Properties

Label 546.2.i.b.235.1
Level $546$
Weight $2$
Character 546.235
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
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] = [546,2,Mod(79,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("546.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.235
Dual form 546.2.i.b.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -1.00000 q^{20} +(2.50000 + 0.866025i) q^{21} -1.00000 q^{22} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +3.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(5.50000 - 9.52628i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} -6.00000 q^{34} +(2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(2.00000 - 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +12.0000 q^{41} +(-0.500000 - 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} +(4.00000 + 6.92820i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(3.00000 + 5.19615i) q^{51} +(0.500000 - 0.866025i) q^{52} +(2.50000 - 4.33013i) q^{53} +(-0.500000 - 0.866025i) q^{54} +1.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} -4.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(2.50000 - 4.33013i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-6.00000 - 10.3923i) q^{61} -11.0000 q^{62} +(-2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-8.00000 + 13.8564i) q^{67} +(3.00000 + 5.19615i) q^{68} -6.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} +6.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(5.00000 - 8.66025i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(2.00000 + 3.46410i) q^{75} -4.00000 q^{76} +(-2.50000 - 0.866025i) q^{77} -1.00000 q^{78} +(-3.50000 - 6.06218i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.00000 - 10.3923i) q^{82} -17.0000 q^{83} +(-2.00000 + 1.73205i) q^{84} +6.00000 q^{85} +(4.00000 + 6.92820i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(0.500000 - 0.866025i) q^{88} +(6.00000 + 10.3923i) q^{89} -1.00000 q^{90} +(0.500000 + 2.59808i) q^{91} -6.00000 q^{92} +(5.50000 + 9.52628i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +13.0000 q^{97} +(5.50000 + 4.33013i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} + q^{10} + q^{11} - q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 6 q^{17} - q^{18} + 4 q^{19} - 2 q^{20} + 5 q^{21} - 2 q^{22} + 6 q^{23} - q^{24} + 4 q^{25} + q^{26} + 2 q^{27} + 5 q^{28} + 6 q^{29} + q^{30} + 11 q^{31} - q^{32} + q^{33} - 12 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{37} + 4 q^{38} + q^{39} + q^{40} + 24 q^{41} - q^{42} - 16 q^{43} + q^{44} + q^{45} + 6 q^{46} + 8 q^{47} + 2 q^{48} - 13 q^{49} - 8 q^{50} + 6 q^{51} + q^{52} + 5 q^{53} - q^{54} + 2 q^{55} - q^{56} - 8 q^{57} - 3 q^{58} + 5 q^{59} + q^{60} - 12 q^{61} - 22 q^{62} - 4 q^{63} + 2 q^{64} - q^{65} + q^{66} - 16 q^{67} + 6 q^{68} - 12 q^{69} - 5 q^{70} + 12 q^{71} - q^{72} + 10 q^{73} - 4 q^{74} + 4 q^{75} - 8 q^{76} - 5 q^{77} - 2 q^{78} - 7 q^{79} + q^{80} - q^{81} - 12 q^{82} - 34 q^{83} - 4 q^{84} + 12 q^{85} + 8 q^{86} - 3 q^{87} + q^{88} + 12 q^{89} - 2 q^{90} + q^{91} - 12 q^{92} + 11 q^{93} + 8 q^{94} - 4 q^{95} - q^{96} + 26 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −1.00000 −0.277350
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) −1.00000 −0.213201
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0.500000 + 0.866025i 0.0980581 + 0.169842i
\(27\) 1.00000 0.192450
\(28\) 2.50000 + 0.866025i 0.472456 + 0.163663i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0.500000 + 0.866025i 0.0912871 + 0.158114i
\(31\) 5.50000 9.52628i 0.987829 1.71097i 0.359211 0.933257i \(-0.383046\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) −6.00000 −1.02899
\(35\) 2.00000 1.73205i 0.338062 0.292770i
\(36\) 1.00000 0.166667
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) −0.500000 2.59808i −0.0771517 0.400892i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −4.00000 −0.565685
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 2.50000 4.33013i 0.343401 0.594789i −0.641661 0.766989i \(-0.721754\pi\)
0.985062 + 0.172200i \(0.0550875\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 1.00000 0.134840
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) −4.00000 −0.529813
\(58\) −1.50000 2.59808i −0.196960 0.341144i
\(59\) 2.50000 4.33013i 0.325472 0.563735i −0.656136 0.754643i \(-0.727810\pi\)
0.981608 + 0.190909i \(0.0611434\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −6.00000 10.3923i −0.768221 1.33060i −0.938527 0.345207i \(-0.887809\pi\)
0.170305 0.985391i \(-0.445525\pi\)
\(62\) −11.0000 −1.39700
\(63\) −2.00000 + 1.73205i −0.251976 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) −0.500000 0.866025i −0.0620174 0.107417i
\(66\) 0.500000 0.866025i 0.0615457 0.106600i
\(67\) −8.00000 + 13.8564i −0.977356 + 1.69283i −0.305424 + 0.952217i \(0.598798\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) −6.00000 −0.722315
\(70\) −2.50000 0.866025i −0.298807 0.103510i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i \(-0.634347\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 2.00000 + 3.46410i 0.230940 + 0.400000i
\(76\) −4.00000 −0.458831
\(77\) −2.50000 0.866025i −0.284901 0.0986928i
\(78\) −1.00000 −0.113228
\(79\) −3.50000 6.06218i −0.393781 0.682048i 0.599164 0.800626i \(-0.295500\pi\)
−0.992945 + 0.118578i \(0.962166\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −6.00000 10.3923i −0.662589 1.14764i
\(83\) −17.0000 −1.86599 −0.932996 0.359886i \(-0.882816\pi\)
−0.932996 + 0.359886i \(0.882816\pi\)
\(84\) −2.00000 + 1.73205i −0.218218 + 0.188982i
\(85\) 6.00000 0.650791
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) −1.50000 + 2.59808i −0.160817 + 0.278543i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 6.00000 + 10.3923i 0.635999 + 1.10158i 0.986303 + 0.164946i \(0.0527450\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0.500000 + 2.59808i 0.0524142 + 0.272352i
\(92\) −6.00000 −0.625543
\(93\) 5.50000 + 9.52628i 0.570323 + 0.987829i
\(94\) 4.00000 6.92820i 0.412568 0.714590i
\(95\) −2.00000 + 3.46410i −0.205196 + 0.355409i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) −1.00000 −0.100504
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 3.00000 5.19615i 0.297044 0.514496i
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0.500000 + 2.59808i 0.0487950 + 0.253546i
\(106\) −5.00000 −0.485643
\(107\) −3.50000 6.06218i −0.338358 0.586053i 0.645766 0.763535i \(-0.276538\pi\)
−0.984124 + 0.177482i \(0.943205\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −6.00000 + 10.3923i −0.574696 + 0.995402i 0.421379 + 0.906885i \(0.361546\pi\)
−0.996075 + 0.0885176i \(0.971787\pi\)
\(110\) −0.500000 0.866025i −0.0476731 0.0825723i
\(111\) 4.00000 0.379663
\(112\) −2.00000 + 1.73205i −0.188982 + 0.163663i
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) −3.00000 + 5.19615i −0.279751 + 0.484544i
\(116\) −1.50000 + 2.59808i −0.139272 + 0.241225i
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) −5.00000 −0.460287
\(119\) −15.0000 5.19615i −1.37505 0.476331i
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) −6.00000 + 10.3923i −0.543214 + 0.940875i
\(123\) −6.00000 + 10.3923i −0.541002 + 0.937043i
\(124\) 5.50000 + 9.52628i 0.493915 + 0.855485i
\(125\) 9.00000 0.804984
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) −0.500000 + 0.866025i −0.0438529 + 0.0759555i
\(131\) −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i \(-0.180577\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 8.00000 6.92820i 0.693688 0.600751i
\(134\) 16.0000 1.38219
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) 4.00000 6.92820i 0.341743 0.591916i −0.643013 0.765855i \(-0.722316\pi\)
0.984757 + 0.173939i \(0.0556494\pi\)
\(138\) 3.00000 + 5.19615i 0.255377 + 0.442326i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0.500000 + 2.59808i 0.0422577 + 0.219578i
\(141\) −8.00000 −0.673722
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −0.500000 + 0.866025i −0.0418121 + 0.0724207i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 1.50000 + 2.59808i 0.124568 + 0.215758i
\(146\) −10.0000 −0.827606
\(147\) 1.00000 6.92820i 0.0824786 0.571429i
\(148\) 4.00000 0.328798
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) −6.50000 + 11.2583i −0.528962 + 0.916190i 0.470467 + 0.882418i \(0.344085\pi\)
−0.999430 + 0.0337724i \(0.989248\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) −6.00000 −0.485071
\(154\) 0.500000 + 2.59808i 0.0402911 + 0.209359i
\(155\) 11.0000 0.883541
\(156\) 0.500000 + 0.866025i 0.0400320 + 0.0693375i
\(157\) 9.00000 15.5885i 0.718278 1.24409i −0.243403 0.969925i \(-0.578264\pi\)
0.961681 0.274169i \(-0.0884028\pi\)
\(158\) −3.50000 + 6.06218i −0.278445 + 0.482281i
\(159\) 2.50000 + 4.33013i 0.198263 + 0.343401i
\(160\) −1.00000 −0.0790569
\(161\) 12.0000 10.3923i 0.945732 0.819028i
\(162\) 1.00000 0.0785674
\(163\) 4.00000 + 6.92820i 0.313304 + 0.542659i 0.979076 0.203497i \(-0.0652307\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) −6.00000 + 10.3923i −0.468521 + 0.811503i
\(165\) −0.500000 + 0.866025i −0.0389249 + 0.0674200i
\(166\) 8.50000 + 14.7224i 0.659728 + 1.14268i
\(167\) −24.0000 −1.85718 −0.928588 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) 2.50000 + 0.866025i 0.192879 + 0.0668153i
\(169\) 1.00000 0.0769231
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 3.00000 0.227429
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) −1.00000 −0.0753778
\(177\) 2.50000 + 4.33013i 0.187912 + 0.325472i
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 2.00000 1.73205i 0.148250 0.128388i
\(183\) 12.0000 0.887066
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) 5.50000 9.52628i 0.403280 0.698501i
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) −8.00000 −0.583460
\(189\) −0.500000 2.59808i −0.0363696 0.188982i
\(190\) 4.00000 0.290191
\(191\) 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −7.50000 + 12.9904i −0.539862 + 0.935068i 0.459049 + 0.888411i \(0.348190\pi\)
−0.998911 + 0.0466572i \(0.985143\pi\)
\(194\) −6.50000 11.2583i −0.466673 0.808301i
\(195\) 1.00000 0.0716115
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0.500000 + 0.866025i 0.0355335 + 0.0615457i
\(199\) −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i \(-0.924846\pi\)
0.688705 + 0.725042i \(0.258180\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) −8.00000 13.8564i −0.564276 0.977356i
\(202\) 10.0000 0.703598
\(203\) −1.50000 7.79423i −0.105279 0.547048i
\(204\) −6.00000 −0.420084
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) 0 0
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) 4.00000 0.276686
\(210\) 2.00000 1.73205i 0.138013 0.119523i
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 2.50000 + 4.33013i 0.171701 + 0.297394i
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) −3.50000 + 6.06218i −0.239255 + 0.414402i
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) 1.00000 0.0680414
\(217\) −27.5000 9.52628i −1.86682 0.646686i
\(218\) 12.0000 0.812743
\(219\) 5.00000 + 8.66025i 0.337869 + 0.585206i
\(220\) −0.500000 + 0.866025i −0.0337100 + 0.0583874i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) −2.00000 3.46410i −0.134231 0.232495i
\(223\) 7.00000 0.468755 0.234377 0.972146i \(-0.424695\pi\)
0.234377 + 0.972146i \(0.424695\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) −4.00000 −0.266667
\(226\) 2.00000 + 3.46410i 0.133038 + 0.230429i
\(227\) 7.50000 12.9904i 0.497792 0.862202i −0.502204 0.864749i \(-0.667477\pi\)
0.999997 + 0.00254715i \(0.000810783\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) −3.00000 5.19615i −0.198246 0.343371i 0.749714 0.661762i \(-0.230191\pi\)
−0.947960 + 0.318390i \(0.896858\pi\)
\(230\) 6.00000 0.395628
\(231\) 2.00000 1.73205i 0.131590 0.113961i
\(232\) 3.00000 0.196960
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 0.500000 0.866025i 0.0326860 0.0566139i
\(235\) −4.00000 + 6.92820i −0.260931 + 0.451946i
\(236\) 2.50000 + 4.33013i 0.162736 + 0.281867i
\(237\) 7.00000 0.454699
\(238\) 3.00000 + 15.5885i 0.194461 + 1.01045i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) 7.50000 12.9904i 0.483117 0.836784i −0.516695 0.856170i \(-0.672838\pi\)
0.999812 + 0.0193858i \(0.00617107\pi\)
\(242\) 5.00000 8.66025i 0.321412 0.556702i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 12.0000 0.768221
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) 12.0000 0.765092
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) 5.50000 9.52628i 0.349250 0.604919i
\(249\) 8.50000 14.7224i 0.538666 0.932996i
\(250\) −4.50000 7.79423i −0.284605 0.492950i
\(251\) 17.0000 1.07303 0.536515 0.843891i \(-0.319740\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(252\) −0.500000 2.59808i −0.0314970 0.163663i
\(253\) 6.00000 0.377217
\(254\) 3.50000 + 6.06218i 0.219610 + 0.380375i
\(255\) −3.00000 + 5.19615i −0.187867 + 0.325396i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) −8.00000 −0.498058
\(259\) −8.00000 + 6.92820i −0.497096 + 0.430498i
\(260\) 1.00000 0.0620174
\(261\) −1.50000 2.59808i −0.0928477 0.160817i
\(262\) −0.500000 + 0.866025i −0.0308901 + 0.0535032i
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0.500000 + 0.866025i 0.0307729 + 0.0533002i
\(265\) 5.00000 0.307148
\(266\) −10.0000 3.46410i −0.613139 0.212398i
\(267\) −12.0000 −0.734388
\(268\) −8.00000 13.8564i −0.488678 0.846415i
\(269\) 4.50000 7.79423i 0.274370 0.475223i −0.695606 0.718423i \(-0.744864\pi\)
0.969976 + 0.243201i \(0.0781974\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 3.50000 + 6.06218i 0.212610 + 0.368251i 0.952531 0.304443i \(-0.0984703\pi\)
−0.739921 + 0.672694i \(0.765137\pi\)
\(272\) −6.00000 −0.363803
\(273\) −2.50000 0.866025i −0.151307 0.0524142i
\(274\) −8.00000 −0.483298
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 0 0
\(279\) −11.0000 −0.658553
\(280\) 2.00000 1.73205i 0.119523 0.103510i
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 4.00000 + 6.92820i 0.238197 + 0.412568i
\(283\) −5.00000 + 8.66025i −0.297219 + 0.514799i −0.975499 0.220005i \(-0.929393\pi\)
0.678280 + 0.734804i \(0.262726\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) −2.00000 3.46410i −0.118470 0.205196i
\(286\) 1.00000 0.0591312
\(287\) −6.00000 31.1769i −0.354169 1.84032i
\(288\) 1.00000 0.0589256
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 1.50000 2.59808i 0.0880830 0.152564i
\(291\) −6.50000 + 11.2583i −0.381037 + 0.659975i
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) −7.00000 −0.408944 −0.204472 0.978872i \(-0.565548\pi\)
−0.204472 + 0.978872i \(0.565548\pi\)
\(294\) −6.50000 + 2.59808i −0.379088 + 0.151523i
\(295\) 5.00000 0.291111
\(296\) −2.00000 3.46410i −0.116248 0.201347i
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) 5.00000 8.66025i 0.289642 0.501675i
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) −4.00000 −0.230940
\(301\) 4.00000 + 20.7846i 0.230556 + 1.19800i
\(302\) 13.0000 0.748066
\(303\) −5.00000 8.66025i −0.287242 0.497519i
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 6.00000 10.3923i 0.343559 0.595062i
\(306\) 3.00000 + 5.19615i 0.171499 + 0.297044i
\(307\) 6.00000 0.342438 0.171219 0.985233i \(-0.445229\pi\)
0.171219 + 0.985233i \(0.445229\pi\)
\(308\) 2.00000 1.73205i 0.113961 0.0986928i
\(309\) 0 0
\(310\) −5.50000 9.52628i −0.312379 0.541056i
\(311\) −1.00000 + 1.73205i −0.0567048 + 0.0982156i −0.892984 0.450088i \(-0.851393\pi\)
0.836280 + 0.548303i \(0.184726\pi\)
\(312\) 0.500000 0.866025i 0.0283069 0.0490290i
\(313\) −6.50000 11.2583i −0.367402 0.636358i 0.621757 0.783210i \(-0.286419\pi\)
−0.989158 + 0.146852i \(0.953086\pi\)
\(314\) −18.0000 −1.01580
\(315\) −2.50000 0.866025i −0.140859 0.0487950i
\(316\) 7.00000 0.393781
\(317\) 1.50000 + 2.59808i 0.0842484 + 0.145922i 0.905071 0.425261i \(-0.139818\pi\)
−0.820822 + 0.571184i \(0.806484\pi\)
\(318\) 2.50000 4.33013i 0.140193 0.242821i
\(319\) 1.50000 2.59808i 0.0839839 0.145464i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 7.00000 0.390702
\(322\) −15.0000 5.19615i −0.835917 0.289570i
\(323\) 24.0000 1.33540
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −2.00000 + 3.46410i −0.110940 + 0.192154i
\(326\) 4.00000 6.92820i 0.221540 0.383718i
\(327\) −6.00000 10.3923i −0.331801 0.574696i
\(328\) 12.0000 0.662589
\(329\) 16.0000 13.8564i 0.882109 0.763928i
\(330\) 1.00000 0.0550482
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 8.50000 14.7224i 0.466498 0.807998i
\(333\) −2.00000 + 3.46410i −0.109599 + 0.189832i
\(334\) 12.0000 + 20.7846i 0.656611 + 1.13728i
\(335\) −16.0000 −0.874173
\(336\) −0.500000 2.59808i −0.0272772 0.141737i
\(337\) 25.0000 1.36184 0.680918 0.732359i \(-0.261581\pi\)
0.680918 + 0.732359i \(0.261581\pi\)
\(338\) −0.500000 0.866025i −0.0271964 0.0471056i
\(339\) 2.00000 3.46410i 0.108625 0.188144i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) −5.50000 9.52628i −0.297842 0.515877i
\(342\) −4.00000 −0.216295
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −8.00000 −0.431331
\(345\) −3.00000 5.19615i −0.161515 0.279751i
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) −10.0000 + 17.3205i −0.536828 + 0.929814i 0.462244 + 0.886753i \(0.347044\pi\)
−0.999072 + 0.0430610i \(0.986289\pi\)
\(348\) −1.50000 2.59808i −0.0804084 0.139272i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 2.00000 + 10.3923i 0.106904 + 0.555492i
\(351\) −1.00000 −0.0533761
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −15.0000 + 25.9808i −0.798369 + 1.38282i 0.122308 + 0.992492i \(0.460970\pi\)
−0.920677 + 0.390324i \(0.872363\pi\)
\(354\) 2.50000 4.33013i 0.132874 0.230144i
\(355\) 3.00000 + 5.19615i 0.159223 + 0.275783i
\(356\) −12.0000 −0.635999
\(357\) 12.0000 10.3923i 0.635107 0.550019i
\(358\) 12.0000 0.634220
\(359\) 11.0000 + 19.0526i 0.580558 + 1.00556i 0.995413 + 0.0956683i \(0.0304988\pi\)
−0.414855 + 0.909887i \(0.636168\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 8.00000 + 13.8564i 0.420471 + 0.728277i
\(363\) −10.0000 −0.524864
\(364\) −2.50000 0.866025i −0.131036 0.0453921i
\(365\) 10.0000 0.523424
\(366\) −6.00000 10.3923i −0.313625 0.543214i
\(367\) 3.50000 6.06218i 0.182699 0.316443i −0.760100 0.649806i \(-0.774850\pi\)
0.942799 + 0.333363i \(0.108183\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) −6.00000 10.3923i −0.312348 0.541002i
\(370\) −4.00000 −0.207950
\(371\) −12.5000 4.33013i −0.648968 0.224809i
\(372\) −11.0000 −0.570323
\(373\) −13.0000 22.5167i −0.673114 1.16587i −0.977016 0.213165i \(-0.931623\pi\)
0.303902 0.952703i \(-0.401711\pi\)
\(374\) −3.00000 + 5.19615i −0.155126 + 0.268687i
\(375\) −4.50000 + 7.79423i −0.232379 + 0.402492i
\(376\) 4.00000 + 6.92820i 0.206284 + 0.357295i
\(377\) −3.00000 −0.154508
\(378\) −2.00000 + 1.73205i −0.102869 + 0.0890871i
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) 3.50000 6.06218i 0.179310 0.310575i
\(382\) 3.00000 5.19615i 0.153493 0.265858i
\(383\) 7.00000 + 12.1244i 0.357683 + 0.619526i 0.987573 0.157159i \(-0.0502334\pi\)
−0.629890 + 0.776684i \(0.716900\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.500000 2.59808i −0.0254824 0.132410i
\(386\) 15.0000 0.763480
\(387\) 4.00000 + 6.92820i 0.203331 + 0.352180i
\(388\) −6.50000 + 11.2583i −0.329988 + 0.571555i
\(389\) −11.0000 + 19.0526i −0.557722 + 0.966003i 0.439964 + 0.898015i \(0.354991\pi\)
−0.997686 + 0.0679877i \(0.978342\pi\)
\(390\) −0.500000 0.866025i −0.0253185 0.0438529i
\(391\) 36.0000 1.82060
\(392\) −6.50000 + 2.59808i −0.328300 + 0.131223i
\(393\) 1.00000 0.0504433
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 3.50000 6.06218i 0.176104 0.305021i
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 9.00000 + 15.5885i 0.451697 + 0.782362i 0.998492 0.0549046i \(-0.0174855\pi\)
−0.546795 + 0.837267i \(0.684152\pi\)
\(398\) 8.00000 0.401004
\(399\) 2.00000 + 10.3923i 0.100125 + 0.520266i
\(400\) −4.00000 −0.200000
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) −8.00000 + 13.8564i −0.399004 + 0.691095i
\(403\) −5.50000 + 9.52628i −0.273975 + 0.474538i
\(404\) −5.00000 8.66025i −0.248759 0.430864i
\(405\) −1.00000 −0.0496904
\(406\) −6.00000 + 5.19615i −0.297775 + 0.257881i
\(407\) −4.00000 −0.198273
\(408\) 3.00000 + 5.19615i 0.148522 + 0.257248i
\(409\) −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i \(0.378758\pi\)
−0.989835 + 0.142222i \(0.954575\pi\)
\(410\) 6.00000 10.3923i 0.296319 0.513239i
\(411\) 4.00000 + 6.92820i 0.197305 + 0.341743i
\(412\) 0 0
\(413\) −12.5000 4.33013i −0.615085 0.213072i
\(414\) −6.00000 −0.294884
\(415\) −8.50000 14.7224i −0.417249 0.722696i
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) 0 0
\(418\) −2.00000 3.46410i −0.0978232 0.169435i
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) −2.50000 0.866025i −0.121988 0.0422577i
\(421\) −36.0000 −1.75453 −0.877266 0.480004i \(-0.840635\pi\)
−0.877266 + 0.480004i \(0.840635\pi\)
\(422\) −6.00000 10.3923i −0.292075 0.505889i
\(423\) 4.00000 6.92820i 0.194487 0.336861i
\(424\) 2.50000 4.33013i 0.121411 0.210290i
\(425\) −12.0000 20.7846i −0.582086 1.00820i
\(426\) 6.00000 0.290701
\(427\) −24.0000 + 20.7846i −1.16144 + 1.00584i
\(428\) 7.00000 0.338358
\(429\) −0.500000 0.866025i −0.0241402 0.0418121i
\(430\) −4.00000 + 6.92820i −0.192897 + 0.334108i
\(431\) 19.0000 32.9090i 0.915198 1.58517i 0.108586 0.994087i \(-0.465368\pi\)
0.806611 0.591082i \(-0.201299\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 5.50000 + 28.5788i 0.264008 + 1.37183i
\(435\) −3.00000 −0.143839
\(436\) −6.00000 10.3923i −0.287348 0.497701i
\(437\) −12.0000 + 20.7846i −0.574038 + 0.994263i
\(438\) 5.00000 8.66025i 0.238909 0.413803i
\(439\) 8.50000 + 14.7224i 0.405683 + 0.702663i 0.994401 0.105675i \(-0.0337004\pi\)
−0.588718 + 0.808339i \(0.700367\pi\)
\(440\) 1.00000 0.0476731
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 6.00000 0.285391
\(443\) 19.5000 + 33.7750i 0.926473 + 1.60470i 0.789175 + 0.614168i \(0.210508\pi\)
0.137298 + 0.990530i \(0.456158\pi\)
\(444\) −2.00000 + 3.46410i −0.0949158 + 0.164399i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −3.50000 6.06218i −0.165730 0.287052i
\(447\) −10.0000 −0.472984
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) 20.0000 0.943858 0.471929 0.881636i \(-0.343558\pi\)
0.471929 + 0.881636i \(0.343558\pi\)
\(450\) 2.00000 + 3.46410i 0.0942809 + 0.163299i
\(451\) 6.00000 10.3923i 0.282529 0.489355i
\(452\) 2.00000 3.46410i 0.0940721 0.162938i
\(453\) −6.50000 11.2583i −0.305397 0.528962i
\(454\) −15.0000 −0.703985
\(455\) −2.00000 + 1.73205i −0.0937614 + 0.0811998i
\(456\) −4.00000 −0.187317
\(457\) 5.50000 + 9.52628i 0.257279 + 0.445621i 0.965512 0.260358i \(-0.0838407\pi\)
−0.708233 + 0.705979i \(0.750507\pi\)
\(458\) −3.00000 + 5.19615i −0.140181 + 0.242800i
\(459\) 3.00000 5.19615i 0.140028 0.242536i
\(460\) −3.00000 5.19615i −0.139876 0.242272i
\(461\) 34.0000 1.58354 0.791769 0.610821i \(-0.209160\pi\)
0.791769 + 0.610821i \(0.209160\pi\)
\(462\) −2.50000 0.866025i −0.116311 0.0402911i
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) −5.50000 + 9.52628i −0.255056 + 0.441771i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i \(-0.256221\pi\)
−0.970799 + 0.239892i \(0.922888\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 40.0000 + 13.8564i 1.84703 + 0.639829i
\(470\) 8.00000 0.369012
\(471\) 9.00000 + 15.5885i 0.414698 + 0.718278i
\(472\) 2.50000 4.33013i 0.115072 0.199310i
\(473\) −4.00000 + 6.92820i −0.183920 + 0.318559i
\(474\) −3.50000 6.06218i −0.160760 0.278445i
\(475\) 16.0000 0.734130
\(476\) 12.0000 10.3923i 0.550019 0.476331i
\(477\) −5.00000 −0.228934
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) −7.00000 + 12.1244i −0.319838 + 0.553976i −0.980454 0.196748i \(-0.936962\pi\)
0.660616 + 0.750724i \(0.270295\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −15.0000 −0.683231
\(483\) 3.00000 + 15.5885i 0.136505 + 0.709299i
\(484\) −10.0000 −0.454545
\(485\) 6.50000 + 11.2583i 0.295150 + 0.511214i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −11.5000 + 19.9186i −0.521115 + 0.902597i 0.478584 + 0.878042i \(0.341150\pi\)
−0.999698 + 0.0245553i \(0.992183\pi\)
\(488\) −6.00000 10.3923i −0.271607 0.470438i
\(489\) −8.00000 −0.361773
\(490\) −1.00000 + 6.92820i −0.0451754 + 0.312984i
\(491\) −35.0000 −1.57953 −0.789764 0.613411i \(-0.789797\pi\)
−0.789764 + 0.613411i \(0.789797\pi\)
\(492\) −6.00000 10.3923i −0.270501 0.468521i
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) −2.00000 + 3.46410i −0.0899843 + 0.155857i
\(495\) −0.500000 0.866025i −0.0224733 0.0389249i
\(496\) −11.0000 −0.493915
\(497\) −3.00000 15.5885i −0.134568 0.699238i
\(498\) −17.0000 −0.761788
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) −8.50000 14.7224i −0.379374 0.657094i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) −2.00000 + 1.73205i −0.0890871 + 0.0771517i
\(505\) −10.0000 −0.444994
\(506\) −3.00000 5.19615i −0.133366 0.230997i
\(507\) −0.500000 + 0.866025i −0.0222058 + 0.0384615i
\(508\) 3.50000 6.06218i 0.155287 0.268966i
\(509\) −6.50000 11.2583i −0.288107 0.499017i 0.685251 0.728307i \(-0.259693\pi\)
−0.973358 + 0.229291i \(0.926359\pi\)
\(510\) 6.00000 0.265684
\(511\) −25.0000 8.66025i −1.10593 0.383107i
\(512\) 1.00000 0.0441942
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) 3.00000 5.19615i 0.132324 0.229192i
\(515\) 0 0
\(516\) 4.00000 + 6.92820i 0.176090 + 0.304997i
\(517\) 8.00000 0.351840
\(518\) 10.0000 + 3.46410i 0.439375 + 0.152204i
\(519\) 6.00000 0.263371
\(520\) −0.500000 0.866025i −0.0219265 0.0379777i
\(521\) −14.0000 + 24.2487i −0.613351 + 1.06236i 0.377320 + 0.926083i \(0.376846\pi\)
−0.990671 + 0.136272i \(0.956488\pi\)
\(522\) −1.50000 + 2.59808i −0.0656532 + 0.113715i
\(523\) −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i \(-0.280422\pi\)
−0.986216 + 0.165460i \(0.947089\pi\)
\(524\) 1.00000 0.0436852
\(525\) 8.00000 6.92820i 0.349149 0.302372i
\(526\) −18.0000 −0.784837
\(527\) −33.0000 57.1577i −1.43750 2.48983i
\(528\) 0.500000 0.866025i 0.0217597 0.0376889i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −2.50000 4.33013i −0.108593 0.188089i
\(531\) −5.00000 −0.216982
\(532\) 2.00000 + 10.3923i 0.0867110 + 0.450564i
\(533\) −12.0000 −0.519778
\(534\) 6.00000 + 10.3923i 0.259645 + 0.449719i
\(535\) 3.50000 6.06218i 0.151318 0.262091i
\(536\) −8.00000 + 13.8564i −0.345547 + 0.598506i
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) −9.00000 −0.388018
\(539\) −1.00000 + 6.92820i −0.0430730 + 0.298419i
\(540\) −1.00000 −0.0430331
\(541\) −16.0000 27.7128i −0.687894 1.19147i −0.972518 0.232828i \(-0.925202\pi\)
0.284624 0.958639i \(-0.408131\pi\)
\(542\) 3.50000 6.06218i 0.150338 0.260393i
\(543\) 8.00000 13.8564i 0.343313 0.594635i
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) −12.0000 −0.514024
\(546\) 0.500000 + 2.59808i 0.0213980 + 0.111187i
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 4.00000 + 6.92820i 0.170872 + 0.295958i
\(549\) −6.00000 + 10.3923i −0.256074 + 0.443533i
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) 6.00000 + 10.3923i 0.255609 + 0.442727i
\(552\) −6.00000 −0.255377
\(553\) −14.0000 + 12.1244i −0.595341 + 0.515580i
\(554\) −10.0000 −0.424859
\(555\) 2.00000 + 3.46410i 0.0848953 + 0.147043i
\(556\) 0 0
\(557\) 8.50000 14.7224i 0.360157 0.623809i −0.627830 0.778351i \(-0.716057\pi\)
0.987986 + 0.154541i \(0.0493899\pi\)
\(558\) 5.50000 + 9.52628i 0.232834 + 0.403280i
\(559\) 8.00000 0.338364
\(560\) −2.50000 0.866025i −0.105644 0.0365963i
\(561\) 6.00000 0.253320
\(562\) −2.00000 3.46410i −0.0843649 0.146124i
\(563\) −10.5000 + 18.1865i −0.442522 + 0.766471i −0.997876 0.0651433i \(-0.979250\pi\)
0.555354 + 0.831614i \(0.312583\pi\)
\(564\) 4.00000 6.92820i 0.168430 0.291730i
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) 10.0000 0.420331
\(567\) 2.50000 + 0.866025i 0.104990 + 0.0363696i
\(568\) 6.00000 0.251754
\(569\) 2.00000 + 3.46410i 0.0838444 + 0.145223i 0.904898 0.425628i \(-0.139947\pi\)
−0.821054 + 0.570851i \(0.806613\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) −14.0000 + 24.2487i −0.585882 + 1.01478i 0.408883 + 0.912587i \(0.365918\pi\)
−0.994765 + 0.102190i \(0.967415\pi\)
\(572\) −0.500000 0.866025i −0.0209061 0.0362103i
\(573\) −6.00000 −0.250654
\(574\) −24.0000 + 20.7846i −1.00174 + 0.867533i
\(575\) 24.0000 1.00087
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −0.500000 + 0.866025i −0.0208153 + 0.0360531i −0.876245 0.481865i \(-0.839960\pi\)
0.855430 + 0.517918i \(0.173293\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) −7.50000 12.9904i −0.311689 0.539862i
\(580\) −3.00000 −0.124568
\(581\) 8.50000 + 44.1673i 0.352639 + 1.83237i
\(582\) 13.0000 0.538867
\(583\) −2.50000 4.33013i −0.103539 0.179336i
\(584\) 5.00000 8.66025i 0.206901 0.358364i
\(585\) −0.500000 + 0.866025i −0.0206725 + 0.0358057i
\(586\) 3.50000 + 6.06218i 0.144584 + 0.250426i
\(587\) 5.00000 0.206372 0.103186 0.994662i \(-0.467096\pi\)
0.103186 + 0.994662i \(0.467096\pi\)
\(588\) 5.50000 + 4.33013i 0.226816 + 0.178571i
\(589\) 44.0000 1.81299
\(590\) −2.50000 4.33013i −0.102923 0.178269i
\(591\) 9.00000 15.5885i 0.370211 0.641223i
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) 18.0000 + 31.1769i 0.739171 + 1.28028i 0.952869 + 0.303383i \(0.0981160\pi\)
−0.213697 + 0.976900i \(0.568551\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −3.00000 15.5885i −0.122988 0.639064i
\(596\) −10.0000 −0.409616
\(597\) −4.00000 6.92820i −0.163709 0.283552i
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) 5.00000 8.66025i 0.204294 0.353848i −0.745613 0.666379i \(-0.767843\pi\)
0.949908 + 0.312531i \(0.101177\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) 11.0000 0.448699 0.224350 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) 16.0000 13.8564i 0.652111 0.564745i
\(603\) 16.0000 0.651570
\(604\) −6.50000 11.2583i −0.264481 0.458095i
\(605\) −5.00000 + 8.66025i −0.203279 + 0.352089i
\(606\) −5.00000 + 8.66025i −0.203111 + 0.351799i
\(607\) −14.5000 25.1147i −0.588537 1.01938i −0.994424 0.105453i \(-0.966371\pi\)
0.405887 0.913923i \(-0.366962\pi\)
\(608\) −4.00000 −0.162221
\(609\) 7.50000 + 2.59808i 0.303915 + 0.105279i
\(610\) −12.0000 −0.485866
\(611\) −4.00000 6.92820i −0.161823 0.280285i
\(612\) 3.00000 5.19615i 0.121268 0.210042i
\(613\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(614\) −3.00000 5.19615i −0.121070 0.209700i
\(615\) −12.0000 −0.483887
\(616\) −2.50000 0.866025i −0.100728 0.0348932i
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) 4.00000 6.92820i 0.160774 0.278468i −0.774373 0.632730i \(-0.781934\pi\)
0.935146 + 0.354262i \(0.115268\pi\)
\(620\) −5.50000 + 9.52628i −0.220885 + 0.382585i
\(621\) 3.00000 + 5.19615i 0.120386 + 0.208514i
\(622\) 2.00000 0.0801927
\(623\) 24.0000 20.7846i 0.961540 0.832718i
\(624\) −1.00000 −0.0400320
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) −6.50000 + 11.2583i −0.259792 + 0.449973i
\(627\) −2.00000 + 3.46410i −0.0798723 + 0.138343i
\(628\) 9.00000 + 15.5885i 0.359139 + 0.622047i
\(629\) −24.0000 −0.956943
\(630\) 0.500000 + 2.59808i 0.0199205 + 0.103510i
\(631\) −29.0000 −1.15447 −0.577236 0.816577i \(-0.695869\pi\)
−0.577236 + 0.816577i \(0.695869\pi\)
\(632\) −3.50000 6.06218i −0.139223 0.241140i
\(633\) −6.00000 + 10.3923i −0.238479 + 0.413057i
\(634\) 1.50000 2.59808i 0.0595726 0.103183i
\(635\) −3.50000 6.06218i −0.138893 0.240570i
\(636\) −5.00000 −0.198263
\(637\) 6.50000 2.59808i 0.257539 0.102940i
\(638\) −3.00000 −0.118771
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 6.00000 10.3923i 0.236986 0.410471i −0.722862 0.690992i \(-0.757174\pi\)
0.959848 + 0.280521i \(0.0905072\pi\)
\(642\) −3.50000 6.06218i −0.138134 0.239255i
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 3.00000 + 15.5885i 0.118217 + 0.614271i
\(645\) 8.00000 0.315000
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) 2.00000 3.46410i 0.0786281 0.136188i −0.824030 0.566546i \(-0.808279\pi\)
0.902658 + 0.430358i \(0.141613\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −2.50000 4.33013i −0.0981336 0.169972i
\(650\) 4.00000 0.156893
\(651\) 22.0000 19.0526i 0.862248 0.746729i
\(652\) −8.00000 −0.313304
\(653\) 5.50000 + 9.52628i 0.215232 + 0.372792i 0.953344 0.301885i \(-0.0976160\pi\)
−0.738113 + 0.674678i \(0.764283\pi\)
\(654\) −6.00000 + 10.3923i −0.234619 + 0.406371i
\(655\) 0.500000 0.866025i 0.0195366 0.0338384i
\(656\) −6.00000 10.3923i −0.234261 0.405751i
\(657\) −10.0000 −0.390137
\(658\) −20.0000 6.92820i −0.779681 0.270089i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) −0.500000 0.866025i −0.0194625 0.0337100i
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) 4.00000 6.92820i 0.155464 0.269272i
\(663\) −3.00000 5.19615i −0.116510 0.201802i
\(664\) −17.0000 −0.659728
\(665\) 10.0000 + 3.46410i 0.387783 + 0.134332i
\(666\) 4.00000 0.154997
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 12.0000 20.7846i 0.464294 0.804181i
\(669\) −3.50000 + 6.06218i −0.135318 + 0.234377i
\(670\) 8.00000 + 13.8564i 0.309067 + 0.535320i
\(671\) −12.0000 −0.463255
\(672\) −2.00000 + 1.73205i −0.0771517 + 0.0668153i
\(673\) −39.0000 −1.50334 −0.751670 0.659540i \(-0.770751\pi\)
−0.751670 + 0.659540i \(0.770751\pi\)
\(674\) −12.5000 21.6506i −0.481482 0.833951i
\(675\) 2.00000 3.46410i 0.0769800 0.133333i
\(676\) −0.500000 + 0.866025i −0.0192308 + 0.0333087i
\(677\) 17.5000 + 30.3109i 0.672580 + 1.16494i 0.977170 + 0.212459i \(0.0681471\pi\)
−0.304590 + 0.952483i \(0.598520\pi\)
\(678\) −4.00000 −0.153619
\(679\) −6.50000 33.7750i −0.249447 1.29617i
\(680\) 6.00000 0.230089
\(681\) 7.50000 + 12.9904i 0.287401 + 0.497792i
\(682\) −5.50000 + 9.52628i −0.210606 + 0.364780i
\(683\) 13.5000 23.3827i 0.516563 0.894714i −0.483252 0.875481i \(-0.660544\pi\)
0.999815 0.0192323i \(-0.00612219\pi\)
\(684\) 2.00000 + 3.46410i 0.0764719 + 0.132453i
\(685\) 8.00000 0.305664
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 6.00000 0.228914
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) −2.50000 + 4.33013i −0.0952424 + 0.164965i
\(690\) −3.00000 + 5.19615i −0.114208 + 0.197814i
\(691\) 20.0000 + 34.6410i 0.760836 + 1.31781i 0.942420 + 0.334431i \(0.108544\pi\)
−0.181584 + 0.983375i \(0.558123\pi\)
\(692\) 6.00000 0.228086
\(693\) 0.500000 + 2.59808i 0.0189934 + 0.0986928i
\(694\) 20.0000 0.759190
\(695\) 0 0
\(696\) −1.50000 + 2.59808i −0.0568574 + 0.0984798i
\(697\) 36.0000 62.3538i 1.36360 2.36182i
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) 6.00000 0.226941
\(700\) 8.00000 6.92820i 0.302372 0.261861i
\(701\) −13.0000 −0.491003 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(702\) 0.500000 + 0.866025i 0.0188713 + 0.0326860i
\(703\) 8.00000 13.8564i 0.301726 0.522604i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −4.00000 6.92820i −0.150649 0.260931i
\(706\) 30.0000 1.12906
\(707\) 25.0000 + 8.66025i 0.940222 + 0.325702i
\(708\) −5.00000 −0.187912
\(709\) −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i \(-0.202606\pi\)
−0.916845 + 0.399244i \(0.869273\pi\)
\(710\) 3.00000 5.19615i 0.112588 0.195008i
\(711\) −3.50000 + 6.06218i −0.131260 + 0.227349i
\(712\) 6.00000 + 10.3923i 0.224860 + 0.389468i
\(713\) 66.0000 2.47172
\(714\) −15.0000 5.19615i −0.561361 0.194461i
\(715\) −1.00000 −0.0373979
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 3.00000 5.19615i 0.112037 0.194054i
\(718\) 11.0000 19.0526i 0.410516 0.711035i
\(719\) −23.0000 39.8372i −0.857755 1.48568i −0.874065 0.485809i \(-0.838525\pi\)
0.0163099 0.999867i \(-0.494808\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 7.50000 + 12.9904i 0.278928 + 0.483117i
\(724\) 8.00000 13.8564i 0.297318 0.514969i
\(725\) 6.00000 10.3923i 0.222834 0.385961i
\(726\) 5.00000 + 8.66025i 0.185567 + 0.321412i
\(727\) 19.0000 0.704671 0.352335 0.935874i \(-0.385388\pi\)
0.352335 + 0.935874i \(0.385388\pi\)
\(728\) 0.500000 + 2.59808i 0.0185312 + 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) −5.00000 8.66025i −0.185058 0.320530i
\(731\) −24.0000 + 41.5692i −0.887672 + 1.53749i
\(732\) −6.00000 + 10.3923i −0.221766 + 0.384111i
\(733\) −1.00000 1.73205i −0.0369358 0.0639748i 0.846967 0.531646i \(-0.178426\pi\)
−0.883902 + 0.467671i \(0.845093\pi\)
\(734\) −7.00000 −0.258375
\(735\) 6.50000 2.59808i 0.239756 0.0958315i
\(736\) −6.00000 −0.221163
\(737\) 8.00000 + 13.8564i 0.294684 + 0.510407i
\(738\) −6.00000 + 10.3923i −0.220863 + 0.382546i
\(739\) 13.0000 22.5167i 0.478213 0.828289i −0.521475 0.853266i \(-0.674618\pi\)
0.999688 + 0.0249776i \(0.00795146\pi\)
\(740\) 2.00000 + 3.46410i 0.0735215 + 0.127343i
\(741\) 4.00000 0.146944
\(742\) 2.50000 + 12.9904i 0.0917779 + 0.476892i
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 5.50000 + 9.52628i 0.201640 + 0.349250i
\(745\) −5.00000 + 8.66025i −0.183186 + 0.317287i
\(746\) −13.0000 + 22.5167i −0.475964 + 0.824394i
\(747\) 8.50000 + 14.7224i 0.310999 + 0.538666i
\(748\) 6.00000 0.219382
\(749\) −14.0000 + 12.1244i −0.511549 + 0.443014i
\(750\) 9.00000 0.328634
\(751\) −12.5000 21.6506i −0.456131 0.790043i 0.542621 0.839978i \(-0.317432\pi\)
−0.998752 + 0.0499348i \(0.984099\pi\)
\(752\) 4.00000 6.92820i 0.145865 0.252646i
\(753\) −8.50000 + 14.7224i −0.309757 + 0.536515i
\(754\) 1.50000 + 2.59808i 0.0546268 + 0.0946164i
\(755\) −13.0000 −0.473118
\(756\) 2.50000 + 0.866025i 0.0909241 + 0.0314970i
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) −8.00000 13.8564i −0.290573 0.503287i
\(759\) −3.00000 + 5.19615i −0.108893 + 0.188608i
\(760\) −2.00000 + 3.46410i −0.0725476 + 0.125656i
\(761\) 14.0000 + 24.2487i 0.507500 + 0.879015i 0.999962 + 0.00868155i \(0.00276346\pi\)
−0.492463 + 0.870334i \(0.663903\pi\)
\(762\) −7.00000 −0.253583
\(763\) 30.0000 + 10.3923i 1.08607 + 0.376227i
\(764\) −6.00000 −0.217072
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) 7.00000 12.1244i 0.252920 0.438071i
\(767\) −2.50000 + 4.33013i −0.0902698 + 0.156352i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 31.0000 1.11789 0.558944 0.829205i \(-0.311207\pi\)
0.558944 + 0.829205i \(0.311207\pi\)
\(770\) −2.00000 + 1.73205i −0.0720750 + 0.0624188i