2.27458i −0.0277362 + 0.0853633i
\(711\) 11.6583 + 2.51842i 0.437221 + 0.0944481i
\(712\) 0.954915 1.31433i 0.0357870 0.0492565i
\(713\) 34.7198 11.2812i 1.30027 0.422482i
\(714\) −24.8990 + 9.51057i −0.931821 + 0.355924i
\(715\) 0 0
\(716\) 8.61803i 0.322071i
\(717\) −10.3980 + 8.39167i −0.388320 + 0.313393i
\(718\) −30.3262 22.0333i −1.13177 0.822276i
\(719\) 17.7068 + 24.3713i 0.660352 + 0.908897i 0.999493 0.0318387i \(-0.0101363\pi\)
−0.339141 + 0.940736i \(0.610136\pi\)
\(720\) −2.49718 + 1.10192i −0.0930642 + 0.0410662i
\(721\) −32.8885 10.6861i −1.22483 0.397972i
\(722\) 11.4984 8.35410i 0.427927 0.310907i
\(723\) 46.6078 + 12.5712i 1.73336 + 0.467530i
\(724\) −1.48278 4.56352i −0.0551071 0.169602i
\(725\) 11.4127 0.423856
\(726\) 0 0
\(727\) −27.8541 −1.03305 −0.516526 0.856272i \(-0.672775\pi\)
−0.516526 + 0.856272i \(0.672775\pi\)
\(728\) −2.12663 6.54508i −0.0788180 0.242577i
\(729\) 0.268157 26.9987i 0.00993173 0.999951i
\(730\) 3.41641 2.48217i 0.126447 0.0918691i
\(731\) 27.8379 + 9.04508i 1.02962 + 0.334545i
\(732\) −0.142616 2.81027i −0.00527123 0.103871i
\(733\) 27.6869 + 38.1078i 1.02264 + 1.40754i 0.910337 + 0.413869i \(0.135823\pi\)
0.112303 + 0.993674i \(0.464177\pi\)
\(734\) 22.8051 + 16.5689i 0.841752 + 0.611569i
\(735\) 1.02717 + 1.27275i 0.0378876 + 0.0469459i
\(736\) 20.9232i 0.771241i
\(737\) 0 0
\(738\) −1.90983 + 1.70820i −0.0703018 + 0.0628799i
\(739\) −12.9271 + 4.20025i −0.475529 + 0.154509i −0.536969 0.843602i \(-0.680431\pi\)
0.0614397 + 0.998111i \(0.480431\pi\)
\(740\) 0.416272 0.572949i 0.0153025 0.0210620i
\(741\) −2.77127 1.80621i −0.101805 0.0663529i
\(742\) −2.07295 + 6.37988i −0.0761004 + 0.234213i
\(743\) −9.07405 + 27.9271i −0.332895 + 1.02454i 0.634855 + 0.772631i \(0.281060\pi\)
−0.967750 + 0.251913i \(0.918940\pi\)
\(744\) 26.1438 + 17.0396i 0.958478 + 0.624701i
\(745\) −2.92705 + 4.02874i −0.107239 + 0.147602i
\(746\) 30.5851 9.93769i 1.11980 0.363845i
\(747\) 14.1473 12.6538i 0.517624 0.462977i
\(748\) 0 0
\(749\) 40.1246i 1.46612i
\(750\) 4.81320 + 5.96396i 0.175753 + 0.217773i
\(751\) 11.7812 + 8.55951i 0.429900 + 0.312341i 0.781609 0.623769i \(-0.214399\pi\)
−0.351709 + 0.936109i \(0.614399\pi\)
\(752\) 11.6574 + 16.0451i 0.425103 + 0.585104i
\(753\) 1.78434 + 35.1608i 0.0650251 + 1.28133i
\(754\) −1.90983 0.620541i −0.0695519 0.0225988i
\(755\) −1.73060 + 1.25735i −0.0629830 + 0.0457598i
\(756\) −8.82859 + 4.44330i −0.321093 + 0.161601i
\(757\) 3.36475 + 10.3556i 0.122294 + 0.376381i 0.993398 0.114716i \(-0.0365958\pi\)
−0.871105 + 0.491098i \(0.836596\pi\)
\(758\) −3.39569 −0.123337
\(759\) 0 0
\(760\) 3.09017 0.112092
\(761\) 10.2496 + 31.5451i 0.371548 + 1.14351i 0.945778 + 0.324814i \(0.105302\pi\)
−0.574229 + 0.818694i \(0.694698\pi\)
\(762\) 25.2927 + 6.82205i 0.916258 + 0.247137i
\(763\) −11.7082 + 8.50651i −0.423865 + 0.307956i
\(764\) −14.2456 4.62868i −0.515388 0.167460i
\(765\) 4.45897 1.96760i 0.161214 0.0711387i
\(766\) −8.57953 11.8087i −0.309991 0.426666i
\(767\) −0.224514 0.163119i −0.00810673 0.00588988i
\(768\) −17.8868 + 14.4355i −0.645433 + 0.520895i
\(769\) 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
\(772\) 5.79180 1.88187i 0.208451 0.0677299i
\(773\) 26.9399 37.0795i 0.968959 1.33366i 0.0263883 0.999652i \(-0.491599\pi\)
0.942571 0.334006i \(-0.108401\pi\)
\(774\) −23.7233 5.12469i −0.852717 0.184203i
\(775\) 8.78115 27.0256i 0.315428 0.970789i
\(776\) −4.16750 + 12.8262i −0.149604 + 0.460435i
\(777\) −8.73212 + 13.3977i −0.313263 + 0.480639i
\(778\) 5.10081 7.02067i 0.182873 0.251703i
\(779\) 1.81636 0.590170i 0.0650777 0.0211450i
\(780\) 0.106001 + 0.277515i 0.00379545 + 0.00993661i
\(781\) 0 0
\(782\) 31.1803i 1.11501i
\(783\) −1.97104 + 12.0568i −0.0704392 + 0.430876i
\(784\) −4.76393 3.46120i −0.170140 0.123614i
\(785\) 2.17963 + 3.00000i 0.0777942 + 0.107075i
\(786\) 21.1663 1.07415i 0.754975 0.0383135i
\(787\) −2.96556 0.963568i −0.105711 0.0343475i 0.255684 0.966760i \(-0.417699\pi\)
−0.361395 + 0.932413i \(0.617699\pi\)
\(788\) −4.30625 + 3.12868i −0.153404 + 0.111455i
\(789\) 4.11682 15.2631i 0.146563 0.543379i
\(790\) −0.551663 1.69784i −0.0196273 0.0604066i
\(791\) −6.32688 −0.224958
\(792\) 0 0
\(793\) 1.90983 0.0678201
\(794\) 8.35524 + 25.7148i 0.296516 + 0.912583i
\(795\) 0.319440 1.18432i 0.0113294 0.0420035i
\(796\) 1.11803 0.812299i 0.0396277 0.0287912i
\(797\) −34.3035 11.1459i −1.21509 0.394808i −0.369801 0.929111i \(-0.620574\pi\)
−0.845293 + 0.534303i \(0.820574\pi\)
\(798\) −16.4516 + 0.834887i −0.582381 + 0.0295547i
\(799\) −20.8156 28.6502i −0.736403 1.01357i
\(800\) 13.1760 + 9.57295i 0.465843 + 0.338455i
\(801\) 0.796332 1.36880i 0.0281370 0.0483642i
\(802\) 32.7445i 1.15625i
\(803\) 0 0
\(804\) 2.79837 + 7.32624i 0.0986910 + 0.258376i
\(805\) 6.97214 2.26538i 0.245736 0.0798443i
\(806\) −2.93893 + 4.04508i −0.103519 + 0.142482i
\(807\) 17.7459 27.2275i 0.624686 0.958454i
\(808\) 15.1631 46.6673i 0.533437 1.64175i
\(809\) −6.62464 + 20.3885i −0.232910 + 0.716823i 0.764482 + 0.644645i \(0.222995\pi\)
−0.997392 + 0.0721778i \(0.977005\pi\)
\(810\) −3.51313 + 1.99741i −0.123439 + 0.0701818i
\(811\) −12.2984 + 16.9273i −0.431854 + 0.594396i −0.968378 0.249489i \(-0.919737\pi\)
0.536523 + 0.843886i \(0.319737\pi\)
\(812\) 4.25325 1.38197i 0.149260 0.0484975i
\(813\) 27.4216 10.4741i 0.961719 0.367344i
\(814\) 0 0
\(815\) 5.58359i 0.195585i
\(816\) −13.6553 + 11.0205i −0.478031 + 0.385794i
\(817\) 14.6353 + 10.6331i 0.512023 + 0.372006i
\(818\) −14.6214 20.1246i −0.511225 0.703641i
\(819\) −2.70817 6.13725i −0.0946311 0.214453i
\(820\) −0.163119 0.0530006i −0.00569636 0.00185086i
\(821\) 37.6260 27.3369i 1.31316 0.954064i 0.313166 0.949699i \(-0.398611\pi\)
0.999990 0.00436519i \(-0.00138949\pi\)
\(822\) −9.25582 2.49652i −0.322834 0.0870761i
\(823\) 8.07295 + 24.8460i 0.281405 + 0.866076i 0.987453 + 0.157912i \(0.0504763\pi\)
−0.706048 + 0.708164i \(0.749524\pi\)
\(824\) −34.5811 −1.20469
\(825\) 0 0
\(826\) −1.38197 −0.0480847
\(827\) 8.05748 + 24.7984i 0.280186 + 0.862324i 0.987800 + 0.155725i \(0.0497714\pi\)
−0.707614 + 0.706599i \(0.750229\pi\)
\(828\) 1.17051 + 11.5029i 0.0406782 + 0.399754i
\(829\) 4.26393 3.09793i 0.148092 0.107595i −0.511272 0.859419i \(-0.670825\pi\)
0.659364 + 0.751824i \(0.270825\pi\)
\(830\) −2.70190 0.877901i −0.0937843 0.0304724i
\(831\) 1.42396 + 28.0594i 0.0493967 + 0.973371i
\(832\) −3.71885 5.11855i −0.128928 0.177454i
\(833\) 8.50651 + 6.18034i 0.294733 + 0.214136i
\(834\) 18.1749 + 22.5203i 0.629347 + 0.779814i
\(835\) 8.05748i 0.278841i
\(836\) 0 0
\(837\) 27.0344 + 13.9443i 0.934447 + 0.481985i
\(838\) −0.954915 + 0.310271i −0.0329870 + 0.0107181i
\(839\) −0.971301 + 1.33688i −0.0335330 + 0.0461543i −0.825454 0.564469i \(-0.809081\pi\)
0.791921 + 0.610623i \(0.209081\pi\)
\(840\) 5.24997 + 3.42174i 0.181141 + 0.118061i
\(841\) −7.25329 + 22.3233i −0.250113 + 0.769770i
\(842\) −6.95515 + 21.4058i −0.239690 + 0.737691i
\(843\) −38.6410 25.1848i −1.33087 0.867411i
\(844\) 7.07295 9.73508i 0.243461 0.335095i
\(845\) 4.53077 1.47214i 0.155863 0.0506430i
\(846\) 19.5762 + 21.8868i 0.673042 + 0.752484i
\(847\) 0 0
\(848\) 4.41641i 0.151660i
\(849\) −23.2484 28.8068i −0.797884 0.988647i
\(850\) 19.6353 + 14.2658i 0.673484 + 0.489315i
\(851\) 10.9964 + 15.1353i 0.376952 + 0.518830i
\(852\) 0.288971 + 5.69423i 0.00989999 + 0.195081i
\(853\) 0.892609 + 0.290026i 0.0305624 + 0.00993031i 0.324258 0.945969i \(-0.394885\pi\)
−0.293696 + 0.955899i \(0.594885\pi\)
\(854\) 7.69421 5.59017i 0.263290 0.191292i
\(855\) 2.99670 0.304938i 0.102485 0.0104287i
\(856\) −12.3992 38.1608i −0.423795 1.30431i
\(857\) −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 \(0.234055\pi\)
\(860\) −0.502029 1.54508i −0.0171190 0.0526870i
\(861\) 3.73935 + 1.00859i 0.127437 + 0.0343728i
\(862\) 5.75329 4.18001i 0.195958 0.142372i
\(863\) 1.06957 + 0.347524i 0.0364086 + 0.0118299i 0.327165 0.944967i \(-0.393907\pi\)
−0.290756 + 0.956797i \(0.593907\pi\)
\(864\) −12.3889 + 12.2664i −0.421477 + 0.417312i
\(865\) 5.18692 + 7.13918i 0.176360 + 0.242739i
\(866\) −5.70634 4.14590i −0.193909 0.140883i
\(867\) 1.46940 1.18587i 0.0499033 0.0402743i
\(868\) 11.1352i 0.377952i
\(869\) 0 0
\(870\) 1.70820 0.652476i 0.0579135 0.0221210i
\(871\) −5.06231 + 1.64484i −0.171530 + 0.0557334i
\(872\) −8.50651 + 11.7082i −0.288067 + 0.396490i
\(873\) −2.77574 + 12.8495i −0.0939446 + 0.434890i
\(874\) −5.95492 + 18.3273i −0.201428 + 0.619932i
\(875\) 3.57971 11.0172i 0.121016 0.372450i
\(876\) 5.49700 8.43403i 0.185726 0.284960i
\(877\) −20.2254 + 27.8379i −0.682964 + 0.940019i −0.999965 0.00840594i \(-0.997324\pi\)
0.317001 + 0.948425i \(0.397324\pi\)
\(878\) −3.05744 + 0.993422i −0.103184 + 0.0335264i
\(879\) 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 \(-0.168163\pi\)
\(882\) −7.53598 4.38423i −0.253750 0.147625i
\(883\) 32.5066 + 23.6174i 1.09393 + 0.794789i 0.980059 0.198706i \(-0.0636739\pi\)
0.113874 + 0.993495i \(0.463674\pi\)
\(884\) 1.12257 + 1.54508i 0.0377561 + 0.0519668i
\(885\) 0.252378 0.0128077i 0.00848359 0.000430526i
\(886\) 1.70820 + 0.555029i 0.0573882 + 0.0186466i
\(887\) −11.2739 + 8.19098i −0.378541 + 0.275026i −0.760744 0.649052i \(-0.775166\pi\)
0.382203 + 0.924079i \(0.375166\pi\)
\(888\) −4.16463 + 15.4403i −0.139756 + 0.518143i
\(889\) −12.2361 37.6587i −0.410385 1.26303i
\(890\) −0.237026 −0.00794512
\(891\) 0 0
\(892\) −1.09017 −0.0365016
\(893\) −6.76340 20.8156i −0.226328 0.696567i
\(894\) 6.91300 25.6299i 0.231205 0.857192i
\(895\) 4.30902 3.13068i 0.144035 0.104647i
\(896\) −10.3229 3.35410i −0.344863 0.112053i
\(897\) −7.83744 + 0.397735i −0.261684 + 0.0132800i
\(898\) 19.2705 + 26.5236i 0.643065 + 0.885103i
\(899\) −11.1352 8.09017i −0.371379 0.269822i
\(900\) 7.77929 + 4.52578i 0.259310 + 0.150859i
\(901\) 7.88597i 0.262720i
\(902\) 0 0
\(903\) 13.0902 + 34.2705i 0.435614 + 1.14045i
\(904\) −6.01722 + 1.95511i −0.200130 + 0.0650261i
\(905\) −1.74311 + 2.39919i −0.0579430 + 0.0797517i
\(906\) 6.22640 9.55316i 0.206858 0.317383i
\(907\) −9.70163 + 29.8585i −0.322137 + 0.991436i 0.650579 + 0.759439i \(0.274526\pi\)
−0.972716 + 0.231998i \(0.925474\pi\)
\(908\) 2.76741 8.51722i 0.0918398 0.282654i
\(909\) 10.0993 46.7520i 0.334973 1.55066i
\(910\) −0.590170 + 0.812299i −0.0195639 + 0.0269275i
\(911\) 30.1688 9.80244i 0.999537 0.324769i 0.236857 0.971545i \(-0.423883\pi\)
0.762681 + 0.646775i \(0.223883\pi\)
\(912\) −10.1311 + 3.86974i −0.335474 + 0.128140i
\(913\) 0 0
\(914\) 29.4721i 0.974852i
\(915\) −1.35333 + 1.09220i −0.0447396 + 0.0361070i
\(916\) −7.56231 5.49434i −0.249866 0.181538i
\(917\) −18.8294 25.9164i −0.621801 0.855835i
\(918\) −18.4622 + 18.2797i −0.609343 + 0.603321i
\(919\) 44.1074 + 14.3314i 1.45497 + 0.472748i 0.926529 0.376223i \(-0.122777\pi\)
0.528439 + 0.848971i \(0.322777\pi\)
\(920\) 5.93085 4.30902i 0.195534 0.142064i
\(921\) 15.9044 + 4.28980i 0.524068 + 0.141354i
\(922\) −11.1565 34.3363i −0.367421 1.13081i
\(923\) −3.86974 −0.127374
\(924\) 0 0
\(925\) 14.5623 0.478806
\(926\) −12.0862 37.1976i −0.397178 1.22239i
\(927\) −33.5350 + 3.41246i −1.10143 + 0.112080i
\(928\) 6.38197 4.63677i 0.209498 0.152209i
\(929\) 30.7238 + 9.98278i 1.00802 + 0.327524i 0.766064 0.642764i \(-0.222212\pi\)
0.241952 + 0.970288i \(0.422212\pi\)
\(930\) −0.230757 4.54711i −0.00756683 0.149106i
\(931\) 3.81966 + 5.25731i 0.125184 + 0.172301i
\(932\) −4.84104 3.51722i −0.158574 0.115210i
\(933\) 5.43893 + 6.73929i 0.178062 + 0.220635i
\(934\) 8.99602i 0.294359i
\(935\) 0 0
\(936\) −4.47214 5.00000i −0.146176 0.163430i
\(937\) 34.7599 11.2942i 1.13556 0.368964i 0.319871 0.947461i \(-0.396361\pi\)
0.815685 + 0.578497i \(0.196361\pi\)
\(938\) −15.5802 + 21.4443i −0.508711 + 0.700180i
\(939\) 15.9616 + 10.4032i 0.520888 + 0.339496i
\(940\) −0.607391 + 1.86936i −0.0198109 + 0.0609717i
\(941\) 11.0619 34.0451i 0.360608 1.10984i −0.592078 0.805881i \(-0.701692\pi\)
0.952686 0.303957i \(-0.0983079\pi\)
\(942\) −16.5604 10.7935i −0.539568 0.351671i
\(943\) 2.66312 3.66547i 0.0867231 0.119364i
\(944\) −0.865300 + 0.281153i −0.0281631 + 0.00915075i
\(945\) 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 \(-0.0898649\pi\)
\(948\) −2.67284 3.31188i −0.0868099 0.107565i
\(949\) 5.52786 + 4.01623i 0.179442 + 0.130372i
\(950\) 8.81678 + 12.1353i 0.286054 + 0.393720i
\(951\) −0.371864 7.32766i −0.0120585 0.237616i
\(952\) 38.3156 + 12.4495i 1.24182 + 0.403490i
\(953\) 3.24920 2.36068i 0.105252 0.0764699i −0.533914 0.845539i \(-0.679280\pi\)
0.639166 + 0.769069i \(0.279280\pi\)
\(954\) 0.661966 + 6.50529i 0.0214320 + 0.210617i
\(955\) 2.86068 + 8.80427i 0.0925694 + 0.284899i
\(956\) 4.76779 0.154201
\(957\) 0 0
\(958\) −23.5410 −0.760576
\(959\) 4.47777 + 13.7812i 0.144595 + 0.445017i
\(960\) 5.56243 + 1.50032i 0.179527 + 0.0484227i
\(961\) −2.64590 + 1.92236i −0.0853515 + 0.0620115i
\(962\) −2.43690 0.791796i −0.0785687 0.0255285i
\(963\) −15.7898 35.7829i −0.508820 1.15309i
\(964\) −10.1246 13.9353i −0.326092 0.448827i
\(965\) −3.04493 2.21227i −0.0980197 0.0712155i
\(966\) −30.4108 + 24.5429i −0.978452 + 0.789656i
\(967\) 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
\(970\) 1.87132 0.608030i 0.0600846 0.0195227i
\(971\) −4.80828 + 6.61803i −0.154305 + 0.212383i −0.879170 0.476508i \(-0.841902\pi\)
0.724865 + 0.688891i \(0.241902\pi\)
\(972\) −6.12476 + 7.43674i −0.196452 + 0.238534i
\(973\) 13.5172 41.6017i 0.433342 1.33369i
\(974\) −0.534785 + 1.64590i −0.0171356 + 0.0527380i
\(975\) −3.33537 + 5.11746i −0.106817 + 0.163890i
\(976\) 3.68034 5.06555i 0.117805 0.162144i
\(977\) −32.3889 + 10.5238i −1.03621 + 0.336686i −0.777244 0.629199i \(-0.783383\pi\)
−0.258969 + 0.965886i \(0.583383\pi\)
\(978\) −10.6206 27.8052i −0.339610 0.889111i
\(979\) 0 0
\(980\) 0.583592i 0.0186422i
\(981\) −7.09383 + 12.1935i −0.226489 + 0.389307i
\(982\) 16.8090 + 12.2125i 0.536397 + 0.389715i
\(983\) 33.6830 + 46.3607i 1.07432 + 1.47868i 0.865623 + 0.500696i \(0.166922\pi\)
0.208698 + 0.977980i \(0.433078\pi\)
\(984\) 3.86801 0.196294i 0.123308 0.00625762i
\(985\) 3.12868 + 1.01657i 0.0996879 + 0.0323906i
\(986\) 9.51057 6.90983i 0.302878 0.220054i
\(987\) 11.5586 42.8533i 0.367913 1.36403i
\(988\) 0.364745 + 1.12257i 0.0116041 + 0.0357137i
\(989\) 42.9161 1.36465
\(990\) 0 0
\(991\) −12.5623 −0.399055 −0.199527 0.979892i \(-0.563941\pi\)
−0.199527 + 0.979892i \(0.563941\pi\)
\(992\) −6.06961 18.6803i −0.192710 0.593101i
\(993\) −5.81346 + 21.5534i −0.184485 + 0.683975i
\(994\) −15.5902 + 11.3269i −0.494490 + 0.359268i
\(995\) −0.812299 0.263932i −0.0257516 0.00836721i
\(996\) −6.76401 + 0.343260i −0.214326 + 0.0108766i
\(997\) 8.65654 + 11.9147i 0.274155 + 0.377343i 0.923787 0.382907i \(-0.125077\pi\)
−0.649632 + 0.760249i \(0.725077\pi\)
\(998\) −34.2178 24.8607i −1.08315 0.786951i
\(999\) −2.51500 + 15.3842i −0.0795711 + 0.486736i
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.e.215.1 8
3.2 odd 2 inner 363.2.f.e.215.2 8
11.2 odd 10 inner 363.2.f.e.233.2 8
11.3 even 5 363.2.d.f.362.3 8
11.4 even 5 363.2.f.b.239.2 8
11.5 even 5 33.2.f.a.29.2 yes 8
11.6 odd 10 363.2.f.b.161.1 8
11.7 odd 10 33.2.f.a.8.1 8
11.8 odd 10 363.2.d.f.362.5 8
11.9 even 5 363.2.f.d.233.1 8
11.10 odd 2 363.2.f.d.215.2 8
33.2 even 10 inner 363.2.f.e.233.1 8
33.5 odd 10 33.2.f.a.29.1 yes 8
33.8 even 10 363.2.d.f.362.4 8
33.14 odd 10 363.2.d.f.362.6 8
33.17 even 10 363.2.f.b.161.2 8
33.20 odd 10 363.2.f.d.233.2 8
33.26 odd 10 363.2.f.b.239.1 8
33.29 even 10 33.2.f.a.8.2 yes 8
33.32 even 2 363.2.f.d.215.1 8
44.7 even 10 528.2.bn.c.305.1 8
44.27 odd 10 528.2.bn.c.161.2 8
55.7 even 20 825.2.bs.a.74.1 8
55.18 even 20 825.2.bs.d.74.2 8
55.27 odd 20 825.2.bs.a.524.2 8
55.29 odd 10 825.2.bi.b.701.2 8
55.38 odd 20 825.2.bs.d.524.1 8
55.49 even 10 825.2.bi.b.326.1 8
99.5 odd 30 891.2.u.a.755.2 16
99.7 odd 30 891.2.u.a.701.2 16
99.16 even 15 891.2.u.a.458.2 16
99.29 even 30 891.2.u.a.701.1 16
99.38 odd 30 891.2.u.a.458.1 16
99.40 odd 30 891.2.u.a.107.1 16
99.49 even 15 891.2.u.a.755.1 16
99.95 even 30 891.2.u.a.107.2 16
132.71 even 10 528.2.bn.c.161.1 8
132.95 odd 10 528.2.bn.c.305.2 8
165.29 even 10 825.2.bi.b.701.1 8
165.38 even 20 825.2.bs.a.524.1 8
165.62 odd 20 825.2.bs.d.74.1 8
165.104 odd 10 825.2.bi.b.326.2 8
165.128 odd 20 825.2.bs.a.74.2 8
165.137 even 20 825.2.bs.d.524.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.f.a.8.1 8 11.7 odd 10
33.2.f.a.8.2 yes 8 33.29 even 10
33.2.f.a.29.1 yes 8 33.5 odd 10
33.2.f.a.29.2 yes 8 11.5 even 5
363.2.d.f.362.3 8 11.3 even 5
363.2.d.f.362.4 8 33.8 even 10
363.2.d.f.362.5 8 11.8 odd 10
363.2.d.f.362.6 8 33.14 odd 10
363.2.f.b.161.1 8 11.6 odd 10
363.2.f.b.161.2 8 33.17 even 10
363.2.f.b.239.1 8 33.26 odd 10
363.2.f.b.239.2 8 11.4 even 5
363.2.f.d.215.1 8 33.32 even 2
363.2.f.d.215.2 8 11.10 odd 2
363.2.f.d.233.1 8 11.9 even 5
363.2.f.d.233.2 8 33.20 odd 10
363.2.f.e.215.1 8 1.1 even 1 trivial
363.2.f.e.215.2 8 3.2 odd 2 inner
363.2.f.e.233.1 8 33.2 even 10 inner
363.2.f.e.233.2 8 11.2 odd 10 inner
528.2.bn.c.161.1 8 132.71 even 10
528.2.bn.c.161.2 8 44.27 odd 10
528.2.bn.c.305.1 8 44.7 even 10
528.2.bn.c.305.2 8 132.95 odd 10
825.2.bi.b.326.1 8 55.49 even 10
825.2.bi.b.326.2 8 165.104 odd 10
825.2.bi.b.701.1 8 165.29 even 10
825.2.bi.b.701.2 8 55.29 odd 10
825.2.bs.a.74.1 8 55.7 even 20
825.2.bs.a.74.2 8 165.128 odd 20
825.2.bs.a.524.1 8 165.38 even 20
825.2.bs.a.524.2 8 55.27 odd 20
825.2.bs.d.74.1 8 165.62 odd 20
825.2.bs.d.74.2 8 55.18 even 20
825.2.bs.d.524.1 8 55.38 odd 20
825.2.bs.d.524.2 8 165.137 even 20
891.2.u.a.107.1 16 99.40 odd 30
891.2.u.a.107.2 16 99.95 even 30
891.2.u.a.458.1 16 99.38 odd 30
891.2.u.a.458.2 16 99.16 even 15
891.2.u.a.701.1 16 99.29 even 30
891.2.u.a.701.2 16 99.7 odd 30
891.2.u.a.755.1 16 99.49 even 15
891.2.u.a.755.2 16 99.5 odd 30