Properties

Label 154.2.e.e.23.1
Level $154$
Weight $2$
Character 154.23
Analytic conductor $1.230$
Analytic rank $0$
Dimension $4$
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] = [154,2,Mod(23,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 23.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 154.23
Dual form 154.2.e.e.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.207107 - 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.70711 - 2.95680i) q^{5} +0.414214 q^{6} +(-2.62132 - 0.358719i) q^{7} +1.00000 q^{8} +(1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.207107 - 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.70711 - 2.95680i) q^{5} +0.414214 q^{6} +(-2.62132 - 0.358719i) q^{7} +1.00000 q^{8} +(1.41421 - 2.44949i) q^{9} +(1.70711 + 2.95680i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.207107 + 0.358719i) q^{12} +1.82843 q^{13} +(1.62132 - 2.09077i) q^{14} -1.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.82843 + 6.63103i) q^{17} +(1.41421 + 2.44949i) q^{18} +(1.70711 - 2.95680i) q^{19} -3.41421 q^{20} +(0.414214 + 1.01461i) q^{21} +1.00000 q^{22} +(-1.12132 + 1.94218i) q^{23} +(-0.207107 - 0.358719i) q^{24} +(-3.32843 - 5.76500i) q^{25} +(-0.914214 + 1.58346i) q^{26} -2.41421 q^{27} +(1.00000 + 2.44949i) q^{28} -8.65685 q^{29} +(0.707107 - 1.22474i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.207107 + 0.358719i) q^{33} -7.65685 q^{34} +(-5.53553 + 7.13834i) q^{35} -2.82843 q^{36} +(3.29289 - 5.70346i) q^{37} +(1.70711 + 2.95680i) q^{38} +(-0.378680 - 0.655892i) q^{39} +(1.70711 - 2.95680i) q^{40} -2.58579 q^{41} +(-1.08579 - 0.148586i) q^{42} +5.65685 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-4.82843 - 8.36308i) q^{45} +(-1.12132 - 1.94218i) q^{46} +(-3.24264 + 5.61642i) q^{47} +0.414214 q^{48} +(6.74264 + 1.88064i) q^{49} +6.65685 q^{50} +(1.58579 - 2.74666i) q^{51} +(-0.914214 - 1.58346i) q^{52} +(5.94975 + 10.3053i) q^{53} +(1.20711 - 2.09077i) q^{54} -3.41421 q^{55} +(-2.62132 - 0.358719i) q^{56} -1.41421 q^{57} +(4.32843 - 7.49706i) q^{58} +(4.20711 + 7.28692i) q^{59} +(0.707107 + 1.22474i) q^{60} +(-3.08579 + 5.34474i) q^{61} -4.00000 q^{62} +(-4.58579 + 5.91359i) q^{63} +1.00000 q^{64} +(3.12132 - 5.40629i) q^{65} +(-0.207107 - 0.358719i) q^{66} +(-5.62132 - 9.73641i) q^{67} +(3.82843 - 6.63103i) q^{68} +0.928932 q^{69} +(-3.41421 - 8.36308i) q^{70} +3.07107 q^{71} +(1.41421 - 2.44949i) q^{72} +(3.29289 + 5.70346i) q^{73} +(3.29289 + 5.70346i) q^{74} +(-1.37868 + 2.38794i) q^{75} -3.41421 q^{76} +(1.00000 + 2.44949i) q^{77} +0.757359 q^{78} +(2.37868 - 4.11999i) q^{79} +(1.70711 + 2.95680i) q^{80} +(-3.74264 - 6.48244i) q^{81} +(1.29289 - 2.23936i) q^{82} +16.1421 q^{83} +(0.671573 - 0.866025i) q^{84} +26.1421 q^{85} +(-2.82843 + 4.89898i) q^{86} +(1.79289 + 3.10538i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(2.24264 - 3.88437i) q^{89} +9.65685 q^{90} +(-4.79289 - 0.655892i) q^{91} +2.24264 q^{92} +(0.828427 - 1.43488i) q^{93} +(-3.24264 - 5.61642i) q^{94} +(-5.82843 - 10.0951i) q^{95} +(-0.207107 + 0.358719i) q^{96} +1.82843 q^{97} +(-5.00000 + 4.89898i) q^{98} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 2 q^{14} - 2 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 4 q^{27} + 4 q^{28} - 12 q^{29} + 8 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} - 8 q^{35} + 16 q^{37} + 4 q^{38} - 10 q^{39} + 4 q^{40} - 16 q^{41} - 10 q^{42} - 2 q^{44} - 8 q^{45} + 4 q^{46} + 4 q^{47} - 4 q^{48} + 10 q^{49} + 4 q^{50} + 12 q^{51} + 2 q^{52} + 4 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} + 6 q^{58} + 14 q^{59} - 18 q^{61} - 16 q^{62} - 24 q^{63} + 4 q^{64} + 4 q^{65} + 2 q^{66} - 14 q^{67} + 4 q^{68} + 32 q^{69} - 8 q^{70} - 16 q^{71} + 16 q^{73} + 16 q^{74} - 14 q^{75} - 8 q^{76} + 4 q^{77} + 20 q^{78} + 18 q^{79} + 4 q^{80} + 2 q^{81} + 8 q^{82} + 8 q^{83} + 14 q^{84} + 48 q^{85} + 10 q^{87} - 2 q^{88} - 8 q^{89} + 16 q^{90} - 22 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} - 12 q^{95} + 2 q^{96} - 4 q^{97} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.207107 0.358719i −0.119573 0.207107i 0.800025 0.599966i \(-0.204819\pi\)
−0.919599 + 0.392859i \(0.871486\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.70711 2.95680i 0.763441 1.32232i −0.177625 0.984098i \(-0.556842\pi\)
0.941067 0.338221i \(-0.109825\pi\)
\(6\) 0.414214 0.169102
\(7\) −2.62132 0.358719i −0.990766 0.135583i
\(8\) 1.00000 0.353553
\(9\) 1.41421 2.44949i 0.471405 0.816497i
\(10\) 1.70711 + 2.95680i 0.539835 + 0.935021i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −0.207107 + 0.358719i −0.0597866 + 0.103553i
\(13\) 1.82843 0.507114 0.253557 0.967320i \(-0.418399\pi\)
0.253557 + 0.967320i \(0.418399\pi\)
\(14\) 1.62132 2.09077i 0.433316 0.558782i
\(15\) −1.41421 −0.365148
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.82843 + 6.63103i 0.928530 + 1.60826i 0.785783 + 0.618502i \(0.212260\pi\)
0.142747 + 0.989759i \(0.454407\pi\)
\(18\) 1.41421 + 2.44949i 0.333333 + 0.577350i
\(19\) 1.70711 2.95680i 0.391637 0.678335i −0.601028 0.799228i \(-0.705242\pi\)
0.992666 + 0.120892i \(0.0385755\pi\)
\(20\) −3.41421 −0.763441
\(21\) 0.414214 + 1.01461i 0.0903888 + 0.221406i
\(22\) 1.00000 0.213201
\(23\) −1.12132 + 1.94218i −0.233811 + 0.404973i −0.958927 0.283654i \(-0.908453\pi\)
0.725115 + 0.688628i \(0.241787\pi\)
\(24\) −0.207107 0.358719i −0.0422755 0.0732233i
\(25\) −3.32843 5.76500i −0.665685 1.15300i
\(26\) −0.914214 + 1.58346i −0.179292 + 0.310543i
\(27\) −2.41421 −0.464616
\(28\) 1.00000 + 2.44949i 0.188982 + 0.462910i
\(29\) −8.65685 −1.60754 −0.803769 0.594942i \(-0.797175\pi\)
−0.803769 + 0.594942i \(0.797175\pi\)
\(30\) 0.707107 1.22474i 0.129099 0.223607i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.207107 + 0.358719i −0.0360527 + 0.0624450i
\(34\) −7.65685 −1.31314
\(35\) −5.53553 + 7.13834i −0.935676 + 1.20660i
\(36\) −2.82843 −0.471405
\(37\) 3.29289 5.70346i 0.541348 0.937643i −0.457479 0.889221i \(-0.651247\pi\)
0.998827 0.0484222i \(-0.0154193\pi\)
\(38\) 1.70711 + 2.95680i 0.276929 + 0.479656i
\(39\) −0.378680 0.655892i −0.0606373 0.105027i
\(40\) 1.70711 2.95680i 0.269917 0.467510i
\(41\) −2.58579 −0.403832 −0.201916 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(42\) −1.08579 0.148586i −0.167540 0.0229274i
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) −4.82843 8.36308i −0.719779 1.24669i
\(46\) −1.12132 1.94218i −0.165330 0.286359i
\(47\) −3.24264 + 5.61642i −0.472988 + 0.819239i −0.999522 0.0309151i \(-0.990158\pi\)
0.526534 + 0.850154i \(0.323491\pi\)
\(48\) 0.414214 0.0597866
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) 6.65685 0.941421
\(51\) 1.58579 2.74666i 0.222055 0.384610i
\(52\) −0.914214 1.58346i −0.126779 0.219587i
\(53\) 5.94975 + 10.3053i 0.817261 + 1.41554i 0.907693 + 0.419634i \(0.137842\pi\)
−0.0904325 + 0.995903i \(0.528825\pi\)
\(54\) 1.20711 2.09077i 0.164266 0.284518i
\(55\) −3.41421 −0.460372
\(56\) −2.62132 0.358719i −0.350289 0.0479359i
\(57\) −1.41421 −0.187317
\(58\) 4.32843 7.49706i 0.568350 0.984412i
\(59\) 4.20711 + 7.28692i 0.547719 + 0.948677i 0.998430 + 0.0560070i \(0.0178369\pi\)
−0.450712 + 0.892670i \(0.648830\pi\)
\(60\) 0.707107 + 1.22474i 0.0912871 + 0.158114i
\(61\) −3.08579 + 5.34474i −0.395094 + 0.684324i −0.993113 0.117158i \(-0.962621\pi\)
0.598019 + 0.801482i \(0.295955\pi\)
\(62\) −4.00000 −0.508001
\(63\) −4.58579 + 5.91359i −0.577755 + 0.745042i
\(64\) 1.00000 0.125000
\(65\) 3.12132 5.40629i 0.387152 0.670567i
\(66\) −0.207107 0.358719i −0.0254931 0.0441553i
\(67\) −5.62132 9.73641i −0.686754 1.18949i −0.972882 0.231301i \(-0.925702\pi\)
0.286129 0.958191i \(-0.407632\pi\)
\(68\) 3.82843 6.63103i 0.464265 0.804131i
\(69\) 0.928932 0.111830
\(70\) −3.41421 8.36308i −0.408077 0.999579i
\(71\) 3.07107 0.364469 0.182234 0.983255i \(-0.441667\pi\)
0.182234 + 0.983255i \(0.441667\pi\)
\(72\) 1.41421 2.44949i 0.166667 0.288675i
\(73\) 3.29289 + 5.70346i 0.385404 + 0.667539i 0.991825 0.127604i \(-0.0407288\pi\)
−0.606421 + 0.795144i \(0.707395\pi\)
\(74\) 3.29289 + 5.70346i 0.382791 + 0.663014i
\(75\) −1.37868 + 2.38794i −0.159196 + 0.275736i
\(76\) −3.41421 −0.391637
\(77\) 1.00000 + 2.44949i 0.113961 + 0.279145i
\(78\) 0.757359 0.0857541
\(79\) 2.37868 4.11999i 0.267622 0.463536i −0.700625 0.713530i \(-0.747095\pi\)
0.968247 + 0.249994i \(0.0804287\pi\)
\(80\) 1.70711 + 2.95680i 0.190860 + 0.330580i
\(81\) −3.74264 6.48244i −0.415849 0.720272i
\(82\) 1.29289 2.23936i 0.142776 0.247296i
\(83\) 16.1421 1.77183 0.885915 0.463848i \(-0.153532\pi\)
0.885915 + 0.463848i \(0.153532\pi\)
\(84\) 0.671573 0.866025i 0.0732746 0.0944911i
\(85\) 26.1421 2.83551
\(86\) −2.82843 + 4.89898i −0.304997 + 0.528271i
\(87\) 1.79289 + 3.10538i 0.192218 + 0.332932i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 2.24264 3.88437i 0.237719 0.411742i −0.722340 0.691538i \(-0.756933\pi\)
0.960060 + 0.279796i \(0.0902668\pi\)
\(90\) 9.65685 1.01792
\(91\) −4.79289 0.655892i −0.502432 0.0687562i
\(92\) 2.24264 0.233811
\(93\) 0.828427 1.43488i 0.0859039 0.148790i
\(94\) −3.24264 5.61642i −0.334453 0.579289i
\(95\) −5.82843 10.0951i −0.597984 1.03574i
\(96\) −0.207107 + 0.358719i −0.0211377 + 0.0366117i
\(97\) 1.82843 0.185649 0.0928243 0.995683i \(-0.470411\pi\)
0.0928243 + 0.995683i \(0.470411\pi\)
\(98\) −5.00000 + 4.89898i −0.505076 + 0.494872i
\(99\) −2.82843 −0.284268
\(100\) −3.32843 + 5.76500i −0.332843 + 0.576500i
\(101\) −5.91421 10.2437i −0.588486 1.01929i −0.994431 0.105390i \(-0.966391\pi\)
0.405945 0.913898i \(-0.366943\pi\)
\(102\) 1.58579 + 2.74666i 0.157016 + 0.271960i
\(103\) −5.29289 + 9.16756i −0.521524 + 0.903307i 0.478162 + 0.878271i \(0.341303\pi\)
−0.999687 + 0.0250350i \(0.992030\pi\)
\(104\) 1.82843 0.179292
\(105\) 3.70711 + 0.507306i 0.361777 + 0.0495080i
\(106\) −11.8995 −1.15578
\(107\) −5.53553 + 9.58783i −0.535140 + 0.926890i 0.464016 + 0.885827i \(0.346408\pi\)
−0.999157 + 0.0410635i \(0.986925\pi\)
\(108\) 1.20711 + 2.09077i 0.116154 + 0.201184i
\(109\) 0.242641 + 0.420266i 0.0232408 + 0.0402542i 0.877412 0.479738i \(-0.159268\pi\)
−0.854171 + 0.519992i \(0.825935\pi\)
\(110\) 1.70711 2.95680i 0.162766 0.281919i
\(111\) −2.72792 −0.258923
\(112\) 1.62132 2.09077i 0.153200 0.197559i
\(113\) −13.8284 −1.30087 −0.650434 0.759562i \(-0.725413\pi\)
−0.650434 + 0.759562i \(0.725413\pi\)
\(114\) 0.707107 1.22474i 0.0662266 0.114708i
\(115\) 3.82843 + 6.63103i 0.357003 + 0.618347i
\(116\) 4.32843 + 7.49706i 0.401884 + 0.696084i
\(117\) 2.58579 4.47871i 0.239056 0.414057i
\(118\) −8.41421 −0.774591
\(119\) −7.65685 18.7554i −0.701903 1.71930i
\(120\) −1.41421 −0.129099
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −3.08579 5.34474i −0.279374 0.483890i
\(123\) 0.535534 + 0.927572i 0.0482875 + 0.0836363i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −5.65685 −0.505964
\(126\) −2.82843 6.92820i −0.251976 0.617213i
\(127\) −9.72792 −0.863213 −0.431607 0.902062i \(-0.642053\pi\)
−0.431607 + 0.902062i \(0.642053\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.17157 2.02922i −0.103151 0.178663i
\(130\) 3.12132 + 5.40629i 0.273758 + 0.474163i
\(131\) 1.70711 2.95680i 0.149151 0.258336i −0.781763 0.623575i \(-0.785679\pi\)
0.930914 + 0.365239i \(0.119013\pi\)
\(132\) 0.414214 0.0360527
\(133\) −5.53553 + 7.13834i −0.479992 + 0.618972i
\(134\) 11.2426 0.971216
\(135\) −4.12132 + 7.13834i −0.354707 + 0.614370i
\(136\) 3.82843 + 6.63103i 0.328285 + 0.568606i
\(137\) 2.67157 + 4.62730i 0.228248 + 0.395337i 0.957289 0.289133i \(-0.0933670\pi\)
−0.729041 + 0.684470i \(0.760034\pi\)
\(138\) −0.464466 + 0.804479i −0.0395380 + 0.0684818i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 8.94975 + 1.22474i 0.756392 + 0.103510i
\(141\) 2.68629 0.226227
\(142\) −1.53553 + 2.65962i −0.128859 + 0.223191i
\(143\) −0.914214 1.58346i −0.0764504 0.132416i
\(144\) 1.41421 + 2.44949i 0.117851 + 0.204124i
\(145\) −14.7782 + 25.5965i −1.22726 + 2.12568i
\(146\) −6.58579 −0.545044
\(147\) −0.721825 2.80821i −0.0595352 0.231617i
\(148\) −6.58579 −0.541348
\(149\) −3.17157 + 5.49333i −0.259825 + 0.450031i −0.966195 0.257812i \(-0.916998\pi\)
0.706370 + 0.707843i \(0.250332\pi\)
\(150\) −1.37868 2.38794i −0.112569 0.194975i
\(151\) −4.86396 8.42463i −0.395824 0.685586i 0.597382 0.801957i \(-0.296207\pi\)
−0.993206 + 0.116370i \(0.962874\pi\)
\(152\) 1.70711 2.95680i 0.138465 0.239828i
\(153\) 21.6569 1.75085
\(154\) −2.62132 0.358719i −0.211232 0.0289064i
\(155\) 13.6569 1.09694
\(156\) −0.378680 + 0.655892i −0.0303186 + 0.0525134i
\(157\) −3.17157 5.49333i −0.253119 0.438415i 0.711264 0.702925i \(-0.248123\pi\)
−0.964383 + 0.264510i \(0.914790\pi\)
\(158\) 2.37868 + 4.11999i 0.189238 + 0.327769i
\(159\) 2.46447 4.26858i 0.195445 0.338520i
\(160\) −3.41421 −0.269917
\(161\) 3.63604 4.68885i 0.286560 0.369533i
\(162\) 7.48528 0.588099
\(163\) 7.86396 13.6208i 0.615953 1.06686i −0.374264 0.927322i \(-0.622104\pi\)
0.990217 0.139539i \(-0.0445622\pi\)
\(164\) 1.29289 + 2.23936i 0.100958 + 0.174864i
\(165\) 0.707107 + 1.22474i 0.0550482 + 0.0953463i
\(166\) −8.07107 + 13.9795i −0.626436 + 1.08502i
\(167\) −11.7279 −0.907534 −0.453767 0.891120i \(-0.649920\pi\)
−0.453767 + 0.891120i \(0.649920\pi\)
\(168\) 0.414214 + 1.01461i 0.0319573 + 0.0782790i
\(169\) −9.65685 −0.742835
\(170\) −13.0711 + 22.6398i −1.00251 + 1.73639i
\(171\) −4.82843 8.36308i −0.369239 0.639541i
\(172\) −2.82843 4.89898i −0.215666 0.373544i
\(173\) 2.08579 3.61269i 0.158579 0.274668i −0.775777 0.631007i \(-0.782642\pi\)
0.934357 + 0.356339i \(0.115975\pi\)
\(174\) −3.58579 −0.271838
\(175\) 6.65685 + 16.3059i 0.503211 + 1.23261i
\(176\) 1.00000 0.0753778
\(177\) 1.74264 3.01834i 0.130985 0.226872i
\(178\) 2.24264 + 3.88437i 0.168093 + 0.291146i
\(179\) 9.44975 + 16.3674i 0.706307 + 1.22336i 0.966218 + 0.257727i \(0.0829736\pi\)
−0.259910 + 0.965633i \(0.583693\pi\)
\(180\) −4.82843 + 8.36308i −0.359890 + 0.623347i
\(181\) 3.65685 0.271812 0.135906 0.990722i \(-0.456606\pi\)
0.135906 + 0.990722i \(0.456606\pi\)
\(182\) 2.96447 3.82282i 0.219741 0.283366i
\(183\) 2.55635 0.188971
\(184\) −1.12132 + 1.94218i −0.0826648 + 0.143180i
\(185\) −11.2426 19.4728i −0.826575 1.43167i
\(186\) 0.828427 + 1.43488i 0.0607432 + 0.105210i
\(187\) 3.82843 6.63103i 0.279962 0.484909i
\(188\) 6.48528 0.472988
\(189\) 6.32843 + 0.866025i 0.460325 + 0.0629941i
\(190\) 11.6569 0.845677
\(191\) 6.41421 11.1097i 0.464116 0.803873i −0.535045 0.844824i \(-0.679705\pi\)
0.999161 + 0.0409507i \(0.0130387\pi\)
\(192\) −0.207107 0.358719i −0.0149466 0.0258883i
\(193\) −1.05025 1.81909i −0.0755988 0.130941i 0.825748 0.564040i \(-0.190754\pi\)
−0.901347 + 0.433099i \(0.857420\pi\)
\(194\) −0.914214 + 1.58346i −0.0656367 + 0.113686i
\(195\) −2.58579 −0.185172
\(196\) −1.74264 6.77962i −0.124474 0.484258i
\(197\) −17.4853 −1.24577 −0.622887 0.782312i \(-0.714041\pi\)
−0.622887 + 0.782312i \(0.714041\pi\)
\(198\) 1.41421 2.44949i 0.100504 0.174078i
\(199\) −9.94975 17.2335i −0.705319 1.22165i −0.966576 0.256379i \(-0.917470\pi\)
0.261257 0.965269i \(-0.415863\pi\)
\(200\) −3.32843 5.76500i −0.235355 0.407647i
\(201\) −2.32843 + 4.03295i −0.164235 + 0.284463i
\(202\) 11.8284 0.832245
\(203\) 22.6924 + 3.10538i 1.59269 + 0.217955i
\(204\) −3.17157 −0.222055
\(205\) −4.41421 + 7.64564i −0.308302 + 0.533995i
\(206\) −5.29289 9.16756i −0.368773 0.638734i
\(207\) 3.17157 + 5.49333i 0.220440 + 0.381813i
\(208\) −0.914214 + 1.58346i −0.0633893 + 0.109793i
\(209\) −3.41421 −0.236166
\(210\) −2.29289 + 2.95680i −0.158225 + 0.204038i
\(211\) 4.58579 0.315699 0.157849 0.987463i \(-0.449544\pi\)
0.157849 + 0.987463i \(0.449544\pi\)
\(212\) 5.94975 10.3053i 0.408630 0.707768i
\(213\) −0.636039 1.10165i −0.0435807 0.0754839i
\(214\) −5.53553 9.58783i −0.378401 0.655410i
\(215\) 9.65685 16.7262i 0.658592 1.14071i
\(216\) −2.41421 −0.164266
\(217\) −4.00000 9.79796i −0.271538 0.665129i
\(218\) −0.485281 −0.0328674
\(219\) 1.36396 2.36245i 0.0921679 0.159640i
\(220\) 1.70711 + 2.95680i 0.115093 + 0.199347i
\(221\) 7.00000 + 12.1244i 0.470871 + 0.815572i
\(222\) 1.36396 2.36245i 0.0915431 0.158557i
\(223\) 11.4142 0.764352 0.382176 0.924089i \(-0.375175\pi\)
0.382176 + 0.924089i \(0.375175\pi\)
\(224\) 1.00000 + 2.44949i 0.0668153 + 0.163663i
\(225\) −18.8284 −1.25523
\(226\) 6.91421 11.9758i 0.459927 0.796616i
\(227\) 11.5858 + 20.0672i 0.768976 + 1.33190i 0.938119 + 0.346313i \(0.112567\pi\)
−0.169143 + 0.985591i \(0.554100\pi\)
\(228\) 0.707107 + 1.22474i 0.0468293 + 0.0811107i
\(229\) −0.343146 + 0.594346i −0.0226757 + 0.0392755i −0.877141 0.480234i \(-0.840552\pi\)
0.854465 + 0.519509i \(0.173885\pi\)
\(230\) −7.65685 −0.504878
\(231\) 0.671573 0.866025i 0.0441863 0.0569803i
\(232\) −8.65685 −0.568350
\(233\) 0.707107 1.22474i 0.0463241 0.0802357i −0.841934 0.539581i \(-0.818583\pi\)
0.888258 + 0.459345i \(0.151916\pi\)
\(234\) 2.58579 + 4.47871i 0.169038 + 0.292783i
\(235\) 11.0711 + 19.1757i 0.722197 + 1.25088i
\(236\) 4.20711 7.28692i 0.273859 0.474338i
\(237\) −1.97056 −0.128002
\(238\) 20.0711 + 2.74666i 1.30101 + 0.178040i
\(239\) −22.2132 −1.43685 −0.718426 0.695603i \(-0.755137\pi\)
−0.718426 + 0.695603i \(0.755137\pi\)
\(240\) 0.707107 1.22474i 0.0456435 0.0790569i
\(241\) −1.87868 3.25397i −0.121016 0.209607i 0.799152 0.601129i \(-0.205282\pi\)
−0.920169 + 0.391522i \(0.871949\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) −5.17157 + 8.95743i −0.331757 + 0.574619i
\(244\) 6.17157 0.395094
\(245\) 17.0711 16.7262i 1.09063 1.06860i
\(246\) −1.07107 −0.0682888
\(247\) 3.12132 5.40629i 0.198605 0.343994i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) −3.34315 5.79050i −0.211863 0.366958i
\(250\) 2.82843 4.89898i 0.178885 0.309839i
\(251\) 2.14214 0.135210 0.0676052 0.997712i \(-0.478464\pi\)
0.0676052 + 0.997712i \(0.478464\pi\)
\(252\) 7.41421 + 1.01461i 0.467052 + 0.0639145i
\(253\) 2.24264 0.140994
\(254\) 4.86396 8.42463i 0.305192 0.528608i
\(255\) −5.41421 9.37769i −0.339051 0.587254i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.57107 + 2.72117i −0.0980005 + 0.169742i −0.910857 0.412722i \(-0.864578\pi\)
0.812856 + 0.582464i \(0.197911\pi\)
\(258\) 2.34315 0.145878
\(259\) −10.6777 + 13.7694i −0.663478 + 0.855587i
\(260\) −6.24264 −0.387152
\(261\) −12.2426 + 21.2049i −0.757800 + 1.31255i
\(262\) 1.70711 + 2.95680i 0.105465 + 0.182671i
\(263\) −15.5208 26.8828i −0.957054 1.65767i −0.729595 0.683879i \(-0.760291\pi\)
−0.227459 0.973788i \(-0.573042\pi\)
\(264\) −0.207107 + 0.358719i −0.0127465 + 0.0220777i
\(265\) 40.6274 2.49572
\(266\) −3.41421 8.36308i −0.209339 0.512773i
\(267\) −1.85786 −0.113699
\(268\) −5.62132 + 9.73641i −0.343377 + 0.594746i
\(269\) −6.82843 11.8272i −0.416337 0.721116i 0.579231 0.815163i \(-0.303353\pi\)
−0.995568 + 0.0940473i \(0.970020\pi\)
\(270\) −4.12132 7.13834i −0.250816 0.434425i
\(271\) 13.2782 22.9985i 0.806592 1.39706i −0.108620 0.994083i \(-0.534643\pi\)
0.915211 0.402974i \(-0.132024\pi\)
\(272\) −7.65685 −0.464265
\(273\) 0.757359 + 1.85514i 0.0458375 + 0.112278i
\(274\) −5.34315 −0.322791
\(275\) −3.32843 + 5.76500i −0.200712 + 0.347643i
\(276\) −0.464466 0.804479i −0.0279576 0.0484239i
\(277\) 1.91421 + 3.31552i 0.115014 + 0.199210i 0.917785 0.397077i \(-0.129975\pi\)
−0.802771 + 0.596287i \(0.796642\pi\)
\(278\) 0 0
\(279\) 11.3137 0.677334
\(280\) −5.53553 + 7.13834i −0.330811 + 0.426597i
\(281\) −16.7279 −0.997904 −0.498952 0.866630i \(-0.666282\pi\)
−0.498952 + 0.866630i \(0.666282\pi\)
\(282\) −1.34315 + 2.32640i −0.0799832 + 0.138535i
\(283\) 10.2929 + 17.8278i 0.611849 + 1.05975i 0.990929 + 0.134389i \(0.0429073\pi\)
−0.379080 + 0.925364i \(0.623759\pi\)
\(284\) −1.53553 2.65962i −0.0911172 0.157820i
\(285\) −2.41421 + 4.18154i −0.143006 + 0.247693i
\(286\) 1.82843 0.108117
\(287\) 6.77817 + 0.927572i 0.400103 + 0.0547528i
\(288\) −2.82843 −0.166667
\(289\) −20.8137 + 36.0504i −1.22434 + 2.12061i
\(290\) −14.7782 25.5965i −0.867804 1.50308i
\(291\) −0.378680 0.655892i −0.0221986 0.0384491i
\(292\) 3.29289 5.70346i 0.192702 0.333770i
\(293\) −5.17157 −0.302127 −0.151063 0.988524i \(-0.548270\pi\)
−0.151063 + 0.988524i \(0.548270\pi\)
\(294\) 2.79289 + 0.778985i 0.162885 + 0.0454314i
\(295\) 28.7279 1.67260
\(296\) 3.29289 5.70346i 0.191396 0.331507i
\(297\) 1.20711 + 2.09077i 0.0700434 + 0.121319i
\(298\) −3.17157 5.49333i −0.183724 0.318220i
\(299\) −2.05025 + 3.55114i −0.118569 + 0.205368i
\(300\) 2.75736 0.159196
\(301\) −14.8284 2.02922i −0.854696 0.116963i
\(302\) 9.72792 0.559779
\(303\) −2.44975 + 4.24309i −0.140734 + 0.243759i
\(304\) 1.70711 + 2.95680i 0.0979093 + 0.169584i
\(305\) 10.5355 + 18.2481i 0.603263 + 1.04488i
\(306\) −10.8284 + 18.7554i −0.619020 + 1.07217i
\(307\) −9.89949 −0.564994 −0.282497 0.959268i \(-0.591163\pi\)
−0.282497 + 0.959268i \(0.591163\pi\)
\(308\) 1.62132 2.09077i 0.0923833 0.119133i
\(309\) 4.38478 0.249441
\(310\) −6.82843 + 11.8272i −0.387829 + 0.671739i
\(311\) 4.36396 + 7.55860i 0.247458 + 0.428609i 0.962820 0.270145i \(-0.0870716\pi\)
−0.715362 + 0.698754i \(0.753738\pi\)
\(312\) −0.378680 0.655892i −0.0214385 0.0371326i
\(313\) 4.67157 8.09140i 0.264053 0.457353i −0.703262 0.710931i \(-0.748274\pi\)
0.967315 + 0.253578i \(0.0816073\pi\)
\(314\) 6.34315 0.357964
\(315\) 9.65685 + 23.6544i 0.544102 + 1.33277i
\(316\) −4.75736 −0.267622
\(317\) −15.6569 + 27.1185i −0.879377 + 1.52312i −0.0273502 + 0.999626i \(0.508707\pi\)
−0.852026 + 0.523499i \(0.824626\pi\)
\(318\) 2.46447 + 4.26858i 0.138200 + 0.239370i
\(319\) 4.32843 + 7.49706i 0.242345 + 0.419755i
\(320\) 1.70711 2.95680i 0.0954302 0.165290i
\(321\) 4.58579 0.255954
\(322\) 2.24264 + 5.49333i 0.124977 + 0.306131i
\(323\) 26.1421 1.45459
\(324\) −3.74264 + 6.48244i −0.207924 + 0.360136i
\(325\) −6.08579 10.5409i −0.337579 0.584703i
\(326\) 7.86396 + 13.6208i 0.435545 + 0.754385i
\(327\) 0.100505 0.174080i 0.00555794 0.00962664i
\(328\) −2.58579 −0.142776
\(329\) 10.5147 13.5592i 0.579695 0.747545i
\(330\) −1.41421 −0.0778499
\(331\) 4.96447 8.59871i 0.272872 0.472628i −0.696724 0.717339i \(-0.745360\pi\)
0.969596 + 0.244711i \(0.0786932\pi\)
\(332\) −8.07107 13.9795i −0.442957 0.767225i
\(333\) −9.31371 16.1318i −0.510388 0.884018i
\(334\) 5.86396 10.1567i 0.320862 0.555749i
\(335\) −38.3848 −2.09718
\(336\) −1.08579 0.148586i −0.0592345 0.00810606i
\(337\) −19.7574 −1.07625 −0.538126 0.842864i \(-0.680868\pi\)
−0.538126 + 0.842864i \(0.680868\pi\)
\(338\) 4.82843 8.36308i 0.262632 0.454892i
\(339\) 2.86396 + 4.96053i 0.155549 + 0.269419i
\(340\) −13.0711 22.6398i −0.708878 1.22781i
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) 9.65685 0.522183
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 5.65685 0.304997
\(345\) 1.58579 2.74666i 0.0853759 0.147875i
\(346\) 2.08579 + 3.61269i 0.112133 + 0.194219i
\(347\) −7.29289 12.6317i −0.391503 0.678103i 0.601145 0.799140i \(-0.294711\pi\)
−0.992648 + 0.121037i \(0.961378\pi\)
\(348\) 1.79289 3.10538i 0.0961092 0.166466i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −17.4497 2.38794i −0.932728 0.127641i
\(351\) −4.41421 −0.235613
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 12.6569 + 21.9223i 0.673656 + 1.16681i 0.976860 + 0.213881i \(0.0686105\pi\)
−0.303203 + 0.952926i \(0.598056\pi\)
\(354\) 1.74264 + 3.01834i 0.0926203 + 0.160423i
\(355\) 5.24264 9.08052i 0.278250 0.481944i
\(356\) −4.48528 −0.237719
\(357\) −5.14214 + 6.63103i −0.272151 + 0.350951i
\(358\) −18.8995 −0.998869
\(359\) −5.37868 + 9.31615i −0.283876 + 0.491687i −0.972336 0.233587i \(-0.924954\pi\)
0.688460 + 0.725274i \(0.258287\pi\)
\(360\) −4.82843 8.36308i −0.254480 0.440773i
\(361\) 3.67157 + 6.35935i 0.193241 + 0.334703i
\(362\) −1.82843 + 3.16693i −0.0961000 + 0.166450i
\(363\) 0.414214 0.0217406
\(364\) 1.82843 + 4.47871i 0.0958356 + 0.234748i
\(365\) 22.4853 1.17693
\(366\) −1.27817 + 2.21386i −0.0668113 + 0.115720i
\(367\) −7.36396 12.7548i −0.384396 0.665793i 0.607290 0.794481i \(-0.292257\pi\)
−0.991685 + 0.128688i \(0.958923\pi\)
\(368\) −1.12132 1.94218i −0.0584529 0.101243i
\(369\) −3.65685 + 6.33386i −0.190368 + 0.329727i
\(370\) 22.4853 1.16895
\(371\) −11.8995 29.1477i −0.617791 1.51327i
\(372\) −1.65685 −0.0859039
\(373\) −6.98528 + 12.0989i −0.361684 + 0.626455i −0.988238 0.152923i \(-0.951131\pi\)
0.626554 + 0.779378i \(0.284465\pi\)
\(374\) 3.82843 + 6.63103i 0.197963 + 0.342882i
\(375\) 1.17157 + 2.02922i 0.0604998 + 0.104789i
\(376\) −3.24264 + 5.61642i −0.167226 + 0.289645i
\(377\) −15.8284 −0.815205
\(378\) −3.91421 + 5.04757i −0.201325 + 0.259619i
\(379\) −25.8701 −1.32886 −0.664428 0.747352i \(-0.731325\pi\)
−0.664428 + 0.747352i \(0.731325\pi\)
\(380\) −5.82843 + 10.0951i −0.298992 + 0.517869i
\(381\) 2.01472 + 3.48960i 0.103217 + 0.178777i
\(382\) 6.41421 + 11.1097i 0.328180 + 0.568424i
\(383\) −15.1924 + 26.3140i −0.776295 + 1.34458i 0.157769 + 0.987476i \(0.449570\pi\)
−0.934064 + 0.357106i \(0.883764\pi\)
\(384\) 0.414214 0.0211377
\(385\) 8.94975 + 1.22474i 0.456121 + 0.0624188i
\(386\) 2.10051 0.106913
\(387\) 8.00000 13.8564i 0.406663 0.704361i
\(388\) −0.914214 1.58346i −0.0464122 0.0803882i
\(389\) −1.36396 2.36245i −0.0691556 0.119781i 0.829374 0.558693i \(-0.188697\pi\)
−0.898530 + 0.438912i \(0.855364\pi\)
\(390\) 1.29289 2.23936i 0.0654682 0.113394i
\(391\) −17.1716 −0.868404
\(392\) 6.74264 + 1.88064i 0.340555 + 0.0949865i
\(393\) −1.41421 −0.0713376
\(394\) 8.74264 15.1427i 0.440448 0.762878i
\(395\) −8.12132 14.0665i −0.408628 0.707764i
\(396\) 1.41421 + 2.44949i 0.0710669 + 0.123091i
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 19.8995 0.997472
\(399\) 3.70711 + 0.507306i 0.185587 + 0.0253971i
\(400\) 6.65685 0.332843
\(401\) 2.15685 3.73578i 0.107708 0.186556i −0.807133 0.590369i \(-0.798982\pi\)
0.914841 + 0.403813i \(0.132315\pi\)
\(402\) −2.32843 4.03295i −0.116131 0.201145i
\(403\) 3.65685 + 6.33386i 0.182161 + 0.315512i
\(404\) −5.91421 + 10.2437i −0.294243 + 0.509644i
\(405\) −25.5563 −1.26991
\(406\) −14.0355 + 18.0995i −0.696572 + 0.898263i
\(407\) −6.58579 −0.326445
\(408\) 1.58579 2.74666i 0.0785081 0.135980i
\(409\) 11.3640 + 19.6830i 0.561912 + 0.973260i 0.997330 + 0.0730312i \(0.0232673\pi\)
−0.435418 + 0.900228i \(0.643399\pi\)
\(410\) −4.41421 7.64564i −0.218002 0.377591i
\(411\) 1.10660 1.91669i 0.0545846 0.0945434i
\(412\) 10.5858 0.521524
\(413\) −8.41421 20.6105i −0.414036 1.01418i
\(414\) −6.34315 −0.311749
\(415\) 27.5563 47.7290i 1.35269 2.34292i
\(416\) −0.914214 1.58346i −0.0448230 0.0776357i
\(417\) 0 0
\(418\) 1.70711 2.95680i 0.0834973 0.144622i
\(419\) 2.14214 0.104650 0.0523251 0.998630i \(-0.483337\pi\)
0.0523251 + 0.998630i \(0.483337\pi\)
\(420\) −1.41421 3.46410i −0.0690066 0.169031i
\(421\) 23.3137 1.13624 0.568120 0.822946i \(-0.307671\pi\)
0.568120 + 0.822946i \(0.307671\pi\)
\(422\) −2.29289 + 3.97141i −0.111616 + 0.193325i
\(423\) 9.17157 + 15.8856i 0.445937 + 0.772386i
\(424\) 5.94975 + 10.3053i 0.288945 + 0.500468i
\(425\) 25.4853 44.1418i 1.23622 2.14119i
\(426\) 1.27208 0.0616324
\(427\) 10.0061 12.9033i 0.484229 0.624436i
\(428\) 11.0711 0.535140
\(429\) −0.378680 + 0.655892i −0.0182828 + 0.0316668i
\(430\) 9.65685 + 16.7262i 0.465695 + 0.806607i
\(431\) 10.2071 + 17.6792i 0.491659 + 0.851578i 0.999954 0.00960469i \(-0.00305731\pi\)
−0.508295 + 0.861183i \(0.669724\pi\)
\(432\) 1.20711 2.09077i 0.0580770 0.100592i
\(433\) −2.14214 −0.102944 −0.0514722 0.998674i \(-0.516391\pi\)
−0.0514722 + 0.998674i \(0.516391\pi\)
\(434\) 10.4853 + 1.43488i 0.503310 + 0.0688763i
\(435\) 12.2426 0.586990
\(436\) 0.242641 0.420266i 0.0116204 0.0201271i
\(437\) 3.82843 + 6.63103i 0.183139 + 0.317205i
\(438\) 1.36396 + 2.36245i 0.0651726 + 0.112882i
\(439\) −4.69239 + 8.12745i −0.223955 + 0.387902i −0.956006 0.293349i \(-0.905230\pi\)
0.732050 + 0.681251i \(0.238564\pi\)
\(440\) −3.41421 −0.162766
\(441\) 14.1421 13.8564i 0.673435 0.659829i
\(442\) −14.0000 −0.665912
\(443\) 16.3137 28.2562i 0.775088 1.34249i −0.159658 0.987172i \(-0.551039\pi\)
0.934745 0.355319i \(-0.115628\pi\)
\(444\) 1.36396 + 2.36245i 0.0647307 + 0.112117i
\(445\) −7.65685 13.2621i −0.362970 0.628682i
\(446\) −5.70711 + 9.88500i −0.270239 + 0.468068i
\(447\) 2.62742 0.124273
\(448\) −2.62132 0.358719i −0.123846 0.0169479i
\(449\) 33.6569 1.58837 0.794183 0.607679i \(-0.207899\pi\)
0.794183 + 0.607679i \(0.207899\pi\)
\(450\) 9.41421 16.3059i 0.443790 0.768667i
\(451\) 1.29289 + 2.23936i 0.0608800 + 0.105447i
\(452\) 6.91421 + 11.9758i 0.325217 + 0.563293i
\(453\) −2.01472 + 3.48960i −0.0946597 + 0.163955i
\(454\) −23.1716 −1.08750
\(455\) −10.1213 + 13.0519i −0.474495 + 0.611884i
\(456\) −1.41421 −0.0662266
\(457\) 0.171573 0.297173i 0.00802584 0.0139012i −0.861985 0.506934i \(-0.830779\pi\)
0.870010 + 0.493033i \(0.164112\pi\)
\(458\) −0.343146 0.594346i −0.0160341 0.0277720i
\(459\) −9.24264 16.0087i −0.431410 0.747223i
\(460\) 3.82843 6.63103i 0.178501 0.309173i
\(461\) 14.3137 0.666656 0.333328 0.942811i \(-0.391828\pi\)
0.333328 + 0.942811i \(0.391828\pi\)
\(462\) 0.414214 + 1.01461i 0.0192710 + 0.0472040i
\(463\) 7.17157 0.333291 0.166646 0.986017i \(-0.446706\pi\)
0.166646 + 0.986017i \(0.446706\pi\)
\(464\) 4.32843 7.49706i 0.200942 0.348042i
\(465\) −2.82843 4.89898i −0.131165 0.227185i
\(466\) 0.707107 + 1.22474i 0.0327561 + 0.0567352i
\(467\) 17.0000 29.4449i 0.786666 1.36255i −0.141332 0.989962i \(-0.545139\pi\)
0.927999 0.372584i \(-0.121528\pi\)
\(468\) −5.17157 −0.239056
\(469\) 11.2426 + 27.5387i 0.519137 + 1.27162i
\(470\) −22.1421 −1.02134
\(471\) −1.31371 + 2.27541i −0.0605325 + 0.104845i
\(472\) 4.20711 + 7.28692i 0.193648 + 0.335408i
\(473\) −2.82843 4.89898i −0.130051 0.225255i
\(474\) 0.985281 1.70656i 0.0452555 0.0783848i
\(475\) −22.7279 −1.04283
\(476\) −12.4142 + 16.0087i −0.569005 + 0.733759i
\(477\) 33.6569 1.54104
\(478\) 11.1066 19.2372i 0.508004 0.879889i
\(479\) 13.0355 + 22.5782i 0.595609 + 1.03162i 0.993461 + 0.114175i \(0.0364224\pi\)
−0.397852 + 0.917450i \(0.630244\pi\)
\(480\) 0.707107 + 1.22474i 0.0322749 + 0.0559017i
\(481\) 6.02082 10.4284i 0.274526 0.475492i
\(482\) 3.75736 0.171143
\(483\) −2.43503 0.333226i −0.110798 0.0151623i
\(484\) 1.00000 0.0454545
\(485\) 3.12132 5.40629i 0.141732 0.245487i
\(486\) −5.17157 8.95743i −0.234587 0.406317i
\(487\) −0.828427 1.43488i −0.0375396 0.0650205i 0.846645 0.532158i \(-0.178619\pi\)
−0.884185 + 0.467137i \(0.845285\pi\)
\(488\) −3.08579 + 5.34474i −0.139687 + 0.241945i
\(489\) −6.51472 −0.294606
\(490\) 5.94975 + 23.1471i 0.268782 + 1.04568i
\(491\) 24.8284 1.12049 0.560246 0.828327i \(-0.310707\pi\)
0.560246 + 0.828327i \(0.310707\pi\)
\(492\) 0.535534 0.927572i 0.0241437 0.0418182i
\(493\) −33.1421 57.4039i −1.49265 2.58534i
\(494\) 3.12132 + 5.40629i 0.140435 + 0.243240i
\(495\) −4.82843 + 8.36308i −0.217022 + 0.375893i
\(496\) −4.00000 −0.179605
\(497\) −8.05025 1.10165i −0.361103 0.0494158i
\(498\) 6.68629 0.299620
\(499\) 3.07107 5.31925i 0.137480 0.238122i −0.789062 0.614313i \(-0.789433\pi\)
0.926542 + 0.376191i \(0.122766\pi\)
\(500\) 2.82843 + 4.89898i 0.126491 + 0.219089i
\(501\) 2.42893 + 4.20703i 0.108517 + 0.187956i
\(502\) −1.07107 + 1.85514i −0.0478041 + 0.0827991i
\(503\) −38.2132 −1.70384 −0.851921 0.523670i \(-0.824563\pi\)
−0.851921 + 0.523670i \(0.824563\pi\)
\(504\) −4.58579 + 5.91359i −0.204267 + 0.263412i
\(505\) −40.3848 −1.79710
\(506\) −1.12132 + 1.94218i −0.0498488 + 0.0863406i
\(507\) 2.00000 + 3.46410i 0.0888231 + 0.153846i
\(508\) 4.86396 + 8.42463i 0.215803 + 0.373782i
\(509\) 6.65685 11.5300i 0.295060 0.511059i −0.679939 0.733269i \(-0.737994\pi\)
0.974999 + 0.222210i \(0.0713271\pi\)
\(510\) 10.8284 0.479491
\(511\) −6.58579 16.1318i −0.291338 0.713630i
\(512\) 1.00000 0.0441942
\(513\) −4.12132 + 7.13834i −0.181961 + 0.315165i
\(514\) −1.57107 2.72117i −0.0692968 0.120026i
\(515\) 18.0711 + 31.3000i 0.796306 + 1.37924i
\(516\) −1.17157 + 2.02922i −0.0515756 + 0.0893316i
\(517\) 6.48528 0.285222
\(518\) −6.58579 16.1318i −0.289363 0.708791i
\(519\) −1.72792 −0.0758474
\(520\) 3.12132 5.40629i 0.136879 0.237081i
\(521\) −14.1421 24.4949i −0.619578 1.07314i −0.989563 0.144103i \(-0.953970\pi\)
0.369984 0.929038i \(-0.379363\pi\)
\(522\) −12.2426 21.2049i −0.535846 0.928112i
\(523\) −6.36396 + 11.0227i −0.278277 + 0.481989i −0.970957 0.239256i \(-0.923097\pi\)
0.692680 + 0.721245i \(0.256430\pi\)
\(524\) −3.41421 −0.149151
\(525\) 4.47056 5.76500i 0.195111 0.251605i
\(526\) 31.0416 1.35348
\(527\) −15.3137 + 26.5241i −0.667076 + 1.15541i
\(528\) −0.207107 0.358719i −0.00901317 0.0156113i
\(529\) 8.98528 + 15.5630i 0.390664 + 0.676651i
\(530\) −20.3137 + 35.1844i −0.882371 + 1.52831i
\(531\) 23.7990 1.03279
\(532\) 8.94975 + 1.22474i 0.388021 + 0.0530994i
\(533\) −4.72792 −0.204789
\(534\) 0.928932 1.60896i 0.0401988 0.0696264i
\(535\) 18.8995 + 32.7349i 0.817096 + 1.41525i
\(536\) −5.62132 9.73641i −0.242804 0.420549i
\(537\) 3.91421 6.77962i 0.168911 0.292562i
\(538\) 13.6569 0.588789
\(539\) −1.74264 6.77962i −0.0750608 0.292019i
\(540\) 8.24264 0.354707
\(541\) 20.5711 35.6301i 0.884419 1.53186i 0.0380415 0.999276i \(-0.487888\pi\)
0.846378 0.532583i \(-0.178779\pi\)
\(542\) 13.2782 + 22.9985i 0.570346 + 0.987869i
\(543\) −0.757359 1.31178i −0.0325014 0.0562941i
\(544\) 3.82843 6.63103i 0.164142 0.284303i
\(545\) 1.65685 0.0709718
\(546\) −1.98528 0.271680i −0.0849622 0.0116268i
\(547\) −18.8701 −0.806825 −0.403413 0.915018i \(-0.632176\pi\)
−0.403413 + 0.915018i \(0.632176\pi\)
\(548\) 2.67157 4.62730i 0.114124 0.197668i
\(549\) 8.72792 + 15.1172i 0.372499 + 0.645187i
\(550\) −3.32843 5.76500i −0.141925 0.245821i
\(551\) −14.7782 + 25.5965i −0.629571 + 1.09045i
\(552\) 0.928932 0.0395380
\(553\) −7.71320 + 9.94655i −0.327999 + 0.422970i
\(554\) −3.82843 −0.162654
\(555\) −4.65685 + 8.06591i −0.197672 + 0.342379i
\(556\) 0 0
\(557\) −12.2426 21.2049i −0.518737 0.898479i −0.999763 0.0217729i \(-0.993069\pi\)
0.481026 0.876707i \(-0.340264\pi\)
\(558\) −5.65685 + 9.79796i −0.239474 + 0.414781i
\(559\) 10.3431 0.437468
\(560\) −3.41421 8.36308i −0.144277 0.353405i
\(561\) −3.17157 −0.133904
\(562\) 8.36396 14.4868i 0.352812 0.611089i
\(563\) 2.53553 + 4.39167i 0.106860 + 0.185087i 0.914497 0.404594i \(-0.132587\pi\)
−0.807637 + 0.589681i \(0.799254\pi\)
\(564\) −1.34315 2.32640i −0.0565566 0.0979590i
\(565\) −23.6066 + 40.8878i −0.993137 + 1.72016i
\(566\) −20.5858 −0.865285
\(567\) 7.48528 + 18.3351i 0.314352 + 0.770003i
\(568\) 3.07107 0.128859
\(569\) 2.00000 3.46410i 0.0838444 0.145223i −0.821054 0.570851i \(-0.806613\pi\)
0.904898 + 0.425628i \(0.139947\pi\)
\(570\) −2.41421 4.18154i −0.101120 0.175145i
\(571\) 5.19239 + 8.99348i 0.217295 + 0.376365i 0.953980 0.299870i \(-0.0969434\pi\)
−0.736685 + 0.676236i \(0.763610\pi\)
\(572\) −0.914214 + 1.58346i −0.0382252 + 0.0662080i
\(573\) −5.31371 −0.221983
\(574\) −4.19239 + 5.40629i −0.174987 + 0.225654i
\(575\) 14.9289 0.622580
\(576\) 1.41421 2.44949i 0.0589256 0.102062i
\(577\) 16.1569 + 27.9845i 0.672619 + 1.16501i 0.977159 + 0.212510i \(0.0681639\pi\)
−0.304540 + 0.952499i \(0.598503\pi\)
\(578\) −20.8137 36.0504i −0.865736 1.49950i
\(579\) −0.435029 + 0.753492i −0.0180792 + 0.0313141i
\(580\) 29.5563 1.22726
\(581\) −42.3137 5.79050i −1.75547 0.240230i
\(582\) 0.757359 0.0313936
\(583\) 5.94975 10.3053i 0.246413 0.426800i
\(584\) 3.29289 + 5.70346i 0.136261 + 0.236011i
\(585\) −8.82843 15.2913i −0.365011 0.632217i
\(586\) 2.58579 4.47871i 0.106818 0.185014i
\(587\) −44.8995 −1.85320 −0.926600 0.376048i \(-0.877283\pi\)
−0.926600 + 0.376048i \(0.877283\pi\)
\(588\) −2.07107 + 2.02922i −0.0854094 + 0.0836838i
\(589\) 13.6569 0.562721
\(590\) −14.3640 + 24.8791i −0.591355 + 1.02426i
\(591\) 3.62132 + 6.27231i 0.148961 + 0.258008i
\(592\) 3.29289 + 5.70346i 0.135337 + 0.234411i
\(593\) 17.8492 30.9158i 0.732981 1.26956i −0.222623 0.974905i \(-0.571462\pi\)
0.955604 0.294655i \(-0.0952047\pi\)
\(594\) −2.41421 −0.0990564
\(595\) −68.5269 9.37769i −2.80933 0.384448i
\(596\) 6.34315 0.259825
\(597\) −4.12132 + 7.13834i −0.168674 + 0.292153i
\(598\) −2.05025 3.55114i −0.0838411 0.145217i
\(599\) 1.31371 + 2.27541i 0.0536767 + 0.0929707i 0.891615 0.452794i \(-0.149573\pi\)
−0.837939 + 0.545765i \(0.816239\pi\)
\(600\) −1.37868 + 2.38794i −0.0562844 + 0.0974874i
\(601\) −35.9411 −1.46607 −0.733035 0.680191i \(-0.761897\pi\)
−0.733035 + 0.680191i \(0.761897\pi\)
\(602\) 9.17157 11.8272i 0.373805 0.482040i
\(603\) −31.7990 −1.29495
\(604\) −4.86396 + 8.42463i −0.197912 + 0.342793i
\(605\) 1.70711 + 2.95680i 0.0694038 + 0.120211i
\(606\) −2.44975 4.24309i −0.0995142 0.172364i
\(607\) 4.51472 7.81972i 0.183247 0.317393i −0.759738 0.650230i \(-0.774673\pi\)
0.942984 + 0.332837i \(0.108006\pi\)
\(608\) −3.41421 −0.138465
\(609\) −3.58579 8.78335i −0.145303 0.355919i
\(610\) −21.0711 −0.853143
\(611\) −5.92893 + 10.2692i −0.239859 + 0.415448i
\(612\) −10.8284 18.7554i −0.437713 0.758142i
\(613\) 8.31371 + 14.3998i 0.335788 + 0.581601i 0.983636 0.180168i \(-0.0576643\pi\)
−0.647848 + 0.761769i \(0.724331\pi\)
\(614\) 4.94975 8.57321i 0.199756 0.345987i
\(615\) 3.65685 0.147459
\(616\) 1.00000 + 2.44949i 0.0402911 + 0.0986928i
\(617\) −8.02944 −0.323253 −0.161626 0.986852i \(-0.551674\pi\)
−0.161626 + 0.986852i \(0.551674\pi\)
\(618\) −2.19239 + 3.79733i −0.0881908 + 0.152751i
\(619\) −22.9706 39.7862i −0.923265 1.59914i −0.794328 0.607489i \(-0.792177\pi\)
−0.128937 0.991653i \(-0.541156\pi\)
\(620\) −6.82843 11.8272i −0.274236 0.474991i
\(621\) 2.70711 4.68885i 0.108632 0.188157i
\(622\) −8.72792 −0.349958
\(623\) −7.27208 + 9.37769i −0.291350 + 0.375709i
\(624\) 0.757359 0.0303186
\(625\) 6.98528 12.0989i 0.279411 0.483954i
\(626\) 4.67157 + 8.09140i 0.186714 + 0.323397i
\(627\) 0.707107 + 1.22474i 0.0282391 + 0.0489116i
\(628\) −3.17157 + 5.49333i −0.126560 + 0.219208i
\(629\) 50.4264 2.01063
\(630\) −25.3137 3.46410i −1.00852 0.138013i
\(631\) 48.7279 1.93983 0.969914 0.243448i \(-0.0782785\pi\)
0.969914 + 0.243448i \(0.0782785\pi\)
\(632\) 2.37868 4.11999i 0.0946188 0.163885i
\(633\) −0.949747 1.64501i −0.0377491 0.0653833i
\(634\) −15.6569 27.1185i −0.621813 1.07701i
\(635\) −16.6066 + 28.7635i −0.659013 + 1.14144i
\(636\) −4.92893 −0.195445
\(637\) 12.3284 + 3.43861i 0.488470 + 0.136243i
\(638\) −8.65685 −0.342728
\(639\) 4.34315 7.52255i 0.171812 0.297587i
\(640\) 1.70711 + 2.95680i 0.0674793 + 0.116878i
\(641\) 20.6421 + 35.7532i 0.815315 + 1.41217i 0.909101 + 0.416575i \(0.136770\pi\)
−0.0937859 + 0.995592i \(0.529897\pi\)
\(642\) −2.29289 + 3.97141i −0.0904933 + 0.156739i
\(643\) 4.41421 0.174080 0.0870398 0.996205i \(-0.472259\pi\)
0.0870398 + 0.996205i \(0.472259\pi\)
\(644\) −5.87868 0.804479i −0.231652 0.0317009i
\(645\) −8.00000 −0.315000
\(646\) −13.0711 + 22.6398i −0.514274 + 0.890749i
\(647\) 23.0919 + 39.9963i 0.907836 + 1.57242i 0.817065 + 0.576546i \(0.195600\pi\)
0.0907706 + 0.995872i \(0.471067\pi\)
\(648\) −3.74264 6.48244i −0.147025 0.254654i
\(649\) 4.20711 7.28692i 0.165143 0.286037i
\(650\) 12.1716 0.477408
\(651\) −2.68629 + 3.46410i −0.105284 + 0.135769i
\(652\) −15.7279 −0.615953
\(653\) −9.19239 + 15.9217i −0.359726 + 0.623064i −0.987915 0.154997i \(-0.950463\pi\)
0.628189 + 0.778061i \(0.283796\pi\)
\(654\) 0.100505 + 0.174080i 0.00393006 + 0.00680706i
\(655\) −5.82843 10.0951i −0.227735 0.394449i
\(656\) 1.29289 2.23936i 0.0504790 0.0874322i
\(657\) 18.6274 0.726725
\(658\) 6.48528 + 15.8856i 0.252823 + 0.619286i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0.707107 1.22474i 0.0275241 0.0476731i
\(661\) 7.48528 + 12.9649i 0.291144 + 0.504276i 0.974080 0.226202i \(-0.0726309\pi\)
−0.682937 + 0.730478i \(0.739298\pi\)
\(662\) 4.96447 + 8.59871i 0.192949 + 0.334198i
\(663\) 2.89949 5.02207i 0.112607 0.195041i
\(664\) 16.1421 0.626436
\(665\) 11.6569 + 28.5533i 0.452033 + 1.10725i
\(666\) 18.6274 0.721798
\(667\) 9.70711 16.8132i 0.375861 0.651010i
\(668\) 5.86396 + 10.1567i 0.226883 + 0.392974i
\(669\) −2.36396 4.09450i −0.0913960 0.158303i
\(670\) 19.1924 33.2422i 0.741467 1.28426i
\(671\) 6.17157 0.238251
\(672\) 0.671573 0.866025i 0.0259065 0.0334077i
\(673\) −25.5563 −0.985125 −0.492562 0.870277i \(-0.663940\pi\)
−0.492562 + 0.870277i \(0.663940\pi\)
\(674\) 9.87868 17.1104i 0.380513 0.659067i
\(675\) 8.03553 + 13.9180i 0.309288 + 0.535702i
\(676\) 4.82843 + 8.36308i 0.185709 + 0.321657i
\(677\) 6.34315 10.9867i 0.243787 0.422251i −0.718003 0.696040i \(-0.754944\pi\)
0.961790 + 0.273789i \(0.0882769\pi\)
\(678\) −5.72792 −0.219980
\(679\) −4.79289 0.655892i −0.183934 0.0251708i
\(680\) 26.1421 1.00251
\(681\) 4.79899 8.31209i 0.183898 0.318520i
\(682\) 2.00000 + 3.46410i 0.0765840 + 0.132647i
\(683\) −8.20711 14.2151i −0.314036 0.543927i 0.665196 0.746669i \(-0.268348\pi\)
−0.979232 + 0.202742i \(0.935015\pi\)
\(684\) −4.82843 + 8.36308i −0.184620 + 0.319770i
\(685\) 18.2426 0.697015
\(686\) 14.8640 11.0482i 0.567509 0.421822i
\(687\) 0.284271 0.0108456
\(688\) −2.82843 + 4.89898i −0.107833 + 0.186772i
\(689\) 10.8787 + 18.8424i 0.414445 + 0.717839i
\(690\) 1.58579 + 2.74666i 0.0603699 + 0.104564i
\(691\) −6.96447 + 12.0628i −0.264941 + 0.458891i −0.967548 0.252687i \(-0.918686\pi\)
0.702607 + 0.711578i \(0.252019\pi\)
\(692\) −4.17157 −0.158579
\(693\) 7.41421 + 1.01461i 0.281643 + 0.0385419i
\(694\) 14.5858 0.553669
\(695\) 0 0
\(696\) 1.79289 + 3.10538i 0.0679594 + 0.117709i
\(697\) −9.89949 17.1464i −0.374970 0.649467i
\(698\) 0 0
\(699\) −0.585786 −0.0221565
\(700\) 10.7929 13.9180i 0.407933 0.526049i
\(701\) 36.1127 1.36396 0.681979 0.731372i \(-0.261120\pi\)
0.681979 + 0.731372i \(0.261120\pi\)
\(702\) 2.20711 3.82282i 0.0833019 0.144283i
\(703\) −11.2426 19.4728i −0.424024 0.734432i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 4.58579 7.94282i 0.172711 0.299144i
\(706\) −25.3137 −0.952694
\(707\) 11.8284 + 28.9736i 0.444854 + 1.08966i
\(708\) −3.48528 −0.130985
\(709\) −18.0208 + 31.2130i −0.676786 + 1.17223i 0.299158 + 0.954204i \(0.403294\pi\)
−0.975943 + 0.218024i \(0.930039\pi\)
\(710\) 5.24264 + 9.08052i 0.196753 + 0.340786i
\(711\) −6.72792 11.6531i −0.252317 0.437026i
\(712\) 2.24264 3.88437i 0.0840465 0.145573i
\(713\) −8.97056 −0.335950
\(714\) −3.17157 7.76874i −0.118693 0.290738i
\(715\) −6.24264 −0.233462
\(716\) 9.44975 16.3674i 0.353154 0.611680i
\(717\) 4.60051 + 7.96831i 0.171809 + 0.297582i
\(718\) −5.37868 9.31615i −0.200731 0.347675i
\(719\) 9.24264 16.0087i 0.344692 0.597025i −0.640605 0.767870i \(-0.721317\pi\)
0.985298 + 0.170846i \(0.0546499\pi\)
\(720\) 9.65685 0.359890
\(721\) 17.1630 22.1324i 0.639182 0.824255i
\(722\) −7.34315 −0.273284
\(723\) −0.778175 + 1.34784i −0.0289406 + 0.0501266i
\(724\) −1.82843 3.16693i −0.0679530 0.117698i
\(725\) 28.8137 + 49.9068i 1.07011 + 1.85349i
\(726\) −0.207107 + 0.358719i −0.00768645 + 0.0133133i
\(727\) −48.4264 −1.79604 −0.898018 0.439959i \(-0.854993\pi\)
−0.898018 + 0.439959i \(0.854993\pi\)
\(728\) −4.79289 0.655892i −0.177636 0.0243090i
\(729\) −18.1716 −0.673021
\(730\) −11.2426 + 19.4728i −0.416109 + 0.720722i
\(731\) 21.6569 + 37.5108i 0.801008 + 1.38739i
\(732\) −1.27817 2.21386i −0.0472427 0.0818267i
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 14.7279 0.543618
\(735\) −9.53553 2.65962i −0.351723 0.0981017i
\(736\) 2.24264 0.0826648
\(737\) −5.62132 + 9.73641i −0.207064 + 0.358645i
\(738\) −3.65685 6.33386i −0.134611 0.233153i
\(739\) −16.2132 28.0821i −0.596412 1.03302i −0.993346 0.115169i \(-0.963259\pi\)
0.396934 0.917847i \(-0.370074\pi\)
\(740\) −11.2426 + 19.4728i −0.413288 + 0.715835i
\(741\) −2.58579 −0.0949912
\(742\) 31.1924 + 4.26858i 1.14511 + 0.156705i
\(743\) 9.31371 0.341687 0.170843 0.985298i \(-0.445351\pi\)
0.170843 + 0.985298i \(0.445351\pi\)
\(744\) 0.828427 1.43488i 0.0303716 0.0526052i
\(745\) 10.8284 + 18.7554i 0.396723 + 0.687144i
\(746\) −6.98528 12.0989i −0.255749 0.442971i
\(747\) 22.8284 39.5400i 0.835248 1.44669i
\(748\) −7.65685 −0.279962
\(749\) 17.9497 23.1471i 0.655869 0.845775i
\(750\) −2.34315 −0.0855596
\(751\) −17.1716 + 29.7420i −0.626600 + 1.08530i 0.361630 + 0.932322i \(0.382220\pi\)
−0.988229 + 0.152980i \(0.951113\pi\)
\(752\) −3.24264 5.61642i −0.118247 0.204810i
\(753\) −0.443651 0.768426i −0.0161675 0.0280030i
\(754\) 7.91421 13.7078i 0.288219 0.499209i
\(755\) −33.2132 −1.20875
\(756\) −2.41421 5.91359i −0.0878041 0.215075i
\(757\) 19.6569 0.714441 0.357220 0.934020i \(-0.383725\pi\)
0.357220 + 0.934020i \(0.383725\pi\)
\(758\) 12.9350 22.4041i 0.469821 0.813755i
\(759\) −0.464466 0.804479i −0.0168591 0.0292007i
\(760\) −5.82843 10.0951i −0.211419 0.366189i
\(761\) 1.48528 2.57258i 0.0538414 0.0932561i −0.837849 0.545903i \(-0.816187\pi\)
0.891690 + 0.452647i \(0.149520\pi\)
\(762\) −4.02944 −0.145971
\(763\) −0.485281 1.18869i −0.0175684 0.0430335i
\(764\) −12.8284 −0.464116
\(765\) 36.9706 64.0349i 1.33667 2.31519i
\(766\) −15.1924 26.3140i −0.548923 0.950763i
\(767\) 7.69239 + 13.3236i 0.277756 + 0.481088i
\(768\) −0.207107 + 0.358719i −0.00747332 + 0.0129442i
\(769\) −10.9706 −0.395609 −0.197804 0.980242i \(-0.563381\pi\)
−0.197804 + 0.980242i \(0.563381\pi\)
\(770\) −5.53553 + 7.13834i −0.199487 + 0.257248i
\(771\) 1.30152 0.0468729