Properties

Label 546.2.i.a.79.1
Level $546$
Weight $2$
Character 546.79
Analytic conductor $4.360$
Analytic rank $1$
Dimension $2$
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: \(1\)
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 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.79
Dual form 546.2.i.a.235.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +3.00000 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} +3.00000 q^{20} +(2.50000 - 0.866025i) q^{21} +3.00000 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} -9.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +6.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{40} -12.0000 q^{41} +(-0.500000 + 2.59808i) q^{42} -4.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(6.00000 - 10.3923i) 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} +(4.50000 + 7.79423i) q^{53} +(-0.500000 + 0.866025i) q^{54} +9.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -4.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-4.00000 + 6.92820i) q^{61} +5.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +(7.50000 - 2.59808i) q^{70} +6.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-2.00000 + 3.46410i) q^{75} -4.00000 q^{76} +(7.50000 - 2.59808i) q^{77} +1.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} +3.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +18.0000 q^{85} +(2.00000 - 3.46410i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{90} +(-0.500000 + 2.59808i) q^{91} +6.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(6.00000 + 10.3923i) q^{94} +(6.00000 + 10.3923i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 2 q^{13} - 4 q^{14} + 6 q^{15} - q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + 6 q^{20} + 5 q^{21} + 6 q^{22} - 6 q^{23} - q^{24} - 4 q^{25} - q^{26} + 2 q^{27} + 5 q^{28} - 18 q^{29} - 3 q^{30} - 5 q^{31} - q^{32} - 3 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{37} + 4 q^{38} - q^{39} - 3 q^{40} - 24 q^{41} - q^{42} - 8 q^{43} - 3 q^{44} - 3 q^{45} - 6 q^{46} + 12 q^{47} + 2 q^{48} - 13 q^{49} + 8 q^{50} - 6 q^{51} - q^{52} + 9 q^{53} - q^{54} + 18 q^{55} - q^{56} - 8 q^{57} + 9 q^{58} + 9 q^{59} - 3 q^{60} - 8 q^{61} + 10 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{65} - 3 q^{66} + 4 q^{67} - 6 q^{68} + 12 q^{69} + 15 q^{70} + 12 q^{71} - q^{72} - 14 q^{73} + 4 q^{74} - 4 q^{75} - 8 q^{76} + 15 q^{77} + 2 q^{78} + q^{79} - 3 q^{80} - q^{81} + 12 q^{82} + 6 q^{83} - 4 q^{84} + 36 q^{85} + 4 q^{86} + 9 q^{87} - 3 q^{88} + 6 q^{90} - q^{91} + 12 q^{92} - 5 q^{93} + 12 q^{94} + 12 q^{95} - q^{96} + 10 q^{97} + 11 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 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
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 1.00000 0.277350
\(14\) −2.00000 1.73205i −0.534522 0.462910i
\(15\) 3.00000 0.774597
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 3.00000 0.670820
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 3.00000 0.639602
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) −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
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) −1.50000 + 2.59808i −0.273861 + 0.474342i
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 6.00000 1.02899
\(35\) −6.00000 5.19615i −1.01419 0.878310i
\(36\) 1.00000 0.166667
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) −0.500000 + 2.59808i −0.0771517 + 0.400892i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 6.00000 10.3923i 0.875190 1.51587i 0.0186297 0.999826i \(-0.494070\pi\)
0.856560 0.516047i \(-0.172597\pi\)
\(48\) 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
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 9.00000 1.21356
\(56\) −0.500000 + 2.59808i −0.0668153 + 0.347183i
\(57\) −4.00000 −0.529813
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i \(0.0325726\pi\)
−0.408919 + 0.912571i \(0.634094\pi\)
\(60\) −1.50000 2.59808i −0.193649 0.335410i
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 5.00000 0.635001
\(63\) −2.00000 1.73205i −0.251976 0.218218i
\(64\) 1.00000 0.125000
\(65\) −1.50000 + 2.59808i −0.186052 + 0.322252i
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 6.00000 0.722315
\(70\) 7.50000 2.59808i 0.896421 0.310530i
\(71\) 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
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) −4.00000 −0.458831
\(77\) 7.50000 2.59808i 0.854704 0.296078i
\(78\) 1.00000 0.113228
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 6.00000 10.3923i 0.662589 1.14764i
\(83\) 3.00000 0.329293 0.164646 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) 18.0000 1.95237
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 4.50000 + 7.79423i 0.482451 + 0.835629i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 3.00000 0.316228
\(91\) −0.500000 + 2.59808i −0.0524142 + 0.272352i
\(92\) 6.00000 0.625543
\(93\) −2.50000 + 4.33013i −0.259238 + 0.449013i
\(94\) 6.00000 + 10.3923i 0.618853 + 1.07188i
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) 5.50000 4.33013i 0.555584 0.437409i
\(99\) 3.00000 0.301511
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −9.00000 15.5885i −0.895533 1.55111i −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 1.00000 0.0980581
\(105\) −1.50000 + 7.79423i −0.146385 + 0.760639i
\(106\) −9.00000 −0.874157
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) −4.50000 + 7.79423i −0.429058 + 0.743151i
\(111\) −4.00000 −0.379663
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 2.00000 3.46410i 0.187317 0.324443i
\(115\) −9.00000 15.5885i −0.839254 1.45363i
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) −9.00000 −0.828517
\(119\) 15.0000 5.19615i 1.37505 0.476331i
\(120\) 3.00000 0.273861
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) 6.00000 + 10.3923i 0.541002 + 0.937043i
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) −3.00000 −0.268328
\(126\) 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
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) −10.5000 + 18.1865i −0.917389 + 1.58896i −0.114024 + 0.993478i \(0.536374\pi\)
−0.803365 + 0.595487i \(0.796959\pi\)
\(132\) 3.00000 0.261116
\(133\) 8.00000 + 6.92820i 0.693688 + 0.600751i
\(134\) −4.00000 −0.345547
\(135\) −1.50000 + 2.59808i −0.129099 + 0.223607i
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) −3.00000 + 5.19615i −0.255377 + 0.442326i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −1.50000 + 7.79423i −0.126773 + 0.658733i
\(141\) −12.0000 −1.01058
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −1.50000 2.59808i −0.125436 0.217262i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 13.5000 23.3827i 1.12111 1.94183i
\(146\) 14.0000 1.15865
\(147\) 1.00000 + 6.92820i 0.0824786 + 0.571429i
\(148\) −4.00000 −0.328798
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) −2.00000 3.46410i −0.163299 0.282843i
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) 2.00000 3.46410i 0.162221 0.280976i
\(153\) 6.00000 0.485071
\(154\) −1.50000 + 7.79423i −0.120873 + 0.628077i
\(155\) 15.0000 1.20483
\(156\) −0.500000 + 0.866025i −0.0400320 + 0.0693375i
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 0.500000 + 0.866025i 0.0397779 + 0.0688973i
\(159\) 4.50000 7.79423i 0.356873 0.618123i
\(160\) 3.00000 0.237171
\(161\) −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 \(-0.934769\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) 6.00000 + 10.3923i 0.468521 + 0.811503i
\(165\) −4.50000 7.79423i −0.350325 0.606780i
\(166\) −1.50000 + 2.59808i −0.116423 + 0.201650i
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 2.50000 0.866025i 0.192879 0.0668153i
\(169\) 1.00000 0.0769231
\(170\) −9.00000 + 15.5885i −0.690268 + 1.19558i
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −9.00000 −0.682288
\(175\) 10.0000 3.46410i 0.755929 0.261861i
\(176\) 3.00000 0.226134
\(177\) 4.50000 7.79423i 0.338241 0.585850i
\(178\) 0 0
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) −1.50000 + 2.59808i −0.111803 + 0.193649i
\(181\) −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
\(183\) 8.00000 0.591377
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 6.00000 + 10.3923i 0.441129 + 0.764057i
\(186\) −2.50000 4.33013i −0.183309 0.317500i
\(187\) −9.00000 + 15.5885i −0.658145 + 1.13994i
\(188\) −12.0000 −0.875190
\(189\) −0.500000 + 2.59808i −0.0363696 + 0.188982i
\(190\) −12.0000 −0.870572
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 0.500000 + 0.866025i 0.0359908 + 0.0623379i 0.883460 0.468507i \(-0.155208\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(194\) −2.50000 + 4.33013i −0.179490 + 0.310885i
\(195\) 3.00000 0.214834
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) 2.00000 3.46410i 0.141069 0.244339i
\(202\) 18.0000 1.26648
\(203\) 4.50000 23.3827i 0.315838 1.64114i
\(204\) 6.00000 0.420084
\(205\) 18.0000 31.1769i 1.25717 2.17749i
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) −12.0000 −0.830057
\(210\) −6.00000 5.19615i −0.414039 0.358569i
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 4.50000 7.79423i 0.309061 0.535310i
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 6.00000 10.3923i 0.409197 0.708749i
\(216\) 1.00000 0.0680414
\(217\) 12.5000 4.33013i 0.848555 0.293948i
\(218\) −16.0000 −1.08366
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 2.00000 3.46410i 0.134231 0.232495i
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 2.50000 0.866025i 0.167038 0.0578638i
\(225\) 4.00000 0.266667
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) −13.0000 + 22.5167i −0.859064 + 1.48794i 0.0137585 + 0.999905i \(0.495620\pi\)
−0.872823 + 0.488037i \(0.837713\pi\)
\(230\) 18.0000 1.18688
\(231\) −6.00000 5.19615i −0.394771 0.341882i
\(232\) −9.00000 −0.590879
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −0.500000 0.866025i −0.0326860 0.0566139i
\(235\) 18.0000 + 31.1769i 1.17419 + 2.03376i
\(236\) 4.50000 7.79423i 0.292925 0.507361i
\(237\) −1.00000 −0.0649570
\(238\) −3.00000 + 15.5885i −0.194461 + 1.01045i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −1.50000 + 2.59808i −0.0968246 + 0.167705i
\(241\) −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i \(-0.982234\pi\)
0.450910 0.892570i \(-0.351100\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 8.00000 0.512148
\(245\) 16.5000 12.9904i 1.05415 0.829925i
\(246\) −12.0000 −0.765092
\(247\) 2.00000 3.46410i 0.127257 0.220416i
\(248\) −2.50000 4.33013i −0.158750 0.274963i
\(249\) −1.50000 2.59808i −0.0950586 0.164646i
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) −0.500000 + 2.59808i −0.0314970 + 0.163663i
\(253\) 18.0000 1.13165
\(254\) 3.50000 6.06218i 0.219610 0.380375i
\(255\) −9.00000 15.5885i −0.563602 0.976187i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.0000 25.9808i 0.935674 1.62064i 0.162247 0.986750i \(-0.448126\pi\)
0.773427 0.633885i \(-0.218541\pi\)
\(258\) −4.00000 −0.249029
\(259\) 8.00000 + 6.92820i 0.497096 + 0.430498i
\(260\) 3.00000 0.186052
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) −10.5000 18.1865i −0.648692 1.12357i
\(263\) −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i \(-0.225891\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) −27.0000 −1.65860
\(266\) −10.0000 + 3.46410i −0.613139 + 0.212398i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −1.50000 2.59808i −0.0914566 0.158408i 0.816668 0.577108i \(-0.195819\pi\)
−0.908124 + 0.418701i \(0.862486\pi\)
\(270\) −1.50000 2.59808i −0.0912871 0.158114i
\(271\) 3.50000 6.06218i 0.212610 0.368251i −0.739921 0.672694i \(-0.765137\pi\)
0.952531 + 0.304443i \(0.0984703\pi\)
\(272\) 6.00000 0.363803
\(273\) 2.50000 0.866025i 0.151307 0.0524142i
\(274\) −12.0000 −0.724947
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) −3.00000 5.19615i −0.180579 0.312772i
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) 5.00000 0.299342
\(280\) −6.00000 5.19615i −0.358569 0.310530i
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 6.00000 10.3923i 0.357295 0.618853i
\(283\) −1.00000 1.73205i −0.0594438 0.102960i 0.834772 0.550596i \(-0.185599\pi\)
−0.894216 + 0.447636i \(0.852266\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 6.00000 10.3923i 0.355409 0.615587i
\(286\) 3.00000 0.177394
\(287\) 6.00000 31.1769i 0.354169 1.84032i
\(288\) 1.00000 0.0589256
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 13.5000 + 23.3827i 0.792747 + 1.37308i
\(291\) −2.50000 4.33013i −0.146553 0.253837i
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) −6.50000 2.59808i −0.379088 0.151523i
\(295\) −27.0000 −1.57200
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) −1.50000 2.59808i −0.0870388 0.150756i
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 4.00000 0.230940
\(301\) 2.00000 10.3923i 0.115278 0.599002i
\(302\) −19.0000 −1.09333
\(303\) −9.00000 + 15.5885i −0.517036 + 0.895533i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) −12.0000 20.7846i −0.687118 1.19012i
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −6.00000 5.19615i −0.341882 0.296078i
\(309\) 8.00000 0.455104
\(310\) −7.50000 + 12.9904i −0.425971 + 0.737804i
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) −0.500000 0.866025i −0.0283069 0.0490290i
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) 2.00000 0.112867
\(315\) 7.50000 2.59808i 0.422577 0.146385i
\(316\) −1.00000 −0.0562544
\(317\) 7.50000 12.9904i 0.421242 0.729612i −0.574819 0.818280i \(-0.694928\pi\)
0.996061 + 0.0886679i \(0.0282610\pi\)
\(318\) 4.50000 + 7.79423i 0.252347 + 0.437079i
\(319\) 13.5000 + 23.3827i 0.755855 + 1.30918i
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) 3.00000 0.167444
\(322\) 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
\(327\) 8.00000 13.8564i 0.442401 0.766261i
\(328\) −12.0000 −0.662589
\(329\) 24.0000 + 20.7846i 1.32316 + 1.14589i
\(330\) 9.00000 0.495434
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) −1.50000 2.59808i −0.0823232 0.142588i
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) −12.0000 −0.655630
\(336\) −0.500000 + 2.59808i −0.0272772 + 0.141737i
\(337\) −31.0000 −1.68868 −0.844339 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) −0.500000 + 0.866025i −0.0271964 + 0.0471056i
\(339\) 6.00000 + 10.3923i 0.325875 + 0.564433i
\(340\) −9.00000 15.5885i −0.488094 0.845403i
\(341\) −7.50000 + 12.9904i −0.406148 + 0.703469i
\(342\) −4.00000 −0.216295
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −4.00000 −0.215666
\(345\) −9.00000 + 15.5885i −0.484544 + 0.839254i
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 4.50000 7.79423i 0.241225 0.417815i
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) −2.00000 + 10.3923i −0.106904 + 0.555492i
\(351\) 1.00000 0.0533761
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 15.0000 + 25.9808i 0.798369 + 1.38282i 0.920677 + 0.390324i \(0.127637\pi\)
−0.122308 + 0.992492i \(0.539030\pi\)
\(354\) 4.50000 + 7.79423i 0.239172 + 0.414259i
\(355\) −9.00000 + 15.5885i −0.477670 + 0.827349i
\(356\) 0 0
\(357\) −12.0000 10.3923i −0.635107 0.550019i
\(358\) 12.0000 0.634220
\(359\) 3.00000 5.19615i 0.158334 0.274242i −0.775934 0.630814i \(-0.782721\pi\)
0.934268 + 0.356572i \(0.116054\pi\)
\(360\) −1.50000 2.59808i −0.0790569 0.136931i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 8.00000 13.8564i 0.420471 0.728277i
\(363\) −2.00000 −0.104973
\(364\) 2.50000 0.866025i 0.131036 0.0453921i
\(365\) 42.0000 2.19838
\(366\) −4.00000 + 6.92820i −0.209083 + 0.362143i
\(367\) 3.50000 + 6.06218i 0.182699 + 0.316443i 0.942799 0.333363i \(-0.108183\pi\)
−0.760100 + 0.649806i \(0.774850\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 6.00000 10.3923i 0.312348 0.541002i
\(370\) −12.0000 −0.623850
\(371\) −22.5000 + 7.79423i −1.16814 + 0.404656i
\(372\) 5.00000 0.259238
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) −9.00000 15.5885i −0.465379 0.806060i
\(375\) 1.50000 + 2.59808i 0.0774597 + 0.134164i
\(376\) 6.00000 10.3923i 0.309426 0.535942i
\(377\) −9.00000 −0.463524
\(378\) −2.00000 1.73205i −0.102869 0.0890871i
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) 3.50000 + 6.06218i 0.179310 + 0.310575i
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) 3.00000 5.19615i 0.153293 0.265511i −0.779143 0.626846i \(-0.784346\pi\)
0.932436 + 0.361335i \(0.117679\pi\)
\(384\) 1.00000 0.0510310
\(385\) −4.50000 + 23.3827i −0.229341 + 1.19169i
\(386\) −1.00000 −0.0508987
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) −15.0000 25.9808i −0.760530 1.31728i −0.942578 0.333987i \(-0.891606\pi\)
0.182047 0.983290i \(-0.441728\pi\)
\(390\) −1.50000 + 2.59808i −0.0759555 + 0.131559i
\(391\) 36.0000 1.82060
\(392\) −6.50000 2.59808i −0.328300 0.131223i
\(393\) 21.0000 1.05931
\(394\) 9.00000 15.5885i 0.453413 0.785335i
\(395\) 1.50000 + 2.59808i 0.0754732 + 0.130723i
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) 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 \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 2.00000 + 3.46410i 0.0997509 + 0.172774i
\(403\) −2.50000 4.33013i −0.124534 0.215699i
\(404\) −9.00000 + 15.5885i −0.447767 + 0.775555i
\(405\) 3.00000 0.149071
\(406\) 18.0000 + 15.5885i 0.893325 + 0.773642i
\(407\) −12.0000 −0.594818
\(408\) −3.00000 + 5.19615i −0.148522 + 0.257248i
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 18.0000 + 31.1769i 0.888957 + 1.53972i
\(411\) 6.00000 10.3923i 0.295958 0.512615i
\(412\) 8.00000 0.394132
\(413\) −22.5000 + 7.79423i −1.10715 + 0.383529i
\(414\) 6.00000 0.294884
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 2.00000 + 3.46410i 0.0979404 + 0.169638i
\(418\) 6.00000 10.3923i 0.293470 0.508304i
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 7.50000 2.59808i 0.365963 0.126773i
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −4.00000 + 6.92820i −0.194717 + 0.337260i
\(423\) 6.00000 + 10.3923i 0.291730 + 0.505291i
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) −12.0000 + 20.7846i −0.582086 + 1.00820i
\(426\) 6.00000 0.290701
\(427\) −16.0000 13.8564i −0.774294 0.670559i
\(428\) 3.00000 0.145010
\(429\) −1.50000 + 2.59808i −0.0724207 + 0.125436i
\(430\) 6.00000 + 10.3923i 0.289346 + 0.501161i
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) −2.50000 + 12.9904i −0.120004 + 0.623558i
\(435\) −27.0000 −1.29455
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) 12.0000 + 20.7846i 0.574038 + 0.994263i
\(438\) −7.00000 12.1244i −0.334473 0.579324i
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) 9.00000 0.429058
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) 6.00000 0.285391
\(443\) 1.50000 2.59808i 0.0712672 0.123438i −0.828190 0.560448i \(-0.810629\pi\)
0.899457 + 0.437009i \(0.143962\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 0 0
\(446\) 0.500000 0.866025i 0.0236757 0.0410075i
\(447\) 6.00000 0.283790
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) −2.00000 + 3.46410i −0.0942809 + 0.163299i
\(451\) 18.0000 + 31.1769i 0.847587 + 1.46806i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 9.50000 16.4545i 0.446349 0.773099i
\(454\) −3.00000 −0.140797
\(455\) −6.00000 5.19615i −0.281284 0.243599i
\(456\) −4.00000 −0.187317
\(457\) 9.50000 16.4545i 0.444391 0.769708i −0.553618 0.832771i \(-0.686753\pi\)
0.998010 + 0.0630623i \(0.0200867\pi\)
\(458\) −13.0000 22.5167i −0.607450 1.05213i
\(459\) −3.00000 5.19615i −0.140028 0.242536i
\(460\) −9.00000 + 15.5885i −0.419627 + 0.726816i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 7.50000 2.59808i 0.348932 0.120873i
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) −7.50000 12.9904i −0.347804 0.602414i
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) 18.0000 31.1769i 0.832941 1.44270i −0.0627555 0.998029i \(-0.519989\pi\)
0.895696 0.444667i \(-0.146678\pi\)
\(468\) 1.00000 0.0462250
\(469\) −10.0000 + 3.46410i −0.461757 + 0.159957i
\(470\) −36.0000 −1.66056
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) 4.50000 + 7.79423i 0.207129 + 0.358758i
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) 0.500000 0.866025i 0.0229658 0.0397779i
\(475\) −16.0000 −0.734130
\(476\) −12.0000 10.3923i −0.550019 0.476331i
\(477\) −9.00000 −0.412082
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) −1.50000 2.59808i −0.0684653 0.118585i
\(481\) 2.00000 3.46410i 0.0911922 0.157949i
\(482\) 17.0000 0.774329
\(483\) −3.00000 + 15.5885i −0.136505 + 0.709299i
\(484\) −2.00000 −0.0909091
\(485\) −7.50000 + 12.9904i −0.340557 + 0.589863i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −11.5000 19.9186i −0.521115 0.902597i −0.999698 0.0245553i \(-0.992183\pi\)
0.478584 0.878042i \(-0.341150\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 8.00000 0.361773
\(490\) 3.00000 + 20.7846i 0.135526 + 0.938953i
\(491\) −15.0000 −0.676941 −0.338470 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) 27.0000 + 46.7654i 1.21602 + 2.10621i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) −4.50000 + 7.79423i −0.202260 + 0.350325i
\(496\) 5.00000 0.224507
\(497\) −3.00000 + 15.5885i −0.134568 + 0.699238i
\(498\) 3.00000 0.134433
\(499\) 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 1.50000 2.59808i 0.0669483 0.115958i
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) −2.00000 1.73205i −0.0890871 0.0771517i
\(505\) 54.0000 2.40297
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) −0.500000 0.866025i −0.0222058 0.0384615i
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) −4.50000 + 7.79423i −0.199459 + 0.345473i −0.948353 0.317217i \(-0.897252\pi\)
0.748894 + 0.662690i \(0.230585\pi\)
\(510\) 18.0000 0.797053
\(511\) 35.0000 12.1244i 1.54831 0.536350i
\(512\) 1.00000 0.0441942
\(513\) 2.00000 3.46410i 0.0883022 0.152944i
\(514\) 15.0000 + 25.9808i 0.661622 + 1.14596i
\(515\) −12.0000 20.7846i −0.528783 0.915879i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) −36.0000 −1.58328
\(518\) −10.0000 + 3.46410i −0.439375 + 0.152204i
\(519\) 6.00000 0.263371
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) −4.00000 + 6.92820i −0.174908 + 0.302949i −0.940129 0.340818i \(-0.889296\pi\)
0.765222 + 0.643767i \(0.222629\pi\)
\(524\) 21.0000 0.917389
\(525\) −8.00000 6.92820i −0.349149 0.302372i
\(526\) 6.00000 0.261612
\(527\) −15.0000 + 25.9808i −0.653410 + 1.13174i
\(528\) −1.50000 2.59808i −0.0652791 0.113067i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 13.5000 23.3827i 0.586403 1.01568i
\(531\) −9.00000 −0.390567
\(532\) 2.00000 10.3923i 0.0867110 0.450564i
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) −4.50000 7.79423i −0.194552 0.336974i
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) 3.00000 0.129339
\(539\) 3.00000 + 20.7846i 0.129219 + 0.895257i
\(540\) 3.00000 0.129099
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) 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
\(545\) −48.0000 −2.05609
\(546\) −0.500000 + 2.59808i −0.0213980 + 0.111187i
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) −4.00000 6.92820i −0.170716 0.295689i
\(550\) −6.00000 10.3923i −0.255841 0.443129i
\(551\) −18.0000 + 31.1769i −0.766826 + 1.32818i
\(552\) 6.00000 0.255377
\(553\) 2.00000 + 1.73205i 0.0850487 + 0.0736543i
\(554\) 2.00000 0.0849719
\(555\) 6.00000 10.3923i 0.254686 0.441129i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 10.5000 + 18.1865i 0.444899 + 0.770588i 0.998045 0.0624962i \(-0.0199061\pi\)
−0.553146 + 0.833084i \(0.686573\pi\)
\(558\) −2.50000 + 4.33013i −0.105833 + 0.183309i
\(559\) −4.00000 −0.169182
\(560\) 7.50000 2.59808i 0.316933 0.109789i
\(561\) 18.0000 0.759961
\(562\) 0 0
\(563\) −16.5000 28.5788i −0.695392 1.20445i −0.970048 0.242912i \(-0.921897\pi\)
0.274656 0.961542i \(-0.411436\pi\)
\(564\) 6.00000 + 10.3923i 0.252646 + 0.437595i
\(565\) 18.0000 31.1769i 0.757266 1.31162i
\(566\) 2.00000 0.0840663
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) 6.00000 0.251754
\(569\) −6.00000 + 10.3923i −0.251533 + 0.435668i −0.963948 0.266090i \(-0.914268\pi\)
0.712415 + 0.701758i \(0.247601\pi\)
\(570\) 6.00000 + 10.3923i 0.251312 + 0.435286i
\(571\) 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i \(0.149011\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(572\) −1.50000 + 2.59808i −0.0627182 + 0.108631i
\(573\) 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
\(577\) −8.50000 14.7224i −0.353860 0.612903i 0.633062 0.774101i \(-0.281798\pi\)
−0.986922 + 0.161198i \(0.948464\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 0.500000 0.866025i 0.0207793 0.0359908i
\(580\) −27.0000 −1.12111
\(581\) −1.50000 + 7.79423i −0.0622305 + 0.323359i
\(582\) 5.00000 0.207257
\(583\) 13.5000 23.3827i 0.559113 0.968412i
\(584\) −7.00000 12.1244i −0.289662 0.501709i
\(585\) −1.50000 2.59808i −0.0620174 0.107417i
\(586\) −10.5000 + 18.1865i −0.433751 + 0.751279i
\(587\) 33.0000 1.36206 0.681028 0.732257i \(-0.261533\pi\)
0.681028 + 0.732257i \(0.261533\pi\)
\(588\) 5.50000 4.33013i 0.226816 0.178571i
\(589\) −20.0000 −0.824086
\(590\) 13.5000 23.3827i 0.555786 0.962650i
\(591\) 9.00000 + 15.5885i 0.370211 + 0.641223i
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) 3.00000 0.123091
\(595\) −9.00000 + 46.7654i −0.368964 + 1.91719i
\(596\) 6.00000 0.245770
\(597\) −4.00000 + 6.92820i −0.163709 + 0.283552i
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) −3.00000 5.19615i −0.122577 0.212309i 0.798206 0.602384i \(-0.205782\pi\)
−0.920783 + 0.390075i \(0.872449\pi\)
\(600\) −2.00000 + 3.46410i −0.0816497 + 0.141421i
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 8.00000 + 6.92820i 0.326056 + 0.282372i
\(603\) −4.00000 −0.162893
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) 3.00000 + 5.19615i 0.121967 + 0.211254i
\(606\) −9.00000 15.5885i −0.365600 0.633238i
\(607\) −2.50000 + 4.33013i −0.101472 + 0.175754i −0.912291 0.409542i \(-0.865689\pi\)
0.810819 + 0.585296i \(0.199022\pi\)
\(608\) −4.00000 −0.162221
\(609\) −22.5000 + 7.79423i −0.911746 + 0.315838i
\(610\) 24.0000 0.971732
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) −3.00000 5.19615i −0.121268 0.210042i
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) −36.0000 −1.45166
\(616\) 7.50000 2.59808i 0.302184 0.104679i
\(617\) 48.0000 1.93241 0.966204 0.257780i \(-0.0829910\pi\)
0.966204 + 0.257780i \(0.0829910\pi\)
\(618\) −4.00000 + 6.92820i −0.160904 + 0.278693i
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) −7.50000 12.9904i −0.301207 0.521706i
\(621\) −3.00000 + 5.19615i −0.120386 + 0.208514i
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 9.50000 + 16.4545i 0.379696 + 0.657653i
\(627\) 6.00000 + 10.3923i 0.239617 + 0.415029i
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) −24.0000 −0.956943
\(630\) −1.50000 + 7.79423i −0.0597614 + 0.310530i
\(631\) −13.0000 −0.517522 −0.258761 0.965941i \(-0.583314\pi\)
−0.258761 + 0.965941i \(0.583314\pi\)
\(632\) 0.500000 0.866025i 0.0198889 0.0344486i
\(633\) −4.00000 6.92820i −0.158986 0.275371i
\(634\) 7.50000 + 12.9904i 0.297863 + 0.515914i
\(635\) 10.5000 18.1865i 0.416680 0.721711i
\(636\) −9.00000 −0.356873
\(637\) −6.50000 2.59808i −0.257539 0.102940i
\(638\) −27.0000 −1.06894
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) −1.50000 + 2.59808i −0.0592003 + 0.102538i
\(643\) 8.00000 0.315489 0.157745 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) −3.00000 + 15.5885i −0.118217 + 0.614271i
\(645\) −12.0000 −0.472500
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 13.5000 23.3827i 0.529921 0.917851i
\(650\) 4.00000 0.156893
\(651\) −10.0000 8.66025i −0.391931 0.339422i
\(652\) 8.00000 0.313304
\(653\) −4.50000 + 7.79423i −0.176099 + 0.305012i −0.940541 0.339680i \(-0.889681\pi\)
0.764442 + 0.644692i \(0.223014\pi\)
\(654\) 8.00000 + 13.8564i 0.312825 + 0.541828i
\(655\) −31.5000 54.5596i −1.23081 2.13182i
\(656\) 6.00000 10.3923i 0.234261 0.405751i
\(657\) 14.0000 0.546192
\(658\) −30.0000 + 10.3923i −1.16952 + 0.405134i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) −4.50000 + 7.79423i −0.175162 + 0.303390i
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −16.0000 27.7128i −0.621858 1.07709i
\(663\) −3.00000 + 5.19615i −0.116510 + 0.201802i
\(664\) 3.00000 0.116423
\(665\) −30.0000 + 10.3923i −1.16335 + 0.402996i
\(666\) −4.00000 −0.154997
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) −6.00000 10.3923i −0.232147 0.402090i
\(669\) 0.500000 + 0.866025i 0.0193311 + 0.0334825i
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) 24.0000 0.926510
\(672\) −2.00000 1.73205i −0.0771517 0.0668153i
\(673\) −31.0000 −1.19496 −0.597481 0.801883i \(-0.703832\pi\)
−0.597481 + 0.801883i \(0.703832\pi\)
\(674\) 15.5000 26.8468i 0.597038 1.03410i
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) −4.50000 + 7.79423i −0.172949 + 0.299557i −0.939450 0.342687i \(-0.888663\pi\)
0.766501 + 0.642244i \(0.221996\pi\)
\(678\) −12.0000 −0.460857
\(679\) −2.50000 + 12.9904i −0.0959412 + 0.498525i
\(680\) 18.0000 0.690268
\(681\) 1.50000 2.59808i 0.0574801 0.0995585i
\(682\) −7.50000 12.9904i −0.287190 0.497427i
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) 2.00000 3.46410i 0.0764719 0.132453i
\(685\) −36.0000 −1.37549
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 26.0000 0.991962
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 4.50000 + 7.79423i 0.171436 + 0.296936i
\(690\) −9.00000 15.5885i −0.342624 0.593442i
\(691\) 20.0000 34.6410i 0.760836 1.31781i −0.181584 0.983375i \(-0.558123\pi\)
0.942420 0.334431i \(-0.108544\pi\)
\(692\) 6.00000 0.228086
\(693\) −1.50000 + 7.79423i −0.0569803 + 0.296078i
\(694\) 12.0000 0.455514
\(695\) 6.00000 10.3923i 0.227593 0.394203i
\(696\) 4.50000 + 7.79423i 0.170572 + 0.295439i
\(697\) 36.0000 + 62.3538i 1.36360 + 2.36182i
\(698\) 17.0000 29.4449i 0.643459 1.11450i
\(699\) −6.00000 −0.226941
\(700\) −8.00000 6.92820i −0.302372 0.261861i
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) −0.500000 + 0.866025i −0.0188713 + 0.0326860i
\(703\) −8.00000 13.8564i −0.301726 0.522604i
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) 18.0000 31.1769i 0.677919 1.17419i
\(706\) −30.0000 −1.12906
\(707\) 45.0000 15.5885i 1.69240 0.586264i
\(708\) −9.00000 −0.338241
\(709\) 17.0000 29.4449i 0.638448 1.10583i −0.347325 0.937745i \(-0.612910\pi\)
0.985773 0.168080i \(-0.0537568\pi\)
\(710\) −9.00000 15.5885i −0.337764 0.585024i
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) 30.0000 1.12351
\(714\) 15.0000 5.19615i 0.561361 0.194461i
\(715\) 9.00000 0.336581
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) −3.00000 5.19615i −0.112037 0.194054i
\(718\) 3.00000 + 5.19615i 0.111959 + 0.193919i
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 3.00000 0.111803
\(721\) −16.0000 13.8564i −0.595871 0.516040i
\(722\) −3.00000 −0.111648
\(723\) −8.50000 + 14.7224i −0.316118 + 0.547533i
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 18.0000 + 31.1769i 0.668503 + 1.15788i
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) −37.0000 −1.37225 −0.686127 0.727482i \(-0.740691\pi\)
−0.686127 + 0.727482i \(0.740691\pi\)
\(728\) −0.500000 + 2.59808i −0.0185312 + 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) −21.0000 + 36.3731i −0.777245 + 1.34623i
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) −4.00000 6.92820i −0.147844 0.256074i
\(733\) −25.0000 + 43.3013i −0.923396 + 1.59937i −0.129275 + 0.991609i \(0.541265\pi\)
−0.794121 + 0.607760i \(0.792068\pi\)
\(734\) −7.00000 −0.258375
\(735\) −19.5000 7.79423i −0.719268 0.287494i
\(736\) 6.00000 0.221163
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 6.00000 + 10.3923i 0.220863 + 0.382546i
\(739\) −19.0000 32.9090i −0.698926 1.21058i −0.968839 0.247691i \(-0.920328\pi\)
0.269913 0.962885i \(-0.413005\pi\)
\(740\) 6.00000 10.3923i 0.220564 0.382029i
\(741\) −4.00000 −0.146944
\(742\) 4.50000 23.3827i 0.165200 0.858405i
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) −2.50000 + 4.33013i −0.0916544 + 0.158750i
\(745\) −9.00000 15.5885i −0.329734 0.571117i
\(746\) −7.00000 12.1244i −0.256288 0.443904i
\(747\) −1.50000 + 2.59808i −0.0548821 + 0.0950586i
\(748\) 18.0000 0.658145
\(749\) −6.00000 5.19615i −0.219235 0.189863i
\(750\) −3.00000 −0.109545
\(751\) 15.5000 26.8468i 0.565603 0.979653i −0.431390 0.902165i \(-0.641977\pi\)
0.996993 0.0774878i \(-0.0246899\pi\)
\(752\) 6.00000 + 10.3923i 0.218797 + 0.378968i
\(753\) 1.50000 + 2.59808i 0.0546630 + 0.0946792i
\(754\) 4.50000 7.79423i 0.163880 0.283849i
\(755\) −57.0000 −2.07444
\(756\) 2.50000 0.866025i 0.0909241 0.0314970i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 8.00000 13.8564i 0.290573 0.503287i
\(759\) −9.00000 15.5885i −0.326679 0.565825i
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) −18.0000 + 31.1769i −0.652499 + 1.13016i 0.330015 + 0.943976i \(0.392946\pi\)
−0.982514 + 0.186187i \(0.940387\pi\)
\(762\) −7.00000 −0.253583
\(763\) −40.0000 + 13.8564i −1.44810 + 0.501636i
\(764\) 6.00000 0.217072
\(765\) −9.00000 + 15.5885i −0.325396 + 0.563602i
\(766\) 3.00000 + 5.19615i 0.108394 + 0.187745i
\(767\) 4.50000 + 7.79423i 0.162486 + 0.281433i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −1.00000 −0.0360609 −0.0180305 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i