Properties

Label 171.2.g.b.121.1
Level $171$
Weight $2$
Character 171.121
Analytic conductor $1.365$
Analytic rank $0$
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] = [171,2,Mod(106,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.g (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: \(1.36544187456\)
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 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 171.121
Dual form 171.2.g.b.106.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +1.73205i q^{12} +(3.00000 + 5.19615i) q^{13} -3.00000 q^{14} +(-1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +3.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} -5.19615i q^{21} -3.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(4.50000 + 2.59808i) q^{24} -4.00000 q^{25} +6.00000 q^{26} +5.19615i q^{27} +(1.50000 - 2.59808i) q^{28} -5.00000 q^{29} +(-1.50000 + 0.866025i) q^{30} +(3.50000 - 6.06218i) q^{31} +(2.50000 + 4.33013i) q^{32} -5.19615i q^{33} -3.00000 q^{34} +(1.50000 + 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{36} +2.00000 q^{37} +(-0.500000 + 4.33013i) q^{38} +10.3923i q^{39} -3.00000 q^{40} -1.00000 q^{41} +(-4.50000 - 2.59808i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{45} -8.00000 q^{46} +9.00000 q^{47} +(1.50000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-2.00000 + 3.46410i) q^{50} -5.19615i q^{51} +(-3.00000 + 5.19615i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(4.50000 + 2.59808i) q^{54} +(1.50000 + 2.59808i) q^{55} +(-4.50000 - 7.79423i) q^{56} +(-7.50000 - 0.866025i) q^{57} +(-2.50000 + 4.33013i) q^{58} +3.00000 q^{59} -1.73205i q^{60} +7.00000 q^{61} +(-3.50000 - 6.06218i) q^{62} +(4.50000 - 7.79423i) q^{63} +7.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(-4.50000 - 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} -13.8564i q^{69} +3.00000 q^{70} +(7.50000 + 12.9904i) q^{71} +(4.50000 + 7.79423i) q^{72} +(2.50000 + 4.33013i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(-3.50000 - 2.59808i) q^{76} +(-4.50000 + 7.79423i) q^{77} +(9.00000 + 5.19615i) q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(0.500000 + 0.866025i) q^{83} +(4.50000 - 2.59808i) q^{84} +(1.50000 + 2.59808i) q^{85} +(4.00000 + 6.92820i) q^{86} +(-7.50000 - 4.33013i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(0.500000 - 0.866025i) q^{89} -3.00000 q^{90} +(9.00000 - 15.5885i) q^{91} +(4.00000 - 6.92820i) q^{92} +(10.5000 - 6.06218i) q^{93} +(4.50000 - 7.79423i) q^{94} +(4.00000 - 1.73205i) q^{95} +8.66025i q^{96} +(1.00000 - 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9} - q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} - 8 q^{19} - q^{20} - 6 q^{22} - 8 q^{23} + 9 q^{24} - 8 q^{25} + 12 q^{26} + 3 q^{28} - 10 q^{29} - 3 q^{30} + 7 q^{31} + 5 q^{32} - 6 q^{34} + 3 q^{35} - 3 q^{36} + 4 q^{37} - q^{38} - 6 q^{40} - 2 q^{41} - 9 q^{42} - 8 q^{43} + 3 q^{44} - 3 q^{45} - 16 q^{46} + 18 q^{47} + 3 q^{48} - 2 q^{49} - 4 q^{50} - 6 q^{52} - 3 q^{53} + 9 q^{54} + 3 q^{55} - 9 q^{56} - 15 q^{57} - 5 q^{58} + 6 q^{59} + 14 q^{61} - 7 q^{62} + 9 q^{63} + 14 q^{64} - 6 q^{65} - 9 q^{66} + 4 q^{67} + 3 q^{68} + 6 q^{70} + 15 q^{71} + 9 q^{72} + 5 q^{73} + 2 q^{74} - 12 q^{75} - 7 q^{76} - 9 q^{77} + 18 q^{78} + 12 q^{79} - q^{80} - 9 q^{81} - q^{82} + q^{83} + 9 q^{84} + 3 q^{85} + 8 q^{86} - 15 q^{87} - 9 q^{88} + q^{89} - 6 q^{90} + 18 q^{91} + 8 q^{92} + 21 q^{93} + 9 q^{94} + 8 q^{95} + 2 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i −0.633316 0.773893i \(-0.718307\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) −3.00000 −0.801784
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 3.00000 0.707107
\(19\) −4.00000 + 1.73205i −0.917663 + 0.397360i
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 5.19615i 1.13389i
\(22\) −3.00000 −0.639602
\(23\) −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) 4.50000 + 2.59808i 0.918559 + 0.530330i
\(25\) −4.00000 −0.800000
\(26\) 6.00000 1.17670
\(27\) 5.19615i 1.00000i
\(28\) 1.50000 2.59808i 0.283473 0.490990i
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −1.50000 + 0.866025i −0.273861 + 0.158114i
\(31\) 3.50000 6.06218i 0.628619 1.08880i −0.359211 0.933257i \(-0.616954\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 2.50000 + 4.33013i 0.441942 + 0.765466i
\(33\) 5.19615i 0.904534i
\(34\) −3.00000 −0.514496
\(35\) 1.50000 + 2.59808i 0.253546 + 0.439155i
\(36\) −1.50000 + 2.59808i −0.250000 + 0.433013i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −0.500000 + 4.33013i −0.0811107 + 0.702439i
\(39\) 10.3923i 1.66410i
\(40\) −3.00000 −0.474342
\(41\) −1.00000 −0.156174 −0.0780869 0.996947i \(-0.524881\pi\)
−0.0780869 + 0.996947i \(0.524881\pi\)
\(42\) −4.50000 2.59808i −0.694365 0.400892i
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) −8.00000 −1.17954
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 1.50000 0.866025i 0.216506 0.125000i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) 5.19615i 0.727607i
\(52\) −3.00000 + 5.19615i −0.416025 + 0.720577i
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 1.50000 + 2.59808i 0.202260 + 0.350325i
\(56\) −4.50000 7.79423i −0.601338 1.04155i
\(57\) −7.50000 0.866025i −0.993399 0.114708i
\(58\) −2.50000 + 4.33013i −0.328266 + 0.568574i
\(59\) 3.00000 0.390567 0.195283 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(60\) 1.73205i 0.223607i
\(61\) 7.00000 0.896258 0.448129 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) −3.50000 6.06218i −0.444500 0.769897i
\(63\) 4.50000 7.79423i 0.566947 0.981981i
\(64\) 7.00000 0.875000
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) −4.50000 2.59808i −0.553912 0.319801i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 1.50000 2.59808i 0.181902 0.315063i
\(69\) 13.8564i 1.66812i
\(70\) 3.00000 0.358569
\(71\) 7.50000 + 12.9904i 0.890086 + 1.54167i 0.839771 + 0.542941i \(0.182689\pi\)
0.0503155 + 0.998733i \(0.483977\pi\)
\(72\) 4.50000 + 7.79423i 0.530330 + 0.918559i
\(73\) 2.50000 + 4.33013i 0.292603 + 0.506803i 0.974424 0.224716i \(-0.0721453\pi\)
−0.681822 + 0.731519i \(0.738812\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −6.00000 3.46410i −0.692820 0.400000i
\(76\) −3.50000 2.59808i −0.401478 0.298020i
\(77\) −4.50000 + 7.79423i −0.512823 + 0.888235i
\(78\) 9.00000 + 5.19615i 1.01905 + 0.588348i
\(79\) 6.00000 10.3923i 0.675053 1.16923i −0.301401 0.953498i \(-0.597454\pi\)
0.976453 0.215728i \(-0.0692125\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −0.500000 + 0.866025i −0.0552158 + 0.0956365i
\(83\) 0.500000 + 0.866025i 0.0548821 + 0.0950586i 0.892161 0.451717i \(-0.149188\pi\)
−0.837279 + 0.546776i \(0.815855\pi\)
\(84\) 4.50000 2.59808i 0.490990 0.283473i
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) −7.50000 4.33013i −0.804084 0.464238i
\(88\) −4.50000 7.79423i −0.479702 0.830868i
\(89\) 0.500000 0.866025i 0.0529999 0.0917985i −0.838308 0.545197i \(-0.816455\pi\)
0.891308 + 0.453398i \(0.149788\pi\)
\(90\) −3.00000 −0.316228
\(91\) 9.00000 15.5885i 0.943456 1.63411i
\(92\) 4.00000 6.92820i 0.417029 0.722315i
\(93\) 10.5000 6.06218i 1.08880 0.628619i
\(94\) 4.50000 7.79423i 0.464140 0.803913i
\(95\) 4.00000 1.73205i 0.410391 0.177705i
\(96\) 8.66025i 0.883883i
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 1.00000 + 1.73205i 0.101015 + 0.174964i
\(99\) 4.50000 7.79423i 0.452267 0.783349i
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −5.00000 −0.497519 −0.248759 0.968565i \(-0.580023\pi\)
−0.248759 + 0.968565i \(0.580023\pi\)
\(102\) −4.50000 2.59808i −0.445566 0.257248i
\(103\) 3.50000 6.06218i 0.344865 0.597324i −0.640464 0.767988i \(-0.721258\pi\)
0.985329 + 0.170664i \(0.0545913\pi\)
\(104\) 9.00000 + 15.5885i 0.882523 + 1.52857i
\(105\) 5.19615i 0.507093i
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) 3.00000 0.286039
\(111\) 3.00000 + 1.73205i 0.284747 + 0.164399i
\(112\) −3.00000 −0.283473
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) −4.50000 + 6.06218i −0.421464 + 0.567775i
\(115\) 4.00000 + 6.92820i 0.373002 + 0.646058i
\(116\) −2.50000 4.33013i −0.232119 0.402042i
\(117\) −9.00000 + 15.5885i −0.832050 + 1.44115i
\(118\) 1.50000 2.59808i 0.138086 0.239172i
\(119\) −4.50000 + 7.79423i −0.412514 + 0.714496i
\(120\) −4.50000 2.59808i −0.410792 0.237171i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 3.50000 6.06218i 0.316875 0.548844i
\(123\) −1.50000 0.866025i −0.135250 0.0780869i
\(124\) 7.00000 0.628619
\(125\) 9.00000 0.804984
\(126\) −4.50000 7.79423i −0.400892 0.694365i
\(127\) −3.50000 + 6.06218i −0.310575 + 0.537931i −0.978487 0.206309i \(-0.933855\pi\)
0.667912 + 0.744240i \(0.267188\pi\)
\(128\) −1.50000 + 2.59808i −0.132583 + 0.229640i
\(129\) −12.0000 + 6.92820i −1.05654 + 0.609994i
\(130\) −6.00000 −0.526235
\(131\) −17.0000 −1.48530 −0.742648 0.669681i \(-0.766431\pi\)
−0.742648 + 0.669681i \(0.766431\pi\)
\(132\) 4.50000 2.59808i 0.391675 0.226134i
\(133\) 10.5000 + 7.79423i 0.910465 + 0.675845i
\(134\) 4.00000 0.345547
\(135\) 5.19615i 0.447214i
\(136\) −4.50000 7.79423i −0.385872 0.668350i
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) −12.0000 6.92820i −1.02151 0.589768i
\(139\) −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i \(-0.220926\pi\)
−0.938293 + 0.345843i \(0.887593\pi\)
\(140\) −1.50000 + 2.59808i −0.126773 + 0.219578i
\(141\) 13.5000 + 7.79423i 1.13691 + 0.656392i
\(142\) 15.0000 1.25877
\(143\) 9.00000 15.5885i 0.752618 1.30357i
\(144\) 3.00000 0.250000
\(145\) 5.00000 0.415227
\(146\) 5.00000 0.413803
\(147\) −3.00000 + 1.73205i −0.247436 + 0.142857i
\(148\) 1.00000 + 1.73205i 0.0821995 + 0.142374i
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) −6.00000 + 3.46410i −0.489898 + 0.282843i
\(151\) −9.50000 16.4545i −0.773099 1.33905i −0.935857 0.352381i \(-0.885372\pi\)
0.162758 0.986666i \(-0.447961\pi\)
\(152\) −12.0000 + 5.19615i −0.973329 + 0.421464i
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) 4.50000 + 7.79423i 0.362620 + 0.628077i
\(155\) −3.50000 + 6.06218i −0.281127 + 0.486926i
\(156\) −9.00000 + 5.19615i −0.720577 + 0.416025i
\(157\) 7.00000 0.558661 0.279330 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) −6.00000 10.3923i −0.477334 0.826767i
\(159\) −4.50000 + 2.59808i −0.356873 + 0.206041i
\(160\) −2.50000 4.33013i −0.197642 0.342327i
\(161\) −12.0000 + 20.7846i −0.945732 + 1.63806i
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −0.500000 0.866025i −0.0390434 0.0676252i
\(165\) 5.19615i 0.404520i
\(166\) 1.00000 0.0776151
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 15.5885i 1.20268i
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 3.00000 0.230089
\(171\) −10.5000 7.79423i −0.802955 0.596040i
\(172\) −8.00000 −0.609994
\(173\) 7.00000 12.1244i 0.532200 0.921798i −0.467093 0.884208i \(-0.654699\pi\)
0.999293 0.0375896i \(-0.0119679\pi\)
\(174\) −7.50000 + 4.33013i −0.568574 + 0.328266i
\(175\) 6.00000 + 10.3923i 0.453557 + 0.785584i
\(176\) −3.00000 −0.226134
\(177\) 4.50000 + 2.59808i 0.338241 + 0.195283i
\(178\) −0.500000 0.866025i −0.0374766 0.0649113i
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) −5.50000 + 9.52628i −0.408812 + 0.708083i −0.994757 0.102268i \(-0.967390\pi\)
0.585945 + 0.810351i \(0.300723\pi\)
\(182\) −9.00000 15.5885i −0.667124 1.15549i
\(183\) 10.5000 + 6.06218i 0.776182 + 0.448129i
\(184\) −12.0000 20.7846i −0.884652 1.53226i
\(185\) −2.00000 −0.147043
\(186\) 12.1244i 0.889001i
\(187\) −4.50000 + 7.79423i −0.329073 + 0.569970i
\(188\) 4.50000 + 7.79423i 0.328196 + 0.568453i
\(189\) 13.5000 7.79423i 0.981981 0.566947i
\(190\) 0.500000 4.33013i 0.0362738 0.314140i
\(191\) 4.50000 + 7.79423i 0.325609 + 0.563971i 0.981635 0.190767i \(-0.0610975\pi\)
−0.656027 + 0.754738i \(0.727764\pi\)
\(192\) 10.5000 + 6.06218i 0.757772 + 0.437500i
\(193\) −17.0000 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 10.3923i 0.744208i
\(196\) −2.00000 −0.142857
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) −4.50000 7.79423i −0.319801 0.553912i
\(199\) 8.50000 14.7224i 0.602549 1.04365i −0.389885 0.920864i \(-0.627485\pi\)
0.992434 0.122782i \(-0.0391815\pi\)
\(200\) −12.0000 −0.848528
\(201\) 6.92820i 0.488678i
\(202\) −2.50000 + 4.33013i −0.175899 + 0.304667i
\(203\) 7.50000 + 12.9904i 0.526397 + 0.911746i
\(204\) 4.50000 2.59808i 0.315063 0.181902i
\(205\) 1.00000 0.0698430
\(206\) −3.50000 6.06218i −0.243857 0.422372i
\(207\) 12.0000 20.7846i 0.834058 1.44463i
\(208\) 6.00000 0.416025
\(209\) 10.5000 + 7.79423i 0.726300 + 0.539138i
\(210\) 4.50000 + 2.59808i 0.310530 + 0.179284i
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) −3.00000 −0.206041
\(213\) 25.9808i 1.78017i
\(214\) −2.00000 + 3.46410i −0.136717 + 0.236801i
\(215\) 4.00000 6.92820i 0.272798 0.472500i
\(216\) 15.5885i 1.06066i
\(217\) −21.0000 −1.42557
\(218\) 1.00000 0.0677285
\(219\) 8.66025i 0.585206i
\(220\) −1.50000 + 2.59808i −0.101130 + 0.175162i
\(221\) 9.00000 15.5885i 0.605406 1.04859i
\(222\) 3.00000 1.73205i 0.201347 0.116248i
\(223\) 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i \(-0.747017\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(224\) 7.50000 12.9904i 0.501115 0.867956i
\(225\) −6.00000 10.3923i −0.400000 0.692820i
\(226\) 7.50000 + 12.9904i 0.498893 + 0.864107i
\(227\) 10.5000 + 18.1865i 0.696909 + 1.20708i 0.969533 + 0.244962i \(0.0787754\pi\)
−0.272623 + 0.962121i \(0.587891\pi\)
\(228\) −3.00000 6.92820i −0.198680 0.458831i
\(229\) −1.50000 + 2.59808i −0.0991228 + 0.171686i −0.911322 0.411695i \(-0.864937\pi\)
0.812199 + 0.583380i \(0.198270\pi\)
\(230\) 8.00000 0.527504
\(231\) −13.5000 + 7.79423i −0.888235 + 0.512823i
\(232\) −15.0000 −0.984798
\(233\) 0.500000 + 0.866025i 0.0327561 + 0.0567352i 0.881939 0.471364i \(-0.156238\pi\)
−0.849183 + 0.528099i \(0.822905\pi\)
\(234\) 9.00000 + 15.5885i 0.588348 + 1.01905i
\(235\) −9.00000 −0.587095
\(236\) 1.50000 + 2.59808i 0.0976417 + 0.169120i
\(237\) 18.0000 10.3923i 1.16923 0.675053i
\(238\) 4.50000 + 7.79423i 0.291692 + 0.505225i
\(239\) 13.5000 23.3827i 0.873242 1.51250i 0.0146191 0.999893i \(-0.495346\pi\)
0.858623 0.512607i \(-0.171320\pi\)
\(240\) −1.50000 + 0.866025i −0.0968246 + 0.0559017i
\(241\) 15.0000 0.966235 0.483117 0.875556i \(-0.339504\pi\)
0.483117 + 0.875556i \(0.339504\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) 1.00000 1.73205i 0.0638877 0.110657i
\(246\) −1.50000 + 0.866025i −0.0956365 + 0.0552158i
\(247\) −21.0000 15.5885i −1.33620 0.991870i
\(248\) 10.5000 18.1865i 0.666751 1.15485i
\(249\) 1.73205i 0.109764i
\(250\) 4.50000 7.79423i 0.284605 0.492950i
\(251\) −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i \(-0.863516\pi\)
0.814795 + 0.579748i \(0.196849\pi\)
\(252\) 9.00000 0.566947
\(253\) −12.0000 + 20.7846i −0.754434 + 1.30672i
\(254\) 3.50000 + 6.06218i 0.219610 + 0.380375i
\(255\) 5.19615i 0.325396i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 1.00000 + 1.73205i 0.0623783 + 0.108042i 0.895528 0.445005i \(-0.146798\pi\)
−0.833150 + 0.553047i \(0.813465\pi\)
\(258\) 13.8564i 0.862662i
\(259\) −3.00000 5.19615i −0.186411 0.322873i
\(260\) 3.00000 5.19615i 0.186052 0.322252i
\(261\) −7.50000 12.9904i −0.464238 0.804084i
\(262\) −8.50000 + 14.7224i −0.525132 + 0.909555i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 15.5885i 0.959403i
\(265\) 1.50000 2.59808i 0.0921443 0.159599i
\(266\) 12.0000 5.19615i 0.735767 0.318597i
\(267\) 1.50000 0.866025i 0.0917985 0.0529999i
\(268\) −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 \(0.862486\pi\)
\(270\) −4.50000 2.59808i −0.273861 0.158114i
\(271\) 7.50000 + 12.9904i 0.455593 + 0.789109i 0.998722 0.0505395i \(-0.0160941\pi\)
−0.543130 + 0.839649i \(0.682761\pi\)
\(272\) −3.00000 −0.181902
\(273\) 27.0000 15.5885i 1.63411 0.943456i
\(274\) 1.50000 2.59808i 0.0906183 0.156956i
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 12.0000 6.92820i 0.722315 0.417029i
\(277\) 2.50000 + 4.33013i 0.150210 + 0.260172i 0.931305 0.364241i \(-0.118672\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) −4.00000 −0.239904
\(279\) 21.0000 1.25724
\(280\) 4.50000 + 7.79423i 0.268926 + 0.465794i
\(281\) −5.00000 −0.298275 −0.149137 0.988816i \(-0.547650\pi\)
−0.149137 + 0.988816i \(0.547650\pi\)
\(282\) 13.5000 7.79423i 0.803913 0.464140i
\(283\) −5.00000 −0.297219 −0.148610 0.988896i \(-0.547480\pi\)
−0.148610 + 0.988896i \(0.547480\pi\)
\(284\) −7.50000 + 12.9904i −0.445043 + 0.770837i
\(285\) 7.50000 + 0.866025i 0.444262 + 0.0512989i
\(286\) −9.00000 15.5885i −0.532181 0.921765i
\(287\) 1.50000 + 2.59808i 0.0885422 + 0.153360i
\(288\) −7.50000 + 12.9904i −0.441942 + 0.765466i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 2.50000 4.33013i 0.146805 0.254274i
\(291\) 3.00000 1.73205i 0.175863 0.101535i
\(292\) −2.50000 + 4.33013i −0.146301 + 0.253402i
\(293\) 12.5000 21.6506i 0.730258 1.26484i −0.226515 0.974008i \(-0.572733\pi\)
0.956773 0.290836i \(-0.0939334\pi\)
\(294\) 3.46410i 0.202031i
\(295\) −3.00000 −0.174667
\(296\) 6.00000 0.348743
\(297\) 13.5000 7.79423i 0.783349 0.452267i
\(298\) 1.50000 2.59808i 0.0868927 0.150503i
\(299\) 24.0000 41.5692i 1.38796 2.40401i
\(300\) 6.92820i 0.400000i
\(301\) 24.0000 1.38334
\(302\) −19.0000 −1.09333
\(303\) −7.50000 4.33013i −0.430864 0.248759i
\(304\) −0.500000 + 4.33013i −0.0286770 + 0.248350i
\(305\) −7.00000 −0.400819
\(306\) −4.50000 7.79423i −0.257248 0.445566i
\(307\) −4.50000 7.79423i −0.256829 0.444840i 0.708562 0.705649i \(-0.249344\pi\)
−0.965391 + 0.260808i \(0.916011\pi\)
\(308\) −9.00000 −0.512823
\(309\) 10.5000 6.06218i 0.597324 0.344865i
\(310\) 3.50000 + 6.06218i 0.198787 + 0.344309i
\(311\) 3.50000 6.06218i 0.198467 0.343755i −0.749565 0.661931i \(-0.769737\pi\)
0.948031 + 0.318177i \(0.103070\pi\)
\(312\) 31.1769i 1.76505i
\(313\) −25.0000 −1.41308 −0.706542 0.707671i \(-0.749746\pi\)
−0.706542 + 0.707671i \(0.749746\pi\)
\(314\) 3.50000 6.06218i 0.197516 0.342108i
\(315\) −4.50000 + 7.79423i −0.253546 + 0.439155i
\(316\) 12.0000 0.675053
\(317\) −21.0000 −1.17948 −0.589739 0.807594i \(-0.700769\pi\)
−0.589739 + 0.807594i \(0.700769\pi\)
\(318\) 5.19615i 0.291386i
\(319\) 7.50000 + 12.9904i 0.419919 + 0.727322i
\(320\) −7.00000 −0.391312
\(321\) −6.00000 3.46410i −0.334887 0.193347i
\(322\) 12.0000 + 20.7846i 0.668734 + 1.15828i
\(323\) 10.5000 + 7.79423i 0.584236 + 0.433682i
\(324\) −9.00000 −0.500000
\(325\) −12.0000 20.7846i −0.665640 1.15292i
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 1.73205i 0.0957826i
\(328\) −3.00000 −0.165647
\(329\) −13.5000 23.3827i −0.744279 1.28913i
\(330\) 4.50000 + 2.59808i 0.247717 + 0.143019i
\(331\) −13.5000 23.3827i −0.742027 1.28523i −0.951571 0.307429i \(-0.900531\pi\)
0.209544 0.977799i \(-0.432802\pi\)
\(332\) −0.500000 + 0.866025i −0.0274411 + 0.0475293i
\(333\) 3.00000 + 5.19615i 0.164399 + 0.284747i
\(334\) −12.0000 −0.656611
\(335\) −2.00000 3.46410i −0.109272 0.189264i
\(336\) −4.50000 2.59808i −0.245495 0.141737i
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) 11.5000 + 19.9186i 0.625518 + 1.08343i
\(339\) −22.5000 + 12.9904i −1.22203 + 0.705541i
\(340\) −1.50000 + 2.59808i −0.0813489 + 0.140900i
\(341\) −21.0000 −1.13721
\(342\) −12.0000 + 5.19615i −0.648886 + 0.280976i
\(343\) −15.0000 −0.809924
\(344\) −12.0000 + 20.7846i −0.646997 + 1.12063i
\(345\) 13.8564i 0.746004i
\(346\) −7.00000 12.1244i −0.376322 0.651809i
\(347\) −33.0000 −1.77153 −0.885766 0.464131i \(-0.846367\pi\)
−0.885766 + 0.464131i \(0.846367\pi\)
\(348\) 8.66025i 0.464238i
\(349\) 2.50000 + 4.33013i 0.133822 + 0.231786i 0.925147 0.379610i \(-0.123942\pi\)
−0.791325 + 0.611396i \(0.790608\pi\)
\(350\) 12.0000 0.641427
\(351\) −27.0000 + 15.5885i −1.44115 + 0.832050i
\(352\) 7.50000 12.9904i 0.399751 0.692390i
\(353\) 14.5000 + 25.1147i 0.771757 + 1.33672i 0.936599 + 0.350403i \(0.113955\pi\)
−0.164842 + 0.986320i \(0.552711\pi\)
\(354\) 4.50000 2.59808i 0.239172 0.138086i
\(355\) −7.50000 12.9904i −0.398059 0.689458i
\(356\) 1.00000 0.0529999
\(357\) −13.5000 + 7.79423i −0.714496 + 0.412514i
\(358\) 2.00000 3.46410i 0.105703 0.183083i
\(359\) −8.50000 14.7224i −0.448613 0.777020i 0.549683 0.835373i \(-0.314748\pi\)
−0.998296 + 0.0583530i \(0.981415\pi\)
\(360\) −4.50000 7.79423i −0.237171 0.410792i
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 5.50000 + 9.52628i 0.289074 + 0.500690i
\(363\) 3.00000 1.73205i 0.157459 0.0909091i
\(364\) 18.0000 0.943456
\(365\) −2.50000 4.33013i −0.130856 0.226649i
\(366\) 10.5000 6.06218i 0.548844 0.316875i
\(367\) −31.0000 −1.61819 −0.809093 0.587680i \(-0.800041\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) −8.00000 −0.417029
\(369\) −1.50000 2.59808i −0.0780869 0.135250i
\(370\) −1.00000 + 1.73205i −0.0519875 + 0.0900450i
\(371\) 9.00000 0.467257
\(372\) 10.5000 + 6.06218i 0.544400 + 0.314309i
\(373\) −11.5000 + 19.9186i −0.595447 + 1.03135i 0.398036 + 0.917370i \(0.369692\pi\)
−0.993484 + 0.113975i \(0.963641\pi\)
\(374\) 4.50000 + 7.79423i 0.232689 + 0.403030i
\(375\) 13.5000 + 7.79423i 0.697137 + 0.402492i
\(376\) 27.0000 1.39242
\(377\) −15.0000 25.9808i −0.772539 1.33808i
\(378\) 15.5885i 0.801784i
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 3.50000 + 2.59808i 0.179546 + 0.133278i
\(381\) −10.5000 + 6.06218i −0.537931 + 0.310575i
\(382\) 9.00000 0.460480
\(383\) 19.0000 0.970855 0.485427 0.874277i \(-0.338664\pi\)
0.485427 + 0.874277i \(0.338664\pi\)
\(384\) −4.50000 + 2.59808i −0.229640 + 0.132583i
\(385\) 4.50000 7.79423i 0.229341 0.397231i
\(386\) −8.50000 + 14.7224i −0.432639 + 0.749352i
\(387\) −24.0000 −1.21999
\(388\) 2.00000 0.101535
\(389\) 15.0000 0.760530 0.380265 0.924878i \(-0.375833\pi\)
0.380265 + 0.924878i \(0.375833\pi\)
\(390\) −9.00000 5.19615i −0.455733 0.263117i
\(391\) −12.0000 + 20.7846i −0.606866 + 1.05112i
\(392\) −3.00000 + 5.19615i −0.151523 + 0.262445i
\(393\) −25.5000 14.7224i −1.28630 0.742648i
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) −6.00000 + 10.3923i −0.301893 + 0.522894i
\(396\) 9.00000 0.452267
\(397\) 6.50000 + 11.2583i 0.326226 + 0.565039i 0.981760 0.190126i \(-0.0608897\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(398\) −8.50000 14.7224i −0.426067 0.737969i
\(399\) 9.00000 + 20.7846i 0.450564 + 1.04053i
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −17.0000 −0.848939 −0.424470 0.905442i \(-0.639539\pi\)
−0.424470 + 0.905442i \(0.639539\pi\)
\(402\) 6.00000 + 3.46410i 0.299253 + 0.172774i
\(403\) 42.0000 2.09217
\(404\) −2.50000 4.33013i −0.124380 0.215432i
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) 15.0000 0.744438
\(407\) −3.00000 5.19615i −0.148704 0.257564i
\(408\) 15.5885i 0.771744i
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) 0.500000 0.866025i 0.0246932 0.0427699i
\(411\) 4.50000 + 2.59808i 0.221969 + 0.128154i
\(412\) 7.00000 0.344865
\(413\) −4.50000 7.79423i −0.221431 0.383529i
\(414\) −12.0000 20.7846i −0.589768 1.02151i
\(415\) −0.500000 0.866025i −0.0245440 0.0425115i
\(416\) −15.0000 + 25.9808i −0.735436 + 1.27381i
\(417\) 6.92820i 0.339276i
\(418\) 12.0000 5.19615i 0.586939 0.254152i
\(419\) 11.5000 19.9186i 0.561812 0.973087i −0.435527 0.900176i \(-0.643438\pi\)
0.997338 0.0729107i \(-0.0232288\pi\)
\(420\) −4.50000 + 2.59808i −0.219578 + 0.126773i
\(421\) −1.00000 + 1.73205i −0.0487370 + 0.0844150i −0.889365 0.457198i \(-0.848853\pi\)
0.840628 + 0.541613i \(0.182186\pi\)
\(422\) 11.5000 19.9186i 0.559811 0.969622i
\(423\) 13.5000 + 23.3827i 0.656392 + 1.13691i
\(424\) −4.50000 + 7.79423i −0.218539 + 0.378521i
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 22.5000 + 12.9904i 1.09013 + 0.629386i
\(427\) −10.5000 18.1865i −0.508131 0.880108i
\(428\) −2.00000 3.46410i −0.0966736 0.167444i
\(429\) 27.0000 15.5885i 1.30357 0.752618i
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) −13.5000 + 23.3827i −0.650272 + 1.12630i 0.332785 + 0.943003i \(0.392012\pi\)
−0.983057 + 0.183301i \(0.941322\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) 14.5000 25.1147i 0.696826 1.20694i −0.272736 0.962089i \(-0.587929\pi\)
0.969561 0.244848i \(-0.0787382\pi\)
\(434\) −10.5000 + 18.1865i −0.504016 + 0.872982i
\(435\) 7.50000 + 4.33013i 0.359597 + 0.207614i
\(436\) −0.500000 + 0.866025i −0.0239457 + 0.0414751i
\(437\) 28.0000 + 20.7846i 1.33942 + 0.994263i
\(438\) 7.50000 + 4.33013i 0.358364 + 0.206901i
\(439\) −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i \(-0.958036\pi\)
0.609503 + 0.792784i \(0.291369\pi\)
\(440\) 4.50000 + 7.79423i 0.214529 + 0.371575i
\(441\) −6.00000 −0.285714
\(442\) −9.00000 15.5885i −0.428086 0.741467i
\(443\) 9.00000 0.427603 0.213801 0.976877i \(-0.431415\pi\)
0.213801 + 0.976877i \(0.431415\pi\)
\(444\) 3.46410i 0.164399i
\(445\) −0.500000 + 0.866025i −0.0237023 + 0.0410535i
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) 4.50000 + 2.59808i 0.212843 + 0.122885i
\(448\) −10.5000 18.1865i −0.496078 0.859233i
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) −12.0000 −0.565685
\(451\) 1.50000 + 2.59808i 0.0706322 + 0.122339i
\(452\) −15.0000 −0.705541
\(453\) 32.9090i 1.54620i
\(454\) 21.0000 0.985579
\(455\) −9.00000 + 15.5885i −0.421927 + 0.730798i
\(456\) −22.5000 2.59808i −1.05366 0.121666i
\(457\) −1.50000 2.59808i −0.0701670 0.121533i 0.828807 0.559534i \(-0.189020\pi\)
−0.898974 + 0.438001i \(0.855687\pi\)
\(458\) 1.50000 + 2.59808i 0.0700904 + 0.121400i
\(459\) 13.5000 7.79423i 0.630126 0.363803i
\(460\) −4.00000 + 6.92820i −0.186501 + 0.323029i
\(461\) 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i \(-0.788712\pi\)
0.927392 + 0.374091i \(0.122045\pi\)
\(462\) 15.5885i 0.725241i
\(463\) −2.50000 + 4.33013i −0.116185 + 0.201238i −0.918253 0.395995i \(-0.870400\pi\)
0.802068 + 0.597233i \(0.203733\pi\)
\(464\) −2.50000 + 4.33013i −0.116060 + 0.201021i
\(465\) −10.5000 + 6.06218i −0.486926 + 0.281127i
\(466\) 1.00000 0.0463241
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) −18.0000 −0.832050
\(469\) 6.00000 10.3923i 0.277054 0.479872i
\(470\) −4.50000 + 7.79423i −0.207570 + 0.359521i
\(471\) 10.5000 + 6.06218i 0.483814 + 0.279330i
\(472\) 9.00000 0.414259
\(473\) 24.0000 1.10352
\(474\) 20.7846i 0.954669i
\(475\) 16.0000 6.92820i 0.734130 0.317888i
\(476\) −9.00000 −0.412514
\(477\) −9.00000 −0.412082
\(478\) −13.5000 23.3827i −0.617476 1.06950i
\(479\) 1.00000 0.0456912 0.0228456 0.999739i \(-0.492727\pi\)
0.0228456 + 0.999739i \(0.492727\pi\)
\(480\) 8.66025i 0.395285i
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) 7.50000 12.9904i 0.341616 0.591696i
\(483\) −36.0000 + 20.7846i −1.63806 + 0.945732i
\(484\) 2.00000 0.0909091
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 15.5885i 0.707107i
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 21.0000 0.950625
\(489\) −6.00000 3.46410i −0.271329 0.156652i
\(490\) −1.00000 1.73205i −0.0451754 0.0782461i
\(491\) 35.0000 1.57953 0.789764 0.613411i \(-0.210203\pi\)
0.789764 + 0.613411i \(0.210203\pi\)
\(492\) 1.73205i 0.0780869i
\(493\) 7.50000 + 12.9904i 0.337783 + 0.585057i
\(494\) −24.0000 + 10.3923i −1.07981 + 0.467572i
\(495\) −4.50000 + 7.79423i −0.202260 + 0.350325i
\(496\) −3.50000 6.06218i −0.157155 0.272200i
\(497\) 22.5000 38.9711i 1.00926 1.74809i
\(498\) 1.50000 + 0.866025i 0.0672166 + 0.0388075i
\(499\) 19.0000 0.850557 0.425278 0.905063i \(-0.360176\pi\)
0.425278 + 0.905063i \(0.360176\pi\)
\(500\) 4.50000 + 7.79423i 0.201246 + 0.348569i
\(501\) 20.7846i 0.928588i
\(502\) 1.50000 + 2.59808i 0.0669483 + 0.115958i
\(503\) −7.50000 + 12.9904i −0.334408 + 0.579212i −0.983371 0.181608i \(-0.941870\pi\)
0.648963 + 0.760820i \(0.275203\pi\)
\(504\) 13.5000 23.3827i 0.601338 1.04155i
\(505\) 5.00000 0.222497
\(506\) 12.0000 + 20.7846i 0.533465 + 0.923989i
\(507\) −34.5000 + 19.9186i −1.53220 + 0.884615i
\(508\) −7.00000 −0.310575
\(509\) 19.0000 + 32.9090i 0.842160 + 1.45866i 0.888065 + 0.459718i \(0.152050\pi\)
−0.0459045 + 0.998946i \(0.514617\pi\)
\(510\) 4.50000 + 2.59808i 0.199263 + 0.115045i
\(511\) 7.50000 12.9904i 0.331780 0.574661i
\(512\) 11.0000 0.486136
\(513\) −9.00000 20.7846i −0.397360 0.917663i
\(514\) 2.00000 0.0882162
\(515\) −3.50000 + 6.06218i −0.154228 + 0.267131i
\(516\) −12.0000 6.92820i −0.528271 0.304997i
\(517\) −13.5000 23.3827i −0.593729 1.02837i
\(518\) −6.00000 −0.263625
\(519\) 21.0000 12.1244i 0.921798 0.532200i
\(520\) −9.00000 15.5885i −0.394676 0.683599i
\(521\) −2.00000 −0.0876216 −0.0438108 0.999040i \(-0.513950\pi\)
−0.0438108 + 0.999040i \(0.513950\pi\)
\(522\) −15.0000 −0.656532
\(523\) −5.50000 + 9.52628i −0.240498 + 0.416555i −0.960856 0.277047i \(-0.910644\pi\)
0.720358 + 0.693602i \(0.243977\pi\)
\(524\) −8.50000 14.7224i −0.371324 0.643152i
\(525\) 20.7846i 0.907115i
\(526\) 12.0000 + 20.7846i 0.523225 + 0.906252i
\(527\) −21.0000 −0.914774
\(528\) −4.50000 2.59808i −0.195837 0.113067i
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) −1.50000 2.59808i −0.0651558 0.112853i
\(531\) 4.50000 + 7.79423i 0.195283 + 0.338241i
\(532\) −1.50000 + 12.9904i −0.0650332 + 0.563204i
\(533\) −3.00000 5.19615i −0.129944 0.225070i
\(534\) 1.73205i 0.0749532i
\(535\) 4.00000 0.172935
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 6.00000 + 3.46410i 0.258919 + 0.149487i
\(538\) −3.00000 −0.129339
\(539\) 6.00000 0.258438
\(540\) 4.50000 2.59808i 0.193649 0.111803i
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 15.0000 0.644305
\(543\) −16.5000 + 9.52628i −0.708083 + 0.408812i
\(544\) 7.50000 12.9904i 0.321560 0.556958i
\(545\) −0.500000 0.866025i −0.0214176 0.0370965i
\(546\) 31.1769i 1.33425i
\(547\) −11.0000 −0.470326 −0.235163 0.971956i \(-0.575562\pi\)
−0.235163 + 0.971956i \(0.575562\pi\)
\(548\) 1.50000 + 2.59808i 0.0640768 + 0.110984i
\(549\) 10.5000 + 18.1865i 0.448129 + 0.776182i
\(550\) 12.0000 0.511682
\(551\) 20.0000 8.66025i 0.852029 0.368939i
\(552\) 41.5692i 1.76930i
\(553\) −36.0000 −1.53088
\(554\) 5.00000 0.212430
\(555\) −3.00000 1.73205i −0.127343 0.0735215i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 4.50000 7.79423i 0.190671 0.330252i −0.754802 0.655953i \(-0.772267\pi\)
0.945473 + 0.325701i \(0.105600\pi\)
\(558\) 10.5000 18.1865i 0.444500 0.769897i
\(559\) −48.0000 −2.03018
\(560\) 3.00000 0.126773
\(561\) −13.5000 + 7.79423i −0.569970 + 0.329073i
\(562\) −2.50000 + 4.33013i −0.105456 + 0.182655i
\(563\) −18.5000 + 32.0429i −0.779682 + 1.35045i 0.152443 + 0.988312i \(0.451286\pi\)
−0.932125 + 0.362137i \(0.882047\pi\)
\(564\) 15.5885i 0.656392i
\(565\) 7.50000 12.9904i 0.315527 0.546509i
\(566\) −2.50000 + 4.33013i −0.105083 + 0.182009i
\(567\) 27.0000 1.13389
\(568\) 22.5000 + 38.9711i 0.944079 + 1.63519i
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 4.50000 6.06218i 0.188484 0.253917i
\(571\) 9.50000 16.4545i 0.397563 0.688599i −0.595862 0.803087i \(-0.703189\pi\)
0.993425 + 0.114488i \(0.0365228\pi\)
\(572\) 18.0000 0.752618
\(573\) 15.5885i 0.651217i
\(574\) 3.00000 0.125218
\(575\) 16.0000 + 27.7128i 0.667246 + 1.15570i
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) 30.0000 1.24892 0.624458 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) −25.5000 14.7224i −1.05974 0.611843i
\(580\) 2.50000 + 4.33013i 0.103807 + 0.179799i
\(581\) 1.50000 2.59808i 0.0622305 0.107786i
\(582\) 3.46410i 0.143592i
\(583\) 9.00000 0.372742
\(584\) 7.50000 + 12.9904i 0.310352 + 0.537546i
\(585\) 9.00000 15.5885i 0.372104 0.644503i
\(586\) −12.5000 21.6506i −0.516370 0.894379i
\(587\) 10.0000 17.3205i 0.412744 0.714894i −0.582445 0.812870i \(-0.697904\pi\)
0.995189 + 0.0979766i \(0.0312370\pi\)
\(588\) −3.00000 1.73205i −0.123718 0.0714286i
\(589\) −3.50000 + 30.3109i −0.144215 + 1.24894i
\(590\) −1.50000 + 2.59808i −0.0617540 + 0.106961i
\(591\) −33.0000 19.0526i −1.35744 0.783718i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 4.50000 7.79423i 0.184793 0.320071i −0.758714 0.651424i \(-0.774172\pi\)
0.943507 + 0.331353i \(0.107505\pi\)
\(594\) 15.5885i 0.639602i
\(595\) 4.50000 7.79423i 0.184482 0.319532i
\(596\) 1.50000 + 2.59808i 0.0614424 + 0.106421i
\(597\) 25.5000 14.7224i 1.04365 0.602549i
\(598\) −24.0000 41.5692i −0.981433 1.69989i
\(599\) −18.0000 31.1769i −0.735460 1.27385i −0.954521 0.298143i \(-0.903633\pi\)
0.219061 0.975711i \(-0.429701\pi\)
\(600\) −18.0000 10.3923i −0.734847 0.424264i
\(601\) 14.5000 + 25.1147i 0.591467 + 1.02445i 0.994035 + 0.109061i \(0.0347845\pi\)
−0.402568 + 0.915390i \(0.631882\pi\)
\(602\) 12.0000 20.7846i 0.489083 0.847117i
\(603\) −6.00000 + 10.3923i −0.244339 + 0.423207i
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) −7.50000 + 4.33013i −0.304667 + 0.175899i
\(607\) 1.50000 2.59808i 0.0608831 0.105453i −0.833977 0.551799i \(-0.813942\pi\)
0.894860 + 0.446346i \(0.147275\pi\)
\(608\) −17.5000 12.9904i −0.709719 0.526830i
\(609\) 25.9808i 1.05279i
\(610\) −3.50000 + 6.06218i −0.141711 + 0.245450i
\(611\) 27.0000 + 46.7654i 1.09230 + 1.89192i
\(612\) 9.00000 0.363803
\(613\) 10.5000 + 18.1865i 0.424091 + 0.734547i 0.996335 0.0855362i \(-0.0272603\pi\)
−0.572244 + 0.820083i \(0.693927\pi\)
\(614\) −9.00000 −0.363210
\(615\) 1.50000 + 0.866025i 0.0604858 + 0.0349215i
\(616\) −13.5000 + 23.3827i −0.543931 + 0.942115i
\(617\) −11.0000 19.0526i −0.442843 0.767027i 0.555056 0.831813i \(-0.312697\pi\)
−0.997899 + 0.0647859i \(0.979364\pi\)
\(618\) 12.1244i 0.487713i
\(619\) −17.5000 30.3109i −0.703384 1.21830i −0.967271 0.253744i \(-0.918338\pi\)
0.263887 0.964554i \(-0.414995\pi\)
\(620\) −7.00000 −0.281127
\(621\) 36.0000 20.7846i 1.44463 0.834058i
\(622\) −3.50000 6.06218i −0.140337 0.243071i
\(623\) −3.00000 −0.120192
\(624\) 9.00000 + 5.19615i 0.360288 + 0.208013i
\(625\) 11.0000 0.440000
\(626\) −12.5000 + 21.6506i −0.499600 + 0.865333i
\(627\) 9.00000 + 20.7846i 0.359425 + 0.830057i
\(628\) 3.50000 + 6.06218i 0.139665 + 0.241907i
\(629\) −3.00000 5.19615i −0.119618 0.207184i
\(630\) 4.50000 + 7.79423i 0.179284 + 0.310530i
\(631\) −21.5000 + 37.2391i −0.855901 + 1.48246i 0.0199047 + 0.999802i \(0.493664\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) 18.0000 31.1769i 0.716002 1.24015i
\(633\) 34.5000 + 19.9186i 1.37125 + 0.791693i
\(634\) −10.5000 + 18.1865i −0.417008 + 0.722280i
\(635\) 3.50000 6.06218i 0.138893 0.240570i
\(636\) −4.50000 2.59808i −0.178437 0.103020i
\(637\) −12.0000 −0.475457
\(638\) 15.0000 0.593856
\(639\) −22.5000 + 38.9711i −0.890086 + 1.54167i
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) −17.0000 + 29.4449i −0.671460 + 1.16300i 0.306031 + 0.952022i \(0.400999\pi\)
−0.977490 + 0.210981i \(0.932334\pi\)
\(642\) −6.00000 + 3.46410i −0.236801 + 0.136717i
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) −24.0000 −0.945732
\(645\) 12.0000 6.92820i 0.472500 0.272798i
\(646\) 12.0000 5.19615i 0.472134 0.204440i
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −13.5000 + 23.3827i −0.530330 + 0.918559i
\(649\) −4.50000 7.79423i −0.176640 0.305950i
\(650\) −24.0000 −0.941357
\(651\) −31.5000 18.1865i −1.23458 0.712786i
\(652\) −2.00000 3.46410i −0.0783260 0.135665i
\(653\) −9.50000 + 16.4545i −0.371764 + 0.643914i −0.989837 0.142207i \(-0.954580\pi\)
0.618073 + 0.786121i \(0.287914\pi\)
\(654\) 1.50000 + 0.866025i 0.0586546 + 0.0338643i
\(655\) 17.0000 0.664245
\(656\) −0.500000 + 0.866025i −0.0195217 + 0.0338126i
\(657\) −7.50000 + 12.9904i −0.292603 + 0.506803i
\(658\) −27.0000 −1.05257
\(659\) −31.0000 −1.20759 −0.603794 0.797140i \(-0.706345\pi\)
−0.603794 + 0.797140i \(0.706345\pi\)
\(660\) −4.50000 + 2.59808i −0.175162 + 0.101130i
\(661\) −21.0000 36.3731i −0.816805 1.41475i −0.908024 0.418917i \(-0.862410\pi\)
0.0912190 0.995831i \(-0.470924\pi\)
\(662\) −27.0000 −1.04938
\(663\) 27.0000 15.5885i 1.04859 0.605406i
\(664\) 1.50000 + 2.59808i 0.0582113 + 0.100825i
\(665\) −10.5000 7.79423i −0.407173 0.302247i
\(666\) 6.00000 0.232495
\(667\) 20.0000 + 34.6410i 0.774403 + 1.34131i
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 12.0000 6.92820i 0.463947 0.267860i
\(670\) −4.00000 −0.154533
\(671\) −10.5000 18.1865i −0.405348 0.702083i
\(672\) 22.5000 12.9904i 0.867956 0.501115i
\(673\) 12.5000 + 21.6506i 0.481840 + 0.834571i 0.999783 0.0208444i \(-0.00663546\pi\)
−0.517943 + 0.855415i \(0.673302\pi\)
\(674\) −6.50000 + 11.2583i −0.250371 + 0.433655i
\(675\) 20.7846i 0.800000i
\(676\) −23.0000 −0.884615
\(677\) −3.50000 6.06218i −0.134516 0.232988i 0.790897 0.611950i \(-0.209615\pi\)
−0.925412 + 0.378962i \(0.876281\pi\)
\(678\) 25.9808i 0.997785i
\(679\) −6.00000 −0.230259
\(680\) 4.50000 + 7.79423i 0.172567 + 0.298895i
\(681\) 36.3731i 1.39382i
\(682\) −10.5000 + 18.1865i −0.402066 + 0.696398i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 1.50000 12.9904i 0.0573539 0.496700i
\(685\) −3.00000 −0.114624
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) −4.50000 + 2.59808i −0.171686 + 0.0991228i
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) −18.0000 −0.685745
\(690\) 12.0000 + 6.92820i 0.456832 + 0.263752i
\(691\) 6.50000 + 11.2583i 0.247272 + 0.428287i 0.962768 0.270330i \(-0.0871327\pi\)
−0.715496 + 0.698617i \(0.753799\pi\)
\(692\) 14.0000 0.532200
\(693\) −27.0000 −1.02565
\(694\) −16.5000 + 28.5788i −0.626331 + 1.08484i
\(695\) 2.00000 + 3.46410i 0.0758643 + 0.131401i
\(696\) −22.5000 12.9904i −0.852860 0.492399i
\(697\) 1.50000 + 2.59808i 0.0568166 + 0.0984092i
\(698\) 5.00000 0.189253
\(699\) 1.73205i 0.0655122i
\(700\) −6.00000 + 10.3923i −0.226779 + 0.392792i
\(701\) −19.5000 33.7750i −0.736505 1.27566i −0.954060 0.299616i \(-0.903142\pi\)
0.217555 0.976048i \(-0.430192\pi\)
\(702\) 31.1769i 1.17670i
\(703\) −8.00000 + 3.46410i −0.301726 + 0.130651i
\(704\) −10.5000 18.1865i −0.395734 0.685431i
\(705\) −13.5000 7.79423i −0.508439 0.293548i
\(706\) 29.0000 1.09143
\(707\) 7.50000 + 12.9904i 0.282067 + 0.488554i
\(708\) 5.19615i 0.195283i
\(709\) 11.0000 0.413114 0.206557 0.978435i \(-0.433774\pi\)
0.206557 + 0.978435i \(0.433774\pi\)
\(710\) −15.0000 −0.562940
\(711\) 36.0000 1.35011
\(712\) 1.50000 2.59808i 0.0562149 0.0973670i
\(713\) −56.0000 −2.09722
\(714\) 15.5885i 0.583383i
\(715\) −9.00000 + 15.5885i −0.336581 + 0.582975i
\(716\) 2.00000 + 3.46410i 0.0747435 + 0.129460i
\(717\) 40.5000 23.3827i 1.51250 0.873242i
\(718\) −17.0000 −0.634434
\(719\) −20.5000 35.5070i −0.764521 1.32419i −0.940499 0.339795i \(-0.889642\pi\)
0.175978 0.984394i \(-0.443691\pi\)
\(720\) −3.00000 −0.111803
\(721\) −21.0000 −0.782081
\(722\) −5.50000 18.1865i −0.204689 0.676833i
\(723\) 22.5000 + 12.9904i 0.836784 + 0.483117i
\(724\) −11.0000 −0.408812
\(725\) 20.0000 0.742781
\(726\) 3.46410i 0.128565i
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) 27.0000 46.7654i 1.00069 1.73324i
\(729\) −27.0000 −1.00000
\(730\) −5.00000 −0.185058
\(731\) 24.0000 0.887672
\(732\) 12.1244i 0.448129i
\(733\) 20.5000 35.5070i 0.757185 1.31148i −0.187096 0.982342i \(-0.559908\pi\)
0.944281 0.329141i \(-0.106759\pi\)
\(734\) −15.5000 + 26.8468i −0.572115 + 0.990933i
\(735\) 3.00000 1.73205i 0.110657 0.0638877i
\(736\) 20.0000 34.6410i 0.737210 1.27688i
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) −3.00000 −0.110432
\(739\) −22.5000 38.9711i −0.827676 1.43358i −0.899857 0.436185i \(-0.856329\pi\)
0.0721811 0.997392i \(-0.477004\pi\)
\(740\) −1.00000 1.73205i −0.0367607 0.0636715i
\(741\) −18.0000 41.5692i −0.661247 1.52708i
\(742\) 4.50000 7.79423i 0.165200 0.286135i
\(743\) −21.0000 −0.770415 −0.385208 0.922830i \(-0.625870\pi\)
−0.385208 + 0.922830i \(0.625870\pi\)
\(744\) 31.5000 18.1865i 1.15485 0.666751i
\(745\) −3.00000 −0.109911
\(746\) 11.5000 + 19.9186i 0.421045 + 0.729271i
\(747\) −1.50000 + 2.59808i −0.0548821 + 0.0950586i
\(748\) −9.00000 −0.329073
\(749\) 6.00000 + 10.3923i 0.219235 + 0.379727i
\(750\) 13.5000 7.79423i 0.492950 0.284605i
\(751\) −20.0000 34.6410i −0.729810 1.26407i −0.956963 0.290209i \(-0.906275\pi\)
0.227153 0.973859i \(-0.427058\pi\)
\(752\) 4.50000 7.79423i 0.164098 0.284226i
\(753\) −4.50000 + 2.59808i −0.163989 + 0.0946792i
\(754\) −30.0000 −1.09254
\(755\) 9.50000 + 16.4545i 0.345740 + 0.598840i
\(756\) 13.5000 + 7.79423i 0.490990 + 0.283473i
\(757\) 6.50000 + 11.2583i 0.236247 + 0.409191i 0.959634 0.281251i \(-0.0907494\pi\)
−0.723388 + 0.690442i \(0.757416\pi\)
\(758\) 6.00000 10.3923i 0.217930 0.377466i
\(759\) −36.0000 + 20.7846i −1.30672 + 0.754434i
\(760\) 12.0000 5.19615i 0.435286 0.188484i
\(761\) 8.50000 14.7224i 0.308125 0.533688i −0.669827 0.742517i \(-0.733632\pi\)
0.977952 + 0.208829i \(0.0669652\pi\)
\(762\) 12.1244i 0.439219i
\(763\) 1.50000 2.59808i 0.0543036 0.0940567i
\(764\) −4.50000 + 7.79423i −0.162804 + 0.281985i
\(765\) −4.50000 + 7.79423i −0.162698 + 0.281801i
\(766\) 9.50000 16.4545i 0.343249 0.594525i
\(767\) 9.00000 + 15.5885i 0.324971 + 0.562867i
\(768\) 29.4449i 1.06250i
\(769\) 21.0000 + 36.3731i 0.757279 + 1.31165i 0.944233 + 0.329278i \(0.106805\pi\)
−0.186954 + 0.982369i \(0.559861\pi\)