Properties

Label 201.3.k.a.14.17
Level $201$
Weight $3$
Character 201.14
Analytic conductor $5.477$
Analytic rank $0$
Dimension $440$
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] = [201,3,Mod(14,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.14");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.k (of order \(22\), degree \(10\), 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: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(44\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 14.17
Character \(\chi\) \(=\) 201.14
Dual form 201.3.k.a.158.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.07136 + 0.489273i) q^{2} +(0.834932 + 2.88147i) q^{3} +(-1.71102 + 1.97463i) q^{4} +(-3.10066 + 0.445807i) q^{5} +(-2.30434 - 2.67858i) q^{6} +(-2.88988 - 6.32795i) q^{7} +(2.19428 - 7.47302i) q^{8} +(-7.60578 + 4.81167i) q^{9} +O(q^{10})\) \(q+(-1.07136 + 0.489273i) q^{2} +(0.834932 + 2.88147i) q^{3} +(-1.71102 + 1.97463i) q^{4} +(-3.10066 + 0.445807i) q^{5} +(-2.30434 - 2.67858i) q^{6} +(-2.88988 - 6.32795i) q^{7} +(2.19428 - 7.47302i) q^{8} +(-7.60578 + 4.81167i) q^{9} +(3.10379 - 1.99469i) q^{10} +(-14.0186 + 2.01557i) q^{11} +(-7.11842 - 3.28159i) q^{12} +(18.0465 - 5.29892i) q^{13} +(6.19219 + 5.36556i) q^{14} +(-3.87342 - 8.56224i) q^{15} +(-0.181872 - 1.26495i) q^{16} +(12.6691 - 10.9778i) q^{17} +(5.79430 - 8.87632i) q^{18} +(-6.46740 + 14.1616i) q^{19} +(4.42499 - 6.88542i) q^{20} +(15.8210 - 13.6105i) q^{21} +(14.0328 - 9.01830i) q^{22} +(5.69560 - 8.86252i) q^{23} +(23.3654 + 0.0832895i) q^{24} +(-14.5720 + 4.27872i) q^{25} +(-16.7416 + 14.5067i) q^{26} +(-20.2150 - 17.8984i) q^{27} +(17.4400 + 5.12084i) q^{28} -11.0751i q^{29} +(8.33909 + 7.27807i) q^{30} +(-44.3459 - 13.0211i) q^{31} +(17.6569 + 27.4747i) q^{32} +(-17.5124 - 38.7113i) q^{33} +(-8.20196 + 17.9598i) q^{34} +(11.7816 + 18.3325i) q^{35} +(3.51242 - 23.2514i) q^{36} -36.2777 q^{37} -18.3365i q^{38} +(30.3363 + 47.5762i) q^{39} +(-3.47218 + 24.1495i) q^{40} +(-36.8922 + 31.9673i) q^{41} +(-10.2907 + 22.3225i) q^{42} +(-53.5804 - 61.8350i) q^{43} +(20.0061 - 31.1301i) q^{44} +(21.4378 - 18.3100i) q^{45} +(-1.76583 + 12.2816i) q^{46} +(34.2391 - 53.2770i) q^{47} +(3.49307 - 1.58021i) q^{48} +(0.396630 - 0.457736i) q^{49} +(13.5184 - 11.7137i) q^{50} +(42.2100 + 27.3398i) q^{51} +(-20.4145 + 44.7016i) q^{52} +(-11.1364 - 9.64973i) q^{53} +(30.4147 + 9.28499i) q^{54} +(42.5682 - 12.4992i) q^{55} +(-53.6301 + 7.71085i) q^{56} +(-46.2062 - 6.81165i) q^{57} +(5.41874 + 11.8654i) q^{58} +(-21.9006 + 74.5866i) q^{59} +(23.5347 + 7.00164i) q^{60} +(-8.86818 + 61.6795i) q^{61} +(53.8812 - 7.74695i) q^{62} +(52.4277 + 34.2239i) q^{63} +(-28.0591 - 18.0325i) q^{64} +(-53.5936 + 24.4754i) q^{65} +(37.7024 + 32.9053i) q^{66} +(15.7827 + 65.1146i) q^{67} +43.7999i q^{68} +(30.2926 + 9.01211i) q^{69} +(-21.5919 - 13.8762i) q^{70} +(-57.4202 - 49.7549i) q^{71} +(19.2685 + 67.3963i) q^{72} +(-6.70035 + 46.6020i) q^{73} +(38.8664 - 17.7497i) q^{74} +(-24.4956 - 38.4164i) q^{75} +(-16.8981 - 37.0016i) q^{76} +(53.2664 + 82.8841i) q^{77} +(-55.7787 - 36.1284i) q^{78} +(-79.5693 + 23.3637i) q^{79} +(1.12785 + 3.84110i) q^{80} +(34.6957 - 73.1929i) q^{81} +(23.8840 - 52.2987i) q^{82} +(79.6924 - 11.4580i) q^{83} +(-0.194375 + 54.5284i) q^{84} +(-34.3884 + 39.6863i) q^{85} +(87.6580 + 40.0321i) q^{86} +(31.9125 - 9.24693i) q^{87} +(-15.6983 + 109.184i) q^{88} +(5.96776 + 9.28602i) q^{89} +(-14.0090 + 30.1056i) q^{90} +(-85.6834 - 98.8839i) q^{91} +(7.75486 + 26.4106i) q^{92} +(0.494250 - 138.653i) q^{93} +(-10.6153 + 73.8311i) q^{94} +(13.7398 - 46.7936i) q^{95} +(-64.4253 + 73.8174i) q^{96} +10.1703 q^{97} +(-0.200975 + 0.684459i) q^{98} +(96.9239 - 82.7827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9} - 34 q^{10} - 123 q^{12} + 10 q^{13} + 19 q^{15} - 226 q^{16} - 33 q^{18} - 100 q^{19} + 85 q^{21} - 454 q^{22} - 251 q^{24} + 142 q^{25} - 53 q^{27} + 642 q^{28} - 80 q^{30} - 130 q^{31} + 104 q^{33} + 26 q^{34} + 67 q^{36} - 144 q^{37} + 117 q^{39} - 182 q^{40} + 193 q^{42} - 156 q^{43} + 341 q^{45} - 746 q^{46} - 485 q^{48} - 354 q^{49} - 125 q^{51} + 1130 q^{52} + 272 q^{54} - 590 q^{55} + 15 q^{57} - 274 q^{58} - 217 q^{60} - 1134 q^{61} + 279 q^{63} + 58 q^{64} + 1288 q^{66} - 87 q^{69} + 1038 q^{70} - 977 q^{72} + 1208 q^{73} - 751 q^{75} + 1126 q^{76} - 11 q^{78} + 678 q^{79} + 125 q^{81} + 510 q^{82} + 191 q^{84} + 166 q^{85} + 1080 q^{87} + 62 q^{88} - 105 q^{90} + 550 q^{91} + 635 q^{93} + 986 q^{94} - 1632 q^{96} - 112 q^{97} - 500 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07136 + 0.489273i −0.535679 + 0.244636i −0.664838 0.746987i \(-0.731499\pi\)
0.129159 + 0.991624i \(0.458772\pi\)
\(3\) 0.834932 + 2.88147i 0.278311 + 0.960491i
\(4\) −1.71102 + 1.97463i −0.427756 + 0.493656i
\(5\) −3.10066 + 0.445807i −0.620131 + 0.0891614i −0.445218 0.895422i \(-0.646874\pi\)
−0.174914 + 0.984584i \(0.555965\pi\)
\(6\) −2.30434 2.67858i −0.384056 0.446430i
\(7\) −2.88988 6.32795i −0.412840 0.903993i −0.995805 0.0914960i \(-0.970835\pi\)
0.582966 0.812497i \(-0.301892\pi\)
\(8\) 2.19428 7.47302i 0.274285 0.934128i
\(9\) −7.60578 + 4.81167i −0.845086 + 0.534630i
\(10\) 3.10379 1.99469i 0.310379 0.199469i
\(11\) −14.0186 + 2.01557i −1.27442 + 0.183233i −0.746111 0.665821i \(-0.768081\pi\)
−0.528305 + 0.849055i \(0.677172\pi\)
\(12\) −7.11842 3.28159i −0.593201 0.273466i
\(13\) 18.0465 5.29892i 1.38819 0.407609i 0.499578 0.866269i \(-0.333489\pi\)
0.888612 + 0.458660i \(0.151670\pi\)
\(14\) 6.19219 + 5.36556i 0.442299 + 0.383254i
\(15\) −3.87342 8.56224i −0.258228 0.570816i
\(16\) −0.181872 1.26495i −0.0113670 0.0790594i
\(17\) 12.6691 10.9778i 0.745238 0.645753i −0.197112 0.980381i \(-0.563156\pi\)
0.942350 + 0.334628i \(0.108611\pi\)
\(18\) 5.79430 8.87632i 0.321905 0.493129i
\(19\) −6.46740 + 14.1616i −0.340390 + 0.745349i −0.999980 0.00627574i \(-0.998002\pi\)
0.659591 + 0.751625i \(0.270730\pi\)
\(20\) 4.42499 6.88542i 0.221250 0.344271i
\(21\) 15.8210 13.6105i 0.753379 0.648120i
\(22\) 14.0328 9.01830i 0.637852 0.409923i
\(23\) 5.69560 8.86252i 0.247635 0.385327i −0.695077 0.718935i \(-0.744630\pi\)
0.942712 + 0.333608i \(0.108266\pi\)
\(24\) 23.3654 + 0.0832895i 0.973558 + 0.00347039i
\(25\) −14.5720 + 4.27872i −0.582880 + 0.171149i
\(26\) −16.7416 + 14.5067i −0.643908 + 0.557950i
\(27\) −20.2150 17.8984i −0.748703 0.662905i
\(28\) 17.4400 + 5.12084i 0.622856 + 0.182887i
\(29\) 11.0751i 0.381899i −0.981600 0.190950i \(-0.938843\pi\)
0.981600 0.190950i \(-0.0611567\pi\)
\(30\) 8.33909 + 7.27807i 0.277970 + 0.242602i
\(31\) −44.3459 13.0211i −1.43051 0.420036i −0.527465 0.849577i \(-0.676857\pi\)
−0.903048 + 0.429541i \(0.858675\pi\)
\(32\) 17.6569 + 27.4747i 0.551778 + 0.858584i
\(33\) −17.5124 38.7113i −0.530677 1.17307i
\(34\) −8.20196 + 17.9598i −0.241234 + 0.528229i
\(35\) 11.7816 + 18.3325i 0.336616 + 0.523785i
\(36\) 3.51242 23.2514i 0.0975672 0.645873i
\(37\) −36.2777 −0.980478 −0.490239 0.871588i \(-0.663090\pi\)
−0.490239 + 0.871588i \(0.663090\pi\)
\(38\) 18.3365i 0.482540i
\(39\) 30.3363 + 47.5762i 0.777853 + 1.21990i
\(40\) −3.47218 + 24.1495i −0.0868044 + 0.603738i
\(41\) −36.8922 + 31.9673i −0.899809 + 0.779689i −0.976083 0.217398i \(-0.930243\pi\)
0.0762737 + 0.997087i \(0.475698\pi\)
\(42\) −10.2907 + 22.3225i −0.245016 + 0.531488i
\(43\) −53.5804 61.8350i −1.24606 1.43802i −0.855791 0.517321i \(-0.826929\pi\)
−0.390264 0.920703i \(-0.627616\pi\)
\(44\) 20.0061 31.1301i 0.454684 0.707503i
\(45\) 21.4378 18.3100i 0.476396 0.406890i
\(46\) −1.76583 + 12.2816i −0.0383877 + 0.266992i
\(47\) 34.2391 53.2770i 0.728491 1.13355i −0.257423 0.966299i \(-0.582873\pi\)
0.985914 0.167255i \(-0.0534904\pi\)
\(48\) 3.49307 1.58021i 0.0727723 0.0329210i
\(49\) 0.396630 0.457736i 0.00809450 0.00934155i
\(50\) 13.5184 11.7137i 0.270367 0.234275i
\(51\) 42.2100 + 27.3398i 0.827647 + 0.536075i
\(52\) −20.4145 + 44.7016i −0.392587 + 0.859646i
\(53\) −11.1364 9.64973i −0.210120 0.182070i 0.543442 0.839447i \(-0.317121\pi\)
−0.753562 + 0.657376i \(0.771666\pi\)
\(54\) 30.4147 + 9.28499i 0.563236 + 0.171944i
\(55\) 42.5682 12.4992i 0.773968 0.227257i
\(56\) −53.6301 + 7.71085i −0.957681 + 0.137694i
\(57\) −46.2062 6.81165i −0.810635 0.119503i
\(58\) 5.41874 + 11.8654i 0.0934265 + 0.204575i
\(59\) −21.9006 + 74.5866i −0.371197 + 1.26418i 0.536267 + 0.844049i \(0.319834\pi\)
−0.907463 + 0.420131i \(0.861984\pi\)
\(60\) 23.5347 + 7.00164i 0.392245 + 0.116694i
\(61\) −8.86818 + 61.6795i −0.145380 + 1.01114i 0.778277 + 0.627921i \(0.216094\pi\)
−0.923657 + 0.383219i \(0.874815\pi\)
\(62\) 53.8812 7.74695i 0.869052 0.124951i
\(63\) 52.4277 + 34.2239i 0.832186 + 0.543236i
\(64\) −28.0591 18.0325i −0.438424 0.281758i
\(65\) −53.5936 + 24.4754i −0.824517 + 0.376544i
\(66\) 37.7024 + 32.9053i 0.571248 + 0.498566i
\(67\) 15.7827 + 65.1146i 0.235563 + 0.971859i
\(68\) 43.7999i 0.644116i
\(69\) 30.2926 + 9.01211i 0.439022 + 0.130610i
\(70\) −21.5919 13.8762i −0.308455 0.198232i
\(71\) −57.4202 49.7549i −0.808735 0.700773i 0.148870 0.988857i \(-0.452436\pi\)
−0.957605 + 0.288084i \(0.906982\pi\)
\(72\) 19.2685 + 67.3963i 0.267618 + 0.936060i
\(73\) −6.70035 + 46.6020i −0.0917857 + 0.638383i 0.891051 + 0.453904i \(0.149969\pi\)
−0.982836 + 0.184480i \(0.940940\pi\)
\(74\) 38.8664 17.7497i 0.525221 0.239861i
\(75\) −24.4956 38.4164i −0.326609 0.512218i
\(76\) −16.8981 37.0016i −0.222343 0.486863i
\(77\) 53.2664 + 82.8841i 0.691771 + 1.07642i
\(78\) −55.7787 36.1284i −0.715112 0.463185i
\(79\) −79.5693 + 23.3637i −1.00721 + 0.295743i −0.743410 0.668836i \(-0.766793\pi\)
−0.263797 + 0.964578i \(0.584975\pi\)
\(80\) 1.12785 + 3.84110i 0.0140981 + 0.0480137i
\(81\) 34.6957 73.1929i 0.428342 0.903617i
\(82\) 23.8840 52.2987i 0.291269 0.637789i
\(83\) 79.6924 11.4580i 0.960149 0.138049i 0.355619 0.934631i \(-0.384270\pi\)
0.604530 + 0.796582i \(0.293361\pi\)
\(84\) −0.194375 + 54.5284i −0.00231398 + 0.649147i
\(85\) −34.3884 + 39.6863i −0.404569 + 0.466898i
\(86\) 87.6580 + 40.0321i 1.01928 + 0.465489i
\(87\) 31.9125 9.24693i 0.366811 0.106287i
\(88\) −15.6983 + 109.184i −0.178389 + 1.24073i
\(89\) 5.96776 + 9.28602i 0.0670535 + 0.104337i 0.873161 0.487432i \(-0.162066\pi\)
−0.806108 + 0.591769i \(0.798430\pi\)
\(90\) −14.0090 + 30.1056i −0.155655 + 0.334506i
\(91\) −85.6834 98.8839i −0.941575 1.08664i
\(92\) 7.75486 + 26.4106i 0.0842920 + 0.287072i
\(93\) 0.494250 138.653i 0.00531452 1.49089i
\(94\) −10.6153 + 73.8311i −0.112929 + 0.785437i
\(95\) 13.7398 46.7936i 0.144630 0.492564i
\(96\) −64.4253 + 73.8174i −0.671097 + 0.768931i
\(97\) 10.1703 0.104848 0.0524242 0.998625i \(-0.483305\pi\)
0.0524242 + 0.998625i \(0.483305\pi\)
\(98\) −0.200975 + 0.684459i −0.00205077 + 0.00698428i
\(99\) 96.9239 82.7827i 0.979030 0.836188i
\(100\) 16.4841 36.0952i 0.164841 0.360952i
\(101\) 83.6333 + 38.1940i 0.828052 + 0.378159i 0.783916 0.620867i \(-0.213219\pi\)
0.0441360 + 0.999026i \(0.485947\pi\)
\(102\) −58.5987 8.63853i −0.574497 0.0846915i
\(103\) 149.475 + 43.8898i 1.45121 + 0.426115i 0.909943 0.414733i \(-0.136125\pi\)
0.541271 + 0.840848i \(0.317943\pi\)
\(104\) 146.489i 1.40855i
\(105\) −42.9877 + 49.2546i −0.409407 + 0.469092i
\(106\) 16.6524 + 4.88959i 0.157098 + 0.0461282i
\(107\) −134.482 19.3356i −1.25684 0.180707i −0.518469 0.855096i \(-0.673498\pi\)
−0.738376 + 0.674389i \(0.764407\pi\)
\(108\) 69.9310 9.29241i 0.647509 0.0860408i
\(109\) 39.0668 11.4711i 0.358411 0.105239i −0.0975693 0.995229i \(-0.531107\pi\)
0.455981 + 0.889990i \(0.349289\pi\)
\(110\) −39.4903 + 34.2186i −0.359003 + 0.311078i
\(111\) −30.2894 104.533i −0.272877 0.941740i
\(112\) −7.47895 + 4.80643i −0.0667763 + 0.0429145i
\(113\) −207.413 29.8215i −1.83551 0.263907i −0.864449 0.502721i \(-0.832332\pi\)
−0.971065 + 0.238814i \(0.923241\pi\)
\(114\) 52.8362 15.3097i 0.463475 0.134296i
\(115\) −13.7091 + 30.0188i −0.119210 + 0.261033i
\(116\) 21.8691 + 18.9497i 0.188527 + 0.163360i
\(117\) −111.761 + 127.136i −0.955220 + 1.08663i
\(118\) −13.0298 90.6243i −0.110422 0.768003i
\(119\) −106.079 48.4446i −0.891420 0.407098i
\(120\) −72.4852 + 10.1582i −0.604043 + 0.0846517i
\(121\) 76.3593 22.4211i 0.631068 0.185298i
\(122\) −20.6771 70.4198i −0.169485 0.577212i
\(123\) −122.915 79.6134i −0.999311 0.647263i
\(124\) 101.589 65.2871i 0.819263 0.526509i
\(125\) 114.512 52.2958i 0.916094 0.418366i
\(126\) −72.9137 11.0145i −0.578680 0.0874169i
\(127\) −52.9963 116.046i −0.417293 0.913745i −0.995220 0.0976565i \(-0.968865\pi\)
0.577927 0.816089i \(-0.303862\pi\)
\(128\) −90.4230 13.0009i −0.706430 0.101569i
\(129\) 133.440 206.018i 1.03442 1.59704i
\(130\) 45.4428 52.4438i 0.349560 0.403414i
\(131\) −23.3430 + 36.3225i −0.178191 + 0.277271i −0.918847 0.394614i \(-0.870878\pi\)
0.740656 + 0.671884i \(0.234515\pi\)
\(132\) 106.404 + 31.6556i 0.806093 + 0.239815i
\(133\) 108.304 0.814317
\(134\) −48.7677 62.0390i −0.363938 0.462977i
\(135\) 70.6590 + 46.4849i 0.523400 + 0.344333i
\(136\) −54.2379 118.764i −0.398808 0.873268i
\(137\) −40.6843 + 63.3060i −0.296966 + 0.462088i −0.957387 0.288807i \(-0.906741\pi\)
0.660421 + 0.750895i \(0.270378\pi\)
\(138\) −36.8636 + 5.16613i −0.267127 + 0.0374357i
\(139\) 5.16340 + 35.9122i 0.0371467 + 0.258361i 0.999929 0.0119170i \(-0.00379340\pi\)
−0.962782 + 0.270278i \(0.912884\pi\)
\(140\) −56.3583 8.10310i −0.402559 0.0578793i
\(141\) 182.104 + 54.1763i 1.29152 + 0.384229i
\(142\) 85.8613 + 25.2112i 0.604657 + 0.177543i
\(143\) −242.305 + 110.657i −1.69444 + 0.773826i
\(144\) 7.46980 + 8.74582i 0.0518736 + 0.0607349i
\(145\) 4.93735 + 34.3400i 0.0340507 + 0.236828i
\(146\) −15.6226 53.2057i −0.107004 0.364423i
\(147\) 1.65011 + 0.760702i 0.0112253 + 0.00517484i
\(148\) 62.0719 71.6348i 0.419405 0.484019i
\(149\) 78.8478 + 36.0086i 0.529180 + 0.241668i 0.662043 0.749466i \(-0.269690\pi\)
−0.132863 + 0.991134i \(0.542417\pi\)
\(150\) 45.0397 + 29.1726i 0.300265 + 0.194484i
\(151\) −64.9100 74.9101i −0.429868 0.496094i 0.498950 0.866631i \(-0.333719\pi\)
−0.928818 + 0.370537i \(0.879174\pi\)
\(152\) 91.6390 + 79.4056i 0.602888 + 0.522405i
\(153\) −43.5365 + 144.454i −0.284552 + 0.944143i
\(154\) −97.6203 62.7368i −0.633898 0.407382i
\(155\) 143.306 + 20.6043i 0.924557 + 0.132931i
\(156\) −145.851 21.5012i −0.934943 0.137828i
\(157\) 86.6991 + 55.7181i 0.552224 + 0.354893i 0.786803 0.617204i \(-0.211735\pi\)
−0.234579 + 0.972097i \(0.575371\pi\)
\(158\) 73.8161 63.9620i 0.467190 0.404823i
\(159\) 18.5073 40.1460i 0.116398 0.252491i
\(160\) −66.9964 77.3180i −0.418728 0.483238i
\(161\) −72.5412 10.4298i −0.450566 0.0647816i
\(162\) −1.36024 + 95.3915i −0.00839652 + 0.588837i
\(163\) −135.601 −0.831907 −0.415953 0.909386i \(-0.636552\pi\)
−0.415953 + 0.909386i \(0.636552\pi\)
\(164\) 127.545i 0.777713i
\(165\) 71.5576 + 112.223i 0.433682 + 0.680141i
\(166\) −79.7730 + 51.2670i −0.480560 + 0.308837i
\(167\) 28.3551 + 12.9493i 0.169791 + 0.0775409i 0.498497 0.866891i \(-0.333885\pi\)
−0.328706 + 0.944432i \(0.606613\pi\)
\(168\) −66.9961 148.096i −0.398786 0.881522i
\(169\) 155.425 99.8853i 0.919672 0.591037i
\(170\) 17.4249 59.3436i 0.102499 0.349080i
\(171\) −18.9514 138.829i −0.110827 0.811867i
\(172\) 213.778 1.24290
\(173\) 21.2279 72.2954i 0.122704 0.417893i −0.875114 0.483918i \(-0.839213\pi\)
0.997818 + 0.0660248i \(0.0210317\pi\)
\(174\) −29.6655 + 25.5207i −0.170491 + 0.146671i
\(175\) 69.1868 + 79.8459i 0.395353 + 0.456262i
\(176\) 5.09918 + 17.3662i 0.0289726 + 0.0986717i
\(177\) −233.205 0.831294i −1.31754 0.00469657i
\(178\) −10.9370 7.02879i −0.0614439 0.0394876i
\(179\) −8.71419 13.5596i −0.0486826 0.0757517i 0.816059 0.577968i \(-0.196154\pi\)
−0.864742 + 0.502217i \(0.832518\pi\)
\(180\) −0.525155 + 73.6606i −0.00291753 + 0.409225i
\(181\) 54.6568 + 35.1258i 0.301971 + 0.194065i 0.682848 0.730561i \(-0.260741\pi\)
−0.380876 + 0.924626i \(0.624378\pi\)
\(182\) 140.179 + 64.0175i 0.770213 + 0.351745i
\(183\) −185.132 + 25.9448i −1.01165 + 0.141775i
\(184\) −53.7321 62.0102i −0.292022 0.337012i
\(185\) 112.485 16.1728i 0.608025 0.0874208i
\(186\) 67.3097 + 148.789i 0.361880 + 0.799941i
\(187\) −155.476 + 179.428i −0.831420 + 0.959510i
\(188\) 46.6184 + 158.768i 0.247970 + 0.844508i
\(189\) −54.8415 + 179.644i −0.290167 + 0.950496i
\(190\) 8.17455 + 56.8552i 0.0430239 + 0.299238i
\(191\) 91.4550 + 142.307i 0.478822 + 0.745062i 0.993684 0.112211i \(-0.0357933\pi\)
−0.514862 + 0.857273i \(0.672157\pi\)
\(192\) 28.5328 95.9076i 0.148608 0.499519i
\(193\) 264.337 + 77.6164i 1.36962 + 0.402157i 0.882145 0.470978i \(-0.156099\pi\)
0.487477 + 0.873136i \(0.337917\pi\)
\(194\) −10.8960 + 4.97605i −0.0561651 + 0.0256497i
\(195\) −115.272 133.993i −0.591139 0.687145i
\(196\) 0.225213 + 1.56639i 0.00114905 + 0.00799180i
\(197\) 86.3760 + 74.8452i 0.438457 + 0.379925i 0.845932 0.533291i \(-0.179045\pi\)
−0.407475 + 0.913216i \(0.633591\pi\)
\(198\) −63.3369 + 136.112i −0.319884 + 0.687435i
\(199\) −82.9720 181.683i −0.416945 0.912982i −0.995267 0.0971737i \(-0.969020\pi\)
0.578323 0.815808i \(-0.303708\pi\)
\(200\) 118.286i 0.591428i
\(201\) −174.448 + 99.8436i −0.867903 + 0.496735i
\(202\) −108.288 −0.536082
\(203\) −70.0825 + 32.0056i −0.345234 + 0.157663i
\(204\) −126.208 + 36.5699i −0.618668 + 0.179264i
\(205\) 100.139 115.566i 0.488482 0.563738i
\(206\) −181.615 + 26.1124i −0.881629 + 0.126759i
\(207\) −0.675950 + 94.8117i −0.00326546 + 0.458027i
\(208\) −9.98502 21.8641i −0.0480049 0.105116i
\(209\) 62.1200 211.561i 0.297225 1.01226i
\(210\) 21.9563 73.8021i 0.104554 0.351438i
\(211\) 167.642 107.737i 0.794512 0.510602i −0.0793084 0.996850i \(-0.525271\pi\)
0.873821 + 0.486248i \(0.161635\pi\)
\(212\) 38.1092 5.47928i 0.179760 0.0258456i
\(213\) 95.4255 206.997i 0.448007 0.971816i
\(214\) 153.539 45.0832i 0.717473 0.210669i
\(215\) 193.701 + 167.843i 0.900934 + 0.780664i
\(216\) −178.113 + 111.793i −0.824596 + 0.517560i
\(217\) 45.7571 + 318.248i 0.210862 + 1.46658i
\(218\) −36.2421 + 31.4040i −0.166248 + 0.144055i
\(219\) −139.877 + 19.6026i −0.638707 + 0.0895095i
\(220\) −48.1541 + 105.443i −0.218882 + 0.479285i
\(221\) 170.461 265.243i 0.771317 1.20019i
\(222\) 83.5960 + 97.1727i 0.376559 + 0.437715i
\(223\) −122.505 + 78.7291i −0.549349 + 0.353045i −0.785686 0.618626i \(-0.787690\pi\)
0.236337 + 0.971671i \(0.424053\pi\)
\(224\) 122.832 191.131i 0.548358 0.853261i
\(225\) 90.2436 102.659i 0.401083 0.456260i
\(226\) 236.805 69.5321i 1.04781 0.307664i
\(227\) −145.170 + 125.791i −0.639517 + 0.554144i −0.913116 0.407699i \(-0.866331\pi\)
0.273600 + 0.961844i \(0.411786\pi\)
\(228\) 92.5103 79.5851i 0.405747 0.349057i
\(229\) −283.089 83.1224i −1.23620 0.362980i −0.402611 0.915371i \(-0.631897\pi\)
−0.833585 + 0.552391i \(0.813715\pi\)
\(230\) 38.8684i 0.168993i
\(231\) −194.355 + 222.688i −0.841362 + 0.964018i
\(232\) −82.7643 24.3018i −0.356743 0.104749i
\(233\) −142.825 222.240i −0.612982 0.953818i −0.999503 0.0315377i \(-0.989960\pi\)
0.386521 0.922281i \(-0.373677\pi\)
\(234\) 57.5316 190.890i 0.245862 0.815768i
\(235\) −82.4123 + 180.458i −0.350691 + 0.767906i
\(236\) −109.808 170.865i −0.465289 0.724004i
\(237\) −133.757 209.770i −0.564374 0.885105i
\(238\) 137.351 0.577106
\(239\) 412.584i 1.72629i 0.504953 + 0.863147i \(0.331510\pi\)
−0.504953 + 0.863147i \(0.668490\pi\)
\(240\) −10.1263 + 6.45691i −0.0421931 + 0.0269038i
\(241\) 7.68845 53.4743i 0.0319023 0.221885i −0.967633 0.252361i \(-0.918793\pi\)
0.999536 + 0.0304755i \(0.00970215\pi\)
\(242\) −70.8381 + 61.3816i −0.292719 + 0.253643i
\(243\) 239.872 + 38.8637i 0.987128 + 0.159933i
\(244\) −106.620 123.046i −0.436969 0.504289i
\(245\) −1.02575 + 1.59610i −0.00418675 + 0.00651470i
\(246\) 170.639 + 25.1553i 0.693654 + 0.102257i
\(247\) −41.6724 + 289.838i −0.168714 + 1.17343i
\(248\) −194.614 + 302.826i −0.784735 + 1.22107i
\(249\) 99.5537 + 220.065i 0.399814 + 0.883794i
\(250\) −97.0962 + 112.055i −0.388385 + 0.448220i
\(251\) 296.262 256.712i 1.18033 1.02276i 0.181099 0.983465i \(-0.442035\pi\)
0.999228 0.0392939i \(-0.0125109\pi\)
\(252\) −157.284 + 44.9674i −0.624144 + 0.178442i
\(253\) −61.9811 + 135.720i −0.244985 + 0.536442i
\(254\) 113.556 + 98.3968i 0.447071 + 0.387389i
\(255\) −143.067 65.9539i −0.561047 0.258643i
\(256\) 231.248 67.9005i 0.903312 0.265236i
\(257\) 297.214 42.7329i 1.15648 0.166276i 0.462732 0.886498i \(-0.346869\pi\)
0.693743 + 0.720222i \(0.255960\pi\)
\(258\) −42.1629 + 286.008i −0.163422 + 1.10856i
\(259\) 104.838 + 229.563i 0.404780 + 0.886345i
\(260\) 43.3702 147.705i 0.166808 0.568097i
\(261\) 53.2896 + 84.2346i 0.204175 + 0.322738i
\(262\) 7.23715 50.3355i 0.0276227 0.192120i
\(263\) −135.096 + 19.4238i −0.513671 + 0.0738548i −0.394276 0.918992i \(-0.629005\pi\)
−0.119395 + 0.992847i \(0.538096\pi\)
\(264\) −327.717 + 45.9269i −1.24135 + 0.173966i
\(265\) 38.8320 + 24.9558i 0.146536 + 0.0941729i
\(266\) −116.032 + 52.9903i −0.436212 + 0.199212i
\(267\) −21.7748 + 24.9491i −0.0815534 + 0.0934425i
\(268\) −155.581 80.2476i −0.580528 0.299431i
\(269\) 498.332i 1.85254i 0.376864 + 0.926268i \(0.377002\pi\)
−0.376864 + 0.926268i \(0.622998\pi\)
\(270\) −98.4449 15.2305i −0.364611 0.0564091i
\(271\) −194.260 124.843i −0.716827 0.460677i 0.130705 0.991421i \(-0.458276\pi\)
−0.847532 + 0.530745i \(0.821912\pi\)
\(272\) −16.1905 14.0292i −0.0595239 0.0515778i
\(273\) 213.392 329.456i 0.781654 1.20680i
\(274\) 12.6136 87.7292i 0.0460349 0.320179i
\(275\) 195.655 89.3524i 0.711471 0.324918i
\(276\) −69.6268 + 44.3965i −0.252271 + 0.160857i
\(277\) −24.7106 54.1088i −0.0892081 0.195338i 0.859769 0.510683i \(-0.170607\pi\)
−0.948977 + 0.315344i \(0.897880\pi\)
\(278\) −23.1027 35.9485i −0.0831033 0.129311i
\(279\) 399.938 114.342i 1.43347 0.409827i
\(280\) 162.851 47.8174i 0.581611 0.170776i
\(281\) −129.793 442.035i −0.461898 1.57308i −0.780478 0.625183i \(-0.785024\pi\)
0.318580 0.947896i \(-0.396794\pi\)
\(282\) −221.605 + 31.0562i −0.785834 + 0.110128i
\(283\) 94.8727 207.742i 0.335239 0.734072i −0.664675 0.747132i \(-0.731430\pi\)
0.999915 + 0.0130607i \(0.00415746\pi\)
\(284\) 196.495 28.2516i 0.691882 0.0994776i
\(285\) 146.306 + 0.521531i 0.513355 + 0.00182993i
\(286\) 205.454 237.107i 0.718372 0.829045i
\(287\) 308.901 + 141.070i 1.07631 + 0.491535i
\(288\) −266.494 124.007i −0.925325 0.430581i
\(289\) −1.13611 + 7.90183i −0.00393118 + 0.0273420i
\(290\) −22.0913 34.3748i −0.0761769 0.118534i
\(291\) 8.49150 + 29.3054i 0.0291804 + 0.100706i
\(292\) −80.5570 92.9677i −0.275880 0.318383i
\(293\) −37.8235 128.815i −0.129090 0.439642i 0.869428 0.494060i \(-0.164488\pi\)
−0.998518 + 0.0544184i \(0.982670\pi\)
\(294\) −2.14005 0.00762854i −0.00727909 2.59474e-5i
\(295\) 34.6550 241.031i 0.117475 0.817054i
\(296\) −79.6033 + 271.104i −0.268930 + 0.915892i
\(297\) 319.461 + 210.166i 1.07563 + 0.707629i
\(298\) −102.092 −0.342591
\(299\) 55.8236 190.118i 0.186701 0.635845i
\(300\) 117.771 + 17.3616i 0.392569 + 0.0578719i
\(301\) −236.448 + 517.749i −0.785542 + 1.72010i
\(302\) 106.193 + 48.4969i 0.351634 + 0.160586i
\(303\) −40.2270 + 272.876i −0.132762 + 0.900582i
\(304\) 19.0900 + 5.60533i 0.0627961 + 0.0184386i
\(305\) 195.201i 0.640002i
\(306\) −24.0342 176.063i −0.0785431 0.575370i
\(307\) −0.923969 0.271302i −0.00300967 0.000883719i 0.280227 0.959934i \(-0.409590\pi\)
−0.283237 + 0.959050i \(0.591408\pi\)
\(308\) −254.805 36.6354i −0.827289 0.118946i
\(309\) −1.66595 + 467.354i −0.00539143 + 1.51247i
\(310\) −163.613 + 48.0413i −0.527785 + 0.154972i
\(311\) −118.149 + 102.376i −0.379899 + 0.329185i −0.823789 0.566897i \(-0.808144\pi\)
0.443889 + 0.896082i \(0.353598\pi\)
\(312\) 422.104 122.308i 1.35290 0.392014i
\(313\) 313.496 201.472i 1.00158 0.643679i 0.0663826 0.997794i \(-0.478854\pi\)
0.935202 + 0.354115i \(0.115218\pi\)
\(314\) −120.147 17.2746i −0.382634 0.0550145i
\(315\) −177.818 82.7438i −0.564501 0.262679i
\(316\) 90.0104 197.095i 0.284843 0.623720i
\(317\) −167.468 145.112i −0.528292 0.457767i 0.349413 0.936969i \(-0.386381\pi\)
−0.877705 + 0.479201i \(0.840926\pi\)
\(318\) −0.185597 + 52.0659i −0.000583638 + 0.163729i
\(319\) 22.3226 + 155.257i 0.0699767 + 0.486699i
\(320\) 95.0408 + 43.4037i 0.297003 + 0.135637i
\(321\) −56.5684 403.651i −0.176226 1.25748i
\(322\) 82.8206 24.3183i 0.257207 0.0755227i
\(323\) 73.5277 + 250.412i 0.227640 + 0.775270i
\(324\) 85.1634 + 193.746i 0.262850 + 0.597981i
\(325\) −240.300 + 154.432i −0.739386 + 0.475174i
\(326\) 145.277 66.3458i 0.445635 0.203515i
\(327\) 65.6717 + 102.993i 0.200831 + 0.314962i
\(328\) 157.940 + 345.841i 0.481526 + 1.05439i
\(329\) −436.081 62.6990i −1.32547 0.190574i
\(330\) −131.572 85.2202i −0.398702 0.258243i
\(331\) 46.6451 53.8313i 0.140922 0.162632i −0.680901 0.732375i \(-0.738412\pi\)
0.821823 + 0.569743i \(0.192957\pi\)
\(332\) −113.730 + 176.968i −0.342561 + 0.533035i
\(333\) 275.920 174.556i 0.828588 0.524192i
\(334\) −36.7142 −0.109923
\(335\) −77.9653 194.862i −0.232732 0.581677i
\(336\) −20.0940 17.5374i −0.0598036 0.0521945i
\(337\) 164.838 + 360.944i 0.489133 + 1.07105i 0.979850 + 0.199733i \(0.0640075\pi\)
−0.490717 + 0.871319i \(0.663265\pi\)
\(338\) −117.644 + 183.058i −0.348060 + 0.541591i
\(339\) −87.2459 622.554i −0.257362 1.83644i
\(340\) −19.5263 135.808i −0.0574303 0.399437i
\(341\) 647.911 + 93.1555i 1.90003 + 0.273183i
\(342\) 88.2292 + 139.463i 0.257980 + 0.407788i
\(343\) −331.109 97.2222i −0.965331 0.283447i
\(344\) −579.665 + 264.724i −1.68507 + 0.769547i
\(345\) −97.9445 14.4388i −0.283897 0.0418517i
\(346\) 12.6296 + 87.8405i 0.0365016 + 0.253874i
\(347\) 34.0598 + 115.997i 0.0981549 + 0.334285i 0.993900 0.110283i \(-0.0351756\pi\)
−0.895745 + 0.444567i \(0.853357\pi\)
\(348\) −36.3439 + 78.8370i −0.104436 + 0.226543i
\(349\) 236.113 272.488i 0.676540 0.780769i −0.308844 0.951113i \(-0.599942\pi\)
0.985385 + 0.170343i \(0.0544877\pi\)
\(350\) −113.190 51.6923i −0.323401 0.147692i
\(351\) −459.652 215.886i −1.30955 0.615059i
\(352\) −302.902 349.567i −0.860516 0.993089i
\(353\) −480.739 416.563i −1.36187 1.18006i −0.965019 0.262179i \(-0.915559\pi\)
−0.396847 0.917885i \(-0.629896\pi\)
\(354\) 250.253 113.210i 0.706928 0.319803i
\(355\) 200.221 + 128.675i 0.564004 + 0.362463i
\(356\) −28.5474 4.10450i −0.0801893 0.0115295i
\(357\) 51.0233 346.112i 0.142922 0.969500i
\(358\) 15.9703 + 10.2635i 0.0446099 + 0.0286690i
\(359\) −470.099 + 407.343i −1.30947 + 1.13466i −0.327659 + 0.944796i \(0.606260\pi\)
−0.981810 + 0.189865i \(0.939195\pi\)
\(360\) −89.7908 200.383i −0.249419 0.556619i
\(361\) 77.6801 + 89.6476i 0.215180 + 0.248331i
\(362\) −75.7432 10.8902i −0.209235 0.0300835i
\(363\) 128.361 + 201.307i 0.353610 + 0.554565i
\(364\) 341.865 0.939189
\(365\) 147.484i 0.404065i
\(366\) 185.649 118.376i 0.507237 0.323433i
\(367\) −217.254 + 139.621i −0.591972 + 0.380438i −0.802059 0.597245i \(-0.796262\pi\)
0.210086 + 0.977683i \(0.432626\pi\)
\(368\) −12.2465 5.59280i −0.0332786 0.0151978i
\(369\) 126.778 420.649i 0.343572 1.13997i
\(370\) −112.598 + 72.3626i −0.304320 + 0.195575i
\(371\) −28.8802 + 98.3570i −0.0778442 + 0.265113i
\(372\) 272.942 + 238.215i 0.733716 + 0.640362i
\(373\) 421.221 1.12928 0.564639 0.825338i \(-0.309015\pi\)
0.564639 + 0.825338i \(0.309015\pi\)
\(374\) 78.7806 268.302i 0.210643 0.717385i
\(375\) 246.298 + 286.299i 0.656796 + 0.763465i
\(376\) −323.011 372.774i −0.859071 0.991420i
\(377\) −58.6860 199.866i −0.155666 0.530149i
\(378\) −29.1399 219.295i −0.0770896 0.580146i
\(379\) −308.308 198.137i −0.813477 0.522790i 0.0665112 0.997786i \(-0.478813\pi\)
−0.879988 + 0.474996i \(0.842450\pi\)
\(380\) 68.8906 + 107.196i 0.181291 + 0.282094i
\(381\) 290.134 249.598i 0.761507 0.655112i
\(382\) −167.608 107.715i −0.438764 0.281977i
\(383\) −402.238 183.696i −1.05023 0.479623i −0.185909 0.982567i \(-0.559523\pi\)
−0.864319 + 0.502944i \(0.832250\pi\)
\(384\) −38.0354 271.406i −0.0990504 0.706787i
\(385\) −202.111 233.249i −0.524964 0.605840i
\(386\) −321.175 + 46.1780i −0.832060 + 0.119632i
\(387\) 705.050 + 212.493i 1.82183 + 0.549077i
\(388\) −17.4016 + 20.0825i −0.0448495 + 0.0517591i
\(389\) −130.080 443.013i −0.334397 1.13885i −0.939456 0.342671i \(-0.888669\pi\)
0.605059 0.796181i \(-0.293150\pi\)
\(390\) 189.057 + 87.1553i 0.484762 + 0.223475i
\(391\) −25.1331 174.805i −0.0642791 0.447071i
\(392\) −2.55035 3.96843i −0.00650600 0.0101235i
\(393\) −124.152 36.9356i −0.315909 0.0939836i
\(394\) −129.159 37.9246i −0.327816 0.0962554i
\(395\) 236.302 107.915i 0.598232 0.273203i
\(396\) −2.37431 + 333.031i −0.00599574 + 0.840989i
\(397\) 56.5548 + 393.347i 0.142455 + 0.990799i 0.928156 + 0.372192i \(0.121394\pi\)
−0.785700 + 0.618607i \(0.787697\pi\)
\(398\) 177.786 + 154.052i 0.446697 + 0.387065i
\(399\) 90.4265 + 312.075i 0.226633 + 0.782144i
\(400\) 8.06261 + 17.6547i 0.0201565 + 0.0441367i
\(401\) 588.165i 1.46675i −0.679827 0.733373i \(-0.737945\pi\)
0.679827 0.733373i \(-0.262055\pi\)
\(402\) 138.046 192.321i 0.343398 0.478411i
\(403\) −869.284 −2.15703
\(404\) −218.517 + 99.7935i −0.540884 + 0.247014i
\(405\) −74.9496 + 242.414i −0.185061 + 0.598553i
\(406\) 59.4240 68.5790i 0.146365 0.168914i
\(407\) 508.561 73.1201i 1.24954 0.179656i
\(408\) 296.932 255.445i 0.727774 0.626092i
\(409\) 58.4847 + 128.064i 0.142994 + 0.313114i 0.967555 0.252659i \(-0.0813051\pi\)
−0.824561 + 0.565773i \(0.808578\pi\)
\(410\) −50.7410 + 172.808i −0.123759 + 0.421483i
\(411\) −216.383 64.3746i −0.526480 0.156629i
\(412\) −342.421 + 220.061i −0.831120 + 0.534128i
\(413\) 535.270 76.9602i 1.29605 0.186344i
\(414\) −45.6646 101.908i −0.110301 0.246155i
\(415\) −241.991 + 71.0549i −0.583110 + 0.171217i
\(416\) 464.231 + 402.258i 1.11594 + 0.966967i
\(417\) −99.1690 + 44.8624i −0.237815 + 0.107584i
\(418\) 36.9585 + 257.052i 0.0884174 + 0.614956i
\(419\) −556.900 + 482.556i −1.32912 + 1.15169i −0.352712 + 0.935732i \(0.614741\pi\)
−0.976404 + 0.215954i \(0.930714\pi\)
\(420\) −23.7064 169.160i −0.0564439 0.402763i
\(421\) −115.650 + 253.237i −0.274702 + 0.601514i −0.995824 0.0912943i \(-0.970900\pi\)
0.721122 + 0.692808i \(0.243627\pi\)
\(422\) −126.892 + 197.448i −0.300692 + 0.467886i
\(423\) −4.06347 + 569.960i −0.00960631 + 1.34742i
\(424\) −96.5490 + 62.0483i −0.227710 + 0.146340i
\(425\) −137.642 + 214.176i −0.323865 + 0.503943i
\(426\) −0.956954 + 268.457i −0.00224637 + 0.630180i
\(427\) 415.933 122.129i 0.974082 0.286016i
\(428\) 268.283 232.469i 0.626830 0.543151i
\(429\) −521.164 605.805i −1.21483 1.41213i
\(430\) −289.644 85.0471i −0.673590 0.197784i
\(431\) 11.5510i 0.0268005i 0.999910 + 0.0134002i \(0.00426556\pi\)
−0.999910 + 0.0134002i \(0.995734\pi\)
\(432\) −18.9641 + 28.8262i −0.0438983 + 0.0667273i
\(433\) 172.394 + 50.6194i 0.398138 + 0.116904i 0.474671 0.880163i \(-0.342567\pi\)
−0.0765331 + 0.997067i \(0.524385\pi\)
\(434\) −204.732 318.570i −0.471734 0.734032i
\(435\) −94.8275 + 42.8984i −0.217994 + 0.0986170i
\(436\) −44.1932 + 96.7696i −0.101361 + 0.221949i
\(437\) 88.6721 + 137.976i 0.202911 + 0.315736i
\(438\) 140.267 89.4393i 0.320244 0.204199i
\(439\) 289.491 0.659432 0.329716 0.944080i \(-0.393047\pi\)
0.329716 + 0.944080i \(0.393047\pi\)
\(440\) 345.540i 0.785318i
\(441\) −0.814210 + 5.38989i −0.00184628 + 0.0122220i
\(442\) −52.8489 + 367.572i −0.119568 + 0.831611i
\(443\) 528.226 457.710i 1.19238 1.03321i 0.193745 0.981052i \(-0.437937\pi\)
0.998639 0.0521545i \(-0.0166088\pi\)
\(444\) 258.240 + 119.048i 0.581621 + 0.268127i
\(445\) −22.6438 26.1323i −0.0508849 0.0587243i
\(446\) 92.7265 144.285i 0.207907 0.323510i
\(447\) −37.9252 + 257.262i −0.0848440 + 0.575531i
\(448\) −33.0214 + 229.669i −0.0737084 + 0.512653i
\(449\) 14.2905 22.2365i 0.0318274 0.0495245i −0.824975 0.565169i \(-0.808811\pi\)
0.856803 + 0.515644i \(0.172447\pi\)
\(450\) −46.4551 + 154.138i −0.103234 + 0.342529i
\(451\) 452.744 522.494i 1.00387 1.15852i
\(452\) 413.775 358.538i 0.915431 0.793225i
\(453\) 161.656 249.581i 0.356857 0.550952i
\(454\) 93.9833 205.795i 0.207012 0.453293i
\(455\) 309.758 + 268.407i 0.680787 + 0.589905i
\(456\) −152.293 + 330.353i −0.333976 + 0.724459i
\(457\) −318.226 + 93.4395i −0.696336 + 0.204463i −0.610698 0.791864i \(-0.709111\pi\)
−0.0856381 + 0.996326i \(0.527293\pi\)
\(458\) 343.959 49.4539i 0.751002 0.107978i
\(459\) −452.590 4.84014i −0.986035 0.0105450i
\(460\) −35.8192 78.4332i −0.0778679 0.170507i
\(461\) −157.514 + 536.445i −0.341680 + 1.16365i 0.592117 + 0.805852i \(0.298292\pi\)
−0.933797 + 0.357803i \(0.883526\pi\)
\(462\) 99.2680 333.671i 0.214866 0.722232i
\(463\) 72.7707 506.131i 0.157172 1.09316i −0.746641 0.665227i \(-0.768335\pi\)
0.903813 0.427928i \(-0.140756\pi\)
\(464\) −14.0094 + 2.01425i −0.0301927 + 0.00434106i
\(465\) 60.2801 + 430.136i 0.129635 + 0.925025i
\(466\) 261.752 + 168.218i 0.561700 + 0.360983i
\(467\) −167.722 + 76.5962i −0.359148 + 0.164017i −0.586814 0.809722i \(-0.699618\pi\)
0.227666 + 0.973739i \(0.426891\pi\)
\(468\) −59.8207 438.218i −0.127822 0.936364i
\(469\) 366.432 288.045i 0.781304 0.614169i
\(470\) 233.657i 0.497143i
\(471\) −88.1625 + 296.342i −0.187181 + 0.629176i
\(472\) 509.331 + 327.327i 1.07909 + 0.693490i
\(473\) 875.753 + 758.844i 1.85149 + 1.60432i
\(474\) 245.936 + 159.295i 0.518853 + 0.336066i
\(475\) 33.6492 234.036i 0.0708405 0.492706i
\(476\) 277.163 126.576i 0.582276 0.265917i
\(477\) 131.132 + 19.8092i 0.274910 + 0.0415286i
\(478\) −201.866 442.025i −0.422314 0.924739i
\(479\) −108.055 168.137i −0.225585 0.351017i 0.709949 0.704253i \(-0.248718\pi\)
−0.935534 + 0.353236i \(0.885081\pi\)
\(480\) 166.852 257.604i 0.347609 0.536674i
\(481\) −654.684 + 192.233i −1.36109 + 0.399652i
\(482\) 17.9265 + 61.0519i 0.0371918 + 0.126664i
\(483\) −30.5136 217.734i −0.0631751 0.450794i
\(484\) −86.3792 + 189.144i −0.178469 + 0.390793i
\(485\) −31.5346 + 4.53399i −0.0650198 + 0.00934843i
\(486\) −276.004 + 75.7259i −0.567909 + 0.155815i
\(487\) −472.155 + 544.896i −0.969517 + 1.11888i 0.0233589 + 0.999727i \(0.492564\pi\)
−0.992876 + 0.119155i \(0.961982\pi\)
\(488\) 441.473 + 201.614i 0.904659 + 0.413144i
\(489\) −113.217 390.730i −0.231528 0.799039i
\(490\) 0.318019 2.21187i 0.000649018 0.00451402i
\(491\) 158.941 + 247.317i 0.323709 + 0.503701i 0.964524 0.263994i \(-0.0850400\pi\)
−0.640815 + 0.767695i \(0.721404\pi\)
\(492\) 367.517 106.491i 0.746987 0.216446i
\(493\) −121.580 140.311i −0.246613 0.284606i
\(494\) −97.1637 330.909i −0.196688 0.669857i
\(495\) −263.623 + 299.890i −0.532571 + 0.605838i
\(496\) −8.40578 + 58.4635i −0.0169471 + 0.117870i
\(497\) −148.909 + 507.138i −0.299616 + 1.02040i
\(498\) −214.329 187.059i −0.430380 0.375621i
\(499\) −878.697 −1.76092 −0.880458 0.474125i \(-0.842765\pi\)
−0.880458 + 0.474125i \(0.842765\pi\)
\(500\) −92.6677 + 315.597i −0.185335 + 0.631194i
\(501\) −13.6386 + 92.5162i −0.0272228 + 0.184663i
\(502\) −191.800 + 419.984i −0.382072 + 0.836621i
\(503\) −295.248 134.835i −0.586974 0.268062i 0.0997116 0.995016i \(-0.468208\pi\)
−0.686686 + 0.726954i \(0.740935\pi\)
\(504\) 370.797 316.697i 0.735708 0.628367i
\(505\) −276.345 81.1423i −0.547218 0.160678i
\(506\) 175.730i 0.347293i
\(507\) 417.586 + 364.454i 0.823640 + 0.718845i
\(508\) 319.824 + 93.9089i 0.629576 + 0.184860i
\(509\) −25.7116 3.69677i −0.0505139 0.00726280i 0.117012 0.993131i \(-0.462669\pi\)
−0.167525 + 0.985868i \(0.553578\pi\)
\(510\) 185.546 + 0.661405i 0.363815 + 0.00129687i
\(511\) 314.258 92.2745i 0.614987 0.180576i
\(512\) 61.6319 53.4043i 0.120375 0.104305i
\(513\) 384.210 170.521i 0.748947 0.332400i
\(514\) −297.515 + 191.201i −0.578822 + 0.371987i
\(515\) −483.037 69.4503i −0.937937 0.134855i
\(516\) 178.490 + 615.996i 0.345911 + 1.19379i
\(517\) −372.600 + 815.879i −0.720696 + 1.57810i
\(518\) −224.638 194.650i −0.433664 0.375772i
\(519\) 226.041 + 0.805758i 0.435532 + 0.00155252i
\(520\) 65.3058 + 454.212i 0.125588 + 0.873485i
\(521\) −183.344 83.7303i −0.351907 0.160711i 0.231615 0.972807i \(-0.425599\pi\)
−0.583523 + 0.812097i \(0.698326\pi\)
\(522\) −98.3059 64.1723i −0.188326 0.122935i
\(523\) 536.540 157.542i 1.02589 0.301228i 0.274851 0.961487i \(-0.411372\pi\)
0.751038 + 0.660259i \(0.229553\pi\)
\(524\) −31.7828 108.242i −0.0606542 0.206569i
\(525\) −172.307 + 266.026i −0.328205 + 0.506716i
\(526\) 135.232 86.9084i 0.257095 0.165225i
\(527\) −704.764 + 321.855i −1.33731 + 0.610730i
\(528\) −45.7828 + 29.1928i −0.0867099 + 0.0552893i
\(529\) 173.650 + 380.241i 0.328261 + 0.718791i
\(530\) −53.8132 7.73717i −0.101534 0.0145984i
\(531\) −192.315 672.668i −0.362175 1.26679i
\(532\) −185.311 + 213.860i −0.348328 + 0.401993i
\(533\) −496.382 + 772.385i −0.931298 + 1.44913i
\(534\) 11.1216 37.3833i 0.0208270 0.0700061i
\(535\) 425.604 0.795521
\(536\) 521.234 + 24.9349i 0.972452 + 0.0465204i
\(537\) 31.7957 36.4310i 0.0592099 0.0678417i
\(538\) −243.821 533.893i −0.453198 0.992365i
\(539\) −4.63759 + 7.21624i −0.00860407 + 0.0133882i
\(540\) −212.689 + 59.9883i −0.393869 + 0.111089i
\(541\) 69.3803 + 482.551i 0.128245 + 0.891961i 0.947778 + 0.318930i \(0.103323\pi\)
−0.819534 + 0.573031i \(0.805768\pi\)
\(542\) 269.205 + 38.7058i 0.496688 + 0.0714129i
\(543\) −55.5794 + 186.820i −0.102356 + 0.344051i
\(544\) 525.308 + 154.244i 0.965639 + 0.283537i
\(545\) −116.019 + 52.9841i −0.212879 + 0.0972185i
\(546\) −67.4250 + 457.372i −0.123489 + 0.837677i
\(547\) −84.7080 589.157i −0.154859 1.07707i −0.907927 0.419127i \(-0.862336\pi\)
0.753068 0.657942i \(-0.228573\pi\)
\(548\) −55.3939 188.654i −0.101084 0.344260i
\(549\) −229.332 511.792i −0.417727 0.932225i
\(550\) −165.898 + 191.457i −0.301633 + 0.348104i
\(551\) 156.841 + 71.6270i 0.284648 + 0.129995i
\(552\) 133.818 206.602i 0.242424 0.374279i
\(553\) 377.790 + 435.993i 0.683164 + 0.788413i
\(554\) 52.9479 + 45.8796i 0.0955738 + 0.0828152i
\(555\) 140.519 + 310.618i 0.253187 + 0.559672i
\(556\) −79.7478 51.2508i −0.143431 0.0921777i
\(557\) 89.9006 + 12.9258i 0.161402 + 0.0232060i 0.222542 0.974923i \(-0.428565\pi\)
−0.0611403 + 0.998129i \(0.519474\pi\)
\(558\) −372.533 + 318.180i −0.667621 + 0.570215i
\(559\) −1294.60 831.986i −2.31591 1.48835i
\(560\) 21.0469 18.2373i 0.0375838 0.0325665i
\(561\) −646.830 298.188i −1.15299 0.531530i
\(562\) 355.331 + 410.074i 0.632261 + 0.729669i
\(563\) −428.605 61.6240i −0.761287 0.109457i −0.249273 0.968433i \(-0.580192\pi\)
−0.512014 + 0.858977i \(0.671101\pi\)
\(564\) −418.561 + 266.890i −0.742130 + 0.473209i
\(565\) 656.411 1.16179
\(566\) 268.985i 0.475238i
\(567\) −563.428 8.03420i −0.993699 0.0141697i
\(568\) −497.815 + 319.927i −0.876436 + 0.563251i
\(569\) 678.033 + 309.647i 1.19162 + 0.544196i 0.909710 0.415244i \(-0.136304\pi\)
0.281913 + 0.959440i \(0.409031\pi\)
\(570\) −157.002 + 71.0250i −0.275441 + 0.124605i
\(571\) 625.872 402.224i 1.09610 0.704420i 0.137878 0.990449i \(-0.455972\pi\)
0.958221 + 0.286029i \(0.0923355\pi\)
\(572\) 196.084 667.799i 0.342803 1.16748i
\(573\) −333.695 + 382.342i −0.582364 + 0.667263i
\(574\) −399.966 −0.696804
\(575\) −45.0759 + 153.514i −0.0783929 + 0.266982i
\(576\) 300.178 + 2.14009i 0.521143 + 0.00371543i
\(577\) −435.873 503.024i −0.755412 0.871792i 0.239669 0.970855i \(-0.422961\pi\)
−0.995081 + 0.0990628i \(0.968416\pi\)
\(578\) −2.64897 9.02156i −0.00458299 0.0156082i
\(579\) −2.94613 + 826.485i −0.00508831 + 1.42743i
\(580\) −76.2566 49.0071i −0.131477 0.0844951i
\(581\) −302.807 471.177i −0.521183 0.810976i
\(582\) −23.4358 27.2420i −0.0402677 0.0468075i
\(583\) 175.566 + 112.829i 0.301142 + 0.193532i
\(584\) 333.555 + 152.330i 0.571156 + 0.260838i
\(585\) 289.854 444.029i 0.495476 0.759024i
\(586\) 103.548 + 119.501i 0.176703 + 0.203927i
\(587\) 745.149 107.136i 1.26942 0.182515i 0.525505 0.850790i \(-0.323876\pi\)
0.743914 + 0.668276i \(0.232967\pi\)
\(588\) −4.32548 + 1.95678i −0.00735626 + 0.00332785i
\(589\) 471.203 543.797i 0.800005 0.923255i
\(590\) 80.8020 + 275.186i 0.136952 + 0.466417i
\(591\) −143.546 + 311.381i −0.242887 + 0.526871i
\(592\) 6.59791 + 45.8894i 0.0111451 + 0.0775159i
\(593\) 353.324 + 549.782i 0.595824 + 0.927120i 0.999923 + 0.0124048i \(0.00394869\pi\)
−0.404099 + 0.914715i \(0.632415\pi\)
\(594\) −445.086 68.8594i −0.749302 0.115925i
\(595\) 350.511 + 102.919i 0.589095 + 0.172974i
\(596\) −206.014 + 94.0833i −0.345661 + 0.157858i
\(597\) 454.240 390.775i 0.760871 0.654564i
\(598\) 33.2124 + 230.997i 0.0555391 + 0.386283i
\(599\) −310.696 269.220i −0.518691 0.449448i 0.355749 0.934581i \(-0.384226\pi\)
−0.874440 + 0.485133i \(0.838771\pi\)
\(600\) −340.837 + 98.7604i −0.568061 + 0.164601i
\(601\) 195.816 + 428.777i 0.325817 + 0.713440i 0.999677 0.0254193i \(-0.00809210\pi\)
−0.673860 + 0.738859i \(0.735365\pi\)
\(602\) 670.383i 1.11359i
\(603\) −433.349 419.306i −0.718656 0.695366i
\(604\) 258.982 0.428778
\(605\) −226.768 + 103.562i −0.374824 + 0.171176i
\(606\) −90.4135 312.030i −0.149197 0.514902i
\(607\) −190.740 + 220.126i −0.314235 + 0.362646i −0.890793 0.454410i \(-0.849850\pi\)
0.576558 + 0.817056i \(0.304395\pi\)
\(608\) −503.281 + 72.3609i −0.827765 + 0.119015i
\(609\) −150.737 175.218i −0.247516 0.287715i
\(610\) 95.5064 + 209.130i 0.156568 + 0.342836i
\(611\) 335.584 1142.89i 0.549237 1.87053i
\(612\) −210.750 333.132i −0.344363 0.544334i
\(613\) 466.885 300.049i 0.761639 0.489476i −0.101255 0.994861i \(-0.532286\pi\)
0.862894 + 0.505385i \(0.168649\pi\)
\(614\) 1.12264 0.161412i 0.00182841 0.000262885i
\(615\) 416.610 + 192.057i 0.677415 + 0.312288i
\(616\) 736.276 216.190i 1.19525 0.350958i
\(617\) −102.875 89.1418i −0.166734 0.144476i 0.567497 0.823375i \(-0.307912\pi\)
−0.734231 + 0.678899i \(0.762457\pi\)
\(618\) −226.879 501.518i −0.367117 0.811518i
\(619\) 44.6258 + 310.379i 0.0720934 + 0.501421i 0.993591 + 0.113036i \(0.0360576\pi\)
−0.921497 + 0.388384i \(0.873033\pi\)
\(620\) −285.886 + 247.722i −0.461107 + 0.399551i
\(621\) −273.762 + 77.2135i −0.440840 + 0.124337i
\(622\) 76.4895 167.489i 0.122974 0.269275i
\(623\) 41.5154 64.5992i 0.0666378 0.103690i
\(624\) 54.6641 47.0266i 0.0876028 0.0753632i
\(625\) −12.3411 + 7.93116i −0.0197458 + 0.0126898i
\(626\) −237.292 + 369.233i −0.379060 + 0.589830i
\(627\) 661.475 + 2.35793i 1.05498 + 0.00376065i
\(628\) −258.367 + 75.8633i −0.411412 + 0.120801i
\(629\) −459.604 + 398.249i −0.730690 + 0.633146i
\(630\) 230.991 + 1.64682i 0.366652 + 0.00261401i
\(631\) −288.415 84.6862i −0.457076 0.134210i 0.0450862 0.998983i \(-0.485644\pi\)
−0.502162 + 0.864774i \(0.667462\pi\)
\(632\) 645.890i 1.02198i
\(633\) 450.411 + 393.103i 0.711550 + 0.621016i
\(634\) 250.418 + 73.5294i 0.394981 + 0.115977i
\(635\) 216.057 + 336.192i 0.340248 + 0.529436i
\(636\) 47.6070 + 105.236i 0.0748537 + 0.165465i
\(637\) 4.73227 10.3622i 0.00742899 0.0162672i
\(638\) −99.8784 155.414i −0.156549 0.243595i
\(639\) 676.129 + 102.138i 1.05811 + 0.159840i
\(640\) 286.167 0.447135
\(641\) 49.6705i 0.0774891i 0.999249 + 0.0387445i \(0.0123359\pi\)
−0.999249 + 0.0387445i \(0.987664\pi\)
\(642\) 258.101 + 404.778i 0.402026 + 0.630495i
\(643\) 14.1569 98.4637i 0.0220170 0.153132i −0.975847 0.218454i \(-0.929899\pi\)
0.997864 + 0.0653226i \(0.0208076\pi\)
\(644\) 144.715 125.396i 0.224712 0.194714i
\(645\) −321.907 + 698.281i −0.499081 + 1.08261i
\(646\) −201.294 232.306i −0.311601 0.359607i
\(647\) 548.960 854.198i 0.848470 1.32024i −0.0972497 0.995260i \(-0.531005\pi\)
0.945719 0.324985i \(-0.105359\pi\)
\(648\) −470.841 419.888i −0.726606 0.647975i
\(649\) 156.681 1089.74i 0.241419 1.67911i
\(650\) 181.889 283.024i 0.279829 0.435422i
\(651\) −878.819 + 397.563i −1.34995 + 0.610696i
\(652\) 232.016 267.761i 0.355853 0.410676i
\(653\) 852.415 738.622i 1.30538 1.13112i 0.322565 0.946547i \(-0.395455\pi\)
0.982819 0.184574i \(-0.0590904\pi\)
\(654\) −120.749 78.2105i −0.184632 0.119588i
\(655\) 56.1859 123.030i 0.0857800 0.187832i
\(656\) 47.1467 + 40.8528i 0.0718699 + 0.0622756i
\(657\) −173.272 386.684i −0.263732 0.588561i
\(658\) 497.876 146.190i 0.756651 0.222173i
\(659\) −231.232 + 33.2461i −0.350883 + 0.0504494i −0.315503 0.948925i \(-0.602173\pi\)
−0.0353800 + 0.999374i \(0.511264\pi\)
\(660\) −344.036 50.7172i −0.521266 0.0768443i
\(661\) −388.032 849.672i −0.587038 1.28543i −0.937216 0.348750i \(-0.886606\pi\)
0.350178 0.936683i \(-0.386121\pi\)
\(662\) −23.6354 + 80.4948i −0.0357031 + 0.121593i
\(663\) 906.613 + 269.720i 1.36744 + 0.406817i
\(664\) 89.2411 620.685i 0.134399 0.934767i
\(665\) −335.814 + 48.2827i −0.504983 + 0.0726056i
\(666\) −210.204 + 322.012i −0.315621 + 0.483502i
\(667\) −98.1531 63.0792i −0.147156 0.0945715i
\(668\) −74.0863 + 33.8341i −0.110908 + 0.0506498i
\(669\) −329.139 287.261i −0.491986 0.429389i
\(670\) 178.869 + 170.621i 0.266969 + 0.254658i
\(671\) 882.534i 1.31525i
\(672\) 653.294 + 194.357i 0.972164 + 0.289221i
\(673\) −516.842 332.154i −0.767967 0.493542i 0.0970535 0.995279i \(-0.469058\pi\)
−0.865020 + 0.501737i \(0.832695\pi\)
\(674\) −353.201 306.050i −0.524037 0.454080i
\(675\) 371.155 + 174.322i 0.549860 + 0.258254i
\(676\) −68.6989 + 477.811i −0.101626 + 0.706821i
\(677\) 287.023 131.079i 0.423963 0.193618i −0.191996 0.981396i \(-0.561496\pi\)
0.615959 + 0.787778i \(0.288769\pi\)
\(678\) 398.070 + 624.291i 0.587125 + 0.920784i
\(679\) −29.3909 64.3571i −0.0432856 0.0947822i
\(680\) 221.119 + 344.068i 0.325175 + 0.505983i
\(681\) −483.670 313.278i −0.710235 0.460026i
\(682\) −739.723 + 217.202i −1.08464 + 0.318478i
\(683\) −55.2167 188.051i −0.0808443 0.275330i 0.909144 0.416483i \(-0.136737\pi\)
−0.989988 + 0.141152i \(0.954919\pi\)
\(684\) 306.562 + 200.118i 0.448190 + 0.292570i
\(685\) 97.9258 214.428i 0.142957 0.313033i
\(686\) 402.304 57.8426i 0.586449 0.0843186i
\(687\) 3.15512 885.115i 0.00459261 1.28838i
\(688\) −68.4734 + 79.0226i −0.0995253 + 0.114858i
\(689\) −252.105 115.133i −0.365901 0.167101i
\(690\) 111.998 32.4524i 0.162316 0.0470325i
\(691\) 151.815 1055.89i 0.219703 1.52807i −0.519433 0.854511i \(-0.673857\pi\)
0.739136 0.673556i \(-0.235234\pi\)
\(692\) 106.435 + 165.616i 0.153808 + 0.239330i
\(693\) −803.943 374.098i −1.16009 0.539824i
\(694\) −93.2443 107.610i −0.134358 0.155057i
\(695\) −32.0198 109.050i −0.0460717 0.156906i
\(696\) 0.922437 258.774i 0.00132534 0.371801i
\(697\) −116.459 + 809.990i −0.167086 + 1.16211i
\(698\) −119.640 + 407.456i −0.171404 + 0.583748i
\(699\) 521.129 597.101i 0.745535 0.854221i
\(700\) −276.046 −0.394351
\(701\) −10.4627 + 35.6326i −0.0149254 + 0.0508311i −0.966619 0.256218i \(-0.917523\pi\)
0.951694 + 0.307049i \(0.0993416\pi\)
\(702\) 598.079 + 6.39604i 0.851964 + 0.00911117i
\(703\) 234.622 513.751i 0.333744 0.730798i
\(704\) 429.695 + 196.235i 0.610362 + 0.278743i
\(705\) −588.793 86.7990i −0.835168 0.123119i
\(706\) 718.856 + 211.075i 1.01821 + 0.298973i
\(707\) 639.603i 0.904672i
\(708\) 400.660 459.070i 0.565904 0.648404i
\(709\) −56.9999 16.7367i −0.0803947 0.0236060i 0.241288 0.970454i \(-0.422430\pi\)
−0.321683 + 0.946848i \(0.604248\pi\)
\(710\) −277.466 39.8936i −0.390797 0.0561881i
\(711\) 492.769 560.560i 0.693064 0.788411i
\(712\) 82.4896 24.2211i 0.115856 0.0340184i
\(713\) −367.976 + 318.853i −0.516096 + 0.447199i
\(714\) 114.679 + 395.774i 0.160615 + 0.554305i
\(715\) 701.974 451.131i 0.981782 0.630953i
\(716\) 41.6852 + 5.99343i 0.0582196 + 0.00837071i
\(717\) −1188.85 + 344.480i −1.65809 + 0.480446i
\(718\) 304.343 666.418i 0.423876 0.928158i
\(719\) 263.105 + 227.982i 0.365932 + 0.317082i 0.818346 0.574726i \(-0.194891\pi\)
−0.452414 + 0.891808i \(0.649437\pi\)
\(720\) −27.0602 23.7877i −0.0375837 0.0330385i
\(721\) −154.232 1072.71i −0.213914 1.48780i
\(722\) −127.085 58.0379i −0.176019 0.0803850i
\(723\) 160.504 22.4934i 0.221998 0.0311111i
\(724\) −162.879 + 47.8257i −0.224972 + 0.0660576i
\(725\) 47.3872 + 161.386i 0.0653617 + 0.222601i
\(726\) −236.014 152.869i −0.325089 0.210563i
\(727\) 299.677 192.591i 0.412211 0.264912i −0.318058 0.948071i \(-0.603031\pi\)
0.730270 + 0.683159i \(0.239394\pi\)
\(728\) −926.975 + 423.335i −1.27332 + 0.581504i
\(729\) 88.2920 + 723.634i 0.121114 + 0.992639i
\(730\) 72.1599 + 158.008i 0.0988491 + 0.216449i
\(731\) −1357.62 195.197i −1.85722 0.267027i
\(732\) 265.534 409.959i 0.362752 0.560053i
\(733\) −78.3726 + 90.4468i −0.106920 + 0.123393i −0.806687 0.590979i \(-0.798742\pi\)
0.699767 + 0.714371i \(0.253287\pi\)
\(734\) 164.444 255.880i 0.224038 0.348610i
\(735\) −5.45556 1.62304i −0.00742253 0.00220822i
\(736\) 344.062 0.467475
\(737\) −352.494 881.002i −0.478282 1.19539i
\(738\) 69.9874 + 512.695i 0.0948339 + 0.694708i
\(739\) 530.404 + 1161.42i 0.717731 + 1.57161i 0.817056 + 0.576558i \(0.195604\pi\)
−0.0993250 + 0.995055i \(0.531668\pi\)
\(740\) −160.528 + 249.787i −0.216930 + 0.337550i
\(741\) −869.953 + 121.917i −1.17403 + 0.164530i
\(742\) −17.1823 119.506i −0.0231568 0.161059i
\(743\) −918.611 132.076i −1.23635 0.177761i −0.507030 0.861929i \(-0.669257\pi\)
−0.729325 + 0.684168i \(0.760166\pi\)
\(744\) −1035.07 307.937i −1.39123 0.413894i
\(745\) −260.533 76.4993i −0.349708 0.102684i
\(746\) −451.278 + 206.092i −0.604931 + 0.276263i
\(747\) −550.990 + 470.600i −0.737604 + 0.629987i
\(748\) −88.2816 614.012i −0.118024 0.820872i
\(749\) 266.283 + 906.875i 0.355518 + 1.21078i
\(750\) −403.952 186.222i −0.538603 0.248296i
\(751\) −340.463 + 392.915i −0.453346 + 0.523189i −0.935704 0.352785i \(-0.885235\pi\)
0.482359 + 0.875974i \(0.339780\pi\)
\(752\) −73.6199 33.6211i −0.0978988 0.0447089i
\(753\) 987.069 + 639.334i 1.31085 + 0.849049i
\(754\) 160.663 + 185.415i 0.213081 + 0.245908i
\(755\) 234.659 + 203.333i 0.310807 + 0.269316i
\(756\) −260.894 415.666i −0.345098 0.549823i
\(757\) 46.2761 + 29.7399i 0.0611310 + 0.0392865i 0.570849 0.821055i \(-0.306614\pi\)
−0.509718 + 0.860341i \(0.670250\pi\)
\(758\) 427.251 + 61.4294i 0.563656 + 0.0810415i
\(759\) −442.823 65.2803i −0.583429 0.0860083i
\(760\) −319.541 205.356i −0.420448 0.270206i
\(761\) −430.025 + 372.619i −0.565079 + 0.489644i −0.889915 0.456127i \(-0.849236\pi\)
0.324836 + 0.945770i \(0.394691\pi\)
\(762\) −188.716 + 409.363i −0.247659 + 0.537222i
\(763\) −185.487 214.063i −0.243102 0.280554i
\(764\) −437.484 62.9007i −0.572623 0.0823308i
\(765\) 70.5932 467.311i 0.0922787 0.610864i
\(766\) 520.818 0.679919
\(767\) 1462.07i 1.90622i
\(768\) 388.730 + 609.643i 0.506159 + 0.793806i
\(769\) 201.820 129.702i 0.262445 0.168663i −0.402801 0.915288i \(-0.631963\pi\)
0.665246 + 0.746625i \(0.268327\pi\)
\(770\) 330.656 + 151.005i 0.429423 + 0.196111i
\(771\) 371.287 + 820.736i 0.481566 + 1.06451i
\(772\) −605.550 + 389.163i −0.784391 + 0.504098i
\(773\) 7.30959 24.8942i 0.00945613 0.0322046i −0.954630 0.297795i \(-0.903749\pi\)
0.964086 + 0.265591i \(0.0855669\pi\)
\(774\) −859.328 + 117.306i −1.11024 + 0.151558i
\(775\) 701.922 0.905705
\(776\) 22.3165 76.0029i 0.0287583 0.0979418i
\(777\) −573.948 + 493.758i −0.738672 + 0.635467i
\(778\) 356.117 + 410.981i 0.457734 + 0.528253i
\(779\) −214.112 729.199i −0.274855 0.936070i
\(780\) 461.820 + 1.64623i 0.592077 + 0.00211055i
\(781\) 905.234 + 581.758i 1.15907 + 0.744889i
\(782\) 112.454 + 174.982i 0.143803 + 0.223762i
\(783\) −198.227 + 223.883i −0.253163 + 0.285929i
\(784\) −0.651149 0.418468i −0.000830547 0.000533760i
\(785\) −293.664 134.112i −0.374094 0.170843i
\(786\) 151.083 21.1730i 0.192217 0.0269377i
\(787\) −95.4464 110.151i −0.121279 0.139963i 0.691863 0.722029i \(-0.256790\pi\)
−0.813142 + 0.582066i \(0.802245\pi\)
\(788\) −295.583 + 42.4984i −0.375105 + 0.0539319i
\(789\) −168.765 373.057i −0.213897 0.472822i
\(790\) −200.364 + 231.232i −0.253625 + 0.292699i
\(791\) 410.689 + 1398.68i 0.519203 + 1.76824i
\(792\) −405.959 905.963i −0.512574 1.14389i
\(793\) 166.796 + 1160.09i 0.210335 + 1.46291i
\(794\) −253.045 393.745i −0.318696 0.495901i
\(795\) −39.4875 + 132.730i −0.0496698 + 0.166956i
\(796\) 500.724 + 147.026i 0.629050 + 0.184706i
\(797\) −382.832 + 174.834i −0.480342 + 0.219365i −0.640845 0.767671i \(-0.721416\pi\)
0.160503 + 0.987035i \(0.448688\pi\)
\(798\) −249.569 290.101i −0.312743 0.363535i
\(799\) −151.088 1050.84i −0.189096 1.31519i
\(800\) −374.853 324.812i −0.468566 0.406015i
\(801\) −90.0707 41.9125i −0.112448 0.0523253i
\(802\) 287.773 + 630.135i 0.358819 + 0.785705i
\(803\) 666.799i 0.830384i
\(804\) 101.331 515.305i 0.126034 0.640927i
\(805\) 229.575 0.285186
\(806\) 931.315 425.317i 1.15548 0.527689i
\(807\) −1435.93 + 416.073i −1.77935 + 0.515581i
\(808\) 468.939 541.185i 0.580371 0.669783i
\(809\) 523.785 75.3090i 0.647448 0.0930889i 0.189236 0.981932i \(-0.439399\pi\)
0.458212 + 0.888843i \(0.348490\pi\)
\(810\) −38.3086 296.383i −0.0472946 0.365905i
\(811\) 188.062 + 411.798i 0.231889 + 0.507765i 0.989428 0.145024i \(-0.0463260\pi\)
−0.757540 + 0.652789i \(0.773599\pi\)
\(812\) 56.7137 193.149i 0.0698444 0.237868i
\(813\) 197.539 663.991i 0.242975 0.816717i
\(814\) −509.076 + 327.163i −0.625400 + 0.401920i
\(815\) 420.451 60.4518i 0.515891 0.0741740i
\(816\) 26.9067 58.3659i 0.0329739 0.0715269i
\(817\) 1222.21 358.874i 1.49597 0.439258i
\(818\) −125.316 108.587i −0.153198 0.132747i
\(819\) 1127.48 + 339.809i 1.37666 + 0.414907i
\(820\) 56.8605 + 395.473i 0.0693420 + 0.482284i
\(821\) 529.627 458.924i 0.645100 0.558982i −0.269672 0.962952i \(-0.586915\pi\)
0.914772 + 0.403970i \(0.132370\pi\)
\(822\) 263.321 36.9023i 0.320342 0.0448932i
\(823\) −646.007 + 1414.56i −0.784941 + 1.71878i −0.0943464 + 0.995539i \(0.530076\pi\)
−0.690595 + 0.723242i \(0.742651\pi\)
\(824\) 655.980 1020.72i 0.796092 1.23874i
\(825\) 420.825 + 489.170i 0.510091 + 0.592934i
\(826\) −535.812 + 344.345i −0.648682 + 0.416883i
\(827\) −434.002 + 675.320i −0.524791 + 0.816590i −0.997924 0.0644004i \(-0.979487\pi\)
0.473133 + 0.880991i \(0.343123\pi\)
\(828\) −186.061 163.560i −0.224711 0.197536i
\(829\) −393.282 + 115.478i −0.474405 + 0.139298i −0.510190 0.860062i \(-0.670425\pi\)
0.0357853 + 0.999360i \(0.488607\pi\)
\(830\) 224.493 194.525i 0.270474 0.234367i
\(831\) 135.281 116.380i 0.162793 0.140048i
\(832\) −601.921 176.740i −0.723463 0.212428i
\(833\) 10.1532i 0.0121887i
\(834\) 84.2955 96.5844i 0.101074 0.115809i
\(835\) −93.6923 27.5105i −0.112206 0.0329467i
\(836\) 311.466 + 484.650i 0.372567 + 0.579725i
\(837\) 663.394 + 1056.94i 0.792585 + 1.26278i
\(838\) 360.537 789.466i 0.430235 0.942084i
\(839\) 250.954 + 390.491i 0.299110 + 0.465425i 0.957981 0.286831i \(-0.0926019\pi\)
−0.658871 + 0.752256i \(0.728966\pi\)
\(840\) 273.754 + 429.327i 0.325898 + 0.511103i
\(841\) 718.343 0.854153
\(842\) 327.892i 0.389421i
\(843\) 1165.34 743.065i 1.38238 0.881453i
\(844\) −74.0991 + 515.371i −0.0877952 + 0.610629i
\(845\) −437.388 + 378.999i −0.517620 + 0.448520i
\(846\) −274.513 612.620i −0.324483 0.724137i
\(847\) −362.549 418.403i −0.428038 0.493983i
\(848\) −10.1810 + 15.8420i −0.0120059 + 0.0186816i
\(849\) 677.816 + 99.9226i 0.798370 + 0.117694i
\(850\) 42.6739 296.804i 0.0502046 0.349181i
\(851\) −206.623 + 321.512i −0.242800 + 0.377805i
\(852\) 245.466 + 542.606i 0.288105 + 0.636861i
\(853\) 394.057 454.765i 0.461965 0.533137i −0.476194 0.879340i \(-0.657984\pi\)
0.938159 + 0.346204i \(0.112529\pi\)
\(854\) −385.859 + 334.349i −0.451825 + 0.391509i
\(855\) 120.653 + 422.013i 0.141115 + 0.493583i
\(856\) −439.587 + 962.562i −0.513537 + 1.12449i
\(857\) −427.355 370.305i −0.498664 0.432095i 0.368864 0.929483i \(-0.379747\pi\)
−0.867528 + 0.497389i \(0.834292\pi\)
\(858\) 854.758 + 394.043i 0.996221 + 0.459258i
\(859\) −195.242 + 57.3284i −0.227290 + 0.0667385i −0.393395 0.919370i \(-0.628699\pi\)
0.166104 + 0.986108i \(0.446881\pi\)
\(860\) −662.853 + 95.3039i −0.770759 + 0.110818i
\(861\) −148.579 + 1007.87i −0.172566 + 1.17059i
\(862\) −5.65159 12.3753i −0.00655637 0.0143565i
\(863\) 375.141 1277.61i 0.434694 1.48043i −0.393151 0.919474i \(-0.628615\pi\)
0.827845 0.560957i \(-0.189567\pi\)
\(864\) 134.820 871.432i 0.156041 1.00860i
\(865\) −33.5905 + 233.627i −0.0388329 + 0.270089i
\(866\) −209.462 + 30.1161i −0.241873 + 0.0347761i
\(867\) −23.7175 + 3.32381i −0.0273558 + 0.00383369i
\(868\) −706.712 454.176i −0.814184 0.523244i
\(869\) 1068.36 487.903i 1.22941 0.561453i
\(870\) 80.6052 92.3561i 0.0926497 0.106156i
\(871\) 629.859 + 1091.46i 0.723145 + 1.25311i
\(872\) 317.118i 0.363668i
\(873\) −77.3530 + 48.9361i −0.0886060 + 0.0560551i
\(874\) −162.508 104.437i −0.185936 0.119494i
\(875\) −661.850 573.496i −0.756400 0.655424i
\(876\) 200.625 309.745i 0.229023 0.353590i
\(877\) 136.289 947.913i 0.155404 1.08086i −0.751564 0.659660i \(-0.770700\pi\)
0.906968 0.421199i \(-0.138390\pi\)
\(878\) −310.148 + 141.640i −0.353244 + 0.161321i
\(879\) 339.597 216.539i 0.386345 0.246347i
\(880\) −23.5528 51.5734i −0.0267645 0.0586062i
\(881\) 600.404 + 934.247i 0.681503 + 1.06044i 0.993878 + 0.110481i \(0.0352390\pi\)
−0.312375 + 0.949959i \(0.601125\pi\)
\(882\) −1.76482 6.17287i −0.00200093 0.00699872i
\(883\) −1472.48 + 432.359i −1.66759 + 0.489648i −0.973202 0.229953i \(-0.926143\pi\)
−0.694387 + 0.719602i \(0.744324\pi\)
\(884\) 232.092 + 790.433i 0.262548 + 0.894155i
\(885\) 723.459 101.387i 0.817467 0.114561i
\(886\) −341.974 + 748.819i −0.385975 + 0.845168i
\(887\) 1505.56 216.467i 1.69736 0.244044i 0.775441 0.631420i \(-0.217528\pi\)
0.921922 + 0.387376i \(0.126619\pi\)
\(888\) −847.642 3.02155i −0.954552 0.00340264i
\(889\) −581.178 + 670.715i −0.653744 + 0.754460i
\(890\) 37.0454 + 16.9181i 0.0416241 + 0.0190091i
\(891\) −338.859 + 1095.99i −0.380314 + 1.23007i
\(892\) 54.1481 376.608i 0.0607042 0.422207i
\(893\) 533.052 + 829.445i 0.596923 + 0.928830i
\(894\) −85.2400 294.176i −0.0953468 0.329056i
\(895\) 33.0647 + 38.1587i 0.0369438 + 0.0426354i
\(896\) 179.043 + 609.763i 0.199824 + 0.680539i
\(897\) 594.428 + 2.11893i 0.662684 + 0.00236224i
\(898\) −4.43056 + 30.8152i −0.00493380 + 0.0343154i
\(899\) −144.210 + 491.134i −0.160412 + 0.546312i
\(900\) 48.3035 + 353.848i 0.0536705 + 0.393165i
\(901\) −247.020 −0.274162
\(902\) −229.409 + 781.294i −0.254333 + 0.866179i
\(903\) −1689.30 249.034i −1.87076 0.275785i
\(904\) −677.979 + 1484.57i −0.749976 + 1.64222i
\(905\) −185.131 84.5467i −0.204565 0.0934218i
\(906\) −51.0783 + 346.485i −0.0563778 + 0.382434i
\(907\) 102.977 + 30.2368i 0.113536 + 0.0333372i 0.338007 0.941144i \(-0.390247\pi\)
−0.224471 + 0.974481i \(0.572065\pi\)
\(908\) 501.888i 0.552740i
\(909\) −819.873 + 111.920i −0.901950 + 0.123124i
\(910\) −463.186 136.004i −0.508995 0.149455i
\(911\) 931.921 + 133.990i 1.02296 + 0.147080i 0.633324 0.773887i \(-0.281690\pi\)
0.389641 + 0.920967i \(0.372599\pi\)
\(912\) −0.212765 + 59.6874i −0.000233295 + 0.0654467i
\(913\) −1094.08 + 321.251i −1.19833 + 0.351863i
\(914\) 295.216 255.806i 0.322994 0.279876i
\(915\) 562.465 162.979i 0.614716 0.178119i
\(916\) 648.507 416.770i 0.707977 0.454989i
\(917\) 297.305 + 42.7460i 0.324215 + 0.0466151i
\(918\) 487.254 216.255i 0.530778 0.235571i
\(919\) 524.664 1148.85i 0.570908 1.25011i −0.375405 0.926861i \(-0.622496\pi\)
0.946313 0.323252i \(-0.104776\pi\)
\(920\) 194.249 + 168.318i 0.211141 + 0.182954i
\(921\) 0.0102980 2.88891i 1.11813e−5 0.00313671i
\(922\) −93.7135 651.792i −0.101642 0.706933i
\(923\) −1299.88 593.635i −1.40832 0.643158i
\(924\) −107.181 764.802i −0.115996 0.827708i
\(925\) 528.638 155.222i 0.571501 0.167808i
\(926\) 169.673 + 577.852i 0.183232 + 0.624031i
\(927\) −1348.06 + 385.408i −1.45422 + 0.415758i
\(928\) 304.284 195.552i 0.327893 0.210724i
\(929\) −456.057 + 208.274i −0.490911 + 0.224192i −0.645461 0.763793i \(-0.723335\pi\)
0.154549 + 0.987985i \(0.450607\pi\)
\(930\) −275.036 431.337i −0.295737 0.463803i
\(931\) 3.91712 + 8.57730i 0.00420743 + 0.00921299i
\(932\) 683.217 + 98.2317i 0.733065 + 0.105399i
\(933\) −393.641 254.965i −0.421909 0.273274i
\(934\) 142.214 164.124i 0.152264 0.175721i
\(935\) 402.086 625.658i 0.430038 0.669153i
\(936\) 704.856 + 1114.16i 0.753051 + 1.19034i
\(937\) −527.533 −0.563002 −0.281501 0.959561i \(-0.590832\pi\)
−0.281501 + 0.959561i \(0.590832\pi\)
\(938\) −251.647 + 487.885i −0.268280 + 0.520133i
\(939\) 842.283 + 735.115i 0.897000 + 0.782870i
\(940\) −215.327 471.501i −0.229072 0.501597i
\(941\) −437.556 + 680.850i −0.464990 + 0.723539i −0.991989 0.126328i \(-0.959681\pi\)
0.526999 + 0.849866i \(0.323317\pi\)
\(942\) −50.5385 360.624i −0.0536502 0.382828i
\(943\) 73.1875 + 509.030i 0.0776114 + 0.539799i
\(944\) 98.3314 + 14.1379i 0.104165 + 0.0149766i
\(945\) 89.9583 581.462i 0.0951940 0.615304i
\(946\) −1309.53 384.512i −1.38428 0.406461i
\(947\) 1343.48 613.547i 1.41867 0.647885i 0.449276 0.893393i \(-0.351682\pi\)
0.969395 + 0.245508i \(0.0789547\pi\)
\(948\) 643.078 + 94.8015i 0.678352 + 0.100002i
\(949\) 126.023 + 876.506i 0.132795 + 0.923610i
\(950\) 78.4569 + 267.200i 0.0825862 + 0.281263i
\(951\) 278.312 603.715i 0.292652 0.634821i
\(952\) −594.795 + 686.430i −0.624784 + 0.721039i
\(953\) 480.624 + 219.494i 0.504328 + 0.230319i 0.651298 0.758822i \(-0.274225\pi\)
−0.146970 + 0.989141i \(0.546952\pi\)
\(954\) −150.182 + 42.9367i −0.157423 + 0.0450070i
\(955\) −347.012 400.473i −0.363363 0.419344i
\(956\) −814.699 705.941i −0.852196 0.738432i
\(957\) −428.731 + 193.951i −0.447994 + 0.202665i
\(958\) 198.031 + 127.267i 0.206713 + 0.132846i
\(959\) 518.170 + 74.5016i 0.540323 + 0.0776868i
\(960\) −45.7140 + 310.097i −0.0476187 + 0.323017i
\(961\) 988.563 + 635.311i 1.02868 + 0.661093i
\(962\) 607.347 526.269i 0.631338 0.547057i
\(963\) 1115.88 500.022i 1.15875 0.519233i
\(964\) 92.4367 + 106.678i 0.0958887 + 0.110661i
\(965\) −854.221 122.818i −0.885203 0.127273i
\(966\) 139.222 + 218.341i 0.144122 + 0.226026i
\(967\) 1212.00 1.25336 0.626679 0.779278i \(-0.284414\pi\)
0.626679 + 0.779278i \(0.284414\pi\)
\(968\) 619.833i 0.640323i
\(969\) −660.166 + 420.945i −0.681286 + 0.434412i
\(970\) 31.5665 20.2866i 0.0325428 0.0209140i
\(971\) −1332.29 608.437i −1.37208 0.626609i −0.413259 0.910613i \(-0.635610\pi\)
−0.958823 + 0.284004i \(0.908337\pi\)
\(972\) −487.168 + 407.161i −0.501201 + 0.418890i
\(973\) 212.329 136.456i 0.218221 0.140242i
\(974\) 239.244 814.791i 0.245631 0.836541i
\(975\) −645.625 563.479i −0.662180 0.577927i
\(976\) 79.6344 0.0815926
\(977\) −389.297 + 1325.83i −0.398462 + 1.35704i 0.479178 + 0.877718i \(0.340935\pi\)
−0.877640 + 0.479320i \(0.840883\pi\)
\(978\) 312.470 + 363.218i 0.319499 + 0.371388i
\(979\) −102.376 118.148i −0.104572 0.120683i
\(980\) −1.39662 4.75644i −0.00142512 0.00485351i
\(981\) −241.939 + 275.223i −0.246625 + 0.280553i
\(982\) −291.288 187.200i −0.296628 0.190631i
\(983\) 627.422 + 976.287i 0.638272 + 0.993171i 0.998187 + 0.0601858i \(0.0191693\pi\)
−0.359915 + 0.932985i \(0.617194\pi\)
\(984\) −864.663 + 743.855i −0.878723 + 0.755950i
\(985\) −301.189 193.562i −0.305775 0.196510i
\(986\) 198.906 + 90.8373i 0.201730 + 0.0921271i
\(987\) −183.432 1308.91i −0.185848 1.32615i
\(988\) −501.018 578.206i −0.507104 0.585229i
\(989\) −853.186 + 122.670i −0.862676 + 0.124034i
\(990\) 135.706 450.273i 0.137077 0.454821i
\(991\) 117.666 135.794i 0.118735 0.137027i −0.693270 0.720678i \(-0.743831\pi\)
0.812005 + 0.583651i \(0.198376\pi\)
\(992\) −425.260 1448.30i −0.428689 1.45998i
\(993\) 194.059 + 89.4612i 0.195427 + 0.0900918i
\(994\) −88.5938 616.183i −0.0891286 0.619903i
\(995\) 338.264 + 526.348i 0.339963 + 0.528993i
\(996\) −604.884 179.955i −0.607313 0.180677i
\(997\) −878.409 257.924i −0.881052 0.258700i −0.190243 0.981737i \(-0.560927\pi\)
−0.690809 + 0.723037i \(0.742746\pi\)
\(998\) 941.399 429.923i 0.943286 0.430784i
\(999\) 733.353 + 649.314i 0.734087 + 0.649964i
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 201.3.k.a.14.17 440
3.2 odd 2 inner 201.3.k.a.14.28 yes 440
67.24 even 11 inner 201.3.k.a.158.28 yes 440
201.158 odd 22 inner 201.3.k.a.158.17 yes 440
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.k.a.14.17 440 1.1 even 1 trivial
201.3.k.a.14.28 yes 440 3.2 odd 2 inner
201.3.k.a.158.17 yes 440 201.158 odd 22 inner
201.3.k.a.158.28 yes 440 67.24 even 11 inner