Properties

Label 273.2.bd.b.127.5
Level $273$
Weight $2$
Character 273.127
Analytic conductor $2.180$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(43,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bd (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} - 132 x^{7} - 45 x^{6} + 864 x^{5} - 243 x^{4} - 1944 x^{3} + 7290 x^{2} - 8748 x + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.5
Root \(0.750089 - 1.56121i\) of defining polynomial
Character \(\chi\) \(=\) 273.127
Dual form 273.2.bd.b.43.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.924500 - 0.533760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.430200 + 0.745128i) q^{4} +0.994065i q^{5} +(0.924500 + 0.533760i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.05354i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.924500 - 0.533760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.430200 + 0.745128i) q^{4} +0.994065i q^{5} +(0.924500 + 0.533760i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.05354i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.530592 + 0.919013i) q^{10} +(-0.215888 + 0.124643i) q^{11} -0.860399 q^{12} +(-3.56641 - 0.529854i) q^{13} +1.06752 q^{14} +(-0.860885 + 0.497032i) q^{15} +(0.769457 + 1.33274i) q^{16} +(3.10350 - 5.37541i) q^{17} +1.06752i q^{18} +(7.28287 + 4.20477i) q^{19} +(-0.740705 - 0.427646i) q^{20} +1.00000i q^{21} +(-0.133059 + 0.230465i) q^{22} +(-0.907804 - 1.57236i) q^{23} +(-2.64444 + 1.52677i) q^{24} +4.01184 q^{25} +(-3.57996 + 1.41376i) q^{26} -1.00000 q^{27} +(-0.745128 + 0.430200i) q^{28} +(-1.34505 - 2.32969i) q^{29} +(-0.530592 + 0.919013i) q^{30} -8.53282i q^{31} +(-3.86615 - 2.23212i) q^{32} +(-0.215888 - 0.124643i) q^{33} -6.62609i q^{34} +(-0.497032 + 0.860885i) q^{35} +(-0.430200 - 0.745128i) q^{36} +(-3.66498 + 2.11598i) q^{37} +8.97735 q^{38} +(-1.32434 - 3.35353i) q^{39} -3.03541 q^{40} +(5.57277 - 3.21744i) q^{41} +(0.533760 + 0.924500i) q^{42} +(-5.71391 + 9.89679i) q^{43} -0.214485i q^{44} +(-0.860885 - 0.497032i) q^{45} +(-1.67853 - 0.969100i) q^{46} -10.6030i q^{47} +(-0.769457 + 1.33274i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.70894 - 2.14136i) q^{50} +6.20699 q^{51} +(1.92908 - 2.42948i) q^{52} -0.601973 q^{53} +(-0.924500 + 0.533760i) q^{54} +(-0.123903 - 0.214607i) q^{55} +(-1.52677 + 2.64444i) q^{56} +8.40953i q^{57} +(-2.48699 - 1.43587i) q^{58} +(-7.71959 - 4.45691i) q^{59} -0.855293i q^{60} +(-2.87430 + 4.97843i) q^{61} +(-4.55448 - 7.88859i) q^{62} +(-0.866025 + 0.500000i) q^{63} -7.84351 q^{64} +(0.526710 - 3.54524i) q^{65} -0.266118 q^{66} +(5.73996 - 3.31397i) q^{67} +(2.67025 + 4.62500i) q^{68} +(0.907804 - 1.57236i) q^{69} +1.06118i q^{70} +(10.4088 + 6.00951i) q^{71} +(-2.64444 - 1.52677i) q^{72} +9.70387i q^{73} +(-2.25885 + 3.91244i) q^{74} +(2.00592 + 3.47435i) q^{75} +(-6.26618 + 3.61778i) q^{76} -0.249286 q^{77} +(-3.01433 - 2.39346i) q^{78} -5.63447 q^{79} +(-1.32483 + 0.764890i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.43468 - 5.94904i) q^{82} -16.5842i q^{83} +(-0.745128 - 0.430200i) q^{84} +(5.34351 + 3.08508i) q^{85} +12.1994i q^{86} +(1.34505 - 2.32969i) q^{87} +(-0.380602 - 0.659221i) q^{88} +(-8.47828 + 4.89494i) q^{89} -1.06118 q^{90} +(-2.82367 - 2.24207i) q^{91} +1.56215 q^{92} +(7.38964 - 4.26641i) q^{93} +(-5.65949 - 9.80252i) q^{94} +(-4.17981 + 7.23964i) q^{95} -4.46425i q^{96} +(2.10869 + 1.21745i) q^{97} +(0.924500 + 0.533760i) q^{98} -0.249286i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.924500 0.533760i 0.653720 0.377426i −0.136160 0.990687i \(-0.543476\pi\)
0.789880 + 0.613261i \(0.210143\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.430200 + 0.745128i −0.215100 + 0.372564i
\(5\) 0.994065i 0.444559i 0.974983 + 0.222280i \(0.0713498\pi\)
−0.974983 + 0.222280i \(0.928650\pi\)
\(6\) 0.924500 + 0.533760i 0.377426 + 0.217907i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 3.05354i 1.07959i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.530592 + 0.919013i 0.167788 + 0.290617i
\(11\) −0.215888 + 0.124643i −0.0650927 + 0.0375813i −0.532193 0.846623i \(-0.678632\pi\)
0.467100 + 0.884204i \(0.345299\pi\)
\(12\) −0.860399 −0.248376
\(13\) −3.56641 0.529854i −0.989143 0.146955i
\(14\) 1.06752 0.285307
\(15\) −0.860885 + 0.497032i −0.222280 + 0.128333i
\(16\) 0.769457 + 1.33274i 0.192364 + 0.333185i
\(17\) 3.10350 5.37541i 0.752708 1.30373i −0.193797 0.981042i \(-0.562080\pi\)
0.946506 0.322688i \(-0.104586\pi\)
\(18\) 1.06752i 0.251617i
\(19\) 7.28287 + 4.20477i 1.67081 + 0.964640i 0.967188 + 0.254060i \(0.0817661\pi\)
0.703617 + 0.710580i \(0.251567\pi\)
\(20\) −0.740705 0.427646i −0.165627 0.0956246i
\(21\) 1.00000i 0.218218i
\(22\) −0.133059 + 0.230465i −0.0283683 + 0.0491353i
\(23\) −0.907804 1.57236i −0.189290 0.327860i 0.755724 0.654891i \(-0.227285\pi\)
−0.945014 + 0.327030i \(0.893952\pi\)
\(24\) −2.64444 + 1.52677i −0.539794 + 0.311650i
\(25\) 4.01184 0.802367
\(26\) −3.57996 + 1.41376i −0.702088 + 0.277260i
\(27\) −1.00000 −0.192450
\(28\) −0.745128 + 0.430200i −0.140816 + 0.0813001i
\(29\) −1.34505 2.32969i −0.249769 0.432612i 0.713693 0.700459i \(-0.247021\pi\)
−0.963462 + 0.267847i \(0.913688\pi\)
\(30\) −0.530592 + 0.919013i −0.0968725 + 0.167788i
\(31\) 8.53282i 1.53254i −0.642519 0.766270i \(-0.722111\pi\)
0.642519 0.766270i \(-0.277889\pi\)
\(32\) −3.86615 2.23212i −0.683446 0.394588i
\(33\) −0.215888 0.124643i −0.0375813 0.0216976i
\(34\) 6.62609i 1.13637i
\(35\) −0.497032 + 0.860885i −0.0840138 + 0.145516i
\(36\) −0.430200 0.745128i −0.0716999 0.124188i
\(37\) −3.66498 + 2.11598i −0.602519 + 0.347864i −0.770032 0.638006i \(-0.779760\pi\)
0.167513 + 0.985870i \(0.446426\pi\)
\(38\) 8.97735 1.45632
\(39\) −1.32434 3.35353i −0.212063 0.536994i
\(40\) −3.03541 −0.479941
\(41\) 5.57277 3.21744i 0.870320 0.502479i 0.00286538 0.999996i \(-0.499088\pi\)
0.867455 + 0.497516i \(0.165755\pi\)
\(42\) 0.533760 + 0.924500i 0.0823610 + 0.142653i
\(43\) −5.71391 + 9.89679i −0.871364 + 1.50925i −0.0107768 + 0.999942i \(0.503430\pi\)
−0.860587 + 0.509304i \(0.829903\pi\)
\(44\) 0.214485i 0.0323349i
\(45\) −0.860885 0.497032i −0.128333 0.0740932i
\(46\) −1.67853 0.969100i −0.247486 0.142886i
\(47\) 10.6030i 1.54661i −0.634032 0.773307i \(-0.718601\pi\)
0.634032 0.773307i \(-0.281399\pi\)
\(48\) −0.769457 + 1.33274i −0.111062 + 0.192364i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 3.70894 2.14136i 0.524524 0.302834i
\(51\) 6.20699 0.869153
\(52\) 1.92908 2.42948i 0.267515 0.336909i
\(53\) −0.601973 −0.0826873 −0.0413436 0.999145i \(-0.513164\pi\)
−0.0413436 + 0.999145i \(0.513164\pi\)
\(54\) −0.924500 + 0.533760i −0.125809 + 0.0726356i
\(55\) −0.123903 0.214607i −0.0167071 0.0289375i
\(56\) −1.52677 + 2.64444i −0.204023 + 0.353378i
\(57\) 8.40953i 1.11387i
\(58\) −2.48699 1.43587i −0.326558 0.188538i
\(59\) −7.71959 4.45691i −1.00501 0.580240i −0.0952798 0.995451i \(-0.530375\pi\)
−0.909725 + 0.415211i \(0.863708\pi\)
\(60\) 0.855293i 0.110418i
\(61\) −2.87430 + 4.97843i −0.368016 + 0.637422i −0.989255 0.146199i \(-0.953296\pi\)
0.621239 + 0.783621i \(0.286629\pi\)
\(62\) −4.55448 7.88859i −0.578420 1.00185i
\(63\) −0.866025 + 0.500000i −0.109109 + 0.0629941i
\(64\) −7.84351 −0.980438
\(65\) 0.526710 3.54524i 0.0653303 0.439733i
\(66\) −0.266118 −0.0327568
\(67\) 5.73996 3.31397i 0.701248 0.404866i −0.106564 0.994306i \(-0.533985\pi\)
0.807812 + 0.589440i \(0.200652\pi\)
\(68\) 2.67025 + 4.62500i 0.323815 + 0.560864i
\(69\) 0.907804 1.57236i 0.109287 0.189290i
\(70\) 1.06118i 0.126836i
\(71\) 10.4088 + 6.00951i 1.23529 + 0.713197i 0.968129 0.250453i \(-0.0805797\pi\)
0.267165 + 0.963651i \(0.413913\pi\)
\(72\) −2.64444 1.52677i −0.311650 0.179931i
\(73\) 9.70387i 1.13575i 0.823114 + 0.567876i \(0.192235\pi\)
−0.823114 + 0.567876i \(0.807765\pi\)
\(74\) −2.25885 + 3.91244i −0.262586 + 0.454812i
\(75\) 2.00592 + 3.47435i 0.231623 + 0.401184i
\(76\) −6.26618 + 3.61778i −0.718780 + 0.414988i
\(77\) −0.249286 −0.0284088
\(78\) −3.01433 2.39346i −0.341305 0.271006i
\(79\) −5.63447 −0.633928 −0.316964 0.948438i \(-0.602663\pi\)
−0.316964 + 0.948438i \(0.602663\pi\)
\(80\) −1.32483 + 0.764890i −0.148120 + 0.0855173i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.43468 5.94904i 0.379297 0.656962i
\(83\) 16.5842i 1.82035i −0.414223 0.910175i \(-0.635947\pi\)
0.414223 0.910175i \(-0.364053\pi\)
\(84\) −0.745128 0.430200i −0.0813001 0.0469386i
\(85\) 5.34351 + 3.08508i 0.579585 + 0.334623i
\(86\) 12.1994i 1.31550i
\(87\) 1.34505 2.32969i 0.144204 0.249769i
\(88\) −0.380602 0.659221i −0.0405723 0.0702732i
\(89\) −8.47828 + 4.89494i −0.898696 + 0.518862i −0.876777 0.480897i \(-0.840311\pi\)
−0.0219191 + 0.999760i \(0.506978\pi\)
\(90\) −1.06118 −0.111859
\(91\) −2.82367 2.24207i −0.296001 0.235033i
\(92\) 1.56215 0.162865
\(93\) 7.38964 4.26641i 0.766270 0.442406i
\(94\) −5.65949 9.80252i −0.583732 1.01105i
\(95\) −4.17981 + 7.23964i −0.428840 + 0.742772i
\(96\) 4.46425i 0.455630i
\(97\) 2.10869 + 1.21745i 0.214105 + 0.123614i 0.603218 0.797577i \(-0.293885\pi\)
−0.389113 + 0.921190i \(0.627218\pi\)
\(98\) 0.924500 + 0.533760i 0.0933886 + 0.0539179i
\(99\) 0.249286i 0.0250542i
\(100\) −1.72589 + 2.98933i −0.172589 + 0.298933i
\(101\) −2.58622 4.47946i −0.257338 0.445723i 0.708190 0.706022i \(-0.249512\pi\)
−0.965528 + 0.260299i \(0.916179\pi\)
\(102\) 5.73837 3.31305i 0.568183 0.328040i
\(103\) 11.3681 1.12013 0.560064 0.828449i \(-0.310777\pi\)
0.560064 + 0.828449i \(0.310777\pi\)
\(104\) 1.61793 10.8901i 0.158651 1.06787i
\(105\) −0.994065 −0.0970108
\(106\) −0.556524 + 0.321309i −0.0540544 + 0.0312083i
\(107\) 5.99438 + 10.3826i 0.579498 + 1.00372i 0.995537 + 0.0943734i \(0.0300848\pi\)
−0.416039 + 0.909347i \(0.636582\pi\)
\(108\) 0.430200 0.745128i 0.0413960 0.0716999i
\(109\) 6.30314i 0.603731i −0.953350 0.301866i \(-0.902391\pi\)
0.953350 0.301866i \(-0.0976094\pi\)
\(110\) −0.229097 0.132269i −0.0218435 0.0126114i
\(111\) −3.66498 2.11598i −0.347864 0.200840i
\(112\) 1.53891i 0.145414i
\(113\) −3.44378 + 5.96479i −0.323963 + 0.561121i −0.981302 0.192475i \(-0.938349\pi\)
0.657339 + 0.753595i \(0.271682\pi\)
\(114\) 4.48868 + 7.77462i 0.420403 + 0.728160i
\(115\) 1.56303 0.902416i 0.145753 0.0841508i
\(116\) 2.31455 0.214901
\(117\) 2.24207 2.82367i 0.207279 0.261049i
\(118\) −9.51568 −0.875990
\(119\) 5.37541 3.10350i 0.492763 0.284497i
\(120\) −1.51771 2.62874i −0.138547 0.239970i
\(121\) −5.46893 + 9.47246i −0.497175 + 0.861133i
\(122\) 6.13674i 0.555594i
\(123\) 5.57277 + 3.21744i 0.502479 + 0.290107i
\(124\) 6.35804 + 3.67082i 0.570969 + 0.329649i
\(125\) 8.95835i 0.801259i
\(126\) −0.533760 + 0.924500i −0.0475512 + 0.0823610i
\(127\) 0.535395 + 0.927332i 0.0475087 + 0.0822874i 0.888802 0.458292i \(-0.151538\pi\)
−0.841293 + 0.540579i \(0.818205\pi\)
\(128\) 0.480982 0.277695i 0.0425132 0.0245450i
\(129\) −11.4278 −1.00616
\(130\) −1.40536 3.55871i −0.123259 0.312120i
\(131\) 6.79609 0.593777 0.296889 0.954912i \(-0.404051\pi\)
0.296889 + 0.954912i \(0.404051\pi\)
\(132\) 0.185750 0.107243i 0.0161674 0.00933428i
\(133\) 4.20477 + 7.28287i 0.364600 + 0.631505i
\(134\) 3.53773 6.12753i 0.305613 0.529338i
\(135\) 0.994065i 0.0855555i
\(136\) 16.4140 + 9.47664i 1.40749 + 0.812615i
\(137\) −16.1702 9.33585i −1.38151 0.797615i −0.389172 0.921165i \(-0.627239\pi\)
−0.992338 + 0.123550i \(0.960572\pi\)
\(138\) 1.93820i 0.164991i
\(139\) 3.10738 5.38214i 0.263564 0.456507i −0.703622 0.710574i \(-0.748435\pi\)
0.967187 + 0.254067i \(0.0817685\pi\)
\(140\) −0.427646 0.740705i −0.0361427 0.0626010i
\(141\) 9.18251 5.30152i 0.773307 0.446469i
\(142\) 12.8305 1.07672
\(143\) 0.835987 0.330138i 0.0699087 0.0276075i
\(144\) −1.53891 −0.128243
\(145\) 2.31586 1.33706i 0.192322 0.111037i
\(146\) 5.17954 + 8.97123i 0.428662 + 0.742464i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) 3.64117i 0.299302i
\(149\) 2.89242 + 1.66994i 0.236957 + 0.136807i 0.613777 0.789479i \(-0.289649\pi\)
−0.376821 + 0.926286i \(0.622983\pi\)
\(150\) 3.70894 + 2.14136i 0.302834 + 0.174841i
\(151\) 9.04809i 0.736324i −0.929762 0.368162i \(-0.879987\pi\)
0.929762 0.368162i \(-0.120013\pi\)
\(152\) −12.8394 + 22.2385i −1.04141 + 1.80378i
\(153\) 3.10350 + 5.37541i 0.250903 + 0.434576i
\(154\) −0.230465 + 0.133059i −0.0185714 + 0.0107222i
\(155\) 8.48218 0.681305
\(156\) 3.06853 + 0.455886i 0.245679 + 0.0365001i
\(157\) −12.0695 −0.963252 −0.481626 0.876377i \(-0.659954\pi\)
−0.481626 + 0.876377i \(0.659954\pi\)
\(158\) −5.20907 + 3.00746i −0.414411 + 0.239261i
\(159\) −0.300986 0.521324i −0.0238698 0.0413436i
\(160\) 2.21888 3.84321i 0.175418 0.303832i
\(161\) 1.81561i 0.143090i
\(162\) −0.924500 0.533760i −0.0726356 0.0419362i
\(163\) −1.64381 0.949055i −0.128753 0.0743358i 0.434240 0.900797i \(-0.357017\pi\)
−0.562993 + 0.826461i \(0.690350\pi\)
\(164\) 5.53656i 0.432333i
\(165\) 0.123903 0.214607i 0.00964585 0.0167071i
\(166\) −8.85198 15.3321i −0.687047 1.19000i
\(167\) 11.8910 6.86525i 0.920150 0.531249i 0.0364674 0.999335i \(-0.488389\pi\)
0.883683 + 0.468086i \(0.155056\pi\)
\(168\) −3.05354 −0.235585
\(169\) 12.4385 + 3.77935i 0.956808 + 0.290719i
\(170\) 6.58677 0.505182
\(171\) −7.28287 + 4.20477i −0.556935 + 0.321547i
\(172\) −4.91625 8.51519i −0.374860 0.649277i
\(173\) −10.9284 + 18.9286i −0.830872 + 1.43911i 0.0664761 + 0.997788i \(0.478824\pi\)
−0.897348 + 0.441324i \(0.854509\pi\)
\(174\) 2.87173i 0.217705i
\(175\) 3.47435 + 2.00592i 0.262636 + 0.151633i
\(176\) −0.332233 0.191815i −0.0250430 0.0144586i
\(177\) 8.91382i 0.670003i
\(178\) −5.22545 + 9.05074i −0.391664 + 0.678382i
\(179\) 3.73571 + 6.47043i 0.279220 + 0.483623i 0.971191 0.238302i \(-0.0765909\pi\)
−0.691971 + 0.721925i \(0.743258\pi\)
\(180\) 0.740705 0.427646i 0.0552089 0.0318749i
\(181\) 6.04007 0.448955 0.224477 0.974479i \(-0.427933\pi\)
0.224477 + 0.974479i \(0.427933\pi\)
\(182\) −3.80721 0.565631i −0.282209 0.0419273i
\(183\) −5.74859 −0.424948
\(184\) 4.80127 2.77201i 0.353954 0.204356i
\(185\) −2.10342 3.64322i −0.154646 0.267855i
\(186\) 4.55448 7.88859i 0.333951 0.578420i
\(187\) 1.54732i 0.113151i
\(188\) 7.90062 + 4.56143i 0.576212 + 0.332676i
\(189\) −0.866025 0.500000i −0.0629941 0.0363696i
\(190\) 8.92407i 0.647420i
\(191\) −6.24095 + 10.8096i −0.451579 + 0.782158i −0.998484 0.0550367i \(-0.982472\pi\)
0.546905 + 0.837194i \(0.315806\pi\)
\(192\) −3.92175 6.79268i −0.283028 0.490219i
\(193\) 4.97792 2.87400i 0.358318 0.206875i −0.310025 0.950729i \(-0.600337\pi\)
0.668343 + 0.743853i \(0.267004\pi\)
\(194\) 2.59931 0.186620
\(195\) 3.33362 1.31648i 0.238726 0.0942748i
\(196\) −0.860399 −0.0614571
\(197\) −12.9690 + 7.48763i −0.924000 + 0.533472i −0.884909 0.465764i \(-0.845780\pi\)
−0.0390912 + 0.999236i \(0.512446\pi\)
\(198\) −0.133059 0.230465i −0.00945609 0.0163784i
\(199\) −1.03719 + 1.79647i −0.0735248 + 0.127349i −0.900444 0.434972i \(-0.856758\pi\)
0.826919 + 0.562321i \(0.190091\pi\)
\(200\) 12.2503i 0.866226i
\(201\) 5.73996 + 3.31397i 0.404866 + 0.233749i
\(202\) −4.78192 2.76084i −0.336455 0.194252i
\(203\) 2.69009i 0.188808i
\(204\) −2.67025 + 4.62500i −0.186955 + 0.323815i
\(205\) 3.19834 + 5.53969i 0.223382 + 0.386909i
\(206\) 10.5098 6.06782i 0.732250 0.422765i
\(207\) 1.81561 0.126194
\(208\) −2.03804 5.16079i −0.141313 0.357836i
\(209\) −2.09638 −0.145010
\(210\) −0.919013 + 0.530592i −0.0634179 + 0.0366144i
\(211\) −10.9283 18.9283i −0.752333 1.30308i −0.946689 0.322148i \(-0.895595\pi\)
0.194356 0.980931i \(-0.437738\pi\)
\(212\) 0.258968 0.448546i 0.0177860 0.0308063i
\(213\) 12.0190i 0.823529i
\(214\) 11.0836 + 6.39912i 0.757660 + 0.437435i
\(215\) −9.83805 5.68000i −0.670949 0.387373i
\(216\) 3.05354i 0.207767i
\(217\) 4.26641 7.38964i 0.289623 0.501641i
\(218\) −3.36437 5.82725i −0.227864 0.394671i
\(219\) −8.40380 + 4.85193i −0.567876 + 0.327863i
\(220\) 0.213212 0.0143748
\(221\) −13.9165 + 17.5265i −0.936126 + 1.17896i
\(222\) −4.51770 −0.303208
\(223\) −10.6138 + 6.12790i −0.710755 + 0.410355i −0.811341 0.584574i \(-0.801262\pi\)
0.100585 + 0.994928i \(0.467928\pi\)
\(224\) −2.23212 3.86615i −0.149140 0.258318i
\(225\) −2.00592 + 3.47435i −0.133728 + 0.231623i
\(226\) 7.35260i 0.489088i
\(227\) −14.1397 8.16356i −0.938485 0.541835i −0.0490001 0.998799i \(-0.515603\pi\)
−0.889485 + 0.456964i \(0.848937\pi\)
\(228\) −6.26618 3.61778i −0.414988 0.239593i
\(229\) 3.88261i 0.256570i −0.991737 0.128285i \(-0.959053\pi\)
0.991737 0.128285i \(-0.0409472\pi\)
\(230\) 0.963348 1.66857i 0.0635213 0.110022i
\(231\) −0.124643 0.215888i −0.00820090 0.0142044i
\(232\) 7.11379 4.10715i 0.467043 0.269647i
\(233\) −18.6257 −1.22021 −0.610106 0.792320i \(-0.708873\pi\)
−0.610106 + 0.792320i \(0.708873\pi\)
\(234\) 0.565631 3.80721i 0.0369764 0.248885i
\(235\) 10.5401 0.687561
\(236\) 6.64193 3.83472i 0.432353 0.249619i
\(237\) −2.81724 4.87960i −0.182999 0.316964i
\(238\) 3.31305 5.73837i 0.214753 0.371963i
\(239\) 17.2578i 1.11631i −0.829736 0.558156i \(-0.811509\pi\)
0.829736 0.558156i \(-0.188491\pi\)
\(240\) −1.32483 0.764890i −0.0855173 0.0493735i
\(241\) 13.2661 + 7.65919i 0.854545 + 0.493372i 0.862182 0.506599i \(-0.169097\pi\)
−0.00763655 + 0.999971i \(0.502431\pi\)
\(242\) 11.6764i 0.750587i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −2.47304 4.28344i −0.158320 0.274219i
\(245\) −0.860885 + 0.497032i −0.0549999 + 0.0317542i
\(246\) 6.86936 0.437975
\(247\) −23.7458 18.8548i −1.51091 1.19970i
\(248\) 26.0553 1.65451
\(249\) 14.3623 8.29209i 0.910175 0.525490i
\(250\) 4.78161 + 8.28199i 0.302416 + 0.523799i
\(251\) 3.92011 6.78983i 0.247435 0.428570i −0.715378 0.698737i \(-0.753746\pi\)
0.962813 + 0.270167i \(0.0870789\pi\)
\(252\) 0.860399i 0.0542001i
\(253\) 0.391968 + 0.226303i 0.0246428 + 0.0142275i
\(254\) 0.989946 + 0.571546i 0.0621148 + 0.0358620i
\(255\) 6.17015i 0.386390i
\(256\) 8.13995 14.0988i 0.508747 0.881176i
\(257\) −3.44069 5.95945i −0.214624 0.371740i 0.738532 0.674218i \(-0.235519\pi\)
−0.953156 + 0.302478i \(0.902186\pi\)
\(258\) −10.5650 + 6.09972i −0.657750 + 0.379752i
\(259\) −4.23195 −0.262961
\(260\) 2.41507 + 1.91763i 0.149776 + 0.118926i
\(261\) 2.69009 0.166513
\(262\) 6.28299 3.62749i 0.388164 0.224107i
\(263\) −12.1976 21.1269i −0.752138 1.30274i −0.946785 0.321867i \(-0.895690\pi\)
0.194647 0.980873i \(-0.437644\pi\)
\(264\) 0.380602 0.659221i 0.0234244 0.0405723i
\(265\) 0.598400i 0.0367594i
\(266\) 7.77462 + 4.48868i 0.476692 + 0.275218i
\(267\) −8.47828 4.89494i −0.518862 0.299565i
\(268\) 5.70267i 0.348346i
\(269\) −7.46508 + 12.9299i −0.455154 + 0.788350i −0.998697 0.0510315i \(-0.983749\pi\)
0.543543 + 0.839381i \(0.317082\pi\)
\(270\) −0.530592 0.919013i −0.0322908 0.0559293i
\(271\) −1.55659 + 0.898700i −0.0945564 + 0.0545922i −0.546533 0.837438i \(-0.684053\pi\)
0.451976 + 0.892030i \(0.350719\pi\)
\(272\) 9.55203 0.579177
\(273\) 0.529854 3.56641i 0.0320682 0.215849i
\(274\) −19.9324 −1.20416
\(275\) −0.866107 + 0.500047i −0.0522282 + 0.0301540i
\(276\) 0.781074 + 1.35286i 0.0470152 + 0.0814326i
\(277\) 6.15944 10.6685i 0.370085 0.641005i −0.619494 0.785002i \(-0.712662\pi\)
0.989578 + 0.143996i \(0.0459953\pi\)
\(278\) 6.63438i 0.397904i
\(279\) 7.38964 + 4.26641i 0.442406 + 0.255423i
\(280\) −2.62874 1.51771i −0.157098 0.0907003i
\(281\) 17.3105i 1.03266i 0.856390 + 0.516329i \(0.172702\pi\)
−0.856390 + 0.516329i \(0.827298\pi\)
\(282\) 5.65949 9.80252i 0.337018 0.583732i
\(283\) −5.78080 10.0126i −0.343633 0.595190i 0.641471 0.767147i \(-0.278324\pi\)
−0.985104 + 0.171957i \(0.944991\pi\)
\(284\) −8.95570 + 5.17058i −0.531423 + 0.306817i
\(285\) −8.35962 −0.495181
\(286\) 0.596655 0.751429i 0.0352810 0.0444329i
\(287\) 6.43488 0.379839
\(288\) 3.86615 2.23212i 0.227815 0.131529i
\(289\) −10.7634 18.6427i −0.633140 1.09663i
\(290\) 1.42734 2.47223i 0.0838165 0.145174i
\(291\) 2.43491i 0.142737i
\(292\) −7.23062 4.17460i −0.423140 0.244300i
\(293\) −2.28791 1.32092i −0.133661 0.0771692i 0.431678 0.902028i \(-0.357922\pi\)
−0.565340 + 0.824858i \(0.691255\pi\)
\(294\) 1.06752i 0.0622591i
\(295\) 4.43045 7.67377i 0.257951 0.446784i
\(296\) −6.46121 11.1911i −0.375550 0.650472i
\(297\) 0.215888 0.124643i 0.0125271 0.00723252i
\(298\) 3.56539 0.206538
\(299\) 2.40448 + 6.08869i 0.139054 + 0.352118i
\(300\) −3.45178 −0.199289
\(301\) −9.89679 + 5.71391i −0.570441 + 0.329344i
\(302\) −4.82951 8.36496i −0.277907 0.481350i
\(303\) 2.58622 4.47946i 0.148574 0.257338i
\(304\) 12.9416i 0.742249i
\(305\) −4.94888 2.85724i −0.283372 0.163605i
\(306\) 5.73837 + 3.31305i 0.328040 + 0.189394i
\(307\) 18.9221i 1.07994i 0.841684 + 0.539971i \(0.181565\pi\)
−0.841684 + 0.539971i \(0.818435\pi\)
\(308\) 0.107243 0.185750i 0.00611072 0.0105841i
\(309\) 5.68403 + 9.84503i 0.323353 + 0.560064i
\(310\) 7.84177 4.52745i 0.445383 0.257142i
\(311\) −16.9499 −0.961140 −0.480570 0.876956i \(-0.659570\pi\)
−0.480570 + 0.876956i \(0.659570\pi\)
\(312\) 10.2401 4.04391i 0.579732 0.228941i
\(313\) −14.0214 −0.792537 −0.396268 0.918135i \(-0.629695\pi\)
−0.396268 + 0.918135i \(0.629695\pi\)
\(314\) −11.1583 + 6.44223i −0.629698 + 0.363556i
\(315\) −0.497032 0.860885i −0.0280046 0.0485054i
\(316\) 2.42395 4.19840i 0.136358 0.236179i
\(317\) 16.4256i 0.922554i −0.887256 0.461277i \(-0.847392\pi\)
0.887256 0.461277i \(-0.152608\pi\)
\(318\) −0.556524 0.321309i −0.0312083 0.0180181i
\(319\) 0.580759 + 0.335301i 0.0325162 + 0.0187733i
\(320\) 7.79695i 0.435863i
\(321\) −5.99438 + 10.3826i −0.334573 + 0.579498i
\(322\) −0.969100 1.67853i −0.0540058 0.0935409i
\(323\) 45.2047 26.0990i 2.51526 1.45218i
\(324\) 0.860399 0.0478000
\(325\) −14.3078 2.12569i −0.793656 0.117912i
\(326\) −2.02627 −0.112225
\(327\) 5.45868 3.15157i 0.301866 0.174282i
\(328\) 9.82456 + 17.0166i 0.542471 + 0.939587i
\(329\) 5.30152 9.18251i 0.292282 0.506248i
\(330\) 0.264538i 0.0145624i
\(331\) 3.84246 + 2.21845i 0.211201 + 0.121937i 0.601869 0.798595i \(-0.294423\pi\)
−0.390668 + 0.920531i \(0.627756\pi\)
\(332\) 12.3573 + 7.13451i 0.678197 + 0.391557i
\(333\) 4.23195i 0.231910i
\(334\) 7.32880 12.6939i 0.401014 0.694577i
\(335\) 3.29430 + 5.70589i 0.179987 + 0.311746i
\(336\) −1.33274 + 0.769457i −0.0727069 + 0.0419773i
\(337\) −18.0752 −0.984618 −0.492309 0.870421i \(-0.663847\pi\)
−0.492309 + 0.870421i \(0.663847\pi\)
\(338\) 13.5167 3.14517i 0.735210 0.171075i
\(339\) −6.88755 −0.374080
\(340\) −4.59755 + 2.65440i −0.249337 + 0.143955i
\(341\) 1.06356 + 1.84213i 0.0575948 + 0.0997571i
\(342\) −4.48868 + 7.77462i −0.242720 + 0.420403i
\(343\) 1.00000i 0.0539949i
\(344\) −30.2202 17.4476i −1.62936 0.940714i
\(345\) 1.56303 + 0.902416i 0.0841508 + 0.0485845i
\(346\) 23.3326i 1.25437i
\(347\) −15.8920 + 27.5257i −0.853126 + 1.47766i 0.0252467 + 0.999681i \(0.491963\pi\)
−0.878373 + 0.477976i \(0.841370\pi\)
\(348\) 1.15728 + 2.00446i 0.0620366 + 0.107450i
\(349\) −4.41576 + 2.54944i −0.236370 + 0.136468i −0.613507 0.789689i \(-0.710242\pi\)
0.377137 + 0.926157i \(0.376909\pi\)
\(350\) 4.28272 0.228921
\(351\) 3.56641 + 0.529854i 0.190361 + 0.0282815i
\(352\) 1.11287 0.0593164
\(353\) 11.6546 6.72880i 0.620313 0.358138i −0.156678 0.987650i \(-0.550078\pi\)
0.776991 + 0.629512i \(0.216745\pi\)
\(354\) −4.75784 8.24082i −0.252876 0.437995i
\(355\) −5.97384 + 10.3470i −0.317058 + 0.549161i
\(356\) 8.42320i 0.446429i
\(357\) 5.37541 + 3.10350i 0.284497 + 0.164254i
\(358\) 6.90732 + 3.98794i 0.365063 + 0.210769i
\(359\) 3.04253i 0.160578i −0.996772 0.0802892i \(-0.974416\pi\)
0.996772 0.0802892i \(-0.0255844\pi\)
\(360\) 1.51771 2.62874i 0.0799901 0.138547i
\(361\) 25.8601 + 44.7911i 1.36106 + 2.35743i
\(362\) 5.58404 3.22395i 0.293491 0.169447i
\(363\) −10.9379 −0.574089
\(364\) 2.88537 1.13946i 0.151235 0.0597238i
\(365\) −9.64627 −0.504909
\(366\) −5.31457 + 3.06837i −0.277797 + 0.160386i
\(367\) −6.44853 11.1692i −0.336611 0.583027i 0.647182 0.762335i \(-0.275947\pi\)
−0.983793 + 0.179309i \(0.942614\pi\)
\(368\) 1.39703 2.41973i 0.0728254 0.126137i
\(369\) 6.43488i 0.334986i
\(370\) −3.88922 2.24544i −0.202191 0.116735i
\(371\) −0.521324 0.300986i −0.0270658 0.0156264i
\(372\) 7.34163i 0.380646i
\(373\) 2.55347 4.42274i 0.132214 0.229001i −0.792316 0.610111i \(-0.791125\pi\)
0.924530 + 0.381110i \(0.124458\pi\)
\(374\) 0.825896 + 1.43049i 0.0427061 + 0.0739691i
\(375\) −7.75816 + 4.47917i −0.400629 + 0.231304i
\(376\) 32.3768 1.66971
\(377\) 3.56259 + 9.02130i 0.183483 + 0.464620i
\(378\) −1.06752 −0.0549073
\(379\) 7.46265 4.30856i 0.383331 0.221316i −0.295936 0.955208i \(-0.595631\pi\)
0.679266 + 0.733892i \(0.262298\pi\)
\(380\) −3.59631 6.22899i −0.184487 0.319540i
\(381\) −0.535395 + 0.927332i −0.0274291 + 0.0475087i
\(382\) 13.3247i 0.681750i
\(383\) 7.59826 + 4.38686i 0.388253 + 0.224158i 0.681403 0.731909i \(-0.261370\pi\)
−0.293150 + 0.956066i \(0.594704\pi\)
\(384\) 0.480982 + 0.277695i 0.0245450 + 0.0141711i
\(385\) 0.247806i 0.0126294i
\(386\) 3.06806 5.31403i 0.156160 0.270477i
\(387\) −5.71391 9.89679i −0.290455 0.503082i
\(388\) −1.81432 + 1.04750i −0.0921079 + 0.0531785i
\(389\) 28.8199 1.46123 0.730614 0.682791i \(-0.239234\pi\)
0.730614 + 0.682791i \(0.239234\pi\)
\(390\) 2.37925 2.99644i 0.120478 0.151730i
\(391\) −11.2695 −0.569922
\(392\) −2.64444 + 1.52677i −0.133564 + 0.0771134i
\(393\) 3.39805 + 5.88559i 0.171409 + 0.296889i
\(394\) −7.99320 + 13.8446i −0.402692 + 0.697483i
\(395\) 5.60103i 0.281818i
\(396\) 0.185750 + 0.107243i 0.00933428 + 0.00538915i
\(397\) −6.22008 3.59116i −0.312177 0.180235i 0.335723 0.941961i \(-0.391019\pi\)
−0.647900 + 0.761725i \(0.724353\pi\)
\(398\) 2.21445i 0.111001i
\(399\) −4.20477 + 7.28287i −0.210502 + 0.364600i
\(400\) 3.08694 + 5.34673i 0.154347 + 0.267336i
\(401\) −7.60538 + 4.39097i −0.379795 + 0.219274i −0.677729 0.735312i \(-0.737036\pi\)
0.297934 + 0.954586i \(0.403702\pi\)
\(402\) 7.07546 0.352892
\(403\) −4.52115 + 30.4315i −0.225215 + 1.51590i
\(404\) 4.45036 0.221414
\(405\) 0.860885 0.497032i 0.0427777 0.0246977i
\(406\) −1.43587 2.48699i −0.0712608 0.123427i
\(407\) 0.527483 0.913627i 0.0261464 0.0452868i
\(408\) 18.9533i 0.938327i
\(409\) 9.11938 + 5.26507i 0.450924 + 0.260341i 0.708220 0.705991i \(-0.249498\pi\)
−0.257296 + 0.966333i \(0.582832\pi\)
\(410\) 5.91373 + 3.41430i 0.292059 + 0.168620i
\(411\) 18.6717i 0.921007i
\(412\) −4.89053 + 8.47065i −0.240939 + 0.417319i
\(413\) −4.45691 7.71959i −0.219310 0.379856i
\(414\) 1.67853 0.969100i 0.0824953 0.0476287i
\(415\) 16.4858 0.809254
\(416\) 12.6056 + 10.0092i 0.618039 + 0.490739i
\(417\) 6.21476 0.304338
\(418\) −1.93810 + 1.11896i −0.0947957 + 0.0547303i
\(419\) 18.7428 + 32.4635i 0.915648 + 1.58595i 0.805950 + 0.591983i \(0.201655\pi\)
0.109697 + 0.993965i \(0.465012\pi\)
\(420\) 0.427646 0.740705i 0.0208670 0.0361427i
\(421\) 11.6873i 0.569602i 0.958587 + 0.284801i \(0.0919276\pi\)
−0.958587 + 0.284801i \(0.908072\pi\)
\(422\) −20.2064 11.6662i −0.983631 0.567900i
\(423\) 9.18251 + 5.30152i 0.446469 + 0.257769i
\(424\) 1.83814i 0.0892682i
\(425\) 12.4507 21.5653i 0.603948 1.04607i
\(426\) 6.41527 + 11.1116i 0.310821 + 0.538358i
\(427\) −4.97843 + 2.87430i −0.240923 + 0.139097i
\(428\) −10.3151 −0.498600
\(429\) 0.703901 + 0.558917i 0.0339847 + 0.0269847i
\(430\) −12.1270 −0.584818
\(431\) 8.16482 4.71396i 0.393286 0.227064i −0.290297 0.956937i \(-0.593754\pi\)
0.683583 + 0.729873i \(0.260421\pi\)
\(432\) −0.769457 1.33274i −0.0370205 0.0641214i
\(433\) −14.7784 + 25.5969i −0.710204 + 1.23011i 0.254577 + 0.967053i \(0.418064\pi\)
−0.964780 + 0.263056i \(0.915270\pi\)
\(434\) 9.10896i 0.437244i
\(435\) 2.31586 + 1.33706i 0.111037 + 0.0641073i
\(436\) 4.69664 + 2.71161i 0.224928 + 0.129862i
\(437\) 15.2684i 0.730388i
\(438\) −5.17954 + 8.97123i −0.247488 + 0.428662i
\(439\) 1.98658 + 3.44086i 0.0948144 + 0.164223i 0.909531 0.415636i \(-0.136441\pi\)
−0.814717 + 0.579859i \(0.803108\pi\)
\(440\) 0.655309 0.378343i 0.0312406 0.0180368i
\(441\) −1.00000 −0.0476190
\(442\) −3.51086 + 23.6313i −0.166995 + 1.12403i
\(443\) 24.4103 1.15977 0.579885 0.814699i \(-0.303098\pi\)
0.579885 + 0.814699i \(0.303098\pi\)
\(444\) 3.15334 1.82058i 0.149651 0.0864011i
\(445\) −4.86589 8.42796i −0.230665 0.399524i
\(446\) −6.54166 + 11.3305i −0.309757 + 0.536514i
\(447\) 3.33988i 0.157971i
\(448\) −6.79268 3.92175i −0.320924 0.185285i
\(449\) 16.6491 + 9.61234i 0.785718 + 0.453634i 0.838453 0.544974i \(-0.183461\pi\)
−0.0527352 + 0.998609i \(0.516794\pi\)
\(450\) 4.28272i 0.201889i
\(451\) −0.802062 + 1.38921i −0.0377676 + 0.0654154i
\(452\) −2.96302 5.13210i −0.139369 0.241394i
\(453\) 7.83588 4.52405i 0.368162 0.212558i
\(454\) −17.4295 −0.818009
\(455\) 2.22876 2.80691i 0.104486 0.131590i
\(456\) −25.6788 −1.20252
\(457\) 20.1012 11.6054i 0.940295 0.542879i 0.0502420 0.998737i \(-0.484001\pi\)
0.890053 + 0.455858i \(0.150667\pi\)
\(458\) −2.07238 3.58947i −0.0968361 0.167725i
\(459\) −3.10350 + 5.37541i −0.144859 + 0.250903i
\(460\) 1.55288i 0.0724033i
\(461\) 11.7802 + 6.80131i 0.548660 + 0.316769i 0.748581 0.663043i \(-0.230735\pi\)
−0.199922 + 0.979812i \(0.564069\pi\)
\(462\) −0.230465 0.133059i −0.0107222 0.00619046i
\(463\) 13.6012i 0.632101i −0.948742 0.316050i \(-0.897643\pi\)
0.948742 0.316050i \(-0.102357\pi\)
\(464\) 2.06991 3.58519i 0.0960932 0.166438i
\(465\) 4.24109 + 7.34578i 0.196676 + 0.340652i
\(466\) −17.2195 + 9.94168i −0.797678 + 0.460539i
\(467\) 9.00148 0.416539 0.208269 0.978072i \(-0.433217\pi\)
0.208269 + 0.978072i \(0.433217\pi\)
\(468\) 1.13946 + 2.88537i 0.0526714 + 0.133376i
\(469\) 6.62794 0.306050
\(470\) 9.74434 5.62590i 0.449473 0.259503i
\(471\) −6.03476 10.4525i −0.278067 0.481626i
\(472\) 13.6093 23.5720i 0.626420 1.08499i
\(473\) 2.84880i 0.130988i
\(474\) −5.20907 3.00746i −0.239261 0.138137i
\(475\) 29.2177 + 16.8688i 1.34060 + 0.773995i
\(476\) 5.34049i 0.244781i
\(477\) 0.300986 0.521324i 0.0137812 0.0238698i
\(478\) −9.21151 15.9548i −0.421325 0.729756i
\(479\) 20.6858 11.9429i 0.945157 0.545687i 0.0535838 0.998563i \(-0.482936\pi\)
0.891573 + 0.452877i \(0.149602\pi\)
\(480\) 4.43775 0.202555
\(481\) 14.1920 5.60452i 0.647098 0.255544i
\(482\) 16.3527 0.744845
\(483\) 1.57236 0.907804i 0.0715450 0.0413065i
\(484\) −4.70546 8.15010i −0.213885 0.370459i
\(485\) −1.21023 + 2.09617i −0.0549536 + 0.0951824i
\(486\) 1.06752i 0.0484237i
\(487\) −17.8192 10.2879i −0.807463 0.466189i 0.0386111 0.999254i \(-0.487707\pi\)
−0.846074 + 0.533065i \(0.821040\pi\)
\(488\) −15.2018 8.77677i −0.688153 0.397306i
\(489\) 1.89811i 0.0858355i
\(490\) −0.530592 + 0.919013i −0.0239697 + 0.0415168i
\(491\) 7.97149 + 13.8070i 0.359748 + 0.623103i 0.987919 0.154973i \(-0.0495292\pi\)
−0.628170 + 0.778076i \(0.716196\pi\)
\(492\) −4.79480 + 2.76828i −0.216166 + 0.124804i
\(493\) −16.6974 −0.752012
\(494\) −32.0169 4.75669i −1.44051 0.214014i
\(495\) 0.247806 0.0111381
\(496\) 11.3720 6.56564i 0.510619 0.294806i
\(497\) 6.00951 + 10.4088i 0.269563 + 0.466897i
\(498\) 8.85198 15.3321i 0.396667 0.687047i
\(499\) 10.3975i 0.465454i −0.972542 0.232727i \(-0.925235\pi\)
0.972542 0.232727i \(-0.0747649\pi\)
\(500\) −6.67511 3.85388i −0.298520 0.172351i
\(501\) 11.8910 + 6.86525i 0.531249 + 0.306717i
\(502\) 8.36960i 0.373553i
\(503\) 11.8034 20.4440i 0.526286 0.911553i −0.473245 0.880931i \(-0.656918\pi\)
0.999531 0.0306227i \(-0.00974903\pi\)
\(504\) −1.52677 2.64444i −0.0680076 0.117793i
\(505\) 4.45287 2.57087i 0.198150 0.114402i
\(506\) 0.483166 0.0214793
\(507\) 2.94624 + 12.6617i 0.130847 + 0.562328i
\(508\) −0.921308 −0.0408764
\(509\) −32.5931 + 18.8177i −1.44467 + 0.834078i −0.998156 0.0607005i \(-0.980667\pi\)
−0.446510 + 0.894779i \(0.647333\pi\)
\(510\) 3.29338 + 5.70431i 0.145833 + 0.252591i
\(511\) −4.85193 + 8.40380i −0.214637 + 0.371762i
\(512\) 16.2684i 0.718967i
\(513\) −7.28287 4.20477i −0.321547 0.185645i
\(514\) −6.36184 3.67301i −0.280609 0.162009i
\(515\) 11.3006i 0.497963i
\(516\) 4.91625 8.51519i 0.216426 0.374860i
\(517\) 1.32160 + 2.28907i 0.0581237 + 0.100673i
\(518\) −3.91244 + 2.25885i −0.171903 + 0.0992481i
\(519\) −21.8568 −0.959408
\(520\) 10.8255 + 1.60833i 0.474730 + 0.0705298i
\(521\) 12.3849 0.542592 0.271296 0.962496i \(-0.412548\pi\)
0.271296 + 0.962496i \(0.412548\pi\)
\(522\) 2.48699 1.43587i 0.108853 0.0628461i
\(523\) −9.17568 15.8927i −0.401225 0.694941i 0.592649 0.805460i \(-0.298082\pi\)
−0.993874 + 0.110519i \(0.964749\pi\)
\(524\) −2.92368 + 5.06396i −0.127721 + 0.221220i
\(525\) 4.01184i 0.175091i
\(526\) −22.5534 13.0212i −0.983375 0.567752i
\(527\) −45.8674 26.4816i −1.99802 1.15356i
\(528\) 0.383630i 0.0166953i
\(529\) 9.85178 17.0638i 0.428338 0.741904i
\(530\) −0.319402 0.553221i −0.0138739 0.0240304i
\(531\) 7.71959 4.45691i 0.335002 0.193413i
\(532\) −7.23556 −0.313701
\(533\) −21.5795 + 8.52194i −0.934713 + 0.369126i
\(534\) −10.4509 −0.452255
\(535\) −10.3209 + 5.95880i −0.446213 + 0.257621i
\(536\) 10.1193 + 17.5272i 0.437088 + 0.757059i
\(537\) −3.73571 + 6.47043i −0.161208 + 0.279220i
\(538\) 15.9383i 0.687147i
\(539\) −0.215888 0.124643i −0.00929895 0.00536875i
\(540\) 0.740705 + 0.427646i 0.0318749 + 0.0184030i
\(541\) 14.4935i 0.623126i −0.950225 0.311563i \(-0.899147\pi\)
0.950225 0.311563i \(-0.100853\pi\)
\(542\) −0.959381 + 1.66170i −0.0412090 + 0.0713760i
\(543\) 3.02003 + 5.23085i 0.129602 + 0.224477i
\(544\) −23.9972 + 13.8548i −1.02887 + 0.594019i
\(545\) 6.26573 0.268394
\(546\) −1.41376 3.57996i −0.0605032 0.153208i
\(547\) 4.86021 0.207808 0.103904 0.994587i \(-0.466867\pi\)
0.103904 + 0.994587i \(0.466867\pi\)
\(548\) 13.9128 8.03256i 0.594325 0.343134i
\(549\) −2.87430 4.97843i −0.122672 0.212474i
\(550\) −0.533811 + 0.924587i −0.0227618 + 0.0394245i
\(551\) 22.6224i 0.963748i
\(552\) 4.80127 + 2.77201i 0.204356 + 0.117985i
\(553\) −4.87960 2.81724i −0.207502 0.119801i
\(554\) 13.1507i 0.558718i
\(555\) 2.10342 3.64322i 0.0892851 0.154646i
\(556\) 2.67359 + 4.63079i 0.113385 + 0.196389i
\(557\) 5.20395 3.00450i 0.220498 0.127305i −0.385683 0.922632i \(-0.626034\pi\)
0.606181 + 0.795327i \(0.292701\pi\)
\(558\) 9.10896 0.385613
\(559\) 25.6220 32.2684i 1.08369 1.36481i
\(560\) −1.52978 −0.0646450
\(561\) −1.34001 + 0.773658i −0.0565755 + 0.0326639i
\(562\) 9.23967 + 16.0036i 0.389752 + 0.675070i
\(563\) 21.2160 36.7472i 0.894149 1.54871i 0.0592944 0.998241i \(-0.481115\pi\)
0.834854 0.550471i \(-0.185552\pi\)
\(564\) 9.12286i 0.384142i
\(565\) −5.92939 3.42334i −0.249451 0.144021i
\(566\) −10.6887 6.17113i −0.449280 0.259392i
\(567\) 1.00000i 0.0419961i
\(568\) −18.3502 + 31.7836i −0.769959 + 1.33361i
\(569\) 11.0476 + 19.1349i 0.463138 + 0.802178i 0.999115 0.0420542i \(-0.0133902\pi\)
−0.535978 + 0.844232i \(0.680057\pi\)
\(570\) −7.72847 + 4.46204i −0.323710 + 0.186894i
\(571\) −29.0504 −1.21572 −0.607861 0.794043i \(-0.707972\pi\)
−0.607861 + 0.794043i \(0.707972\pi\)
\(572\) −0.113646 + 0.764942i −0.00475178 + 0.0319838i
\(573\) −12.4819 −0.521439
\(574\) 5.94904 3.43468i 0.248308 0.143361i
\(575\) −3.64196 6.30806i −0.151880 0.263064i
\(576\) 3.92175 6.79268i 0.163406 0.283028i
\(577\) 29.4874i 1.22758i −0.789471 0.613788i \(-0.789645\pi\)
0.789471 0.613788i \(-0.210355\pi\)
\(578\) −19.9015 11.4901i −0.827793 0.477926i
\(579\) 4.97792 + 2.87400i 0.206875 + 0.119439i
\(580\) 2.30082i 0.0955362i
\(581\) 8.29209 14.3623i 0.344014 0.595850i
\(582\) 1.29966 + 2.25107i 0.0538725 + 0.0933099i
\(583\) 0.129959 0.0750316i 0.00538233 0.00310749i
\(584\) −29.6311 −1.22614
\(585\) 2.80691 + 2.22876i 0.116052 + 0.0921480i
\(586\) −2.82023 −0.116503
\(587\) −33.4815 + 19.3305i −1.38193 + 0.797857i −0.992388 0.123152i \(-0.960700\pi\)
−0.389541 + 0.921009i \(0.627366\pi\)
\(588\) −0.430200 0.745128i −0.0177411 0.0307285i
\(589\) 35.8785 62.1434i 1.47835 2.56058i
\(590\) 9.45921i 0.389429i
\(591\) −12.9690 7.48763i −0.533472 0.308000i
\(592\) −5.64009 3.25631i −0.231806 0.133833i
\(593\) 34.9446i 1.43500i −0.696556 0.717502i \(-0.745285\pi\)
0.696556 0.717502i \(-0.254715\pi\)
\(594\) 0.133059 0.230465i 0.00545947 0.00945609i
\(595\) 3.08508 + 5.34351i 0.126476 + 0.219062i
\(596\) −2.48864 + 1.43682i −0.101939 + 0.0588543i
\(597\) −2.07439 −0.0848991
\(598\) 5.47284 + 4.34558i 0.223801 + 0.177704i
\(599\) 15.4209 0.630080 0.315040 0.949078i \(-0.397982\pi\)
0.315040 + 0.949078i \(0.397982\pi\)
\(600\) −10.6091 + 6.12514i −0.433113 + 0.250058i
\(601\) 6.34569 + 10.9911i 0.258846 + 0.448334i 0.965933 0.258792i \(-0.0833245\pi\)
−0.707087 + 0.707126i \(0.749991\pi\)
\(602\) −6.09972 + 10.5650i −0.248606 + 0.430598i
\(603\) 6.62794i 0.269910i
\(604\) 6.74199 + 3.89249i 0.274328 + 0.158383i
\(605\) −9.41624 5.43647i −0.382825 0.221024i
\(606\) 5.52168i 0.224303i
\(607\) −9.58410 + 16.6002i −0.389007 + 0.673780i −0.992316 0.123728i \(-0.960515\pi\)
0.603309 + 0.797507i \(0.293848\pi\)
\(608\) −18.7711 32.5125i −0.761270 1.31856i
\(609\) 2.32969 1.34505i 0.0944038 0.0545040i
\(610\) −6.10032 −0.246995
\(611\) −5.61807 + 37.8148i −0.227283 + 1.52982i
\(612\) −5.34049 −0.215877
\(613\) 15.6414 9.03055i 0.631749 0.364740i −0.149680 0.988734i \(-0.547824\pi\)
0.781429 + 0.623994i \(0.214491\pi\)
\(614\) 10.0999 + 17.4935i 0.407598 + 0.705980i
\(615\) −3.19834 + 5.53969i −0.128970 + 0.223382i
\(616\) 0.761203i 0.0306698i
\(617\) −1.19682 0.690982i −0.0481820 0.0278179i 0.475715 0.879599i \(-0.342189\pi\)
−0.523898 + 0.851781i \(0.675523\pi\)
\(618\) 10.5098 + 6.06782i 0.422765 + 0.244083i
\(619\) 17.0392i 0.684863i 0.939543 + 0.342432i \(0.111251\pi\)
−0.939543 + 0.342432i \(0.888749\pi\)
\(620\) −3.64903 + 6.32030i −0.146549 + 0.253830i
\(621\) 0.907804 + 1.57236i 0.0364289 + 0.0630968i
\(622\) −15.6702 + 9.04718i −0.628317 + 0.362759i
\(623\) −9.78988 −0.392223
\(624\) 3.45035 4.34539i 0.138125 0.173955i
\(625\) 11.1540 0.446160
\(626\) −12.9628 + 7.48407i −0.518097 + 0.299124i
\(627\) −1.04819 1.81552i −0.0418606 0.0725048i
\(628\) 5.19230 8.99333i 0.207195 0.358873i
\(629\) 26.2677i 1.04736i
\(630\) −0.919013 0.530592i −0.0366144 0.0211393i
\(631\) 40.8243 + 23.5699i 1.62519 + 0.938303i 0.985501 + 0.169669i \(0.0542698\pi\)
0.639688 + 0.768635i \(0.279064\pi\)
\(632\) 17.2051i 0.684381i
\(633\) 10.9283 18.9283i 0.434360 0.752333i
\(634\) −8.76733 15.1855i −0.348195 0.603092i
\(635\) −0.921828 + 0.532218i −0.0365816 + 0.0211204i
\(636\) 0.517937 0.0205375
\(637\) −1.32434 3.35353i −0.0524721 0.132872i
\(638\) 0.715882 0.0283420
\(639\) −10.4088 + 6.00951i −0.411765 + 0.237732i
\(640\) 0.276047 + 0.478127i 0.0109117 + 0.0188996i
\(641\) −15.6362 + 27.0826i −0.617592 + 1.06970i 0.372332 + 0.928100i \(0.378558\pi\)
−0.989924 + 0.141601i \(0.954775\pi\)
\(642\) 12.7982i 0.505106i
\(643\) 13.1376 + 7.58497i 0.518095 + 0.299122i 0.736155 0.676813i \(-0.236640\pi\)
−0.218060 + 0.975935i \(0.569973\pi\)
\(644\) 1.35286 + 0.781074i 0.0533102 + 0.0307786i
\(645\) 11.3600i 0.447299i
\(646\) 27.8612 48.2570i 1.09618 1.89865i
\(647\) 3.09449 + 5.35981i 0.121657 + 0.210716i 0.920421 0.390928i \(-0.127846\pi\)
−0.798764 + 0.601644i \(0.794513\pi\)
\(648\) 2.64444 1.52677i 0.103883 0.0599771i
\(649\) 2.22209 0.0872246
\(650\) −14.3622 + 5.67176i −0.563332 + 0.222465i
\(651\) 8.53282 0.334428
\(652\) 1.41433 0.816567i 0.0553896 0.0319792i
\(653\) 13.8477 + 23.9849i 0.541901 + 0.938600i 0.998795 + 0.0490789i \(0.0156286\pi\)
−0.456894 + 0.889521i \(0.651038\pi\)
\(654\) 3.36437 5.82725i 0.131557 0.227864i
\(655\) 6.75576i 0.263969i
\(656\) 8.57601 + 4.95136i 0.334837 + 0.193318i
\(657\) −8.40380 4.85193i −0.327863 0.189292i
\(658\) 11.3190i 0.441260i
\(659\) −12.7045 + 22.0048i −0.494896 + 0.857185i −0.999983 0.00588335i \(-0.998127\pi\)
0.505086 + 0.863069i \(0.331461\pi\)
\(660\) 0.106606 + 0.184647i 0.00414964 + 0.00718739i
\(661\) 6.35256 3.66765i 0.247086 0.142655i −0.371343 0.928496i \(-0.621103\pi\)
0.618429 + 0.785841i \(0.287769\pi\)
\(662\) 4.73648 0.184088
\(663\) −22.1367 3.28880i −0.859716 0.127727i
\(664\) 50.6404 1.96523
\(665\) −7.23964 + 4.17981i −0.280741 + 0.162086i
\(666\) −2.25885 3.91244i −0.0875286 0.151604i
\(667\) −2.44208 + 4.22980i −0.0945577 + 0.163779i
\(668\) 11.8137i 0.457086i
\(669\) −10.6138 6.12790i −0.410355 0.236918i
\(670\) 6.09116 + 3.51673i 0.235322 + 0.135863i
\(671\) 1.43304i 0.0553220i
\(672\) 2.23212 3.86615i 0.0861061 0.149140i
\(673\) −2.03837 3.53055i −0.0785732 0.136093i 0.824061 0.566501i \(-0.191703\pi\)
−0.902635 + 0.430408i \(0.858370\pi\)
\(674\) −16.7105 + 9.64781i −0.643665 + 0.371620i
\(675\) −4.01184 −0.154416
\(676\) −8.16714 + 7.64240i −0.314121 + 0.293938i
\(677\) 7.12994 0.274026 0.137013 0.990569i \(-0.456250\pi\)
0.137013 + 0.990569i \(0.456250\pi\)
\(678\) −6.36754 + 3.67630i −0.244544 + 0.141188i
\(679\) 1.21745 + 2.10869i 0.0467216 + 0.0809241i
\(680\) −9.42039 + 16.3166i −0.361255 + 0.625713i
\(681\) 16.3271i 0.625657i
\(682\) 1.96651 + 1.13537i 0.0753017 + 0.0434755i
\(683\) 26.6854 + 15.4068i 1.02109 + 0.589525i 0.914419 0.404770i \(-0.132648\pi\)
0.106668 + 0.994295i \(0.465982\pi\)
\(684\) 7.23556i 0.276658i
\(685\) 9.28043 16.0742i 0.354587 0.614163i
\(686\) 0.533760 + 0.924500i 0.0203791 + 0.0352976i
\(687\) 3.36244 1.94131i 0.128285 0.0740654i
\(688\) −17.5864 −0.670477
\(689\) 2.14688 + 0.318958i 0.0817896 + 0.0121513i
\(690\) 1.92670 0.0733481
\(691\) −3.76220 + 2.17211i −0.143121 + 0.0826309i −0.569851 0.821748i \(-0.692999\pi\)
0.426730 + 0.904379i \(0.359666\pi\)
\(692\) −9.40280 16.2861i −0.357441 0.619106i
\(693\) 0.124643 0.215888i 0.00473479 0.00820090i
\(694\) 33.9300i 1.28797i
\(695\) 5.35019 + 3.08894i 0.202944 + 0.117170i
\(696\) 7.11379 + 4.10715i 0.269647 + 0.155681i
\(697\) 39.9412i 1.51288i
\(698\) −2.72158 + 4.71391i −0.103013 + 0.178424i
\(699\) −9.31287 16.1304i −0.352245 0.610106i
\(700\) −2.98933 + 1.72589i −0.112986 + 0.0652325i
\(701\) −28.8256 −1.08873 −0.544365 0.838849i \(-0.683229\pi\)
−0.544365 + 0.838849i \(0.683229\pi\)
\(702\) 3.57996 1.41376i 0.135117 0.0533588i
\(703\) −35.5887 −1.34225
\(704\) 1.69332 0.977638i 0.0638193 0.0368461i
\(705\) 5.27006 + 9.12801i 0.198482 + 0.343781i
\(706\) 7.18314 12.4416i 0.270341 0.468244i
\(707\) 5.17244i 0.194529i
\(708\) 6.64193 + 3.83472i 0.249619 + 0.144118i
\(709\) −3.96199 2.28745i −0.148796 0.0859072i 0.423754 0.905777i \(-0.360712\pi\)
−0.572549 + 0.819870i \(0.694046\pi\)
\(710\) 12.7544i 0.478664i
\(711\) 2.81724 4.87960i 0.105655 0.182999i
\(712\) −14.9469 25.8887i −0.560158 0.970221i
\(713\) −13.4167 + 7.74613i −0.502459 + 0.290095i
\(714\) 6.62609 0.247975
\(715\) 0.328179 + 0.831025i 0.0122732 + 0.0310786i
\(716\) −6.42840 −0.240240
\(717\) 14.9457 8.62888i 0.558156 0.322252i
\(718\) −1.62398 2.81282i −0.0606064 0.104973i
\(719\) 9.72262 16.8401i 0.362593 0.628029i −0.625794 0.779988i \(-0.715225\pi\)
0.988387 + 0.151959i \(0.0485583\pi\)
\(720\) 1.52978i 0.0570116i
\(721\) 9.84503 + 5.68403i 0.366648 + 0.211684i
\(722\) 47.8154 + 27.6062i 1.77951 + 1.02740i
\(723\) 15.3184i 0.569697i
\(724\) −2.59843 + 4.50062i −0.0965701 + 0.167264i
\(725\) −5.39611 9.34633i −0.200406 0.347114i
\(726\) −10.1120 + 5.83819i −0.375293 + 0.216676i
\(727\) −30.2589 −1.12224 −0.561120 0.827734i \(-0.689630\pi\)
−0.561120 + 0.827734i \(0.689630\pi\)
\(728\) 6.84624 8.62218i 0.253739 0.319559i
\(729\) 1.00000 0.0370370
\(730\) −8.91798 + 5.14880i −0.330069 + 0.190566i
\(731\) 35.4662 + 61.4293i 1.31177 + 2.27204i
\(732\) 2.47304 4.28344i 0.0914063 0.158320i
\(733\) 31.9678i 1.18076i 0.807126 + 0.590379i \(0.201022\pi\)
−0.807126 + 0.590379i \(0.798978\pi\)
\(734\) −11.9233 6.88394i −0.440098 0.254091i
\(735\) −0.860885 0.497032i −0.0317542 0.0183333i
\(736\) 8.10533i 0.298766i
\(737\) −0.826125 + 1.43089i −0.0304307 + 0.0527076i
\(738\) 3.43468 + 5.94904i 0.126432 + 0.218987i
\(739\) 20.8353 12.0293i 0.766439 0.442504i −0.0651639 0.997875i \(-0.520757\pi\)
0.831603 + 0.555371i \(0.187424\pi\)
\(740\) 3.61956 0.133058
\(741\) 4.45583 29.9918i 0.163689 1.10178i
\(742\) −0.642618 −0.0235913
\(743\) 18.0539 10.4234i 0.662332 0.382398i −0.130833 0.991404i \(-0.541765\pi\)
0.793165 + 0.609007i \(0.208432\pi\)
\(744\) 13.0276 + 22.5645i 0.477616 + 0.827256i
\(745\) −1.66003 + 2.87526i −0.0608188 + 0.105341i
\(746\) 5.45177i 0.199603i
\(747\) 14.3623 + 8.29209i 0.525490 + 0.303392i
\(748\) −1.15295 0.665655i −0.0421559 0.0243387i
\(749\) 11.9888i 0.438059i
\(750\) −4.78161 + 8.28199i −0.174600 + 0.302416i
\(751\) 16.3766 + 28.3652i 0.597592 + 1.03506i 0.993175 + 0.116630i \(0.0372091\pi\)
−0.395583 + 0.918430i \(0.629458\pi\)
\(752\) 14.1311 8.15859i 0.515308 0.297513i
\(753\) 7.84022 0.285714
\(754\) 8.10882 + 6.43862i 0.295306 + 0.234481i
\(755\) 8.99439 0.327339
\(756\) 0.745128 0.430200i 0.0271000 0.0156462i
\(757\) 17.6920 + 30.6435i 0.643028 + 1.11376i 0.984753 + 0.173958i \(0.0556556\pi\)
−0.341725 + 0.939800i \(0.611011\pi\)
\(758\) 4.59948 7.96653i 0.167061 0.289358i
\(759\) 0.452606i 0.0164285i
\(760\) −22.1065 12.7632i −0.801888 0.462970i
\(761\) −11.8090 6.81792i −0.428075 0.247149i 0.270451 0.962734i \(-0.412827\pi\)
−0.698526 + 0.715584i \(0.746160\pi\)
\(762\) 1.14309i 0.0414098i
\(763\) 3.15157 5.45868i 0.114094 0.197617i
\(764\) −5.36971 9.30060i −0.194269 0.336484i
\(765\) −5.34351 + 3.08508i −0.193195 + 0.111541i
\(766\) 9.36612 0.338412
\(767\) 25.1697 + 19.9854i 0.908825 + 0.721631i
\(768\) 16.2799 0.587450
\(769\) −18.1442 + 10.4756i −0.654298 + 0.377759i −0.790101 0.612977i \(-0.789972\pi\)
0.135803 + 0.990736i \(0.456639\pi\)