Properties

Label 966.2.i.k.277.1
Level $966$
Weight $2$
Character 966.277
Analytic conductor $7.714$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(277,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.29428272.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 277.1
Root \(-0.0741344 + 2.64471i\) of defining polynomial
Character \(\chi\) \(=\) 966.277
Dual form 966.2.i.k.415.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.25332 + 1.38656i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.25332 + 1.38656i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.82746 - 3.16525i) q^{11} +(0.500000 + 0.866025i) q^{12} -0.851731 q^{13} +(-2.32746 - 1.25815i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.08078 - 5.33606i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.75332 - 4.76889i) q^{19} +1.00000 q^{20} +(0.0741344 + 2.64471i) q^{21} +3.65491 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.425866 - 0.737621i) q^{26} -1.00000 q^{27} +(-0.0741344 - 2.64471i) q^{28} +4.14827 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-1.67919 + 2.90844i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.82746 - 3.16525i) q^{33} +6.16155 q^{34} +(2.32746 + 1.25815i) q^{35} +1.00000 q^{36} +(-3.40823 - 5.90323i) q^{37} +(2.75332 - 4.76889i) q^{38} +(-0.425866 + 0.737621i) q^{39} +(0.500000 + 0.866025i) q^{40} -2.49336 q^{41} +(-2.25332 + 1.38656i) q^{42} +7.30982 q^{43} +(1.82746 + 3.16525i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-1.17919 - 2.04241i) q^{47} -1.00000 q^{48} +(3.15491 - 6.24872i) q^{49} +4.00000 q^{50} +(-3.08078 - 5.33606i) q^{51} +(0.425866 - 0.737621i) q^{52} +(-3.15491 + 5.46447i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.65491 q^{55} +(2.25332 - 1.38656i) q^{56} -5.50664 q^{57} +(2.07413 + 3.59251i) q^{58} +(-1.58078 + 2.73799i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-5.00000 - 8.66025i) q^{61} -3.35837 q^{62} +(2.32746 + 1.25815i) q^{63} +1.00000 q^{64} +(0.425866 + 0.737621i) q^{65} +(1.82746 - 3.16525i) q^{66} +(5.17919 - 8.97061i) q^{67} +(3.08078 + 5.33606i) q^{68} +1.00000 q^{69} +(0.0741344 + 2.64471i) q^{70} -8.45809 q^{71} +(0.500000 + 0.866025i) q^{72} +(-0.672545 + 1.16488i) q^{73} +(3.40823 - 5.90323i) q^{74} +(-2.00000 - 3.46410i) q^{75} +5.50664 q^{76} +(0.270955 + 9.66619i) q^{77} -0.851731 q^{78} +(5.72905 + 9.92300i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.24668 - 2.15931i) q^{82} -7.65491 q^{83} +(-2.32746 - 1.25815i) q^{84} -6.16155 q^{85} +(3.65491 + 6.33049i) q^{86} +(2.07413 - 3.59251i) q^{87} +(-1.82746 + 3.16525i) q^{88} +(3.40823 + 5.90323i) q^{89} -1.00000 q^{90} +(1.91922 - 1.18098i) q^{91} -1.00000 q^{92} +(1.67919 + 2.90844i) q^{93} +(1.17919 - 2.04241i) q^{94} +(-2.75332 + 4.76889i) q^{95} +(-0.500000 - 0.866025i) q^{96} +0.444807 q^{97} +(6.98901 - 0.392129i) q^{98} -3.65491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 6 q^{15} - 3 q^{16} - 3 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{23} - 3 q^{24} + 12 q^{25} - 3 q^{26} - 6 q^{27} + 24 q^{29} - 3 q^{30} + 3 q^{32} - 6 q^{34} + 3 q^{35} + 6 q^{36} + 12 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 36 q^{41} - 3 q^{42} - 3 q^{45} - 3 q^{46} + 3 q^{47} - 6 q^{48} - 3 q^{49} + 24 q^{50} + 3 q^{51} + 3 q^{52} + 3 q^{53} - 3 q^{54} + 3 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} + 3 q^{60} - 30 q^{61} + 3 q^{63} + 6 q^{64} + 3 q^{65} + 21 q^{67} - 3 q^{68} + 6 q^{69} - 6 q^{71} + 3 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} + 12 q^{76} + 24 q^{77} - 6 q^{78} + 12 q^{79} - 3 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} - 3 q^{84} + 6 q^{85} + 12 q^{87} - 12 q^{89} - 6 q^{90} + 33 q^{91} - 6 q^{92} - 3 q^{94} - 6 q^{95} - 3 q^{96} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.25332 + 1.38656i −0.851675 + 0.524070i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 1.82746 3.16525i 0.550999 0.954357i −0.447204 0.894432i \(-0.647580\pi\)
0.998203 0.0599256i \(-0.0190864\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −0.851731 −0.236228 −0.118114 0.993000i \(-0.537685\pi\)
−0.118114 + 0.993000i \(0.537685\pi\)
\(14\) −2.32746 1.25815i −0.622039 0.336256i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.08078 5.33606i 0.747198 1.29418i −0.201963 0.979393i \(-0.564732\pi\)
0.949161 0.314792i \(-0.101935\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −2.75332 4.76889i −0.631655 1.09406i −0.987213 0.159405i \(-0.949043\pi\)
0.355558 0.934654i \(-0.384291\pi\)
\(20\) 1.00000 0.223607
\(21\) 0.0741344 + 2.64471i 0.0161775 + 0.577124i
\(22\) 3.65491 0.779230
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) −0.425866 0.737621i −0.0835191 0.144659i
\(27\) −1.00000 −0.192450
\(28\) −0.0741344 2.64471i −0.0140101 0.499804i
\(29\) 4.14827 0.770314 0.385157 0.922851i \(-0.374147\pi\)
0.385157 + 0.922851i \(0.374147\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) −1.67919 + 2.90844i −0.301591 + 0.522371i −0.976496 0.215533i \(-0.930851\pi\)
0.674906 + 0.737904i \(0.264184\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.82746 3.16525i −0.318119 0.550999i
\(34\) 6.16155 1.05670
\(35\) 2.32746 + 1.25815i 0.393412 + 0.212667i
\(36\) 1.00000 0.166667
\(37\) −3.40823 5.90323i −0.560310 0.970485i −0.997469 0.0711010i \(-0.977349\pi\)
0.437159 0.899384i \(-0.355985\pi\)
\(38\) 2.75332 4.76889i 0.446648 0.773616i
\(39\) −0.425866 + 0.737621i −0.0681931 + 0.118114i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −2.49336 −0.389397 −0.194699 0.980863i \(-0.562373\pi\)
−0.194699 + 0.980863i \(0.562373\pi\)
\(42\) −2.25332 + 1.38656i −0.347695 + 0.213951i
\(43\) 7.30982 1.11474 0.557369 0.830265i \(-0.311811\pi\)
0.557369 + 0.830265i \(0.311811\pi\)
\(44\) 1.82746 + 3.16525i 0.275499 + 0.477179i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) −1.17919 2.04241i −0.172002 0.297916i 0.767118 0.641506i \(-0.221690\pi\)
−0.939120 + 0.343590i \(0.888357\pi\)
\(48\) −1.00000 −0.144338
\(49\) 3.15491 6.24872i 0.450702 0.892675i
\(50\) 4.00000 0.565685
\(51\) −3.08078 5.33606i −0.431395 0.747198i
\(52\) 0.425866 0.737621i 0.0590569 0.102290i
\(53\) −3.15491 + 5.46447i −0.433360 + 0.750602i −0.997160 0.0753093i \(-0.976006\pi\)
0.563800 + 0.825911i \(0.309339\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −3.65491 −0.492828
\(56\) 2.25332 1.38656i 0.301113 0.185287i
\(57\) −5.50664 −0.729373
\(58\) 2.07413 + 3.59251i 0.272347 + 0.471719i
\(59\) −1.58078 + 2.73799i −0.205800 + 0.356455i −0.950387 0.311069i \(-0.899313\pi\)
0.744588 + 0.667525i \(0.232646\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) −3.35837 −0.426514
\(63\) 2.32746 + 1.25815i 0.293232 + 0.158512i
\(64\) 1.00000 0.125000
\(65\) 0.425866 + 0.737621i 0.0528221 + 0.0914906i
\(66\) 1.82746 3.16525i 0.224944 0.389615i
\(67\) 5.17919 8.97061i 0.632738 1.09593i −0.354251 0.935150i \(-0.615264\pi\)
0.986990 0.160785i \(-0.0514025\pi\)
\(68\) 3.08078 + 5.33606i 0.373599 + 0.647092i
\(69\) 1.00000 0.120386
\(70\) 0.0741344 + 2.64471i 0.00886076 + 0.316104i
\(71\) −8.45809 −1.00379 −0.501895 0.864928i \(-0.667364\pi\)
−0.501895 + 0.864928i \(0.667364\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −0.672545 + 1.16488i −0.0787154 + 0.136339i −0.902696 0.430279i \(-0.858415\pi\)
0.823981 + 0.566618i \(0.191749\pi\)
\(74\) 3.40823 5.90323i 0.396199 0.686237i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 5.50664 0.631655
\(77\) 0.270955 + 9.66619i 0.0308782 + 1.10156i
\(78\) −0.851731 −0.0964396
\(79\) 5.72905 + 9.92300i 0.644568 + 1.11642i 0.984401 + 0.175939i \(0.0562961\pi\)
−0.339833 + 0.940486i \(0.610371\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.24668 2.15931i −0.137673 0.238456i
\(83\) −7.65491 −0.840236 −0.420118 0.907470i \(-0.638011\pi\)
−0.420118 + 0.907470i \(0.638011\pi\)
\(84\) −2.32746 1.25815i −0.253946 0.137276i
\(85\) −6.16155 −0.668314
\(86\) 3.65491 + 6.33049i 0.394119 + 0.682634i
\(87\) 2.07413 3.59251i 0.222371 0.385157i
\(88\) −1.82746 + 3.16525i −0.194807 + 0.337416i
\(89\) 3.40823 + 5.90323i 0.361272 + 0.625741i 0.988170 0.153360i \(-0.0490093\pi\)
−0.626899 + 0.779101i \(0.715676\pi\)
\(90\) −1.00000 −0.105409
\(91\) 1.91922 1.18098i 0.201189 0.123800i
\(92\) −1.00000 −0.104257
\(93\) 1.67919 + 2.90844i 0.174124 + 0.301591i
\(94\) 1.17919 2.04241i 0.121624 0.210659i
\(95\) −2.75332 + 4.76889i −0.282485 + 0.489278i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 0.444807 0.0451633 0.0225816 0.999745i \(-0.492811\pi\)
0.0225816 + 0.999745i \(0.492811\pi\)
\(98\) 6.98901 0.392129i 0.705996 0.0396110i
\(99\) −3.65491 −0.367332
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) −0.654911 + 1.13434i −0.0651661 + 0.112871i −0.896768 0.442502i \(-0.854091\pi\)
0.831602 + 0.555373i \(0.187424\pi\)
\(102\) 3.08078 5.33606i 0.305042 0.528349i
\(103\) −1.82081 3.15374i −0.179410 0.310747i 0.762269 0.647261i \(-0.224086\pi\)
−0.941679 + 0.336513i \(0.890752\pi\)
\(104\) 0.851731 0.0835191
\(105\) 2.25332 1.38656i 0.219902 0.135314i
\(106\) −6.30982 −0.612864
\(107\) 3.17254 + 5.49501i 0.306701 + 0.531223i 0.977639 0.210292i \(-0.0674413\pi\)
−0.670937 + 0.741514i \(0.734108\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −1.65491 + 2.86639i −0.158512 + 0.274550i −0.934332 0.356403i \(-0.884003\pi\)
0.775820 + 0.630954i \(0.217336\pi\)
\(110\) −1.82746 3.16525i −0.174241 0.301794i
\(111\) −6.81646 −0.646990
\(112\) 2.32746 + 1.25815i 0.219924 + 0.118884i
\(113\) 9.17484 0.863096 0.431548 0.902090i \(-0.357968\pi\)
0.431548 + 0.902090i \(0.357968\pi\)
\(114\) −2.75332 4.76889i −0.257872 0.446648i
\(115\) 0.500000 0.866025i 0.0466252 0.0807573i
\(116\) −2.07413 + 3.59251i −0.192579 + 0.333556i
\(117\) 0.425866 + 0.737621i 0.0393713 + 0.0681931i
\(118\) −3.16155 −0.291045
\(119\) 0.456783 + 16.2955i 0.0418733 + 1.49381i
\(120\) 1.00000 0.0912871
\(121\) −1.17919 2.04241i −0.107199 0.185674i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) −1.24668 + 2.15931i −0.112409 + 0.194699i
\(124\) −1.67919 2.90844i −0.150795 0.261185i
\(125\) −9.00000 −0.804984
\(126\) 0.0741344 + 2.64471i 0.00660442 + 0.235610i
\(127\) −8.34509 −0.740507 −0.370253 0.928931i \(-0.620729\pi\)
−0.370253 + 0.928931i \(0.620729\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 3.65491 6.33049i 0.321797 0.557369i
\(130\) −0.425866 + 0.737621i −0.0373509 + 0.0646936i
\(131\) −2.54986 4.41648i −0.222782 0.385870i 0.732870 0.680369i \(-0.238181\pi\)
−0.955652 + 0.294499i \(0.904847\pi\)
\(132\) 3.65491 0.318119
\(133\) 12.8165 + 6.92820i 1.11133 + 0.600751i
\(134\) 10.3584 0.894827
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) −3.08078 + 5.33606i −0.264174 + 0.457563i
\(137\) 1.47572 2.55603i 0.126080 0.218376i −0.796075 0.605198i \(-0.793094\pi\)
0.922154 + 0.386822i \(0.126427\pi\)
\(138\) 0.500000 + 0.866025i 0.0425628 + 0.0737210i
\(139\) 16.0266 1.35936 0.679678 0.733511i \(-0.262120\pi\)
0.679678 + 0.733511i \(0.262120\pi\)
\(140\) −2.25332 + 1.38656i −0.190440 + 0.117186i
\(141\) −2.35837 −0.198611
\(142\) −4.22905 7.32492i −0.354894 0.614694i
\(143\) −1.55650 + 2.69594i −0.130161 + 0.225446i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −2.07413 3.59251i −0.172247 0.298341i
\(146\) −1.34509 −0.111320
\(147\) −3.83410 5.85659i −0.316231 0.483044i
\(148\) 6.81646 0.560310
\(149\) 9.98237 + 17.2900i 0.817787 + 1.41645i 0.907309 + 0.420464i \(0.138133\pi\)
−0.0895218 + 0.995985i \(0.528534\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) −1.17254 + 2.03091i −0.0954203 + 0.165273i −0.909784 0.415082i \(-0.863753\pi\)
0.814364 + 0.580355i \(0.197086\pi\)
\(152\) 2.75332 + 4.76889i 0.223324 + 0.386808i
\(153\) −6.16155 −0.498132
\(154\) −8.23569 + 5.06775i −0.663651 + 0.408371i
\(155\) 3.35837 0.269751
\(156\) −0.425866 0.737621i −0.0340965 0.0590569i
\(157\) 12.4215 21.5147i 0.991345 1.71706i 0.381978 0.924172i \(-0.375243\pi\)
0.609367 0.792888i \(-0.291424\pi\)
\(158\) −5.72905 + 9.92300i −0.455778 + 0.789431i
\(159\) 3.15491 + 5.46447i 0.250201 + 0.433360i
\(160\) −1.00000 −0.0790569
\(161\) −2.32746 1.25815i −0.183429 0.0991564i
\(162\) −1.00000 −0.0785674
\(163\) 11.4215 + 19.7826i 0.894602 + 1.54950i 0.834296 + 0.551316i \(0.185874\pi\)
0.0603059 + 0.998180i \(0.480792\pi\)
\(164\) 1.24668 2.15931i 0.0973493 0.168614i
\(165\) −1.82746 + 3.16525i −0.142267 + 0.246414i
\(166\) −3.82746 6.62935i −0.297068 0.514537i
\(167\) 4.06184 0.314314 0.157157 0.987574i \(-0.449767\pi\)
0.157157 + 0.987574i \(0.449767\pi\)
\(168\) −0.0741344 2.64471i −0.00571960 0.204044i
\(169\) −12.2746 −0.944196
\(170\) −3.08078 5.33606i −0.236285 0.409257i
\(171\) −2.75332 + 4.76889i −0.210552 + 0.364686i
\(172\) −3.65491 + 6.33049i −0.278684 + 0.482695i
\(173\) 1.85173 + 3.20729i 0.140785 + 0.243846i 0.927792 0.373097i \(-0.121704\pi\)
−0.787008 + 0.616943i \(0.788371\pi\)
\(174\) 4.14827 0.314479
\(175\) 0.296538 + 10.5788i 0.0224161 + 0.799686i
\(176\) −3.65491 −0.275499
\(177\) 1.58078 + 2.73799i 0.118818 + 0.205800i
\(178\) −3.40823 + 5.90323i −0.255458 + 0.442466i
\(179\) −7.48901 + 12.9713i −0.559755 + 0.969524i 0.437762 + 0.899091i \(0.355771\pi\)
−0.997517 + 0.0704327i \(0.977562\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −1.70346 −0.126617 −0.0633087 0.997994i \(-0.520165\pi\)
−0.0633087 + 0.997994i \(0.520165\pi\)
\(182\) 1.98237 + 1.07161i 0.146943 + 0.0794329i
\(183\) −10.0000 −0.739221
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) −3.40823 + 5.90323i −0.250578 + 0.434014i
\(186\) −1.67919 + 2.90844i −0.123124 + 0.213257i
\(187\) −11.2600 19.5028i −0.823410 1.42619i
\(188\) 2.35837 0.172002
\(189\) 2.25332 1.38656i 0.163905 0.100857i
\(190\) −5.50664 −0.399494
\(191\) 11.4215 + 19.7826i 0.826432 + 1.43142i 0.900820 + 0.434193i \(0.142966\pi\)
−0.0743882 + 0.997229i \(0.523700\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 8.95809 15.5159i 0.644817 1.11686i −0.339526 0.940597i \(-0.610267\pi\)
0.984344 0.176260i \(-0.0563999\pi\)
\(194\) 0.222403 + 0.385214i 0.0159676 + 0.0276567i
\(195\) 0.851731 0.0609937
\(196\) 3.83410 + 5.85659i 0.273864 + 0.418328i
\(197\) 5.01328 0.357182 0.178591 0.983923i \(-0.442846\pi\)
0.178591 + 0.983923i \(0.442846\pi\)
\(198\) −1.82746 3.16525i −0.129872 0.224944i
\(199\) −7.16155 + 12.4042i −0.507669 + 0.879309i 0.492292 + 0.870430i \(0.336159\pi\)
−0.999961 + 0.00887817i \(0.997174\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) −5.17919 8.97061i −0.365312 0.632738i
\(202\) −1.30982 −0.0921587
\(203\) −9.34738 + 5.75182i −0.656058 + 0.403698i
\(204\) 6.16155 0.431395
\(205\) 1.24668 + 2.15931i 0.0870718 + 0.150813i
\(206\) 1.82081 3.15374i 0.126862 0.219732i
\(207\) 0.500000 0.866025i 0.0347524 0.0601929i
\(208\) 0.425866 + 0.737621i 0.0295285 + 0.0511448i
\(209\) −20.1263 −1.39216
\(210\) 2.32746 + 1.25815i 0.160610 + 0.0868209i
\(211\) −9.01328 −0.620500 −0.310250 0.950655i \(-0.600413\pi\)
−0.310250 + 0.950655i \(0.600413\pi\)
\(212\) −3.15491 5.46447i −0.216680 0.375301i
\(213\) −4.22905 + 7.32492i −0.289769 + 0.501895i
\(214\) −3.17254 + 5.49501i −0.216871 + 0.375631i
\(215\) −3.65491 6.33049i −0.249263 0.431736i
\(216\) 1.00000 0.0680414
\(217\) −0.248971 8.88193i −0.0169013 0.602945i
\(218\) −3.30982 −0.224169
\(219\) 0.672545 + 1.16488i 0.0454464 + 0.0787154i
\(220\) 1.82746 3.16525i 0.123207 0.213401i
\(221\) −2.62399 + 4.54489i −0.176509 + 0.305722i
\(222\) −3.40823 5.90323i −0.228746 0.396199i
\(223\) −15.9780 −1.06997 −0.534984 0.844862i \(-0.679682\pi\)
−0.534984 + 0.844862i \(0.679682\pi\)
\(224\) 0.0741344 + 2.64471i 0.00495332 + 0.176707i
\(225\) −4.00000 −0.266667
\(226\) 4.58742 + 7.94564i 0.305151 + 0.528536i
\(227\) 6.98901 12.1053i 0.463877 0.803458i −0.535273 0.844679i \(-0.679791\pi\)
0.999150 + 0.0412208i \(0.0131247\pi\)
\(228\) 2.75332 4.76889i 0.182343 0.315828i
\(229\) −14.2600 24.6990i −0.942325 1.63215i −0.761021 0.648727i \(-0.775302\pi\)
−0.181304 0.983427i \(-0.558032\pi\)
\(230\) 1.00000 0.0659380
\(231\) 8.50664 + 4.59844i 0.559696 + 0.302555i
\(232\) −4.14827 −0.272347
\(233\) −5.56978 9.64715i −0.364889 0.632006i 0.623870 0.781528i \(-0.285560\pi\)
−0.988758 + 0.149523i \(0.952226\pi\)
\(234\) −0.425866 + 0.737621i −0.0278397 + 0.0482198i
\(235\) −1.17919 + 2.04241i −0.0769216 + 0.133232i
\(236\) −1.58078 2.73799i −0.102900 0.178228i
\(237\) 11.4581 0.744283
\(238\) −13.8840 + 8.54335i −0.899963 + 0.553783i
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) −8.28424 + 14.3487i −0.533635 + 0.924282i 0.465593 + 0.884999i \(0.345841\pi\)
−0.999228 + 0.0392837i \(0.987492\pi\)
\(242\) 1.17919 2.04241i 0.0758010 0.131291i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 10.0000 0.640184
\(245\) −6.98901 + 0.392129i −0.446511 + 0.0250522i
\(246\) −2.49336 −0.158971
\(247\) 2.34509 + 4.06181i 0.149214 + 0.258447i
\(248\) 1.67919 2.90844i 0.106628 0.184686i
\(249\) −3.82746 + 6.62935i −0.242555 + 0.420118i
\(250\) −4.50000 7.79423i −0.284605 0.492950i
\(251\) 30.2746 1.91091 0.955456 0.295132i \(-0.0953637\pi\)
0.955456 + 0.295132i \(0.0953637\pi\)
\(252\) −2.25332 + 1.38656i −0.141946 + 0.0873450i
\(253\) 3.65491 0.229782
\(254\) −4.17254 7.22706i −0.261809 0.453466i
\(255\) −3.08078 + 5.33606i −0.192926 + 0.334157i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.06314 + 12.2337i 0.440587 + 0.763119i 0.997733 0.0672957i \(-0.0214371\pi\)
−0.557146 + 0.830414i \(0.688104\pi\)
\(258\) 7.30982 0.455090
\(259\) 15.8650 + 8.57616i 0.985804 + 0.532897i
\(260\) −0.851731 −0.0528221
\(261\) −2.07413 3.59251i −0.128386 0.222371i
\(262\) 2.54986 4.41648i 0.157531 0.272851i
\(263\) 7.65491 13.2587i 0.472022 0.817566i −0.527466 0.849576i \(-0.676858\pi\)
0.999488 + 0.0320103i \(0.0101909\pi\)
\(264\) 1.82746 + 3.16525i 0.112472 + 0.194807i
\(265\) 6.30982 0.387609
\(266\) 0.408232 + 14.5635i 0.0250303 + 0.892945i
\(267\) 6.81646 0.417161
\(268\) 5.17919 + 8.97061i 0.316369 + 0.547967i
\(269\) 11.2357 19.4608i 0.685052 1.18654i −0.288369 0.957519i \(-0.593113\pi\)
0.973420 0.229025i \(-0.0735538\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 7.18583 + 12.4462i 0.436508 + 0.756054i 0.997417 0.0718232i \(-0.0228817\pi\)
−0.560909 + 0.827877i \(0.689548\pi\)
\(272\) −6.16155 −0.373599
\(273\) −0.0631426 2.25258i −0.00382156 0.136333i
\(274\) 2.95145 0.178304
\(275\) −7.30982 12.6610i −0.440799 0.763486i
\(276\) −0.500000 + 0.866025i −0.0300965 + 0.0521286i
\(277\) 5.98237 10.3618i 0.359446 0.622578i −0.628423 0.777872i \(-0.716299\pi\)
0.987868 + 0.155294i \(0.0496325\pi\)
\(278\) 8.01328 + 13.8794i 0.480605 + 0.832432i
\(279\) 3.35837 0.201061
\(280\) −2.32746 1.25815i −0.139092 0.0751891i
\(281\) 11.0512 0.659257 0.329629 0.944111i \(-0.393076\pi\)
0.329629 + 0.944111i \(0.393076\pi\)
\(282\) −1.17919 2.04241i −0.0702195 0.121624i
\(283\) −1.96908 + 3.41055i −0.117050 + 0.202736i −0.918597 0.395195i \(-0.870677\pi\)
0.801547 + 0.597931i \(0.204010\pi\)
\(284\) 4.22905 7.32492i 0.250948 0.434654i
\(285\) 2.75332 + 4.76889i 0.163093 + 0.282485i
\(286\) −3.11300 −0.184076
\(287\) 5.61834 3.45719i 0.331640 0.204071i
\(288\) −1.00000 −0.0589256
\(289\) −10.4824 18.1560i −0.616610 1.06800i
\(290\) 2.07413 3.59251i 0.121797 0.210959i
\(291\) 0.222403 0.385214i 0.0130375 0.0225816i
\(292\) −0.672545 1.16488i −0.0393577 0.0681695i
\(293\) 13.0266 0.761020 0.380510 0.924777i \(-0.375748\pi\)
0.380510 + 0.924777i \(0.375748\pi\)
\(294\) 3.15491 6.24872i 0.183998 0.364433i
\(295\) 3.16155 0.184073
\(296\) 3.40823 + 5.90323i 0.198099 + 0.343118i
\(297\) −1.82746 + 3.16525i −0.106040 + 0.183666i
\(298\) −9.98237 + 17.2900i −0.578263 + 1.00158i
\(299\) −0.425866 0.737621i −0.0246284 0.0426577i
\(300\) 4.00000 0.230940
\(301\) −16.4714 + 10.1355i −0.949394 + 0.584200i
\(302\) −2.34509 −0.134945
\(303\) 0.654911 + 1.13434i 0.0376236 + 0.0651661i
\(304\) −2.75332 + 4.76889i −0.157914 + 0.273515i
\(305\) −5.00000 + 8.66025i −0.286299 + 0.495885i
\(306\) −3.08078 5.33606i −0.176116 0.305042i
\(307\) −25.4095 −1.45020 −0.725099 0.688644i \(-0.758206\pi\)
−0.725099 + 0.688644i \(0.758206\pi\)
\(308\) −8.50664 4.59844i −0.484711 0.262020i
\(309\) −3.64163 −0.207165
\(310\) 1.67919 + 2.90844i 0.0953714 + 0.165188i
\(311\) 2.77095 4.79943i 0.157126 0.272151i −0.776705 0.629865i \(-0.783110\pi\)
0.933831 + 0.357714i \(0.116444\pi\)
\(312\) 0.425866 0.737621i 0.0241099 0.0417596i
\(313\) −9.58078 16.5944i −0.541537 0.937970i −0.998816 0.0486469i \(-0.984509\pi\)
0.457279 0.889324i \(-0.348824\pi\)
\(314\) 24.8430 1.40197
\(315\) −0.0741344 2.64471i −0.00417700 0.149013i
\(316\) −11.4581 −0.644568
\(317\) −4.28424 7.42052i −0.240627 0.416778i 0.720266 0.693698i \(-0.244020\pi\)
−0.960893 + 0.276920i \(0.910686\pi\)
\(318\) −3.15491 + 5.46447i −0.176919 + 0.306432i
\(319\) 7.58078 13.1303i 0.424442 0.735155i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 6.34509 0.354148
\(322\) −0.0741344 2.64471i −0.00413135 0.147384i
\(323\) −33.9295 −1.88789
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −1.70346 + 2.95048i −0.0944911 + 0.163663i
\(326\) −11.4215 + 19.7826i −0.632579 + 1.09566i
\(327\) 1.65491 + 2.86639i 0.0915168 + 0.158512i
\(328\) 2.49336 0.137673
\(329\) 5.48901 + 2.96720i 0.302619 + 0.163587i
\(330\) −3.65491 −0.201196
\(331\) −8.56978 14.8433i −0.471038 0.815862i 0.528413 0.848987i \(-0.322787\pi\)
−0.999451 + 0.0331256i \(0.989454\pi\)
\(332\) 3.82746 6.62935i 0.210059 0.363833i
\(333\) −3.40823 + 5.90323i −0.186770 + 0.323495i
\(334\) 2.03092 + 3.51765i 0.111127 + 0.192477i
\(335\) −10.3584 −0.565938
\(336\) 2.25332 1.38656i 0.122929 0.0756430i
\(337\) −14.5685 −0.793596 −0.396798 0.917906i \(-0.629879\pi\)
−0.396798 + 0.917906i \(0.629879\pi\)
\(338\) −6.13728 10.6301i −0.333824 0.578200i
\(339\) 4.58742 7.94564i 0.249154 0.431548i
\(340\) 3.08078 5.33606i 0.167079 0.289389i
\(341\) 6.13728 + 10.6301i 0.332352 + 0.575651i
\(342\) −5.50664 −0.297765
\(343\) 1.55519 + 18.4548i 0.0839725 + 0.996468i
\(344\) −7.30982 −0.394119
\(345\) −0.500000 0.866025i −0.0269191 0.0466252i
\(346\) −1.85173 + 3.20729i −0.0995497 + 0.172425i
\(347\) −3.52428 + 6.10422i −0.189193 + 0.327692i −0.944981 0.327124i \(-0.893921\pi\)
0.755788 + 0.654816i \(0.227254\pi\)
\(348\) 2.07413 + 3.59251i 0.111185 + 0.192579i
\(349\) 22.4581 1.20215 0.601077 0.799191i \(-0.294738\pi\)
0.601077 + 0.799191i \(0.294738\pi\)
\(350\) −9.01328 + 5.54623i −0.481780 + 0.296459i
\(351\) 0.851731 0.0454620
\(352\) −1.82746 3.16525i −0.0974037 0.168708i
\(353\) −5.56978 + 9.64715i −0.296450 + 0.513466i −0.975321 0.220791i \(-0.929136\pi\)
0.678871 + 0.734257i \(0.262469\pi\)
\(354\) −1.58078 + 2.73799i −0.0840173 + 0.145522i
\(355\) 4.22905 + 7.32492i 0.224454 + 0.388766i
\(356\) −6.81646 −0.361272
\(357\) 14.3407 + 7.75218i 0.758992 + 0.410289i
\(358\) −14.9780 −0.791613
\(359\) 14.0133 + 24.2717i 0.739593 + 1.28101i 0.952679 + 0.303979i \(0.0983152\pi\)
−0.213086 + 0.977033i \(0.568351\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) −5.66155 + 9.80610i −0.297976 + 0.516110i
\(362\) −0.851731 1.47524i −0.0447660 0.0775370i
\(363\) −2.35837 −0.123782
\(364\) 0.0631426 + 2.25258i 0.00330957 + 0.118067i
\(365\) 1.34509 0.0704052
\(366\) −5.00000 8.66025i −0.261354 0.452679i
\(367\) 3.89495 6.74625i 0.203315 0.352151i −0.746280 0.665632i \(-0.768162\pi\)
0.949594 + 0.313481i \(0.101495\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 1.24668 + 2.15931i 0.0648995 + 0.112409i
\(370\) −6.81646 −0.354371
\(371\) −0.467775 16.6877i −0.0242857 0.866380i
\(372\) −3.35837 −0.174124
\(373\) −6.35837 11.0130i −0.329224 0.570233i 0.653134 0.757242i \(-0.273454\pi\)
−0.982358 + 0.187009i \(0.940120\pi\)
\(374\) 11.2600 19.5028i 0.582239 1.00847i
\(375\) −4.50000 + 7.79423i −0.232379 + 0.402492i
\(376\) 1.17919 + 2.04241i 0.0608119 + 0.105329i
\(377\) −3.53321 −0.181970
\(378\) 2.32746 + 1.25815i 0.119711 + 0.0647125i
\(379\) −22.2613 −1.14348 −0.571742 0.820433i \(-0.693732\pi\)
−0.571742 + 0.820433i \(0.693732\pi\)
\(380\) −2.75332 4.76889i −0.141242 0.244639i
\(381\) −4.17254 + 7.22706i −0.213766 + 0.370253i
\(382\) −11.4215 + 19.7826i −0.584376 + 1.01217i
\(383\) 11.1117 + 19.2460i 0.567781 + 0.983426i 0.996785 + 0.0801230i \(0.0255313\pi\)
−0.429004 + 0.903303i \(0.641135\pi\)
\(384\) 1.00000 0.0510310
\(385\) 8.23569 5.06775i 0.419729 0.258276i
\(386\) 17.9162 0.911910
\(387\) −3.65491 6.33049i −0.185790 0.321797i
\(388\) −0.222403 + 0.385214i −0.0112908 + 0.0195563i
\(389\) 15.3717 26.6245i 0.779374 1.34992i −0.152929 0.988237i \(-0.548871\pi\)
0.932303 0.361678i \(-0.117796\pi\)
\(390\) 0.425866 + 0.737621i 0.0215645 + 0.0373509i
\(391\) 6.16155 0.311603
\(392\) −3.15491 + 6.24872i −0.159347 + 0.315608i
\(393\) −5.09972 −0.257247
\(394\) 2.50664 + 4.34163i 0.126283 + 0.218728i
\(395\) 5.72905 9.92300i 0.288260 0.499280i
\(396\) 1.82746 3.16525i 0.0918331 0.159060i
\(397\) 3.08078 + 5.33606i 0.154620 + 0.267809i 0.932920 0.360082i \(-0.117251\pi\)
−0.778301 + 0.627892i \(0.783918\pi\)
\(398\) −14.3231 −0.717952
\(399\) 12.4082 7.63528i 0.621189 0.382242i
\(400\) −4.00000 −0.200000
\(401\) 7.98237 + 13.8259i 0.398620 + 0.690431i 0.993556 0.113343i \(-0.0361558\pi\)
−0.594936 + 0.803773i \(0.702822\pi\)
\(402\) 5.17919 8.97061i 0.258314 0.447414i
\(403\) 1.43022 2.47721i 0.0712441 0.123398i
\(404\) −0.654911 1.13434i −0.0325830 0.0564355i
\(405\) 1.00000 0.0496904
\(406\) −9.65491 5.21916i −0.479165 0.259023i
\(407\) −24.9136 −1.23492
\(408\) 3.08078 + 5.33606i 0.152521 + 0.264174i
\(409\) 7.36502 12.7566i 0.364177 0.630772i −0.624467 0.781051i \(-0.714684\pi\)
0.988644 + 0.150279i \(0.0480171\pi\)
\(410\) −1.24668 + 2.15931i −0.0615691 + 0.106641i
\(411\) −1.47572 2.55603i −0.0727921 0.126080i
\(412\) 3.64163 0.179410
\(413\) −0.234380 8.36140i −0.0115331 0.411437i
\(414\) 1.00000 0.0491473
\(415\) 3.82746 + 6.62935i 0.187882 + 0.325422i
\(416\) −0.425866 + 0.737621i −0.0208798 + 0.0361648i
\(417\) 8.01328 13.8794i 0.392412 0.679678i
\(418\) −10.0631 17.4299i −0.492204 0.852523i
\(419\) 24.9427 1.21853 0.609267 0.792966i \(-0.291464\pi\)
0.609267 + 0.792966i \(0.291464\pi\)
\(420\) 0.0741344 + 2.64471i 0.00361739 + 0.129049i
\(421\) 32.3497 1.57663 0.788313 0.615274i \(-0.210955\pi\)
0.788313 + 0.615274i \(0.210955\pi\)
\(422\) −4.50664 7.80573i −0.219380 0.379977i
\(423\) −1.17919 + 2.04241i −0.0573340 + 0.0993054i
\(424\) 3.15491 5.46447i 0.153216 0.265378i
\(425\) −12.3231 21.3442i −0.597758 1.03535i
\(426\) −8.45809 −0.409796
\(427\) 23.2746 + 12.5815i 1.12633 + 0.608863i
\(428\) −6.34509 −0.306701
\(429\) 1.55650 + 2.69594i 0.0751486 + 0.130161i
\(430\) 3.65491 6.33049i 0.176255 0.305283i
\(431\) −2.29654 + 3.97772i −0.110620 + 0.191600i −0.916021 0.401131i \(-0.868617\pi\)
0.805400 + 0.592731i \(0.201950\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 27.2393 1.30904 0.654518 0.756046i \(-0.272871\pi\)
0.654518 + 0.756046i \(0.272871\pi\)
\(434\) 7.56749 4.65658i 0.363251 0.223523i
\(435\) −4.14827 −0.198894
\(436\) −1.65491 2.86639i −0.0792559 0.137275i
\(437\) 2.75332 4.76889i 0.131709 0.228127i
\(438\) −0.672545 + 1.16488i −0.0321354 + 0.0556602i
\(439\) 7.97572 + 13.8144i 0.380661 + 0.659323i 0.991157 0.132696i \(-0.0423633\pi\)
−0.610496 + 0.792019i \(0.709030\pi\)
\(440\) 3.65491 0.174241
\(441\) −6.98901 + 0.392129i −0.332810 + 0.0186728i
\(442\) −5.24799 −0.249621
\(443\) 14.5631 + 25.2241i 0.691916 + 1.19843i 0.971209 + 0.238228i \(0.0765664\pi\)
−0.279294 + 0.960206i \(0.590100\pi\)
\(444\) 3.40823 5.90323i 0.161748 0.280155i
\(445\) 3.40823 5.90323i 0.161566 0.279840i
\(446\) −7.98901 13.8374i −0.378291 0.655218i
\(447\) 19.9647 0.944299
\(448\) −2.25332 + 1.38656i −0.106459 + 0.0655087i
\(449\) −18.2234 −0.860015 −0.430007 0.902825i \(-0.641489\pi\)
−0.430007 + 0.902825i \(0.641489\pi\)
\(450\) −2.00000 3.46410i −0.0942809 0.163299i
\(451\) −4.55650 + 7.89209i −0.214557 + 0.371624i
\(452\) −4.58742 + 7.94564i −0.215774 + 0.373732i
\(453\) 1.17254 + 2.03091i 0.0550910 + 0.0954203i
\(454\) 13.9780 0.656021
\(455\) −1.98237 1.07161i −0.0929348 0.0502378i
\(456\) 5.50664 0.257872
\(457\) −5.13597 8.89576i −0.240251 0.416126i 0.720535 0.693419i \(-0.243896\pi\)
−0.960786 + 0.277292i \(0.910563\pi\)
\(458\) 14.2600 24.6990i 0.666324 1.15411i
\(459\) −3.08078 + 5.33606i −0.143798 + 0.249066i
\(460\) 0.500000 + 0.866025i 0.0233126 + 0.0403786i
\(461\) 20.6196 0.960353 0.480176 0.877172i \(-0.340573\pi\)
0.480176 + 0.877172i \(0.340573\pi\)
\(462\) 0.270955 + 9.66619i 0.0126060 + 0.449712i
\(463\) 15.3098 0.711508 0.355754 0.934580i \(-0.384224\pi\)
0.355754 + 0.934580i \(0.384224\pi\)
\(464\) −2.07413 3.59251i −0.0962893 0.166778i
\(465\) 1.67919 2.90844i 0.0778704 0.134876i
\(466\) 5.56978 9.64715i 0.258015 0.446896i
\(467\) −3.65491 6.33049i −0.169129 0.292940i 0.768985 0.639267i \(-0.220762\pi\)
−0.938114 + 0.346327i \(0.887429\pi\)
\(468\) −0.851731 −0.0393713
\(469\) 0.767912 + 27.3949i 0.0354589 + 1.26498i
\(470\) −2.35837 −0.108784
\(471\) −12.4215 21.5147i −0.572353 0.991345i
\(472\) 1.58078 2.73799i 0.0727611 0.126026i
\(473\) 13.3584 23.1374i 0.614219 1.06386i
\(474\) 5.72905 + 9.92300i 0.263144 + 0.455778i
\(475\) −22.0266 −1.01065
\(476\) −14.3407 7.75218i −0.657307 0.355321i
\(477\) 6.30982 0.288907
\(478\) −8.00000 13.8564i −0.365911 0.633777i
\(479\) 16.5565 28.6767i 0.756486 1.31027i −0.188146 0.982141i \(-0.560248\pi\)
0.944632 0.328131i \(-0.106419\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) 2.90290 + 5.02797i 0.132361 + 0.229255i
\(482\) −16.5685 −0.754673
\(483\) −2.25332 + 1.38656i −0.102530 + 0.0630906i
\(484\) 2.35837 0.107199
\(485\) −0.222403 0.385214i −0.0100988 0.0174917i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 13.6925 23.7161i 0.620465 1.07468i −0.368934 0.929456i \(-0.620277\pi\)
0.989399 0.145221i \(-0.0463895\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 22.8430 1.03300
\(490\) −3.83410 5.85659i −0.173207 0.264574i
\(491\) 19.8165 0.894304 0.447152 0.894458i \(-0.352438\pi\)
0.447152 + 0.894458i \(0.352438\pi\)
\(492\) −1.24668 2.15931i −0.0562046 0.0973493i
\(493\) 12.7799 22.1354i 0.575577 0.996929i
\(494\) −2.34509 + 4.06181i −0.105511 + 0.182750i
\(495\) 1.82746 + 3.16525i 0.0821380 + 0.142267i
\(496\) 3.35837 0.150795
\(497\) 19.0588 11.7276i 0.854904 0.526056i
\(498\) −7.65491 −0.343025
\(499\) 18.1748 + 31.4797i 0.813617 + 1.40923i 0.910316 + 0.413913i \(0.135838\pi\)
−0.0966990 + 0.995314i \(0.530828\pi\)
\(500\) 4.50000 7.79423i 0.201246 0.348569i
\(501\) 2.03092 3.51765i 0.0907347 0.157157i
\(502\) 15.1373 + 26.2185i 0.675610 + 1.17019i
\(503\) −38.9427 −1.73637 −0.868186 0.496239i \(-0.834714\pi\)
−0.868186 + 0.496239i \(0.834714\pi\)
\(504\) −2.32746 1.25815i −0.103673 0.0560426i
\(505\) 1.30982 0.0582863
\(506\) 1.82746 + 3.16525i 0.0812403 + 0.140712i
\(507\) −6.13728 + 10.6301i −0.272566 + 0.472098i
\(508\) 4.17254 7.22706i 0.185127 0.320649i
\(509\) −8.08742 14.0078i −0.358469 0.620886i 0.629237 0.777214i \(-0.283368\pi\)
−0.987705 + 0.156328i \(0.950034\pi\)
\(510\) −6.16155 −0.272838
\(511\) −0.0997174 3.55737i −0.00441124 0.157369i
\(512\) −1.00000 −0.0441942
\(513\) 2.75332 + 4.76889i 0.121562 + 0.210552i
\(514\) −7.06314 + 12.2337i −0.311542 + 0.539606i
\(515\) −1.82081 + 3.15374i −0.0802346 + 0.138970i
\(516\) 3.65491 + 6.33049i 0.160898 + 0.278684i
\(517\) −8.61964 −0.379091
\(518\) 0.505335 + 18.0276i 0.0222031 + 0.792087i
\(519\) 3.70346 0.162564
\(520\) −0.425866 0.737621i −0.0186754 0.0323468i
\(521\) 10.4890 18.1675i 0.459532 0.795932i −0.539404 0.842047i \(-0.681351\pi\)
0.998936 + 0.0461145i \(0.0146839\pi\)
\(522\) 2.07413 3.59251i 0.0907824 0.157240i
\(523\) 13.1306 + 22.7429i 0.574163 + 0.994479i 0.996132 + 0.0878687i \(0.0280056\pi\)
−0.421969 + 0.906610i \(0.638661\pi\)
\(524\) 5.09972 0.222782
\(525\) 9.30982 + 5.03262i 0.406314 + 0.219641i
\(526\) 15.3098 0.667540
\(527\) 10.3464 + 17.9205i 0.450696 + 0.780629i
\(528\) −1.82746 + 3.16525i −0.0795298 + 0.137750i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) 3.15491 + 5.46447i 0.137041 + 0.237361i
\(531\) 3.16155 0.137200
\(532\) −12.4082 + 7.63528i −0.537965 + 0.331031i
\(533\) 2.12367 0.0919864
\(534\) 3.40823 + 5.90323i 0.147489 + 0.255458i
\(535\) 3.17254 5.49501i 0.137161 0.237570i
\(536\) −5.17919 + 8.97061i −0.223707 + 0.387472i
\(537\) 7.48901 + 12.9713i 0.323175 + 0.559755i
\(538\) 22.4714 0.968810
\(539\) −14.0133 21.4053i −0.603595 0.921993i
\(540\) −1.00000 −0.0430331
\(541\) −4.08078 7.06811i −0.175446 0.303882i 0.764869 0.644185i \(-0.222803\pi\)
−0.940316 + 0.340304i \(0.889470\pi\)
\(542\) −7.18583 + 12.4462i −0.308658 + 0.534611i
\(543\) −0.851731 + 1.47524i −0.0365513 + 0.0633087i
\(544\) −3.08078 5.33606i −0.132087 0.228782i
\(545\) 3.30982 0.141777
\(546\) 1.91922 1.18098i 0.0821352 0.0505411i
\(547\) 21.7326 0.929221 0.464610 0.885515i \(-0.346194\pi\)
0.464610 + 0.885515i \(0.346194\pi\)
\(548\) 1.47572 + 2.55603i 0.0630398 + 0.109188i
\(549\) −5.00000 + 8.66025i −0.213395 + 0.369611i
\(550\) 7.30982 12.6610i 0.311692 0.539866i
\(551\) −11.4215 19.7826i −0.486573 0.842769i
\(552\) −1.00000 −0.0425628
\(553\) −26.6682 14.4160i −1.13405 0.613032i
\(554\) 11.9647 0.508333
\(555\) 3.40823 + 5.90323i 0.144671 + 0.250578i
\(556\) −8.01328 + 13.8794i −0.339839 + 0.588618i
\(557\) 18.2988 31.6945i 0.775346 1.34294i −0.159253 0.987238i \(-0.550909\pi\)
0.934600 0.355701i \(-0.115758\pi\)
\(558\) 1.67919 + 2.90844i 0.0710856 + 0.123124i
\(559\) −6.22600 −0.263332
\(560\) −0.0741344 2.64471i −0.00313275 0.111760i
\(561\) −22.5199 −0.950792
\(562\) 5.52558 + 9.57059i 0.233083 + 0.403711i
\(563\) −3.64392 + 6.31145i −0.153573 + 0.265996i −0.932538 0.361071i \(-0.882411\pi\)
0.778966 + 0.627067i \(0.215745\pi\)
\(564\) 1.17919 2.04241i 0.0496527 0.0860010i
\(565\) −4.58742 7.94564i −0.192994 0.334276i
\(566\) −3.93816 −0.165533
\(567\) −0.0741344 2.64471i −0.00311335 0.111067i
\(568\) 8.45809 0.354894
\(569\) 6.67254 + 11.5572i 0.279728 + 0.484502i 0.971317 0.237788i \(-0.0764225\pi\)
−0.691589 + 0.722291i \(0.743089\pi\)
\(570\) −2.75332 + 4.76889i −0.115324 + 0.199747i
\(571\) 15.7975 27.3621i 0.661106 1.14507i −0.319220 0.947681i \(-0.603421\pi\)
0.980325 0.197388i \(-0.0632459\pi\)
\(572\) −1.55650 2.69594i −0.0650806 0.112723i
\(573\) 22.8430 0.954281
\(574\) 5.80318 + 3.13703i 0.242220 + 0.130937i
\(575\) 4.00000 0.166812
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −0.369365 + 0.639759i −0.0153769 + 0.0266335i −0.873611 0.486624i \(-0.838228\pi\)
0.858235 + 0.513258i \(0.171561\pi\)
\(578\) 10.4824 18.1560i 0.436009 0.755190i
\(579\) −8.95809 15.5159i −0.372286 0.644817i
\(580\) 4.14827 0.172247
\(581\) 17.2490 10.6140i 0.715608 0.440342i
\(582\) 0.444807 0.0184378
\(583\) 11.5309 + 19.9721i 0.477562 + 0.827161i
\(584\) 0.672545 1.16488i 0.0278301 0.0482031i
\(585\) 0.425866 0.737621i 0.0176074 0.0304969i
\(586\) 6.51328 + 11.2813i 0.269061 + 0.466028i
\(587\) −42.2367 −1.74329 −0.871647 0.490134i \(-0.836948\pi\)
−0.871647 + 0.490134i \(0.836948\pi\)
\(588\) 6.98901 0.392129i 0.288222 0.0161711i
\(589\) 18.4934 0.762006
\(590\) 1.58078 + 2.73799i 0.0650795 + 0.112721i
\(591\) 2.50664 4.34163i 0.103109 0.178591i
\(592\) −3.40823 + 5.90323i −0.140077 + 0.242621i
\(593\) 0.331805 + 0.574704i 0.0136256 + 0.0236002i 0.872758 0.488153i \(-0.162329\pi\)
−0.859132 + 0.511754i \(0.828996\pi\)
\(594\) −3.65491 −0.149963
\(595\) 13.8840 8.54335i 0.569187 0.350243i
\(596\) −19.9647 −0.817787
\(597\) 7.16155 + 12.4042i 0.293103 + 0.507669i
\(598\) 0.425866 0.737621i 0.0174149 0.0301636i
\(599\) −14.9458 + 25.8869i −0.610668 + 1.05771i 0.380459 + 0.924798i \(0.375766\pi\)
−0.991128 + 0.132911i \(0.957567\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) −18.9647 −0.773588 −0.386794 0.922166i \(-0.626417\pi\)
−0.386794 + 0.922166i \(0.626417\pi\)
\(602\) −17.0133 9.19688i −0.693410 0.374837i
\(603\) −10.3584 −0.421826
\(604\) −1.17254 2.03091i −0.0477102 0.0826364i
\(605\) −1.17919 + 2.04241i −0.0479408 + 0.0830358i
\(606\) −0.654911 + 1.13434i −0.0266039 + 0.0460794i
\(607\) −11.7789 20.4017i −0.478091 0.828078i 0.521594 0.853194i \(-0.325338\pi\)
−0.999685 + 0.0251162i \(0.992004\pi\)
\(608\) −5.50664 −0.223324
\(609\) 0.307530 + 10.9710i 0.0124617 + 0.444566i
\(610\) −10.0000 −0.404888
\(611\) 1.00435 + 1.73959i 0.0406316 + 0.0703761i
\(612\) 3.08078 5.33606i 0.124533 0.215697i
\(613\) 21.9647 38.0440i 0.887147 1.53658i 0.0439145 0.999035i \(-0.486017\pi\)
0.843233 0.537549i \(-0.180650\pi\)
\(614\) −12.7048 22.0053i −0.512723 0.888062i
\(615\) 2.49336 0.100542
\(616\) −0.270955 9.66619i −0.0109171 0.389462i
\(617\) 30.2878 1.21934 0.609671 0.792654i \(-0.291301\pi\)
0.609671 + 0.792654i \(0.291301\pi\)
\(618\) −1.82081 3.15374i −0.0732439 0.126862i
\(619\) 12.4524 21.5682i 0.500506 0.866901i −0.499494 0.866317i \(-0.666481\pi\)
1.00000 0.000583862i \(-0.000185849\pi\)
\(620\) −1.67919 + 2.90844i −0.0674378 + 0.116806i
\(621\) −0.500000 0.866025i −0.0200643 0.0347524i
\(622\) 5.54191 0.222210
\(623\) −15.8650 8.57616i −0.635618 0.343597i
\(624\) 0.851731 0.0340965
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 9.58078 16.5944i 0.382925 0.663245i
\(627\) −10.0631 + 17.4299i −0.401883 + 0.696082i
\(628\) 12.4215 + 21.5147i 0.495672 + 0.858530i
\(629\) −42.0000 −1.67465
\(630\) 2.25332 1.38656i 0.0897745 0.0552418i
\(631\) −28.4095 −1.13097 −0.565483 0.824760i \(-0.691310\pi\)
−0.565483 + 0.824760i \(0.691310\pi\)
\(632\) −5.72905 9.92300i −0.227889 0.394716i
\(633\) −4.50664 + 7.80573i −0.179123 + 0.310250i
\(634\) 4.28424 7.42052i 0.170149 0.294706i
\(635\) 4.17254 + 7.22706i 0.165582 + 0.286797i
\(636\) −6.30982 −0.250201
\(637\) −2.68714 + 5.32223i −0.106468 + 0.210875i
\(638\) 15.1616 0.600252
\(639\) 4.22905 + 7.32492i 0.167298 + 0.289769i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 7.52558 13.0347i 0.297243 0.514839i −0.678261 0.734821i \(-0.737266\pi\)
0.975504 + 0.219981i \(0.0705996\pi\)
\(642\) 3.17254 + 5.49501i 0.125210 + 0.216871i
\(643\) 9.80318 0.386600 0.193300 0.981140i \(-0.438081\pi\)
0.193300 + 0.981140i \(0.438081\pi\)
\(644\) 2.25332 1.38656i 0.0887933 0.0546381i
\(645\) −7.30982 −0.287824
\(646\) −16.9647 29.3838i −0.667468 1.15609i
\(647\) 15.7546 27.2878i 0.619378 1.07279i −0.370221 0.928944i \(-0.620718\pi\)
0.989599 0.143851i \(-0.0459486\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 5.77760 + 10.0071i 0.226791 + 0.392813i
\(650\) −3.40692 −0.133631
\(651\) −7.81646 4.22535i −0.306351 0.165605i
\(652\) −22.8430 −0.894602
\(653\) 20.7556 + 35.9498i 0.812230 + 1.40682i 0.911300 + 0.411743i \(0.135080\pi\)
−0.0990701 + 0.995080i \(0.531587\pi\)
\(654\) −1.65491 + 2.86639i −0.0647121 + 0.112085i
\(655\) −2.54986 + 4.41648i −0.0996312 + 0.172566i
\(656\) 1.24668 + 2.15931i 0.0486746 + 0.0843069i
\(657\) 1.34509 0.0524769
\(658\) 0.174837 + 6.23722i 0.00681584 + 0.243152i
\(659\) −43.6329 −1.69970 −0.849849 0.527027i \(-0.823307\pi\)
−0.849849 + 0.527027i \(0.823307\pi\)
\(660\) −1.82746 3.16525i −0.0711336 0.123207i
\(661\) −18.9913 + 32.8939i −0.738676 + 1.27942i 0.214416 + 0.976742i \(0.431215\pi\)
−0.953092 + 0.302682i \(0.902118\pi\)
\(662\) 8.56978 14.8433i 0.333074 0.576901i
\(663\) 2.62399 + 4.54489i 0.101907 + 0.176509i
\(664\) 7.65491 0.297068
\(665\) −0.408232 14.5635i −0.0158305 0.564748i
\(666\) −6.81646 −0.264133
\(667\) 2.07413 + 3.59251i 0.0803108 + 0.139102i
\(668\) −2.03092 + 3.51765i −0.0785786 + 0.136102i
\(669\) −7.98901 + 13.8374i −0.308873 + 0.534984i
\(670\) −5.17919 8.97061i −0.200089 0.346565i
\(671\) −36.5491 −1.41096
\(672\) 2.32746 + 1.25815i 0.0897835 + 0.0485343i
\(673\) 36.2040 1.39556 0.697781 0.716311i \(-0.254171\pi\)
0.697781 + 0.716311i \(0.254171\pi\)
\(674\) −7.28424 12.6167i −0.280578 0.485976i
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) 6.13728 10.6301i 0.236049 0.408849i
\(677\) 14.8098 + 25.6514i 0.569188 + 0.985862i 0.996647 + 0.0818272i \(0.0260756\pi\)
−0.427459 + 0.904035i \(0.640591\pi\)
\(678\) 9.17484 0.352357
\(679\) −1.00229 + 0.616750i −0.0384644 + 0.0236687i
\(680\) 6.16155 0.236285
\(681\) −6.98901 12.1053i −0.267819 0.463877i
\(682\) −6.13728 + 10.6301i −0.235008 + 0.407047i
\(683\) −18.4282 + 31.9185i −0.705134 + 1.22133i 0.261509 + 0.965201i \(0.415780\pi\)
−0.966643 + 0.256127i \(0.917554\pi\)
\(684\) −2.75332 4.76889i −0.105276 0.182343i
\(685\) −2.95145 −0.112769
\(686\) −15.2048 + 10.5743i −0.580521 + 0.403727i
\(687\) −28.5199 −1.08810
\(688\) −3.65491 6.33049i −0.139342 0.241348i
\(689\) 2.68714 4.65426i 0.102372 0.177313i
\(690\) 0.500000 0.866025i 0.0190347 0.0329690i
\(691\) 6.27325 + 10.8656i 0.238646 + 0.413346i 0.960326 0.278880i \(-0.0899633\pi\)
−0.721680 + 0.692226i \(0.756630\pi\)
\(692\) −3.70346 −0.140785
\(693\) 8.23569 5.06775i 0.312848 0.192508i
\(694\) −7.04855 −0.267559
\(695\) −8.01328 13.8794i −0.303961 0.526476i
\(696\) −2.07413 + 3.59251i −0.0786199 + 0.136174i
\(697\) −7.68148 + 13.3047i −0.290957 + 0.503952i
\(698\) 11.2290 + 19.4493i 0.425026 + 0.736166i
\(699\) −11.1396 −0.421337
\(700\) −9.30982 5.03262i −0.351878 0.190215i
\(701\) −12.6769 −0.478800 −0.239400 0.970921i \(-0.576951\pi\)
−0.239400 + 0.970921i \(0.576951\pi\)
\(702\) 0.425866 + 0.737621i 0.0160733 + 0.0278397i
\(703\) −18.7679 + 32.5070i −0.707845 + 1.22602i
\(704\) 1.82746 3.16525i 0.0688748 0.119295i
\(705\) 1.17919 + 2.04241i 0.0444107 + 0.0769216i
\(706\) −11.1396 −0.419243
\(707\) −0.0971029 3.46410i −0.00365193 0.130281i
\(708\) −3.16155 −0.118818
\(709\) 14.0146 + 24.2740i 0.526329 + 0.911629i 0.999529 + 0.0306738i \(0.00976531\pi\)
−0.473200 + 0.880955i \(0.656901\pi\)
\(710\) −4.22905 + 7.32492i −0.158713 + 0.274899i
\(711\) 5.72905 9.92300i 0.214856 0.372141i
\(712\) −3.40823 5.90323i −0.127729 0.221233i
\(713\) −3.35837 −0.125772
\(714\) 0.456783 + 16.2955i 0.0170947 + 0.609845i
\(715\) 3.11300 0.116420
\(716\) −7.48901 12.9713i −0.279877 0.484762i
\(717\) −8.00000 + 13.8564i −0.298765 + 0.517477i
\(718\) −14.0133 + 24.2717i −0.522971 + 0.905813i
\(719\) 7.63728 + 13.2282i 0.284822 + 0.493327i 0.972566 0.232627i \(-0.0747320\pi\)
−0.687744 + 0.725954i \(0.741399\pi\)
\(720\) 1.00000 0.0372678
\(721\) 8.47572 + 4.58173i 0.315652 + 0.170632i
\(722\) −11.3231 −0.421402
\(723\) 8.28424 + 14.3487i 0.308094 + 0.533635i
\(724\) 0.851731 1.47524i 0.0316543 0.0548269i
\(725\) 8.29654 14.3700i 0.308126 0.533689i
\(726\) −1.17919 2.04241i −0.0437637 0.0758010i
\(727\) −2.51534 −0.0932889 −0.0466444 0.998912i \(-0.514853\pi\)
−0.0466444 + 0.998912i \(0.514853\pi\)
\(728\) −1.91922 + 1.18098i −0.0711312 + 0.0437698i
\(729\) 1.00000 0.0370370
\(730\) 0.672545 + 1.16488i 0.0248920 + 0.0431142i
\(731\) 22.5199 39.0057i 0.832930 1.44268i
\(732\) 5.00000 8.66025i 0.184805 0.320092i
\(733\) −22.4348 38.8582i −0.828648 1.43526i −0.899099 0.437746i \(-0.855777\pi\)
0.0704507 0.997515i \(-0.477556\pi\)
\(734\) 7.78990 0.287530
\(735\) −3.15491 + 6.24872i −0.116371 + 0.230488i
\(736\) 1.00000 0.0368605
\(737\) −18.9295 32.7868i −0.697276 1.20772i
\(738\) −1.24668 + 2.15931i −0.0458909 + 0.0794854i
\(739\) −17.4847 + 30.2843i −0.643184 + 1.11403i 0.341534 + 0.939869i \(0.389053\pi\)
−0.984718 + 0.174157i \(0.944280\pi\)
\(740\) −3.40823 5.90323i −0.125289 0.217007i
\(741\) 4.69018 0.172298
\(742\) 14.2181 8.74894i 0.521961 0.321184i
\(743\) −39.4627 −1.44775 −0.723873 0.689934i \(-0.757640\pi\)
−0.723873 + 0.689934i \(0.757640\pi\)
\(744\) −1.67919 2.90844i −0.0615620 0.106628i
\(745\) 9.98237 17.2900i 0.365726 0.633455i
\(746\) 6.35837 11.0130i 0.232797 0.403216i
\(747\) 3.82746 + 6.62935i 0.140039 + 0.242555i
\(748\) 22.5199 0.823410
\(749\) −14.7679 7.98310i −0.539608 0.291696i
\(750\) −9.00000 −0.328634
\(751\) −9.53222 16.5103i −0.347836 0.602469i 0.638029 0.770012i \(-0.279750\pi\)
−0.985865 + 0.167543i \(0.946417\pi\)
\(752\) −1.17919 + 2.04241i −0.0430005 + 0.0744791i
\(753\) 15.1373 26.2185i 0.551633 0.955456i
\(754\) −1.76660 3.05985i −0.0643360 0.111433i
\(755\) 2.34509 0.0853465
\(756\) 0.0741344 + 2.64471i 0.00269624 + 0.0961873i
\(757\) 13.2101 0.480129 0.240065 0.970757i \(-0.422831\pi\)
0.240065 + 0.970757i \(0.422831\pi\)
\(758\) −11.1306 19.2788i −0.404283 0.700238i
\(759\) 1.82746 3.16525i 0.0663324 0.114891i
\(760\) 2.75332 4.76889i 0.0998734 0.172986i
\(761\) −25.1761 43.6064i −0.912635 1.58073i −0.810328 0.585976i \(-0.800711\pi\)
−0.102306 0.994753i \(-0.532622\pi\)
\(762\) −8.34509 −0.302311
\(763\) −0.245372 8.75353i −0.00888305 0.316899i
\(764\) −22.8430 −0.826432
\(765\) 3.08078 + 5.33606i 0.111386 + 0.192926i
\(766\) −11.1117 + 19.2460i −0.401482 + 0.695387i
\(767\) 1.34640 2.33203i 0.0486156 0.0842046i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 42.4008 1.52901 0.764507 0.644616i \(-0.222983\pi\)
0.764507 + 0.644616i \(0.222983\pi\)
\(770\) 8.50664 + 4.59844i 0.306558 + 0.165716i</