Properties

Label 143.2.e.b.133.1
Level $143$
Weight $2$
Character 143.133
Analytic conductor $1.142$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [143,2,Mod(100,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.3518667.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 133.1
Root \(-1.25351 - 2.17114i\) of defining polynomial
Character \(\chi\) \(=\) 143.133
Dual form 143.2.e.b.100.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25351 - 2.17114i) q^{2} +(-1.14257 - 1.97899i) q^{3} +(-2.14257 + 3.71104i) q^{4} -1.22188 q^{5} +(-2.86445 + 4.96137i) q^{6} +(-0.389062 + 0.673875i) q^{7} +5.72889 q^{8} +(-1.11094 + 1.92420i) q^{9} +O(q^{10})\) \(q+(-1.25351 - 2.17114i) q^{2} +(-1.14257 - 1.97899i) q^{3} +(-2.14257 + 3.71104i) q^{4} -1.22188 q^{5} +(-2.86445 + 4.96137i) q^{6} +(-0.389062 + 0.673875i) q^{7} +5.72889 q^{8} +(-1.11094 + 1.92420i) q^{9} +(1.53163 + 2.65287i) q^{10} +(-0.500000 - 0.866025i) q^{11} +9.79216 q^{12} +(-2.50000 - 2.59808i) q^{13} +1.95077 q^{14} +(1.39608 + 2.41808i) q^{15} +(-2.89608 - 5.01616i) q^{16} +(2.14257 - 3.71104i) q^{17} +5.57028 q^{18} +(-4.14959 + 7.18730i) q^{19} +(2.61796 - 4.53443i) q^{20} +1.77812 q^{21} +(-1.25351 + 2.17114i) q^{22} +(1.36445 + 2.36329i) q^{23} +(-6.54567 - 11.3374i) q^{24} -3.50702 q^{25} +(-2.50702 + 8.68457i) q^{26} -1.77812 q^{27} +(-1.66719 - 2.88765i) q^{28} +(-3.68122 - 6.37607i) q^{29} +(3.50000 - 6.06218i) q^{30} -1.44375 q^{31} +(-1.53163 + 2.65287i) q^{32} +(-1.14257 + 1.97899i) q^{33} -10.7429 q^{34} +(0.475385 - 0.823392i) q^{35} +(-4.76053 - 8.24548i) q^{36} +(0.396081 + 0.686032i) q^{37} +20.8062 q^{38} +(-2.28514 + 7.91597i) q^{39} -7.00000 q^{40} +(-4.87147 - 8.43763i) q^{41} +(-2.22889 - 3.86056i) q^{42} +(4.83983 - 8.38284i) q^{43} +4.28514 q^{44} +(1.35743 - 2.35114i) q^{45} +(3.42070 - 5.92482i) q^{46} -3.38049 q^{47} +(-6.61796 + 11.4626i) q^{48} +(3.19726 + 5.53782i) q^{49} +(4.39608 + 7.61423i) q^{50} -9.79216 q^{51} +(14.9980 - 3.71104i) q^{52} +1.79216 q^{53} +(2.22889 + 3.86056i) q^{54} +(0.610938 + 1.05818i) q^{55} +(-2.22889 + 3.86056i) q^{56} +18.9648 q^{57} +(-9.22889 + 15.9849i) q^{58} +(-2.60392 + 4.51012i) q^{59} -11.9648 q^{60} +(7.26053 - 12.5756i) q^{61} +(1.80976 + 3.13459i) q^{62} +(-0.864447 - 1.49727i) q^{63} -3.90466 q^{64} +(3.05469 + 3.17453i) q^{65} +5.72889 q^{66} +(-3.03163 - 5.25094i) q^{67} +(9.18122 + 15.9023i) q^{68} +(3.11796 - 5.40046i) q^{69} -2.38360 q^{70} +(3.25351 - 5.63524i) q^{71} +(-6.36445 + 11.0235i) q^{72} -2.00000 q^{73} +(0.992981 - 1.71989i) q^{74} +(4.00702 + 6.94036i) q^{75} +(-17.7816 - 30.7986i) q^{76} +0.778124 q^{77} +(20.0511 - 4.96137i) q^{78} +13.5843 q^{79} +(3.53865 + 6.12912i) q^{80} +(5.36445 + 9.29150i) q^{81} +(-12.2129 + 21.1533i) q^{82} -13.3624 q^{83} +(-3.80976 + 6.59869i) q^{84} +(-2.61796 + 4.53443i) q^{85} -24.2671 q^{86} +(-8.41212 + 14.5702i) q^{87} +(-2.86445 - 4.96137i) q^{88} +(2.38906 + 4.13798i) q^{89} -6.80620 q^{90} +(2.72343 - 0.673875i) q^{91} -11.6937 q^{92} +(1.64959 + 2.85717i) q^{93} +(4.23747 + 7.33951i) q^{94} +(5.07028 - 8.78199i) q^{95} +7.00000 q^{96} +(2.07028 - 3.58584i) q^{97} +(8.01559 - 13.8834i) q^{98} +2.22188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} - q^{3} - 7 q^{4} - 2 q^{5} - 6 q^{6} - 5 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 3 q^{11} + 30 q^{12} - 15 q^{13} - 16 q^{14} - 6 q^{15} - 3 q^{16} + 7 q^{17} + 10 q^{18} - 2 q^{19} - 4 q^{20} + 16 q^{21} + q^{22} - 3 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 21 q^{30} + 2 q^{31} - 6 q^{32} - q^{33} - 8 q^{34} - 11 q^{35} - 3 q^{36} - 12 q^{37} + 62 q^{38} - 2 q^{39} - 42 q^{40} - q^{41} + 9 q^{42} + 4 q^{43} + 14 q^{44} + 14 q^{45} + 20 q^{46} - 16 q^{47} - 20 q^{48} + 12 q^{50} - 30 q^{51} + 49 q^{52} - 18 q^{53} - 9 q^{54} + q^{55} + 9 q^{56} + 52 q^{57} - 33 q^{58} - 30 q^{59} - 10 q^{60} + 18 q^{61} + 13 q^{62} + 6 q^{63} - 16 q^{64} + 5 q^{65} + 12 q^{66} - 15 q^{67} + 29 q^{68} - q^{69} - 58 q^{70} + 11 q^{71} - 27 q^{72} - 12 q^{73} + 23 q^{74} + 7 q^{75} - 30 q^{76} + 10 q^{77} + 42 q^{78} + 24 q^{79} + q^{80} + 21 q^{81} - 44 q^{82} - 28 q^{83} - 25 q^{84} + 4 q^{85} - 86 q^{86} - 43 q^{87} - 6 q^{88} + 17 q^{89} + 22 q^{90} + 35 q^{91} + 14 q^{92} - 13 q^{93} + 10 q^{94} + 7 q^{95} + 42 q^{96} - 11 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25351 2.17114i −0.886365 1.53523i −0.844141 0.536121i \(-0.819889\pi\)
−0.0422238 0.999108i \(-0.513444\pi\)
\(3\) −1.14257 1.97899i −0.659664 1.14257i −0.980703 0.195505i \(-0.937365\pi\)
0.321039 0.947066i \(-0.395968\pi\)
\(4\) −2.14257 + 3.71104i −1.07129 + 1.85552i
\(5\) −1.22188 −0.546440 −0.273220 0.961952i \(-0.588089\pi\)
−0.273220 + 0.961952i \(0.588089\pi\)
\(6\) −2.86445 + 4.96137i −1.16941 + 2.02547i
\(7\) −0.389062 + 0.673875i −0.147052 + 0.254701i −0.930136 0.367214i \(-0.880312\pi\)
0.783085 + 0.621915i \(0.213645\pi\)
\(8\) 5.72889 2.02547
\(9\) −1.11094 + 1.92420i −0.370313 + 0.641400i
\(10\) 1.53163 + 2.65287i 0.484345 + 0.838910i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 9.79216 2.82675
\(13\) −2.50000 2.59808i −0.693375 0.720577i
\(14\) 1.95077 0.521365
\(15\) 1.39608 + 2.41808i 0.360466 + 0.624346i
\(16\) −2.89608 5.01616i −0.724020 1.25404i
\(17\) 2.14257 3.71104i 0.519650 0.900060i −0.480089 0.877220i \(-0.659396\pi\)
0.999739 0.0228403i \(-0.00727093\pi\)
\(18\) 5.57028 1.31293
\(19\) −4.14959 + 7.18730i −0.951981 + 1.64888i −0.210851 + 0.977518i \(0.567624\pi\)
−0.741130 + 0.671362i \(0.765710\pi\)
\(20\) 2.61796 4.53443i 0.585393 1.01393i
\(21\) 1.77812 0.388018
\(22\) −1.25351 + 2.17114i −0.267249 + 0.462889i
\(23\) 1.36445 + 2.36329i 0.284507 + 0.492780i 0.972489 0.232947i \(-0.0748368\pi\)
−0.687983 + 0.725727i \(0.741503\pi\)
\(24\) −6.54567 11.3374i −1.33613 2.31424i
\(25\) −3.50702 −0.701404
\(26\) −2.50702 + 8.68457i −0.491667 + 1.70318i
\(27\) −1.77812 −0.342200
\(28\) −1.66719 2.88765i −0.315068 0.545715i
\(29\) −3.68122 6.37607i −0.683586 1.18401i −0.973879 0.227068i \(-0.927086\pi\)
0.290293 0.956938i \(-0.406247\pi\)
\(30\) 3.50000 6.06218i 0.639010 1.10680i
\(31\) −1.44375 −0.259306 −0.129653 0.991559i \(-0.541386\pi\)
−0.129653 + 0.991559i \(0.541386\pi\)
\(32\) −1.53163 + 2.65287i −0.270757 + 0.468965i
\(33\) −1.14257 + 1.97899i −0.198896 + 0.344498i
\(34\) −10.7429 −1.84240
\(35\) 0.475385 0.823392i 0.0803548 0.139179i
\(36\) −4.76053 8.24548i −0.793421 1.37425i
\(37\) 0.396081 + 0.686032i 0.0651152 + 0.112783i 0.896745 0.442547i \(-0.145925\pi\)
−0.831630 + 0.555330i \(0.812592\pi\)
\(38\) 20.8062 3.37521
\(39\) −2.28514 + 7.91597i −0.365916 + 1.26757i
\(40\) −7.00000 −1.10680
\(41\) −4.87147 8.43763i −0.760795 1.31774i −0.942441 0.334372i \(-0.891476\pi\)
0.181646 0.983364i \(-0.441857\pi\)
\(42\) −2.22889 3.86056i −0.343926 0.595697i
\(43\) 4.83983 8.38284i 0.738068 1.27837i −0.215297 0.976549i \(-0.569072\pi\)
0.953364 0.301822i \(-0.0975948\pi\)
\(44\) 4.28514 0.646010
\(45\) 1.35743 2.35114i 0.202354 0.350487i
\(46\) 3.42070 5.92482i 0.504354 0.873567i
\(47\) −3.38049 −0.493095 −0.246547 0.969131i \(-0.579296\pi\)
−0.246547 + 0.969131i \(0.579296\pi\)
\(48\) −6.61796 + 11.4626i −0.955220 + 1.65449i
\(49\) 3.19726 + 5.53782i 0.456752 + 0.791117i
\(50\) 4.39608 + 7.61423i 0.621700 + 1.07682i
\(51\) −9.79216 −1.37118
\(52\) 14.9980 3.71104i 2.07985 0.514629i
\(53\) 1.79216 0.246172 0.123086 0.992396i \(-0.460721\pi\)
0.123086 + 0.992396i \(0.460721\pi\)
\(54\) 2.22889 + 3.86056i 0.303314 + 0.525356i
\(55\) 0.610938 + 1.05818i 0.0823789 + 0.142684i
\(56\) −2.22889 + 3.86056i −0.297849 + 0.515889i
\(57\) 18.9648 2.51195
\(58\) −9.22889 + 15.9849i −1.21181 + 2.09892i
\(59\) −2.60392 + 4.51012i −0.339001 + 0.587168i −0.984245 0.176809i \(-0.943422\pi\)
0.645244 + 0.763977i \(0.276756\pi\)
\(60\) −11.9648 −1.54465
\(61\) 7.26053 12.5756i 0.929615 1.61014i 0.145650 0.989336i \(-0.453473\pi\)
0.783965 0.620805i \(-0.213194\pi\)
\(62\) 1.80976 + 3.13459i 0.229839 + 0.398093i
\(63\) −0.864447 1.49727i −0.108910 0.188638i
\(64\) −3.90466 −0.488082
\(65\) 3.05469 + 3.17453i 0.378888 + 0.393752i
\(66\) 5.72889 0.705178
\(67\) −3.03163 5.25094i −0.370373 0.641505i 0.619250 0.785194i \(-0.287437\pi\)
−0.989623 + 0.143689i \(0.954103\pi\)
\(68\) 9.18122 + 15.9023i 1.11339 + 1.92844i
\(69\) 3.11796 5.40046i 0.375358 0.650139i
\(70\) −2.38360 −0.284895
\(71\) 3.25351 5.63524i 0.386121 0.668780i −0.605803 0.795614i \(-0.707148\pi\)
0.991924 + 0.126834i \(0.0404815\pi\)
\(72\) −6.36445 + 11.0235i −0.750057 + 1.29914i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0.992981 1.71989i 0.115432 0.199934i
\(75\) 4.00702 + 6.94036i 0.462691 + 0.801404i
\(76\) −17.7816 30.7986i −2.03969 3.53284i
\(77\) 0.778124 0.0886754
\(78\) 20.0511 4.96137i 2.27034 0.561764i
\(79\) 13.5843 1.52836 0.764178 0.645006i \(-0.223145\pi\)
0.764178 + 0.645006i \(0.223145\pi\)
\(80\) 3.53865 + 6.12912i 0.395633 + 0.685257i
\(81\) 5.36445 + 9.29150i 0.596050 + 1.03239i
\(82\) −12.2129 + 21.1533i −1.34868 + 2.33599i
\(83\) −13.3624 −1.46672 −0.733360 0.679841i \(-0.762049\pi\)
−0.733360 + 0.679841i \(0.762049\pi\)
\(84\) −3.80976 + 6.59869i −0.415679 + 0.719976i
\(85\) −2.61796 + 4.53443i −0.283957 + 0.491828i
\(86\) −24.2671 −2.61679
\(87\) −8.41212 + 14.5702i −0.901874 + 1.56209i
\(88\) −2.86445 4.96137i −0.305351 0.528884i
\(89\) 2.38906 + 4.13798i 0.253240 + 0.438625i 0.964416 0.264389i \(-0.0851704\pi\)
−0.711176 + 0.703014i \(0.751837\pi\)
\(90\) −6.80620 −0.717436
\(91\) 2.72343 0.673875i 0.285493 0.0706413i
\(92\) −11.6937 −1.21915
\(93\) 1.64959 + 2.85717i 0.171055 + 0.296275i
\(94\) 4.23747 + 7.33951i 0.437062 + 0.757013i
\(95\) 5.07028 8.78199i 0.520200 0.901013i
\(96\) 7.00000 0.714435
\(97\) 2.07028 3.58584i 0.210206 0.364087i −0.741573 0.670872i \(-0.765920\pi\)
0.951779 + 0.306785i \(0.0992533\pi\)
\(98\) 8.01559 13.8834i 0.809697 1.40244i
\(99\) 2.22188 0.223307
\(100\) 7.51404 13.0147i 0.751404 1.30147i
\(101\) −2.41212 4.17791i −0.240015 0.415718i 0.720703 0.693244i \(-0.243819\pi\)
−0.960718 + 0.277526i \(0.910486\pi\)
\(102\) 12.2746 + 21.2602i 1.21536 + 2.10507i
\(103\) 9.76008 0.961690 0.480845 0.876806i \(-0.340330\pi\)
0.480845 + 0.876806i \(0.340330\pi\)
\(104\) −14.3222 14.8841i −1.40441 1.45951i
\(105\) −2.17265 −0.212029
\(106\) −2.24649 3.89104i −0.218198 0.377931i
\(107\) −1.18122 2.04594i −0.114193 0.197788i 0.803264 0.595623i \(-0.203095\pi\)
−0.917457 + 0.397835i \(0.869762\pi\)
\(108\) 3.80976 6.59869i 0.366594 0.634959i
\(109\) −2.86946 −0.274845 −0.137422 0.990513i \(-0.543882\pi\)
−0.137422 + 0.990513i \(0.543882\pi\)
\(110\) 1.53163 2.65287i 0.146035 0.252941i
\(111\) 0.905101 1.56768i 0.0859083 0.148798i
\(112\) 4.50702 0.425873
\(113\) 2.80118 4.85179i 0.263513 0.456418i −0.703660 0.710537i \(-0.748452\pi\)
0.967173 + 0.254119i \(0.0817855\pi\)
\(114\) −23.7726 41.1753i −2.22650 3.85642i
\(115\) −1.66719 2.88765i −0.155466 0.269275i
\(116\) 31.5491 2.92926
\(117\) 7.77657 1.92420i 0.718944 0.177892i
\(118\) 13.0561 1.20192
\(119\) 1.66719 + 2.88765i 0.152831 + 0.264710i
\(120\) 7.99800 + 13.8529i 0.730114 + 1.26459i
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −36.4046 −3.29591
\(123\) −11.1320 + 19.2812i −1.00374 + 1.73853i
\(124\) 3.09334 5.35783i 0.277790 0.481147i
\(125\) 10.3945 0.929714
\(126\) −2.16719 + 3.75368i −0.193068 + 0.334404i
\(127\) −3.61796 6.26648i −0.321042 0.556061i 0.659662 0.751563i \(-0.270700\pi\)
−0.980703 + 0.195502i \(0.937366\pi\)
\(128\) 7.95779 + 13.7833i 0.703376 + 1.21828i
\(129\) −22.1194 −1.94751
\(130\) 3.06327 10.6115i 0.268666 0.930687i
\(131\) −10.3484 −0.904145 −0.452072 0.891981i \(-0.649315\pi\)
−0.452072 + 0.891981i \(0.649315\pi\)
\(132\) −4.89608 8.48026i −0.426149 0.738112i
\(133\) −3.22889 5.59261i −0.279981 0.484941i
\(134\) −7.60036 + 13.1642i −0.656571 + 1.13721i
\(135\) 2.17265 0.186992
\(136\) 12.2746 21.2602i 1.05254 1.82304i
\(137\) 2.46837 4.27534i 0.210887 0.365267i −0.741106 0.671389i \(-0.765698\pi\)
0.951992 + 0.306122i \(0.0990315\pi\)
\(138\) −15.6336 −1.33082
\(139\) −8.23591 + 14.2650i −0.698561 + 1.20994i 0.270404 + 0.962747i \(0.412843\pi\)
−0.968965 + 0.247196i \(0.920491\pi\)
\(140\) 2.03709 + 3.52835i 0.172166 + 0.298200i
\(141\) 3.86245 + 6.68995i 0.325277 + 0.563396i
\(142\) −16.3132 −1.36897
\(143\) −1.00000 + 3.46410i −0.0836242 + 0.289683i
\(144\) 12.8695 1.07246
\(145\) 4.49800 + 7.79076i 0.373538 + 0.646988i
\(146\) 2.50702 + 4.34228i 0.207482 + 0.359370i
\(147\) 7.30620 12.6547i 0.602605 1.04374i
\(148\) −3.39452 −0.279028
\(149\) 0.952328 1.64948i 0.0780178 0.135131i −0.824377 0.566041i \(-0.808474\pi\)
0.902395 + 0.430911i \(0.141808\pi\)
\(150\) 10.0457 17.3996i 0.820226 1.42067i
\(151\) 18.4086 1.49807 0.749034 0.662532i \(-0.230518\pi\)
0.749034 + 0.662532i \(0.230518\pi\)
\(152\) −23.7726 + 41.1753i −1.92821 + 3.33976i
\(153\) 4.76053 + 8.24548i 0.384866 + 0.666607i
\(154\) −0.975385 1.68942i −0.0785988 0.136137i
\(155\) 1.76409 0.141695
\(156\) −24.4804 25.4408i −1.96000 2.03689i
\(157\) −12.1054 −0.966114 −0.483057 0.875589i \(-0.660474\pi\)
−0.483057 + 0.875589i \(0.660474\pi\)
\(158\) −17.0281 29.4935i −1.35468 2.34638i
\(159\) −2.04767 3.54667i −0.162391 0.281269i
\(160\) 1.87147 3.24147i 0.147952 0.256261i
\(161\) −2.12342 −0.167349
\(162\) 13.4488 23.2940i 1.05664 1.83015i
\(163\) −0.959347 + 1.66164i −0.0751418 + 0.130149i −0.901148 0.433512i \(-0.857274\pi\)
0.826006 + 0.563661i \(0.190608\pi\)
\(164\) 41.7499 3.26012
\(165\) 1.39608 2.41808i 0.108685 0.188247i
\(166\) 16.7500 + 29.0118i 1.30005 + 2.25175i
\(167\) 3.53008 + 6.11427i 0.273165 + 0.473136i 0.969671 0.244415i \(-0.0785960\pi\)
−0.696505 + 0.717552i \(0.745263\pi\)
\(168\) 10.1867 0.785920
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 13.1265 1.00676
\(171\) −9.21987 15.9693i −0.705061 1.22120i
\(172\) 20.7394 + 35.9216i 1.58136 + 2.73900i
\(173\) −0.823794 + 1.42685i −0.0626319 + 0.108482i −0.895641 0.444778i \(-0.853283\pi\)
0.833009 + 0.553259i \(0.186616\pi\)
\(174\) 42.1787 3.19756
\(175\) 1.36445 2.36329i 0.103143 0.178648i
\(176\) −2.89608 + 5.01616i −0.218300 + 0.378107i
\(177\) 11.9007 0.894508
\(178\) 5.98942 10.3740i 0.448926 0.777563i
\(179\) −3.66719 6.35175i −0.274098 0.474752i 0.695809 0.718227i \(-0.255046\pi\)
−0.969907 + 0.243475i \(0.921713\pi\)
\(180\) 5.81678 + 10.0750i 0.433557 + 0.750943i
\(181\) 11.7750 0.875230 0.437615 0.899163i \(-0.355823\pi\)
0.437615 + 0.899163i \(0.355823\pi\)
\(182\) −4.87693 5.06825i −0.361502 0.375684i
\(183\) −33.1827 −2.45293
\(184\) 7.81678 + 13.5391i 0.576260 + 0.998112i
\(185\) −0.483961 0.838246i −0.0355815 0.0616291i
\(186\) 4.13555 7.16299i 0.303233 0.525216i
\(187\) −4.28514 −0.313361
\(188\) 7.24293 12.5451i 0.528245 0.914947i
\(189\) 0.691800 1.19823i 0.0503211 0.0871586i
\(190\) −25.4226 −1.84435
\(191\) −7.37147 + 12.7678i −0.533381 + 0.923842i 0.465859 + 0.884859i \(0.345745\pi\)
−0.999240 + 0.0389834i \(0.987588\pi\)
\(192\) 4.46135 + 7.72728i 0.321970 + 0.557669i
\(193\) 4.45077 + 7.70896i 0.320374 + 0.554903i 0.980565 0.196194i \(-0.0628583\pi\)
−0.660192 + 0.751097i \(0.729525\pi\)
\(194\) −10.3805 −0.745275
\(195\) 2.79216 9.67233i 0.199951 0.692650i
\(196\) −27.4014 −1.95725
\(197\) 3.05625 + 5.29358i 0.217749 + 0.377152i 0.954119 0.299427i \(-0.0967954\pi\)
−0.736371 + 0.676578i \(0.763462\pi\)
\(198\) −2.78514 4.82401i −0.197931 0.342827i
\(199\) −4.67265 + 8.09326i −0.331235 + 0.573716i −0.982754 0.184916i \(-0.940799\pi\)
0.651519 + 0.758632i \(0.274132\pi\)
\(200\) −20.0913 −1.42067
\(201\) −6.92771 + 11.9992i −0.488643 + 0.846355i
\(202\) −6.04723 + 10.4741i −0.425481 + 0.736956i
\(203\) 5.72889 0.402090
\(204\) 20.9804 36.3391i 1.46892 2.54425i
\(205\) 5.95233 + 10.3097i 0.415729 + 0.720063i
\(206\) −12.2344 21.1905i −0.852408 1.47641i
\(207\) −6.06327 −0.421426
\(208\) −5.79216 + 20.0646i −0.401614 + 1.39123i
\(209\) 8.29918 0.574066
\(210\) 2.72343 + 4.71713i 0.187935 + 0.325513i
\(211\) 2.59334 + 4.49180i 0.178533 + 0.309228i 0.941378 0.337353i \(-0.109532\pi\)
−0.762845 + 0.646581i \(0.776198\pi\)
\(212\) −3.83983 + 6.65079i −0.263721 + 0.456778i
\(213\) −14.8695 −1.01884
\(214\) −2.96135 + 5.12921i −0.202434 + 0.350625i
\(215\) −5.91368 + 10.2428i −0.403309 + 0.698552i
\(216\) −10.1867 −0.693116
\(217\) 0.561709 0.972909i 0.0381313 0.0660453i
\(218\) 3.59690 + 6.23001i 0.243613 + 0.421950i
\(219\) 2.28514 + 3.95798i 0.154416 + 0.267456i
\(220\) −5.23591 −0.353005
\(221\) −14.9980 + 3.71104i −1.00887 + 0.249632i
\(222\) −4.53821 −0.304585
\(223\) −8.41714 14.5789i −0.563653 0.976276i −0.997174 0.0751322i \(-0.976062\pi\)
0.433520 0.901144i \(-0.357271\pi\)
\(224\) −1.19180 2.06426i −0.0796305 0.137924i
\(225\) 3.89608 6.74821i 0.259739 0.449881i
\(226\) −14.0452 −0.934275
\(227\) 8.80820 15.2562i 0.584621 1.01259i −0.410302 0.911950i \(-0.634577\pi\)
0.994923 0.100643i \(-0.0320900\pi\)
\(228\) −40.6335 + 70.3792i −2.69102 + 4.66098i
\(229\) 26.8554 1.77466 0.887328 0.461138i \(-0.152559\pi\)
0.887328 + 0.461138i \(0.152559\pi\)
\(230\) −4.17967 + 7.23939i −0.275599 + 0.477351i
\(231\) −0.889062 1.53990i −0.0584960 0.101318i
\(232\) −21.0893 36.5278i −1.38458 2.39817i
\(233\) −27.1406 −1.77804 −0.889019 0.457870i \(-0.848612\pi\)
−0.889019 + 0.457870i \(0.848612\pi\)
\(234\) −13.9257 14.4720i −0.910352 0.946066i
\(235\) 4.13054 0.269446
\(236\) −11.1582 19.3265i −0.726335 1.25805i
\(237\) −15.5211 26.8833i −1.00820 1.74626i
\(238\) 4.17967 7.23939i 0.270927 0.469260i
\(239\) 0.746047 0.0482577 0.0241289 0.999709i \(-0.492319\pi\)
0.0241289 + 0.999709i \(0.492319\pi\)
\(240\) 8.08632 14.0059i 0.521970 0.904078i
\(241\) −8.08632 + 14.0059i −0.520886 + 0.902201i 0.478819 + 0.877914i \(0.341065\pi\)
−0.999705 + 0.0242873i \(0.992268\pi\)
\(242\) 2.50702 0.161157
\(243\) 9.59134 16.6127i 0.615285 1.06570i
\(244\) 31.1124 + 53.8883i 1.99177 + 3.44984i
\(245\) −3.90666 6.76653i −0.249587 0.432298i
\(246\) 55.8162 3.55871
\(247\) 29.0471 7.18730i 1.84822 0.457317i
\(248\) −8.27111 −0.525216
\(249\) 15.2675 + 26.4442i 0.967541 + 1.67583i
\(250\) −13.0296 22.5680i −0.824066 1.42732i
\(251\) 5.51404 9.55059i 0.348043 0.602828i −0.637859 0.770153i \(-0.720180\pi\)
0.985902 + 0.167325i \(0.0535130\pi\)
\(252\) 7.40856 0.466695
\(253\) 1.36445 2.36329i 0.0857821 0.148579i
\(254\) −9.07028 + 15.7102i −0.569120 + 0.985745i
\(255\) 11.9648 0.749265
\(256\) 16.0457 27.7919i 1.00285 1.73699i
\(257\) −9.42616 16.3266i −0.587987 1.01842i −0.994496 0.104777i \(-0.966587\pi\)
0.406508 0.913647i \(-0.366746\pi\)
\(258\) 27.7269 + 48.0244i 1.72620 + 2.98987i
\(259\) −0.616399 −0.0383012
\(260\) −18.3257 + 4.53443i −1.13651 + 0.281214i
\(261\) 16.3584 1.01256
\(262\) 12.9718 + 22.4679i 0.801402 + 1.38807i
\(263\) 7.77612 + 13.4686i 0.479496 + 0.830512i 0.999723 0.0235160i \(-0.00748607\pi\)
−0.520227 + 0.854028i \(0.674153\pi\)
\(264\) −6.54567 + 11.3374i −0.402858 + 0.697771i
\(265\) −2.18980 −0.134518
\(266\) −8.09490 + 14.0208i −0.496330 + 0.859669i
\(267\) 5.45935 9.45587i 0.334107 0.578690i
\(268\) 25.9820 1.58710
\(269\) 2.61094 4.52228i 0.159192 0.275728i −0.775386 0.631488i \(-0.782445\pi\)
0.934577 + 0.355760i \(0.115778\pi\)
\(270\) −2.72343 4.71713i −0.165743 0.287075i
\(271\) −12.9684 22.4619i −0.787772 1.36446i −0.927329 0.374247i \(-0.877901\pi\)
0.139557 0.990214i \(-0.455432\pi\)
\(272\) −24.8202 −1.50495
\(273\) −4.44531 4.61970i −0.269042 0.279597i
\(274\) −12.3765 −0.747691
\(275\) 1.75351 + 3.03717i 0.105741 + 0.183148i
\(276\) 13.3609 + 23.1417i 0.804231 + 1.39297i
\(277\) 8.88706 15.3928i 0.533972 0.924866i −0.465241 0.885184i \(-0.654032\pi\)
0.999212 0.0396819i \(-0.0126345\pi\)
\(278\) 41.2952 2.47672
\(279\) 1.60392 2.77807i 0.0960241 0.166319i
\(280\) 2.72343 4.71713i 0.162756 0.281902i
\(281\) 7.41168 0.442143 0.221072 0.975258i \(-0.429045\pi\)
0.221072 + 0.975258i \(0.429045\pi\)
\(282\) 9.68322 16.7718i 0.576628 0.998748i
\(283\) −4.65861 8.06895i −0.276926 0.479649i 0.693694 0.720270i \(-0.255982\pi\)
−0.970619 + 0.240621i \(0.922649\pi\)
\(284\) 13.9418 + 24.1478i 0.827291 + 1.43291i
\(285\) −23.1726 −1.37263
\(286\) 8.77457 2.17114i 0.518851 0.128382i
\(287\) 7.58121 0.447505
\(288\) −3.40310 5.89434i −0.200530 0.347327i
\(289\) −0.681223 1.17991i −0.0400719 0.0694066i
\(290\) 11.2766 19.5316i 0.662183 1.14693i
\(291\) −9.46179 −0.554660
\(292\) 4.28514 7.42208i 0.250769 0.434345i
\(293\) 14.3765 24.9008i 0.839883 1.45472i −0.0501087 0.998744i \(-0.515957\pi\)
0.889992 0.455976i \(-0.150710\pi\)
\(294\) −36.6336 −2.13651
\(295\) 3.18167 5.51081i 0.185244 0.320852i
\(296\) 2.26910 + 3.93020i 0.131889 + 0.228438i
\(297\) 0.889062 + 1.53990i 0.0515886 + 0.0893541i
\(298\) −4.77501 −0.276609
\(299\) 2.72889 9.45317i 0.157816 0.546691i
\(300\) −34.3413 −1.98270
\(301\) 3.76599 + 6.52288i 0.217068 + 0.375973i
\(302\) −23.0753 39.9676i −1.32783 2.29988i
\(303\) −5.51204 + 9.54713i −0.316658 + 0.548468i
\(304\) 48.0702 2.75701
\(305\) −8.87147 + 15.3658i −0.507979 + 0.879845i
\(306\) 11.9347 20.6716i 0.682263 1.18171i
\(307\) −0.792161 −0.0452110 −0.0226055 0.999744i \(-0.507196\pi\)
−0.0226055 + 0.999744i \(0.507196\pi\)
\(308\) −1.66719 + 2.88765i −0.0949967 + 0.164539i
\(309\) −11.1516 19.3151i −0.634392 1.09880i
\(310\) −2.21130 3.83008i −0.125593 0.217534i
\(311\) 25.8022 1.46311 0.731554 0.681783i \(-0.238795\pi\)
0.731554 + 0.681783i \(0.238795\pi\)
\(312\) −13.0913 + 45.3497i −0.741151 + 2.56742i
\(313\) −26.2780 −1.48532 −0.742661 0.669668i \(-0.766437\pi\)
−0.742661 + 0.669668i \(0.766437\pi\)
\(314\) 15.1742 + 26.2825i 0.856330 + 1.48321i
\(315\) 1.05625 + 1.82947i 0.0595128 + 0.103079i
\(316\) −29.1054 + 50.4120i −1.63731 + 2.83590i
\(317\) 10.9788 0.616633 0.308317 0.951284i \(-0.400234\pi\)
0.308317 + 0.951284i \(0.400234\pi\)
\(318\) −5.13355 + 8.89157i −0.287875 + 0.498615i
\(319\) −3.68122 + 6.37607i −0.206109 + 0.356991i
\(320\) 4.77101 0.266707
\(321\) −2.69926 + 4.67526i −0.150658 + 0.260948i
\(322\) 2.66172 + 4.61024i 0.148332 + 0.256919i
\(323\) 17.7816 + 30.7986i 0.989394 + 1.71368i
\(324\) −45.9748 −2.55416
\(325\) 8.76755 + 9.11150i 0.486336 + 0.505415i
\(326\) 4.81020 0.266412
\(327\) 3.27857 + 5.67865i 0.181305 + 0.314030i
\(328\) −27.9081 48.3383i −1.54097 2.66903i
\(329\) 1.31522 2.27803i 0.0725103 0.125592i
\(330\) −7.00000 −0.385337
\(331\) −5.02807 + 8.70888i −0.276368 + 0.478683i −0.970479 0.241184i \(-0.922464\pi\)
0.694111 + 0.719868i \(0.255798\pi\)
\(332\) 28.6300 49.5886i 1.57127 2.72153i
\(333\) −1.76008 −0.0964520
\(334\) 8.84997 15.3286i 0.484249 0.838743i
\(335\) 3.70428 + 6.41600i 0.202386 + 0.350544i
\(336\) −5.14959 8.91935i −0.280933 0.486591i
\(337\) 19.7398 1.07530 0.537648 0.843169i \(-0.319313\pi\)
0.537648 + 0.843169i \(0.319313\pi\)
\(338\) 28.8307 15.1980i 1.56818 0.826662i
\(339\) −12.8022 −0.695320
\(340\) −11.2183 19.4307i −0.608399 1.05378i
\(341\) 0.721876 + 1.25033i 0.0390918 + 0.0677090i
\(342\) −23.1144 + 40.0353i −1.24988 + 2.16486i
\(343\) −10.4226 −0.562767
\(344\) 27.7269 48.0244i 1.49493 2.58930i
\(345\) −3.80976 + 6.59869i −0.205110 + 0.355262i
\(346\) 4.13054 0.222059
\(347\) −9.15661 + 15.8597i −0.491553 + 0.851394i −0.999953 0.00972702i \(-0.996904\pi\)
0.508400 + 0.861121i \(0.330237\pi\)
\(348\) −36.0471 62.4355i −1.93233 3.34689i
\(349\) −8.68824 15.0485i −0.465071 0.805526i 0.534134 0.845400i \(-0.320638\pi\)
−0.999205 + 0.0398735i \(0.987305\pi\)
\(350\) −6.84139 −0.365688
\(351\) 4.44531 + 4.61970i 0.237273 + 0.246581i
\(352\) 3.06327 0.163273
\(353\) −16.8835 29.2431i −0.898618 1.55645i −0.829262 0.558860i \(-0.811239\pi\)
−0.0693563 0.997592i \(-0.522095\pi\)
\(354\) −14.9176 25.8380i −0.792860 1.37327i
\(355\) −3.97539 + 6.88557i −0.210992 + 0.365448i
\(356\) −20.4749 −1.08517
\(357\) 3.80976 6.59869i 0.201634 0.349240i
\(358\) −9.19370 + 15.9240i −0.485902 + 0.841607i
\(359\) −4.72889 −0.249582 −0.124791 0.992183i \(-0.539826\pi\)
−0.124791 + 0.992183i \(0.539826\pi\)
\(360\) 7.77657 13.4694i 0.409861 0.709900i
\(361\) −24.9382 43.1942i −1.31254 2.27338i
\(362\) −14.7601 25.5652i −0.775773 1.34368i
\(363\) 2.28514 0.119939
\(364\) −3.33437 + 11.5506i −0.174769 + 0.605416i
\(365\) 2.44375 0.127912
\(366\) 41.5948 + 72.0443i 2.17420 + 3.76582i
\(367\) −3.21330 5.56560i −0.167733 0.290522i 0.769890 0.638177i \(-0.220311\pi\)
−0.937622 + 0.347655i \(0.886978\pi\)
\(368\) 7.90310 13.6886i 0.411978 0.713566i
\(369\) 21.6476 1.12693
\(370\) −1.21330 + 2.10150i −0.0630765 + 0.109252i
\(371\) −0.697262 + 1.20769i −0.0362000 + 0.0627003i
\(372\) −14.1375 −0.732993
\(373\) 2.20584 3.82062i 0.114214 0.197824i −0.803251 0.595640i \(-0.796898\pi\)
0.917465 + 0.397816i \(0.130232\pi\)
\(374\) 5.37147 + 9.30365i 0.277752 + 0.481080i
\(375\) −11.8765 20.5707i −0.613299 1.06226i
\(376\) −19.3664 −0.998748
\(377\) −7.36245 + 25.5043i −0.379185 + 1.31354i
\(378\) −3.46871 −0.178411
\(379\) −9.75351 16.8936i −0.501004 0.867765i −0.999999 0.00115985i \(-0.999631\pi\)
0.498995 0.866605i \(-0.333703\pi\)
\(380\) 21.7269 + 37.6321i 1.11457 + 1.93049i
\(381\) −8.26755 + 14.3198i −0.423559 + 0.733626i
\(382\) 36.9608 1.89108
\(383\) −13.8152 + 23.9287i −0.705925 + 1.22270i 0.260432 + 0.965492i \(0.416135\pi\)
−0.966357 + 0.257205i \(0.917198\pi\)
\(384\) 18.1847 31.4968i 0.927983 1.60731i
\(385\) −0.950771 −0.0484558
\(386\) 11.1582 19.3265i 0.567936 0.983693i
\(387\) 10.7535 + 18.6256i 0.546632 + 0.946794i
\(388\) 8.87147 + 15.3658i 0.450380 + 0.780082i
\(389\) −28.9960 −1.47016 −0.735078 0.677983i \(-0.762854\pi\)
−0.735078 + 0.677983i \(0.762854\pi\)
\(390\) −24.5000 + 6.06218i −1.24061 + 0.306970i
\(391\) 11.6937 0.591376
\(392\) 18.3168 + 31.7256i 0.925137 + 1.60238i
\(393\) 11.8238 + 20.4794i 0.596432 + 1.03305i
\(394\) 7.66207 13.2711i 0.386010 0.668588i
\(395\) −16.5984 −0.835154
\(396\) −4.76053 + 8.24548i −0.239226 + 0.414351i
\(397\) −17.3293 + 30.0152i −0.869730 + 1.50642i −0.00745819 + 0.999972i \(0.502374\pi\)
−0.862272 + 0.506445i \(0.830959\pi\)
\(398\) 23.4288 1.17438
\(399\) −7.37848 + 12.7799i −0.369386 + 0.639796i
\(400\) 10.1566 + 17.5918i 0.507830 + 0.879588i
\(401\) 7.29372 + 12.6331i 0.364231 + 0.630866i 0.988652 0.150221i \(-0.0479986\pi\)
−0.624422 + 0.781088i \(0.714665\pi\)
\(402\) 34.7358 1.73246
\(403\) 3.60938 + 3.75098i 0.179796 + 0.186850i
\(404\) 20.6725 1.02850
\(405\) −6.55469 11.3531i −0.325705 0.564138i
\(406\) −7.18122 12.4382i −0.356398 0.617300i
\(407\) 0.396081 0.686032i 0.0196330 0.0340053i
\(408\) −56.0983 −2.77728
\(409\) −8.30074 + 14.3773i −0.410445 + 0.710912i −0.994938 0.100487i \(-0.967960\pi\)
0.584493 + 0.811398i \(0.301293\pi\)
\(410\) 14.9226 25.8467i 0.736975 1.27648i
\(411\) −11.2811 −0.556458
\(412\) −20.9117 + 36.2201i −1.03024 + 1.78444i
\(413\) −2.02617 3.50943i −0.0997014 0.172688i
\(414\) 7.60036 + 13.1642i 0.373537 + 0.646986i
\(415\) 16.3273 0.801473
\(416\) 10.7214 2.65287i 0.525661 0.130067i
\(417\) 37.6405 1.84326
\(418\) −10.4031 18.0187i −0.508832 0.881323i
\(419\) 11.1476 + 19.3082i 0.544595 + 0.943267i 0.998632 + 0.0522839i \(0.0166501\pi\)
−0.454037 + 0.890983i \(0.650017\pi\)
\(420\) 4.65505 8.06279i 0.227143 0.393424i
\(421\) −3.45779 −0.168522 −0.0842612 0.996444i \(-0.526853\pi\)
−0.0842612 + 0.996444i \(0.526853\pi\)
\(422\) 6.50156 11.2610i 0.316491 0.548178i
\(423\) 3.75551 6.50474i 0.182599 0.316271i
\(424\) 10.2671 0.498615
\(425\) −7.51404 + 13.0147i −0.364484 + 0.631305i
\(426\) 18.6390 + 32.2837i 0.903063 + 1.56415i
\(427\) 5.64959 + 9.78538i 0.273403 + 0.473548i
\(428\) 10.1234 0.489334
\(429\) 7.99800 1.97899i 0.386147 0.0955466i
\(430\) 29.6514 1.42992
\(431\) −12.9402 22.4131i −0.623307 1.07960i −0.988866 0.148811i \(-0.952455\pi\)
0.365558 0.930788i \(-0.380878\pi\)
\(432\) 5.14959 + 8.91935i 0.247760 + 0.429132i
\(433\) −7.19024 + 12.4539i −0.345541 + 0.598495i −0.985452 0.169955i \(-0.945638\pi\)
0.639911 + 0.768449i \(0.278971\pi\)
\(434\) −2.81643 −0.135193
\(435\) 10.2786 17.8030i 0.492820 0.853589i
\(436\) 6.14803 10.6487i 0.294437 0.509980i
\(437\) −22.6476 −1.08338
\(438\) 5.72889 9.92274i 0.273737 0.474127i
\(439\) −2.28314 3.95452i −0.108968 0.188739i 0.806384 0.591392i \(-0.201421\pi\)
−0.915353 + 0.402653i \(0.868088\pi\)
\(440\) 3.50000 + 6.06218i 0.166856 + 0.289003i
\(441\) −14.2078 −0.676564
\(442\) 26.8573 + 27.9110i 1.27747 + 1.32759i
\(443\) 18.1718 0.863366 0.431683 0.902025i \(-0.357920\pi\)
0.431683 + 0.902025i \(0.357920\pi\)
\(444\) 3.87848 + 6.71773i 0.184065 + 0.318809i
\(445\) −2.91914 5.05609i −0.138380 0.239682i
\(446\) −21.1019 + 36.5496i −0.999205 + 1.73067i
\(447\) −4.35241 −0.205862
\(448\) 1.51915 2.63125i 0.0717732 0.124315i
\(449\) 6.31477 10.9375i 0.298013 0.516173i −0.677669 0.735367i \(-0.737010\pi\)
0.975681 + 0.219194i \(0.0703429\pi\)
\(450\) −19.5351 −0.920893
\(451\) −4.87147 + 8.43763i −0.229388 + 0.397312i
\(452\) 12.0035 + 20.7906i 0.564595 + 0.977908i
\(453\) −21.0331 36.4304i −0.988221 1.71165i
\(454\) −44.1646 −2.07275
\(455\) −3.32770 + 0.823392i −0.156005 + 0.0386012i
\(456\) 108.647 5.08788
\(457\) 12.8941 + 22.3332i 0.603160 + 1.04470i 0.992339 + 0.123541i \(0.0394251\pi\)
−0.389180 + 0.921162i \(0.627242\pi\)
\(458\) −33.6635 58.3069i −1.57299 2.72450i
\(459\) −3.80976 + 6.59869i −0.177824 + 0.308001i
\(460\) 14.2883 0.666193
\(461\) 6.31678 10.9410i 0.294202 0.509572i −0.680597 0.732658i \(-0.738280\pi\)
0.974799 + 0.223086i \(0.0716130\pi\)
\(462\) −2.22889 + 3.86056i −0.103698 + 0.179609i
\(463\) −3.47494 −0.161494 −0.0807471 0.996735i \(-0.525731\pi\)
−0.0807471 + 0.996735i \(0.525731\pi\)
\(464\) −21.3222 + 36.9312i −0.989860 + 1.71449i
\(465\) −2.01559 3.49111i −0.0934710 0.161896i
\(466\) 34.0210 + 58.9260i 1.57599 + 2.72970i
\(467\) −18.7258 −0.866526 −0.433263 0.901268i \(-0.642638\pi\)
−0.433263 + 0.901268i \(0.642638\pi\)
\(468\) −9.52106 + 32.9819i −0.440111 + 1.52459i
\(469\) 4.71797 0.217856
\(470\) −5.17766 8.96798i −0.238828 0.413662i
\(471\) 13.8313 + 23.9564i 0.637311 + 1.10385i
\(472\) −14.9176 + 25.8380i −0.686637 + 1.18929i
\(473\) −9.67967 −0.445072
\(474\) −38.9116 + 67.3968i −1.78727 + 3.09564i
\(475\) 14.5527 25.2060i 0.667723 1.15653i
\(476\) −14.2883 −0.654901
\(477\) −1.99098 + 3.44848i −0.0911607 + 0.157895i
\(478\) −0.935176 1.61977i −0.0427740 0.0740867i
\(479\) −4.64257 8.04117i −0.212124 0.367410i 0.740255 0.672327i \(-0.234705\pi\)
−0.952379 + 0.304916i \(0.901372\pi\)
\(480\) −8.55313 −0.390395
\(481\) 0.792161 2.74413i 0.0361194 0.125121i
\(482\) 40.5451 1.84678
\(483\) 2.42616 + 4.20223i 0.110394 + 0.191208i
\(484\) −2.14257 3.71104i −0.0973896 0.168684i
\(485\) −2.52963 + 4.38145i −0.114865 + 0.198951i
\(486\) −48.0913 −2.18147
\(487\) 19.9648 34.5801i 0.904692 1.56697i 0.0833614 0.996519i \(-0.473434\pi\)
0.821330 0.570453i \(-0.193232\pi\)
\(488\) 41.5948 72.0443i 1.88291 3.26129i
\(489\) 4.38449 0.198273
\(490\) −9.79406 + 16.9638i −0.442451 + 0.766347i
\(491\) 20.5913 + 35.6652i 0.929274 + 1.60955i 0.784539 + 0.620080i \(0.212900\pi\)
0.144735 + 0.989470i \(0.453767\pi\)
\(492\) −47.7022 82.6226i −2.15058 3.72491i
\(493\) −31.5491 −1.42090
\(494\) −52.0155 54.0561i −2.34029 2.43210i
\(495\) −2.71486 −0.122024
\(496\) 4.18122 + 7.24209i 0.187742 + 0.325179i
\(497\) 2.53163 + 4.38492i 0.113559 + 0.196690i
\(498\) 38.2760 66.2960i 1.71519 2.97080i
\(499\) 19.3132 0.864578 0.432289 0.901735i \(-0.357706\pi\)
0.432289 + 0.901735i \(0.357706\pi\)
\(500\) −22.2710 + 38.5745i −0.995990 + 1.72510i
\(501\) 8.06673 13.9720i 0.360395 0.624222i
\(502\) −27.6476 −1.23397
\(503\) −9.84485 + 17.0518i −0.438960 + 0.760301i −0.997610 0.0691026i \(-0.977986\pi\)
0.558649 + 0.829404i \(0.311320\pi\)
\(504\) −4.95233 8.57768i −0.220594 0.382080i
\(505\) 2.94731 + 5.10489i 0.131154 + 0.227165i
\(506\) −6.84139 −0.304137
\(507\) 26.2791 13.8529i 1.16710 0.615231i
\(508\) 31.0069 1.37571
\(509\) −6.73747 11.6696i −0.298633 0.517248i 0.677190 0.735808i \(-0.263197\pi\)
−0.975823 + 0.218560i \(0.929864\pi\)
\(510\) −14.9980 25.9773i −0.664123 1.15029i
\(511\) 0.778124 1.34775i 0.0344222 0.0596210i
\(512\) −48.6224 −2.14883
\(513\) 7.37848 12.7799i 0.325768 0.564247i
\(514\) −23.6315 + 40.9310i −1.04234 + 1.80539i
\(515\) −11.9256 −0.525505
\(516\) 47.3924 82.0861i 2.08634 3.61364i
\(517\) 1.69024 + 2.92759i 0.0743368 + 0.128755i
\(518\) 0.772662 + 1.33829i 0.0339488 + 0.0588011i
\(519\) 3.76497 0.165264
\(520\) 17.5000 + 18.1865i 0.767426 + 0.797532i
\(521\) 19.4266 0.851095 0.425547 0.904936i \(-0.360082\pi\)
0.425547 + 0.904936i \(0.360082\pi\)
\(522\) −20.5055 35.5165i −0.897500 1.55452i
\(523\) −5.46135 9.45933i −0.238808 0.413628i 0.721564 0.692347i \(-0.243423\pi\)
−0.960373 + 0.278720i \(0.910090\pi\)
\(524\) 22.1722 38.4034i 0.968597 1.67766i
\(525\) −6.23591 −0.272158
\(526\) 19.4949 33.7661i 0.850017 1.47227i
\(527\) −3.09334 + 5.35783i −0.134748 + 0.233391i
\(528\) 13.2359 0.576019
\(529\) 7.77657 13.4694i 0.338112 0.585626i
\(530\) 2.74493 + 4.75436i 0.119232 + 0.206516i
\(531\) −5.78559 10.0209i −0.251073 0.434871i
\(532\) 27.6725 1.19976
\(533\) −9.74293 + 33.7505i −0.422013 + 1.46190i
\(534\) −27.3734 −1.18456
\(535\) 1.44331 + 2.49988i 0.0623997 + 0.108079i
\(536\) −17.3679 30.0821i −0.750179 1.29935i
\(537\) −8.38004 + 14.5147i −0.361626 + 0.626354i
\(538\) −13.0913 −0.564408
\(539\) 3.19726 5.53782i 0.137716 0.238531i
\(540\) −4.65505 + 8.06279i −0.200322 + 0.346967i
\(541\) −16.9820 −0.730111 −0.365056 0.930986i \(-0.618950\pi\)
−0.365056 + 0.930986i \(0.618950\pi\)
\(542\) −32.5119 + 56.3123i −1.39651 + 2.41882i
\(543\) −13.4538 23.3026i −0.577357 1.00001i
\(544\) 6.56327 + 11.3679i 0.281398 + 0.487395i
\(545\) 3.50613 0.150186
\(546\) −4.45779 + 15.4422i −0.190776 + 0.660867i
\(547\) 1.13345 0.0484629 0.0242315 0.999706i \(-0.492286\pi\)
0.0242315 + 0.999706i \(0.492286\pi\)
\(548\) 10.5773 + 18.3204i 0.451840 + 0.782610i
\(549\) 16.1320 + 27.9414i 0.688497 + 1.19251i
\(550\) 4.39608 7.61423i 0.187450 0.324672i
\(551\) 61.1023 2.60304
\(552\) 17.8624 30.9387i 0.760276 1.31684i
\(553\) −5.28514 + 9.15414i −0.224747 + 0.389273i
\(554\) −44.5601 −1.89318
\(555\) −1.10592 + 1.91551i −0.0469437 + 0.0813089i
\(556\) −35.2921 61.1276i −1.49672 2.59239i
\(557\) 10.1336 + 17.5518i 0.429372 + 0.743695i 0.996818 0.0797164i \(-0.0254015\pi\)
−0.567445 + 0.823411i \(0.692068\pi\)
\(558\) −8.04211 −0.340450
\(559\) −33.8788 + 8.38284i −1.43292 + 0.354556i
\(560\) −5.50702 −0.232714
\(561\) 4.89608 + 8.48026i 0.206713 + 0.358037i
\(562\) −9.29060 16.0918i −0.391900 0.678792i
\(563\) −0.156609 + 0.271254i −0.00660026 + 0.0114320i −0.869307 0.494273i \(-0.835434\pi\)
0.862706 + 0.505705i \(0.168768\pi\)
\(564\) −33.1023 −1.39386
\(565\) −3.42270 + 5.92828i −0.143994 + 0.249405i
\(566\) −11.6792 + 20.2290i −0.490914 + 0.850289i
\(567\) −8.34841 −0.350600
\(568\) 18.6390 32.2837i 0.782076 1.35459i
\(569\) 5.54211 + 9.59922i 0.232337 + 0.402420i 0.958496 0.285108i \(-0.0920293\pi\)
−0.726158 + 0.687528i \(0.758696\pi\)
\(570\) 29.0471 + 50.3111i 1.21665 + 2.10730i
\(571\) 41.7037 1.74525 0.872624 0.488393i \(-0.162417\pi\)
0.872624 + 0.488393i \(0.162417\pi\)
\(572\) −10.7129 11.1331i −0.447927 0.465499i
\(573\) 33.6897 1.40741
\(574\) −9.50311 16.4599i −0.396652 0.687022i
\(575\) −4.78514 8.28811i −0.199554 0.345638i
\(576\) 4.33783 7.51334i 0.180743 0.313056i
\(577\) 19.1867 0.798752 0.399376 0.916787i \(-0.369227\pi\)
0.399376 + 0.916787i \(0.369227\pi\)
\(578\) −1.70784 + 2.95806i −0.0710367 + 0.123039i
\(579\) 10.1706 17.6161i 0.422678 0.732099i
\(580\) −38.5491 −1.60067
\(581\) 5.19882 9.00462i 0.215683 0.373575i
\(582\) 11.8604 + 20.5429i 0.491631 + 0.851530i
\(583\) −0.896081 1.55206i −0.0371119 0.0642796i
\(584\) −11.4578 −0.474127
\(585\) −9.50200 + 2.35114i −0.392859 + 0.0972075i
\(586\) −72.0842 −2.97777
\(587\) 6.29216 + 10.8983i 0.259705 + 0.449823i 0.966163 0.257933i \(-0.0830412\pi\)
−0.706458 + 0.707755i \(0.749708\pi\)
\(588\) 31.3081 + 54.2272i 1.29112 + 2.23629i
\(589\) 5.99098 10.3767i 0.246854 0.427564i
\(590\) −15.9530 −0.656775
\(591\) 6.98396 12.0966i 0.287282 0.497587i
\(592\) 2.29416 3.97361i 0.0942895 0.163314i
\(593\) −13.7117 −0.563074 −0.281537 0.959550i \(-0.590844\pi\)
−0.281537 + 0.959550i \(0.590844\pi\)
\(594\) 2.22889 3.86056i 0.0914527 0.158401i
\(595\) −2.03709 3.52835i −0.0835127 0.144648i
\(596\) 4.08086 + 7.06826i 0.167159 + 0.289527i
\(597\) 21.3553 0.874015
\(598\) −23.9449 + 5.92482i −0.979178 + 0.242284i
\(599\) −15.3905 −0.628840 −0.314420 0.949284i \(-0.601810\pi\)
−0.314420 + 0.949284i \(0.601810\pi\)
\(600\) 22.9558 + 39.7606i 0.937166 + 1.62322i
\(601\) 8.10738 + 14.0424i 0.330707 + 0.572801i 0.982651 0.185466i \(-0.0593795\pi\)
−0.651944 + 0.758267i \(0.726046\pi\)
\(602\) 9.44141 16.3530i 0.384803 0.666498i
\(603\) 13.4718 0.548615
\(604\) −39.4417 + 68.3149i −1.60486 + 2.77970i
\(605\) 0.610938 1.05818i 0.0248382 0.0430210i
\(606\) 27.6376 1.12270
\(607\) −1.34139 + 2.32336i −0.0544453 + 0.0943021i −0.891964 0.452107i \(-0.850672\pi\)
0.837518 + 0.546409i \(0.184006\pi\)
\(608\) −12.7113 22.0166i −0.515511 0.892892i
\(609\) −6.54567 11.3374i −0.265244 0.459416i
\(610\) 44.4819 1.80102
\(611\) 8.45122 + 8.78276i 0.341900 + 0.355312i
\(612\) −40.7991 −1.64921
\(613\) 18.0457 + 31.2560i 0.728858 + 1.26242i 0.957366 + 0.288877i \(0.0932818\pi\)
−0.228509 + 0.973542i \(0.573385\pi\)
\(614\) 0.992981 + 1.71989i 0.0400735 + 0.0694093i
\(615\) 13.6019 23.5592i 0.548482 0.949999i
\(616\) 4.45779 0.179609
\(617\) 9.58588 16.6032i 0.385913 0.668421i −0.605982 0.795478i \(-0.707220\pi\)
0.991895 + 0.127057i \(0.0405532\pi\)
\(618\) −27.9572 + 48.4234i −1.12461 + 1.94787i
\(619\) 6.38049 0.256453 0.128227 0.991745i \(-0.459071\pi\)
0.128227 + 0.991745i \(0.459071\pi\)
\(620\) −3.77968 + 6.54660i −0.151796 + 0.262918i
\(621\) −2.42616 4.20223i −0.0973583 0.168630i
\(622\) −32.3433 56.0202i −1.29685 2.24621i
\(623\) −3.71797 −0.148957
\(624\) 46.3257 11.4626i 1.85451 0.458873i
\(625\) 4.83427 0.193371
\(626\) 32.9397 + 57.0533i 1.31654 + 2.28031i
\(627\) −9.48240 16.4240i −0.378691 0.655912i
\(628\) 25.9366 44.9236i 1.03498 1.79265i
\(629\) 3.39452 0.135349
\(630\) 2.64803 4.58653i 0.105500 0.182732i
\(631\) 10.4503 18.1005i 0.416021 0.720569i −0.579514 0.814962i \(-0.696758\pi\)
0.995535 + 0.0943928i \(0.0300910\pi\)
\(632\) 77.8232 3.09564
\(633\) 5.92616 10.2644i 0.235544 0.407973i
\(634\) −13.7621 23.8366i −0.546562 0.946674i
\(635\) 4.42070 + 7.65687i 0.175430 + 0.303854i
\(636\) 17.5491 0.695868
\(637\) 6.39452 22.1513i 0.253360 0.877666i
\(638\) 18.4578 0.730751
\(639\) 7.22889 + 12.5208i 0.285971 + 0.495316i
\(640\) −9.72343 16.8415i −0.384352 0.665718i
\(641\) −9.55425 + 16.5484i −0.377370 + 0.653624i −0.990679 0.136219i \(-0.956505\pi\)
0.613309 + 0.789843i \(0.289838\pi\)
\(642\) 13.5342 0.534152
\(643\) 1.75351 3.03717i 0.0691517 0.119774i −0.829376 0.558690i \(-0.811304\pi\)
0.898528 + 0.438916i \(0.144637\pi\)
\(644\) 4.54957 7.88009i 0.179278 0.310519i
\(645\) 27.0272 1.06419
\(646\) 44.5788 77.2127i 1.75393 3.03789i
\(647\) −10.4171 18.0430i −0.409540 0.709344i 0.585298 0.810818i \(-0.300977\pi\)
−0.994838 + 0.101474i \(0.967644\pi\)
\(648\) 30.7324 + 53.2300i 1.20728 + 2.09107i
\(649\) 5.20784 0.204426
\(650\) 8.79216 30.4569i 0.344857 1.19462i
\(651\) −2.56717 −0.100615
\(652\) −4.11094 7.12035i −0.160997 0.278855i
\(653\) 6.33783 + 10.9774i 0.248019 + 0.429581i 0.962976 0.269587i \(-0.0868873\pi\)
−0.714957 + 0.699168i \(0.753554\pi\)
\(654\) 8.21943 14.2365i 0.321405 0.556690i
\(655\) 12.6445 0.494060
\(656\) −28.2163 + 48.8721i −1.10166 + 1.90813i
\(657\) 2.22188 3.84840i 0.0866836 0.150140i
\(658\) −6.59455 −0.257082
\(659\) −2.18980 + 3.79284i −0.0853025 + 0.147748i −0.905520 0.424303i \(-0.860519\pi\)
0.820218 + 0.572052i \(0.193852\pi\)
\(660\) 5.98240 + 10.3618i 0.232865 + 0.403334i
\(661\) 0.561265 + 0.972140i 0.0218307 + 0.0378118i 0.876734 0.480975i \(-0.159717\pi\)
−0.854904 + 0.518787i \(0.826384\pi\)
\(662\) 25.2110 0.979852
\(663\) 24.4804 + 25.4408i 0.950740 + 0.988038i
\(664\) −76.5520 −2.97080
\(665\) 3.94531 + 6.83348i 0.152993 + 0.264991i
\(666\) 2.20628 + 3.82139i 0.0854917 + 0.148076i
\(667\) 10.0457 17.3996i 0.388970 0.673716i
\(668\) −30.2538 −1.17055
\(669\) −19.2344 + 33.3149i −0.743643 + 1.28803i
\(670\) 9.28670 16.0850i 0.358777 0.621419i
\(671\) −14.5211 −0.560579
\(672\) −2.72343 + 4.71713i −0.105059 + 0.181967i
\(673\) −9.02461 15.6311i −0.347873 0.602534i 0.637998 0.770038i \(-0.279763\pi\)
−0.985871 + 0.167504i \(0.946429\pi\)
\(674\) −24.7440 42.8579i −0.953105 1.65083i
\(675\) 6.23591 0.240020
\(676\) −47.1366 29.6883i −1.81294 1.14186i
\(677\) −26.7037 −1.02631 −0.513154 0.858297i \(-0.671523\pi\)
−0.513154 + 0.858297i \(0.671523\pi\)
\(678\) 16.0477 + 27.7954i 0.616307 + 1.06748i
\(679\) 1.61094 + 2.79023i 0.0618221 + 0.107079i
\(680\) −14.9980 + 25.9773i −0.575147 + 0.996184i
\(681\) −40.2560 −1.54261
\(682\) 1.80976 3.13459i 0.0692992 0.120030i
\(683\) −15.4894 + 26.8285i −0.592686 + 1.02656i 0.401183 + 0.915998i \(0.368599\pi\)
−0.993869 + 0.110565i \(0.964734\pi\)
\(684\) 79.0170 3.02129
\(685\) −3.01604 + 5.22393i −0.115237 + 0.199596i
\(686\) 13.0648 + 22.6289i 0.498817 + 0.863977i
\(687\) −30.6842 53.1467i −1.17068 2.02767i
\(688\) −56.0662 −2.13750
\(689\) −4.48040 4.65617i −0.170690 0.177386i
\(690\) 19.1023 0.727211
\(691\) 1.16563 + 2.01893i 0.0443426 + 0.0768036i 0.887345 0.461106i \(-0.152547\pi\)
−0.843002 + 0.537910i \(0.819214\pi\)
\(692\) −3.53008 6.11427i −0.134193 0.232430i
\(693\) −0.864447 + 1.49727i −0.0328376 + 0.0568765i
\(694\) 45.9116 1.74278
\(695\) 10.0633 17.4301i 0.381721 0.661161i
\(696\) −48.1921 + 83.4712i −1.82672 + 3.16397i
\(697\) −41.7499 −1.58139
\(698\) −21.7816 + 37.7268i −0.824445 + 1.42798i
\(699\) 31.0100 + 53.7110i 1.17291 + 2.03153i
\(700\) 5.84685 + 10.1270i 0.220990 + 0.382766i
\(701\) −22.5834 −0.852965 −0.426482 0.904496i \(-0.640247\pi\)
−0.426482 + 0.904496i \(0.640247\pi\)
\(702\) 4.45779 15.4422i 0.168248 0.582830i
\(703\) −6.57429 −0.247954
\(704\) 1.95233 + 3.38153i 0.0735811 + 0.127446i
\(705\) −4.71943 8.17429i −0.177744 0.307862i
\(706\) −42.3273 + 73.3130i −1.59301 + 2.75917i
\(707\) 3.75385 0.141178
\(708\) −25.4980 + 44.1638i −0.958273 + 1.65978i
\(709\) 7.86089 13.6155i 0.295222 0.511339i −0.679815 0.733384i \(-0.737940\pi\)
0.975036 + 0.222045i \(0.0712731\pi\)
\(710\) 19.9327 0.748062
\(711\) −15.0913 + 26.1390i −0.565970 + 0.980288i
\(712\) 13.6867 + 23.7060i 0.512930 + 0.888421i
\(713\) −1.96992 3.41201i −0.0737742 0.127781i
\(714\) −19.1023 −0.714884
\(715\) 1.22188 4.23270i 0.0456956 0.158294i
\(716\) 31.4288 1.17455
\(717\) −0.852411 1.47642i −0.0318339 0.0551379i
\(718\) 5.92771 + 10.2671i 0.221220 + 0.383165i
\(719\) 14.9151 25.8338i 0.556241 0.963437i −0.441565 0.897229i \(-0.645577\pi\)
0.997806 0.0662079i \(-0.0210901\pi\)
\(720\) −15.7249 −0.586032
\(721\) −3.79728 + 6.57708i −0.141418 + 0.244943i
\(722\) −62.5205 + 108.289i −2.32677 + 4.03009i
\(723\) 36.9568 1.37444
\(724\) −25.2288 + 43.6976i −0.937621 + 1.62401i
\(725\) 12.9101 + 22.3610i 0.479470 + 0.830466i
\(726\) −2.86445 4.96137i −0.106310 0.184134i
\(727\) −36.6053 −1.35761 −0.678807 0.734316i \(-0.737503\pi\)
−0.678807 + 0.734316i \(0.737503\pi\)
\(728\) 15.6023 3.86056i 0.578258 0.143082i
\(729\) −11.6485 −0.431425
\(730\) −3.06327 5.30573i −0.113377 0.196374i
\(731\) −20.7394 35.9216i −0.767073 1.32861i
\(732\) 71.0963 123.142i 2.62779 4.55147i
\(733\) 29.8695 1.10325 0.551627 0.834091i \(-0.314007\pi\)
0.551627 + 0.834091i \(0.314007\pi\)
\(734\) −8.05580 + 13.9531i −0.297345 + 0.515017i
\(735\) −8.92727 + 15.4625i −0.329287 + 0.570342i
\(736\) −8.35933 −0.308129
\(737\) −3.03163 + 5.25094i −0.111672 + 0.193421i
\(738\) −27.1355 47.0000i −0.998870 1.73009i
\(739\) −15.1284 26.2032i −0.556508 0.963901i −0.997784 0.0665295i \(-0.978807\pi\)
0.441276 0.897371i \(-0.354526\pi\)
\(740\) 4.14769 0.152472
\(741\) −47.4120 49.2720i −1.74172 1.81005i
\(742\) 3.49610 0.128346
\(743\) −19.6210 33.9845i −0.719824 1.24677i −0.961069 0.276307i \(-0.910889\pi\)
0.241246 0.970464i \(-0.422444\pi\)
\(744\) 9.45033 + 16.3684i 0.346466 + 0.600096i
\(745\) −1.16363 + 2.01546i −0.0426320 + 0.0738408i
\(746\) −11.0602 −0.404941
\(747\) 14.8449 25.7120i 0.543145 0.940754i
\(748\) 9.18122 15.9023i 0.335699 0.581447i
\(749\) 1.83828 0.0671691
\(750\) −29.7746 + 51.5711i −1.08721 + 1.88311i
\(751\) −3.41168 5.90919i −0.124494 0.215630i 0.797041 0.603925i \(-0.206397\pi\)
−0.921535 + 0.388295i \(0.873064\pi\)
\(752\) 9.79016 + 16.9571i 0.357010 + 0.618360i
\(753\) −25.2007 −0.918365
\(754\) 64.6023 15.9849i 2.35268 0.582136i
\(755\) −22.4930 −0.818603
\(756\) 2.96446 + 5.13460i 0.107816 + 0.186744i
\(757\) 0.376483 + 0.652088i 0.0136835 + 0.0237006i 0.872786 0.488103i \(-0.162311\pi\)
−0.859103 + 0.511803i \(0.828978\pi\)
\(758\) −24.4522 + 42.3525i −0.888145 + 1.53831i
\(759\) −6.23591 −0.226349
\(760\) 29.0471 50.3111i 1.05365 1.82498i
\(761\) −17.4874 + 30.2891i −0.633919 + 1.09798i 0.352825 + 0.935689i \(0.385221\pi\)
−0.986743 + 0.162290i \(0.948112\pi\)
\(762\) 41.4538 1.50171
\(763\) 1.11640 1.93366i 0.0404164 0.0700032i
\(764\) −31.5878 54.7116i −1.14281 1.97940i
\(765\) −5.81678 10.0750i −0.210306 0.364261i
\(766\) 69.2700 2.50283
\(767\) 18.2274 4.51012i 0.658155 0.162851i
\(768\) −73.3333 −2.64619
\(769\) −7.73245 13.3930i −0.278839 0.482964i 0.692257 0.721651i \(-0.256616\pi\)
−0.971097 + 0.238687i \(0.923283\pi\)
\(770\)