Properties

Label 285.2.k.d.248.1
Level $285$
Weight $2$
Character 285.248
Analytic conductor $2.276$
Analytic rank $0$
Dimension $36$
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] = [285,2,Mod(77,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.k (of order \(4\), 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: \(2.27573645761\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 248.1
Character \(\chi\) \(=\) 285.248
Dual form 285.2.k.d.77.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.91639 - 1.91639i) q^{2} +(-0.520717 + 1.65192i) q^{3} +5.34506i q^{4} +(0.478119 + 2.18435i) q^{5} +(4.16362 - 2.16783i) q^{6} +(-1.54943 + 1.54943i) q^{7} +(6.41043 - 6.41043i) q^{8} +(-2.45771 - 1.72037i) q^{9} +O(q^{10})\) \(q+(-1.91639 - 1.91639i) q^{2} +(-0.520717 + 1.65192i) q^{3} +5.34506i q^{4} +(0.478119 + 2.18435i) q^{5} +(4.16362 - 2.16783i) q^{6} +(-1.54943 + 1.54943i) q^{7} +(6.41043 - 6.41043i) q^{8} +(-2.45771 - 1.72037i) q^{9} +(3.26980 - 5.10232i) q^{10} +2.77537i q^{11} +(-8.82964 - 2.78327i) q^{12} +(-3.18746 - 3.18746i) q^{13} +5.93863 q^{14} +(-3.85735 - 0.347614i) q^{15} -13.8796 q^{16} +(-3.06903 - 3.06903i) q^{17} +(1.41302 + 8.00681i) q^{18} -1.00000i q^{19} +(-11.6755 + 2.55558i) q^{20} +(-1.75273 - 3.36636i) q^{21} +(5.31867 - 5.31867i) q^{22} +(1.05802 - 1.05802i) q^{23} +(7.25153 + 13.9276i) q^{24} +(-4.54280 + 2.08876i) q^{25} +12.2168i q^{26} +(4.12169 - 3.16412i) q^{27} +(-8.28182 - 8.28182i) q^{28} +0.341074 q^{29} +(6.72601 + 8.05833i) q^{30} +6.05973 q^{31} +(13.7778 + 13.7778i) q^{32} +(-4.58469 - 1.44518i) q^{33} +11.7629i q^{34} +(-4.12533 - 2.64370i) q^{35} +(9.19549 - 13.1366i) q^{36} +(-5.33202 + 5.33202i) q^{37} +(-1.91639 + 1.91639i) q^{38} +(6.92521 - 3.60568i) q^{39} +(17.0676 + 10.9377i) q^{40} +0.460773i q^{41} +(-3.09234 + 9.81016i) q^{42} +(-3.43474 - 3.43474i) q^{43} -14.8345 q^{44} +(2.58282 - 6.19105i) q^{45} -4.05513 q^{46} +(1.93023 + 1.93023i) q^{47} +(7.22733 - 22.9280i) q^{48} +2.19851i q^{49} +(12.7086 + 4.70289i) q^{50} +(6.66790 - 3.47171i) q^{51} +(17.0372 - 17.0372i) q^{52} +(-4.19597 + 4.19597i) q^{53} +(-13.9624 - 1.83507i) q^{54} +(-6.06238 + 1.32695i) q^{55} +19.8651i q^{56} +(1.65192 + 0.520717i) q^{57} +(-0.653630 - 0.653630i) q^{58} -12.0249 q^{59} +(1.85802 - 20.6178i) q^{60} -12.4849 q^{61} +(-11.6128 - 11.6128i) q^{62} +(6.47366 - 1.14246i) q^{63} -25.0478i q^{64} +(5.43856 - 8.48653i) q^{65} +(6.01652 + 11.5556i) q^{66} +(-2.96882 + 2.96882i) q^{67} +(16.4042 - 16.4042i) q^{68} +(1.19683 + 2.29869i) q^{69} +(2.83937 + 12.9721i) q^{70} -9.44996i q^{71} +(-26.7833 + 4.72666i) q^{72} +(11.0638 + 11.0638i) q^{73} +20.4364 q^{74} +(-1.08496 - 8.59202i) q^{75} +5.34506 q^{76} +(-4.30025 - 4.30025i) q^{77} +(-20.1812 - 6.36150i) q^{78} -1.95283i q^{79} +(-6.63609 - 30.3179i) q^{80} +(3.08066 + 8.45633i) q^{81} +(0.883018 - 0.883018i) q^{82} +(-1.98775 + 1.98775i) q^{83} +(17.9934 - 9.36846i) q^{84} +(5.23649 - 8.17121i) q^{85} +13.1646i q^{86} +(-0.177603 + 0.563429i) q^{87} +(17.7913 + 17.7913i) q^{88} +2.63417 q^{89} +(-16.8141 + 6.91475i) q^{90} +9.87752 q^{91} +(5.65516 + 5.65516i) q^{92} +(-3.15540 + 10.0102i) q^{93} -7.39814i q^{94} +(2.18435 - 0.478119i) q^{95} +(-29.9341 + 15.5855i) q^{96} +(-7.00016 + 7.00016i) q^{97} +(4.21319 - 4.21319i) q^{98} +(4.77465 - 6.82104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.91639 1.91639i −1.35509 1.35509i −0.879865 0.475224i \(-0.842367\pi\)
−0.475224 0.879865i \(-0.657633\pi\)
\(3\) −0.520717 + 1.65192i −0.300636 + 0.953739i
\(4\) 5.34506i 2.67253i
\(5\) 0.478119 + 2.18435i 0.213821 + 0.976873i
\(6\) 4.16362 2.16783i 1.69979 0.885013i
\(7\) −1.54943 + 1.54943i −0.585631 + 0.585631i −0.936445 0.350814i \(-0.885905\pi\)
0.350814 + 0.936445i \(0.385905\pi\)
\(8\) 6.41043 6.41043i 2.26643 2.26643i
\(9\) −2.45771 1.72037i −0.819236 0.573457i
\(10\) 3.26980 5.10232i 1.03400 1.61350i
\(11\) 2.77537i 0.836804i 0.908262 + 0.418402i \(0.137410\pi\)
−0.908262 + 0.418402i \(0.862590\pi\)
\(12\) −8.82964 2.78327i −2.54890 0.803459i
\(13\) −3.18746 3.18746i −0.884043 0.884043i 0.109900 0.993943i \(-0.464947\pi\)
−0.993943 + 0.109900i \(0.964947\pi\)
\(14\) 5.93863 1.58716
\(15\) −3.85735 0.347614i −0.995964 0.0897535i
\(16\) −13.8796 −3.46990
\(17\) −3.06903 3.06903i −0.744349 0.744349i 0.229063 0.973412i \(-0.426434\pi\)
−0.973412 + 0.229063i \(0.926434\pi\)
\(18\) 1.41302 + 8.00681i 0.333053 + 1.88722i
\(19\) 1.00000i 0.229416i
\(20\) −11.6755 + 2.55558i −2.61072 + 0.571444i
\(21\) −1.75273 3.36636i −0.382477 0.734601i
\(22\) 5.31867 5.31867i 1.13394 1.13394i
\(23\) 1.05802 1.05802i 0.220611 0.220611i −0.588144 0.808756i \(-0.700141\pi\)
0.808756 + 0.588144i \(0.200141\pi\)
\(24\) 7.25153 + 13.9276i 1.48021 + 2.84295i
\(25\) −4.54280 + 2.08876i −0.908561 + 0.417752i
\(26\) 12.2168i 2.39591i
\(27\) 4.12169 3.16412i 0.793220 0.608936i
\(28\) −8.28182 8.28182i −1.56512 1.56512i
\(29\) 0.341074 0.0633359 0.0316680 0.999498i \(-0.489918\pi\)
0.0316680 + 0.999498i \(0.489918\pi\)
\(30\) 6.72601 + 8.05833i 1.22800 + 1.47124i
\(31\) 6.05973 1.08836 0.544180 0.838969i \(-0.316841\pi\)
0.544180 + 0.838969i \(0.316841\pi\)
\(32\) 13.7778 + 13.7778i 2.43559 + 2.43559i
\(33\) −4.58469 1.44518i −0.798093 0.251573i
\(34\) 11.7629i 2.01732i
\(35\) −4.12533 2.64370i −0.697307 0.446867i
\(36\) 9.19549 13.1366i 1.53258 2.18943i
\(37\) −5.33202 + 5.33202i −0.876579 + 0.876579i −0.993179 0.116600i \(-0.962801\pi\)
0.116600 + 0.993179i \(0.462801\pi\)
\(38\) −1.91639 + 1.91639i −0.310879 + 0.310879i
\(39\) 6.92521 3.60568i 1.10892 0.577371i
\(40\) 17.0676 + 10.9377i 2.69862 + 1.72940i
\(41\) 0.460773i 0.0719606i 0.999352 + 0.0359803i \(0.0114554\pi\)
−0.999352 + 0.0359803i \(0.988545\pi\)
\(42\) −3.09234 + 9.81016i −0.477159 + 1.51374i
\(43\) −3.43474 3.43474i −0.523794 0.523794i 0.394921 0.918715i \(-0.370772\pi\)
−0.918715 + 0.394921i \(0.870772\pi\)
\(44\) −14.8345 −2.23639
\(45\) 2.58282 6.19105i 0.385024 0.922907i
\(46\) −4.05513 −0.597896
\(47\) 1.93023 + 1.93023i 0.281553 + 0.281553i 0.833728 0.552175i \(-0.186202\pi\)
−0.552175 + 0.833728i \(0.686202\pi\)
\(48\) 7.22733 22.9280i 1.04318 3.30937i
\(49\) 2.19851i 0.314073i
\(50\) 12.7086 + 4.70289i 1.79727 + 0.665089i
\(51\) 6.66790 3.47171i 0.933693 0.486137i
\(52\) 17.0372 17.0372i 2.36263 2.36263i
\(53\) −4.19597 + 4.19597i −0.576360 + 0.576360i −0.933899 0.357538i \(-0.883616\pi\)
0.357538 + 0.933899i \(0.383616\pi\)
\(54\) −13.9624 1.83507i −1.90005 0.249722i
\(55\) −6.06238 + 1.32695i −0.817451 + 0.178926i
\(56\) 19.8651i 2.65458i
\(57\) 1.65192 + 0.520717i 0.218803 + 0.0689706i
\(58\) −0.653630 0.653630i −0.0858258 0.0858258i
\(59\) −12.0249 −1.56551 −0.782757 0.622327i \(-0.786187\pi\)
−0.782757 + 0.622327i \(0.786187\pi\)
\(60\) 1.85802 20.6178i 0.239869 2.66175i
\(61\) −12.4849 −1.59853 −0.799263 0.600981i \(-0.794777\pi\)
−0.799263 + 0.600981i \(0.794777\pi\)
\(62\) −11.6128 11.6128i −1.47482 1.47482i
\(63\) 6.47366 1.14246i 0.815604 0.143936i
\(64\) 25.0478i 3.13098i
\(65\) 5.43856 8.48653i 0.674570 1.05262i
\(66\) 6.01652 + 11.5556i 0.740582 + 1.42239i
\(67\) −2.96882 + 2.96882i −0.362699 + 0.362699i −0.864806 0.502107i \(-0.832558\pi\)
0.502107 + 0.864806i \(0.332558\pi\)
\(68\) 16.4042 16.4042i 1.98930 1.98930i
\(69\) 1.19683 + 2.29869i 0.144082 + 0.276730i
\(70\) 2.83937 + 12.9721i 0.339369 + 1.55046i
\(71\) 9.44996i 1.12150i −0.827984 0.560752i \(-0.810512\pi\)
0.827984 0.560752i \(-0.189488\pi\)
\(72\) −26.7833 + 4.72666i −3.15644 + 0.557042i
\(73\) 11.0638 + 11.0638i 1.29492 + 1.29492i 0.931706 + 0.363214i \(0.118321\pi\)
0.363214 + 0.931706i \(0.381679\pi\)
\(74\) 20.4364 2.37569
\(75\) −1.08496 8.59202i −0.125280 0.992121i
\(76\) 5.34506 0.613121
\(77\) −4.30025 4.30025i −0.490058 0.490058i
\(78\) −20.1812 6.36150i −2.28508 0.720298i
\(79\) 1.95283i 0.219710i −0.993948 0.109855i \(-0.964961\pi\)
0.993948 0.109855i \(-0.0350387\pi\)
\(80\) −6.63609 30.3179i −0.741937 3.38965i
\(81\) 3.08066 + 8.45633i 0.342295 + 0.939593i
\(82\) 0.883018 0.883018i 0.0975130 0.0975130i
\(83\) −1.98775 + 1.98775i −0.218184 + 0.218184i −0.807733 0.589549i \(-0.799306\pi\)
0.589549 + 0.807733i \(0.299306\pi\)
\(84\) 17.9934 9.36846i 1.96324 1.02218i
\(85\) 5.23649 8.17121i 0.567977 0.886292i
\(86\) 13.1646i 1.41957i
\(87\) −0.177603 + 0.563429i −0.0190411 + 0.0604059i
\(88\) 17.7913 + 17.7913i 1.89656 + 1.89656i
\(89\) 2.63417 0.279222 0.139611 0.990206i \(-0.455415\pi\)
0.139611 + 0.990206i \(0.455415\pi\)
\(90\) −16.8141 + 6.91475i −1.77236 + 0.728878i
\(91\) 9.87752 1.03545
\(92\) 5.65516 + 5.65516i 0.589591 + 0.589591i
\(93\) −3.15540 + 10.0102i −0.327200 + 1.03801i
\(94\) 7.39814i 0.763060i
\(95\) 2.18435 0.478119i 0.224110 0.0490540i
\(96\) −29.9341 + 15.5855i −3.05514 + 1.59069i
\(97\) −7.00016 + 7.00016i −0.710759 + 0.710759i −0.966694 0.255935i \(-0.917617\pi\)
0.255935 + 0.966694i \(0.417617\pi\)
\(98\) 4.21319 4.21319i 0.425596 0.425596i
\(99\) 4.77465 6.82104i 0.479871 0.685540i
\(100\) −11.1646 24.2816i −1.11646 2.42816i
\(101\) 4.85779i 0.483369i 0.970355 + 0.241684i \(0.0776998\pi\)
−0.970355 + 0.241684i \(0.922300\pi\)
\(102\) −19.4314 6.12513i −1.92400 0.606479i
\(103\) 5.35243 + 5.35243i 0.527391 + 0.527391i 0.919793 0.392403i \(-0.128356\pi\)
−0.392403 + 0.919793i \(0.628356\pi\)
\(104\) −40.8660 −4.00724
\(105\) 6.51532 5.43811i 0.635830 0.530705i
\(106\) 16.0822 1.56204
\(107\) 11.6658 + 11.6658i 1.12778 + 1.12778i 0.990538 + 0.137240i \(0.0438231\pi\)
0.137240 + 0.990538i \(0.456177\pi\)
\(108\) 16.9124 + 22.0307i 1.62740 + 2.11991i
\(109\) 8.24149i 0.789391i −0.918812 0.394696i \(-0.870850\pi\)
0.918812 0.394696i \(-0.129150\pi\)
\(110\) 14.1608 + 9.07490i 1.35018 + 0.865258i
\(111\) −6.03163 11.5846i −0.572497 1.09956i
\(112\) 21.5055 21.5055i 2.03208 2.03208i
\(113\) −1.81897 + 1.81897i −0.171114 + 0.171114i −0.787469 0.616355i \(-0.788609\pi\)
0.616355 + 0.787469i \(0.288609\pi\)
\(114\) −2.16783 4.16362i −0.203036 0.389958i
\(115\) 2.81694 + 1.80522i 0.262681 + 0.168338i
\(116\) 1.82306i 0.169267i
\(117\) 2.35024 + 13.3175i 0.217279 + 1.23120i
\(118\) 23.0444 + 23.0444i 2.12141 + 2.12141i
\(119\) 9.51052 0.871828
\(120\) −26.9556 + 22.4989i −2.46070 + 2.05386i
\(121\) 3.29735 0.299759
\(122\) 23.9259 + 23.9259i 2.16615 + 2.16615i
\(123\) −0.761161 0.239932i −0.0686316 0.0216339i
\(124\) 32.3897i 2.90868i
\(125\) −6.73459 8.92442i −0.602360 0.798224i
\(126\) −14.5954 10.2166i −1.30026 0.910170i
\(127\) 2.22493 2.22493i 0.197430 0.197430i −0.601467 0.798897i \(-0.705417\pi\)
0.798897 + 0.601467i \(0.205417\pi\)
\(128\) −20.4458 + 20.4458i −1.80717 + 1.80717i
\(129\) 7.46247 3.88541i 0.657034 0.342091i
\(130\) −26.6858 + 5.84109i −2.34050 + 0.512297i
\(131\) 10.5155i 0.918741i 0.888245 + 0.459370i \(0.151925\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(132\) 7.72458 24.5055i 0.672338 2.13293i
\(133\) 1.54943 + 1.54943i 0.134353 + 0.134353i
\(134\) 11.3788 0.982977
\(135\) 8.88222 + 7.49041i 0.764460 + 0.644671i
\(136\) −39.3476 −3.37403
\(137\) −10.5193 10.5193i −0.898728 0.898728i 0.0965958 0.995324i \(-0.469205\pi\)
−0.995324 + 0.0965958i \(0.969205\pi\)
\(138\) 2.11157 6.69877i 0.179749 0.570237i
\(139\) 4.15876i 0.352741i −0.984324 0.176371i \(-0.943564\pi\)
0.984324 0.176371i \(-0.0564357\pi\)
\(140\) 14.1307 22.0501i 1.19427 1.86358i
\(141\) −4.19370 + 2.18349i −0.353174 + 0.183883i
\(142\) −18.1098 + 18.1098i −1.51974 + 1.51974i
\(143\) 8.84637 8.84637i 0.739771 0.739771i
\(144\) 34.1120 + 23.8780i 2.84266 + 1.98983i
\(145\) 0.163074 + 0.745027i 0.0135426 + 0.0618711i
\(146\) 42.4050i 3.50946i
\(147\) −3.63177 1.14480i −0.299543 0.0944215i
\(148\) −28.5000 28.5000i −2.34269 2.34269i
\(149\) −7.19933 −0.589792 −0.294896 0.955529i \(-0.595285\pi\)
−0.294896 + 0.955529i \(0.595285\pi\)
\(150\) −14.3864 + 18.5448i −1.17465 + 1.51418i
\(151\) −12.0309 −0.979064 −0.489532 0.871985i \(-0.662832\pi\)
−0.489532 + 0.871985i \(0.662832\pi\)
\(152\) −6.41043 6.41043i −0.519955 0.519955i
\(153\) 2.26291 + 12.8226i 0.182946 + 1.03665i
\(154\) 16.4819i 1.32815i
\(155\) 2.89727 + 13.2366i 0.232714 + 1.06319i
\(156\) 19.2726 + 37.0157i 1.54304 + 2.96363i
\(157\) −16.2197 + 16.2197i −1.29447 + 1.29447i −0.362483 + 0.931990i \(0.618071\pi\)
−0.931990 + 0.362483i \(0.881929\pi\)
\(158\) −3.74237 + 3.74237i −0.297727 + 0.297727i
\(159\) −4.74651 9.11633i −0.376423 0.722972i
\(160\) −23.5081 + 36.6829i −1.85848 + 2.90004i
\(161\) 3.27865i 0.258394i
\(162\) 10.3019 22.1093i 0.809391 1.73707i
\(163\) 6.98240 + 6.98240i 0.546904 + 0.546904i 0.925544 0.378640i \(-0.123608\pi\)
−0.378640 + 0.925544i \(0.623608\pi\)
\(164\) −2.46286 −0.192317
\(165\) 0.964756 10.7056i 0.0751061 0.833427i
\(166\) 7.61860 0.591318
\(167\) 3.03997 + 3.03997i 0.235240 + 0.235240i 0.814876 0.579636i \(-0.196805\pi\)
−0.579636 + 0.814876i \(0.696805\pi\)
\(168\) −32.8156 10.3441i −2.53178 0.798063i
\(169\) 7.31982i 0.563063i
\(170\) −25.6943 + 5.62406i −1.97066 + 0.431345i
\(171\) −1.72037 + 2.45771i −0.131560 + 0.187946i
\(172\) 18.3589 18.3589i 1.39986 1.39986i
\(173\) 7.67046 7.67046i 0.583175 0.583175i −0.352600 0.935774i \(-0.614702\pi\)
0.935774 + 0.352600i \(0.114702\pi\)
\(174\) 1.42010 0.739391i 0.107658 0.0560531i
\(175\) 3.80238 10.2752i 0.287433 0.776730i
\(176\) 38.5209i 2.90362i
\(177\) 6.26159 19.8643i 0.470650 1.49309i
\(178\) −5.04809 5.04809i −0.378370 0.378370i
\(179\) 1.98934 0.148691 0.0743453 0.997233i \(-0.476313\pi\)
0.0743453 + 0.997233i \(0.476313\pi\)
\(180\) 33.0915 + 13.8053i 2.46650 + 1.02899i
\(181\) 4.67919 0.347801 0.173901 0.984763i \(-0.444363\pi\)
0.173901 + 0.984763i \(0.444363\pi\)
\(182\) −18.9291 18.9291i −1.40312 1.40312i
\(183\) 6.50109 20.6241i 0.480575 1.52458i
\(184\) 13.5647i 1.00000i
\(185\) −14.1964 9.09769i −1.04374 0.668875i
\(186\) 25.2304 13.1365i 1.84998 0.963212i
\(187\) 8.51768 8.51768i 0.622874 0.622874i
\(188\) −10.3172 + 10.3172i −0.752461 + 0.752461i
\(189\) −1.48369 + 11.2889i −0.107923 + 0.821146i
\(190\) −5.10232 3.26980i −0.370161 0.237217i
\(191\) 16.7170i 1.20960i 0.796377 + 0.604801i \(0.206747\pi\)
−0.796377 + 0.604801i \(0.793253\pi\)
\(192\) 41.3771 + 13.0428i 2.98614 + 0.941286i
\(193\) −7.47975 7.47975i −0.538404 0.538404i 0.384656 0.923060i \(-0.374320\pi\)
−0.923060 + 0.384656i \(0.874320\pi\)
\(194\) 26.8300 1.92628
\(195\) 11.1872 + 13.4032i 0.801129 + 0.959821i
\(196\) −11.7512 −0.839369
\(197\) 7.94055 + 7.94055i 0.565741 + 0.565741i 0.930932 0.365192i \(-0.118997\pi\)
−0.365192 + 0.930932i \(0.618997\pi\)
\(198\) −22.2218 + 3.92166i −1.57924 + 0.278700i
\(199\) 2.10866i 0.149479i −0.997203 0.0747396i \(-0.976187\pi\)
0.997203 0.0747396i \(-0.0238126\pi\)
\(200\) −15.7315 + 42.5112i −1.11238 + 3.00600i
\(201\) −3.35835 6.45017i −0.236879 0.454960i
\(202\) 9.30941 9.30941i 0.655007 0.655007i
\(203\) −0.528472 + 0.528472i −0.0370915 + 0.0370915i
\(204\) 18.5565 + 35.6404i 1.29922 + 2.49532i
\(205\) −1.00649 + 0.220304i −0.0702963 + 0.0153867i
\(206\) 20.5146i 1.42932i
\(207\) −4.42047 + 0.780115i −0.307244 + 0.0542217i
\(208\) 44.2406 + 44.2406i 3.06754 + 3.06754i
\(209\) 2.77537 0.191976
\(210\) −22.9074 2.06435i −1.58076 0.142454i
\(211\) 2.30777 0.158874 0.0794368 0.996840i \(-0.474688\pi\)
0.0794368 + 0.996840i \(0.474688\pi\)
\(212\) −22.4277 22.4277i −1.54034 1.54034i
\(213\) 15.6106 + 4.92075i 1.06962 + 0.337164i
\(214\) 44.7124i 3.05648i
\(215\) 5.86048 9.14491i 0.399682 0.623678i
\(216\) 6.13843 46.7052i 0.417667 3.17789i
\(217\) −9.38915 + 9.38915i −0.637377 + 0.637377i
\(218\) −15.7939 + 15.7939i −1.06970 + 1.06970i
\(219\) −24.0377 + 12.5155i −1.62432 + 0.845716i
\(220\) −7.09266 32.4038i −0.478187 2.18466i
\(221\) 19.5648i 1.31607i
\(222\) −10.6416 + 33.7594i −0.714217 + 2.26578i
\(223\) 10.1353 + 10.1353i 0.678708 + 0.678708i 0.959708 0.281000i \(-0.0906661\pi\)
−0.281000 + 0.959708i \(0.590666\pi\)
\(224\) −42.6955 −2.85271
\(225\) 14.7583 + 2.68174i 0.983889 + 0.178783i
\(226\) 6.97169 0.463750
\(227\) 5.56895 + 5.56895i 0.369624 + 0.369624i 0.867340 0.497716i \(-0.165828\pi\)
−0.497716 + 0.867340i \(0.665828\pi\)
\(228\) −2.78327 + 8.82964i −0.184326 + 0.584757i
\(229\) 17.5759i 1.16145i −0.814101 0.580723i \(-0.802770\pi\)
0.814101 0.580723i \(-0.197230\pi\)
\(230\) −1.93883 8.85784i −0.127843 0.584069i
\(231\) 9.34289 4.86447i 0.614717 0.320059i
\(232\) 2.18643 2.18643i 0.143546 0.143546i
\(233\) −3.20196 + 3.20196i −0.209767 + 0.209767i −0.804169 0.594401i \(-0.797389\pi\)
0.594401 + 0.804169i \(0.297389\pi\)
\(234\) 21.0174 30.0253i 1.37395 1.96282i
\(235\) −3.29343 + 5.13919i −0.214840 + 0.335244i
\(236\) 64.2741i 4.18389i
\(237\) 3.22593 + 1.01687i 0.209546 + 0.0660529i
\(238\) −18.2258 18.2258i −1.18140 1.18140i
\(239\) −3.93355 −0.254440 −0.127220 0.991875i \(-0.540605\pi\)
−0.127220 + 0.991875i \(0.540605\pi\)
\(240\) 53.5384 + 4.82474i 3.45589 + 0.311435i
\(241\) 13.4170 0.864268 0.432134 0.901809i \(-0.357761\pi\)
0.432134 + 0.901809i \(0.357761\pi\)
\(242\) −6.31899 6.31899i −0.406200 0.406200i
\(243\) −15.5734 + 0.685655i −0.999032 + 0.0439848i
\(244\) 66.7325i 4.27211i
\(245\) −4.80232 + 1.05115i −0.306809 + 0.0671554i
\(246\) 0.998876 + 1.91848i 0.0636860 + 0.122318i
\(247\) −3.18746 + 3.18746i −0.202813 + 0.202813i
\(248\) 38.8455 38.8455i 2.46669 2.46669i
\(249\) −2.24856 4.31868i −0.142497 0.273685i
\(250\) −4.19654 + 30.0087i −0.265413 + 1.89792i
\(251\) 22.6412i 1.42910i 0.699583 + 0.714551i \(0.253369\pi\)
−0.699583 + 0.714551i \(0.746631\pi\)
\(252\) 6.10650 + 34.6021i 0.384674 + 2.17973i
\(253\) 2.93638 + 2.93638i 0.184609 + 0.184609i
\(254\) −8.52763 −0.535071
\(255\) 10.7715 + 12.9052i 0.674537 + 0.808153i
\(256\) 28.2683 1.76677
\(257\) −17.9072 17.9072i −1.11702 1.11702i −0.992176 0.124844i \(-0.960157\pi\)
−0.124844 0.992176i \(-0.539843\pi\)
\(258\) −21.7469 6.85502i −1.35390 0.426775i
\(259\) 16.5232i 1.02670i
\(260\) 45.3610 + 29.0694i 2.81317 + 1.80281i
\(261\) −0.838261 0.586774i −0.0518871 0.0363204i
\(262\) 20.1517 20.1517i 1.24498 1.24498i
\(263\) −17.9317 + 17.9317i −1.10572 + 1.10572i −0.112008 + 0.993707i \(0.535728\pi\)
−0.993707 + 0.112008i \(0.964272\pi\)
\(264\) −38.6541 + 20.1256i −2.37899 + 1.23865i
\(265\) −11.1716 7.15931i −0.686269 0.439793i
\(266\) 5.93863i 0.364120i
\(267\) −1.37166 + 4.35145i −0.0839441 + 0.266304i
\(268\) −15.8685 15.8685i −0.969323 0.969323i
\(269\) −7.65484 −0.466724 −0.233362 0.972390i \(-0.574973\pi\)
−0.233362 + 0.972390i \(0.574973\pi\)
\(270\) −2.66725 31.3763i −0.162324 1.90950i
\(271\) 23.6973 1.43951 0.719754 0.694230i \(-0.244255\pi\)
0.719754 + 0.694230i \(0.244255\pi\)
\(272\) 42.5969 + 42.5969i 2.58281 + 2.58281i
\(273\) −5.14339 + 16.3169i −0.311292 + 0.987545i
\(274\) 40.3182i 2.43571i
\(275\) −5.79708 12.6079i −0.349577 0.760288i
\(276\) −12.2866 + 6.39716i −0.739568 + 0.385064i
\(277\) −19.2242 + 19.2242i −1.15507 + 1.15507i −0.169547 + 0.985522i \(0.554230\pi\)
−0.985522 + 0.169547i \(0.945770\pi\)
\(278\) −7.96978 + 7.96978i −0.477996 + 0.477996i
\(279\) −14.8930 10.4250i −0.891624 0.624127i
\(280\) −43.3924 + 9.49787i −2.59319 + 0.567606i
\(281\) 13.1510i 0.784521i 0.919854 + 0.392260i \(0.128307\pi\)
−0.919854 + 0.392260i \(0.871693\pi\)
\(282\) 12.2212 + 3.85234i 0.727760 + 0.229403i
\(283\) −6.91873 6.91873i −0.411276 0.411276i 0.470907 0.882183i \(-0.343927\pi\)
−0.882183 + 0.470907i \(0.843927\pi\)
\(284\) 50.5106 2.99725
\(285\) −0.347614 + 3.85735i −0.0205909 + 0.228490i
\(286\) −33.9061 −2.00491
\(287\) −0.713937 0.713937i −0.0421424 0.0421424i
\(288\) −10.1589 57.5646i −0.598617 3.39202i
\(289\) 1.83789i 0.108111i
\(290\) 1.11525 1.74027i 0.0654895 0.102192i
\(291\) −7.91864 15.2088i −0.464199 0.891558i
\(292\) −59.1367 + 59.1367i −3.46072 + 3.46072i
\(293\) 0.0332012 0.0332012i 0.00193964 0.00193964i −0.706136 0.708076i \(-0.749563\pi\)
0.708076 + 0.706136i \(0.249563\pi\)
\(294\) 4.76599 + 9.15375i 0.277958 + 0.533857i
\(295\) −5.74935 26.2667i −0.334740 1.52931i
\(296\) 68.3612i 3.97341i
\(297\) 8.78159 + 11.4392i 0.509560 + 0.663770i
\(298\) 13.7967 + 13.7967i 0.799221 + 0.799221i
\(299\) −6.74477 −0.390060
\(300\) 45.9249 5.79918i 2.65148 0.334816i
\(301\) 10.6438 0.613500
\(302\) 23.0559 + 23.0559i 1.32672 + 1.32672i
\(303\) −8.02471 2.52954i −0.461007 0.145318i
\(304\) 13.8796i 0.796049i
\(305\) −5.96926 27.2714i −0.341799 1.56156i
\(306\) 20.2365 28.9097i 1.15684 1.65266i
\(307\) 14.8603 14.8603i 0.848121 0.848121i −0.141778 0.989899i \(-0.545282\pi\)
0.989899 + 0.141778i \(0.0452818\pi\)
\(308\) 22.9851 22.9851i 1.30970 1.30970i
\(309\) −11.6289 + 6.05471i −0.661546 + 0.344440i
\(310\) 19.8141 30.9187i 1.12537 1.75606i
\(311\) 20.7689i 1.17770i 0.808244 + 0.588848i \(0.200418\pi\)
−0.808244 + 0.588848i \(0.799582\pi\)
\(312\) 21.2796 67.5076i 1.20472 3.82186i
\(313\) 17.9949 + 17.9949i 1.01713 + 1.01713i 0.999851 + 0.0172821i \(0.00550135\pi\)
0.0172821 + 0.999851i \(0.494499\pi\)
\(314\) 62.1664 3.50825
\(315\) 5.59071 + 13.5945i 0.315001 + 0.765965i
\(316\) 10.4380 0.587183
\(317\) −20.9864 20.9864i −1.17871 1.17871i −0.980073 0.198640i \(-0.936348\pi\)
−0.198640 0.980073i \(-0.563652\pi\)
\(318\) −8.37426 + 26.5665i −0.469605 + 1.48978i
\(319\) 0.946606i 0.0529998i
\(320\) 54.7134 11.9758i 3.05857 0.669470i
\(321\) −25.3456 + 13.1965i −1.41466 + 0.736555i
\(322\) 6.28316 6.28316i 0.350147 0.350147i
\(323\) −3.06903 + 3.06903i −0.170765 + 0.170765i
\(324\) −45.1996 + 16.4663i −2.51109 + 0.914795i
\(325\) 21.1379 + 7.82217i 1.17252 + 0.433896i
\(326\) 26.7619i 1.48221i
\(327\) 13.6143 + 4.29148i 0.752873 + 0.237320i
\(328\) 2.95375 + 2.95375i 0.163094 + 0.163094i
\(329\) −5.98154 −0.329773
\(330\) −22.3648 + 18.6671i −1.23114 + 1.02759i
\(331\) 2.39369 0.131569 0.0657845 0.997834i \(-0.479045\pi\)
0.0657845 + 0.997834i \(0.479045\pi\)
\(332\) −10.6247 10.6247i −0.583105 0.583105i
\(333\) 22.2776 3.93150i 1.22081 0.215445i
\(334\) 11.6515i 0.637542i
\(335\) −7.90439 5.06550i −0.431863 0.276758i
\(336\) 24.3272 + 46.7237i 1.32716 + 2.54899i
\(337\) 1.11402 1.11402i 0.0606843 0.0606843i −0.676113 0.736798i \(-0.736337\pi\)
0.736798 + 0.676113i \(0.236337\pi\)
\(338\) 14.0276 14.0276i 0.763001 0.763001i
\(339\) −2.05763 3.95197i −0.111755 0.214641i
\(340\) 43.6756 + 27.9894i 2.36864 + 1.51794i
\(341\) 16.8180i 0.910744i
\(342\) 8.00681 1.41302i 0.432958 0.0764076i
\(343\) −14.2525 14.2525i −0.769562 0.769562i
\(344\) −44.0364 −2.37428
\(345\) −4.44892 + 3.71336i −0.239522 + 0.199920i
\(346\) −29.3991 −1.58051
\(347\) 15.4836 + 15.4836i 0.831203 + 0.831203i 0.987681 0.156478i \(-0.0500141\pi\)
−0.156478 + 0.987681i \(0.550014\pi\)
\(348\) −3.01156 0.949300i −0.161437 0.0508878i
\(349\) 0.845815i 0.0452755i −0.999744 0.0226377i \(-0.992794\pi\)
0.999744 0.0226377i \(-0.00720643\pi\)
\(350\) −26.9780 + 12.4044i −1.44204 + 0.663042i
\(351\) −23.2232 3.05221i −1.23957 0.162915i
\(352\) −38.2383 + 38.2383i −2.03811 + 2.03811i
\(353\) 14.1758 14.1758i 0.754502 0.754502i −0.220814 0.975316i \(-0.570871\pi\)
0.975316 + 0.220814i \(0.0708713\pi\)
\(354\) −50.0673 + 26.0680i −2.66105 + 1.38550i
\(355\) 20.6420 4.51820i 1.09557 0.239801i
\(356\) 14.0798i 0.746229i
\(357\) −4.95229 + 15.7107i −0.262103 + 0.831496i
\(358\) −3.81235 3.81235i −0.201489 0.201489i
\(359\) −23.0208 −1.21499 −0.607496 0.794322i \(-0.707826\pi\)
−0.607496 + 0.794322i \(0.707826\pi\)
\(360\) −23.1303 56.2443i −1.21907 2.96433i
\(361\) −1.00000 −0.0526316
\(362\) −8.96712 8.96712i −0.471301 0.471301i
\(363\) −1.71698 + 5.44697i −0.0901183 + 0.285892i
\(364\) 52.7960i 2.76726i
\(365\) −18.8774 + 29.4571i −0.988091 + 1.54185i
\(366\) −51.9823 + 27.0651i −2.71716 + 1.41472i
\(367\) 7.92943 7.92943i 0.413913 0.413913i −0.469186 0.883099i \(-0.655453\pi\)
0.883099 + 0.469186i \(0.155453\pi\)
\(368\) −14.6848 + 14.6848i −0.765499 + 0.765499i
\(369\) 0.792699 1.13244i 0.0412663 0.0589527i
\(370\) 9.77104 + 44.6404i 0.507972 + 2.32074i
\(371\) 13.0027i 0.675069i
\(372\) −53.5053 16.8658i −2.77412 0.874453i
\(373\) −6.69493 6.69493i −0.346650 0.346650i 0.512210 0.858860i \(-0.328827\pi\)
−0.858860 + 0.512210i \(0.828827\pi\)
\(374\) −32.6463 −1.68810
\(375\) 18.2493 6.47795i 0.942389 0.334520i
\(376\) 24.7473 1.27624
\(377\) −1.08716 1.08716i −0.0559917 0.0559917i
\(378\) 24.4772 18.7905i 1.25897 0.966481i
\(379\) 10.8622i 0.557952i 0.960298 + 0.278976i \(0.0899950\pi\)
−0.960298 + 0.278976i \(0.910005\pi\)
\(380\) 2.55558 + 11.6755i 0.131098 + 0.598941i
\(381\) 2.51685 + 4.83397i 0.128942 + 0.247652i
\(382\) 32.0363 32.0363i 1.63912 1.63912i
\(383\) 12.3305 12.3305i 0.630059 0.630059i −0.318024 0.948083i \(-0.603019\pi\)
0.948083 + 0.318024i \(0.103019\pi\)
\(384\) −23.1284 44.4214i −1.18027 2.26687i
\(385\) 7.33723 11.4493i 0.373940 0.583510i
\(386\) 28.6682i 1.45917i
\(387\) 2.53257 + 14.3506i 0.128738 + 0.729483i
\(388\) −37.4163 37.4163i −1.89953 1.89953i
\(389\) 22.3582 1.13360 0.566802 0.823854i \(-0.308180\pi\)
0.566802 + 0.823854i \(0.308180\pi\)
\(390\) 4.24673 47.1245i 0.215042 2.38624i
\(391\) −6.49416 −0.328424
\(392\) 14.0934 + 14.0934i 0.711823 + 0.711823i
\(393\) −17.3708 5.47558i −0.876239 0.276207i
\(394\) 30.4343i 1.53326i
\(395\) 4.26567 0.933684i 0.214629 0.0469788i
\(396\) 36.4589 + 25.5208i 1.83213 + 1.28247i
\(397\) 2.17078 2.17078i 0.108948 0.108948i −0.650531 0.759479i \(-0.725454\pi\)
0.759479 + 0.650531i \(0.225454\pi\)
\(398\) −4.04101 + 4.04101i −0.202558 + 0.202558i
\(399\) −3.36636 + 1.75273i −0.168529 + 0.0877463i
\(400\) 63.0522 28.9911i 3.15261 1.44956i
\(401\) 31.8732i 1.59167i −0.605512 0.795836i \(-0.707032\pi\)
0.605512 0.795836i \(-0.292968\pi\)
\(402\) −5.92513 + 18.7969i −0.295518 + 0.937504i
\(403\) −19.3152 19.3152i −0.962157 0.962157i
\(404\) −25.9652 −1.29182
\(405\) −16.9987 + 10.7724i −0.844672 + 0.535284i
\(406\) 2.02551 0.100525
\(407\) −14.7983 14.7983i −0.733525 0.733525i
\(408\) 20.4890 64.9993i 1.01435 3.21794i
\(409\) 25.4247i 1.25717i 0.777740 + 0.628586i \(0.216366\pi\)
−0.777740 + 0.628586i \(0.783634\pi\)
\(410\) 2.35101 + 1.50664i 0.116108 + 0.0744074i
\(411\) 22.8548 11.8996i 1.12734 0.586962i
\(412\) −28.6091 + 28.6091i −1.40947 + 1.40947i
\(413\) 18.6319 18.6319i 0.916814 0.916814i
\(414\) 9.96633 + 6.97632i 0.489818 + 0.342868i
\(415\) −5.29234 3.39158i −0.259791 0.166486i
\(416\) 87.8322i 4.30633i
\(417\) 6.86995 + 2.16554i 0.336423 + 0.106047i
\(418\) −5.31867 5.31867i −0.260145 0.260145i
\(419\) 17.7057 0.864980 0.432490 0.901639i \(-0.357635\pi\)
0.432490 + 0.901639i \(0.357635\pi\)
\(420\) 29.0670 + 34.8248i 1.41833 + 1.69928i
\(421\) −11.7072 −0.570573 −0.285286 0.958442i \(-0.592089\pi\)
−0.285286 + 0.958442i \(0.592089\pi\)
\(422\) −4.42258 4.42258i −0.215288 0.215288i
\(423\) −1.42323 8.06466i −0.0692000 0.392117i
\(424\) 53.7959i 2.61256i
\(425\) 20.3525 + 7.53153i 0.987240 + 0.365333i
\(426\) −20.4859 39.3460i −0.992545 1.90632i
\(427\) 19.3445 19.3445i 0.936147 0.936147i
\(428\) −62.3546 + 62.3546i −3.01402 + 3.01402i
\(429\) 10.0071 + 19.2200i 0.483146 + 0.927950i
\(430\) −28.7561 + 6.29424i −1.38674 + 0.303535i
\(431\) 21.6064i 1.04074i −0.853940 0.520371i \(-0.825794\pi\)
0.853940 0.520371i \(-0.174206\pi\)
\(432\) −57.2074 + 43.9167i −2.75239 + 2.11294i
\(433\) 0.0582172 + 0.0582172i 0.00279774 + 0.00279774i 0.708504 0.705707i \(-0.249370\pi\)
−0.705707 + 0.708504i \(0.749370\pi\)
\(434\) 35.9865 1.72741
\(435\) −1.31564 0.118562i −0.0630803 0.00568462i
\(436\) 44.0513 2.10967
\(437\) −1.05802 1.05802i −0.0506117 0.0506117i
\(438\) 70.0499 + 22.0810i 3.34711 + 1.05507i
\(439\) 23.8132i 1.13654i −0.822841 0.568272i \(-0.807612\pi\)
0.822841 0.568272i \(-0.192388\pi\)
\(440\) −30.3561 + 47.3688i −1.44717 + 2.25822i
\(441\) 3.78225 5.40329i 0.180107 0.257300i
\(442\) 37.4937 37.4937i 1.78340 1.78340i
\(443\) 2.17649 2.17649i 0.103408 0.103408i −0.653510 0.756918i \(-0.726704\pi\)
0.756918 + 0.653510i \(0.226704\pi\)
\(444\) 61.9203 32.2394i 2.93861 1.53002i
\(445\) 1.25945 + 5.75396i 0.0597035 + 0.272764i
\(446\) 38.8462i 1.83942i
\(447\) 3.74881 11.8928i 0.177313 0.562508i
\(448\) 38.8100 + 38.8100i 1.83360 + 1.83360i
\(449\) 8.53457 0.402771 0.201386 0.979512i \(-0.435456\pi\)
0.201386 + 0.979512i \(0.435456\pi\)
\(450\) −23.1434 33.4219i −1.09099 1.57552i
\(451\) −1.27881 −0.0602169
\(452\) −9.72251 9.72251i −0.457308 0.457308i
\(453\) 6.26471 19.8742i 0.294342 0.933771i
\(454\) 21.3445i 1.00175i
\(455\) 4.72263 + 21.5760i 0.221400 + 1.01150i
\(456\) 13.9276 7.25153i 0.652218 0.339584i
\(457\) 7.83972 7.83972i 0.366727 0.366727i −0.499555 0.866282i \(-0.666503\pi\)
0.866282 + 0.499555i \(0.166503\pi\)
\(458\) −33.6821 + 33.6821i −1.57386 + 1.57386i
\(459\) −22.3604 2.93881i −1.04369 0.137172i
\(460\) −9.64903 + 15.0567i −0.449889 + 0.702023i
\(461\) 0.162959i 0.00758975i 0.999993 + 0.00379487i \(0.00120795\pi\)
−0.999993 + 0.00379487i \(0.998792\pi\)
\(462\) −27.2268 8.58238i −1.26670 0.399288i
\(463\) −0.535845 0.535845i −0.0249028 0.0249028i 0.694546 0.719449i \(-0.255605\pi\)
−0.719449 + 0.694546i \(0.755605\pi\)
\(464\) −4.73397 −0.219769
\(465\) −23.3745 2.10645i −1.08397 0.0976842i
\(466\) 12.2724 0.568507
\(467\) 18.3999 + 18.3999i 0.851446 + 0.851446i 0.990311 0.138865i \(-0.0443455\pi\)
−0.138865 + 0.990311i \(0.544345\pi\)
\(468\) −71.1827 + 12.5622i −3.29042 + 0.580686i
\(469\) 9.19997i 0.424815i
\(470\) 16.1602 3.53719i 0.745412 0.163158i
\(471\) −18.3479 35.2396i −0.845425 1.62376i
\(472\) −77.0851 + 77.0851i −3.54813 + 3.54813i
\(473\) 9.53267 9.53267i 0.438313 0.438313i
\(474\) −4.23340 8.13083i −0.194447 0.373462i
\(475\) 2.08876 + 4.54280i 0.0958389 + 0.208438i
\(476\) 50.8343i 2.32999i
\(477\) 17.5311 3.09385i 0.802693 0.141657i
\(478\) 7.53820 + 7.53820i 0.344789 + 0.344789i
\(479\) 13.7799 0.629620 0.314810 0.949155i \(-0.398059\pi\)
0.314810 + 0.949155i \(0.398059\pi\)
\(480\) −48.3563 57.9350i −2.20716 2.64436i
\(481\) 33.9912 1.54987
\(482\) −25.7122 25.7122i −1.17116 1.17116i
\(483\) −5.41608 1.70725i −0.246440 0.0776825i
\(484\) 17.6245i 0.801115i
\(485\) −18.6377 11.9439i −0.846297 0.542346i
\(486\) 31.1586 + 28.5306i 1.41338 + 1.29417i
\(487\) −0.179630 + 0.179630i −0.00813983 + 0.00813983i −0.711165 0.703025i \(-0.751832\pi\)
0.703025 + 0.711165i \(0.251832\pi\)
\(488\) −80.0335 + 80.0335i −3.62295 + 3.62295i
\(489\) −15.1703 + 7.89855i −0.686023 + 0.357185i
\(490\) 11.2175 + 7.18869i 0.506755 + 0.324752i
\(491\) 28.1070i 1.26845i −0.773148 0.634225i \(-0.781319\pi\)
0.773148 0.634225i \(-0.218681\pi\)
\(492\) 1.28245 4.06846i 0.0578174 0.183420i
\(493\) −1.04677 1.04677i −0.0471440 0.0471440i
\(494\) 12.2168 0.549660
\(495\) 17.1824 + 7.16827i 0.772292 + 0.322190i
\(496\) −84.1066 −3.77650
\(497\) 14.6421 + 14.6421i 0.656787 + 0.656787i
\(498\) −3.96714 + 12.5854i −0.177772 + 0.563963i
\(499\) 24.5089i 1.09717i 0.836096 + 0.548584i \(0.184833\pi\)
−0.836096 + 0.548584i \(0.815167\pi\)
\(500\) 47.7016 35.9968i 2.13328 1.60983i
\(501\) −6.60477 + 3.43884i −0.295079 + 0.153636i
\(502\) 43.3893 43.3893i 1.93656 1.93656i
\(503\) 9.04409 9.04409i 0.403256 0.403256i −0.476123 0.879379i \(-0.657958\pi\)
0.879379 + 0.476123i \(0.157958\pi\)
\(504\) 34.1753 48.8226i 1.52229 2.17473i
\(505\) −10.6111 + 2.32260i −0.472190 + 0.103354i
\(506\) 11.2545i 0.500322i
\(507\) −12.0918 3.81155i −0.537015 0.169277i
\(508\) 11.8924 + 11.8924i 0.527639 + 0.527639i
\(509\) −23.6478 −1.04817 −0.524086 0.851665i \(-0.675593\pi\)
−0.524086 + 0.851665i \(0.675593\pi\)
\(510\) 4.08894 45.3736i 0.181061 2.00918i
\(511\) −34.2853 −1.51669
\(512\) −13.2814 13.2814i −0.586961 0.586961i
\(513\) −3.16412 4.12169i −0.139699 0.181977i
\(514\) 68.6342i 3.02733i
\(515\) −9.13251 + 14.2507i −0.402426 + 0.627961i
\(516\) 20.7678 + 39.8874i 0.914250 + 1.75594i
\(517\) −5.35710 + 5.35710i −0.235605 + 0.235605i
\(518\) −31.6649 + 31.6649i −1.39128 + 1.39128i
\(519\) 8.67689 + 16.6652i 0.380873 + 0.731520i
\(520\) −19.5388 89.2658i −0.856833 3.91457i
\(521\) 31.8364i 1.39478i 0.716693 + 0.697389i \(0.245655\pi\)
−0.716693 + 0.697389i \(0.754345\pi\)
\(522\) 0.481946 + 2.73092i 0.0210942 + 0.119529i
\(523\) 10.3448 + 10.3448i 0.452346 + 0.452346i 0.896132 0.443787i \(-0.146365\pi\)
−0.443787 + 0.896132i \(0.646365\pi\)
\(524\) −56.2059 −2.45536
\(525\) 14.9938 + 11.6317i 0.654385 + 0.507649i
\(526\) 68.7281 2.99669
\(527\) −18.5975 18.5975i −0.810120 0.810120i
\(528\) 63.6336 + 20.0585i 2.76930 + 0.872934i
\(529\) 20.7612i 0.902661i
\(530\) 7.68919 + 35.1292i 0.333997 + 1.52591i
\(531\) 29.5538 + 20.6874i 1.28253 + 0.897755i
\(532\) −8.28182 + 8.28182i −0.359063 + 0.359063i
\(533\) 1.46869 1.46869i 0.0636162 0.0636162i
\(534\) 10.9677 5.71043i 0.474618 0.247115i
\(535\) −19.9046 + 31.0599i −0.860553 + 1.34284i
\(536\) 38.0628i 1.64406i
\(537\) −1.03589 + 3.28625i −0.0447018 + 0.141812i
\(538\) 14.6696 + 14.6696i 0.632452 + 0.632452i
\(539\) −6.10166 −0.262817
\(540\) −40.0367 + 47.4760i −1.72291 + 2.04304i
\(541\) −13.8983 −0.597535 −0.298767 0.954326i \(-0.596575\pi\)
−0.298767 + 0.954326i \(0.596575\pi\)
\(542\) −45.4131 45.4131i −1.95066 1.95066i
\(543\) −2.43653 + 7.72966i −0.104562 + 0.331712i
\(544\) 84.5687i 3.62585i
\(545\) 18.0023 3.94041i 0.771135 0.168789i
\(546\) 41.1262 21.4128i 1.76004 0.916382i
\(547\) −27.6535 + 27.6535i −1.18238 + 1.18238i −0.203253 + 0.979126i \(0.565151\pi\)
−0.979126 + 0.203253i \(0.934849\pi\)
\(548\) 56.2266 56.2266i 2.40188 2.40188i
\(549\) 30.6842 + 21.4786i 1.30957 + 0.916686i
\(550\) −13.0522 + 35.2711i −0.556550 + 1.50396i
\(551\) 0.341074i 0.0145303i
\(552\) 22.4078 + 7.06335i 0.953740 + 0.300636i
\(553\) 3.02578 + 3.02578i 0.128669 + 0.128669i
\(554\) 73.6818 3.13044
\(555\) 22.4210 18.7140i 0.951718 0.794365i
\(556\) 22.2288 0.942712
\(557\) −10.7082 10.7082i −0.453720 0.453720i 0.442867 0.896587i \(-0.353961\pi\)
−0.896587 + 0.442867i \(0.853961\pi\)
\(558\) 8.56254 + 48.5191i 0.362481 + 2.05398i
\(559\) 21.8962i 0.926112i
\(560\) 57.2578 + 36.6934i 2.41958 + 1.55058i
\(561\) 9.63526 + 18.5059i 0.406801 + 0.781318i
\(562\) 25.2023 25.2023i 1.06310 1.06310i
\(563\) 8.16092 8.16092i 0.343942 0.343942i −0.513905 0.857847i \(-0.671802\pi\)
0.857847 + 0.513905i \(0.171802\pi\)
\(564\) −11.6709 22.4156i −0.491434 0.943868i
\(565\) −4.84296 3.10359i −0.203745 0.130569i
\(566\) 26.5179i 1.11463i
\(567\) −17.8758 8.32926i −0.750713 0.349796i
\(568\) −60.5783 60.5783i −2.54181 2.54181i
\(569\) 15.6913 0.657812 0.328906 0.944363i \(-0.393320\pi\)
0.328906 + 0.944363i \(0.393320\pi\)
\(570\) 8.05833 6.72601i 0.337526 0.281722i
\(571\) −2.89052 −0.120965 −0.0604823 0.998169i \(-0.519264\pi\)
−0.0604823 + 0.998169i \(0.519264\pi\)
\(572\) 47.2844 + 47.2844i 1.97706 + 1.97706i
\(573\) −27.6153 8.70484i −1.15364 0.363650i
\(574\) 2.73636i 0.114213i
\(575\) −2.59642 + 7.01630i −0.108278 + 0.292600i
\(576\) −43.0916 + 61.5603i −1.79548 + 2.56501i
\(577\) 33.4230 33.4230i 1.39142 1.39142i 0.569265 0.822154i \(-0.307228\pi\)
0.822154 0.569265i \(-0.192772\pi\)
\(578\) 3.52210 3.52210i 0.146500 0.146500i
\(579\) 16.2508 8.46115i 0.675361 0.351633i
\(580\) −3.98222 + 0.871641i −0.165353 + 0.0361929i
\(581\) 6.15979i 0.255551i
\(582\) −13.9708 + 44.3212i −0.579110 + 1.83717i
\(583\) −11.6453 11.6453i −0.482301 0.482301i
\(584\) 141.847 5.86969
\(585\) −27.9664 + 11.5011i −1.15627 + 0.475511i
\(586\) −0.127253 −0.00525676
\(587\) 32.6911 + 32.6911i 1.34931 + 1.34931i 0.886413 + 0.462895i \(0.153189\pi\)
0.462895 + 0.886413i \(0.346811\pi\)
\(588\) 6.11903 19.4120i 0.252345 0.800539i
\(589\) 6.05973i 0.249687i
\(590\) −39.3192 + 61.3552i −1.61875 + 2.52595i
\(591\) −17.2520 + 8.98241i −0.709651 + 0.369487i
\(592\) 74.0063 74.0063i 3.04164 3.04164i
\(593\) 3.73463 3.73463i 0.153363 0.153363i −0.626255 0.779618i \(-0.715413\pi\)
0.779618 + 0.626255i \(0.215413\pi\)
\(594\) 5.09299 38.7508i 0.208968 1.58997i
\(595\) 4.54716 + 20.7743i 0.186415 + 0.851665i
\(596\) 38.4809i 1.57624i
\(597\) 3.48335 + 1.09802i 0.142564 + 0.0449388i
\(598\) 12.9256 + 12.9256i 0.528566 + 0.528566i
\(599\) 18.9926 0.776015 0.388007 0.921656i \(-0.373163\pi\)
0.388007 + 0.921656i \(0.373163\pi\)
\(600\) −62.0336 48.1235i −2.53251 1.96463i
\(601\) −34.2389 −1.39663 −0.698316 0.715789i \(-0.746067\pi\)
−0.698316 + 0.715789i \(0.746067\pi\)
\(602\) −20.3977 20.3977i −0.831347 0.831347i
\(603\) 12.4039 2.18902i 0.505128 0.0891438i
\(604\) 64.3061i 2.61658i
\(605\) 1.57652 + 7.20257i 0.0640948 + 0.292826i
\(606\) 10.5309 + 20.2260i 0.427787 + 0.821625i
\(607\) −0.971775 + 0.971775i −0.0394431 + 0.0394431i −0.726553 0.687110i \(-0.758879\pi\)
0.687110 + 0.726553i \(0.258879\pi\)
\(608\) 13.7778 13.7778i 0.558762 0.558762i
\(609\) −0.597812 1.14818i −0.0242246 0.0465266i
\(610\) −40.8231 + 63.7020i −1.65288 + 2.57922i
\(611\) 12.3051i 0.497811i
\(612\) −68.5379 + 12.0954i −2.77048 + 0.488928i
\(613\) −0.868747 0.868747i −0.0350884 0.0350884i 0.689345 0.724433i \(-0.257898\pi\)
−0.724433 + 0.689345i \(0.757898\pi\)
\(614\) −56.9560 −2.29856
\(615\) 0.160171 1.77736i 0.00645872 0.0716701i
\(616\) −55.1329 −2.22137
\(617\) 21.7676 + 21.7676i 0.876329 + 0.876329i 0.993153 0.116823i \(-0.0372711\pi\)
−0.116823 + 0.993153i \(0.537271\pi\)
\(618\) 33.8886 + 10.6823i 1.36320 + 0.429706i
\(619\) 38.6157i 1.55210i −0.630674 0.776048i \(-0.717222\pi\)
0.630674 0.776048i \(-0.282778\pi\)
\(620\) −70.7505 + 15.4861i −2.84141 + 0.621937i
\(621\) 1.01312 7.70850i 0.0406552 0.309332i
\(622\) 39.8012 39.8012i 1.59588 1.59588i
\(623\) −4.08147 + 4.08147i −0.163521 + 0.163521i
\(624\) −96.1190 + 50.0453i −3.84784 + 2.00342i
\(625\) 16.2742 18.9777i 0.650966 0.759107i
\(626\) 68.9704i 2.75661i
\(627\) −1.44518 + 4.58469i −0.0577149 + 0.183095i
\(628\) −86.6954 86.6954i −3.45952 3.45952i
\(629\) 32.7283 1.30496
\(630\) 15.3384 36.7663i 0.611097 1.46480i
\(631\) −28.7544 −1.14469 −0.572347 0.820011i \(-0.693967\pi\)
−0.572347 + 0.820011i \(0.693967\pi\)
\(632\) −12.5185 12.5185i −0.497958 0.497958i
\(633\) −1.20170 + 3.81226i −0.0477631 + 0.151524i
\(634\) 80.4360i 3.19452i
\(635\) 5.92381 + 3.79625i 0.235079 + 0.150649i
\(636\) 48.7274 25.3704i 1.93217 1.00600i
\(637\) 7.00766 7.00766i 0.277654 0.277654i
\(638\) 1.81406 1.81406i 0.0718194 0.0718194i
\(639\) −16.2574 + 23.2252i −0.643134 + 0.918776i
\(640\) −54.4363 34.8853i −2.15179 1.37896i
\(641\) 15.2356i 0.601769i 0.953661 + 0.300885i \(0.0972819\pi\)
−0.953661 + 0.300885i \(0.902718\pi\)
\(642\) 73.8615 + 23.2825i 2.91508 + 0.918887i
\(643\) 14.6770 + 14.6770i 0.578805 + 0.578805i 0.934574 0.355769i \(-0.115781\pi\)
−0.355769 + 0.934574i \(0.615781\pi\)
\(644\) −17.5246 −0.690566
\(645\) 12.0551 + 14.4430i 0.474667 + 0.568692i
\(646\) 11.7629 0.462805
\(647\) −8.15999 8.15999i −0.320802 0.320802i 0.528273 0.849075i \(-0.322840\pi\)
−0.849075 + 0.528273i \(0.822840\pi\)
\(648\) 73.9571 + 34.4604i 2.90531 + 1.35373i
\(649\) 33.3736i 1.31003i
\(650\) −25.5180 55.4986i −1.00090 2.17683i
\(651\) −10.6211 20.3993i −0.416273 0.799510i
\(652\) −37.3214 + 37.3214i −1.46162 + 1.46162i
\(653\) 18.7646 18.7646i 0.734317 0.734317i −0.237154 0.971472i \(-0.576215\pi\)
0.971472 + 0.237154i \(0.0762147\pi\)
\(654\) −17.8661 34.3144i −0.698621 1.34180i
\(655\) −22.9695 + 5.02764i −0.897493 + 0.196446i
\(656\) 6.39533i 0.249696i
\(657\) −8.15776 46.2254i −0.318265 1.80343i
\(658\) 11.4629 + 11.4629i 0.446872 + 0.446872i
\(659\) −19.8613 −0.773688 −0.386844 0.922145i \(-0.626435\pi\)
−0.386844 + 0.922145i \(0.626435\pi\)
\(660\) 57.2219 + 5.15668i 2.22736 + 0.200724i
\(661\) 1.81809 0.0707156 0.0353578 0.999375i \(-0.488743\pi\)
0.0353578 + 0.999375i \(0.488743\pi\)
\(662\) −4.58723 4.58723i −0.178288 0.178288i
\(663\) −32.3196 10.1877i −1.25519 0.395659i
\(664\) 25.4847i 0.988999i
\(665\) −2.64370 + 4.12533i −0.102518 + 0.159973i
\(666\) −50.2268 35.1582i −1.94625 1.36235i
\(667\) 0.360862 0.360862i 0.0139726 0.0139726i
\(668\) −16.2488 + 16.2488i −0.628686 + 0.628686i
\(669\) −22.0203 + 11.4651i −0.851354 + 0.443266i
\(670\) 5.44041 + 24.8553i 0.210181 + 0.960244i
\(671\) 34.6501i 1.33765i
\(672\) 22.2323 70.5297i 0.857628 2.72074i
\(673\) −26.1329 26.1329i −1.00735 1.00735i −0.999973 0.00737644i \(-0.997652\pi\)
−0.00737644 0.999973i \(-0.502348\pi\)
\(674\) −4.26976 −0.164465
\(675\) −12.1149 + 22.9832i −0.466304 + 0.884624i
\(676\) −39.1249 −1.50480
\(677\) −23.2430 23.2430i −0.893303 0.893303i 0.101530 0.994832i \(-0.467626\pi\)
−0.994832 + 0.101530i \(0.967626\pi\)
\(678\) −3.63028 + 11.5167i −0.139420 + 0.442297i
\(679\) 21.6926i 0.832485i
\(680\) −18.8128 85.9491i −0.721439 3.29600i
\(681\) −12.0993 + 6.29964i −0.463647 + 0.241403i
\(682\) 32.2297 32.2297i 1.23414 1.23414i
\(683\) −6.69635 + 6.69635i −0.256229 + 0.256229i −0.823518 0.567290i \(-0.807992\pi\)
0.567290 + 0.823518i \(0.307992\pi\)
\(684\) −13.1366 9.19549i −0.502291 0.351598i
\(685\) 17.9485 28.0075i 0.685776 1.07011i
\(686\) 54.6265i 2.08565i
\(687\) 29.0340 + 9.15205i 1.10772 + 0.349172i
\(688\) 47.6728 + 47.6728i 1.81751 + 1.81751i
\(689\) 26.7490 1.01905
\(690\) 15.6421 + 1.40962i 0.595483 + 0.0536633i
\(691\) 14.0822 0.535713 0.267856 0.963459i \(-0.413685\pi\)
0.267856 + 0.963459i \(0.413685\pi\)
\(692\) 40.9991 + 40.9991i 1.55855 + 1.55855i
\(693\) 3.17073 + 17.9668i 0.120446 + 0.682501i
\(694\) 59.3451i 2.25271i
\(695\) 9.08420 1.98838i 0.344583 0.0754236i
\(696\) 2.47331 + 4.75034i 0.0937506 + 0.180061i
\(697\) 1.41412 1.41412i 0.0535638 0.0535638i
\(698\) −1.62091 + 1.62091i −0.0613523 + 0.0613523i
\(699\) −3.62208 6.95671i −0.137000 0.263127i
\(700\) 54.9215 + 20.3240i 2.07584 + 0.768173i
\(701\) 8.36037i 0.315767i 0.987458 + 0.157883i \(0.0504670\pi\)
−0.987458 + 0.157883i \(0.949533\pi\)
\(702\) 38.6555 + 50.3539i 1.45896 + 1.90049i
\(703\) 5.33202 + 5.33202i 0.201101 + 0.201101i
\(704\) 69.5169 2.62002
\(705\) −6.77461 8.11656i −0.255147 0.305687i
\(706\) −54.3326 −2.04484
\(707\) −7.52683 7.52683i −0.283076 0.283076i
\(708\) 106.176 + 33.4686i 3.99034 + 1.25783i
\(709\) 18.9746i 0.712607i 0.934370 + 0.356303i \(0.115963\pi\)
−0.934370 + 0.356303i \(0.884037\pi\)
\(710\) −48.2167 30.8995i −1.80954 1.15964i
\(711\) −3.35959 + 4.79948i −0.125994 + 0.179995i
\(712\) 16.8862 16.8862i 0.632836 0.632836i
\(713\) 6.41129 6.41129i 0.240105 0.240105i
\(714\) 39.5982 20.6172i 1.48192 0.771579i
\(715\) 23.5532 + 15.0940i 0.880840 + 0.564483i
\(716\) 10.6332i 0.397380i
\(717\) 2.04827 6.49793i 0.0764939 0.242670i
\(718\) 44.1168 + 44.1168i 1.64642 + 1.64642i
\(719\) 16.5292 0.616434 0.308217 0.951316i \(-0.400268\pi\)
0.308217 + 0.951316i \(0.400268\pi\)
\(720\) −35.8485 + 85.9291i −1.33599 + 3.20239i
\(721\) −16.5865 −0.617713
\(722\) 1.91639 + 1.91639i 0.0713205 + 0.0713205i
\(723\) −6.98648 + 22.1639i −0.259830 + 0.824286i
\(724\) 25.0105i 0.929510i
\(725\) −1.54943 + 0.712423i −0.0575445 + 0.0264587i
\(726\) 13.7289 7.14809i 0.509527 0.265290i
\(727\) −4.61397 + 4.61397i −0.171123 + 0.171123i −0.787472 0.616350i \(-0.788611\pi\)
0.616350 + 0.787472i \(0.288611\pi\)
\(728\) 63.3192 63.3192i 2.34677 2.34677i
\(729\) 6.97667 26.0831i 0.258395 0.966039i
\(730\) 92.6275 20.2746i 3.42830 0.750398i
\(731\) 21.0827i 0.779771i
\(732\) 110.237 + 34.7488i 4.07448 + 1.28435i
\(733\) −29.2126 29.2126i −1.07899 1.07899i −0.996600 0.0823910i \(-0.973744\pi\)
−0.0823910 0.996600i \(-0.526256\pi\)
\(734\) −30.3917 −1.12178
\(735\) 0.764232 8.48042i 0.0281891 0.312805i
\(736\) 29.1542 1.07464
\(737\) −8.23955 8.23955i −0.303508 0.303508i
\(738\) −3.68932 + 0.651083i −0.135806 + 0.0239667i
\(739\) 49.6356i 1.82587i 0.408101 + 0.912937i \(0.366191\pi\)
−0.408101 + 0.912937i \(0.633809\pi\)
\(740\) 48.6277 75.8805i 1.78759 2.78942i
\(741\) −3.60568 6.92521i −0.132458 0.254404i
\(742\) −24.9183 + 24.9183i −0.914779 + 0.914779i
\(743\) 0.289869 0.289869i 0.0106343 0.0106343i −0.701770 0.712404i \(-0.747606\pi\)
0.712404 + 0.701770i \(0.247606\pi\)
\(744\) 43.9423 + 84.3973i 1.61100 + 3.09416i
\(745\) −3.44214 15.7259i −0.126110 0.576152i
\(746\) 25.6601i 0.939484i
\(747\) 8.30499 1.46565i 0.303864 0.0536252i
\(748\) 45.5275 + 45.5275i 1.66465 + 1.66465i
\(749\) −36.1508 −1.32092
\(750\) −47.3869 22.5584i −1.73032 0.823717i
\(751\) −43.9824 −1.60494 −0.802471 0.596691i \(-0.796482\pi\)
−0.802471 + 0.596691i \(0.796482\pi\)
\(752\) −26.7908 26.7908i −0.976961 0.976961i
\(753\) −37.4016 11.7897i −1.36299 0.429640i
\(754\) 4.16684i 0.151747i
\(755\) −5.75222 26.2798i −0.209345 0.956421i
\(756\) −60.3398 7.93042i −2.19454 0.288427i
\(757\) 10.7580 10.7580i 0.391005 0.391005i −0.484040 0.875046i \(-0.660831\pi\)
0.875046 + 0.484040i \(0.160831\pi\)
\(758\) 20.8161 20.8161i 0.756075 0.756075i
\(759\) −6.37970 + 3.32165i −0.231568 + 0.120568i
\(760\) 10.9377 17.0676i 0.396752 0.619107i
\(761\) 43.6178i 1.58114i −0.612370 0.790571i \(-0.709784\pi\)
0.612370 0.790571i \(-0.290216\pi\)
\(762\) 4.44048 14.0870i 0.160862 0.510318i
\(763\) 12.7696 + 12.7696i 0.462292 + 0.462292i
\(764\) −89.3536 −3.23270
\(765\) −26.9273 + 11.0737i −0.973557 + 0.400372i
\(766\) −47.2600 −1.70757
\(767\) 38.3290 + 38.3290i 1.38398 + 1.38398i
\(768\) −14.7198 + 46.6971i −0.531155 + 1.68504i
\(769\) 30.3590i 1.09477i −0.836880 0.547386i \(-0.815623\pi\)
0.836880 0.547386i \(-0.184377\pi\)
\(770\) −36.0022 + 7.88028i −1.29743 + 0.283986i
\(771\) 38.9059 20.2568i 1.40116 0.729530i
\(772\) 39.9797 &minus