Properties

Label 546.2.cg.a.145.5
Level $546$
Weight $2$
Character 546.145
Analytic conductor $4.360$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(145,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 10, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.145");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.cg (of order \(12\), degree \(4\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.5
Character \(\chi\) \(=\) 546.145
Dual form 546.2.cg.a.241.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-3.46134 + 0.927465i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-1.74330 + 1.99020i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-3.46134 + 0.927465i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-1.74330 + 1.99020i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.79172 + 3.10336i) q^{10} +(-3.84991 + 1.03158i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.05596 - 1.91340i) q^{13} +(0.174582 + 2.63999i) q^{14} +(-3.46134 - 0.927465i) q^{15} -1.00000 q^{16} -4.31782 q^{17} +(0.965926 + 0.258819i) q^{18} +(1.87046 - 6.98067i) q^{19} +(0.927465 + 3.46134i) q^{20} +(-2.50484 + 0.851912i) q^{21} +(-1.99286 + 3.45173i) q^{22} +0.712056i q^{23} +(-0.258819 - 0.965926i) q^{24} +(6.79059 - 3.92055i) q^{25} +(-3.51387 + 0.807915i) q^{26} +1.00000i q^{27} +(1.99020 + 1.74330i) q^{28} +(4.49789 + 7.79058i) q^{29} +(-3.10336 + 1.79172i) q^{30} +(-1.93392 + 7.21748i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.84991 - 1.03158i) q^{33} +(-3.05316 + 3.05316i) q^{34} +(4.18833 - 8.50562i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.627321 + 0.627321i) q^{37} +(-3.61346 - 6.25869i) q^{38} +(-1.68984 - 3.18503i) q^{39} +(3.10336 + 1.79172i) q^{40} +(-0.511837 + 1.91020i) q^{41} +(-1.16880 + 2.37359i) q^{42} +(10.1649 + 5.86869i) q^{43} +(1.03158 + 3.84991i) q^{44} +(-2.53388 - 2.53388i) q^{45} +(0.503500 + 0.503500i) q^{46} +(-0.430209 - 1.60556i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.921790 - 6.93904i) q^{49} +(2.02943 - 7.57392i) q^{50} +(-3.73934 - 2.15891i) q^{51} +(-1.91340 + 3.05596i) q^{52} +(-0.862951 - 1.49467i) q^{53} +(0.707107 + 0.707107i) q^{54} +(12.3691 - 7.14131i) q^{55} +(2.63999 - 0.174582i) q^{56} +(5.11020 - 5.11020i) q^{57} +(8.68926 + 2.32828i) q^{58} +(-2.86582 + 2.86582i) q^{59} +(-0.927465 + 3.46134i) q^{60} +(-7.04381 + 4.06674i) q^{61} +(3.73604 + 6.47102i) q^{62} +(-2.59521 - 0.514645i) q^{63} +1.00000i q^{64} +(12.3523 + 3.78863i) q^{65} +(-3.45173 + 1.99286i) q^{66} +(-3.29307 - 12.2899i) q^{67} +4.31782i q^{68} +(-0.356028 + 0.616658i) q^{69} +(-3.05278 - 8.97598i) q^{70} +(-0.167008 - 0.623283i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-3.77262 - 1.01087i) q^{73} +0.887166 q^{74} +7.84110 q^{75} +(-6.98067 - 1.87046i) q^{76} +(4.65851 - 9.46044i) q^{77} +(-3.44706 - 1.05726i) q^{78} +(-2.49494 + 4.32136i) q^{79} +(3.46134 - 0.927465i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.988794 + 1.71264i) q^{82} +(-7.15916 - 7.15916i) q^{83} +(0.851912 + 2.50484i) q^{84} +(14.9455 - 4.00462i) q^{85} +(11.3374 - 3.03786i) q^{86} +8.99579i q^{87} +(3.45173 + 1.99286i) q^{88} +(-11.8393 + 11.8393i) q^{89} -3.58345 q^{90} +(9.13551 - 2.74634i) q^{91} +0.712056 q^{92} +(-5.28357 + 5.28357i) q^{93} +(-1.43951 - 0.831100i) q^{94} +25.8973i q^{95} +(-0.965926 + 0.258819i) q^{96} +(8.33554 - 2.23350i) q^{97} +(-5.55845 - 4.25484i) q^{98} +(-2.81833 - 2.81833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 1.00000i 0.500000i
\(5\) −3.46134 + 0.927465i −1.54796 + 0.414775i −0.928828 0.370512i \(-0.879182\pi\)
−0.619133 + 0.785286i \(0.712516\pi\)
\(6\) 0.965926 0.258819i 0.394338 0.105662i
\(7\) −1.74330 + 1.99020i −0.658907 + 0.752225i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −1.79172 + 3.10336i −0.566593 + 0.981368i
\(11\) −3.84991 + 1.03158i −1.16079 + 0.311033i −0.787282 0.616593i \(-0.788512\pi\)
−0.373509 + 0.927626i \(0.621846\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −3.05596 1.91340i −0.847572 0.530681i
\(14\) 0.174582 + 2.63999i 0.0466591 + 0.705566i
\(15\) −3.46134 0.927465i −0.893715 0.239470i
\(16\) −1.00000 −0.250000
\(17\) −4.31782 −1.04722 −0.523612 0.851957i \(-0.675416\pi\)
−0.523612 + 0.851957i \(0.675416\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) 1.87046 6.98067i 0.429114 1.60147i −0.325658 0.945487i \(-0.605586\pi\)
0.754772 0.655987i \(-0.227747\pi\)
\(20\) 0.927465 + 3.46134i 0.207387 + 0.773980i
\(21\) −2.50484 + 0.851912i −0.546602 + 0.185902i
\(22\) −1.99286 + 3.45173i −0.424879 + 0.735912i
\(23\) 0.712056i 0.148474i 0.997241 + 0.0742370i \(0.0236521\pi\)
−0.997241 + 0.0742370i \(0.976348\pi\)
\(24\) −0.258819 0.965926i −0.0528312 0.197169i
\(25\) 6.79059 3.92055i 1.35812 0.784110i
\(26\) −3.51387 + 0.807915i −0.689126 + 0.158445i
\(27\) 1.00000i 0.192450i
\(28\) 1.99020 + 1.74330i 0.376112 + 0.329453i
\(29\) 4.49789 + 7.79058i 0.835238 + 1.44667i 0.893837 + 0.448393i \(0.148003\pi\)
−0.0585987 + 0.998282i \(0.518663\pi\)
\(30\) −3.10336 + 1.79172i −0.566593 + 0.327123i
\(31\) −1.93392 + 7.21748i −0.347342 + 1.29630i 0.542510 + 0.840049i \(0.317474\pi\)
−0.889852 + 0.456249i \(0.849193\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −3.84991 1.03158i −0.670183 0.179575i
\(34\) −3.05316 + 3.05316i −0.523612 + 0.523612i
\(35\) 4.18833 8.50562i 0.707957 1.43771i
\(36\) 0.866025 0.500000i 0.144338 0.0833333i
\(37\) 0.627321 + 0.627321i 0.103131 + 0.103131i 0.756790 0.653659i \(-0.226767\pi\)
−0.653659 + 0.756790i \(0.726767\pi\)
\(38\) −3.61346 6.25869i −0.586180 1.01529i
\(39\) −1.68984 3.18503i −0.270591 0.510013i
\(40\) 3.10336 + 1.79172i 0.490684 + 0.283296i
\(41\) −0.511837 + 1.91020i −0.0799356 + 0.298324i −0.994307 0.106553i \(-0.966019\pi\)
0.914371 + 0.404876i \(0.132685\pi\)
\(42\) −1.16880 + 2.37359i −0.180350 + 0.366252i
\(43\) 10.1649 + 5.86869i 1.55013 + 0.894967i 0.998130 + 0.0611213i \(0.0194676\pi\)
0.551998 + 0.833846i \(0.313866\pi\)
\(44\) 1.03158 + 3.84991i 0.155517 + 0.580395i
\(45\) −2.53388 2.53388i −0.377729 0.377729i
\(46\) 0.503500 + 0.503500i 0.0742370 + 0.0742370i
\(47\) −0.430209 1.60556i −0.0627524 0.234195i 0.927426 0.374008i \(-0.122017\pi\)
−0.990178 + 0.139813i \(0.955350\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) −0.921790 6.93904i −0.131684 0.991292i
\(50\) 2.02943 7.57392i 0.287004 1.07111i
\(51\) −3.73934 2.15891i −0.523612 0.302308i
\(52\) −1.91340 + 3.05596i −0.265341 + 0.423786i
\(53\) −0.862951 1.49467i −0.118535 0.205309i 0.800652 0.599130i \(-0.204487\pi\)
−0.919187 + 0.393820i \(0.871153\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 12.3691 7.14131i 1.66785 0.962934i
\(56\) 2.63999 0.174582i 0.352783 0.0233296i
\(57\) 5.11020 5.11020i 0.676863 0.676863i
\(58\) 8.68926 + 2.32828i 1.14096 + 0.305718i
\(59\) −2.86582 + 2.86582i −0.373098 + 0.373098i −0.868605 0.495506i \(-0.834983\pi\)
0.495506 + 0.868605i \(0.334983\pi\)
\(60\) −0.927465 + 3.46134i −0.119735 + 0.446858i
\(61\) −7.04381 + 4.06674i −0.901867 + 0.520693i −0.877805 0.479017i \(-0.840993\pi\)
−0.0240615 + 0.999710i \(0.507660\pi\)
\(62\) 3.73604 + 6.47102i 0.474478 + 0.821820i
\(63\) −2.59521 0.514645i −0.326966 0.0648391i
\(64\) 1.00000i 0.125000i
\(65\) 12.3523 + 3.78863i 1.53212 + 0.469922i
\(66\) −3.45173 + 1.99286i −0.424879 + 0.245304i
\(67\) −3.29307 12.2899i −0.402312 1.50145i −0.808959 0.587865i \(-0.799969\pi\)
0.406647 0.913586i \(-0.366698\pi\)
\(68\) 4.31782i 0.523612i
\(69\) −0.356028 + 0.616658i −0.0428607 + 0.0742370i
\(70\) −3.05278 8.97598i −0.364877 1.07283i
\(71\) −0.167008 0.623283i −0.0198202 0.0739701i 0.955307 0.295614i \(-0.0955243\pi\)
−0.975128 + 0.221644i \(0.928858\pi\)
\(72\) 0.258819 0.965926i 0.0305021 0.113835i
\(73\) −3.77262 1.01087i −0.441551 0.118313i 0.0311922 0.999513i \(-0.490070\pi\)
−0.472743 + 0.881200i \(0.656736\pi\)
\(74\) 0.887166 0.103131
\(75\) 7.84110 0.905412
\(76\) −6.98067 1.87046i −0.800737 0.214557i
\(77\) 4.65851 9.46044i 0.530886 1.07812i
\(78\) −3.44706 1.05726i −0.390302 0.119711i
\(79\) −2.49494 + 4.32136i −0.280703 + 0.486191i −0.971558 0.236802i \(-0.923901\pi\)
0.690855 + 0.722993i \(0.257234\pi\)
\(80\) 3.46134 0.927465i 0.386990 0.103694i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0.988794 + 1.71264i 0.109194 + 0.189130i
\(83\) −7.15916 7.15916i −0.785820 0.785820i 0.194986 0.980806i \(-0.437534\pi\)
−0.980806 + 0.194986i \(0.937534\pi\)
\(84\) 0.851912 + 2.50484i 0.0929512 + 0.273301i
\(85\) 14.9455 4.00462i 1.62106 0.434362i
\(86\) 11.3374 3.03786i 1.22255 0.327581i
\(87\) 8.99579i 0.964450i
\(88\) 3.45173 + 1.99286i 0.367956 + 0.212439i
\(89\) −11.8393 + 11.8393i −1.25497 + 1.25497i −0.301503 + 0.953465i \(0.597488\pi\)
−0.953465 + 0.301503i \(0.902512\pi\)
\(90\) −3.58345 −0.377729
\(91\) 9.13551 2.74634i 0.957662 0.287895i
\(92\) 0.712056 0.0742370
\(93\) −5.28357 + 5.28357i −0.547880 + 0.547880i
\(94\) −1.43951 0.831100i −0.148474 0.0857214i
\(95\) 25.8973i 2.65700i
\(96\) −0.965926 + 0.258819i −0.0985844 + 0.0264156i
\(97\) 8.33554 2.23350i 0.846346 0.226778i 0.190514 0.981684i \(-0.438985\pi\)
0.655832 + 0.754907i \(0.272318\pi\)
\(98\) −5.55845 4.25484i −0.561488 0.429804i
\(99\) −2.81833 2.81833i −0.283253 0.283253i
\(100\) −3.92055 6.79059i −0.392055 0.679059i
\(101\) 2.68348 4.64792i 0.267016 0.462486i −0.701074 0.713089i \(-0.747296\pi\)
0.968090 + 0.250603i \(0.0806290\pi\)
\(102\) −4.17069 + 1.11753i −0.412960 + 0.110652i
\(103\) −1.95134 + 3.37982i −0.192271 + 0.333024i −0.946003 0.324159i \(-0.894919\pi\)
0.753731 + 0.657183i \(0.228252\pi\)
\(104\) 0.807915 + 3.51387i 0.0792226 + 0.344563i
\(105\) 7.88001 5.27192i 0.769010 0.514486i
\(106\) −1.66709 0.446696i −0.161922 0.0433870i
\(107\) −19.4175 −1.87716 −0.938582 0.345056i \(-0.887860\pi\)
−0.938582 + 0.345056i \(0.887860\pi\)
\(108\) 1.00000 0.0962250
\(109\) −12.9072 3.45849i −1.23629 0.331263i −0.419264 0.907864i \(-0.637712\pi\)
−0.817026 + 0.576601i \(0.804379\pi\)
\(110\) 3.69661 13.7959i 0.352458 1.31539i
\(111\) 0.229615 + 0.856937i 0.0217941 + 0.0813368i
\(112\) 1.74330 1.99020i 0.164727 0.188056i
\(113\) −0.175668 + 0.304265i −0.0165254 + 0.0286229i −0.874170 0.485620i \(-0.838594\pi\)
0.857644 + 0.514243i \(0.171927\pi\)
\(114\) 7.22692i 0.676863i
\(115\) −0.660407 2.46467i −0.0615832 0.229832i
\(116\) 7.79058 4.49789i 0.723337 0.417619i
\(117\) 0.129070 3.60324i 0.0119325 0.333120i
\(118\) 4.05289i 0.373098i
\(119\) 7.52726 8.59332i 0.690023 0.787748i
\(120\) 1.79172 + 3.10336i 0.163561 + 0.283296i
\(121\) 4.23136 2.44297i 0.384669 0.222089i
\(122\) −2.10510 + 7.85634i −0.190587 + 0.711280i
\(123\) −1.39837 + 1.39837i −0.126086 + 0.126086i
\(124\) 7.21748 + 1.93392i 0.648149 + 0.173671i
\(125\) −7.19900 + 7.19900i −0.643898 + 0.643898i
\(126\) −2.19900 + 1.47119i −0.195903 + 0.131064i
\(127\) 2.86847 1.65611i 0.254535 0.146956i −0.367304 0.930101i \(-0.619719\pi\)
0.621839 + 0.783145i \(0.286386\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 5.86869 + 10.1649i 0.516709 + 0.894967i
\(130\) 11.4134 6.05546i 1.00102 0.531099i
\(131\) −1.14746 0.662484i −0.100254 0.0578815i 0.449035 0.893514i \(-0.351768\pi\)
−0.549289 + 0.835633i \(0.685101\pi\)
\(132\) −1.03158 + 3.84991i −0.0897875 + 0.335091i
\(133\) 10.6321 + 15.8920i 0.921923 + 1.37801i
\(134\) −11.0188 6.36172i −0.951881 0.549569i
\(135\) −0.927465 3.46134i −0.0798234 0.297905i
\(136\) 3.05316 + 3.05316i 0.261806 + 0.261806i
\(137\) 1.52374 + 1.52374i 0.130182 + 0.130182i 0.769195 0.639014i \(-0.220657\pi\)
−0.639014 + 0.769195i \(0.720657\pi\)
\(138\) 0.184294 + 0.687793i 0.0156881 + 0.0585488i
\(139\) 4.27921 + 2.47060i 0.362958 + 0.209554i 0.670377 0.742020i \(-0.266132\pi\)
−0.307420 + 0.951574i \(0.599466\pi\)
\(140\) −8.50562 4.18833i −0.718856 0.353979i
\(141\) 0.430209 1.60556i 0.0362301 0.135213i
\(142\) −0.558821 0.322635i −0.0468952 0.0270749i
\(143\) 13.7390 + 4.21394i 1.14891 + 0.352387i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −22.7942 22.7942i −1.89296 1.89296i
\(146\) −3.38243 + 1.95285i −0.279932 + 0.161619i
\(147\) 2.67123 6.47028i 0.220319 0.533660i
\(148\) 0.627321 0.627321i 0.0515655 0.0515655i
\(149\) 7.16290 + 1.91929i 0.586808 + 0.157235i 0.539994 0.841669i \(-0.318427\pi\)
0.0468138 + 0.998904i \(0.485093\pi\)
\(150\) 5.54449 5.54449i 0.452706 0.452706i
\(151\) −2.94021 + 10.9730i −0.239271 + 0.892970i 0.736906 + 0.675995i \(0.236286\pi\)
−0.976177 + 0.216976i \(0.930381\pi\)
\(152\) −6.25869 + 3.61346i −0.507647 + 0.293090i
\(153\) −2.15891 3.73934i −0.174537 0.302308i
\(154\) −3.39548 9.98360i −0.273616 0.804502i
\(155\) 26.7758i 2.15069i
\(156\) −3.18503 + 1.68984i −0.255007 + 0.135296i
\(157\) 18.0270 10.4079i 1.43871 0.830641i 0.440952 0.897531i \(-0.354641\pi\)
0.997760 + 0.0668898i \(0.0213076\pi\)
\(158\) 1.29148 + 4.81985i 0.102744 + 0.383447i
\(159\) 1.72590i 0.136873i
\(160\) 1.79172 3.10336i 0.141648 0.245342i
\(161\) −1.41713 1.24133i −0.111686 0.0978304i
\(162\) 0.258819 + 0.965926i 0.0203347 + 0.0758903i
\(163\) −2.21749 + 8.27580i −0.173688 + 0.648211i 0.823084 + 0.567920i \(0.192252\pi\)
−0.996771 + 0.0802909i \(0.974415\pi\)
\(164\) 1.91020 + 0.511837i 0.149162 + 0.0399678i
\(165\) 14.2826 1.11190
\(166\) −10.1246 −0.785820
\(167\) −10.7973 2.89312i −0.835519 0.223877i −0.184399 0.982851i \(-0.559034\pi\)
−0.651120 + 0.758975i \(0.725701\pi\)
\(168\) 2.37359 + 1.16880i 0.183126 + 0.0901749i
\(169\) 5.67782 + 11.6945i 0.436755 + 0.899580i
\(170\) 7.73634 13.3997i 0.593350 1.02771i
\(171\) 6.98067 1.87046i 0.533825 0.143038i
\(172\) 5.86869 10.1649i 0.447483 0.775064i
\(173\) −3.47656 6.02158i −0.264318 0.457812i 0.703067 0.711124i \(-0.251814\pi\)
−0.967385 + 0.253312i \(0.918480\pi\)
\(174\) 6.36098 + 6.36098i 0.482225 + 0.482225i
\(175\) −4.03538 + 20.3493i −0.305046 + 1.53827i
\(176\) 3.84991 1.03158i 0.290198 0.0777583i
\(177\) −3.91479 + 1.04896i −0.294253 + 0.0788450i
\(178\) 16.7434i 1.25497i
\(179\) −15.3799 8.87956i −1.14954 0.663690i −0.200768 0.979639i \(-0.564344\pi\)
−0.948776 + 0.315949i \(0.897677\pi\)
\(180\) −2.53388 + 2.53388i −0.188864 + 0.188864i
\(181\) 13.6380 1.01371 0.506853 0.862032i \(-0.330809\pi\)
0.506853 + 0.862032i \(0.330809\pi\)
\(182\) 4.51783 8.40174i 0.334883 0.622778i
\(183\) −8.13349 −0.601245
\(184\) 0.503500 0.503500i 0.0371185 0.0371185i
\(185\) −2.75319 1.58956i −0.202419 0.116867i
\(186\) 7.47209i 0.547880i
\(187\) 16.6232 4.45417i 1.21561 0.325721i
\(188\) −1.60556 + 0.430209i −0.117098 + 0.0313762i
\(189\) −1.99020 1.74330i −0.144766 0.126807i
\(190\) 18.3121 + 18.3121i 1.32850 + 1.32850i
\(191\) −5.06856 8.77900i −0.366748 0.635226i 0.622307 0.782773i \(-0.286196\pi\)
−0.989055 + 0.147547i \(0.952862\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 12.4154 3.32669i 0.893678 0.239460i 0.217379 0.976087i \(-0.430249\pi\)
0.676299 + 0.736627i \(0.263583\pi\)
\(194\) 4.31479 7.47344i 0.309784 0.536562i
\(195\) 8.80313 + 9.45723i 0.630405 + 0.677246i
\(196\) −6.93904 + 0.921790i −0.495646 + 0.0658421i
\(197\) 14.3021 + 3.83225i 1.01899 + 0.273036i 0.729379 0.684110i \(-0.239809\pi\)
0.289606 + 0.957146i \(0.406476\pi\)
\(198\) −3.98572 −0.283253
\(199\) −21.6106 −1.53194 −0.765969 0.642877i \(-0.777740\pi\)
−0.765969 + 0.642877i \(0.777740\pi\)
\(200\) −7.57392 2.02943i −0.535557 0.143502i
\(201\) 3.29307 12.2899i 0.232275 0.866863i
\(202\) −1.38907 5.18408i −0.0977347 0.364751i
\(203\) −23.3460 4.62963i −1.63857 0.324937i
\(204\) −2.15891 + 3.73934i −0.151154 + 0.261806i
\(205\) 7.08658i 0.494948i
\(206\) 1.01009 + 3.76970i 0.0703762 + 0.262648i
\(207\) −0.616658 + 0.356028i −0.0428607 + 0.0247457i
\(208\) 3.05596 + 1.91340i 0.211893 + 0.132670i
\(209\) 28.8045i 1.99245i
\(210\) 1.84420 9.29982i 0.127262 0.641748i
\(211\) −11.9473 20.6934i −0.822487 1.42459i −0.903825 0.427903i \(-0.859252\pi\)
0.0813372 0.996687i \(-0.474081\pi\)
\(212\) −1.49467 + 0.862951i −0.102655 + 0.0592677i
\(213\) 0.167008 0.623283i 0.0114432 0.0427067i
\(214\) −13.7303 + 13.7303i −0.938582 + 0.938582i
\(215\) −40.6271 10.8860i −2.77075 0.742419i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) −10.9928 16.4311i −0.746242 1.11542i
\(218\) −11.5723 + 6.68128i −0.783776 + 0.452514i
\(219\) −2.76175 2.76175i −0.186621 0.186621i
\(220\) −7.14131 12.3691i −0.481467 0.833925i
\(221\) 13.1951 + 8.26170i 0.887598 + 0.555742i
\(222\) 0.768308 + 0.443583i 0.0515655 + 0.0297713i
\(223\) −5.54886 + 20.7086i −0.371579 + 1.38675i 0.486700 + 0.873569i \(0.338200\pi\)
−0.858279 + 0.513183i \(0.828466\pi\)
\(224\) −0.174582 2.63999i −0.0116648 0.176391i
\(225\) 6.79059 + 3.92055i 0.452706 + 0.261370i
\(226\) 0.0909323 + 0.339364i 0.00604873 + 0.0225742i
\(227\) −1.86102 1.86102i −0.123520 0.123520i 0.642644 0.766165i \(-0.277837\pi\)
−0.766165 + 0.642644i \(0.777837\pi\)
\(228\) −5.11020 5.11020i −0.338431 0.338431i
\(229\) 5.43526 + 20.2847i 0.359172 + 1.34045i 0.875152 + 0.483848i \(0.160761\pi\)
−0.515980 + 0.856601i \(0.672572\pi\)
\(230\) −2.20976 1.27581i −0.145707 0.0841243i
\(231\) 8.76461 5.86373i 0.576669 0.385805i
\(232\) 2.32828 8.68926i 0.152859 0.570478i
\(233\) 16.1588 + 9.32927i 1.05860 + 0.611181i 0.925044 0.379861i \(-0.124028\pi\)
0.133553 + 0.991042i \(0.457362\pi\)
\(234\) −2.45661 2.63914i −0.160594 0.172526i
\(235\) 2.97820 + 5.15840i 0.194277 + 0.336497i
\(236\) 2.86582 + 2.86582i 0.186549 + 0.186549i
\(237\) −4.32136 + 2.49494i −0.280703 + 0.162064i
\(238\) −0.753815 11.3990i −0.0488626 0.738886i
\(239\) 8.43037 8.43037i 0.545315 0.545315i −0.379767 0.925082i \(-0.623996\pi\)
0.925082 + 0.379767i \(0.123996\pi\)
\(240\) 3.46134 + 0.927465i 0.223429 + 0.0598676i
\(241\) −10.6320 + 10.6320i −0.684866 + 0.684866i −0.961092 0.276227i \(-0.910916\pi\)
0.276227 + 0.961092i \(0.410916\pi\)
\(242\) 1.26458 4.71946i 0.0812901 0.303379i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 4.06674 + 7.04381i 0.260347 + 0.450933i
\(245\) 9.62635 + 23.1635i 0.615005 + 1.47986i
\(246\) 1.97759i 0.126086i
\(247\) −19.0729 + 17.7537i −1.21358 + 1.12964i
\(248\) 6.47102 3.73604i 0.410910 0.237239i
\(249\) −2.62043 9.77959i −0.166063 0.619756i
\(250\) 10.1809i 0.643898i
\(251\) 5.32365 9.22082i 0.336026 0.582013i −0.647656 0.761933i \(-0.724250\pi\)
0.983681 + 0.179920i \(0.0575838\pi\)
\(252\) −0.514645 + 2.59521i −0.0324196 + 0.163483i
\(253\) −0.734542 2.74135i −0.0461803 0.172347i
\(254\) 0.857266 3.19936i 0.0537896 0.200746i
\(255\) 14.9455 + 4.00462i 0.935921 + 0.250779i
\(256\) 1.00000 0.0625000
\(257\) 12.6998 0.792194 0.396097 0.918209i \(-0.370364\pi\)
0.396097 + 0.918209i \(0.370364\pi\)
\(258\) 11.3374 + 3.03786i 0.705838 + 0.189129i
\(259\) −2.34211 + 0.154884i −0.145531 + 0.00962400i
\(260\) 3.78863 12.3523i 0.234961 0.766060i
\(261\) −4.49789 + 7.79058i −0.278413 + 0.482225i
\(262\) −1.27982 + 0.342927i −0.0790676 + 0.0211861i
\(263\) −9.33453 + 16.1679i −0.575592 + 0.996954i 0.420385 + 0.907346i \(0.361895\pi\)
−0.995977 + 0.0896086i \(0.971438\pi\)
\(264\) 1.99286 + 3.45173i 0.122652 + 0.212439i
\(265\) 4.37323 + 4.37323i 0.268645 + 0.268645i
\(266\) 18.7554 + 3.71929i 1.14997 + 0.228045i
\(267\) −16.1728 + 4.33350i −0.989762 + 0.265206i
\(268\) −12.2899 + 3.29307i −0.750725 + 0.201156i
\(269\) 15.5528i 0.948269i 0.880452 + 0.474135i \(0.157239\pi\)
−0.880452 + 0.474135i \(0.842761\pi\)
\(270\) −3.10336 1.79172i −0.188864 0.109041i
\(271\) −9.71103 + 9.71103i −0.589903 + 0.589903i −0.937605 0.347702i \(-0.886962\pi\)
0.347702 + 0.937605i \(0.386962\pi\)
\(272\) 4.31782 0.261806
\(273\) 9.28476 + 2.18935i 0.561939 + 0.132506i
\(274\) 2.15489 0.130182
\(275\) −22.0988 + 22.0988i −1.33261 + 1.33261i
\(276\) 0.616658 + 0.356028i 0.0371185 + 0.0214304i
\(277\) 1.85671i 0.111559i 0.998443 + 0.0557794i \(0.0177643\pi\)
−0.998443 + 0.0557794i \(0.982236\pi\)
\(278\) 4.77283 1.27888i 0.286256 0.0767020i
\(279\) −7.21748 + 1.93392i −0.432099 + 0.115781i
\(280\) −8.97598 + 3.05278i −0.536417 + 0.182439i
\(281\) 12.6667 + 12.6667i 0.755630 + 0.755630i 0.975524 0.219894i \(-0.0705710\pi\)
−0.219894 + 0.975524i \(0.570571\pi\)
\(282\) −0.831100 1.43951i −0.0494913 0.0857214i
\(283\) 3.73778 6.47402i 0.222188 0.384841i −0.733284 0.679922i \(-0.762014\pi\)
0.955472 + 0.295082i \(0.0953468\pi\)
\(284\) −0.623283 + 0.167008i −0.0369851 + 0.00991012i
\(285\) −12.9486 + 22.4277i −0.767011 + 1.32850i
\(286\) 12.6946 6.73523i 0.750650 0.398263i
\(287\) −2.90940 4.34872i −0.171736 0.256697i
\(288\) −0.965926 0.258819i −0.0569177 0.0152511i
\(289\) 1.64354 0.0966791
\(290\) −32.2359 −1.89296
\(291\) 8.33554 + 2.23350i 0.488638 + 0.130930i
\(292\) −1.01087 + 3.77262i −0.0591566 + 0.220776i
\(293\) 0.984079 + 3.67263i 0.0574905 + 0.214557i 0.988695 0.149939i \(-0.0479078\pi\)
−0.931205 + 0.364497i \(0.881241\pi\)
\(294\) −2.68634 6.46402i −0.156670 0.376989i
\(295\) 7.26165 12.5776i 0.422790 0.732294i
\(296\) 0.887166i 0.0515655i
\(297\) −1.03158 3.84991i −0.0598583 0.223394i
\(298\) 6.42208 3.70779i 0.372021 0.214786i
\(299\) 1.36245 2.17602i 0.0787923 0.125842i
\(300\) 7.84110i 0.452706i
\(301\) −29.4003 + 9.99922i −1.69461 + 0.576345i
\(302\) 5.68004 + 9.83813i 0.326850 + 0.566121i
\(303\) 4.64792 2.68348i 0.267016 0.154162i
\(304\) −1.87046 + 6.98067i −0.107278 + 0.400369i
\(305\) 20.6093 20.6093i 1.18008 1.18008i
\(306\) −4.17069 1.11753i −0.238423 0.0638851i
\(307\) −11.3549 + 11.3549i −0.648060 + 0.648060i −0.952524 0.304464i \(-0.901523\pi\)
0.304464 + 0.952524i \(0.401523\pi\)
\(308\) −9.46044 4.65851i −0.539059 0.265443i
\(309\) −3.37982 + 1.95134i −0.192271 + 0.111008i
\(310\) −18.9334 18.9334i −1.07534 1.07534i
\(311\) 5.29988 + 9.17966i 0.300529 + 0.520531i 0.976256 0.216621i \(-0.0695036\pi\)
−0.675727 + 0.737152i \(0.736170\pi\)
\(312\) −1.05726 + 3.44706i −0.0598555 + 0.195151i
\(313\) 17.3619 + 10.0239i 0.981352 + 0.566584i 0.902678 0.430316i \(-0.141598\pi\)
0.0786742 + 0.996900i \(0.474931\pi\)
\(314\) 5.38753 20.1065i 0.304036 1.13468i
\(315\) 9.46025 0.625607i 0.533025 0.0352490i
\(316\) 4.32136 + 2.49494i 0.243096 + 0.140351i
\(317\) −1.66934 6.23006i −0.0937594 0.349915i 0.903069 0.429495i \(-0.141309\pi\)
−0.996828 + 0.0795806i \(0.974642\pi\)
\(318\) −1.22040 1.22040i −0.0684364 0.0684364i
\(319\) −25.3531 25.3531i −1.41950 1.41950i
\(320\) −0.927465 3.46134i −0.0518468 0.193495i
\(321\) −16.8161 9.70877i −0.938582 0.541891i
\(322\) −1.87982 + 0.124312i −0.104758 + 0.00692766i
\(323\) −8.07632 + 30.1412i −0.449378 + 1.67710i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) −28.2534 1.01205i −1.56721 0.0561385i
\(326\) 4.28387 + 7.41988i 0.237262 + 0.410949i
\(327\) −9.44876 9.44876i −0.522518 0.522518i
\(328\) 1.71264 0.988794i 0.0945648 0.0545970i
\(329\) 3.94537 + 1.94278i 0.217515 + 0.107109i
\(330\) 10.0993 10.0993i 0.555950 0.555950i
\(331\) 19.4177 + 5.20295i 1.06729 + 0.285980i 0.749380 0.662140i \(-0.230352\pi\)
0.317912 + 0.948120i \(0.397018\pi\)
\(332\) −7.15916 + 7.15916i −0.392910 + 0.392910i
\(333\) −0.229615 + 0.856937i −0.0125828 + 0.0469598i
\(334\) −9.68058 + 5.58909i −0.529698 + 0.305821i
\(335\) 22.7969 + 39.4854i 1.24553 + 2.15732i
\(336\) 2.50484 0.851912i 0.136650 0.0464756i
\(337\) 2.51782i 0.137154i −0.997646 0.0685772i \(-0.978154\pi\)
0.997646 0.0685772i \(-0.0218460\pi\)
\(338\) 12.2841 + 4.25447i 0.668168 + 0.231413i
\(339\) −0.304265 + 0.175668i −0.0165254 + 0.00954096i
\(340\) −4.00462 14.9455i −0.217181 0.810531i
\(341\) 29.7816i 1.61277i
\(342\) 3.61346 6.25869i 0.195393 0.338431i
\(343\) 15.4170 + 10.2623i 0.832442 + 0.554112i
\(344\) −3.03786 11.3374i −0.163790 0.611274i
\(345\) 0.660407 2.46467i 0.0355551 0.132693i
\(346\) −6.71620 1.79960i −0.361065 0.0967472i
\(347\) 17.7585 0.953328 0.476664 0.879086i \(-0.341846\pi\)
0.476664 + 0.879086i \(0.341846\pi\)
\(348\) 8.99579 0.482225
\(349\) 4.09488 + 1.09722i 0.219194 + 0.0587329i 0.366745 0.930322i \(-0.380472\pi\)
−0.147551 + 0.989055i \(0.547139\pi\)
\(350\) 11.5357 + 17.2426i 0.616610 + 0.921656i
\(351\) 1.91340 3.05596i 0.102130 0.163115i
\(352\) 1.99286 3.45173i 0.106220 0.183978i
\(353\) 28.6691 7.68186i 1.52590 0.408864i 0.604222 0.796816i \(-0.293484\pi\)
0.921680 + 0.387952i \(0.126817\pi\)
\(354\) −2.02644 + 3.50990i −0.107704 + 0.186549i
\(355\) 1.15615 + 2.00250i 0.0613619 + 0.106282i
\(356\) 11.8393 + 11.8393i 0.627484 + 0.627484i
\(357\) 10.8155 3.67840i 0.572415 0.194682i
\(358\) −17.1540 + 4.59640i −0.906617 + 0.242927i
\(359\) 0.500851 0.134203i 0.0264339 0.00708294i −0.245578 0.969377i \(-0.578978\pi\)
0.272012 + 0.962294i \(0.412311\pi\)
\(360\) 3.58345i 0.188864i
\(361\) −28.7766 16.6142i −1.51456 0.874429i
\(362\) 9.64354 9.64354i 0.506853 0.506853i
\(363\) 4.88595 0.256446
\(364\) −2.74634 9.13551i −0.143948 0.478831i
\(365\) 13.9959 0.732577
\(366\) −5.75124 + 5.75124i −0.300622 + 0.300622i
\(367\) −29.0561 16.7755i −1.51671 0.875675i −0.999807 0.0196332i \(-0.993750\pi\)
−0.516907 0.856042i \(-0.672917\pi\)
\(368\) 0.712056i 0.0371185i
\(369\) −1.91020 + 0.511837i −0.0994412 + 0.0266452i
\(370\) −3.07079 + 0.822815i −0.159643 + 0.0427761i
\(371\) 4.47908 + 0.888226i 0.232542 + 0.0461144i
\(372\) 5.28357 + 5.28357i 0.273940 + 0.273940i
\(373\) −15.3407 26.5709i −0.794314 1.37579i −0.923274 0.384142i \(-0.874497\pi\)
0.128960 0.991650i \(-0.458836\pi\)
\(374\) 8.60480 14.9040i 0.444944 0.770665i
\(375\) −9.83402 + 2.63502i −0.507827 + 0.136072i
\(376\) −0.831100 + 1.43951i −0.0428607 + 0.0742369i
\(377\) 1.16109 32.4140i 0.0597990 1.66941i
\(378\) −2.63999 + 0.174582i −0.135786 + 0.00897955i
\(379\) 2.21846 + 0.594436i 0.113955 + 0.0305341i 0.315346 0.948977i \(-0.397879\pi\)
−0.201391 + 0.979511i \(0.564546\pi\)
\(380\) 25.8973 1.32850
\(381\) 3.31222 0.169690
\(382\) −9.79170 2.62368i −0.500987 0.134239i
\(383\) −3.80442 + 14.1983i −0.194397 + 0.725498i 0.798026 + 0.602624i \(0.205878\pi\)
−0.992422 + 0.122875i \(0.960789\pi\)
\(384\) 0.258819 + 0.965926i 0.0132078 + 0.0492922i
\(385\) −7.35047 + 37.0665i −0.374615 + 1.88908i
\(386\) 6.42667 11.1313i 0.327109 0.566569i
\(387\) 11.7374i 0.596645i
\(388\) −2.23350 8.33554i −0.113389 0.423173i
\(389\) −28.5510 + 16.4839i −1.44759 + 0.835767i −0.998338 0.0576369i \(-0.981643\pi\)
−0.449254 + 0.893404i \(0.648310\pi\)
\(390\) 12.9120 + 0.462516i 0.653826 + 0.0234204i
\(391\) 3.07453i 0.155486i
\(392\) −4.25484 + 5.55845i −0.214902 + 0.280744i
\(393\) −0.662484 1.14746i −0.0334179 0.0578815i
\(394\) 12.8230 7.40333i 0.646011 0.372975i
\(395\) 4.62794 17.2717i 0.232857 0.869033i
\(396\) −2.81833 + 2.81833i −0.141626 + 0.141626i
\(397\) 12.7620 + 3.41956i 0.640506 + 0.171623i 0.564433 0.825479i \(-0.309095\pi\)
0.0760733 + 0.997102i \(0.475762\pi\)
\(398\) −15.2810 + 15.2810i −0.765969 + 0.765969i
\(399\) 1.26169 + 19.0790i 0.0631636 + 0.955142i
\(400\) −6.79059 + 3.92055i −0.339530 + 0.196027i
\(401\) −10.4686 10.4686i −0.522777 0.522777i 0.395632 0.918409i \(-0.370526\pi\)
−0.918409 + 0.395632i \(0.870526\pi\)
\(402\) −6.36172 11.0188i −0.317294 0.549569i
\(403\) 19.7199 18.3560i 0.982318 0.914378i
\(404\) −4.64792 2.68348i −0.231243 0.133508i
\(405\) 0.927465 3.46134i 0.0460861 0.171996i
\(406\) −19.7818 + 13.2345i −0.981752 + 0.656816i
\(407\) −3.06226 1.76800i −0.151791 0.0876364i
\(408\) 1.11753 + 4.17069i 0.0553261 + 0.206480i
\(409\) −14.9768 14.9768i −0.740556 0.740556i 0.232129 0.972685i \(-0.425431\pi\)
−0.972685 + 0.232129i \(0.925431\pi\)
\(410\) −5.01097 5.01097i −0.247474 0.247474i
\(411\) 0.557727 + 2.08146i 0.0275106 + 0.102671i
\(412\) 3.37982 + 1.95134i 0.166512 + 0.0961357i
\(413\) −0.707563 10.6996i −0.0348169 0.526491i
\(414\) −0.184294 + 0.687793i −0.00905754 + 0.0338032i
\(415\) 31.4202 + 18.1405i 1.54236 + 0.890480i
\(416\) 3.51387 0.807915i 0.172282 0.0396113i
\(417\) 2.47060 + 4.27921i 0.120986 + 0.209554i
\(418\) 20.3678 + 20.3678i 0.996223 + 0.996223i
\(419\) 7.81110 4.50974i 0.381597 0.220315i −0.296916 0.954904i \(-0.595958\pi\)
0.678513 + 0.734588i \(0.262625\pi\)
\(420\) −5.27192 7.88001i −0.257243 0.384505i
\(421\) −5.07143 + 5.07143i −0.247166 + 0.247166i −0.819807 0.572640i \(-0.805919\pi\)
0.572640 + 0.819807i \(0.305919\pi\)
\(422\) −23.0804 6.18439i −1.12354 0.301051i
\(423\) 1.17535 1.17535i 0.0571476 0.0571476i
\(424\) −0.446696 + 1.66709i −0.0216935 + 0.0809612i
\(425\) −29.3205 + 16.9282i −1.42225 + 0.821139i
\(426\) −0.322635 0.558821i −0.0156317 0.0270749i
\(427\) 4.18586 21.1081i 0.202568 1.02149i
\(428\) 19.4175i 0.938582i
\(429\) 9.79135 + 10.5189i 0.472731 + 0.507856i
\(430\) −36.4253 + 21.0301i −1.75658 + 1.01416i
\(431\) −3.90772 14.5838i −0.188228 0.702477i −0.993916 0.110137i \(-0.964871\pi\)
0.805688 0.592340i \(-0.201796\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −18.3240 + 31.7381i −0.880596 + 1.52524i −0.0299168 + 0.999552i \(0.509524\pi\)
−0.850679 + 0.525685i \(0.823809\pi\)
\(434\) −19.3917 3.84547i −0.930830 0.184589i
\(435\) −8.34327 31.1375i −0.400029 1.49293i
\(436\) −3.45849 + 12.9072i −0.165631 + 0.618145i
\(437\) 4.97062 + 1.33187i 0.237777 + 0.0637122i
\(438\) −3.90570 −0.186621
\(439\) −27.7745 −1.32561 −0.662803 0.748794i \(-0.730633\pi\)
−0.662803 + 0.748794i \(0.730633\pi\)
\(440\) −13.7959 3.69661i −0.657696 0.176229i
\(441\) 5.54849 4.26781i 0.264214 0.203229i
\(442\) 15.1722 3.48843i 0.721670 0.165928i
\(443\) 7.82321 13.5502i 0.371692 0.643789i −0.618134 0.786073i \(-0.712111\pi\)
0.989826 + 0.142283i \(0.0454445\pi\)
\(444\) 0.856937 0.229615i 0.0406684 0.0108971i
\(445\) 29.9995 51.9606i 1.42211 2.46317i
\(446\) 10.7196 + 18.5668i 0.507587 + 0.879166i
\(447\) 5.24361 + 5.24361i 0.248014 + 0.248014i
\(448\) −1.99020 1.74330i −0.0940281 0.0823633i
\(449\) 9.64984 2.58567i 0.455404 0.122025i −0.0238228 0.999716i \(-0.507584\pi\)
0.479227 + 0.877691i \(0.340917\pi\)
\(450\) 7.57392 2.02943i 0.357038 0.0956680i
\(451\) 7.88211i 0.371154i
\(452\) 0.304265 + 0.175668i 0.0143114 + 0.00826271i
\(453\) −8.03280 + 8.03280i −0.377414 + 0.377414i
\(454\) −2.63188 −0.123520
\(455\) −29.0740 + 17.9789i −1.36301 + 0.842864i
\(456\) −7.22692 −0.338431
\(457\) −10.0672 + 10.0672i −0.470924 + 0.470924i −0.902214 0.431289i \(-0.858059\pi\)
0.431289 + 0.902214i \(0.358059\pi\)
\(458\) 18.1867 + 10.5001i 0.849811 + 0.490638i
\(459\) 4.31782i 0.201538i
\(460\) −2.46467 + 0.660407i −0.114916 + 0.0307916i
\(461\) 27.4644 7.35907i 1.27915 0.342746i 0.445617 0.895223i \(-0.352984\pi\)
0.833528 + 0.552478i \(0.186318\pi\)
\(462\) 2.05123 10.3438i 0.0954318 0.481237i
\(463\) 9.63165 + 9.63165i 0.447621 + 0.447621i 0.894563 0.446942i \(-0.147487\pi\)
−0.446942 + 0.894563i \(0.647487\pi\)
\(464\) −4.49789 7.79058i −0.208809 0.361669i
\(465\) 13.3879 23.1886i 0.620850 1.07534i
\(466\) 18.0228 4.82918i 0.834888 0.223708i
\(467\) 15.3719 26.6250i 0.711329 1.23206i −0.253030 0.967458i \(-0.581427\pi\)
0.964359 0.264599i \(-0.0852396\pi\)
\(468\) −3.60324 0.129070i −0.166560 0.00596627i
\(469\) 30.2002 + 14.8712i 1.39451 + 0.686686i
\(470\) 5.75345 + 1.54163i 0.265387 + 0.0711101i
\(471\) 20.8158 0.959142
\(472\) 4.05289 0.186549
\(473\) −45.1878 12.1080i −2.07774 0.556728i
\(474\) −1.29148 + 4.81985i −0.0593195 + 0.221383i
\(475\) −14.6665 54.7361i −0.672945 2.51146i
\(476\) −8.59332 7.52726i −0.393874 0.345012i
\(477\) 0.862951 1.49467i 0.0395118 0.0684364i
\(478\) 11.9223i 0.545315i
\(479\) 4.08006 + 15.2270i 0.186423 + 0.695739i 0.994322 + 0.106418i \(0.0339380\pi\)
−0.807899 + 0.589321i \(0.799395\pi\)
\(480\) 3.10336 1.79172i 0.141648 0.0817806i
\(481\) −0.716755 3.11738i −0.0326812 0.142141i
\(482\) 15.0359i 0.684866i
\(483\) −0.606609 1.78359i −0.0276017 0.0811561i
\(484\) −2.44297 4.23136i −0.111044 0.192334i
\(485\) −26.7807 + 15.4618i −1.21605 + 0.702086i
\(486\) −0.258819 + 0.965926i −0.0117403 + 0.0438153i
\(487\) −13.1445 + 13.1445i −0.595635 + 0.595635i −0.939148 0.343513i \(-0.888383\pi\)
0.343513 + 0.939148i \(0.388383\pi\)
\(488\) 7.85634 + 2.10510i 0.355640 + 0.0952935i
\(489\) −6.05831 + 6.05831i −0.273966 + 0.273966i
\(490\) 23.1859 + 9.57220i 1.04743 + 0.432428i
\(491\) −11.0514 + 6.38052i −0.498742 + 0.287949i −0.728194 0.685371i \(-0.759640\pi\)
0.229452 + 0.973320i \(0.426307\pi\)
\(492\) 1.39837 + 1.39837i 0.0630432 + 0.0630432i
\(493\) −19.4211 33.6383i −0.874682 1.51499i
\(494\) −0.932779 + 26.0403i −0.0419677 + 1.17161i
\(495\) 12.3691 + 7.14131i 0.555950 + 0.320978i
\(496\) 1.93392 7.21748i 0.0868355 0.324075i
\(497\) 1.53160 + 0.754192i 0.0687018 + 0.0338301i
\(498\) −8.76814 5.06229i −0.392910 0.226847i
\(499\) 8.34647 + 31.1495i 0.373639 + 1.39444i 0.855323 + 0.518096i \(0.173359\pi\)
−0.481683 + 0.876345i \(0.659974\pi\)
\(500\) 7.19900 + 7.19900i 0.321949 + 0.321949i
\(501\) −7.90416 7.90416i −0.353132 0.353132i
\(502\) −2.75572 10.2845i −0.122994 0.459019i
\(503\) −27.5872 15.9275i −1.23005 0.710170i −0.263010 0.964793i \(-0.584715\pi\)
−0.967040 + 0.254623i \(0.918049\pi\)
\(504\) 1.47119 + 2.19900i 0.0655318 + 0.0979514i
\(505\) −4.97766 + 18.5769i −0.221503 + 0.826661i
\(506\) −2.45783 1.41903i −0.109264 0.0630834i
\(507\) −0.930141 + 12.9667i −0.0413090 + 0.575871i
\(508\) −1.65611 2.86847i −0.0734780 0.127268i
\(509\) −5.42481 5.42481i −0.240451 0.240451i 0.576586 0.817037i \(-0.304385\pi\)
−0.817037 + 0.576586i \(0.804385\pi\)
\(510\) 13.3997 7.73634i 0.593350 0.342571i
\(511\) 8.58864 5.74601i 0.379939 0.254188i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 6.98067 + 1.87046i 0.308204 + 0.0825830i
\(514\) 8.98014 8.98014i 0.396097 0.396097i
\(515\) 3.61960 13.5085i 0.159499 0.595257i
\(516\) 10.1649 5.86869i 0.447483 0.258355i
\(517\) 3.31253 + 5.73747i 0.145685 + 0.252334i
\(518\) −1.54660 + 1.76564i −0.0679537 + 0.0775777i
\(519\) 6.95312i 0.305208i
\(520\) −6.05546 11.4134i −0.265550 0.500511i
\(521\) 17.2643 9.96755i 0.756363 0.436686i −0.0716253 0.997432i \(-0.522819\pi\)
0.827988 + 0.560745i \(0.189485\pi\)
\(522\) 2.32828 + 8.68926i 0.101906 + 0.380319i
\(523\) 5.77080i 0.252340i −0.992009 0.126170i \(-0.959732\pi\)
0.992009 0.126170i \(-0.0402684\pi\)
\(524\) −0.662484 + 1.14746i −0.0289407 + 0.0501268i
\(525\) −13.6694 + 15.6054i −0.596582 + 0.681073i
\(526\) 4.83191 + 18.0329i 0.210681 + 0.786273i
\(527\) 8.35031 31.1638i 0.363745 1.35752i
\(528\) 3.84991 + 1.03158i 0.167546 + 0.0448937i
\(529\) 22.4930 0.977955
\(530\) 6.18468 0.268645
\(531\) −3.91479 1.04896i −0.169887 0.0455212i
\(532\) 15.8920 10.6321i 0.689006 0.460961i
\(533\) 5.21914 4.85816i 0.226066 0.210430i
\(534\) −8.37168 + 14.5002i −0.362278 + 0.627484i
\(535\) 67.2108 18.0091i 2.90578 0.778600i
\(536\) −6.36172 + 11.0188i −0.274785 + 0.475941i
\(537\) −8.87956 15.3799i −0.383181 0.663690i
\(538\) 10.9975 + 10.9975i 0.474135 + 0.474135i
\(539\) 10.7070 + 25.7638i 0.461182 + 1.10972i
\(540\) −3.46134 + 0.927465i −0.148953 + 0.0399117i
\(541\) 28.0638 7.51967i 1.20656 0.323296i 0.401147 0.916014i \(-0.368612\pi\)
0.805410 + 0.592718i \(0.201945\pi\)
\(542\) 13.7335i 0.589903i
\(543\) 11.8109 + 6.81901i 0.506853 + 0.292632i
\(544\) 3.05316 3.05316i 0.130903 0.130903i
\(545\) 47.8841 2.05113
\(546\) 8.11342 5.01721i 0.347222 0.214717i
\(547\) −7.46165 −0.319037 −0.159519 0.987195i \(-0.550994\pi\)
−0.159519 + 0.987195i \(0.550994\pi\)
\(548\) 1.52374 1.52374i 0.0650908 0.0650908i
\(549\) −7.04381 4.06674i −0.300622 0.173564i
\(550\) 31.2524i 1.33261i
\(551\) 62.7966 16.8263i 2.67522 0.716824i
\(552\) 0.687793 0.184294i 0.0292744 0.00784406i
\(553\) −4.25094 12.4989i −0.180768 0.531506i
\(554\) 1.31289 + 1.31289i 0.0557794 + 0.0557794i
\(555\) −1.58956 2.75319i −0.0674729 0.116867i
\(556\) 2.47060 4.27921i 0.104777 0.181479i
\(557\) 6.38717 1.71144i 0.270633 0.0725160i −0.120950 0.992659i \(-0.538594\pi\)
0.391583 + 0.920143i \(0.371927\pi\)
\(558\) −3.73604 + 6.47102i −0.158159 + 0.273940i
\(559\) −19.8343 37.3839i −0.838902 1.58117i
\(560\) −4.18833 + 8.50562i −0.176989 + 0.359428i
\(561\) 16.6232 + 4.45417i 0.701832 + 0.188055i
\(562\) 17.9134 0.755630
\(563\) 40.4902 1.70646 0.853230 0.521535i \(-0.174640\pi\)
0.853230 + 0.521535i \(0.174640\pi\)
\(564\) −1.60556 0.430209i −0.0676063 0.0181151i
\(565\) 0.325851 1.21609i 0.0137087 0.0511614i
\(566\) −1.93482 7.22083i −0.0813264 0.303514i
\(567\) −0.851912 2.50484i −0.0357769 0.105194i
\(568\) −0.322635 + 0.558821i −0.0135375 + 0.0234476i
\(569\) 3.73110i 0.156416i −0.996937 0.0782080i \(-0.975080\pi\)
0.996937 0.0782080i \(-0.0249198\pi\)
\(570\) 6.70271 + 25.0148i 0.280746 + 1.04776i
\(571\) −17.2895 + 9.98211i −0.723544 + 0.417738i −0.816056 0.577973i \(-0.803844\pi\)
0.0925116 + 0.995712i \(0.470510\pi\)
\(572\) 4.21394 13.7390i 0.176194 0.574456i
\(573\) 10.1371i 0.423484i
\(574\) −5.13227 1.01776i −0.214217 0.0424803i
\(575\) 2.79165 + 4.83528i 0.116420 + 0.201645i
\(576\) −0.866025 + 0.500000i −0.0360844 + 0.0208333i
\(577\) −1.83883 + 6.86259i −0.0765513 + 0.285693i −0.993581 0.113127i \(-0.963913\pi\)
0.917029 + 0.398820i \(0.130580\pi\)
\(578\) 1.16216 1.16216i 0.0483395 0.0483395i
\(579\) 12.4154 + 3.32669i 0.515965 + 0.138252i
\(580\) −22.7942 + 22.7942i −0.946480 + 0.946480i
\(581\) 26.7287 1.76757i 1.10889 0.0733313i
\(582\) 7.47344 4.31479i 0.309784 0.178854i
\(583\) 4.86416 + 4.86416i 0.201453 + 0.201453i
\(584\) 1.95285 + 3.38243i 0.0808095 + 0.139966i
\(585\) 2.89512 + 12.5918i 0.119699 + 0.520605i
\(586\) 3.29279 + 1.90109i 0.136024 + 0.0785335i
\(587\) 6.45668 24.0967i 0.266496 0.994576i −0.694833 0.719171i \(-0.744522\pi\)
0.961328 0.275404i \(-0.0888117\pi\)
\(588\) −6.47028 2.67123i −0.266830 0.110160i
\(589\) 46.7655 + 27.0001i 1.92694 + 1.11252i
\(590\) −3.75891 14.0284i −0.154752 0.577542i
\(591\) 10.4699 + 10.4699i 0.430674 + 0.430674i
\(592\) −0.627321 0.627321i −0.0257827 0.0257827i
\(593\) −8.49895 31.7185i −0.349010 1.30252i −0.887857 0.460120i \(-0.847806\pi\)
0.538847 0.842404i \(-0.318860\pi\)
\(594\) −3.45173 1.99286i −0.141626 0.0817680i
\(595\) −18.0845 + 36.7257i −0.741390 + 1.50561i
\(596\) 1.91929 7.16290i 0.0786173 0.293404i
\(597\) −18.7154 10.8053i −0.765969 0.442232i
\(598\) −0.575281 2.50207i −0.0235250 0.102317i
\(599\) 15.6586 + 27.1214i 0.639792 + 1.10815i 0.985478 + 0.169802i \(0.0543129\pi\)
−0.345686 + 0.938350i \(0.612354\pi\)
\(600\) −5.54449 5.54449i −0.226353 0.226353i
\(601\) −24.7157 + 14.2696i −1.00817 + 0.582069i −0.910656 0.413165i \(-0.864423\pi\)
−0.0975167 + 0.995234i \(0.531090\pi\)
\(602\) −13.7186 + 27.8597i −0.559130 + 1.13548i
\(603\) 8.99683 8.99683i 0.366379 0.366379i
\(604\) 10.9730 + 2.94021i 0.446485 + 0.119635i
\(605\) −12.3804 + 12.3804i −0.503335 + 0.503335i
\(606\) 1.38907 5.18408i 0.0564272 0.210589i
\(607\) −16.7950 + 9.69658i −0.681687 + 0.393572i −0.800490 0.599346i \(-0.795427\pi\)
0.118803 + 0.992918i \(0.462094\pi\)
\(608\) 3.61346 + 6.25869i 0.146545 + 0.253824i
\(609\) −17.9034 15.6824i −0.725483 0.635482i
\(610\) 29.1459i 1.18008i
\(611\) −1.75738 + 5.72970i −0.0710958 + 0.231799i
\(612\) −3.73934 + 2.15891i −0.151154 + 0.0872687i
\(613\) −0.0218165 0.0814203i −0.000881160 0.00328853i 0.965484 0.260463i \(-0.0838752\pi\)
−0.966365 + 0.257174i \(0.917209\pi\)
\(614\) 16.0583i 0.648060i
\(615\) 3.54329 6.13716i 0.142879 0.247474i
\(616\) −9.98360 + 3.39548i −0.402251 + 0.136808i
\(617\) −7.58497 28.3075i −0.305360 1.13962i −0.932635 0.360820i \(-0.882497\pi\)
0.627276 0.778797i \(-0.284170\pi\)
\(618\) −1.01009 + 3.76970i −0.0406317 + 0.151640i
\(619\) 12.1835 + 3.26457i 0.489698 + 0.131214i 0.495215 0.868771i \(-0.335089\pi\)
−0.00551671 + 0.999985i \(0.501756\pi\)
\(620\) −26.7758 −1.07534
\(621\) −0.712056 −0.0285738
\(622\) 10.2386 + 2.74342i 0.410530 + 0.110001i
\(623\) −2.92310 44.2022i −0.117111 1.77092i
\(624\) 1.68984 + 3.18503i 0.0676478 + 0.127503i
\(625\) −1.36134 + 2.35790i −0.0544535 + 0.0943161i
\(626\) 19.3647 5.18875i 0.773968 0.207384i
\(627\) −14.4022 + 24.9454i −0.575170 + 0.996223i
\(628\) −10.4079 18.0270i −0.415320 0.719356i
\(629\) −2.70866 2.70866i −0.108001 0.108001i
\(630\) 6.24703 7.13178i 0.248888 0.284137i
\(631\) 18.9752 5.08439i 0.755392 0.202407i 0.139483 0.990224i \(-0.455456\pi\)
0.615908 + 0.787818i \(0.288789\pi\)
\(632\) 4.81985 1.29148i 0.191723 0.0513722i
\(633\) 23.8946i 0.949727i
\(634\) −5.58571 3.22491i −0.221837 0.128078i
\(635\) −8.39277 + 8.39277i −0.333057 + 0.333057i
\(636\) −1.72590 −0.0684364
\(637\) −10.4602 + 22.9692i −0.414448 + 0.910073i
\(638\) −35.8547 −1.41950
\(639\) 0.456275 0.456275i 0.0180500 0.0180500i
\(640\) −3.10336 1.79172i −0.122671 0.0708241i
\(641\) 29.8364i 1.17847i 0.807962 + 0.589234i \(0.200570\pi\)
−0.807962 + 0.589234i \(0.799430\pi\)
\(642\) −18.7559 + 5.02563i −0.740237 + 0.198346i
\(643\) −24.2952 + 6.50987i −0.958108 + 0.256724i −0.703799 0.710399i \(-0.748515\pi\)
−0.254309 + 0.967123i \(0.581848\pi\)
\(644\) −1.24133 + 1.41713i −0.0489152 + 0.0558429i
\(645\) −29.7411 29.7411i −1.17106 1.17106i
\(646\) 15.6023 + 27.0239i 0.613862 + 1.06324i
\(647\) 10.1862 17.6431i 0.400462 0.693620i −0.593320 0.804967i \(-0.702183\pi\)
0.993782 + 0.111347i \(0.0355164\pi\)
\(648\) 0.965926 0.258819i 0.0379452 0.0101674i
\(649\) 8.07683 13.9895i 0.317043 0.549135i
\(650\) −20.6938 + 19.2625i −0.811676 + 0.755538i
\(651\) −1.30450 19.7262i −0.0511272 0.773131i
\(652\) 8.27580 + 2.21749i 0.324105 + 0.0868438i
\(653\) −37.3896 −1.46317 −0.731584 0.681752i \(-0.761219\pi\)
−0.731584 + 0.681752i \(0.761219\pi\)
\(654\) −13.3626 −0.522518
\(655\) 4.58617 + 1.22886i 0.179196 + 0.0480155i
\(656\) 0.511837 1.91020i 0.0199839 0.0745809i
\(657\) −1.01087 3.77262i −0.0394378 0.147184i
\(658\) 4.16355 1.41605i 0.162312 0.0552033i
\(659\) −14.5963 + 25.2816i −0.568593 + 0.984832i 0.428113 + 0.903725i \(0.359179\pi\)
−0.996705 + 0.0811063i \(0.974155\pi\)
\(660\) 14.2826i 0.555950i
\(661\) 2.36366 + 8.82130i 0.0919357 + 0.343109i 0.996537 0.0831499i \(-0.0264980\pi\)
−0.904601 + 0.426259i \(0.859831\pi\)
\(662\) 17.4094 10.0513i 0.676636 0.390656i
\(663\) 7.29643 + 13.7524i 0.283370 + 0.534099i
\(664\) 10.1246i 0.392910i
\(665\) −51.5408 45.1468i −1.99866 1.75072i
\(666\) 0.443583 + 0.768308i 0.0171885 + 0.0297713i
\(667\) −5.54733 + 3.20275i −0.214793 + 0.124011i
\(668\) −2.89312 + 10.7973i −0.111938 + 0.417760i
\(669\) −15.1598 + 15.1598i −0.586110 + 0.586110i
\(670\) 44.0402 + 11.8005i 1.70142 + 0.455895i
\(671\) 22.9228 22.9228i 0.884926 0.884926i
\(672\) 1.16880 2.37359i 0.0450874 0.0915630i
\(673\) −31.7383 + 18.3241i −1.22342 + 0.706342i −0.965645 0.259863i \(-0.916322\pi\)
−0.257774 + 0.966205i \(0.582989\pi\)
\(674\) −1.78037 1.78037i −0.0685772 0.0685772i
\(675\) 3.92055 + 6.79059i 0.150902 + 0.261370i
\(676\) 11.6945 5.67782i 0.449790 0.218378i
\(677\) −7.40989 4.27810i −0.284785 0.164421i 0.350803 0.936449i \(-0.385909\pi\)
−0.635588 + 0.772029i \(0.719242\pi\)
\(678\) −0.0909323 + 0.339364i −0.00349223 + 0.0130332i
\(679\) −10.0863 + 20.4831i −0.387075 + 0.786068i
\(680\) −13.3997 7.73634i −0.513856 0.296675i
\(681\) −0.681182 2.54220i −0.0261029 0.0974175i
\(682\) −21.0588 21.0588i −0.806383 0.806383i
\(683\) 8.05282 + 8.05282i 0.308133 + 0.308133i 0.844185 0.536052i \(-0.180085\pi\)
−0.536052 + 0.844185i \(0.680085\pi\)
\(684\) −1.87046 6.98067i −0.0715190 0.266912i
\(685\) −6.68739 3.86097i −0.255512 0.147520i
\(686\) 18.1580 3.64495i 0.693277 0.139165i
\(687\) −5.43526 + 20.2847i −0.207368 + 0.773909i
\(688\) −10.1649 5.86869i −0.387532 0.223742i
\(689\) −0.222762 + 6.21884i −0.00848656 + 0.236919i
\(690\) −1.27581 2.20976i −0.0485692 0.0841243i
\(691\) −5.36678 5.36678i −0.204162 0.204162i 0.597619 0.801781i \(-0.296114\pi\)
−0.801781 + 0.597619i \(0.796114\pi\)
\(692\) −6.02158 + 3.47656i −0.228906 + 0.132159i
\(693\) 10.5222 0.695836i 0.399707 0.0264326i
\(694\) 12.5572 12.5572i 0.476664 0.476664i
\(695\) −17.1032 4.58279i −0.648761 0.173835i
\(696\) 6.36098 6.36098i 0.241112 0.241112i
\(697\) 2.21002 8.24791i 0.0837105 0.312412i
\(698\) 3.67137 2.11967i 0.138963 0.0802306i
\(699\) 9.32927 + 16.1588i 0.352865 + 0.611181i
\(700\) 20.3493 + 4.03538i 0.769133 + 0.152523i
\(701\) 7.89055i 0.298022i 0.988836 + 0.149011i \(0.0476090\pi\)
−0.988836 + 0.149011i \(0.952391\pi\)
\(702\) −0.807915 3.51387i −0.0304928 0.132622i
\(703\) 5.55250 3.20574i 0.209417 0.120907i
\(704\) −1.03158 3.84991i −0.0388791 0.145099i
\(705\) 5.95641i 0.224331i
\(706\) 14.8402 25.7040i 0.558519 0.967383i
\(707\) 4.57218 + 13.4434i 0.171954 + 0.505591i
\(708\) 1.04896 + 3.91479i 0.0394225 + 0.147127i
\(709\) 3.37772 12.6058i 0.126853 0.473422i −0.873046 0.487638i \(-0.837859\pi\)
0.999899 + 0.0142160i \(0.00452525\pi\)
\(710\) 2.23350 + 0.598465i 0.0838219 + 0.0224600i
\(711\) −4.98988 −0.187135
\(712\) 16.7434 0.627484
\(713\) −5.13925 1.37706i −0.192467 0.0515712i
\(714\) 5.04666 10.2487i 0.188867 0.383548i
\(715\) −51.4637 1.84346i −1.92463 0.0689414i
\(716\) −8.87956 + 15.3799i −0.331845 + 0.574772i
\(717\) 11.5161 3.08573i 0.430077 0.115239i
\(718\) 0.259260 0.449051i 0.00967548 0.0167584i
\(719\) 20.3699 + 35.2816i 0.759667 + 1.31578i 0.943020 + 0.332735i \(0.107972\pi\)
−0.183353 + 0.983047i \(0.558695\pi\)
\(720\) 2.53388 + 2.53388i 0.0944321 + 0.0944321i
\(721\) −3.32474 9.77561i −0.123820 0.364063i
\(722\) −32.0961 + 8.60012i −1.19449 + 0.320063i
\(723\) −14.5235 + 3.89157i −0.540136 + 0.144729i
\(724\) 13.6380i 0.506853i
\(725\) 61.0867 + 35.2684i 2.26870 + 1.30984i
\(726\) 3.45489 3.45489i 0.128223 0.128223i
\(727\) 24.1295 0.894913 0.447457 0.894306i \(-0.352330\pi\)
0.447457 + 0.894306i \(0.352330\pi\)
\(728\) −8.40174 4.51783i −0.311389 0.167442i
\(729\) −1.00000 −0.0370370
\(730\) 9.89657 9.89657i 0.366289 0.366289i
\(731\) −43.8900 25.3399i −1.62333 0.937231i
\(732\) 8.13349i 0.300622i
\(733\) −21.4643 + 5.75135i −0.792804 + 0.212431i −0.632422 0.774624i \(-0.717939\pi\)
−0.160382 + 0.987055i \(0.551272\pi\)
\(734\) −32.4078 + 8.68365i −1.19619 + 0.320519i
\(735\) −3.24508 + 24.8733i −0.119697 + 0.917467i
\(736\) −0.503500 0.503500i −0.0185592 0.0185592i
\(737\) 25.3560 + 43.9179i 0.934001 + 1.61774i
\(738\) −0.988794 + 1.71264i −0.0363980 + 0.0630432i
\(739\) −14.8523 + 3.97967i −0.546351 + 0.146394i −0.521428 0.853295i \(-0.674601\pi\)
−0.0249227 + 0.999689i \(0.507934\pi\)
\(740\) −1.58956 + 2.75319i −0.0584333 + 0.101209i
\(741\) −25.3944 + 5.83873i −0.932888 + 0.214491i
\(742\) 3.79526 2.53912i 0.139328 0.0932140i
\(743\) −49.3360 13.2195i −1.80996 0.484978i −0.814501 0.580162i \(-0.802989\pi\)
−0.995460 + 0.0951843i \(0.969656\pi\)
\(744\) 7.47209 0.273940
\(745\) −26.5733 −0.973572
\(746\) −29.6360 7.94095i −1.08505 0.290739i
\(747\) 2.62043 9.77959i 0.0958767 0.357817i
\(748\) −4.45417 16.6232i −0.162861 0.607804i
\(749\) 33.8507 38.6448i 1.23688 1.41205i
\(750\) −5.09046 + 8.81694i −0.185877 + 0.321949i
\(751\) 18.6065i 0.678962i −0.940613 0.339481i \(-0.889749\pi\)
0.940613 0.339481i \(-0.110251\pi\)
\(752\) 0.430209 + 1.60556i 0.0156881 + 0.0585488i
\(753\) 9.22082 5.32365i 0.336026 0.194004i
\(754\) −22.0991 23.7412i −0.804803 0.864602i
\(755\) 40.7083i 1.48153i
\(756\) −1.74330 + 1.99020i −0.0634033 + 0.0723829i
\(757\) −9.09650 15.7556i −0.330618 0.572647i 0.652015 0.758206i \(-0.273924\pi\)
−0.982633 + 0.185559i \(0.940590\pi\)
\(758\) 1.98902 1.14836i 0.0722445 0.0417104i
\(759\) 0.734542 2.74135i 0.0266622 0.0995047i
\(760\) 18.3121 18.3121i 0.664251 0.664251i
\(761\) 21.5729 + 5.78044i 0.782017 + 0.209541i 0.627674 0.778476i \(-0.284007\pi\)
0.154343 + 0.988017i \(0.450674\pi\)
\(762\) 2.34209 2.34209i 0.0848451 0.0848451i
\(763\) 29.3843 19.6588i 1.06378 0.711697i
\(764\) −8.77900 + 5.06856i −0.317613 + 0.183374i
\(765\) 10.9408 + 10.9408i 0.395567 + 0.395567i
\(766\) 7.34957 + 12.7298i 0.265551 + 0.459947i
\(767\) 14.2413 3.27439i 0.514224 0.118231i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) −4.19052 + 15.6392i −0.151114 + 0.563966i 0.848293 + 0.529528i \(0.177631\pi\)
−0.999407 + 0.0344380i \(0.989036\pi\)
\(770\) 21.0124 + 31.4075i 0.757233 + 1.13185i
\(771\) 10.9984 + 6.34992i 0.396097 + 0.228687i
\(772\) −3.32669 12.4154i −0.119730 0.446839i
\(773\) −11.9898 11.9898i −0.431241 0.431241i 0.457809 0.889050i \(-0.348634\pi\)
−0.889050 + 0.457809i \(0.848634\pi\)
\(774\) 8.29958 + 8.29958i 0.298322 + 0.298322i
\(775\) 15.1640 + 56.5930i 0.544709 + 2.03288i
\(776\) −7.47344 4.31479i −0.268281 0.154892i
\(777\) −2.10576 1.03692i −0.0755439 0.0371993i
\(778\) −8.53270 + 31.8445i −0.305912 + 1.14168i
\(779\) 12.3771 + 7.14593i 0.443456 + 0.256030i
\(780\) 9.45723 8.80313i 0.338623 0.315203i
\(781\) 1.28593 + 2.22730i 0.0460143 + 0.0796991i
\(782\) −2.17402 2.17402i −0.0777428 0.0777428i
\(783\) −7.79058 + 4.49789i −0.278413 + 0.160742i
\(784\) 0.921790 + 6.93904i 0.0329211 + 0.247823i
\(785\) −52.7447 + 52.7447i −1.88254 + 1.88254i
\(786\) −1.27982 0.342927i −0.0456497 0.0122318i
\(787\) 11.5739 11.5739i 0.412565 0.412565i −0.470066 0.882631i \(-0.655770\pi\)
0.882631 + 0.470066i \(0.155770\pi\)
\(788\) 3.83225 14.3021i 0.136518 0.509493i
\(789\) −16.1679 + 9.33453i −0.575592 + 0.332318i
\(790\) −8.94049 15.4854i −0.318088 0.550945i
\(791\) −0.299307 0.880041i −0.0106421 0.0312906i
\(792\) 3.98572i 0.141626i
\(793\) 29.3069 + 1.04979i 1.04072 + 0.0372791i
\(794\) 11.4421 6.60609i 0.406064 0.234441i
\(795\) 1.60071 + 5.97394i 0.0567714 + 0.211874i
\(796\) 21.6106i 0.765969i
\(797\) 12.8616 22.2770i 0.455581 0.789090i −0.543140 0.839642i \(-0.682765\pi\)
0.998721 + 0.0505519i \(0.0160980\pi\)
\(798\) 14.3830 + 12.5987i 0.509153 + 0.445989i
\(799\) 1.85756 + 6.93252i 0.0657159 + 0.245255i
\(800\) −2.02943 + 7.57392i −0.0717510 + 0.267778i
\(801\) −16.1728 4.33350i −0.571439 0.153117i
\(802\) −14.8048 −0.522777
\(803\) 15.5670 0.549348
\(804\) −12.2899 3.29307i −0.433431 0.116138i
\(805\) 6.05648 + 2.98233i 0.213463 + 0.105113i
\(806\) 0.964423 26.9237i 0.0339704 0.948348i
\(807\) −7.77639 + 13.4691i −0.273742 + 0.474135i
\(808\) −5.18408 + 1.38907i −0.182375 + 0.0488673i
\(809\) −5.36185 + 9.28700i −0.188513 + 0.326514i −0.944755 0.327779i \(-0.893700\pi\)
0.756242 + 0.654292i \(0.227033\pi\)
\(810\) −1.79172 3.10336i −0.0629548 0.109041i
\(811\) −28.0122 28.0122i −0.983641 0.983641i 0.0162272 0.999868i \(-0.494834\pi\)
−0.999868 + 0.0162272i \(0.994834\pi\)
\(812\) −4.62963 + 23.3460i −0.162468 + 0.819284i
\(813\) −13.2655 + 3.55448i −0.465242 + 0.124661i
\(814\) −3.41551 + 0.915183i −0.119713 + 0.0320771i
\(815\) 30.7020i 1.07545i
\(816\) 3.73934 + 2.15891i 0.130903 + 0.0755769i
\(817\) 59.9804 59.9804i 2.09845 2.09845i
\(818\) −21.1804 −0.740556
\(819\) 6.94616 + 6.53841i 0.242718 + 0.228471i
\(820\) −7.08658 −0.247474
\(821\) −26.2639 + 26.2639i −0.916618 + 0.916618i −0.996782 0.0801641i \(-0.974456\pi\)
0.0801641 + 0.996782i \(0.474456\pi\)
\(822\) 1.86619 + 1.07745i 0.0650908 + 0.0375802i
\(823\) 32.9801i 1.14961i −0.818289 0.574807i \(-0.805077\pi\)
0.818289 0.574807i \(-0.194923\pi\)
\(824\) 3.76970 1.01009i 0.131324 0.0351881i
\(825\) −30.1875 + 8.08872i −1.05099 + 0.281613i
\(826\) −8.06605 7.06541i −0.280654 0.245837i
\(827\) −5.18018 5.18018i −0.180132 0.180132i 0.611281 0.791414i \(-0.290654\pi\)
−0.791414 + 0.611281i \(0.790654\pi\)
\(828\) 0.356028 + 0.616658i 0.0123728 + 0.0214304i
\(829\) −24.0315 + 41.6237i −0.834648 + 1.44565i 0.0596693 + 0.998218i \(0.480995\pi\)
−0.894317 + 0.447434i \(0.852338\pi\)
\(830\) 35.0447 9.39019i 1.21642 0.325938i
\(831\) −0.928354 + 1.60796i −0.0322042 + 0.0557794i
\(832\) 1.91340 3.05596i 0.0663351 0.105946i
\(833\) 3.98012 + 29.9615i 0.137903 + 1.03810i
\(834\) 4.77283 + 1.27888i 0.165270 + 0.0442839i
\(835\) 40.0564 1.38621
\(836\) 28.8045 0.996223
\(837\) −7.21748 1.93392i −0.249473 0.0668460i
\(838\) 2.33441 8.71215i 0.0806410 0.300956i
\(839\) −3.47079 12.9532i −0.119825 0.447193i 0.879778 0.475385i \(-0.157691\pi\)
−0.999603 + 0.0281929i \(0.991025\pi\)
\(840\) −9.29982 1.84420i −0.320874 0.0636310i
\(841\) −25.9621 + 44.9677i −0.895245 + 1.55061i
\(842\) 7.17208i 0.247166i
\(843\) 4.63632 + 17.3030i 0.159683 + 0.595947i
\(844\) −20.6934 + 11.9473i −0.712295 + 0.411244i
\(845\) −30.4992 35.2129i −1.04920 1.21136i
\(846\) 1.66220i 0.0571476i
\(847\) −2.51453 + 12.6801i −0.0864002 + 0.435693i
\(848\) 0.862951 + 1.49467i 0.0296338 + 0.0513273i
\(849\) 6.47402 3.73778i 0.222188 0.128280i
\(850\) −8.76269 + 32.7028i −0.300558 + 1.12170i
\(851\) −0.446688 + 0.446688i −0.0153123 + 0.0153123i
\(852\) −0.623283 0.167008i −0.0213533 0.00572161i
\(853\) 34.5255 34.5255i 1.18213 1.18213i 0.202939 0.979191i \(-0.434951\pi\)
0.979191 0.202939i \(-0.0650492\pi\)
\(854\) −11.9659 17.8856i −0.409464 0.612031i
\(855\) −22.4277 + 12.9486i −0.767011 + 0.442834i
\(856\) 13.7303 + 13.7303i 0.469291 + 0.469291i
\(857\) 20.6789 + 35.8169i 0.706377 + 1.22348i 0.966192 + 0.257823i \(0.0830051\pi\)
−0.259815 + 0.965658i \(0.583662\pi\)
\(858\) 14.3615 + 0.514437i 0.490294 + 0.0175626i
\(859\) 30.9750 + 17.8834i 1.05685 + 0.610175i 0.924560 0.381036i \(-0.124433\pi\)
0.132293 + 0.991211i \(0.457766\pi\)
\(860\) −10.8860 + 40.6271i −0.371210 + 1.38537i
\(861\) −0.345252 5.22080i −0.0117662 0.177924i
\(862\) −13.0755 7.54913i −0.445352 0.257124i
\(863\) 0.863708 + 3.22340i 0.0294010 + 0.109726i 0.979067 0.203538i \(-0.0652441\pi\)
−0.949666 + 0.313264i \(0.898577\pi\)
\(864\) −0.707107 0.707107i −0.0240563 0.0240563i
\(865\) 17.6184 + 17.6184i 0.599043 + 0.599043i
\(866\) 9.48521 + 35.3993i 0.322321 + 1.20292i
\(867\) 1.42335 + 0.821772i 0.0483395 + 0.0279088i
\(868\) −16.4311 + 10.9928i −0.557709 + 0.373121i
\(869\) 5.14746 19.2106i 0.174616 0.651674i
\(870\) −27.9171 16.1180i −0.946480 0.546450i
\(871\) −13.4520 + 43.8584i −0.455803 + 1.48609i
\(872\) 6.68128 + 11.5723i 0.226257 + 0.391888i
\(873\) 6.10204 + 6.10204i 0.206523 + 0.206523i
\(874\) 4.45654 2.57298i 0.150745 0.0870325i
\(875\) −1.77741 26.8775i −0.0600874 0.908625i
\(876\) −2.76175 + 2.76175i −0.0933107 + 0.0933107i
\(877\) −14.8962 3.99142i −0.503008 0.134781i −0.00161249 0.999999i \(-0.500513\pi\)
−0.501396 + 0.865218i \(0.667180\pi\)
\(878\) −19.6396 + 19.6396i −0.662803 + 0.662803i
\(879\) −0.984079 + 3.67263i −0.0331922 + 0.123875i
\(880\) −12.3691 + 7.14131i −0.416962 + 0.240733i
\(881\) 0.913525 + 1.58227i 0.0307774 + 0.0533081i 0.881004 0.473109i \(-0.156868\pi\)
−0.850226 + 0.526417i \(0.823535\pi\)
\(882\) 0.905576 6.94118i 0.0304923 0.233722i
\(883\) 2.82109i 0.0949371i −0.998873 0.0474686i \(-0.984885\pi\)
0.998873 0.0474686i \(-0.0151154\pi\)
\(884\) 8.26170 13.1951i 0.277871 0.443799i
\(885\) 12.5776 7.26165i 0.422790 0.244098i
\(886\) −4.04959 15.1133i −0.136049 0.507741i
\(887\) 5.81024i 0.195089i −0.995231 0.0975445i \(-0.968901\pi\)
0.995231 0.0975445i \(-0.0310988\pi\)
\(888\) 0.443583 0.768308i 0.0148857 0.0257827i
\(889\) −1.70462 + 8.59592i −0.0571710 + 0.288298i
\(890\) −15.5289 57.9545i −0.520529 1.94264i
\(891\) 1.03158 3.84991i 0.0345592 0.128977i
\(892\) 20.7086 + 5.54886i 0.693376 + 0.185790i
\(893\) −12.0126 −0.401986
\(894\) 7.41558 0.248014
\(895\) 61.4704 + 16.4710i 2.05473 + 0.550563i
\(896\) −2.63999 + 0.174582i −0.0881957 + 0.00583239i
\(897\) 2.26792 1.20326i 0.0757237 0.0401758i
\(898\) 4.99512 8.65181i 0.166689 0.288715i
\(899\) −64.9270 + 17.3971i −2.16544 + 0.580227i
\(900\) 3.92055 6.79059i 0.130685 0.226353i
\(901\) 3.72606 + 6.45373i 0.124133 + 0.215005i
\(902\) −5.57349 5.57349i −0.185577 0.185577i
\(903\) −30.4610 6.04058i −1.01368 0.201018i
\(904\) 0.339364 0.0909323i 0.0112871 0.00302436i
\(905\) −47.2059 + 12.6488i −1.56918 + 0.420460i
\(906\) 11.3601i 0.377414i
\(907\) 10.6409 + 6.14352i 0.353325 + 0.203992i 0.666149 0.745819i \(-0.267942\pi\)
−0.312824 + 0.949811i \(0.601275\pi\)
\(908\) −1.86102 + 1.86102i −0.0617602 + 0.0617602i
\(909\) 5.36696 0.178011
\(910\) −7.84543 + 33.2714i −0.260074 + 1.10294i
\(911\) −55.2245 −1.82967 −0.914834 0.403830i \(-0.867679\pi\)
−0.914834 + 0.403830i \(0.867679\pi\)
\(912\) −5.11020 + 5.11020i −0.169216 + 0.169216i
\(913\) 34.9473 + 20.1769i 1.15659 + 0.667757i
\(914\) 14.2372i 0.470924i
\(915\) 28.1528 7.54352i 0.930703 0.249381i
\(916\) 20.2847 5.43526i 0.670225 0.179586i
\(917\) 3.31884 1.12876i 0.109598 0.0372748i
\(918\) −3.05316 3.05316i −0.100769 0.100769i
\(919\) −10.9433 18.9543i −0.360985 0.625245i 0.627138 0.778908i \(-0.284226\pi\)
−0.988123 + 0.153664i \(0.950893\pi\)
\(920\) −1.27581 + 2.20976i −0.0420621 + 0.0728537i
\(921\) −15.5111 + 4.15619i −0.511109 + 0.136951i
\(922\) 14.2166 24.6239i 0.468200 0.810946i
\(923\) −0.682218 + 2.22428i −0.0224555 + 0.0732132i
\(924\) −5.86373 8.76461i −0.192903 0.288334i
\(925\) 6.71932 + 1.80044i 0.220930 + 0.0591980i
\(926\) 13.6212 0.447621
\(927\) −3.90268 −0.128181
\(928\) −8.68926 2.32828i −0.285239 0.0764296i
\(929\) 3.75511 14.0143i 0.123201 0.459793i −0.876568 0.481278i \(-0.840173\pi\)
0.999769 + 0.0214851i \(0.00683944\pi\)
\(930\) −6.93010 25.8635i −0.227247 0.848097i
\(931\) −50.1633 6.54452i −1.64404 0.214488i
\(932\) 9.32927 16.1588i 0.305590 0.529298i
\(933\) 10.5998i 0.347020i
\(934\) −7.95710 29.6963i −0.260364 0.971693i
\(935\) −53.4075 + 30.8349i −1.74661 + 1.00841i
\(936\) −2.63914 + 2.45661i −0.0862631 + 0.0802968i
\(937\) 20.5964i 0.672856i 0.941709 + 0.336428i \(0.109219\pi\)
−0.941709 + 0.336428i \(0.890781\pi\)
\(938\) 31.8702 10.8393i 1.04060 0.353914i
\(939\) 10.0239 + 17.3619i 0.327117 + 0.566584i
\(940\) 5.15840 2.97820i 0.168248 0.0971383i
\(941\) 8.56080 31.9494i 0.279074 1.04152i −0.673987 0.738743i \(-0.735420\pi\)
0.953062 0.302776i \(-0.0979135\pi\)
\(942\) 14.7190 14.7190i 0.479571 0.479571i
\(943\) −1.36017 0.364457i −0.0442933 0.0118683i
\(944\) 2.86582 2.86582i 0.0932746 0.0932746i
\(945\) 8.50562 + 4.18833i 0.276688 + 0.136246i
\(946\) −40.5143 + 23.3909i −1.31723 + 0.760505i
\(947\) −22.6911 22.6911i −0.737360 0.737360i 0.234706 0.972066i \(-0.424587\pi\)
−0.972066 + 0.234706i \(0.924587\pi\)
\(948\) 2.49494 + 4.32136i 0.0810319 + 0.140351i
\(949\) 9.59478 + 10.3077i 0.311460 + 0.334602i
\(950\) −49.0750 28.3335i −1.59220 0.919259i
\(951\) 1.66934 6.23006i 0.0541320 0.202023i
\(952\) −11.3990 + 0.753815i −0.369443 + 0.0244313i
\(953\) 33.5501 + 19.3702i 1.08679 + 0.627461i 0.932721 0.360598i \(-0.117427\pi\)
0.154073 + 0.988059i \(0.450761\pi\)
\(954\) −0.446696 1.66709i −0.0144623 0.0539741i
\(955\) 25.6862 + 25.6862i 0.831187 + 0.831187i
\(956\) −8.43037 8.43037i −0.272658 0.272658i
\(957\) −9.27987 34.6330i −0.299976 1.11952i
\(958\) 13.6521 + 7.88207i 0.441081 + 0.254658i
\(959\) −5.68888 + 0.376206i −0.183703 + 0.0121483i
\(960\) 0.927465 3.46134i 0.0299338 0.111714i
\(961\) −21.5052 12.4161i −0.693718 0.400518i
\(962\) −2.71115 1.69750i −0.0874109 0.0547297i
\(963\) −9.70877 16.8161i −0.312861 0.541891i
\(964\) 10.6320 + 10.6320i 0.342433 + 0.342433i
\(965\) −39.8885 + 23.0296i −1.28406 + 0.741350i
\(966\) −1.69013 0.832251i −0.0543789 0.0267772i
\(967\) 13.3179 13.3179i 0.428274 0.428274i −0.459766 0.888040i \(-0.652067\pi\)
0.888040 + 0.459766i \(0.152067\pi\)
\(968\) −4.71946 1.26458i −0.151689 0.0406450i
\(969\) −22.0649 + 22.0649i −0.708827 + 0.708827i
\(970\) −8.00364 + 29.8700i −0.256981 + 0.959067i
\(971\) −15.6269 + 9.02220i −0.501491 + 0.289536i −0.729329 0.684163i \(-0.760168\pi\)
0.227838 + 0.973699i \(0.426834\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) −12.3769 + 4.20947i −0.396787 + 0.134949i
\(974\) 18.5892i 0.595635i
\(975\) −23.9621 15.0031i −0.767401 0.480485i
\(976\) 7.04381 4.06674i 0.225467 0.130173i
\(977\) 2.63296 + 9.82635i 0.0842360 + 0.314373i 0.995168 0.0981827i \(-0.0313029\pi\)
−0.910932 + 0.412556i \(0.864636\pi\)
\(978\) 8.56774i 0.273966i
\(979\) 33.3672 57.7936i 1.06642 1.84709i
\(980\) 23.1635 9.62635i 0.739931 0.307502i
\(981\) −3.45849 12.9072i −0.110421 0.412097i
\(982\) −3.30280 + 12.3262i −0.105397 + 0.393345i
\(983\) −2.10554 0.564179i −0.0671564 0.0179945i 0.225084 0.974339i \(-0.427734\pi\)
−0.292241 + 0.956345i \(0.594401\pi\)
\(984\) 1.97759 0.0630432
\(985\) −53.0589 −1.69060
\(986\) −37.5186 10.0531i −1.19484 0.320156i
\(987\) 2.44540 + 3.65518i 0.0778381 + 0.116346i
\(988\) 17.7537 + 19.0729i 0.564821 + 0.606788i
\(989\) −4.17884 + 7.23796i −0.132879 + 0.230154i
\(990\) 13.7959 3.69661i 0.438464 0.117486i
\(991\) 17.3203 29.9997i 0.550198 0.952971i −0.448062 0.894003i \(-0.647886\pi\)
0.998260 0.0589682i \(-0.0187811\pi\)
\(992\) −3.73604 6.47102i −0.118620 0.205455i
\(993\) 14.2147 + 14.2147i 0.451091 + 0.451091i
\(994\) 1.61630 0.549714i 0.0512660 0.0174359i
\(995\) 74.8019 20.0431i 2.37138 0.635409i
\(996\) −9.77959 + 2.62043i −0.309878 + 0.0830316i
\(997\) 4.80515i 0.152181i −0.997101 0.0760903i \(-0.975756\pi\)
0.997101 0.0760903i \(-0.0242437\pi\)
\(998\) 27.9278 + 16.1241i 0.884040 + 0.510401i
\(999\) −0.627321 + 0.627321i −0.0198476 + 0.0198476i
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 546.2.cg.a.145.5 yes 32
7.3 odd 6 546.2.by.a.535.5 yes 32
13.7 odd 12 546.2.by.a.397.5 32
91.59 even 12 inner 546.2.cg.a.241.5 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.by.a.397.5 32 13.7 odd 12
546.2.by.a.535.5 yes 32 7.3 odd 6
546.2.cg.a.145.5 yes 32 1.1 even 1 trivial
546.2.cg.a.241.5 yes 32 91.59 even 12 inner