Properties

Label 117.2.l.a.4.1
Level $117$
Weight $2$
Character 117.4
Analytic conductor $0.934$
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] = [117,2,Mod(4,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 117.l (of order \(6\), 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: \(0.934249703649\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.4
Dual form 117.2.l.a.88.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.73205i q^{2} +1.73205i q^{3} -1.00000 q^{4} +(1.50000 + 0.866025i) q^{5} +3.00000 q^{6} +(1.50000 + 0.866025i) q^{7} -1.73205i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.73205i q^{2} +1.73205i q^{3} -1.00000 q^{4} +(1.50000 + 0.866025i) q^{5} +3.00000 q^{6} +(1.50000 + 0.866025i) q^{7} -1.73205i q^{8} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{10} -3.46410i q^{11} -1.73205i q^{12} +(-1.00000 + 3.46410i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-1.50000 + 2.59808i) q^{15} -5.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +5.19615i q^{18} +(-1.50000 + 0.866025i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{21} -6.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +3.00000 q^{24} +(-1.00000 - 1.73205i) q^{25} +(6.00000 + 1.73205i) q^{26} -5.19615i q^{27} +(-1.50000 - 0.866025i) q^{28} -6.00000 q^{29} +(4.50000 + 2.59808i) q^{30} +(7.50000 + 4.33013i) q^{31} +5.19615i q^{32} +6.00000 q^{33} +(-4.50000 + 2.59808i) q^{34} +(1.50000 + 2.59808i) q^{35} +3.00000 q^{36} +(-4.50000 - 2.59808i) q^{37} +(1.50000 + 2.59808i) q^{38} +(-6.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-10.5000 + 6.06218i) q^{41} +(4.50000 + 2.59808i) q^{42} +(0.500000 - 0.866025i) q^{43} +3.46410i q^{44} +(-4.50000 - 2.59808i) q^{45} +(4.50000 - 2.59808i) q^{46} +(4.50000 - 2.59808i) q^{47} -8.66025i q^{48} +(-2.00000 - 3.46410i) q^{49} +(-3.00000 + 1.73205i) q^{50} +(4.50000 - 2.59808i) q^{51} +(1.00000 - 3.46410i) q^{52} +6.00000 q^{53} -9.00000 q^{54} +(3.00000 - 5.19615i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{57} +10.3923i q^{58} -3.46410i q^{59} +(1.50000 - 2.59808i) q^{60} +(2.50000 - 4.33013i) q^{61} +(7.50000 - 12.9904i) q^{62} +(-4.50000 - 2.59808i) q^{63} -1.00000 q^{64} +(-4.50000 + 4.33013i) q^{65} -10.3923i q^{66} +(10.5000 - 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-4.50000 + 2.59808i) q^{69} +(4.50000 - 2.59808i) q^{70} +(-7.50000 + 4.33013i) q^{71} +5.19615i q^{72} +6.92820i q^{73} +(-4.50000 + 7.79423i) q^{74} +(3.00000 - 1.73205i) q^{75} +(1.50000 - 0.866025i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-3.00000 + 10.3923i) q^{78} +(5.50000 + 9.52628i) q^{79} +(-7.50000 - 4.33013i) q^{80} +9.00000 q^{81} +(10.5000 + 18.1865i) q^{82} +(4.50000 - 2.59808i) q^{83} +(1.50000 - 2.59808i) q^{84} -5.19615i q^{85} +(-1.50000 - 0.866025i) q^{86} -10.3923i q^{87} -6.00000 q^{88} +(13.5000 + 7.79423i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(-4.50000 + 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +(-7.50000 + 12.9904i) q^{93} +(-4.50000 - 7.79423i) q^{94} -3.00000 q^{95} -9.00000 q^{96} +(13.5000 + 7.79423i) q^{97} +(-6.00000 + 3.46410i) q^{98} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} + 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} + 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{9} + 3 q^{10} - 2 q^{13} + 3 q^{14} - 3 q^{15} - 10 q^{16} - 3 q^{17} - 3 q^{19} - 3 q^{20} - 3 q^{21} - 12 q^{22} + 3 q^{23} + 6 q^{24} - 2 q^{25} + 12 q^{26} - 3 q^{28} - 12 q^{29} + 9 q^{30} + 15 q^{31} + 12 q^{33} - 9 q^{34} + 3 q^{35} + 6 q^{36} - 9 q^{37} + 3 q^{38} - 12 q^{39} + 3 q^{40} - 21 q^{41} + 9 q^{42} + q^{43} - 9 q^{45} + 9 q^{46} + 9 q^{47} - 4 q^{49} - 6 q^{50} + 9 q^{51} + 2 q^{52} + 12 q^{53} - 18 q^{54} + 6 q^{55} + 3 q^{56} - 3 q^{57} + 3 q^{60} + 5 q^{61} + 15 q^{62} - 9 q^{63} - 2 q^{64} - 9 q^{65} + 21 q^{67} + 3 q^{68} - 9 q^{69} + 9 q^{70} - 15 q^{71} - 9 q^{74} + 6 q^{75} + 3 q^{76} + 6 q^{77} - 6 q^{78} + 11 q^{79} - 15 q^{80} + 18 q^{81} + 21 q^{82} + 9 q^{83} + 3 q^{84} - 3 q^{86} - 12 q^{88} + 27 q^{89} - 9 q^{90} - 9 q^{91} - 3 q^{92} - 15 q^{93} - 9 q^{94} - 6 q^{95} - 18 q^{96} + 27 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.22474i −0.790569 0.612372i \(-0.790215\pi\)
0.790569 0.612372i \(-0.209785\pi\)
\(3\) 1.73205i 1.00000i
\(4\) −1.00000 −0.500000
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 3.00000 1.22474
\(7\) 1.50000 + 0.866025i 0.566947 + 0.327327i 0.755929 0.654654i \(-0.227186\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.73205i 0.612372i
\(9\) −3.00000 −1.00000
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 3.46410i 1.04447i −0.852803 0.522233i \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 1.73205i 0.500000i
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) −1.50000 + 2.59808i −0.387298 + 0.670820i
\(16\) −5.00000 −1.25000
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 5.19615i 1.22474i
\(19\) −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i \(-0.730332\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(20\) −1.50000 0.866025i −0.335410 0.193649i
\(21\) −1.50000 + 2.59808i −0.327327 + 0.566947i
\(22\) −6.00000 −1.27920
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 3.00000 0.612372
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 6.00000 + 1.73205i 1.17670 + 0.339683i
\(27\) 5.19615i 1.00000i
\(28\) −1.50000 0.866025i −0.283473 0.163663i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 4.50000 + 2.59808i 0.821584 + 0.474342i
\(31\) 7.50000 + 4.33013i 1.34704 + 0.777714i 0.987829 0.155543i \(-0.0497126\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 5.19615i 0.918559i
\(33\) 6.00000 1.04447
\(34\) −4.50000 + 2.59808i −0.771744 + 0.445566i
\(35\) 1.50000 + 2.59808i 0.253546 + 0.439155i
\(36\) 3.00000 0.500000
\(37\) −4.50000 2.59808i −0.739795 0.427121i 0.0821995 0.996616i \(-0.473806\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 1.50000 + 2.59808i 0.243332 + 0.421464i
\(39\) −6.00000 1.73205i −0.960769 0.277350i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) −10.5000 + 6.06218i −1.63982 + 0.946753i −0.658932 + 0.752202i \(0.728992\pi\)
−0.980892 + 0.194551i \(0.937675\pi\)
\(42\) 4.50000 + 2.59808i 0.694365 + 0.400892i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 3.46410i 0.522233i
\(45\) −4.50000 2.59808i −0.670820 0.387298i
\(46\) 4.50000 2.59808i 0.663489 0.383065i
\(47\) 4.50000 2.59808i 0.656392 0.378968i −0.134509 0.990912i \(-0.542946\pi\)
0.790901 + 0.611944i \(0.209612\pi\)
\(48\) 8.66025i 1.25000i
\(49\) −2.00000 3.46410i −0.285714 0.494872i
\(50\) −3.00000 + 1.73205i −0.424264 + 0.244949i
\(51\) 4.50000 2.59808i 0.630126 0.363803i
\(52\) 1.00000 3.46410i 0.138675 0.480384i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −9.00000 −1.22474
\(55\) 3.00000 5.19615i 0.404520 0.700649i
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) −1.50000 2.59808i −0.198680 0.344124i
\(58\) 10.3923i 1.36458i
\(59\) 3.46410i 0.450988i −0.974245 0.225494i \(-0.927600\pi\)
0.974245 0.225494i \(-0.0723995\pi\)
\(60\) 1.50000 2.59808i 0.193649 0.335410i
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 7.50000 12.9904i 0.952501 1.64978i
\(63\) −4.50000 2.59808i −0.566947 0.327327i
\(64\) −1.00000 −0.125000
\(65\) −4.50000 + 4.33013i −0.558156 + 0.537086i
\(66\) 10.3923i 1.27920i
\(67\) 10.5000 6.06218i 1.28278 0.740613i 0.305424 0.952217i \(-0.401202\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) −4.50000 + 2.59808i −0.541736 + 0.312772i
\(70\) 4.50000 2.59808i 0.537853 0.310530i
\(71\) −7.50000 + 4.33013i −0.890086 + 0.513892i −0.873971 0.485979i \(-0.838463\pi\)
−0.0161155 + 0.999870i \(0.505130\pi\)
\(72\) 5.19615i 0.612372i
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) −4.50000 + 7.79423i −0.523114 + 0.906061i
\(75\) 3.00000 1.73205i 0.346410 0.200000i
\(76\) 1.50000 0.866025i 0.172062 0.0993399i
\(77\) 3.00000 5.19615i 0.341882 0.592157i
\(78\) −3.00000 + 10.3923i −0.339683 + 1.17670i
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) −7.50000 4.33013i −0.838525 0.484123i
\(81\) 9.00000 1.00000
\(82\) 10.5000 + 18.1865i 1.15953 + 2.00837i
\(83\) 4.50000 2.59808i 0.493939 0.285176i −0.232268 0.972652i \(-0.574615\pi\)
0.726207 + 0.687476i \(0.241281\pi\)
\(84\) 1.50000 2.59808i 0.163663 0.283473i
\(85\) 5.19615i 0.563602i
\(86\) −1.50000 0.866025i −0.161749 0.0933859i
\(87\) 10.3923i 1.11417i
\(88\) −6.00000 −0.639602
\(89\) 13.5000 + 7.79423i 1.43100 + 0.826187i 0.997197 0.0748225i \(-0.0238390\pi\)
0.433800 + 0.901009i \(0.357172\pi\)
\(90\) −4.50000 + 7.79423i −0.474342 + 0.821584i
\(91\) −4.50000 + 4.33013i −0.471728 + 0.453921i
\(92\) −1.50000 2.59808i −0.156386 0.270868i
\(93\) −7.50000 + 12.9904i −0.777714 + 1.34704i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) −3.00000 −0.307794
\(96\) −9.00000 −0.918559
\(97\) 13.5000 + 7.79423i 1.37072 + 0.791384i 0.991018 0.133726i \(-0.0426942\pi\)
0.379699 + 0.925110i \(0.376028\pi\)
\(98\) −6.00000 + 3.46410i −0.606092 + 0.349927i
\(99\) 10.3923i 1.04447i
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −4.50000 7.79423i −0.445566 0.771744i
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 6.00000 + 1.73205i 0.588348 + 0.169842i
\(105\) −4.50000 + 2.59808i −0.439155 + 0.253546i
\(106\) 10.3923i 1.00939i
\(107\) −7.50000 + 12.9904i −0.725052 + 1.25583i 0.233900 + 0.972261i \(0.424851\pi\)
−0.958952 + 0.283567i \(0.908482\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −9.00000 5.19615i −0.858116 0.495434i
\(111\) 4.50000 7.79423i 0.427121 0.739795i
\(112\) −7.50000 4.33013i −0.708683 0.409159i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −4.50000 + 2.59808i −0.421464 + 0.243332i
\(115\) 5.19615i 0.484544i
\(116\) 6.00000 0.557086
\(117\) 3.00000 10.3923i 0.277350 0.960769i
\(118\) −6.00000 −0.552345
\(119\) 5.19615i 0.476331i
\(120\) 4.50000 + 2.59808i 0.410792 + 0.237171i
\(121\) −1.00000 −0.0909091
\(122\) −7.50000 4.33013i −0.679018 0.392031i
\(123\) −10.5000 18.1865i −0.946753 1.63982i
\(124\) −7.50000 4.33013i −0.673520 0.388857i
\(125\) 12.1244i 1.08444i
\(126\) −4.50000 + 7.79423i −0.400892 + 0.694365i
\(127\) 2.50000 4.33013i 0.221839 0.384237i −0.733527 0.679660i \(-0.762127\pi\)
0.955366 + 0.295423i \(0.0954607\pi\)
\(128\) 12.1244i 1.07165i
\(129\) 1.50000 + 0.866025i 0.132068 + 0.0762493i
\(130\) 7.50000 + 7.79423i 0.657794 + 0.683599i
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) −6.00000 −0.522233
\(133\) −3.00000 −0.260133
\(134\) −10.5000 18.1865i −0.907062 1.57108i
\(135\) 4.50000 7.79423i 0.387298 0.670820i
\(136\) −4.50000 + 2.59808i −0.385872 + 0.222783i
\(137\) −4.50000 2.59808i −0.384461 0.221969i 0.295296 0.955406i \(-0.404582\pi\)
−0.679757 + 0.733437i \(0.737915\pi\)
\(138\) 4.50000 + 7.79423i 0.383065 + 0.663489i
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −1.50000 2.59808i −0.126773 0.219578i
\(141\) 4.50000 + 7.79423i 0.378968 + 0.656392i
\(142\) 7.50000 + 12.9904i 0.629386 + 1.09013i
\(143\) 12.0000 + 3.46410i 1.00349 + 0.289683i
\(144\) 15.0000 1.25000
\(145\) −9.00000 5.19615i −0.747409 0.431517i
\(146\) 12.0000 0.993127
\(147\) 6.00000 3.46410i 0.494872 0.285714i
\(148\) 4.50000 + 2.59808i 0.369898 + 0.213561i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −3.00000 5.19615i −0.244949 0.424264i
\(151\) 10.5000 6.06218i 0.854478 0.493333i −0.00768132 0.999970i \(-0.502445\pi\)
0.862159 + 0.506637i \(0.169112\pi\)
\(152\) 1.50000 + 2.59808i 0.121666 + 0.210732i
\(153\) 4.50000 + 7.79423i 0.363803 + 0.630126i
\(154\) −9.00000 5.19615i −0.725241 0.418718i
\(155\) 7.50000 + 12.9904i 0.602414 + 1.04341i
\(156\) 6.00000 + 1.73205i 0.480384 + 0.138675i
\(157\) −11.5000 + 19.9186i −0.917800 + 1.58968i −0.115050 + 0.993360i \(0.536703\pi\)
−0.802749 + 0.596316i \(0.796630\pi\)
\(158\) 16.5000 9.52628i 1.31267 0.757870i
\(159\) 10.3923i 0.824163i
\(160\) −4.50000 + 7.79423i −0.355756 + 0.616188i
\(161\) 5.19615i 0.409514i
\(162\) 15.5885i 1.22474i
\(163\) 10.5000 6.06218i 0.822423 0.474826i −0.0288280 0.999584i \(-0.509178\pi\)
0.851251 + 0.524758i \(0.175844\pi\)
\(164\) 10.5000 6.06218i 0.819912 0.473377i
\(165\) 9.00000 + 5.19615i 0.700649 + 0.404520i
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) 4.50000 2.59808i 0.348220 0.201045i −0.315681 0.948865i \(-0.602233\pi\)
0.663901 + 0.747820i \(0.268900\pi\)
\(168\) 4.50000 + 2.59808i 0.347183 + 0.200446i
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) −9.00000 −0.690268
\(171\) 4.50000 2.59808i 0.344124 0.198680i
\(172\) −0.500000 + 0.866025i −0.0381246 + 0.0660338i
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) −18.0000 −1.36458
\(175\) 3.46410i 0.261861i
\(176\) 17.3205i 1.30558i
\(177\) 6.00000 0.450988
\(178\) 13.5000 23.3827i 1.01187 1.75261i
\(179\) −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i \(-0.869096\pi\)
0.804508 + 0.593942i \(0.202429\pi\)
\(180\) 4.50000 + 2.59808i 0.335410 + 0.193649i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 7.50000 + 7.79423i 0.555937 + 0.577747i
\(183\) 7.50000 + 4.33013i 0.554416 + 0.320092i
\(184\) 4.50000 2.59808i 0.331744 0.191533i
\(185\) −4.50000 7.79423i −0.330847 0.573043i
\(186\) 22.5000 + 12.9904i 1.64978 + 0.952501i
\(187\) −9.00000 + 5.19615i −0.658145 + 0.379980i
\(188\) −4.50000 + 2.59808i −0.328196 + 0.189484i
\(189\) 4.50000 7.79423i 0.327327 0.566947i
\(190\) 5.19615i 0.376969i
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) 1.73205i 0.125000i
\(193\) −4.50000 + 2.59808i −0.323917 + 0.187014i −0.653137 0.757240i \(-0.726548\pi\)
0.329220 + 0.944253i \(0.393214\pi\)
\(194\) 13.5000 23.3827i 0.969244 1.67878i
\(195\) −7.50000 7.79423i −0.537086 0.558156i
\(196\) 2.00000 + 3.46410i 0.142857 + 0.247436i
\(197\) 7.50000 + 4.33013i 0.534353 + 0.308509i 0.742787 0.669528i \(-0.233503\pi\)
−0.208434 + 0.978036i \(0.566837\pi\)
\(198\) 18.0000 1.27920
\(199\) −6.50000 11.2583i −0.460773 0.798082i 0.538227 0.842800i \(-0.319094\pi\)
−0.999000 + 0.0447181i \(0.985761\pi\)
\(200\) −3.00000 + 1.73205i −0.212132 + 0.122474i
\(201\) 10.5000 + 18.1865i 0.740613 + 1.28278i
\(202\) 10.3923i 0.731200i
\(203\) −9.00000 5.19615i −0.631676 0.364698i
\(204\) −4.50000 + 2.59808i −0.315063 + 0.181902i
\(205\) −21.0000 −1.46670
\(206\) −19.5000 11.2583i −1.35863 0.784405i
\(207\) −4.50000 7.79423i −0.312772 0.541736i
\(208\) 5.00000 17.3205i 0.346688 1.20096i
\(209\) 3.00000 + 5.19615i 0.207514 + 0.359425i
\(210\) 4.50000 + 7.79423i 0.310530 + 0.537853i
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) −6.00000 −0.412082
\(213\) −7.50000 12.9904i −0.513892 0.890086i
\(214\) 22.5000 + 12.9904i 1.53807 + 0.888004i
\(215\) 1.50000 0.866025i 0.102299 0.0590624i
\(216\) −9.00000 −0.612372
\(217\) 7.50000 + 12.9904i 0.509133 + 0.881845i
\(218\) 0 0
\(219\) −12.0000 −0.810885
\(220\) −3.00000 + 5.19615i −0.202260 + 0.350325i
\(221\) 10.5000 2.59808i 0.706306 0.174766i
\(222\) −13.5000 7.79423i −0.906061 0.523114i
\(223\) 3.46410i 0.231973i 0.993251 + 0.115987i \(0.0370030\pi\)
−0.993251 + 0.115987i \(0.962997\pi\)
\(224\) −4.50000 + 7.79423i −0.300669 + 0.520774i
\(225\) 3.00000 + 5.19615i 0.200000 + 0.346410i
\(226\) 10.3923i 0.691286i
\(227\) −10.5000 6.06218i −0.696909 0.402361i 0.109286 0.994010i \(-0.465144\pi\)
−0.806195 + 0.591649i \(0.798477\pi\)
\(228\) 1.50000 + 2.59808i 0.0993399 + 0.172062i
\(229\) 7.50000 + 4.33013i 0.495614 + 0.286143i 0.726900 0.686743i \(-0.240960\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 9.00000 0.593442
\(231\) 9.00000 + 5.19615i 0.592157 + 0.341882i
\(232\) 10.3923i 0.682288i
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) −18.0000 5.19615i −1.17670 0.339683i
\(235\) 9.00000 0.587095
\(236\) 3.46410i 0.225494i
\(237\) −16.5000 + 9.52628i −1.07179 + 0.618798i
\(238\) −9.00000 −0.583383
\(239\) −4.50000 2.59808i −0.291081 0.168056i 0.347348 0.937736i \(-0.387082\pi\)
−0.638429 + 0.769681i \(0.720415\pi\)
\(240\) 7.50000 12.9904i 0.484123 0.838525i
\(241\) −4.50000 2.59808i −0.289870 0.167357i 0.348013 0.937490i \(-0.386857\pi\)
−0.637883 + 0.770133i \(0.720190\pi\)
\(242\) 1.73205i 0.111340i
\(243\) 15.5885i 1.00000i
\(244\) −2.50000 + 4.33013i −0.160046 + 0.277208i
\(245\) 6.92820i 0.442627i
\(246\) −31.5000 + 18.1865i −2.00837 + 1.15953i
\(247\) −1.50000 6.06218i −0.0954427 0.385727i
\(248\) 7.50000 12.9904i 0.476250 0.824890i
\(249\) 4.50000 + 7.79423i 0.285176 + 0.493939i
\(250\) −21.0000 −1.32816
\(251\) −4.50000 7.79423i −0.284037 0.491967i 0.688338 0.725390i \(-0.258341\pi\)
−0.972375 + 0.233423i \(0.925007\pi\)
\(252\) 4.50000 + 2.59808i 0.283473 + 0.163663i
\(253\) 9.00000 5.19615i 0.565825 0.326679i
\(254\) −7.50000 4.33013i −0.470592 0.271696i
\(255\) 9.00000 0.563602
\(256\) 19.0000 1.18750
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 1.50000 2.59808i 0.0933859 0.161749i
\(259\) −4.50000 7.79423i −0.279616 0.484310i
\(260\) 4.50000 4.33013i 0.279078 0.268543i
\(261\) 18.0000 1.11417
\(262\) 22.5000 + 12.9904i 1.39005 + 0.802548i
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 10.3923i 0.639602i
\(265\) 9.00000 + 5.19615i 0.552866 + 0.319197i
\(266\) 5.19615i 0.318597i
\(267\) −13.5000 + 23.3827i −0.826187 + 1.43100i
\(268\) −10.5000 + 6.06218i −0.641390 + 0.370306i
\(269\) −1.50000 2.59808i −0.0914566 0.158408i 0.816668 0.577108i \(-0.195819\pi\)
−0.908124 + 0.418701i \(0.862486\pi\)
\(270\) −13.5000 7.79423i −0.821584 0.474342i
\(271\) 13.5000 + 7.79423i 0.820067 + 0.473466i 0.850439 0.526073i \(-0.176336\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) 7.50000 + 12.9904i 0.454754 + 0.787658i
\(273\) −7.50000 7.79423i −0.453921 0.471728i
\(274\) −4.50000 + 7.79423i −0.271855 + 0.470867i
\(275\) −6.00000 + 3.46410i −0.361814 + 0.208893i
\(276\) 4.50000 2.59808i 0.270868 0.156386i
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) 27.7128i 1.66210i
\(279\) −22.5000 12.9904i −1.34704 0.777714i
\(280\) 4.50000 2.59808i 0.268926 0.155265i
\(281\) −4.50000 + 2.59808i −0.268447 + 0.154988i −0.628182 0.778067i \(-0.716201\pi\)
0.359734 + 0.933055i \(0.382867\pi\)
\(282\) 13.5000 7.79423i 0.803913 0.464140i
\(283\) 11.5000 + 19.9186i 0.683604 + 1.18404i 0.973873 + 0.227092i \(0.0729218\pi\)
−0.290269 + 0.956945i \(0.593745\pi\)
\(284\) 7.50000 4.33013i 0.445043 0.256946i
\(285\) 5.19615i 0.307794i
\(286\) 6.00000 20.7846i 0.354787 1.22902i
\(287\) −21.0000 −1.23959
\(288\) 15.5885i 0.918559i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −9.00000 + 15.5885i −0.528498 + 0.915386i
\(291\) −13.5000 + 23.3827i −0.791384 + 1.37072i
\(292\) 6.92820i 0.405442i
\(293\) 13.8564i 0.809500i −0.914427 0.404750i \(-0.867359\pi\)
0.914427 0.404750i \(-0.132641\pi\)
\(294\) −6.00000 10.3923i −0.349927 0.606092i
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) −4.50000 + 7.79423i −0.261557 + 0.453030i
\(297\) −18.0000 −1.04447
\(298\) 0 0
\(299\) −10.5000 + 2.59808i −0.607231 + 0.150251i
\(300\) −3.00000 + 1.73205i −0.173205 + 0.100000i
\(301\) 1.50000 0.866025i 0.0864586 0.0499169i
\(302\) −10.5000 18.1865i −0.604207 1.04652i
\(303\) 10.3923i 0.597022i
\(304\) 7.50000 4.33013i 0.430155 0.248350i
\(305\) 7.50000 4.33013i 0.429449 0.247942i
\(306\) 13.5000 7.79423i 0.771744 0.445566i
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) −3.00000 + 5.19615i −0.170941 + 0.296078i
\(309\) 19.5000 + 11.2583i 1.10932 + 0.640464i
\(310\) 22.5000 12.9904i 1.27791 0.737804i
\(311\) −13.5000 + 23.3827i −0.765515 + 1.32591i 0.174459 + 0.984664i \(0.444182\pi\)
−0.939974 + 0.341246i \(0.889151\pi\)
\(312\) −3.00000 + 10.3923i −0.169842 + 0.588348i
\(313\) −9.50000 16.4545i −0.536972 0.930062i −0.999065 0.0432311i \(-0.986235\pi\)
0.462093 0.886831i \(-0.347098\pi\)
\(314\) 34.5000 + 19.9186i 1.94695 + 1.12407i
\(315\) −4.50000 7.79423i −0.253546 0.439155i
\(316\) −5.50000 9.52628i −0.309399 0.535895i
\(317\) 7.50000 4.33013i 0.421242 0.243204i −0.274367 0.961625i \(-0.588468\pi\)
0.695609 + 0.718421i \(0.255135\pi\)
\(318\) 18.0000 1.00939
\(319\) 20.7846i 1.16371i
\(320\) −1.50000 0.866025i −0.0838525 0.0484123i
\(321\) −22.5000 12.9904i −1.25583 0.725052i
\(322\) 9.00000 0.501550
\(323\) 4.50000 + 2.59808i 0.250387 + 0.144561i
\(324\) −9.00000 −0.500000
\(325\) 7.00000 1.73205i 0.388290 0.0960769i
\(326\) −10.5000 18.1865i −0.581541 1.00726i
\(327\) 0 0
\(328\) 10.5000 + 18.1865i 0.579766 + 1.00418i
\(329\) 9.00000 0.496186
\(330\) 9.00000 15.5885i 0.495434 0.858116i
\(331\) 13.5000 + 7.79423i 0.742027 + 0.428410i 0.822806 0.568323i \(-0.192407\pi\)
−0.0807788 + 0.996732i \(0.525741\pi\)
\(332\) −4.50000 + 2.59808i −0.246970 + 0.142588i
\(333\) 13.5000 + 7.79423i 0.739795 + 0.427121i
\(334\) −4.50000 7.79423i −0.246229 0.426481i
\(335\) 21.0000 1.14735
\(336\) 7.50000 12.9904i 0.409159 0.708683i
\(337\) 14.5000 25.1147i 0.789865 1.36809i −0.136184 0.990684i \(-0.543484\pi\)
0.926049 0.377403i \(-0.123183\pi\)
\(338\) −12.0000 + 19.0526i −0.652714 + 1.03632i
\(339\) 10.3923i 0.564433i
\(340\) 5.19615i 0.281801i
\(341\) 15.0000 25.9808i 0.812296 1.40694i
\(342\) −4.50000 7.79423i −0.243332 0.421464i
\(343\) 19.0526i 1.02874i
\(344\) −1.50000 0.866025i −0.0808746 0.0466930i
\(345\) −9.00000 −0.484544
\(346\) −31.5000 18.1865i −1.69345 0.977714i
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 10.3923i 0.557086i
\(349\) 27.7128i 1.48343i −0.670714 0.741716i \(-0.734012\pi\)
0.670714 0.741716i \(-0.265988\pi\)
\(350\) −6.00000 −0.320713
\(351\) 18.0000 + 5.19615i 0.960769 + 0.277350i
\(352\) 18.0000 0.959403
\(353\) 6.92820i 0.368751i 0.982856 + 0.184376i \(0.0590263\pi\)
−0.982856 + 0.184376i \(0.940974\pi\)
\(354\) 10.3923i 0.552345i
\(355\) −15.0000 −0.796117
\(356\) −13.5000 7.79423i −0.715499 0.413093i
\(357\) 9.00000 0.476331
\(358\) 4.50000 + 2.59808i 0.237832 + 0.137313i
\(359\) 10.3923i 0.548485i −0.961661 0.274242i \(-0.911573\pi\)
0.961661 0.274242i \(-0.0884271\pi\)
\(360\) −4.50000 + 7.79423i −0.237171 + 0.410792i
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) 38.1051i 2.00276i
\(363\) 1.73205i 0.0909091i
\(364\) 4.50000 4.33013i 0.235864 0.226960i
\(365\) −6.00000 + 10.3923i −0.314054 + 0.543958i
\(366\) 7.50000 12.9904i 0.392031 0.679018i
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) −7.50000 12.9904i −0.390965 0.677170i
\(369\) 31.5000 18.1865i 1.63982 0.946753i
\(370\) −13.5000 + 7.79423i −0.701832 + 0.405203i
\(371\) 9.00000 + 5.19615i 0.467257 + 0.269771i
\(372\) 7.50000 12.9904i 0.388857 0.673520i
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 21.0000 1.08444
\(376\) −4.50000 7.79423i −0.232070 0.401957i
\(377\) 6.00000 20.7846i 0.309016 1.07046i
\(378\) −13.5000 7.79423i −0.694365 0.400892i
\(379\) −10.5000 6.06218i −0.539349 0.311393i 0.205466 0.978664i \(-0.434129\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 3.00000 0.153897
\(381\) 7.50000 + 4.33013i 0.384237 + 0.221839i
\(382\) 4.50000 + 2.59808i 0.230240 + 0.132929i
\(383\) 3.46410i 0.177007i 0.996076 + 0.0885037i \(0.0282085\pi\)
−0.996076 + 0.0885037i \(0.971792\pi\)
\(384\) −21.0000 −1.07165
\(385\) 9.00000 5.19615i 0.458682 0.264820i
\(386\) 4.50000 + 7.79423i 0.229044 + 0.396716i
\(387\) −1.50000 + 2.59808i −0.0762493 + 0.132068i
\(388\) −13.5000 7.79423i −0.685359 0.395692i
\(389\) −1.50000 2.59808i −0.0760530 0.131728i 0.825491 0.564416i \(-0.190898\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(390\) −13.5000 + 12.9904i −0.683599 + 0.657794i
\(391\) 4.50000 7.79423i 0.227575 0.394171i
\(392\) −6.00000 + 3.46410i −0.303046 + 0.174964i
\(393\) −22.5000 12.9904i −1.13497 0.655278i
\(394\) 7.50000 12.9904i 0.377845 0.654446i
\(395\) 19.0526i 0.958638i
\(396\) 10.3923i 0.522233i
\(397\) −22.5000 + 12.9904i −1.12924 + 0.651969i −0.943744 0.330676i \(-0.892723\pi\)
−0.185498 + 0.982645i \(0.559390\pi\)
\(398\) −19.5000 + 11.2583i −0.977447 + 0.564329i
\(399\) 5.19615i 0.260133i
\(400\) 5.00000 + 8.66025i 0.250000 + 0.433013i
\(401\) 25.5000 14.7224i 1.27341 0.735203i 0.297781 0.954634i \(-0.403753\pi\)
0.975628 + 0.219431i \(0.0704201\pi\)
\(402\) 31.5000 18.1865i 1.57108 0.907062i
\(403\) −22.5000 + 21.6506i −1.12080 + 1.07849i
\(404\) 6.00000 0.298511
\(405\) 13.5000 + 7.79423i 0.670820 + 0.387298i
\(406\) −9.00000 + 15.5885i −0.446663 + 0.773642i
\(407\) −9.00000 + 15.5885i −0.446113 + 0.772691i
\(408\) −4.50000 7.79423i −0.222783 0.385872i
\(409\) 6.92820i 0.342578i −0.985221 0.171289i \(-0.945207\pi\)
0.985221 0.171289i \(-0.0547931\pi\)
\(410\) 36.3731i 1.79634i
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) −6.50000 + 11.2583i −0.320232 + 0.554658i
\(413\) 3.00000 5.19615i 0.147620 0.255686i
\(414\) −13.5000 + 7.79423i −0.663489 + 0.383065i
\(415\) 9.00000 0.441793
\(416\) −18.0000 5.19615i −0.882523 0.254762i
\(417\) 27.7128i 1.35710i
\(418\) 9.00000 5.19615i 0.440204 0.254152i
\(419\) −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) 4.50000 2.59808i 0.219578 0.126773i
\(421\) 7.50000 4.33013i 0.365528 0.211037i −0.305975 0.952039i \(-0.598982\pi\)
0.671503 + 0.741002i \(0.265649\pi\)
\(422\) −19.5000 + 11.2583i −0.949245 + 0.548047i
\(423\) −13.5000 + 7.79423i −0.656392 + 0.378968i
\(424\) 10.3923i 0.504695i
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) −22.5000 + 12.9904i −1.09013 + 0.629386i
\(427\) 7.50000 4.33013i 0.362950 0.209550i
\(428\) 7.50000 12.9904i 0.362526 0.627914i
\(429\) −6.00000 + 20.7846i −0.289683 + 1.00349i
\(430\) −1.50000 2.59808i −0.0723364 0.125290i
\(431\) 19.5000 + 11.2583i 0.939282 + 0.542295i 0.889735 0.456477i \(-0.150889\pi\)
0.0495468 + 0.998772i \(0.484222\pi\)
\(432\) 25.9808i 1.25000i
\(433\) 2.50000 + 4.33013i 0.120142 + 0.208093i 0.919824 0.392332i \(-0.128332\pi\)
−0.799681 + 0.600425i \(0.794998\pi\)
\(434\) 22.5000 12.9904i 1.08003 0.623558i
\(435\) 9.00000 15.5885i 0.431517 0.747409i
\(436\) 0 0
\(437\) −4.50000 2.59808i −0.215264 0.124283i
\(438\) 20.7846i 0.993127i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) −9.00000 5.19615i −0.429058 0.247717i
\(441\) 6.00000 + 10.3923i 0.285714 + 0.494872i
\(442\) −4.50000 18.1865i −0.214043 0.865045i
\(443\) −10.5000 18.1865i −0.498870 0.864068i 0.501129 0.865373i \(-0.332918\pi\)
−0.999999 + 0.00130426i \(0.999585\pi\)
\(444\) −4.50000 + 7.79423i −0.213561 + 0.369898i
\(445\) 13.5000 + 23.3827i 0.639961 + 1.10845i
\(446\) 6.00000 0.284108
\(447\) 0 0
\(448\) −1.50000 0.866025i −0.0708683 0.0409159i
\(449\) 13.5000 7.79423i 0.637104 0.367832i −0.146394 0.989226i \(-0.546767\pi\)
0.783498 + 0.621394i \(0.213433\pi\)
\(450\) 9.00000 5.19615i 0.424264 0.244949i
\(451\) 21.0000 + 36.3731i 0.988851 + 1.71274i
\(452\) −6.00000 −0.282216
\(453\) 10.5000 + 18.1865i 0.493333 + 0.854478i
\(454\) −10.5000 + 18.1865i −0.492789 + 0.853536i
\(455\) −10.5000 + 2.59808i −0.492248 + 0.121800i
\(456\) −4.50000 + 2.59808i −0.210732 + 0.121666i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 7.50000 12.9904i 0.350452 0.607001i
\(459\) −13.5000 + 7.79423i −0.630126 + 0.363803i
\(460\) 5.19615i 0.242272i
\(461\) 1.50000 + 0.866025i 0.0698620 + 0.0403348i 0.534524 0.845153i \(-0.320491\pi\)
−0.464662 + 0.885488i \(0.653824\pi\)
\(462\) 9.00000 15.5885i 0.418718 0.725241i
\(463\) −22.5000 12.9904i −1.04566 0.603714i −0.124231 0.992253i \(-0.539647\pi\)
−0.921432 + 0.388539i \(0.872980\pi\)
\(464\) 30.0000 1.39272
\(465\) −22.5000 + 12.9904i −1.04341 + 0.602414i
\(466\) 31.1769i 1.44424i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −3.00000 + 10.3923i −0.138675 + 0.480384i
\(469\) 21.0000 0.969690
\(470\) 15.5885i 0.719042i
\(471\) −34.5000 19.9186i −1.58968 0.917800i
\(472\) −6.00000 −0.276172
\(473\) −3.00000 1.73205i −0.137940 0.0796398i
\(474\) 16.5000 + 28.5788i 0.757870 + 1.31267i
\(475\) 3.00000 + 1.73205i 0.137649 + 0.0794719i
\(476\) 5.19615i 0.238165i
\(477\) −18.0000 −0.824163
\(478\) −4.50000 + 7.79423i −0.205825 + 0.356500i
\(479\) 24.2487i 1.10795i −0.832533 0.553976i \(-0.813110\pi\)
0.832533 0.553976i \(-0.186890\pi\)
\(480\) −13.5000 7.79423i −0.616188 0.355756i
\(481\) 13.5000 12.9904i 0.615547 0.592310i
\(482\) −4.50000 + 7.79423i −0.204969 + 0.355017i
\(483\) −9.00000 −0.409514
\(484\) 1.00000 0.0454545
\(485\) 13.5000 + 23.3827i 0.613003 + 1.06175i
\(486\) 27.0000 1.22474
\(487\) −7.50000 + 4.33013i −0.339857 + 0.196217i −0.660209 0.751082i \(-0.729532\pi\)
0.320352 + 0.947299i \(0.396199\pi\)
\(488\) −7.50000 4.33013i −0.339509 0.196016i
\(489\) 10.5000 + 18.1865i 0.474826 + 0.822423i
\(490\) −12.0000 −0.542105
\(491\) 1.50000 + 2.59808i 0.0676941 + 0.117250i 0.897886 0.440228i \(-0.145102\pi\)
−0.830192 + 0.557478i \(0.811769\pi\)
\(492\) 10.5000 + 18.1865i 0.473377 + 0.819912i
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) −10.5000 + 2.59808i −0.472417 + 0.116893i
\(495\) −9.00000 + 15.5885i −0.404520 + 0.700649i
\(496\) −37.5000 21.6506i −1.68380 0.972142i
\(497\) −15.0000 −0.672842
\(498\) 13.5000 7.79423i 0.604949 0.349268i
\(499\) −22.5000 12.9904i −1.00724 0.581529i −0.0968564 0.995298i \(-0.530879\pi\)
−0.910382 + 0.413769i \(0.864212\pi\)
\(500\) 12.1244i 0.542218i
\(501\) 4.50000 + 7.79423i 0.201045 + 0.348220i
\(502\) −13.5000 + 7.79423i −0.602534 + 0.347873i
\(503\) −10.5000 18.1865i −0.468172 0.810897i 0.531167 0.847267i \(-0.321754\pi\)
−0.999338 + 0.0363700i \(0.988421\pi\)
\(504\) −4.50000 + 7.79423i −0.200446 + 0.347183i
\(505\) −9.00000 5.19615i −0.400495 0.231226i
\(506\) −9.00000 15.5885i −0.400099 0.692991i
\(507\) 12.0000 19.0526i 0.532939 0.846154i
\(508\) −2.50000 + 4.33013i −0.110920 + 0.192118i
\(509\) 1.50000 0.866025i 0.0664863 0.0383859i −0.466388 0.884580i \(-0.654445\pi\)
0.532875 + 0.846194i \(0.321112\pi\)
\(510\) 15.5885i 0.690268i
\(511\) −6.00000 + 10.3923i −0.265424 + 0.459728i
\(512\) 8.66025i 0.382733i
\(513\) 4.50000 + 7.79423i 0.198680 + 0.344124i
\(514\) −4.50000 + 2.59808i −0.198486 + 0.114596i
\(515\) 19.5000 11.2583i 0.859273 0.496101i
\(516\) −1.50000 0.866025i −0.0660338 0.0381246i
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) −13.5000 + 7.79423i −0.593156 + 0.342459i
\(519\) 31.5000 + 18.1865i 1.38270 + 0.798300i
\(520\) 7.50000 + 7.79423i 0.328897 + 0.341800i
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 31.1769i 1.36458i
\(523\) 12.5000 21.6506i 0.546587 0.946716i −0.451918 0.892059i \(-0.649260\pi\)
0.998505 0.0546569i \(-0.0174065\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 6.00000 0.261861
\(526\) 41.5692i 1.81250i
\(527\) 25.9808i 1.13174i
\(528\) −30.0000 −1.30558
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 9.00000 15.5885i 0.390935 0.677119i
\(531\) 10.3923i 0.450988i
\(532\) 3.00000 0.130066
\(533\) −10.5000 42.4352i −0.454805 1.83807i
\(534\) 40.5000 + 23.3827i 1.75261 + 1.01187i
\(535\) −22.5000 + 12.9904i −0.972760 + 0.561623i
\(536\) −10.5000 18.1865i −0.453531 0.785539i
\(537\) −4.50000 2.59808i −0.194189 0.112115i
\(538\) −4.50000 + 2.59808i −0.194009 + 0.112011i
\(539\) −12.0000 + 6.92820i −0.516877 + 0.298419i
\(540\) −4.50000 + 7.79423i −0.193649 + 0.335410i
\(541\) 13.8564i 0.595733i −0.954607 0.297867i \(-0.903725\pi\)
0.954607 0.297867i \(-0.0962751\pi\)
\(542\) 13.5000 23.3827i 0.579875 1.00437i
\(543\) 38.1051i 1.63525i
\(544\) 13.5000 7.79423i 0.578808 0.334175i
\(545\) 0 0
\(546\) −13.5000 + 12.9904i −0.577747 + 0.555937i
\(547\) −8.50000 14.7224i −0.363434 0.629486i 0.625090 0.780553i \(-0.285062\pi\)
−0.988524 + 0.151067i \(0.951729\pi\)
\(548\) 4.50000 + 2.59808i 0.192230 + 0.110984i
\(549\) −7.50000 + 12.9904i −0.320092 + 0.554416i
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) 9.00000 5.19615i 0.383413 0.221364i
\(552\) 4.50000 + 7.79423i 0.191533 + 0.331744i
\(553\) 19.0526i 0.810197i
\(554\) 34.5000 + 19.9186i 1.46576 + 0.846260i
\(555\) 13.5000 7.79423i 0.573043 0.330847i
\(556\) 16.0000 0.678551
\(557\) −16.5000 9.52628i −0.699127 0.403641i 0.107895 0.994162i \(-0.465589\pi\)
−0.807022 + 0.590521i \(0.798922\pi\)
\(558\) −22.5000 + 38.9711i −0.952501 + 1.64978i
\(559\) 2.50000 + 2.59808i 0.105739 + 0.109887i
\(560\) −7.50000 12.9904i −0.316933 0.548944i
\(561\) −9.00000 15.5885i −0.379980 0.658145i
\(562\) 4.50000 + 7.79423i 0.189821 + 0.328780i
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −4.50000 7.79423i −0.189484 0.328196i
\(565\) 9.00000 + 5.19615i 0.378633 + 0.218604i
\(566\) 34.5000 19.9186i 1.45014 0.837241i
\(567\) 13.5000 + 7.79423i 0.566947 + 0.327327i
\(568\) 7.50000 + 12.9904i 0.314693 + 0.545064i
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) −9.00000 −0.376969
\(571\) 2.50000 4.33013i 0.104622 0.181210i −0.808962 0.587861i \(-0.799970\pi\)
0.913584 + 0.406651i \(0.133303\pi\)
\(572\) −12.0000 3.46410i −0.501745 0.144841i
\(573\) −4.50000 2.59808i −0.187990 0.108536i
\(574\) 36.3731i 1.51818i
\(575\) 3.00000 5.19615i 0.125109 0.216695i
\(576\) 3.00000 0.125000
\(577\) 6.92820i 0.288425i 0.989547 + 0.144212i \(0.0460649\pi\)
−0.989547 + 0.144212i \(0.953935\pi\)
\(578\) −12.0000 6.92820i −0.499134 0.288175i
\(579\) −4.50000 7.79423i −0.187014 0.323917i
\(580\) 9.00000 + 5.19615i 0.373705 + 0.215758i
\(581\) 9.00000 0.373383
\(582\) 40.5000 + 23.3827i 1.67878 + 0.969244i
\(583\) 20.7846i 0.860811i
\(584\) 12.0000 0.496564
\(585\) 13.5000 12.9904i 0.558156 0.537086i
\(586\) −24.0000 −0.991431
\(587\) 10.3923i 0.428936i 0.976731 + 0.214468i \(0.0688018\pi\)
−0.976731 + 0.214468i \(0.931198\pi\)
\(588\) −6.00000 + 3.46410i −0.247436 + 0.142857i
\(589\) −15.0000 −0.618064
\(590\) −9.00000 5.19615i −0.370524 0.213922i
\(591\) −7.50000 + 12.9904i −0.308509 + 0.534353i
\(592\) 22.5000 + 12.9904i 0.924744 + 0.533901i
\(593\) 27.7128i 1.13803i 0.822328 + 0.569014i \(0.192675\pi\)
−0.822328 + 0.569014i \(0.807325\pi\)
\(594\) 31.1769i 1.27920i
\(595\) 4.50000 7.79423i 0.184482 0.319532i
\(596\) 0 0
\(597\) 19.5000 11.2583i 0.798082 0.460773i
\(598\) 4.50000 + 18.1865i 0.184019 + 0.743703i
\(599\) −13.5000 + 23.3827i −0.551595 + 0.955391i 0.446565 + 0.894751i \(0.352647\pi\)
−0.998160 + 0.0606393i \(0.980686\pi\)
\(600\) −3.00000 5.19615i −0.122474 0.212132i
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −1.50000 2.59808i −0.0611354 0.105890i
\(603\) −31.5000 + 18.1865i −1.28278 + 0.740613i
\(604\) −10.5000 + 6.06218i −0.427239 + 0.246667i
\(605\) −1.50000 0.866025i −0.0609837 0.0352089i
\(606\) −18.0000 −0.731200
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) −4.50000 7.79423i −0.182499 0.316098i
\(609\) 9.00000 15.5885i 0.364698 0.631676i
\(610\) −7.50000 12.9904i −0.303666 0.525965i
\(611\) 4.50000 + 18.1865i 0.182051 + 0.735748i
\(612\) −4.50000 7.79423i −0.181902 0.315063i
\(613\) −10.5000 6.06218i −0.424091 0.244849i 0.272735 0.962089i \(-0.412072\pi\)
−0.696826 + 0.717240i \(0.745405\pi\)
\(614\) 42.0000 1.69498
\(615\) 36.3731i 1.46670i
\(616\) −9.00000 5.19615i −0.362620 0.209359i
\(617\) 27.7128i 1.11568i 0.829950 + 0.557838i \(0.188369\pi\)
−0.829950 + 0.557838i \(0.811631\pi\)
\(618\) 19.5000 33.7750i 0.784405 1.35863i
\(619\) 22.5000 12.9904i 0.904351 0.522127i 0.0257420 0.999669i \(-0.491805\pi\)
0.878609 + 0.477541i \(0.158472\pi\)
\(620\) −7.50000 12.9904i −0.301207 0.521706i
\(621\) 13.5000 7.79423i 0.541736 0.312772i
\(622\) 40.5000 + 23.3827i 1.62390 + 0.937560i
\(623\) 13.5000 + 23.3827i 0.540866 + 0.936808i
\(624\) 30.0000 + 8.66025i 1.20096 + 0.346688i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −28.5000 + 16.4545i −1.13909 + 0.657653i
\(627\) −9.00000 + 5.19615i −0.359425 + 0.207514i
\(628\) 11.5000 19.9186i 0.458900 0.794838i
\(629\) 15.5885i 0.621552i
\(630\) −13.5000 + 7.79423i −0.537853 + 0.310530i
\(631\) −7.50000 + 4.33013i −0.298570 + 0.172380i −0.641800 0.766872i \(-0.721812\pi\)
0.343230 + 0.939251i \(0.388479\pi\)
\(632\) 16.5000 9.52628i 0.656335 0.378935i
\(633\) 19.5000 11.2583i 0.775055 0.447478i
\(634\) −7.50000 12.9904i −0.297863 0.515914i
\(635\) 7.50000 4.33013i 0.297628 0.171836i
\(636\) 10.3923i 0.412082i
\(637\) 14.0000 3.46410i 0.554700 0.137253i
\(638\) 36.0000 1.42525
\(639\) 22.5000 12.9904i 0.890086 0.513892i
\(640\) −10.5000 + 18.1865i −0.415049 + 0.718886i
\(641\) −19.5000 + 33.7750i −0.770204 + 1.33403i 0.167247 + 0.985915i \(0.446512\pi\)
−0.937451 + 0.348117i \(0.886821\pi\)
\(642\) −22.5000 + 38.9711i −0.888004 + 1.53807i
\(643\) 3.46410i 0.136611i 0.997664 + 0.0683054i \(0.0217592\pi\)
−0.997664 + 0.0683054i \(0.978241\pi\)
\(644\) 5.19615i 0.204757i
\(645\) 1.50000 + 2.59808i 0.0590624 + 0.102299i
\(646\) 4.50000 7.79423i 0.177050 0.306660i
\(647\) 4.50000 7.79423i 0.176913 0.306423i −0.763908 0.645325i \(-0.776722\pi\)
0.940822 + 0.338902i \(0.110055\pi\)
\(648\) 15.5885i 0.612372i
\(649\) −12.0000 −0.471041
\(650\) −3.00000 12.1244i −0.117670 0.475556i
\(651\) −22.5000 + 12.9904i −0.881845 + 0.509133i
\(652\) −10.5000 + 6.06218i −0.411212 + 0.237413i
\(653\) 22.5000 + 38.9711i 0.880493 + 1.52506i 0.850794 + 0.525500i \(0.176122\pi\)
0.0296993 + 0.999559i \(0.490545\pi\)
\(654\) 0 0
\(655\) −22.5000 + 12.9904i −0.879148 + 0.507576i
\(656\) 52.5000 30.3109i 2.04978 1.18344i
\(657\) 20.7846i 0.810885i
\(658\) 15.5885i 0.607701i
\(659\) −19.5000 + 33.7750i −0.759612 + 1.31569i 0.183436 + 0.983032i \(0.441278\pi\)
−0.943049 + 0.332655i \(0.892055\pi\)
\(660\) −9.00000 5.19615i −0.350325 0.202260i
\(661\) −40.5000 + 23.3827i −1.57527 + 0.909481i −0.579761 + 0.814787i \(0.696854\pi\)
−0.995506 + 0.0946945i \(0.969813\pi\)
\(662\) 13.5000 23.3827i 0.524692 0.908794i
\(663\) 4.50000 + 18.1865i 0.174766 + 0.706306i
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) −4.50000 2.59808i −0.174503 0.100749i
\(666\) 13.5000 23.3827i 0.523114 0.906061i
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) −4.50000 + 2.59808i −0.174110 + 0.100523i
\(669\) −6.00000 −0.231973
\(670\) 36.3731i 1.40521i
\(671\) −15.0000 8.66025i −0.579069 0.334325i
\(672\) −13.5000 7.79423i −0.520774 0.300669i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −43.5000 25.1147i −1.67556 0.967384i
\(675\) −9.00000 + 5.19615i −0.346410 + 0.200000i
\(676\) 11.0000 + 6.92820i 0.423077 + 0.266469i
\(677\) 10.5000 + 18.1865i 0.403548 + 0.698965i 0.994151 0.107997i \(-0.0344436\pi\)
−0.590603 + 0.806962i \(0.701110\pi\)
\(678\) 18.0000 0.691286
\(679\) 13.5000 + 23.3827i 0.518082 + 0.897345i
\(680\) −9.00000 −0.345134
\(681\) 10.5000 18.1865i 0.402361 0.696909i
\(682\) −45.0000 25.9808i −1.72314 0.994855i
\(683\) −19.5000 + 11.2583i −0.746147 + 0.430788i −0.824300 0.566153i \(-0.808431\pi\)
0.0781532 + 0.996941i \(0.475098\pi\)
\(684\) −4.50000 + 2.59808i −0.172062 + 0.0993399i
\(685\) −4.50000 7.79423i −0.171936 0.297802i
\(686\) −33.0000 −1.25995
\(687\) −7.50000 + 12.9904i −0.286143 + 0.495614i
\(688\) −2.50000 + 4.33013i −0.0953116 + 0.165085i
\(689\) −6.00000 + 20.7846i −0.228582 + 0.791831i
\(690\) 15.5885i 0.593442i
\(691\) 17.3205i 0.658903i −0.944172 0.329452i \(-0.893136\pi\)
0.944172 0.329452i \(-0.106864\pi\)
\(692\) −10.5000 + 18.1865i −0.399150 + 0.691348i
\(693\) −9.00000 + 15.5885i −0.341882 + 0.592157i
\(694\) 20.7846i 0.788973i
\(695\) −24.0000 13.8564i −0.910372 0.525603i
\(696\) −18.0000 −0.682288
\(697\) 31.5000 + 18.1865i 1.19315 + 0.688864i
\(698\) −48.0000 −1.81683
\(699\) 31.1769i 1.17922i
\(700\) 3.46410i 0.130931i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 9.00000 31.1769i 0.339683 1.17670i
\(703\) 9.00000 0.339441
\(704\) 3.46410i 0.130558i
\(705\) 15.5885i 0.587095i
\(706\) 12.0000 0.451626
\(707\) −9.00000 5.19615i −0.338480 0.195421i
\(708\) −6.00000 −0.225494
\(709\) −10.5000 6.06218i −0.394336 0.227670i 0.289701 0.957117i \(-0.406444\pi\)
−0.684037 + 0.729447i \(0.739777\pi\)
\(710\) 25.9808i 0.975041i
\(711\) −16.5000 28.5788i −0.618798 1.07179i
\(712\) 13.5000 23.3827i 0.505934 0.876303i
\(713\) 25.9808i 0.972987i
\(714\) 15.5885i 0.583383i
\(715\) 15.0000 + 15.5885i 0.560968 + 0.582975i
\(716\) 1.50000 2.59808i 0.0560576 0.0970947i
\(717\) 4.50000 7.79423i 0.168056 0.291081i
\(718\) −18.0000 −0.671754
\(719\) 19.5000 + 33.7750i 0.727227 + 1.25959i 0.958051 + 0.286599i \(0.0925247\pi\)
−0.230823 + 0.972996i \(0.574142\pi\)
\(720\) 22.5000 + 12.9904i 0.838525 + 0.484123i
\(721\) 19.5000 11.2583i 0.726218 0.419282i
\(722\) 24.0000 + 13.8564i 0.893188 + 0.515682i
\(723\) 4.50000 7.79423i 0.167357 0.289870i
\(724\) 22.0000 0.817624
\(725\) 6.00000 + 10.3923i 0.222834 + 0.385961i
\(726\) −3.00000 −0.111340
\(727\) −0.500000 0.866025i −0.0185440 0.0321191i 0.856605 0.515974i \(-0.172570\pi\)
−0.875148 + 0.483854i \(0.839236\pi\)
\(728\) 7.50000 + 7.79423i 0.277968 + 0.288873i
\(729\) −27.0000 −1.00000
\(730\) 18.0000 + 10.3923i 0.666210 + 0.384636i
\(731\) −3.00000 −0.110959
\(732\) −7.50000 4.33013i −0.277208 0.160046i
\(733\) −16.5000 9.52628i −0.609441 0.351861i 0.163305 0.986576i \(-0.447784\pi\)
−0.772747 + 0.634714i \(0.781118\pi\)
\(734\) 13.8564i 0.511449i
\(735\) 12.0000 0.442627
\(736\) −13.5000 + 7.79423i −0.497617 + 0.287299i
\(737\) −21.0000 36.3731i −0.773545 1.33982i
\(738\) −31.5000 54.5596i −1.15953 2.00837i
\(739\) −28.5000 16.4545i −1.04839 0.605288i −0.126191 0.992006i \(-0.540275\pi\)
−0.922198 + 0.386718i \(0.873609\pi\)
\(740\) 4.50000 + 7.79423i 0.165423 + 0.286522i
\(741\) 10.5000 2.59808i 0.385727 0.0954427i
\(742\) 9.00000 15.5885i 0.330400 0.572270i
\(743\) 10.5000 6.06218i 0.385208 0.222400i −0.294874 0.955536i \(-0.595278\pi\)
0.680082 + 0.733136i \(0.261944\pi\)
\(744\) 22.5000 + 12.9904i 0.824890 + 0.476250i
\(745\) 0 0
\(746\) 24.2487i 0.887808i
\(747\) −13.5000 + 7.79423i −0.493939 + 0.285176i
\(748\) 9.00000 5.19615i 0.329073 0.189990i
\(749\) −22.5000 + 12.9904i −0.822132 + 0.474658i
\(750\) 36.3731i 1.32816i
\(751\) 9.50000 + 16.4545i 0.346660 + 0.600433i 0.985654 0.168779i \(-0.0539825\pi\)
−0.638994 + 0.769212i \(0.720649\pi\)
\(752\) −22.5000 + 12.9904i −0.820491 + 0.473710i
\(753\) 13.5000 7.79423i 0.491967 0.284037i
\(754\) −36.0000 10.3923i −1.31104 0.378465i
\(755\) 21.0000 0.764268
\(756\) −4.50000 + 7.79423i −0.163663 + 0.283473i
\(757\) −3.50000 + 6.06218i −0.127210 + 0.220334i −0.922595 0.385771i \(-0.873935\pi\)
0.795385 + 0.606105i \(0.207269\pi\)
\(758\) −10.5000 + 18.1865i −0.381377 + 0.660565i
\(759\) 9.00000 + 15.5885i 0.326679 + 0.565825i
\(760\) 5.19615i 0.188484i
\(761\) 13.8564i 0.502294i −0.967949 0.251147i \(-0.919192\pi\)
0.967949 0.251147i \(-0.0808078\pi\)
\(762\) 7.50000 12.9904i 0.271696 0.470592i
\(763\) 0 0
\(764\) 1.50000 2.59808i 0.0542681 0.0939951i
\(765\) 15.5885i 0.563602i
\(766\) 6.00000 0.216789
\(767\) 12.0000 + 3.46410i 0.433295 + 0.125081i
\(768\) 32.9090i 1.18750i
\(769\) 19.5000 11.2583i 0.703188 0.405986i