Properties

Label 192.3.q.a.5.11
Level $192$
Weight $3$
Character 192.5
Analytic conductor $5.232$
Analytic rank $0$
Dimension $496$
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] = [192,3,Mod(5,192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(192, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([0, 1, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("192.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.q (of order \(16\), degree \(8\), 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: \(5.23162107572\)
Analytic rank: \(0\)
Dimension: \(496\)
Relative dimension: \(62\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 5.11
Character \(\chi\) \(=\) 192.5
Dual form 192.3.q.a.77.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.74186 + 0.982818i) q^{2} +(-0.766801 - 2.90035i) q^{3} +(2.06814 - 3.42386i) q^{4} +(1.45744 - 7.32705i) q^{5} +(4.18617 + 4.29837i) q^{6} +(4.63081 - 11.1798i) q^{7} +(-0.237375 + 7.99648i) q^{8} +(-7.82403 + 4.44798i) q^{9} +O(q^{10})\) \(q+(-1.74186 + 0.982818i) q^{2} +(-0.766801 - 2.90035i) q^{3} +(2.06814 - 3.42386i) q^{4} +(1.45744 - 7.32705i) q^{5} +(4.18617 + 4.29837i) q^{6} +(4.63081 - 11.1798i) q^{7} +(-0.237375 + 7.99648i) q^{8} +(-7.82403 + 4.44798i) q^{9} +(4.66250 + 14.1951i) q^{10} +(-11.2914 + 7.54469i) q^{11} +(-11.5162 - 3.37290i) q^{12} +(11.3601 - 2.25967i) q^{13} +(2.92146 + 24.0248i) q^{14} +(-22.3685 + 1.39130i) q^{15} +(-7.44561 - 14.1620i) q^{16} +(6.02985 + 6.02985i) q^{17} +(9.25680 - 15.4373i) q^{18} +(2.66875 + 13.4167i) q^{19} +(-22.0726 - 20.1434i) q^{20} +(-35.9761 - 4.85831i) q^{21} +(12.2530 - 24.2392i) q^{22} +(-9.27341 - 22.3880i) q^{23} +(23.3746 - 5.44323i) q^{24} +(-28.4645 - 11.7904i) q^{25} +(-17.5669 + 15.1010i) q^{26} +(18.9002 + 19.2817i) q^{27} +(-28.7008 - 38.9765i) q^{28} +(20.1199 + 13.4437i) q^{29} +(37.5954 - 24.4077i) q^{30} -32.6756i q^{31} +(26.8879 + 17.3506i) q^{32} +(30.5405 + 26.9638i) q^{33} +(-16.4294 - 4.57690i) q^{34} +(-75.1656 - 50.2240i) q^{35} +(-0.951943 + 35.9874i) q^{36} +(-8.00748 + 40.2563i) q^{37} +(-17.8347 - 20.7471i) q^{38} +(-15.2648 - 31.2156i) q^{39} +(58.2446 + 13.3936i) q^{40} +(-0.296995 - 0.717010i) q^{41} +(67.4401 - 26.8955i) q^{42} +(6.68847 - 4.46910i) q^{43} +(2.47971 + 54.2637i) q^{44} +(21.1875 + 63.8097i) q^{45} +(38.1563 + 29.8826i) q^{46} +(-37.6255 - 37.6255i) q^{47} +(-35.3655 + 32.4543i) q^{48} +(-68.8946 - 68.8946i) q^{49} +(61.1689 - 7.43824i) q^{50} +(12.8650 - 22.1124i) q^{51} +(15.7575 - 43.5687i) q^{52} +(11.9581 - 7.99012i) q^{53} +(-51.8718 - 15.0106i) q^{54} +(38.8237 + 93.7287i) q^{55} +(88.2995 + 39.6840i) q^{56} +(36.8667 - 18.0282i) q^{57} +(-48.2588 - 3.64280i) q^{58} +(-2.59794 + 13.0607i) q^{59} +(-41.4976 + 79.4641i) q^{60} +(68.3844 + 45.6930i) q^{61} +(32.1141 + 56.9162i) q^{62} +(13.4957 + 108.069i) q^{63} +(-63.8873 - 3.79632i) q^{64} -86.5295i q^{65} +(-79.6977 - 16.9513i) q^{66} +(-25.9270 - 17.3239i) q^{67} +(33.1159 - 8.17479i) q^{68} +(-57.8221 + 44.0632i) q^{69} +(180.289 + 13.6091i) q^{70} +(31.1044 + 12.8839i) q^{71} +(-33.7109 - 63.6205i) q^{72} +(36.2193 + 87.4412i) q^{73} +(-25.6167 - 77.9907i) q^{74} +(-12.3696 + 91.5978i) q^{75} +(51.4562 + 18.6102i) q^{76} +(32.0594 + 161.173i) q^{77} +(57.2683 + 39.3706i) q^{78} +(-87.0954 - 87.0954i) q^{79} +(-114.617 + 33.9140i) q^{80} +(41.4310 - 69.6022i) q^{81} +(1.22201 + 0.957037i) q^{82} +(95.9127 - 19.0782i) q^{83} +(-91.0378 + 113.129i) q^{84} +(52.9692 - 35.3929i) q^{85} +(-7.25806 + 14.3581i) q^{86} +(23.5635 - 68.6634i) q^{87} +(-57.6506 - 92.0825i) q^{88} +(52.6944 - 127.216i) q^{89} +(-99.6189 - 90.3240i) q^{90} +(27.3440 - 137.468i) q^{91} +(-95.8320 - 14.5506i) q^{92} +(-94.7705 + 25.0556i) q^{93} +(102.517 + 28.5593i) q^{94} +102.194 q^{95} +(29.7050 - 91.2886i) q^{96} +87.5637i q^{97} +(187.715 + 52.2937i) q^{98} +(54.7859 - 109.254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 496 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 496 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} + 272 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} + 72 q^{30} - 16 q^{34} - 408 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 448 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} - 544 q^{52} - 8 q^{54} + 496 q^{55} - 8 q^{57} - 736 q^{58} - 8 q^{60} - 16 q^{61} - 16 q^{63} + 80 q^{64} - 40 q^{66} - 528 q^{67} - 8 q^{69} + 656 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 1440 q^{76} - 416 q^{78} - 528 q^{79} - 8 q^{81} - 1056 q^{82} - 1240 q^{84} - 16 q^{85} - 8 q^{87} - 576 q^{88} - 728 q^{90} - 16 q^{91} + 64 q^{93} - 112 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.74186 + 0.982818i −0.870929 + 0.491409i
\(3\) −0.766801 2.90035i −0.255600 0.966783i
\(4\) 2.06814 3.42386i 0.517035 0.855964i
\(5\) 1.45744 7.32705i 0.291488 1.46541i −0.506240 0.862392i \(-0.668965\pi\)
0.797728 0.603017i \(-0.206035\pi\)
\(6\) 4.18617 + 4.29837i 0.697695 + 0.716395i
\(7\) 4.63081 11.1798i 0.661544 1.59711i −0.133839 0.991003i \(-0.542730\pi\)
0.795383 0.606107i \(-0.207270\pi\)
\(8\) −0.237375 + 7.99648i −0.0296719 + 0.999560i
\(9\) −7.82403 + 4.44798i −0.869337 + 0.494220i
\(10\) 4.66250 + 14.1951i 0.466250 + 1.41951i
\(11\) −11.2914 + 7.54469i −1.02649 + 0.685881i −0.950339 0.311216i \(-0.899264\pi\)
−0.0761534 + 0.997096i \(0.524264\pi\)
\(12\) −11.5162 3.37290i −0.959686 0.281075i
\(13\) 11.3601 2.25967i 0.873855 0.173821i 0.262266 0.964996i \(-0.415530\pi\)
0.611590 + 0.791175i \(0.290530\pi\)
\(14\) 2.92146 + 24.0248i 0.208676 + 1.71606i
\(15\) −22.3685 + 1.39130i −1.49124 + 0.0927534i
\(16\) −7.44561 14.1620i −0.465350 0.885127i
\(17\) 6.02985 + 6.02985i 0.354697 + 0.354697i 0.861854 0.507157i \(-0.169303\pi\)
−0.507157 + 0.861854i \(0.669303\pi\)
\(18\) 9.25680 15.4373i 0.514267 0.857630i
\(19\) 2.66875 + 13.4167i 0.140460 + 0.706142i 0.985261 + 0.171060i \(0.0547192\pi\)
−0.844800 + 0.535082i \(0.820281\pi\)
\(20\) −22.0726 20.1434i −1.10363 1.00717i
\(21\) −35.9761 4.85831i −1.71315 0.231348i
\(22\) 12.2530 24.2392i 0.556954 1.10178i
\(23\) −9.27341 22.3880i −0.403192 0.973391i −0.986886 0.161418i \(-0.948393\pi\)
0.583694 0.811973i \(-0.301607\pi\)
\(24\) 23.3746 5.44323i 0.973941 0.226801i
\(25\) −28.4645 11.7904i −1.13858 0.471615i
\(26\) −17.5669 + 15.1010i −0.675649 + 0.580806i
\(27\) 18.9002 + 19.2817i 0.700006 + 0.714137i
\(28\) −28.7008 38.9765i −1.02503 1.39202i
\(29\) 20.1199 + 13.4437i 0.693791 + 0.463576i 0.851804 0.523861i \(-0.175509\pi\)
−0.158013 + 0.987437i \(0.550509\pi\)
\(30\) 37.5954 24.4077i 1.25318 0.813589i
\(31\) 32.6756i 1.05405i −0.849850 0.527025i \(-0.823307\pi\)
0.849850 0.527025i \(-0.176693\pi\)
\(32\) 26.8879 + 17.3506i 0.840246 + 0.542205i
\(33\) 30.5405 + 26.9638i 0.925469 + 0.817084i
\(34\) −16.4294 4.57690i −0.483218 0.134615i
\(35\) −75.1656 50.2240i −2.14759 1.43497i
\(36\) −0.951943 + 35.9874i −0.0264429 + 0.999650i
\(37\) −8.00748 + 40.2563i −0.216418 + 1.08801i 0.707878 + 0.706334i \(0.249652\pi\)
−0.924297 + 0.381674i \(0.875348\pi\)
\(38\) −17.8347 20.7471i −0.469335 0.545976i
\(39\) −15.2648 31.2156i −0.391404 0.800400i
\(40\) 58.2446 + 13.3936i 1.45612 + 0.334841i
\(41\) −0.296995 0.717010i −0.00724378 0.0174880i 0.920216 0.391410i \(-0.128013\pi\)
−0.927460 + 0.373922i \(0.878013\pi\)
\(42\) 67.4401 26.8955i 1.60572 0.640369i
\(43\) 6.68847 4.46910i 0.155546 0.103932i −0.475362 0.879791i \(-0.657683\pi\)
0.630907 + 0.775858i \(0.282683\pi\)
\(44\) 2.47971 + 54.2637i 0.0563571 + 1.23327i
\(45\) 21.1875 + 63.8097i 0.470833 + 1.41799i
\(46\) 38.1563 + 29.8826i 0.829485 + 0.649623i
\(47\) −37.6255 37.6255i −0.800542 0.800542i 0.182638 0.983180i \(-0.441536\pi\)
−0.983180 + 0.182638i \(0.941536\pi\)
\(48\) −35.3655 + 32.4543i −0.736781 + 0.676131i
\(49\) −68.8946 68.8946i −1.40601 1.40601i
\(50\) 61.1689 7.43824i 1.22338 0.148765i
\(51\) 12.8650 22.1124i 0.252254 0.433576i
\(52\) 15.7575 43.5687i 0.303029 0.837861i
\(53\) 11.9581 7.99012i 0.225624 0.150757i −0.437621 0.899160i \(-0.644179\pi\)
0.663245 + 0.748403i \(0.269179\pi\)
\(54\) −51.8718 15.0106i −0.960589 0.277974i
\(55\) 38.8237 + 93.7287i 0.705885 + 1.70416i
\(56\) 88.2995 + 39.6840i 1.57678 + 0.708642i
\(57\) 36.8667 18.0282i 0.646784 0.316284i
\(58\) −48.2588 3.64280i −0.832048 0.0628070i
\(59\) −2.59794 + 13.0607i −0.0440329 + 0.221368i −0.996536 0.0831600i \(-0.973499\pi\)
0.952503 + 0.304528i \(0.0984987\pi\)
\(60\) −41.4976 + 79.4641i −0.691627 + 1.32440i
\(61\) 68.3844 + 45.6930i 1.12106 + 0.749065i 0.970873 0.239593i \(-0.0770141\pi\)
0.150182 + 0.988658i \(0.452014\pi\)
\(62\) 32.1141 + 56.9162i 0.517970 + 0.918003i
\(63\) 13.4957 + 108.069i 0.214218 + 1.71537i
\(64\) −63.8873 3.79632i −0.998239 0.0593176i
\(65\) 86.5295i 1.33122i
\(66\) −79.6977 16.9513i −1.20754 0.256838i
\(67\) −25.9270 17.3239i −0.386970 0.258565i 0.346833 0.937927i \(-0.387257\pi\)
−0.733804 + 0.679361i \(0.762257\pi\)
\(68\) 33.1159 8.17479i 0.486999 0.120218i
\(69\) −57.8221 + 44.0632i −0.838002 + 0.638598i
\(70\) 180.289 + 13.6091i 2.57555 + 0.194415i
\(71\) 31.1044 + 12.8839i 0.438090 + 0.181463i 0.590817 0.806805i \(-0.298805\pi\)
−0.152727 + 0.988268i \(0.548805\pi\)
\(72\) −33.7109 63.6205i −0.468207 0.883619i
\(73\) 36.2193 + 87.4412i 0.496155 + 1.19782i 0.951539 + 0.307529i \(0.0995022\pi\)
−0.455383 + 0.890295i \(0.650498\pi\)
\(74\) −25.6167 77.9907i −0.346172 1.05393i
\(75\) −12.3696 + 91.5978i −0.164928 + 1.22130i
\(76\) 51.4562 + 18.6102i 0.677055 + 0.244871i
\(77\) 32.0594 + 161.173i 0.416356 + 2.09316i
\(78\) 57.2683 + 39.3706i 0.734209 + 0.504752i
\(79\) −87.0954 87.0954i −1.10247 1.10247i −0.994112 0.108362i \(-0.965439\pi\)
−0.108362 0.994112i \(-0.534561\pi\)
\(80\) −114.617 + 33.9140i −1.43272 + 0.423925i
\(81\) 41.4310 69.6022i 0.511494 0.859287i
\(82\) 1.22201 + 0.957037i 0.0149026 + 0.0116712i
\(83\) 95.9127 19.0782i 1.15557 0.229858i 0.420143 0.907458i \(-0.361980\pi\)
0.735431 + 0.677600i \(0.236980\pi\)
\(84\) −91.0378 + 113.129i −1.08378 + 1.34678i
\(85\) 52.9692 35.3929i 0.623167 0.416387i
\(86\) −7.25806 + 14.3581i −0.0843961 + 0.166954i
\(87\) 23.5635 68.6634i 0.270844 0.789235i
\(88\) −57.6506 92.0825i −0.655121 1.04639i
\(89\) 52.6944 127.216i 0.592072 1.42939i −0.289425 0.957201i \(-0.593464\pi\)
0.881498 0.472189i \(-0.156536\pi\)
\(90\) −99.6189 90.3240i −1.10688 1.00360i
\(91\) 27.3440 137.468i 0.300484 1.51063i
\(92\) −95.8320 14.5506i −1.04165 0.158159i
\(93\) −94.7705 + 25.0556i −1.01904 + 0.269415i
\(94\) 102.517 + 28.5593i 1.09061 + 0.303822i
\(95\) 102.194 1.07573
\(96\) 29.7050 91.2886i 0.309427 0.950923i
\(97\) 87.5637i 0.902719i 0.892342 + 0.451359i \(0.149061\pi\)
−0.892342 + 0.451359i \(0.850939\pi\)
\(98\) 187.715 + 52.2937i 1.91546 + 0.533610i
\(99\) 54.7859 109.254i 0.553393 1.10357i
\(100\) −99.2371 + 73.0742i −0.992371 + 0.730742i
\(101\) −92.6302 18.4253i −0.917131 0.182429i −0.286112 0.958196i \(-0.592363\pi\)
−0.631019 + 0.775767i \(0.717363\pi\)
\(102\) −0.676534 + 51.1605i −0.00663268 + 0.501574i
\(103\) −43.5492 18.0387i −0.422807 0.175133i 0.161127 0.986934i \(-0.448487\pi\)
−0.583934 + 0.811801i \(0.698487\pi\)
\(104\) 15.3728 + 91.3773i 0.147815 + 0.878628i
\(105\) −88.0301 + 256.518i −0.838382 + 2.44303i
\(106\) −12.9764 + 25.6703i −0.122419 + 0.242172i
\(107\) −54.4849 81.5424i −0.509205 0.762079i 0.484418 0.874837i \(-0.339031\pi\)
−0.993622 + 0.112758i \(0.964031\pi\)
\(108\) 105.106 24.8342i 0.973203 0.229946i
\(109\) −24.8834 125.097i −0.228288 1.14768i −0.909535 0.415628i \(-0.863562\pi\)
0.681247 0.732054i \(-0.261438\pi\)
\(110\) −159.744 125.105i −1.45221 1.13732i
\(111\) 122.897 7.64410i 1.10718 0.0688657i
\(112\) −192.807 + 17.6585i −1.72149 + 0.157665i
\(113\) 25.9075 25.9075i 0.229270 0.229270i −0.583118 0.812388i \(-0.698167\pi\)
0.812388 + 0.583118i \(0.198167\pi\)
\(114\) −46.4981 + 67.6358i −0.407878 + 0.593297i
\(115\) −177.553 + 35.3176i −1.54394 + 0.307109i
\(116\) 87.6402 41.0843i 0.755519 0.354175i
\(117\) −78.8310 + 68.2093i −0.673769 + 0.582985i
\(118\) −8.31107 25.3032i −0.0704328 0.214434i
\(119\) 95.3355 39.4892i 0.801138 0.331842i
\(120\) −5.81577 179.200i −0.0484648 1.49333i
\(121\) 24.2692 58.5910i 0.200572 0.484223i
\(122\) −164.024 12.3813i −1.34446 0.101486i
\(123\) −1.85184 + 1.41119i −0.0150556 + 0.0114731i
\(124\) −111.876 67.5776i −0.902229 0.544980i
\(125\) −24.1130 + 36.0876i −0.192904 + 0.288701i
\(126\) −129.719 174.976i −1.02952 1.38870i
\(127\) 168.650 1.32795 0.663975 0.747755i \(-0.268868\pi\)
0.663975 + 0.747755i \(0.268868\pi\)
\(128\) 115.014 56.1769i 0.898545 0.438882i
\(129\) −18.0907 15.9720i −0.140238 0.123814i
\(130\) 85.0427 + 150.722i 0.654175 + 1.15940i
\(131\) 29.4444 44.0667i 0.224767 0.336387i −0.701897 0.712278i \(-0.747663\pi\)
0.926664 + 0.375891i \(0.122663\pi\)
\(132\) 155.482 48.8014i 1.17789 0.369708i
\(133\) 162.354 + 32.2942i 1.22071 + 0.242814i
\(134\) 62.1874 + 4.69420i 0.464085 + 0.0350314i
\(135\) 168.824 110.380i 1.25055 0.817632i
\(136\) −49.6489 + 46.7863i −0.365066 + 0.344017i
\(137\) 125.915 52.1557i 0.919087 0.380698i 0.127559 0.991831i \(-0.459286\pi\)
0.791528 + 0.611133i \(0.209286\pi\)
\(138\) 57.4118 133.581i 0.416027 0.967975i
\(139\) 12.1798 + 18.2283i 0.0876242 + 0.131139i 0.872692 0.488271i \(-0.162372\pi\)
−0.785068 + 0.619409i \(0.787372\pi\)
\(140\) −327.413 + 153.486i −2.33866 + 1.09633i
\(141\) −80.2758 + 137.978i −0.569332 + 0.978569i
\(142\) −66.8420 + 8.12810i −0.470718 + 0.0572401i
\(143\) −111.223 + 111.223i −0.777786 + 0.777786i
\(144\) 121.247 + 77.6863i 0.841993 + 0.539488i
\(145\) 127.826 127.826i 0.881561 0.881561i
\(146\) −149.028 116.713i −1.02074 0.799405i
\(147\) −146.990 + 252.647i −0.999931 + 1.71868i
\(148\) 121.271 + 110.672i 0.819401 + 0.747785i
\(149\) −31.4391 47.0519i −0.211000 0.315784i 0.710840 0.703353i \(-0.248315\pi\)
−0.921841 + 0.387569i \(0.873315\pi\)
\(150\) −68.4778 171.707i −0.456519 1.14472i
\(151\) 271.707 112.545i 1.79939 0.745330i 0.812702 0.582680i \(-0.197996\pi\)
0.986684 0.162650i \(-0.0520042\pi\)
\(152\) −107.920 + 18.1558i −0.709998 + 0.119446i
\(153\) −73.9984 20.3571i −0.483650 0.133053i
\(154\) −214.247 249.233i −1.39121 1.61839i
\(155\) −239.415 47.6227i −1.54461 0.307243i
\(156\) −138.447 12.2937i −0.887483 0.0788060i
\(157\) −10.8191 + 16.1920i −0.0689116 + 0.103133i −0.864325 0.502934i \(-0.832254\pi\)
0.795413 + 0.606067i \(0.207254\pi\)
\(158\) 237.307 + 66.1089i 1.50194 + 0.418411i
\(159\) −32.3436 28.5557i −0.203419 0.179596i
\(160\) 166.316 171.721i 1.03947 1.07326i
\(161\) −293.236 −1.82134
\(162\) −3.76060 + 161.956i −0.0232136 + 0.999731i
\(163\) −144.416 + 216.133i −0.885985 + 1.32597i 0.0587960 + 0.998270i \(0.481274\pi\)
−0.944782 + 0.327701i \(0.893726\pi\)
\(164\) −3.06917 0.466006i −0.0187144 0.00284150i
\(165\) 242.076 184.473i 1.46713 1.11802i
\(166\) −148.316 + 127.496i −0.893469 + 0.768050i
\(167\) −86.0035 + 207.631i −0.514991 + 1.24330i 0.425955 + 0.904744i \(0.359938\pi\)
−0.940947 + 0.338555i \(0.890062\pi\)
\(168\) 47.3892 286.529i 0.282079 1.70553i
\(169\) −32.1894 + 13.3333i −0.190470 + 0.0788952i
\(170\) −57.4800 + 113.708i −0.338118 + 0.668873i
\(171\) −80.5575 93.1021i −0.471096 0.544457i
\(172\) −1.46886 32.1431i −0.00853987 0.186878i
\(173\) 95.7142 19.0387i 0.553261 0.110050i 0.0894610 0.995990i \(-0.471486\pi\)
0.463800 + 0.885940i \(0.346486\pi\)
\(174\) 26.4395 + 142.761i 0.151951 + 0.820463i
\(175\) −263.627 + 263.627i −1.50644 + 1.50644i
\(176\) 190.919 + 103.735i 1.08477 + 0.589401i
\(177\) 39.8727 2.48004i 0.225270 0.0140115i
\(178\) 33.2436 + 273.381i 0.186762 + 1.53585i
\(179\) 10.9514 + 55.0566i 0.0611812 + 0.307579i 0.999244 0.0388877i \(-0.0123815\pi\)
−0.938062 + 0.346466i \(0.887381\pi\)
\(180\) 262.294 + 59.4244i 1.45719 + 0.330136i
\(181\) 29.0497 + 43.4759i 0.160495 + 0.240198i 0.902998 0.429645i \(-0.141361\pi\)
−0.742502 + 0.669843i \(0.766361\pi\)
\(182\) 87.4762 + 266.323i 0.480639 + 1.46331i
\(183\) 80.0883 233.376i 0.437641 1.27528i
\(184\) 181.226 68.8403i 0.984926 0.374132i
\(185\) 283.290 + 117.342i 1.53129 + 0.634283i
\(186\) 140.452 136.785i 0.755116 0.735406i
\(187\) −113.579 22.5923i −0.607374 0.120814i
\(188\) −206.639 + 51.0096i −1.09914 + 0.271328i
\(189\) 303.088 122.009i 1.60364 0.645552i
\(190\) −178.008 + 100.438i −0.936884 + 0.528623i
\(191\) 215.201i 1.12671i 0.826216 + 0.563353i \(0.190489\pi\)
−0.826216 + 0.563353i \(0.809511\pi\)
\(192\) 37.9782 + 188.206i 0.197803 + 0.980242i
\(193\) 85.6217 0.443636 0.221818 0.975088i \(-0.428801\pi\)
0.221818 + 0.975088i \(0.428801\pi\)
\(194\) −86.0592 152.524i −0.443604 0.786204i
\(195\) −250.966 + 66.3509i −1.28700 + 0.340261i
\(196\) −378.369 + 93.4017i −1.93045 + 0.476539i
\(197\) 20.2044 101.574i 0.102560 0.515605i −0.895017 0.446033i \(-0.852837\pi\)
0.997577 0.0695724i \(-0.0221635\pi\)
\(198\) 11.9474 + 244.149i 0.0603406 + 1.23308i
\(199\) −111.199 + 268.459i −0.558791 + 1.34904i 0.351934 + 0.936025i \(0.385524\pi\)
−0.910724 + 0.413015i \(0.864476\pi\)
\(200\) 101.038 224.817i 0.505191 1.12408i
\(201\) −30.3644 + 88.4813i −0.151067 + 0.440206i
\(202\) 179.457 58.9444i 0.888403 0.291804i
\(203\) 243.469 162.681i 1.19936 0.801384i
\(204\) −49.1031 89.7793i −0.240701 0.440095i
\(205\) −5.68642 + 1.13110i −0.0277386 + 0.00551755i
\(206\) 93.5852 11.3801i 0.454297 0.0552433i
\(207\) 172.137 + 133.917i 0.831579 + 0.646940i
\(208\) −116.584 144.058i −0.560502 0.692585i
\(209\) −131.359 131.359i −0.628510 0.628510i
\(210\) −98.7745 533.336i −0.470355 2.53969i
\(211\) 48.1887 + 242.261i 0.228383 + 1.14816i 0.909411 + 0.415900i \(0.136533\pi\)
−0.681028 + 0.732257i \(0.738467\pi\)
\(212\) −2.62611 57.4674i −0.0123873 0.271073i
\(213\) 13.5168 100.093i 0.0634592 0.469920i
\(214\) 175.046 + 88.4866i 0.817973 + 0.413489i
\(215\) −22.9972 55.5202i −0.106964 0.258233i
\(216\) −158.672 + 146.558i −0.734593 + 0.678508i
\(217\) −365.305 151.314i −1.68343 0.697301i
\(218\) 166.291 + 193.446i 0.762804 + 0.887367i
\(219\) 225.837 172.099i 1.03122 0.785839i
\(220\) 401.206 + 60.9171i 1.82367 + 0.276896i
\(221\) 82.1253 + 54.8744i 0.371608 + 0.248300i
\(222\) −206.557 + 134.101i −0.930438 + 0.604058i
\(223\) 350.850i 1.57332i −0.617387 0.786659i \(-0.711809\pi\)
0.617387 0.786659i \(-0.288191\pi\)
\(224\) 318.488 220.253i 1.42182 0.983273i
\(225\) 275.150 34.3611i 1.22289 0.152716i
\(226\) −19.6649 + 70.5897i −0.0870127 + 0.312344i
\(227\) 343.431 + 229.473i 1.51291 + 1.01090i 0.987066 + 0.160317i \(0.0512517\pi\)
0.525847 + 0.850579i \(0.323748\pi\)
\(228\) 14.5193 163.511i 0.0636812 0.717154i
\(229\) 68.0711 342.217i 0.297254 1.49440i −0.486696 0.873572i \(-0.661798\pi\)
0.783950 0.620824i \(-0.213202\pi\)
\(230\) 274.562 236.021i 1.19375 1.02618i
\(231\) 442.876 216.571i 1.91721 0.937538i
\(232\) −112.278 + 157.697i −0.483958 + 0.679730i
\(233\) −127.769 308.463i −0.548367 1.32387i −0.918693 0.394973i \(-0.870754\pi\)
0.370326 0.928902i \(-0.379246\pi\)
\(234\) 70.2751 196.287i 0.300321 0.838835i
\(235\) −330.521 + 220.847i −1.40647 + 0.939774i
\(236\) 39.3451 + 35.9063i 0.166717 + 0.152146i
\(237\) −185.822 + 319.392i −0.784060 + 1.34764i
\(238\) −127.250 + 162.482i −0.534664 + 0.682698i
\(239\) −238.944 238.944i −0.999766 0.999766i 0.000234107 1.00000i \(-0.499925\pi\)
−1.00000 0.000234107i \(0.999925\pi\)
\(240\) 186.251 + 306.425i 0.776046 + 1.27677i
\(241\) 99.6708 + 99.6708i 0.413572 + 0.413572i 0.882981 0.469409i \(-0.155533\pi\)
−0.469409 + 0.882981i \(0.655533\pi\)
\(242\) 15.3108 + 125.909i 0.0632678 + 0.520287i
\(243\) −233.640 66.7933i −0.961482 0.274869i
\(244\) 297.875 139.639i 1.22080 0.572291i
\(245\) −605.203 + 404.384i −2.47022 + 1.65055i
\(246\) 1.83870 4.27812i 0.00747439 0.0173907i
\(247\) 60.6345 + 146.385i 0.245484 + 0.592651i
\(248\) 261.289 + 7.75635i 1.05359 + 0.0312756i
\(249\) −128.879 263.551i −0.517588 1.05844i
\(250\) 6.53383 86.5582i 0.0261353 0.346233i
\(251\) 22.9324 115.289i 0.0913642 0.459319i −0.907836 0.419326i \(-0.862266\pi\)
0.999200 0.0399929i \(-0.0127335\pi\)
\(252\) 397.923 + 177.293i 1.57906 + 0.703545i
\(253\) 273.620 + 182.827i 1.08150 + 0.722638i
\(254\) −293.764 + 165.752i −1.15655 + 0.652567i
\(255\) −143.268 126.490i −0.561837 0.496038i
\(256\) −145.126 + 210.890i −0.566898 + 0.823788i
\(257\) 39.1255i 0.152239i 0.997099 + 0.0761197i \(0.0242531\pi\)
−0.997099 + 0.0761197i \(0.975747\pi\)
\(258\) 47.2089 + 10.0411i 0.182980 + 0.0389191i
\(259\) 412.975 + 275.941i 1.59450 + 1.06541i
\(260\) −296.265 178.955i −1.13948 0.688288i
\(261\) −217.216 15.6910i −0.832247 0.0601189i
\(262\) −7.97847 + 105.696i −0.0304522 + 0.403421i
\(263\) 20.6596 + 8.55747i 0.0785534 + 0.0325379i 0.421614 0.906775i \(-0.361464\pi\)
−0.343061 + 0.939313i \(0.611464\pi\)
\(264\) −222.865 + 237.816i −0.844185 + 0.900817i
\(265\) −41.1158 99.2624i −0.155154 0.374575i
\(266\) −314.537 + 103.312i −1.18247 + 0.388393i
\(267\) −409.376 55.2832i −1.53324 0.207053i
\(268\) −112.935 + 52.9423i −0.421400 + 0.197546i
\(269\) −65.3010 328.290i −0.242755 1.22041i −0.889225 0.457471i \(-0.848755\pi\)
0.646470 0.762940i \(-0.276245\pi\)
\(270\) −185.583 + 358.190i −0.687346 + 1.32663i
\(271\) −173.151 173.151i −0.638934 0.638934i 0.311358 0.950293i \(-0.399216\pi\)
−0.950293 + 0.311358i \(0.899216\pi\)
\(272\) 40.4990 130.291i 0.148893 0.479011i
\(273\) −419.671 + 26.1031i −1.53726 + 0.0956158i
\(274\) −168.066 + 214.599i −0.613381 + 0.783208i
\(275\) 410.359 81.6255i 1.49222 0.296820i
\(276\) 31.2822 + 289.104i 0.113341 + 1.04748i
\(277\) −176.162 + 117.708i −0.635965 + 0.424938i −0.831320 0.555794i \(-0.812414\pi\)
0.195355 + 0.980733i \(0.437414\pi\)
\(278\) −39.1305 19.7806i −0.140757 0.0711533i
\(279\) 145.340 + 255.655i 0.520932 + 0.916325i
\(280\) 419.458 589.138i 1.49806 2.10406i
\(281\) −150.035 + 362.217i −0.533933 + 1.28903i 0.394966 + 0.918696i \(0.370757\pi\)
−0.928899 + 0.370333i \(0.879243\pi\)
\(282\) 4.22148 319.235i 0.0149698 1.13204i
\(283\) −2.41890 + 12.1606i −0.00854736 + 0.0429705i −0.984824 0.173558i \(-0.944474\pi\)
0.976276 + 0.216529i \(0.0694735\pi\)
\(284\) 108.441 79.8515i 0.381834 0.281167i
\(285\) −78.3626 296.399i −0.274957 1.04000i
\(286\) 84.4230 303.048i 0.295185 1.05961i
\(287\) −9.39133 −0.0327224
\(288\) −287.547 16.1547i −0.998426 0.0560927i
\(289\) 216.282i 0.748380i
\(290\) −97.0253 + 348.285i −0.334570 + 1.20098i
\(291\) 253.965 67.1439i 0.872733 0.230735i
\(292\) 374.293 + 56.8307i 1.28182 + 0.194626i
\(293\) 49.2656 + 9.79953i 0.168142 + 0.0334455i 0.278443 0.960453i \(-0.410182\pi\)
−0.110301 + 0.993898i \(0.535182\pi\)
\(294\) 7.72979 584.539i 0.0262918 1.98823i
\(295\) 91.9101 + 38.0704i 0.311560 + 0.129052i
\(296\) −320.008 73.5875i −1.08111 0.248606i
\(297\) −358.884 75.1221i −1.20836 0.252936i
\(298\) 101.006 + 51.0588i 0.338946 + 0.171338i
\(299\) −155.937 233.376i −0.521527 0.780520i
\(300\) 288.036 + 231.789i 0.960119 + 0.772629i
\(301\) −18.9904 95.4711i −0.0630910 0.317180i
\(302\) −362.664 + 463.076i −1.20088 + 1.53336i
\(303\) 17.5891 + 282.788i 0.0580500 + 0.933295i
\(304\) 170.137 137.690i 0.559661 0.452928i
\(305\) 434.461 434.461i 1.42446 1.42446i
\(306\) 148.902 37.2677i 0.486608 0.121790i
\(307\) −195.822 + 38.9513i −0.637855 + 0.126877i −0.503415 0.864044i \(-0.667923\pi\)
−0.134440 + 0.990922i \(0.542923\pi\)
\(308\) 618.138 + 223.562i 2.00694 + 0.725851i
\(309\) −18.9248 + 140.140i −0.0612454 + 0.453527i
\(310\) 463.832 152.350i 1.49623 0.491451i
\(311\) 216.025 89.4807i 0.694616 0.287719i −0.00730607 0.999973i \(-0.502326\pi\)
0.701922 + 0.712254i \(0.252326\pi\)
\(312\) 253.238 114.655i 0.811661 0.367483i
\(313\) −6.04998 + 14.6059i −0.0193290 + 0.0466644i −0.933249 0.359229i \(-0.883040\pi\)
0.913920 + 0.405894i \(0.133040\pi\)
\(314\) 2.93163 38.8373i 0.00933639 0.123686i
\(315\) 811.493 + 58.6197i 2.57617 + 0.186094i
\(316\) −478.328 + 118.077i −1.51370 + 0.373661i
\(317\) −83.1228 + 124.402i −0.262217 + 0.392435i −0.939094 0.343661i \(-0.888333\pi\)
0.676877 + 0.736096i \(0.263333\pi\)
\(318\) 84.4030 + 17.9521i 0.265418 + 0.0564533i
\(319\) −328.611 −1.03013
\(320\) −120.928 + 462.572i −0.377899 + 1.44554i
\(321\) −194.722 + 220.552i −0.606612 + 0.687078i
\(322\) 510.776 288.198i 1.58626 0.895024i
\(323\) −64.8085 + 96.9928i −0.200646 + 0.300287i
\(324\) −152.623 285.801i −0.471059 0.882102i
\(325\) −350.002 69.6198i −1.07693 0.214215i
\(326\) 39.1319 518.408i 0.120037 1.59021i
\(327\) −343.745 + 168.095i −1.05121 + 0.514053i
\(328\) 5.80405 2.20472i 0.0176953 0.00672169i
\(329\) −594.881 + 246.408i −1.80815 + 0.748960i
\(330\) −240.358 + 559.243i −0.728357 + 1.69468i
\(331\) 48.3952 + 72.4286i 0.146209 + 0.218818i 0.897345 0.441331i \(-0.145493\pi\)
−0.751135 + 0.660148i \(0.770493\pi\)
\(332\) 133.040 367.848i 0.400722 1.10798i
\(333\) −116.408 350.584i −0.349575 1.05280i
\(334\) −54.2574 446.189i −0.162447 1.33590i
\(335\) −164.720 + 164.720i −0.491701 + 0.491701i
\(336\) 199.061 + 545.668i 0.592442 + 1.62401i
\(337\) 338.619 338.619i 1.00480 1.00480i 0.00481492 0.999988i \(-0.498467\pi\)
0.999988 0.00481492i \(-0.00153264\pi\)
\(338\) 42.9652 54.8610i 0.127116 0.162311i
\(339\) −95.0068 55.2750i −0.280256 0.163053i
\(340\) −11.6326 254.556i −0.0342135 0.748695i
\(341\) 246.527 + 368.953i 0.722952 + 1.08197i
\(342\) 231.822 + 82.9973i 0.677842 + 0.242682i
\(343\) −541.454 + 224.278i −1.57858 + 0.653871i
\(344\) 34.1493 + 54.5451i 0.0992713 + 0.158561i
\(345\) 238.581 + 487.885i 0.691540 + 1.41416i
\(346\) −148.009 + 127.232i −0.427771 + 0.367724i
\(347\) 190.609 + 37.9144i 0.549304 + 0.109263i 0.461937 0.886913i \(-0.347155\pi\)
0.0873674 + 0.996176i \(0.472155\pi\)
\(348\) −186.361 222.683i −0.535521 0.639895i
\(349\) −273.169 + 408.826i −0.782719 + 1.17142i 0.198797 + 0.980041i \(0.436296\pi\)
−0.981516 + 0.191381i \(0.938704\pi\)
\(350\) 200.104 718.299i 0.571725 2.05228i
\(351\) 258.278 + 176.334i 0.735836 + 0.502377i
\(352\) −434.507 + 6.94814i −1.23439 + 0.0197390i
\(353\) 30.5913 0.0866609 0.0433305 0.999061i \(-0.486203\pi\)
0.0433305 + 0.999061i \(0.486203\pi\)
\(354\) −67.0152 + 43.5075i −0.189308 + 0.122903i
\(355\) 139.734 209.126i 0.393616 0.589087i
\(356\) −326.589 443.518i −0.917385 1.24584i
\(357\) −187.636 246.226i −0.525591 0.689708i
\(358\) −73.1865 85.1375i −0.204431 0.237814i
\(359\) −164.609 + 397.402i −0.458521 + 1.10697i 0.510475 + 0.859893i \(0.329470\pi\)
−0.968996 + 0.247076i \(0.920530\pi\)
\(360\) −515.282 + 154.278i −1.43134 + 0.428551i
\(361\) 160.635 66.5373i 0.444973 0.184314i
\(362\) −93.3293 47.1783i −0.257816 0.130327i
\(363\) −188.544 25.4615i −0.519405 0.0701418i
\(364\) −414.118 377.924i −1.13769 1.03825i
\(365\) 693.473 137.940i 1.89993 0.377919i
\(366\) 89.8634 + 485.220i 0.245529 + 1.32574i
\(367\) −158.439 + 158.439i −0.431715 + 0.431715i −0.889211 0.457497i \(-0.848746\pi\)
0.457497 + 0.889211i \(0.348746\pi\)
\(368\) −248.013 + 298.023i −0.673949 + 0.809844i
\(369\) 5.51294 + 4.28888i 0.0149402 + 0.0116230i
\(370\) −608.776 + 74.0283i −1.64534 + 0.200076i
\(371\) −33.9522 170.689i −0.0915153 0.460078i
\(372\) −110.211 + 376.299i −0.296267 + 1.01156i
\(373\) 88.4847 + 132.427i 0.237224 + 0.355031i 0.930911 0.365245i \(-0.119015\pi\)
−0.693687 + 0.720277i \(0.744015\pi\)
\(374\) 220.042 72.2749i 0.588349 0.193248i
\(375\) 123.157 + 42.2640i 0.328418 + 0.112704i
\(376\) 309.803 291.940i 0.823944 0.776436i
\(377\) 258.943 + 107.258i 0.686852 + 0.284503i
\(378\) −408.023 + 510.403i −1.07943 + 1.35027i
\(379\) −18.3350 3.64706i −0.0483774 0.00962285i 0.170842 0.985298i \(-0.445351\pi\)
−0.219220 + 0.975676i \(0.570351\pi\)
\(380\) 211.352 349.899i 0.556189 0.920786i
\(381\) −129.321 489.143i −0.339424 1.28384i
\(382\) −211.503 374.849i −0.553673 0.981281i
\(383\) 65.5435i 0.171132i 0.996333 + 0.0855659i \(0.0272698\pi\)
−0.996333 + 0.0855659i \(0.972730\pi\)
\(384\) −251.125 290.503i −0.653972 0.756519i
\(385\) 1227.65 3.18870
\(386\) −149.141 + 84.1506i −0.386375 + 0.218007i
\(387\) −32.4524 + 64.7165i −0.0838564 + 0.167226i
\(388\) 299.806 + 181.094i 0.772695 + 0.466737i
\(389\) −95.8688 + 481.965i −0.246449 + 1.23898i 0.637150 + 0.770740i \(0.280113\pi\)
−0.883599 + 0.468244i \(0.844887\pi\)
\(390\) 371.936 362.227i 0.953681 0.928788i
\(391\) 79.0790 190.914i 0.202248 0.488270i
\(392\) 567.268 534.560i 1.44711 1.36367i
\(393\) −150.387 51.6087i −0.382663 0.131320i
\(394\) 64.6358 + 196.785i 0.164050 + 0.499454i
\(395\) −765.088 + 511.216i −1.93693 + 1.29422i
\(396\) −260.765 413.531i −0.658497 1.04427i
\(397\) 604.050 120.153i 1.52154 0.302653i 0.637640 0.770334i \(-0.279911\pi\)
0.883897 + 0.467681i \(0.154911\pi\)
\(398\) −70.1528 576.906i −0.176263 1.44951i
\(399\) −30.8287 495.646i −0.0772649 1.24222i
\(400\) 44.9598 + 490.901i 0.112399 + 1.22725i
\(401\) −42.4390 42.4390i −0.105833 0.105833i 0.652208 0.758040i \(-0.273843\pi\)
−0.758040 + 0.652208i \(0.773843\pi\)
\(402\) −34.0705 183.965i −0.0847525 0.457623i
\(403\) −73.8359 371.198i −0.183216 0.921087i
\(404\) −254.658 + 279.047i −0.630341 + 0.690710i
\(405\) −449.596 405.008i −1.11011 1.00002i
\(406\) −264.203 + 522.653i −0.650746 + 1.28732i
\(407\) −213.305 514.965i −0.524092 1.26527i
\(408\) 173.767 + 108.123i 0.425900 + 0.265008i
\(409\) −125.262 51.8854i −0.306265 0.126859i 0.224258 0.974530i \(-0.428004\pi\)
−0.530523 + 0.847671i \(0.678004\pi\)
\(410\) 8.79327 7.55892i 0.0214470 0.0184364i
\(411\) −247.821 325.204i −0.602971 0.791250i
\(412\) −151.827 + 111.800i −0.368513 + 0.271359i
\(413\) 133.985 + 89.5261i 0.324419 + 0.216770i
\(414\) −431.453 64.0845i −1.04216 0.154793i
\(415\) 730.562i 1.76039i
\(416\) 344.656 + 136.347i 0.828500 + 0.327757i
\(417\) 43.5289 49.3030i 0.104386 0.118233i
\(418\) 357.910 + 99.7065i 0.856243 + 0.238532i
\(419\) 404.519 + 270.291i 0.965440 + 0.645086i 0.935074 0.354453i \(-0.115333\pi\)
0.0303656 + 0.999539i \(0.490333\pi\)
\(420\) 696.223 + 831.917i 1.65767 + 1.98076i
\(421\) 98.5653 495.521i 0.234122 1.17701i −0.667542 0.744572i \(-0.732654\pi\)
0.901664 0.432438i \(-0.142346\pi\)
\(422\) −322.036 374.624i −0.763120 0.887734i
\(423\) 461.740 + 127.026i 1.09159 + 0.300297i
\(424\) 61.0543 + 97.5190i 0.143996 + 0.229998i
\(425\) −100.542 242.731i −0.236571 0.571132i
\(426\) 74.8288 + 187.632i 0.175654 + 0.440451i
\(427\) 827.512 552.926i 1.93797 1.29491i
\(428\) −391.872 + 17.9076i −0.915589 + 0.0418401i
\(429\) 407.873 + 237.300i 0.950752 + 0.553148i
\(430\) 94.6241 + 74.1062i 0.220056 + 0.172340i
\(431\) 358.285 + 358.285i 0.831287 + 0.831287i 0.987693 0.156405i \(-0.0499907\pi\)
−0.156405 + 0.987693i \(0.549991\pi\)
\(432\) 132.345 411.228i 0.306354 0.951918i
\(433\) −254.855 254.855i −0.588580 0.588580i 0.348667 0.937247i \(-0.386635\pi\)
−0.937247 + 0.348667i \(0.886635\pi\)
\(434\) 785.024 95.4603i 1.80881 0.219955i
\(435\) −468.758 272.723i −1.07760 0.626950i
\(436\) −479.778 173.521i −1.10041 0.397985i
\(437\) 275.624 184.166i 0.630720 0.421433i
\(438\) −224.234 + 521.728i −0.511950 + 1.19116i
\(439\) −31.1750 75.2631i −0.0710137 0.171442i 0.884387 0.466754i \(-0.154577\pi\)
−0.955401 + 0.295312i \(0.904577\pi\)
\(440\) −758.715 + 288.204i −1.72435 + 0.655009i
\(441\) 845.475 + 232.592i 1.91718 + 0.527419i
\(442\) −196.982 14.8692i −0.445661 0.0336406i
\(443\) −13.8087 + 69.4210i −0.0311709 + 0.156707i −0.993236 0.116113i \(-0.962956\pi\)
0.962065 + 0.272820i \(0.0879564\pi\)
\(444\) 227.997 436.593i 0.513506 0.983317i
\(445\) −855.316 571.504i −1.92206 1.28428i
\(446\) 344.822 + 611.131i 0.773143 + 1.37025i
\(447\) −112.359 + 127.264i −0.251363 + 0.284706i
\(448\) −338.292 + 696.665i −0.755116 + 1.55506i
\(449\) 47.5988i 0.106011i 0.998594 + 0.0530053i \(0.0168800\pi\)
−0.998594 + 0.0530053i \(0.983120\pi\)
\(450\) −445.502 + 330.275i −0.990005 + 0.733944i
\(451\) 8.76311 + 5.85532i 0.0194304 + 0.0129830i
\(452\) −35.1234 142.284i −0.0777066 0.314788i
\(453\) −534.764 701.746i −1.18050 1.54911i
\(454\) −823.739 62.1798i −1.81440 0.136960i
\(455\) −967.379 400.702i −2.12611 0.880663i
\(456\) 135.411 + 299.083i 0.296954 + 0.655884i
\(457\) 219.114 + 528.989i 0.479462 + 1.15752i 0.959861 + 0.280474i \(0.0904918\pi\)
−0.480399 + 0.877050i \(0.659508\pi\)
\(458\) 217.766 + 662.994i 0.475472 + 1.44759i
\(459\) −2.30071 + 230.231i −0.00501243 + 0.501593i
\(460\) −246.283 + 680.959i −0.535397 + 1.48035i
\(461\) 148.015 + 744.120i 0.321073 + 1.61414i 0.717829 + 0.696219i \(0.245136\pi\)
−0.396757 + 0.917924i \(0.629864\pi\)
\(462\) −558.577 + 812.503i −1.20904 + 1.75866i
\(463\) 469.193 + 469.193i 1.01338 + 1.01338i 0.999909 + 0.0134669i \(0.00428677\pi\)
0.0134669 + 0.999909i \(0.495713\pi\)
\(464\) 40.5850 385.036i 0.0874677 0.829818i
\(465\) 45.4615 + 730.905i 0.0977667 + 1.57184i
\(466\) 525.719 + 411.724i 1.12815 + 0.883528i
\(467\) 257.221 51.1644i 0.550795 0.109560i 0.0881557 0.996107i \(-0.471903\pi\)
0.462639 + 0.886547i \(0.346903\pi\)
\(468\) 70.5054 + 410.972i 0.150653 + 0.878146i
\(469\) −313.740 + 209.634i −0.668955 + 0.446982i
\(470\) 358.668 709.525i 0.763123 1.50963i
\(471\) 55.2584 + 18.9632i 0.117321 + 0.0402616i
\(472\) −103.823 23.8746i −0.219964 0.0505819i
\(473\) −41.8044 + 100.925i −0.0883815 + 0.213372i
\(474\) 9.77188 738.964i 0.0206158 1.55900i
\(475\) 82.2234 413.365i 0.173102 0.870242i
\(476\) 61.9614 408.084i 0.130171 0.857320i
\(477\) −58.0204 + 115.704i −0.121636 + 0.242566i
\(478\) 651.045 + 181.368i 1.36202 + 0.379431i
\(479\) −310.103 −0.647397 −0.323699 0.946160i \(-0.604926\pi\)
−0.323699 + 0.946160i \(0.604926\pi\)
\(480\) −625.583 350.698i −1.30330 0.730620i
\(481\) 475.411i 0.988380i
\(482\) −271.570 75.6541i −0.563424 0.156959i
\(483\) 224.854 + 850.486i 0.465535 + 1.76084i
\(484\) −150.415 204.269i −0.310775 0.422042i
\(485\) 641.583 + 127.619i 1.32285 + 0.263132i
\(486\) 472.613 113.281i 0.972455 0.233089i
\(487\) 120.263 + 49.8147i 0.246947 + 0.102289i 0.502724 0.864447i \(-0.332331\pi\)
−0.255777 + 0.966736i \(0.582331\pi\)
\(488\) −381.616 + 535.988i −0.781999 + 1.09834i
\(489\) 737.600 + 253.124i 1.50838 + 0.517637i
\(490\) 656.743 1299.18i 1.34029 2.65140i
\(491\) 289.645 + 433.485i 0.589909 + 0.882861i 0.999568 0.0293778i \(-0.00935258\pi\)
−0.409660 + 0.912238i \(0.634353\pi\)
\(492\) 1.00186 + 9.25898i 0.00203630 + 0.0188191i
\(493\) 40.2567 + 202.384i 0.0816565 + 0.410515i
\(494\) −249.486 195.389i −0.505033 0.395524i
\(495\) −720.661 560.650i −1.45588 1.13263i
\(496\) −462.752 + 243.289i −0.932968 + 0.490503i
\(497\) 288.077 288.077i 0.579632 0.579632i
\(498\) 483.512 + 332.403i 0.970908 + 0.667477i
\(499\) 834.052 165.903i 1.67145 0.332471i 0.733616 0.679565i \(-0.237831\pi\)
0.937831 + 0.347093i \(0.112831\pi\)
\(500\) 73.6900 + 157.194i 0.147380 + 0.314387i
\(501\) 668.149 + 90.2287i 1.33363 + 0.180097i
\(502\) 73.3631 + 223.355i 0.146142 + 0.444931i
\(503\) 137.677 57.0275i 0.273711 0.113375i −0.241606 0.970374i \(-0.577674\pi\)
0.515317 + 0.857000i \(0.327674\pi\)
\(504\) −867.372 + 82.2655i −1.72098 + 0.163225i
\(505\) −270.006 + 651.852i −0.534665 + 1.29080i
\(506\) −656.294 49.5402i −1.29702 0.0979055i
\(507\) 63.3540 + 83.1365i 0.124959 + 0.163977i
\(508\) 348.791 577.433i 0.686596 1.13668i
\(509\) −38.6923 + 57.9071i −0.0760163 + 0.113766i −0.867530 0.497385i \(-0.834294\pi\)
0.791513 + 0.611152i \(0.209294\pi\)
\(510\) 373.870 + 79.5204i 0.733078 + 0.155922i
\(511\) 1145.30 2.24129
\(512\) 45.5225 509.972i 0.0889111 0.996040i
\(513\) −208.257 + 305.035i −0.405959 + 0.594611i
\(514\) −38.4533 68.1511i −0.0748118 0.132590i
\(515\) −195.640 + 292.796i −0.379884 + 0.568537i
\(516\) −92.0998 + 28.9075i −0.178488 + 0.0560224i
\(517\) 708.718 + 140.973i 1.37083 + 0.272675i
\(518\) −990.544 74.7710i −1.91225 0.144346i
\(519\) −128.613 263.005i −0.247809 0.506754i
\(520\) 691.931 + 20.5399i 1.33064 + 0.0394998i
\(521\) −120.250 + 49.8093i −0.230807 + 0.0956033i −0.495090 0.868842i \(-0.664865\pi\)
0.264283 + 0.964445i \(0.414865\pi\)
\(522\) 393.781 186.153i 0.754371 0.356614i
\(523\) −189.767 284.006i −0.362842 0.543032i 0.604467 0.796630i \(-0.293386\pi\)
−0.967310 + 0.253598i \(0.918386\pi\)
\(524\) −89.9829 191.949i −0.171723 0.366316i
\(525\) 966.761 + 562.461i 1.84145 + 1.07136i
\(526\) −44.3964 + 5.39868i −0.0844039 + 0.0102637i
\(527\) 197.029 197.029i 0.373869 0.373869i
\(528\) 154.469 633.277i 0.292555 1.19939i
\(529\) −41.1668 + 41.1668i −0.0778199 + 0.0778199i
\(530\) 169.175 + 132.492i 0.319198 + 0.249984i
\(531\) −37.7674 113.743i −0.0711251 0.214205i
\(532\) 446.341 489.088i 0.838987 0.919338i
\(533\) −4.99411 7.47421i −0.00936980 0.0140229i
\(534\) 767.408 306.046i 1.43709 0.573120i
\(535\) −676.874 + 280.370i −1.26518 + 0.524056i
\(536\) 144.684 203.213i 0.269934 0.379128i
\(537\) 151.286 73.9804i 0.281724 0.137766i
\(538\) 436.395 + 507.656i 0.811143 + 0.943599i
\(539\) 1297.71 + 258.130i 2.40762 + 0.478905i
\(540\) −28.7757 806.311i −0.0532884 1.49317i
\(541\) −369.786 + 553.424i −0.683523 + 1.02297i 0.313774 + 0.949498i \(0.398407\pi\)
−0.997298 + 0.0734675i \(0.976593\pi\)
\(542\) 471.781 + 131.429i 0.870444 + 0.242488i
\(543\) 103.820 117.592i 0.191197 0.216559i
\(544\) 57.5086 + 266.751i 0.105714 + 0.490352i
\(545\) −952.860 −1.74837
\(546\) 705.353 457.928i 1.29186 0.838697i
\(547\) −241.382 + 361.253i −0.441283 + 0.660426i −0.983728 0.179665i \(-0.942499\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(548\) 81.8359 538.980i 0.149336 0.983540i
\(549\) −738.283 53.3313i −1.34478 0.0971426i
\(550\) −634.565 + 545.488i −1.15375 + 0.991797i
\(551\) −126.675 + 305.821i −0.229900 + 0.555029i
\(552\) −338.625 472.833i −0.613452 0.856581i
\(553\) −1377.03 + 570.384i −2.49011 + 1.03144i
\(554\) 191.164 378.166i 0.345062 0.682610i
\(555\) 123.107 911.616i 0.221815 1.64255i
\(556\) 87.6005 4.00312i 0.157555 0.00719986i
\(557\) −251.464 + 50.0193i −0.451462 + 0.0898013i −0.415584 0.909555i \(-0.636423\pi\)
−0.0358778 + 0.999356i \(0.511423\pi\)
\(558\) −504.424 302.471i −0.903985 0.542063i
\(559\) 65.8832 65.8832i 0.117859 0.117859i
\(560\) −151.621 + 1438.44i −0.270751 + 2.56865i
\(561\) 21.5670 + 346.742i 0.0384439 + 0.618079i
\(562\) −94.6534 778.388i −0.168422 1.38503i
\(563\) 18.3577 + 92.2904i 0.0326069 + 0.163926i 0.993658 0.112445i \(-0.0358682\pi\)
−0.961051 + 0.276371i \(0.910868\pi\)
\(564\) 306.397 + 560.211i 0.543256 + 0.993282i
\(565\) −152.067 227.584i −0.269145 0.402804i
\(566\) −7.73831 23.5595i −0.0136719 0.0416245i
\(567\) −586.278 785.504i −1.03400 1.38537i
\(568\) −110.409 + 245.667i −0.194382 + 0.432513i
\(569\) −682.897 282.865i −1.20017 0.497127i −0.309117 0.951024i \(-0.600033\pi\)
−0.891054 + 0.453897i \(0.850033\pi\)
\(570\) 427.803 + 439.269i 0.750531 + 0.770647i
\(571\) −900.959 179.212i −1.57786 0.313856i −0.673026 0.739618i \(-0.735006\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 150.788 + 610.839i 0.263615 + 1.06790i
\(573\) 624.157 165.016i 1.08928 0.287986i
\(574\) 16.3584 9.22997i 0.0284989 0.0160801i
\(575\) 746.600i 1.29843i
\(576\) 516.742 254.467i 0.897122 0.441782i
\(577\) −185.309 −0.321159 −0.160580 0.987023i \(-0.551336\pi\)
−0.160580 + 0.987023i \(0.551336\pi\)
\(578\) 212.566 + 376.732i 0.367760 + 0.651786i
\(579\) −65.6548 248.333i −0.113393 0.428900i
\(580\) −173.297 702.022i −0.298787 1.21038i
\(581\) 230.863 1160.63i 0.397355 1.99764i
\(582\) −376.381 + 366.557i −0.646703 + 0.629823i
\(583\) −74.7405 + 180.440i −0.128200 + 0.309502i
\(584\) −707.819 + 268.871i −1.21202 + 0.460395i
\(585\) 384.881 + 677.009i 0.657916 + 1.15728i
\(586\) −95.4448 + 31.3497i −0.162875 + 0.0534977i
\(587\) 529.217 353.611i 0.901561 0.602404i −0.0160551 0.999871i \(-0.505111\pi\)
0.917616 + 0.397467i \(0.130111\pi\)
\(588\) 561.031 + 1025.78i 0.954134 + 1.74452i
\(589\) 438.398 87.2027i 0.744309 0.148052i
\(590\) −197.511 + 24.0176i −0.334764 + 0.0407079i
\(591\) −310.093 + 19.2875i −0.524692 + 0.0326353i
\(592\) 629.732 186.331i 1.06374 0.314748i
\(593\) 110.696 + 110.696i 0.186671 + 0.186671i 0.794255 0.607584i \(-0.207861\pi\)
−0.607584 + 0.794255i \(0.707861\pi\)
\(594\) 698.956 221.865i 1.17669 0.373511i
\(595\) −150.394 756.081i −0.252763 1.27072i
\(596\) −226.119 + 10.3331i −0.379395 + 0.0173374i
\(597\) 863.892 + 116.662i 1.44706 + 0.195414i
\(598\) 500.985 + 253.250i 0.837767 + 0.423495i
\(599\) −109.139 263.486i −0.182203 0.439876i 0.806217 0.591620i \(-0.201511\pi\)
−0.988420 + 0.151743i \(0.951511\pi\)
\(600\) −729.524 120.656i −1.21587 0.201094i
\(601\) 12.3425 + 5.11243i 0.0205366 + 0.00850654i 0.392928 0.919569i \(-0.371462\pi\)
−0.372391 + 0.928076i \(0.621462\pi\)
\(602\) 126.909 + 147.633i 0.210813 + 0.245238i
\(603\) 279.910 + 20.2198i 0.464196 + 0.0335321i
\(604\) 176.591 1163.05i 0.292369 1.92557i
\(605\) −393.928 263.214i −0.651121 0.435065i
\(606\) −308.567 475.290i −0.509187 0.784307i
\(607\) 546.365i 0.900106i 0.893002 + 0.450053i \(0.148595\pi\)
−0.893002 + 0.450053i \(0.851405\pi\)
\(608\) −161.030 + 407.051i −0.264852 + 0.669491i
\(609\) −658.523 581.401i −1.08132 0.954682i
\(610\) −329.773 + 1183.76i −0.540612 + 1.94060i
\(611\) −512.451 342.409i −0.838709 0.560408i
\(612\) −222.739 + 211.259i −0.363952 + 0.345194i
\(613\) −96.6037 + 485.659i −0.157592 + 0.792267i 0.818432 + 0.574603i \(0.194844\pi\)
−0.976024 + 0.217664i \(0.930156\pi\)
\(614\) 302.811 260.305i 0.493178 0.423949i
\(615\) 7.64093 + 15.6253i 0.0124243 + 0.0254069i
\(616\) −1296.43 + 218.104i −2.10459 + 0.354064i
\(617\) 344.824 + 832.478i 0.558872 + 1.34924i 0.910660 + 0.413156i \(0.135574\pi\)
−0.351789 + 0.936079i \(0.614426\pi\)
\(618\) −104.767 262.703i −0.169527 0.425086i
\(619\) −593.178 + 396.349i −0.958284 + 0.640305i −0.933191 0.359380i \(-0.882988\pi\)
−0.0250929 + 0.999685i \(0.507988\pi\)
\(620\) −658.197 + 721.234i −1.06161 + 1.16328i
\(621\) 256.410 601.944i 0.412898 0.969314i
\(622\) −288.342 + 368.176i −0.463573 + 0.591923i
\(623\) −1178.22 1178.22i −1.89121 1.89121i
\(624\) −328.420 + 448.599i −0.526315 + 0.718909i
\(625\) −315.372 315.372i −0.504595 0.504595i
\(626\) −3.81678 31.3875i −0.00609709 0.0501398i
\(627\) −280.260 + 481.712i −0.446985 + 0.768280i
\(628\) 33.0635 + 70.5303i 0.0526489 + 0.112309i
\(629\) −291.024 + 194.456i −0.462677 + 0.309151i
\(630\) −1471.12 + 695.443i −2.33511 + 1.10388i
\(631\) 5.85195 + 14.1279i 0.00927409 + 0.0223896i 0.928449 0.371461i \(-0.121143\pi\)
−0.919175 + 0.393850i \(0.871143\pi\)
\(632\) 717.131 675.782i 1.13470 1.06928i
\(633\) 665.690 325.530i 1.05164 0.514266i
\(634\) 22.5235 298.385i 0.0355261 0.470639i
\(635\) 245.797 1235.70i 0.387082 1.94599i
\(636\) −164.662 + 51.6827i −0.258902 + 0.0812621i
\(637\) −938.329 626.972i −1.47304 0.984257i
\(638\) 572.394 322.965i 0.897169 0.506215i
\(639\) −300.669 + 37.5479i −0.470531 + 0.0587604i
\(640\) −243.985 924.585i −0.381227 1.44466i
\(641\) 468.390i 0.730717i 0.930867 + 0.365359i \(0.119054\pi\)
−0.930867 + 0.365359i \(0.880946\pi\)
\(642\) 122.416 575.547i 0.190679 0.896490i
\(643\) 596.885 + 398.826i 0.928281 + 0.620258i 0.925094 0.379737i \(-0.123986\pi\)
0.00318693 + 0.999995i \(0.498986\pi\)
\(644\) −606.453 + 1004.00i −0.941697 + 1.55900i
\(645\) −143.394 + 109.273i −0.222316 + 0.169415i
\(646\) 17.5610 232.643i 0.0271842 0.360128i
\(647\) 673.324 + 278.900i 1.04069 + 0.431066i 0.836558 0.547878i \(-0.184564\pi\)
0.204128 + 0.978944i \(0.434564\pi\)
\(648\) 546.738 + 347.824i 0.843732 + 0.536765i
\(649\) −69.2046 167.075i −0.106633 0.257434i
\(650\) 678.078 222.721i 1.04320 0.342647i
\(651\) −158.748 + 1175.54i −0.243852 + 1.80574i
\(652\) 441.338 + 941.452i 0.676899 + 1.44394i
\(653\) −52.7284 265.083i −0.0807479 0.405947i −0.999927 0.0121066i \(-0.996146\pi\)
0.919179 0.393840i \(-0.128854\pi\)
\(654\) 433.548 630.637i 0.662918 0.964276i
\(655\) −279.965 279.965i −0.427428 0.427428i
\(656\) −7.94300 + 9.54463i −0.0121082 + 0.0145497i
\(657\) −672.318 523.040i −1.02331 0.796104i
\(658\) 794.024 1013.87i 1.20672 1.54083i
\(659\) −369.319 + 73.4622i −0.560424 + 0.111475i −0.467171 0.884167i \(-0.654727\pi\)
−0.0932532 + 0.995642i \(0.529727\pi\)
\(660\) −130.965 1210.35i −0.198431 1.83386i
\(661\) 120.623 80.5980i 0.182486 0.121934i −0.460972 0.887415i \(-0.652499\pi\)
0.643458 + 0.765481i \(0.277499\pi\)
\(662\) −155.482 78.5966i −0.234867 0.118726i
\(663\) 96.1811 280.270i 0.145069 0.422730i
\(664\) 129.791 + 771.492i 0.195469 + 1.16189i
\(665\) 473.242 1142.51i 0.711643 1.71806i
\(666\) 547.327 + 496.259i 0.821812 + 0.745134i
\(667\) 114.397 575.114i 0.171510 0.862240i
\(668\) 533.032 + 723.873i 0.797951 + 1.08364i
\(669\) −1017.59 + 269.032i −1.52106 + 0.402141i
\(670\) 125.029 448.808i 0.186611 0.669863i
\(671\) −1116.90 −1.66452
\(672\) −883.027 754.836i −1.31403 1.12327i
\(673\) 896.920i 1.33272i 0.745630 + 0.666360i \(0.232149\pi\)
−0.745630 + 0.666360i \(0.767851\pi\)
\(674\) −257.025 + 922.626i −0.381343 + 1.36888i
\(675\) −310.645 771.684i −0.460214 1.14324i
\(676\) −20.9209 + 137.787i −0.0309480 + 0.203827i
\(677\) 842.597 + 167.603i 1.24460 + 0.247567i 0.773093 0.634293i \(-0.218709\pi\)
0.471512 + 0.881860i \(0.343709\pi\)
\(678\) 219.814 + 2.90676i 0.324209 + 0.00428725i
\(679\) 978.942 + 405.491i 1.44174 + 0.597189i
\(680\) 270.445 + 431.968i 0.397713 + 0.635247i
\(681\) 402.209 1172.03i 0.590616 1.72104i
\(682\) −792.029 400.373i −1.16133 0.587058i
\(683\) 284.099 + 425.185i 0.415958 + 0.622525i 0.978990 0.203910i \(-0.0653650\pi\)
−0.563032 + 0.826435i \(0.690365\pi\)
\(684\) −485.372 + 83.2693i −0.709609 + 0.121739i
\(685\) −198.633 998.598i −0.289976 1.45781i
\(686\) 722.712 922.811i 1.05352 1.34521i
\(687\) −1044.74 + 64.9820i −1.52073 + 0.0945881i
\(688\) −113.091 61.4472i −0.164377 0.0893128i
\(689\) 117.790 117.790i 0.170958 0.170958i
\(690\) −895.077 615.344i −1.29721 0.891803i
\(691\) −100.509 + 19.9924i −0.145454 + 0.0289326i −0.267280 0.963619i \(-0.586125\pi\)
0.121826 + 0.992551i \(0.461125\pi\)
\(692\) 132.764 367.087i 0.191856 0.530472i
\(693\) −967.730 1118.43i −1.39644 1.61389i
\(694\) −369.276 + 121.292i −0.532098 + 0.174772i
\(695\) 151.311 62.6750i 0.217713 0.0901799i
\(696\) 543.472 + 204.724i 0.780851 + 0.294143i
\(697\) 2.53263 6.11430i 0.00363361 0.00877231i
\(698\) 74.0198 980.592i 0.106046 1.40486i
\(699\) −796.676 + 607.105i −1.13974 + 0.868534i
\(700\) 357.405 + 1447.84i 0.510578 + 2.06834i
\(701\) 475.833 712.135i 0.678792 1.01588i −0.318887 0.947793i \(-0.603309\pi\)
0.997679 0.0680914i \(-0.0216910\pi\)
\(702\) −623.189 53.3090i −0.887733 0.0759388i
\(703\) −561.477 −0.798686
\(704\) 750.020 439.144i 1.06537 0.623784i
\(705\) 893.976 + 789.279i 1.26805 + 1.11955i
\(706\) −53.2857 + 30.0657i −0.0754755 + 0.0425859i
\(707\) −634.944 + 950.260i −0.898082 + 1.34407i
\(708\) 73.9710 141.648i 0.104479 0.200067i
\(709\) −353.988 70.4127i −0.499279 0.0993127i −0.0609743 0.998139i \(-0.519421\pi\)
−0.438304 + 0.898827i \(0.644421\pi\)
\(710\) −37.8632 + 501.600i −0.0533285 + 0.706479i
\(711\) 1068.84 + 294.039i 1.50329 + 0.413557i
\(712\) 1004.77 + 451.568i 1.41119 + 0.634224i
\(713\) −731.540 + 303.014i −1.02600 + 0.424984i
\(714\) 568.830 + 244.478i 0.796681 + 0.342407i
\(715\) 652.838 + 977.041i 0.913060 + 1.36649i
\(716\) 211.155 + 76.3685i 0.294909 + 0.106660i
\(717\) −509.798 + 876.243i −0.711016 + 1.22210i
\(718\) −103.848 853.998i −0.144635 1.18941i
\(719\) 258.783 258.783i 0.359921 0.359921i −0.503863 0.863784i \(-0.668088\pi\)
0.863784 + 0.503863i \(0.168088\pi\)
\(720\) 745.921 775.160i 1.03600 1.07661i
\(721\) −403.336 + 403.336i −0.559412 + 0.559412i
\(722\) −214.410 + 273.774i −0.296966 + 0.379188i
\(723\) 212.652 365.507i 0.294125 0.505543i
\(724\) 208.934 9.54776i 0.288583 0.0131875i
\(725\) −414.197 619.890i −0.571307 0.855021i
\(726\) 353.441 140.954i 0.486833 0.194152i
\(727\) 896.400 371.301i 1.23301 0.510730i 0.331488 0.943459i \(-0.392449\pi\)
0.901524 + 0.432729i \(0.142449\pi\)
\(728\) 1092.77 + 251.287i 1.50105 + 0.345175i
\(729\) −14.5684 + 728.854i −0.0199841 + 0.999800i
\(730\) −1072.36 + 921.831i −1.46899 + 1.26278i
\(731\) 67.2785 + 13.3825i 0.0920363 + 0.0183072i
\(732\) −633.412 756.865i −0.865317 1.03397i
\(733\) 226.209 338.545i 0.308607 0.461863i −0.644453 0.764644i \(-0.722915\pi\)
0.953060 + 0.302781i \(0.0979151\pi\)
\(734\) 120.262 431.696i 0.163844 0.588141i
\(735\) 1636.92 + 1445.22i 2.22711 + 1.96628i
\(736\) 139.102 762.865i 0.188997 1.03650i
\(737\) 423.456 0.574567
\(738\) −13.8180 2.05240i −0.0187235 0.00278103i
\(739\) 632.251 946.231i 0.855550 1.28042i −0.102765 0.994706i \(-0.532769\pi\)
0.958315 0.285715i \(-0.0922311\pi\)
\(740\) 987.646 727.263i 1.33466 0.982788i
\(741\) 378.072 288.109i 0.510219 0.388811i
\(742\) 226.896 + 263.947i 0.305790 + 0.355724i
\(743\) 176.935 427.160i 0.238137 0.574912i −0.758954 0.651145i \(-0.774289\pi\)
0.997090 + 0.0762324i \(0.0242891\pi\)
\(744\) −177.861 763.777i −0.239060 1.02658i
\(745\) −390.572 + 161.780i −0.524258 + 0.217155i
\(746\) −284.279 143.704i −0.381071 0.192633i
\(747\) −665.565 + 575.886i −0.890983 + 0.770932i
\(748\) −312.250 + 342.154i −0.417446 + 0.457426i
\(749\) −1163.93 + 231.521i −1.55398 + 0.309107i
\(750\) −256.059 + 47.4225i −0.341412 + 0.0632300i
\(751\) 607.594 607.594i 0.809046 0.809046i −0.175443 0.984490i \(-0.556136\pi\)
0.984490 + 0.175443i \(0.0561359\pi\)
\(752\) −252.709 + 812.998i −0.336049 + 1.08111i
\(753\) −351.963 + 21.8917i −0.467414 + 0.0290727i
\(754\) −556.457 + 67.6662i −0.738007 + 0.0897429i
\(755\) −428.624 2154.84i −0.567714 2.85409i
\(756\) 209.085 1290.06i 0.276568 1.70643i
\(757\) 532.638 + 797.150i 0.703617 + 1.05304i 0.995330 + 0.0965317i \(0.0307749\pi\)
−0.291713 + 0.956506i \(0.594225\pi\)
\(758\) 35.5214 11.6673i 0.0468620 0.0153922i
\(759\) 320.450 933.786i 0.422201 1.23029i
\(760\) −24.2583 + 817.194i −0.0319189 + 1.07526i
\(761\) 940.607 + 389.612i 1.23601 + 0.511974i 0.902467 0.430760i \(-0.141754\pi\)
0.333547 + 0.942733i \(0.391754\pi\)
\(762\) 705.996 + 724.918i 0.926504 + 0.951337i
\(763\) −1513.79 301.111i −1.98400 0.394641i
\(764\) 736.817 + 445.065i 0.964420 + 0.582546i
\(765\) −257.006 + 512.521i −0.335955 + 0.669962i
\(766\) −64.4173 114.167i −0.0840957 0.149044i
\(767\) 154.242i 0.201098i
\(768\) 722.936 + 259.205i 0.941323 + 0.337507i
\(769\) 397.909 0.517437 0.258718 0.965953i \(-0.416700\pi\)
0.258718 + 0.965953i \(0.416700\pi\)
\(770\) −2138.39 + 1206.56i −2.77713 + 1.56696i
\(771\) 113.478 30.0015i 0.147182 0.0389124i
\(772\) 177.078 293.157i 0.229375 0.379737i
\(773\) −198.492 + 997.885i −0.256781 + 1.29092i 0.610066 + 0.792351i \(0.291143\pi\)
−0.866847 + 0.498574i \(0.833857\pi\)
\(774\) −7.07706 144.622i −0.00914349 0.186850i
\(775\) −385.257 + 930.093i −0.497106 + 1.20012i
\(776\) −700.201 20.7854i −0.902321 0.0267853i
\(777\) 483.656 1409.36i 0.622466 1.81385i
\(778\) −306.694 933.736i −0.394208 1.20017i
\(779\) 8.82729 5.89821i 0.0113316 0.00757151i
\(780\) −291.856 + 996.493i −0.374174 + 1.27756i
\(781\) −448.418 + 89.1958i −0.574158 + 0.114207i
\(782\) 49.8889 + 410.265i 0.0637966 + 0.524635i
\(783\) 121.052 + 642.035i 0.154600 + 0.819968i
\(784\) −462.725 + 1488.65i −0.590210 + 1.89879i
\(785\) 102.871 + 102.871i 0.131046 + 0.131046i
\(786\) 312.674 57.9077i 0.397804 0.0736739i
\(787\) 36.5214 + 183.605i 0.0464058 + 0.233298i 0.997027 0.0770567i \(-0.0245522\pi\)
−0.950621 + 0.310354i \(0.899552\pi\)
\(788\) −305.990 279.246i −0.388312 0.354374i
\(789\) 8.97787 66.4818i 0.0113788 0.0842608i
\(790\) 830.243 1642.41i 1.05094 2.07900i
\(791\) −169.667 409.613i −0.214497 0.517842i
\(792\) 860.641 + 464.028i 1.08667 + 0.585894i
\(793\) 880.106 + 364.552i 1.10984 + 0.459712i
\(794\) −934.081 + 802.961i −1.17642 + 1.01129i
\(795\) −256.368 + 195.365i −0.322475 + 0.245742i
\(796\) 689.190 + 935.941i 0.865816 + 1.17581i
\(797\) −296.861 198.356i −0.372473 0.248878i 0.355218 0.934783i \(-0.384407\pi\)
−0.727691 + 0.685905i \(0.759407\pi\)
\(798\) 540.829 + 833.046i 0.677731 + 1.04392i
\(799\) 453.752i 0.567900i
\(800\) −560.780 810.893i −0.700975 1.01362i
\(801\) 153.569 + 1229.72i 0.191722 + 1.53523i
\(802\) 115.633 + 32.2129i 0.144180 + 0.0401657i
\(803\) −1068.68 714.072i −1.33086 0.889255i
\(804\) 240.150 + 286.955i 0.298694 + 0.356909i
\(805\) −427.374 + 2148.55i −0.530899 + 2.66901i
\(806\) 493.432 + 574.007i 0.612198 + 0.712168i
\(807\) −902.083 + 441.129i −1.11782 + 0.546628i
\(808\) 169.326 736.342i 0.209561 0.911314i
\(809\) −505.763 1221.02i −0.625171 1.50930i −0.845558 0.533883i \(-0.820732\pi\)
0.220388 0.975412i \(-0.429268\pi\)
\(810\) 1181.18 + 263.596i 1.45825 + 0.325427i
\(811\) −207.381 + 138.567i −0.255710 + 0.170860i −0.676818 0.736151i \(-0.736641\pi\)
0.421108 + 0.907011i \(0.361641\pi\)
\(812\) −53.4684 1170.05i −0.0658477 1.44095i
\(813\) −369.426 + 634.971i −0.454399 + 0.781022i
\(814\) 877.665 + 687.355i 1.07821 + 0.844417i
\(815\) 1373.14 + 1373.14i 1.68484 + 1.68484i
\(816\) −408.943 17.5541i −0.501156 0.0215124i
\(817\) 77.8103 + 77.8103i 0.0952390 + 0.0952390i
\(818\) 269.183 32.7331i 0.329075 0.0400161i
\(819\) 397.512 + 1197.18i 0.485363 + 1.46175i
\(820\) −7.88758 + 21.8088i −0.00961899 + 0.0265960i
\(821\) −712.809 + 476.284i −0.868220 + 0.580126i −0.907947 0.419084i \(-0.862351\pi\)
0.0397271 + 0.999211i \(0.487351\pi\)
\(822\) 751.285 + 322.896i 0.913973 + 0.392818i
\(823\) 52.4924 + 126.728i 0.0637817 + 0.153983i 0.952557 0.304361i \(-0.0984429\pi\)
−0.888775 + 0.458344i \(0.848443\pi\)
\(824\) 154.583 343.958i 0.187601 0.417425i
\(825\) −551.406 1127.59i −0.668371 1.36678i
\(826\) −321.371 24.2586i −0.389069 0.0293688i
\(827\) −19.7276 + 99.1775i −0.0238545 + 0.119924i −0.990878 0.134763i \(-0.956973\pi\)
0.967023 + 0.254688i \(0.0819726\pi\)
\(828\) 814.514 312.414i 0.983712 0.377312i
\(829\) −3.64269 2.43397i −0.00439408 0.00293603i 0.553371 0.832935i \(-0.313341\pi\)
−0.557765 + 0.829999i \(0.688341\pi\)
\(830\) 718.009 + 1272.54i 0.865071 + 1.53317i
\(831\) 476.475 + 420.674i 0.573376 + 0.506226i
\(832\) −734.346 + 101.237i −0.882627 + 0.121680i
\(833\) 830.848i 0.997417i
\(834\) −27.3654 + 128.660i −0.0328122 + 0.154268i
\(835\) 1395.98 + 932.762i 1.67183 + 1.11708i
\(836\) −721.421 + 178.085i −0.862944 + 0.213021i
\(837\) 630.040 617.573i 0.752736 0.737841i
\(838\) −970.262 73.2400i −1.15783 0.0873986i
\(839\) 405.021 + 167.765i 0.482743 + 0.199959i 0.610764 0.791813i \(-0.290863\pi\)
−0.128021 + 0.991771i \(0.540863\pi\)
\(840\) −2030.34 764.822i −2.41708 0.910502i
\(841\) −97.7584 236.010i −0.116241 0.280630i
\(842\) 315.320 + 959.999i 0.374490 + 1.14014i
\(843\) 1165.60 + 157.406i 1.38268 + 0.186721i
\(844\) 929.129 + 336.038i 1.10086 + 0.398149i
\(845\) 50.7795 + 255.286i 0.0600941 + 0.302113i
\(846\) −929.130 + 232.546i −1.09826 + 0.274877i
\(847\) −542.648 542.648i −0.640670 0.640670i
\(848\) −202.191 109.859i −0.238433 0.129551i
\(849\) 37.1249 2.30913i 0.0437278 0.00271983i
\(850\) 413.691 + 323.988i 0.486695 + 0.381162i
\(851\) 975.515 194.042i 1.14632 0.228016i
\(852\) −314.749 253.286i −0.369424 0.297284i
\(853\) 720.251 481.256i 0.844374 0.564192i −0.0564362 0.998406i \(-0.517974\pi\)
0.900810 + 0.434214i \(0.142974\pi\)
\(854\) −897.983 + 1776.41i −1.05150 + 2.08011i
\(855\) −799.571 + 454.558i −0.935171 + 0.531646i
\(856\) 664.985 416.331i 0.776852 0.486368i
\(857\) 334.553 807.683i 0.390377 0.942453i −0.599481 0.800389i \(-0.704626\pi\)
0.989857 0.142064i \(-0.0453739\pi\)
\(858\) −943.679 12.4790i −1.09986 0.0145443i
\(859\) −51.3640 + 258.224i −0.0597951 + 0.300610i −0.999097 0.0424807i \(-0.986474\pi\)
0.939302 + 0.343091i \(0.111474\pi\)
\(860\) −237.655 36.0842i −0.276343 0.0419584i
\(861\) 7.20128 + 27.2381i 0.00836385 + 0.0316355i
\(862\) −976.210 271.953i −1.13249 0.315490i
\(863\) 181.297 0.210077 0.105039 0.994468i \(-0.466503\pi\)
0.105039 + 0.994468i \(0.466503\pi\)
\(864\) 173.637 + 846.372i 0.200968 + 0.979598i
\(865\) 729.050i 0.842832i
\(866\) 694.398 + 193.445i 0.801845 + 0.223378i
\(867\) −627.292 + 165.845i −0.723520 + 0.191286i
\(868\) −1273.58 + 937.814i −1.46726 + 1.08043i
\(869\) 1640.54 + 326.323i 1.88785 + 0.375516i
\(870\) 1084.55 + 14.3418i 1.24661 + 0.0164848i
\(871\) −333.680 138.215i −0.383100 0.158685i
\(872\) 1006.24 169.285i 1.15395 0.194134i
\(873\) −389.481 685.101i −0.446141 0.784767i
\(874\) −299.097 + 591.680i −0.342216 + 0.676980i
\(875\) 291.789 + 436.693i 0.333473 + 0.499077i
\(876\) −122.179 1129.16i −0.139474 1.28899i
\(877\) 56.3934 + 283.509i 0.0643026 + 0.323271i 0.999526 0.0307872i \(-0.00980143\pi\)
−0.935223 + 0.354058i \(0.884801\pi\)
\(878\) 128.272 + 100.458i 0.146096 + 0.114417i
\(879\) −9.35482 150.402i −0.0106426 0.171105i
\(880\) 1038.32 1247.69i 1.17991 1.41783i
\(881\) −773.249 + 773.249i −0.877695 + 0.877695i −0.993296 0.115601i \(-0.963121\pi\)
0.115601 + 0.993296i \(0.463121\pi\)
\(882\) −1701.29 + 425.806i −1.92890 + 0.482773i
\(883\) −612.046 + 121.743i −0.693144 + 0.137875i −0.529076 0.848574i \(-0.677461\pi\)
−0.164067 + 0.986449i \(0.552461\pi\)
\(884\) 357.729 167.698i 0.404670 0.189703i
\(885\) 39.9407 295.764i 0.0451308 0.334196i
\(886\) −44.1754 134.493i −0.0498594 0.151798i
\(887\) 4.14547 1.71711i 0.00467358 0.00193586i −0.380345 0.924845i \(-0.624195\pi\)
0.385019 + 0.922909i \(0.374195\pi\)
\(888\) 31.9531 + 984.561i 0.0359832 + 1.10874i
\(889\) 780.985 1885.46i 0.878498 2.12088i
\(890\) 2051.52 + 154.859i 2.30508 + 0.173999i
\(891\) 57.3122 + 1098.49i 0.0643234 + 1.23288i
\(892\) −1201.26 725.606i −1.34670 0.813460i
\(893\) 404.397 605.222i 0.452852 0.677741i
\(894\) 70.6370 332.104i 0.0790123 0.371481i
\(895\) 419.363 0.468562
\(896\) −95.4381 1545.97i −0.106516 1.72541i
\(897\) −557.298 + 631.223i −0.621291 + 0.703704i
\(898\) −46.7809 82.9103i −0.0520946 0.0923278i
\(899\) 439.281 657.430i 0.488633 0.731290i
\(900\) 451.402 1013.14i 0.501558 1.12571i
\(901\) 120.285 + 23.9261i 0.133501 + 0.0265550i
\(902\) −21.0188 1.58660i −0.0233024 0.00175898i
\(903\) −262.338 + 128.286i −0.290518 + 0.142066i
\(904\) 201.019 + 213.319i 0.222366 + 0.235972i
\(905\) 360.888 149.485i 0.398771 0.165177i
\(906\) 1621.17 + 696.766i 1.78937 + 0.769057i
\(907\) −374.780 560.898i −0.413209 0.618410i 0.565234 0.824931i \(-0.308786\pi\)
−0.978442 + 0.206520i \(0.933786\pi\)
\(908\) 1495.95 701.277i 1.64752 0.772332i
\(909\) 806.697 267.857i 0.887456 0.294672i
\(910\) 2078.85 252.792i 2.28446 0.277794i
\(911\) −679.415 + 679.415i −0.745791 + 0.745791i −0.973686 0.227895i \(-0.926816\pi\)
0.227895 + 0.973686i \(0.426816\pi\)
\(912\) −529.811 387.876i −0.580933 0.425302i
\(913\) −939.051 + 939.051i −1.02853 + 1.02853i
\(914\) −901.565 706.074i −0.986395 0.772510i
\(915\) −1593.23 926.942i −1.74124 1.01305i
\(916\) −1030.92 940.817i −1.12546 1.02709i
\(917\) −356.304 533.246i −0.388554 0.581512i
\(918\) −222.268 403.291i −0.242122 0.439315i
\(919\) −1293.50 + 535.785i −1.40751 + 0.583009i −0.951689 0.307063i \(-0.900654\pi\)
−0.455820 + 0.890072i \(0.650654\pi\)
\(920\) −240.269 1428.18i −0.261162 1.55237i
\(921\) 263.129 + 538.083i 0.285699 + 0.584237i
\(922\) −989.155 1150.68i −1.07284 1.24803i
\(923\) 382.463 + 76.0767i 0.414370 + 0.0824232i
\(924\) 174.419 1964.24i 0.188765 2.12580i
\(925\) 702.566 1051.46i 0.759531 1.13672i
\(926\) −1278.40 356.136i −1.38056 0.384597i
\(927\) 420.966 52.5706i 0.454116 0.0567105i
\(928\) 307.726 + 710.565i 0.331602 + 0.765695i
\(929\) 1009.61 1.08677 0.543385 0.839484i \(-0.317143\pi\)
0.543385 + 0.839484i \(0.317143\pi\)
\(930\) −797.534 1228.45i −0.857563 1.32092i
\(931\) 740.475 1108.20i 0.795354 1.19033i
\(932\) −1320.38 200.479i −1.41671 0.215106i
\(933\) −425.174 557.935i −0.455706 0.598001i
\(934\) −397.757 + 341.923i −0.425864 + 0.366084i
\(935\) −331.069 + 799.271i −0.354085 + 0.854836i
\(936\) −526.721 646.562i −0.562737 0.690771i
\(937\) 481.672 199.515i 0.514057 0.212929i −0.110547 0.993871i \(-0.535260\pi\)
0.624604 + 0.780941i \(0.285260\pi\)
\(938\) 340.458 673.503i 0.362962 0.718020i
\(939\) 47.0014 + 6.34720i 0.0500548 + 0.00675953i
\(940\) 72.5858 + 1588.40i 0.0772189 + 1.68978i
\(941\) −597.933 + 118.936i −0.635423 + 0.126394i −0.502283 0.864704i \(-0.667506\pi\)
−0.133141 + 0.991097i \(0.542506\pi\)
\(942\) −114.890 + 21.2777i −0.121964 + 0.0225878i
\(943\) −13.2983 + 13.2983i −0.0141021 + 0.0141021i
\(944\) 204.309 60.4529i 0.216429 0.0640391i
\(945\) −452.236 2398.56i −0.478556 2.53816i
\(946\) −26.3733 216.883i −0.0278788 0.229263i
\(947\) −0.204800 1.02960i −0.000216262 0.00108722i 0.980677 0.195634i \(-0.0626764\pi\)
−0.980893 + 0.194547i \(0.937676\pi\)
\(948\) 709.246 + 1296.78i 0.748150 + 1.36791i
\(949\) 609.044 + 911.499i 0.641775 + 0.960484i
\(950\) 263.041 + 800.833i 0.276885 + 0.842983i
\(951\) 424.548 + 145.693i 0.446422 + 0.153200i
\(952\) 293.145 + 771.722i 0.307925 + 0.810632i
\(953\) 433.073 + 179.385i 0.454431 + 0.188231i 0.598145 0.801388i \(-0.295905\pi\)
−0.143714 + 0.989619i \(0.545905\pi\)
\(954\) −12.6528 258.564i −0.0132629 0.271031i
\(955\) 1576.79 + 313.642i 1.65109 + 0.328421i
\(956\) −1312.28 + 323.941i −1.37268 + 0.338851i
\(957\) 251.979 + 953.087i 0.263301 + 0.995911i
\(958\) 540.156 304.775i 0.563837 0.318137i
\(959\) 1649.22i 1.71973i
\(960\) 1434.35 3.96817i 1.49411 0.00413351i
\(961\) −106.692 −0.111021
\(962\) −467.242 828.098i −0.485699 0.860809i
\(963\) 788.990 + 395.643i 0.819305 + 0.410844i
\(964\) 547.391 135.126i 0.567833 0.140172i
\(965\) 124.789 627.354i 0.129315 0.650108i
\(966\) −1227.54 1260.44i −1.27074 1.30480i
\(967\) −34.8367 + 84.1032i −0.0360255 + 0.0869734i −0.940868 0.338773i \(-0.889988\pi\)
0.904843 + 0.425746i \(0.139988\pi\)
\(968\) 462.761 + 207.976i 0.478059 + 0.214851i
\(969\) 331.008 + 113.593i 0.341598 + 0.117227i
\(970\) −1242.97 + 408.266i −1.28142 + 0.420892i
\(971\) −281.112 + 187.833i −0.289508 + 0.193443i −0.691840 0.722051i \(-0.743200\pi\)
0.402332 + 0.915494i \(0.368200\pi\)
\(972\) −711.891 + 661.813i −0.732398 + 0.680877i
\(973\) 260.190 51.7551i 0.267410 0.0531912i
\(974\) −258.440 + 31.4268i −0.265339 + 0.0322657i
\(975\) 66.4604 + 1068.51i 0.0681645 + 1.09591i
\(976\) 137.942 1308.67i 0.141334 1.34085i
\(977\) −465.872 465.872i −0.476840 0.476840i 0.427280 0.904119i \(-0.359472\pi\)
−0.904119 + 0.427280i \(0.859472\pi\)
\(978\) −1533.57 + 284.019i −1.56807 + 0.290408i
\(979\) 364.807 + 1834.01i 0.372632 + 1.87335i
\(980\) 132.909 + 2908.45i 0.135621 + 2.96781i
\(981\) 751.119 + 868.085i 0.765666 + 0.884898i
\(982\) −930.557 470.400i −0.947614 0.479023i
\(983\) 169.698 + 409.687i 0.172633 + 0.416772i 0.986388 0.164436i \(-0.0525803\pi\)
−0.813755 + 0.581208i \(0.802580\pi\)
\(984\) −10.8450 15.1432i −0.0110213 0.0153894i
\(985\) −714.792 296.077i −0.725677 0.300585i
\(986\) −269.028 312.959i −0.272848 0.317403i
\(987\) 1170.82 + 1536.42i 1.18624 + 1.55665i
\(988\) 626.601 + 95.1398i 0.634212 + 0.0962954i
\(989\) −162.079 108.298i −0.163882 0.109502i
\(990\) 1806.31 + 268.293i 1.82455 + 0.271003i
\(991\) 288.466i 0.291086i −0.989352 0.145543i \(-0.953507\pi\)
0.989352 0.145543i \(-0.0464929\pi\)
\(992\) 566.939 878.576i 0.571511 0.885662i
\(993\) 172.959 195.901i 0.174178 0.197282i
\(994\) −218.662 + 784.917i −0.219982 + 0.789655i
\(995\) 1804.95 + 1206.03i 1.81402 + 1.21209i
\(996\) −1168.90 103.795i −1.17360 0.104212i
\(997\) 32.6694 164.240i 0.0327677 0.164734i −0.960937 0.276768i \(-0.910737\pi\)
0.993704 + 0.112034i \(0.0357366\pi\)
\(998\) −1289.75 + 1108.70i −1.29233 + 1.11092i
\(999\) −927.553 + 606.453i −0.928482 + 0.607060i
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 192.3.q.a.5.11 496
3.2 odd 2 inner 192.3.q.a.5.52 yes 496
64.13 even 16 inner 192.3.q.a.77.52 yes 496
192.77 odd 16 inner 192.3.q.a.77.11 yes 496
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
192.3.q.a.5.11 496 1.1 even 1 trivial
192.3.q.a.5.52 yes 496 3.2 odd 2 inner
192.3.q.a.77.11 yes 496 192.77 odd 16 inner
192.3.q.a.77.52 yes 496 64.13 even 16 inner