Properties

Label 72.3.p.b.43.20
Level $72$
Weight $3$
Character 72.43
Analytic conductor $1.962$
Analytic rank $0$
Dimension $40$
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] = [72,3,Mod(43,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.p (of order \(6\), degree \(2\), 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: \(1.96185790339\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.20
Character \(\chi\) \(=\) 72.43
Dual form 72.3.p.b.67.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.99426 - 0.151428i) q^{2} +(1.33710 + 2.68555i) q^{3} +(3.95414 - 0.603974i) q^{4} +(-1.70411 + 0.983869i) q^{5} +(3.07320 + 5.15320i) q^{6} +(-8.69613 - 5.02071i) q^{7} +(7.79412 - 1.80325i) q^{8} +(-5.42431 + 7.18171i) q^{9} +O(q^{10})\) \(q+(1.99426 - 0.151428i) q^{2} +(1.33710 + 2.68555i) q^{3} +(3.95414 - 0.603974i) q^{4} +(-1.70411 + 0.983869i) q^{5} +(3.07320 + 5.15320i) q^{6} +(-8.69613 - 5.02071i) q^{7} +(7.79412 - 1.80325i) q^{8} +(-5.42431 + 7.18171i) q^{9} +(-3.24945 + 2.22014i) q^{10} +(6.08627 - 10.5417i) q^{11} +(6.90909 + 9.81144i) q^{12} +(4.28857 - 2.47601i) q^{13} +(-18.1026 - 8.69576i) q^{14} +(-4.92080 - 3.26093i) q^{15} +(15.2704 - 4.77640i) q^{16} +4.71370 q^{17} +(-9.72996 + 15.1436i) q^{18} -20.5288 q^{19} +(-6.14406 + 4.91959i) q^{20} +(1.85572 - 30.0671i) q^{21} +(10.5413 - 21.9446i) q^{22} +(-3.33400 + 1.92488i) q^{23} +(15.2643 + 18.5203i) q^{24} +(-10.5640 + 18.2974i) q^{25} +(8.17758 - 5.58721i) q^{26} +(-26.5397 - 4.96454i) q^{27} +(-37.4181 - 14.6004i) q^{28} +(40.7608 + 23.5333i) q^{29} +(-10.3071 - 5.75800i) q^{30} +(-49.9323 + 28.8285i) q^{31} +(29.7299 - 11.8377i) q^{32} +(36.4483 + 2.24957i) q^{33} +(9.40035 - 0.713788i) q^{34} +19.7589 q^{35} +(-17.1109 + 31.6736i) q^{36} -7.93672i q^{37} +(-40.9398 + 3.10864i) q^{38} +(12.3837 + 8.20647i) q^{39} +(-11.5079 + 10.7413i) q^{40} +(-11.3426 - 19.6460i) q^{41} +(-0.852206 - 60.2425i) q^{42} +(30.7806 - 53.3136i) q^{43} +(17.6990 - 45.3594i) q^{44} +(2.17777 - 17.5752i) q^{45} +(-6.35737 + 4.34358i) q^{46} +(44.7133 + 25.8152i) q^{47} +(33.2454 + 34.6229i) q^{48} +(25.9151 + 44.8862i) q^{49} +(-18.2966 + 38.0894i) q^{50} +(6.30271 + 12.6589i) q^{51} +(15.4622 - 12.3807i) q^{52} +51.0133i q^{53} +(-53.6787 - 5.88172i) q^{54} +23.9524i q^{55} +(-76.8322 - 23.4507i) q^{56} +(-27.4491 - 55.1310i) q^{57} +(84.8513 + 40.7591i) q^{58} +(16.7094 + 28.9415i) q^{59} +(-21.4270 - 9.92214i) q^{60} +(39.7329 + 22.9398i) q^{61} +(-95.2126 + 65.0526i) q^{62} +(83.2277 - 35.2191i) q^{63} +(57.4966 - 28.1095i) q^{64} +(-4.87213 + 8.43878i) q^{65} +(73.0280 - 1.03307i) q^{66} +(26.9209 + 46.6284i) q^{67} +(18.6386 - 2.84696i) q^{68} +(-9.62726 - 6.37983i) q^{69} +(39.4043 - 2.99205i) q^{70} -132.571i q^{71} +(-29.3273 + 65.7564i) q^{72} +24.6995 q^{73} +(-1.20184 - 15.8279i) q^{74} +(-63.2636 - 3.90460i) q^{75} +(-81.1738 + 12.3989i) q^{76} +(-105.854 + 61.1148i) q^{77} +(25.9390 + 14.4906i) q^{78} +(-84.3214 - 48.6830i) q^{79} +(-21.3232 + 23.1636i) q^{80} +(-22.1538 - 77.9116i) q^{81} +(-25.5951 - 37.4616i) q^{82} +(0.187458 - 0.324687i) q^{83} +(-10.8219 - 120.010i) q^{84} +(-8.03267 + 4.63767i) q^{85} +(53.3113 - 110.982i) q^{86} +(-8.69822 + 140.932i) q^{87} +(28.4278 - 93.1386i) q^{88} -134.821 q^{89} +(1.68164 - 35.3793i) q^{90} -49.7252 q^{91} +(-12.0205 + 9.62490i) q^{92} +(-144.185 - 95.5489i) q^{93} +(93.0790 + 44.7114i) q^{94} +(34.9834 - 20.1977i) q^{95} +(71.5428 + 64.0127i) q^{96} +(10.8826 - 18.8492i) q^{97} +(58.4784 + 85.5905i) q^{98} +(42.6938 + 100.891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9} - 12 q^{10} - 16 q^{11} - 12 q^{12} + 6 q^{14} + 31 q^{16} - 4 q^{17} - 114 q^{18} - 76 q^{19} - 12 q^{20} + 35 q^{22} + 39 q^{24} + 118 q^{25} - 72 q^{26} - 144 q^{27} - 36 q^{28} - 90 q^{30} - 5 q^{32} + 156 q^{33} + 5 q^{34} - 108 q^{35} + 51 q^{36} - 169 q^{38} - 6 q^{40} + 20 q^{41} - 42 q^{42} - 16 q^{43} + 362 q^{44} - 96 q^{46} + 183 q^{48} + 166 q^{49} + 73 q^{50} + 330 q^{51} - 24 q^{52} + 57 q^{54} + 186 q^{56} - 258 q^{57} + 36 q^{58} - 64 q^{59} + 150 q^{60} + 384 q^{62} - 518 q^{64} - 102 q^{65} + 486 q^{66} - 64 q^{67} - 295 q^{68} - 6 q^{70} - 225 q^{72} - 292 q^{73} + 318 q^{74} + 138 q^{75} + 197 q^{76} + 174 q^{78} - 720 q^{80} - 42 q^{81} + 386 q^{82} + 554 q^{83} - 720 q^{84} - 295 q^{86} + 59 q^{88} - 688 q^{89} - 696 q^{90} - 204 q^{91} - 378 q^{92} - 66 q^{94} - 222 q^{96} + 92 q^{97} - 614 q^{98} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99426 0.151428i 0.997130 0.0757141i
\(3\) 1.33710 + 2.68555i 0.445701 + 0.895182i
\(4\) 3.95414 0.603974i 0.988535 0.150994i
\(5\) −1.70411 + 0.983869i −0.340822 + 0.196774i −0.660636 0.750707i \(-0.729713\pi\)
0.319813 + 0.947481i \(0.396380\pi\)
\(6\) 3.07320 + 5.15320i 0.512200 + 0.858866i
\(7\) −8.69613 5.02071i −1.24230 0.717244i −0.272741 0.962087i \(-0.587930\pi\)
−0.969563 + 0.244843i \(0.921264\pi\)
\(8\) 7.79412 1.80325i 0.974265 0.225406i
\(9\) −5.42431 + 7.18171i −0.602701 + 0.797967i
\(10\) −3.24945 + 2.22014i −0.324945 + 0.222014i
\(11\) 6.08627 10.5417i 0.553298 0.958339i −0.444736 0.895662i \(-0.646703\pi\)
0.998034 0.0626779i \(-0.0199641\pi\)
\(12\) 6.90909 + 9.81144i 0.575758 + 0.817620i
\(13\) 4.28857 2.47601i 0.329890 0.190462i −0.325902 0.945403i \(-0.605668\pi\)
0.655792 + 0.754941i \(0.272335\pi\)
\(14\) −18.1026 8.69576i −1.29304 0.621126i
\(15\) −4.92080 3.26093i −0.328053 0.217395i
\(16\) 15.2704 4.77640i 0.954402 0.298525i
\(17\) 4.71370 0.277277 0.138638 0.990343i \(-0.455727\pi\)
0.138638 + 0.990343i \(0.455727\pi\)
\(18\) −9.72996 + 15.1436i −0.540553 + 0.841310i
\(19\) −20.5288 −1.08046 −0.540232 0.841516i \(-0.681663\pi\)
−0.540232 + 0.841516i \(0.681663\pi\)
\(20\) −6.14406 + 4.91959i −0.307203 + 0.245980i
\(21\) 1.85572 30.0671i 0.0883678 1.43176i
\(22\) 10.5413 21.9446i 0.479149 0.997481i
\(23\) −3.33400 + 1.92488i −0.144956 + 0.0836906i −0.570724 0.821142i \(-0.693337\pi\)
0.425768 + 0.904832i \(0.360004\pi\)
\(24\) 15.2643 + 18.5203i 0.636011 + 0.771680i
\(25\) −10.5640 + 18.2974i −0.422560 + 0.731896i
\(26\) 8.17758 5.58721i 0.314522 0.214893i
\(27\) −26.5397 4.96454i −0.982950 0.183872i
\(28\) −37.4181 14.6004i −1.33636 0.521441i
\(29\) 40.7608 + 23.5333i 1.40555 + 0.811492i 0.994955 0.100327i \(-0.0319889\pi\)
0.410592 + 0.911819i \(0.365322\pi\)
\(30\) −10.3071 5.75800i −0.343571 0.191933i
\(31\) −49.9323 + 28.8285i −1.61072 + 0.929950i −0.621517 + 0.783400i \(0.713483\pi\)
−0.989203 + 0.146550i \(0.953183\pi\)
\(32\) 29.7299 11.8377i 0.929060 0.369930i
\(33\) 36.4483 + 2.24957i 1.10449 + 0.0681688i
\(34\) 9.40035 0.713788i 0.276481 0.0209938i
\(35\) 19.7589 0.564540
\(36\) −17.1109 + 31.6736i −0.475303 + 0.879822i
\(37\) 7.93672i 0.214506i −0.994232 0.107253i \(-0.965795\pi\)
0.994232 0.107253i \(-0.0342055\pi\)
\(38\) −40.9398 + 3.10864i −1.07736 + 0.0818063i
\(39\) 12.3837 + 8.20647i 0.317530 + 0.210422i
\(40\) −11.5079 + 10.7413i −0.287697 + 0.268533i
\(41\) −11.3426 19.6460i −0.276649 0.479171i 0.693901 0.720071i \(-0.255891\pi\)
−0.970550 + 0.240900i \(0.922557\pi\)
\(42\) −0.852206 60.2425i −0.0202906 1.43435i
\(43\) 30.7806 53.3136i 0.715828 1.23985i −0.246811 0.969064i \(-0.579383\pi\)
0.962639 0.270787i \(-0.0872840\pi\)
\(44\) 17.6990 45.3594i 0.402251 1.03090i
\(45\) 2.17777 17.5752i 0.0483948 0.390561i
\(46\) −6.35737 + 4.34358i −0.138204 + 0.0944256i
\(47\) 44.7133 + 25.8152i 0.951346 + 0.549260i 0.893499 0.449066i \(-0.148243\pi\)
0.0578471 + 0.998325i \(0.481576\pi\)
\(48\) 33.2454 + 34.6229i 0.692612 + 0.721310i
\(49\) 25.9151 + 44.8862i 0.528879 + 0.916045i
\(50\) −18.2966 + 38.0894i −0.365932 + 0.761789i
\(51\) 6.30271 + 12.6589i 0.123583 + 0.248213i
\(52\) 15.4622 12.3807i 0.297349 0.238090i
\(53\) 51.0133i 0.962515i 0.876579 + 0.481258i \(0.159820\pi\)
−0.876579 + 0.481258i \(0.840180\pi\)
\(54\) −53.6787 5.88172i −0.994050 0.108921i
\(55\) 23.9524i 0.435498i
\(56\) −76.8322 23.4507i −1.37200 0.418763i
\(57\) −27.4491 55.1310i −0.481564 0.967211i
\(58\) 84.8513 + 40.7591i 1.46295 + 0.702743i
\(59\) 16.7094 + 28.9415i 0.283209 + 0.490533i 0.972173 0.234262i \(-0.0752675\pi\)
−0.688964 + 0.724796i \(0.741934\pi\)
\(60\) −21.4270 9.92214i −0.357117 0.165369i
\(61\) 39.7329 + 22.9398i 0.651359 + 0.376062i 0.788977 0.614423i \(-0.210611\pi\)
−0.137618 + 0.990485i \(0.543945\pi\)
\(62\) −95.2126 + 65.0526i −1.53569 + 1.04923i
\(63\) 83.2277 35.2191i 1.32108 0.559034i
\(64\) 57.4966 28.1095i 0.898384 0.439211i
\(65\) −4.87213 + 8.43878i −0.0749559 + 0.129827i
\(66\) 73.0280 1.03307i 1.10648 0.0156526i
\(67\) 26.9209 + 46.6284i 0.401805 + 0.695946i 0.993944 0.109889i \(-0.0350497\pi\)
−0.592139 + 0.805836i \(0.701716\pi\)
\(68\) 18.6386 2.84696i 0.274098 0.0418670i
\(69\) −9.62726 6.37983i −0.139525 0.0924613i
\(70\) 39.4043 2.99205i 0.562919 0.0427436i
\(71\) 132.571i 1.86720i −0.358313 0.933601i \(-0.616648\pi\)
0.358313 0.933601i \(-0.383352\pi\)
\(72\) −29.3273 + 65.7564i −0.407323 + 0.913284i
\(73\) 24.6995 0.338349 0.169175 0.985586i \(-0.445890\pi\)
0.169175 + 0.985586i \(0.445890\pi\)
\(74\) −1.20184 15.8279i −0.0162411 0.213890i
\(75\) −63.2636 3.90460i −0.843515 0.0520614i
\(76\) −81.1738 + 12.3989i −1.06808 + 0.163143i
\(77\) −105.854 + 61.1148i −1.37473 + 0.793699i
\(78\) 25.9390 + 14.4906i 0.332551 + 0.185777i
\(79\) −84.3214 48.6830i −1.06736 0.616241i −0.139901 0.990166i \(-0.544678\pi\)
−0.927459 + 0.373925i \(0.878012\pi\)
\(80\) −21.3232 + 23.1636i −0.266539 + 0.289545i
\(81\) −22.1538 77.9116i −0.273503 0.961871i
\(82\) −25.5951 37.4616i −0.312135 0.456849i
\(83\) 0.187458 0.324687i 0.00225853 0.00391189i −0.864894 0.501955i \(-0.832614\pi\)
0.867152 + 0.498043i \(0.165948\pi\)
\(84\) −10.8219 120.010i −0.128833 1.42869i
\(85\) −8.03267 + 4.63767i −0.0945021 + 0.0545608i
\(86\) 53.3113 110.982i 0.619899 1.29049i
\(87\) −8.69822 + 140.932i −0.0999796 + 1.61990i
\(88\) 28.4278 93.1386i 0.323043 1.05839i
\(89\) −134.821 −1.51485 −0.757423 0.652925i \(-0.773542\pi\)
−0.757423 + 0.652925i \(0.773542\pi\)
\(90\) 1.68164 35.3793i 0.0186849 0.393104i
\(91\) −49.7252 −0.546431
\(92\) −12.0205 + 9.62490i −0.130658 + 0.104618i
\(93\) −144.185 95.5489i −1.55037 1.02741i
\(94\) 93.0790 + 44.7114i 0.990202 + 0.475653i
\(95\) 34.9834 20.1977i 0.368246 0.212607i
\(96\) 71.5428 + 64.0127i 0.745237 + 0.666799i
\(97\) 10.8826 18.8492i 0.112192 0.194322i −0.804462 0.594004i \(-0.797546\pi\)
0.916654 + 0.399682i \(0.130880\pi\)
\(98\) 58.4784 + 85.5905i 0.596719 + 0.873372i
\(99\) 42.6938 + 100.891i 0.431251 + 1.01911i
\(100\) −30.7204 + 78.7308i −0.307204 + 0.787308i
\(101\) −40.3177 23.2774i −0.399185 0.230470i 0.286947 0.957946i \(-0.407360\pi\)
−0.686132 + 0.727477i \(0.740693\pi\)
\(102\) 14.4862 + 24.2907i 0.142021 + 0.238144i
\(103\) 87.3356 50.4232i 0.847918 0.489546i −0.0120298 0.999928i \(-0.503829\pi\)
0.859948 + 0.510382i \(0.170496\pi\)
\(104\) 28.9608 27.0316i 0.278469 0.259920i
\(105\) 26.4197 + 53.0634i 0.251616 + 0.505365i
\(106\) 7.72485 + 101.734i 0.0728760 + 0.959752i
\(107\) −12.9467 −0.120997 −0.0604986 0.998168i \(-0.519269\pi\)
−0.0604986 + 0.998168i \(0.519269\pi\)
\(108\) −107.940 3.60121i −0.999444 0.0333445i
\(109\) 117.693i 1.07975i −0.841745 0.539875i \(-0.818471\pi\)
0.841745 0.539875i \(-0.181529\pi\)
\(110\) 3.62707 + 47.7672i 0.0329733 + 0.434248i
\(111\) 21.3144 10.6122i 0.192022 0.0956055i
\(112\) −156.774 35.1323i −1.39977 0.313681i
\(113\) 14.6904 + 25.4446i 0.130004 + 0.225173i 0.923678 0.383170i \(-0.125168\pi\)
−0.793674 + 0.608343i \(0.791834\pi\)
\(114\) −63.0891 105.789i −0.553413 0.927974i
\(115\) 3.78766 6.56043i 0.0329362 0.0570472i
\(116\) 175.388 + 68.4354i 1.51196 + 0.589960i
\(117\) −5.48057 + 44.2299i −0.0468425 + 0.378033i
\(118\) 37.7053 + 55.1865i 0.319537 + 0.467682i
\(119\) −40.9910 23.6661i −0.344462 0.198875i
\(120\) −44.2336 16.5427i −0.368613 0.137856i
\(121\) −13.5854 23.5307i −0.112276 0.194468i
\(122\) 82.7114 + 39.7312i 0.677962 + 0.325666i
\(123\) 37.5940 56.7299i 0.305642 0.461219i
\(124\) −180.028 + 144.150i −1.45184 + 1.16250i
\(125\) 90.7678i 0.726143i
\(126\) 160.644 82.8391i 1.27496 0.657453i
\(127\) 112.463i 0.885532i 0.896637 + 0.442766i \(0.146003\pi\)
−0.896637 + 0.442766i \(0.853997\pi\)
\(128\) 110.407 64.7642i 0.862551 0.505970i
\(129\) 184.333 + 11.3769i 1.42894 + 0.0881933i
\(130\) −8.43842 + 17.5669i −0.0649109 + 0.135130i
\(131\) 89.1863 + 154.475i 0.680812 + 1.17920i 0.974733 + 0.223371i \(0.0717062\pi\)
−0.293922 + 0.955829i \(0.594961\pi\)
\(132\) 145.480 13.1187i 1.10212 0.0993842i
\(133\) 178.521 + 103.069i 1.34226 + 0.774956i
\(134\) 60.7482 + 88.9125i 0.453344 + 0.663526i
\(135\) 50.1110 17.6514i 0.371192 0.130751i
\(136\) 36.7392 8.49999i 0.270141 0.0624999i
\(137\) 64.0732 110.978i 0.467688 0.810059i −0.531631 0.846976i \(-0.678420\pi\)
0.999318 + 0.0369173i \(0.0117538\pi\)
\(138\) −20.1653 11.2652i −0.146126 0.0816318i
\(139\) −96.3171 166.826i −0.692929 1.20019i −0.970874 0.239591i \(-0.922987\pi\)
0.277945 0.960597i \(-0.410347\pi\)
\(140\) 78.1294 11.9339i 0.558067 0.0852418i
\(141\) −9.54166 + 154.597i −0.0676713 + 1.09643i
\(142\) −20.0751 264.382i −0.141374 1.86184i
\(143\) 60.2786i 0.421529i
\(144\) −48.5288 + 135.576i −0.337006 + 0.941503i
\(145\) −92.6146 −0.638722
\(146\) 49.2572 3.74020i 0.337378 0.0256178i
\(147\) −85.8928 + 129.614i −0.584305 + 0.881725i
\(148\) −4.79357 31.3829i −0.0323890 0.212046i
\(149\) −31.9061 + 18.4210i −0.214135 + 0.123631i −0.603231 0.797566i \(-0.706120\pi\)
0.389097 + 0.921197i \(0.372787\pi\)
\(150\) −126.755 + 1.79311i −0.845036 + 0.0119541i
\(151\) −1.53781 0.887854i −0.0101842 0.00587983i 0.494899 0.868950i \(-0.335205\pi\)
−0.505083 + 0.863071i \(0.668538\pi\)
\(152\) −160.004 + 37.0186i −1.05266 + 0.243543i
\(153\) −25.5686 + 33.8524i −0.167115 + 0.221258i
\(154\) −201.846 + 137.908i −1.31069 + 0.895507i
\(155\) 56.7268 98.2538i 0.365980 0.633895i
\(156\) 53.9233 + 24.9701i 0.345662 + 0.160065i
\(157\) 28.4676 16.4358i 0.181322 0.104686i −0.406592 0.913610i \(-0.633283\pi\)
0.587914 + 0.808924i \(0.299949\pi\)
\(158\) −175.531 84.3179i −1.11095 0.533657i
\(159\) −136.999 + 68.2101i −0.861626 + 0.428994i
\(160\) −39.0163 + 49.4232i −0.243852 + 0.308895i
\(161\) 38.6571 0.240106
\(162\) −55.9784 152.021i −0.345546 0.938402i
\(163\) 26.1023 0.160137 0.0800686 0.996789i \(-0.474486\pi\)
0.0800686 + 0.996789i \(0.474486\pi\)
\(164\) −56.7160 70.8324i −0.345829 0.431905i
\(165\) −64.3252 + 32.0268i −0.389850 + 0.194102i
\(166\) 0.324673 0.675896i 0.00195586 0.00407166i
\(167\) −113.333 + 65.4331i −0.678643 + 0.391815i −0.799344 0.600874i \(-0.794819\pi\)
0.120700 + 0.992689i \(0.461486\pi\)
\(168\) −39.7547 237.693i −0.236635 1.41484i
\(169\) −72.2388 + 125.121i −0.427448 + 0.740362i
\(170\) −15.3170 + 10.4651i −0.0900998 + 0.0615593i
\(171\) 111.355 147.432i 0.651196 0.862174i
\(172\) 89.5108 229.400i 0.520412 1.33372i
\(173\) 159.107 + 91.8606i 0.919695 + 0.530986i 0.883538 0.468360i \(-0.155155\pi\)
0.0361571 + 0.999346i \(0.488488\pi\)
\(174\) 3.99450 + 282.371i 0.0229569 + 1.62282i
\(175\) 183.732 106.078i 1.04990 0.606158i
\(176\) 42.5885 190.047i 0.241980 1.07981i
\(177\) −55.3815 + 83.5715i −0.312890 + 0.472155i
\(178\) −268.869 + 20.4157i −1.51050 + 0.114695i
\(179\) −24.4312 −0.136487 −0.0682435 0.997669i \(-0.521739\pi\)
−0.0682435 + 0.997669i \(0.521739\pi\)
\(180\) −2.00380 70.8102i −0.0111322 0.393390i
\(181\) 101.654i 0.561622i −0.959763 0.280811i \(-0.909397\pi\)
0.959763 0.280811i \(-0.0906034\pi\)
\(182\) −99.1650 + 7.52981i −0.544863 + 0.0413726i
\(183\) −8.47886 + 137.377i −0.0463326 + 0.750696i
\(184\) −22.5145 + 21.0148i −0.122361 + 0.114211i
\(185\) 7.80869 + 13.5250i 0.0422091 + 0.0731084i
\(186\) −302.011 168.716i −1.62371 0.907074i
\(187\) 28.6889 49.6906i 0.153417 0.265725i
\(188\) 192.394 + 75.0713i 1.02337 + 0.399315i
\(189\) 205.867 + 176.420i 1.08924 + 0.933440i
\(190\) 66.7074 45.5768i 0.351092 0.239878i
\(191\) −25.0116 14.4405i −0.130951 0.0756046i 0.433093 0.901349i \(-0.357422\pi\)
−0.564044 + 0.825744i \(0.690755\pi\)
\(192\) 152.368 + 116.824i 0.793584 + 0.608460i
\(193\) −142.662 247.098i −0.739181 1.28030i −0.952864 0.303396i \(-0.901879\pi\)
0.213683 0.976903i \(-0.431454\pi\)
\(194\) 18.8484 39.2382i 0.0971569 0.202259i
\(195\) −29.1773 1.80081i −0.149627 0.00923491i
\(196\) 129.582 + 161.834i 0.661132 + 0.825685i
\(197\) 191.958i 0.974405i −0.873289 0.487202i \(-0.838017\pi\)
0.873289 0.487202i \(-0.161983\pi\)
\(198\) 100.420 + 194.739i 0.507173 + 0.983528i
\(199\) 33.7936i 0.169817i 0.996389 + 0.0849085i \(0.0270598\pi\)
−0.996389 + 0.0849085i \(0.972940\pi\)
\(200\) −49.3423 + 161.662i −0.246712 + 0.808308i
\(201\) −89.2266 + 134.644i −0.443914 + 0.669873i
\(202\) −83.9288 40.3160i −0.415489 0.199584i
\(203\) −236.308 409.297i −1.16408 2.01624i
\(204\) 32.5674 + 46.2482i 0.159644 + 0.226707i
\(205\) 38.6582 + 22.3193i 0.188576 + 0.108875i
\(206\) 166.534 113.782i 0.808419 0.552340i
\(207\) 4.26067 34.3849i 0.0205830 0.166111i
\(208\) 53.6619 58.2936i 0.257990 0.280258i
\(209\) −124.944 + 216.409i −0.597818 + 1.03545i
\(210\) 60.7230 + 101.821i 0.289157 + 0.484864i
\(211\) 129.688 + 224.627i 0.614636 + 1.06458i 0.990448 + 0.137885i \(0.0440306\pi\)
−0.375812 + 0.926696i \(0.622636\pi\)
\(212\) 30.8107 + 201.714i 0.145334 + 0.951480i
\(213\) 356.027 177.262i 1.67149 0.832215i
\(214\) −25.8191 + 1.96050i −0.120650 + 0.00916120i
\(215\) 121.136i 0.563425i
\(216\) −215.806 + 9.16342i −0.999100 + 0.0424232i
\(217\) 578.957 2.66801
\(218\) −17.8220 234.710i −0.0817524 1.07665i
\(219\) 33.0258 + 66.3316i 0.150803 + 0.302884i
\(220\) 14.4666 + 94.7110i 0.0657574 + 0.430505i
\(221\) 20.2150 11.6712i 0.0914708 0.0528107i
\(222\) 40.8995 24.3911i 0.184232 0.109870i
\(223\) −107.192 61.8873i −0.480681 0.277521i 0.240019 0.970768i \(-0.422846\pi\)
−0.720700 + 0.693247i \(0.756180\pi\)
\(224\) −317.969 46.3228i −1.41950 0.206798i
\(225\) −74.1041 175.118i −0.329351 0.778303i
\(226\) 33.1495 + 48.5185i 0.146679 + 0.214684i
\(227\) −127.486 + 220.813i −0.561614 + 0.972745i 0.435741 + 0.900072i \(0.356486\pi\)
−0.997356 + 0.0726729i \(0.976847\pi\)
\(228\) −141.835 201.417i −0.622085 0.883409i
\(229\) −216.736 + 125.132i −0.946444 + 0.546430i −0.891975 0.452085i \(-0.850680\pi\)
−0.0544698 + 0.998515i \(0.517347\pi\)
\(230\) 6.56015 13.6568i 0.0285224 0.0593772i
\(231\) −305.664 202.559i −1.32322 0.876878i
\(232\) 360.131 + 109.919i 1.55229 + 0.473790i
\(233\) 231.979 0.995619 0.497810 0.867286i \(-0.334138\pi\)
0.497810 + 0.867286i \(0.334138\pi\)
\(234\) −4.23202 + 89.0357i −0.0180856 + 0.380494i
\(235\) −101.595 −0.432320
\(236\) 83.5510 + 104.347i 0.354030 + 0.442146i
\(237\) 17.9939 291.543i 0.0759237 1.23014i
\(238\) −85.3303 40.9892i −0.358531 0.172224i
\(239\) −209.313 + 120.847i −0.875786 + 0.505635i −0.869267 0.494344i \(-0.835408\pi\)
−0.00651903 + 0.999979i \(0.502075\pi\)
\(240\) −90.7182 26.2922i −0.377992 0.109551i
\(241\) −115.503 + 200.057i −0.479266 + 0.830113i −0.999717 0.0237786i \(-0.992430\pi\)
0.520451 + 0.853891i \(0.325764\pi\)
\(242\) −30.6561 44.8690i −0.126678 0.185409i
\(243\) 179.613 163.671i 0.739149 0.673542i
\(244\) 170.964 + 66.7095i 0.700674 + 0.273400i
\(245\) −88.3243 50.9941i −0.360507 0.208139i
\(246\) 66.3816 118.827i 0.269844 0.483036i
\(247\) −88.0392 + 50.8294i −0.356434 + 0.205787i
\(248\) −337.194 + 314.733i −1.35965 + 1.26908i
\(249\) 1.12261 + 0.0692871i 0.00450848 + 0.000278261i
\(250\) −13.7448 181.015i −0.0549792 0.724058i
\(251\) −78.5229 −0.312840 −0.156420 0.987691i \(-0.549995\pi\)
−0.156420 + 0.987691i \(0.549995\pi\)
\(252\) 307.823 189.529i 1.22152 0.752098i
\(253\) 46.8615i 0.185223i
\(254\) 17.0300 + 224.280i 0.0670473 + 0.882991i
\(255\) −23.1952 15.3711i −0.0909615 0.0602787i
\(256\) 210.372 145.875i 0.821766 0.569825i
\(257\) 130.836 + 226.615i 0.509090 + 0.881770i 0.999945 + 0.0105283i \(0.00335132\pi\)
−0.490855 + 0.871242i \(0.663315\pi\)
\(258\) 369.330 5.22464i 1.43151 0.0202506i
\(259\) −39.8480 + 69.0187i −0.153853 + 0.266481i
\(260\) −14.1683 + 36.3107i −0.0544934 + 0.139657i
\(261\) −390.108 + 165.081i −1.49467 + 0.632493i
\(262\) 201.253 + 294.558i 0.768140 + 1.12427i
\(263\) 275.353 + 158.975i 1.04697 + 0.604469i 0.921800 0.387667i \(-0.126719\pi\)
0.125171 + 0.992135i \(0.460052\pi\)
\(264\) 288.139 48.1919i 1.09143 0.182545i
\(265\) −50.1904 86.9323i −0.189398 0.328046i
\(266\) 371.625 + 178.514i 1.39709 + 0.671104i
\(267\) −180.270 362.069i −0.675169 1.35606i
\(268\) 134.611 + 168.116i 0.502281 + 0.627297i
\(269\) 135.043i 0.502020i −0.967985 0.251010i \(-0.919237\pi\)
0.967985 0.251010i \(-0.0807627\pi\)
\(270\) 97.2613 42.7897i 0.360227 0.158480i
\(271\) 161.415i 0.595628i 0.954624 + 0.297814i \(0.0962575\pi\)
−0.954624 + 0.297814i \(0.903742\pi\)
\(272\) 71.9803 22.5145i 0.264633 0.0827740i
\(273\) −66.4878 133.539i −0.243545 0.489155i
\(274\) 110.973 231.022i 0.405012 0.843144i
\(275\) 128.591 + 222.726i 0.467603 + 0.809912i
\(276\) −41.9208 19.4121i −0.151887 0.0703337i
\(277\) −367.934 212.427i −1.32828 0.766884i −0.343248 0.939245i \(-0.611527\pi\)
−0.985034 + 0.172361i \(0.944860\pi\)
\(278\) −217.344 318.109i −0.781811 1.14428i
\(279\) 63.8109 514.974i 0.228713 1.84578i
\(280\) 154.003 35.6302i 0.550011 0.127251i
\(281\) 80.5450 139.508i 0.286637 0.496470i −0.686368 0.727255i \(-0.740796\pi\)
0.973005 + 0.230785i \(0.0741293\pi\)
\(282\) 4.38183 + 309.752i 0.0155384 + 1.09841i
\(283\) 182.383 + 315.897i 0.644464 + 1.11625i 0.984425 + 0.175805i \(0.0562530\pi\)
−0.339960 + 0.940440i \(0.610414\pi\)
\(284\) −80.0697 524.206i −0.281936 1.84580i
\(285\) 101.018 + 66.9430i 0.354449 + 0.234888i
\(286\) −9.12788 120.211i −0.0319157 0.420319i
\(287\) 227.792i 0.793701i
\(288\) −76.2490 + 277.723i −0.264753 + 0.964316i
\(289\) −266.781 −0.923118
\(290\) −184.698 + 14.0245i −0.636888 + 0.0483602i
\(291\) 65.1717 + 4.02236i 0.223958 + 0.0138226i
\(292\) 97.6653 14.9179i 0.334470 0.0510886i
\(293\) 437.041 252.326i 1.49161 0.861180i 0.491654 0.870790i \(-0.336392\pi\)
0.999954 + 0.00961009i \(0.00305903\pi\)
\(294\) −151.665 + 271.490i −0.515869 + 0.923435i
\(295\) −56.9492 32.8796i −0.193048 0.111456i
\(296\) −14.3119 61.8597i −0.0483510 0.208986i
\(297\) −213.862 + 249.558i −0.720076 + 0.840264i
\(298\) −60.8395 + 41.5677i −0.204159 + 0.139489i
\(299\) −9.53204 + 16.5100i −0.0318797 + 0.0552173i
\(300\) −252.512 + 22.7703i −0.841705 + 0.0759009i
\(301\) −535.344 + 309.081i −1.77855 + 1.02685i
\(302\) −3.20124 1.53774i −0.0106001 0.00509187i
\(303\) 8.60366 139.399i 0.0283949 0.460064i
\(304\) −313.484 + 98.0537i −1.03120 + 0.322545i
\(305\) −90.2790 −0.295997
\(306\) −45.8642 + 71.3823i −0.149883 + 0.233276i
\(307\) 42.6361 0.138880 0.0694400 0.997586i \(-0.477879\pi\)
0.0694400 + 0.997586i \(0.477879\pi\)
\(308\) −381.650 + 305.590i −1.23912 + 0.992174i
\(309\) 252.190 + 167.123i 0.816150 + 0.540850i
\(310\) 98.2496 204.533i 0.316934 0.659785i
\(311\) 170.776 98.5973i 0.549117 0.317033i −0.199649 0.979868i \(-0.563980\pi\)
0.748766 + 0.662834i \(0.230647\pi\)
\(312\) 111.318 + 41.6313i 0.356789 + 0.133434i
\(313\) 73.0920 126.599i 0.233521 0.404470i −0.725321 0.688411i \(-0.758309\pi\)
0.958842 + 0.283941i \(0.0916420\pi\)
\(314\) 54.2829 37.0880i 0.172876 0.118115i
\(315\) −107.178 + 141.902i −0.340248 + 0.450484i
\(316\) −362.822 141.571i −1.14817 0.448011i
\(317\) −61.0328 35.2373i −0.192533 0.111159i 0.400635 0.916238i \(-0.368790\pi\)
−0.593168 + 0.805079i \(0.702123\pi\)
\(318\) −262.882 + 156.774i −0.826672 + 0.493000i
\(319\) 496.163 286.460i 1.55537 0.897993i
\(320\) −70.3245 + 104.471i −0.219764 + 0.326471i
\(321\) −17.3111 34.7690i −0.0539286 0.108315i
\(322\) 77.0923 5.85378i 0.239417 0.0181794i
\(323\) −96.7667 −0.299587
\(324\) −134.656 294.693i −0.415604 0.909546i
\(325\) 104.626i 0.321927i
\(326\) 52.0548 3.95263i 0.159677 0.0121246i
\(327\) 316.069 157.368i 0.966573 0.481246i
\(328\) −123.832 132.670i −0.377538 0.404481i
\(329\) −259.221 448.985i −0.787907 1.36470i
\(330\) −123.431 + 73.6104i −0.374034 + 0.223062i
\(331\) 54.0633 93.6405i 0.163333 0.282902i −0.772729 0.634736i \(-0.781109\pi\)
0.936062 + 0.351835i \(0.114442\pi\)
\(332\) 0.545133 1.39708i 0.00164197 0.00420806i
\(333\) 56.9992 + 43.0512i 0.171169 + 0.129283i
\(334\) −216.108 + 147.652i −0.647029 + 0.442073i
\(335\) −91.7525 52.9733i −0.273888 0.158129i
\(336\) −115.274 468.000i −0.343079 1.39286i
\(337\) −168.695 292.189i −0.500580 0.867030i −1.00000 0.000669822i \(-0.999787\pi\)
0.499420 0.866360i \(-0.333547\pi\)
\(338\) −125.116 + 260.463i −0.370166 + 0.770601i
\(339\) −48.6899 + 73.4738i −0.143628 + 0.216737i
\(340\) −28.9613 + 23.1895i −0.0851802 + 0.0682044i
\(341\) 701.831i 2.05816i
\(342\) 199.745 310.880i 0.584048 0.909004i
\(343\) 28.4187i 0.0828534i
\(344\) 143.770 471.038i 0.417936 1.36930i
\(345\) 22.6828 + 1.39997i 0.0657473 + 0.00405789i
\(346\) 331.211 + 159.100i 0.957258 + 0.459828i
\(347\) 12.3560 + 21.4012i 0.0356081 + 0.0616750i 0.883280 0.468845i \(-0.155330\pi\)
−0.847672 + 0.530520i \(0.821997\pi\)
\(348\) 50.7250 + 562.516i 0.145762 + 1.61643i
\(349\) −12.1159 6.99512i −0.0347160 0.0200433i 0.482542 0.875873i \(-0.339714\pi\)
−0.517258 + 0.855830i \(0.673047\pi\)
\(350\) 350.346 239.368i 1.00099 0.683910i
\(351\) −126.109 + 44.4216i −0.359286 + 0.126557i
\(352\) 56.1540 385.453i 0.159528 1.09504i
\(353\) 157.831 273.371i 0.447113 0.774422i −0.551084 0.834450i \(-0.685786\pi\)
0.998197 + 0.0600276i \(0.0191189\pi\)
\(354\) −97.7899 + 175.049i −0.276243 + 0.494490i
\(355\) 130.433 + 225.916i 0.367417 + 0.636384i
\(356\) −533.102 + 81.4286i −1.49748 + 0.228732i
\(357\) 8.74733 141.727i 0.0245023 0.396995i
\(358\) −48.7221 + 3.69957i −0.136095 + 0.0103340i
\(359\) 629.848i 1.75445i 0.480078 + 0.877226i \(0.340608\pi\)
−0.480078 + 0.877226i \(0.659392\pi\)
\(360\) −14.7188 140.910i −0.0408855 0.391418i
\(361\) 60.4319 0.167401
\(362\) −15.3932 202.724i −0.0425227 0.560010i
\(363\) 45.0275 67.9472i 0.124043 0.187182i
\(364\) −196.621 + 30.0328i −0.540166 + 0.0825076i
\(365\) −42.0907 + 24.3011i −0.115317 + 0.0665783i
\(366\) 3.89376 + 275.250i 0.0106387 + 0.752049i
\(367\) 224.072 + 129.368i 0.610550 + 0.352501i 0.773181 0.634186i \(-0.218665\pi\)
−0.162631 + 0.986687i \(0.551998\pi\)
\(368\) −41.7175 + 45.3183i −0.113363 + 0.123147i
\(369\) 202.618 + 25.1066i 0.549099 + 0.0680395i
\(370\) 17.6206 + 25.7900i 0.0476233 + 0.0697027i
\(371\) 256.123 443.618i 0.690359 1.19574i
\(372\) −627.836 290.730i −1.68773 0.781532i
\(373\) −107.907 + 62.3003i −0.289296 + 0.167025i −0.637624 0.770348i \(-0.720083\pi\)
0.348329 + 0.937373i \(0.386749\pi\)
\(374\) 49.6885 103.440i 0.132857 0.276578i
\(375\) 243.761 121.366i 0.650030 0.323643i
\(376\) 395.052 + 120.578i 1.05067 + 0.320685i
\(377\) 233.074 0.618234
\(378\) 437.267 + 320.654i 1.15679 + 0.848290i
\(379\) −154.148 −0.406724 −0.203362 0.979104i \(-0.565187\pi\)
−0.203362 + 0.979104i \(0.565187\pi\)
\(380\) 126.130 100.993i 0.331922 0.265772i
\(381\) −302.023 + 150.374i −0.792712 + 0.394683i
\(382\) −52.0664 25.0106i −0.136299 0.0654727i
\(383\) 344.678 199.000i 0.899944 0.519583i 0.0227617 0.999741i \(-0.492754\pi\)
0.877182 + 0.480158i \(0.159421\pi\)
\(384\) 321.552 + 209.905i 0.837375 + 0.546628i
\(385\) 120.258 208.293i 0.312358 0.541020i
\(386\) −321.922 471.174i −0.833996 1.22066i
\(387\) 215.919 + 510.247i 0.557930 + 1.31847i
\(388\) 31.6469 81.1053i 0.0815642 0.209034i
\(389\) −279.310 161.260i −0.718020 0.414549i 0.0960032 0.995381i \(-0.469394\pi\)
−0.814024 + 0.580832i \(0.802727\pi\)
\(390\) −58.4597 + 0.826986i −0.149897 + 0.00212048i
\(391\) −15.7155 + 9.07333i −0.0401930 + 0.0232054i
\(392\) 282.926 + 303.117i 0.721751 + 0.773258i
\(393\) −295.599 + 446.063i −0.752160 + 1.13502i
\(394\) −29.0678 382.813i −0.0737762 0.971608i
\(395\) 191.591 0.485040
\(396\) 229.753 + 373.153i 0.580185 + 0.942305i
\(397\) 286.878i 0.722615i −0.932447 0.361308i \(-0.882330\pi\)
0.932447 0.361308i \(-0.117670\pi\)
\(398\) 5.11730 + 67.3931i 0.0128575 + 0.169329i
\(399\) −38.0958 + 617.241i −0.0954782 + 1.54697i
\(400\) −73.9213 + 329.867i −0.184803 + 0.824667i
\(401\) 296.251 + 513.122i 0.738781 + 1.27961i 0.953044 + 0.302831i \(0.0979317\pi\)
−0.214263 + 0.976776i \(0.568735\pi\)
\(402\) −157.552 + 282.027i −0.391921 + 0.701560i
\(403\) −142.759 + 247.266i −0.354240 + 0.613562i
\(404\) −173.481 67.6913i −0.429408 0.167553i
\(405\) 114.407 + 110.974i 0.282487 + 0.274009i
\(406\) −533.238 780.460i −1.31339 1.92232i
\(407\) −83.6668 48.3050i −0.205569 0.118686i
\(408\) 71.9512 + 87.2994i 0.176351 + 0.213969i
\(409\) 258.131 + 447.095i 0.631126 + 1.09314i 0.987322 + 0.158731i \(0.0507403\pi\)
−0.356196 + 0.934411i \(0.615926\pi\)
\(410\) 80.4742 + 38.6566i 0.196279 + 0.0942843i
\(411\) 383.709 + 23.6823i 0.933599 + 0.0576213i
\(412\) 314.883 252.129i 0.764278 0.611963i
\(413\) 335.571i 0.812522i
\(414\) 3.29004 69.2176i 0.00794695 0.167192i
\(415\) 0.737736i 0.00177768i
\(416\) 98.1884 124.378i 0.236030 0.298987i
\(417\) 319.233 481.728i 0.765547 1.15522i
\(418\) −216.400 + 450.496i −0.517704 + 1.07774i
\(419\) −155.891 270.011i −0.372054 0.644417i 0.617827 0.786314i \(-0.288013\pi\)
−0.989881 + 0.141897i \(0.954680\pi\)
\(420\) 136.516 + 193.863i 0.325038 + 0.461579i
\(421\) 567.466 + 327.627i 1.34790 + 0.778211i 0.987952 0.154761i \(-0.0494608\pi\)
0.359949 + 0.932972i \(0.382794\pi\)
\(422\) 292.647 + 428.325i 0.693476 + 1.01499i
\(423\) −427.936 + 181.088i −1.01167 + 0.428104i
\(424\) 91.9897 + 397.604i 0.216957 + 0.937745i
\(425\) −49.7956 + 86.2485i −0.117166 + 0.202938i
\(426\) 683.167 407.418i 1.60368 0.956381i
\(427\) −230.348 398.975i −0.539457 0.934367i
\(428\) −51.1931 + 7.81948i −0.119610 + 0.0182698i
\(429\) 161.881 80.5987i 0.377345 0.187876i
\(430\) 18.3435 + 241.577i 0.0426592 + 0.561808i
\(431\) 204.753i 0.475064i −0.971380 0.237532i \(-0.923662\pi\)
0.971380 0.237532i \(-0.0763384\pi\)
\(432\) −428.985 + 50.9533i −0.993020 + 0.117947i
\(433\) −561.451 −1.29665 −0.648327 0.761362i \(-0.724531\pi\)
−0.648327 + 0.761362i \(0.724531\pi\)
\(434\) 1154.59 87.6705i 2.66035 0.202006i
\(435\) −123.835 248.721i −0.284679 0.571772i
\(436\) −71.0835 465.374i −0.163035 1.06737i
\(437\) 68.4429 39.5155i 0.156620 0.0904246i
\(438\) 75.9065 + 127.281i 0.173302 + 0.290597i
\(439\) −261.544 151.002i −0.595771 0.343969i 0.171605 0.985166i \(-0.445105\pi\)
−0.767376 + 0.641197i \(0.778438\pi\)
\(440\) 43.1921 + 186.688i 0.0981639 + 0.424290i
\(441\) −462.931 57.3623i −1.04973 0.130073i
\(442\) 38.5467 26.3364i 0.0872097 0.0595847i
\(443\) −228.326 + 395.472i −0.515408 + 0.892713i 0.484432 + 0.874829i \(0.339026\pi\)
−0.999840 + 0.0178842i \(0.994307\pi\)
\(444\) 77.8706 54.8355i 0.175384 0.123503i
\(445\) 229.750 132.646i 0.516293 0.298082i
\(446\) −223.140 107.187i −0.500314 0.240330i
\(447\) −92.1321 61.0544i −0.206112 0.136587i
\(448\) −641.127 44.2301i −1.43109 0.0987279i
\(449\) 418.640 0.932384 0.466192 0.884684i \(-0.345626\pi\)
0.466192 + 0.884684i \(0.345626\pi\)
\(450\) −174.301 338.010i −0.387335 0.751133i
\(451\) −276.137 −0.612278
\(452\) 73.4558 + 91.7387i 0.162513 + 0.202962i
\(453\) 0.328163 5.31701i 0.000724422 0.0117373i
\(454\) −220.804 + 459.664i −0.486352 + 1.01247i
\(455\) 84.7373 48.9231i 0.186236 0.107523i
\(456\) −313.357 380.200i −0.687186 0.833772i
\(457\) 117.305 203.178i 0.256684 0.444590i −0.708668 0.705543i \(-0.750703\pi\)
0.965352 + 0.260953i \(0.0840367\pi\)
\(458\) −413.279 + 282.366i −0.902355 + 0.616521i
\(459\) −125.100 23.4014i −0.272549 0.0509834i
\(460\) 11.0146 28.2285i 0.0239448 0.0613663i
\(461\) −104.947 60.5913i −0.227651 0.131435i 0.381837 0.924230i \(-0.375292\pi\)
−0.609488 + 0.792795i \(0.708625\pi\)
\(462\) −640.247 357.669i −1.38582 0.774174i
\(463\) −213.979 + 123.541i −0.462157 + 0.266827i −0.712951 0.701214i \(-0.752642\pi\)
0.250794 + 0.968041i \(0.419308\pi\)
\(464\) 734.840 + 164.673i 1.58371 + 0.354900i
\(465\) 339.715 + 20.9670i 0.730569 + 0.0450904i
\(466\) 462.627 35.1282i 0.992761 0.0753824i
\(467\) −276.509 −0.592097 −0.296049 0.955173i \(-0.595669\pi\)
−0.296049 + 0.955173i \(0.595669\pi\)
\(468\) 5.04277 + 178.201i 0.0107751 + 0.380772i
\(469\) 540.649i 1.15277i
\(470\) −202.607 + 15.3844i −0.431079 + 0.0327327i
\(471\) 82.2031 + 54.4747i 0.174529 + 0.115658i
\(472\) 182.423 + 195.442i 0.386490 + 0.414072i
\(473\) −374.678 648.962i −0.792132 1.37201i
\(474\) −8.26336 584.138i −0.0174333 1.23236i
\(475\) 216.866 375.624i 0.456561 0.790787i
\(476\) −176.378 68.8217i −0.370541 0.144583i
\(477\) −366.362 276.712i −0.768055 0.580109i
\(478\) −399.124 + 272.696i −0.834988 + 0.570493i
\(479\) −613.932 354.454i −1.28169 0.739987i −0.304536 0.952501i \(-0.598501\pi\)
−0.977158 + 0.212514i \(0.931835\pi\)
\(480\) −184.897 38.6961i −0.385202 0.0806168i
\(481\) −19.6514 34.0372i −0.0408552 0.0707633i
\(482\) −200.049 + 416.456i −0.415039 + 0.864017i
\(483\) 51.6886 + 103.815i 0.107016 + 0.214939i
\(484\) −67.9306 84.8382i −0.140352 0.175286i
\(485\) 42.8283i 0.0883057i
\(486\) 333.411 353.600i 0.686030 0.727573i
\(487\) 204.394i 0.419699i 0.977734 + 0.209850i \(0.0672975\pi\)
−0.977734 + 0.209850i \(0.932703\pi\)
\(488\) 351.049 + 107.147i 0.719363 + 0.219564i
\(489\) 34.9015 + 70.0990i 0.0713733 + 0.143352i
\(490\) −183.864 88.3206i −0.375232 0.180246i
\(491\) 113.951 + 197.369i 0.232080 + 0.401974i 0.958420 0.285361i \(-0.0921136\pi\)
−0.726340 + 0.687335i \(0.758780\pi\)
\(492\) 114.388 247.024i 0.232497 0.502081i
\(493\) 192.135 + 110.929i 0.389725 + 0.225008i
\(494\) −167.876 + 114.699i −0.339830 + 0.232184i
\(495\) −172.019 129.925i −0.347513 0.262475i
\(496\) −624.792 + 678.720i −1.25966 + 1.36839i
\(497\) −665.603 + 1152.86i −1.33924 + 2.31963i
\(498\) 2.24927 0.0318188i 0.00451661 6.38931e-5i
\(499\) −190.463 329.891i −0.381689 0.661105i 0.609615 0.792698i \(-0.291324\pi\)
−0.991304 + 0.131593i \(0.957991\pi\)
\(500\) −54.8214 358.909i −0.109643 0.717817i
\(501\) −327.262 216.871i −0.653218 0.432877i
\(502\) −156.595 + 11.8906i −0.311942 + 0.0236864i
\(503\) 697.917i 1.38751i −0.720212 0.693754i \(-0.755955\pi\)
0.720212 0.693754i \(-0.244045\pi\)
\(504\) 585.178 424.582i 1.16107 0.842426i
\(505\) 91.6077 0.181401
\(506\) 7.09615 + 93.4539i 0.0140240 + 0.184691i
\(507\) −432.610 26.7005i −0.853273 0.0526636i
\(508\) 67.9245 + 444.693i 0.133710 + 0.875380i
\(509\) −64.0084 + 36.9552i −0.125753 + 0.0726036i −0.561557 0.827438i \(-0.689797\pi\)
0.435804 + 0.900042i \(0.356464\pi\)
\(510\) −48.5848 27.1415i −0.0952644 0.0532186i
\(511\) −214.790 124.009i −0.420333 0.242679i
\(512\) 397.447 322.769i 0.776263 0.630409i
\(513\) 544.827 + 101.916i 1.06204 + 0.198667i
\(514\) 295.237 + 432.116i 0.574391 + 0.840693i
\(515\) −99.2196 + 171.853i −0.192659 + 0.333696i
\(516\) 735.749 66.3463i 1.42587 0.128578i
\(517\) 544.274 314.237i 1.05275 0.607808i
\(518\) −69.0158 + 143.675i −0.133235 + 0.277365i
\(519\) −33.9529 + 550.117i −0.0654199 + 1.05996i
\(520\) −22.7567 + 74.5585i −0.0437630 + 0.143382i
\(521\) −994.276 −1.90840 −0.954200 0.299171i \(-0.903290\pi\)
−0.954200 + 0.299171i \(0.903290\pi\)
\(522\) −752.979 + 388.287i −1.44249 + 0.743845i
\(523\) 342.943 0.655722 0.327861 0.944726i \(-0.393672\pi\)
0.327861 + 0.944726i \(0.393672\pi\)
\(524\) 445.954 + 556.950i 0.851058 + 1.06288i
\(525\) 530.545 + 351.583i 1.01056 + 0.669683i
\(526\) 573.199 + 275.342i 1.08973 + 0.523463i
\(527\) −235.366 + 135.889i −0.446615 + 0.257854i
\(528\) 567.326 139.740i 1.07448 0.264658i
\(529\) −257.090 + 445.292i −0.485992 + 0.841762i
\(530\) −113.257 165.765i −0.213692 0.312765i
\(531\) −298.486 36.9857i −0.562120 0.0696529i
\(532\) 768.148 + 299.728i 1.44389 + 0.563398i
\(533\) −97.2872 56.1688i −0.182528 0.105382i
\(534\) −414.333 694.761i −0.775904 1.30105i
\(535\) 22.0626 12.7379i 0.0412385 0.0238091i
\(536\) 293.908 + 314.882i 0.548335 + 0.587467i
\(537\) −32.6670 65.6110i −0.0608324 0.122181i
\(538\) −20.4494 269.311i −0.0380100 0.500579i
\(539\) 630.905 1.17051
\(540\) 187.485 100.062i 0.347194 0.185300i
\(541\) 571.225i 1.05587i 0.849285 + 0.527934i \(0.177033\pi\)
−0.849285 + 0.527934i \(0.822967\pi\)
\(542\) 24.4428 + 321.904i 0.0450974 + 0.593918i
\(543\) 272.995 135.921i 0.502754 0.250316i
\(544\) 140.138 55.7996i 0.257607 0.102573i
\(545\) 115.794 + 200.562i 0.212467 + 0.368003i
\(546\) −152.816 256.244i −0.279882 0.469311i
\(547\) 390.615 676.565i 0.714104 1.23686i −0.249200 0.968452i \(-0.580168\pi\)
0.963304 0.268413i \(-0.0864990\pi\)
\(548\) 186.327 477.521i 0.340012 0.871389i
\(549\) −380.270 + 160.917i −0.692660 + 0.293110i
\(550\) 290.170 + 424.701i 0.527583 + 0.772183i
\(551\) −836.771 483.110i −1.51864 0.876788i
\(552\) −86.5404 32.3648i −0.156776 0.0586318i
\(553\) 488.847 + 846.707i 0.883990 + 1.53112i
\(554\) −765.923 367.918i −1.38253 0.664113i
\(555\) −25.8811 + 39.0550i −0.0466326 + 0.0703693i
\(556\) −481.610 601.481i −0.866205 1.08180i
\(557\) 439.321i 0.788727i 0.918954 + 0.394364i \(0.129035\pi\)
−0.918954 + 0.394364i \(0.870965\pi\)
\(558\) 49.2740 1036.65i 0.0883046 1.85780i
\(559\) 304.852i 0.545352i
\(560\) 301.727 94.3763i 0.538798 0.168529i
\(561\) 171.806 + 10.6038i 0.306250 + 0.0189016i
\(562\) 139.502 290.412i 0.248224 0.516747i
\(563\) 16.1013 + 27.8883i 0.0285992 + 0.0495352i 0.879971 0.475028i \(-0.157562\pi\)
−0.851372 + 0.524563i \(0.824229\pi\)
\(564\) 55.6436 + 617.061i 0.0986589 + 1.09408i
\(565\) −50.0682 28.9069i −0.0886163 0.0511626i
\(566\) 411.556 + 602.363i 0.727130 + 1.06425i
\(567\) −198.519 + 788.756i −0.350122 + 1.39110i
\(568\) −239.059 1033.28i −0.420879 1.81915i
\(569\) 402.885 697.818i 0.708058 1.22639i −0.257518 0.966274i \(-0.582905\pi\)
0.965576 0.260120i \(-0.0837620\pi\)
\(570\) 211.593 + 118.205i 0.371216 + 0.207377i
\(571\) 250.021 + 433.050i 0.437866 + 0.758406i 0.997525 0.0703173i \(-0.0224012\pi\)
−0.559659 + 0.828723i \(0.689068\pi\)
\(572\) −36.4067 238.350i −0.0636481 0.416696i
\(573\) 5.33740 86.4783i 0.00931483 0.150922i
\(574\) 34.4942 + 454.277i 0.0600944 + 0.791423i
\(575\) 81.3379i 0.141457i
\(576\) −110.005 + 565.398i −0.190981 + 0.981594i
\(577\) 408.301 0.707628 0.353814 0.935316i \(-0.384885\pi\)
0.353814 + 0.935316i \(0.384885\pi\)
\(578\) −532.030 + 40.3982i −0.920468 + 0.0698930i
\(579\) 472.838 713.520i 0.816647 1.23233i
\(580\) −366.211 + 55.9369i −0.631399 + 0.0964429i
\(581\) −3.26032 + 1.88235i −0.00561156 + 0.00323984i
\(582\) 130.578 1.84719i 0.224361 0.00317387i
\(583\) 537.769 + 310.481i 0.922416 + 0.532557i
\(584\) 192.511 44.5394i 0.329642 0.0762660i
\(585\) −34.1769 80.7647i −0.0584220 0.138059i
\(586\) 833.364 569.384i 1.42212 0.971644i
\(587\) −231.965 + 401.775i −0.395171 + 0.684456i −0.993123 0.117076i \(-0.962648\pi\)
0.597952 + 0.801532i \(0.295981\pi\)
\(588\) −261.349 + 564.387i −0.444471 + 0.959843i
\(589\) 1025.05 591.814i 1.74032 1.00478i
\(590\) −118.550 56.9468i −0.200933 0.0965200i
\(591\) 515.511 256.667i 0.872269 0.434293i
\(592\) −37.9089 121.197i −0.0640353 0.204725i
\(593\) −80.8523 −0.136344 −0.0681722 0.997674i \(-0.521717\pi\)
−0.0681722 + 0.997674i \(0.521717\pi\)
\(594\) −388.707 + 530.069i −0.654389 + 0.892372i
\(595\) 93.1375 0.156534
\(596\) −115.035 + 92.1095i −0.193012 + 0.154546i
\(597\) −90.7541 + 45.1855i −0.152017 + 0.0756876i
\(598\) −16.5093 + 34.3686i −0.0276075 + 0.0574726i
\(599\) 153.902 88.8554i 0.256932 0.148339i −0.366002 0.930614i \(-0.619274\pi\)
0.622934 + 0.782274i \(0.285941\pi\)
\(600\) −500.125 + 83.6472i −0.833542 + 0.139412i
\(601\) 99.6250 172.555i 0.165765 0.287114i −0.771161 0.636640i \(-0.780324\pi\)
0.936927 + 0.349526i \(0.113657\pi\)
\(602\) −1020.81 + 697.454i −1.69570 + 1.15856i
\(603\) −480.899 59.5887i −0.797511 0.0988204i
\(604\) −6.61695 2.58190i −0.0109552 0.00427467i
\(605\) 46.3022 + 26.7326i 0.0765325 + 0.0441861i
\(606\) −3.95107 279.301i −0.00651991 0.460893i
\(607\) −967.595 + 558.641i −1.59406 + 0.920332i −0.601461 + 0.798902i \(0.705415\pi\)
−0.992600 + 0.121430i \(0.961252\pi\)
\(608\) −610.320 + 243.015i −1.00382 + 0.399695i
\(609\) 783.217 1181.89i 1.28607 1.94070i
\(610\) −180.040 + 13.6708i −0.295147 + 0.0224111i
\(611\) 255.674 0.418453
\(612\) −80.6557 + 149.300i −0.131790 + 0.243954i
\(613\) 131.929i 0.215218i 0.994193 + 0.107609i \(0.0343194\pi\)
−0.994193 + 0.107609i \(0.965681\pi\)
\(614\) 85.0275 6.45631i 0.138481 0.0105152i
\(615\) −8.24953 + 133.662i −0.0134139 + 0.217336i
\(616\) −714.833 + 667.217i −1.16044 + 1.08315i
\(617\) −57.7694 100.060i −0.0936295 0.162171i 0.815406 0.578889i \(-0.196514\pi\)
−0.909036 + 0.416718i \(0.863180\pi\)
\(618\) 528.240 + 295.097i 0.854758 + 0.477503i
\(619\) −337.518 + 584.599i −0.545264 + 0.944424i 0.453327 + 0.891344i \(0.350237\pi\)
−0.998590 + 0.0530799i \(0.983096\pi\)
\(620\) 164.963 422.771i 0.266069 0.681888i
\(621\) 98.0392 34.5340i 0.157873 0.0556103i
\(622\) 325.640 222.489i 0.523537 0.357699i
\(623\) 1172.42 + 676.899i 1.88190 + 1.08651i
\(624\) 228.302 + 66.1669i 0.365868 + 0.106037i
\(625\) −174.796 302.756i −0.279674 0.484410i
\(626\) 126.594 263.540i 0.202226 0.420990i
\(627\) −748.240 46.1810i −1.19336 0.0736539i
\(628\) 102.638 82.1830i 0.163436 0.130865i
\(629\) 37.4113i 0.0594775i
\(630\) −192.253 + 299.220i −0.305164 + 0.474953i
\(631\) 214.708i 0.340267i −0.985421 0.170133i \(-0.945580\pi\)
0.985421 0.170133i \(-0.0544199\pi\)
\(632\) −744.999 227.389i −1.17880 0.359792i
\(633\) −429.838 + 648.633i −0.679050 + 1.02470i
\(634\) −127.051 61.0303i −0.200396 0.0962622i
\(635\) −110.648 191.649i −0.174250 0.301809i
\(636\) −500.514 + 352.456i −0.786972 + 0.554176i
\(637\) 222.277 + 128.332i 0.348944 + 0.201463i
\(638\) 946.100 646.408i 1.48291 1.01318i
\(639\) 952.089 + 719.108i 1.48997 + 1.12536i
\(640\) −124.425 + 218.991i −0.194415 + 0.342173i
\(641\) 90.7182 157.129i 0.141526 0.245130i −0.786545 0.617532i \(-0.788132\pi\)
0.928072 + 0.372402i \(0.121466\pi\)
\(642\) −39.7878 66.7169i −0.0619748 0.103920i
\(643\) −544.280 942.721i −0.846470 1.46613i −0.884338 0.466847i \(-0.845390\pi\)
0.0378680 0.999283i \(-0.487943\pi\)
\(644\) 152.856 23.3479i 0.237353 0.0362545i
\(645\) −325.317 + 161.972i −0.504368 + 0.251119i
\(646\) −192.978 + 14.6532i −0.298727 + 0.0226830i
\(647\) 162.166i 0.250643i −0.992116 0.125321i \(-0.960004\pi\)
0.992116 0.125321i \(-0.0399962\pi\)
\(648\) −313.163 567.303i −0.483276 0.875468i
\(649\) 406.791 0.626796
\(650\) 15.8434 + 208.652i 0.0243744 + 0.321003i
\(651\) 774.126 + 1554.82i 1.18913 + 2.38835i
\(652\) 103.212 15.7651i 0.158301 0.0241797i
\(653\) −441.606 + 254.961i −0.676272 + 0.390446i −0.798449 0.602062i \(-0.794346\pi\)
0.122177 + 0.992508i \(0.461013\pi\)
\(654\) 606.495 361.694i 0.927362 0.553048i
\(655\) −303.967 175.495i −0.464071 0.267932i
\(656\) −267.044 245.826i −0.407079 0.374735i
\(657\) −133.978 + 177.385i −0.203923 + 0.269992i
\(658\) −584.944 856.138i −0.888972 1.30112i
\(659\) 392.592 679.989i 0.595739 1.03185i −0.397703 0.917514i \(-0.630193\pi\)
0.993442 0.114336i \(-0.0364740\pi\)
\(660\) −235.007 + 165.489i −0.356072 + 0.250741i
\(661\) 219.088 126.491i 0.331450 0.191363i −0.325035 0.945702i \(-0.605376\pi\)
0.656485 + 0.754339i \(0.272043\pi\)
\(662\) 93.6365 194.930i 0.141445 0.294456i
\(663\) 58.3730 + 38.6829i 0.0880438 + 0.0583452i
\(664\) 0.875579 2.86868i 0.00131864 0.00432030i
\(665\) −405.626 −0.609964
\(666\) 120.190 + 77.2240i 0.180466 + 0.115952i
\(667\) −181.195 −0.271657
\(668\) −408.616 + 327.182i −0.611701 + 0.489793i
\(669\) 22.8744 370.618i 0.0341919 0.553989i
\(670\) −191.000 91.7486i −0.285074 0.136938i
\(671\) 483.650 279.236i 0.720790 0.416149i
\(672\) −300.756 915.858i −0.447553 1.36288i
\(673\) −54.8126 + 94.9383i −0.0814452 + 0.141067i −0.903871 0.427805i \(-0.859287\pi\)
0.822426 + 0.568873i \(0.192620\pi\)
\(674\) −380.668 557.156i −0.564789 0.826640i
\(675\) 371.203 433.161i 0.549931 0.641720i
\(676\) −210.072 + 538.377i −0.310758 + 0.796416i
\(677\) 415.870 + 240.103i 0.614284 + 0.354657i 0.774640 0.632402i \(-0.217931\pi\)
−0.160356 + 0.987059i \(0.551264\pi\)
\(678\) −85.9742 + 153.899i −0.126806 + 0.226989i
\(679\) −189.273 + 109.277i −0.278753 + 0.160938i
\(680\) −54.2448 + 50.6314i −0.0797717 + 0.0744580i
\(681\) −763.466 47.1208i −1.12110 0.0691935i
\(682\) 106.277 + 1399.63i 0.155831 + 2.05225i
\(683\) −27.4345 −0.0401677 −0.0200838 0.999798i \(-0.506393\pi\)
−0.0200838 + 0.999798i \(0.506393\pi\)
\(684\) 351.266 650.221i 0.513547 0.950616i
\(685\) 252.159i 0.368115i
\(686\) −4.30339 56.6743i −0.00627317 0.0826155i
\(687\) −625.847 414.739i −0.910986 0.603695i
\(688\) 215.386 961.142i 0.313062 1.39701i
\(689\) 126.309 + 218.774i 0.183323 + 0.317524i
\(690\) 45.4474 0.642911i 0.0658658 0.000931755i
\(691\) 4.69502 8.13201i 0.00679452 0.0117685i −0.862608 0.505873i \(-0.831171\pi\)
0.869403 + 0.494104i \(0.164504\pi\)
\(692\) 684.613 + 267.133i 0.989326 + 0.386030i
\(693\) 135.276 1091.72i 0.195203 1.57535i
\(694\) 27.8818 + 40.8085i 0.0401755 + 0.0588019i
\(695\) 328.270 + 189.527i 0.472331 + 0.272701i
\(696\) 186.340 + 1114.12i 0.267729 + 1.60075i
\(697\) −53.4658 92.6055i −0.0767084 0.132863i
\(698\) −25.2215 12.1154i −0.0361339 0.0173573i
\(699\) 310.180 + 622.991i 0.443749 + 0.891260i
\(700\) 662.433 530.415i 0.946333 0.757736i
\(701\) 821.246i 1.17153i 0.810479 + 0.585767i \(0.199207\pi\)
−0.810479 + 0.585767i \(0.800793\pi\)
\(702\) −244.768 + 107.685i −0.348672 + 0.153397i
\(703\) 162.931i 0.231766i
\(704\) 53.6172 777.196i 0.0761608 1.10397i
\(705\) −135.843 272.838i −0.192685 0.387005i
\(706\) 273.360 569.073i 0.387195 0.806052i
\(707\) 233.738 + 404.847i 0.330606 + 0.572626i
\(708\) −168.511 + 363.902i −0.238010 + 0.513986i
\(709\) −719.455 415.378i −1.01475 0.585864i −0.102168 0.994767i \(-0.532578\pi\)
−0.912578 + 0.408903i \(0.865911\pi\)
\(710\) 294.327 + 430.785i 0.414545 + 0.606739i
\(711\) 807.012 341.500i 1.13504 0.480310i
\(712\) −1050.81 + 243.116i −1.47586 + 0.341456i
\(713\) 110.983 192.228i 0.155656 0.269604i
\(714\) −4.01705 283.965i −0.00562612 0.397711i
\(715\) 59.3062 + 102.721i 0.0829458 + 0.143666i
\(716\) −96.6042 + 14.7558i −0.134922 + 0.0206087i
\(717\) −604.412 400.534i −0.842974 0.558625i
\(718\) 95.3768 + 1256.08i 0.132837 + 1.74942i
\(719\) 195.460i 0.271850i −0.990719 0.135925i \(-0.956599\pi\)
0.990719 0.135925i \(-0.0434006\pi\)
\(720\) −50.6909 278.783i −0.0704040 0.387199i
\(721\) −1012.64 −1.40450
\(722\) 120.517 9.15110i 0.166921 0.0126746i
\(723\) −691.702 42.6915i −0.956711 0.0590478i
\(724\) −61.3961 401.952i −0.0848013 0.555183i
\(725\) −861.195 + 497.211i −1.18786 + 0.685809i
\(726\) 79.5074 142.323i 0.109514 0.196037i
\(727\) 208.982 + 120.656i 0.287457 + 0.165964i 0.636795 0.771033i \(-0.280260\pi\)
−0.349337 + 0.936997i \(0.613593\pi\)
\(728\) −387.564 + 89.6670i −0.532369 + 0.123169i
\(729\) 679.707 + 263.514i 0.932382 + 0.361474i
\(730\) −80.2599 + 54.8363i −0.109945 + 0.0751183i
\(731\) 145.091 251.304i 0.198482 0.343782i
\(732\) 49.4458 + 548.330i 0.0675489 + 0.749085i
\(733\) −907.973 + 524.218i −1.23871 + 0.715168i −0.968830 0.247726i \(-0.920317\pi\)
−0.269878 + 0.962895i \(0.586983\pi\)
\(734\) 466.447 + 224.062i 0.635487 + 0.305262i
\(735\) 18.8481 305.383i 0.0256437 0.415487i
\(736\) −76.3331 + 96.6936i −0.103713 + 0.131377i
\(737\) 655.392 0.889271
\(738\) 407.874 + 19.3870i 0.552675 + 0.0262696i
\(739\) −166.542 −0.225362 −0.112681 0.993631i \(-0.535944\pi\)
−0.112681 + 0.993631i \(0.535944\pi\)
\(740\) 39.0454 + 48.7637i 0.0527641 + 0.0658968i
\(741\) −254.222 168.469i −0.343080 0.227354i
\(742\) 443.599 923.474i 0.597843 1.24457i
\(743\) 242.538 140.029i 0.326430 0.188465i −0.327825 0.944739i \(-0.606316\pi\)
0.654255 + 0.756274i \(0.272982\pi\)
\(744\) −1296.09 484.719i −1.74206 0.651503i
\(745\) 36.2476 62.7828i 0.0486545 0.0842722i
\(746\) −205.761 + 140.583i −0.275819 + 0.188449i
\(747\) 1.31498 + 3.10747i 0.00176034 + 0.00415993i
\(748\) 83.4280 213.811i 0.111535 0.285844i
\(749\) 112.586 + 65.0017i 0.150315 + 0.0867846i
\(750\) 467.745 278.948i 0.623659 0.371930i
\(751\) −189.292 + 109.288i −0.252053 + 0.145523i −0.620704 0.784045i \(-0.713153\pi\)
0.368651 + 0.929568i \(0.379820\pi\)
\(752\) 806.094 + 180.641i 1.07193 + 0.240214i
\(753\) −104.993 210.877i −0.139433 0.280049i
\(754\) 464.810 35.2940i 0.616459 0.0468090i
\(755\) 3.49413 0.00462799
\(756\) 920.579 + 573.252i 1.21770 + 0.758270i
\(757\) 1241.72i 1.64031i 0.572138 + 0.820157i \(0.306114\pi\)
−0.572138 + 0.820157i \(0.693886\pi\)
\(758\) −307.412 + 23.3424i −0.405556 + 0.0307947i
\(759\) −125.849 + 62.6586i −0.165808 + 0.0825542i
\(760\) 236.243 220.507i 0.310846 0.290140i
\(761\) −353.625 612.496i −0.464684 0.804857i 0.534503 0.845167i \(-0.320499\pi\)
−0.999187 + 0.0403097i \(0.987166\pi\)
\(762\) −579.542 + 345.620i −0.760554 + 0.453570i
\(763\) −590.902 + 1023.47i −0.774445 + 1.34138i
\(764\) −107.621 41.9933i −0.140865 0.0549650i
\(765\) 10.2653 82.8444i 0.0134187 0.108293i
\(766\) 657.244 449.052i 0.858021 0.586230i
\(767\) 143.318 + 82.7449i 0.186856 + 0.107881i
\(768\) 673.044 + 369.913i 0.876359 + 0.481658i
\(769\) −469.232 812.734i −0.610185 1.05687i −0.991209 0.132307i \(-0.957762\pi\)
0.381024 0.924565i \(-0.375572\pi\)
\(770\) 208.284 433.600i 0.270499 0.563117i
\(771\) −433.643 + 654.374i −0.562442 + 0.848734i
\(772\) −713.346 890.895i −0.924023 1.15401i
\(773\) 419.774i 0.543045i −0.962432 0.271522i \(-0.912473\pi\)
0.962432 0.271522i \(-0.0875271\pi\)
\(774\) 507.864 + 984.868i 0.656155 + 1.27244i
\(775\) 1218.18i 1.57184i
\(776\) 50.8305 166.537i 0.0655032 0.214610i
\(777\) −238.634 14.7284i −0.307122 0.0189554i
\(778\) −581.436 279.298i −0.747347 0.358995i
\(779\) 232.851 + 403.309i 0.298910 + 0.517727i
\(780\) −116.459 + 10.5017i −0.149306 + 0.0134637i
\(781\) −1397.53 806.866i −1.78941 1.03312i
\(782\) −29.9668 + 20.4743i −0.0383207 + 0.0261820i
\(783\) −964.947 826.924i −1.23237 1.05610i
\(784\) 610.129 + 561.651i 0.778225 + 0.716392i
\(785\) −32.3413 + 56.0168i −0.0411991 + 0.0713589i
\(786\) −521.954 + 934.328i −0.664064 + 1.18871i
\(787\) 43.1357 + 74.7132i 0.0548103 + 0.0949341i 0.892129 0.451781i \(-0.149211\pi\)
−0.837318 + 0.546715i \(0.815878\pi\)
\(788\) −115.938 759.027i −0.147129 0.963233i
\(789\) −58.7594 + 952.040i −0.0744733 + 1.20664i
\(790\) 382.082 29.0123i 0.483648 0.0367244i
\(791\) 295.025i 0.372978i
\(792\) 514.693 + 709.372i 0.649865 + 0.895672i
\(793\) 227.196 0.286502
\(794\) −43.4415 572.110i −0.0547122 0.720541i
\(795\) 166.351 251.026i 0.209246 0.315756i
\(796\) 20.4104 + 133.624i 0.0256413 + 0.167870i
\(797\) 865.089 499.459i 1.08543 0.626674i 0.153075 0.988215i \(-0.451082\pi\)
0.932356 + 0.361540i \(0.117749\pi\)
\(798\) 17.4948 + 1236.71i 0.0219233 + 1.54976i
\(799\) 210.765 + 121.685i 0.263786 + 0.152297i
\(800\) −97.4670 + 669.034i −0.121834 + 0.836292i
\(801\) 731.312 968.247i 0.912999 1.20880i
\(802\) 668.503 + 978.438i 0.833545 + 1.22000i
\(803\) 150.328 260.376i 0.187208 0.324253i
\(804\) −271.493 + 586.293i −0.337678 + 0.729220i
\(805\) −65.8760 + 38.0335i −0.0818336 + 0.0472466i
\(806\) −247.255 + 514.729i −0.306768 + 0.638622i
\(807\) 362.665 180.567i 0.449399 0.223751i
\(808\) −356.216 108.724i −0.440861 0.134560i
\(809\) 526.876 0.651268 0.325634 0.945496i \(-0.394422\pi\)
0.325634 + 0.945496i \(0.394422\pi\)
\(810\) 244.962 + 203.985i 0.302422 + 0.251834i
\(811\) 980.131 1.20855 0.604273 0.796777i \(-0.293464\pi\)
0.604273 + 0.796777i \(0.293464\pi\)
\(812\) −1181.60 1475.69i −1.45517 1.81736i
\(813\) −433.488 + 215.829i −0.533195 + 0.265472i
\(814\) −174.168 83.6632i −0.213966 0.102780i
\(815\) −44.4813 + 25.6813i −0.0545783 + 0.0315108i
\(816\) 156.709 + 163.202i 0.192045 + 0.200003i
\(817\) −631.889 + 1094.46i −0.773426 + 1.33961i
\(818\) 582.482 + 852.536i 0.712081 + 1.04222i
\(819\) 269.725 357.112i 0.329335 0.436034i
\(820\) 166.340 + 64.9051i 0.202854 + 0.0791526i
\(821\) 1151.54 + 664.844i 1.40261 + 0.809798i 0.994660 0.103205i \(-0.0329099\pi\)
0.407951 + 0.913004i \(0.366243\pi\)
\(822\) 768.802 10.8757i 0.935282 0.0132307i
\(823\) −354.999 + 204.959i −0.431347 + 0.249038i −0.699920 0.714221i \(-0.746781\pi\)
0.268573 + 0.963259i \(0.413448\pi\)
\(824\) 589.778 550.492i 0.715750 0.668073i
\(825\) −426.201 + 643.144i −0.516607 + 0.779569i
\(826\) −50.8150 669.216i −0.0615194 0.810189i
\(827\) 756.431 0.914668 0.457334 0.889295i \(-0.348804\pi\)
0.457334 + 0.889295i \(0.348804\pi\)
\(828\) −3.92032 138.536i −0.00473469 0.167314i
\(829\) 1028.26i 1.24036i −0.784460 0.620179i \(-0.787060\pi\)
0.784460 0.620179i \(-0.212940\pi\)
\(830\) 0.111714 + 1.47124i 0.000134595 + 0.00177258i
\(831\) 78.5159 1272.14i 0.0944836 1.53085i
\(832\) 176.979 262.911i 0.212715 0.315999i
\(833\) 122.156 + 211.580i 0.146646 + 0.253998i
\(834\) 563.687 1009.03i 0.675883 1.20987i
\(835\) 128.755 223.010i 0.154198 0.267078i
\(836\) −363.340 + 931.175i −0.434617 + 1.11385i
\(837\) 1468.31 517.206i 1.75425 0.617928i
\(838\) −351.774 514.865i −0.419778 0.614398i
\(839\) 140.269 + 80.9842i 0.167186 + 0.0965247i 0.581258 0.813719i \(-0.302561\pi\)
−0.414072 + 0.910244i \(0.635894\pi\)
\(840\) 301.605 + 365.941i 0.359053 + 0.435644i
\(841\) 687.130 + 1190.14i 0.817040 + 1.41515i
\(842\) 1181.29 + 567.442i 1.40295 + 0.673922i
\(843\) 482.352 + 29.7705i 0.572185 + 0.0353150i
\(844\) 648.474 + 809.877i 0.768334 + 0.959570i
\(845\) 284.294i 0.336443i
\(846\) −825.993 + 425.938i −0.976351 + 0.503472i
\(847\) 272.834i 0.322118i
\(848\) 243.660 + 778.995i 0.287335 + 0.918626i
\(849\) −604.491 + 912.187i −0.712004 + 1.07442i
\(850\) −86.2449 + 179.542i −0.101465 + 0.211226i
\(851\) 15.2773 + 26.4610i 0.0179521 + 0.0310940i
\(852\) 1300.72 915.948i 1.52666 1.07506i
\(853\) 64.6457 + 37.3232i 0.0757863 + 0.0437552i 0.537414 0.843318i \(-0.319401\pi\)
−0.461628 + 0.887074i \(0.652734\pi\)
\(854\) −519.790 760.778i −0.608653 0.890840i
\(855\) −44.7069 + 360.798i −0.0522888 + 0.421987i
\(856\) −100.908 + 23.3461i −0.117883 + 0.0272735i
\(857\) 619.475 1072.96i 0.722841 1.25200i −0.237015 0.971506i \(-0.576169\pi\)
0.959856 0.280492i \(-0.0904976\pi\)
\(858\) 310.628 185.248i 0.362037 0.215907i
\(859\) −59.7685 103.522i −0.0695792 0.120515i 0.829137 0.559046i \(-0.188832\pi\)
−0.898716 + 0.438531i \(0.855499\pi\)
\(860\) 73.1632 + 478.990i 0.0850735 + 0.556965i
\(861\) −611.746 + 304.582i −0.710507 + 0.353753i
\(862\) −31.0053 408.330i −0.0359690 0.473700i
\(863\) 1262.84i 1.46332i 0.681672 + 0.731658i \(0.261253\pi\)
−0.681672 + 0.731658i \(0.738747\pi\)
\(864\) −847.791 + 166.574i −0.981239 + 0.192794i
\(865\) −361.515 −0.417936
\(866\) −1119.68 + 85.0195i −1.29293 + 0.0981749i
\(867\) −356.714 716.452i −0.411435 0.826358i
\(868\) 2289.28 349.675i 2.63742 0.402852i
\(869\) −1026.41 + 592.596i −1.18114 + 0.681929i
\(870\) −284.623 477.262i −0.327153 0.548577i
\(871\) 230.904 + 133.313i 0.265103 + 0.153057i
\(872\) −212.230 917.312i −0.243383 1.05196i
\(873\) 76.3390 + 180.400i 0.0874445 + 0.206644i
\(874\) 130.509 89.1684i 0.149324 0.102023i
\(875\) −455.719 + 789.328i −0.520822 + 0.902090i
\(876\) 170.651 + 242.338i 0.194807 + 0.276641i
\(877\) 329.652 190.325i 0.375886 0.217018i −0.300141 0.953895i \(-0.597034\pi\)
0.676027 + 0.736877i \(0.263700\pi\)
\(878\) −544.452 261.533i −0.620104 0.297873i
\(879\) 1262.00 + 836.308i 1.43572 + 0.951431i
\(880\) 114.406 + 365.763i 0.130007 + 0.415640i
\(881\) −1191.72 −1.35268 −0.676342 0.736587i \(-0.736436\pi\)
−0.676342 + 0.736587i \(0.736436\pi\)
\(882\) −931.891 44.2944i −1.05657 0.0502204i
\(883\) 1390.74 1.57502 0.787509 0.616303i \(-0.211370\pi\)
0.787509 + 0.616303i \(0.211370\pi\)
\(884\) 72.8840 58.3588i 0.0824480 0.0660167i
\(885\) 12.1528 196.903i 0.0137319 0.222489i
\(886\) −395.455 + 823.248i −0.446338 + 0.929174i
\(887\) −1389.31 + 802.119i −1.56630 + 0.904306i −0.569709 + 0.821847i \(0.692944\pi\)
−0.996594 + 0.0824589i \(0.973723\pi\)
\(888\) 146.991 121.148i 0.165530 0.136428i
\(889\) 564.642 977.989i 0.635143 1.10010i
\(890\) 438.095 299.322i 0.492242 0.336317i
\(891\) −956.157 240.652i −1.07313 0.270092i
\(892\) −461.230 179.970i −0.517074 0.201760i
\(893\) −917.910 529.955i −1.02789 0.593455i
\(894\) −192.981 107.807i −0.215862 0.120589i
\(895\) 41.6334 24.0371i 0.0465178 0.0268570i
\(896\) −1285.27 + 8.87848i −1.43445 + 0.00990902i
\(897\) −57.0836 3.52317i −0.0636384 0.00392773i
\(898\) 834.877 63.3940i 0.929708 0.0705946i
\(899\) −2713.71 −3.01859
\(900\) −398.785 647.685i −0.443094 0.719650i
\(901\) 240.462i 0.266883i
\(902\) −550.689 + 41.8150i −0.610520 + 0.0463581i
\(903\) −1545.86 1024.42i −1.71192 1.13446i
\(904\) 160.382 + 171.827i 0.177413 + 0.190075i
\(905\) 100.014 + 173.229i 0.110512 + 0.191413i
\(906\) −0.150703 10.6532i −0.000166339 0.0117585i
\(907\) −321.020 + 556.023i −0.353936 + 0.613035i −0.986935 0.161117i \(-0.948490\pi\)
0.632999 + 0.774152i \(0.281824\pi\)
\(908\) −370.734 + 950.124i −0.408297 + 1.04639i
\(909\) 385.867 163.286i 0.424496 0.179632i
\(910\) 161.580 110.397i 0.177560 0.121315i
\(911\) 23.6696 + 13.6656i 0.0259820 + 0.0150007i 0.512935 0.858428i \(-0.328558\pi\)
−0.486953 + 0.873428i \(0.661892\pi\)
\(912\) −682.488 710.767i −0.748342 0.779349i
\(913\) −2.28184 3.95227i −0.00249928 0.00432888i
\(914\) 203.169 422.952i 0.222286 0.462748i
\(915\) −120.712 242.448i −0.131926 0.264971i
\(916\) −781.427 + 625.694i −0.853086 + 0.683072i
\(917\) 1791.12i 1.95323i
\(918\) −253.026 27.7247i −0.275627 0.0302012i
\(919\) 678.306i 0.738091i 0.929411 + 0.369046i \(0.120315\pi\)
−0.929411 + 0.369046i \(0.879685\pi\)
\(920\) 17.6914 57.9629i 0.0192298 0.0630031i
\(921\) 57.0089 + 114.501i 0.0618990 + 0.124323i
\(922\) −218.467 104.943i −0.236949 0.113821i
\(923\) −328.248 568.542i −0.355631 0.615971i
\(924\) −1330.98 616.332i −1.44045 0.667026i
\(925\) 145.221 + 83.8435i 0.156996 + 0.0906416i
\(926\) −408.022 + 278.775i −0.440628 + 0.301053i
\(927\) −111.610 + 900.729i −0.120399 + 0.971660i
\(928\) 1490.40 + 217.126i 1.60603 + 0.233972i
\(929\) −635.493 + 1100.71i −0.684062 + 1.18483i 0.289669 + 0.957127i \(0.406455\pi\)
−0.973731 + 0.227703i \(0.926879\pi\)
\(930\) 680.654 9.62871i 0.731886 0.0103534i
\(931\) −532.006 921.461i −0.571435 0.989754i
\(932\) 917.278 140.110i 0.984204 0.150332i
\(933\) 493.132 + 326.791i 0.528545 + 0.350258i
\(934\) −551.431 + 41.8713i −0.590398 + 0.0448301i
\(935\) 112.904i 0.120753i
\(936\) 37.0413 + 354.616i 0.0395740 + 0.378863i
\(937\) 1049.34 1.11990 0.559948 0.828528i \(-0.310821\pi\)
0.559948 + 0.828528i \(0.310821\pi\)
\(938\) −81.8695 1078.19i −0.0872809 1.14946i
\(939\) 437.719 + 27.0158i 0.466155 + 0.0287708i
\(940\) −401.721 + 61.3608i −0.427363 + 0.0652775i
\(941\) 1206.53 696.589i 1.28218 0.740265i 0.304931 0.952374i \(-0.401367\pi\)
0.977246 + 0.212109i \(0.0680333\pi\)
\(942\) 172.183 + 96.1888i 0.182785 + 0.102111i
\(943\) 75.6325 + 43.6665i 0.0802042 + 0.0463059i
\(944\) 393.395 + 362.138i 0.416732 + 0.383621i
\(945\) −524.394 98.0937i −0.554914 0.103803i
\(946\) −845.477 1237.46i −0.893739 1.30810i
\(947\) 751.624 1301.85i 0.793690 1.37471i −0.129978 0.991517i \(-0.541491\pi\)
0.923668 0.383194i \(-0.125176\pi\)
\(948\) −104.934 1163.67i −0.110690 1.22750i
\(949\) 105.925 61.1561i 0.111618 0.0644427i
\(950\) 375.608 781.931i 0.395377 0.823085i
\(951\) 13.0242 211.022i 0.0136953 0.221895i
\(952\) −362.164 110.540i −0.380425 0.116113i
\(953\) 788.992 0.827903 0.413951 0.910299i \(-0.364148\pi\)
0.413951 + 0.910299i \(0.364148\pi\)
\(954\) −772.524 496.357i −0.809773 0.520291i
\(955\) 56.8301 0.0595080
\(956\) −754.663 + 604.264i −0.789397 + 0.632076i
\(957\) 1432.72 + 949.442i 1.49710 + 0.992102i
\(958\) −1278.01 613.906i −1.33404 0.640820i
\(959\) −1114.38 + 643.386i −1.16202 + 0.670893i
\(960\) −374.592 49.1714i −0.390200 0.0512202i
\(961\) 1181.66 2046.69i 1.22961 2.12975i
\(962\) −44.3441 64.9031i −0.0460957 0.0674669i
\(963\) 70.2269 92.9794i 0.0729251 0.0965518i
\(964\) −335.886 + 860.815i −0.348429 + 0.892961i
\(965\) 486.224 + 280.721i 0.503859 + 0.290903i
\(966\) 118.801 + 199.208i 0.122982 + 0.206219i
\(967\) 396.835 229.113i 0.410377 0.236931i −0.280575 0.959832i \(-0.590525\pi\)
0.690952 + 0.722901i \(0.257192\pi\)
\(968\) −148.318 158.903i −0.153221 0.164156i
\(969\) −129.387 259.871i −0.133526 0.268185i
\(970\) 6.48541 + 85.4106i 0.00668599 + 0.0880522i
\(971\) −25.2266 −0.0259800 −0.0129900 0.999916i \(-0.504135\pi\)
−0.0129900 + 0.999916i \(0.504135\pi\)
\(972\) 611.362 755.659i 0.628973 0.777427i
\(973\) 1934.32i 1.98800i
\(974\) 30.9510 + 407.614i 0.0317772 + 0.418495i
\(975\) −280.978 + 139.896i −0.288183 + 0.143483i
\(976\) 716.308 + 160.520i 0.733922 + 0.164468i
\(977\) 736.113 + 1274.98i 0.753442 + 1.30500i 0.946145 + 0.323743i \(0.104941\pi\)
−0.192703 + 0.981257i \(0.561726\pi\)
\(978\) 80.2177 + 134.511i 0.0820222 + 0.137536i
\(979\) −820.559 + 1421.25i −0.838160 + 1.45174i
\(980\) −380.046 148.292i −0.387802 0.151318i
\(981\) 845.235 + 638.402i 0.861606 + 0.650767i
\(982\) 257.136 + 376.350i 0.261849 + 0.383249i
\(983\) 909.975 + 525.374i 0.925712 + 0.534460i 0.885453 0.464729i \(-0.153848\pi\)
0.0402592 + 0.999189i \(0.487182\pi\)
\(984\) 190.714 509.951i 0.193815 0.518243i
\(985\) 188.861 + 327.117i 0.191737 + 0.332099i
\(986\) 399.964 + 192.126i 0.405643 + 0.194854i
\(987\) 859.163 1296.49i 0.870479 1.31357i
\(988\) −317.420 + 254.160i −0.321275 + 0.257247i
\(989\) 236.996i 0.239632i
\(990\) −362.725 233.056i −0.366388 0.235410i
\(991\) 1021.63i 1.03091i −0.856917 0.515454i \(-0.827623\pi\)
0.856917 0.515454i \(-0.172377\pi\)
\(992\) −1143.22 + 1448.15i −1.15244 + 1.45983i
\(993\) 323.764 + 19.9826i 0.326046 + 0.0201234i
\(994\) −1152.81 + 2399.89i −1.15977 + 2.41437i
\(995\) −33.2484 57.5880i −0.0334155 0.0578774i
\(996\) 4.48081 0.404058i 0.00449881 0.000405681i
\(997\) −331.758 191.540i −0.332756 0.192117i 0.324308 0.945952i \(-0.394869\pi\)
−0.657064 + 0.753835i \(0.728202\pi\)
\(998\) −429.787 629.047i −0.430648 0.630308i
\(999\) −39.4021 + 210.638i −0.0394416 + 0.210849i
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 72.3.p.b.43.20 yes 40
3.2 odd 2 216.3.p.b.19.1 40
4.3 odd 2 288.3.t.b.79.5 40
8.3 odd 2 inner 72.3.p.b.43.8 40
8.5 even 2 288.3.t.b.79.6 40
9.2 odd 6 648.3.b.e.163.16 20
9.4 even 3 inner 72.3.p.b.67.8 yes 40
9.5 odd 6 216.3.p.b.91.13 40
9.7 even 3 648.3.b.f.163.5 20
12.11 even 2 864.3.t.b.559.13 40
24.5 odd 2 864.3.t.b.559.8 40
24.11 even 2 216.3.p.b.19.13 40
36.7 odd 6 2592.3.b.e.1135.8 20
36.11 even 6 2592.3.b.f.1135.13 20
36.23 even 6 864.3.t.b.847.8 40
36.31 odd 6 288.3.t.b.175.6 40
72.5 odd 6 864.3.t.b.847.13 40
72.11 even 6 648.3.b.e.163.15 20
72.13 even 6 288.3.t.b.175.5 40
72.29 odd 6 2592.3.b.f.1135.8 20
72.43 odd 6 648.3.b.f.163.6 20
72.59 even 6 216.3.p.b.91.1 40
72.61 even 6 2592.3.b.e.1135.13 20
72.67 odd 6 inner 72.3.p.b.67.20 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.p.b.43.8 40 8.3 odd 2 inner
72.3.p.b.43.20 yes 40 1.1 even 1 trivial
72.3.p.b.67.8 yes 40 9.4 even 3 inner
72.3.p.b.67.20 yes 40 72.67 odd 6 inner
216.3.p.b.19.1 40 3.2 odd 2
216.3.p.b.19.13 40 24.11 even 2
216.3.p.b.91.1 40 72.59 even 6
216.3.p.b.91.13 40 9.5 odd 6
288.3.t.b.79.5 40 4.3 odd 2
288.3.t.b.79.6 40 8.5 even 2
288.3.t.b.175.5 40 72.13 even 6
288.3.t.b.175.6 40 36.31 odd 6
648.3.b.e.163.15 20 72.11 even 6
648.3.b.e.163.16 20 9.2 odd 6
648.3.b.f.163.5 20 9.7 even 3
648.3.b.f.163.6 20 72.43 odd 6
864.3.t.b.559.8 40 24.5 odd 2
864.3.t.b.559.13 40 12.11 even 2
864.3.t.b.847.8 40 36.23 even 6
864.3.t.b.847.13 40 72.5 odd 6
2592.3.b.e.1135.8 20 36.7 odd 6
2592.3.b.e.1135.13 20 72.61 even 6
2592.3.b.f.1135.8 20 72.29 odd 6
2592.3.b.f.1135.13 20 36.11 even 6