Properties

Label 126.2.f.a.43.1
Level $126$
Weight $2$
Character 126.43
Analytic conductor $1.006$
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] = [126,2,Mod(43,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.f (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.00611506547\)
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 43.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.43
Dual form 126.2.f.a.85.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +3.00000 q^{10} +(3.00000 - 5.19615i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-4.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} -7.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 - 2.59808i) q^{23} -1.73205i q^{24} +(-2.00000 + 3.46410i) q^{25} -2.00000 q^{26} -5.19615i q^{27} +1.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +5.19615i q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(9.00000 + 5.19615i) q^{33} +(3.00000 - 5.19615i) q^{34} -3.00000 q^{35} +(1.50000 + 2.59808i) q^{36} +2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +(3.00000 - 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-1.50000 + 0.866025i) q^{42} +(-1.00000 + 1.73205i) q^{43} -6.00000 q^{44} +(-4.50000 - 7.79423i) q^{45} -3.00000 q^{46} +(-1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.00000 + 3.46410i) q^{50} +10.3923i q^{51} +(-1.00000 + 1.73205i) q^{52} +6.00000 q^{53} +(-4.50000 - 2.59808i) q^{54} +18.0000 q^{55} +(0.500000 - 0.866025i) q^{56} -12.1244i q^{57} +(3.00000 + 5.19615i) q^{58} +(4.50000 + 2.59808i) q^{60} +(-2.50000 + 4.33013i) q^{61} -2.00000 q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(9.00000 - 5.19615i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(4.50000 - 2.59808i) q^{69} +(-1.50000 + 2.59808i) q^{70} +3.00000 q^{71} +3.00000 q^{72} +2.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(3.50000 + 6.06218i) q^{76} +(3.00000 + 5.19615i) q^{77} -3.46410i q^{78} +(-2.50000 + 4.33013i) q^{79} -3.00000 q^{80} +9.00000 q^{81} +(-6.00000 + 10.3923i) q^{83} +1.73205i q^{84} +(9.00000 + 15.5885i) q^{85} +(1.00000 + 1.73205i) q^{86} +(-9.00000 - 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} -9.00000 q^{90} +2.00000 q^{91} +(-1.50000 + 2.59808i) q^{92} +(3.00000 - 1.73205i) q^{93} +(-10.5000 - 18.1865i) q^{95} +(-1.50000 + 0.866025i) q^{96} +(-1.00000 + 1.73205i) q^{97} -1.00000 q^{98} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 3 q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 3 q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9} + 6 q^{10} + 6 q^{11} + 3 q^{12} - 2 q^{13} + q^{14} - 9 q^{15} - q^{16} + 12 q^{17} - 3 q^{18} - 14 q^{19} + 3 q^{20} - 3 q^{21} - 6 q^{22} - 3 q^{23} - 4 q^{25} - 4 q^{26} + 2 q^{28} - 6 q^{29} - 2 q^{31} + q^{32} + 18 q^{33} + 6 q^{34} - 6 q^{35} + 3 q^{36} + 4 q^{37} - 7 q^{38} + 6 q^{39} - 3 q^{40} - 3 q^{42} - 2 q^{43} - 12 q^{44} - 9 q^{45} - 6 q^{46} - 3 q^{48} - q^{49} + 4 q^{50} - 2 q^{52} + 12 q^{53} - 9 q^{54} + 36 q^{55} + q^{56} + 6 q^{58} + 9 q^{60} - 5 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} + 6 q^{65} + 18 q^{66} - 8 q^{67} - 6 q^{68} + 9 q^{69} - 3 q^{70} + 6 q^{71} + 6 q^{72} + 4 q^{73} + 2 q^{74} - 12 q^{75} + 7 q^{76} + 6 q^{77} - 5 q^{79} - 6 q^{80} + 18 q^{81} - 12 q^{83} + 18 q^{85} + 2 q^{86} - 18 q^{87} - 6 q^{88} - 18 q^{90} + 4 q^{91} - 3 q^{92} + 6 q^{93} - 21 q^{95} - 3 q^{96} - 2 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.73205i 1.00000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 1.50000 + 0.866025i 0.612372 + 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) 3.00000 0.948683
\(11\) 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) −4.50000 + 2.59808i −1.16190 + 0.670820i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) −1.50000 0.866025i −0.327327 0.188982i
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −2.00000 −0.392232
\(27\) 5.19615i 1.00000i
\(28\) 1.00000 0.188982
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 5.19615i 0.948683i
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 9.00000 + 5.19615i 1.56670 + 0.904534i
\(34\) 3.00000 5.19615i 0.514496 0.891133i
\(35\) −3.00000 −0.507093
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −3.50000 + 6.06218i −0.567775 + 0.983415i
\(39\) 3.00000 1.73205i 0.480384 0.277350i
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) −1.50000 + 0.866025i −0.231455 + 0.133631i
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) −6.00000 −0.904534
\(45\) −4.50000 7.79423i −0.670820 1.16190i
\(46\) −3.00000 −0.442326
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −1.50000 0.866025i −0.216506 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 10.3923i 1.45521i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 18.0000 2.42712
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 12.1244i 1.60591i
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 4.50000 + 2.59808i 0.580948 + 0.335410i
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) −2.00000 −0.254000
\(63\) 1.50000 2.59808i 0.188982 0.327327i
\(64\) 1.00000 0.125000
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 9.00000 5.19615i 1.10782 0.639602i
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 4.50000 2.59808i 0.541736 0.312772i
\(70\) −1.50000 + 2.59808i −0.179284 + 0.310530i
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 3.00000 0.353553
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −6.00000 3.46410i −0.692820 0.400000i
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) 3.00000 + 5.19615i 0.341882 + 0.592157i
\(78\) 3.46410i 0.392232i
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) −3.00000 −0.335410
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 1.73205i 0.188982i
\(85\) 9.00000 + 15.5885i 0.976187 + 1.69081i
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) −9.00000 5.19615i −0.964901 0.557086i
\(88\) −3.00000 + 5.19615i −0.319801 + 0.553912i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −9.00000 −0.948683
\(91\) 2.00000 0.209657
\(92\) −1.50000 + 2.59808i −0.156386 + 0.270868i
\(93\) 3.00000 1.73205i 0.311086 0.179605i
\(94\) 0 0
\(95\) −10.5000 18.1865i −1.07728 1.86590i
\(96\) −1.50000 + 0.866025i −0.153093 + 0.0883883i
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −1.00000 −0.101015
\(99\) −9.00000 + 15.5885i −0.904534 + 1.56670i
\(100\) 4.00000 0.400000
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 9.00000 + 5.19615i 0.891133 + 0.514496i
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 5.19615i 0.507093i
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 9.00000 15.5885i 0.858116 1.48630i
\(111\) 3.46410i 0.328798i
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −7.50000 12.9904i −0.705541 1.22203i −0.966496 0.256681i \(-0.917371\pi\)
0.260955 0.965351i \(-0.415962\pi\)
\(114\) −10.5000 6.06218i −0.983415 0.567775i
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 6.00000 0.557086
\(117\) 3.00000 + 5.19615i 0.277350 + 0.480384i
\(118\) 0 0
\(119\) −3.00000 + 5.19615i −0.275010 + 0.476331i
\(120\) 4.50000 2.59808i 0.410792 0.237171i
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 2.50000 + 4.33013i 0.226339 + 0.392031i
\(123\) 0 0
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 3.00000 0.268328
\(126\) −1.50000 2.59808i −0.133631 0.231455i
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −3.00000 1.73205i −0.264135 0.152499i
\(130\) −3.00000 5.19615i −0.263117 0.455733i
\(131\) 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i \(-0.0380462\pi\)
−0.599699 + 0.800226i \(0.704713\pi\)
\(132\) 10.3923i 0.904534i
\(133\) 3.50000 6.06218i 0.303488 0.525657i
\(134\) −8.00000 −0.691095
\(135\) 13.5000 7.79423i 1.16190 0.670820i
\(136\) −6.00000 −0.514496
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 5.19615i 0.442326i
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 1.50000 + 2.59808i 0.126773 + 0.219578i
\(141\) 0 0
\(142\) 1.50000 2.59808i 0.125877 0.218026i
\(143\) −12.0000 −1.00349
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) −18.0000 −1.49482
\(146\) 1.00000 1.73205i 0.0827606 0.143346i
\(147\) 1.50000 0.866025i 0.123718 0.0714286i
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) −6.00000 + 3.46410i −0.489898 + 0.282843i
\(151\) −11.5000 + 19.9186i −0.935857 + 1.62095i −0.162758 + 0.986666i \(0.552039\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 7.00000 0.567775
\(153\) −18.0000 −1.45521
\(154\) 6.00000 0.483494
\(155\) 3.00000 5.19615i 0.240966 0.417365i
\(156\) −3.00000 1.73205i −0.240192 0.138675i
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 2.50000 + 4.33013i 0.198889 + 0.344486i
\(159\) 10.3923i 0.824163i
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 3.00000 0.236433
\(162\) 4.50000 7.79423i 0.353553 0.612372i
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 0 0
\(165\) 31.1769i 2.42712i
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 1.50000 + 0.866025i 0.115728 + 0.0668153i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 18.0000 1.38054
\(171\) 21.0000 1.60591
\(172\) 2.00000 0.152499
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −9.00000 + 5.19615i −0.682288 + 0.393919i
\(175\) −2.00000 3.46410i −0.151186 0.261861i
\(176\) 3.00000 + 5.19615i 0.226134 + 0.391675i
\(177\) 0 0
\(178\) 0 0
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) −4.50000 + 7.79423i −0.335410 + 0.580948i
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 1.00000 1.73205i 0.0741249 0.128388i
\(183\) −7.50000 4.33013i −0.554416 0.320092i
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 3.46410i 0.254000i
\(187\) 18.0000 31.1769i 1.31629 2.27988i
\(188\) 0 0
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) −21.0000 −1.52350
\(191\) 4.50000 7.79423i 0.325609 0.563971i −0.656027 0.754738i \(-0.727764\pi\)
0.981635 + 0.190767i \(0.0610975\pi\)
\(192\) 1.73205i 0.125000i
\(193\) −8.50000 14.7224i −0.611843 1.05974i −0.990930 0.134382i \(-0.957095\pi\)
0.379086 0.925361i \(-0.376238\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 9.00000 + 5.19615i 0.644503 + 0.372104i
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 9.00000 + 15.5885i 0.639602 + 1.10782i
\(199\) 14.0000 0.992434 0.496217 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 12.0000 6.92820i 0.846415 0.488678i
\(202\) 4.50000 + 7.79423i 0.316619 + 0.548400i
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) 9.00000 5.19615i 0.630126 0.363803i
\(205\) 0 0
\(206\) 10.0000 0.696733
\(207\) 4.50000 + 7.79423i 0.312772 + 0.541736i
\(208\) 2.00000 0.138675
\(209\) −21.0000 + 36.3731i −1.45260 + 2.51598i
\(210\) −4.50000 2.59808i −0.310530 0.179284i
\(211\) −4.00000 6.92820i −0.275371 0.476957i 0.694857 0.719148i \(-0.255467\pi\)
−0.970229 + 0.242190i \(0.922134\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 5.19615i 0.356034i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −6.00000 −0.409197
\(216\) 5.19615i 0.353553i
\(217\) 2.00000 0.135769
\(218\) −5.00000 + 8.66025i −0.338643 + 0.586546i
\(219\) 3.46410i 0.234082i
\(220\) −9.00000 15.5885i −0.606780 1.05097i
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 3.00000 + 1.73205i 0.201347 + 0.116248i
\(223\) 14.0000 24.2487i 0.937509 1.62381i 0.167412 0.985887i \(-0.446459\pi\)
0.770097 0.637927i \(-0.220208\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 6.00000 10.3923i 0.400000 0.692820i
\(226\) −15.0000 −0.997785
\(227\) 7.50000 12.9904i 0.497792 0.862202i −0.502204 0.864749i \(-0.667477\pi\)
0.999997 + 0.00254715i \(0.000810783\pi\)
\(228\) −10.5000 + 6.06218i −0.695379 + 0.401478i
\(229\) 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i \(-0.156147\pi\)
−0.849032 + 0.528341i \(0.822814\pi\)
\(230\) −4.50000 7.79423i −0.296721 0.513936i
\(231\) −9.00000 + 5.19615i −0.592157 + 0.341882i
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 9.00000 0.589610 0.294805 0.955557i \(-0.404745\pi\)
0.294805 + 0.955557i \(0.404745\pi\)
\(234\) 6.00000 0.392232
\(235\) 0 0
\(236\) 0 0
\(237\) −7.50000 4.33013i −0.487177 0.281272i
\(238\) 3.00000 + 5.19615i 0.194461 + 0.336817i
\(239\) 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) 5.19615i 0.335410i
\(241\) −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) −25.0000 −1.60706
\(243\) 15.5885i 1.00000i
\(244\) 5.00000 0.320092
\(245\) 1.50000 2.59808i 0.0958315 0.165985i
\(246\) 0 0
\(247\) 7.00000 + 12.1244i 0.445399 + 0.771454i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) −18.0000 10.3923i −1.14070 0.658586i
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) −3.00000 −0.188982
\(253\) −18.0000 −1.13165
\(254\) 8.50000 14.7224i 0.533337 0.923768i
\(255\) −27.0000 + 15.5885i −1.69081 + 0.976187i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) −3.00000 + 1.73205i −0.186772 + 0.107833i
\(259\) −1.00000 + 1.73205i −0.0621370 + 0.107624i
\(260\) −6.00000 −0.372104
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 9.00000 0.556022
\(263\) 10.5000 18.1865i 0.647458 1.12143i −0.336270 0.941766i \(-0.609166\pi\)
0.983728 0.179664i \(-0.0575011\pi\)
\(264\) −9.00000 5.19615i −0.553912 0.319801i
\(265\) 9.00000 + 15.5885i 0.552866 + 0.957591i
\(266\) −3.50000 6.06218i −0.214599 0.371696i
\(267\) 0 0
\(268\) −4.00000 + 6.92820i −0.244339 + 0.423207i
\(269\) −9.00000 −0.548740 −0.274370 0.961624i \(-0.588469\pi\)
−0.274370 + 0.961624i \(0.588469\pi\)
\(270\) 15.5885i 0.948683i
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 3.46410i 0.209657i
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) 12.0000 + 20.7846i 0.723627 + 1.25336i
\(276\) −4.50000 2.59808i −0.270868 0.156386i
\(277\) 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) −5.00000 −0.299880
\(279\) 3.00000 + 5.19615i 0.179605 + 0.311086i
\(280\) 3.00000 0.179284
\(281\) 13.5000 23.3827i 0.805342 1.39489i −0.110717 0.993852i \(-0.535315\pi\)
0.916060 0.401042i \(-0.131352\pi\)
\(282\) 0 0
\(283\) 9.50000 + 16.4545i 0.564716 + 0.978117i 0.997076 + 0.0764162i \(0.0243478\pi\)
−0.432360 + 0.901701i \(0.642319\pi\)
\(284\) −1.50000 2.59808i −0.0890086 0.154167i
\(285\) 31.5000 18.1865i 1.86590 1.07728i
\(286\) −6.00000 + 10.3923i −0.354787 + 0.614510i
\(287\) 0 0
\(288\) −1.50000 2.59808i −0.0883883 0.153093i
\(289\) 19.0000 1.11765
\(290\) −9.00000 + 15.5885i −0.528498 + 0.915386i
\(291\) −3.00000 1.73205i −0.175863 0.101535i
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) 1.50000 + 2.59808i 0.0876309 + 0.151781i 0.906509 0.422186i \(-0.138737\pi\)
−0.818878 + 0.573967i \(0.805404\pi\)
\(294\) 1.73205i 0.101015i
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) −27.0000 15.5885i −1.56670 0.904534i
\(298\) 6.00000 0.347571
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 6.92820i 0.400000i
\(301\) −1.00000 1.73205i −0.0576390 0.0998337i
\(302\) 11.5000 + 19.9186i 0.661751 + 1.14619i
\(303\) −13.5000 7.79423i −0.775555 0.447767i
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) −15.0000 −0.858898
\(306\) −9.00000 + 15.5885i −0.514496 + 0.891133i
\(307\) −25.0000 −1.42683 −0.713413 0.700744i \(-0.752851\pi\)
−0.713413 + 0.700744i \(0.752851\pi\)
\(308\) 3.00000 5.19615i 0.170941 0.296078i
\(309\) −15.0000 + 8.66025i −0.853320 + 0.492665i
\(310\) −3.00000 5.19615i −0.170389 0.295122i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) −3.00000 + 1.73205i −0.169842 + 0.0980581i
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 13.0000 0.733632
\(315\) 9.00000 0.507093
\(316\) 5.00000 0.281272
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 9.00000 + 5.19615i 0.504695 + 0.291386i
\(319\) 18.0000 + 31.1769i 1.00781 + 1.74557i
\(320\) 1.50000 + 2.59808i 0.0838525 + 0.145237i
\(321\) 20.7846i 1.16008i
\(322\) 1.50000 2.59808i 0.0835917 0.144785i
\(323\) −42.0000 −2.33694
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 8.00000 0.443760
\(326\) 1.00000 1.73205i 0.0553849 0.0959294i
\(327\) 17.3205i 0.957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 27.0000 + 15.5885i 1.48630 + 0.858116i
\(331\) −13.0000 + 22.5167i −0.714545 + 1.23763i 0.248590 + 0.968609i \(0.420033\pi\)
−0.963135 + 0.269019i \(0.913301\pi\)
\(332\) 12.0000 0.658586
\(333\) −6.00000 −0.328798
\(334\) 0 0
\(335\) 12.0000 20.7846i 0.655630 1.13558i
\(336\) 1.50000 0.866025i 0.0818317 0.0472456i
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 22.5000 12.9904i 1.22203 0.705541i
\(340\) 9.00000 15.5885i 0.488094 0.845403i
\(341\) −12.0000 −0.649836
\(342\) 10.5000 18.1865i 0.567775 0.983415i
\(343\) 1.00000 0.0539949
\(344\) 1.00000 1.73205i 0.0539164 0.0933859i
\(345\) 13.5000 + 7.79423i 0.726816 + 0.419627i
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) 10.3923i 0.557086i
\(349\) −13.0000 + 22.5167i −0.695874 + 1.20529i 0.274011 + 0.961727i \(0.411649\pi\)
−0.969885 + 0.243563i \(0.921684\pi\)
\(350\) −4.00000 −0.213809
\(351\) −9.00000 + 5.19615i −0.480384 + 0.277350i
\(352\) 6.00000 0.319801
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) 0 0
\(355\) 4.50000 + 7.79423i 0.238835 + 0.413675i
\(356\) 0 0
\(357\) −9.00000 5.19615i −0.476331 0.275010i
\(358\) 9.00000 15.5885i 0.475665 0.823876i
\(359\) −3.00000 −0.158334 −0.0791670 0.996861i \(-0.525226\pi\)
−0.0791670 + 0.996861i \(0.525226\pi\)
\(360\) 4.50000 + 7.79423i 0.237171 + 0.410792i
\(361\) 30.0000 1.57895
\(362\) −12.5000 + 21.6506i −0.656985 + 1.13793i
\(363\) 37.5000 21.6506i 1.96824 1.13636i
\(364\) −1.00000 1.73205i −0.0524142 0.0907841i
\(365\) 3.00000 + 5.19615i 0.157027 + 0.271979i
\(366\) −7.50000 + 4.33013i −0.392031 + 0.226339i
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) 6.00000 0.311925
\(371\) −3.00000 + 5.19615i −0.155752 + 0.269771i
\(372\) −3.00000 1.73205i −0.155543 0.0898027i
\(373\) −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) −18.0000 31.1769i −0.930758 1.61212i
\(375\) 5.19615i 0.268328i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 4.50000 2.59808i 0.231455 0.133631i
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) −10.5000 + 18.1865i −0.538639 + 0.932949i
\(381\) 29.4449i 1.50851i
\(382\) −4.50000 7.79423i −0.230240 0.398787i
\(383\) 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i \(-0.0145596\pi\)
−0.539076 + 0.842257i \(0.681226\pi\)
\(384\) 1.50000 + 0.866025i 0.0765466 + 0.0441942i
\(385\) −9.00000 + 15.5885i −0.458682 + 0.794461i
\(386\) −17.0000 −0.865277
\(387\) 3.00000 5.19615i 0.152499 0.264135i
\(388\) 2.00000 0.101535
\(389\) −12.0000 + 20.7846i −0.608424 + 1.05382i 0.383076 + 0.923717i \(0.374865\pi\)
−0.991500 + 0.130105i \(0.958469\pi\)
\(390\) 9.00000 5.19615i 0.455733 0.263117i
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) −13.5000 + 7.79423i −0.680985 + 0.393167i
\(394\) 9.00000 15.5885i 0.453413 0.785335i
\(395\) −15.0000 −0.754732
\(396\) 18.0000 0.904534
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 7.00000 12.1244i 0.350878 0.607739i
\(399\) 10.5000 + 6.06218i 0.525657 + 0.303488i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 13.8564i 0.691095i
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) 9.00000 0.447767
\(405\) 13.5000 + 23.3827i 0.670820 + 1.16190i
\(406\) −6.00000 −0.297775
\(407\) 6.00000 10.3923i 0.297409 0.515127i
\(408\) 10.3923i 0.514496i
\(409\) −16.0000 27.7128i −0.791149 1.37031i −0.925256 0.379344i \(-0.876150\pi\)
0.134107 0.990967i \(-0.457183\pi\)
\(410\) 0 0
\(411\) −9.00000 5.19615i −0.443937 0.256307i
\(412\) 5.00000 8.66025i 0.246332 0.426660i
\(413\) 0 0
\(414\) 9.00000 0.442326
\(415\) −36.0000 −1.76717
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) 7.50000 4.33013i 0.367277 0.212047i
\(418\) 21.0000 + 36.3731i 1.02714 + 1.77906i
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) −4.50000 + 2.59808i −0.219578 + 0.126773i
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −8.00000 −0.389434
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) −12.0000 + 20.7846i −0.582086 + 1.00820i
\(426\) 4.50000 + 2.59808i 0.218026 + 0.125877i
\(427\) −2.50000 4.33013i −0.120983 0.209550i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 20.7846i 1.00349i
\(430\) −3.00000 + 5.19615i −0.144673 + 0.250581i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 1.00000 1.73205i 0.0480015 0.0831411i
\(435\) 31.1769i 1.49482i
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 10.5000 + 18.1865i 0.502283 + 0.869980i
\(438\) 3.00000 + 1.73205i 0.143346 + 0.0827606i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) −18.0000 −0.858116
\(441\) 1.50000 + 2.59808i 0.0714286 + 0.123718i
\(442\) −12.0000 −0.570782
\(443\) −9.00000 + 15.5885i −0.427603 + 0.740630i −0.996660 0.0816684i \(-0.973975\pi\)
0.569057 + 0.822298i \(0.307309\pi\)
\(444\) 3.00000 1.73205i 0.142374 0.0821995i
\(445\) 0 0
\(446\) −14.0000 24.2487i −0.662919 1.14821i
\(447\) −9.00000 + 5.19615i −0.425685 + 0.245770i
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) −6.00000 10.3923i −0.282843 0.489898i
\(451\) 0 0
\(452\) −7.50000 + 12.9904i −0.352770 + 0.611016i
\(453\) −34.5000 19.9186i −1.62095 0.935857i
\(454\) −7.50000 12.9904i −0.351992 0.609669i
\(455\) 3.00000 + 5.19615i 0.140642 + 0.243599i
\(456\) 12.1244i 0.567775i
\(457\) −14.5000 + 25.1147i −0.678281 + 1.17482i 0.297217 + 0.954810i \(0.403942\pi\)
−0.975498 + 0.220008i \(0.929392\pi\)
\(458\) 1.00000 0.0467269
\(459\) 31.1769i 1.45521i
\(460\) −9.00000 −0.419627
\(461\) 16.5000 28.5788i 0.768482 1.33105i −0.169904 0.985461i \(-0.554346\pi\)
0.938386 0.345589i \(-0.112321\pi\)
\(462\) 10.3923i 0.483494i
\(463\) 6.50000 + 11.2583i 0.302081 + 0.523219i 0.976607 0.215032i \(-0.0689855\pi\)
−0.674526 + 0.738251i \(0.735652\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 9.00000 + 5.19615i 0.417365 + 0.240966i
\(466\) 4.50000 7.79423i 0.208458 0.361061i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 3.00000 5.19615i 0.138675 0.240192i
\(469\) 8.00000 0.369406
\(470\) 0 0
\(471\) −19.5000 + 11.2583i −0.898513 + 0.518756i
\(472\) 0 0
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) −7.50000 + 4.33013i −0.344486 + 0.198889i
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) 6.00000 0.275010
\(477\) −18.0000 −0.824163
\(478\) 15.0000 0.686084
\(479\) 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) −4.50000 2.59808i −0.205396 0.118585i
\(481\) −2.00000 3.46410i −0.0911922 0.157949i
\(482\) 4.00000 + 6.92820i 0.182195 + 0.315571i
\(483\) 5.19615i 0.236433i
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) −6.00000 −0.272446
\(486\) 13.5000 + 7.79423i 0.612372 + 0.353553i
\(487\) 29.0000 1.31412 0.657058 0.753840i \(-0.271801\pi\)
0.657058 + 0.753840i \(0.271801\pi\)
\(488\) 2.50000 4.33013i 0.113170 0.196016i
\(489\) 3.46410i 0.156652i
\(490\) −1.50000 2.59808i −0.0677631 0.117369i
\(491\) −9.00000 15.5885i −0.406164 0.703497i 0.588292 0.808649i \(-0.299801\pi\)
−0.994456 + 0.105151i \(0.966467\pi\)
\(492\) 0 0
\(493\) −18.0000 + 31.1769i −0.810679 + 1.40414i
\(494\) 14.0000 0.629890
\(495\) −54.0000 −2.42712
\(496\) 2.00000 0.0898027
\(497\) −1.50000 + 2.59808i −0.0672842 + 0.116540i
\(498\) −18.0000 + 10.3923i −0.806599 + 0.465690i
\(499\) −16.0000 27.7128i −0.716258 1.24060i −0.962472 0.271380i \(-0.912520\pi\)
0.246214 0.969216i \(-0.420813\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 1.50000 2.59808i 0.0669483 0.115958i
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) −1.50000 + 2.59808i −0.0668153 + 0.115728i
\(505\) −27.0000 −1.20148
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) 13.5000 + 7.79423i 0.599556 + 0.346154i
\(508\) −8.50000 14.7224i −0.377127 0.653202i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 31.1769i 1.38054i
\(511\) −1.00000 + 1.73205i −0.0442374 + 0.0766214i
\(512\) −1.00000 −0.0441942
\(513\) 36.3731i 1.60591i
\(514\) −18.0000 −0.793946
\(515\) −15.0000 + 25.9808i −0.660979 + 1.14485i
\(516\) 3.46410i 0.152499i
\(517\) 0 0
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) 9.00000 + 5.19615i 0.395056 + 0.228086i
\(520\) −3.00000 + 5.19615i −0.131559 + 0.227866i
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) −13.0000 −0.568450 −0.284225 0.958758i \(-0.591736\pi\)
−0.284225 + 0.958758i \(0.591736\pi\)
\(524\) 4.50000 7.79423i 0.196583 0.340492i
\(525\) 6.00000 3.46410i 0.261861 0.151186i
\(526\) −10.5000 18.1865i −0.457822 0.792971i
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) −9.00000 + 5.19615i −0.391675 + 0.226134i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 18.0000 0.781870
\(531\) 0 0
\(532\) −7.00000 −0.303488
\(533\) 0 0
\(534\) 0 0
\(535\) −18.0000 31.1769i −0.778208 1.34790i
\(536\) 4.00000 + 6.92820i 0.172774 + 0.299253i
\(537\) 31.1769i 1.34538i
\(538\) −4.50000 + 7.79423i −0.194009 + 0.336033i
\(539\) −6.00000 −0.258438
\(540\) −13.5000 7.79423i −0.580948 0.335410i
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −14.0000 + 24.2487i −0.601351 + 1.04157i
\(543\) 43.3013i 1.85824i
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) −15.0000 25.9808i −0.642529 1.11289i
\(546\) 3.00000 + 1.73205i 0.128388 + 0.0741249i
\(547\) −16.0000 + 27.7128i −0.684111 + 1.18491i 0.289605 + 0.957146i \(0.406476\pi\)
−0.973715 + 0.227768i \(0.926857\pi\)
\(548\) 6.00000 0.256307
\(549\) 7.50000 12.9904i 0.320092 0.554416i
\(550\) 24.0000 1.02336
\(551\) 21.0000 36.3731i 0.894630 1.54954i
\(552\) −4.50000 + 2.59808i −0.191533 + 0.110581i
\(553\) −2.50000 4.33013i −0.106311 0.184136i
\(554\) −8.00000 13.8564i −0.339887 0.588702i
\(555\) −9.00000 + 5.19615i −0.382029 + 0.220564i
\(556\) −2.50000 + 4.33013i −0.106024 + 0.183638i
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) 6.00000 0.254000
\(559\) 4.00000 0.169182
\(560\) 1.50000 2.59808i 0.0633866 0.109789i
\(561\) 54.0000 + 31.1769i 2.27988 + 1.31629i
\(562\) −13.5000 23.3827i −0.569463 0.986339i
\(563\) 16.5000 + 28.5788i 0.695392 + 1.20445i 0.970048 + 0.242912i \(0.0781026\pi\)
−0.274656 + 0.961542i \(0.588564\pi\)
\(564\) 0 0
\(565\) 22.5000 38.9711i 0.946582 1.63953i
\(566\) 19.0000 0.798630
\(567\) −4.50000 + 7.79423i −0.188982 + 0.327327i
\(568\) −3.00000 −0.125877
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 36.3731i 1.52350i
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 6.00000 + 10.3923i 0.250873 + 0.434524i
\(573\) 13.5000 + 7.79423i 0.563971 + 0.325609i
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) −3.00000 −0.125000
\(577\) −4.00000 −0.166522 −0.0832611 0.996528i \(-0.526534\pi\)
−0.0832611 + 0.996528i \(0.526534\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) 25.5000 14.7224i 1.05974 0.611843i
\(580\) 9.00000 + 15.5885i 0.373705 + 0.647275i
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) −3.00000 + 1.73205i −0.124354 + 0.0717958i
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) −2.00000 −0.0827606
\(585\) −9.00000 + 15.5885i −0.372104 + 0.644503i
\(586\) 3.00000 0.123929
\(587\) 1.50000 2.59808i 0.0619116 0.107234i −0.833408 0.552658i \(-0.813614\pi\)
0.895320 + 0.445424i \(0.146947\pi\)
\(588\) −1.50000 0.866025i −0.0618590 0.0357143i
\(589\) 7.00000 + 12.1244i 0.288430 + 0.499575i
\(590\) 0 0
\(591\) 31.1769i 1.28245i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) −27.0000 + 15.5885i −1.10782 + 0.639602i
\(595\) −18.0000 −0.737928
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) 24.2487i 0.992434i
\(598\) 3.00000 + 5.19615i 0.122679 + 0.212486i
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 6.00000 + 3.46410i 0.244949 + 0.141421i
\(601\) −7.00000 + 12.1244i −0.285536 + 0.494563i −0.972739 0.231903i \(-0.925505\pi\)
0.687203 + 0.726465i \(0.258838\pi\)
\(602\) −2.00000 −0.0815139
\(603\) 12.0000 + 20.7846i 0.488678 + 0.846415i
\(604\) 23.0000 0.935857
\(605\) 37.5000 64.9519i 1.52459 2.64067i
\(606\) −13.5000 + 7.79423i −0.548400 + 0.316619i
\(607\) 11.0000 + 19.0526i 0.446476 + 0.773320i 0.998154 0.0607380i \(-0.0193454\pi\)
−0.551678 + 0.834058i \(0.686012\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 9.00000 5.19615i 0.364698 0.210559i
\(610\) −7.50000 + 12.9904i −0.303666 + 0.525965i
\(611\) 0 0
\(612\) 9.00000 + 15.5885i 0.363803 + 0.630126i
\(613\) 8.00000 0.323117 0.161558 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) −12.5000 + 21.6506i −0.504459 + 0.873749i
\(615\) 0 0
\(616\) −3.00000 5.19615i −0.120873 0.209359i
\(617\) −21.0000 36.3731i −0.845428 1.46432i −0.885249 0.465118i \(-0.846012\pi\)
0.0398207 0.999207i \(-0.487321\pi\)
\(618\) 17.3205i 0.696733i
\(619\) 3.50000 6.06218i 0.140677 0.243659i −0.787075 0.616858i \(-0.788405\pi\)
0.927752 + 0.373198i \(0.121739\pi\)
\(620\) −6.00000 −0.240966
\(621\) −13.5000 + 7.79423i −0.541736 + 0.312772i
\(622\) −12.0000 −0.481156
\(623\) 0 0
\(624\) 3.46410i 0.138675i
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) −63.0000 36.3731i −2.51598 1.45260i
\(628\) 6.50000 11.2583i 0.259378 0.449256i
\(629\) 12.0000 0.478471
\(630\) 4.50000 7.79423i 0.179284 0.310530i
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) 2.50000 4.33013i 0.0994447 0.172243i
\(633\) 12.0000 6.92820i 0.476957 0.275371i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 25.5000 + 44.1673i 1.01194 + 1.75273i
\(636\) 9.00000 5.19615i 0.356873 0.206041i
\(637\) −1.00000 + 1.73205i −0.0396214 + 0.0686264i
\(638\) 36.0000 1.42525
\(639\) −9.00000 −0.356034
\(640\) 3.00000 0.118585
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) −18.0000 10.3923i −0.710403 0.410152i
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) −1.50000 2.59808i −0.0591083 0.102379i
\(645\) 10.3923i 0.409197i
\(646\) −21.0000 + 36.3731i −0.826234 + 1.43108i
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −9.00000 −0.353553
\(649\) 0 0
\(650\) 4.00000 6.92820i 0.156893 0.271746i
\(651\) 3.46410i 0.135769i
\(652\) −1.00000 1.73205i −0.0391630 0.0678323i
\(653\) 18.0000 + 31.1769i 0.704394 + 1.22005i 0.966910 + 0.255119i \(0.0821147\pi\)
−0.262515 + 0.964928i \(0.584552\pi\)
\(654\) −15.0000 8.66025i −0.586546 0.338643i
\(655\) −13.5000 + 23.3827i −0.527489 + 0.913637i
\(656\) 0 0
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −21.0000 + 36.3731i −0.818044 + 1.41689i 0.0890776 + 0.996025i \(0.471608\pi\)
−0.907122 + 0.420869i \(0.861725\pi\)
\(660\) 27.0000 15.5885i 1.05097 0.606780i
\(661\) −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i \(-0.197668\pi\)
−0.910541 + 0.413419i \(0.864334\pi\)
\(662\) 13.0000 + 22.5167i 0.505259 + 0.875135i
\(663\) 18.0000 10.3923i 0.699062 0.403604i
\(664\) 6.00000 10.3923i 0.232845 0.403300i
\(665\) 21.0000 0.814345
\(666\) −3.00000 + 5.19615i −0.116248 + 0.201347i
\(667\) 18.0000 0.696963
\(668\) 0 0
\(669\) 42.0000 + 24.2487i 1.62381 + 0.937509i
\(670\) −12.0000 20.7846i −0.463600 0.802980i
\(671\) 15.0000 + 25.9808i 0.579069 + 1.00298i
\(672\) 1.73205i 0.0668153i
\(673\) 18.5000 32.0429i 0.713123 1.23516i −0.250557 0.968102i \(-0.580614\pi\)
0.963679 0.267063i \(-0.0860531\pi\)
\(674\) 22.0000 0.847408
\(675\) 18.0000 + 10.3923i 0.692820 + 0.400000i
\(676\) −9.00000 −0.346154
\(677\) −21.0000 + 36.3731i −0.807096 + 1.39793i 0.107772 + 0.994176i \(0.465628\pi\)
−0.914867 + 0.403755i \(0.867705\pi\)
\(678\) 25.9808i 0.997785i
\(679\) −1.00000 1.73205i −0.0383765 0.0664700i
\(680\) −9.00000 15.5885i −0.345134 0.597790i
\(681\) 22.5000 + 12.9904i 0.862202 + 0.497792i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) −6.00000 −0.229584 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) −10.5000 18.1865i −0.401478 0.695379i
\(685\) −18.0000 −0.687745
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) −1.50000 + 0.866025i −0.0572286 + 0.0330409i
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 13.5000 7.79423i 0.513936 0.296721i
\(691\) −23.5000 + 40.7032i −0.893982 + 1.54842i −0.0589228 + 0.998263i \(0.518767\pi\)
−0.835059 + 0.550160i \(0.814567\pi\)
\(692\) −6.00000 −0.228086
\(693\) −9.00000 15.5885i −0.341882 0.592157i
\(694\) 24.0000 0.911028
\(695\) 7.50000 12.9904i 0.284491 0.492753i
\(696\) 9.00000 + 5.19615i 0.341144 + 0.196960i
\(697\) 0 0
\(698\) 13.0000 + 22.5167i 0.492057 + 0.852268i
\(699\) 15.5885i 0.589610i
\(700\) −2.00000 + 3.46410i −0.0755929 + 0.130931i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 10.3923i 0.392232i
\(703\) −14.0000 −0.528020
\(704\) 3.00000 5.19615i 0.113067 0.195837i
\(705\) 0 0
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) −4.50000 7.79423i −0.169240 0.293132i
\(708\) 0 0
\(709\) 26.0000 45.0333i 0.976450 1.69126i 0.301388 0.953502i \(-0.402550\pi\)
0.675063 0.737760i \(-0.264116\pi\)
\(710\) 9.00000 0.337764
\(711\) 7.50000 12.9904i 0.281272 0.487177i
\(712\) 0 0
\(713\) −3.00000 + 5.19615i −0.112351 + 0.194597i
\(714\) −9.00000 + 5.19615i −0.336817 + 0.194461i
\(715\) −18.0000 31.1769i −0.673162 1.16595i
\(716\) −9.00000 15.5885i −0.336346 0.582568i
\(717\) −22.5000 + 12.9904i −0.840278 + 0.485135i
\(718\) −1.50000 + 2.59808i −0.0559795 + 0.0969593i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 9.00000 0.335410
\(721\) −10.0000 −0.372419
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) −12.0000 6.92820i −0.446285 0.257663i
\(724\) 12.5000 + 21.6506i 0.464559 + 0.804640i
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 43.3013i 1.60706i
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) −2.00000 −0.0741249
\(729\) −27.0000 −1.00000
\(730\) 6.00000 0.222070
\(731\) −6.00000 + 10.3923i −0.221918 + 0.384373i
\(732\) 8.66025i 0.320092i
\(733\) −14.5000 25.1147i −0.535570 0.927634i −0.999136 0.0415715i \(-0.986764\pi\)
0.463566 0.886062i \(-0.346570\pi\)
\(734\) 4.00000 + 6.92820i 0.147643 + 0.255725i
\(735\) 4.50000 + 2.59808i 0.165985 + 0.0958315i
\(736\) 1.50000 2.59808i 0.0552907 0.0957664i
\(737\) −48.0000 −1.76810
\(738\) 0 0
\(739\) 26.0000 0.956425 0.478213 0.878244i \(-0.341285\pi\)
0.478213 + 0.878244i \(0.341285\pi\)
\(740\) 3.00000 5.19615i 0.110282 0.191014i
\(741\) −21.0000 + 12.1244i −0.771454 + 0.445399i
\(742\) 3.00000 + 5.19615i 0.110133 + 0.190757i
\(743\) −18.0000 31.1769i −0.660356 1.14377i −0.980522 0.196409i \(-0.937072\pi\)
0.320166 0.947361i \(-0.396261\pi\)
\(744\) −3.00000 + 1.73205i −0.109985 + 0.0635001i
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) −14.0000 −0.512576
\(747\) 18.0000 31.1769i 0.658586 1.14070i
\(748\) −36.0000 −1.31629
\(749\) 6.00000 10.3923i 0.219235 0.379727i
\(750\) 4.50000 + 2.59808i 0.164317 + 0.0948683i
\(751\) 15.5000 + 26.8468i 0.565603 + 0.979653i 0.996993 + 0.0774878i \(0.0246899\pi\)
−0.431390 + 0.902165i \(0.641977\pi\)
\(752\) 0 0
\(753\) 5.19615i 0.189358i
\(754\) 6.00000 10.3923i 0.218507 0.378465i
\(755\) −69.0000 −2.51117
\(756\) 5.19615i 0.188982i
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 1.00000 1.73205i 0.0363216 0.0629109i
\(759\) 31.1769i 1.13165i
\(760\) 10.5000 + 18.1865i 0.380875 + 0.659695i
\(761\) 21.0000 + 36.3731i 0.761249 + 1.31852i 0.942207 + 0.335032i \(0.108747\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(762\) 25.5000 + 14.7224i 0.923768 + 0.533337i
\(763\) 5.00000 8.66025i 0.181012 0.313522i
\(764\) −9.00000 −0.325609
\(765\) −27.0000 46.7654i −0.976187 1.69081i
\(766\) 18.0000 0.650366
\(767\) 0 0
\(768\) 1.50000 0.866025i 0.0541266 0.0312500i
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) 9.00000 + 15.5885i 0.324337 + 0.561769i
\(771\) 27.0000 15.5885i 0.972381 0.561405i
\(772\) −8.50000 + 14.7224i −0.305922 + 0.529872i
\(773\) −51.0000 −1.83434 −0.917171 0.398493i \(-0.869533\pi\)
−0.917171 + 0.398493i \(0.869533\pi\)
\(774\)